%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP567-1 : 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 : n013.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 10:14:52 AM UTC 2026
% Result : Unsatisfiable 0.44s 1.01s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 8
% Syntax : Number of formulae : 122 ( 40 unt; 3 def)
% Number of atoms : 208 ( 109 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 171 ( 85 ~; 83 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 9 ( 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 : 200 ( 0 sgn 200 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),double_divide(identity,identity)) = X1,
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(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),inverse(identity)) = X1,
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,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(superposition,[],[f12,f3]) ).
fof(f14,plain,
! [X0] : inverse(identity) = multiply(inverse(X0),X0),
inference(superposition,[],[f12,f4]) ).
fof(f19,plain,
! [X0] : identity = double_divide(identity,multiply(inverse(X0),X0)),
inference(superposition,[],[f4,f14]) ).
fof(f21,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,identity),double_divide(identity,inverse(X0)))),inverse(identity)) = X1,
inference(superposition,[],[f11,f4]) ).
fof(f23,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,identity)),inverse(identity))),inverse(identity)) = X1,
inference(superposition,[],[f11,f3]) ).
fof(f24,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,inverse(identity))),identity)),inverse(identity)) = X1,
inference(superposition,[],[f11,f4]) ).
fof(f27,plain,
! [X0,X1] : double_divide(double_divide(X0,inverse(double_divide(X1,double_divide(X0,inverse(identity))))),inverse(identity)) = X1,
inference(forward_demodulation,[],[f24,f3]) ).
fof(f28,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,inverse(X0)),inverse(identity))),inverse(identity)) = X1,
inference(forward_demodulation,[],[f23,f3]) ).
fof(f30,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(inverse(X1),double_divide(identity,inverse(X0)))),inverse(identity)) = X1,
inference(forward_demodulation,[],[f21,f3]) ).
fof(f32,plain,
! [X0,X1] : double_divide(double_divide(X0,multiply(double_divide(X0,inverse(identity)),X1)),inverse(identity)) = X1,
inference(forward_demodulation,[],[f27,f12]) ).
fof(f39,plain,
! [X0] : double_divide(double_divide(identity,double_divide(double_divide(X0,identity),identity)),inverse(identity)) = X0,
inference(superposition,[],[f11,f19]) ).
fof(f42,plain,
! [X0] : double_divide(double_divide(identity,inverse(double_divide(X0,identity))),inverse(identity)) = X0,
inference(forward_demodulation,[],[f39,f3]) ).
fof(f46,plain,
! [X0] : double_divide(double_divide(identity,multiply(identity,X0)),inverse(identity)) = X0,
inference(forward_demodulation,[],[f42,f12]) ).
fof(f48,plain,
! [X0] : double_divide(double_divide(identity,inverse(inverse(X0))),inverse(identity)) = X0,
inference(forward_demodulation,[],[f46,f13]) ).
fof(f153,plain,
! [X0] : double_divide(double_divide(X0,double_divide(identity,inverse(identity))),inverse(identity)) = X0,
inference(superposition,[],[f28,f4]) ).
fof(f154,plain,
! [X2,X0,X1] : double_divide(X1,double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(identity,X2))) = double_divide(double_divide(identity,double_divide(X0,inverse(identity))),inverse(identity)),
inference(superposition,[],[f28,f11]) ).
fof(f157,plain,
! [X0] : double_divide(identity,inverse(inverse(X0))) = double_divide(double_divide(identity,double_divide(X0,inverse(identity))),inverse(identity)),
inference(superposition,[],[f28,f48]) ).
fof(f158,plain,
! [X0] : identity = double_divide(double_divide(inverse(X0),X0),inverse(identity)),
inference(superposition,[],[f28,f48]) ).
fof(f170,plain,
! [X2,X0,X1] : double_divide(X1,double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(identity,X2))) = double_divide(identity,inverse(inverse(X0))),
inference(forward_demodulation,[],[f154,f157]) ).
fof(f171,plain,
! [X0] : double_divide(double_divide(X0,identity),inverse(identity)) = X0,
inference(forward_demodulation,[],[f153,f4]) ).
fof(f180,plain,
! [X0] : double_divide(inverse(X0),inverse(identity)) = X0,
inference(forward_demodulation,[],[f171,f3]) ).
fof(f183,plain,
! [X0,X1] : double_divide(X1,X0) = double_divide(multiply(X0,X1),inverse(identity)),
inference(superposition,[],[f180,f12]) ).
fof(f186,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),multiply(X0,X1)),inverse(identity)) = X1,
inference(superposition,[],[f32,f180]) ).
fof(f233,plain,
identity = double_divide(inverse(inverse(identity)),inverse(identity)),
inference(superposition,[],[f158,f3]) ).
fof(f242,plain,
identity = inverse(identity),
inference(forward_demodulation,[],[f233,f180]) ).
fof(f246,definition,
( spl0_2
<=> identity = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f248,plain,
( identity = inverse(identity)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f249,plain,
spl0_2,
inference(avatar_split_clause,[],[f242,f246]) ).
fof(f253,plain,
( ! [X0,X1] : double_divide(double_divide(X0,double_divide(inverse(X1),double_divide(identity,inverse(X0)))),identity) = X1
| ~ spl0_2 ),
inference(backward_demodulation,[],[f30,f248]) ).
fof(f254,plain,
( ! [X0,X1] : double_divide(double_divide(X0,multiply(double_divide(X0,identity),X1)),identity) = X1
| ~ spl0_2 ),
inference(backward_demodulation,[],[f32,f248]) ).
fof(f256,plain,
( ! [X0] : double_divide(double_divide(identity,inverse(inverse(X0))),identity) = X0
| ~ spl0_2 ),
inference(backward_demodulation,[],[f48,f248]) ).
fof(f265,plain,
( ! [X0] : identity = double_divide(double_divide(inverse(X0),X0),identity)
| ~ spl0_2 ),
inference(backward_demodulation,[],[f158,f248]) ).
fof(f268,plain,
( ! [X0] : double_divide(inverse(X0),identity) = X0
| ~ spl0_2 ),
inference(backward_demodulation,[],[f180,f248]) ).
fof(f269,plain,
( ! [X0,X1] : double_divide(X1,X0) = double_divide(multiply(X0,X1),identity)
| ~ spl0_2 ),
inference(backward_demodulation,[],[f183,f248]) ).
fof(f270,plain,
( ! [X0,X1] : double_divide(double_divide(inverse(X0),multiply(X0,X1)),identity) = X1
| ~ spl0_2 ),
inference(backward_demodulation,[],[f186,f248]) ).
fof(f287,plain,
( ! [X0,X1] : inverse(double_divide(inverse(X0),multiply(X0,X1))) = X1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f270,f3]) ).
fof(f288,plain,
( ! [X0,X1] : double_divide(X1,X0) = inverse(multiply(X0,X1))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f269,f3]) ).
fof(f289,plain,
( ! [X0] : inverse(inverse(X0)) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f268,f3]) ).
fof(f292,plain,
( ! [X0] : identity = inverse(double_divide(inverse(X0),X0))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f265,f3]) ).
fof(f301,plain,
( ! [X0] : inverse(double_divide(identity,inverse(inverse(X0)))) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f256,f3]) ).
fof(f303,plain,
( ! [X0,X1] : inverse(double_divide(X0,multiply(double_divide(X0,identity),X1))) = X1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f254,f3]) ).
fof(f304,plain,
( ! [X0,X1] : inverse(double_divide(X0,double_divide(inverse(X1),double_divide(identity,inverse(X0))))) = X1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f253,f3]) ).
fof(f311,plain,
( ! [X0,X1] : multiply(multiply(X0,X1),inverse(X0)) = X1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f287,f12]) ).
fof(f314,plain,
( ! [X2,X0,X1] : double_divide(identity,inverse(inverse(X0))) = double_divide(X1,double_divide(double_divide(X0,inverse(multiply(X2,X1))),double_divide(identity,X2)))
| ~ spl0_2 ),
inference(backward_demodulation,[],[f170,f288]) ).
fof(f329,plain,
( ! [X0] : multiply(identity,X0) = X0
| ~ spl0_2 ),
inference(backward_demodulation,[],[f13,f289]) ).
fof(f332,plain,
( ! [X0] : identity = inverse(inverse(multiply(X0,inverse(X0))))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f292,f288]) ).
fof(f341,plain,
( ! [X0] : inverse(inverse(multiply(inverse(inverse(X0)),identity))) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f301,f288]) ).
fof(f343,plain,
( ! [X0,X1] : inverse(inverse(multiply(multiply(double_divide(X0,identity),X1),X0))) = X1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f303,f288]) ).
fof(f344,plain,
( ! [X0,X1] : inverse(inverse(multiply(double_divide(inverse(X1),double_divide(identity,inverse(X0))),X0))) = X1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f304,f288]) ).
fof(f361,plain,
( ! [X2,X0,X1] : double_divide(identity,inverse(inverse(X0))) = inverse(multiply(double_divide(double_divide(X0,inverse(multiply(X2,X1))),double_divide(identity,X2)),X1))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f314,f288]) ).
fof(f365,plain,
( ! [X0] : identity = multiply(X0,inverse(X0))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f332,f289]) ).
fof(f374,plain,
( ! [X0] : multiply(inverse(inverse(X0)),identity) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f341,f289]) ).
fof(f376,plain,
( ! [X0,X1] : multiply(multiply(double_divide(X0,identity),X1),X0) = X1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f343,f289]) ).
fof(f377,plain,
( ! [X0,X1] : multiply(double_divide(inverse(X1),double_divide(identity,inverse(X0))),X0) = X1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f344,f289]) ).
fof(f390,plain,
( ! [X2,X0,X1] : double_divide(identity,inverse(inverse(X0))) = inverse(multiply(inverse(multiply(double_divide(identity,X2),double_divide(X0,inverse(multiply(X2,X1))))),X1))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f361,f288]) ).
fof(f401,plain,
( ! [X0] : multiply(X0,identity) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f374,f289]) ).
fof(f403,plain,
( ! [X0,X1] : multiply(multiply(inverse(multiply(identity,X0)),X1),X0) = X1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f376,f288]) ).
fof(f404,plain,
( ! [X0,X1] : multiply(inverse(multiply(double_divide(identity,inverse(X0)),inverse(X1))),X0) = X1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f377,f288]) ).
fof(f415,plain,
( ! [X2,X0,X1] : double_divide(identity,inverse(inverse(X0))) = inverse(multiply(inverse(multiply(double_divide(identity,X2),inverse(multiply(inverse(multiply(X2,X1)),X0)))),X1))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f390,f288]) ).
fof(f425,plain,
( ! [X0,X1] : multiply(multiply(inverse(X0),X1),X0) = X1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f403,f329]) ).
fof(f426,plain,
( ! [X0,X1] : multiply(inverse(multiply(inverse(multiply(inverse(X0),identity)),inverse(X1))),X0) = X1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f404,f288]) ).
fof(f436,plain,
( ! [X2,X0,X1] : double_divide(identity,inverse(inverse(X0))) = inverse(multiply(inverse(multiply(inverse(multiply(X2,identity)),inverse(multiply(inverse(multiply(X2,X1)),X0)))),X1))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f415,f288]) ).
fof(f444,plain,
( ! [X0,X1] : multiply(inverse(multiply(inverse(inverse(X0)),inverse(X1))),X0) = X1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f426,f401]) ).
fof(f451,plain,
( ! [X2,X0,X1] : double_divide(identity,inverse(inverse(X0))) = inverse(multiply(inverse(multiply(inverse(X2),inverse(multiply(inverse(multiply(X2,X1)),X0)))),X1))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f436,f401]) ).
fof(f457,plain,
( ! [X0,X1] : multiply(inverse(multiply(X0,inverse(X1))),X0) = X1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f444,f289]) ).
fof(f463,plain,
( ! [X2,X0,X1] : inverse(multiply(inverse(inverse(X0)),identity)) = inverse(multiply(inverse(multiply(inverse(X2),inverse(multiply(inverse(multiply(X2,X1)),X0)))),X1))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f451,f288]) ).
fof(f470,plain,
( ! [X2,X0,X1] : inverse(inverse(inverse(X0))) = inverse(multiply(inverse(multiply(inverse(X2),inverse(multiply(inverse(multiply(X2,X1)),X0)))),X1))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f463,f401]) ).
fof(f473,plain,
( ! [X2,X0,X1] : inverse(X0) = inverse(multiply(inverse(multiply(inverse(X2),inverse(multiply(inverse(multiply(X2,X1)),X0)))),X1))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f470,f289]) ).
fof(f547,plain,
( ! [X0,X1] : multiply(multiply(X0,inverse(X0)),X1) = X1
| ~ spl0_2 ),
inference(superposition,[],[f329,f365]) ).
fof(f548,plain,
( ! [X0] : multiply(X0,inverse(X0)) = inverse(multiply(X0,inverse(X0)))
| ~ spl0_2 ),
inference(superposition,[],[f248,f365]) ).
fof(f572,plain,
( ! [X0,X1] : inverse(X0) = multiply(inverse(multiply(X1,X0)),X1)
| ~ spl0_2 ),
inference(superposition,[],[f457,f289]) ).
fof(f583,plain,
( ! [X0,X1] : multiply(X0,multiply(X1,inverse(X0))) = X1
| ~ spl0_2 ),
inference(superposition,[],[f425,f457]) ).
fof(f775,plain,
( ! [X0,X1] : inverse(X1) = multiply(X0,inverse(multiply(X1,X0)))
| ~ spl0_2 ),
inference(superposition,[],[f311,f311]) ).
fof(f1033,plain,
( ! [X0,X1] : multiply(inverse(X0),X1) = inverse(multiply(X0,inverse(X1)))
| ~ spl0_2 ),
inference(superposition,[],[f572,f583]) ).
fof(f1051,plain,
( ! [X0,X1] : inverse(multiply(inverse(X1),X0)) = multiply(X1,inverse(X0))
| ~ spl0_2 ),
inference(superposition,[],[f583,f572]) ).
fof(f1058,plain,
( ! [X2,X0,X1] : inverse(X0) = multiply(multiply(inverse(X2),inverse(multiply(inverse(multiply(X2,X1)),X0))),inverse(X1))
| ~ spl0_2 ),
inference(backward_demodulation,[],[f473,f1051]) ).
fof(f1086,plain,
( ! [X2,X0,X1] : inverse(X0) = multiply(inverse(multiply(X2,inverse(inverse(multiply(inverse(multiply(X2,X1)),X0))))),inverse(X1))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1058,f1033]) ).
fof(f1112,plain,
( ! [X2,X0,X1] : inverse(X0) = inverse(multiply(multiply(X2,inverse(inverse(multiply(inverse(multiply(X2,X1)),X0)))),inverse(inverse(X1))))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1086,f1033]) ).
fof(f1128,plain,
( ! [X2,X0,X1] : inverse(X0) = inverse(multiply(multiply(X2,inverse(inverse(multiply(inverse(multiply(X2,X1)),X0)))),X1))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1112,f289]) ).
fof(f1137,plain,
( ! [X2,X0,X1] : inverse(X0) = inverse(multiply(multiply(X2,multiply(inverse(multiply(X2,X1)),X0)),X1))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1128,f289]) ).
fof(f1140,plain,
( ! [X2,X0,X1] : inverse(X0) = inverse(multiply(multiply(X2,inverse(multiply(multiply(X2,X1),inverse(X0)))),X1))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1137,f1033]) ).
fof(f1322,plain,
( ! [X2,X0,X1] : inverse(multiply(X0,multiply(X1,X2))) = inverse(multiply(multiply(X1,inverse(inverse(X0))),X2))
| ~ spl0_2 ),
inference(superposition,[],[f1140,f775]) ).
fof(f1334,plain,
( ! [X2,X0,X1] : inverse(inverse(X0)) = multiply(multiply(X1,inverse(multiply(multiply(X1,X2),inverse(X0)))),X2)
| ~ spl0_2 ),
inference(superposition,[],[f289,f1140]) ).
fof(f1344,plain,
( ! [X2,X0,X1] : multiply(multiply(X1,inverse(multiply(multiply(X1,X2),inverse(X0)))),X2) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1334,f289]) ).
fof(f1353,plain,
( ! [X2,X0,X1] : inverse(multiply(X0,multiply(X1,X2))) = inverse(multiply(multiply(X1,X0),X2))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1322,f289]) ).
fof(f1383,plain,
( ! [X2,X0,X1] : multiply(multiply(X1,inverse(multiply(X2,multiply(X1,inverse(X0))))),X2) = X0
| ~ spl0_2 ),
inference(backward_demodulation,[],[f1344,f1353]) ).
fof(f1467,plain,
( ! [X0,X1] : multiply(multiply(X0,inverse(X0)),X1) = inverse(multiply(multiply(X0,inverse(X0)),inverse(X1)))
| ~ spl0_2 ),
inference(superposition,[],[f1033,f548]) ).
fof(f1468,plain,
( ! [X0,X1] : multiply(multiply(X0,inverse(X0)),X1) = inverse(multiply(inverse(X0),multiply(X0,inverse(X1))))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1467,f1353]) ).
fof(f1483,plain,
( ! [X0,X1] : multiply(multiply(X0,inverse(X0)),X1) = inverse(inverse(multiply(X0,inverse(multiply(X0,inverse(X1))))))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1468,f1033]) ).
fof(f1487,plain,
( ! [X0,X1] : multiply(multiply(X0,inverse(X0)),X1) = multiply(X0,inverse(multiply(X0,inverse(X1))))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1483,f289]) ).
fof(f1489,plain,
( ! [X0,X1] : multiply(X0,inverse(multiply(X0,inverse(X1)))) = X1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1487,f547]) ).
fof(f1500,plain,
( ! [X0,X1] : multiply(X0,X1) = multiply(X1,inverse(inverse(X0)))
| ~ spl0_2 ),
inference(superposition,[],[f1489,f775]) ).
fof(f1527,plain,
( ! [X0,X1] : multiply(X0,X1) = multiply(X1,X0)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1500,f289]) ).
fof(f1583,plain,
( multiply(a3,multiply(b3,c3)) != multiply(c3,multiply(a3,b3))
| spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f9,f1527]) ).
fof(f1586,definition,
( spl0_3
<=> multiply(a3,multiply(b3,c3)) = multiply(c3,multiply(a3,b3)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f1588,plain,
( multiply(a3,multiply(b3,c3)) != multiply(c3,multiply(a3,b3))
| spl0_3 ),
inference(avatar_component_clause,[],[f1586]) ).
fof(f1589,plain,
( ~ spl0_3
| spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f1583,f246,f7,f1586]) ).
fof(f1641,plain,
( ! [X2,X0,X1] : multiply(X1,X0) = multiply(X2,inverse(multiply(inverse(X1),multiply(X2,inverse(X0)))))
| ~ spl0_2 ),
inference(superposition,[],[f583,f1383]) ).
fof(f1642,plain,
( ! [X2,X0,X1] : multiply(X1,X0) = multiply(X2,inverse(inverse(multiply(X1,inverse(multiply(X2,inverse(X0)))))))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1641,f1033]) ).
fof(f1672,plain,
( ! [X2,X0,X1] : multiply(X1,X0) = multiply(X2,multiply(X1,inverse(multiply(X2,inverse(X0)))))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1642,f289]) ).
fof(f2607,plain,
( ! [X2,X0,X1] : multiply(X1,multiply(X0,X2)) = multiply(X2,multiply(X1,inverse(inverse(X0))))
| ~ spl0_2 ),
inference(superposition,[],[f1672,f775]) ).
fof(f2674,plain,
( ! [X2,X0,X1] : multiply(X1,multiply(X0,X2)) = multiply(X2,multiply(X1,X0))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f2607,f289]) ).
fof(f2710,plain,
( $false
| ~ spl0_2
| spl0_3 ),
inference(backward_subsumption_resolution,[],[f1588,f2674]) ).
fof(f2711,plain,
( ~ spl0_2
| spl0_3 ),
inference(avatar_contradiction_clause,[],[f2710]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f10]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f249]) ).
cnf(s3,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f1589]) ).
cnf(s5,plain,
( ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f2711]) ).
cnf(s6,plain,
spl0_3,
inference(rat,[],[s5,s2]) ).
cnf(s7,plain,
spl0_1,
inference(rat,[],[s3,s6,s2]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s7]) ).
fof(f2760,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP567-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 % Computer : n013.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sun Sep 27 10:06:51 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.46 Running first-order theorem proving
% 0.15/0.46 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
% 0.44/1.01 % (4179749)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.44/1.01 % (4179759)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3751406604:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.44/1.01 % (4179754)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=3167607728:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.44/1.01 % (4179755)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=1787372615:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.44/1.01 % (4179757)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2503682698:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.44/1.01 % (4179756)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2193762061:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.44/1.01 % (4179759)First to succeed.
% 0.44/1.01 % (4179759)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4179749"
% 0.44/1.01 % (4179758)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2588336977:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.44/1.01 % (4179760)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1684047683:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.44/1.01 % (4179757)Also succeeded, but the first one will report.
% 0.44/1.01 % (4179758)Instruction limit reached!
% 0.44/1.01 % (4179758)------------------------------
% 0.44/1.01 % (4179758)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.44/1.01 % (4179758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/1.01 % (4179758)CaDiCaL version: 2.1.3
% 0.44/1.01 % (4179758)Termination reason: Instruction limit
% 0.44/1.01 % (4179758)Termination phase: Saturation
% 0.44/1.01 % (4179758)Time elapsed: 0.098 s
% 0.44/1.01 % (4179758)Peak memory usage: 89 MB
% 0.44/1.01 % (4179758)Instructions burned: 183 (million)
% 0.44/1.01 % (4179759)Refutation found. Thanks to Tanya!
% 0.44/1.01 % SZS status Unsatisfiable for theBenchmark
% 0.44/1.01 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/1.20 % (4179759)------------------------------
% 0.22/1.20 % (4179759)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.22/1.20 % (4179759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/1.20 % (4179759)CaDiCaL version: 2.1.3
% 0.22/1.20 % (4179759)Termination reason: Refutation
% 0.22/1.20 % (4179759)Time elapsed: 0.037 s
% 0.22/1.20 % (4179759)Peak memory usage: 90 MB
% 0.22/1.20 % (4179759)Instructions burned: 80 (million)
% 0.22/1.20 % (4179759)------------------------------
% 0.22/1.20 % (4179759)------------------------------
% 0.22/1.20 % (4179749)Success in time 0.331 s
% 0.22/1.20 % Vampire exiting
%------------------------------------------------------------------------------