%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP408-1 : TPTP v9.2.1. Released v2.6.0.
% 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 : n025.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 04:26:03 PM UTC 2026
% Result : Unsatisfiable 6.46s 4.67s
% Output : CNFRefutation 6.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 2
% Syntax : Number of clauses : 45 ( 45 unt; 0 nHn; 3 RR)
% Number of literals : 45 ( 44 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 19 ( 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 : 145 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),multiply(inverse(X2),multiply(inverse(X2),X2))))) = X3,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
cnf(c_0_2,axiom,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),multiply(inverse(X2),multiply(inverse(X2),X2))))) = X3,
single_axiom ).
cnf(c_0_3,plain,
multiply(X1,inverse(multiply(inverse(X2),multiply(inverse(X3),multiply(inverse(X3),X3))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X3)),X4)),X2)),multiply(inverse(X4),multiply(inverse(X4),X4)))),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(X1,inverse(multiply(inverse(multiply(inverse(X2),X3)),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X1,X4)),X2)),multiply(inverse(X4),multiply(inverse(X4),X4))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X1,X4)),X2)),multiply(inverse(X4),multiply(inverse(X4),X4))))),inverse(multiply(inverse(multiply(inverse(multiply(X1,X4)),X2)),multiply(inverse(X4),multiply(inverse(X4),X4))))))))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_5,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(multiply(inverse(X3),multiply(inverse(X2),multiply(inverse(X2),X2)))))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_6,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(X1),X2)),multiply(inverse(X1),X3))),multiply(inverse(X2),multiply(inverse(X2),X2)))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_4]),c_0_2]) ).
cnf(c_0_7,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(multiply(inverse(X4),X2)),multiply(inverse(X4),X3)),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(multiply(X4,X2)),multiply(X4,X3)),
inference(spm,[status(thm)],[c_0_7,c_0_7]) ).
cnf(c_0_9,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3))),multiply(inverse(X2),multiply(inverse(X2),X2)))) = X3,
inference(spm,[status(thm)],[c_0_6,c_0_6]) ).
cnf(c_0_10,plain,
multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),multiply(inverse(multiply(X4,X2)),multiply(X4,X5))) = multiply(inverse(multiply(X6,X3)),multiply(X6,multiply(X1,X5))),
inference(spm,[status(thm)],[c_0_8,c_0_8]) ).
cnf(c_0_11,plain,
multiply(inverse(multiply(X1,multiply(X2,inverse(multiply(inverse(X3),multiply(inverse(X4),multiply(inverse(X4),X4))))))),multiply(X1,X5)) = multiply(inverse(X3),multiply(inverse(multiply(X2,X4)),X5)),
inference(spm,[status(thm)],[c_0_8,c_0_5]) ).
cnf(c_0_12,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X1,multiply(inverse(multiply(X2,X3)),X3))),multiply(X1,X4))),multiply(inverse(multiply(X5,X3)),multiply(X5,multiply(X2,X3))))) = X4,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
multiply(inverse(multiply(X1,multiply(X2,inverse(multiply(X3,multiply(inverse(X4),multiply(inverse(X4),X4))))))),multiply(X1,X5)) = multiply(X3,multiply(inverse(multiply(X2,X4)),X5)),
inference(spm,[status(thm)],[c_0_11,c_0_9]) ).
cnf(c_0_14,plain,
multiply(inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X3)),X4)),multiply(inverse(X3),multiply(inverse(X3),X3)))))),multiply(X1,X5)) = multiply(inverse(X4),multiply(X2,X5)),
inference(spm,[status(thm)],[c_0_8,c_0_2]) ).
cnf(c_0_15,plain,
multiply(inverse(multiply(X1,multiply(inverse(multiply(X2,X3)),X3))),multiply(X1,inverse(multiply(inverse(X4),multiply(inverse(multiply(X5,X3)),multiply(X5,multiply(X2,X3))))))) = X4,
inference(spm,[status(thm)],[c_0_5,c_0_10]) ).
cnf(c_0_16,plain,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X1,multiply(inverse(multiply(X2,X3)),X3))),X4)),multiply(inverse(multiply(X5,X3)),multiply(X5,multiply(X2,X3)))))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_10]) ).
cnf(c_0_17,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),multiply(inverse(multiply(inverse(X3),X2)),X4))),multiply(inverse(X3),multiply(X1,X3)))) = X4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_2]),c_0_13]),c_0_14]) ).
cnf(c_0_18,plain,
multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),multiply(inverse(multiply(inverse(X3),X2)),inverse(multiply(inverse(X4),multiply(inverse(X3),multiply(X1,X3)))))) = X4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_2]),c_0_14]),c_0_13]) ).
cnf(c_0_19,plain,
multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),inverse(multiply(X2,multiply(inverse(multiply(X4,X2)),multiply(X4,multiply(inverse(X3),X2)))))) = multiply(inverse(X3),multiply(X1,X3)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
multiply(X1,inverse(multiply(inverse(X2),multiply(inverse(inverse(multiply(inverse(X3),multiply(inverse(X4),multiply(inverse(X4),X4))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(X3),multiply(inverse(X4),multiply(inverse(X4),X4))))),X4)),X5)),X3)),multiply(inverse(X5),multiply(inverse(X5),X5)))))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X3),multiply(inverse(X4),multiply(inverse(X4),X4)))))),X6)),X2)),multiply(inverse(X6),multiply(inverse(X6),X6)))),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_21,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(X1),inverse(X2)))),multiply(inverse(X1),multiply(inverse(X1),X1))) = X2,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
multiply(X1,inverse(multiply(inverse(X2),X2))) = inverse(multiply(X3,multiply(inverse(multiply(X1,X3)),multiply(inverse(multiply(X1,X3)),multiply(X1,X3))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_9]),c_0_13]),c_0_2]) ).
cnf(c_0_23,plain,
multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(X3)))),multiply(inverse(X2),multiply(inverse(X2),X2))) = X3,
inference(spm,[status(thm)],[c_0_21,c_0_8]) ).
cnf(c_0_24,plain,
multiply(X1,inverse(multiply(inverse(X2),X2))) = multiply(X1,inverse(multiply(inverse(X3),X3))),
inference(spm,[status(thm)],[c_0_22,c_0_22]) ).
cnf(c_0_25,plain,
multiply(X1,multiply(X2,inverse(multiply(inverse(X3),multiply(inverse(X4),multiply(inverse(X4),X4)))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X5)),X6)),multiply(inverse(multiply(inverse(multiply(X2,X4)),X5)),X3))),multiply(inverse(X6),multiply(inverse(X6),X6)))),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_26,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_23]) ).
cnf(c_0_27,plain,
inverse(multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(X2),multiply(inverse(X2),X2)))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_5]) ).
cnf(c_0_28,plain,
inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(inverse(X2),X2)))) = X2,
inference(spm,[status(thm)],[c_0_27,c_0_8]) ).
cnf(c_0_29,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(multiply(inverse(multiply(X3,X4)),multiply(X3,multiply(inverse(X2),X2)))))) = multiply(inverse(X2),X4),
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_30,plain,
inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(inverse(X3),X3)))) = X2,
inference(spm,[status(thm)],[c_0_28,c_0_26]) ).
cnf(c_0_31,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X3,X4)))),multiply(inverse(X2),multiply(X3,X2)))) = multiply(inverse(X2),X4),
inference(spm,[status(thm)],[c_0_17,c_0_10]) ).
cnf(c_0_32,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(X2),X3),
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X1,multiply(X2,X3))),multiply(X1,X4))),multiply(inverse(multiply(X2,X3)),multiply(inverse(multiply(X5,X3)),multiply(X5,X3))))) = X4,
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_34,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_32]),c_0_32]) ).
cnf(c_0_35,plain,
multiply(inverse(inverse(X1)),multiply(inverse(X2),X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_32]),c_0_32]) ).
cnf(c_0_36,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_32]),c_0_32]),c_0_32]),c_0_34]),c_0_34]) ).
cnf(c_0_37,plain,
multiply(inverse(X1),multiply(inverse(inverse(X1)),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_35]),c_0_34]),c_0_36]) ).
cnf(c_0_38,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_35,c_0_37]) ).
cnf(c_0_39,plain,
multiply(X1,multiply(inverse(X2),X2)) = X1,
inference(rw,[status(thm)],[c_0_35,c_0_38]) ).
cnf(c_0_40,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_39]),c_0_39]) ).
cnf(c_0_41,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_40]),c_0_38]) ).
cnf(c_0_42,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
prove_these_axioms_3 ).
cnf(c_0_43,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_32,c_0_41]),c_0_38]),c_0_38]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP408-1 : TPTP v9.2.1. Released v2.6.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n025.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 18:34:28 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 6.46/4.67 % Version : CSE_E---1.7
% 6.46/4.67 % Problem : theBenchmark.p
% 6.46/4.67 % SZS status Unsatisfiable for theBenchmark.p
% 6.46/4.67 % SZS output start CNFRefutation
% See solution above
% 6.46/4.69 % Total time : 3.369s
%------------------------------------------------------------------------------