%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP579-1 : 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 : n001.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 10:14:54 AM UTC 2026
% Result : Unsatisfiable 3.12s 1.33s
% Output : Refutation 3.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 9
% Syntax : Number of formulae : 120 ( 61 unt; 4 def)
% Number of atoms : 183 ( 104 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 124 ( 61 ~; 59 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 171 ( 0 sgn 171 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(double_divide(X1,X0),X2),double_divide(X1,identity))),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(double_divide(X1,X0),X2),inverse(X1))),double_divide(identity,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(X0,double_divide(double_divide(double_divide(X1,X0),X2),inverse(X1))),inverse(identity)) = X2,
inference(forward_demodulation,[],[f11,f3]) ).
fof(f14,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(superposition,[],[f12,f3]) ).
fof(f15,plain,
! [X0] : inverse(identity) = multiply(inverse(X0),X0),
inference(superposition,[],[f12,f4]) ).
fof(f18,plain,
! [X0,X1] : inverse(identity) = multiply(multiply(X0,X1),double_divide(X1,X0)),
inference(superposition,[],[f15,f12]) ).
fof(f20,plain,
! [X0] : identity = double_divide(identity,multiply(inverse(X0),X0)),
inference(superposition,[],[f4,f15]) ).
fof(f21,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(double_divide(inverse(X0),X1),inverse(X0))),inverse(identity)) = X1,
inference(superposition,[],[f13,f3]) ).
fof(f22,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),double_divide(double_divide(identity,X1),inverse(X0))),inverse(identity)) = X1,
inference(superposition,[],[f13,f4]) ).
fof(f25,plain,
! [X0,X1] : identity = double_divide(double_divide(X1,double_divide(inverse(double_divide(X0,X1)),inverse(X0))),inverse(identity)),
inference(superposition,[],[f13,f3]) ).
fof(f26,plain,
! [X0,X1] : inverse(double_divide(X1,X0)) = double_divide(double_divide(X0,double_divide(identity,inverse(X1))),inverse(identity)),
inference(superposition,[],[f13,f4]) ).
fof(f31,plain,
! [X2,X0,X1] : inverse(X0) = multiply(inverse(identity),double_divide(X1,double_divide(double_divide(double_divide(X2,X1),X0),inverse(X2)))),
inference(superposition,[],[f12,f13]) ).
fof(f32,plain,
! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X0,double_divide(identity,inverse(X1))),inverse(identity)),
inference(forward_demodulation,[],[f26,f12]) ).
fof(f33,plain,
! [X0,X1] : identity = double_divide(double_divide(X1,double_divide(multiply(X1,X0),inverse(X0))),inverse(identity)),
inference(forward_demodulation,[],[f25,f12]) ).
fof(f83,plain,
! [X0,X1] : multiply(X1,identity) = double_divide(double_divide(X1,double_divide(identity,multiply(inverse(X0),X0))),multiply(inverse(X0),X0)),
inference(superposition,[],[f32,f15]) ).
fof(f84,plain,
! [X0] : multiply(X0,identity) = double_divide(double_divide(X0,identity),inverse(identity)),
inference(superposition,[],[f32,f4]) ).
fof(f93,plain,
! [X0] : multiply(X0,identity) = double_divide(inverse(X0),inverse(identity)),
inference(forward_demodulation,[],[f84,f3]) ).
fof(f94,plain,
! [X0,X1] : multiply(X1,identity) = double_divide(double_divide(X1,identity),multiply(inverse(X0),X0)),
inference(forward_demodulation,[],[f83,f20]) ).
fof(f95,plain,
! [X0,X1] : multiply(X1,identity) = double_divide(inverse(X1),multiply(inverse(X0),X0)),
inference(forward_demodulation,[],[f94,f3]) ).
fof(f162,plain,
! [X0,X1] : inverse(identity) = double_divide(double_divide(double_divide(multiply(X0,X1),inverse(X1)),double_divide(identity,inverse(X0))),inverse(identity)),
inference(superposition,[],[f13,f33]) ).
fof(f170,plain,
! [X0,X1] : inverse(identity) = multiply(double_divide(multiply(X0,X1),inverse(X1)),X0),
inference(forward_demodulation,[],[f162,f32]) ).
fof(f194,plain,
! [X2,X0,X1] : multiply(double_divide(X1,X0),identity) = double_divide(multiply(X0,X1),multiply(inverse(X2),X2)),
inference(superposition,[],[f95,f12]) ).
fof(f248,plain,
! [X0] : double_divide(multiply(inverse(identity),X0),inverse(X0)) = double_divide(double_divide(identity,identity),inverse(identity)),
inference(superposition,[],[f21,f33]) ).
fof(f258,plain,
! [X0] : double_divide(inverse(identity),inverse(identity)) = double_divide(multiply(inverse(identity),X0),inverse(X0)),
inference(forward_demodulation,[],[f248,f3]) ).
fof(f261,plain,
! [X0] : multiply(identity,identity) = double_divide(multiply(inverse(identity),X0),inverse(X0)),
inference(forward_demodulation,[],[f258,f93]) ).
fof(f262,plain,
! [X0] : inverse(inverse(identity)) = double_divide(multiply(inverse(identity),X0),inverse(X0)),
inference(forward_demodulation,[],[f261,f14]) ).
fof(f269,plain,
! [X0] : inverse(multiply(inverse(X0),X0)) = double_divide(multiply(multiply(inverse(X0),X0),identity),multiply(inverse(X0),X0)),
inference(superposition,[],[f262,f15]) ).
fof(f280,plain,
! [X0] : inverse(multiply(inverse(X0),X0)) = multiply(double_divide(identity,multiply(inverse(X0),X0)),identity),
inference(forward_demodulation,[],[f269,f194]) ).
fof(f286,plain,
! [X0] : multiply(identity,identity) = inverse(multiply(inverse(X0),X0)),
inference(forward_demodulation,[],[f280,f20]) ).
fof(f290,plain,
! [X0] : inverse(inverse(identity)) = inverse(multiply(inverse(X0),X0)),
inference(forward_demodulation,[],[f286,f14]) ).
fof(f324,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X1),X1)) = double_divide(double_divide(X0,double_divide(identity,inverse(inverse(identity)))),inverse(identity)),
inference(superposition,[],[f32,f290]) ).
fof(f336,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X1),X1)) = multiply(X0,inverse(identity)),
inference(forward_demodulation,[],[f324,f32]) ).
fof(f389,plain,
! [X0] : double_divide(identity,inverse(X0)) = double_divide(double_divide(inverse(identity),multiply(identity,X0)),inverse(identity)),
inference(superposition,[],[f22,f32]) ).
fof(f391,plain,
! [X0] : double_divide(double_divide(inverse(double_divide(identity,X0)),identity),inverse(identity)) = X0,
inference(superposition,[],[f22,f4]) ).
fof(f401,plain,
! [X0] : double_divide(inverse(inverse(double_divide(identity,X0))),inverse(identity)) = X0,
inference(forward_demodulation,[],[f391,f3]) ).
fof(f403,plain,
! [X0] : double_divide(identity,inverse(X0)) = double_divide(double_divide(inverse(identity),inverse(inverse(X0))),inverse(identity)),
inference(forward_demodulation,[],[f389,f14]) ).
fof(f407,plain,
! [X0] : multiply(inverse(double_divide(identity,X0)),identity) = X0,
inference(forward_demodulation,[],[f401,f93]) ).
fof(f409,plain,
! [X0] : multiply(multiply(X0,identity),identity) = X0,
inference(forward_demodulation,[],[f407,f12]) ).
fof(f415,plain,
identity = multiply(inverse(inverse(identity)),identity),
inference(superposition,[],[f409,f14]) ).
fof(f425,plain,
! [X0] : inverse(identity) = multiply(X0,double_divide(identity,multiply(X0,identity))),
inference(superposition,[],[f18,f409]) ).
fof(f431,definition,
( spl0_2
<=> identity = multiply(inverse(inverse(identity)),identity) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f433,plain,
( identity = multiply(inverse(inverse(identity)),identity)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f431]) ).
fof(f434,plain,
spl0_2,
inference(avatar_split_clause,[],[f415,f431]) ).
fof(f478,plain,
! [X0] : inverse(identity) = multiply(double_divide(inverse(identity),inverse(double_divide(identity,multiply(X0,identity)))),X0),
inference(superposition,[],[f170,f425]) ).
fof(f489,plain,
! [X0] : inverse(identity) = multiply(double_divide(inverse(identity),multiply(multiply(X0,identity),identity)),X0),
inference(forward_demodulation,[],[f478,f12]) ).
fof(f499,plain,
! [X0] : inverse(identity) = multiply(double_divide(inverse(identity),X0),X0),
inference(forward_demodulation,[],[f489,f409]) ).
fof(f541,plain,
! [X0,X1] : inverse(X0) = multiply(inverse(identity),double_divide(multiply(inverse(X1),X1),double_divide(double_divide(identity,X0),inverse(identity)))),
inference(superposition,[],[f31,f20]) ).
fof(f559,plain,
! [X2,X0,X1] : inverse(double_divide(double_divide(double_divide(X1,double_divide(identity,X2)),X0),inverse(X1))) = multiply(inverse(identity),double_divide(X2,X0)),
inference(superposition,[],[f31,f13]) ).
fof(f574,plain,
! [X2,X0,X1] : multiply(inverse(identity),double_divide(X2,X0)) = multiply(inverse(X1),double_divide(double_divide(X1,double_divide(identity,X2)),X0)),
inference(forward_demodulation,[],[f559,f12]) ).
fof(f595,plain,
inverse(identity) = multiply(inverse(inverse(identity)),identity),
inference(superposition,[],[f499,f3]) ).
fof(f610,plain,
( identity = inverse(identity)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f595,f433]) ).
fof(f623,definition,
( spl0_6
<=> identity = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f625,plain,
( identity = inverse(identity)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f623]) ).
fof(f626,plain,
( spl0_6
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f610,f431,f623]) ).
fof(f639,plain,
( ! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(double_divide(X1,X0),X2),inverse(X1))),identity) = X2
| ~ spl0_6 ),
inference(backward_demodulation,[],[f13,f625]) ).
fof(f647,plain,
( ! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X0,double_divide(identity,inverse(X1))),identity)
| ~ spl0_6 ),
inference(backward_demodulation,[],[f32,f625]) ).
fof(f656,plain,
( ! [X0] : multiply(X0,identity) = double_divide(inverse(X0),identity)
| ~ spl0_6 ),
inference(backward_demodulation,[],[f93,f625]) ).
fof(f704,plain,
( ! [X0,X1] : multiply(X0,identity) = multiply(X0,multiply(inverse(X1),X1))
| ~ spl0_6 ),
inference(backward_demodulation,[],[f336,f625]) ).
fof(f709,plain,
( ! [X0] : double_divide(identity,inverse(X0)) = double_divide(double_divide(identity,inverse(inverse(X0))),identity)
| ~ spl0_6 ),
inference(backward_demodulation,[],[f403,f625]) ).
fof(f720,plain,
( ! [X0,X1] : inverse(X0) = multiply(identity,double_divide(multiply(inverse(X1),X1),double_divide(double_divide(identity,X0),identity)))
| ~ spl0_6 ),
inference(backward_demodulation,[],[f541,f625]) ).
fof(f734,plain,
( ! [X2,X0,X1] : multiply(inverse(X1),double_divide(double_divide(X1,double_divide(identity,X2)),X0)) = multiply(identity,double_divide(X2,X0))
| ~ spl0_6 ),
inference(backward_demodulation,[],[f574,f625]) ).
fof(f756,plain,
( ! [X2,X0,X1] : multiply(inverse(X1),double_divide(double_divide(X1,double_divide(identity,X2)),X0)) = inverse(inverse(double_divide(X2,X0)))
| ~ spl0_6 ),
inference(forward_demodulation,[],[f734,f14]) ).
fof(f770,plain,
( ! [X0,X1] : inverse(X0) = inverse(inverse(double_divide(multiply(inverse(X1),X1),double_divide(double_divide(identity,X0),identity))))
| ~ spl0_6 ),
inference(forward_demodulation,[],[f720,f14]) ).
fof(f779,plain,
( ! [X0] : double_divide(identity,inverse(X0)) = inverse(double_divide(identity,inverse(inverse(X0))))
| ~ spl0_6 ),
inference(forward_demodulation,[],[f709,f3]) ).
fof(f824,plain,
( ! [X0] : inverse(inverse(X0)) = multiply(X0,identity)
| ~ spl0_6 ),
inference(forward_demodulation,[],[f656,f3]) ).
fof(f833,plain,
( ! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X0,double_divide(identity,inverse(X1))))
| ~ spl0_6 ),
inference(forward_demodulation,[],[f647,f3]) ).
fof(f839,plain,
( ! [X2,X0,X1] : inverse(double_divide(X0,double_divide(double_divide(double_divide(X1,X0),X2),inverse(X1)))) = X2
| ~ spl0_6 ),
inference(forward_demodulation,[],[f639,f3]) ).
fof(f848,plain,
( ! [X2,X0,X1] : multiply(inverse(X1),double_divide(double_divide(X1,double_divide(identity,X2)),X0)) = inverse(multiply(X0,X2))
| ~ spl0_6 ),
inference(forward_demodulation,[],[f756,f12]) ).
fof(f861,plain,
( ! [X0,X1] : inverse(X0) = inverse(multiply(double_divide(double_divide(identity,X0),identity),multiply(inverse(X1),X1)))
| ~ spl0_6 ),
inference(forward_demodulation,[],[f770,f12]) ).
fof(f868,plain,
( ! [X0] : double_divide(identity,inverse(X0)) = multiply(inverse(inverse(X0)),identity)
| ~ spl0_6 ),
inference(forward_demodulation,[],[f779,f12]) ).
fof(f916,plain,
( ! [X0] : multiply(inverse(inverse(X0)),identity) = X0
| ~ spl0_6 ),
inference(backward_demodulation,[],[f409,f824]) ).
fof(f920,plain,
( ! [X0,X1] : inverse(inverse(X0)) = multiply(X0,multiply(inverse(X1),X1))
| ~ spl0_6 ),
inference(backward_demodulation,[],[f704,f824]) ).
fof(f937,plain,
( ! [X0,X1] : multiply(X0,X1) = multiply(double_divide(identity,inverse(X1)),X0)
| ~ spl0_6 ),
inference(forward_demodulation,[],[f833,f12]) ).
fof(f943,plain,
( ! [X2,X0,X1] : multiply(double_divide(double_divide(double_divide(X1,X0),X2),inverse(X1)),X0) = X2
| ~ spl0_6 ),
inference(forward_demodulation,[],[f839,f12]) ).
fof(f958,plain,
( ! [X0,X1] : inverse(X0) = inverse(multiply(inverse(double_divide(identity,X0)),multiply(inverse(X1),X1)))
| ~ spl0_6 ),
inference(forward_demodulation,[],[f861,f3]) ).
fof(f962,plain,
( ! [X0] : double_divide(identity,inverse(X0)) = inverse(inverse(inverse(inverse(X0))))
| ~ spl0_6 ),
inference(forward_demodulation,[],[f868,f824]) ).
fof(f997,plain,
( ! [X0] : inverse(inverse(inverse(inverse(X0)))) = X0
| ~ spl0_6 ),
inference(forward_demodulation,[],[f916,f824]) ).
fof(f1016,plain,
( ! [X0] : inverse(X0) = inverse(inverse(inverse(inverse(double_divide(identity,X0)))))
| ~ spl0_6 ),
inference(forward_demodulation,[],[f958,f920]) ).
fof(f1025,plain,
( ! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(inverse(inverse(X1)))),X0)
| ~ spl0_6 ),
inference(backward_demodulation,[],[f937,f962]) ).
fof(f1052,plain,
( ! [X0] : double_divide(identity,inverse(X0)) = X0
| ~ spl0_6 ),
inference(backward_demodulation,[],[f962,f997]) ).
fof(f1064,plain,
( ! [X0] : inverse(X0) = double_divide(identity,X0)
| ~ spl0_6 ),
inference(forward_demodulation,[],[f1016,f997]) ).
fof(f1068,plain,
( ! [X0,X1] : multiply(X0,X1) = multiply(X1,X0)
| ~ spl0_6 ),
inference(forward_demodulation,[],[f1025,f997]) ).
fof(f1099,plain,
( ! [X2,X0,X1] : inverse(multiply(X0,X2)) = multiply(inverse(X1),double_divide(double_divide(X1,inverse(X2)),X0))
| ~ spl0_6 ),
inference(backward_demodulation,[],[f848,f1064]) ).
fof(f1110,plain,
( ! [X0] : inverse(inverse(X0)) = X0
| ~ spl0_6 ),
inference(backward_demodulation,[],[f1052,f1064]) ).
fof(f1198,plain,
( ! [X0,X1] : double_divide(X1,X0) = inverse(multiply(X0,X1))
| ~ spl0_6 ),
inference(superposition,[],[f1110,f12]) ).
fof(f1210,plain,
( ! [X2,X0,X1] : multiply(double_divide(double_divide(inverse(multiply(X0,X1)),X2),inverse(X1)),X0) = X2
| ~ spl0_6 ),
inference(backward_demodulation,[],[f943,f1198]) ).
fof(f1221,plain,
( ! [X2,X0,X1] : inverse(multiply(X0,X2)) = multiply(inverse(X1),double_divide(inverse(multiply(inverse(X2),X1)),X0))
| ~ spl0_6 ),
inference(backward_demodulation,[],[f1099,f1198]) ).
fof(f1246,plain,
( ! [X2,X0,X1] : inverse(multiply(X0,X2)) = multiply(inverse(X1),inverse(multiply(X0,inverse(multiply(inverse(X2),X1)))))
| ~ spl0_6 ),
inference(forward_demodulation,[],[f1221,f1198]) ).
fof(f1253,plain,
( ! [X2,X0,X1] : multiply(inverse(multiply(inverse(X1),double_divide(inverse(multiply(X0,X1)),X2))),X0) = X2
| ~ spl0_6 ),
inference(forward_demodulation,[],[f1210,f1198]) ).
fof(f1263,plain,
( ! [X2,X0,X1] : multiply(inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(X0,X1)))))),X0) = X2
| ~ spl0_6 ),
inference(forward_demodulation,[],[f1253,f1198]) ).
fof(f1280,plain,
( ! [X2,X3,X0,X1] : inverse(multiply(inverse(X2),inverse(multiply(X0,inverse(multiply(inverse(multiply(X3,X1)),X2)))))) = multiply(inverse(multiply(inverse(X1),inverse(X0))),X3)
| ~ spl0_6 ),
inference(superposition,[],[f1263,f1263]) ).
fof(f1281,plain,
( ! [X3,X0,X1] : multiply(inverse(multiply(inverse(X1),inverse(X0))),X3) = inverse(inverse(multiply(X0,multiply(X3,X1))))
| ~ spl0_6 ),
inference(forward_demodulation,[],[f1280,f1246]) ).
fof(f1289,plain,
( ! [X3,X0,X1] : multiply(inverse(multiply(inverse(X1),inverse(X0))),X3) = multiply(X0,multiply(X3,X1))
| ~ spl0_6 ),
inference(forward_demodulation,[],[f1281,f1110]) ).
fof(f1384,plain,
( multiply(a3,multiply(b3,c3)) != multiply(c3,multiply(a3,b3))
| spl0_1
| ~ spl0_6 ),
inference(superposition,[],[f9,f1068]) ).
fof(f1390,definition,
( spl0_9
<=> multiply(a3,multiply(b3,c3)) = multiply(c3,multiply(a3,b3)) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f1392,plain,
( multiply(a3,multiply(b3,c3)) != multiply(c3,multiply(a3,b3))
| spl0_9 ),
inference(avatar_component_clause,[],[f1390]) ).
fof(f1393,plain,
( ~ spl0_9
| spl0_1
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f1384,f623,f7,f1390]) ).
fof(f1477,plain,
( ! [X2,X0,X1] : multiply(inverse(multiply(inverse(X0),inverse(X1))),X2) = multiply(X0,multiply(X2,X1))
| ~ spl0_6 ),
inference(superposition,[],[f1289,f1068]) ).
fof(f1491,plain,
( ! [X2,X0,X1] : multiply(X2,multiply(X0,X1)) = multiply(inverse(multiply(inverse(X0),inverse(X2))),X1)
| ~ spl0_6 ),
inference(superposition,[],[f1289,f1068]) ).
fof(f1557,plain,
( ! [X2,X0,X1] : multiply(X0,multiply(X2,X1)) = multiply(X1,multiply(X0,X2))
| ~ spl0_6 ),
inference(forward_demodulation,[],[f1477,f1491]) ).
fof(f1575,plain,
( $false
| ~ spl0_6
| spl0_9 ),
inference(backward_subsumption_resolution,[],[f1392,f1557]) ).
fof(f1576,plain,
( ~ spl0_6
| spl0_9 ),
inference(avatar_contradiction_clause,[],[f1575]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f10]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f434]) ).
cnf(s6,plain,
( ~ spl0_2
| spl0_6 ),
inference(sat_conversion,[],[f626]) ).
cnf(s9,plain,
( spl0_1
| ~ spl0_6
| ~ spl0_9 ),
inference(sat_conversion,[],[f1393]) ).
cnf(s11,plain,
( ~ spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f1576]) ).
cnf(s12,plain,
spl0_6,
inference(rat,[],[s6,s2]) ).
cnf(s15,plain,
spl0_9,
inference(rat,[],[s11,s12]) ).
cnf(s16,plain,
spl0_1,
inference(rat,[],[s9,s15,s12]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s1,s16]) ).
fof(f1591,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP579-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 10:13:00 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 3.12/1.33 % (3331614)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.12/1.33 % (3331654)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3345258614:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.12/1.33 % (3331652)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=339869037:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.12/1.33 % (3331651)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=496628716:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.12/1.33 % (3331653)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3202381150:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.12/1.33 % (3331655)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1356309618:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.12/1.33 % (3331658)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3066607240:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.12/1.33 % (3331656)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3159948295:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.12/1.33 % (3331654)Instruction limit reached!
% 3.12/1.33 % (3331654)------------------------------
% 3.12/1.33 % (3331654)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.33 % (3331654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.33 % (3331654)CaDiCaL version: 2.1.3
% 3.12/1.33 % (3331654)Termination reason: Instruction limit
% 3.12/1.33 % (3331654)Termination phase: Saturation
% 3.12/1.33 % (3331654)Time elapsed: 0.048 s
% 3.12/1.33 % (3331654)Peak memory usage: 88 MB
% 3.12/1.33 % (3331654)Instructions burned: 139 (million)
% 3.12/1.33 % (3331656)First to succeed.
% 3.12/1.33 % (3331656)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3331614"
% 3.12/1.33 % (3331655)Instruction limit reached!
% 3.12/1.33 % (3331655)------------------------------
% 3.12/1.33 % (3331655)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.33 % (3331655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.33 % (3331655)CaDiCaL version: 2.1.3
% 3.12/1.33 % (3331655)Termination reason: Instruction limit
% 3.12/1.33 % (3331655)Termination phase: Saturation
% 3.12/1.33 % (3331655)Time elapsed: 0.101 s
% 3.12/1.33 % (3331655)Peak memory usage: 89 MB
% 3.12/1.33 % (3331655)Instructions burned: 182 (million)
% 3.12/1.33 % (3331728)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=736228252:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 3.12/1.33 % (3331658)Also succeeded, but the first one will report.
% 3.12/1.33 % (3331760)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1826375572:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 3.12/1.33 % (3331656)Refutation found. Thanks to Tanya!
% 3.12/1.33 % SZS status Unsatisfiable for theBenchmark
% 3.12/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.89/1.43 % (3331656)------------------------------
% 3.89/1.43 % (3331656)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.43 % (3331656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.43 % (3331656)CaDiCaL version: 2.1.3
% 3.89/1.43 % (3331656)Termination reason: Refutation
% 3.89/1.43 % (3331656)Time elapsed: 0.052 s
% 3.89/1.43 % (3331656)Peak memory usage: 89 MB
% 3.89/1.43 % (3331656)Instructions burned: 77 (million)
% 3.89/1.43 % (3331656)------------------------------
% 3.89/1.43 % (3331656)------------------------------
% 3.89/1.43 % (3331614)Success in time 0.468 s
% 3.89/1.43 % Vampire exiting
%------------------------------------------------------------------------------