%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP607-1 : 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 : 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 04:26:30 PM UTC 2026
% Result : Unsatisfiable 2.09s 1.94s
% Output : CNFRefutation 2.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of clauses : 39 ( 39 unt; 0 nHn; 8 RR)
% Number of literals : 39 ( 38 equ; 7 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(inverse(double_divide(X1,inverse(double_divide(inverse(X2),double_divide(X1,X3))))),X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
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(X1,inverse(double_divide(inverse(X2),double_divide(X1,X3))))),X3) = X2,
single_axiom ).
cnf(c_0_4,plain,
double_divide(inverse(double_divide(inverse(double_divide(X1,inverse(double_divide(inverse(X2),double_divide(X1,X3))))),inverse(double_divide(inverse(X4),X2)))),X3) = X4,
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_5,plain,
double_divide(inverse(X1),inverse(double_divide(inverse(X2),X1))) = X2,
inference(spm,[status(thm)],[c_0_4,c_0_3]) ).
cnf(c_0_6,plain,
double_divide(inverse(inverse(double_divide(inverse(X1),X2))),inverse(X1)) = X2,
inference(spm,[status(thm)],[c_0_5,c_0_5]) ).
cnf(c_0_7,plain,
double_divide(inverse(inverse(X1)),inverse(X2)) = inverse(double_divide(inverse(X1),X2)),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
inverse(double_divide(inverse(double_divide(inverse(X1),X2)),X1)) = X2,
inference(rw,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,plain,
inverse(double_divide(X1,double_divide(inverse(X2),X1))) = X2,
inference(spm,[status(thm)],[c_0_8,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_7,c_0_8]) ).
cnf(c_0_11,plain,
inverse(double_divide(double_divide(inverse(X1),X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_9]),c_0_10]) ).
cnf(c_0_12,plain,
double_divide(X1,inverse(double_divide(inverse(X2),double_divide(X1,double_divide(X3,X4))))) = double_divide(inverse(double_divide(X3,inverse(X2))),X4),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_13,plain,
double_divide(inverse(X1),double_divide(inverse(X2),X2)) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_14,plain,
double_divide(inverse(inverse(double_divide(double_divide(X1,inverse(double_divide(inverse(X2),double_divide(X1,X3)))),double_divide(inverse(X4),X2)))),X3) = X4,
inference(rw,[status(thm)],[c_0_4,c_0_10]) ).
cnf(c_0_15,plain,
double_divide(inverse(inverse(double_divide(X1,X2))),X1) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_10]),c_0_9]),c_0_10]) ).
cnf(c_0_16,plain,
inverse(double_divide(double_divide(inverse(X1),X2),X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_9]),c_0_11]),c_0_10]) ).
cnf(c_0_17,plain,
double_divide(inverse(X1),double_divide(inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_17]) ).
cnf(c_0_19,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
prove_these_axioms_3 ).
cnf(c_0_20,axiom,
multiply(X1,X2) = inverse(double_divide(X2,X1)),
multiply ).
cnf(c_0_21,plain,
inverse(inverse(double_divide(X1,double_divide(X2,X1)))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_10]) ).
cnf(c_0_22,plain,
inverse(double_divide(inverse(X1),X2)) = double_divide(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_8,c_0_17]) ).
cnf(c_0_23,plain,
inverse(double_divide(X1,inverse(X2))) = double_divide(inverse(X1),X2),
inference(spm,[status(thm)],[c_0_10,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_20]),c_0_20]),c_0_20]) ).
cnf(c_0_25,plain,
double_divide(X1,double_divide(X2,X1)) = X2,
inference(rw,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_26,plain,
double_divide(X1,double_divide(inverse(double_divide(X1,double_divide(X2,X3))),X4)) = double_divide(double_divide(inverse(X2),X4),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_22]),c_0_23]) ).
cnf(c_0_27,negated_conjecture,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != double_divide(inverse(a3),double_divide(c3,b3)),
inference(rw,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_28,plain,
inverse(double_divide(X1,double_divide(inverse(X2),X3))) = double_divide(inverse(X1),double_divide(inverse(X3),X2)),
inference(spm,[status(thm)],[c_0_10,c_0_22]) ).
cnf(c_0_29,plain,
inverse(double_divide(X1,double_divide(X2,X3))) = double_divide(double_divide(inverse(X2),X1),X3),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
double_divide(inverse(c3),double_divide(b3,a3)) != double_divide(inverse(a3),double_divide(c3,b3)),
inference(rw,[status(thm)],[c_0_27,c_0_23]) ).
cnf(c_0_31,plain,
double_divide(inverse(X1),X2) = double_divide(X2,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_18]),c_0_22]) ).
cnf(c_0_32,plain,
double_divide(inverse(X1),double_divide(inverse(X2),X3)) = double_divide(double_divide(X3,X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29]),c_0_18]) ).
cnf(c_0_33,negated_conjecture,
double_divide(double_divide(c3,b3),inverse(a3)) != double_divide(double_divide(b3,a3),inverse(c3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_31]) ).
cnf(c_0_34,plain,
double_divide(X1,X2) = double_divide(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_10]),c_0_18]),c_0_18]) ).
cnf(c_0_35,plain,
double_divide(inverse(X1),double_divide(X2,X3)) = double_divide(double_divide(X3,X1),inverse(X2)),
inference(spm,[status(thm)],[c_0_32,c_0_18]) ).
cnf(c_0_36,negated_conjecture,
double_divide(double_divide(b3,c3),inverse(a3)) != double_divide(double_divide(a3,b3),inverse(c3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34]),c_0_34]) ).
cnf(c_0_37,plain,
double_divide(double_divide(X1,X2),inverse(X3)) = double_divide(double_divide(X2,X3),inverse(X1)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP607-1 : TPTP v9.2.1. Released v2.6.0.
% 0.00/0.09 % 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
% 0.11/0.29 % Computer : n001.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Mon May 4 18:46:48 EDT 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.30 % start to proof: theBenchmark
% 2.09/1.94 % Version : CSE_E---1.7
% 2.09/1.94 % Problem : theBenchmark.p
% 2.09/1.94 % SZS status Unsatisfiable for theBenchmark.p
% 2.09/1.94 % SZS output start CNFRefutation
% See solution above
% 2.09/1.94 % Total time : 1.368s
%------------------------------------------------------------------------------