%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP512-1 : 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 : n019.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 07:30:15 AM UTC 2026
% Result : Unsatisfiable 0.13s 5.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 2
% Syntax : Number of formulae : 80 ( 80 unt; 0 def)
% Number of atoms : 80 ( 79 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 247 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(multiply(VAR_0,VAR_1),VAR_2),inverse(multiply(VAR_0,VAR_2))) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(prove_these_axioms_4,axiom,
multiply(a,b) != multiply(b,a),
file('theBenchmark.p',prove_these_axioms_4) ).
cnf(c_2,plain,
multiply(a,b) != multiply(b,a),
inference(clausify,[status(thm)],[prove_these_axioms_4]) ).
cnf(c_3,plain,
multiply(b,a) != multiply(a,b),
inference(copy,[status(thm)],[c_2]) ).
cnf(c_4,plain,
multiply(multiply(A,B),inverse(multiply(multiply(multiply(C,A),D),B))) = inverse(multiply(C,D)),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_5,plain,
multiply(A,inverse(multiply(multiply(B,A),inverse(multiply(B,C))))) = C,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
multiply(multiply(multiply(multiply(multiply(A,B),C),D),inverse(multiply(A,C))),inverse(B)) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_198,plain,
multiply(A,inverse(multiply(multiply(B,A),inverse(C)))) = inverse(multiply(multiply(D,B),inverse(multiply(D,C)))),
inference(paramod,[status(thm)],[c_5,c_5]) ).
cnf(c_28,plain,
inverse(multiply(multiply(A,B),inverse(multiply(A,C)))) = multiply(D,inverse(multiply(multiply(B,D),inverse(C)))),
inference(copy,[status(thm)],[c_198]) ).
cnf(c_199,plain,
multiply(multiply(A,inverse(B)),inverse(A)) = inverse(multiply(multiply(multiply(C,B),D),inverse(multiply(C,D)))),
inference(paramod,[status(thm)],[c_6,c_4]) ).
cnf(c_32,plain,
multiply(multiply(A,inverse(B)),inverse(A)) = inverse(B),
inference(paramod,[status(thm)],[c_1,c_199]) ).
cnf(c_200,plain,
multiply(multiply(inverse(multiply(A,B)),inverse(multiply(C,D))),inverse(E)) = inverse(multiply(multiply(multiply(A,multiply(C,E)),B),D)),
inference(paramod,[status(thm)],[c_4,c_6]) ).
cnf(c_35,plain,
inverse(multiply(multiply(multiply(A,multiply(B,C)),D),E)) = multiply(multiply(inverse(multiply(A,D)),inverse(multiply(B,E))),inverse(C)),
inference(copy,[status(thm)],[c_200]) ).
cnf(c_47,plain,
multiply(inverse(A),inverse(multiply(B,inverse(B)))) = inverse(A),
inference(paramod,[status(thm)],[c_32,c_1]) ).
cnf(c_48,plain,
multiply(multiply(multiply(multiply(A,inverse(B)),C),inverse(A)),inverse(inverse(B))) = C,
inference(paramod,[status(thm)],[c_32,c_1]) ).
cnf(c_49,plain,
multiply(A,inverse(multiply(multiply(B,A),C))) = inverse(multiply(B,C)),
inference(paramod,[status(thm)],[c_1,c_32]) ).
cnf(c_201,plain,
multiply(inverse(multiply(A,B)),inverse(multiply(C,D))) = inverse(multiply(multiply(multiply(A,C),B),D)),
inference(paramod,[status(thm)],[c_4,c_32]) ).
cnf(c_54,plain,
inverse(multiply(multiply(multiply(A,B),C),D)) = multiply(inverse(multiply(A,C)),inverse(multiply(B,D))),
inference(copy,[status(thm)],[c_201]) ).
cnf(c_202,plain,
multiply(A,inverse(multiply(multiply(multiply(B,inverse(C)),A),inverse(inverse(C))))) = inverse(B),
inference(paramod,[status(thm)],[c_32,c_5]) ).
cnf(c_203,plain,
multiply(A,multiply(inverse(multiply(B,A)),inverse(multiply(inverse(C),inverse(inverse(C)))))) = inverse(B),
inference(paramod,[status(thm)],[c_54,c_202]) ).
cnf(c_56,plain,
multiply(A,inverse(multiply(B,A))) = inverse(B),
inference(paramod,[status(thm)],[c_47,c_203]) ).
cnf(c_204,plain,
multiply(A,inverse(B)) = inverse(multiply(multiply(C,B),inverse(multiply(C,A)))),
inference(paramod,[status(thm)],[c_5,c_32]) ).
cnf(c_57,plain,
inverse(multiply(multiply(A,B),inverse(multiply(A,C)))) = multiply(C,inverse(B)),
inference(copy,[status(thm)],[c_204]) ).
cnf(c_59,plain,
multiply(multiply(multiply(inverse(A),B),inverse(multiply(C,inverse(C)))),inverse(inverse(A))) = B,
inference(paramod,[status(thm)],[c_32,c_6]) ).
cnf(c_205,plain,
multiply(multiply(inverse(A),inverse(multiply(B,inverse(A)))),inverse(C)) = inverse(multiply(B,C)),
inference(paramod,[status(thm)],[c_32,c_6]) ).
cnf(c_206,plain,
multiply(inverse(B),inverse(C)) = inverse(multiply(B,C)),
inference(paramod,[status(thm)],[c_56,c_205]) ).
cnf(c_60,plain,
inverse(multiply(A,B)) = multiply(inverse(A),inverse(B)),
inference(copy,[status(thm)],[c_206]) ).
cnf(c_207,plain,
inverse(multiply(multiply(A,B),multiply(inverse(A),inverse(C)))) = multiply(D,inverse(multiply(multiply(B,D),inverse(C)))),
inference(paramod,[status(thm)],[c_60,c_28]) ).
cnf(c_208,plain,
multiply(inverse(multiply(A,B)),inverse(multiply(inverse(A),inverse(C)))) = multiply(D,inverse(multiply(multiply(B,D),inverse(C)))),
inference(paramod,[status(thm)],[c_60,c_207]) ).
cnf(c_209,plain,
multiply(multiply(inverse(A),inverse(B)),inverse(multiply(inverse(A),inverse(C)))) = multiply(D,inverse(multiply(multiply(B,D),inverse(C)))),
inference(paramod,[status(thm)],[c_60,c_208]) ).
cnf(c_210,plain,
multiply(multiply(inverse(A),inverse(B)),multiply(inverse(inverse(A)),inverse(inverse(C)))) = multiply(D,inverse(multiply(multiply(B,D),inverse(C)))),
inference(paramod,[status(thm)],[c_60,c_209]) ).
cnf(c_211,plain,
multiply(multiply(inverse(A),inverse(B)),multiply(inverse(inverse(A)),inverse(inverse(C)))) = multiply(D,multiply(inverse(multiply(B,D)),inverse(inverse(C)))),
inference(paramod,[status(thm)],[c_60,c_210]) ).
cnf(c_64,plain,
multiply(multiply(inverse(A),inverse(B)),multiply(inverse(inverse(A)),inverse(inverse(C)))) = multiply(D,multiply(multiply(inverse(B),inverse(D)),inverse(inverse(C)))),
inference(paramod,[status(thm)],[c_60,c_211]) ).
cnf(c_212,plain,
multiply(inverse(multiply(multiply(A,multiply(B,C)),D)),inverse(E)) = multiply(multiply(inverse(multiply(A,D)),inverse(multiply(B,E))),inverse(C)),
inference(paramod,[status(thm)],[c_60,c_35]) ).
cnf(c_213,plain,
multiply(multiply(inverse(multiply(A,multiply(B,C))),inverse(D)),inverse(E)) = multiply(multiply(inverse(multiply(A,D)),inverse(multiply(B,E))),inverse(C)),
inference(paramod,[status(thm)],[c_60,c_212]) ).
cnf(c_214,plain,
multiply(multiply(multiply(inverse(A),inverse(multiply(B,C))),inverse(D)),inverse(E)) = multiply(multiply(inverse(multiply(A,D)),inverse(multiply(B,E))),inverse(C)),
inference(paramod,[status(thm)],[c_60,c_213]) ).
cnf(c_215,plain,
multiply(multiply(multiply(inverse(A),multiply(inverse(B),inverse(C))),inverse(D)),inverse(E)) = multiply(multiply(inverse(multiply(A,D)),inverse(multiply(B,E))),inverse(C)),
inference(paramod,[status(thm)],[c_60,c_214]) ).
cnf(c_216,plain,
multiply(multiply(multiply(inverse(A),multiply(inverse(B),inverse(C))),inverse(D)),inverse(E)) = multiply(multiply(multiply(inverse(A),inverse(D)),inverse(multiply(B,E))),inverse(C)),
inference(paramod,[status(thm)],[c_60,c_215]) ).
cnf(c_217,plain,
multiply(multiply(multiply(inverse(A),multiply(inverse(B),inverse(C))),inverse(D)),inverse(E)) = multiply(multiply(multiply(inverse(A),inverse(D)),multiply(inverse(B),inverse(E))),inverse(C)),
inference(paramod,[status(thm)],[c_60,c_216]) ).
cnf(c_68,plain,
multiply(multiply(multiply(inverse(A),inverse(B)),multiply(inverse(C),inverse(D))),inverse(E)) = multiply(multiply(multiply(inverse(A),multiply(inverse(C),inverse(E))),inverse(B)),inverse(D)),
inference(copy,[status(thm)],[c_217]) ).
cnf(c_76,plain,
multiply(multiply(multiply(inverse(A),B),multiply(inverse(C),inverse(inverse(C)))),inverse(inverse(A))) = B,
inference(paramod,[status(thm)],[c_60,c_59]) ).
cnf(c_218,plain,
inverse(multiply(multiply(A,B),multiply(inverse(A),inverse(C)))) = multiply(C,inverse(B)),
inference(paramod,[status(thm)],[c_60,c_57]) ).
cnf(c_219,plain,
multiply(inverse(multiply(A,B)),inverse(multiply(inverse(A),inverse(C)))) = multiply(C,inverse(B)),
inference(paramod,[status(thm)],[c_60,c_218]) ).
cnf(c_220,plain,
multiply(multiply(inverse(A),inverse(B)),inverse(multiply(inverse(A),inverse(C)))) = multiply(C,inverse(B)),
inference(paramod,[status(thm)],[c_60,c_219]) ).
cnf(c_78,plain,
multiply(multiply(inverse(A),inverse(B)),multiply(inverse(inverse(A)),inverse(inverse(C)))) = multiply(C,inverse(B)),
inference(paramod,[status(thm)],[c_60,c_220]) ).
cnf(c_79,plain,
multiply(A,multiply(inverse(B),inverse(A))) = inverse(B),
inference(paramod,[status(thm)],[c_60,c_56]) ).
cnf(c_221,plain,
multiply(inverse(multiply(multiply(A,B),C)),inverse(D)) = multiply(inverse(multiply(A,C)),inverse(multiply(B,D))),
inference(paramod,[status(thm)],[c_60,c_54]) ).
cnf(c_222,plain,
multiply(multiply(inverse(multiply(A,B)),inverse(C)),inverse(D)) = multiply(inverse(multiply(A,C)),inverse(multiply(B,D))),
inference(paramod,[status(thm)],[c_60,c_221]) ).
cnf(c_223,plain,
multiply(multiply(multiply(inverse(A),inverse(B)),inverse(C)),inverse(D)) = multiply(inverse(multiply(A,C)),inverse(multiply(B,D))),
inference(paramod,[status(thm)],[c_60,c_222]) ).
cnf(c_224,plain,
multiply(multiply(multiply(inverse(A),inverse(B)),inverse(C)),inverse(D)) = multiply(multiply(inverse(A),inverse(C)),inverse(multiply(B,D))),
inference(paramod,[status(thm)],[c_60,c_223]) ).
cnf(c_81,plain,
multiply(multiply(multiply(inverse(A),inverse(B)),inverse(C)),inverse(D)) = multiply(multiply(inverse(A),inverse(C)),multiply(inverse(B),inverse(D))),
inference(paramod,[status(thm)],[c_60,c_224]) ).
cnf(c_225,plain,
multiply(A,multiply(inverse(multiply(B,A)),inverse(C))) = inverse(multiply(B,C)),
inference(paramod,[status(thm)],[c_60,c_49]) ).
cnf(c_226,plain,
multiply(A,multiply(multiply(inverse(B),inverse(A)),inverse(C))) = inverse(multiply(B,C)),
inference(paramod,[status(thm)],[c_60,c_225]) ).
cnf(c_85,plain,
multiply(A,multiply(multiply(inverse(B),inverse(A)),inverse(C))) = multiply(inverse(B),inverse(C)),
inference(paramod,[status(thm)],[c_60,c_226]) ).
cnf(c_97,plain,
multiply(multiply(inverse(A),inverse(B)),multiply(inverse(inverse(A)),inverse(inverse(C)))) = multiply(inverse(B),inverse(inverse(C))),
inference(paramod,[status(thm)],[c_85,c_64]) ).
cnf(c_98,plain,
multiply(inverse(A),inverse(inverse(B))) = multiply(B,inverse(A)),
inference(paramod,[status(thm)],[c_97,c_78]) ).
cnf(c_110,plain,
multiply(inverse(A),multiply(A,inverse(B))) = inverse(B),
inference(paramod,[status(thm)],[c_98,c_79]) ).
cnf(c_111,plain,
multiply(inverse(inverse(A)),inverse(inverse(inverse(B)))) = multiply(A,inverse(B)),
inference(paramod,[status(thm)],[c_98,c_98]) ).
cnf(c_114,plain,
inverse(inverse(inverse(A))) = inverse(A),
inference(paramod,[status(thm)],[c_110,c_79]) ).
cnf(c_116,plain,
multiply(inverse(inverse(A)),inverse(B)) = multiply(A,inverse(B)),
inference(paramod,[status(thm)],[c_114,c_111]) ).
cnf(c_126,plain,
multiply(A,inverse(inverse(B))) = multiply(B,inverse(inverse(A))),
inference(paramod,[status(thm)],[c_116,c_98]) ).
cnf(c_227,plain,
multiply(multiply(multiply(multiply(inverse(A),multiply(inverse(B),inverse(inverse(A)))),inverse(C)),inverse(D)),inverse(inverse(C))) = multiply(inverse(B),inverse(D)),
inference(paramod,[status(thm)],[c_68,c_48]) ).
cnf(c_228,plain,
multiply(multiply(multiply(inverse(B),inverse(C)),inverse(D)),inverse(inverse(C))) = multiply(inverse(B),inverse(D)),
inference(paramod,[status(thm)],[c_79,c_227]) ).
cnf(c_162,plain,
multiply(multiply(inverse(A),inverse(B)),multiply(inverse(C),inverse(inverse(C)))) = multiply(inverse(A),inverse(B)),
inference(paramod,[status(thm)],[c_81,c_228]) ).
cnf(c_229,plain,
multiply(inverse(inverse(A)),inverse(inverse(multiply(multiply(inverse(A),B),multiply(inverse(C),inverse(inverse(C))))))) = B,
inference(paramod,[status(thm)],[c_76,c_98]) ).
cnf(c_230,plain,
multiply(inverse(inverse(A)),inverse(multiply(inverse(multiply(inverse(A),B)),inverse(multiply(inverse(C),inverse(inverse(C))))))) = B,
inference(paramod,[status(thm)],[c_60,c_229]) ).
cnf(c_231,plain,
multiply(inverse(inverse(A)),inverse(multiply(multiply(inverse(inverse(A)),inverse(B)),inverse(multiply(inverse(C),inverse(inverse(C))))))) = B,
inference(paramod,[status(thm)],[c_60,c_230]) ).
cnf(c_232,plain,
multiply(inverse(inverse(A)),inverse(multiply(multiply(A,inverse(B)),inverse(multiply(inverse(C),inverse(inverse(C))))))) = B,
inference(paramod,[status(thm)],[c_116,c_231]) ).
cnf(c_233,plain,
multiply(inverse(inverse(A)),inverse(multiply(multiply(A,inverse(B)),multiply(inverse(inverse(C)),inverse(inverse(inverse(C))))))) = B,
inference(paramod,[status(thm)],[c_60,c_232]) ).
cnf(c_234,plain,
multiply(inverse(inverse(A)),inverse(multiply(multiply(A,inverse(B)),multiply(inverse(inverse(C)),inverse(C))))) = B,
inference(paramod,[status(thm)],[c_114,c_233]) ).
cnf(c_235,plain,
multiply(inverse(inverse(A)),inverse(multiply(multiply(A,inverse(B)),multiply(C,inverse(C))))) = B,
inference(paramod,[status(thm)],[c_116,c_234]) ).
cnf(c_236,plain,
multiply(inverse(inverse(A)),multiply(inverse(multiply(A,inverse(B))),inverse(multiply(C,inverse(C))))) = B,
inference(paramod,[status(thm)],[c_60,c_235]) ).
cnf(c_237,plain,
multiply(inverse(inverse(A)),multiply(multiply(inverse(A),inverse(inverse(B))),inverse(multiply(C,inverse(C))))) = B,
inference(paramod,[status(thm)],[c_60,c_236]) ).
cnf(c_238,plain,
multiply(inverse(inverse(A)),multiply(multiply(inverse(A),inverse(inverse(B))),multiply(inverse(C),inverse(inverse(C))))) = B,
inference(paramod,[status(thm)],[c_60,c_237]) ).
cnf(c_239,plain,
multiply(inverse(inverse(A)),multiply(inverse(A),inverse(inverse(B)))) = B,
inference(paramod,[status(thm)],[c_162,c_238]) ).
cnf(c_166,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_110,c_239]) ).
cnf(c_240,plain,
multiply(A,B) = multiply(B,inverse(inverse(A))),
inference(paramod,[status(thm)],[c_166,c_126]) ).
cnf(c_196,plain,
multiply(A,B) = multiply(B,A),
inference(paramod,[status(thm)],[c_166,c_240]) ).
cnf(c_197,plain,
$false,
inference(resolve,[status(thm)],[c_196,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP512-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.37 % Computer : n019.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Fri Sep 25 14:57:56 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/5.37 % Process 3040228 was started by sandbox2 on n019,
% 0.08/5.37 % Fri Sep 25 14:57:56 2026
% 0.08/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/5.38
% 0.08/5.38 % From the command line: assign(max_seconds, 300).
% 0.13/5.40
% 0.13/5.40 % SZS status Unsatisfiable for theBenchmark
% 0.13/5.40
% 0.13/5.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/5.40 % Length of proof is 35.
% 0.13/5.40 % Level of proof is 14.
% 0.13/5.40 % Maximum clause weight is 89.000.
% 0.13/5.40 % Given clauses 14.
% 0.13/5.40
% 0.13/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------