============================== Prover9 ===============================
Prover9 (32) version August-2006A, August 2006.
Process 10674 was started by mccune on cleo.thornwood,
Sat Aug 12 20:58:11 2006
The command was "/home/mccune/bin/prover9 -f cg1.in".
============================== end of head ===========================

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

% Reading from file cg1.in


formulas(sos).
(all x all y all z (x * y = x * z -> y = z)).
(all x all y all z (y * x = z * x -> y = z)).
end_of_list.

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

formulas(goals).
(x * (y * z)) * ((u * v) * w) = (x * (u * z)) * ((y * v) * w).
end_of_list.

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

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

% Formulas that are not ordinary clauses:
1 (all x all y all z (x * y = x * z -> y = z)).  [assumption].
2 (all x all y all z (y * x = z * x -> y = z)).  [assumption].
3 (x * (y * z)) * ((u * v) * w) = (x * (u * z)) * ((y * v) * w).  [goal].

============================== 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.  [clausify(1)].
x * y != z * y | x = z.  [clausify(2)].
(x * y) * (z * u) = (x * z) * (y * u).  [assumption].
(c1 * (c4 * c3)) * ((c2 * c5) * c6) != (c1 * (c2 * c3)) * ((c4 * c5) * c6).  [deny(3)].
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([ c1, c2, c3, c4, c5, c6, * ]).
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).
4 x * y != x * z | y = z.  [clausify(1)].
5 x * y != z * y | x = z.  [clausify(2)].
6 (x * y) * (z * u) = (x * z) * (y * u).  [assumption].
8 (c1 * (c2 * c3)) * ((c4 * c5) * c6) != (c1 * (c4 * c3)) * ((c2 * c5) * c6).  [copy(7),flip(a)].
end_of_list.

formulas(demodulators).
end_of_list.

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

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

% Starting search at 0.00 seconds.

given #1 (I,wt=10): 4 x * y != x * z | y = z.  [clausify(1)].

given #2 (I,wt=10): 5 x * y != z * y | x = z.  [clausify(2)].

given #3 (I,wt=15): 6 (x * y) * (z * u) = (x * z) * (y * u).  [assumption].

given #4 (I,wt=23): 8 (c1 * (c2 * c3)) * ((c4 * c5) * c6) != (c1 * (c4 * c3)) * ((c2 * c5) * c6).  [copy(7),flip(a)].

given #5 (T,wt=18): 9 (x * y) * (z * u) != (x * z) * v | y * u = v.  [para(6(a,1),4(a,1))].

given #6 (A,wt=18): 10 (x * y) * (z * u) != v * (y * u) | x * z = v.  [para(6(a,1),5(a,1))].

given #7 (F,wt=23): 15 (c1 * (c4 * c5)) * ((c2 * c3) * c6) != (c1 * (c4 * c3)) * ((c2 * c5) * c6).  [para(6(a,1),8(a,1))].

given #8 (F,wt=23): 16 (c1 * (c2 * c3)) * ((c4 * c5) * c6) != (c1 * (c2 * c5)) * ((c4 * c3) * c6).  [para(6(a,1),8(a,2))].

given #9 (T,wt=22): 22 (x * y) * (z * u) != (x * v) * (z * w) | y * u = v * w.  [para(6(a,1),9(a,2))].

given #10 (T,wt=22): 28 (x * y) * (z * u) != (v * y) * (w * u) | x * z = v * w.  [para(6(a,1),10(a,2))].

given #11 (A,wt=23): 11 ((x * y) * (z * u)) * (v * w) = ((x * z) * v) * ((y * u) * w).  [para(6(a,1),6(a,1,1))].

given #12 (F,wt=23): 35 (c1 * (c4 * c5)) * ((c2 * c3) * c6) != (c1 * (c2 * c5)) * ((c4 * c3) * c6).  [para(6(a,1),15(a,2))].

given #13 (F,wt=27): 13 ((c1 * (c2 * c3)) * ((c4 * c5) * c6)) * x != ((c1 * (c4 * c3)) * ((c2 * c5) * c6)) * x.  [ur(5,b,8,a)].

given #14 (T,wt=22): 47 (x * y) * (z * u) != (x * v) * (y * w) | z * u = v * w.  [para(6(a,1),22(a,1))].

given #15 (T,wt=22): 48 (x * y) * (z * u) != (x * v) * (y * w) | v * w = z * u.  [para(6(a,1),22(a,2)),flip(a)].

given #16 (A,wt=23): 12 (x * (y * z)) * (u * (v * w)) = (x * u) * ((y * v) * (z * w)).  [para(6(a,1),6(a,1,2)),flip(a)].

given #17 (F,wt=27): 14 x * ((c1 * (c2 * c3)) * ((c4 * c5) * c6)) != x * ((c1 * (c4 * c3)) * ((c2 * c5) * c6)).  [ur(4,b,8,a)].

given #18 (F,wt=27): 31 ((c1 * (c4 * c5)) * ((c2 * c3) * c6)) * x != ((c1 * (c4 * c3)) * ((c2 * c5) * c6)) * x.  [ur(5,b,15,a)].

given #19 (T,wt=22): 54 (x * y) * (z * u) != (v * w) * (y * u) | v * w = x * z.  [para(6(a,1),28(a,1)),flip(a)].

given #20 (T,wt=22): 136 (x * y) * (z * u) != (x * v) * (z * w) | v * w = y * u.  [para(6(a,1),48(a,1))].

given #21 (A,wt=31): 17 (x * (c1 * (c2 * c3))) * (y * ((c4 * c5) * c6)) != (x * y) * ((c1 * (c4 * c3)) * ((c2 * c5) * c6)).  [ur(9,b,8,a)].

given #22 (F,wt=27): 32 x * ((c1 * (c4 * c5)) * ((c2 * c3) * c6)) != x * ((c1 * (c4 * c3)) * ((c2 * c5) * c6)).  [ur(4,b,15,a)].

given #23 (F,wt=27): 38 ((c1 * (c2 * c3)) * ((c4 * c5) * c6)) * x != ((c1 * (c2 * c5)) * ((c4 * c3) * c6)) * x.  [ur(5,b,16,a)].

given #24 (T,wt=22): 137 (x * y) * (z * u) != (x * y) * (v * w) | v * w = z * u.  [para(6(a,1),48(a,2))].

given #25 (T,wt=22): 258 (x * y) * (z * u) != (v * w) * (z * u) | v * w = x * y.  [para(6(a,1),54(a,1))].

given #26 (A,wt=31): 18 (x * (c1 * (c4 * c3))) * (y * ((c2 * c5) * c6)) != (x * y) * ((c1 * (c2 * c3)) * ((c4 * c5) * c6)).  [ur(9,b,8,a(flip))].

given #27 (F,wt=27): 39 x * ((c1 * (c2 * c3)) * ((c4 * c5) * c6)) != x * ((c1 * (c2 * c5)) * ((c4 * c3) * c6)).  [ur(4,b,16,a)].

given #28 (F,wt=27): 118 ((c1 * (c4 * c5)) * ((c2 * c3) * c6)) * x != ((c1 * (c2 * c5)) * ((c4 * c3) * c6)) * x.  [ur(5,b,35,a)].

given #29 (T,wt=22): 259 (x * y) * (z * u) != (v * y) * (w * u) | v * w = x * z.  [para(6(a,1),54(a,2))].

given #30 (T,wt=23): 58 ((x * y) * z) * ((u * v) * w) = ((x * u) * z) * ((y * v) * w).  [para(11(a,1),6(a,1))].

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

% Proof 1 at 0.09 (+ 0.00) seconds.
% Length of proof is 14.
% Level of proof is 5.
% Maximum clause weight is 39.
% Given clauses 30.

1 (all x all y all z (x * y = x * z -> y = z)) # label(non_clause).  [assumption].
3 (x * (y * z)) * ((u * v) * w) = (x * (u * z)) * ((y * v) * w).  [goal].
4 x * y != x * z | y = z.  [clausify(1)].
6 (x * y) * (z * u) = (x * z) * (y * u).  [assumption].
7 (c1 * (c4 * c3)) * ((c2 * c5) * c6) != (c1 * (c2 * c3)) * ((c4 * c5) * c6).  [deny(3)].
8 (c1 * (c2 * c3)) * ((c4 * c5) * c6) != (c1 * (c4 * c3)) * ((c2 * c5) * c6).  [copy(7),flip(a)].
9 (x * y) * (z * u) != (x * z) * v | y * u = v.  [para(6(a,1),4(a,1))].
11 ((x * y) * (z * u)) * (v * w) = ((x * z) * v) * ((y * u) * w).  [para(6(a,1),6(a,1,1))].
12 (x * (y * z)) * (u * (v * w)) = (x * u) * ((y * v) * (z * w)).  [para(6(a,1),6(a,1,2)),flip(a)].
17 (x * (c1 * (c2 * c3))) * (y * ((c4 * c5) * c6)) != (x * y) * ((c1 * (c4 * c3)) * ((c2 * c5) * c6)).  [ur(9,b,8,a)].
58 ((x * y) * z) * ((u * v) * w) = ((x * u) * z) * ((y * v) * w).  [para(11(a,1),6(a,1))].
417 ((x * y) * ((z * u) * (v * w))) * ((v6 * v7) * v8) = ((x * v6) * (y * (u * w))) * (((z * v) * v7) * v8).  [para(12(a,1),58(a,1,1))].
427 (x * ((y * z) * u)) * ((c1 * (c4 * c3)) * ((c2 * c5) * c6)) != (x * (c1 * (c2 * c3))) * (((y * c4) * u) * ((z * c5) * c6)).  [para(58(a,1),17(a,1,2)),flip(a)].
428 $F.  [resolve(427,a,417,a)].

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

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

Given=30. Generated=1244. Kept=423. proofs=1.
Usable=30. Sos=329. Demods=0. Limbo=50, Disabled=17. Hints=0.
Weight_deleted=0. Literals_deleted=0.
Forward_subsumed=821. Back_subsumed=13.
Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0.
New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0.
Demod_attempts=0. Demod_rewrites=0.
Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
Nonunit_fsub_feature_tests=12994. Nonunit_bsub_feature_tests=1925.
Megabytes=0.62.
User_CPU=0.09, System_CPU=0.00, Wall_clock=0.

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

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

THEOREM PROVED

Exiting with 1 proof.

Process 10674 exit (max_proofs) Sat Aug 12 20:58:11 2006