%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP413-1 : 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 : n014.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 10:13:56 AM UTC 2026
% Result : Unsatisfiable 11.99s 2.54s
% Output : Refutation 12.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 9
% Syntax : Number of formulae : 151 ( 55 unt; 7 def)
% Number of atoms : 337 ( 137 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 373 ( 187 ~; 182 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 17 ( 3 avg)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 416 ( 0 sgn 416 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(X0,inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(X0,inverse(X1))),X2))),X1))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
fof(f3,plain,
a2 != multiply(multiply(inverse(b2),b2),a2),
inference(reorient_equations,[],[f2]) ).
fof(f4,definition,
sF0 = inverse(b2),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f5,plain,
inverse(b2) = sF0,
inference(reorient_equations,[],[f4]) ).
fof(f6,definition,
sF1 = multiply(sF0,b2),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f7,plain,
multiply(sF0,b2) = sF1,
inference(reorient_equations,[],[f6]) ).
fof(f8,definition,
sF2 = multiply(sF1,a2),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f9,plain,
multiply(sF1,a2) = sF2,
inference(reorient_equations,[],[f8]) ).
fof(f10,plain,
a2 != sF2,
inference(definition_folding,[],[f3,f9,f7,f5]) ).
fof(f12,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(multiply(inverse(X3),X3),inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(X2))),inverse(X3))),X0))),X3)) = multiply(X1,inverse(multiply(multiply(multiply(inverse(X2),X2),inverse(X0)),X2))),
inference(superposition,[],[f1,f1]) ).
fof(f14,definition,
( spl3_1
<=> multiply(sF1,a2) = sF2 ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f16,plain,
( multiply(sF1,a2) = sF2
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f14]) ).
fof(f17,plain,
spl3_1,
inference(avatar_split_clause,[],[f9,f14]) ).
fof(f19,definition,
( spl3_2
<=> multiply(sF0,b2) = sF1 ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f21,plain,
( multiply(sF0,b2) = sF1
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f19]) ).
fof(f22,plain,
spl3_2,
inference(avatar_split_clause,[],[f7,f19]) ).
fof(f24,definition,
( spl3_3
<=> inverse(b2) = sF0 ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f26,plain,
( inverse(b2) = sF0
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f27,plain,
spl3_3,
inference(avatar_split_clause,[],[f5,f24]) ).
fof(f29,definition,
( spl3_4
<=> a2 = sF2 ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f31,plain,
( a2 != sF2
| spl3_4 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f32,plain,
~ spl3_4,
inference(avatar_split_clause,[],[f10,f29]) ).
fof(f57,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(X2)),X1)))) = X2,
inference(superposition,[],[f1,f12]) ).
fof(f60,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(multiply(inverse(X0),X0),inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(X2))),inverse(X0))),multiply(inverse(multiply(X1,inverse(X2))),X3)))),X0)) = X3,
inference(superposition,[],[f1,f12]) ).
fof(f75,plain,
! [X2,X3,X0,X1] : multiply(multiply(multiply(inverse(X3),X3),inverse(multiply(inverse(multiply(multiply(inverse(X2),X2),inverse(X3))),X0))),X3) = multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,inverse(multiply(X0,X2)))),
inference(superposition,[],[f57,f1]) ).
fof(f97,plain,
! [X0,X1,X5] : inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,X5)))),X1)) = X5,
inference(superposition,[],[f60,f60]) ).
fof(f133,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,X0)) = multiply(inverse(multiply(X3,inverse(X2))),multiply(X3,X0)),
inference(superposition,[],[f57,f97]) ).
fof(f161,plain,
! [X0,X1,X4,X5] : multiply(inverse(multiply(X1,X0)),multiply(X1,X4)) = multiply(inverse(multiply(X5,X0)),multiply(X5,X4)),
inference(superposition,[],[f133,f97]) ).
fof(f165,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,X3)) = multiply(X0,multiply(multiply(multiply(inverse(inverse(X2)),inverse(X2)),inverse(multiply(inverse(multiply(X4,inverse(inverse(X2)))),multiply(X4,X0)))),X3)),
inference(superposition,[],[f133,f97]) ).
fof(f328,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X4,inverse(X2))),multiply(X4,inverse(multiply(X3,X2)))) = multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(multiply(inverse(X2),X2),inverse(X1))),X0))),X1)),multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(multiply(inverse(X2),X2),inverse(X1))),X0))),X1)),inverse(multiply(inverse(X0),X3))),multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(multiply(inverse(X2),X2),inverse(X1))),X0))),X1)),
inference(superposition,[],[f75,f1]) ).
fof(f342,plain,
( ! [X2,X0,X1] : multiply(multiply(multiply(inverse(X0),X0),inverse(multiply(inverse(multiply(multiply(sF0,b2),inverse(X0))),X1))),X0) = multiply(inverse(multiply(X2,sF0)),multiply(X2,inverse(multiply(X1,b2))))
| ~ spl3_3 ),
inference(superposition,[],[f75,f26]) ).
fof(f359,plain,
! [X2,X3,X0,X1,X4,X5] : multiply(multiply(multiply(inverse(X3),X3),inverse(multiply(inverse(multiply(multiply(inverse(multiply(X4,X2)),multiply(X4,X2)),inverse(X3))),inverse(multiply(X4,X1))))),X3) = multiply(inverse(multiply(X5,inverse(multiply(X4,X2)))),multiply(X5,inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2))))),
inference(superposition,[],[f75,f161]) ).
fof(f375,plain,
! [X2,X0,X1] : multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(multiply(X2,X1)))))) = X2,
inference(superposition,[],[f1,f75]) ).
fof(f376,plain,
! [X2,X0,X1] : inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(multiply(multiply(multiply(inverse(X1),X1),X2),X1))))) = X2,
inference(superposition,[],[f97,f75]) ).
fof(f378,plain,
! [X2,X3,X0,X1,X4,X5] : inverse(multiply(multiply(multiply(inverse(X3),X3),inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(X5))),inverse(X3))),multiply(inverse(multiply(multiply(inverse(X1),X1),inverse(X5))),X2)))),X3)) = multiply(X4,inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(multiply(X2,X1)))))),
inference(superposition,[],[f12,f75]) ).
fof(f395,plain,
! [X2,X0,X1] : multiply(multiply(multiply(inverse(X0),X0),inverse(multiply(inverse(multiply(multiply(inverse(X1),X1),inverse(X0))),multiply(multiply(inverse(X1),X1),inverse(X2))))),X0) = X2,
inference(superposition,[],[f57,f75]) ).
fof(f420,plain,
( ! [X2,X0,X1] : multiply(inverse(multiply(X2,sF0)),multiply(X2,inverse(multiply(X1,b2)))) = multiply(multiply(multiply(inverse(X0),X0),inverse(multiply(inverse(multiply(sF1,inverse(X0))),X1))),X0)
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f342,f21]) ).
fof(f434,plain,
( ! [X0,X1] : multiply(multiply(sF0,b2),inverse(multiply(inverse(multiply(X0,sF0)),multiply(X0,inverse(multiply(X1,b2)))))) = X1
| ~ spl3_3 ),
inference(superposition,[],[f375,f26]) ).
fof(f488,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(multiply(inverse(multiply(X3,inverse(X4))),multiply(X3,inverse(multiply(X0,X4))))))) = multiply(inverse(multiply(multiply(inverse(X4),X4),X2)),X0),
inference(superposition,[],[f161,f375]) ).
fof(f497,plain,
( ! [X0,X1] : multiply(sF1,inverse(multiply(inverse(multiply(X0,sF0)),multiply(X0,inverse(multiply(X1,b2)))))) = X1
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f434,f21]) ).
fof(f526,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,X0))) = inverse(multiply(inverse(multiply(X3,inverse(X2))),multiply(X3,X0))),
inference(superposition,[],[f376,f97]) ).
fof(f548,plain,
! [X2,X3,X0,X1,X4] : inverse(multiply(multiply(multiply(X0,multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,inverse(multiply(multiply(multiply(inverse(X2),X2),X0),X2))))),inverse(multiply(inverse(multiply(X3,X0)),multiply(X3,X4)))),multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,inverse(multiply(multiply(multiply(inverse(X2),X2),X0),X2)))))) = X4,
inference(superposition,[],[f97,f376]) ).
fof(f663,plain,
! [X2,X0,X1] : multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(X2))))),X1) = X2,
inference(superposition,[],[f395,f161]) ).
fof(f917,plain,
! [X0,X1,X4,X5] : inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,X4))) = inverse(multiply(inverse(multiply(X5,X0)),multiply(X5,X4))),
inference(superposition,[],[f526,f376]) ).
fof(f1269,plain,
! [X2,X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,inverse(X2))),
inference(superposition,[],[f165,f663]) ).
fof(f1321,plain,
! [X2,X3,X0,X1,X6,X4,X5] : multiply(multiply(multiply(inverse(X3),X3),inverse(multiply(inverse(multiply(multiply(inverse(multiply(multiply(multiply(inverse(inverse(X1)),inverse(X1)),inverse(multiply(inverse(multiply(X4,inverse(inverse(X1)))),multiply(X4,X5)))),X2)),multiply(multiply(multiply(inverse(inverse(X1)),inverse(X1)),inverse(multiply(inverse(multiply(X4,inverse(inverse(X1)))),multiply(X4,X5)))),X2)),inverse(X3))),X5))),X3) = multiply(inverse(multiply(X6,inverse(multiply(multiply(multiply(inverse(inverse(X1)),inverse(X1)),inverse(multiply(inverse(multiply(X4,inverse(inverse(X1)))),multiply(X4,X5)))),X2)))),multiply(X6,inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,X2))))),
inference(superposition,[],[f75,f165]) ).
fof(f1430,plain,
! [X0,X1] : multiply(inverse(X1),X1) = multiply(inverse(X0),X0),
inference(superposition,[],[f1269,f1269]) ).
fof(f1472,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X2,X3)),multiply(X2,X4)) = multiply(inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(X1)))),multiply(inverse(X3),X4)),
inference(superposition,[],[f161,f1269]) ).
fof(f1473,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X2,X3)),multiply(X2,X4)) = multiply(inverse(multiply(inverse(X4),X3)),multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(X1)))),
inference(superposition,[],[f161,f1269]) ).
fof(f1483,plain,
! [X2,X3,X0,X1,X4] : inverse(multiply(inverse(multiply(X2,X3)),multiply(X2,X4))) = inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(X1)))),multiply(inverse(X3),X4))),
inference(superposition,[],[f917,f1269]) ).
fof(f1505,plain,
! [X0,X1] : multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(X0),X0))),X1) = X1,
inference(superposition,[],[f663,f1269]) ).
fof(f1512,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,X3)) = multiply(inverse(inverse(X2)),multiply(multiply(multiply(inverse(inverse(X2)),inverse(X2)),inverse(multiply(inverse(X0),X0))),X3)),
inference(superposition,[],[f165,f1269]) ).
fof(f1598,plain,
( ! [X0] : multiply(sF0,b2) = multiply(inverse(X0),X0)
| ~ spl3_3 ),
inference(superposition,[],[f1430,f26]) ).
fof(f1601,plain,
! [X2,X3,X0,X1] : multiply(inverse(X1),X1) = multiply(X0,multiply(inverse(multiply(X2,inverse(X3))),multiply(X2,inverse(multiply(multiply(multiply(inverse(X3),X3),X0),X3))))),
inference(superposition,[],[f1430,f376]) ).
fof(f1694,plain,
! [X2,X3,X0,X1,X4] : multiply(X2,inverse(multiply(multiply(multiply(inverse(X3),X3),inverse(X4)),X3))) = inverse(multiply(multiply(multiply(inverse(X0),X0),inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(X3))),inverse(X1))),X4))),X1)),
inference(superposition,[],[f12,f1430]) ).
fof(f1695,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,inverse(multiply(multiply(multiply(inverse(X0),X0),inverse(X3)),X2)))) = X3,
inference(superposition,[],[f57,f1430]) ).
fof(f1697,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X4,inverse(X2))),multiply(X4,inverse(multiply(X3,X2)))) = multiply(multiply(multiply(inverse(X0),X0),inverse(multiply(inverse(multiply(multiply(inverse(X2),X2),inverse(X1))),X3))),X1),
inference(superposition,[],[f75,f1430]) ).
fof(f1698,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(multiply(inverse(X0),X0),inverse(multiply(inverse(multiply(X2,inverse(X1))),multiply(X2,X3)))),X1)) = X3,
inference(superposition,[],[f97,f1430]) ).
fof(f1723,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X3,inverse(X2))),multiply(X3,inverse(multiply(inverse(X0),X0)))) = multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(multiply(inverse(X0),X0),inverse(X1))),inverse(X2)))),X1),
inference(superposition,[],[f75,f1430]) ).
fof(f1742,plain,
! [X2,X0,X1] : multiply(inverse(inverse(X1)),inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(inverse(X0),X0)),X2))),X1))) = X2,
inference(superposition,[],[f1,f1430]) ).
fof(f1819,plain,
( ! [X0] : sF1 = multiply(inverse(X0),X0)
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f1598,f21]) ).
fof(f1910,plain,
( ! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X4,inverse(X2))),multiply(X4,inverse(multiply(X3,X2)))) = multiply(multiply(multiply(inverse(multiply(multiply(sF1,inverse(multiply(inverse(multiply(multiply(inverse(X2),X2),inverse(X1))),X0))),X1)),multiply(multiply(sF1,inverse(multiply(inverse(multiply(multiply(inverse(X2),X2),inverse(X1))),X0))),X1)),inverse(multiply(inverse(X0),X3))),multiply(multiply(sF1,inverse(multiply(inverse(multiply(multiply(inverse(X2),X2),inverse(X1))),X0))),X1))
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f328,f1819]) ).
fof(f1922,plain,
( ! [X2,X3,X0,X1,X4,X5] : multiply(inverse(multiply(X5,inverse(multiply(X4,X2)))),multiply(X5,inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2))))) = multiply(multiply(sF1,inverse(multiply(inverse(multiply(multiply(inverse(multiply(X4,X2)),multiply(X4,X2)),inverse(X3))),inverse(multiply(X4,X1))))),X3)
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f359,f1819]) ).
fof(f1926,plain,
( ! [X2,X3,X0,X1,X4,X5] : multiply(X4,inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(multiply(X2,X1)))))) = inverse(multiply(multiply(multiply(inverse(X3),X3),inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(X5))),inverse(X3))),multiply(inverse(multiply(sF1,inverse(X5))),X2)))),X3))
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f378,f1819]) ).
fof(f1941,plain,
( ! [X2,X0,X1] : multiply(inverse(multiply(X2,sF0)),multiply(X2,inverse(multiply(X1,b2)))) = multiply(multiply(sF1,inverse(multiply(inverse(multiply(sF1,inverse(X0))),X1))),X0)
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f420,f1819]) ).
fof(f1963,plain,
( ! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(multiply(inverse(multiply(X3,inverse(X4))),multiply(X3,inverse(multiply(X0,X4))))))) = multiply(inverse(multiply(sF1,X2)),X0)
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f488,f1819]) ).
fof(f1987,plain,
( ! [X2,X3,X0,X1,X4] : inverse(multiply(multiply(multiply(X0,multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,inverse(multiply(multiply(sF1,X0),X2))))),inverse(multiply(inverse(multiply(X3,X0)),multiply(X3,X4)))),multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,inverse(multiply(multiply(sF1,X0),X2)))))) = X4
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f548,f1819]) ).
fof(f2085,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : multiply(inverse(multiply(X6,inverse(multiply(multiply(multiply(inverse(inverse(X1)),inverse(X1)),inverse(multiply(inverse(multiply(X4,inverse(inverse(X1)))),multiply(X4,X5)))),X2)))),multiply(X6,inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,X2))))) = multiply(multiply(sF1,inverse(multiply(inverse(multiply(multiply(inverse(multiply(multiply(multiply(inverse(inverse(X1)),inverse(X1)),inverse(multiply(inverse(multiply(X4,inverse(inverse(X1)))),multiply(X4,X5)))),X2)),multiply(multiply(multiply(inverse(inverse(X1)),inverse(X1)),inverse(multiply(inverse(multiply(X4,inverse(inverse(X1)))),multiply(X4,X5)))),X2)),inverse(X3))),X5))),X3)
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f1321,f1819]) ).
fof(f2109,plain,
( ! [X0,X1] : multiply(multiply(sF1,inverse(multiply(inverse(X0),X0))),X1) = X1
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f1505,f1819]) ).
fof(f2110,plain,
( ! [X2,X3,X1] : multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,X3)) = multiply(inverse(inverse(X2)),multiply(multiply(multiply(inverse(inverse(X2)),inverse(X2)),inverse(sF1)),X3))
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f1512,f1819]) ).
fof(f2125,plain,
( ! [X2,X3,X0] : sF1 = multiply(X0,multiply(inverse(multiply(X2,inverse(X3))),multiply(X2,inverse(multiply(multiply(multiply(inverse(X3),X3),X0),X3)))))
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f1601,f1819]) ).
fof(f2129,plain,
( ! [X2,X3,X1,X4] : multiply(X2,inverse(multiply(multiply(multiply(inverse(X3),X3),inverse(X4)),X3))) = inverse(multiply(multiply(sF1,inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(X3))),inverse(X1))),X4))),X1))
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f1694,f1819]) ).
fof(f2130,plain,
( ! [X2,X3,X1] : multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,inverse(multiply(multiply(sF1,inverse(X3)),X2)))) = X3
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f1695,f1819]) ).
fof(f2132,plain,
( ! [X2,X3,X1,X4] : multiply(inverse(multiply(X4,inverse(X2))),multiply(X4,inverse(multiply(X3,X2)))) = multiply(multiply(sF1,inverse(multiply(inverse(multiply(multiply(inverse(X2),X2),inverse(X1))),X3))),X1)
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f1697,f1819]) ).
fof(f2133,plain,
( ! [X2,X3,X1] : inverse(multiply(multiply(sF1,inverse(multiply(inverse(multiply(X2,inverse(X1))),multiply(X2,X3)))),X1)) = X3
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f1698,f1819]) ).
fof(f2139,plain,
( ! [X2,X3,X0,X1] : multiply(inverse(multiply(X3,inverse(X2))),multiply(X3,inverse(multiply(inverse(X0),X0)))) = multiply(multiply(sF1,inverse(multiply(inverse(multiply(multiply(inverse(X0),X0),inverse(X1))),inverse(X2)))),X1)
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f1723,f1819]) ).
fof(f2149,plain,
( ! [X2,X0,X1] : multiply(inverse(inverse(X1)),inverse(multiply(multiply(sF1,inverse(multiply(inverse(multiply(inverse(X0),X0)),X2))),X1))) = X2
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f1742,f1819]) ).
fof(f2195,plain,
( ! [X2,X3,X4] : multiply(inverse(multiply(X2,X3)),multiply(X2,X4)) = multiply(inverse(sF1),multiply(inverse(X3),X4))
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f1472,f1819]) ).
fof(f2196,plain,
( ! [X2,X3,X4] : multiply(inverse(multiply(X2,X3)),multiply(X2,X4)) = multiply(inverse(multiply(inverse(X4),X3)),sF1)
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f1473,f1819]) ).
fof(f2197,plain,
( ! [X2,X3,X4] : inverse(multiply(inverse(multiply(X2,X3)),multiply(X2,X4))) = inverse(multiply(inverse(sF1),multiply(inverse(X3),X4)))
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f1483,f1819]) ).
fof(f2240,plain,
( ! [X2,X1] : multiply(inverse(inverse(X1)),inverse(multiply(multiply(sF1,inverse(multiply(inverse(sF1),X2))),X1))) = X2
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f2149,f1819]) ).
fof(f2243,plain,
( ! [X2,X3,X1] : multiply(inverse(multiply(X3,inverse(X2))),multiply(X3,inverse(sF1))) = multiply(multiply(sF1,inverse(multiply(inverse(multiply(sF1,inverse(X1))),inverse(X2)))),X1)
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f2139,f1819]) ).
fof(f2244,plain,
( ! [X2,X3,X1,X4] : multiply(inverse(multiply(X4,inverse(X2))),multiply(X4,inverse(multiply(X3,X2)))) = multiply(multiply(sF1,inverse(multiply(inverse(multiply(sF1,inverse(X1))),X3))),X1)
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f2132,f1819]) ).
fof(f2246,plain,
( ! [X2,X3,X1,X4] : inverse(multiply(multiply(sF1,inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(X3))),inverse(X1))),X4))),X1)) = multiply(X2,inverse(multiply(multiply(sF1,inverse(X4)),X3)))
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f2129,f1819]) ).
fof(f2248,plain,
( ! [X2,X3,X0] : sF1 = multiply(X0,multiply(inverse(multiply(X2,inverse(X3))),multiply(X2,inverse(multiply(multiply(sF1,X0),X3)))))
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f2125,f1819]) ).
fof(f2256,plain,
( ! [X2,X3,X1] : multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,X3)) = multiply(inverse(inverse(X2)),multiply(multiply(sF1,inverse(sF1)),X3))
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f2110,f1819]) ).
fof(f2257,plain,
( ! [X1] : multiply(multiply(sF1,inverse(sF1)),X1) = X1
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f2109,f1819]) ).
fof(f2280,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : multiply(inverse(multiply(X6,inverse(multiply(multiply(multiply(inverse(inverse(X1)),inverse(X1)),inverse(multiply(inverse(multiply(X4,inverse(inverse(X1)))),multiply(X4,X5)))),X2)))),multiply(X6,inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,X2))))) = multiply(multiply(sF1,inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(X2),X2)),sF1),inverse(X3))),X5))),X3)
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f2085,f2196]) ).
fof(f2401,plain,
( ! [X2,X3,X0,X1,X4,X5] : multiply(X4,inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(multiply(X2,X1)))))) = inverse(multiply(multiply(sF1,inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(X5))),inverse(X3))),multiply(inverse(multiply(sF1,inverse(X5))),X2)))),X3))
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f1926,f1819]) ).
fof(f2405,plain,
( ! [X2,X3,X0,X1,X4,X5] : multiply(inverse(multiply(X5,inverse(multiply(X4,X2)))),multiply(X5,inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2))))) = multiply(multiply(sF1,inverse(multiply(inverse(multiply(sF1,inverse(X3))),inverse(multiply(X4,X1))))),X3)
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f1922,f1819]) ).
fof(f2417,plain,
( ! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X4,inverse(X2))),multiply(X4,inverse(multiply(X3,X2)))) = multiply(multiply(multiply(inverse(multiply(multiply(sF1,inverse(multiply(inverse(multiply(sF1,inverse(X1))),X0))),X1)),multiply(multiply(sF1,inverse(multiply(inverse(multiply(sF1,inverse(X1))),X0))),X1)),inverse(multiply(inverse(X0),X3))),multiply(multiply(sF1,inverse(multiply(inverse(multiply(sF1,inverse(X1))),X0))),X1))
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f1910,f1819]) ).
fof(f2497,plain,
( ! [X2,X3,X0,X1,X4] : inverse(multiply(multiply(sF1,inverse(multiply(inverse(multiply(X3,X0)),multiply(X3,X4)))),multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,inverse(multiply(multiply(sF1,X0),X2)))))) = X4
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f1987,f2248]) ).
fof(f2507,plain,
( ! [X2,X3,X1] : multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,X3)) = multiply(inverse(inverse(X2)),X3)
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f2256,f2257]) ).
fof(f2517,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : multiply(inverse(multiply(X6,inverse(multiply(multiply(multiply(inverse(inverse(X1)),inverse(X1)),inverse(multiply(inverse(multiply(X4,inverse(inverse(X1)))),multiply(X4,X5)))),X2)))),multiply(X6,inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,X2))))) = multiply(multiply(sF1,inverse(multiply(inverse(multiply(multiply(inverse(sF1),sF1),inverse(X3))),X5))),X3)
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f2280,f1819]) ).
fof(f2583,plain,
( ! [X2,X0,X1,X4,X5] : multiply(X4,inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(multiply(X2,X1)))))) = multiply(X4,inverse(multiply(multiply(sF1,inverse(multiply(inverse(multiply(sF1,inverse(X5))),X2))),X5)))
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f2401,f2246]) ).
fof(f2596,plain,
( ! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X4,inverse(X2))),multiply(X4,inverse(multiply(X3,X2)))) = multiply(multiply(multiply(inverse(multiply(inverse(X1),X1)),sF1),inverse(multiply(inverse(X0),X3))),multiply(multiply(sF1,inverse(multiply(inverse(multiply(sF1,inverse(X1))),X0))),X1))
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f2417,f2196]) ).
fof(f2666,plain,
( ! [X3,X1] : inverse(multiply(multiply(sF1,inverse(multiply(inverse(inverse(X1)),X3))),X1)) = X3
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f2133,f2507]) ).
fof(f2706,plain,
( ! [X2,X0,X1,X4] : multiply(inverse(multiply(sF1,X2)),X0) = multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(multiply(inverse(inverse(X4)),inverse(multiply(X0,X4))))))
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f1963,f2507]) ).
fof(f2714,plain,
( ! [X2,X3,X1] : multiply(inverse(inverse(X2)),inverse(multiply(X3,X2))) = multiply(multiply(sF1,inverse(multiply(inverse(multiply(sF1,inverse(X1))),X3))),X1)
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f2244,f2507]) ).
fof(f2732,plain,
( ! [X2,X3,X0,X4] : inverse(multiply(multiply(sF1,inverse(multiply(inverse(multiply(X3,X0)),multiply(X3,X4)))),multiply(inverse(inverse(X2)),inverse(multiply(multiply(sF1,X0),X2))))) = X4
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f2497,f2507]) ).
fof(f2735,plain,
( ! [X2,X3] : multiply(inverse(inverse(X2)),inverse(multiply(multiply(sF1,inverse(X3)),X2))) = X3
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f2130,f2507]) ).
fof(f2738,plain,
( ! [X2,X1] : multiply(multiply(sF1,inverse(multiply(inverse(multiply(sF1,inverse(X1))),inverse(X2)))),X1) = multiply(inverse(inverse(X2)),inverse(sF1))
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f2243,f2507]) ).
fof(f2768,plain,
( ! [X2,X3,X0,X1,X4] : multiply(multiply(sF1,inverse(multiply(inverse(multiply(sF1,inverse(X3))),inverse(multiply(X4,X1))))),X3) = multiply(inverse(inverse(multiply(X4,X2))),inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2))))
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f2405,f2507]) ).
fof(f2787,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : multiply(inverse(multiply(X6,inverse(multiply(multiply(multiply(inverse(inverse(X1)),inverse(X1)),inverse(multiply(inverse(multiply(X4,inverse(inverse(X1)))),multiply(X4,X5)))),X2)))),multiply(X6,inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,X2))))) = multiply(multiply(sF1,inverse(multiply(inverse(multiply(sF1,inverse(X3))),X5))),X3)
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f2517,f1819]) ).
fof(f2838,plain,
( ! [X2,X1,X4,X5] : multiply(X4,inverse(multiply(multiply(sF1,inverse(multiply(inverse(multiply(sF1,inverse(X5))),X2))),X5))) = multiply(X4,inverse(multiply(inverse(inverse(X1)),inverse(multiply(X2,X1)))))
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f2583,f2507]) ).
fof(f2850,plain,
( ! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X4,inverse(X2))),multiply(X4,inverse(multiply(X3,X2)))) = multiply(multiply(multiply(inverse(sF1),sF1),inverse(multiply(inverse(X0),X3))),multiply(multiply(sF1,inverse(multiply(inverse(multiply(sF1,inverse(X1))),X0))),X1))
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f2596,f1819]) ).
fof(f2903,plain,
( ! [X2,X0,X1,X4] : multiply(inverse(inverse(multiply(X4,X2))),inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2)))) = multiply(inverse(inverse(multiply(X4,X1))),inverse(sF1))
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f2768,f2738]) ).
fof(f2909,plain,
( ! [X2] : multiply(inverse(sF1),X2) = X2
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f2240,f2735]) ).
fof(f2951,plain,
( ! [X2,X3,X0,X1,X4,X5] : multiply(multiply(sF1,inverse(multiply(inverse(multiply(sF1,inverse(X3))),X5))),X3) = multiply(inverse(inverse(multiply(multiply(multiply(inverse(inverse(X1)),inverse(X1)),inverse(multiply(inverse(multiply(X4,inverse(inverse(X1)))),multiply(X4,X5)))),X2))),inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,X2))))
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f2787,f2507]) ).
fof(f2988,plain,
( ! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X4,inverse(X2))),multiply(X4,inverse(multiply(X3,X2)))) = multiply(multiply(sF1,inverse(multiply(inverse(X0),X3))),multiply(multiply(sF1,inverse(multiply(inverse(multiply(sF1,inverse(X1))),X0))),X1))
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f2850,f1819]) ).
fof(f3054,plain,
( ! [X2,X3,X4] : multiply(inverse(X3),X4) = multiply(inverse(multiply(X2,X3)),multiply(X2,X4))
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f2195,f2909]) ).
fof(f3055,plain,
( ! [X2,X3,X4] : inverse(multiply(inverse(X3),X4)) = inverse(multiply(inverse(multiply(X2,X3)),multiply(X2,X4)))
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f2197,f2909]) ).
fof(f3072,plain,
( ! [X3,X1,X4,X5] : multiply(multiply(sF1,inverse(multiply(inverse(multiply(sF1,inverse(X3))),X5))),X3) = multiply(inverse(inverse(multiply(multiply(multiply(inverse(inverse(X1)),inverse(X1)),inverse(multiply(inverse(multiply(X4,inverse(inverse(X1)))),multiply(X4,X5)))),inverse(X1)))),inverse(sF1))
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f2951,f2903]) ).
fof(f3091,plain,
( ! [X2,X3,X0,X1] : multiply(inverse(inverse(X2)),inverse(multiply(X3,X2))) = multiply(multiply(sF1,inverse(multiply(inverse(X0),X3))),multiply(multiply(sF1,inverse(multiply(inverse(multiply(sF1,inverse(X1))),X0))),X1))
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f2988,f2507]) ).
fof(f3136,plain,
( ! [X2,X0,X4] : inverse(multiply(multiply(sF1,inverse(multiply(inverse(X0),X4))),multiply(inverse(inverse(X2)),inverse(multiply(multiply(sF1,X0),X2))))) = X4
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f2732,f3055]) ).
fof(f3161,plain,
( ! [X1] : multiply(sF1,inverse(multiply(inverse(sF0),inverse(multiply(X1,b2))))) = X1
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f497,f3055]) ).
fof(f3181,plain,
( ! [X2,X0,X4] : multiply(inverse(multiply(sF1,X2)),X0) = multiply(inverse(X2),inverse(multiply(inverse(inverse(X4)),inverse(multiply(X0,X4)))))
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f2706,f3054]) ).
fof(f3192,plain,
( ! [X0,X1] : multiply(multiply(sF1,inverse(multiply(inverse(multiply(sF1,inverse(X0))),X1))),X0) = multiply(inverse(sF0),inverse(multiply(X1,b2)))
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f1941,f3054]) ).
fof(f3215,plain,
( ! [X3,X1,X5] : multiply(multiply(sF1,inverse(multiply(inverse(multiply(sF1,inverse(X3))),X5))),X3) = multiply(inverse(inverse(multiply(multiply(multiply(inverse(inverse(X1)),inverse(X1)),inverse(multiply(inverse(inverse(inverse(X1))),X5))),inverse(X1)))),inverse(sF1))
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f3072,f3054]) ).
fof(f3280,plain,
( ! [X2,X3] : multiply(inverse(inverse(X2)),inverse(multiply(X3,X2))) = multiply(inverse(sF0),inverse(multiply(X3,b2)))
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f2714,f3192]) ).
fof(f3285,plain,
( ! [X2,X1,X4] : multiply(X4,inverse(multiply(inverse(inverse(X1)),inverse(multiply(X2,X1))))) = multiply(X4,inverse(multiply(inverse(sF0),inverse(multiply(X2,b2)))))
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f2838,f3192]) ).
fof(f3293,plain,
( ! [X2,X3,X0] : multiply(inverse(inverse(X2)),inverse(multiply(X3,X2))) = multiply(multiply(sF1,inverse(multiply(inverse(X0),X3))),multiply(inverse(sF0),inverse(multiply(X0,b2))))
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f3091,f3192]) ).
fof(f3329,plain,
( ! [X3,X1,X5] : multiply(multiply(sF1,inverse(multiply(inverse(multiply(sF1,inverse(X3))),X5))),X3) = multiply(inverse(inverse(multiply(multiply(sF1,inverse(multiply(inverse(inverse(inverse(X1))),X5))),inverse(X1)))),inverse(sF1))
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f3215,f1819]) ).
fof(f3367,plain,
( ! [X3,X5] : multiply(multiply(sF1,inverse(multiply(inverse(multiply(sF1,inverse(X3))),X5))),X3) = multiply(inverse(X5),inverse(sF1))
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f3329,f2666]) ).
fof(f3376,plain,
( ! [X5] : multiply(inverse(sF0),inverse(multiply(X5,b2))) = multiply(inverse(X5),inverse(sF1))
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f3367,f3192]) ).
fof(f3380,plain,
( ! [X1] : multiply(sF1,inverse(multiply(inverse(X1),inverse(sF1)))) = X1
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f3161,f3376]) ).
fof(f3383,plain,
( ! [X2,X3] : multiply(inverse(inverse(X2)),inverse(multiply(X3,X2))) = multiply(inverse(X3),inverse(sF1))
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f3280,f3376]) ).
fof(f3386,plain,
( ! [X2,X1,X4] : multiply(X4,inverse(multiply(inverse(inverse(X1)),inverse(multiply(X2,X1))))) = multiply(X4,inverse(multiply(inverse(X2),inverse(sF1))))
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f3285,f3376]) ).
fof(f3390,plain,
( ! [X2,X3,X0] : multiply(inverse(inverse(X2)),inverse(multiply(X3,X2))) = multiply(multiply(sF1,inverse(multiply(inverse(X0),X3))),multiply(inverse(X0),inverse(sF1)))
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f3293,f3376]) ).
fof(f3400,plain,
( ! [X2,X0] : multiply(inverse(multiply(sF1,X2)),X0) = multiply(inverse(X2),inverse(multiply(inverse(X0),inverse(sF1))))
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f3181,f3386]) ).
fof(f3418,plain,
( ! [X0,X4] : inverse(multiply(multiply(sF1,inverse(multiply(inverse(X0),X4))),multiply(inverse(multiply(sF1,X0)),inverse(sF1)))) = X4
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f3136,f3383]) ).
fof(f3434,plain,
( ! [X3,X0] : multiply(inverse(X3),inverse(sF1)) = multiply(multiply(sF1,inverse(multiply(inverse(X0),X3))),multiply(inverse(X0),inverse(sF1)))
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f3390,f3383]) ).
fof(f3600,plain,
( ! [X0] : multiply(inverse(X0),inverse(sF1)) = multiply(inverse(multiply(sF1,X0)),inverse(sF1))
| ~ spl3_2
| ~ spl3_3 ),
inference(superposition,[],[f3400,f1819]) ).
fof(f3603,plain,
( ! [X0] : inverse(multiply(inverse(X0),inverse(sF1))) = multiply(inverse(multiply(sF1,sF1)),X0)
| ~ spl3_2
| ~ spl3_3 ),
inference(superposition,[],[f2909,f3400]) ).
fof(f3620,plain,
( ! [X1] : multiply(sF1,multiply(inverse(multiply(sF1,sF1)),X1)) = X1
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f3380,f3603]) ).
fof(f3640,plain,
( ! [X0,X4] : inverse(multiply(multiply(sF1,inverse(multiply(inverse(X0),X4))),multiply(inverse(X0),inverse(sF1)))) = X4
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f3418,f3600]) ).
fof(f3660,plain,
( ! [X4] : inverse(multiply(inverse(X4),inverse(sF1))) = X4
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f3640,f3434]) ).
fof(f3668,plain,
( ! [X4] : multiply(inverse(multiply(sF1,sF1)),X4) = X4
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f3660,f3603]) ).
fof(f3682,plain,
( ! [X1] : multiply(sF1,X1) = X1
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f3620,f3668]) ).
fof(f3787,plain,
( a2 = sF2
| ~ spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[],[f16,f3682]) ).
fof(f3812,plain,
( $false
| ~ spl3_1
| ~ spl3_2
| ~ spl3_3
| spl3_4 ),
inference(forward_subsumption_resolution,[],[f3787,f31]) ).
fof(f3813,plain,
( ~ spl3_1
| ~ spl3_2
| ~ spl3_3
| spl3_4 ),
inference(avatar_contradiction_clause,[],[f3812]) ).
cnf(s1,plain,
spl3_1,
inference(sat_conversion,[],[f17]) ).
cnf(s2,plain,
spl3_2,
inference(sat_conversion,[],[f22]) ).
cnf(s3,plain,
spl3_3,
inference(sat_conversion,[],[f27]) ).
cnf(s4,plain,
~ spl3_4,
inference(sat_conversion,[],[f32]) ).
cnf(s5,plain,
( ~ spl3_1
| ~ spl3_2
| ~ spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f3813]) ).
cnf(s6,plain,
~ spl3_1,
inference(rat,[],[s5,s4,s3,s2]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s6]) ).
fof(f4123,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP413-1 : 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 : n014.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 10:03:32 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 11.99/2.54 % (561174)Detected a unit-equality problem, will run specialized UEQ schedule.
% 11.99/2.54 % (561182)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1789511640:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 11.99/2.54 % (561185)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=280009370:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 11.99/2.54 % (561180)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=1613949368:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 11.99/2.54 % (561184)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=4117449526:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 11.99/2.54 % (561179)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=2638562102:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 11.99/2.54 % (561181)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=741813003:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 11.99/2.54 % (561183)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3402439321:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 11.99/2.54 % (561182)Instruction limit reached!
% 11.99/2.54 % (561182)------------------------------
% 11.99/2.54 % (561182)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.99/2.54 % (561182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.99/2.54 % (561182)CaDiCaL version: 2.1.3
% 11.99/2.54 % (561182)Termination reason: Instruction limit
% 11.99/2.54 % (561182)Termination phase: Saturation
% 11.99/2.54 % (561182)Time elapsed: 0.041 s
% 11.99/2.54 % (561182)Peak memory usage: 89 MB
% 11.99/2.54 % (561182)Instructions burned: 138 (million)
% 11.99/2.54 % (561183)Instruction limit reached!
% 11.99/2.54 % (561183)------------------------------
% 11.99/2.54 % (561183)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.99/2.54 % (561183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.99/2.54 % (561183)CaDiCaL version: 2.1.3
% 11.99/2.54 % (561183)Termination reason: Instruction limit
% 11.99/2.54 % (561183)Termination phase: Saturation
% 11.99/2.54 % (561183)Time elapsed: 0.103 s
% 11.99/2.54 % (561183)Peak memory usage: 89 MB
% 11.99/2.54 % (561183)Instructions burned: 181 (million)
% 11.99/2.54 % (561193)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3535183214:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 11.99/2.54 % (561184)Instruction limit reached!
% 11.99/2.54 % (561184)------------------------------
% 11.99/2.54 % (561184)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.99/2.54 % (561184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.99/2.54 % (561184)CaDiCaL version: 2.1.3
% 11.99/2.54 % (561184)Termination reason: Instruction limit
% 11.99/2.54 % (561184)Termination phase: Saturation
% 11.99/2.54 % (561184)Time elapsed: 0.148 s
% 11.99/2.54 % (561184)Peak memory usage: 90 MB
% 11.99/2.54 % (561184)Instructions burned: 257 (million)
% 11.99/2.54 % (561194)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=248817861:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 11.99/2.54 % (561196)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=309539156:i=215:ep=RSTC_2997 on theBenchmark for (2997ds/215Mi)
% 11.99/2.54 % (561196)Instruction limit reached!
% 11.99/2.54 % (561196)------------------------------
% 11.99/2.54 % (561196)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.99/2.54 % (561196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.99/2.54 % (561196)CaDiCaL version: 2.1.3
% 11.99/2.54 % (561196)Termination reason: Instruction limit
% 11.99/2.54 % (561196)Termination phase: Saturation
% 11.99/2.54 % (561196)Time elapsed: 0.127 s
% 11.99/2.54 % (561196)Peak memory usage: 91 MB
% 11.99/2.54 % (561196)Instructions burned: 216 (million)
% 11.99/2.54 % (561199)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=662349375:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2994 on theBenchmark for (2994ds/317Mi)
% 11.99/2.54 % (561185)Instruction limit reached!
% 11.99/2.54 % (561185)------------------------------
% 11.99/2.54 % (561185)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.99/2.54 % (561185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.99/2.54 % (561185)CaDiCaL version: 2.1.3
% 11.99/2.54 % (561185)Termination reason: Instruction limit
% 11.99/2.54 % (561185)Termination phase: Saturation
% 11.99/2.54 % (561185)Time elapsed: 0.611 s
% 11.99/2.54 % (561185)Peak memory usage: 97 MB
% 11.99/2.54 % (561185)Instructions burned: 1187 (million)
% 11.99/2.54 % (561199)Instruction limit reached!
% 11.99/2.54 % (561199)------------------------------
% 11.99/2.54 % (561199)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.99/2.54 % (561199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.99/2.54 % (561199)CaDiCaL version: 2.1.3
% 11.99/2.54 % (561199)Termination reason: Instruction limit
% 11.99/2.54 % (561199)Termination phase: Saturation
% 11.99/2.54 % (561199)Time elapsed: 0.174 s
% 11.99/2.54 % (561199)Peak memory usage: 91 MB
% 11.99/2.54 % (561199)Instructions burned: 319 (million)
% 11.99/2.54 % (561201)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=2603798989:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2992 on theBenchmark for (2992ds/12125Mi)
% 11.99/2.54 % (561193)Instruction limit reached!
% 11.99/2.54 % (561193)------------------------------
% 11.99/2.54 % (561193)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.99/2.54 % (561193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.99/2.54 % (561193)CaDiCaL version: 2.1.3
% 11.99/2.54 % (561193)Termination reason: Instruction limit
% 11.99/2.54 % (561193)Termination phase: Saturation
% 11.99/2.54 % (561193)Time elapsed: 0.684 s
% 11.99/2.54 % (561193)Peak memory usage: 137 MB
% 11.99/2.54 % (561193)Instructions burned: 2053 (million)
% 11.99/2.54 % (561202)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=2723955730:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2991 on theBenchmark for (2991ds/2836Mi)
% 11.99/2.54 % (561204)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=1841761781:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2990 on theBenchmark for (2990ds/14534Mi)
% 11.99/2.54 % (561179)First to succeed.
% 11.99/2.54 % (561179)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-561174"
% 11.99/2.54 % (561179)Refutation found. Thanks to Tanya!
% 11.99/2.54 % SZS status Unsatisfiable for theBenchmark
% 11.99/2.54 % SZS output start Proof for theBenchmark
% See solution above
% 12.50/2.74 % (561179)------------------------------
% 12.50/2.74 % (561179)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.50/2.74 % (561179)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.50/2.74 % (561179)CaDiCaL version: 2.1.3
% 12.50/2.74 % (561179)Termination reason: Refutation
% 12.50/2.74 % (561179)Time elapsed: 1.276 s
% 12.50/2.74 % (561179)Peak memory usage: 136 MB
% 12.50/2.74 % (561179)Instructions burned: 2102 (million)
% 12.50/2.74 % (561179)------------------------------
% 12.50/2.74 % (561179)------------------------------
% 12.50/2.74 % (561174)Success in time 1.681 s
% 12.50/2.74 % Vampire exiting
%------------------------------------------------------------------------------