%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP444-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 : Thu Sep 24 12:34:13 PM UTC 2026
% Result : Unsatisfiable 130.98s 16.99s
% Output : CNFRefutation 119.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 77
% Number of leaves : 6
% Syntax : Number of formulae : 178 ( 178 unt; 4 def)
% Number of atoms : 178 ( 177 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 15 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 289 ( 289 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C,D] : inverse(multiply(A,multiply(B,multiply(multiply(C,inverse(C)),inverse(multiply(D,multiply(A,B))))))) = D,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2,X3] : inverse(multiply(X0,multiply(X1,multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,multiply(X0,X1))))))) = X3,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f5,definition,
sF1_fnc = multiply(a3,b3),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f6,definition,
sF0_fnc = multiply(sF1_fnc,c3),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f7,definition,
sF3_fnc = multiply(b3,c3),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f8,definition,
sF2_fnc = multiply(a3,sF3_fnc),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f9,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f4,f8,f7,f6,f5]) ).
fof(f10,plain,
! [X0,X1,X2,X3,X4,X5,X6] : inverse(multiply(X0,multiply(X1,multiply(multiply(multiply(X2,multiply(X3,multiply(multiply(X4,inverse(X4)),inverse(multiply(X5,multiply(X2,X3)))))),X5),inverse(multiply(X6,multiply(X0,X1))))))) = X6,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f11,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(X0,multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,multiply(X3,X0)))),multiply(multiply(X4,inverse(X4)),X2)))) = X3,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f12,plain,
! [X0,X1] : inverse(multiply(b3,multiply(c3,multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,sF3_fnc)))))) = X1,
inference(paramodulation,[status(thm)],[f7,f3]) ).
fof(f13,plain,
! [X0,X1] : inverse(multiply(sF1_fnc,multiply(c3,multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,sF0_fnc)))))) = X1,
inference(paramodulation,[status(thm)],[f6,f3]) ).
fof(f15,plain,
! [X0,X1] : inverse(multiply(a3,multiply(b3,multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,sF1_fnc)))))) = X1,
inference(paramodulation,[status(thm)],[f5,f3]) ).
fof(f23,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(X0,multiply(X1,multiply(multiply(multiply(a3,multiply(b3,multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,sF1_fnc))))),X3),inverse(multiply(X4,multiply(X0,X1))))))) = X4,
inference(paramodulation,[status(thm)],[f5,f10]) ).
fof(f30,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] : inverse(multiply(X0,multiply(multiply(multiply(multiply(X1,multiply(X2,multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,multiply(X1,X2)))))),X4),inverse(multiply(X5,multiply(X6,X0)))),multiply(multiply(X7,inverse(X7)),X5)))) = X6,
inference(paramodulation,[status(thm)],[f10,f3]) ).
fof(f35,plain,
! [X0] : inverse(multiply(b3,multiply(c3,multiply(multiply(X0,inverse(X0)),inverse(sF2_fnc))))) = a3,
inference(paramodulation,[status(thm)],[f8,f12]) ).
fof(f39,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] : inverse(multiply(X0,multiply(X1,multiply(multiply(multiply(X2,multiply(X3,multiply(multiply(multiply(b3,multiply(c3,multiply(multiply(X4,inverse(X4)),inverse(multiply(X5,sF3_fnc))))),X5),inverse(multiply(X6,multiply(X2,X3)))))),X6),inverse(multiply(X7,multiply(X0,X1))))))) = X7,
inference(paramodulation,[status(thm)],[f12,f10]) ).
fof(f47,plain,
! [X0,X1] : inverse(multiply(c3,multiply(multiply(multiply(X0,inverse(X0)),inverse(sF2_fnc)),multiply(multiply(X1,inverse(X1)),a3)))) = b3,
inference(paramodulation,[status(thm)],[f35,f3]) ).
fof(f58,plain,
! [X0,X1,X2] : inverse(multiply(c3,multiply(multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,sF0_fnc))),multiply(multiply(X2,inverse(X2)),X1)))) = sF1_fnc,
inference(paramodulation,[status(thm)],[f13,f3]) ).
fof(f111,plain,
! [X0,X1,X2] : inverse(multiply(multiply(multiply(X0,inverse(X0)),inverse(sF2_fnc)),multiply(multiply(multiply(X1,inverse(X1)),a3),multiply(multiply(X2,inverse(X2)),b3)))) = c3,
inference(paramodulation,[status(thm)],[f47,f3]) ).
fof(f128,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(multiply(X0,inverse(X0)),a3),multiply(multiply(multiply(X1,inverse(X1)),b3),multiply(multiply(X2,inverse(X2)),c3)))) = multiply(multiply(X3,inverse(X3)),inverse(sF2_fnc)),
inference(paramodulation,[status(thm)],[f47,f11]) ).
fof(f129,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,sF1_fnc))),multiply(multiply(multiply(X2,inverse(X2)),X1),multiply(multiply(X3,inverse(X3)),a3)))) = b3,
inference(paramodulation,[status(thm)],[f15,f11]) ).
fof(f131,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,sF0_fnc))),multiply(multiply(multiply(X2,inverse(X2)),X1),multiply(multiply(X3,inverse(X3)),sF1_fnc)))) = c3,
inference(paramodulation,[status(thm)],[f13,f11]) ).
fof(f134,plain,
! [X0,X1,X2,X3,X4,X5,X6] : inverse(multiply(multiply(multiply(X0,inverse(X0)),X1),multiply(multiply(multiply(X2,inverse(X2)),X3),multiply(multiply(X4,inverse(X4)),X5)))) = multiply(multiply(X6,inverse(X6)),inverse(multiply(X1,multiply(X3,X5)))),
inference(paramodulation,[status(thm)],[f11,f11]) ).
fof(f136,plain,
! [X0,X1,X2,X3,X4,X5] : inverse(multiply(multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,multiply(X2,X3)))),multiply(multiply(multiply(X4,inverse(X4)),X1),multiply(multiply(X5,inverse(X5)),X2)))) = X3,
inference(paramodulation,[status(thm)],[f3,f11]) ).
fof(f9314,plain,
! [X0] : multiply(multiply(X0,inverse(X0)),inverse(sF2_fnc)) = multiply(multiply(a3,inverse(a3)),inverse(sF2_fnc)),
inference(equality_split,[status(thm)],[f128]) ).
fof(f9757,plain,
! [X0,X1,X2,X3,X4,X5,X6] : inverse(multiply(inverse(sF2_fnc),multiply(multiply(multiply(multiply(X0,multiply(X1,multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,multiply(X0,X1)))))),X3),inverse(multiply(X4,multiply(multiply(a3,inverse(a3)),inverse(sF2_fnc))))),multiply(multiply(X5,inverse(X5)),X4)))) = multiply(X6,inverse(X6)),
inference(paramodulation,[status(thm)],[f9314,f30]) ).
fof(f9831,plain,
! [X0] : multiply(a3,inverse(a3)) = multiply(X0,inverse(X0)),
inference(forward_demodulation,[status(thm)],[f30,f9757]) ).
fof(f9836,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = multiply(X1,inverse(X1)),
inference(paramodulation,[status(thm)],[f9831,f9831]) ).
fof(f9849,plain,
! [X0,X1] : multiply(a3,inverse(a3)) = multiply(multiply(c3,multiply(multiply(multiply(X0,inverse(X0)),inverse(sF2_fnc)),multiply(multiply(X1,inverse(X1)),a3))),b3),
inference(paramodulation,[status(thm)],[f47,f9831]) ).
fof(f9887,plain,
! [X0,X1] : multiply(a3,inverse(a3)) = multiply(multiply(b3,multiply(c3,multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,sF3_fnc))))),X1),
inference(paramodulation,[status(thm)],[f12,f9831]) ).
fof(f9904,plain,
! [X0,X1,X2,X3] : multiply(a3,inverse(a3)) = multiply(multiply(X0,multiply(X1,multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,multiply(X0,X1)))))),X3),
inference(paramodulation,[status(thm)],[f3,f9831]) ).
fof(f10048,plain,
! [X0,X1,X2] : inverse(multiply(X0,multiply(X1,multiply(a3,inverse(a3))))) = multiply(a3,multiply(b3,multiply(multiply(X2,inverse(X2)),inverse(multiply(multiply(X0,X1),sF1_fnc))))),
inference(paramodulation,[status(thm)],[f9831,f23]) ).
fof(f10101,plain,
! [X0,X1] : inverse(multiply(c3,multiply(multiply(multiply(X0,inverse(X0)),inverse(multiply(inverse(multiply(X1,inverse(X1))),sF0_fnc))),multiply(a3,inverse(a3))))) = sF1_fnc,
inference(paramodulation,[status(thm)],[f9831,f58]) ).
fof(f10103,plain,
! [X0,X1,X2,X3] : inverse(multiply(X0,multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(inverse(multiply(X2,inverse(X2))),multiply(X3,X0)))),multiply(a3,inverse(a3))))) = X3,
inference(paramodulation,[status(thm)],[f9831,f11]) ).
fof(f10240,plain,
! [X0,X1,X2,X3] : inverse(multiply(inverse(X0),multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,multiply(a3,inverse(a3))))),multiply(multiply(X3,inverse(X3)),X2)))) = X0,
inference(paramodulation,[status(thm)],[f9831,f11]) ).
fof(f10243,plain,
! [X0,X1,X2] : inverse(multiply(X0,multiply(inverse(X0),multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,multiply(a3,inverse(a3)))))))) = X2,
inference(paramodulation,[status(thm)],[f9831,f3]) ).
fof(f10245,plain,
! [X0] : multiply(a3,inverse(a3)) = multiply(multiply(c3,multiply(multiply(multiply(a3,inverse(a3)),inverse(sF2_fnc)),multiply(multiply(X0,inverse(X0)),a3))),b3),
inference(forward_demodulation,[status(thm)],[f9314,f9849]) ).
fof(f10256,plain,
! [X0] : multiply(X0,inverse(X0)) = multiply(a3,inverse(a3)),
inference(equality_split,[status(thm)],[f9836]) ).
fof(f11744,plain,
! [X0,X1] : inverse(multiply(X0,multiply(inverse(X0),multiply(multiply(a3,inverse(a3)),inverse(multiply(X1,multiply(a3,inverse(a3)))))))) = X1,
inference(forward_demodulation,[status(thm)],[f10256,f10243]) ).
fof(f14332,plain,
! [X0] : multiply(a3,inverse(a3)) = multiply(multiply(b3,multiply(c3,multiply(multiply(a3,inverse(a3)),inverse(multiply(X0,sF3_fnc))))),X0),
inference(forward_demodulation,[status(thm)],[f10256,f9887]) ).
fof(f14838,plain,
! [X0,X1,X2] : multiply(a3,inverse(a3)) = multiply(multiply(X0,multiply(X1,multiply(multiply(a3,inverse(a3)),inverse(multiply(X2,multiply(X0,X1)))))),X2),
inference(forward_demodulation,[status(thm)],[f10256,f9904]) ).
fof(f16881,plain,
! [X0] : inverse(multiply(c3,multiply(multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(multiply(X0,inverse(X0))),sF0_fnc))),multiply(a3,inverse(a3))))) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f10256,f10101]) ).
fof(f16882,plain,
inverse(multiply(c3,multiply(multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(multiply(a3,inverse(a3))),sF0_fnc))),multiply(a3,inverse(a3))))) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f10256,f16881]) ).
fof(f17511,plain,
! [X0,X1,X2] : inverse(multiply(X0,multiply(multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(multiply(X1,inverse(X1))),multiply(X2,X0)))),multiply(a3,inverse(a3))))) = X2,
inference(forward_demodulation,[status(thm)],[f10256,f10103]) ).
fof(f17512,plain,
! [X0,X1] : inverse(multiply(X0,multiply(multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(multiply(a3,inverse(a3))),multiply(X1,X0)))),multiply(a3,inverse(a3))))) = X1,
inference(forward_demodulation,[status(thm)],[f10256,f17511]) ).
fof(f17902,plain,
! [X0,X1,X2] : inverse(multiply(inverse(X0),multiply(multiply(multiply(a3,inverse(a3)),inverse(multiply(X1,multiply(a3,inverse(a3))))),multiply(multiply(X2,inverse(X2)),X1)))) = X0,
inference(forward_demodulation,[status(thm)],[f10256,f10240]) ).
fof(f17903,plain,
! [X0,X1] : inverse(multiply(inverse(X0),multiply(multiply(multiply(a3,inverse(a3)),inverse(multiply(X1,multiply(a3,inverse(a3))))),multiply(multiply(a3,inverse(a3)),X1)))) = X0,
inference(forward_demodulation,[status(thm)],[f10256,f17902]) ).
fof(f18964,plain,
multiply(a3,inverse(a3)) = multiply(multiply(c3,multiply(multiply(multiply(a3,inverse(a3)),inverse(sF2_fnc)),multiply(multiply(a3,inverse(a3)),a3))),b3),
inference(forward_demodulation,[status(thm)],[f10256,f10245]) ).
fof(f22750,plain,
! [X0,X1] : inverse(multiply(X0,multiply(X1,multiply(a3,inverse(a3))))) = multiply(a3,multiply(b3,multiply(multiply(a3,inverse(a3)),inverse(multiply(multiply(X0,X1),sF1_fnc))))),
inference(forward_demodulation,[status(thm)],[f10256,f10048]) ).
fof(f22793,plain,
! [X0,X1] : inverse(inverse(multiply(X0,multiply(X1,multiply(a3,inverse(a3)))))) = multiply(X0,X1),
inference(paramodulation,[status(thm)],[f22750,f15]) ).
fof(f23103,plain,
inverse(sF1_fnc) = multiply(c3,multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(multiply(a3,inverse(a3))),sF0_fnc)))),
inference(paramodulation,[status(thm)],[f16882,f22793]) ).
fof(f23105,plain,
! [X0,X1] : inverse(X0) = multiply(X1,multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(multiply(a3,inverse(a3))),multiply(X0,X1))))),
inference(paramodulation,[status(thm)],[f17512,f22793]) ).
fof(f24890,plain,
inverse(multiply(c3,multiply(multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(multiply(a3,inverse(a3))),sF0_fnc))),multiply(a3,inverse(a3))))) = multiply(a3,multiply(b3,multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(sF1_fnc),sF1_fnc))))),
inference(paramodulation,[status(thm)],[f23103,f22750]) ).
fof(f25037,plain,
sF1_fnc = multiply(a3,multiply(b3,multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(sF1_fnc),sF1_fnc))))),
inference(forward_demodulation,[status(thm)],[f16882,f24890]) ).
fof(f25219,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,sF1_fnc))),multiply(multiply(multiply(X2,inverse(X2)),X1),multiply(multiply(X3,inverse(X3)),a3)))) = multiply(b3,multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(sF1_fnc),sF1_fnc)))),
inference(paramodulation,[status(thm)],[f25037,f136]) ).
fof(f25406,plain,
b3 = multiply(b3,multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(sF1_fnc),sF1_fnc)))),
inference(forward_demodulation,[status(thm)],[f129,f25219]) ).
fof(f26044,plain,
! [X0] : inverse(multiply(b3,multiply(c3,multiply(multiply(a3,inverse(a3)),inverse(multiply(X0,sF3_fnc)))))) = multiply(X0,multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(multiply(a3,inverse(a3))),multiply(a3,inverse(a3)))))),
inference(paramodulation,[status(thm)],[f14332,f23105]) ).
fof(f26161,plain,
! [X0,X1] : inverse(multiply(X0,multiply(multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(multiply(a3,inverse(a3))),multiply(X1,X0)))),multiply(a3,inverse(a3))))) = multiply(a3,multiply(b3,multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(X1),sF1_fnc))))),
inference(paramodulation,[status(thm)],[f23105,f22750]) ).
fof(f26267,plain,
! [X0] : X0 = multiply(X0,multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(multiply(a3,inverse(a3))),multiply(a3,inverse(a3)))))),
inference(forward_demodulation,[status(thm)],[f12,f26044]) ).
fof(f26444,plain,
! [X0] : X0 = multiply(a3,multiply(b3,multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(X0),sF1_fnc))))),
inference(forward_demodulation,[status(thm)],[f17512,f26161]) ).
fof(f33307,plain,
! [X0,X1,X2,X3,X4,X5] : inverse(multiply(multiply(multiply(a3,inverse(a3)),X0),multiply(multiply(multiply(X1,inverse(X1)),X2),multiply(multiply(X3,inverse(X3)),X4)))) = multiply(multiply(X5,inverse(X5)),inverse(multiply(X0,multiply(X2,X4)))),
inference(forward_demodulation,[status(thm)],[f10256,f134]) ).
fof(f33308,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(multiply(multiply(a3,inverse(a3)),X0),multiply(multiply(multiply(a3,inverse(a3)),X1),multiply(multiply(X2,inverse(X2)),X3)))) = multiply(multiply(X4,inverse(X4)),inverse(multiply(X0,multiply(X1,X3)))),
inference(forward_demodulation,[status(thm)],[f10256,f33307]) ).
fof(f33309,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(multiply(a3,inverse(a3)),X0),multiply(multiply(multiply(a3,inverse(a3)),X1),multiply(multiply(a3,inverse(a3)),X2)))) = multiply(multiply(X3,inverse(X3)),inverse(multiply(X0,multiply(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f10256,f33308]) ).
fof(f33310,plain,
! [X0,X1,X2] : inverse(multiply(multiply(multiply(a3,inverse(a3)),X0),multiply(multiply(multiply(a3,inverse(a3)),X1),multiply(multiply(a3,inverse(a3)),X2)))) = multiply(multiply(a3,inverse(a3)),inverse(multiply(X0,multiply(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f10256,f33309]) ).
fof(f33312,plain,
! [X0,X1,X2] : X0 = multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(multiply(X1,multiply(X2,X0))),multiply(X1,X2)))),
inference(paramodulation,[status(thm)],[f136,f33310]) ).
fof(f33317,plain,
c3 = multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(sF2_fnc),multiply(a3,b3)))),
inference(paramodulation,[status(thm)],[f111,f33310]) ).
fof(f33318,plain,
! [X0,X1,X2] : X0 = multiply(multiply(a3,inverse(a3)),inverse(multiply(X1,multiply(inverse(multiply(X2,multiply(X0,multiply(multiply(a3,inverse(a3)),X1)))),X2)))),
inference(paramodulation,[status(thm)],[f11,f33310]) ).
fof(f33510,plain,
c3 = multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(sF2_fnc),sF1_fnc))),
inference(forward_demodulation,[status(thm)],[f5,f33317]) ).
fof(f34110,plain,
! [X0] : X0 = multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(multiply(a3,multiply(b3,X0))),sF1_fnc))),
inference(paramodulation,[status(thm)],[f5,f33312]) ).
fof(f34118,plain,
! [X0,X1] : inverse(multiply(inverse(X0),multiply(X1,multiply(multiply(a3,inverse(a3)),inverse(multiply(a3,multiply(inverse(a3),X1))))))) = X0,
inference(paramodulation,[status(thm)],[f33312,f17903]) ).
fof(f34119,plain,
! [X0,X1] : inverse(multiply(X0,multiply(inverse(X0),X1))) = inverse(multiply(a3,multiply(inverse(a3),X1))),
inference(paramodulation,[status(thm)],[f33312,f11744]) ).
fof(f34683,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = multiply(a3,multiply(b3,multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(multiply(a3,multiply(inverse(a3),X1))),sF1_fnc))))),
inference(paramodulation,[status(thm)],[f34119,f26444]) ).
fof(f35334,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = multiply(a3,multiply(inverse(a3),X1)),
inference(forward_demodulation,[status(thm)],[f26444,f34683]) ).
fof(f35712,plain,
! [X0,X1,X2] : multiply(X0,multiply(inverse(X0),X1)) = multiply(X2,multiply(inverse(X2),X1)),
inference(paramodulation,[status(thm)],[f35334,f35334]) ).
fof(f36796,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = multiply(a3,multiply(inverse(a3),X1)),
inference(equality_split,[status(thm)],[f35712]) ).
fof(f48106,plain,
! [X0,X1,X2] : inverse(multiply(inverse(multiply(X0,multiply(X1,multiply(multiply(a3,inverse(a3)),X2)))),multiply(X0,X1))) = X2,
inference(paramodulation,[status(thm)],[f33318,f3]) ).
fof(f48401,plain,
! [X0] : inverse(multiply(inverse(multiply(X0,b3)),multiply(X0,b3))) = inverse(multiply(inverse(sF1_fnc),sF1_fnc)),
inference(paramodulation,[status(thm)],[f25406,f48106]) ).
fof(f48418,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(X0,multiply(X1,c3))),multiply(X0,X1))) = inverse(multiply(inverse(sF2_fnc),sF1_fnc)),
inference(paramodulation,[status(thm)],[f33510,f48106]) ).
fof(f48475,plain,
! [X0] : inverse(multiply(inverse(multiply(sF1_fnc,multiply(c3,multiply(multiply(a3,inverse(a3)),X0)))),sF0_fnc)) = X0,
inference(paramodulation,[status(thm)],[f6,f48106]) ).
fof(f48910,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(inverse(sF1_fnc),sF1_fnc)),multiply(X0,multiply(multiply(a3,inverse(a3)),inverse(multiply(a3,multiply(inverse(a3),X0))))))) = multiply(inverse(multiply(X1,b3)),multiply(X1,b3)),
inference(paramodulation,[status(thm)],[f48401,f34118]) ).
fof(f49151,plain,
! [X0] : multiply(inverse(sF1_fnc),sF1_fnc) = multiply(inverse(multiply(X0,b3)),multiply(X0,b3)),
inference(forward_demodulation,[status(thm)],[f34118,f48910]) ).
fof(f49235,plain,
multiply(inverse(sF1_fnc),sF1_fnc) = multiply(inverse(multiply(a3,inverse(a3))),multiply(multiply(c3,multiply(multiply(multiply(a3,inverse(a3)),inverse(sF2_fnc)),multiply(multiply(a3,inverse(a3)),a3))),b3)),
inference(paramodulation,[status(thm)],[f18964,f49151]) ).
fof(f49364,plain,
multiply(inverse(sF1_fnc),sF1_fnc) = multiply(inverse(multiply(a3,inverse(a3))),multiply(a3,inverse(a3))),
inference(forward_demodulation,[status(thm)],[f18964,f49235]) ).
fof(f49750,plain,
! [X0,X1,X2] : inverse(multiply(inverse(multiply(inverse(sF2_fnc),sF1_fnc)),multiply(X0,multiply(multiply(a3,inverse(a3)),inverse(multiply(a3,multiply(inverse(a3),X0))))))) = multiply(inverse(multiply(X1,multiply(X2,c3))),multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f48418,f34118]) ).
fof(f49998,plain,
! [X0,X1] : multiply(inverse(sF2_fnc),sF1_fnc) = multiply(inverse(multiply(X0,multiply(X1,c3))),multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f34118,f49750]) ).
fof(f50108,plain,
! [X0] : multiply(inverse(sF2_fnc),sF1_fnc) = multiply(inverse(multiply(X0,sF3_fnc)),multiply(X0,b3)),
inference(paramodulation,[status(thm)],[f7,f49998]) ).
fof(f50109,plain,
! [X0] : multiply(inverse(sF2_fnc),sF1_fnc) = multiply(inverse(multiply(X0,sF0_fnc)),multiply(X0,sF1_fnc)),
inference(paramodulation,[status(thm)],[f6,f49998]) ).
fof(f52955,plain,
! [X0] : X0 = multiply(X0,multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(sF1_fnc),sF1_fnc)))),
inference(backward_demodulation,[status(thm)],[f49364,f26267]) ).
fof(f52967,plain,
! [X0] : inverse(inverse(multiply(X0,multiply(inverse(sF1_fnc),sF1_fnc)))) = multiply(X0,inverse(multiply(a3,inverse(a3)))),
inference(paramodulation,[status(thm)],[f49364,f22793]) ).
fof(f53306,plain,
inverse(multiply(inverse(multiply(sF1_fnc,c3)),sF0_fnc)) = inverse(multiply(inverse(sF1_fnc),sF1_fnc)),
inference(paramodulation,[status(thm)],[f52955,f48475]) ).
fof(f53434,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X1))) = inverse(multiply(inverse(sF1_fnc),sF1_fnc)),
inference(paramodulation,[status(thm)],[f52955,f48106]) ).
fof(f53553,plain,
inverse(multiply(inverse(sF0_fnc),sF0_fnc)) = inverse(multiply(inverse(sF1_fnc),sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f6,f53306]) ).
fof(f54382,plain,
! [X0] : X0 = multiply(X0,multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(sF0_fnc),sF0_fnc)))),
inference(backward_demodulation,[status(thm)],[f53553,f52955]) ).
fof(f54402,plain,
! [X0] : inverse(multiply(inverse(multiply(inverse(sF0_fnc),sF0_fnc)),multiply(X0,multiply(multiply(a3,inverse(a3)),inverse(multiply(a3,multiply(inverse(a3),X0))))))) = multiply(inverse(sF1_fnc),sF1_fnc),
inference(paramodulation,[status(thm)],[f53553,f34118]) ).
fof(f54537,plain,
multiply(inverse(sF0_fnc),sF0_fnc) = multiply(inverse(sF1_fnc),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f34118,f54402]) ).
fof(f54627,plain,
multiply(inverse(sF2_fnc),sF1_fnc) = multiply(inverse(multiply(inverse(sF1_fnc),sF0_fnc)),multiply(inverse(sF0_fnc),sF0_fnc)),
inference(paramodulation,[status(thm)],[f54537,f50109]) ).
fof(f55824,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X1))) = inverse(multiply(inverse(sF0_fnc),sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f54537,f53434]) ).
fof(f55951,plain,
! [X0] : inverse(multiply(inverse(X0),multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(multiply(a3,multiply(b3,X0))),sF1_fnc))))) = inverse(multiply(inverse(sF0_fnc),sF0_fnc)),
inference(paramodulation,[status(thm)],[f34110,f55824]) ).
fof(f56427,plain,
! [X0] : inverse(multiply(inverse(X0),X0)) = inverse(multiply(inverse(sF0_fnc),sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f34110,f55951]) ).
fof(f56941,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(inverse(sF0_fnc),sF0_fnc)),multiply(X0,multiply(multiply(a3,inverse(a3)),inverse(multiply(a3,multiply(inverse(a3),X0))))))) = multiply(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f56427,f34118]) ).
fof(f57520,plain,
! [X0] : multiply(inverse(sF0_fnc),sF0_fnc) = multiply(inverse(X0),X0),
inference(forward_demodulation,[status(thm)],[f34118,f56941]) ).
fof(f57715,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f57520,f57520]) ).
fof(f57899,plain,
! [X0] : multiply(X0,multiply(inverse(sF0_fnc),sF0_fnc)) = multiply(a3,multiply(inverse(a3),X0)),
inference(paramodulation,[status(thm)],[f57520,f36796]) ).
fof(f57901,plain,
! [X0] : inverse(multiply(X0,multiply(inverse(sF0_fnc),sF0_fnc))) = inverse(multiply(a3,multiply(inverse(a3),X0))),
inference(paramodulation,[status(thm)],[f57520,f34119]) ).
fof(f58644,plain,
! [X0] : multiply(inverse(X0),X0) = multiply(inverse(a3),a3),
inference(equality_split,[status(thm)],[f57715]) ).
fof(f58645,plain,
! [X0] : multiply(inverse(X0),X0) = multiply(inverse(a3),a3),
inference(equality_split,[status(thm)],[f57715]) ).
fof(f58756,plain,
multiply(inverse(sF2_fnc),sF1_fnc) = multiply(inverse(multiply(inverse(b3),sF3_fnc)),multiply(inverse(a3),a3)),
inference(paramodulation,[status(thm)],[f58644,f50108]) ).
fof(f61342,plain,
! [X0] : multiply(X0,multiply(inverse(a3),a3)) = multiply(a3,multiply(inverse(a3),X0)),
inference(forward_demodulation,[status(thm)],[f58645,f57899]) ).
fof(f61346,plain,
multiply(inverse(a3),a3) = multiply(a3,multiply(inverse(a3),inverse(multiply(inverse(a3),a3)))),
inference(paramodulation,[status(thm)],[f58645,f61342]) ).
fof(f62207,plain,
! [X0] : X0 = multiply(X0,multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(a3),a3)))),
inference(forward_demodulation,[status(thm)],[f58645,f54382]) ).
fof(f63638,plain,
! [X0] : inverse(multiply(X0,multiply(inverse(a3),a3))) = inverse(multiply(a3,multiply(inverse(a3),X0))),
inference(forward_demodulation,[status(thm)],[f58645,f57901]) ).
fof(f64369,plain,
! [X0] : inverse(inverse(multiply(X0,multiply(inverse(a3),a3)))) = multiply(X0,inverse(multiply(a3,inverse(a3)))),
inference(forward_demodulation,[status(thm)],[f58645,f52967]) ).
fof(f64373,plain,
! [X0] : inverse(inverse(multiply(a3,multiply(inverse(a3),X0)))) = multiply(X0,inverse(multiply(a3,inverse(a3)))),
inference(paramodulation,[status(thm)],[f63638,f64369]) ).
fof(f64598,plain,
multiply(inverse(sF2_fnc),sF1_fnc) = multiply(inverse(multiply(inverse(sF1_fnc),sF0_fnc)),multiply(inverse(a3),a3)),
inference(forward_demodulation,[status(thm)],[f58645,f54627]) ).
fof(f64599,plain,
multiply(inverse(sF2_fnc),sF1_fnc) = multiply(a3,multiply(inverse(a3),inverse(multiply(inverse(sF1_fnc),sF0_fnc)))),
inference(paramodulation,[status(thm)],[f61342,f64598]) ).
fof(f64615,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(inverse(a3),multiply(a3,multiply(multiply(multiply(X0,multiply(X1,multiply(multiply(multiply(b3,multiply(c3,multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,sF3_fnc))))),X3),inverse(multiply(X4,multiply(X0,X1)))))),X4),inverse(multiply(inverse(sF2_fnc),sF1_fnc)))))) = inverse(multiply(inverse(sF1_fnc),sF0_fnc)),
inference(paramodulation,[status(thm)],[f64598,f39]) ).
fof(f64724,plain,
! [X0,X1,X2,X3] : inverse(multiply(inverse(a3),multiply(a3,multiply(multiply(multiply(X0,multiply(X1,multiply(multiply(multiply(b3,multiply(c3,multiply(multiply(a3,inverse(a3)),inverse(multiply(X2,sF3_fnc))))),X2),inverse(multiply(X3,multiply(X0,X1)))))),X3),inverse(multiply(inverse(sF2_fnc),sF1_fnc)))))) = inverse(multiply(inverse(sF1_fnc),sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f10256,f64615]) ).
fof(f64725,plain,
! [X0,X1,X2] : inverse(multiply(inverse(a3),multiply(a3,multiply(multiply(multiply(X0,multiply(X1,multiply(multiply(a3,inverse(a3)),inverse(multiply(X2,multiply(X0,X1)))))),X2),inverse(multiply(inverse(sF2_fnc),sF1_fnc)))))) = inverse(multiply(inverse(sF1_fnc),sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f14332,f64724]) ).
fof(f64726,plain,
inverse(multiply(inverse(a3),multiply(a3,multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(sF2_fnc),sF1_fnc)))))) = inverse(multiply(inverse(sF1_fnc),sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f14838,f64725]) ).
fof(f64727,plain,
inverse(multiply(inverse(a3),multiply(a3,c3))) = inverse(multiply(inverse(sF1_fnc),sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f33510,f64726]) ).
fof(f64998,plain,
! [X0] : inverse(multiply(inverse(multiply(inverse(sF1_fnc),sF0_fnc)),multiply(X0,multiply(multiply(a3,inverse(a3)),inverse(multiply(a3,multiply(inverse(a3),X0))))))) = multiply(inverse(a3),multiply(a3,c3)),
inference(paramodulation,[status(thm)],[f64727,f34118]) ).
fof(f65204,plain,
multiply(inverse(sF1_fnc),sF0_fnc) = multiply(inverse(a3),multiply(a3,c3)),
inference(forward_demodulation,[status(thm)],[f34118,f64998]) ).
fof(f66616,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(inverse(a3),multiply(a3,multiply(multiply(multiply(X0,multiply(X1,multiply(multiply(multiply(b3,multiply(c3,multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,sF3_fnc))))),X3),inverse(multiply(X4,multiply(X0,X1)))))),X4),inverse(multiply(inverse(sF2_fnc),sF1_fnc)))))) = inverse(multiply(inverse(b3),sF3_fnc)),
inference(paramodulation,[status(thm)],[f58756,f39]) ).
fof(f66729,plain,
! [X0,X1,X2,X3] : inverse(multiply(inverse(a3),multiply(a3,multiply(multiply(multiply(X0,multiply(X1,multiply(multiply(multiply(b3,multiply(c3,multiply(multiply(a3,inverse(a3)),inverse(multiply(X2,sF3_fnc))))),X2),inverse(multiply(X3,multiply(X0,X1)))))),X3),inverse(multiply(inverse(sF2_fnc),sF1_fnc)))))) = inverse(multiply(inverse(b3),sF3_fnc)),
inference(forward_demodulation,[status(thm)],[f10256,f66616]) ).
fof(f66730,plain,
! [X0,X1,X2] : inverse(multiply(inverse(a3),multiply(a3,multiply(multiply(multiply(X0,multiply(X1,multiply(multiply(a3,inverse(a3)),inverse(multiply(X2,multiply(X0,X1)))))),X2),inverse(multiply(inverse(sF2_fnc),sF1_fnc)))))) = inverse(multiply(inverse(b3),sF3_fnc)),
inference(forward_demodulation,[status(thm)],[f14332,f66729]) ).
fof(f66731,plain,
inverse(multiply(inverse(a3),multiply(a3,multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(sF2_fnc),sF1_fnc)))))) = inverse(multiply(inverse(b3),sF3_fnc)),
inference(forward_demodulation,[status(thm)],[f14838,f66730]) ).
fof(f66732,plain,
inverse(multiply(inverse(a3),multiply(a3,c3))) = inverse(multiply(inverse(b3),sF3_fnc)),
inference(forward_demodulation,[status(thm)],[f33510,f66731]) ).
fof(f66733,plain,
inverse(multiply(inverse(sF1_fnc),sF0_fnc)) = inverse(multiply(inverse(b3),sF3_fnc)),
inference(forward_demodulation,[status(thm)],[f65204,f66732]) ).
fof(f67011,plain,
! [X0] : inverse(multiply(inverse(multiply(inverse(b3),sF3_fnc)),multiply(X0,multiply(multiply(a3,inverse(a3)),inverse(multiply(a3,multiply(inverse(a3),X0))))))) = multiply(inverse(sF1_fnc),sF0_fnc),
inference(paramodulation,[status(thm)],[f66733,f34118]) ).
fof(f67156,plain,
multiply(inverse(b3),sF3_fnc) = multiply(inverse(sF1_fnc),sF0_fnc),
inference(forward_demodulation,[status(thm)],[f34118,f67011]) ).
fof(f68061,plain,
! [X0] : inverse(multiply(inverse(X0),multiply(inverse(multiply(inverse(a3),a3)),multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(a3),a3)))))) = X0,
inference(paramodulation,[status(thm)],[f61346,f34118]) ).
fof(f68170,plain,
! [X0] : inverse(multiply(inverse(X0),inverse(multiply(inverse(a3),a3)))) = X0,
inference(forward_demodulation,[status(thm)],[f62207,f68061]) ).
fof(f68511,plain,
! [X0] : multiply(multiply(inverse(X0),inverse(multiply(inverse(a3),a3))),X0) = multiply(a3,inverse(a3)),
inference(paramodulation,[status(thm)],[f68170,f10256]) ).
fof(f69056,plain,
! [X0] : inverse(multiply(inverse(X0),multiply(multiply(multiply(a3,inverse(a3)),inverse(multiply(a3,inverse(a3)))),multiply(multiply(a3,inverse(a3)),multiply(inverse(multiply(a3,inverse(a3))),inverse(multiply(inverse(a3),a3))))))) = X0,
inference(paramodulation,[status(thm)],[f68511,f17903]) ).
fof(f69529,plain,
! [X0] : inverse(multiply(inverse(X0),multiply(multiply(a3,inverse(a3)),multiply(multiply(a3,inverse(a3)),multiply(inverse(multiply(a3,inverse(a3))),inverse(multiply(inverse(a3),a3))))))) = X0,
inference(forward_demodulation,[status(thm)],[f10256,f69056]) ).
fof(f69530,plain,
! [X0] : inverse(multiply(inverse(X0),multiply(multiply(a3,inverse(a3)),multiply(a3,multiply(inverse(a3),inverse(multiply(inverse(a3),a3))))))) = X0,
inference(forward_demodulation,[status(thm)],[f36796,f69529]) ).
fof(f69531,plain,
! [X0] : inverse(multiply(inverse(X0),multiply(multiply(a3,inverse(a3)),multiply(inverse(a3),a3)))) = X0,
inference(forward_demodulation,[status(thm)],[f61346,f69530]) ).
fof(f69773,plain,
inverse(multiply(inverse(sF0_fnc),sF0_fnc)) = multiply(multiply(a3,inverse(a3)),multiply(inverse(a3),a3)),
inference(paramodulation,[status(thm)],[f56427,f69531]) ).
fof(f70048,plain,
inverse(multiply(inverse(a3),a3)) = multiply(multiply(a3,inverse(a3)),multiply(inverse(a3),a3)),
inference(forward_demodulation,[status(thm)],[f58645,f69773]) ).
fof(f71278,plain,
multiply(inverse(sF2_fnc),sF1_fnc) = multiply(a3,multiply(inverse(a3),inverse(multiply(inverse(b3),sF3_fnc)))),
inference(forward_demodulation,[status(thm)],[f67156,f64599]) ).
fof(f71280,plain,
! [X0] : inverse(multiply(inverse(X0),multiply(inverse(multiply(inverse(b3),sF3_fnc)),multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(sF2_fnc),sF1_fnc)))))) = X0,
inference(paramodulation,[status(thm)],[f71278,f34118]) ).
fof(f71389,plain,
! [X0] : inverse(multiply(inverse(X0),multiply(inverse(multiply(inverse(b3),sF3_fnc)),c3))) = X0,
inference(forward_demodulation,[status(thm)],[f33510,f71280]) ).
fof(f71623,plain,
! [X0] : X0 = multiply(inverse(multiply(inverse(b3),sF3_fnc)),multiply(c3,multiply(multiply(a3,inverse(a3)),X0))),
inference(paramodulation,[status(thm)],[f48106,f71389]) ).
fof(f71734,plain,
! [X0] : X0 = multiply(multiply(a3,inverse(a3)),multiply(inverse(multiply(inverse(b3),sF3_fnc)),multiply(c3,X0))),
inference(paramodulation,[status(thm)],[f71389,f33312]) ).
fof(f74167,plain,
inverse(inverse(multiply(a3,multiply(inverse(a3),c3)))) = multiply(inverse(b3),sF3_fnc),
inference(paramodulation,[status(thm)],[f71623,f34118]) ).
fof(f74306,plain,
multiply(c3,inverse(multiply(a3,inverse(a3)))) = multiply(inverse(b3),sF3_fnc),
inference(forward_demodulation,[status(thm)],[f64373,f74167]) ).
fof(f76411,plain,
inverse(multiply(a3,inverse(a3))) = multiply(multiply(a3,inverse(a3)),multiply(inverse(multiply(inverse(b3),sF3_fnc)),multiply(inverse(b3),sF3_fnc))),
inference(paramodulation,[status(thm)],[f74306,f71734]) ).
fof(f76568,plain,
inverse(multiply(a3,inverse(a3))) = multiply(multiply(a3,inverse(a3)),multiply(inverse(a3),a3)),
inference(forward_demodulation,[status(thm)],[f58645,f76411]) ).
fof(f76569,plain,
inverse(multiply(a3,inverse(a3))) = inverse(multiply(inverse(a3),a3)),
inference(forward_demodulation,[status(thm)],[f70048,f76568]) ).
fof(f76796,plain,
! [X0] : X0 = multiply(X0,multiply(multiply(a3,inverse(a3)),inverse(multiply(a3,inverse(a3))))),
inference(backward_demodulation,[status(thm)],[f76569,f62207]) ).
fof(f76800,plain,
! [X0] : inverse(multiply(inverse(multiply(a3,inverse(a3))),multiply(X0,multiply(multiply(a3,inverse(a3)),inverse(multiply(a3,multiply(inverse(a3),X0))))))) = multiply(inverse(a3),a3),
inference(paramodulation,[status(thm)],[f76569,f34118]) ).
fof(f76913,plain,
! [X0] : X0 = multiply(X0,multiply(a3,inverse(a3))),
inference(forward_demodulation,[status(thm)],[f10256,f76796]) ).
fof(f76916,plain,
multiply(a3,inverse(a3)) = multiply(inverse(a3),a3),
inference(forward_demodulation,[status(thm)],[f34118,f76800]) ).
fof(f77014,plain,
! [X0,X1] : inverse(multiply(X0,multiply(multiply(a3,inverse(a3)),inverse(multiply(inverse(multiply(a3,inverse(a3))),multiply(X1,X0)))))) = X1,
inference(backward_demodulation,[status(thm)],[f76913,f17512]) ).
fof(f77280,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f23105,f77014]) ).
fof(f78223,plain,
! [X0] : multiply(X0,multiply(a3,inverse(a3))) = multiply(a3,multiply(inverse(a3),X0)),
inference(backward_demodulation,[status(thm)],[f76916,f61342]) ).
fof(f78287,plain,
! [X0] : X0 = multiply(a3,multiply(inverse(a3),X0)),
inference(forward_demodulation,[status(thm)],[f76913,f78223]) ).
fof(f78462,plain,
! [X0] : inverse(multiply(inverse(multiply(multiply(a3,inverse(a3)),X0)),multiply(a3,inverse(a3)))) = X0,
inference(paramodulation,[status(thm)],[f78287,f48106]) ).
fof(f78611,plain,
! [X0] : inverse(inverse(multiply(multiply(a3,inverse(a3)),X0))) = X0,
inference(forward_demodulation,[status(thm)],[f76913,f78462]) ).
fof(f78612,plain,
! [X0] : multiply(multiply(a3,inverse(a3)),X0) = X0,
inference(forward_demodulation,[status(thm)],[f77280,f78611]) ).
fof(f81965,plain,
! [X0,X1,X2] : inverse(multiply(multiply(multiply(X0,inverse(X0)),inverse(sF0_fnc)),multiply(multiply(multiply(X1,inverse(X1)),multiply(a3,inverse(a3))),multiply(multiply(X2,inverse(X2)),sF1_fnc)))) = c3,
inference(paramodulation,[status(thm)],[f78612,f131]) ).
fof(f82531,plain,
! [X0,X1] : inverse(multiply(multiply(multiply(a3,inverse(a3)),inverse(sF0_fnc)),multiply(multiply(multiply(X0,inverse(X0)),multiply(a3,inverse(a3))),multiply(multiply(X1,inverse(X1)),sF1_fnc)))) = c3,
inference(forward_demodulation,[status(thm)],[f10256,f81965]) ).
fof(f82532,plain,
! [X0,X1] : inverse(multiply(inverse(sF0_fnc),multiply(multiply(multiply(X0,inverse(X0)),multiply(a3,inverse(a3))),multiply(multiply(X1,inverse(X1)),sF1_fnc)))) = c3,
inference(forward_demodulation,[status(thm)],[f78612,f82531]) ).
fof(f82533,plain,
! [X0,X1] : inverse(multiply(inverse(sF0_fnc),multiply(multiply(X0,inverse(X0)),multiply(multiply(X1,inverse(X1)),sF1_fnc)))) = c3,
inference(forward_demodulation,[status(thm)],[f76913,f82532]) ).
fof(f82534,plain,
! [X0] : inverse(multiply(inverse(sF0_fnc),multiply(multiply(a3,inverse(a3)),multiply(multiply(X0,inverse(X0)),sF1_fnc)))) = c3,
inference(forward_demodulation,[status(thm)],[f10256,f82533]) ).
fof(f82535,plain,
! [X0] : inverse(multiply(inverse(sF0_fnc),multiply(multiply(X0,inverse(X0)),sF1_fnc))) = c3,
inference(forward_demodulation,[status(thm)],[f78612,f82534]) ).
fof(f82536,plain,
inverse(multiply(inverse(sF0_fnc),multiply(multiply(a3,inverse(a3)),sF1_fnc))) = c3,
inference(forward_demodulation,[status(thm)],[f10256,f82535]) ).
fof(f82537,plain,
inverse(multiply(inverse(sF0_fnc),sF1_fnc)) = c3,
inference(forward_demodulation,[status(thm)],[f78612,f82536]) ).
fof(f86432,plain,
! [X0] : inverse(multiply(a3,multiply(b3,multiply(multiply(X0,inverse(X0)),c3)))) = inverse(sF0_fnc),
inference(paramodulation,[status(thm)],[f82537,f15]) ).
fof(f86578,plain,
inverse(multiply(a3,multiply(b3,multiply(multiply(a3,inverse(a3)),c3)))) = inverse(sF0_fnc),
inference(forward_demodulation,[status(thm)],[f10256,f86432]) ).
fof(f86579,plain,
inverse(multiply(a3,multiply(b3,c3))) = inverse(sF0_fnc),
inference(forward_demodulation,[status(thm)],[f78612,f86578]) ).
fof(f86580,plain,
inverse(multiply(a3,sF3_fnc)) = inverse(sF0_fnc),
inference(forward_demodulation,[status(thm)],[f7,f86579]) ).
fof(f86581,plain,
inverse(sF2_fnc) = inverse(sF0_fnc),
inference(forward_demodulation,[status(thm)],[f8,f86580]) ).
fof(f86730,plain,
inverse(inverse(sF0_fnc)) = sF2_fnc,
inference(paramodulation,[status(thm)],[f86581,f77280]) ).
fof(f86846,plain,
sF0_fnc = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f77280,f86730]) ).
fof(f86847,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f86846,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP444-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:15:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 130.98/16.99 % Refutation found
% 130.98/16.99 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 130.98/16.99 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 12.48/17.13 % Elapsed time: 16.749377 seconds
% 12.48/17.13 % CPU time: 132.516521 seconds
% 12.48/17.13 % Total memory used: 1.107 GB
% 12.48/17.13 % Net memory used: 1.099 GB
%------------------------------------------------------------------------------