%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP410-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 12:33:38 PM UTC 2026
% Result : Unsatisfiable 1.41s 0.60s
% Output : CNFRefutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 5
% Syntax : Number of formulae : 101 ( 101 unt; 3 def)
% Number of atoms : 101 ( 100 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 14 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 160 ( 160 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))),inverse(multiply(inverse(C),C))) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2] : multiply(multiply(inverse(multiply(X0,inverse(multiply(X1,X2)))),multiply(X0,inverse(X2))),inverse(multiply(inverse(X2),X2))) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f5,definition,
sF2_fnc = inverse(b2),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f6,definition,
sF1_fnc = multiply(sF2_fnc,b2),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f7,definition,
sF0_fnc = multiply(sF1_fnc,a2),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f8,plain,
sF0_fnc != a2,
inference(definition_folding,[],[f4,f7,f6,f5]) ).
fof(f10,plain,
! [X0,X1,X2,X3] : multiply(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(inverse(multiply(inverse(X2),X2))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))) = multiply(inverse(multiply(X3,inverse(multiply(X1,X2)))),multiply(X3,inverse(X2))),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f12,plain,
! [X0] : multiply(multiply(inverse(multiply(X0,inverse(sF1_fnc))),multiply(X0,inverse(b2))),inverse(multiply(inverse(b2),b2))) = sF2_fnc,
inference(paramodulation,[status(thm)],[f6,f3]) ).
fof(f13,plain,
! [X0,X1,X2,X3] : multiply(multiply(inverse(multiply(multiply(inverse(multiply(X0,inverse(multiply(X1,X2)))),multiply(X0,inverse(X2))),inverse(multiply(X3,multiply(inverse(X2),X2))))),X1),inverse(multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(X2),X2)))) = X3,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f16,plain,
! [X0] : multiply(multiply(inverse(multiply(X0,inverse(sF1_fnc))),multiply(X0,sF2_fnc)),inverse(multiply(inverse(b2),b2))) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f5,f12]) ).
fof(f17,plain,
! [X0] : multiply(multiply(inverse(multiply(X0,inverse(sF1_fnc))),multiply(X0,sF2_fnc)),inverse(multiply(sF2_fnc,b2))) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f5,f16]) ).
fof(f18,plain,
! [X0] : multiply(multiply(inverse(multiply(X0,inverse(sF1_fnc))),multiply(X0,sF2_fnc)),inverse(sF1_fnc)) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f6,f17]) ).
fof(f24,plain,
! [X0,X1] : multiply(multiply(inverse(multiply(multiply(inverse(multiply(X0,inverse(sF1_fnc))),multiply(X0,sF2_fnc)),inverse(multiply(X1,sF1_fnc)))),sF2_fnc),inverse(multiply(inverse(sF1_fnc),sF1_fnc))) = X1,
inference(paramodulation,[status(thm)],[f18,f3]) ).
fof(f110,plain,
! [X0,X1,X2] : X0 = multiply(inverse(multiply(X1,inverse(multiply(multiply(X0,inverse(multiply(inverse(X2),X2))),X2)))),multiply(X1,inverse(X2))),
inference(paramodulation,[status(thm)],[f3,f10]) ).
fof(f111,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(X0,inverse(multiply(X1,X2)))),multiply(X0,inverse(X2))) = multiply(inverse(multiply(X3,inverse(multiply(X1,X2)))),multiply(X3,inverse(X2))),
inference(paramodulation,[status(thm)],[f10,f10]) ).
fof(f204,plain,
! [X0,X1] : X0 = multiply(inverse(multiply(multiply(inverse(multiply(X1,inverse(sF1_fnc))),multiply(X1,sF2_fnc)),inverse(multiply(multiply(X0,inverse(multiply(inverse(sF1_fnc),sF1_fnc))),sF1_fnc)))),sF2_fnc),
inference(paramodulation,[status(thm)],[f18,f110]) ).
fof(f287,plain,
! [X0,X1,X2,X3,X4] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(multiply(X2,inverse(X3))))) = multiply(inverse(multiply(X4,inverse(multiply(inverse(multiply(X2,inverse(multiply(multiply(X1,inverse(multiply(inverse(X3),X3))),X3)))),multiply(X2,inverse(X3)))))),multiply(X4,inverse(multiply(X2,inverse(X3))))),
inference(paramodulation,[status(thm)],[f110,f111]) ).
fof(f367,plain,
! [X0,X1,X2,X3,X4] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(multiply(X2,inverse(X3))))) = multiply(inverse(multiply(X4,inverse(X1))),multiply(X4,inverse(multiply(X2,inverse(X3))))),
inference(forward_demodulation,[status(thm)],[f110,f287]) ).
fof(f1182,plain,
! [X0,X1,X2,X3,X4] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(X2))) = multiply(inverse(multiply(X3,inverse(X1))),multiply(X3,inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(X4,inverse(sF1_fnc))),multiply(X4,sF2_fnc)),inverse(multiply(X2,sF1_fnc)))),sF2_fnc),inverse(multiply(inverse(sF1_fnc),sF1_fnc)))))),
inference(paramodulation,[status(thm)],[f24,f367]) ).
fof(f1298,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(X2))) = multiply(inverse(multiply(X3,inverse(X1))),multiply(X3,inverse(X2))),
inference(forward_demodulation,[status(thm)],[f24,f1182]) ).
fof(f1343,plain,
! [X0,X1,X2] : multiply(inverse(multiply(X0,sF2_fnc)),multiply(X0,inverse(X1))) = multiply(inverse(multiply(X2,inverse(b2))),multiply(X2,inverse(X1))),
inference(paramodulation,[status(thm)],[f5,f1298]) ).
fof(f1453,plain,
! [X0,X1,X2] : multiply(inverse(multiply(X0,sF2_fnc)),multiply(X0,inverse(X1))) = multiply(inverse(multiply(X2,sF2_fnc)),multiply(X2,inverse(X1))),
inference(forward_demodulation,[status(thm)],[f5,f1343]) ).
fof(f1475,plain,
! [X0,X1] : multiply(inverse(multiply(X0,sF2_fnc)),multiply(X0,sF2_fnc)) = multiply(inverse(multiply(X1,sF2_fnc)),multiply(X1,inverse(b2))),
inference(paramodulation,[status(thm)],[f5,f1453]) ).
fof(f1505,plain,
! [X0,X1] : multiply(inverse(multiply(X0,sF2_fnc)),multiply(X0,sF2_fnc)) = multiply(inverse(multiply(X1,sF2_fnc)),multiply(X1,sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f5,f1475]) ).
fof(f3153,plain,
! [X0,X1,X2] : multiply(inverse(multiply(X0,sF2_fnc)),multiply(X0,sF2_fnc)) = multiply(inverse(multiply(inverse(multiply(multiply(inverse(multiply(X1,inverse(sF1_fnc))),multiply(X1,sF2_fnc)),inverse(multiply(multiply(X2,inverse(multiply(inverse(sF1_fnc),sF1_fnc))),sF1_fnc)))),sF2_fnc)),X2),
inference(paramodulation,[status(thm)],[f204,f1505]) ).
fof(f3180,plain,
! [X0,X1] : multiply(inverse(multiply(X0,sF2_fnc)),multiply(X0,sF2_fnc)) = multiply(inverse(X1),X1),
inference(forward_demodulation,[status(thm)],[f204,f3153]) ).
fof(f3184,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f3180,f3180]) ).
fof(f3329,plain,
! [X0] : multiply(sF2_fnc,b2) = multiply(inverse(X0),X0),
inference(paramodulation,[status(thm)],[f5,f3184]) ).
fof(f3687,plain,
! [X0] : sF1_fnc = multiply(inverse(X0),X0),
inference(forward_demodulation,[status(thm)],[f6,f3329]) ).
fof(f3718,plain,
! [X0,X1,X2,X3] : multiply(multiply(inverse(multiply(multiply(inverse(multiply(X0,inverse(multiply(X1,X2)))),multiply(X0,inverse(X2))),inverse(multiply(X3,multiply(inverse(X2),X2))))),X1),inverse(sF1_fnc)) = X3,
inference(backward_demodulation,[status(thm)],[f3687,f13]) ).
fof(f3723,plain,
! [X0,X1,X2] : X0 = multiply(inverse(multiply(X1,inverse(multiply(multiply(X0,inverse(sF1_fnc)),X2)))),multiply(X1,inverse(X2))),
inference(backward_demodulation,[status(thm)],[f3687,f110]) ).
fof(f3725,plain,
! [X0,X1,X2] : multiply(multiply(inverse(multiply(X0,inverse(multiply(X1,X2)))),multiply(X0,inverse(X2))),inverse(sF1_fnc)) = X1,
inference(backward_demodulation,[status(thm)],[f3687,f3]) ).
fof(f3781,plain,
! [X0,X1,X2,X3] : multiply(multiply(inverse(multiply(multiply(inverse(multiply(X0,inverse(multiply(X1,X2)))),multiply(X0,inverse(X2))),inverse(multiply(X3,sF1_fnc)))),X1),inverse(sF1_fnc)) = X3,
inference(forward_demodulation,[status(thm)],[f3687,f3718]) ).
fof(f3827,plain,
! [X0,X1,X2,X3] : multiply(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(inverse(sF1_fnc)))),inverse(sF1_fnc)) = multiply(inverse(multiply(X2,inverse(multiply(X1,X3)))),multiply(X2,inverse(X3))),
inference(paramodulation,[status(thm)],[f3725,f3725]) ).
fof(f3838,plain,
! [X0,X1,X2,X3] : multiply(multiply(inverse(multiply(multiply(inverse(multiply(X0,inverse(multiply(X1,X2)))),multiply(X0,inverse(X2))),inverse(multiply(X3,sF1_fnc)))),X1),inverse(sF1_fnc)) = X3,
inference(paramodulation,[status(thm)],[f3725,f3725]) ).
fof(f4121,plain,
! [X0,X1,X2] : multiply(multiply(inverse(multiply(multiply(inverse(multiply(X0,inverse(multiply(X1,X2)))),multiply(X0,inverse(X2))),inverse(sF1_fnc))),X1),inverse(sF1_fnc)) = inverse(sF1_fnc),
inference(paramodulation,[status(thm)],[f3687,f3781]) ).
fof(f4148,plain,
! [X0] : multiply(multiply(inverse(X0),X0),inverse(sF1_fnc)) = inverse(sF1_fnc),
inference(forward_demodulation,[status(thm)],[f3725,f4121]) ).
fof(f4149,plain,
multiply(sF1_fnc,inverse(sF1_fnc)) = inverse(sF1_fnc),
inference(forward_demodulation,[status(thm)],[f3687,f4148]) ).
fof(f4172,plain,
! [X0] : multiply(multiply(inverse(multiply(X0,inverse(inverse(sF1_fnc)))),multiply(X0,inverse(inverse(sF1_fnc)))),inverse(sF1_fnc)) = sF1_fnc,
inference(paramodulation,[status(thm)],[f4149,f3725]) ).
fof(f4175,plain,
multiply(sF1_fnc,inverse(sF1_fnc)) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f3687,f4172]) ).
fof(f4176,plain,
inverse(sF1_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f4149,f4175]) ).
fof(f4177,plain,
multiply(sF1_fnc,inverse(sF1_fnc)) = sF1_fnc,
inference(backward_demodulation,[status(thm)],[f4176,f4149]) ).
fof(f4181,plain,
! [X0,X1,X2] : X0 = multiply(inverse(multiply(X1,inverse(multiply(multiply(X0,sF1_fnc),X2)))),multiply(X1,inverse(X2))),
inference(backward_demodulation,[status(thm)],[f4176,f3723]) ).
fof(f4185,plain,
! [X0,X1,X2] : multiply(multiply(inverse(multiply(X0,inverse(multiply(X1,X2)))),multiply(X0,inverse(X2))),sF1_fnc) = X1,
inference(backward_demodulation,[status(thm)],[f4176,f3725]) ).
fof(f4205,plain,
multiply(sF1_fnc,sF1_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f4176,f4177]) ).
fof(f4239,plain,
! [X0,X1] : multiply(multiply(inverse(sF1_fnc),multiply(inverse(inverse(multiply(X0,X1))),inverse(X1))),sF1_fnc) = X0,
inference(paramodulation,[status(thm)],[f3687,f4185]) ).
fof(f4250,plain,
! [X0,X1] : multiply(multiply(inverse(multiply(X0,inverse(sF1_fnc))),multiply(X0,inverse(X1))),sF1_fnc) = inverse(X1),
inference(paramodulation,[status(thm)],[f3687,f4185]) ).
fof(f4258,plain,
! [X0,X1] : multiply(multiply(sF1_fnc,multiply(inverse(inverse(multiply(X0,X1))),inverse(X1))),sF1_fnc) = X0,
inference(forward_demodulation,[status(thm)],[f4176,f4239]) ).
fof(f4263,plain,
! [X0,X1] : multiply(multiply(inverse(multiply(X0,sF1_fnc)),multiply(X0,inverse(X1))),sF1_fnc) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f4176,f4250]) ).
fof(f4345,plain,
! [X0] : multiply(multiply(sF1_fnc,multiply(inverse(inverse(sF1_fnc)),inverse(X0))),sF1_fnc) = inverse(X0),
inference(paramodulation,[status(thm)],[f3687,f4258]) ).
fof(f4347,plain,
multiply(multiply(sF1_fnc,multiply(inverse(inverse(sF0_fnc)),inverse(a2))),sF1_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f7,f4258]) ).
fof(f4360,plain,
! [X0] : multiply(multiply(sF1_fnc,multiply(inverse(sF1_fnc),inverse(X0))),sF1_fnc) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f4176,f4345]) ).
fof(f4361,plain,
! [X0] : multiply(multiply(sF1_fnc,multiply(sF1_fnc,inverse(X0))),sF1_fnc) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f4176,f4360]) ).
fof(f4396,plain,
! [X0] : multiply(multiply(inverse(multiply(inverse(inverse(X0)),sF1_fnc)),sF1_fnc),sF1_fnc) = inverse(X0),
inference(paramodulation,[status(thm)],[f3687,f4263]) ).
fof(f4416,plain,
multiply(multiply(sF1_fnc,multiply(inverse(inverse(sF1_fnc)),inverse(sF1_fnc))),sF1_fnc) = multiply(sF1_fnc,multiply(inverse(inverse(sF0_fnc)),inverse(a2))),
inference(paramodulation,[status(thm)],[f4347,f4258]) ).
fof(f4421,plain,
multiply(multiply(sF1_fnc,sF1_fnc),sF1_fnc) = multiply(sF1_fnc,multiply(inverse(inverse(sF0_fnc)),inverse(a2))),
inference(forward_demodulation,[status(thm)],[f3687,f4416]) ).
fof(f4422,plain,
multiply(sF1_fnc,sF1_fnc) = multiply(sF1_fnc,multiply(inverse(inverse(sF0_fnc)),inverse(a2))),
inference(forward_demodulation,[status(thm)],[f4205,f4421]) ).
fof(f4423,plain,
sF1_fnc = multiply(sF1_fnc,multiply(inverse(inverse(sF0_fnc)),inverse(a2))),
inference(forward_demodulation,[status(thm)],[f4205,f4422]) ).
fof(f4431,plain,
multiply(multiply(sF1_fnc,multiply(inverse(inverse(sF1_fnc)),inverse(multiply(inverse(inverse(sF0_fnc)),inverse(a2))))),sF1_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f4423,f4258]) ).
fof(f4434,plain,
multiply(multiply(sF1_fnc,multiply(inverse(sF1_fnc),inverse(multiply(inverse(inverse(sF0_fnc)),inverse(a2))))),sF1_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f4176,f4431]) ).
fof(f4435,plain,
multiply(multiply(sF1_fnc,multiply(sF1_fnc,inverse(multiply(inverse(inverse(sF0_fnc)),inverse(a2))))),sF1_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f4176,f4434]) ).
fof(f4436,plain,
inverse(multiply(inverse(inverse(sF0_fnc)),inverse(a2))) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f4361,f4435]) ).
fof(f4445,plain,
multiply(multiply(sF1_fnc,multiply(inverse(sF1_fnc),inverse(inverse(a2)))),sF1_fnc) = inverse(inverse(sF0_fnc)),
inference(paramodulation,[status(thm)],[f4436,f4258]) ).
fof(f4464,plain,
multiply(multiply(sF1_fnc,multiply(sF1_fnc,inverse(inverse(a2)))),sF1_fnc) = inverse(inverse(sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f4176,f4445]) ).
fof(f4465,plain,
inverse(inverse(a2)) = inverse(inverse(sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f4361,f4464]) ).
fof(f4574,plain,
! [X0,X1,X2,X3] : multiply(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(sF1_fnc))),inverse(sF1_fnc)) = multiply(inverse(multiply(X2,inverse(multiply(X1,X3)))),multiply(X2,inverse(X3))),
inference(forward_demodulation,[status(thm)],[f4176,f3827]) ).
fof(f4575,plain,
! [X0,X1,X2,X3] : multiply(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,sF1_fnc)),inverse(sF1_fnc)) = multiply(inverse(multiply(X2,inverse(multiply(X1,X3)))),multiply(X2,inverse(X3))),
inference(forward_demodulation,[status(thm)],[f4176,f4574]) ).
fof(f4576,plain,
! [X0,X1,X2,X3] : multiply(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,sF1_fnc)),sF1_fnc) = multiply(inverse(multiply(X2,inverse(multiply(X1,X3)))),multiply(X2,inverse(X3))),
inference(forward_demodulation,[status(thm)],[f4176,f4575]) ).
fof(f4581,plain,
! [X0,X1,X2] : multiply(multiply(inverse(multiply(X0,sF1_fnc)),multiply(X0,sF1_fnc)),sF1_fnc) = multiply(inverse(multiply(X1,inverse(multiply(sF1_fnc,X2)))),multiply(X1,inverse(X2))),
inference(paramodulation,[status(thm)],[f4176,f4576]) ).
fof(f4640,plain,
! [X0,X1] : multiply(sF1_fnc,sF1_fnc) = multiply(inverse(multiply(X0,inverse(multiply(sF1_fnc,X1)))),multiply(X0,inverse(X1))),
inference(forward_demodulation,[status(thm)],[f3687,f4581]) ).
fof(f4641,plain,
! [X0,X1] : sF1_fnc = multiply(inverse(multiply(X0,inverse(multiply(sF1_fnc,X1)))),multiply(X0,inverse(X1))),
inference(forward_demodulation,[status(thm)],[f4205,f4640]) ).
fof(f4708,plain,
! [X0,X1,X2,X3] : multiply(multiply(inverse(multiply(multiply(inverse(multiply(X0,inverse(multiply(X1,X2)))),multiply(X0,inverse(X2))),inverse(multiply(X3,sF1_fnc)))),X1),sF1_fnc) = X3,
inference(forward_demodulation,[status(thm)],[f4176,f3838]) ).
fof(f4911,plain,
multiply(multiply(inverse(multiply(inverse(inverse(sF0_fnc)),sF1_fnc)),sF1_fnc),sF1_fnc) = inverse(a2),
inference(paramodulation,[status(thm)],[f4465,f4396]) ).
fof(f4926,plain,
inverse(sF0_fnc) = inverse(a2),
inference(forward_demodulation,[status(thm)],[f4396,f4911]) ).
fof(f5000,plain,
! [X0] : sF1_fnc = multiply(inverse(sF1_fnc),multiply(inverse(inverse(multiply(sF1_fnc,X0))),inverse(X0))),
inference(paramodulation,[status(thm)],[f3687,f4641]) ).
fof(f5020,plain,
! [X0] : sF1_fnc = multiply(sF1_fnc,multiply(inverse(inverse(multiply(sF1_fnc,X0))),inverse(X0))),
inference(forward_demodulation,[status(thm)],[f4176,f5000]) ).
fof(f5048,plain,
! [X0] : multiply(multiply(sF1_fnc,multiply(inverse(inverse(sF1_fnc)),inverse(multiply(inverse(inverse(multiply(sF1_fnc,X0))),inverse(X0))))),sF1_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f5020,f4258]) ).
fof(f5067,plain,
! [X0] : multiply(multiply(sF1_fnc,multiply(inverse(sF1_fnc),inverse(multiply(inverse(inverse(multiply(sF1_fnc,X0))),inverse(X0))))),sF1_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f4176,f5048]) ).
fof(f5068,plain,
! [X0] : multiply(multiply(sF1_fnc,multiply(sF1_fnc,inverse(multiply(inverse(inverse(multiply(sF1_fnc,X0))),inverse(X0))))),sF1_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f4176,f5067]) ).
fof(f5069,plain,
! [X0] : inverse(multiply(inverse(inverse(multiply(sF1_fnc,X0))),inverse(X0))) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f4361,f5068]) ).
fof(f5093,plain,
! [X0] : multiply(multiply(sF1_fnc,multiply(inverse(sF1_fnc),inverse(inverse(X0)))),sF1_fnc) = inverse(inverse(multiply(sF1_fnc,X0))),
inference(paramodulation,[status(thm)],[f5069,f4258]) ).
fof(f5133,plain,
! [X0] : multiply(multiply(sF1_fnc,multiply(sF1_fnc,inverse(inverse(X0)))),sF1_fnc) = inverse(inverse(multiply(sF1_fnc,X0))),
inference(forward_demodulation,[status(thm)],[f4176,f5093]) ).
fof(f5134,plain,
! [X0] : inverse(inverse(X0)) = inverse(inverse(multiply(sF1_fnc,X0))),
inference(forward_demodulation,[status(thm)],[f4361,f5133]) ).
fof(f5171,plain,
! [X0] : multiply(multiply(inverse(multiply(inverse(inverse(X0)),sF1_fnc)),sF1_fnc),sF1_fnc) = inverse(multiply(sF1_fnc,X0)),
inference(paramodulation,[status(thm)],[f5134,f4396]) ).
fof(f5203,plain,
! [X0] : inverse(X0) = inverse(multiply(sF1_fnc,X0)),
inference(forward_demodulation,[status(thm)],[f4396,f5171]) ).
fof(f5238,plain,
! [X0,X1,X2] : multiply(multiply(inverse(multiply(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(X1))),inverse(multiply(X2,sF1_fnc)))),sF1_fnc),sF1_fnc) = X2,
inference(paramodulation,[status(thm)],[f5203,f4708]) ).
fof(f5274,plain,
! [X0] : multiply(multiply(inverse(multiply(sF1_fnc,inverse(multiply(X0,sF1_fnc)))),sF1_fnc),sF1_fnc) = X0,
inference(forward_demodulation,[status(thm)],[f3687,f5238]) ).
fof(f5275,plain,
! [X0] : multiply(multiply(inverse(inverse(multiply(X0,sF1_fnc))),sF1_fnc),sF1_fnc) = X0,
inference(forward_demodulation,[status(thm)],[f5203,f5274]) ).
fof(f6130,plain,
! [X0,X1] : X0 = multiply(inverse(inverse(multiply(multiply(X0,sF1_fnc),X1))),multiply(sF1_fnc,inverse(X1))),
inference(paramodulation,[status(thm)],[f5203,f4181]) ).
fof(f6193,plain,
! [X0] : inverse(inverse(multiply(X0,sF1_fnc))) = multiply(inverse(inverse(X0)),multiply(sF1_fnc,inverse(sF1_fnc))),
inference(paramodulation,[status(thm)],[f5275,f6130]) ).
fof(f6223,plain,
! [X0] : X0 = multiply(inverse(inverse(multiply(multiply(X0,sF1_fnc),sF1_fnc))),multiply(sF1_fnc,sF1_fnc)),
inference(paramodulation,[status(thm)],[f4176,f6130]) ).
fof(f6232,plain,
! [X0] : inverse(inverse(multiply(X0,sF1_fnc))) = multiply(inverse(inverse(X0)),multiply(sF1_fnc,sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f4176,f6193]) ).
fof(f6233,plain,
! [X0] : inverse(inverse(multiply(X0,sF1_fnc))) = multiply(inverse(inverse(X0)),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f4205,f6232]) ).
fof(f6252,plain,
! [X0] : X0 = multiply(inverse(inverse(multiply(multiply(X0,sF1_fnc),sF1_fnc))),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f4205,f6223]) ).
fof(f6850,plain,
! [X0] : X0 = multiply(multiply(inverse(inverse(multiply(X0,sF1_fnc))),sF1_fnc),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f6233,f6252]) ).
fof(f6851,plain,
! [X0] : X0 = multiply(multiply(multiply(inverse(inverse(X0)),sF1_fnc),sF1_fnc),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f6233,f6850]) ).
fof(f6856,plain,
a2 = multiply(multiply(multiply(inverse(inverse(sF0_fnc)),sF1_fnc),sF1_fnc),sF1_fnc),
inference(paramodulation,[status(thm)],[f4926,f6851]) ).
fof(f6884,plain,
a2 = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f6851,f6856]) ).
fof(f6885,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f6884,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP410-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.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 20:10:35 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 1.41/0.60 % Refutation found
% 1.41/0.60 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.41/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.41/0.65 % Elapsed time: 0.276229 seconds
% 1.41/0.65 % CPU time: 1.906569 seconds
% 1.41/0.65 % Total memory used: 119.142 MB
% 1.41/0.65 % Net memory used: 118.658 MB
%------------------------------------------------------------------------------