%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP500-1 : 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 : n009.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 04:26:16 PM UTC 2026
% Result : Unsatisfiable 1.85s 1.91s
% Output : CNFRefutation 1.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 3
% Syntax : Number of clauses : 43 ( 43 unt; 0 nHn; 5 RR)
% Number of literals : 43 ( 42 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 12 ( 3 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 : 125 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(inverse(X1),inverse(double_divide(inverse(double_divide(X1,double_divide(X2,X3))),double_divide(X4,double_divide(X2,X4))))) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
cnf(multiply,axiom,
multiply(X1,X2) = inverse(double_divide(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
cnf(c_0_3,axiom,
double_divide(inverse(X1),inverse(double_divide(inverse(double_divide(X1,double_divide(X2,X3))),double_divide(X4,double_divide(X2,X4))))) = X3,
single_axiom ).
cnf(c_0_4,plain,
double_divide(inverse(X1),inverse(double_divide(inverse(double_divide(X1,X2)),double_divide(X3,double_divide(inverse(X4),X3))))) = inverse(double_divide(inverse(double_divide(X4,double_divide(X5,X2))),double_divide(X6,double_divide(X5,X6)))),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_5,plain,
inverse(double_divide(inverse(double_divide(X1,double_divide(X2,double_divide(inverse(X1),X3)))),double_divide(X4,double_divide(X2,X4)))) = X3,
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_6,plain,
double_divide(inverse(inverse(double_divide(X1,double_divide(X2,double_divide(inverse(X1),X3))))),inverse(double_divide(X3,double_divide(X4,double_divide(X5,X4))))) = double_divide(X2,X5),
inference(spm,[status(thm)],[c_0_3,c_0_5]) ).
cnf(c_0_7,plain,
double_divide(inverse(inverse(double_divide(X1,double_divide(X2,double_divide(inverse(X1),inverse(double_divide(X3,double_divide(X4,double_divide(inverse(X3),X5))))))))),X5) = double_divide(X2,X4),
inference(spm,[status(thm)],[c_0_6,c_0_5]) ).
cnf(c_0_8,plain,
double_divide(inverse(inverse(double_divide(inverse(double_divide(X1,double_divide(X2,double_divide(inverse(X1),X3)))),double_divide(X4,double_divide(X2,inverse(X3)))))),X5) = double_divide(X4,X5),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_9,plain,
double_divide(inverse(X1),inverse(double_divide(inverse(double_divide(X1,double_divide(inverse(X2),X3))),double_divide(inverse(double_divide(inverse(double_divide(X2,double_divide(X4,X5))),double_divide(X6,double_divide(X4,X6)))),X5)))) = X3,
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_10,plain,
double_divide(X1,inverse(inverse(double_divide(inverse(double_divide(X2,double_divide(X3,double_divide(inverse(X2),X4)))),double_divide(X5,double_divide(X3,inverse(X4))))))) = double_divide(X1,X5),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_7]) ).
cnf(c_0_11,plain,
double_divide(inverse(X1),double_divide(inverse(X2),inverse(double_divide(inverse(double_divide(X2,X3)),double_divide(X4,double_divide(inverse(X1),X4)))))) = X3,
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_12,plain,
inverse(inverse(double_divide(inverse(double_divide(X1,double_divide(X2,double_divide(inverse(X1),X3)))),double_divide(X4,double_divide(X2,inverse(X3)))))) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_9]) ).
cnf(c_0_13,plain,
double_divide(X1,double_divide(inverse(X2),inverse(double_divide(inverse(double_divide(X2,X3)),double_divide(X4,double_divide(X1,X4)))))) = X3,
inference(spm,[status(thm)],[c_0_11,c_0_5]) ).
cnf(c_0_14,plain,
inverse(inverse(double_divide(inverse(double_divide(X1,double_divide(inverse(X2),double_divide(inverse(X1),double_divide(inverse(double_divide(X2,X3)),double_divide(X4,double_divide(X5,X4))))))),X3))) = X5,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,plain,
inverse(double_divide(inverse(double_divide(X1,double_divide(X2,double_divide(inverse(X1),X2)))),double_divide(X3,double_divide(X4,X3)))) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_4]),c_0_3]) ).
cnf(c_0_16,plain,
double_divide(X1,double_divide(inverse(X2),X1)) = double_divide(X3,double_divide(inverse(X2),X3)),
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_17,plain,
double_divide(X1,double_divide(X2,X1)) = double_divide(X3,double_divide(X2,X3)),
inference(spm,[status(thm)],[c_0_16,c_0_5]) ).
cnf(c_0_18,plain,
double_divide(inverse(X1),inverse(double_divide(inverse(double_divide(X2,double_divide(X3,X2))),double_divide(X4,double_divide(X3,X4))))) = X1,
inference(spm,[status(thm)],[c_0_3,c_0_17]) ).
cnf(c_0_19,plain,
inverse(double_divide(X1,double_divide(X2,double_divide(inverse(X1),inverse(double_divide(X3,double_divide(X4,X3))))))) = double_divide(X2,X4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_18]),c_0_18]) ).
cnf(c_0_20,plain,
inverse(double_divide(double_divide(inverse(double_divide(X1,double_divide(X2,X1))),X2),double_divide(X3,double_divide(X4,X3)))) = X4,
inference(spm,[status(thm)],[c_0_15,c_0_19]) ).
cnf(c_0_21,plain,
inverse(double_divide(inverse(double_divide(inverse(double_divide(X1,double_divide(X2,X1))),X2)),double_divide(X3,double_divide(X4,X3)))) = X4,
inference(spm,[status(thm)],[c_0_5,c_0_20]) ).
cnf(c_0_22,plain,
double_divide(X1,double_divide(inverse(inverse(double_divide(X2,double_divide(X3,X2)))),X1)) = X3,
inference(spm,[status(thm)],[c_0_13,c_0_21]) ).
cnf(c_0_23,plain,
double_divide(inverse(X1),inverse(double_divide(inverse(X2),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_22]),c_0_22]) ).
cnf(c_0_24,plain,
double_divide(inverse(X1),inverse(double_divide(X2,inverse(X2)))) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_6]) ).
cnf(c_0_25,plain,
double_divide(inverse(X1),inverse(inverse(double_divide(inverse(X2),X2)))) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_23]) ).
cnf(c_0_26,plain,
double_divide(inverse(X1),inverse(inverse(double_divide(X2,inverse(X2))))) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,plain,
double_divide(double_divide(inverse(X1),inverse(double_divide(inverse(double_divide(X1,X2)),X3))),X2) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_13]),c_0_22]) ).
cnf(c_0_28,plain,
double_divide(inverse(X1),inverse(inverse(inverse(inverse(double_divide(X2,inverse(X2))))))) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,plain,
inverse(inverse(double_divide(X1,X2))) = double_divide(X1,X2),
inference(spm,[status(thm)],[c_0_27,c_0_24]) ).
cnf(c_0_30,plain,
double_divide(inverse(X1),double_divide(X2,inverse(X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29]),c_0_29]) ).
cnf(c_0_31,plain,
double_divide(X1,double_divide(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_17,c_0_30]) ).
cnf(c_0_32,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_27]) ).
cnf(c_0_33,plain,
inverse(double_divide(double_divide(inverse(X1),X1),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_31]),c_0_31]) ).
cnf(c_0_34,plain,
double_divide(double_divide(inverse(X1),X1),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_35,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
prove_these_axioms_2 ).
cnf(c_0_36,axiom,
multiply(X1,X2) = inverse(double_divide(X2,X1)),
multiply ).
cnf(c_0_37,plain,
double_divide(double_divide(X1,inverse(X1)),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_34,c_0_32]) ).
cnf(c_0_38,negated_conjecture,
inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36]),c_0_36]) ).
cnf(c_0_39,plain,
double_divide(X1,inverse(X1)) = double_divide(X2,inverse(X2)),
inference(spm,[status(thm)],[c_0_31,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
inverse(double_divide(a2,inverse(double_divide(X1,inverse(X1))))) != a2,
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_41,plain,
double_divide(X1,inverse(double_divide(inverse(X2),X2))) = inverse(X1),
inference(spm,[status(thm)],[c_0_23,c_0_32]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_32]),c_0_41]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.16 % Problem : GRP500-1 : TPTP v9.2.1. Released v2.6.0.
% 0.10/0.16 % 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
% 0.20/0.37 % Computer : n009.cluster.edu
% 0.20/0.37 % Model : x86_64 x86_64
% 0.20/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.37 % Memory : 8042.1875MB
% 0.20/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.37 % CPULimit : 300
% 0.20/0.37 % WCLimit : 300
% 0.20/0.37 % DateTime : Mon May 4 18:39:11 EDT 2026
% 0.20/0.37 % CPUTime :
% 0.20/0.38 % start to proof: theBenchmark
% 1.85/1.91 % Version : CSE_E---1.7
% 1.85/1.91 % Problem : theBenchmark.p
% 1.85/1.91 % SZS status Unsatisfiable for theBenchmark.p
% 1.85/1.91 % SZS output start CNFRefutation
% See solution above
% 1.85/1.91 % Total time : 1.370s
%------------------------------------------------------------------------------