%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP429-1 : 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 : n024.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 04:26:06 PM UTC 2026
% Result : Unsatisfiable 1.94s 1.87s
% Output : CNFRefutation 1.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 2
% Syntax : Number of clauses : 48 ( 48 unt; 0 nHn; 3 RR)
% Number of literals : 48 ( 47 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 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 : 128 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(X1,inverse(multiply(multiply(inverse(multiply(inverse(X2),multiply(inverse(X1),X3))),X4),inverse(multiply(X2,X4))))) = X3,
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,
multiply(X1,inverse(multiply(multiply(inverse(multiply(inverse(X2),multiply(inverse(X1),X3))),X4),inverse(multiply(X2,X4))))) = X3,
single_axiom ).
cnf(c_0_3,plain,
multiply(X1,inverse(multiply(multiply(inverse(multiply(inverse(X2),X3)),X4),inverse(multiply(X2,X4))))) = inverse(multiply(multiply(inverse(multiply(inverse(X5),multiply(inverse(inverse(X1)),X3))),X6),inverse(multiply(X5,X6)))),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(inverse(X1),multiply(X1,inverse(multiply(multiply(inverse(multiply(inverse(X2),X3)),X4),inverse(multiply(X2,X4)))))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
inverse(multiply(multiply(inverse(multiply(inverse(X1),multiply(inverse(inverse(X2)),multiply(inverse(X2),X3)))),X4),inverse(multiply(X1,X4)))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_6,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(inverse(inverse(X3)),multiply(inverse(X3),X2)),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(inverse(X3),multiply(X3,X2)),
inference(spm,[status(thm)],[c_0_6,c_0_6]) ).
cnf(c_0_8,plain,
multiply(X1,inverse(multiply(multiply(inverse(multiply(inverse(X2),multiply(X2,X3))),X4),inverse(multiply(inverse(X1),X4))))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_7]) ).
cnf(c_0_9,plain,
multiply(X1,inverse(multiply(multiply(inverse(multiply(inverse(X2),multiply(X2,X3))),multiply(X1,X4)),inverse(multiply(inverse(X5),multiply(X5,X4)))))) = X3,
inference(spm,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_10,plain,
multiply(inverse(X1),multiply(X1,inverse(multiply(multiply(inverse(multiply(inverse(X2),multiply(X2,X3))),X4),inverse(multiply(X5,X4)))))) = multiply(X5,X3),
inference(spm,[status(thm)],[c_0_4,c_0_7]) ).
cnf(c_0_11,plain,
multiply(multiply(inverse(X1),multiply(X1,X2)),inverse(multiply(X3,inverse(X3)))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_4]),c_0_4]) ).
cnf(c_0_12,plain,
multiply(inverse(multiply(inverse(X1),multiply(X1,X2))),X2) = multiply(inverse(multiply(inverse(X3),multiply(X3,X4))),X4),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,plain,
multiply(multiply(inverse(inverse(X1)),multiply(inverse(X2),multiply(X2,X3))),inverse(multiply(X4,inverse(X4)))) = multiply(X1,X3),
inference(spm,[status(thm)],[c_0_11,c_0_7]) ).
cnf(c_0_14,plain,
multiply(inverse(inverse(X1)),multiply(inverse(multiply(inverse(X2),multiply(X2,X3))),X3)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_12]),c_0_4]) ).
cnf(c_0_15,plain,
multiply(X1,inverse(multiply(X2,inverse(X2)))) = multiply(X1,inverse(multiply(X3,inverse(X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_11]),c_0_14]) ).
cnf(c_0_16,plain,
inverse(multiply(X1,inverse(X1))) = inverse(multiply(X2,inverse(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_15]),c_0_2]) ).
cnf(c_0_17,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_16]),c_0_14]) ).
cnf(c_0_18,plain,
multiply(inverse(X1),multiply(X2,inverse(X2))) = multiply(inverse(X3),multiply(X3,inverse(X1))),
inference(spm,[status(thm)],[c_0_7,c_0_17]) ).
cnf(c_0_19,plain,
inverse(multiply(multiply(inverse(multiply(inverse(X1),multiply(inverse(X2),multiply(X2,X3)))),X4),inverse(multiply(X1,X4)))) = X3,
inference(spm,[status(thm)],[c_0_5,c_0_5]) ).
cnf(c_0_20,plain,
multiply(X1,multiply(X2,inverse(X2))) = multiply(inverse(X3),multiply(X3,X1)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,plain,
multiply(X1,inverse(multiply(multiply(inverse(X2),multiply(X2,X3)),inverse(multiply(X4,multiply(multiply(inverse(X4),multiply(inverse(X1),X5)),X3)))))) = X5,
inference(spm,[status(thm)],[c_0_2,c_0_7]) ).
cnf(c_0_22,plain,
multiply(multiply(X1,multiply(X2,inverse(X2))),inverse(multiply(X3,inverse(X3)))) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_20]) ).
cnf(c_0_23,plain,
multiply(X1,inverse(inverse(multiply(X2,inverse(X2))))) = inverse(inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_11]) ).
cnf(c_0_24,plain,
multiply(inverse(inverse(X1)),inverse(inverse(inverse(multiply(inverse(X2),inverse(inverse(X2))))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_23]),c_0_23]) ).
cnf(c_0_25,plain,
multiply(X1,inverse(X1)) = inverse(inverse(inverse(multiply(X2,inverse(X2))))),
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_26,plain,
multiply(inverse(inverse(X1)),multiply(X2,inverse(X2))) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,plain,
multiply(X1,inverse(multiply(X2,inverse(X2)))) = inverse(inverse(X1)),
inference(spm,[status(thm)],[c_0_22,c_0_26]) ).
cnf(c_0_28,plain,
multiply(inverse(X1),multiply(X1,X2)) = inverse(inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_27]),c_0_23]) ).
cnf(c_0_29,plain,
inverse(inverse(inverse(inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_23]) ).
cnf(c_0_30,plain,
multiply(X1,inverse(multiply(multiply(inverse(inverse(inverse(X2))),X3),inverse(multiply(inverse(X1),X3))))) = X2,
inference(rw,[status(thm)],[c_0_8,c_0_28]) ).
cnf(c_0_31,plain,
multiply(X1,multiply(X2,inverse(X2))) = inverse(inverse(X1)),
inference(spm,[status(thm)],[c_0_26,c_0_29]) ).
cnf(c_0_32,plain,
multiply(X1,inverse(multiply(inverse(X2),X1))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_31]),c_0_29]),c_0_29]) ).
cnf(c_0_33,plain,
multiply(inverse(multiply(X1,inverse(X1))),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_27]),c_0_29]) ).
cnf(c_0_34,plain,
multiply(multiply(X1,inverse(X1)),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_31]),c_0_29]) ).
cnf(c_0_35,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_33]),c_0_34]) ).
cnf(c_0_36,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[c_0_28,c_0_35]) ).
cnf(c_0_37,plain,
multiply(multiply(X1,X2),inverse(X2)) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_36]) ).
cnf(c_0_38,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_36,c_0_35]) ).
cnf(c_0_39,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(spm,[status(thm)],[c_0_32,c_0_35]) ).
cnf(c_0_40,plain,
multiply(multiply(X1,inverse(X2)),X2) = X1,
inference(spm,[status(thm)],[c_0_37,c_0_35]) ).
cnf(c_0_41,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,plain,
multiply(multiply(X1,X2),multiply(inverse(X2),X3)) = multiply(X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_28]),c_0_28]),c_0_35]),c_0_42]),c_0_43]),c_0_35]) ).
cnf(c_0_45,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
prove_these_axioms_3 ).
cnf(c_0_46,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_38]),c_0_35]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : GRP429-1 : TPTP v9.2.1. Released v2.6.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 13:35:11 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 1.94/1.87 % Version : CSE_E---1.7
% 1.94/1.87 % Problem : theBenchmark.p
% 1.94/1.87 % SZS status Unsatisfiable for theBenchmark.p
% 1.94/1.87 % SZS output start CNFRefutation
% See solution above
% 1.94/1.87 % Total time : 1.361s
%------------------------------------------------------------------------------