%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP581-1 : 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 04:26:26 PM UTC 2026
% Result : Unsatisfiable 1.14s 1.62s
% Output : CNFRefutation 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of clauses : 22 ( 22 unt; 0 nHn; 4 RR)
% Number of literals : 22 ( 21 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(X1,double_divide(double_divide(identity,X2),double_divide(X3,double_divide(X2,X1)))),double_divide(identity,identity)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(inverse,axiom,
inverse(X1) = double_divide(X1,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(multiply,axiom,
multiply(X1,X2) = double_divide(double_divide(X2,X1),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(identity,axiom,
identity = double_divide(X1,inverse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).
cnf(c_0_5,axiom,
double_divide(double_divide(X1,double_divide(double_divide(identity,X2),double_divide(X3,double_divide(X2,X1)))),double_divide(identity,identity)) = X3,
single_axiom ).
cnf(c_0_6,axiom,
inverse(X1) = double_divide(X1,identity),
inverse ).
cnf(c_0_7,axiom,
multiply(X1,X2) = double_divide(double_divide(X2,X1),identity),
multiply ).
cnf(c_0_8,plain,
double_divide(double_divide(X1,double_divide(double_divide(identity,X2),double_divide(X3,double_divide(X2,X1)))),inverse(identity)) = X3,
inference(rw,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_9,axiom,
identity = double_divide(X1,inverse(X1)),
identity ).
cnf(c_0_10,plain,
inverse(double_divide(X1,X2)) = multiply(X2,X1),
inference(rw,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_11,plain,
double_divide(double_divide(inverse(X1),double_divide(double_divide(identity,X1),inverse(X2))),inverse(identity)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_6]) ).
cnf(c_0_12,plain,
inverse(inverse(X1)) = multiply(identity,X1),
inference(spm,[status(thm)],[c_0_10,c_0_6]) ).
cnf(c_0_13,plain,
double_divide(multiply(identity,X1),inverse(identity)) = double_divide(identity,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_9]),c_0_6]),c_0_12]) ).
cnf(c_0_14,plain,
multiply(identity,double_divide(X1,X2)) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_15,plain,
double_divide(identity,double_divide(X1,X2)) = double_divide(inverse(multiply(X2,X1)),inverse(identity)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,plain,
double_divide(double_divide(inverse(multiply(double_divide(X1,inverse(X2)),double_divide(identity,X2))),inverse(identity)),inverse(identity)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_6]),c_0_15]) ).
cnf(c_0_17,negated_conjecture,
multiply(inverse(a1),a1) != identity,
prove_these_axioms_1 ).
cnf(c_0_18,plain,
multiply(inverse(X1),X1) = inverse(identity),
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_19,plain,
double_divide(double_divide(identity,multiply(X1,identity)),inverse(identity)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_9]),c_0_14]),c_0_12]),c_0_13]) ).
cnf(c_0_20,negated_conjecture,
inverse(identity) != identity,
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_18]),c_0_9]),c_0_9]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : GRP581-1 : 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
% 0.07/0.25 % Computer : n024.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Mon May 4 13:44:11 EDT 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 % start to proof: theBenchmark
% 1.14/1.62 % Version : CSE_E---1.7
% 1.14/1.62 % Problem : theBenchmark.p
% 1.14/1.62 % SZS status Unsatisfiable for theBenchmark.p
% 1.14/1.62 % SZS output start CNFRefutation
% See solution above
% 1.14/1.62 % Total time : 1.361s
%------------------------------------------------------------------------------