%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP518-1 : 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 : n026.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 04:26:18 PM UTC 2026
% Result : Unsatisfiable 1.28s 1.73s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 4 RR)
% Number of literals : 18 ( 17 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 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 : 39 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(X1,multiply(multiply(inverse(multiply(X1,X2)),X3),X2)) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
cnf(c_0_2,axiom,
multiply(X1,multiply(multiply(inverse(multiply(X1,X2)),X3),X2)) = X3,
single_axiom ).
cnf(c_0_3,plain,
multiply(X1,multiply(multiply(inverse(X2),X3),multiply(multiply(inverse(multiply(X1,X4)),X2),X4))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),X4),X3) = multiply(X1,multiply(X4,X2)),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_5,plain,
multiply(multiply(inverse(X1),X2),X1) = X2,
inference(spm,[status(thm)],[c_0_3,c_0_2]) ).
cnf(c_0_6,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X3,X2))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_4]) ).
cnf(c_0_7,plain,
multiply(X1,multiply(X2,X3)) = multiply(X2,multiply(X1,X3)),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
multiply(multiply(X1,multiply(inverse(X2),X3)),X2) = multiply(X1,X3),
inference(spm,[status(thm)],[c_0_5,c_0_7]) ).
cnf(c_0_9,plain,
multiply(X1,multiply(inverse(multiply(X1,X2)),X3)) = multiply(inverse(X2),X3),
inference(spm,[status(thm)],[c_0_2,c_0_8]) ).
cnf(c_0_10,plain,
multiply(inverse(X1),multiply(X2,multiply(X3,X1))) = multiply(X2,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_2]),c_0_4]) ).
cnf(c_0_11,plain,
multiply(inverse(X1),multiply(X2,X1)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7]),c_0_9]) ).
cnf(c_0_12,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_7]),c_0_10]) ).
cnf(c_0_13,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
prove_these_axioms_2 ).
cnf(c_0_14,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_11]),c_0_12]) ).
cnf(c_0_15,negated_conjecture,
multiply(b2,multiply(a2,inverse(b2))) != a2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_12]),c_0_12]),c_0_7]) ).
cnf(c_0_16,plain,
multiply(X1,multiply(X2,inverse(X1))) = X2,
inference(spm,[status(thm)],[c_0_7,c_0_14]) ).
cnf(c_0_17,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP518-1 : 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
% 0.17/0.33 % Computer : n026.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Mon May 4 18:40:23 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 1.28/1.73 % Version : CSE_E---1.7
% 1.28/1.73 % Problem : theBenchmark.p
% 1.28/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.28/1.73 % SZS output start CNFRefutation
% See solution above
% 1.28/1.73 % Total time : 1.374s
%------------------------------------------------------------------------------