%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP420-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 : Tue Sep 29 10:13:57 AM UTC 2026
% Result : Unsatisfiable 14.46s 2.98s
% Output : Refutation 15.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 12
% Syntax : Number of formulae : 244 ( 168 unt; 10 def)
% Number of atoms : 407 ( 225 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 324 ( 161 ~; 157 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 24 ( 3 avg)
% Number of predicates : 8 ( 6 usr; 7 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 697 ( 0 sgn 697 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
fof(f3,definition,
sF0 = multiply(a3,b3),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f4,plain,
multiply(a3,b3) = sF0,
inference(reorient_equations,[],[f3]) ).
fof(f5,definition,
sF1 = multiply(sF0,c3),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f6,plain,
multiply(sF0,c3) = sF1,
inference(reorient_equations,[],[f5]) ).
fof(f7,definition,
sF2 = multiply(b3,c3),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f8,plain,
multiply(b3,c3) = sF2,
inference(reorient_equations,[],[f7]) ).
fof(f9,definition,
sF3 = multiply(a3,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f10,plain,
multiply(a3,sF2) = sF3,
inference(reorient_equations,[],[f9]) ).
fof(f11,plain,
sF1 != sF3,
inference(definition_folding,[],[f2,f10,f8,f6,f4]) ).
fof(f12,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X2,inverse(multiply(inverse(X0),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X2,X3)) = inverse(multiply(inverse(multiply(X1,inverse(multiply(X0,inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X1,X4))),
inference(superposition,[],[f1,f1]) ).
fof(f15,definition,
( spl4_1
<=> multiply(a3,sF2) = sF3 ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f17,plain,
( multiply(a3,sF2) = sF3
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f15]) ).
fof(f18,plain,
spl4_1,
inference(avatar_split_clause,[],[f10,f15]) ).
fof(f20,definition,
( spl4_2
<=> multiply(sF0,c3) = sF1 ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f22,plain,
( multiply(sF0,c3) = sF1
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f23,plain,
spl4_2,
inference(avatar_split_clause,[],[f6,f20]) ).
fof(f25,definition,
( spl4_3
<=> multiply(a3,b3) = sF0 ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f27,plain,
( multiply(a3,b3) = sF0
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f28,plain,
spl4_3,
inference(avatar_split_clause,[],[f4,f25]) ).
fof(f31,definition,
( spl4_4
<=> multiply(b3,c3) = sF2 ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f33,plain,
( multiply(b3,c3) = sF2
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f34,plain,
spl4_4,
inference(avatar_split_clause,[],[f8,f31]) ).
fof(f39,definition,
( spl4_5
<=> sF1 = sF3 ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f41,plain,
( sF1 != sF3
| spl4_5 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f42,plain,
~ spl4_5,
inference(avatar_split_clause,[],[f11,f39]) ).
fof(f63,plain,
! [X2,X0,X1] : inverse(inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2)))) = X1,
inference(superposition,[],[f1,f12]) ).
fof(f65,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(X1)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2)) = X1,
inference(superposition,[],[f1,f12]) ).
fof(f104,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(inverse(X0)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(inverse(X3),inverse(multiply(multiply(X1,X2),inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X2))))))))),X0)) = X3,
inference(superposition,[],[f1,f65]) ).
fof(f227,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),inverse(multiply(inverse(X0),inverse(multiply(multiply(X2,X4),inverse(multiply(inverse(multiply(X2,X4)),multiply(X2,X4)))))))) = inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,X3))),
inference(superposition,[],[f1,f104]) ).
fof(f278,plain,
! [X2,X0,X1,X5] : inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2))) = inverse(multiply(inverse(multiply(X5,X1)),multiply(X5,X2))),
inference(superposition,[],[f227,f227]) ).
fof(f294,plain,
! [X2,X0,X1] : inverse(multiply(inverse(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2)))),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))) = X1,
inference(superposition,[],[f104,f227]) ).
fof(f297,plain,
! [X2,X3,X0,X1,X4,X5] : inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,X2)))),inverse(multiply(inverse(X5),inverse(multiply(multiply(inverse(multiply(X3,inverse(multiply(inverse(inverse(inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X3,X4)),inverse(multiply(inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(inverse(inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X3,X4))),multiply(inverse(multiply(X3,inverse(multiply(inverse(inverse(inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X3,X4)))))))))),X1)) = X5,
inference(superposition,[],[f104,f227]) ).
fof(f298,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,X2)))),multiply(inverse(multiply(X3,inverse(multiply(inverse(inverse(inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X3,X4))) = X1,
inference(superposition,[],[f65,f227]) ).
fof(f331,plain,
! [X2,X0,X1] : multiply(inverse(inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,X2)))),inverse(multiply(X2,inverse(multiply(inverse(X2),X2))))) = X1,
inference(forward_demodulation,[],[f298,f65]) ).
fof(f332,plain,
! [X2,X0,X1,X5] : inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,X2)))),inverse(multiply(inverse(X5),inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))),inverse(multiply(inverse(inverse(multiply(X2,inverse(multiply(inverse(X2),X2))))),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))))))),X1)) = X5,
inference(forward_demodulation,[],[f297,f65]) ).
fof(f372,plain,
( ! [X0,X1] : inverse(multiply(inverse(multiply(X0,b3)),multiply(X0,X1))) = inverse(multiply(inverse(sF0),multiply(a3,X1)))
| ~ spl4_3 ),
inference(superposition,[],[f278,f27]) ).
fof(f454,plain,
! [X2,X3,X0,X1,X6,X4,X5] : multiply(inverse(multiply(X6,X1)),multiply(X6,X2)) = inverse(multiply(inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(inverse(X4)),inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))))),inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2))),inverse(multiply(multiply(X3,X5),inverse(multiply(inverse(multiply(X3,X5)),multiply(X3,X5))))))))),X4)),
inference(superposition,[],[f104,f278]) ).
fof(f458,plain,
! [X2,X0,X1,X6] : multiply(inverse(multiply(X0,X1)),multiply(X0,X2)) = multiply(inverse(multiply(X6,X1)),multiply(X6,X2)),
inference(forward_demodulation,[],[f454,f104]) ).
fof(f500,plain,
( ! [X0,X1] : multiply(inverse(multiply(X0,b3)),multiply(X0,X1)) = multiply(inverse(sF0),multiply(a3,X1))
| ~ spl4_3 ),
inference(superposition,[],[f458,f27]) ).
fof(f501,plain,
( ! [X0,X1] : multiply(inverse(multiply(X0,sF2)),multiply(X0,X1)) = multiply(inverse(sF3),multiply(a3,X1))
| ~ spl4_1 ),
inference(superposition,[],[f458,f17]) ).
fof(f502,plain,
( ! [X0,X1] : multiply(inverse(multiply(X0,c3)),multiply(X0,X1)) = multiply(inverse(sF2),multiply(b3,X1))
| ~ spl4_4 ),
inference(superposition,[],[f458,f33]) ).
fof(f504,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X1,multiply(X2,X3))),multiply(X1,X4)) = multiply(X0,multiply(inverse(multiply(X2,inverse(multiply(inverse(X0),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),X4)),
inference(superposition,[],[f458,f1]) ).
fof(f720,plain,
( multiply(inverse(sF1),sF1) = multiply(inverse(sF2),multiply(b3,c3))
| ~ spl4_2
| ~ spl4_4 ),
inference(superposition,[],[f502,f22]) ).
fof(f778,plain,
( multiply(inverse(sF2),sF2) = multiply(inverse(sF1),sF1)
| ~ spl4_2
| ~ spl4_4 ),
inference(forward_demodulation,[],[f720,f33]) ).
fof(f790,plain,
! [X2,X3,X0,X1,X4,X5] : inverse(multiply(inverse(X1),inverse(multiply(multiply(X3,X4),inverse(multiply(inverse(multiply(X3,X4)),multiply(X3,X4))))))) = inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2)))),multiply(inverse(multiply(X3,inverse(multiply(inverse(inverse(inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),X5)))),inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))),
inference(superposition,[],[f294,f227]) ).
fof(f804,plain,
! [X2,X3,X0,X1] : inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))) = inverse(multiply(inverse(inverse(multiply(X0,multiply(inverse(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,X2)))),X3)))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))),
inference(superposition,[],[f294,f294]) ).
fof(f845,plain,
! [X2,X3,X0,X1] : inverse(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,X3)))) = inverse(inverse(multiply(inverse(multiply(X2,X0)),multiply(X2,X3)))),
inference(superposition,[],[f63,f294]) ).
fof(f852,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))),multiply(X1,X3)) = multiply(X0,multiply(inverse(inverse(multiply(inverse(multiply(X4,X0)),multiply(X4,X2)))),X3)),
inference(superposition,[],[f458,f294]) ).
fof(f1165,definition,
( spl4_6
<=> multiply(inverse(sF2),sF2) = multiply(inverse(sF1),sF1) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
fof(f1167,plain,
( multiply(inverse(sF2),sF2) = multiply(inverse(sF1),sF1)
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f1165]) ).
fof(f1168,plain,
( spl4_6
| ~ spl4_2
| ~ spl4_4 ),
inference(avatar_split_clause,[],[f778,f31,f20,f1165]) ).
fof(f1611,plain,
( ! [X2,X3,X0,X1] : multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(X3)),inverse(multiply(multiply(inverse(sF0),multiply(a3,X1)),inverse(multiply(inverse(multiply(inverse(multiply(X0,b3)),multiply(X0,X1))),multiply(inverse(sF0),multiply(a3,X1)))))))))),multiply(X2,multiply(inverse(sF0),multiply(a3,X1)))) = X3
| ~ spl4_3 ),
inference(superposition,[],[f65,f372]) ).
fof(f1927,plain,
! [X2,X3,X0,X1] : multiply(X2,inverse(multiply(inverse(X2),X2))) = multiply(inverse(inverse(multiply(X0,multiply(inverse(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,X2)))),X3)))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3))))),
inference(superposition,[],[f331,f294]) ).
fof(f2058,plain,
( ! [X2,X0,X1] : multiply(inverse(multiply(X0,multiply(inverse(sF2),sF2))),multiply(X0,X1)) = multiply(X2,multiply(inverse(multiply(inverse(sF1),inverse(multiply(inverse(X2),inverse(multiply(sF1,inverse(multiply(inverse(sF2),sF2)))))))),X1))
| ~ spl4_6 ),
inference(superposition,[],[f504,f1167]) ).
fof(f2092,plain,
( ! [X2,X3,X0,X1,X4] : multiply(X4,multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X1,X0))) = multiply(inverse(multiply(inverse(multiply(X1,b3)),multiply(X2,X3))),multiply(inverse(sF0),multiply(a3,X0)))
| ~ spl4_3 ),
inference(superposition,[],[f504,f500]) ).
fof(f2094,plain,
( ! [X2,X3,X0,X1,X4] : multiply(X4,multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X1,X0))) = multiply(inverse(multiply(inverse(multiply(X1,sF2)),multiply(X2,X3))),multiply(inverse(sF3),multiply(a3,X0)))
| ~ spl4_1 ),
inference(superposition,[],[f504,f501]) ).
fof(f2145,plain,
! [X2,X3,X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(multiply(X1,multiply(X2,X3))),multiply(X1,multiply(X2,X3))),
inference(superposition,[],[f504,f65]) ).
fof(f2227,plain,
! [X2,X3,X0,X1,X6,X4,X5] : multiply(inverse(multiply(X4,multiply(inverse(multiply(X1,inverse(multiply(inverse(X5),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),X3))),multiply(X4,X6)) = multiply(inverse(multiply(inverse(multiply(X0,multiply(X1,X2))),multiply(X0,X3))),multiply(X5,X6)),
inference(superposition,[],[f458,f504]) ).
fof(f2286,plain,
( ! [X2,X3,X0,X1] : multiply(inverse(multiply(inverse(multiply(X1,b3)),multiply(X2,X3))),multiply(inverse(sF0),multiply(a3,X0))) = multiply(inverse(multiply(inverse(multiply(X1,sF2)),multiply(X2,X3))),multiply(inverse(sF3),multiply(a3,X0)))
| ~ spl4_1
| ~ spl4_3 ),
inference(forward_demodulation,[],[f2092,f2094]) ).
fof(f2375,plain,
( ! [X2,X3,X0,X1] : multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(X3)),inverse(multiply(multiply(inverse(sF0),multiply(a3,X1)),inverse(multiply(inverse(multiply(inverse(multiply(X0,sF2)),multiply(X0,X1))),multiply(inverse(sF3),multiply(a3,X1)))))))))),multiply(X2,multiply(inverse(sF0),multiply(a3,X1)))) = X3
| ~ spl4_1
| ~ spl4_3 ),
inference(backward_demodulation,[],[f1611,f2286]) ).
fof(f2537,plain,
! [X0,X1] : multiply(inverse(X1),X1) = multiply(inverse(X0),X0),
inference(superposition,[],[f2145,f2145]) ).
fof(f2838,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),inverse(multiply(X3,inverse(multiply(inverse(X0),X0)))))))),multiply(X1,X3))) = X2,
inference(superposition,[],[f1,f2537]) ).
fof(f2841,plain,
! [X2,X3,X0,X1] : inverse(inverse(multiply(inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(X3,inverse(multiply(inverse(X0),X0)))))))),multiply(X1,X3)))) = X2,
inference(superposition,[],[f63,f2537]) ).
fof(f2849,plain,
! [X2,X0,X1] : inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))) = inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X0),X0)))),multiply(X1,X2))),
inference(superposition,[],[f1,f2537]) ).
fof(f2852,plain,
! [X2,X0,X1] : multiply(X2,inverse(multiply(inverse(X2),X2))) = multiply(inverse(multiply(X1,inverse(multiply(inverse(X0),X0)))),multiply(X1,X2)),
inference(superposition,[],[f65,f2537]) ).
fof(f2857,plain,
! [X2,X0,X1] : inverse(multiply(inverse(X0),X0)) = inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X2))),
inference(superposition,[],[f278,f2537]) ).
fof(f2858,plain,
! [X2,X0] : inverse(multiply(inverse(inverse(multiply(inverse(X0),X0))),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))) = X2,
inference(superposition,[],[f294,f2537]) ).
fof(f2864,plain,
! [X2,X0] : multiply(inverse(inverse(multiply(inverse(X0),X0))),inverse(multiply(inverse(X2),inverse(multiply(inverse(inverse(X2)),inverse(X2)))))) = X2,
inference(superposition,[],[f331,f2537]) ).
fof(f2876,plain,
! [X2,X0,X1] : multiply(inverse(multiply(inverse(X1),inverse(multiply(inverse(inverse(X2)),inverse(multiply(X1,inverse(multiply(inverse(X0),X0)))))))),multiply(inverse(X0),X0)) = X2,
inference(superposition,[],[f65,f2537]) ).
fof(f3103,plain,
! [X0,X1] : inverse(multiply(inverse(X1),X1)) = inverse(multiply(inverse(X0),X0)),
inference(superposition,[],[f2857,f2857]) ).
fof(f4218,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(multiply(inverse(X1),inverse(multiply(inverse(X2),inverse(multiply(X1,inverse(multiply(inverse(X3),X3)))))))),multiply(inverse(X0),X0))) = X2,
inference(superposition,[],[f2838,f2537]) ).
fof(f4239,plain,
! [X2,X0] : inverse(multiply(X0,inverse(multiply(inverse(X0),X0)))) = inverse(multiply(X0,inverse(multiply(inverse(X2),X2)))),
inference(superposition,[],[f2838,f2852]) ).
fof(f6024,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),X1)))),multiply(X0,X2))))) = X2,
inference(superposition,[],[f2858,f2849]) ).
fof(f6025,plain,
! [X2,X0,X1] : inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(X0,inverse(multiply(inverse(X1),X1)))))) = X0,
inference(superposition,[],[f2858,f4239]) ).
fof(f9743,plain,
! [X0,X1] : inverse(multiply(inverse(X1),X1)) = inverse(inverse(multiply(inverse(X0),X0))),
inference(superposition,[],[f3103,f6025]) ).
fof(f9762,plain,
! [X2,X0,X1] : multiply(X1,inverse(multiply(inverse(X1),X1))) = multiply(inverse(inverse(multiply(inverse(X0),X0))),multiply(inverse(inverse(multiply(inverse(X2),X2))),X1)),
inference(superposition,[],[f2852,f6025]) ).
fof(f10120,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(inverse(multiply(inverse(X0),X0))),multiply(inverse(X2),X3)),
inference(superposition,[],[f458,f9743]) ).
fof(f10147,plain,
( ! [X0,X1] : multiply(inverse(sF0),multiply(a3,X1)) = multiply(inverse(inverse(multiply(inverse(X0),X0))),multiply(inverse(b3),X1))
| ~ spl4_3 ),
inference(superposition,[],[f500,f9743]) ).
fof(f10213,plain,
! [X2,X3,X0,X1,X4] : inverse(multiply(inverse(X2),X2)) = inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(X0),X0)),inverse(multiply(X3,inverse(multiply(inverse(X4),X4)))))))),multiply(X1,X3))),
inference(superposition,[],[f2838,f9743]) ).
fof(f10246,plain,
! [X2,X0] : inverse(multiply(inverse(X2),X2)) = multiply(inverse(X0),X0),
inference(forward_demodulation,[],[f10213,f2838]) ).
fof(f10530,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),inverse(multiply(X3,multiply(inverse(X0),X0))))))),multiply(X1,X3))) = X2,
inference(superposition,[],[f2838,f10246]) ).
fof(f10531,plain,
! [X2,X3,X0,X1] : inverse(inverse(multiply(inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(X3,multiply(inverse(X0),X0))))))),multiply(X1,X3)))) = X2,
inference(superposition,[],[f2841,f10246]) ).
fof(f10555,plain,
! [X2,X0,X1] : inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(X2,multiply(inverse(X0),X0))))) = X2,
inference(superposition,[],[f6025,f10246]) ).
fof(f10587,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3))) = inverse(multiply(multiply(inverse(X0),X0),multiply(inverse(X2),X3))),
inference(superposition,[],[f278,f10246]) ).
fof(f10589,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(multiply(inverse(X0),X0),multiply(inverse(X2),X3)),
inference(superposition,[],[f458,f10246]) ).
fof(f10660,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(inverse(multiply(multiply(inverse(X0),X0),multiply(inverse(X1),X1)))),inverse(multiply(X2,inverse(multiply(inverse(X3),X3)))))) = X2,
inference(superposition,[],[f6025,f10246]) ).
fof(f10749,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3))) = inverse(multiply(inverse(multiply(inverse(X3),X2)),inverse(multiply(inverse(X0),X0)))),
inference(superposition,[],[f278,f10246]) ).
fof(f10761,plain,
! [X2,X3,X0,X1] : inverse(inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,X1)))) = inverse(inverse(multiply(inverse(multiply(inverse(X1),X2)),inverse(multiply(inverse(X0),X0))))),
inference(superposition,[],[f845,f10246]) ).
fof(f10773,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(multiply(inverse(X1),inverse(multiply(inverse(X2),inverse(multiply(X1,inverse(multiply(inverse(X3),X3)))))))),inverse(multiply(inverse(X0),X0)))) = X2,
inference(superposition,[],[f2838,f10246]) ).
fof(f11366,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(multiply(inverse(X1),X2)),inverse(multiply(inverse(X0),X0)))) = inverse(multiply(multiply(inverse(X3),X3),multiply(inverse(X2),X1))),
inference(superposition,[],[f10587,f10246]) ).
fof(f12249,plain,
! [X2,X3,X0,X1] : multiply(inverse(inverse(multiply(inverse(X0),X0))),multiply(inverse(X1),X2)) = multiply(multiply(inverse(X3),X3),multiply(inverse(X1),X2)),
inference(superposition,[],[f10589,f9743]) ).
fof(f12261,plain,
! [X2,X3,X0,X1,X4,X5] : multiply(X0,multiply(inverse(multiply(X1,inverse(multiply(inverse(X0),inverse(multiply(X2,inverse(multiply(inverse(X3),X3)))))))),X4)) = multiply(multiply(inverse(X5),X5),multiply(inverse(multiply(X1,X2)),X4)),
inference(superposition,[],[f10589,f2838]) ).
fof(f12296,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),X2)))),X3)),multiply(X0,inverse(multiply(inverse(X0),X0)))) = multiply(multiply(inverse(X4),X4),multiply(inverse(X3),multiply(X1,X0))),
inference(superposition,[],[f10589,f2852]) ).
fof(f12600,plain,
! [X2,X3,X0,X1,X4] : multiply(multiply(X3,X2),inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,X2)))) = multiply(inverse(multiply(inverse(multiply(X3,X1)),inverse(multiply(inverse(X4),X4)))),multiply(multiply(inverse(X0),X0),multiply(inverse(X1),X2))),
inference(superposition,[],[f2852,f10589]) ).
fof(f13223,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(inverse(multiply(inverse(X0),X0))),multiply(inverse(X1),X2))) = inverse(multiply(inverse(multiply(inverse(X2),X1)),inverse(multiply(inverse(X3),X3)))),
inference(superposition,[],[f10749,f9743]) ).
fof(f13225,plain,
! [X2,X3,X0,X1,X4] : inverse(multiply(X0,multiply(inverse(inverse(multiply(inverse(X1),X1))),X3))) = inverse(multiply(inverse(multiply(inverse(X3),inverse(multiply(X0,inverse(multiply(inverse(X2),X2)))))),inverse(multiply(inverse(X4),X4)))),
inference(superposition,[],[f10749,f6025]) ).
fof(f13278,plain,
( ! [X2,X3,X0,X1] : inverse(multiply(inverse(multiply(inverse(multiply(X1,sF2)),X2)),multiply(inverse(sF3),multiply(a3,X0)))) = inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),X2)),inverse(multiply(inverse(X3),X3))))
| ~ spl4_1 ),
inference(superposition,[],[f10749,f501]) ).
fof(f13689,plain,
! [X2,X3,X0,X1,X6,X4,X5] : inverse(multiply(inverse(multiply(X3,multiply(inverse(multiply(X4,X1)),multiply(X4,X0)))),multiply(X3,X5))) = inverse(multiply(multiply(inverse(X6),X6),multiply(inverse(multiply(inverse(multiply(inverse(X0),X1)),inverse(multiply(inverse(X2),X2)))),X5))),
inference(superposition,[],[f10587,f10749]) ).
fof(f13711,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(X2),X1)) = inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2))))),
inference(superposition,[],[f6025,f10749]) ).
fof(f13796,plain,
! [X2,X1] : inverse(multiply(inverse(X2),inverse(multiply(inverse(X1),X1)))) = X2,
inference(backward_demodulation,[],[f6024,f13711]) ).
fof(f13984,plain,
! [X2,X3,X0,X1] : multiply(multiply(X3,X2),inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,X2)))) = multiply(multiply(X3,X1),multiply(multiply(inverse(X0),X0),multiply(inverse(X1),X2))),
inference(backward_demodulation,[],[f12600,f13796]) ).
fof(f13988,plain,
! [X2,X3,X1] : inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3))) = multiply(inverse(X3),X2),
inference(backward_demodulation,[],[f10749,f13796]) ).
fof(f13989,plain,
! [X2,X3,X1] : inverse(inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,X1)))) = inverse(multiply(inverse(X1),X2)),
inference(backward_demodulation,[],[f10761,f13796]) ).
fof(f13993,plain,
! [X2,X3,X1] : multiply(inverse(X1),X2) = inverse(multiply(multiply(inverse(X3),X3),multiply(inverse(X2),X1))),
inference(backward_demodulation,[],[f11366,f13796]) ).
fof(f13999,plain,
! [X2,X0,X1] : multiply(inverse(X2),X1) = inverse(multiply(inverse(inverse(multiply(inverse(X0),X0))),multiply(inverse(X1),X2))),
inference(backward_demodulation,[],[f13223,f13796]) ).
fof(f14052,plain,
! [X3,X0,X1,X6,X4,X5] : inverse(multiply(inverse(multiply(X3,multiply(inverse(multiply(X4,X1)),multiply(X4,X0)))),multiply(X3,X5))) = inverse(multiply(multiply(inverse(X6),X6),multiply(multiply(inverse(X0),X1),X5))),
inference(backward_demodulation,[],[f13689,f13796]) ).
fof(f14098,plain,
! [X2,X3,X1] : multiply(inverse(X1),inverse(multiply(inverse(X2),inverse(multiply(X1,inverse(multiply(inverse(X3),X3))))))) = X2,
inference(backward_demodulation,[],[f10773,f13796]) ).
fof(f14099,plain,
! [X2,X3,X0,X1] : inverse(multiply(X0,multiply(inverse(inverse(multiply(inverse(X1),X1))),X3))) = multiply(inverse(X3),inverse(multiply(X0,inverse(multiply(inverse(X2),X2))))),
inference(backward_demodulation,[],[f13225,f13796]) ).
fof(f14128,plain,
( ! [X2,X0,X1] : multiply(inverse(multiply(X1,X0)),X2) = inverse(multiply(inverse(multiply(inverse(multiply(X1,sF2)),X2)),multiply(inverse(sF3),multiply(a3,X0))))
| ~ spl4_1 ),
inference(backward_demodulation,[],[f13278,f13796]) ).
fof(f14148,plain,
! [X2,X0,X1,X5] : inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,X2)))),inverse(multiply(inverse(X5),multiply(X2,inverse(multiply(inverse(X2),X2))))))),X1)) = X5,
inference(backward_demodulation,[],[f332,f13796]) ).
fof(f14166,plain,
! [X2,X0] : multiply(inverse(inverse(multiply(inverse(X0),X0))),X2) = X2,
inference(backward_demodulation,[],[f2864,f13796]) ).
fof(f14383,plain,
! [X0,X1] : multiply(X1,inverse(multiply(inverse(X1),X1))) = multiply(inverse(inverse(multiply(inverse(X0),X0))),X1),
inference(backward_demodulation,[],[f9762,f14166]) ).
fof(f14533,plain,
! [X2,X0] : inverse(inverse(multiply(X2,multiply(inverse(X0),X0)))) = X2,
inference(backward_demodulation,[],[f10555,f14166]) ).
fof(f14539,plain,
! [X2,X3,X1] : multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(X2),X3),
inference(backward_demodulation,[],[f10120,f14166]) ).
fof(f14546,plain,
! [X2,X3,X1] : multiply(inverse(X1),X2) = multiply(multiply(inverse(X3),X3),multiply(inverse(X1),X2)),
inference(backward_demodulation,[],[f12249,f14166]) ).
fof(f14585,plain,
( ! [X1] : multiply(inverse(sF0),multiply(a3,X1)) = multiply(inverse(b3),X1)
| ~ spl4_3 ),
inference(backward_demodulation,[],[f10147,f14166]) ).
fof(f14664,plain,
( ! [X2,X3,X0,X1] : multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(X3)),inverse(multiply(multiply(inverse(sF0),multiply(a3,X1)),multiply(inverse(multiply(X0,X1)),multiply(X0,X1)))))))),multiply(X2,multiply(inverse(sF0),multiply(a3,X1)))) = X3
| ~ spl4_1
| ~ spl4_3 ),
inference(backward_demodulation,[],[f2375,f14128]) ).
fof(f15208,plain,
! [X2,X3,X0] : inverse(multiply(X0,X3)) = multiply(inverse(X3),inverse(multiply(X0,inverse(multiply(inverse(X2),X2))))),
inference(forward_demodulation,[],[f14099,f14166]) ).
fof(f15210,plain,
! [X2,X0] : multiply(inverse(inverse(X2)),multiply(inverse(X0),X0)) = X2,
inference(backward_demodulation,[],[f2876,f14098]) ).
fof(f15213,plain,
! [X2,X0] : inverse(multiply(inverse(X2),multiply(inverse(X0),X0))) = X2,
inference(backward_demodulation,[],[f4218,f14098]) ).
fof(f15222,plain,
( ! [X2,X0,X1] : multiply(inverse(multiply(X0,multiply(inverse(sF2),sF2))),multiply(X0,X1)) = multiply(X2,multiply(inverse(X2),X1))
| ~ spl4_6 ),
inference(backward_demodulation,[],[f2058,f14098]) ).
fof(f15346,plain,
! [X2,X1] : inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(forward_demodulation,[],[f13999,f14166]) ).
fof(f15396,plain,
! [X2,X3,X1] : inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(X2,inverse(multiply(inverse(X3),X3)))))) = X2,
inference(backward_demodulation,[],[f10660,f13993]) ).
fof(f15882,plain,
! [X2,X3,X1,X4,X5] : inverse(multiply(inverse(X1),inverse(multiply(multiply(X3,X4),inverse(multiply(inverse(multiply(X3,X4)),multiply(X3,X4))))))) = inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(X2),X1)),multiply(inverse(multiply(X3,inverse(multiply(inverse(inverse(inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),X5)))),inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))),
inference(backward_demodulation,[],[f790,f13989]) ).
fof(f15883,plain,
! [X2,X3,X0] : inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))) = inverse(multiply(inverse(inverse(multiply(X0,multiply(inverse(multiply(inverse(X2),X0)),X3)))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))),
inference(backward_demodulation,[],[f804,f13989]) ).
fof(f15887,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))),multiply(X1,X3)) = multiply(X0,multiply(inverse(multiply(inverse(X2),X0)),X3)),
inference(backward_demodulation,[],[f852,f13989]) ).
fof(f15908,plain,
! [X2,X3,X0] : multiply(X2,inverse(multiply(inverse(X2),X2))) = multiply(inverse(inverse(multiply(X0,multiply(inverse(multiply(inverse(X2),X0)),X3)))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3))))),
inference(backward_demodulation,[],[f1927,f13989]) ).
fof(f15982,plain,
! [X2,X1,X5] : inverse(multiply(inverse(multiply(inverse(multiply(inverse(X2),inverse(X1))),inverse(multiply(inverse(X5),multiply(X2,inverse(multiply(inverse(X2),X2))))))),X1)) = X5,
inference(backward_demodulation,[],[f14148,f13989]) ).
fof(f16022,plain,
! [X2,X3,X0] : inverse(multiply(inverse(X3),inverse(multiply(X2,inverse(multiply(X3,multiply(inverse(X0),X0))))))) = X2,
inference(backward_demodulation,[],[f10531,f13989]) ).
fof(f16629,plain,
! [X2,X3,X0] : multiply(inverse(X3),inverse(multiply(inverse(X2),inverse(multiply(X3,multiply(inverse(X0),X0)))))) = X2,
inference(backward_demodulation,[],[f10530,f13988]) ).
fof(f16665,plain,
! [X2,X3,X1,X6,X4,X5] : multiply(inverse(multiply(X4,multiply(inverse(multiply(X1,inverse(multiply(inverse(X5),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),X3))),multiply(X4,X6)) = multiply(multiply(inverse(X3),multiply(X1,X2)),multiply(X5,X6)),
inference(backward_demodulation,[],[f2227,f13988]) ).
fof(f16677,plain,
! [X0,X1,X6,X4,X5] : inverse(multiply(multiply(inverse(X6),X6),multiply(multiply(inverse(X0),X1),X5))) = multiply(inverse(X5),multiply(inverse(multiply(X4,X1)),multiply(X4,X0))),
inference(backward_demodulation,[],[f14052,f13988]) ).
fof(f16763,plain,
! [X2,X3,X0,X1] : multiply(multiply(X3,X1),multiply(multiply(inverse(X0),X0),multiply(inverse(X1),X2))) = multiply(multiply(X3,X2),multiply(inverse(X2),X2)),
inference(forward_demodulation,[],[f13984,f13988]) ).
fof(f17148,plain,
! [X2,X3,X0,X1,X4] : multiply(X0,multiply(inverse(multiply(X1,inverse(multiply(inverse(X0),inverse(multiply(X2,inverse(multiply(inverse(X3),X3)))))))),X4)) = multiply(inverse(multiply(X1,X2)),X4),
inference(backward_demodulation,[],[f12261,f14546]) ).
fof(f17164,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),X2)))),X3)),multiply(X0,inverse(multiply(inverse(X0),X0)))) = multiply(inverse(X3),multiply(X1,X0)),
inference(backward_demodulation,[],[f12296,f14546]) ).
fof(f17535,plain,
! [X1] : multiply(X1,inverse(multiply(inverse(X1),X1))) = X1,
inference(forward_demodulation,[],[f14383,f14166]) ).
fof(f17602,plain,
( ! [X3,X0,X1] : multiply(inverse(inverse(multiply(inverse(inverse(X3)),inverse(multiply(multiply(inverse(sF0),multiply(a3,X1)),multiply(inverse(multiply(X0,X1)),multiply(X0,X1))))))),multiply(inverse(sF0),multiply(a3,X1))) = X3
| ~ spl4_1
| ~ spl4_3 ),
inference(forward_demodulation,[],[f14664,f14539]) ).
fof(f17990,plain,
( ! [X2,X1] : multiply(inverse(multiply(inverse(sF2),sF2)),X1) = multiply(X2,multiply(inverse(X2),X1))
| ~ spl4_6 ),
inference(forward_demodulation,[],[f15222,f14539]) ).
fof(f18230,plain,
! [X2,X3,X0] : inverse(multiply(X0,X3)) = multiply(inverse(X3),inverse(multiply(X0,multiply(inverse(X2),X2)))),
inference(backward_demodulation,[],[f15208,f15346]) ).
fof(f18234,plain,
! [X2,X0] : multiply(inverse(multiply(inverse(X0),X0)),X2) = X2,
inference(backward_demodulation,[],[f15213,f15346]) ).
fof(f18463,plain,
! [X2,X3,X1] : multiply(inverse(inverse(multiply(X2,inverse(multiply(inverse(X3),X3))))),multiply(inverse(X1),X1)) = X2,
inference(forward_demodulation,[],[f15396,f15346]) ).
fof(f18769,plain,
! [X2,X3,X0] : multiply(inverse(inverse(multiply(X2,inverse(multiply(X3,multiply(inverse(X0),X0)))))),X3) = X2,
inference(forward_demodulation,[],[f16022,f15346]) ).
fof(f18809,plain,
! [X2,X1,X5] : multiply(inverse(X1),multiply(inverse(multiply(inverse(X2),inverse(X1))),inverse(multiply(inverse(X5),multiply(X2,inverse(multiply(inverse(X2),X2))))))) = X5,
inference(forward_demodulation,[],[f15982,f15346]) ).
fof(f18883,plain,
! [X2,X3,X0] : multiply(X2,inverse(multiply(inverse(X2),X2))) = multiply(inverse(inverse(multiply(X0,multiply(inverse(multiply(inverse(X2),X0)),X3)))),inverse(multiply(X3,multiply(inverse(X3),X3)))),
inference(forward_demodulation,[],[f15908,f15346]) ).
fof(f18904,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))),multiply(X1,X3)) = multiply(X0,multiply(multiply(inverse(X0),X2),X3)),
inference(forward_demodulation,[],[f15887,f15346]) ).
fof(f18908,plain,
! [X2,X3,X0] : inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))) = multiply(inverse(inverse(multiply(X3,inverse(multiply(inverse(X3),X3))))),inverse(multiply(X0,multiply(inverse(multiply(inverse(X2),X0)),X3)))),
inference(forward_demodulation,[],[f15883,f15346]) ).
fof(f18909,plain,
! [X2,X3,X1,X4,X5] : inverse(multiply(inverse(X1),inverse(multiply(multiply(X3,X4),inverse(multiply(inverse(multiply(X3,X4)),multiply(X3,X4))))))) = multiply(inverse(inverse(multiply(X5,inverse(multiply(inverse(X5),X5))))),inverse(multiply(inverse(multiply(inverse(X2),X1)),multiply(inverse(multiply(X3,inverse(multiply(inverse(inverse(inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),X5)))),
inference(forward_demodulation,[],[f15882,f15346]) ).
fof(f18992,plain,
! [X0,X1,X6,X5] : inverse(multiply(multiply(inverse(X6),X6),multiply(multiply(inverse(X0),X1),X5))) = multiply(inverse(X5),multiply(inverse(X1),X0)),
inference(forward_demodulation,[],[f16677,f14539]) ).
fof(f19002,plain,
! [X2,X3,X1,X6,X5] : multiply(multiply(inverse(X3),multiply(X1,X2)),multiply(X5,X6)) = multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X5),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),X3)),X6),
inference(forward_demodulation,[],[f16665,f14539]) ).
fof(f19036,plain,
! [X2,X3,X0] : multiply(inverse(X3),multiply(inverse(inverse(multiply(X3,multiply(inverse(X0),X0)))),X2)) = X2,
inference(forward_demodulation,[],[f16629,f15346]) ).
fof(f19627,plain,
! [X2,X3,X1] : multiply(multiply(X3,X2),multiply(inverse(X2),X2)) = multiply(multiply(X3,X1),multiply(inverse(X1),X2)),
inference(forward_demodulation,[],[f16763,f14546]) ).
fof(f19938,plain,
! [X2,X3,X0,X1] : multiply(inverse(X3),multiply(X1,X0)) = multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),X2)))),X3)),multiply(X0,multiply(inverse(X0),X0))),
inference(forward_demodulation,[],[f17164,f15346]) ).
fof(f19955,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X1,X2)),X4) = multiply(X0,multiply(inverse(multiply(X1,multiply(inverse(inverse(multiply(X2,inverse(multiply(inverse(X3),X3))))),X0))),X4)),
inference(forward_demodulation,[],[f17148,f15346]) ).
fof(f20345,plain,
! [X1] : multiply(X1,multiply(inverse(X1),X1)) = X1,
inference(forward_demodulation,[],[f17535,f15346]) ).
fof(f20407,plain,
( ! [X3,X0,X1] : multiply(inverse(inverse(multiply(inverse(inverse(X3)),inverse(multiply(multiply(inverse(b3),X1),multiply(inverse(multiply(X0,X1)),multiply(X0,X1))))))),multiply(inverse(b3),X1)) = X3
| ~ spl4_1
| ~ spl4_3 ),
inference(forward_demodulation,[],[f17602,f14585]) ).
fof(f20713,plain,
( ! [X2,X1] : multiply(X2,multiply(inverse(X2),X1)) = multiply(multiply(inverse(sF2),sF2),X1)
| ~ spl4_6 ),
inference(forward_demodulation,[],[f17990,f15346]) ).
fof(f20750,plain,
! [X2,X0] : multiply(multiply(inverse(X0),X0),X2) = X2,
inference(forward_demodulation,[],[f18234,f15346]) ).
fof(f21076,plain,
! [X2,X3] : multiply(X2,inverse(multiply(inverse(X3),X3))) = X2,
inference(forward_demodulation,[],[f18463,f15210]) ).
fof(f21378,plain,
! [X2,X1,X5] : multiply(inverse(X1),multiply(inverse(multiply(inverse(X2),inverse(X1))),multiply(inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))),X5))) = X5,
inference(forward_demodulation,[],[f18809,f15346]) ).
fof(f21452,plain,
! [X2,X3,X0] : multiply(X2,inverse(multiply(inverse(X2),X2))) = inverse(multiply(X3,inverse(multiply(X0,multiply(inverse(multiply(inverse(X2),X0)),X3))))),
inference(forward_demodulation,[],[f18883,f18230]) ).
fof(f21473,plain,
! [X2,X3,X0] : multiply(inverse(inverse(multiply(X2,inverse(multiply(inverse(X2),X2))))),X3) = multiply(X0,multiply(multiply(inverse(X0),X2),X3)),
inference(forward_demodulation,[],[f18904,f14539]) ).
fof(f21477,plain,
! [X2,X3,X0] : inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))) = multiply(inverse(inverse(multiply(X3,inverse(multiply(inverse(X3),X3))))),inverse(multiply(X0,multiply(multiply(inverse(X0),X2),X3)))),
inference(forward_demodulation,[],[f18908,f15346]) ).
fof(f21478,plain,
! [X2,X3,X1,X4,X5] : inverse(multiply(inverse(X1),inverse(multiply(multiply(X3,X4),inverse(multiply(inverse(multiply(X3,X4)),multiply(X3,X4))))))) = multiply(inverse(inverse(multiply(X5,inverse(multiply(inverse(X5),X5))))),multiply(inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(inverse(inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),X5)),multiply(inverse(X2),X1))),
inference(forward_demodulation,[],[f18909,f15346]) ).
fof(f21553,plain,
! [X2,X3,X1,X6,X5] : multiply(multiply(inverse(X3),multiply(X1,X2)),multiply(X5,X6)) = multiply(multiply(inverse(X3),multiply(X1,inverse(multiply(inverse(X5),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),X6),
inference(forward_demodulation,[],[f19002,f15346]) ).
fof(f21584,plain,
! [X2,X3] : multiply(inverse(X3),multiply(X3,X2)) = X2,
inference(forward_demodulation,[],[f19036,f14533]) ).
fof(f22396,plain,
! [X2,X3,X0,X1] : multiply(inverse(X3),multiply(X1,X0)) = multiply(multiply(inverse(X3),multiply(X1,inverse(multiply(inverse(X2),X2)))),multiply(X0,multiply(inverse(X0),X0))),
inference(forward_demodulation,[],[f19938,f15346]) ).
fof(f22410,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X1,X2)),X4) = multiply(X0,multiply(inverse(multiply(X1,multiply(inverse(inverse(multiply(X2,multiply(inverse(X3),X3)))),X0))),X4)),
inference(forward_demodulation,[],[f19955,f15346]) ).
fof(f22786,plain,
( ! [X3] : inverse(inverse(X3)) = X3
| ~ spl4_1
| ~ spl4_3 ),
inference(forward_demodulation,[],[f20407,f18769]) ).
fof(f23084,plain,
! [X0,X1,X5] : inverse(multiply(multiply(inverse(X0),X1),X5)) = multiply(inverse(X5),multiply(inverse(X1),X0)),
inference(backward_demodulation,[],[f18992,f20750]) ).
fof(f23088,plain,
( ! [X2,X1] : multiply(X2,multiply(inverse(X2),X1)) = X1
| ~ spl4_6 ),
inference(backward_demodulation,[],[f20713,f20750]) ).
fof(f23339,plain,
! [X2,X3] : multiply(X2,multiply(inverse(X3),X3)) = X2,
inference(forward_demodulation,[],[f21076,f15346]) ).
fof(f23596,plain,
! [X2,X1,X5] : multiply(inverse(X1),multiply(inverse(multiply(inverse(X2),inverse(X1))),multiply(inverse(multiply(X2,multiply(inverse(X2),X2))),X5))) = X5,
inference(forward_demodulation,[],[f21378,f15346]) ).
fof(f23665,plain,
! [X2,X3,X0] : multiply(X2,inverse(multiply(inverse(X2),X2))) = inverse(multiply(X3,inverse(multiply(X0,multiply(multiply(inverse(X0),X2),X3))))),
inference(forward_demodulation,[],[f21452,f15346]) ).
fof(f23686,plain,
! [X2,X3,X0] : multiply(X0,multiply(multiply(inverse(X0),X2),X3)) = multiply(inverse(inverse(multiply(X2,multiply(inverse(X2),X2)))),X3),
inference(forward_demodulation,[],[f21473,f15346]) ).
fof(f23690,plain,
! [X2,X3,X0] : inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))) = multiply(inverse(inverse(multiply(X3,multiply(inverse(X3),X3)))),inverse(multiply(X0,multiply(multiply(inverse(X0),X2),X3)))),
inference(forward_demodulation,[],[f21477,f15346]) ).
fof(f23691,plain,
! [X2,X3,X1,X4,X5] : inverse(multiply(inverse(X1),inverse(multiply(multiply(X3,X4),inverse(multiply(inverse(multiply(X3,X4)),multiply(X3,X4))))))) = multiply(inverse(inverse(multiply(X5,inverse(multiply(inverse(X5),X5))))),multiply(multiply(inverse(X5),multiply(X3,inverse(multiply(inverse(inverse(inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(inverse(X2),X1))),
inference(forward_demodulation,[],[f21478,f15346]) ).
fof(f23754,plain,
! [X2,X3,X1,X6,X5] : multiply(multiply(inverse(X3),multiply(X1,X2)),multiply(X5,X6)) = multiply(multiply(inverse(X3),multiply(X1,multiply(inverse(inverse(multiply(X2,inverse(multiply(inverse(X2),X2))))),X5))),X6),
inference(forward_demodulation,[],[f21553,f15346]) ).
fof(f24481,plain,
! [X2,X3,X0,X1] : multiply(inverse(X3),multiply(X1,X0)) = multiply(multiply(inverse(X3),multiply(X1,inverse(multiply(inverse(X2),X2)))),X0),
inference(forward_demodulation,[],[f22396,f20345]) ).
fof(f24487,plain,
! [X2,X0,X1,X4] : multiply(inverse(multiply(X1,X2)),X4) = multiply(X0,multiply(inverse(multiply(X1,multiply(X2,X0))),X4)),
inference(forward_demodulation,[],[f22410,f14533]) ).
fof(f25237,plain,
! [X3,X0] : inverse(multiply(X0,X3)) = multiply(inverse(X3),inverse(X0)),
inference(backward_demodulation,[],[f18230,f23339]) ).
fof(f25248,plain,
! [X2,X3,X1] : multiply(X3,X2) = multiply(multiply(X3,X1),multiply(inverse(X1),X2)),
inference(backward_demodulation,[],[f19627,f23339]) ).
fof(f25444,plain,
! [X2,X1,X5] : inverse(multiply(multiply(inverse(multiply(inverse(multiply(X2,multiply(inverse(X2),X2))),X5)),multiply(inverse(X2),inverse(X1))),X1)) = X5,
inference(forward_demodulation,[],[f23596,f23084]) ).
fof(f25508,plain,
! [X2,X3,X0] : multiply(X2,multiply(inverse(X2),X2)) = inverse(multiply(X3,inverse(multiply(X0,multiply(multiply(inverse(X0),X2),X3))))),
inference(forward_demodulation,[],[f23665,f15346]) ).
fof(f25529,plain,
( ! [X2,X3,X0] : multiply(X0,multiply(multiply(inverse(X0),X2),X3)) = multiply(multiply(X2,multiply(inverse(X2),X2)),X3)
| ~ spl4_1
| ~ spl4_3 ),
inference(forward_demodulation,[],[f23686,f22786]) ).
fof(f25532,plain,
( ! [X2,X3,X0] : inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))) = multiply(multiply(X3,multiply(inverse(X3),X3)),inverse(multiply(X0,multiply(multiply(inverse(X0),X2),X3))))
| ~ spl4_1
| ~ spl4_3 ),
inference(forward_demodulation,[],[f23690,f22786]) ).
fof(f25533,plain,
! [X2,X3,X1,X4,X5] : inverse(multiply(inverse(X1),inverse(multiply(multiply(X3,X4),inverse(multiply(inverse(multiply(X3,X4)),multiply(X3,X4))))))) = multiply(inverse(inverse(multiply(X5,inverse(multiply(inverse(X5),X5))))),multiply(multiply(inverse(X5),multiply(X3,multiply(inverse(inverse(multiply(X4,inverse(multiply(inverse(X4),X4))))),inverse(inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(inverse(X2),X1))),
inference(forward_demodulation,[],[f23691,f15346]) ).
fof(f25585,plain,
( ! [X2,X3,X1,X6,X5] : multiply(multiply(inverse(X3),multiply(X1,X2)),multiply(X5,X6)) = multiply(multiply(inverse(X3),multiply(X1,multiply(multiply(X2,inverse(multiply(inverse(X2),X2))),X5))),X6)
| ~ spl4_1
| ~ spl4_3 ),
inference(forward_demodulation,[],[f23754,f22786]) ).
fof(f26220,plain,
! [X2,X3,X0,X1] : multiply(inverse(X3),multiply(X1,X0)) = multiply(multiply(inverse(X3),multiply(X1,multiply(inverse(X2),X2))),X0),
inference(forward_demodulation,[],[f24481,f15346]) ).
fof(f26990,plain,
! [X2,X1,X5] : inverse(multiply(inverse(multiply(multiply(inverse(inverse(X1)),X2),multiply(inverse(multiply(X2,multiply(inverse(X2),X2))),X5))),X1)) = X5,
inference(forward_demodulation,[],[f25444,f23084]) ).
fof(f27045,plain,
( ! [X2,X3,X0] : inverse(multiply(X3,inverse(multiply(X0,multiply(multiply(inverse(X0),X2),X3))))) = X2
| ~ spl4_6 ),
inference(forward_demodulation,[],[f25508,f23088]) ).
fof(f27066,plain,
( ! [X2,X3,X0] : multiply(X2,X3) = multiply(X0,multiply(multiply(inverse(X0),X2),X3))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f25529,f23088]) ).
fof(f27069,plain,
( ! [X2,X3,X0] : inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))) = multiply(X3,inverse(multiply(X0,multiply(multiply(inverse(X0),X2),X3))))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f25532,f23088]) ).
fof(f27070,plain,
! [X2,X3,X1,X4,X5] : inverse(multiply(inverse(X1),inverse(multiply(multiply(X3,X4),inverse(multiply(inverse(multiply(X3,X4)),multiply(X3,X4))))))) = multiply(inverse(inverse(multiply(X5,inverse(multiply(inverse(X5),X5))))),multiply(multiply(inverse(X5),multiply(X3,inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(inverse(X2),X1))),
inference(forward_demodulation,[],[f25533,f25237]) ).
fof(f27117,plain,
( ! [X2,X3,X1,X6,X5] : multiply(multiply(inverse(X3),multiply(X1,X2)),multiply(X5,X6)) = multiply(multiply(inverse(X3),multiply(X1,multiply(multiply(X2,multiply(inverse(X2),X2)),X5))),X6)
| ~ spl4_1
| ~ spl4_3 ),
inference(forward_demodulation,[],[f25585,f15346]) ).
fof(f27658,plain,
! [X3,X0,X1] : multiply(inverse(X3),multiply(X1,X0)) = multiply(multiply(inverse(X3),X1),X0),
inference(forward_demodulation,[],[f26220,f23339]) ).
fof(f28192,plain,
! [X2,X1,X5] : multiply(inverse(X1),multiply(multiply(inverse(inverse(X1)),X2),multiply(inverse(multiply(X2,multiply(inverse(X2),X2))),X5))) = X5,
inference(forward_demodulation,[],[f26990,f15346]) ).
fof(f28261,plain,
( ! [X2,X3] : inverse(multiply(X3,inverse(multiply(X2,X3)))) = X2
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(backward_demodulation,[],[f27045,f27066]) ).
fof(f28264,plain,
( ! [X2,X3] : inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))) = multiply(X3,inverse(multiply(X2,X3)))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f27069,f27066]) ).
fof(f28265,plain,
! [X2,X3,X1,X4,X5] : inverse(multiply(inverse(X1),inverse(multiply(multiply(X3,X4),inverse(multiply(inverse(multiply(X3,X4)),multiply(X3,X4))))))) = multiply(inverse(inverse(multiply(X5,inverse(multiply(inverse(X5),X5))))),multiply(multiply(inverse(X5),multiply(X3,multiply(inverse(inverse(multiply(X4,inverse(multiply(inverse(X4),X4))))),multiply(X2,inverse(multiply(inverse(X2),X2)))))),multiply(inverse(X2),X1))),
inference(forward_demodulation,[],[f27070,f15346]) ).
fof(f28308,plain,
( ! [X2,X3,X1,X6,X5] : multiply(multiply(inverse(X3),multiply(X1,X2)),multiply(X5,X6)) = multiply(multiply(inverse(X3),multiply(X1,multiply(X2,X5))),X6)
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f27117,f23088]) ).
fof(f28759,plain,
! [X0,X1,X5] : multiply(inverse(X5),multiply(inverse(X1),X0)) = inverse(multiply(inverse(X0),multiply(X1,X5))),
inference(backward_demodulation,[],[f23084,f27658]) ).
fof(f29189,plain,
! [X2,X1,X5] : multiply(inverse(X1),multiply(inverse(inverse(X1)),multiply(X2,multiply(inverse(multiply(X2,multiply(inverse(X2),X2))),X5)))) = X5,
inference(forward_demodulation,[],[f28192,f27658]) ).
fof(f29252,plain,
( ! [X2,X3] : inverse(X2) = multiply(X3,inverse(multiply(X2,X3)))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f28264,f28261]) ).
fof(f29253,plain,
! [X2,X3,X1,X4,X5] : inverse(multiply(inverse(X1),inverse(multiply(multiply(X3,X4),inverse(multiply(inverse(multiply(X3,X4)),multiply(X3,X4))))))) = multiply(inverse(inverse(multiply(X5,inverse(multiply(inverse(X5),X5))))),multiply(inverse(X5),multiply(multiply(X3,multiply(inverse(inverse(multiply(X4,inverse(multiply(inverse(X4),X4))))),multiply(X2,inverse(multiply(inverse(X2),X2))))),multiply(inverse(X2),X1)))),
inference(forward_demodulation,[],[f28265,f27658]) ).
fof(f29294,plain,
( ! [X2,X3,X1,X6,X5] : multiply(multiply(inverse(X3),multiply(X1,X2)),multiply(X5,X6)) = multiply(inverse(X3),multiply(multiply(X1,multiply(X2,X5)),X6))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f28308,f27658]) ).
fof(f29682,plain,
! [X0,X1,X5] : multiply(inverse(X5),multiply(inverse(X1),X0)) = multiply(inverse(multiply(X1,X5)),X0),
inference(forward_demodulation,[],[f28759,f15346]) ).
fof(f30010,plain,
( ! [X2,X5] : multiply(X2,multiply(inverse(multiply(X2,multiply(inverse(X2),X2))),X5)) = X5
| ~ spl4_6 ),
inference(forward_demodulation,[],[f29189,f23088]) ).
fof(f30066,plain,
( ! [X2,X3,X1,X4,X5] : inverse(multiply(inverse(X1),inverse(multiply(multiply(X3,X4),inverse(multiply(inverse(multiply(X3,X4)),multiply(X3,X4))))))) = multiply(inverse(inverse(multiply(X5,inverse(multiply(inverse(X5),X5))))),multiply(inverse(X5),multiply(multiply(X3,multiply(inverse(inverse(multiply(X4,inverse(multiply(inverse(X4),X4))))),inverse(inverse(X2)))),multiply(inverse(X2),X1))))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f29253,f29252]) ).
fof(f30097,plain,
( ! [X2,X3,X1,X6,X5] : multiply(inverse(X3),multiply(multiply(X1,multiply(X2,X5)),X6)) = multiply(inverse(X3),multiply(multiply(X1,X2),multiply(X5,X6)))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f29294,f27658]) ).
fof(f30678,plain,
( ! [X2,X5] : multiply(inverse(multiply(X2,inverse(X2))),X5) = X5
| ~ spl4_6 ),
inference(forward_demodulation,[],[f30010,f24487]) ).
fof(f30717,plain,
( ! [X2,X3,X1,X4,X5] : inverse(multiply(inverse(X1),inverse(multiply(multiply(X3,X4),inverse(multiply(inverse(multiply(X3,X4)),multiply(X3,X4))))))) = multiply(inverse(multiply(X5,inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))),multiply(multiply(X3,multiply(inverse(inverse(multiply(X4,inverse(multiply(inverse(X4),X4))))),inverse(inverse(X2)))),multiply(inverse(X2),X1)))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f30066,f29682]) ).
fof(f31267,plain,
( ! [X2,X3,X1,X4,X5] : inverse(multiply(inverse(X1),inverse(multiply(multiply(X3,X4),inverse(multiply(inverse(multiply(X3,X4)),multiply(X3,X4))))))) = multiply(inverse(multiply(X5,inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))),multiply(multiply(X3,inverse(inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))),multiply(inverse(inverse(X2)),multiply(inverse(X2),X1))))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f30717,f30097]) ).
fof(f31733,plain,
( ! [X3,X1,X4,X5] : inverse(multiply(inverse(X1),inverse(multiply(multiply(X3,X4),inverse(multiply(inverse(multiply(X3,X4)),multiply(X3,X4))))))) = multiply(inverse(multiply(X5,inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))),multiply(multiply(X3,inverse(inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))),X1))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f31267,f21584]) ).
fof(f32129,plain,
( ! [X3,X1,X4,X5] : inverse(multiply(inverse(X1),inverse(multiply(multiply(X3,X4),inverse(multiply(inverse(multiply(X3,X4)),multiply(X3,X4))))))) = multiply(inverse(multiply(X5,inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))),multiply(multiply(X3,multiply(X4,inverse(multiply(inverse(X4),X4)))),X1))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f31733,f22786]) ).
fof(f32445,plain,
( ! [X3,X1,X4,X5] : inverse(multiply(inverse(X1),inverse(multiply(multiply(X3,X4),inverse(multiply(inverse(multiply(X3,X4)),multiply(X3,X4))))))) = multiply(inverse(multiply(X5,inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))),multiply(multiply(X3,X4),multiply(inverse(multiply(inverse(X4),X4)),X1)))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f32129,f30097]) ).
fof(f32719,plain,
( ! [X3,X1,X4,X5] : inverse(multiply(inverse(X1),inverse(multiply(multiply(X3,X4),inverse(multiply(inverse(multiply(X3,X4)),multiply(X3,X4))))))) = multiply(inverse(multiply(X5,inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))),multiply(multiply(X3,X4),multiply(multiply(inverse(X4),X4),X1)))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f32445,f15346]) ).
fof(f32950,plain,
( ! [X3,X1,X4,X5] : inverse(multiply(inverse(X1),inverse(multiply(multiply(X3,X4),inverse(multiply(inverse(multiply(X3,X4)),multiply(X3,X4))))))) = multiply(inverse(multiply(X5,inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))),multiply(multiply(X3,X4),multiply(inverse(X4),multiply(X4,X1))))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f32719,f27658]) ).
fof(f33160,plain,
( ! [X3,X1,X4,X5] : inverse(multiply(inverse(X1),inverse(multiply(multiply(X3,X4),inverse(multiply(inverse(multiply(X3,X4)),multiply(X3,X4))))))) = multiply(inverse(multiply(X5,inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))),multiply(X3,multiply(X4,X1)))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f32950,f25248]) ).
fof(f33362,plain,
( ! [X3,X1,X4,X5] : inverse(multiply(inverse(X1),inverse(multiply(multiply(X3,X4),inverse(multiply(inverse(multiply(X3,X4)),multiply(X3,X4))))))) = multiply(inverse(multiply(X5,inverse(inverse(inverse(X5))))),multiply(X3,multiply(X4,X1)))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f33160,f29252]) ).
fof(f33549,plain,
( ! [X3,X1,X4,X5] : inverse(multiply(inverse(X1),inverse(multiply(multiply(X3,X4),inverse(multiply(inverse(multiply(X3,X4)),multiply(X3,X4))))))) = multiply(inverse(multiply(X5,inverse(X5))),multiply(X3,multiply(X4,X1)))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f33362,f22786]) ).
fof(f33716,plain,
( ! [X3,X1,X4] : inverse(multiply(inverse(X1),inverse(multiply(multiply(X3,X4),inverse(multiply(inverse(multiply(X3,X4)),multiply(X3,X4))))))) = multiply(X3,multiply(X4,X1))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f33549,f30678]) ).
fof(f33855,plain,
( ! [X3,X1,X4] : multiply(X3,multiply(X4,X1)) = multiply(inverse(inverse(multiply(multiply(X3,X4),inverse(multiply(inverse(multiply(X3,X4)),multiply(X3,X4)))))),X1)
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f33716,f15346]) ).
fof(f33974,plain,
( ! [X3,X1,X4] : multiply(X3,multiply(X4,X1)) = multiply(multiply(multiply(X3,X4),inverse(multiply(inverse(multiply(X3,X4)),multiply(X3,X4)))),X1)
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f33855,f22786]) ).
fof(f34077,plain,
( ! [X3,X1,X4] : multiply(X3,multiply(X4,X1)) = multiply(inverse(inverse(multiply(X3,X4))),X1)
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f33974,f29252]) ).
fof(f34168,plain,
( ! [X3,X1,X4] : multiply(X3,multiply(X4,X1)) = multiply(multiply(X3,X4),X1)
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f34077,f22786]) ).
fof(f35328,plain,
( ! [X0] : multiply(sF0,X0) = multiply(a3,multiply(b3,X0))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6 ),
inference(superposition,[],[f34168,f27]) ).
fof(f35386,plain,
( multiply(sF0,c3) = multiply(a3,sF2)
| ~ spl4_1
| ~ spl4_3
| ~ spl4_4
| ~ spl4_6 ),
inference(superposition,[],[f35328,f33]) ).
fof(f35405,plain,
( multiply(sF0,c3) = sF3
| ~ spl4_1
| ~ spl4_3
| ~ spl4_4
| ~ spl4_6 ),
inference(forward_demodulation,[],[f35386,f17]) ).
fof(f35408,plain,
( sF1 = sF3
| ~ spl4_1
| ~ spl4_2
| ~ spl4_3
| ~ spl4_4
| ~ spl4_6 ),
inference(forward_demodulation,[],[f35405,f22]) ).
fof(f35409,plain,
( $false
| ~ spl4_1
| ~ spl4_2
| ~ spl4_3
| ~ spl4_4
| spl4_5
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f35408,f41]) ).
fof(f35410,plain,
( ~ spl4_1
| ~ spl4_2
| ~ spl4_3
| ~ spl4_4
| spl4_5
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f35409]) ).
cnf(s1,plain,
spl4_1,
inference(sat_conversion,[],[f18]) ).
cnf(s2,plain,
spl4_2,
inference(sat_conversion,[],[f23]) ).
cnf(s3,plain,
spl4_3,
inference(sat_conversion,[],[f28]) ).
cnf(s4,plain,
spl4_4,
inference(sat_conversion,[],[f34]) ).
cnf(s5,plain,
~ spl4_5,
inference(sat_conversion,[],[f42]) ).
cnf(s6,plain,
( ~ spl4_2
| ~ spl4_4
| spl4_6 ),
inference(sat_conversion,[],[f1168]) ).
cnf(s7,plain,
( ~ spl4_1
| ~ spl4_2
| ~ spl4_3
| ~ spl4_4
| spl4_5
| ~ spl4_6 ),
inference(sat_conversion,[],[f35410]) ).
cnf(s8,plain,
spl4_6,
inference(rat,[],[s6,s4,s2]) ).
cnf(s9,plain,
~ spl4_1,
inference(rat,[],[s7,s2,s5,s4,s3,s8]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s9]) ).
fof(f35411,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP420-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n015.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 10:07:15 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.46/2.98 % (1422675)Detected a unit-equality problem, will run specialized UEQ schedule.
% 14.46/2.98 % (1422680)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=2431308439:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 14.46/2.98 % (1422681)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1104377963:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 14.46/2.98 % (1422683)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2420352577:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 14.46/2.98 % (1422686)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1874962102:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 14.46/2.98 % (1422684)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1844223143:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 14.46/2.98 % (1422682)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3411364707:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 14.46/2.98 % (1422685)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2981951920:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 14.46/2.98 % (1422683)Instruction limit reached!
% 14.46/2.98 % (1422683)------------------------------
% 14.46/2.98 % (1422683)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.46/2.98 % (1422683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.46/2.98 % (1422683)CaDiCaL version: 2.1.3
% 14.46/2.98 % (1422683)Termination reason: Instruction limit
% 14.46/2.98 % (1422683)Termination phase: Saturation
% 14.46/2.98 % (1422683)Time elapsed: 0.071 s
% 14.46/2.98 % (1422683)Peak memory usage: 89 MB
% 14.46/2.98 % (1422683)Instructions burned: 138 (million)
% 14.46/2.98 % (1422684)Instruction limit reached!
% 14.46/2.98 % (1422684)------------------------------
% 14.46/2.98 % (1422684)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.46/2.98 % (1422684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.46/2.98 % (1422684)CaDiCaL version: 2.1.3
% 14.46/2.98 % (1422684)Termination reason: Instruction limit
% 14.46/2.98 % (1422684)Termination phase: Saturation
% 14.46/2.98 % (1422684)Time elapsed: 0.089 s
% 14.46/2.98 % (1422684)Peak memory usage: 88 MB
% 14.46/2.98 % (1422684)Instructions burned: 183 (million)
% 14.46/2.98 % (1422685)Instruction limit reached!
% 14.46/2.98 % (1422685)------------------------------
% 14.46/2.98 % (1422685)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.46/2.98 % (1422685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.46/2.98 % (1422685)CaDiCaL version: 2.1.3
% 14.46/2.98 % (1422685)Termination reason: Instruction limit
% 14.46/2.98 % (1422685)Termination phase: Saturation
% 14.46/2.98 % (1422685)Time elapsed: 0.134 s
% 14.46/2.98 % (1422685)Peak memory usage: 91 MB
% 14.46/2.98 % (1422685)Instructions burned: 259 (million)
% 14.46/2.98 % (1422694)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=269573695:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 14.46/2.98 % (1422695)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=595950380:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 14.46/2.98 % (1422696)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2696340992:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 14.46/2.98 % (1422696)Instruction limit reached!
% 14.46/2.98 % (1422696)------------------------------
% 14.46/2.98 % (1422696)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.46/2.98 % (1422696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.46/2.98 % (1422696)CaDiCaL version: 2.1.3
% 14.46/2.98 % (1422696)Termination reason: Instruction limit
% 14.46/2.98 % (1422696)Termination phase: Saturation
% 14.46/2.98 % (1422696)Time elapsed: 0.127 s
% 14.46/2.98 % (1422696)Peak memory usage: 89 MB
% 14.46/2.98 % (1422696)Instructions burned: 215 (million)
% 14.46/2.98 % (1422686)Instruction limit reached!
% 14.46/2.98 % (1422686)------------------------------
% 14.46/2.98 % (1422686)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.46/2.98 % (1422686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.46/2.98 % (1422686)CaDiCaL version: 2.1.3
% 14.46/2.98 % (1422686)Termination reason: Instruction limit
% 14.46/2.98 % (1422686)Termination phase: Saturation
% 14.46/2.98 % (1422686)Time elapsed: 0.582 s
% 14.46/2.98 % (1422686)Peak memory usage: 93 MB
% 14.46/2.98 % (1422686)Instructions burned: 1188 (million)
% 14.46/2.98 % (1422700)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=3545496316:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2993 on theBenchmark for (2993ds/317Mi)
% 14.46/2.98 % (1422701)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=227551979:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2992 on theBenchmark for (2992ds/12125Mi)
% 14.46/2.98 % (1422700)Instruction limit reached!
% 14.46/2.98 % (1422700)------------------------------
% 14.46/2.98 % (1422700)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.46/2.98 % (1422700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.46/2.98 % (1422700)CaDiCaL version: 2.1.3
% 14.46/2.98 % (1422700)Termination reason: Instruction limit
% 14.46/2.98 % (1422700)Termination phase: Saturation
% 14.46/2.98 % (1422700)Time elapsed: 0.154 s
% 14.46/2.98 % (1422700)Peak memory usage: 95 MB
% 14.46/2.98 % (1422700)Instructions burned: 319 (million)
% 14.46/2.98 % (1422704)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=1020405087:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2990 on theBenchmark for (2990ds/2836Mi)
% 14.46/2.98 % (1422694)Instruction limit reached!
% 14.46/2.98 % (1422694)------------------------------
% 14.46/2.98 % (1422694)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.46/2.98 % (1422694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.46/2.98 % (1422694)CaDiCaL version: 2.1.3
% 14.46/2.98 % (1422694)Termination reason: Instruction limit
% 14.46/2.98 % (1422694)Termination phase: Saturation
% 14.46/2.98 % (1422694)Time elapsed: 1.212 s
% 14.46/2.98 % (1422694)Peak memory usage: 138 MB
% 14.46/2.98 % (1422694)Instructions burned: 2052 (million)
% 14.46/2.98 % (1422706)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=1888455978:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2983 on theBenchmark for (2983ds/14534Mi)
% 14.46/2.98 % (1422680)First to succeed.
% 14.46/2.98 % (1422680)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1422675"
% 14.46/2.98 % (1422680)Refutation found. Thanks to Tanya!
% 14.46/2.98 % SZS status Unsatisfiable for theBenchmark
% 14.46/2.98 % SZS output start Proof for theBenchmark
% See solution above
% 15.64/3.18 % (1422680)------------------------------
% 15.64/3.18 % (1422680)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.64/3.18 % (1422680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.64/3.18 % (1422680)CaDiCaL version: 2.1.3
% 15.64/3.18 % (1422680)Termination reason: Refutation
% 15.64/3.18 % (1422680)Time elapsed: 1.803 s
% 15.64/3.18 % (1422680)Peak memory usage: 165 MB
% 15.64/3.18 % (1422680)Instructions burned: 5819 (million)
% 15.64/3.18 % (1422680)------------------------------
% 15.64/3.18 % (1422680)------------------------------
% 15.64/3.18 % (1422675)Success in time 2.127 s
% 15.64/3.18 % Vampire exiting
%------------------------------------------------------------------------------