%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP406-1 : 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 : n004.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 4.93s 3.50s
% Output : CNFRefutation 4.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 3 RR)
% Number of literals : 20 ( 19 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 62 ( 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/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).
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,
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_10,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_11,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_12,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_9,c_0_10]) ).
cnf(c_0_13,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_11,c_0_10]),c_0_12]),c_0_2]) ).
cnf(c_0_14,plain,
multiply(X1,inverse(multiply(inverse(X2),X2))) = multiply(X1,inverse(multiply(inverse(X3),X3))),
inference(spm,[status(thm)],[c_0_13,c_0_13]) ).
cnf(c_0_15,plain,
multiply(inverse(multiply(X1,multiply(X2,X3))),multiply(X1,inverse(multiply(inverse(X4),multiply(inverse(multiply(X2,X3)),multiply(inverse(multiply(X5,X3)),multiply(X5,X3))))))) = X4,
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_16,plain,
inverse(multiply(inverse(X1),X1)) = inverse(multiply(inverse(X2),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_14]),c_0_2]) ).
cnf(c_0_17,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
prove_these_axioms_1 ).
cnf(c_0_18,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_15]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_17,c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP406-1 : 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
% 0.16/0.33 % Computer : n004.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:34:17 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 4.93/3.50 % Version : CSE_E---1.7
% 4.93/3.50 % Problem : theBenchmark.p
% 4.93/3.50 % SZS status Unsatisfiable for theBenchmark.p
% 4.93/3.50 % SZS output start CNFRefutation
% See solution above
% 4.93/3.51 % Total time : 2.372s
%------------------------------------------------------------------------------