%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP498-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 10:14:09 AM UTC 2026
% Result : Unsatisfiable 3.17s 1.36s
% Output : Refutation 4.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 8
% Syntax : Number of formulae : 136 ( 38 unt; 3 def)
% Number of atoms : 238 ( 123 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 203 ( 101 ~; 99 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 253 ( 0 sgn 253 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(double_divide(identity,double_divide(X0,double_divide(X1,identity))),double_divide(double_divide(X1,double_divide(X2,X0)),identity)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X1,X0),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f3,axiom,
! [X0] : inverse(X0) = double_divide(X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f4,axiom,
! [X0] : identity = double_divide(X0,inverse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
fof(f5,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
fof(f7,definition,
( spl0_1
<=> multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f9,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| spl0_1 ),
inference(avatar_component_clause,[],[f7]) ).
fof(f10,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f5,f7]) ).
fof(f11,plain,
! [X2,X0,X1] : double_divide(double_divide(identity,double_divide(X0,inverse(X1))),double_divide(double_divide(X1,double_divide(X2,X0)),identity)) = X2,
inference(backward_demodulation,[],[f1,f3]) ).
fof(f12,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(forward_demodulation,[],[f2,f3]) ).
fof(f13,plain,
! [X2,X0,X1] : double_divide(double_divide(identity,double_divide(X0,inverse(X1))),inverse(double_divide(X1,double_divide(X2,X0)))) = X2,
inference(forward_demodulation,[],[f11,f3]) ).
fof(f14,plain,
! [X2,X0,X1] : double_divide(double_divide(identity,double_divide(X0,inverse(X1))),multiply(double_divide(X2,X0),X1)) = X2,
inference(forward_demodulation,[],[f13,f12]) ).
fof(f15,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(superposition,[],[f12,f3]) ).
fof(f16,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(identity),
inference(superposition,[],[f12,f4]) ).
fof(f17,plain,
! [X0,X1] : identity = double_divide(double_divide(X1,X0),multiply(X0,X1)),
inference(superposition,[],[f4,f12]) ).
fof(f25,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(identity,inverse(X1))),multiply(inverse(X0),X1)) = X0,
inference(superposition,[],[f14,f3]) ).
fof(f26,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(inverse(X0),inverse(X1))),multiply(identity,X1)) = X0,
inference(superposition,[],[f14,f4]) ).
fof(f28,plain,
! [X2,X0,X1] : inverse(X0) = multiply(multiply(double_divide(X0,X1),X2),double_divide(identity,double_divide(X1,inverse(X2)))),
inference(superposition,[],[f12,f14]) ).
fof(f29,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(inverse(X0),inverse(X1))),inverse(inverse(X1))) = X0,
inference(forward_demodulation,[],[f26,f15]) ).
fof(f48,plain,
identity = inverse(identity),
inference(superposition,[],[f14,f17]) ).
fof(f49,plain,
! [X2,X0,X1] : double_divide(X1,X0) = double_divide(double_divide(identity,double_divide(multiply(X0,X1),inverse(X2))),multiply(identity,X2)),
inference(superposition,[],[f14,f17]) ).
fof(f51,plain,
! [X2,X0,X1] : double_divide(X1,X0) = double_divide(double_divide(identity,double_divide(multiply(X0,X1),inverse(X2))),inverse(inverse(X2))),
inference(forward_demodulation,[],[f49,f15]) ).
fof(f53,definition,
( spl0_2
<=> identity = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f55,plain,
( identity = inverse(identity)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f56,plain,
spl0_2,
inference(avatar_split_clause,[],[f48,f53]) ).
fof(f66,plain,
( ! [X0] : identity = multiply(inverse(X0),X0)
| ~ spl0_2 ),
inference(backward_demodulation,[],[f16,f55]) ).
fof(f88,plain,
! [X0,X1] : inverse(X0) = multiply(multiply(inverse(X0),X1),double_divide(identity,double_divide(identity,inverse(X1)))),
inference(superposition,[],[f12,f25]) ).
fof(f102,plain,
! [X2,X0,X1] : double_divide(double_divide(identity,double_divide(inverse(X2),multiply(X0,X1))),inverse(multiply(X0,X1))) = X2,
inference(superposition,[],[f29,f12]) ).
fof(f106,plain,
! [X0,X1] : inverse(X0) = multiply(inverse(inverse(X1)),double_divide(identity,double_divide(inverse(X0),inverse(X1)))),
inference(superposition,[],[f12,f29]) ).
fof(f125,plain,
( ! [X0] : double_divide(double_divide(identity,double_divide(identity,inverse(X0))),identity) = X0
| ~ spl0_2 ),
inference(superposition,[],[f25,f66]) ).
fof(f128,plain,
( ! [X0] : inverse(double_divide(identity,double_divide(identity,inverse(X0)))) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f125,f3]) ).
fof(f138,plain,
( ! [X0] : multiply(double_divide(identity,inverse(X0)),identity) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f128,f12]) ).
fof(f151,plain,
! [X0] : inverse(X0) = multiply(multiply(inverse(X0),identity),double_divide(identity,identity)),
inference(superposition,[],[f88,f4]) ).
fof(f154,plain,
! [X0] : inverse(X0) = multiply(multiply(inverse(X0),identity),inverse(identity)),
inference(forward_demodulation,[],[f151,f3]) ).
fof(f158,plain,
( ! [X0] : inverse(X0) = multiply(multiply(inverse(X0),identity),identity)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f154,f55]) ).
fof(f164,plain,
! [X2,X3,X0,X1] : inverse(double_divide(identity,double_divide(X1,inverse(X2)))) = multiply(multiply(X0,X3),double_divide(identity,double_divide(multiply(double_divide(X0,X1),X2),inverse(X3)))),
inference(superposition,[],[f28,f14]) ).
fof(f165,plain,
! [X2,X0,X1] : inverse(double_divide(identity,double_divide(identity,inverse(X1)))) = multiply(multiply(X0,X2),double_divide(identity,double_divide(multiply(inverse(X0),X1),inverse(X2)))),
inference(superposition,[],[f28,f25]) ).
fof(f167,plain,
! [X2,X0,X1] : inverse(double_divide(identity,double_divide(inverse(X0),inverse(X1)))) = multiply(multiply(X0,X2),double_divide(identity,double_divide(inverse(inverse(X1)),inverse(X2)))),
inference(superposition,[],[f28,f29]) ).
fof(f175,plain,
! [X2,X0,X1] : multiply(multiply(X0,X2),double_divide(identity,double_divide(inverse(inverse(X1)),inverse(X2)))) = multiply(double_divide(inverse(X0),inverse(X1)),identity),
inference(forward_demodulation,[],[f167,f12]) ).
fof(f177,plain,
! [X2,X0,X1] : multiply(double_divide(identity,inverse(X1)),identity) = multiply(multiply(X0,X2),double_divide(identity,double_divide(multiply(inverse(X0),X1),inverse(X2)))),
inference(forward_demodulation,[],[f165,f12]) ).
fof(f178,plain,
! [X2,X3,X0,X1] : multiply(multiply(X0,X3),double_divide(identity,double_divide(multiply(double_divide(X0,X1),X2),inverse(X3)))) = multiply(double_divide(X1,inverse(X2)),identity),
inference(forward_demodulation,[],[f164,f12]) ).
fof(f182,plain,
( ! [X2,X0,X1] : multiply(multiply(X0,X2),double_divide(identity,double_divide(multiply(inverse(X0),X1),inverse(X2)))) = X1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f177,f138]) ).
fof(f198,plain,
( ! [X0] : double_divide(double_divide(identity,double_divide(inverse(X0),identity)),inverse(identity)) = X0
| ~ spl0_2 ),
inference(superposition,[],[f102,f66]) ).
fof(f212,plain,
( ! [X0] : double_divide(double_divide(identity,double_divide(inverse(X0),identity)),identity) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f198,f55]) ).
fof(f213,plain,
( ! [X0] : inverse(double_divide(identity,double_divide(inverse(X0),identity))) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f212,f3]) ).
fof(f214,plain,
( ! [X0] : multiply(double_divide(inverse(X0),identity),identity) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f213,f12]) ).
fof(f215,plain,
( ! [X0] : multiply(inverse(inverse(X0)),identity) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f214,f3]) ).
fof(f321,plain,
( ! [X0,X1] : double_divide(X0,X1) = double_divide(double_divide(identity,double_divide(multiply(X1,X0),identity)),inverse(identity))
| ~ spl0_2 ),
inference(superposition,[],[f51,f55]) ).
fof(f326,plain,
( ! [X0] : identity = multiply(inverse(inverse(X0)),double_divide(identity,double_divide(identity,inverse(X0))))
| ~ spl0_2 ),
inference(superposition,[],[f106,f55]) ).
fof(f332,plain,
( ! [X0,X1] : double_divide(X0,X1) = double_divide(double_divide(identity,double_divide(multiply(X1,X0),identity)),identity)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f321,f55]) ).
fof(f344,plain,
( ! [X0,X1] : double_divide(X0,X1) = inverse(double_divide(identity,double_divide(multiply(X1,X0),identity)))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f332,f3]) ).
fof(f350,plain,
( ! [X0,X1] : double_divide(X0,X1) = multiply(double_divide(multiply(X1,X0),identity),identity)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f344,f12]) ).
fof(f355,plain,
( ! [X0,X1] : double_divide(X0,X1) = multiply(inverse(multiply(X1,X0)),identity)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f350,f3]) ).
fof(f362,plain,
( ! [X2,X0,X1] : inverse(X0) = multiply(multiply(multiply(inverse(multiply(X1,X0)),identity),X2),double_divide(identity,double_divide(X1,inverse(X2))))
| ~ spl0_2 ),
inference(backward_demodulation,[],[f28,f355]) ).
fof(f373,plain,
( ! [X2,X3,X0,X1] : multiply(double_divide(X1,inverse(X2)),identity) = multiply(multiply(X0,X3),double_divide(identity,double_divide(multiply(multiply(inverse(multiply(X1,X0)),identity),X2),inverse(X3))))
| ~ spl0_2 ),
inference(backward_demodulation,[],[f178,f355]) ).
fof(f404,plain,
( ! [X0] : identity = multiply(inverse(inverse(X0)),multiply(inverse(multiply(double_divide(identity,inverse(X0)),identity)),identity))
| ~ spl0_2 ),
inference(backward_demodulation,[],[f326,f355]) ).
fof(f406,plain,
( ! [X2,X0,X1] : multiply(multiply(X0,X2),multiply(inverse(multiply(double_divide(multiply(inverse(X0),X1),inverse(X2)),identity)),identity)) = X1
| ~ spl0_2 ),
inference(backward_demodulation,[],[f182,f355]) ).
fof(f410,plain,
( ! [X2,X0,X1] : multiply(double_divide(inverse(X0),inverse(X1)),identity) = multiply(multiply(X0,X2),multiply(inverse(multiply(double_divide(inverse(inverse(X1)),inverse(X2)),identity)),identity))
| ~ spl0_2 ),
inference(backward_demodulation,[],[f175,f355]) ).
fof(f419,plain,
( ! [X0] : multiply(multiply(inverse(multiply(inverse(X0),identity)),identity),identity) = X0
| ~ spl0_2 ),
inference(backward_demodulation,[],[f138,f355]) ).
fof(f432,plain,
( ! [X0] : inverse(multiply(inverse(X0),identity)) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f419,f158]) ).
fof(f441,plain,
( ! [X2,X0,X1] : multiply(double_divide(inverse(X0),inverse(X1)),identity) = multiply(multiply(X0,X2),multiply(inverse(multiply(multiply(inverse(multiply(inverse(X2),inverse(inverse(X1)))),identity),identity)),identity))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f410,f355]) ).
fof(f445,plain,
( ! [X2,X0,X1] : multiply(multiply(X0,X2),multiply(inverse(multiply(multiply(inverse(multiply(inverse(X2),multiply(inverse(X0),X1))),identity),identity)),identity)) = X1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f406,f355]) ).
fof(f447,plain,
( ! [X0] : identity = multiply(inverse(inverse(X0)),multiply(inverse(multiply(multiply(inverse(multiply(inverse(X0),identity)),identity),identity)),identity))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f404,f355]) ).
fof(f477,plain,
( ! [X2,X3,X0,X1] : multiply(double_divide(X1,inverse(X2)),identity) = multiply(multiply(X0,X3),multiply(inverse(multiply(double_divide(multiply(multiply(inverse(multiply(X1,X0)),identity),X2),inverse(X3)),identity)),identity))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f373,f355]) ).
fof(f487,plain,
( ! [X2,X0,X1] : inverse(X0) = multiply(multiply(multiply(inverse(multiply(X1,X0)),identity),X2),multiply(inverse(multiply(double_divide(X1,inverse(X2)),identity)),identity))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f362,f355]) ).
fof(f502,plain,
( ! [X2,X0,X1] : multiply(double_divide(inverse(X0),inverse(X1)),identity) = multiply(multiply(X0,X2),multiply(inverse(inverse(multiply(inverse(X2),inverse(inverse(X1))))),identity))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f441,f158]) ).
fof(f506,plain,
( ! [X2,X0,X1] : multiply(multiply(X0,X2),multiply(inverse(inverse(multiply(inverse(X2),multiply(inverse(X0),X1)))),identity)) = X1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f445,f158]) ).
fof(f508,plain,
( ! [X0] : identity = multiply(inverse(inverse(X0)),multiply(inverse(inverse(multiply(inverse(X0),identity))),identity))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f447,f158]) ).
fof(f535,plain,
( ! [X2,X3,X0,X1] : multiply(double_divide(X1,inverse(X2)),identity) = multiply(multiply(X0,X3),multiply(inverse(multiply(multiply(inverse(multiply(inverse(X3),multiply(multiply(inverse(multiply(X1,X0)),identity),X2))),identity),identity)),identity))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f477,f355]) ).
fof(f545,plain,
( ! [X2,X0,X1] : inverse(X0) = multiply(multiply(multiply(inverse(multiply(X1,X0)),identity),X2),multiply(inverse(multiply(multiply(inverse(multiply(inverse(X2),X1)),identity),identity)),identity))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f487,f355]) ).
fof(f559,plain,
( ! [X2,X0,X1] : multiply(double_divide(inverse(X0),inverse(X1)),identity) = multiply(multiply(X0,X2),multiply(inverse(X2),inverse(inverse(X1))))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f502,f215]) ).
fof(f563,plain,
( ! [X2,X0,X1] : multiply(multiply(X0,X2),multiply(inverse(X2),multiply(inverse(X0),X1))) = X1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f506,f215]) ).
fof(f565,plain,
( ! [X0] : identity = multiply(inverse(inverse(X0)),multiply(inverse(X0),identity))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f508,f215]) ).
fof(f592,plain,
( ! [X2,X3,X0,X1] : multiply(double_divide(X1,inverse(X2)),identity) = multiply(multiply(X0,X3),multiply(inverse(inverse(multiply(inverse(X3),multiply(multiply(inverse(multiply(X1,X0)),identity),X2)))),identity))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f535,f158]) ).
fof(f600,plain,
( ! [X2,X0,X1] : inverse(X0) = multiply(multiply(multiply(inverse(multiply(X1,X0)),identity),X2),multiply(inverse(inverse(multiply(inverse(X2),X1))),identity))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f545,f158]) ).
fof(f610,plain,
( ! [X2,X0,X1] : multiply(multiply(inverse(multiply(inverse(X1),inverse(X0))),identity),identity) = multiply(multiply(X0,X2),multiply(inverse(X2),inverse(inverse(X1))))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f559,f355]) ).
fof(f634,plain,
( ! [X2,X3,X0,X1] : multiply(double_divide(X1,inverse(X2)),identity) = multiply(multiply(X0,X3),multiply(inverse(X3),multiply(multiply(inverse(multiply(X1,X0)),identity),X2)))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f592,f215]) ).
fof(f642,plain,
( ! [X2,X0,X1] : inverse(X0) = multiply(multiply(multiply(inverse(multiply(X1,X0)),identity),X2),multiply(inverse(X2),X1))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f600,f215]) ).
fof(f651,plain,
( ! [X2,X0,X1] : inverse(multiply(inverse(X1),inverse(X0))) = multiply(multiply(X0,X2),multiply(inverse(X2),inverse(inverse(X1))))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f610,f158]) ).
fof(f674,plain,
( ! [X2,X3,X0,X1] : multiply(multiply(inverse(multiply(inverse(X2),X1)),identity),identity) = multiply(multiply(X0,X3),multiply(inverse(X3),multiply(multiply(inverse(multiply(X1,X0)),identity),X2)))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f634,f355]) ).
fof(f701,plain,
( ! [X2,X3,X0,X1] : inverse(multiply(inverse(X2),X1)) = multiply(multiply(X0,X3),multiply(inverse(X3),multiply(multiply(inverse(multiply(X1,X0)),identity),X2)))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f674,f158]) ).
fof(f754,plain,
( ! [X0] : multiply(inverse(X0),identity) = inverse(multiply(X0,identity))
| ~ spl0_2 ),
inference(superposition,[],[f432,f432]) ).
fof(f761,plain,
( ! [X0] : identity = multiply(X0,multiply(inverse(X0),identity))
| ~ spl0_2 ),
inference(superposition,[],[f66,f432]) ).
fof(f767,plain,
( ! [X0] : inverse(X0) = multiply(inverse(multiply(X0,identity)),identity)
| ~ spl0_2 ),
inference(backward_demodulation,[],[f158,f754]) ).
fof(f768,plain,
( ! [X0] : inverse(inverse(multiply(X0,identity))) = X0
| ~ spl0_2 ),
inference(backward_demodulation,[],[f432,f754]) ).
fof(f769,plain,
( ! [X0] : identity = multiply(inverse(inverse(X0)),inverse(multiply(X0,identity)))
| ~ spl0_2 ),
inference(backward_demodulation,[],[f565,f754]) ).
fof(f774,plain,
( ! [X0] : identity = multiply(X0,inverse(multiply(X0,identity)))
| ~ spl0_2 ),
inference(backward_demodulation,[],[f761,f754]) ).
fof(f782,plain,
( ! [X2,X0,X1] : inverse(X0) = multiply(multiply(inverse(multiply(multiply(X1,X0),identity)),X2),multiply(inverse(X2),X1))
| ~ spl0_2 ),
inference(backward_demodulation,[],[f642,f754]) ).
fof(f786,plain,
( ! [X2,X3,X0,X1] : inverse(multiply(inverse(X2),X1)) = multiply(multiply(X0,X3),multiply(inverse(X3),multiply(inverse(multiply(multiply(X1,X0),identity)),X2)))
| ~ spl0_2 ),
inference(backward_demodulation,[],[f701,f754]) ).
fof(f822,plain,
( ! [X0] : inverse(X0) = inverse(multiply(multiply(X0,identity),identity))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f767,f754]) ).
fof(f915,plain,
( ! [X0,X1] : inverse(inverse(multiply(X0,identity))) = multiply(multiply(inverse(multiply(identity,identity)),X1),multiply(inverse(X1),X0))
| ~ spl0_2 ),
inference(superposition,[],[f782,f774]) ).
fof(f922,plain,
( ! [X0,X1] : inverse(inverse(multiply(X0,identity))) = multiply(multiply(inverse(inverse(inverse(identity))),X1),multiply(inverse(X1),X0))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f915,f15]) ).
fof(f930,plain,
( ! [X0,X1] : inverse(inverse(multiply(X0,identity))) = multiply(multiply(inverse(inverse(identity)),X1),multiply(inverse(X1),X0))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f922,f55]) ).
fof(f935,plain,
( ! [X0,X1] : inverse(inverse(multiply(X0,identity))) = multiply(multiply(inverse(identity),X1),multiply(inverse(X1),X0))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f930,f55]) ).
fof(f940,plain,
( ! [X0,X1] : inverse(inverse(multiply(X0,identity))) = multiply(multiply(identity,X1),multiply(inverse(X1),X0))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f935,f55]) ).
fof(f944,plain,
( ! [X0,X1] : inverse(inverse(multiply(X0,identity))) = multiply(inverse(inverse(X1)),multiply(inverse(X1),X0))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f940,f15]) ).
fof(f948,plain,
( ! [X0,X1] : multiply(inverse(inverse(X1)),multiply(inverse(X1),X0)) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f944,f768]) ).
fof(f1023,plain,
( ! [X0] : inverse(inverse(X0)) = multiply(X0,identity)
| ~ spl0_2 ),
inference(superposition,[],[f768,f822]) ).
fof(f1034,plain,
( ! [X0] : inverse(inverse(inverse(inverse(X0)))) = X0
| ~ spl0_2 ),
inference(backward_demodulation,[],[f768,f1023]) ).
fof(f1035,plain,
( ! [X0] : identity = multiply(inverse(inverse(X0)),inverse(inverse(inverse(X0))))
| ~ spl0_2 ),
inference(backward_demodulation,[],[f769,f1023]) ).
fof(f1059,plain,
( ! [X2,X0,X1] : inverse(X0) = multiply(multiply(inverse(inverse(inverse(multiply(X1,X0)))),X2),multiply(inverse(X2),X1))
| ~ spl0_2 ),
inference(backward_demodulation,[],[f782,f1023]) ).
fof(f1061,plain,
( ! [X2,X3,X0,X1] : inverse(multiply(inverse(X2),X1)) = multiply(multiply(X0,X3),multiply(inverse(X3),multiply(inverse(inverse(inverse(multiply(X1,X0)))),X2)))
| ~ spl0_2 ),
inference(backward_demodulation,[],[f786,f1023]) ).
fof(f1474,plain,
( ! [X0,X1] : inverse(X0) = multiply(identity,multiply(inverse(inverse(inverse(inverse(inverse(multiply(X1,X0)))))),X1))
| ~ spl0_2 ),
inference(superposition,[],[f1059,f1035]) ).
fof(f1477,plain,
( ! [X0,X1] : inverse(inverse(inverse(inverse(X0)))) = multiply(multiply(inverse(inverse(inverse(identity))),X1),multiply(inverse(X1),inverse(inverse(X0))))
| ~ spl0_2 ),
inference(superposition,[],[f1059,f1035]) ).
fof(f1478,plain,
( ! [X0,X1] : inverse(inverse(inverse(inverse(X0)))) = multiply(multiply(inverse(inverse(identity)),X1),multiply(inverse(X1),inverse(inverse(X0))))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1477,f55]) ).
fof(f1481,plain,
( ! [X0,X1] : inverse(X0) = inverse(inverse(multiply(inverse(inverse(inverse(inverse(inverse(multiply(X1,X0)))))),X1)))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1474,f15]) ).
fof(f1484,plain,
( ! [X0,X1] : inverse(inverse(inverse(inverse(X0)))) = multiply(multiply(inverse(identity),X1),multiply(inverse(X1),inverse(inverse(X0))))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1478,f55]) ).
fof(f1487,plain,
( ! [X0,X1] : inverse(X0) = inverse(inverse(multiply(inverse(multiply(X1,X0)),X1)))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1481,f1034]) ).
fof(f1489,plain,
( ! [X0,X1] : inverse(inverse(inverse(inverse(X0)))) = multiply(multiply(identity,X1),multiply(inverse(X1),inverse(inverse(X0))))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1484,f55]) ).
fof(f1492,plain,
( ! [X0,X1] : inverse(inverse(inverse(inverse(X0)))) = multiply(inverse(inverse(X1)),multiply(inverse(X1),inverse(inverse(X0))))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1489,f15]) ).
fof(f1494,plain,
( ! [X0] : inverse(inverse(X0)) = inverse(inverse(inverse(inverse(X0))))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1492,f948]) ).
fof(f1495,plain,
( ! [X0] : inverse(inverse(X0)) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1494,f1034]) ).
fof(f1498,plain,
( ! [X2,X0,X1] : inverse(multiply(inverse(X1),inverse(X0))) = multiply(multiply(X0,X2),multiply(inverse(X2),X1))
| ~ spl0_2 ),
inference(backward_demodulation,[],[f651,f1495]) ).
fof(f1500,plain,
( ! [X0,X1] : multiply(X1,multiply(inverse(X1),X0)) = X0
| ~ spl0_2 ),
inference(backward_demodulation,[],[f948,f1495]) ).
fof(f1540,plain,
( ! [X0,X1] : inverse(X0) = multiply(inverse(multiply(X1,X0)),X1)
| ~ spl0_2 ),
inference(backward_demodulation,[],[f1487,f1495]) ).
fof(f1544,plain,
( ! [X2,X3,X0,X1] : inverse(multiply(inverse(X2),X1)) = multiply(multiply(X0,X3),multiply(inverse(X3),multiply(inverse(multiply(X1,X0)),X2)))
| ~ spl0_2 ),
inference(backward_demodulation,[],[f1061,f1495]) ).
fof(f1970,plain,
( ! [X2,X0,X1] : multiply(multiply(X1,X2),multiply(inverse(X2),X0)) = multiply(inverse(inverse(X1)),X0)
| ~ spl0_2 ),
inference(superposition,[],[f563,f1500]) ).
fof(f1992,plain,
( ! [X2,X0,X1] : multiply(X1,X0) = multiply(multiply(X1,X2),multiply(inverse(X2),X0))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1970,f1495]) ).
fof(f2012,plain,
( ! [X2,X0,X1] : inverse(multiply(inverse(X2),X1)) = multiply(X0,multiply(inverse(multiply(X1,X0)),X2))
| ~ spl0_2 ),
inference(backward_demodulation,[],[f1544,f1992]) ).
fof(f2039,plain,
( ! [X0,X1] : multiply(X0,X1) = inverse(multiply(inverse(X1),inverse(X0)))
| ~ spl0_2 ),
inference(backward_demodulation,[],[f1498,f1992]) ).
fof(f2478,plain,
( multiply(a3,multiply(b3,c3)) != inverse(multiply(inverse(c3),inverse(multiply(a3,b3))))
| spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f9,f2039]) ).
fof(f2518,definition,
( spl0_3
<=> multiply(a3,multiply(b3,c3)) = inverse(multiply(inverse(c3),inverse(multiply(a3,b3)))) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f2520,plain,
( multiply(a3,multiply(b3,c3)) != inverse(multiply(inverse(c3),inverse(multiply(a3,b3))))
| spl0_3 ),
inference(avatar_component_clause,[],[f2518]) ).
fof(f2521,plain,
( ~ spl0_3
| spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f2478,f53,f7,f2518]) ).
fof(f2859,plain,
( ! [X2,X0,X1] : inverse(multiply(inverse(X1),inverse(multiply(X2,X0)))) = multiply(X2,multiply(inverse(inverse(X0)),X1))
| ~ spl0_2 ),
inference(superposition,[],[f2012,f1540]) ).
fof(f3020,plain,
( ! [X2,X0,X1] : multiply(X2,multiply(X0,X1)) = inverse(multiply(inverse(X1),inverse(multiply(X2,X0))))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f2859,f1495]) ).
fof(f3073,plain,
( $false
| ~ spl0_2
| spl0_3 ),
inference(backward_subsumption_resolution,[],[f2520,f3020]) ).
fof(f3074,plain,
( ~ spl0_2
| spl0_3 ),
inference(avatar_contradiction_clause,[],[f3073]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f10]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f56]) ).
cnf(s4,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f2521]) ).
cnf(s5,plain,
( ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f3074]) ).
cnf(s6,plain,
spl0_3,
inference(rat,[],[s5,s2]) ).
cnf(s7,plain,
spl0_1,
inference(rat,[],[s4,s6,s2]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s7]) ).
fof(f3091,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP498-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n004.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 10:05:54 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.17/1.36 % (3274786)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.17/1.36 % (3274791)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=226193714:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.17/1.36 % (3274792)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=2902396053:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.17/1.36 % (3274796)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1647345691:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.17/1.36 % (3274794)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2320684894:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.17/1.36 % (3274793)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1522316713:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.17/1.36 % (3274795)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1703020878:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.17/1.36 % (3274797)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3765347961:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.17/1.36 % (3274794)Instruction limit reached!
% 3.17/1.36 % (3274794)------------------------------
% 3.17/1.36 % (3274794)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.17/1.36 % (3274794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/1.36 % (3274794)CaDiCaL version: 2.1.3
% 3.17/1.36 % (3274794)Termination reason: Instruction limit
% 3.17/1.36 % (3274794)Termination phase: Saturation
% 3.17/1.36 % (3274794)Time elapsed: 0.083 s
% 3.17/1.36 % (3274794)Peak memory usage: 88 MB
% 3.17/1.36 % (3274794)Instructions burned: 137 (million)
% 3.17/1.36 % (3274796)First to succeed.
% 3.17/1.36 % (3274796)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3274786"
% 3.17/1.36 % (3274795)Instruction limit reached!
% 3.17/1.36 % (3274795)------------------------------
% 3.17/1.36 % (3274795)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.17/1.36 % (3274795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/1.36 % (3274795)CaDiCaL version: 2.1.3
% 3.17/1.36 % (3274795)Termination reason: Instruction limit
% 3.17/1.36 % (3274795)Termination phase: Saturation
% 3.17/1.36 % (3274795)Time elapsed: 0.095 s
% 3.17/1.36 % (3274795)Peak memory usage: 89 MB
% 3.17/1.36 % (3274795)Instructions burned: 183 (million)
% 3.17/1.36 % (3274797)Also succeeded, but the first one will report.
% 3.17/1.36 % (3274805)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1723761986:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 3.17/1.36 % (3274806)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=214198037:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 3.17/1.36 % (3274796)Refutation found. Thanks to Tanya!
% 3.17/1.36 % SZS status Unsatisfiable for theBenchmark
% 3.17/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 4.12/1.57 % (3274796)------------------------------
% 4.12/1.57 % (3274796)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.12/1.57 % (3274796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/1.57 % (3274796)CaDiCaL version: 2.1.3
% 4.12/1.57 % (3274796)Termination reason: Refutation
% 4.12/1.57 % (3274796)Time elapsed: 0.093 s
% 4.12/1.57 % (3274796)Peak memory usage: 90 MB
% 4.12/1.57 % (3274796)Instructions burned: 157 (million)
% 4.12/1.57 % (3274796)------------------------------
% 4.12/1.57 % (3274796)------------------------------
% 4.12/1.57 % (3274786)Success in time 0.495 s
% 4.12/1.57 % Vampire exiting
%------------------------------------------------------------------------------