%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP085-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 07:27:17 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.58s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 2
% Syntax : Number of formulae : 82 ( 69 unt; 0 def)
% Number of atoms : 116 ( 115 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 84 ( 50 ~; 34 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 205 ( 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,axiom,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('theBenchmark.p',prove_these_axioms) ).
cnf(c_2,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(clausify,[status(thm)],[prove_these_axioms]) ).
cnf(c_226,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(b1),b1) != multiply(inverse(a1),a1) ),
inference(copy,[status(thm)],[c_2]) ).
cnf(c_3,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(b1),b1) != multiply(inverse(a1),a1) ),
inference(copy,[status(thm)],[c_226]) ).
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_12,plain,
multiply(multiply(A,inverse(multiply(B,C))),inverse(A)) = inverse(multiply(B,C)),
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_17,plain,
multiply(A,inverse(multiply(B,inverse(multiply(multiply(C,multiply(B,D)),inverse(multiply(C,A))))))) = D,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_227,plain,
multiply(multiply(inverse(multiply(multiply(A,B),inverse(multiply(A,C)))),D),inverse(multiply(multiply(C,E),D))) = inverse(multiply(B,E)),
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_21,plain,
inverse(multiply(A,B)) = multiply(multiply(inverse(multiply(multiply(C,A),inverse(multiply(C,D)))),E),inverse(multiply(multiply(D,B),E))),
inference(copy,[status(thm)],[c_227]) ).
cnf(c_228,plain,
multiply(multiply(A,B),inverse(multiply(C,B))) = inverse(multiply(D,inverse(multiply(multiply(E,multiply(D,A)),inverse(multiply(E,C)))))),
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_22,plain,
inverse(multiply(A,inverse(multiply(multiply(B,multiply(A,C)),inverse(multiply(B,D)))))) = multiply(multiply(C,E),inverse(multiply(D,E))),
inference(copy,[status(thm)],[c_228]) ).
cnf(c_229,plain,
A = inverse(multiply(B,multiply(C,inverse(multiply(multiply(B,C),A))))),
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_24,plain,
inverse(multiply(A,multiply(B,inverse(multiply(multiply(A,B),C))))) = C,
inference(copy,[status(thm)],[c_229]) ).
cnf(c_230,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_230]) ).
cnf(c_29,plain,
multiply(multiply(multiply(A,B),multiply(C,inverse(multiply(multiply(A,C),D)))),D) = B,
inference(paramod,[status(thm)],[c_24,c_1]) ).
cnf(c_35,plain,
inverse(multiply(multiply(A,B),inverse(multiply(A,multiply(B,C))))) = C,
inference(paramod,[status(thm)],[c_4,c_24]) ).
cnf(c_231,plain,
inverse(multiply(A,multiply(B,inverse(C)))) = inverse(multiply(multiply(D,multiply(A,B)),inverse(multiply(D,C)))),
inference(paramod,[status(thm)],[c_5,c_24]) ).
cnf(c_38,plain,
inverse(multiply(multiply(A,multiply(B,C)),inverse(multiply(A,D)))) = inverse(multiply(B,multiply(C,inverse(D)))),
inference(copy,[status(thm)],[c_231]) ).
cnf(c_41,plain,
inverse(multiply(A,inverse(multiply(A,multiply(B,inverse(C)))))) = multiply(multiply(B,D),inverse(multiply(C,D))),
inference(paramod,[status(thm)],[c_38,c_22]) ).
cnf(c_42,plain,
multiply(A,inverse(multiply(B,inverse(multiply(B,multiply(C,inverse(A))))))) = C,
inference(paramod,[status(thm)],[c_38,c_17]) ).
cnf(c_47,plain,
inverse(multiply(A,inverse(multiply(B,multiply(inverse(multiply(multiply(C,B),inverse(multiply(C,A)))),D))))) = D,
inference(paramod,[status(thm)],[c_5,c_35]) ).
cnf(c_53,plain,
multiply(A,inverse(multiply(multiply(B,A),C))) = inverse(multiply(B,C)),
inference(paramod,[status(thm)],[c_1,c_12]) ).
cnf(c_232,plain,
multiply(multiply(inverse(multiply(A,B)),C),inverse(multiply(inverse(multiply(A,B)),C))) = inverse(multiply(D,inverse(D))),
inference(paramod,[status(thm)],[c_12,c_4]) ).
cnf(c_56,plain,
inverse(multiply(A,inverse(A))) = multiply(multiply(inverse(multiply(B,C)),D),inverse(multiply(inverse(multiply(B,C)),D))),
inference(copy,[status(thm)],[c_232]) ).
cnf(c_233,plain,
multiply(A,inverse(B)) = inverse(multiply(multiply(C,B),inverse(multiply(C,A)))),
inference(paramod,[status(thm)],[c_5,c_12]) ).
cnf(c_63,plain,
inverse(multiply(multiply(A,B),inverse(multiply(A,C)))) = multiply(C,inverse(B)),
inference(copy,[status(thm)],[c_233]) ).
cnf(c_76,plain,
multiply(multiply(multiply(A,B),inverse(multiply(A,C))),C) = B,
inference(paramod,[status(thm)],[c_53,c_29]) ).
cnf(c_234,plain,
multiply(C,inverse(B)) = multiply(D,inverse(multiply(multiply(B,D),inverse(C)))),
inference(paramod,[status(thm)],[c_63,c_28]) ).
cnf(c_235,plain,
multiply(C,inverse(B)) = inverse(multiply(B,inverse(C))),
inference(paramod,[status(thm)],[c_53,c_234]) ).
cnf(c_77,plain,
inverse(multiply(A,inverse(B))) = multiply(B,inverse(A)),
inference(copy,[status(thm)],[c_235]) ).
cnf(c_236,plain,
inverse(multiply(A,inverse(multiply(A,C)))) = C,
inference(paramod,[status(thm)],[c_53,c_24]) ).
cnf(c_78,plain,
multiply(multiply(A,B),inverse(A)) = B,
inference(paramod,[status(thm)],[c_77,c_236]) ).
cnf(c_237,plain,
inverse(multiply(A,inverse(multiply(B,multiply(multiply(multiply(C,A),inverse(multiply(C,B))),D))))) = D,
inference(paramod,[status(thm)],[c_77,c_47]) ).
cnf(c_96,plain,
multiply(multiply(A,multiply(multiply(multiply(B,C),inverse(multiply(B,A))),D)),inverse(C)) = D,
inference(paramod,[status(thm)],[c_77,c_237]) ).
cnf(c_101,plain,
inverse(multiply(A,B)) = multiply(multiply(multiply(multiply(C,D),inverse(multiply(C,A))),E),inverse(multiply(multiply(D,B),E))),
inference(paramod,[status(thm)],[c_77,c_21]) ).
cnf(c_238,plain,
multiply(A,multiply(multiply(B,multiply(C,inverse(A))),inverse(B))) = C,
inference(paramod,[status(thm)],[c_77,c_42]) ).
cnf(c_104,plain,
multiply(A,multiply(B,inverse(A))) = B,
inference(paramod,[status(thm)],[c_78,c_238]) ).
cnf(c_239,plain,
multiply(multiply(A,multiply(B,inverse(C))),inverse(A)) = multiply(multiply(B,D),inverse(multiply(C,D))),
inference(paramod,[status(thm)],[c_77,c_41]) ).
cnf(c_240,plain,
multiply(B,inverse(C)) = multiply(multiply(B,D),inverse(multiply(C,D))),
inference(paramod,[status(thm)],[c_78,c_239]) ).
cnf(c_105,plain,
multiply(multiply(A,B),inverse(multiply(C,B))) = multiply(A,inverse(C)),
inference(copy,[status(thm)],[c_240]) ).
cnf(c_106,plain,
multiply(multiply(A,B),inverse(multiply(A,C))) = multiply(B,inverse(C)),
inference(paramod,[status(thm)],[c_77,c_63]) ).
cnf(c_241,plain,
multiply(A,inverse(A)) = multiply(multiply(inverse(multiply(B,C)),D),inverse(multiply(inverse(multiply(B,C)),D))),
inference(paramod,[status(thm)],[c_77,c_56]) ).
cnf(c_107,plain,
multiply(A,inverse(A)) = multiply(B,inverse(B)),
inference(paramod,[status(thm)],[c_106,c_241]) ).
cnf(c_242,plain,
inverse(multiply(A,B)) = multiply(multiply(multiply(D,inverse(A)),E),inverse(multiply(multiply(D,B),E))),
inference(paramod,[status(thm)],[c_106,c_101]) ).
cnf(c_243,plain,
inverse(multiply(A,B)) = multiply(multiply(D,inverse(A)),inverse(multiply(D,B))),
inference(paramod,[status(thm)],[c_105,c_242]) ).
cnf(c_110,plain,
inverse(multiply(A,B)) = multiply(inverse(A),inverse(B)),
inference(paramod,[status(thm)],[c_106,c_243]) ).
cnf(c_120,plain,
multiply(multiply(A,multiply(multiply(multiply(B,C),multiply(inverse(B),inverse(A))),D)),inverse(C)) = D,
inference(paramod,[status(thm)],[c_110,c_96]) ).
cnf(c_124,plain,
multiply(multiply(multiply(A,B),multiply(inverse(A),inverse(C))),C) = B,
inference(paramod,[status(thm)],[c_110,c_76]) ).
cnf(c_128,plain,
multiply(multiply(A,B),multiply(inverse(A),inverse(C))) = multiply(B,inverse(C)),
inference(paramod,[status(thm)],[c_110,c_106]) ).
cnf(c_152,plain,
multiply(multiply(A,inverse(B)),B) = A,
inference(paramod,[status(thm)],[c_128,c_124]) ).
cnf(c_153,plain,
multiply(multiply(A,multiply(multiply(B,inverse(A)),C)),inverse(B)) = C,
inference(paramod,[status(thm)],[c_128,c_120]) ).
cnf(c_244,plain,
multiply(A,inverse(multiply(A,inverse(B)))) = B,
inference(paramod,[status(thm)],[c_152,c_78]) ).
cnf(c_158,plain,
multiply(A,multiply(inverse(A),inverse(inverse(B)))) = B,
inference(paramod,[status(thm)],[c_110,c_244]) ).
cnf(c_245,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_152,c_78]) ).
cnf(c_159,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_245]) ).
cnf(c_160,plain,
multiply(A,B) = multiply(B,A),
inference(paramod,[status(thm)],[c_78,c_152]) ).
cnf(c_161,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(paramod,[status(thm)],[c_159,c_158]) ).
cnf(c_246,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(b1,inverse(b1)) != multiply(inverse(a1),a1) ),
inference(paramod,[status(thm)],[c_160,c_3]) ).
cnf(c_247,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_160,c_246]) ).
cnf(c_248,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(b2,inverse(b2)),a2) != a2
| multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_160,c_247]) ).
cnf(c_249,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a2,multiply(b2,inverse(b2))) != a2
| multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_160,c_248]) ).
cnf(c_250,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3))
| multiply(a2,multiply(b2,inverse(b2))) != a2
| multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_160,c_249]) ).
cnf(c_251,plain,
( multiply(a4,b4) != multiply(a4,b4)
| multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3))
| multiply(a2,multiply(b2,inverse(b2))) != a2
| multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_160,c_250]) ).
cnf(c_252,plain,
( multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3))
| multiply(a2,multiply(b2,inverse(b2))) != a2
| multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) ),
inference(copy,[status(thm)],[c_251]) ).
cnf(c_180,plain,
( multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3))
| multiply(a2,multiply(b2,inverse(b2))) != a2 ),
inference(resolve,[status(thm)],[c_107,c_252]) ).
cnf(c_185,plain,
multiply(A,multiply(B,inverse(B))) = A,
inference(paramod,[status(thm)],[c_107,c_104]) ).
cnf(c_253,plain,
( multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_185,c_180]) ).
cnf(c_186,plain,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(copy,[status(thm)],[c_253]) ).
cnf(c_254,plain,
multiply(A,B) = multiply(C,multiply(multiply(A,inverse(C)),B)),
inference(paramod,[status(thm)],[c_153,c_104]) ).
cnf(c_195,plain,
multiply(A,multiply(multiply(B,inverse(A)),C)) = multiply(B,C),
inference(copy,[status(thm)],[c_254]) ).
cnf(c_255,plain,
multiply(A,multiply(B,C)) = multiply(multiply(A,B),C),
inference(paramod,[status(thm)],[c_78,c_195]) ).
cnf(c_204,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(copy,[status(thm)],[c_255]) ).
cnf(c_256,plain,
multiply(A,multiply(B,C)) = multiply(multiply(B,inverse(inverse(A))),C),
inference(paramod,[status(thm)],[c_195,c_161]) ).
cnf(c_257,plain,
multiply(A,multiply(B,C)) = multiply(multiply(B,A),C),
inference(paramod,[status(thm)],[c_159,c_256]) ).
cnf(c_211,plain,
multiply(A,multiply(B,C)) = multiply(B,multiply(A,C)),
inference(paramod,[status(thm)],[c_204,c_257]) ).
cnf(c_258,plain,
multiply(a3,multiply(c3,b3)) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_211,c_186]) ).
cnf(c_259,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_160,c_258]) ).
cnf(c_225,plain,
$false,
inference(copy,[status(thm)],[c_259]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP085-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.45 % Computer : n008.cluster.edu
% 0.11/0.45 % Model : x86_64 x86_64
% 0.11/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.45 % Memory : 8046.5625MB
% 0.11/0.45 % OS : Linux 6.8.0-71-generic
% 0.11/0.45 % CPULimit : 300
% 0.11/0.45 % WCLimit : 300
% 0.11/0.46 % DateTime : Fri Sep 25 14:22:24 UTC 2026
% 0.11/0.46 % CPUTime :
% 0.11/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.46 % Process 1245762 was started by sandbox on n008,
% 0.11/0.46 % Fri Sep 25 14:22:24 2026
% 0.11/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.47
% 0.11/0.47 % From the command line: assign(max_seconds, 300).
% 0.15/0.58
% 0.15/0.58 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.58
% 0.15/0.58 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.15/0.58 % Length of proof is 46.
% 0.15/0.58 % Level of proof is 13.
% 0.15/0.58 % Maximum clause weight is 35.000.
% 0.15/0.58 % Given clauses 23.
% 0.15/0.58
% 0.15/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------