%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP577-1 : 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 : 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 04:26:26 PM UTC 2026
% Result : Unsatisfiable 1.27s 1.73s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of clauses : 24 ( 24 unt; 0 nHn; 5 RR)
% Number of literals : 24 ( 23 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X2,X1),X3),double_divide(X2,identity))),double_divide(identity,identity)) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(inverse,axiom,
inverse(X1) = double_divide(X1,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
cnf(multiply,axiom,
multiply(X1,X2) = double_divide(double_divide(X2,X1),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
cnf(identity,axiom,
identity = double_divide(X1,inverse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_1) ).
cnf(c_0_5,axiom,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X2,X1),X3),double_divide(X2,identity))),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(double_divide(X2,X1),X3),inverse(X2))),inverse(identity)) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5,c_0_6]),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(X1,double_divide(identity,inverse(X2))),inverse(identity)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
cnf(c_0_12,plain,
double_divide(inverse(X1),inverse(identity)) = multiply(X1,identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_9]),c_0_6]) ).
cnf(c_0_13,plain,
double_divide(double_divide(double_divide(X1,double_divide(identity,X2)),X3),inverse(X1)) = double_divide(double_divide(X2,X3),inverse(identity)),
inference(spm,[status(thm)],[c_0_8,c_0_8]) ).
cnf(c_0_14,plain,
double_divide(multiply(X1,X2),inverse(identity)) = multiply(double_divide(X2,X1),identity),
inference(spm,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_15,plain,
double_divide(multiply(X1,X2),inverse(X1)) = multiply(double_divide(identity,X2),identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_11]),c_0_12]),c_0_14]) ).
cnf(c_0_16,plain,
multiply(double_divide(identity,X1),identity) = multiply(inverse(X1),identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_6]) ).
cnf(c_0_17,plain,
inverse(inverse(X1)) = multiply(identity,X1),
inference(spm,[status(thm)],[c_0_10,c_0_6]) ).
cnf(c_0_18,negated_conjecture,
multiply(inverse(a1),a1) != identity,
prove_these_axioms_1 ).
cnf(c_0_19,plain,
multiply(inverse(X1),X1) = inverse(identity),
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_20,plain,
double_divide(multiply(X1,X2),inverse(X1)) = multiply(inverse(X2),identity),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
multiply(multiply(identity,identity),identity) = multiply(identity,identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_9]),c_0_17]) ).
cnf(c_0_22,negated_conjecture,
inverse(identity) != identity,
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_9]),c_0_19]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP577-1 : 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
% 0.16/0.34 % Computer : n001.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon May 4 18:45:33 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.27/1.73 % Version : CSE_E---1.7
% 1.27/1.73 % Problem : theBenchmark.p
% 1.27/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.27/1.73 % SZS output start CNFRefutation
% See solution above
% 1.27/1.73 % Total time : 1.369s
%------------------------------------------------------------------------------