%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP605-1 : 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 : n018.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 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of clauses : 33 ( 33 unt; 0 nHn; 5 RR)
% Number of literals : 33 ( 32 equ; 4 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 63 ( 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_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(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(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_19,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_20,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_17]) ).
cnf(c_0_21,plain,
inverse(double_divide(X1,double_divide(inverse(X2),X2))) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_11]) ).
cnf(c_0_22,plain,
double_divide(X1,X2) = double_divide(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_10]),c_0_20]),c_0_20]) ).
cnf(c_0_23,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
prove_these_axioms_1 ).
cnf(c_0_24,axiom,
multiply(X1,X2) = inverse(double_divide(X2,X1)),
multiply ).
cnf(c_0_25,plain,
inverse(double_divide(X1,double_divide(X2,inverse(X2)))) = X1,
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
inverse(double_divide(b1,inverse(b1))) != inverse(double_divide(a1,inverse(a1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_24]) ).
cnf(c_0_27,plain,
inverse(double_divide(X1,inverse(X2))) = double_divide(inverse(X1),X2),
inference(spm,[status(thm)],[c_0_10,c_0_20]) ).
cnf(c_0_28,plain,
double_divide(X1,double_divide(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_17,c_0_11]) ).
cnf(c_0_29,plain,
double_divide(X1,double_divide(X2,inverse(X2))) = inverse(X1),
inference(spm,[status(thm)],[c_0_20,c_0_25]) ).
cnf(c_0_30,negated_conjecture,
double_divide(a1,inverse(a1)) != double_divide(b1,inverse(b1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_22]),c_0_27]),c_0_22]) ).
cnf(c_0_31,plain,
double_divide(X1,inverse(X1)) = double_divide(X2,inverse(X2)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_30,c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP605-1 : TPTP v9.2.1. Released v2.6.0.
% 0.00/0.12 % 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
% 0.14/0.32 % Computer : n018.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 18:53:03 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------