%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP615-1 : TPTP v9.3.1. Released v2.6.0.
% 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 07:30:29 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.44s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 3
% Syntax : Number of formulae : 74 ( 74 unt; 0 def)
% Number of atoms : 74 ( 73 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 22 ( 22 ~; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 134 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : double_divide(inverse(double_divide(inverse(double_divide(VAR_0,inverse(VAR_1))),VAR_2)),double_divide(VAR_0,VAR_2)) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(inverse(double_divide(inverse(double_divide(A,inverse(B))),C)),double_divide(A,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_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_202,plain,
multiply(inverse(double_divide(b3,a3)),c3) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_203,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_202]) ).
cnf(c_204,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != multiply(a3,inverse(double_divide(c3,b3))),
inference(paramod,[status(thm)],[c_2,c_203]) ).
cnf(c_205,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_204]) ).
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_205]) ).
cnf(c_5,plain,
double_divide(inverse(A),double_divide(inverse(double_divide(B,inverse(A))),double_divide(B,inverse(C)))) = C,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(A,inverse(B))),C)),inverse(D))),double_divide(A,C))),B) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_8,plain,
double_divide(inverse(double_divide(inverse(double_divide(inverse(A),inverse(B))),double_divide(inverse(double_divide(C,inverse(A))),double_divide(C,inverse(D))))),D) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_206,plain,
double_divide(inverse(double_divide(inverse(A),double_divide(inverse(B),double_divide(inverse(double_divide(C,inverse(B))),double_divide(C,inverse(inverse(D))))))),A) = D,
inference(paramod,[status(thm)],[c_8,c_6]) ).
cnf(c_13,plain,
double_divide(inverse(double_divide(inverse(A),inverse(B))),A) = B,
inference(paramod,[status(thm)],[c_5,c_206]) ).
cnf(c_15,plain,
double_divide(inverse(A),double_divide(inverse(B),B)) = A,
inference(paramod,[status(thm)],[c_13,c_1]) ).
cnf(c_16,plain,
double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(A),inverse(B))),inverse(C))),A)),B) = C,
inference(paramod,[status(thm)],[c_13,c_1]) ).
cnf(c_36,plain,
double_divide(inverse(double_divide(inverse(A),A)),inverse(B)) = B,
inference(paramod,[status(thm)],[c_15,c_13]) ).
cnf(c_207,plain,
double_divide(inverse(A),double_divide(inverse(A),double_divide(inverse(double_divide(inverse(B),B)),inverse(C)))) = C,
inference(paramod,[status(thm)],[c_36,c_5]) ).
cnf(c_39,plain,
double_divide(inverse(A),double_divide(inverse(A),B)) = B,
inference(paramod,[status(thm)],[c_36,c_207]) ).
cnf(c_55,plain,
double_divide(inverse(A),A) = double_divide(inverse(B),B),
inference(paramod,[status(thm)],[c_15,c_39]) ).
cnf(c_56,plain,
double_divide(inverse(double_divide(inverse(A),A)),B) = inverse(B),
inference(paramod,[status(thm)],[c_36,c_39]) ).
cnf(c_68,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_56,c_36]) ).
cnf(c_208,plain,
double_divide(inverse(double_divide(inverse(double_divide(inverse(A),A)),B)),double_divide(inverse(inverse(C)),B)) = C,
inference(paramod,[status(thm)],[c_55,c_1]) ).
cnf(c_209,plain,
double_divide(inverse(inverse(B)),double_divide(inverse(inverse(C)),B)) = C,
inference(paramod,[status(thm)],[c_56,c_208]) ).
cnf(c_210,plain,
double_divide(B,double_divide(inverse(inverse(C)),B)) = C,
inference(paramod,[status(thm)],[c_68,c_209]) ).
cnf(c_81,plain,
double_divide(A,double_divide(B,A)) = B,
inference(paramod,[status(thm)],[c_68,c_210]) ).
cnf(c_211,plain,
double_divide(A,double_divide(inverse(inverse(A)),B)) = B,
inference(paramod,[status(thm)],[c_68,c_39]) ).
cnf(c_92,plain,
double_divide(A,double_divide(A,B)) = B,
inference(paramod,[status(thm)],[c_68,c_211]) ).
cnf(c_212,plain,
double_divide(A,inverse(A)) = double_divide(inverse(B),B),
inference(paramod,[status(thm)],[c_68,c_55]) ).
cnf(c_93,plain,
double_divide(inverse(A),A) = double_divide(B,inverse(B)),
inference(copy,[status(thm)],[c_212]) ).
cnf(c_213,plain,
double_divide(inverse(double_divide(inverse(double_divide(inverse(A),A)),B)),C) = inverse(double_divide(inverse(B),inverse(C))),
inference(paramod,[status(thm)],[c_93,c_16]) ).
cnf(c_214,plain,
double_divide(inverse(inverse(B)),C) = inverse(double_divide(inverse(B),inverse(C))),
inference(paramod,[status(thm)],[c_56,c_213]) ).
cnf(c_215,plain,
double_divide(B,C) = inverse(double_divide(inverse(B),inverse(C))),
inference(paramod,[status(thm)],[c_68,c_214]) ).
cnf(c_103,plain,
inverse(double_divide(inverse(A),inverse(B))) = double_divide(A,B),
inference(copy,[status(thm)],[c_215]) ).
cnf(c_216,plain,
double_divide(A,B) = inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(C),inverse(A))),inverse(B))),C)),
inference(paramod,[status(thm)],[c_16,c_81]) ).
cnf(c_217,plain,
double_divide(A,B) = inverse(double_divide(inverse(double_divide(double_divide(C,A),inverse(B))),C)),
inference(paramod,[status(thm)],[c_103,c_216]) ).
cnf(c_105,plain,
inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),A)) = double_divide(B,C),
inference(copy,[status(thm)],[c_217]) ).
cnf(c_121,plain,
double_divide(A,B) = double_divide(B,A),
inference(paramod,[status(thm)],[c_81,c_92]) ).
cnf(c_135,plain,
inverse(double_divide(A,inverse(double_divide(double_divide(A,B),inverse(C))))) = double_divide(B,C),
inference(paramod,[status(thm)],[c_121,c_105]) ).
cnf(c_218,plain,
inverse(double_divide(inverse(double_divide(b3,c3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))),
inference(paramod,[status(thm)],[c_121,c_4]) ).
cnf(c_219,plain,
inverse(double_divide(a3,inverse(double_divide(b3,c3)))) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))),
inference(paramod,[status(thm)],[c_121,c_218]) ).
cnf(c_220,plain,
inverse(double_divide(a3,inverse(double_divide(b3,c3)))) != inverse(double_divide(c3,inverse(double_divide(a3,b3)))),
inference(paramod,[status(thm)],[c_121,c_219]) ).
cnf(c_145,plain,
inverse(double_divide(c3,inverse(double_divide(a3,b3)))) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(copy,[status(thm)],[c_220]) ).
cnf(c_146,plain,
inverse(double_divide(A,B)) = double_divide(inverse(A),inverse(B)),
inference(paramod,[status(thm)],[c_103,c_68]) ).
cnf(c_221,plain,
inverse(double_divide(c3,double_divide(inverse(a3),inverse(b3)))) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_146,c_145]) ).
cnf(c_222,plain,
double_divide(inverse(c3),inverse(double_divide(inverse(a3),inverse(b3)))) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_146,c_221]) ).
cnf(c_223,plain,
double_divide(inverse(c3),double_divide(inverse(inverse(a3)),inverse(inverse(b3)))) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_146,c_222]) ).
cnf(c_224,plain,
double_divide(inverse(c3),double_divide(a3,inverse(inverse(b3)))) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_68,c_223]) ).
cnf(c_225,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_68,c_224]) ).
cnf(c_226,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != inverse(double_divide(a3,double_divide(inverse(b3),inverse(c3)))),
inference(paramod,[status(thm)],[c_146,c_225]) ).
cnf(c_227,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(inverse(a3),inverse(double_divide(inverse(b3),inverse(c3)))),
inference(paramod,[status(thm)],[c_146,c_226]) ).
cnf(c_228,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(inverse(a3),double_divide(inverse(inverse(b3)),inverse(inverse(c3)))),
inference(paramod,[status(thm)],[c_146,c_227]) ).
cnf(c_229,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(inverse(a3),double_divide(b3,inverse(inverse(c3)))),
inference(paramod,[status(thm)],[c_68,c_228]) ).
cnf(c_148,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(inverse(a3),double_divide(b3,c3)),
inference(paramod,[status(thm)],[c_68,c_229]) ).
cnf(c_230,plain,
inverse(double_divide(A,double_divide(inverse(double_divide(A,B)),inverse(inverse(C))))) = double_divide(B,C),
inference(paramod,[status(thm)],[c_146,c_135]) ).
cnf(c_231,plain,
inverse(double_divide(A,double_divide(double_divide(inverse(A),inverse(B)),inverse(inverse(C))))) = double_divide(B,C),
inference(paramod,[status(thm)],[c_146,c_230]) ).
cnf(c_232,plain,
inverse(double_divide(A,double_divide(double_divide(inverse(A),inverse(B)),C))) = double_divide(B,C),
inference(paramod,[status(thm)],[c_68,c_231]) ).
cnf(c_233,plain,
double_divide(inverse(A),inverse(double_divide(double_divide(inverse(A),inverse(B)),C))) = double_divide(B,C),
inference(paramod,[status(thm)],[c_146,c_232]) ).
cnf(c_234,plain,
double_divide(inverse(A),double_divide(inverse(double_divide(inverse(A),inverse(B))),inverse(C))) = double_divide(B,C),
inference(paramod,[status(thm)],[c_146,c_233]) ).
cnf(c_235,plain,
double_divide(inverse(A),double_divide(double_divide(inverse(inverse(A)),inverse(inverse(B))),inverse(C))) = double_divide(B,C),
inference(paramod,[status(thm)],[c_146,c_234]) ).
cnf(c_236,plain,
double_divide(inverse(A),double_divide(double_divide(A,inverse(inverse(B))),inverse(C))) = double_divide(B,C),
inference(paramod,[status(thm)],[c_68,c_235]) ).
cnf(c_155,plain,
double_divide(inverse(A),double_divide(double_divide(A,B),inverse(C))) = double_divide(B,C),
inference(paramod,[status(thm)],[c_68,c_236]) ).
cnf(c_237,plain,
double_divide(inverse(A),double_divide(B,inverse(C))) = double_divide(double_divide(B,A),C),
inference(paramod,[status(thm)],[c_81,c_155]) ).
cnf(c_187,plain,
double_divide(double_divide(A,B),C) = double_divide(inverse(B),double_divide(A,inverse(C))),
inference(copy,[status(thm)],[c_237]) ).
cnf(c_238,plain,
double_divide(inverse(A),double_divide(B,C)) = double_divide(double_divide(A,B),inverse(C)),
inference(paramod,[status(thm)],[c_155,c_92]) ).
cnf(c_239,plain,
double_divide(inverse(A),double_divide(B,C)) = double_divide(inverse(B),double_divide(A,inverse(inverse(C)))),
inference(paramod,[status(thm)],[c_187,c_238]) ).
cnf(c_189,plain,
double_divide(inverse(A),double_divide(B,C)) = double_divide(inverse(B),double_divide(A,C)),
inference(paramod,[status(thm)],[c_68,c_239]) ).
cnf(c_240,plain,
double_divide(inverse(A),double_divide(B,C)) = double_divide(double_divide(A,C),inverse(B)),
inference(paramod,[status(thm)],[c_189,c_121]) ).
cnf(c_241,plain,
double_divide(inverse(A),double_divide(B,C)) = double_divide(inverse(C),double_divide(A,inverse(inverse(B)))),
inference(paramod,[status(thm)],[c_187,c_240]) ).
cnf(c_200,plain,
double_divide(inverse(A),double_divide(B,C)) = double_divide(inverse(C),double_divide(A,B)),
inference(paramod,[status(thm)],[c_68,c_241]) ).
cnf(c_242,plain,
double_divide(inverse(a3),double_divide(b3,c3)) != double_divide(inverse(c3),double_divide(a3,b3)),
inference(copy,[status(thm)],[c_148]) ).
cnf(c_201,plain,
$false,
inference(resolve,[status(thm)],[c_200,c_242]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP615-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n015.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 25 15:06:12 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 1681503 was started by sandbox2 on n015,
% 0.07/0.35 % Fri Sep 25 15:06:12 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.36
% 0.07/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.44
% 0.13/0.44 % Assigning unary symbol inverse kb_weight 0 and highest precedence (7).
% 0.13/0.44
% 0.13/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.44
% 0.13/0.44 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.13/0.44 % Length of proof is 30.
% 0.13/0.44 % Level of proof is 17.
% 0.13/0.44 % Maximum clause weight is 81.000.
% 0.13/0.44 % Given clauses 29.
% 0.13/0.44
% 0.13/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------