%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP583-1 : 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 : n006.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 10:14:55 AM UTC 2026
% Result : Unsatisfiable 2.93s 1.42s
% Output : Refutation 4.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 7
% Syntax : Number of formulae : 152 ( 50 unt; 2 def)
% Number of atoms : 255 ( 142 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 206 ( 103 ~; 101 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 26 ( 3 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 282 ( 0 sgn 282 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,X0)))),double_divide(identity,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(X0,double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,X0)))),inverse(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,
! [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(f15,plain,
! [X0,X1] : identity = double_divide(double_divide(X1,X0),multiply(X0,X1)),
inference(superposition,[],[f4,f12]) ).
fof(f18,plain,
! [X0] : multiply(inverse(X0),X0) = multiply(multiply(inverse(X0),X0),identity),
inference(superposition,[],[f14,f14]) ).
fof(f19,plain,
! [X0] : identity = double_divide(identity,multiply(inverse(X0),X0)),
inference(superposition,[],[f4,f14]) ).
fof(f20,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(inverse(identity),double_divide(X1,double_divide(identity,X0)))),inverse(identity)) = X1,
inference(superposition,[],[f11,f3]) ).
fof(f22,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(double_divide(identity,X0),double_divide(X1,inverse(X0)))),inverse(identity)) = X1,
inference(superposition,[],[f11,f3]) ).
fof(f23,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),double_divide(double_divide(identity,X0),double_divide(X1,identity))),inverse(identity)) = X1,
inference(superposition,[],[f11,f4]) ).
fof(f27,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),double_divide(double_divide(identity,X0),inverse(X1))),inverse(identity)) = X1,
inference(forward_demodulation,[],[f23,f3]) ).
fof(f46,plain,
! [X2,X0,X1] : double_divide(double_divide(multiply(X0,X1),double_divide(double_divide(identity,double_divide(X1,X0)),double_divide(X2,identity))),inverse(identity)) = X2,
inference(superposition,[],[f11,f15]) ).
fof(f48,plain,
! [X2,X0,X1] : double_divide(double_divide(multiply(X0,X1),double_divide(double_divide(identity,double_divide(X1,X0)),inverse(X2))),inverse(identity)) = X2,
inference(forward_demodulation,[],[f46,f3]) ).
fof(f83,plain,
! [X0,X1] : identity = double_divide(double_divide(inverse(X1),double_divide(double_divide(identity,X1),multiply(inverse(X0),X0))),multiply(inverse(X0),X0)),
inference(superposition,[],[f27,f14]) ).
fof(f85,plain,
! [X0] : double_divide(identity,X0) = double_divide(double_divide(inverse(X0),identity),inverse(identity)),
inference(superposition,[],[f27,f4]) ).
fof(f91,plain,
! [X0] : double_divide(identity,X0) = double_divide(inverse(inverse(X0)),inverse(identity)),
inference(forward_demodulation,[],[f85,f3]) ).
fof(f125,plain,
! [X0,X1] : double_divide(identity,X1) = double_divide(inverse(inverse(X1)),multiply(inverse(X0),X0)),
inference(superposition,[],[f91,f14]) ).
fof(f136,plain,
! [X0] : inverse(double_divide(identity,X0)) = multiply(inverse(identity),inverse(inverse(X0))),
inference(superposition,[],[f12,f91]) ).
fof(f137,plain,
! [X0] : multiply(X0,identity) = multiply(inverse(identity),inverse(inverse(X0))),
inference(forward_demodulation,[],[f136,f12]) ).
fof(f150,plain,
! [X0] : double_divide(double_divide(identity,double_divide(inverse(identity),double_divide(X0,inverse(identity)))),inverse(identity)) = X0,
inference(superposition,[],[f20,f3]) ).
fof(f212,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(inverse(identity),double_divide(X2,double_divide(inverse(inverse(X0)),multiply(inverse(X1),X1))))),inverse(identity)) = X2,
inference(superposition,[],[f20,f125]) ).
fof(f213,plain,
! [X0,X1] : double_divide(inverse(inverse(X0)),inverse(identity)) = double_divide(inverse(inverse(X0)),multiply(inverse(X1),X1)),
inference(superposition,[],[f91,f125]) ).
fof(f215,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(X2,double_divide(double_divide(inverse(inverse(X0)),multiply(inverse(X1),X1)),double_divide(X3,double_divide(X0,X2)))),inverse(identity)) = X3,
inference(superposition,[],[f11,f125]) ).
fof(f372,plain,
! [X0] : double_divide(double_divide(identity,double_divide(double_divide(identity,X0),identity)),inverse(identity)) = X0,
inference(superposition,[],[f22,f4]) ).
fof(f379,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(double_divide(identity,identity),X0)),inverse(identity)) = double_divide(identity,double_divide(double_divide(identity,X1),double_divide(X0,inverse(X1)))),
inference(superposition,[],[f22,f22]) ).
fof(f395,plain,
! [X0,X1] : double_divide(identity,double_divide(double_divide(identity,X1),double_divide(X0,inverse(X1)))) = double_divide(double_divide(identity,double_divide(inverse(identity),X0)),inverse(identity)),
inference(forward_demodulation,[],[f379,f3]) ).
fof(f400,plain,
! [X0] : double_divide(double_divide(identity,inverse(double_divide(identity,X0))),inverse(identity)) = X0,
inference(forward_demodulation,[],[f372,f3]) ).
fof(f404,plain,
! [X0] : double_divide(double_divide(identity,multiply(X0,identity)),inverse(identity)) = X0,
inference(forward_demodulation,[],[f400,f12]) ).
fof(f415,plain,
! [X0] : multiply(inverse(X0),X0) = double_divide(double_divide(identity,multiply(inverse(X0),X0)),inverse(identity)),
inference(superposition,[],[f404,f18]) ).
fof(f420,plain,
inverse(identity) = double_divide(identity,inverse(identity)),
inference(superposition,[],[f404,f19]) ).
fof(f423,plain,
! [X0] : double_divide(double_divide(identity,double_divide(double_divide(identity,identity),X0)),inverse(identity)) = double_divide(identity,multiply(X0,identity)),
inference(superposition,[],[f22,f404]) ).
fof(f430,plain,
! [X0] : double_divide(double_divide(identity,double_divide(inverse(identity),X0)),inverse(identity)) = double_divide(identity,multiply(X0,identity)),
inference(forward_demodulation,[],[f423,f3]) ).
fof(f431,plain,
identity = inverse(identity),
inference(forward_demodulation,[],[f420,f4]) ).
fof(f436,plain,
! [X0] : multiply(inverse(X0),X0) = double_divide(identity,inverse(identity)),
inference(forward_demodulation,[],[f415,f19]) ).
fof(f441,plain,
! [X0,X1] : double_divide(identity,double_divide(double_divide(identity,X1),double_divide(X0,inverse(X1)))) = double_divide(identity,multiply(X0,identity)),
inference(backward_demodulation,[],[f395,f430]) ).
fof(f442,plain,
! [X0] : double_divide(identity,multiply(double_divide(X0,inverse(identity)),identity)) = X0,
inference(backward_demodulation,[],[f150,f430]) ).
fof(f445,definition,
( spl0_9
<=> identity = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f447,plain,
( identity = inverse(identity)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f448,plain,
spl0_9,
inference(avatar_split_clause,[],[f431,f445]) ).
fof(f457,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(forward_demodulation,[],[f436,f4]) ).
fof(f480,plain,
( ! [X2,X0,X1] : double_divide(double_divide(multiply(X0,X1),double_divide(double_divide(identity,double_divide(X1,X0)),inverse(X2))),identity) = X2
| ~ spl0_9 ),
inference(backward_demodulation,[],[f48,f447]) ).
fof(f485,plain,
( ! [X0] : double_divide(identity,X0) = double_divide(inverse(inverse(X0)),identity)
| ~ spl0_9 ),
inference(backward_demodulation,[],[f91,f447]) ).
fof(f497,plain,
( ! [X0] : multiply(X0,identity) = multiply(identity,inverse(inverse(X0)))
| ~ spl0_9 ),
inference(backward_demodulation,[],[f137,f447]) ).
fof(f504,plain,
( ! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(identity,double_divide(X2,double_divide(inverse(inverse(X0)),multiply(inverse(X1),X1))))),identity) = X2
| ~ spl0_9 ),
inference(backward_demodulation,[],[f212,f447]) ).
fof(f505,plain,
( ! [X0,X1] : double_divide(inverse(inverse(X0)),multiply(inverse(X1),X1)) = double_divide(inverse(inverse(X0)),identity)
| ~ spl0_9 ),
inference(backward_demodulation,[],[f213,f447]) ).
fof(f507,plain,
( ! [X2,X3,X0,X1] : double_divide(double_divide(X2,double_divide(double_divide(inverse(inverse(X0)),multiply(inverse(X1),X1)),double_divide(X3,double_divide(X0,X2)))),identity) = X3
| ~ spl0_9 ),
inference(backward_demodulation,[],[f215,f447]) ).
fof(f547,plain,
( ! [X0] : double_divide(identity,multiply(double_divide(X0,identity),identity)) = X0
| ~ spl0_9 ),
inference(backward_demodulation,[],[f442,f447]) ).
fof(f549,plain,
( ! [X0] : double_divide(identity,multiply(inverse(X0),identity)) = X0
| ~ spl0_9 ),
inference(forward_demodulation,[],[f547,f3]) ).
fof(f582,plain,
( ! [X2,X3,X0,X1] : inverse(double_divide(X2,double_divide(double_divide(inverse(inverse(X0)),multiply(inverse(X1),X1)),double_divide(X3,double_divide(X0,X2))))) = X3
| ~ spl0_9 ),
inference(forward_demodulation,[],[f507,f3]) ).
fof(f584,plain,
( ! [X0,X1] : double_divide(inverse(inverse(X0)),multiply(inverse(X1),X1)) = inverse(inverse(inverse(X0)))
| ~ spl0_9 ),
inference(forward_demodulation,[],[f505,f3]) ).
fof(f585,plain,
( ! [X2,X0,X1] : inverse(double_divide(X0,double_divide(identity,double_divide(X2,double_divide(inverse(inverse(X0)),multiply(inverse(X1),X1)))))) = X2
| ~ spl0_9 ),
inference(forward_demodulation,[],[f504,f3]) ).
fof(f592,plain,
( ! [X0] : multiply(X0,identity) = inverse(inverse(inverse(inverse(X0))))
| ~ spl0_9 ),
inference(forward_demodulation,[],[f497,f13]) ).
fof(f603,plain,
( ! [X0] : double_divide(identity,X0) = inverse(inverse(inverse(X0)))
| ~ spl0_9 ),
inference(forward_demodulation,[],[f485,f3]) ).
fof(f608,plain,
( ! [X2,X0,X1] : inverse(double_divide(multiply(X0,X1),double_divide(double_divide(identity,double_divide(X1,X0)),inverse(X2)))) = X2
| ~ spl0_9 ),
inference(forward_demodulation,[],[f480,f3]) ).
fof(f644,plain,
( ! [X2,X3,X0,X1] : multiply(double_divide(double_divide(inverse(inverse(X0)),multiply(inverse(X1),X1)),double_divide(X3,double_divide(X0,X2))),X2) = X3
| ~ spl0_9 ),
inference(forward_demodulation,[],[f582,f12]) ).
fof(f652,plain,
( ! [X2,X0,X1] : multiply(double_divide(identity,double_divide(X2,double_divide(inverse(inverse(X0)),multiply(inverse(X1),X1)))),X0) = X2
| ~ spl0_9 ),
inference(forward_demodulation,[],[f585,f12]) ).
fof(f660,plain,
( ! [X0,X1] : double_divide(identity,double_divide(double_divide(identity,X1),double_divide(X0,inverse(X1)))) = double_divide(identity,inverse(inverse(inverse(inverse(X0)))))
| ~ spl0_9 ),
inference(backward_demodulation,[],[f441,f592]) ).
fof(f666,plain,
( ! [X0] : double_divide(identity,inverse(inverse(inverse(inverse(inverse(X0)))))) = X0
| ~ spl0_9 ),
inference(backward_demodulation,[],[f549,f592]) ).
fof(f677,plain,
( ! [X0,X1] : identity = double_divide(double_divide(inverse(X1),double_divide(inverse(inverse(inverse(X1))),multiply(inverse(X0),X0))),multiply(inverse(X0),X0))
| ~ spl0_9 ),
inference(backward_demodulation,[],[f83,f603]) ).
fof(f689,plain,
( ! [X2,X0,X1] : multiply(double_divide(double_divide(identity,double_divide(X1,X0)),inverse(X2)),multiply(X0,X1)) = X2
| ~ spl0_9 ),
inference(forward_demodulation,[],[f608,f12]) ).
fof(f718,plain,
( ! [X2,X3,X0] : multiply(double_divide(inverse(inverse(inverse(X0))),double_divide(X3,double_divide(X0,X2))),X2) = X3
| ~ spl0_9 ),
inference(forward_demodulation,[],[f644,f584]) ).
fof(f722,plain,
( ! [X2,X0,X1] : multiply(inverse(inverse(inverse(double_divide(X2,double_divide(inverse(inverse(X0)),multiply(inverse(X1),X1)))))),X0) = X2
| ~ spl0_9 ),
inference(forward_demodulation,[],[f652,f603]) ).
fof(f727,plain,
( ! [X0] : inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(X0)))))))) = X0
| ~ spl0_9 ),
inference(forward_demodulation,[],[f666,f603]) ).
fof(f732,plain,
( ! [X0,X1] : double_divide(identity,double_divide(double_divide(identity,X1),double_divide(X0,inverse(X1)))) = inverse(inverse(inverse(inverse(inverse(inverse(inverse(X0)))))))
| ~ spl0_9 ),
inference(forward_demodulation,[],[f660,f603]) ).
fof(f742,plain,
( ! [X0,X1] : identity = double_divide(double_divide(inverse(X1),inverse(inverse(inverse(inverse(X1))))),multiply(inverse(X0),X0))
| ~ spl0_9 ),
inference(forward_demodulation,[],[f677,f584]) ).
fof(f747,plain,
( ! [X2,X0,X1] : multiply(double_divide(inverse(inverse(inverse(double_divide(X1,X0)))),inverse(X2)),multiply(X0,X1)) = X2
| ~ spl0_9 ),
inference(forward_demodulation,[],[f689,f603]) ).
fof(f773,plain,
( ! [X2,X0,X1] : multiply(inverse(inverse(multiply(double_divide(inverse(inverse(X0)),multiply(inverse(X1),X1)),X2))),X0) = X2
| ~ spl0_9 ),
inference(forward_demodulation,[],[f722,f12]) ).
fof(f781,plain,
( ! [X0,X1] : inverse(inverse(inverse(inverse(inverse(inverse(inverse(X0))))))) = inverse(inverse(inverse(double_divide(double_divide(identity,X1),double_divide(X0,inverse(X1))))))
| ~ spl0_9 ),
inference(forward_demodulation,[],[f732,f603]) ).
fof(f789,plain,
( ! [X2,X0,X1] : multiply(double_divide(inverse(inverse(multiply(X0,X1))),inverse(X2)),multiply(X0,X1)) = X2
| ~ spl0_9 ),
inference(forward_demodulation,[],[f747,f12]) ).
fof(f806,plain,
( ! [X2,X0] : multiply(inverse(inverse(multiply(inverse(inverse(inverse(X0))),X2))),X0) = X2
| ~ spl0_9 ),
inference(forward_demodulation,[],[f773,f584]) ).
fof(f813,plain,
( ! [X0,X1] : inverse(inverse(inverse(inverse(inverse(inverse(inverse(X0))))))) = inverse(inverse(multiply(double_divide(X0,inverse(X1)),double_divide(identity,X1))))
| ~ spl0_9 ),
inference(forward_demodulation,[],[f781,f12]) ).
fof(f831,plain,
( ! [X0,X1] : inverse(inverse(inverse(inverse(inverse(inverse(inverse(X0))))))) = inverse(inverse(multiply(double_divide(X0,inverse(X1)),inverse(inverse(inverse(X1))))))
| ~ spl0_9 ),
inference(forward_demodulation,[],[f813,f603]) ).
fof(f851,plain,
! [X0,X1] : inverse(X1) = double_divide(X1,multiply(inverse(X0),X0)),
inference(superposition,[],[f3,f457]) ).
fof(f861,plain,
( ! [X1] : identity = inverse(double_divide(inverse(X1),inverse(inverse(inverse(inverse(X1))))))
| ~ spl0_9 ),
inference(backward_demodulation,[],[f742,f851]) ).
fof(f863,plain,
( ! [X1] : identity = multiply(inverse(inverse(inverse(inverse(X1)))),inverse(X1))
| ~ spl0_9 ),
inference(forward_demodulation,[],[f861,f12]) ).
fof(f1203,plain,
( ! [X0,X1] : double_divide(X1,X0) = inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(X0,X1))))))))
| ~ spl0_9 ),
inference(superposition,[],[f727,f12]) ).
fof(f1219,plain,
( ! [X0] : identity = multiply(inverse(inverse(inverse(X0))),X0)
| ~ spl0_9 ),
inference(superposition,[],[f863,f727]) ).
fof(f1225,plain,
( ! [X2,X3,X0] : multiply(double_divide(inverse(inverse(inverse(X0))),double_divide(X3,inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(X2,X0)))))))))),X2) = X3
| ~ spl0_9 ),
inference(backward_demodulation,[],[f718,f1203]) ).
fof(f1236,plain,
( ! [X0,X1] : inverse(inverse(inverse(inverse(inverse(inverse(inverse(X0))))))) = inverse(inverse(multiply(inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(inverse(X1),X0)))))))),inverse(inverse(inverse(X1))))))
| ~ spl0_9 ),
inference(backward_demodulation,[],[f831,f1203]) ).
fof(f1246,plain,
( ! [X2,X0,X1] : multiply(inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(inverse(X2),inverse(inverse(multiply(X0,X1))))))))))),multiply(X0,X1)) = X2
| ~ spl0_9 ),
inference(backward_demodulation,[],[f789,f1203]) ).
fof(f1263,plain,
( ! [X2,X3,X0] : multiply(inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(double_divide(X3,inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(X2,X0))))))))),inverse(inverse(inverse(X0))))))))))),X2) = X3
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1225,f1203]) ).
fof(f1270,plain,
( ! [X2,X3,X0] : multiply(inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(X2,X0)))))))),X3)))))))),inverse(inverse(inverse(X0))))))))))),X2) = X3
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1263,f1203]) ).
fof(f1603,plain,
( ! [X0,X1] : multiply(inverse(inverse(multiply(X0,X1))),inverse(inverse(inverse(inverse(inverse(X0)))))) = X1
| ~ spl0_9 ),
inference(superposition,[],[f806,f727]) ).
fof(f1605,plain,
( ! [X0] : multiply(inverse(inverse(identity)),X0) = X0
| ~ spl0_9 ),
inference(superposition,[],[f806,f1219]) ).
fof(f1613,plain,
( ! [X0] : inverse(X0) = multiply(inverse(inverse(identity)),inverse(X0))
| ~ spl0_9 ),
inference(superposition,[],[f806,f863]) ).
fof(f1624,plain,
( ! [X0] : inverse(X0) = multiply(inverse(identity),inverse(X0))
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1613,f447]) ).
fof(f1632,plain,
( ! [X0] : multiply(inverse(identity),X0) = X0
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1605,f447]) ).
fof(f1639,plain,
( ! [X0] : inverse(X0) = multiply(identity,inverse(X0))
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1624,f447]) ).
fof(f1646,plain,
( ! [X0] : multiply(identity,X0) = X0
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1632,f447]) ).
fof(f1653,plain,
( ! [X0] : inverse(X0) = inverse(inverse(inverse(X0)))
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1639,f13]) ).
fof(f1656,plain,
( ! [X0] : inverse(inverse(X0)) = X0
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1646,f13]) ).
fof(f1680,plain,
( ! [X0,X1] : inverse(inverse(inverse(inverse(inverse(X0))))) = inverse(inverse(multiply(inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(inverse(X1),X0)))))))),inverse(inverse(inverse(X1))))))
| ~ spl0_9 ),
inference(backward_demodulation,[],[f1236,f1653]) ).
fof(f1689,plain,
( ! [X0,X1] : multiply(inverse(inverse(multiply(X0,X1))),inverse(inverse(inverse(X0)))) = X1
| ~ spl0_9 ),
inference(backward_demodulation,[],[f1603,f1653]) ).
fof(f1692,plain,
( ! [X2,X3,X0] : multiply(inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(inverse(inverse(inverse(inverse(inverse(multiply(X2,X0)))))),X3)))))))),inverse(inverse(inverse(X0))))))))))),X2) = X3
| ~ spl0_9 ),
inference(backward_demodulation,[],[f1270,f1653]) ).
fof(f1696,plain,
( ! [X2,X0,X1] : multiply(inverse(inverse(inverse(inverse(inverse(multiply(inverse(X2),inverse(inverse(multiply(X0,X1))))))))),multiply(X0,X1)) = X2
| ~ spl0_9 ),
inference(backward_demodulation,[],[f1246,f1653]) ).
fof(f1704,plain,
( ! [X2,X0] : multiply(inverse(inverse(multiply(inverse(X0),X2))),X0) = X2
| ~ spl0_9 ),
inference(backward_demodulation,[],[f806,f1653]) ).
fof(f1720,plain,
( ! [X2,X0] : multiply(multiply(inverse(X0),X2),X0) = X2
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1704,f1656]) ).
fof(f1728,plain,
( ! [X2,X0,X1] : multiply(inverse(inverse(inverse(multiply(inverse(X2),inverse(inverse(multiply(X0,X1))))))),multiply(X0,X1)) = X2
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1696,f1656]) ).
fof(f1732,plain,
( ! [X2,X3,X0] : multiply(inverse(inverse(inverse(inverse(inverse(multiply(inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(inverse(inverse(inverse(inverse(inverse(multiply(X2,X0)))))),X3)))))))),inverse(inverse(inverse(X0))))))))),X2) = X3
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1692,f1656]) ).
fof(f1735,plain,
( ! [X0,X1] : multiply(inverse(inverse(multiply(X0,X1))),inverse(X0)) = X1
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1689,f1656]) ).
fof(f1744,plain,
( ! [X0,X1] : inverse(inverse(inverse(inverse(inverse(X0))))) = multiply(inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(inverse(X1),X0)))))))),inverse(inverse(inverse(X1))))
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1680,f1656]) ).
fof(f1772,plain,
( ! [X2,X0,X1] : multiply(inverse(multiply(inverse(X2),inverse(inverse(multiply(X0,X1))))),multiply(X0,X1)) = X2
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1728,f1656]) ).
fof(f1776,plain,
( ! [X2,X3,X0] : multiply(inverse(inverse(inverse(multiply(inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(inverse(inverse(inverse(inverse(inverse(multiply(X2,X0)))))),X3)))))))),inverse(inverse(inverse(X0))))))),X2) = X3
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1732,f1656]) ).
fof(f1779,plain,
( ! [X0,X1] : multiply(multiply(X0,X1),inverse(X0)) = X1
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1735,f1656]) ).
fof(f1788,plain,
( ! [X0,X1] : inverse(inverse(inverse(inverse(inverse(X0))))) = multiply(inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(inverse(X1),X0)))))))),inverse(X1))
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1744,f1656]) ).
fof(f1811,plain,
( ! [X2,X0,X1] : multiply(inverse(multiply(inverse(X2),multiply(X0,X1))),multiply(X0,X1)) = X2
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1772,f1656]) ).
fof(f1814,plain,
( ! [X2,X3,X0] : multiply(inverse(multiply(inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(inverse(inverse(inverse(inverse(inverse(multiply(X2,X0)))))),X3)))))))),inverse(inverse(inverse(X0))))),X2) = X3
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1776,f1656]) ).
fof(f1822,plain,
( ! [X0,X1] : inverse(inverse(inverse(inverse(inverse(X0))))) = multiply(inverse(inverse(inverse(inverse(inverse(multiply(inverse(X1),X0)))))),inverse(X1))
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1788,f1656]) ).
fof(f1833,plain,
( ! [X2,X3,X0] : multiply(inverse(multiply(inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(inverse(inverse(inverse(inverse(inverse(multiply(X2,X0)))))),X3)))))))),inverse(X0))),X2) = X3
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1814,f1656]) ).
fof(f1839,plain,
( ! [X0,X1] : inverse(inverse(inverse(inverse(inverse(X0))))) = multiply(inverse(inverse(inverse(multiply(inverse(X1),X0)))),inverse(X1))
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1822,f1656]) ).
fof(f1843,plain,
( ! [X2,X3,X0] : multiply(inverse(multiply(inverse(inverse(inverse(inverse(inverse(multiply(inverse(inverse(inverse(inverse(inverse(multiply(X2,X0)))))),X3)))))),inverse(X0))),X2) = X3
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1833,f1656]) ).
fof(f1849,plain,
( ! [X0,X1] : inverse(inverse(inverse(inverse(inverse(X0))))) = multiply(inverse(multiply(inverse(X1),X0)),inverse(X1))
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1839,f1656]) ).
fof(f1853,plain,
( ! [X2,X3,X0] : multiply(inverse(multiply(inverse(inverse(inverse(multiply(inverse(inverse(inverse(inverse(inverse(multiply(X2,X0)))))),X3)))),inverse(X0))),X2) = X3
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1843,f1656]) ).
fof(f1854,plain,
( ! [X0,X1] : inverse(inverse(inverse(X0))) = multiply(inverse(multiply(inverse(X1),X0)),inverse(X1))
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1849,f1656]) ).
fof(f1857,plain,
( ! [X2,X3,X0] : multiply(inverse(multiply(inverse(multiply(inverse(inverse(inverse(inverse(inverse(multiply(X2,X0)))))),X3)),inverse(X0))),X2) = X3
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1853,f1656]) ).
fof(f1858,plain,
( ! [X0,X1] : inverse(X0) = multiply(inverse(multiply(inverse(X1),X0)),inverse(X1))
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1854,f1656]) ).
fof(f1859,plain,
( ! [X2,X3,X0] : multiply(inverse(multiply(inverse(multiply(inverse(inverse(inverse(multiply(X2,X0)))),X3)),inverse(X0))),X2) = X3
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1857,f1656]) ).
fof(f1868,plain,
( ! [X2,X3,X0] : multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X0)),X3)),inverse(X0))),X2) = X3
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1859,f1656]) ).
fof(f1907,plain,
( ! [X0,X1] : inverse(X1) = multiply(inverse(multiply(X0,X1)),X0)
| ~ spl0_9 ),
inference(superposition,[],[f1858,f1656]) ).
fof(f1934,plain,
( ! [X0,X1] : multiply(inverse(multiply(inverse(X1),X0)),X0) = X1
| ~ spl0_9 ),
inference(superposition,[],[f1811,f1811]) ).
fof(f2109,plain,
( ! [X0,X1] : inverse(X1) = multiply(X0,inverse(multiply(X1,X0)))
| ~ spl0_9 ),
inference(superposition,[],[f1779,f1779]) ).
fof(f2139,plain,
( ! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1
| ~ spl0_9 ),
inference(superposition,[],[f1720,f1934]) ).
fof(f2182,plain,
( ! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X1)),X0)
| ~ spl0_9 ),
inference(superposition,[],[f1720,f2139]) ).
fof(f2183,plain,
( ! [X0,X1] : multiply(X0,X1) = multiply(X1,X0)
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2182,f1656]) ).
fof(f2249,plain,
( ! [X0,X1] : multiply(X1,multiply(X0,inverse(X1))) = X0
| ~ spl0_9 ),
inference(superposition,[],[f2139,f2183]) ).
fof(f2622,plain,
( ! [X0,X1] : multiply(inverse(X0),X1) = inverse(multiply(X0,inverse(X1)))
| ~ spl0_9 ),
inference(superposition,[],[f1907,f2249]) ).
fof(f2649,plain,
( ! [X0,X1] : inverse(multiply(inverse(X1),X0)) = multiply(X1,inverse(X0))
| ~ spl0_9 ),
inference(superposition,[],[f2249,f1907]) ).
fof(f2651,plain,
( ! [X2,X3,X0] : multiply(inverse(multiply(multiply(multiply(X2,X0),inverse(X3)),inverse(X0))),X2) = X3
| ~ spl0_9 ),
inference(backward_demodulation,[],[f1868,f2649]) ).
fof(f2692,plain,
( ! [X2,X3,X0] : inverse(multiply(multiply(multiply(multiply(X2,X0),inverse(X3)),inverse(X0)),inverse(X2))) = X3
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2651,f2622]) ).
fof(f3054,plain,
( ! [X2,X0,X1] : multiply(X0,multiply(X1,X2)) = inverse(multiply(multiply(inverse(X0),inverse(X2)),inverse(X1)))
| ~ spl0_9 ),
inference(superposition,[],[f2692,f2109]) ).
fof(f3144,plain,
( ! [X2,X0,X1] : multiply(X0,multiply(X1,X2)) = inverse(multiply(inverse(multiply(X0,inverse(inverse(X2)))),inverse(X1)))
| ~ spl0_9 ),
inference(forward_demodulation,[],[f3054,f2622]) ).
fof(f3199,plain,
( ! [X2,X0,X1] : multiply(X0,multiply(X1,X2)) = inverse(inverse(multiply(multiply(X0,inverse(inverse(X2))),inverse(inverse(X1)))))
| ~ spl0_9 ),
inference(forward_demodulation,[],[f3144,f2622]) ).
fof(f3245,plain,
( ! [X2,X0,X1] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,inverse(inverse(X2))),inverse(inverse(X1)))
| ~ spl0_9 ),
inference(forward_demodulation,[],[f3199,f1656]) ).
fof(f3274,plain,
( ! [X2,X0,X1] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,inverse(inverse(X2))),X1)
| ~ spl0_9 ),
inference(forward_demodulation,[],[f3245,f1656]) ).
fof(f3287,plain,
( ! [X2,X0,X1] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X2),X1)
| ~ spl0_9 ),
inference(forward_demodulation,[],[f3274,f1656]) ).
fof(f4006,plain,
( ! [X2,X0,X1] : multiply(multiply(X2,X0),X1) = multiply(X2,multiply(X0,X1))
| ~ spl0_9 ),
inference(superposition,[],[f3287,f2183]) ).
fof(f4188,plain,
( $false
| spl0_1
| ~ spl0_9 ),
inference(backward_subsumption_resolution,[],[f9,f4006]) ).
fof(f4235,plain,
( spl0_1
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f4188]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f10]) ).
cnf(s10,plain,
spl0_9,
inference(sat_conversion,[],[f448]) ).
cnf(s18,plain,
( spl0_1
| ~ spl0_9 ),
inference(sat_conversion,[],[f4235]) ).
cnf(s21,plain,
spl0_1,
inference(rat,[],[s18,s10]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s1,s21]) ).
fof(f4511,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP583-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 % Computer : n006.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 10:07:25 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
% 2.93/1.42 % (2758723)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.93/1.42 % (2758858)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=640880703:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.93/1.42 % (2758855)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=436652134:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.93/1.42 % (2758862)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=444017705:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.93/1.42 % (2758856)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2418818662:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.93/1.42 % (2758852)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=403901273:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.93/1.42 % (2758850)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=3029356537:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.93/1.42 % (2758860)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=988914511:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.93/1.42 % (2758858)Instruction limit reached!
% 2.93/1.42 % (2758858)------------------------------
% 2.93/1.42 % (2758858)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.93/1.42 % (2758858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/1.42 % (2758858)CaDiCaL version: 2.1.3
% 2.93/1.42 % (2758858)Termination reason: Instruction limit
% 2.93/1.42 % (2758858)Termination phase: Saturation
% 2.93/1.42 % (2758858)Time elapsed: 0.052 s
% 2.93/1.42 % (2758858)Peak memory usage: 89 MB
% 2.93/1.42 % (2758858)Instructions burned: 181 (million)
% 2.93/1.42 % (2758856)Instruction limit reached!
% 2.93/1.42 % (2758856)------------------------------
% 2.93/1.42 % (2758856)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.93/1.42 % (2758856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/1.42 % (2758856)CaDiCaL version: 2.1.3
% 2.93/1.42 % (2758856)Termination reason: Instruction limit
% 2.93/1.42 % (2758856)Termination phase: Saturation
% 2.93/1.42 % (2758856)Time elapsed: 0.083 s
% 2.93/1.42 % (2758856)Peak memory usage: 88 MB
% 2.93/1.42 % (2758856)Instructions burned: 136 (million)
% 2.93/1.42 % (2758860)First to succeed.
% 2.93/1.42 % (2758860)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2758723"
% 2.93/1.42 % (2758894)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=4142207656:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 2.93/1.42 % (2758895)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2670682293:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 2.93/1.42 % (2758860)Refutation found. Thanks to Tanya!
% 2.93/1.42 % SZS status Unsatisfiable for theBenchmark
% 2.93/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 4.19/1.51 % (2758860)------------------------------
% 4.19/1.51 % (2758860)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/1.51 % (2758860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/1.51 % (2758860)CaDiCaL version: 2.1.3
% 4.19/1.51 % (2758860)Termination reason: Refutation
% 4.19/1.51 % (2758860)Time elapsed: 0.095 s
% 4.19/1.51 % (2758860)Peak memory usage: 90 MB
% 4.19/1.51 % (2758860)Instructions burned: 158 (million)
% 4.19/1.51 % (2758860)------------------------------
% 4.19/1.51 % (2758860)------------------------------
% 4.19/1.51 % (2758723)Success in time 0.51 s
% 4.19/1.51 % Vampire exiting
%------------------------------------------------------------------------------