%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP431-1 : 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 : n002.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 1.83s 1.91s
% Output : CNFRefutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 2
% Syntax : Number of clauses : 41 ( 41 unt; 0 nHn; 3 RR)
% Number of literals : 41 ( 40 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 121 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(X1,inverse(multiply(X2,multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,X2))),X1)))) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
cnf(c_0_2,axiom,
multiply(X1,inverse(multiply(X2,multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,X2))),X1)))) = X4,
single_axiom ).
cnf(c_0_3,plain,
multiply(X1,inverse(multiply(multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X4))),multiply(X5,inverse(X5))),multiply(X3,X1)))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(X1,inverse(multiply(multiply(X2,multiply(X3,inverse(X3))),multiply(X4,X1)))) = multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(X2,X4))),multiply(X6,inverse(X6))),
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,multiply(X3,inverse(multiply(multiply(X4,multiply(X5,inverse(X5))),multiply(X2,X3))))))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_4]) ).
cnf(c_0_6,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,X3))) = multiply(multiply(X4,inverse(X4)),inverse(multiply(X2,X3))),
inference(spm,[status(thm)],[c_0_5,c_0_3]) ).
cnf(c_0_7,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_6]),c_0_2]) ).
cnf(c_0_8,plain,
multiply(X1,inverse(multiply(multiply(multiply(multiply(X2,inverse(X2)),inverse(X3)),multiply(X4,inverse(X4))),multiply(X5,X1)))) = inverse(multiply(X6,multiply(multiply(multiply(X7,inverse(X7)),inverse(multiply(X3,X6))),X5))),
inference(spm,[status(thm)],[c_0_3,c_0_2]) ).
cnf(c_0_9,plain,
multiply(X1,inverse(multiply(multiply(multiply(X2,inverse(X2)),multiply(X3,inverse(X3))),multiply(X4,X1)))) = inverse(X4),
inference(spm,[status(thm)],[c_0_3,c_0_7]) ).
cnf(c_0_10,plain,
multiply(X1,inverse(multiply(inverse(X2),multiply(multiply(X3,inverse(X3)),X1)))) = X2,
inference(spm,[status(thm)],[c_0_2,c_0_7]) ).
cnf(c_0_11,plain,
multiply(X1,inverse(multiply(inverse(multiply(X2,multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,X2))),X5))),multiply(multiply(multiply(X6,inverse(X6)),inverse(X4)),X1)))) = X5,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_12,plain,
inverse(multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(multiply(X3,X4),X1))),X3))) = X4,
inference(spm,[status(thm)],[c_0_3,c_0_8]) ).
cnf(c_0_13,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,inverse(X2)))) = multiply(X3,inverse(X3)),
inference(spm,[status(thm)],[c_0_5,c_0_9]) ).
cnf(c_0_14,plain,
multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(multiply(X3,inverse(X3)),X1))),X4)) = X4,
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(X1))),X2)),multiply(X3,inverse(X3)))) = X2,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,plain,
multiply(inverse(multiply(X1,inverse(X1))),multiply(multiply(X2,inverse(X2)),X3)) = X3,
inference(spm,[status(thm)],[c_0_14,c_0_7]) ).
cnf(c_0_17,plain,
inverse(multiply(inverse(multiply(X1,X2)),multiply(multiply(X3,inverse(X3)),X1))) = X2,
inference(spm,[status(thm)],[c_0_12,c_0_7]) ).
cnf(c_0_18,plain,
inverse(multiply(inverse(X1),multiply(X2,inverse(X2)))) = multiply(multiply(X3,inverse(X3)),X1),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
multiply(multiply(X1,inverse(X1)),multiply(inverse(multiply(X2,inverse(X2))),X3)) = X3,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,plain,
inverse(multiply(inverse(multiply(multiply(inverse(multiply(X1,inverse(X1))),X2),X3)),X2)) = X3,
inference(spm,[status(thm)],[c_0_12,c_0_19]) ).
cnf(c_0_21,plain,
multiply(multiply(multiply(X1,inverse(X1)),inverse(X2)),X3) = inverse(multiply(inverse(X3),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_14]),c_0_19]) ).
cnf(c_0_22,plain,
inverse(multiply(X1,inverse(multiply(inverse(X2),multiply(multiply(X2,X3),X1))))) = X3,
inference(rw,[status(thm)],[c_0_12,c_0_21]) ).
cnf(c_0_23,plain,
multiply(X1,inverse(multiply(inverse(inverse(multiply(X2,inverse(X2)))),multiply(X3,X1)))) = inverse(X3),
inference(spm,[status(thm)],[c_0_9,c_0_19]) ).
cnf(c_0_24,plain,
inverse(inverse(multiply(inverse(multiply(X1,inverse(X1))),X2))) = X2,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,plain,
multiply(multiply(X1,inverse(X1)),X2) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_24,c_0_16]) ).
cnf(c_0_26,plain,
multiply(inverse(multiply(inverse(inverse(X1)),multiply(X2,inverse(X2)))),X3) = inverse(multiply(inverse(X3),X1)),
inference(spm,[status(thm)],[c_0_21,c_0_21]) ).
cnf(c_0_27,plain,
multiply(inverse(inverse(inverse(X1))),X2) = inverse(multiply(inverse(X2),X1)),
inference(rw,[status(thm)],[c_0_21,c_0_25]) ).
cnf(c_0_28,plain,
multiply(X1,inverse(multiply(multiply(X2,inverse(multiply(multiply(X3,multiply(X4,inverse(X4))),multiply(X5,X2)))),multiply(X3,X1)))) = X5,
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_29,plain,
inverse(multiply(inverse(X1),inverse(X2))) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_24]) ).
cnf(c_0_30,plain,
multiply(multiply(inverse(multiply(X1,inverse(X1))),X2),inverse(multiply(inverse(X3),X2))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_19]),c_0_9]) ).
cnf(c_0_31,plain,
inverse(multiply(X1,multiply(X2,inverse(X2)))) = inverse(X1),
inference(spm,[status(thm)],[c_0_24,c_0_29]) ).
cnf(c_0_32,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_30]) ).
cnf(c_0_33,plain,
inverse(inverse(inverse(inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_27]),c_0_24]) ).
cnf(c_0_34,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_32]),c_0_25]),c_0_33]) ).
cnf(c_0_35,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_34,c_0_34]) ).
cnf(c_0_36,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_35]),c_0_32]) ).
cnf(c_0_37,plain,
multiply(multiply(X1,inverse(X1)),X2) = X2,
inference(rw,[status(thm)],[c_0_25,c_0_36]) ).
cnf(c_0_38,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
prove_these_axioms_2 ).
cnf(c_0_39,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(spm,[status(thm)],[c_0_37,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP431-1 : 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
% 0.15/0.33 % Computer : n002.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 18:35:31 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.83/1.91 % Version : CSE_E---1.7
% 1.83/1.91 % Problem : theBenchmark.p
% 1.83/1.91 % SZS status Unsatisfiable for theBenchmark.p
% 1.83/1.91 % SZS output start CNFRefutation
% See solution above
% 1.83/1.91 % Total time : 1.373s
%------------------------------------------------------------------------------