%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP589-1 : 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 04:26:28 PM UTC 2026
% Result : Unsatisfiable 1.13s 1.61s
% Output : CNFRefutation 1.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of clauses : 27 ( 27 unt; 0 nHn; 5 RR)
% Number of literals : 27 ( 26 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 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 : 47 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(inverse(double_divide(double_divide(X1,X2),inverse(double_divide(X1,inverse(X3))))),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(multiply,axiom,
multiply(X1,X2) = inverse(double_divide(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(c_0_3,axiom,
double_divide(inverse(double_divide(double_divide(X1,X2),inverse(double_divide(X1,inverse(X3))))),X2) = X3,
single_axiom ).
cnf(c_0_4,plain,
double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(X1,inverse(X2)),inverse(double_divide(X1,inverse(X3))))),X4),inverse(X3))),X4) = X2,
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_5,plain,
double_divide(inverse(double_divide(X1,inverse(X1))),inverse(X2)) = X2,
inference(spm,[status(thm)],[c_0_4,c_0_3]) ).
cnf(c_0_6,plain,
double_divide(inverse(double_divide(X1,inverse(X2))),inverse(X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_5]),c_0_5]) ).
cnf(c_0_7,plain,
double_divide(inverse(X1),inverse(inverse(double_divide(X2,inverse(X1))))) = X2,
inference(spm,[status(thm)],[c_0_6,c_0_6]) ).
cnf(c_0_8,plain,
double_divide(inverse(X1),inverse(inverse(X2))) = inverse(double_divide(X1,inverse(X2))),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,plain,
inverse(double_divide(X1,inverse(double_divide(X2,inverse(X1))))) = X2,
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,plain,
double_divide(inverse(X1),inverse(X2)) = inverse(double_divide(X1,X2)),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,plain,
inverse(double_divide(double_divide(X1,inverse(X1)),X2)) = X2,
inference(rw,[status(thm)],[c_0_5,c_0_10]) ).
cnf(c_0_12,plain,
inverse(double_divide(X1,inverse(double_divide(X2,inverse(X2))))) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_13,plain,
inverse(double_divide(double_divide(X1,inverse(X2)),X1)) = X2,
inference(rw,[status(thm)],[c_0_6,c_0_10]) ).
cnf(c_0_14,plain,
double_divide(double_divide(X1,X2),X2) = X1,
inference(spm,[status(thm)],[c_0_3,c_0_12]) ).
cnf(c_0_15,plain,
inverse(inverse(double_divide(double_divide(X1,X2),X1))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_10]),c_0_10]) ).
cnf(c_0_16,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
prove_these_axioms_1 ).
cnf(c_0_18,axiom,
multiply(X1,X2) = inverse(double_divide(X2,X1)),
multiply ).
cnf(c_0_19,plain,
double_divide(double_divide(X1,X2),X1) = X2,
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
inverse(double_divide(b1,inverse(b1))) != inverse(double_divide(a1,inverse(a1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_18]) ).
cnf(c_0_21,plain,
inverse(double_divide(X1,inverse(X2))) = double_divide(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_9,c_0_14]) ).
cnf(c_0_22,plain,
double_divide(X1,double_divide(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_19,c_0_19]) ).
cnf(c_0_23,plain,
double_divide(double_divide(X1,inverse(X1)),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_16,c_0_11]) ).
cnf(c_0_24,negated_conjecture,
double_divide(a1,inverse(a1)) != double_divide(b1,inverse(b1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_21]) ).
cnf(c_0_25,plain,
double_divide(X1,inverse(X1)) = double_divide(X2,inverse(X2)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_24,c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : GRP589-1 : 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
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 13:45:26 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.24 % start to proof: theBenchmark
% 1.13/1.61 % Version : CSE_E---1.7
% 1.13/1.61 % Problem : theBenchmark.p
% 1.13/1.61 % SZS status Unsatisfiable for theBenchmark.p
% 1.13/1.61 % SZS output start CNFRefutation
% See solution above
% 1.13/1.61 % Total time : 1.361s
%------------------------------------------------------------------------------