%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG245-1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:08:22 PM UTC 2026
% Result : Unsatisfiable 4.07s 3.12s
% Output : CNFRefutation 4.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 23 ( 23 unt; 0 nHn; 3 RR)
% Number of literals : 23 ( 22 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c02,axiom,
mult(mult(X1,X2),X3) = mult(mult(X1,X3),mult(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
cnf(c05,axiom,
mult(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).
cnf(c01,axiom,
mult(X1,mult(X2,X3)) = mult(mult(X1,X2),mult(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c01) ).
cnf(c03,axiom,
mult(mult(mult(X1,X2),mult(X3,X4)),mult(mult(mult(X1,X2),mult(X3,X4)),mult(mult(X1,X3),mult(X2,X4)))) = mult(mult(X1,X3),mult(X2,X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c03) ).
cnf(c04,axiom,
mult(mult(mult(mult(X1,X2),mult(X3,X4)),mult(mult(X1,X3),mult(X2,X4))),mult(mult(X1,X3),mult(X2,X4))) = mult(mult(X1,X2),mult(X3,X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).
cnf(goals,negated_conjecture,
mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))) != mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c_0_6,axiom,
mult(mult(X1,X2),X3) = mult(mult(X1,X3),mult(X2,X3)),
c02 ).
cnf(c_0_7,axiom,
mult(X1,X1) = X1,
c05 ).
cnf(c_0_8,axiom,
mult(X1,mult(X2,X3)) = mult(mult(X1,X2),mult(X1,X3)),
c01 ).
cnf(c_0_9,plain,
mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,plain,
mult(mult(mult(X1,X2),X3),mult(X1,mult(X2,X4))) = mult(mult(X1,X2),mult(X3,mult(X1,X4))),
inference(spm,[status(thm)],[c_0_8,c_0_8]) ).
cnf(c_0_11,plain,
mult(mult(X1,mult(X2,X3)),mult(mult(X1,X2),X4)) = mult(mult(X1,X2),mult(mult(X1,X3),X4)),
inference(spm,[status(thm)],[c_0_8,c_0_8]) ).
cnf(c_0_12,plain,
mult(mult(X1,mult(X2,X1)),mult(X3,X1)) = mult(mult(mult(X1,X2),X3),X1),
inference(spm,[status(thm)],[c_0_6,c_0_9]) ).
cnf(c_0_13,plain,
mult(mult(X1,mult(X2,X1)),mult(X2,X3)) = mult(mult(X1,X2),mult(mult(X2,X1),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_10]),c_0_6]),c_0_9]) ).
cnf(c_0_14,plain,
mult(mult(X1,mult(X1,X2)),mult(X2,X3)) = mult(mult(X1,X2),mult(mult(X1,X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_11]),c_0_6]) ).
cnf(c_0_15,plain,
mult(mult(X1,mult(X2,X3)),mult(mult(X4,X2),X3)) = mult(mult(X1,mult(X4,X3)),mult(X2,X3)),
inference(spm,[status(thm)],[c_0_6,c_0_6]) ).
cnf(c_0_16,plain,
mult(mult(X1,X2),mult(mult(X2,X1),X1)) = mult(mult(mult(X1,X2),X2),X1),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
mult(mult(mult(X1,mult(X1,X2)),X2),X1) = mult(X1,mult(X2,mult(mult(X2,X1),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_8]),c_0_8]),c_0_13]),c_0_16]),c_0_12]),c_0_6]) ).
cnf(c_0_18,axiom,
mult(mult(mult(X1,X2),mult(X3,X4)),mult(mult(mult(X1,X2),mult(X3,X4)),mult(mult(X1,X3),mult(X2,X4)))) = mult(mult(X1,X3),mult(X2,X4)),
c03 ).
cnf(c_0_19,axiom,
mult(mult(mult(mult(X1,X2),mult(X3,X4)),mult(mult(X1,X3),mult(X2,X4))),mult(mult(X1,X3),mult(X2,X4))) = mult(mult(X1,X2),mult(X3,X4)),
c04 ).
cnf(c_0_20,negated_conjecture,
mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))) != mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))),
goals ).
cnf(c_0_21,plain,
mult(mult(mult(X1,X2),mult(X3,X4)),mult(mult(X1,X3),mult(X2,X4))) = mult(mult(mult(X1,X3),mult(X2,X4)),mult(mult(X1,X2),mult(X3,X4))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_8]),c_0_8]),c_0_7]),c_0_19]),c_0_8]),c_0_8]),c_0_7]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : ALG245-1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.07/0.24 % Computer : n012.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Tue May 5 10:30:46 EDT 2026
% 0.07/0.24 % CPUTime :
% 0.07/0.25 % start to proof: theBenchmark
% 4.07/3.12 % Version : CSE_E---1.7
% 4.07/3.12 % Problem : theBenchmark.p
% 4.07/3.12 % SZS status Unsatisfiable for theBenchmark.p
% 4.07/3.12 % SZS output start CNFRefutation
% See solution above
% 4.07/3.13 % Total time : 2.361s
%------------------------------------------------------------------------------