%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO462+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 09:52:43 AM UTC 2026
% Result : Theorem 30.62s 6.48s
% Output : Refutation 32.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 6 unt; 1 def)
% Number of atoms : 133 ( 14 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 159 ( 55 ~; 49 |; 42 &)
% ( 7 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 13 con; 0-2 aty)
% Number of variables : 99 ( 82 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1700,axiom,
! [X0,X1] :
( ? [X2] : p(s(bool,i(s(fun(fun(X0,bool),bool),i(s(fun(X0,fun(fun(X0,bool),bool)),in),s(X0,X2))),s(fun(X0,bool),X1))))
<=> s(fun(X0,bool),X1) != s(fun(X0,bool),empty) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aMEMBERu_NOTu_EMPTY) ).
fof(f3294,axiom,
! [X0,X1] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),subspace),s(fun(cart(real,X0),bool),X1))))
<=> ( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X0),bool),X1))))
& ! [X2,X3] :
( ( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X2))),s(fun(cart(real,X0),bool),X1))))
& p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X3))),s(fun(cart(real,X0),bool),X1)))) )
=> p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(cart(real,X0),fun(cart(real,X0),cart(real,X0))),vectoru_add),s(cart(real,X0),X2))),s(cart(real,X0),X3))))),s(fun(cart(real,X0),bool),X1)))) )
& ! [X4,X2] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X2))),s(fun(cart(real,X0),bool),X1))))
=> p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(real,fun(cart(real,X0),cart(real,X0))),r_),s(real,X4))),s(cart(real,X0),X2))))),s(fun(cart(real,X0),bool),X1)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',asubspace) ).
fof(f3299,conjecture,
! [X0,X1] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),subspace),s(fun(cart(real,X0),bool),X1))))
=> s(fun(cart(real,X0),bool),X1) != s(fun(cart(real,X0),bool),empty) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSUBSPACEu_IMPu_NONEMPTY) ).
fof(f3300,negated_conjecture,
~ ! [X0,X1] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),subspace),s(fun(cart(real,X0),bool),X1))))
=> s(fun(cart(real,X0),bool),X1) != s(fun(cart(real,X0),bool),empty) ),
inference(negated_conjecture,[status(cth)],[f3299]) ).
fof(f3355,plain,
! [X0,X1] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),subspace),s(fun(cart(real,X0),bool),X1))))
<=> ( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X0),bool),X1))))
& ! [X2,X3] :
( ( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X2))),s(fun(cart(real,X0),bool),X1))))
& p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X3))),s(fun(cart(real,X0),bool),X1)))) )
=> p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(cart(real,X0),fun(cart(real,X0),cart(real,X0))),vectoru_add),s(cart(real,X0),X2))),s(cart(real,X0),X3))))),s(fun(cart(real,X0),bool),X1)))) )
& ! [X4,X5] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X5))),s(fun(cart(real,X0),bool),X1))))
=> p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(real,fun(cart(real,X0),cart(real,X0))),r_),s(real,X4))),s(cart(real,X0),X5))))),s(fun(cart(real,X0),bool),X1)))) ) ) ),
inference(rectify,[],[f3294]) ).
fof(f3356,plain,
? [X0,X1] :
( s(fun(cart(real,X0),bool),X1) = s(fun(cart(real,X0),bool),empty)
& p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),subspace),s(fun(cart(real,X0),bool),X1)))) ),
inference(ennf_transformation,[],[f3300]) ).
fof(f3409,plain,
! [X0,X1] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),subspace),s(fun(cart(real,X0),bool),X1))))
<=> ( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X0),bool),X1))))
& ! [X2,X3] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(cart(real,X0),fun(cart(real,X0),cart(real,X0))),vectoru_add),s(cart(real,X0),X2))),s(cart(real,X0),X3))))),s(fun(cart(real,X0),bool),X1))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X2))),s(fun(cart(real,X0),bool),X1))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X3))),s(fun(cart(real,X0),bool),X1)))) )
& ! [X4,X5] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(real,fun(cart(real,X0),cart(real,X0))),r_),s(real,X4))),s(cart(real,X0),X5))))),s(fun(cart(real,X0),bool),X1))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X5))),s(fun(cart(real,X0),bool),X1)))) ) ) ),
inference(ennf_transformation,[],[f3355]) ).
fof(f3410,plain,
! [X0,X1] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),subspace),s(fun(cart(real,X0),bool),X1))))
<=> ( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X0),bool),X1))))
& ! [X2,X3] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(cart(real,X0),fun(cart(real,X0),cart(real,X0))),vectoru_add),s(cart(real,X0),X2))),s(cart(real,X0),X3))))),s(fun(cart(real,X0),bool),X1))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X2))),s(fun(cart(real,X0),bool),X1))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X3))),s(fun(cart(real,X0),bool),X1)))) )
& ! [X4,X5] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(real,fun(cart(real,X0),cart(real,X0))),r_),s(real,X4))),s(cart(real,X0),X5))))),s(fun(cart(real,X0),bool),X1))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X5))),s(fun(cart(real,X0),bool),X1)))) ) ) ),
inference(flattening,[],[f3409]) ).
fof(f3433,definition,
! [X1,X0] :
( sP11(X1,X0)
<=> ( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X0),bool),X1))))
& ! [X2,X3] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(cart(real,X0),fun(cart(real,X0),cart(real,X0))),vectoru_add),s(cart(real,X0),X2))),s(cart(real,X0),X3))))),s(fun(cart(real,X0),bool),X1))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X2))),s(fun(cart(real,X0),bool),X1))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X3))),s(fun(cart(real,X0),bool),X1)))) )
& ! [X4,X5] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(real,fun(cart(real,X0),cart(real,X0))),r_),s(real,X4))),s(cart(real,X0),X5))))),s(fun(cart(real,X0),bool),X1))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X5))),s(fun(cart(real,X0),bool),X1)))) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])],[predicate_definition_introduction]) ).
fof(f3434,plain,
! [X0,X1] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),subspace),s(fun(cart(real,X0),bool),X1))))
<=> sP11(X1,X0) ),
inference(definition_folding,[],[f3410,f3433]) ).
fof(f3435,plain,
( s(fun(cart(real,sK12),bool),sK13) = s(fun(cart(real,sK12),bool),empty)
& p(s(bool,i(s(fun(fun(cart(real,sK12),bool),bool),subspace),s(fun(cart(real,sK12),bool),sK13)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X0,sK12),skolemize(X1,sK13)],[f3356]) ).
fof(f3702,plain,
! [X0,X1] :
( ( ? [X2] : p(s(bool,i(s(fun(fun(X0,bool),bool),i(s(fun(X0,fun(fun(X0,bool),bool)),in),s(X0,X2))),s(fun(X0,bool),X1))))
| s(fun(X0,bool),X1) = s(fun(X0,bool),empty) )
& ( s(fun(X0,bool),X1) != s(fun(X0,bool),empty)
| ! [X2] : ~ p(s(bool,i(s(fun(fun(X0,bool),bool),i(s(fun(X0,fun(fun(X0,bool),bool)),in),s(X0,X2))),s(fun(X0,bool),X1)))) ) ),
inference(nnf_transformation,[],[f1700]) ).
fof(f3703,plain,
! [X0,X1] :
( ( ? [X2] : p(s(bool,i(s(fun(fun(X0,bool),bool),i(s(fun(X0,fun(fun(X0,bool),bool)),in),s(X0,X2))),s(fun(X0,bool),X1))))
| s(fun(X0,bool),X1) = s(fun(X0,bool),empty) )
& ( s(fun(X0,bool),X1) != s(fun(X0,bool),empty)
| ! [X3] : ~ p(s(bool,i(s(fun(fun(X0,bool),bool),i(s(fun(X0,fun(fun(X0,bool),bool)),in),s(X0,X3))),s(fun(X0,bool),X1)))) ) ),
inference(rectify,[],[f3702]) ).
fof(f3704,plain,
! [X0,X1] :
( ( p(s(bool,i(s(fun(fun(X0,bool),bool),i(s(fun(X0,fun(fun(X0,bool),bool)),in),s(X0,sK182(X0,X1)))),s(fun(X0,bool),X1))))
| s(fun(X0,bool),X1) = s(fun(X0,bool),empty) )
& ( s(fun(X0,bool),X1) != s(fun(X0,bool),empty)
| ! [X3] : ~ p(s(bool,i(s(fun(fun(X0,bool),bool),i(s(fun(X0,fun(fun(X0,bool),bool)),in),s(X0,X3))),s(fun(X0,bool),X1)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK182]),skolemize(X2,sK182(X0,X1))],[f3703]) ).
fof(f3705,plain,
! [X1,X0] :
( ( sP11(X1,X0)
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X0),bool),X1))))
| ? [X2,X3] :
( ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(cart(real,X0),fun(cart(real,X0),cart(real,X0))),vectoru_add),s(cart(real,X0),X2))),s(cart(real,X0),X3))))),s(fun(cart(real,X0),bool),X1))))
& p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X2))),s(fun(cart(real,X0),bool),X1))))
& p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X3))),s(fun(cart(real,X0),bool),X1)))) )
| ? [X4,X5] :
( ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(real,fun(cart(real,X0),cart(real,X0))),r_),s(real,X4))),s(cart(real,X0),X5))))),s(fun(cart(real,X0),bool),X1))))
& p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X5))),s(fun(cart(real,X0),bool),X1)))) ) )
& ( ( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X0),bool),X1))))
& ! [X2,X3] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(cart(real,X0),fun(cart(real,X0),cart(real,X0))),vectoru_add),s(cart(real,X0),X2))),s(cart(real,X0),X3))))),s(fun(cart(real,X0),bool),X1))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X2))),s(fun(cart(real,X0),bool),X1))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X3))),s(fun(cart(real,X0),bool),X1)))) )
& ! [X4,X5] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(real,fun(cart(real,X0),cart(real,X0))),r_),s(real,X4))),s(cart(real,X0),X5))))),s(fun(cart(real,X0),bool),X1))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X5))),s(fun(cart(real,X0),bool),X1)))) ) )
| ~ sP11(X1,X0) ) ),
inference(nnf_transformation,[],[f3433]) ).
fof(f3706,plain,
! [X1,X0] :
( ( sP11(X1,X0)
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X0),bool),X1))))
| ? [X2,X3] :
( ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(cart(real,X0),fun(cart(real,X0),cart(real,X0))),vectoru_add),s(cart(real,X0),X2))),s(cart(real,X0),X3))))),s(fun(cart(real,X0),bool),X1))))
& p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X2))),s(fun(cart(real,X0),bool),X1))))
& p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X3))),s(fun(cart(real,X0),bool),X1)))) )
| ? [X4,X5] :
( ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(real,fun(cart(real,X0),cart(real,X0))),r_),s(real,X4))),s(cart(real,X0),X5))))),s(fun(cart(real,X0),bool),X1))))
& p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X5))),s(fun(cart(real,X0),bool),X1)))) ) )
& ( ( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X0),bool),X1))))
& ! [X2,X3] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(cart(real,X0),fun(cart(real,X0),cart(real,X0))),vectoru_add),s(cart(real,X0),X2))),s(cart(real,X0),X3))))),s(fun(cart(real,X0),bool),X1))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X2))),s(fun(cart(real,X0),bool),X1))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X3))),s(fun(cart(real,X0),bool),X1)))) )
& ! [X4,X5] :
( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(real,fun(cart(real,X0),cart(real,X0))),r_),s(real,X4))),s(cart(real,X0),X5))))),s(fun(cart(real,X0),bool),X1))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),X5))),s(fun(cart(real,X0),bool),X1)))) ) )
| ~ sP11(X1,X0) ) ),
inference(flattening,[],[f3705]) ).
fof(f3707,plain,
! [X0,X1] :
( ( sP11(X0,X1)
| ~ p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),i(s(fun(num,cart(real,X1)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X1),bool),X0))))
| ? [X2,X3] :
( ~ p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),i(s(fun(cart(real,X1),cart(real,X1)),i(s(fun(cart(real,X1),fun(cart(real,X1),cart(real,X1))),vectoru_add),s(cart(real,X1),X2))),s(cart(real,X1),X3))))),s(fun(cart(real,X1),bool),X0))))
& p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),X2))),s(fun(cart(real,X1),bool),X0))))
& p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),X3))),s(fun(cart(real,X1),bool),X0)))) )
| ? [X4,X5] :
( ~ p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),i(s(fun(cart(real,X1),cart(real,X1)),i(s(fun(real,fun(cart(real,X1),cart(real,X1))),r_),s(real,X4))),s(cart(real,X1),X5))))),s(fun(cart(real,X1),bool),X0))))
& p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),X5))),s(fun(cart(real,X1),bool),X0)))) ) )
& ( ( p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),i(s(fun(num,cart(real,X1)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X1),bool),X0))))
& ! [X6,X7] :
( p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),i(s(fun(cart(real,X1),cart(real,X1)),i(s(fun(cart(real,X1),fun(cart(real,X1),cart(real,X1))),vectoru_add),s(cart(real,X1),X6))),s(cart(real,X1),X7))))),s(fun(cart(real,X1),bool),X0))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),X6))),s(fun(cart(real,X1),bool),X0))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),X7))),s(fun(cart(real,X1),bool),X0)))) )
& ! [X8,X9] :
( p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),i(s(fun(cart(real,X1),cart(real,X1)),i(s(fun(real,fun(cart(real,X1),cart(real,X1))),r_),s(real,X8))),s(cart(real,X1),X9))))),s(fun(cart(real,X1),bool),X0))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),X9))),s(fun(cart(real,X1),bool),X0)))) ) )
| ~ sP11(X0,X1) ) ),
inference(rectify,[],[f3706]) ).
fof(f3708,plain,
! [X0,X1] :
( ( sP11(X0,X1)
| ~ p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),i(s(fun(num,cart(real,X1)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X1),bool),X0))))
| ( ~ p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),i(s(fun(cart(real,X1),cart(real,X1)),i(s(fun(cart(real,X1),fun(cart(real,X1),cart(real,X1))),vectoru_add),s(cart(real,X1),sK183(X0,X1)))),s(cart(real,X1),sK184(X0,X1)))))),s(fun(cart(real,X1),bool),X0))))
& p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),sK183(X0,X1)))),s(fun(cart(real,X1),bool),X0))))
& p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),sK184(X0,X1)))),s(fun(cart(real,X1),bool),X0)))) )
| ( ~ p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),i(s(fun(cart(real,X1),cart(real,X1)),i(s(fun(real,fun(cart(real,X1),cart(real,X1))),r_),s(real,sK185(X0,X1)))),s(cart(real,X1),sK186(X0,X1)))))),s(fun(cart(real,X1),bool),X0))))
& p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),sK186(X0,X1)))),s(fun(cart(real,X1),bool),X0)))) ) )
& ( ( p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),i(s(fun(num,cart(real,X1)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X1),bool),X0))))
& ! [X6,X7] :
( p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),i(s(fun(cart(real,X1),cart(real,X1)),i(s(fun(cart(real,X1),fun(cart(real,X1),cart(real,X1))),vectoru_add),s(cart(real,X1),X6))),s(cart(real,X1),X7))))),s(fun(cart(real,X1),bool),X0))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),X6))),s(fun(cart(real,X1),bool),X0))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),X7))),s(fun(cart(real,X1),bool),X0)))) )
& ! [X8,X9] :
( p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),i(s(fun(cart(real,X1),cart(real,X1)),i(s(fun(real,fun(cart(real,X1),cart(real,X1))),r_),s(real,X8))),s(cart(real,X1),X9))))),s(fun(cart(real,X1),bool),X0))))
| ~ p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),X9))),s(fun(cart(real,X1),bool),X0)))) ) )
| ~ sP11(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK183,sK184,sK185,sK186]),skolemize(X2,sK183(X0,X1)),skolemize(X3,sK184(X0,X1)),skolemize(X4,sK185(X0,X1)),skolemize(X5,sK186(X0,X1))],[f3707]) ).
fof(f3709,plain,
! [X0,X1] :
( ( p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),subspace),s(fun(cart(real,X0),bool),X1))))
| ~ sP11(X1,X0) )
& ( sP11(X1,X0)
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),subspace),s(fun(cart(real,X0),bool),X1)))) ) ),
inference(nnf_transformation,[],[f3434]) ).
fof(f3710,plain,
p(s(bool,i(s(fun(fun(cart(real,sK12),bool),bool),subspace),s(fun(cart(real,sK12),bool),sK13)))),
inference(cnf_transformation,[],[f3435]) ).
fof(f3711,plain,
s(fun(cart(real,sK12),bool),sK13) = s(fun(cart(real,sK12),bool),empty),
inference(cnf_transformation,[],[f3435]) ).
fof(f4061,plain,
! [X3,X0,X1] :
( ~ p(s(bool,i(s(fun(fun(X0,bool),bool),i(s(fun(X0,fun(fun(X0,bool),bool)),in),s(X0,X3))),s(fun(X0,bool),X1))))
| s(fun(X0,bool),X1) != s(fun(X0,bool),empty) ),
inference(cnf_transformation,[],[f3704]) ).
fof(f4069,plain,
! [X0,X1] :
( ~ sP11(X0,X1)
| p(s(bool,i(s(fun(fun(cart(real,X1),bool),bool),i(s(fun(cart(real,X1),fun(fun(cart(real,X1),bool),bool)),in),s(cart(real,X1),i(s(fun(num,cart(real,X1)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X1),bool),X0)))) ),
inference(cnf_transformation,[],[f3708]) ).
fof(f4076,plain,
! [X0,X1] :
( sP11(X1,X0)
| ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),subspace),s(fun(cart(real,X0),bool),X1)))) ),
inference(cnf_transformation,[],[f3709]) ).
fof(f6411,plain,
! [X0,X1] :
( ~ p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),subspace),s(fun(cart(real,X0),bool),X1))))
| p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X0),bool),X1)))) ),
inference(resolution,[],[f4069,f4076]) ).
fof(f8676,plain,
p(s(bool,i(s(fun(fun(cart(real,sK12),bool),bool),i(s(fun(cart(real,sK12),fun(fun(cart(real,sK12),bool),bool)),in),s(cart(real,sK12),i(s(fun(num,cart(real,sK12)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,sK12),bool),sK13)))),
inference(resolution,[],[f6411,f3710]) ).
fof(f8750,plain,
p(s(bool,i(s(fun(fun(cart(real,sK12),bool),bool),i(s(fun(cart(real,sK12),fun(fun(cart(real,sK12),bool),bool)),in),s(cart(real,sK12),i(s(fun(num,cart(real,sK12)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,sK12),bool),empty)))),
inference(forward_demodulation,[],[f8676,f3711]) ).
fof(f8754,plain,
s(fun(cart(real,sK12),bool),empty) != s(fun(cart(real,sK12),bool),empty),
inference(resolution,[],[f8750,f4061]) ).
fof(f8757,plain,
$false,
inference(trivial_inequality_removal,[],[f8754]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO462+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.43 % Computer : n018.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Sun Sep 27 08:17:53 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.49 Running first-order theorem proving
% 0.21/0.49 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.85/5.12 % (2019327)Detected formulas, will run a generic FOF schedule.
% 21.85/5.12 % (2019335)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=271545660:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2987 on theBenchmark for (2987ds/134677Mi)
% 21.85/5.12 % (2019338)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2848112448:i=119:av=off:ss=axioms_2987 on theBenchmark for (2987ds/119Mi)
% 21.85/5.12 % (2019334)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=993688660:i=141193_2987 on theBenchmark for (2987ds/141193Mi)
% 21.85/5.12 % (2019337)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1228303641:i=109:sd=1:ins=1:gsp=on:ss=axioms_2987 on theBenchmark for (2987ds/109Mi)
% 21.85/5.12 % (2019339)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3583000573:s2a=on:i=139:gtg=position_2987 on theBenchmark for (2987ds/139Mi)
% 21.85/5.12 % (2019340)dis-21_1_sil=8000:lcm=predicate:random_seed=3806346318:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2987 on theBenchmark for (2987ds/129Mi)
% 21.85/5.12 % (2019336)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=4118857240:i=141695:sd=1:nm=32:gsp=on:ss=included_2987 on theBenchmark for (2987ds/141695Mi)
% 21.85/5.12 % (2019337)Instruction limit reached!
% 21.85/5.12 % (2019337)------------------------------
% 21.85/5.12 % (2019337)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.85/5.12 % (2019337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.85/5.12 % (2019337)CaDiCaL version: 2.1.3
% 21.85/5.12 % (2019337)Termination reason: Instruction limit
% 21.85/5.12 % (2019337)Termination phase: Property scanning
% 21.85/5.12 % (2019337)Time elapsed: 0.091 s
% 21.85/5.12 % (2019337)Peak memory usage: 92 MB
% 21.85/5.12 % (2019337)Instructions burned: 109 (million)
% 21.85/5.12 % (2019340)Instruction limit reached!
% 21.85/5.12 % (2019340)------------------------------
% 21.85/5.12 % (2019340)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.85/5.12 % (2019340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.85/5.12 % (2019340)CaDiCaL version: 2.1.3
% 21.85/5.12 % (2019340)Termination reason: Instruction limit
% 21.85/5.12 % (2019340)Termination phase: SInE selection
% 21.85/5.12 % (2019340)Time elapsed: 0.100 s
% 21.85/5.12 % (2019340)Peak memory usage: 90 MB
% 21.85/5.12 % (2019340)Instructions burned: 131 (million)
% 21.85/5.12 % (2019338)Instruction limit reached!
% 21.85/5.12 % (2019338)------------------------------
% 21.85/5.12 % (2019338)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.85/5.12 % (2019338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.85/5.12 % (2019338)CaDiCaL version: 2.1.3
% 21.85/5.12 % (2019338)Termination reason: Instruction limit
% 21.85/5.12 % (2019338)Termination phase: Naming
% 21.85/5.12 % (2019338)Time elapsed: 0.100 s
% 21.85/5.12 % (2019338)Peak memory usage: 91 MB
% 21.85/5.12 % (2019338)Instructions burned: 119 (million)
% 21.85/5.12 % (2019339)Instruction limit reached!
% 21.85/5.12 % (2019339)------------------------------
% 21.85/5.12 % (2019339)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.85/5.12 % (2019339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.85/5.12 % (2019339)CaDiCaL version: 2.1.3
% 21.85/5.12 % (2019339)Termination reason: Instruction limit
% 21.85/5.12 % (2019339)Termination phase: Property scanning
% 21.85/5.12 % (2019339)Time elapsed: 0.104 s
% 21.85/5.12 % (2019339)Peak memory usage: 90 MB
% 21.85/5.12 % (2019339)Instructions burned: 140 (million)
% 21.85/5.12 % (2019349)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3838509721:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2983 on theBenchmark for (2983ds/157Mi)
% 21.85/5.12 % (2019350)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3048545951:i=325:sd=1:ss=axioms:sgt=32_2983 on theBenchmark for (2983ds/325Mi)
% 21.85/5.12 % (2019348)lrs+10_1_sil=8000:sp=occurrence:random_seed=2264086703:i=285:sd=3:ss=axioms:sgt=8_2983 on theBenchmark for (2983ds/285Mi)
% 21.85/5.12 % (2019351)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=885419377:s2a=on:i=248:s2at=1.23:gtg=position_2983 on theBenchmark for (2983ds/248Mi)
% 21.85/5.12 % (2019349)Instruction limit reached!
% 30.62/6.48 % (2019349)------------------------------
% 30.62/6.48 % (2019349)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 30.62/6.48 % (2019349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.62/6.48 % (2019349)CaDiCaL version: 2.1.3
% 30.62/6.48 % (2019349)Termination reason: Instruction limit
% 30.62/6.48 % (2019349)Termination phase: Property scanning
% 30.62/6.48 % (2019349)Time elapsed: 0.109 s
% 30.62/6.48 % (2019349)Peak memory usage: 90 MB
% 30.62/6.48 % (2019349)Instructions burned: 158 (million)
% 30.62/6.48 % (2019351)Instruction limit reached!
% 30.62/6.48 % (2019351)------------------------------
% 30.62/6.48 % (2019351)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 30.62/6.48 % (2019351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.62/6.48 % (2019351)CaDiCaL version: 2.1.3
% 30.62/6.48 % (2019351)Termination reason: Instruction limit
% 30.62/6.48 % (2019351)Termination phase: Property scanning
% 30.62/6.48 % (2019351)Time elapsed: 0.185 s
% 30.62/6.48 % (2019351)Peak memory usage: 90 MB
% 30.62/6.48 % (2019351)Instructions burned: 249 (million)
% 30.62/6.48 % (2019348)Instruction limit reached!
% 30.62/6.48 % (2019348)------------------------------
% 30.62/6.48 % (2019348)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 30.62/6.48 % (2019348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.62/6.48 % (2019348)CaDiCaL version: 2.1.3
% 30.62/6.48 % (2019348)Termination reason: Instruction limit
% 30.62/6.48 % (2019348)Termination phase: Property scanning
% 30.62/6.48 % (2019348)Time elapsed: 0.230 s
% 30.62/6.48 % (2019348)Peak memory usage: 94 MB
% 30.62/6.48 % (2019348)Instructions burned: 285 (million)
% 30.62/6.48 % (2019350)Instruction limit reached!
% 30.62/6.48 % (2019350)------------------------------
% 30.62/6.48 % (2019350)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 30.62/6.48 % (2019350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.62/6.48 % (2019350)CaDiCaL version: 2.1.3
% 30.62/6.48 % (2019350)Termination reason: Instruction limit
% 30.62/6.48 % (2019350)Termination phase: Saturation
% 30.62/6.48 % (2019350)Time elapsed: 0.301 s
% 30.62/6.48 % (2019350)Peak memory usage: 96 MB
% 30.62/6.48 % (2019350)Instructions burned: 326 (million)
% 30.62/6.48 % (2019356)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2965323578:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2980 on theBenchmark for (2980ds/294Mi)
% 30.62/6.48 % (2019357)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1975584121:i=2350_2979 on theBenchmark for (2979ds/2350Mi)
% 30.62/6.48 % (2019358)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1631471440:cts=off:i=113:fsr=off:ss=included:sgt=4_2978 on theBenchmark for (2978ds/113Mi)
% 30.62/6.48 % (2019359)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1571306073:i=127:av=off:fsr=off:sup=off_2978 on theBenchmark for (2978ds/127Mi)
% 30.62/6.48 % (2019358)Instruction limit reached!
% 30.62/6.48 % (2019358)------------------------------
% 30.62/6.48 % (2019358)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 30.62/6.48 % (2019358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.62/6.48 % (2019358)CaDiCaL version: 2.1.3
% 30.62/6.48 % (2019358)Termination reason: Instruction limit
% 30.62/6.48 % (2019358)Termination phase: Preprocessing 1
% 30.62/6.48 % (2019358)Time elapsed: 0.097 s
% 30.62/6.48 % (2019358)Peak memory usage: 90 MB
% 30.62/6.48 % (2019358)Instructions burned: 113 (million)
% 30.62/6.48 % (2019356)Instruction limit reached!
% 30.62/6.48 % (2019356)------------------------------
% 30.62/6.48 % (2019356)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 30.62/6.48 % (2019356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.62/6.48 % (2019356)CaDiCaL version: 2.1.3
% 30.62/6.48 % (2019356)Termination reason: Instruction limit
% 30.62/6.48 % (2019356)Termination phase: Preprocessing 3
% 30.62/6.48 % (2019356)Time elapsed: 0.240 s
% 30.62/6.48 % (2019356)Peak memory usage: 95 MB
% 30.62/6.48 % (2019356)Instructions burned: 294 (million)
% 30.62/6.48 % (2019359)Instruction limit reached!
% 30.62/6.48 % (2019359)------------------------------
% 30.62/6.48 % (2019359)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 30.62/6.48 % (2019359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.62/6.48 % (2019359)CaDiCaL version: 2.1.3
% 30.62/6.48 % (2019359)Termination reason: Instruction limit
% 30.62/6.48 % (2019359)Termination phase: Naming
% 30.62/6.48 % (2019359)Time elapsed: 0.116 s
% 30.62/6.48 % (2019359)Peak memory usage: 93 MB
% 30.62/6.48 % (2019359)Instructions burned: 128 (million)
% 30.62/6.48 % (2019364)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2390943284:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2975 on theBenchmark for (2975ds/114Mi)
% 30.62/6.48 % (2019365)lrs+10_1_sil=8000:sp=occurrence:random_seed=3292791308:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2975 on theBenchmark for (2975ds/907Mi)
% 30.62/6.48 % (2019364)Instruction limit reached!
% 30.62/6.48 % (2019364)------------------------------
% 30.62/6.48 % (2019364)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 30.62/6.48 % (2019364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.62/6.48 % (2019364)CaDiCaL version: 2.1.3
% 30.62/6.48 % (2019364)Termination reason: Instruction limit
% 30.62/6.48 % (2019364)Termination phase: Property scanning
% 30.62/6.48 % (2019364)Time elapsed: 0.086 s
% 30.62/6.48 % (2019364)Peak memory usage: 90 MB
% 30.62/6.48 % (2019364)Instructions burned: 114 (million)
% 30.62/6.48 % (2019366)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2000023723:i=437:sd=1:aac=none:ss=included_2974 on theBenchmark for (2974ds/437Mi)
% 30.62/6.48 % (2019369)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3662420537:i=5202:ss=axioms:sgt=16_2972 on theBenchmark for (2972ds/5202Mi)
% 30.62/6.48 % (2019366)Instruction limit reached!
% 30.62/6.48 % (2019366)------------------------------
% 30.62/6.48 % (2019366)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 30.62/6.48 % (2019366)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.62/6.48 % (2019366)CaDiCaL version: 2.1.3
% 30.62/6.48 % (2019366)Termination reason: Instruction limit
% 30.62/6.48 % (2019366)Termination phase: Property scanning
% 30.62/6.48 % (2019366)Time elapsed: 0.357 s
% 30.62/6.48 % (2019366)Peak memory usage: 99 MB
% 30.62/6.48 % (2019366)Instructions burned: 438 (million)
% 30.62/6.48 % (2019365)Instruction limit reached!
% 30.62/6.48 % (2019365)------------------------------
% 30.62/6.48 % (2019365)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 30.62/6.48 % (2019365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.62/6.48 % (2019365)CaDiCaL version: 2.1.3
% 30.62/6.48 % (2019365)Termination reason: Instruction limit
% 30.62/6.48 % (2019365)Termination phase: Property scanning
% 30.62/6.48 % (2019365)Time elapsed: 0.666 s
% 30.62/6.48 % (2019365)Peak memory usage: 99 MB
% 30.62/6.48 % (2019365)Instructions burned: 908 (million)
% 30.62/6.48 % (2019372)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=230074952:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2968 on theBenchmark for (2968ds/134Mi)
% 30.62/6.48 % (2019372)Instruction limit reached!
% 30.62/6.48 % (2019372)------------------------------
% 30.62/6.48 % (2019372)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 30.62/6.48 % (2019372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.62/6.48 % (2019372)CaDiCaL version: 2.1.3
% 30.62/6.48 % (2019372)Termination reason: Instruction limit
% 30.62/6.48 % (2019372)Termination phase: Preprocessing 1
% 30.62/6.48 % (2019372)Time elapsed: 0.118 s
% 30.62/6.48 % (2019372)Peak memory usage: 91 MB
% 30.62/6.48 % (2019372)Instructions burned: 135 (million)
% 30.62/6.48 % (2019373)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=4102082348:st=8:i=592:sd=3:ep=RST:ss=axioms_2965 on theBenchmark for (2965ds/592Mi)
% 30.62/6.48 % (2019375)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=4214999814:st=3:i=13193:sd=3:ss=axioms_2964 on theBenchmark for (2964ds/13193Mi)
% 30.62/6.48 % (2019357)Instruction limit reached!
% 30.62/6.48 % (2019357)------------------------------
% 30.62/6.48 % (2019357)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 30.62/6.48 % (2019357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.62/6.48 % (2019357)CaDiCaL version: 2.1.3
% 30.62/6.48 % (2019357)Termination reason: Instruction limit
% 30.62/6.48 % (2019357)Termination phase: Twee Goal Transformation
% 30.62/6.48 % (2019357)Time elapsed: 1.743 s
% 30.62/6.48 % (2019357)Peak memory usage: 105 MB
% 30.62/6.48 % (2019357)Instructions burned: 2351 (million)
% 30.62/6.48 % (2019373)Instruction limit reached!
% 30.62/6.48 % (2019373)------------------------------
% 30.62/6.48 % (2019373)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 30.62/6.48 % (2019373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.62/6.48 % (2019373)CaDiCaL version: 2.1.3
% 30.62/6.48 % (2019373)Termination reason: Instruction limit
% 30.62/6.48 % (2019373)Termination phase: Preprocessing 3
% 30.62/6.48 % (2019373)Time elapsed: 0.484 s
% 30.62/6.48 % (2019373)Peak memory usage: 102 MB
% 30.62/6.48 % (2019373)Instructions burned: 593 (million)
% 30.62/6.48 % (2019378)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=2242063943:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2959 on theBenchmark for (2959ds/125Mi)
% 30.62/6.48 % (2019378)Instruction limit reached!
% 30.62/6.48 % (2019378)------------------------------
% 30.62/6.48 % (2019378)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 30.62/6.48 % (2019378)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.62/6.48 % (2019378)CaDiCaL version: 2.1.3
% 30.62/6.48 % (2019378)Termination reason: Instruction limit
% 30.62/6.48 % (2019378)Termination phase: Property scanning
% 30.62/6.48 % (2019378)Time elapsed: 0.095 s
% 30.62/6.48 % (2019378)Peak memory usage: 90 MB
% 30.62/6.48 % (2019378)Instructions burned: 125 (million)
% 30.62/6.48 % (2019379)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=3558834085:i=134:gtgl=5:slsql=off:gtg=exists_sym_2958 on theBenchmark for (2958ds/134Mi)
% 30.62/6.48 % (2019379)Instruction limit reached!
% 30.62/6.48 % (2019379)------------------------------
% 30.62/6.48 % (2019379)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 30.62/6.48 % (2019379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.62/6.48 % (2019379)CaDiCaL version: 2.1.3
% 30.62/6.48 % (2019379)Termination reason: Instruction limit
% 30.62/6.48 % (2019379)Termination phase: Property scanning
% 30.62/6.48 % (2019379)Time elapsed: 0.093 s
% 30.62/6.48 % (2019379)Peak memory usage: 90 MB
% 30.62/6.48 % (2019379)Instructions burned: 135 (million)
% 30.62/6.48 % (2019381)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=3482720714:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2955 on theBenchmark for (2955ds/141Mi)
% 30.62/6.48 % (2019383)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=1759585272:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2954 on theBenchmark for (2954ds/431Mi)
% 30.62/6.48 % (2019381)Instruction limit reached!
% 30.62/6.48 % (2019381)------------------------------
% 30.62/6.48 % (2019381)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 30.62/6.48 % (2019381)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.62/6.48 % (2019381)CaDiCaL version: 2.1.3
% 30.62/6.48 % (2019381)Termination reason: Instruction limit
% 30.62/6.48 % (2019381)Termination phase: Saturation
% 30.62/6.48 % (2019381)Time elapsed: 0.125 s
% 30.62/6.48 % (2019381)Peak memory usage: 94 MB
% 30.62/6.48 % (2019381)Instructions burned: 142 (million)
% 30.62/6.48 % (2019383)First to succeed.
% 30.62/6.48 % (2019383)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2019327"
% 30.62/6.48 % (2019386)lrs+1010_1_ncem=casc2026/models/loop6.pt:sil=64000:tgt=full:npcc=on:prc=on:urr=ec_only:bsr=on:fd=preordered:gs=on:sac=on:newcnf=on:random_seed=1715260544:i=6060:aac=none:ins=25_2951 on theBenchmark for (2951ds/6060Mi)
% 30.62/6.48 % (2019383)Refutation found. Thanks to Tanya!
% 30.62/6.48 % SZS status Theorem for theBenchmark
% 30.62/6.48 % SZS output start Proof for theBenchmark
% See solution above
% 32.09/6.71 % (2019383)------------------------------
% 32.09/6.71 % (2019383)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.09/6.71 % (2019383)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.09/6.71 % (2019383)CaDiCaL version: 2.1.3
% 32.09/6.71 % (2019383)Termination reason: Refutation
% 32.09/6.71 % (2019383)Time elapsed: 0.297 s
% 32.09/6.71 % (2019383)Peak memory usage: 97 MB
% 32.09/6.71 % (2019383)Instructions burned: 338 (million)
% 32.09/6.71 % (2019383)------------------------------
% 32.09/6.71 % (2019383)------------------------------
% 32.09/6.71 % (2019327)Success in time 5.519 s
% 32.09/6.71 % Vampire exiting
%------------------------------------------------------------------------------