============================== Prover9 ===============================
Prover9 (32) version March-2007, March 2007.
Process 20998 was started by mccune on cleo,
Mon Mar 19 17:01:53 2007
The command was "/home/mccune/bin/prover9 -f cs.in AN.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 AN.in


formulas(sos).
(x @ y) @ z = u @ (v @ w).
end_of_list.

formulas(sos).
(A @ B) * C != C * (A @ B) # answer(N).
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 = u @ (v @ w).  [assumption].
(A @ B) * C != C * (A @ B) # answer(N).  [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 = u @ (v @ w).  [assumption].
6 (A @ B) * C != C * (A @ B) # answer(N).  [assumption].
end_of_list.

formulas(demodulators).
3 (x * y) * z = x * y * z.  [assumption].
4 x * y * (y @ x) = y * x.  [assumption].
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 = u @ (v @ w).  [assumption].

given #6 (I,wt=11): 6 (A @ B) * C != C * (A @ B) # answer(N).  [assumption].

given #7 (A,wt=14): 7 x * y * z != x * y * u | z = u.  [para(3(a,1),1(a,1)),rewrite(3(4))].

given #8 (F,wt=15): 20 (A @ B) * C * x != C * (A @ B) * x # answer(N).  [ur(2,b,6,a),rewrite(3(6),3(12))].

given #9 (F,wt=15): 21 x * (A @ B) * C != x * C * (A @ B) # answer(N).  [ur(1,b,6,a)].

given #10 (F,wt=17): 29 C * (A @ B) * (C @ (A @ B)) != C * (A @ B) # answer(N).  [para(4(a,1),20(a,1)),flip(a)].

given #11 (F,wt=17): 31 (A @ B) * C * ((A @ B) @ C) != (A @ B) * C # answer(N).  [para(4(a,1),20(a,2))].

given #12 (T,wt=7): 9 x * (x @ x) = x.  [hyper(1,a,4,a)].

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

% Proof 1 at 0.00 (+ 0.00) seconds: N.
% Length of proof is 11.
% Level of proof is 3.
% Maximum clause weight is 19.
% Given clauses 12.

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 = u @ (v @ w).  [assumption].
6 (A @ B) * C != C * (A @ B) # answer(N).  [assumption].
9 x * (x @ x) = x.  [hyper(1,a,4,a)].
17 (x @ y) * z * ((u @ v) @ w) = z * (x @ y).  [para(5(a,2),4(a,1,2,2))].
20 (A @ B) * C * x != C * (A @ B) * x # answer(N).  [ur(2,b,6,a),rewrite(3(6),3(12))].
50 (A @ B) * C * ((A @ B) @ (A @ B)) != C * (A @ B) # answer(N).  [para(9(a,1),20(a,2,2))].
51 $F # answer(N).  [resolve(50,a,17,a)].

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

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

Given=12. Generated=114. Kept=50. proofs=1.
Usable=12. Sos=28. Demods=10. Limbo=9, Disabled=6. Hints=0.
Weight_deleted=0. Literals_deleted=0.
Forward_subsumed=64. Back_subsumed=0.
Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0.
New_demodulators=10 (0 lex), Back_demodulated=0. Back_unit_deleted=0.
Demod_attempts=1241. Demod_rewrites=74.
Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
Nonunit_fsub_feature_tests=63. Nonunit_bsub_feature_tests=16.
Megabytes=0.08.
User_CPU=0.00, System_CPU=0.00, Wall_clock=0.

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

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

THEOREM PROVED

Exiting with 1 proof.

Process 20998 exit (max_proofs) Mon Mar 19 17:01:53 2007