%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP608-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:30:28 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.42s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of formulae : 39 ( 39 unt; 0 def)
% Number of atoms : 39 ( 38 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 11 ( 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 : 99 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : double_divide(inverse(double_divide(VAR_0,inverse(double_divide(inverse(VAR_1),double_divide(VAR_0,VAR_2))))),VAR_2) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C) = B,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = inverse(double_divide(VAR_1,VAR_0)),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = inverse(double_divide(B,A)),
inference(clausify,[status(thm)],[multiply]) ).
fof(prove_these_axioms_4,axiom,
multiply(a,b) != multiply(b,a),
file('theBenchmark.p',prove_these_axioms_4) ).
cnf(c_3,plain,
multiply(a,b) != multiply(b,a),
inference(clausify,[status(thm)],[prove_these_axioms_4]) ).
cnf(c_247,plain,
inverse(double_divide(b,a)) != multiply(b,a),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_4,plain,
inverse(double_divide(b,a)) != inverse(double_divide(a,b)),
inference(paramod,[status(thm)],[c_2,c_247]) ).
cnf(c_5,plain,
double_divide(inverse(double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),inverse(double_divide(inverse(D),B)))),C) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
double_divide(inverse(double_divide(A,inverse(B))),C) = double_divide(D,inverse(double_divide(inverse(B),double_divide(D,double_divide(A,C))))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_7,plain,
double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),inverse(double_divide(inverse(D),B)))),inverse(double_divide(inverse(E),D)))),C) = E,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_11,plain,
double_divide(inverse(A),inverse(double_divide(inverse(B),A))) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_248,plain,
double_divide(inverse(double_divide(A,inverse(B))),C) = double_divide(inverse(double_divide(inverse(double_divide(D,inverse(double_divide(inverse(E),double_divide(D,double_divide(A,C)))))),inverse(double_divide(inverse(F),E)))),inverse(double_divide(inverse(B),F))),
inference(paramod,[status(thm)],[c_5,c_6]) ).
cnf(c_23,plain,
double_divide(inverse(double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,double_divide(C,D)))))),inverse(double_divide(inverse(E),B)))),inverse(double_divide(inverse(F),E))) = double_divide(inverse(double_divide(C,inverse(F))),D),
inference(copy,[status(thm)],[c_248]) ).
cnf(c_249,plain,
double_divide(inverse(A),inverse(B)) = double_divide(C,inverse(double_divide(inverse(B),double_divide(C,A)))),
inference(paramod,[status(thm)],[c_1,c_11]) ).
cnf(c_32,plain,
double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C)))) = double_divide(inverse(C),inverse(B)),
inference(copy,[status(thm)],[c_249]) ).
cnf(c_250,plain,
double_divide(inverse(A),inverse(B)) = double_divide(inverse(double_divide(C,inverse(double_divide(inverse(D),double_divide(C,A))))),inverse(double_divide(inverse(B),D))),
inference(paramod,[status(thm)],[c_5,c_11]) ).
cnf(c_251,plain,
double_divide(inverse(A),inverse(B)) = double_divide(inverse(double_divide(inverse(A),inverse(D))),inverse(double_divide(inverse(B),D))),
inference(paramod,[status(thm)],[c_32,c_250]) ).
cnf(c_35,plain,
double_divide(inverse(double_divide(inverse(A),inverse(B))),inverse(double_divide(inverse(C),B))) = double_divide(inverse(A),inverse(C)),
inference(copy,[status(thm)],[c_251]) ).
cnf(c_252,plain,
double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(C,D)),inverse(B))),inverse(double_divide(inverse(E),B)))),inverse(double_divide(inverse(F),E))) = double_divide(inverse(double_divide(C,inverse(F))),D),
inference(paramod,[status(thm)],[c_32,c_23]) ).
cnf(c_253,plain,
double_divide(inverse(double_divide(inverse(double_divide(C,D)),inverse(E))),inverse(double_divide(inverse(F),E))) = double_divide(inverse(double_divide(C,inverse(F))),D),
inference(paramod,[status(thm)],[c_35,c_252]) ).
cnf(c_254,plain,
double_divide(inverse(double_divide(C,D)),inverse(F)) = double_divide(inverse(double_divide(C,inverse(F))),D),
inference(paramod,[status(thm)],[c_35,c_253]) ).
cnf(c_48,plain,
double_divide(inverse(double_divide(A,inverse(B))),C) = double_divide(inverse(double_divide(A,C)),inverse(B)),
inference(copy,[status(thm)],[c_254]) ).
cnf(c_255,plain,
double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(C),inverse(B))),inverse(double_divide(inverse(D),B)))),inverse(double_divide(inverse(E),D)))),C) = E,
inference(paramod,[status(thm)],[c_32,c_7]) ).
cnf(c_256,plain,
double_divide(inverse(double_divide(inverse(double_divide(inverse(C),inverse(D))),inverse(double_divide(inverse(E),D)))),C) = E,
inference(paramod,[status(thm)],[c_35,c_255]) ).
cnf(c_53,plain,
double_divide(inverse(double_divide(inverse(A),inverse(B))),A) = B,
inference(paramod,[status(thm)],[c_35,c_256]) ).
cnf(c_56,plain,
double_divide(inverse(double_divide(inverse(A),A)),inverse(B)) = B,
inference(paramod,[status(thm)],[c_48,c_53]) ).
cnf(c_257,plain,
double_divide(inverse(double_divide(inverse(double_divide(inverse(A),A)),inverse(B))),inverse(C)) = double_divide(inverse(C),inverse(B)),
inference(paramod,[status(thm)],[c_56,c_48]) ).
cnf(c_63,plain,
double_divide(inverse(A),inverse(B)) = double_divide(inverse(B),inverse(A)),
inference(paramod,[status(thm)],[c_56,c_257]) ).
cnf(c_73,plain,
double_divide(inverse(double_divide(inverse(A),inverse(B))),B) = A,
inference(paramod,[status(thm)],[c_63,c_53]) ).
cnf(c_158,plain,
double_divide(inverse(A),double_divide(inverse(A),B)) = B,
inference(paramod,[status(thm)],[c_11,c_73]) ).
cnf(c_258,plain,
double_divide(inverse(A),double_divide(inverse(A),inverse(inverse(B)))) = B,
inference(paramod,[status(thm)],[c_73,c_53]) ).
cnf(c_159,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_158,c_258]) ).
cnf(c_259,plain,
double_divide(inverse(A),B) = double_divide(inverse(inverse(B)),inverse(A)),
inference(paramod,[status(thm)],[c_53,c_73]) ).
cnf(c_160,plain,
double_divide(inverse(A),B) = double_divide(B,inverse(A)),
inference(paramod,[status(thm)],[c_159,c_259]) ).
cnf(c_260,plain,
double_divide(A,B) = double_divide(B,inverse(inverse(A))),
inference(paramod,[status(thm)],[c_159,c_160]) ).
cnf(c_244,plain,
double_divide(A,B) = double_divide(B,A),
inference(paramod,[status(thm)],[c_159,c_260]) ).
cnf(c_261,plain,
inverse(double_divide(a,b)) != inverse(double_divide(a,b)),
inference(paramod,[status(thm)],[c_244,c_4]) ).
cnf(c_246,plain,
$false,
inference(copy,[status(thm)],[c_261]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP608-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 15:04:58 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1679661 was started by sandbox2 on n015,
% 0.09/0.37 % Fri Sep 25 15:04:58 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.16/0.42
% 0.16/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.42
% 0.16/0.42 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.16/0.42 % Length of proof is 21.
% 0.16/0.42 % Level of proof is 13.
% 0.16/0.42 % Maximum clause weight is 93.000.
% 0.16/0.42 % Given clauses 20.
% 0.16/0.42
% 0.16/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------