============================== Prover9 ===============================
Prover9 (32) version November-2006, November 2006.
Process 3874 was started by mccune on cleo.thornwood,
Wed Nov 22 11:24:24 2006
The command was "/home/mccune/bin/prover9 -f cs.in ND.in".
============================== end of head ===========================

============================== INPUT =================================

% Reading from file cs.in

op(450,infix,@).
op(400,infix_right,*).
assign(new_constants,1).
assign(max_weight,25).

formulas(sos).
x * y != x * z | y = z.
y * x != z * x | y = z.
(x * y) * z = x * y * z.
y * x * (x @ y) = x * y.
end_of_list.

% Reading from file ND.in


formulas(sos).
(x @ y) * z = z * (x @ y).
end_of_list.

formulas(sos).
(A @ C) * (B @ C) != A * B @ C # answer(D).
end_of_list.

============================== end of input ==========================

============================== PROCESS NON-CLAUSAL FORMULAS ==========

% Formulas that are not ordinary clauses:

============================== end of process non-clausal formulas ===

============================== PROCESS INITIAL CLAUSES ===============

% Clauses before input processing:

formulas(usable).
end_of_list.

formulas(sos).
x * y != x * z | y = z.  [assumption].
x * y != z * y | x = z.  [assumption].
(x * y) * z = x * y * z.  [assumption].
x * y * (y @ x) = y * x.  [assumption].
(x @ y) * z = z * (x @ y).  [assumption].
(A @ C) * (B @ C) != A * B @ C # answer(D).  [assumption].
end_of_list.

formulas(demodulators).
end_of_list.

============================== PREDICATE ELIMINATION =================

No predicates eliminated.

============================== end predicate elimination =============

Auto_denials:  (no changes).

Term ordering decisions:
Relation symbol precedence:  lex([ = ]).
Function symbol precedence:  lex([ A, B, C, *, @ ]).
After inverse_order:  (no changes).
Unfolding symbols: (none).

Auto_inference settings:
  % set(paramodulation).  % (positive equality literals)
    % set(paramodulation) -> set(back_demod).
  % set(hyper_resolution).  % (nonunit Horn with equality)
  % set(neg_ur_resolution).  % (nonunit Horn with equality)
  % assign(para_lit_limit, 2).  % (nonunit Horn with equality)

Auto_process settings:  (no changes).

============================== end of process initial clauses ========

============================== CLAUSES FOR SEARCH ====================

% Clauses after input processing:

formulas(usable).
end_of_list.

formulas(sos).
1 x * y != x * z | y = z.  [assumption].
2 x * y != z * y | x = z.  [assumption].
3 (x * y) * z = x * y * z.  [assumption].
4 x * y * (y @ x) = y * x.  [assumption].
5 (x @ y) * z = z * (x @ y).  [assumption].
7 A * B @ C != (A @ C) * (B @ C) # answer(D).  [copy(6),flip(a)].
end_of_list.

formulas(demodulators).
3 (x * y) * z = x * y * z.  [assumption].
4 x * y * (y @ x) = y * x.  [assumption].
5 (x @ y) * z = z * (x @ y).  [assumption].
        % (lex-dep)
end_of_list.

============================== end of clauses for search =============

============================== SEARCH ================================

% Starting search at 0.00 seconds.

given #1 (I,wt=10): 1 x * y != x * z | y = z.  [assumption].

given #2 (I,wt=10): 2 x * y != z * y | x = z.  [assumption].

given #3 (I,wt=11): 3 (x * y) * z = x * y * z.  [assumption].

given #4 (I,wt=11): 4 x * y * (y @ x) = y * x.  [assumption].

given #5 (I,wt=11): 5 (x @ y) * z = z * (x @ y).  [assumption].

given #6 (I,wt=13): 7 A * B @ C != (A @ C) * (B @ C) # answer(D).  [copy(6),flip(a)].

given #7 (F,wt=17): 24 (A * B @ C) * x != (A @ C) * (B @ C) * x # answer(D).  [ur(2,b,7,a),rewrite(3(14))].

given #8 (F,wt=17): 25 x * (A * B @ C) != x * (A @ C) * (B @ C) # answer(D).  [ur(1,b,7,a)].

given #9 (T,wt=7): 10 x * (x @ x) = x.  [hyper(1,a,4,a)].

given #10 (T,wt=10): 35 x * y != x | x @ x = y.  [para(10(a,1),1(a,1)),flip(a)].

given #11 (A,wt=14): 8 x * y * z != x * y * u | z = u.  [para(3(a,1),1(a,1)),rewrite(3(4))].

given #12 (F,wt=17): 30 (A @ C) * (B @ C) * x != x * (A * B @ C) # answer(D).  [para(5(a,1),24(a,1)),flip(a)].

given #13 (F,wt=17): 31 (A * B @ C) * x != (A @ C) * x * (B @ C) # answer(D).  [para(5(a,1),24(a,2,2))].

given #14 (T,wt=10): 36 x * (y @ y) != y | y = x.  [para(10(a,1),2(a,1)),flip(a)].

given #15 (T,wt=10): 37 x * (y @ y) != y | x = y.  [para(10(a,1),2(a,2))].

given #16 (A,wt=14): 9 x * y * z != u * z | x * y = u.  [para(3(a,1),2(a,1))].

given #17 (F,wt=17): 34 (A * B @ C) * x != x * (A @ C) * (B @ C) # answer(D).  [para(5(a,2),25(a,1))].

given #18 (F,wt=17): 62 (A @ C) * x * (B @ C) != x * (A * B @ C) # answer(D).  [para(5(a,1),30(a,1,2))].

given #19 (T,wt=10): 69 (x @ x) * y != x | x = y.  [para(5(a,2),36(a,1))].

given #20 (T,wt=10): 70 (x @ x) * y != x | y = x.  [para(5(a,2),37(a,1))].

given #21 (A,wt=14): 11 x * y != z * x | z * (z @ x) = y.  [para(4(a,1),1(a,1)),flip(a)].

given #22 (F,wt=19): 98 C * A * B * (A @ C) * (B @ C) != A * B * C # answer(D).  [ur(11,b,25,a),rewrite(3(12),3(18))].

given #23 (F,wt=19): 99 C * (A @ C) * A * B * (B @ C) != A * B * C # answer(D).  [ur(11,b,62,a(flip)),rewrite(3(11),3(18))].

given #24 (T,wt=9): 93 x * (x @ (y @ z)) = x.  [hyper(11,a,5,a)].

given #25 (T,wt=9): 94 x * (x @ x * x) = x.  [hyper(11,a,3,a)].

given #26 (A,wt=14): 12 x * y * (y @ z) != y * z | z = x.  [para(4(a,1),2(a,1)),flip(a)].

given #27 (F,wt=21): 26 x * (A * B @ C) * y != x * (A @ C) * (B @ C) * y # answer(D).  [ur(1,b,24,a)].

given #28 (F,wt=21): 32 x * y * (A * B @ C) != x * y * (A @ C) * (B @ C) # answer(D).  [ur(1,b,25,a)].

given #29 (T,wt=9): 111 x @ (y @ z) = x @ x.  [hyper(35,a,93,a),flip(a)].

given #30 (T,wt=9): 125 x @ x * x = x @ x.  [hyper(35,a,94,a),flip(a)].

given #31 (A,wt=14): 13 x * y * (y @ z) != y * z | x = z.  [para(4(a,1),2(a,2))].

given #32 (F,wt=21): 58 (A @ C) * (B @ C) * x * y != x * (A * B @ C) * y # answer(D).  [ur(2,b,30,a),rewrite(3(9),3(8),3(16))].

given #33 (F,wt=21): 59 x * (A @ C) * (B @ C) * y != x * y * (A * B @ C) # answer(D).  [ur(1,b,30,a)].

given #34 (T,wt=10): 130 x * y != y * y | y = x.  [para(10(a,1),12(a,1,2))].

given #35 (T,wt=10): 131 x * y != y | y @ y = x.  [para(10(a,1),12(a,2)),rewrite(93(3))].

given #36 (A,wt=15): 14 x * y * (y @ x) * z = y * x * z.  [para(4(a,1),3(a,1,1)),rewrite(3(2),3(5)),flip(a)].

given #37 (F,wt=17): 185 C * A * (A * B @ C) != A * C * (B @ C) # answer(D).  [para(14(a,1),32(a,2))].

given #38 (F,wt=21): 60 (A @ C) * (B @ C) * x * y != x * y * (A * B @ C) # answer(D).  [para(3(a,1),30(a,2))].

given #39 (T,wt=6): 191 x != y | y = x.  [back_rewrite(69),rewrite(163(2))].

given #40 (T,wt=7): 163 (x @ x) * y = y.  [hyper(8,a,14,a)].

NOTE: New constant: x @ x = c_0.  [new_symbol(199)].
NOTE: New Function symbol precedence:  lex([ A, B, C, c_0, *, @ ]).

given #41 (A,wt=17): 15 x * y * z * (z @ x * y) = z * x * y.  [para(4(a,1),3(a,1)),flip(a)].

given #42 (F,wt=17): 215 (B @ C) * (A @ C) * x != x * (A * B @ C) # answer(D).  [back_rewrite(198),rewrite(209(14)),flip(a)].

given #43 (F,wt=17): 216 (A * B @ C) * x != (B @ C) * (A @ C) * x # answer(D).  [back_rewrite(186),rewrite(209(14))].

given #44 (T,wt=5): 212 x @ x = c_0.  [new_symbol(199)].

given #45 (T,wt=5): 214 x * c_0 = x.  [back_rewrite(141),rewrite(209(3),212(1)),flip(a)].

given #46 (A,wt=17): 16 x * y * z * (y * z @ x) = y * z * x.  [para(3(a,1),4(a,1,2)),rewrite(3(7))].

given #47 (F,wt=17): 255 (B @ C) * x * (A @ C) != x * (A * B @ C) # answer(D).  [para(4(a,1),215(a,1,2)),rewrite(232(12),214(10))].

given #48 (F,wt=17): 260 (A * B @ C) * x != (B @ C) * x * (A @ C) # answer(D).  [para(4(a,1),216(a,2,2)),rewrite(232(9),214(7))].

given #49 (T,wt=5): 226 c_0 * x = x.  [back_rewrite(163),rewrite(212(1))].

given #50 (T,wt=7): 223 x * (c_0 @ x) = x.  [back_rewrite(202),rewrite(212(1))].

given #51 (A,wt=14): 17 (x @ y) * z != u * (x @ y) | u = z.  [para(5(a,1),1(a,1)),flip(a)].

given #52 (F,wt=19): 196 (A @ C) * C * A * B * (B @ C) != A * B * C # answer(D).  [para(4(a,1),60(a,2)),rewrite(5(12),3(12),3(11),3(18))].

given #53 (F,wt=21): 64 (A * B @ C) * x * y != (A @ C) * x * (B @ C) * y # answer(D).  [ur(2,b,31,a),rewrite(3(7),3(16),3(15))].

given #54 (T,wt=7): 230 x @ x * x = c_0.  [back_rewrite(125),rewrite(212(3))].

given #55 (T,wt=7): 232 x @ (y @ z) = c_0.  [back_rewrite(111),rewrite(212(3))].

given #56 (A,wt=14): 18 (x @ y) * z != z * u | x @ y = u.  [para(5(a,2),1(a,1))].

given #57 (F,wt=21): 65 x * (A * B @ C) * y != x * (A @ C) * y * (B @ C) # answer(D).  [ur(1,b,31,a)].

given #58 (F,wt=21): 66 (A * B @ C) * x * y != (A @ C) * x * y * (B @ C) # answer(D).  [para(3(a,1),31(a,2,2))].

given #59 (T,wt=5): 324 x @ c_0 = c_0.  [para(212(a,1),232(a,1,2))].

given #60 (T,wt=8): 224 x * y != y | c_0 = x.  [back_rewrite(201),rewrite(212(3))].

given #61 (A,wt=14): 19 (x @ y) * z != u * (x @ y) | z = u.  [para(5(a,1),1(a,2))].

given #62 (F,wt=17): 331 C * B * (A * B @ C) != B * C * (A @ C) # answer(D).  [para(4(a,1),66(a,2,2)),rewrite(5(9),3(9),5(16),3(16))].

given #63 (F,wt=21): 82 (A * B @ C) * x * y != x * (A @ C) * (B @ C) * y # answer(D).  [ur(9,b,34,a),rewrite(3(16),3(15))].

given #64 (T,wt=8): 236 x * y != x | c_0 = y.  [back_rewrite(35),rewrite(212(3))].

given #65 (T,wt=5): 354 c_0 @ x = c_0.  [hyper(236,a,223,a),flip(a)].

given #66 (A,wt=14): 20 x * (y @ z) != u * x | y @ z = u.  [para(5(a,1),2(a,1))].

given #67 (F,wt=21): 84 x * (A * B @ C) * y != x * y * (A @ C) * (B @ C) # answer(D).  [ur(1,b,34,a)].

given #68 (F,wt=21): 85 (A * B @ C) * x * y != x * y * (A @ C) * (B @ C) # answer(D).  [para(3(a,1),34(a,2))].

given #69 (T,wt=9): 263 x * (x * x @ x) = x.  [hyper(8,a,16,a)].

given #70 (T,wt=7): 364 x * x @ x = c_0.  [hyper(236,a,263,a),flip(a)].

given #71 (A,wt=15): 21 (x @ y) * z * u = z * (x @ y) * u.  [para(5(a,1),3(a,1,1)),rewrite(3(3)),flip(a)].

============================== PROOF =================================

% Proof 1 at 0.07 (+ 0.00) seconds: D.
% Length of proof is 12.
% Level of proof is 4.
% Maximum clause weight is 19.
% Given clauses 71.

1 x * y != x * z | y = z.  [assumption].
3 (x * y) * z = x * y * z.  [assumption].
4 x * y * (y @ x) = y * x.  [assumption].
5 (x @ y) * z = z * (x @ y).  [assumption].
6 (A @ C) * (B @ C) != A * B @ C # answer(D).  [assumption].
7 A * B @ C != (A @ C) * (B @ C) # answer(D).  [copy(6),flip(a)].
11 x * y != z * x | z * (z @ x) = y.  [para(4(a,1),1(a,1)),flip(a)].
14 x * y * (y @ x) * z = y * x * z.  [para(4(a,1),3(a,1,1)),rewrite(3(2),3(5)),flip(a)].
21 (x @ y) * z * u = z * (x @ y) * u.  [para(5(a,1),3(a,1,1)),rewrite(3(3)),flip(a)].
25 x * (A * B @ C) != x * (A @ C) * (B @ C) # answer(D).  [ur(1,b,7,a)].
98 C * A * B * (A @ C) * (B @ C) != A * B * C # answer(D).  [ur(11,b,25,a),rewrite(3(12),3(18))].
389 $F # answer(D).  [para(21(a,2),98(a,1,2,2)),rewrite(14(13),4(8)),xx(a)].

============================== end of proof ==========================

============================== STATISTICS ============================

Given=71. Generated=2327. Kept=387. proofs=1.
Usable=57. Sos=201. Demods=36. Limbo=21, Disabled=114. Hints=0.
Weight_deleted=441. Literals_deleted=0.
Forward_subsumed=1498. Back_subsumed=15.
Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0.
New_demodulators=63 (1 lex), Back_demodulated=93. Back_unit_deleted=0.
Demod_attempts=39529. Demod_rewrites=3217.
Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
Nonunit_fsub_feature_tests=3848. Nonunit_bsub_feature_tests=1794.
Megabytes=0.38.
User_CPU=0.07, System_CPU=0.00, Wall_clock=0.

============================== end of statistics =====================

============================== end of search =========================

THEOREM PROVED

Exiting with 1 proof.

Process 3874 exit (max_proofs) Wed Nov 22 11:24:24 2006