%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP012-4 : TPTP v9.2.1. Released v1.0.0.
% 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 : n001.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 04:23:33 PM UTC 2026
% Result : Unsatisfiable 1.26s 1.71s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 17 ( 17 unt; 0 nHn; 3 RR)
% Number of literals : 17 ( 16 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 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 : 22 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(right_inverse,axiom,
multiply(X1,inverse(X1)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
cnf(right_identity,axiom,
multiply(X1,identity) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
cnf(prove_inverse_of_product_is_product_of_inverses,negated_conjecture,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_of_product_is_product_of_inverses) ).
cnf(c_0_6,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_7,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_8,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_9,axiom,
multiply(X1,inverse(X1)) = identity,
right_inverse ).
cnf(c_0_10,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8]) ).
cnf(c_0_11,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_9,c_0_6]) ).
cnf(c_0_12,axiom,
multiply(X1,identity) = X1,
right_identity ).
cnf(c_0_13,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
cnf(c_0_14,negated_conjecture,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
prove_inverse_of_product_is_product_of_inverses ).
cnf(c_0_15,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_10,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP012-4 : TPTP v9.2.1. Released v1.0.0.
% 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
% 0.15/0.32 % Computer : n001.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 18:18:03 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.26/1.71 % Version : CSE_E---1.7
% 1.26/1.71 % Problem : theBenchmark.p
% 1.26/1.71 % SZS status Unsatisfiable for theBenchmark.p
% 1.26/1.71 % SZS output start CNFRefutation
% See solution above
% 1.26/1.71 % Total time : 1.369s
%------------------------------------------------------------------------------