%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP438-1 : 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 : n009.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 07:29:33 AM UTC 2026
% Result : Unsatisfiable 2.60s 0.81s
% Output : CNFRefutation 2.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 2
% Syntax : Number of formulae : 142 ( 142 unt; 0 def)
% Number of atoms : 142 ( 141 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 16 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 597 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : multiply(VAR_0,inverse(multiply(VAR_1,multiply(VAR_2,multiply(multiply(inverse(VAR_2),inverse(multiply(VAR_3,VAR_1))),VAR_0))))) = VAR_3,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),A))))) = D,
inference(clausify,[status(thm)],[single_axiom]) ).
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_2,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(clausify,[status(thm)],[prove_these_axioms_3]) ).
cnf(c_3,plain,
multiply(A,inverse(multiply(multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,D))),inverse(E))),multiply(E,multiply(C,A))))) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_4,plain,
multiply(inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),multiply(inverse(D),inverse(multiply(E,F))))))),inverse(multiply(F,multiply(D,C)))) = E,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_518,plain,
multiply(A,inverse(multiply(multiply(B,multiply(C,inverse(D))),multiply(D,multiply(E,A))))) = multiply(F,multiply(multiply(inverse(F),inverse(multiply(C,E))),inverse(B))),
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_5,plain,
multiply(A,multiply(multiply(inverse(A),inverse(multiply(B,C))),inverse(D))) = multiply(E,inverse(multiply(multiply(D,multiply(B,inverse(F))),multiply(F,multiply(C,E))))),
inference(copy,[status(thm)],[c_518]) ).
cnf(c_6,plain,
multiply(inverse(A),inverse(multiply(B,multiply(C,inverse(multiply(multiply(A,multiply(D,inverse(E))),multiply(E,multiply(B,C)))))))) = D,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_7,plain,
multiply(A,multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,D))),C))),inverse(B))) = D,
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_8,plain,
multiply(A,multiply(multiply(inverse(A),inverse(multiply(B,C))),inverse(D))) = multiply(E,multiply(multiply(inverse(E),inverse(multiply(B,C))),inverse(D))),
inference(paramod,[status(thm)],[c_5,c_5]) ).
cnf(c_519,plain,
multiply(A,multiply(multiply(inverse(A),inverse(B)),inverse(C))) = multiply(D,multiply(multiply(inverse(D),inverse(multiply(E,inverse(multiply(F,multiply(V6,multiply(multiply(inverse(V6),inverse(multiply(B,F))),E))))))),inverse(C))),
inference(paramod,[status(thm)],[c_1,c_8]) ).
cnf(c_9,plain,
multiply(A,multiply(multiply(inverse(A),inverse(B)),inverse(C))) = multiply(D,multiply(multiply(inverse(D),inverse(B)),inverse(C))),
inference(paramod,[status(thm)],[c_1,c_519]) ).
cnf(c_520,plain,
multiply(A,multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(C)),D))),inverse(B))) = multiply(multiply(inverse(D),inverse(multiply(multiply(inverse(E),inverse(multiply(F,C))),F))),inverse(E)),
inference(paramod,[status(thm)],[c_7,c_7]) ).
cnf(c_11,plain,
multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,D))),C))),inverse(B)) = multiply(E,multiply(multiply(inverse(E),inverse(multiply(multiply(inverse(F),inverse(D)),A))),inverse(F))),
inference(copy,[status(thm)],[c_520]) ).
cnf(c_12,plain,
multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(A,multiply(D,inverse(B)))))),C))) = D,
inference(paramod,[status(thm)],[c_1,c_6]) ).
cnf(c_521,plain,
multiply(inverse(A),inverse(multiply(B,multiply(C,inverse(multiply(D,multiply(E,multiply(B,C)))))))) = multiply(inverse(A),inverse(multiply(multiply(inverse(E),inverse(multiply(F,D))),F))),
inference(paramod,[status(thm)],[c_7,c_6]) ).
cnf(c_13,plain,
multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,D))),C))) = multiply(inverse(A),inverse(multiply(E,multiply(F,inverse(multiply(D,multiply(B,multiply(E,F)))))))),
inference(copy,[status(thm)],[c_521]) ).
cnf(c_15,plain,
multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,D))),C))) = multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(E,D))),E))),
inference(paramod,[status(thm)],[c_7,c_12]) ).
cnf(c_522,plain,
multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(multiply(inverse(C),inverse(D)),A))),inverse(C)))) = multiply(E,inverse(multiply(multiply(F,multiply(multiply(inverse(F),inverse(multiply(V6,D))),inverse(V7))),multiply(V7,multiply(V6,E))))),
inference(paramod,[status(thm)],[c_11,c_5]) ).
cnf(c_16,plain,
multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(multiply(inverse(C),inverse(D)),A))),inverse(C)))) = D,
inference(paramod,[status(thm)],[c_3,c_522]) ).
cnf(c_17,plain,
multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(A,D)))),C))),inverse(B)) = D,
inference(paramod,[status(thm)],[c_11,c_7]) ).
cnf(c_523,plain,
multiply(A,inverse(multiply(multiply(B,multiply(multiply(inverse(B),inverse(multiply(inverse(C),inverse(multiply(D,multiply(E,inverse(multiply(F,multiply(V6,multiply(D,E)))))))))),inverse(V7))),multiply(V7,multiply(inverse(C),A))))) = inverse(multiply(multiply(inverse(V6),inverse(multiply(V8,F))),V8)),
inference(paramod,[status(thm)],[c_13,c_3]) ).
cnf(c_524,plain,
inverse(multiply(D,multiply(E,inverse(multiply(F,multiply(V6,multiply(D,E))))))) = inverse(multiply(multiply(inverse(V6),inverse(multiply(V8,F))),V8)),
inference(paramod,[status(thm)],[c_3,c_523]) ).
cnf(c_19,plain,
inverse(multiply(multiply(inverse(A),inverse(multiply(B,C))),B)) = inverse(multiply(D,multiply(E,inverse(multiply(C,multiply(A,multiply(D,E))))))),
inference(copy,[status(thm)],[c_524]) ).
cnf(c_525,plain,
multiply(A,inverse(multiply(inverse(B),multiply(C,multiply(multiply(inverse(C),inverse(D)),A))))) = multiply(inverse(E),inverse(multiply(multiply(inverse(B),inverse(multiply(F,multiply(E,D)))),F))),
inference(paramod,[status(thm)],[c_17,c_1]) ).
cnf(c_26,plain,
multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(A,D)))),C))) = multiply(E,inverse(multiply(inverse(B),multiply(F,multiply(multiply(inverse(F),inverse(D)),E))))),
inference(copy,[status(thm)],[c_525]) ).
cnf(c_27,plain,
multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,D))),C))),inverse(B)) = inverse(multiply(E,multiply(F,multiply(multiply(inverse(F),inverse(multiply(D,E))),A)))),
inference(paramod,[status(thm)],[c_1,c_17]) ).
cnf(c_526,plain,
multiply(multiply(inverse(A),inverse(multiply(B,C))),inverse(D)) = inverse(multiply(multiply(D,multiply(B,inverse(E))),multiply(E,multiply(C,A)))),
inference(paramod,[status(thm)],[c_6,c_17]) ).
cnf(c_29,plain,
inverse(multiply(multiply(A,multiply(B,inverse(C))),multiply(C,multiply(D,E)))) = multiply(multiply(inverse(E),inverse(multiply(B,D))),inverse(A)),
inference(copy,[status(thm)],[c_526]) ).
cnf(c_527,plain,
multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(multiply(inverse(C),inverse(multiply(D,multiply(E,inverse(multiply(F,multiply(V6,multiply(D,E)))))))),A))),inverse(C)))) = multiply(multiply(inverse(V6),inverse(multiply(V7,F))),V7),
inference(paramod,[status(thm)],[c_13,c_16]) ).
cnf(c_528,plain,
multiply(D,multiply(E,inverse(multiply(F,multiply(V6,multiply(D,E)))))) = multiply(multiply(inverse(V6),inverse(multiply(V7,F))),V7),
inference(paramod,[status(thm)],[c_16,c_527]) ).
cnf(c_41,plain,
multiply(multiply(inverse(A),inverse(multiply(B,C))),B) = multiply(D,multiply(E,inverse(multiply(C,multiply(A,multiply(D,E)))))),
inference(copy,[status(thm)],[c_528]) ).
cnf(c_529,plain,
multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(multiply(inverse(C),inverse(multiply(multiply(inverse(D),inverse(multiply(E,F))),E))),A))),inverse(C)))) = multiply(multiply(inverse(D),inverse(multiply(V6,F))),V6),
inference(paramod,[status(thm)],[c_15,c_16]) ).
cnf(c_43,plain,
multiply(multiply(inverse(A),inverse(multiply(B,C))),B) = multiply(multiply(inverse(A),inverse(multiply(D,C))),D),
inference(paramod,[status(thm)],[c_16,c_529]) ).
cnf(c_48,plain,
multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),D))))) = A,
inference(paramod,[status(thm)],[c_43,c_1]) ).
cnf(c_50,plain,
multiply(inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),C)))),inverse(multiply(D,multiply(E,multiply(inverse(E),inverse(multiply(F,D))))))) = F,
inference(paramod,[status(thm)],[c_43,c_4]) ).
cnf(c_530,plain,
multiply(A,multiply(multiply(inverse(A),inverse(multiply(B,C))),B)) = multiply(D,multiply(multiply(inverse(D),inverse(multiply(inverse(E),C))),inverse(E))),
inference(paramod,[status(thm)],[c_43,c_9]) ).
cnf(c_51,plain,
multiply(A,multiply(multiply(inverse(A),inverse(multiply(inverse(B),C))),inverse(B))) = multiply(D,multiply(multiply(inverse(D),inverse(multiply(E,C))),E)),
inference(copy,[status(thm)],[c_530]) ).
cnf(c_531,plain,
multiply(A,multiply(inverse(A),inverse(B))) = multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,multiply(E,multiply(multiply(inverse(E),inverse(multiply(F,D))),F))))),inverse(B))),
inference(paramod,[status(thm)],[c_48,c_9]) ).
cnf(c_62,plain,
multiply(A,multiply(inverse(A),inverse(B))) = multiply(C,multiply(inverse(C),inverse(B))),
inference(paramod,[status(thm)],[c_48,c_531]) ).
cnf(c_532,plain,
multiply(multiply(inverse(A),inverse(B)),B) = multiply(multiply(inverse(A),inverse(multiply(C,inverse(multiply(D,multiply(E,multiply(multiply(inverse(E),inverse(multiply(F,D))),F))))))),C),
inference(paramod,[status(thm)],[c_48,c_43]) ).
cnf(c_70,plain,
multiply(multiply(inverse(A),inverse(B)),B) = multiply(multiply(inverse(A),inverse(C)),C),
inference(paramod,[status(thm)],[c_48,c_532]) ).
cnf(c_91,plain,
inverse(multiply(multiply(inverse(A),inverse(multiply(B,C))),B)) = inverse(multiply(D,multiply(inverse(D),inverse(multiply(C,multiply(A,multiply(E,inverse(E)))))))),
inference(paramod,[status(thm)],[c_62,c_19]) ).
cnf(c_533,plain,
multiply(A,inverse(A)) = multiply(B,multiply(inverse(B),inverse(multiply(C,multiply(D,multiply(multiply(inverse(D),inverse(multiply(E,C))),E)))))),
inference(paramod,[status(thm)],[c_48,c_62]) ).
cnf(c_96,plain,
multiply(A,inverse(A)) = multiply(B,inverse(B)),
inference(paramod,[status(thm)],[c_48,c_533]) ).
cnf(c_101,plain,
multiply(A,multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,inverse(C)))),D))),inverse(B))) = inverse(D),
inference(paramod,[status(thm)],[c_96,c_7]) ).
cnf(c_122,plain,
multiply(multiply(inverse(A),inverse(multiply(B,inverse(B)))),C) = multiply(D,multiply(E,inverse(multiply(inverse(C),multiply(A,multiply(D,E)))))),
inference(paramod,[status(thm)],[c_96,c_41]) ).
cnf(c_534,plain,
multiply(A,multiply(B,inverse(B))) = multiply(C,multiply(inverse(C),inverse(inverse(A)))),
inference(paramod,[status(thm)],[c_96,c_62]) ).
cnf(c_125,plain,
multiply(A,multiply(inverse(A),inverse(inverse(B)))) = multiply(B,multiply(C,inverse(C))),
inference(copy,[status(thm)],[c_534]) ).
cnf(c_152,plain,
multiply(multiply(inverse(A),inverse(multiply(B,multiply(inverse(C),inverse(multiply(A,multiply(D,E))))))),B) = multiply(D,multiply(E,inverse(multiply(multiply(inverse(C),inverse(F)),F)))),
inference(paramod,[status(thm)],[c_70,c_41]) ).
cnf(c_535,plain,
multiply(multiply(A,inverse(A)),inverse(B)) = multiply(multiply(inverse(B),inverse(C)),C),
inference(paramod,[status(thm)],[c_96,c_70]) ).
cnf(c_154,plain,
multiply(multiply(inverse(A),inverse(B)),B) = multiply(multiply(C,inverse(C)),inverse(A)),
inference(copy,[status(thm)],[c_535]) ).
cnf(c_536,plain,
multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(A,D)))),C))) = multiply(inverse(multiply(inverse(E),inverse(D))),inverse(multiply(inverse(B),multiply(E,multiply(F,inverse(F)))))),
inference(paramod,[status(thm)],[c_96,c_26]) ).
cnf(c_164,plain,
multiply(inverse(multiply(inverse(A),inverse(B))),inverse(multiply(inverse(C),multiply(A,multiply(D,inverse(D)))))) = multiply(inverse(E),inverse(multiply(multiply(inverse(C),inverse(multiply(F,multiply(E,B)))),F))),
inference(copy,[status(thm)],[c_536]) ).
cnf(c_168,plain,
multiply(multiply(inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),multiply(D,inverse(D)))))),inverse(E)),E) = C,
inference(paramod,[status(thm)],[c_154,c_1]) ).
cnf(c_198,plain,
multiply(multiply(inverse(A),inverse(multiply(multiply(B,inverse(B)),inverse(C)))),multiply(inverse(C),inverse(D))) = multiply(multiply(inverse(A),inverse(multiply(E,D))),E),
inference(paramod,[status(thm)],[c_154,c_43]) ).
cnf(c_207,plain,
multiply(multiply(inverse(multiply(A,inverse(A))),inverse(B)),B) = multiply(C,inverse(C)),
inference(paramod,[status(thm)],[c_154,c_96]) ).
cnf(c_208,plain,
multiply(multiply(A,inverse(A)),inverse(B)) = multiply(multiply(C,inverse(C)),inverse(B)),
inference(paramod,[status(thm)],[c_96,c_154]) ).
cnf(c_209,plain,
multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(A,D)))),C))) = multiply(D,inverse(multiply(inverse(B),multiply(E,multiply(multiply(F,inverse(F)),inverse(E)))))),
inference(paramod,[status(thm)],[c_154,c_26]) ).
cnf(c_211,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),multiply(E,inverse(E))))))) = D,
inference(paramod,[status(thm)],[c_208,c_1]) ).
cnf(c_222,plain,
multiply(multiply(inverse(A),inverse(multiply(multiply(B,inverse(B)),inverse(C)))),multiply(D,inverse(D))) = multiply(E,multiply(F,inverse(multiply(inverse(C),multiply(A,multiply(E,F)))))),
inference(paramod,[status(thm)],[c_208,c_41]) ).
cnf(c_224,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(B)))) = multiply(C,inverse(C)),
inference(paramod,[status(thm)],[c_208,c_96]) ).
cnf(c_537,plain,
multiply(A,multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,inverse(C)))),multiply(D,inverse(D))))),inverse(B))) = inverse(multiply(E,inverse(E))),
inference(paramod,[status(thm)],[c_224,c_7]) ).
cnf(c_232,plain,
inverse(multiply(A,inverse(A))) = inverse(multiply(B,inverse(B))),
inference(paramod,[status(thm)],[c_101,c_537]) ).
cnf(c_244,plain,
inverse(multiply(multiply(A,multiply(multiply(B,inverse(B)),inverse(multiply(C,inverse(C))))),multiply(D,multiply(E,F)))) = multiply(multiply(inverse(F),inverse(multiply(D,E))),inverse(A)),
inference(paramod,[status(thm)],[c_224,c_29]) ).
cnf(c_253,plain,
multiply(A,inverse(multiply(inverse(multiply(B,inverse(B))),multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,inverse(D)))),multiply(E,inverse(E))))))) = A,
inference(paramod,[status(thm)],[c_224,c_48]) ).
cnf(c_538,plain,
multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(A,inverse(D))))),C))) = multiply(inverse(multiply(E,inverse(E))),inverse(multiply(inverse(B),multiply(D,multiply(F,inverse(F)))))),
inference(paramod,[status(thm)],[c_224,c_26]) ).
cnf(c_257,plain,
multiply(inverse(multiply(A,inverse(A))),inverse(multiply(inverse(B),multiply(C,multiply(D,inverse(D)))))) = multiply(inverse(E),inverse(multiply(multiply(inverse(B),inverse(multiply(F,multiply(E,inverse(C))))),F))),
inference(copy,[status(thm)],[c_538]) ).
cnf(c_292,plain,
multiply(multiply(inverse(A),inverse(multiply(B,inverse(B)))),multiply(C,inverse(C))) = multiply(multiply(D,inverse(D)),inverse(A)),
inference(paramod,[status(thm)],[c_232,c_154]) ).
cnf(c_539,plain,
multiply(A,multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,inverse(C)))),multiply(inverse(multiply(D,inverse(D))),inverse(E))))),inverse(B))) = E,
inference(paramod,[status(thm)],[c_207,c_7]) ).
cnf(c_303,plain,
inverse(multiply(inverse(multiply(A,inverse(A))),inverse(B))) = B,
inference(paramod,[status(thm)],[c_101,c_539]) ).
cnf(c_540,plain,
multiply(multiply(inverse(multiply(inverse(multiply(A,inverse(A))),inverse(B))),inverse(multiply(multiply(inverse(C),inverse(multiply(D,multiply(E,inverse(E))))),D))),inverse(C)) = B,
inference(paramod,[status(thm)],[c_207,c_17]) ).
cnf(c_319,plain,
multiply(multiply(A,inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(D,inverse(D))))),C))),inverse(B)) = A,
inference(paramod,[status(thm)],[c_303,c_540]) ).
cnf(c_326,plain,
multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,inverse(C)))),inverse(multiply(D,inverse(D)))))) = A,
inference(paramod,[status(thm)],[c_207,c_16]) ).
cnf(c_341,plain,
multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(A,D)))),C))) = multiply(D,inverse(multiply(inverse(B),multiply(multiply(E,inverse(E)),multiply(F,inverse(F)))))),
inference(paramod,[status(thm)],[c_207,c_26]) ).
cnf(c_541,plain,
inverse(A) = multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(A,B))),inverse(multiply(D,inverse(D)))))),
inference(paramod,[status(thm)],[c_1,c_303]) ).
cnf(c_347,plain,
multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),inverse(multiply(D,inverse(D)))))) = inverse(C),
inference(copy,[status(thm)],[c_541]) ).
cnf(c_353,plain,
multiply(A,multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),C),inverse(multiply(D,inverse(D)))))),inverse(B))) = inverse(C),
inference(paramod,[status(thm)],[c_303,c_7]) ).
cnf(c_542,plain,
multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(D,inverse(D))))),C))),inverse(B)) = inverse(multiply(inverse(multiply(E,inverse(E))),multiply(F,multiply(multiply(inverse(F),inverse(multiply(V6,inverse(V6)))),A)))),
inference(paramod,[status(thm)],[c_224,c_27]) ).
cnf(c_543,plain,
inverse(A) = inverse(multiply(inverse(multiply(E,inverse(E))),multiply(F,multiply(multiply(inverse(F),inverse(multiply(V6,inverse(V6)))),A)))),
inference(paramod,[status(thm)],[c_319,c_542]) ).
cnf(c_406,plain,
inverse(multiply(inverse(multiply(A,inverse(A))),multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,inverse(C)))),D)))) = inverse(D),
inference(copy,[status(thm)],[c_543]) ).
cnf(c_410,plain,
multiply(A,inverse(multiply(B,inverse(B)))) = A,
inference(paramod,[status(thm)],[c_406,c_253]) ).
cnf(c_419,plain,
multiply(A,multiply(multiply(inverse(A),inverse(multiply(inverse(B),C))),inverse(B))) = inverse(C),
inference(paramod,[status(thm)],[c_410,c_353]) ).
cnf(c_420,plain,
multiply(A,multiply(B,multiply(inverse(B),inverse(multiply(C,A))))) = inverse(C),
inference(paramod,[status(thm)],[c_410,c_347]) ).
cnf(c_544,plain,
multiply(A,multiply(B,multiply(inverse(B),inverse(multiply(D,inverse(D)))))) = A,
inference(paramod,[status(thm)],[c_410,c_326]) ).
cnf(c_427,plain,
multiply(A,multiply(B,inverse(B))) = A,
inference(paramod,[status(thm)],[c_410,c_544]) ).
cnf(c_545,plain,
multiply(inverse(A),multiply(C,inverse(C))) = multiply(multiply(D,inverse(D)),inverse(A)),
inference(paramod,[status(thm)],[c_410,c_292]) ).
cnf(c_546,plain,
inverse(A) = multiply(multiply(D,inverse(D)),inverse(A)),
inference(paramod,[status(thm)],[c_427,c_545]) ).
cnf(c_437,plain,
multiply(multiply(A,inverse(A)),inverse(B)) = inverse(B),
inference(copy,[status(thm)],[c_546]) ).
cnf(c_547,plain,
inverse(multiply(multiply(A,multiply(B,inverse(B))),multiply(D,multiply(E,F)))) = multiply(multiply(inverse(F),inverse(multiply(D,E))),inverse(A)),
inference(paramod,[status(thm)],[c_410,c_244]) ).
cnf(c_446,plain,
inverse(multiply(A,multiply(B,multiply(C,D)))) = multiply(multiply(inverse(D),inverse(multiply(B,C))),inverse(A)),
inference(paramod,[status(thm)],[c_427,c_547]) ).
cnf(c_548,plain,
multiply(inverse(A),C) = multiply(D,multiply(E,inverse(multiply(inverse(C),multiply(A,multiply(D,E)))))),
inference(paramod,[status(thm)],[c_410,c_122]) ).
cnf(c_549,plain,
multiply(inverse(A),C) = multiply(D,multiply(E,multiply(multiply(inverse(E),inverse(multiply(A,D))),inverse(inverse(C))))),
inference(paramod,[status(thm)],[c_446,c_548]) ).
cnf(c_451,plain,
multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),inverse(inverse(D))))) = multiply(inverse(C),D),
inference(copy,[status(thm)],[c_549]) ).
cnf(c_550,plain,
multiply(multiply(inverse(A),inverse(inverse(C))),multiply(D,inverse(D))) = multiply(E,multiply(F,inverse(multiply(inverse(C),multiply(A,multiply(E,F)))))),
inference(paramod,[status(thm)],[c_437,c_222]) ).
cnf(c_551,plain,
multiply(inverse(A),inverse(inverse(C))) = multiply(E,multiply(F,inverse(multiply(inverse(C),multiply(A,multiply(E,F)))))),
inference(paramod,[status(thm)],[c_427,c_550]) ).
cnf(c_552,plain,
multiply(inverse(A),inverse(inverse(C))) = multiply(E,multiply(F,multiply(multiply(inverse(F),inverse(multiply(A,E))),inverse(inverse(C))))),
inference(paramod,[status(thm)],[c_446,c_551]) ).
cnf(c_455,plain,
multiply(inverse(A),inverse(inverse(B))) = multiply(inverse(A),B),
inference(paramod,[status(thm)],[c_451,c_552]) ).
cnf(c_553,plain,
inverse(C) = multiply(D,multiply(multiply(inverse(D),inverse(multiply(E,C))),E)),
inference(paramod,[status(thm)],[c_419,c_51]) ).
cnf(c_457,plain,
multiply(A,multiply(multiply(inverse(A),inverse(multiply(B,C))),B)) = inverse(C),
inference(copy,[status(thm)],[c_553]) ).
cnf(c_554,plain,
multiply(inverse(multiply(A,inverse(A))),inverse(multiply(D,multiply(E,multiply(inverse(E),inverse(multiply(F,D))))))) = F,
inference(paramod,[status(thm)],[c_457,c_50]) ).
cnf(c_555,plain,
multiply(inverse(multiply(A,inverse(A))),inverse(inverse(F))) = F,
inference(paramod,[status(thm)],[c_420,c_554]) ).
cnf(c_458,plain,
multiply(inverse(multiply(A,inverse(A))),B) = B,
inference(paramod,[status(thm)],[c_455,c_555]) ).
cnf(c_556,plain,
multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(A,D)))),C))) = multiply(D,inverse(multiply(inverse(B),multiply(E,inverse(E))))),
inference(paramod,[status(thm)],[c_427,c_341]) ).
cnf(c_461,plain,
multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(A,D)))),C))) = multiply(D,inverse(inverse(B))),
inference(paramod,[status(thm)],[c_427,c_556]) ).
cnf(c_557,plain,
multiply(inverse(multiply(A,inverse(A))),inverse(multiply(inverse(B),C))) = multiply(inverse(E),inverse(multiply(multiply(inverse(B),inverse(multiply(F,multiply(E,inverse(C))))),F))),
inference(paramod,[status(thm)],[c_427,c_257]) ).
cnf(c_558,plain,
inverse(multiply(inverse(B),C)) = multiply(inverse(E),inverse(multiply(multiply(inverse(B),inverse(multiply(F,multiply(E,inverse(C))))),F))),
inference(paramod,[status(thm)],[c_458,c_557]) ).
cnf(c_559,plain,
inverse(multiply(inverse(B),C)) = multiply(inverse(C),inverse(inverse(B))),
inference(paramod,[status(thm)],[c_461,c_558]) ).
cnf(c_471,plain,
inverse(multiply(inverse(A),B)) = multiply(inverse(B),A),
inference(paramod,[status(thm)],[c_455,c_559]) ).
cnf(c_560,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,multiply(inverse(C),inverse(multiply(D,B))))))) = D,
inference(paramod,[status(thm)],[c_427,c_211]) ).
cnf(c_561,plain,
multiply(multiply(A,inverse(A)),inverse(inverse(D))) = D,
inference(paramod,[status(thm)],[c_420,c_560]) ).
cnf(c_475,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_437,c_561]) ).
cnf(c_562,plain,
multiply(multiply(inverse(multiply(A,multiply(B,multiply(inverse(B),inverse(multiply(C,A)))))),inverse(E)),E) = C,
inference(paramod,[status(thm)],[c_427,c_168]) ).
cnf(c_563,plain,
multiply(multiply(inverse(inverse(C)),inverse(E)),E) = C,
inference(paramod,[status(thm)],[c_420,c_562]) ).
cnf(c_477,plain,
multiply(multiply(A,inverse(B)),B) = A,
inference(paramod,[status(thm)],[c_475,c_563]) ).
cnf(c_564,plain,
multiply(multiply(inverse(inverse(B)),A),inverse(multiply(inverse(C),multiply(A,multiply(D,inverse(D)))))) = multiply(inverse(E),inverse(multiply(multiply(inverse(C),inverse(multiply(F,multiply(E,B)))),F))),
inference(paramod,[status(thm)],[c_471,c_164]) ).
cnf(c_565,plain,
multiply(multiply(B,A),inverse(multiply(inverse(C),multiply(A,multiply(D,inverse(D)))))) = multiply(inverse(E),inverse(multiply(multiply(inverse(C),inverse(multiply(F,multiply(E,B)))),F))),
inference(paramod,[status(thm)],[c_475,c_564]) ).
cnf(c_566,plain,
multiply(multiply(B,A),inverse(multiply(inverse(C),A))) = multiply(inverse(E),inverse(multiply(multiply(inverse(C),inverse(multiply(F,multiply(E,B)))),F))),
inference(paramod,[status(thm)],[c_427,c_565]) ).
cnf(c_567,plain,
multiply(multiply(B,A),multiply(inverse(A),C)) = multiply(inverse(E),inverse(multiply(multiply(inverse(C),inverse(multiply(F,multiply(E,B)))),F))),
inference(paramod,[status(thm)],[c_471,c_566]) ).
cnf(c_568,plain,
multiply(multiply(B,A),multiply(inverse(A),C)) = multiply(B,inverse(inverse(C))),
inference(paramod,[status(thm)],[c_461,c_567]) ).
cnf(c_478,plain,
multiply(multiply(A,B),multiply(inverse(B),C)) = multiply(A,C),
inference(paramod,[status(thm)],[c_475,c_568]) ).
cnf(c_569,plain,
multiply(A,multiply(inverse(A),B)) = multiply(B,multiply(C,inverse(C))),
inference(paramod,[status(thm)],[c_475,c_125]) ).
cnf(c_479,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(paramod,[status(thm)],[c_427,c_569]) ).
cnf(c_570,plain,
inverse(multiply(multiply(inverse(A),inverse(multiply(B,C))),B)) = inverse(multiply(D,multiply(inverse(D),inverse(multiply(C,A))))),
inference(paramod,[status(thm)],[c_427,c_91]) ).
cnf(c_571,plain,
inverse(multiply(multiply(inverse(A),inverse(multiply(B,C))),B)) = inverse(inverse(multiply(C,A))),
inference(paramod,[status(thm)],[c_479,c_570]) ).
cnf(c_482,plain,
inverse(multiply(multiply(inverse(A),inverse(multiply(B,C))),B)) = multiply(C,A),
inference(paramod,[status(thm)],[c_475,c_571]) ).
cnf(c_572,plain,
multiply(inverse(A),multiply(multiply(A,D),B)) = multiply(D,inverse(multiply(inverse(B),multiply(E,multiply(multiply(F,inverse(F)),inverse(E)))))),
inference(paramod,[status(thm)],[c_482,c_209]) ).
cnf(c_573,plain,
multiply(inverse(A),multiply(multiply(A,D),B)) = multiply(D,inverse(multiply(inverse(B),multiply(E,inverse(E))))),
inference(paramod,[status(thm)],[c_437,c_572]) ).
cnf(c_574,plain,
multiply(inverse(A),multiply(multiply(A,D),B)) = multiply(D,inverse(inverse(B))),
inference(paramod,[status(thm)],[c_427,c_573]) ).
cnf(c_488,plain,
multiply(inverse(A),multiply(multiply(A,B),C)) = multiply(B,C),
inference(paramod,[status(thm)],[c_475,c_574]) ).
cnf(c_575,plain,
multiply(multiply(inverse(A),inverse(inverse(C))),multiply(inverse(C),inverse(D))) = multiply(multiply(inverse(A),inverse(multiply(E,D))),E),
inference(paramod,[status(thm)],[c_437,c_198]) ).
cnf(c_576,plain,
multiply(multiply(inverse(A),C),multiply(inverse(C),inverse(D))) = multiply(multiply(inverse(A),inverse(multiply(E,D))),E),
inference(paramod,[status(thm)],[c_475,c_575]) ).
cnf(c_577,plain,
multiply(inverse(A),inverse(D)) = multiply(multiply(inverse(A),inverse(multiply(E,D))),E),
inference(paramod,[status(thm)],[c_478,c_576]) ).
cnf(c_492,plain,
multiply(multiply(inverse(A),inverse(multiply(B,C))),B) = multiply(inverse(A),inverse(C)),
inference(copy,[status(thm)],[c_577]) ).
cnf(c_578,plain,
multiply(inverse(A),inverse(multiply(inverse(C),inverse(multiply(A,multiply(D,E)))))) = multiply(D,multiply(E,inverse(multiply(multiply(inverse(C),inverse(F)),F)))),
inference(paramod,[status(thm)],[c_492,c_152]) ).
cnf(c_579,plain,
multiply(inverse(A),multiply(inverse(inverse(multiply(A,multiply(D,E)))),C)) = multiply(D,multiply(E,inverse(multiply(multiply(inverse(C),inverse(F)),F)))),
inference(paramod,[status(thm)],[c_471,c_578]) ).
cnf(c_580,plain,
multiply(inverse(A),multiply(multiply(A,multiply(D,E)),C)) = multiply(D,multiply(E,inverse(multiply(multiply(inverse(C),inverse(F)),F)))),
inference(paramod,[status(thm)],[c_475,c_579]) ).
cnf(c_581,plain,
multiply(multiply(D,E),C) = multiply(D,multiply(E,inverse(multiply(multiply(inverse(C),inverse(F)),F)))),
inference(paramod,[status(thm)],[c_488,c_580]) ).
cnf(c_582,plain,
multiply(multiply(D,E),C) = multiply(D,multiply(E,inverse(inverse(C)))),
inference(paramod,[status(thm)],[c_477,c_581]) ).
cnf(c_516,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(paramod,[status(thm)],[c_475,c_582]) ).
cnf(c_517,plain,
$false,
inference(resolve,[status(thm)],[c_516,c_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP438-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n009.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 14:54:13 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 1882131 was started by sandbox2 on n009,
% 0.16/0.44 % Fri Sep 25 14:54:13 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.44
% 0.16/0.44 % From the command line: assign(max_seconds, 300).
% 2.60/0.81
% 2.60/0.81 % SZS status Unsatisfiable for theBenchmark
% 2.60/0.81
% 2.60/0.81 % Proof 1 at 0.27 (+ 0.08) seconds.
% 2.60/0.81 % Length of proof is 75.
% 2.60/0.81 % Level of proof is 25.
% 2.60/0.81 % Maximum clause weight is 100.000.
% 2.60/0.81 % Given clauses 39.
% 2.60/0.81
% 2.60/0.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------