%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP591-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 07:30:26 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.43s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 3
% Syntax : Number of formulae : 79 ( 79 unt; 0 def)
% Number of atoms : 79 ( 78 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 14 ( 14 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 12 ( 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 : 166 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : double_divide(inverse(double_divide(double_divide(VAR_0,VAR_1),inverse(double_divide(VAR_0,inverse(VAR_2))))),VAR_1) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B) = C,
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_3,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('theBenchmark.p',prove_these_axioms_3) ).
cnf(c_3,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(clausify,[status(thm)],[prove_these_axioms_3]) ).
cnf(c_235,plain,
multiply(inverse(double_divide(b3,a3)),c3) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_236,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_235]) ).
cnf(c_237,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != multiply(a3,inverse(double_divide(c3,b3))),
inference(paramod,[status(thm)],[c_2,c_236]) ).
cnf(c_238,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference(paramod,[status(thm)],[c_2,c_237]) ).
cnf(c_4,plain,
inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))),
inference(copy,[status(thm)],[c_238]) ).
cnf(c_5,plain,
double_divide(inverse(double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(B,C),inverse(double_divide(B,inverse(A))))),inverse(D))))),C) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(A,inverse(B)),inverse(double_divide(A,inverse(C))))),D),inverse(C))),D) = B,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_7,plain,
double_divide(inverse(double_divide(A,inverse(A))),inverse(B)) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_239,plain,
double_divide(inverse(double_divide(A,inverse(double_divide(inverse(double_divide(B,inverse(B))),inverse(C))))),inverse(A)) = C,
inference(paramod,[status(thm)],[c_7,c_1]) ).
cnf(c_8,plain,
double_divide(inverse(double_divide(A,inverse(B))),inverse(A)) = B,
inference(paramod,[status(thm)],[c_7,c_239]) ).
cnf(c_17,plain,
double_divide(inverse(double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(A,inverse(B))),C),inverse(B))),inverse(D))))),C) = D,
inference(paramod,[status(thm)],[c_8,c_5]) ).
cnf(c_20,plain,
double_divide(inverse(A),inverse(inverse(double_divide(B,inverse(B))))) = A,
inference(paramod,[status(thm)],[c_7,c_8]) ).
cnf(c_240,plain,
double_divide(inverse(double_divide(A,inverse(double_divide(inverse(A),inverse(B))))),inverse(inverse(double_divide(C,inverse(C))))) = B,
inference(paramod,[status(thm)],[c_20,c_1]) ).
cnf(c_28,plain,
double_divide(A,inverse(double_divide(inverse(A),inverse(B)))) = B,
inference(paramod,[status(thm)],[c_20,c_240]) ).
cnf(c_241,plain,
double_divide(A,inverse(A)) = inverse(double_divide(B,inverse(B))),
inference(paramod,[status(thm)],[c_20,c_7]) ).
cnf(c_33,plain,
inverse(double_divide(A,inverse(A))) = double_divide(B,inverse(B)),
inference(copy,[status(thm)],[c_241]) ).
cnf(c_37,plain,
double_divide(inverse(double_divide(double_divide(A,B),double_divide(C,inverse(C)))),B) = A,
inference(paramod,[status(thm)],[c_33,c_1]) ).
cnf(c_38,plain,
double_divide(double_divide(A,inverse(A)),inverse(B)) = B,
inference(paramod,[status(thm)],[c_33,c_1]) ).
cnf(c_242,plain,
double_divide(inverse(double_divide(double_divide(A,inverse(A)),inverse(B))),double_divide(C,inverse(C))) = B,
inference(paramod,[status(thm)],[c_33,c_8]) ).
cnf(c_51,plain,
double_divide(inverse(A),double_divide(B,inverse(B))) = A,
inference(paramod,[status(thm)],[c_38,c_242]) ).
cnf(c_57,plain,
double_divide(A,inverse(A)) = double_divide(B,inverse(B)),
inference(paramod,[status(thm)],[c_33,c_33]) ).
cnf(c_84,plain,
double_divide(inverse(A),double_divide(double_divide(B,inverse(B)),double_divide(C,inverse(C)))) = A,
inference(paramod,[status(thm)],[c_33,c_51]) ).
cnf(c_87,plain,
double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B) = double_divide(inverse(A),inverse(C)),
inference(paramod,[status(thm)],[c_28,c_1]) ).
cnf(c_92,plain,
double_divide(inverse(A),inverse(B)) = double_divide(inverse(B),inverse(A)),
inference(paramod,[status(thm)],[c_28,c_8]) ).
cnf(c_94,plain,
double_divide(A,double_divide(B,inverse(B))) = inverse(A),
inference(paramod,[status(thm)],[c_33,c_28]) ).
cnf(c_96,plain,
double_divide(A,inverse(double_divide(B,inverse(B)))) = inverse(A),
inference(paramod,[status(thm)],[c_57,c_28]) ).
cnf(c_243,plain,
double_divide(inverse(double_divide(double_divide(inverse(double_divide(A,inverse(double_divide(B,inverse(C))))),D),inverse(C))),D) = double_divide(inverse(B),inverse(A)),
inference(paramod,[status(thm)],[c_28,c_6]) ).
cnf(c_244,plain,
double_divide(inverse(inverse(double_divide(A,inverse(double_divide(B,inverse(C)))))),inverse(C)) = double_divide(inverse(B),inverse(A)),
inference(paramod,[status(thm)],[c_87,c_243]) ).
cnf(c_97,plain,
double_divide(inverse(A),inverse(inverse(double_divide(B,inverse(double_divide(C,inverse(A))))))) = double_divide(inverse(C),inverse(B)),
inference(paramod,[status(thm)],[c_92,c_244]) ).
cnf(c_245,plain,
double_divide(inverse(inverse(double_divide(double_divide(A,inverse(B)),inverse(double_divide(A,inverse(C)))))),inverse(C)) = B,
inference(paramod,[status(thm)],[c_87,c_6]) ).
cnf(c_246,plain,
double_divide(inverse(C),inverse(inverse(double_divide(double_divide(A,inverse(B)),inverse(double_divide(A,inverse(C))))))) = B,
inference(paramod,[status(thm)],[c_92,c_245]) ).
cnf(c_106,plain,
double_divide(inverse(A),inverse(double_divide(A,inverse(B)))) = B,
inference(paramod,[status(thm)],[c_97,c_246]) ).
cnf(c_247,plain,
double_divide(inverse(A),inverse(double_divide(B,inverse(B)))) = A,
inference(paramod,[status(thm)],[c_94,c_84]) ).
cnf(c_111,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_96,c_247]) ).
cnf(c_248,plain,
double_divide(inverse(inverse(double_divide(A,B))),B) = A,
inference(paramod,[status(thm)],[c_94,c_37]) ).
cnf(c_116,plain,
double_divide(double_divide(A,B),B) = A,
inference(paramod,[status(thm)],[c_111,c_248]) ).
cnf(c_249,plain,
double_divide(inverse(double_divide(A,double_divide(B,inverse(B)))),C) = inverse(double_divide(double_divide(inverse(double_divide(A,inverse(D))),C),inverse(D))),
inference(paramod,[status(thm)],[c_33,c_17]) ).
cnf(c_250,plain,
double_divide(inverse(inverse(A)),C) = inverse(double_divide(double_divide(inverse(double_divide(A,inverse(D))),C),inverse(D))),
inference(paramod,[status(thm)],[c_94,c_249]) ).
cnf(c_251,plain,
double_divide(A,C) = inverse(double_divide(double_divide(inverse(double_divide(A,inverse(D))),C),inverse(D))),
inference(paramod,[status(thm)],[c_111,c_250]) ).
cnf(c_139,plain,
inverse(double_divide(double_divide(inverse(double_divide(A,inverse(B))),C),inverse(B))) = double_divide(A,C),
inference(copy,[status(thm)],[c_251]) ).
cnf(c_252,plain,
double_divide(A,B) = inverse(double_divide(C,inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(C,inverse(D))),B),inverse(D))),inverse(A))))),
inference(paramod,[status(thm)],[c_17,c_116]) ).
cnf(c_253,plain,
double_divide(A,B) = inverse(double_divide(C,inverse(double_divide(double_divide(C,B),inverse(A))))),
inference(paramod,[status(thm)],[c_139,c_252]) ).
cnf(c_143,plain,
inverse(double_divide(A,inverse(double_divide(double_divide(A,B),inverse(C))))) = double_divide(C,B),
inference(copy,[status(thm)],[c_253]) ).
cnf(c_254,plain,
double_divide(A,inverse(B)) = double_divide(inverse(B),inverse(inverse(A))),
inference(paramod,[status(thm)],[c_111,c_92]) ).
cnf(c_255,plain,
double_divide(A,inverse(B)) = double_divide(inverse(B),A),
inference(paramod,[status(thm)],[c_111,c_254]) ).
cnf(c_149,plain,
double_divide(inverse(A),B) = double_divide(B,inverse(A)),
inference(copy,[status(thm)],[c_255]) ).
cnf(c_256,plain,
inverse(double_divide(a3,inverse(double_divide(c3,b3)))) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))),
inference(paramod,[status(thm)],[c_149,c_4]) ).
cnf(c_164,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(a3,inverse(double_divide(c3,b3)))),
inference(copy,[status(thm)],[c_256]) ).
cnf(c_257,plain,
double_divide(A,B) = double_divide(B,inverse(inverse(A))),
inference(paramod,[status(thm)],[c_111,c_149]) ).
cnf(c_166,plain,
double_divide(A,B) = double_divide(B,A),
inference(paramod,[status(thm)],[c_111,c_257]) ).
cnf(c_258,plain,
inverse(double_divide(c3,inverse(double_divide(a3,b3)))) != inverse(double_divide(a3,inverse(double_divide(c3,b3)))),
inference(paramod,[status(thm)],[c_166,c_164]) ).
cnf(c_169,plain,
inverse(double_divide(c3,inverse(double_divide(a3,b3)))) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_166,c_258]) ).
cnf(c_172,plain,
double_divide(A,double_divide(B,A)) = B,
inference(paramod,[status(thm)],[c_166,c_116]) ).
cnf(c_173,plain,
double_divide(A,double_divide(A,B)) = B,
inference(paramod,[status(thm)],[c_166,c_172]) ).
cnf(c_183,plain,
double_divide(inverse(A),inverse(double_divide(A,B))) = inverse(B),
inference(paramod,[status(thm)],[c_111,c_106]) ).
cnf(c_259,plain,
double_divide(inverse(A),B) = inverse(double_divide(A,inverse(B))),
inference(paramod,[status(thm)],[c_106,c_173]) ).
cnf(c_186,plain,
inverse(double_divide(A,inverse(B))) = double_divide(inverse(A),B),
inference(copy,[status(thm)],[c_259]) ).
cnf(c_260,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_186,c_169]) ).
cnf(c_188,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(inverse(a3),double_divide(b3,c3)),
inference(paramod,[status(thm)],[c_186,c_260]) ).
cnf(c_196,plain,
inverse(double_divide(A,double_divide(inverse(double_divide(A,B)),C))) = double_divide(C,B),
inference(paramod,[status(thm)],[c_186,c_143]) ).
cnf(c_261,plain,
double_divide(inverse(A),inverse(B)) = inverse(double_divide(B,A)),
inference(paramod,[status(thm)],[c_172,c_183]) ).
cnf(c_206,plain,
inverse(double_divide(A,B)) = double_divide(inverse(B),inverse(A)),
inference(copy,[status(thm)],[c_261]) ).
cnf(c_262,plain,
inverse(double_divide(A,double_divide(double_divide(inverse(B),inverse(A)),C))) = double_divide(C,B),
inference(paramod,[status(thm)],[c_206,c_196]) ).
cnf(c_263,plain,
double_divide(inverse(double_divide(double_divide(inverse(B),inverse(A)),C)),inverse(A)) = double_divide(C,B),
inference(paramod,[status(thm)],[c_206,c_262]) ).
cnf(c_264,plain,
double_divide(double_divide(inverse(C),inverse(double_divide(inverse(B),inverse(A)))),inverse(A)) = double_divide(C,B),
inference(paramod,[status(thm)],[c_206,c_263]) ).
cnf(c_265,plain,
double_divide(double_divide(inverse(C),double_divide(inverse(inverse(A)),inverse(inverse(B)))),inverse(A)) = double_divide(C,B),
inference(paramod,[status(thm)],[c_206,c_264]) ).
cnf(c_266,plain,
double_divide(double_divide(inverse(C),double_divide(A,inverse(inverse(B)))),inverse(A)) = double_divide(C,B),
inference(paramod,[status(thm)],[c_111,c_265]) ).
cnf(c_267,plain,
double_divide(double_divide(inverse(C),double_divide(A,B)),inverse(A)) = double_divide(C,B),
inference(paramod,[status(thm)],[c_111,c_266]) ).
cnf(c_212,plain,
double_divide(inverse(A),double_divide(inverse(B),double_divide(A,C))) = double_divide(B,C),
inference(paramod,[status(thm)],[c_166,c_267]) ).
cnf(c_227,plain,
double_divide(inverse(A),double_divide(B,C)) = double_divide(inverse(B),double_divide(A,C)),
inference(paramod,[status(thm)],[c_212,c_173]) ).
cnf(c_233,plain,
double_divide(inverse(A),double_divide(B,C)) = double_divide(inverse(C),double_divide(A,B)),
inference(paramod,[status(thm)],[c_166,c_227]) ).
cnf(c_268,plain,
double_divide(inverse(a3),double_divide(b3,c3)) != double_divide(inverse(c3),double_divide(a3,b3)),
inference(copy,[status(thm)],[c_188]) ).
cnf(c_234,plain,
$false,
inference(resolve,[status(thm)],[c_233,c_268]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP591-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.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 15:01:14 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2307778 was started by sandbox on n011,
% 0.09/0.36 % Fri Sep 25 15:01:14 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.43
% 0.09/0.43 % Assigning unary symbol inverse kb_weight 0 and highest precedence (7).
% 0.09/0.43
% 0.09/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.43
% 0.09/0.43 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.09/0.43 % Length of proof is 42.
% 0.09/0.43 % Level of proof is 19.
% 0.09/0.43 % Maximum clause weight is 84.000.
% 0.09/0.43 % Given clauses 37.
% 0.09/0.43
% 0.09/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------