%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP402-1 : TPTP v9.2.1. Released v2.5.0.
% 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 : n015.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 04:26:02 PM UTC 2026
% Result : Unsatisfiable 1.78s 1.93s
% Output : CNFRefutation 1.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of clauses : 32 ( 22 unt; 0 nHn; 15 RR)
% Number of literals : 42 ( 41 equ; 15 neg)
% Maximal clause size : 2 ( 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; 3 con; 0-2 aty)
% Number of variables : 84 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_cancellation,axiom,
( X2 = X3
| multiply(X1,X2) != multiply(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP008-1.ax',left_cancellation) ).
cnf(commutator,axiom,
multiply(X1,X2) = multiply(X2,multiply(X1,commutator(X1,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutator) ).
cnf(associativity_of_multiply,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP008-0.ax',associativity_of_multiply) ).
cnf(nilpotency,axiom,
multiply(commutator(X1,X2),X3) = multiply(X3,commutator(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nilpotency) ).
cnf(prove_commutator_is_associative,negated_conjecture,
commutator(commutator(a,b),c) != commutator(a,commutator(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutator_is_associative) ).
cnf(c_0_5,axiom,
( X2 = X3
| multiply(X1,X2) != multiply(X1,X3) ),
left_cancellation ).
cnf(c_0_6,axiom,
multiply(X1,X2) = multiply(X2,multiply(X1,commutator(X1,X2))),
commutator ).
cnf(c_0_7,plain,
( X1 = multiply(X2,commutator(X2,X3))
| multiply(X3,X1) != multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity_of_multiply ).
cnf(c_0_9,plain,
multiply(X1,commutator(X1,X1)) = X1,
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( X1 = X2
| multiply(X3,multiply(X4,X1)) != multiply(X3,multiply(X4,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_8]),c_0_8]) ).
cnf(c_0_11,plain,
multiply(X1,multiply(commutator(X1,X1),X2)) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,axiom,
multiply(commutator(X1,X2),X3) = multiply(X3,commutator(X1,X2)),
nilpotency ).
cnf(c_0_13,plain,
( X1 = commutator(X2,X2)
| multiply(X3,multiply(X2,X1)) != multiply(X3,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_14,plain,
multiply(X1,multiply(X2,commutator(X1,X1))) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
commutator(X1,X1) = commutator(X2,X2),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,plain,
( X1 = commutator(X2,X3)
| multiply(X4,X1) != multiply(commutator(X2,X3),X4) ),
inference(spm,[status(thm)],[c_0_5,c_0_12]) ).
cnf(c_0_17,plain,
multiply(X1,commutator(X2,X2)) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_15]) ).
cnf(c_0_18,plain,
( multiply(X1,commutator(X1,X2)) = commutator(X3,X4)
| multiply(X1,X2) != multiply(commutator(X3,X4),X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_6]) ).
cnf(c_0_19,plain,
( X1 = commutator(X2,X2)
| multiply(X3,X1) != X3 ),
inference(spm,[status(thm)],[c_0_5,c_0_17]) ).
cnf(c_0_20,plain,
multiply(commutator(X1,X2),commutator(commutator(X1,X2),X3)) = commutator(X1,X2),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_21,negated_conjecture,
commutator(commutator(a,b),c) != commutator(a,commutator(b,c)),
prove_commutator_is_associative ).
cnf(c_0_22,plain,
commutator(commutator(X1,X2),X3) = commutator(X4,X4),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
( X1 = commutator(X2,X3)
| multiply(X3,multiply(X2,X1)) != multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_10,c_0_6]) ).
cnf(c_0_24,plain,
multiply(commutator(X1,X2),multiply(X3,X4)) = multiply(X3,multiply(X4,commutator(X1,X2))),
inference(spm,[status(thm)],[c_0_8,c_0_12]) ).
cnf(c_0_25,negated_conjecture,
commutator(X1,X1) != commutator(a,commutator(b,c)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
( X1 = commutator(X2,multiply(X3,X4))
| multiply(X3,multiply(X4,multiply(X2,X1))) != multiply(X2,multiply(X3,X4)) ),
inference(spm,[status(thm)],[c_0_23,c_0_8]) ).
cnf(c_0_27,plain,
multiply(X1,multiply(commutator(X2,X3),commutator(X1,commutator(X2,X3)))) = multiply(X1,commutator(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_24]),c_0_12]) ).
cnf(c_0_28,negated_conjecture,
commutator(commutator(X1,X2),X3) != commutator(a,commutator(b,c)),
inference(spm,[status(thm)],[c_0_25,c_0_22]) ).
cnf(c_0_29,plain,
commutator(commutator(X1,X2),multiply(X3,X4)) = commutator(X4,commutator(X1,X2)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_24]) ).
cnf(c_0_30,negated_conjecture,
commutator(X1,commutator(X2,X3)) != commutator(a,commutator(b,c)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(er,[status(thm)],[c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP402-1 : TPTP v9.2.1. Released v2.5.0.
% 0.00/0.11 % 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
% 0.12/0.31 % Computer : n015.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Mon May 4 18:34:46 EDT 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.32 % start to proof: theBenchmark
% 1.78/1.93 % Version : CSE_E---1.7
% 1.78/1.93 % Problem : theBenchmark.p
% 1.78/1.93 % SZS status Unsatisfiable for theBenchmark.p
% 1.78/1.93 % SZS output start CNFRefutation
% See solution above
% 1.78/1.93 % Total time : 1.372s
%------------------------------------------------------------------------------