%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP423-1 : TPTP v9.2.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/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 04:26:05 PM UTC 2026
% Result : Unsatisfiable 33.57s 20.13s
% Output : CNFRefutation 33.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 2
% Syntax : Number of clauses : 39 ( 39 unt; 0 nHn; 3 RR)
% Number of literals : 39 ( 38 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 20 ( 3 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 : 109 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))))),multiply(X1,X3))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
cnf(c_0_2,axiom,
inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))))),multiply(X1,X3))) = X2,
single_axiom ).
cnf(c_0_3,plain,
inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3))) = multiply(inverse(X3),inverse(multiply(inverse(X2),multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(multiply(inverse(X3),X3)))))))),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3))) = inverse(multiply(inverse(multiply(X4,X2)),multiply(X4,X3))),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_5,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(multiply(X4,X2)),multiply(X4,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_4]),c_0_2]) ).
cnf(c_0_6,plain,
inverse(multiply(inverse(multiply(X1,inverse(multiply(X2,multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))))),multiply(X1,X3))) = multiply(inverse(multiply(X4,inverse(multiply(inverse(X2),multiply(inverse(X5),inverse(multiply(inverse(X5),X5))))))),multiply(X4,X5)),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_7,plain,
inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),multiply(inverse(multiply(X3,X4)),inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,X4)))))))),multiply(X1,multiply(X3,X4)))) = X2,
inference(spm,[status(thm)],[c_0_2,c_0_5]) ).
cnf(c_0_8,plain,
multiply(inverse(multiply(X1,inverse(multiply(inverse(inverse(X2)),multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))))),multiply(X1,X3)) = X2,
inference(spm,[status(thm)],[c_0_2,c_0_6]) ).
cnf(c_0_9,plain,
inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),multiply(inverse(X3),inverse(multiply(inverse(multiply(X4,multiply(X5,X6))),multiply(X4,multiply(X5,X6))))))))),multiply(X1,X3))) = X2,
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,plain,
multiply(inverse(multiply(X1,inverse(multiply(inverse(inverse(X2)),multiply(inverse(multiply(X3,X4)),inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,X4)))))))),multiply(X1,multiply(X3,X4))) = X2,
inference(spm,[status(thm)],[c_0_8,c_0_5]) ).
cnf(c_0_11,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,X3)))),multiply(inverse(X3),inverse(multiply(inverse(X3),X3)))) = X2,
inference(spm,[status(thm)],[c_0_8,c_0_3]) ).
cnf(c_0_12,plain,
inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),multiply(inverse(X3),inverse(multiply(inverse(X4),X4))))))),multiply(X1,X3))) = X2,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3)))),multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))) = X2,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_14,plain,
multiply(inverse(X1),multiply(inverse(X2),inverse(multiply(inverse(X2),X2)))) = multiply(inverse(X1),multiply(inverse(X2),inverse(multiply(inverse(X3),X3)))),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
multiply(inverse(X1),inverse(multiply(inverse(X1),X1))) = multiply(inverse(X1),inverse(multiply(inverse(X2),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_13]) ).
cnf(c_0_16,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_15]),c_0_11]) ).
cnf(c_0_17,plain,
inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),multiply(inverse(X2),inverse(multiply(inverse(X2),X2))))) = X2,
inference(spm,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_18,plain,
inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),multiply(inverse(X2),inverse(multiply(inverse(X3),X3))))) = X2,
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_19,plain,
inverse(multiply(inverse(multiply(inverse(X1),inverse(multiply(inverse(X2),multiply(inverse(inverse(multiply(inverse(X3),multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(X1),X1)))))))),inverse(multiply(inverse(inverse(multiply(inverse(X3),multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(X1),X1)))))))),inverse(multiply(inverse(X3),multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(X1),X1)))))))))))))),inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,X1))))) = X2,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_20,plain,
inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),multiply(inverse(X2),X2))) = inverse(multiply(inverse(X3),X3)),
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_21,plain,
inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),multiply(inverse(X3),X3))))),multiply(X1,inverse(multiply(inverse(X4),X4))))) = X2,
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_22,plain,
multiply(inverse(inverse(multiply(inverse(X1),X1))),multiply(inverse(X2),X2)) = multiply(inverse(X3),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_19]) ).
cnf(c_0_23,plain,
multiply(inverse(inverse(multiply(inverse(X1),X1))),multiply(inverse(inverse(X2)),inverse(multiply(inverse(inverse(X2)),inverse(X2))))) = X2,
inference(spm,[status(thm)],[c_0_11,c_0_16]) ).
cnf(c_0_24,plain,
inverse(multiply(inverse(X1),X1)) = multiply(inverse(X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_21]) ).
cnf(c_0_25,plain,
multiply(inverse(inverse(multiply(inverse(X1),X1))),multiply(inverse(inverse(X2)),inverse(multiply(inverse(X3),X3)))) = X2,
inference(spm,[status(thm)],[c_0_23,c_0_16]) ).
cnf(c_0_26,plain,
multiply(inverse(X1),inverse(multiply(inverse(inverse(multiply(inverse(X2),multiply(inverse(X1),inverse(multiply(inverse(X1),X1)))))),multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(X1),X1)))))))) = X2,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_27,plain,
inverse(multiply(inverse(X1),multiply(inverse(X2),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_24]),c_0_25]) ).
cnf(c_0_28,plain,
multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(X2),X3)) = multiply(inverse(multiply(X4,X2)),multiply(X4,X3)),
inference(spm,[status(thm)],[c_0_5,c_0_16]) ).
cnf(c_0_29,plain,
multiply(inverse(multiply(inverse(X1),X1)),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_27]),c_0_27]),c_0_27]) ).
cnf(c_0_30,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(X2),X3),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_31,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_27]),c_0_29]) ).
cnf(c_0_32,plain,
multiply(X1,multiply(inverse(X2),X2)) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_16]) ).
cnf(c_0_33,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_32]),c_0_32]) ).
cnf(c_0_34,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_31]) ).
cnf(c_0_35,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_33]),c_0_34]) ).
cnf(c_0_36,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
prove_these_axioms_3 ).
cnf(c_0_37,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_35]),c_0_34]),c_0_34]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP423-1 : TPTP v9.2.1. Released v2.6.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.33 % Computer : n015.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 18:35:47 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 33.57/20.13 % Version : CSE_E---1.7
% 33.57/20.13 % Problem : theBenchmark.p
% 33.57/20.13 % SZS status Unsatisfiable for theBenchmark.p
% 33.57/20.13 % SZS output start CNFRefutation
% See solution above
% 33.65/20.26 % Total time : 14.393s
%------------------------------------------------------------------------------