%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LAT386+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 11:47:34 AM UTC 2026
% Result : Theorem 4.25s 1.53s
% Output : Refutation 5.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 23
% Syntax : Number of formulae : 164 ( 17 unt; 13 def)
% Number of atoms : 805 ( 29 equ)
% Maximal formula atoms : 37 ( 4 avg)
% Number of connectives : 982 ( 341 ~; 319 |; 258 &)
% ( 12 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 29 ( 27 usr; 11 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-3 aty)
% Number of variables : 200 ( 0 sgn 167 !; 33 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f9,axiom,
! [X0,X1,X2] :
( ( aElement0(X0)
& aElement0(X1)
& aElement0(X2) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTrans) ).
fof(f21,axiom,
! [X0] :
( aFunction0(X0)
=> ! [X1] :
( aElementOf0(X1,szDzozmdt0(X0))
=> aElementOf0(sdtlpdtrp0(X0,X1),szRzazndt0(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgSort) ).
fof(f23,axiom,
! [X0] :
( aFunction0(X0)
=> ( isMonotone0(X0)
<=> ! [X1,X2] :
( ( aElementOf0(X1,szDzozmdt0(X0))
& aElementOf0(X2,szDzozmdt0(X0)) )
=> ( sdtlseqdt0(X1,X2)
=> sdtlseqdt0(sdtlpdtrp0(X0,X1),sdtlpdtrp0(X0,X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMonot) ).
fof(f24,axiom,
( aSet0(xU)
& ! [X0] :
( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xU) ) )
| aSubsetOf0(X0,xU) )
=> ? [X1] :
( aElementOf0(X1,xU)
& aElementOf0(X1,xU)
& ! [X2] :
( aElementOf0(X2,X0)
=> sdtlseqdt0(X1,X2) )
& aLowerBoundOfIn0(X1,X0,xU)
& ! [X2] :
( ( ( aElementOf0(X2,xU)
& ! [X3] :
( aElementOf0(X3,X0)
=> sdtlseqdt0(X2,X3) ) )
| aLowerBoundOfIn0(X2,X0,xU) )
=> sdtlseqdt0(X2,X1) )
& aInfimumOfIn0(X1,X0,xU)
& ? [X2] :
( aElementOf0(X2,xU)
& aElementOf0(X2,xU)
& ! [X3] :
( aElementOf0(X3,X0)
=> sdtlseqdt0(X3,X2) )
& aUpperBoundOfIn0(X2,X0,xU)
& ! [X3] :
( ( ( aElementOf0(X3,xU)
& ! [X4] :
( aElementOf0(X4,X0)
=> sdtlseqdt0(X4,X3) ) )
| aUpperBoundOfIn0(X3,X0,xU) )
=> sdtlseqdt0(X2,X3) )
& aSupremumOfIn0(X2,X0,xU) ) ) )
& aCompleteLattice0(xU)
& aFunction0(xf)
& ! [X0,X1] :
( ( aElementOf0(X0,szDzozmdt0(xf))
& aElementOf0(X1,szDzozmdt0(xf)) )
=> ( sdtlseqdt0(X0,X1)
=> sdtlseqdt0(sdtlpdtrp0(xf,X0),sdtlpdtrp0(xf,X1)) ) )
& isMonotone0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& szRzazndt0(xf) = xU
& isOn0(xf,xU) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1123) ).
fof(f25,axiom,
( aSet0(xS)
& ! [X0] :
( ( aElementOf0(X0,xS)
=> ( aElementOf0(X0,szDzozmdt0(xf))
& sdtlpdtrp0(xf,X0) = X0
& aFixedPointOf0(X0,xf) ) )
& ( ( ( aElementOf0(X0,szDzozmdt0(xf))
& sdtlpdtrp0(xf,X0) = X0 )
| aFixedPointOf0(X0,xf) )
=> aElementOf0(X0,xS) ) )
& xS = cS1142(xf) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1144) ).
fof(f26,axiom,
( aSet0(xT)
& ! [X0] :
( aElementOf0(X0,xT)
=> aElementOf0(X0,xS) )
& aSubsetOf0(xT,xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1173) ).
fof(f27,axiom,
( aSet0(xP)
& ! [X0] :
( ( aElementOf0(X0,xP)
=> ( aElementOf0(X0,xU)
& sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
& ! [X1] :
( aElementOf0(X1,xT)
=> sdtlseqdt0(X1,X0) )
& aUpperBoundOfIn0(X0,xT,xU) ) )
& ( ( aElementOf0(X0,xU)
& sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
& ( ! [X1] :
( aElementOf0(X1,xT)
=> sdtlseqdt0(X1,X0) )
| aUpperBoundOfIn0(X0,xT,xU) ) )
=> aElementOf0(X0,xP) ) )
& xP = cS1241(xU,xf,xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1244) ).
fof(f28,axiom,
( aElementOf0(xp,xU)
& aElementOf0(xp,xU)
& ! [X0] :
( aElementOf0(X0,xP)
=> sdtlseqdt0(xp,X0) )
& aLowerBoundOfIn0(xp,xP,xU)
& ! [X0] :
( ( ( aElementOf0(X0,xU)
& ! [X1] :
( aElementOf0(X1,xP)
=> sdtlseqdt0(X0,X1) ) )
| aLowerBoundOfIn0(X0,xP,xU) )
=> sdtlseqdt0(X0,xp) )
& aInfimumOfIn0(xp,xP,xU) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1261) ).
fof(f29,conjecture,
( ( ! [X0] :
( aElementOf0(X0,xP)
=> sdtlseqdt0(sdtlpdtrp0(xf,xp),X0) )
| aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU) )
& ( ! [X0] :
( aElementOf0(X0,xT)
=> sdtlseqdt0(X0,sdtlpdtrp0(xf,xp)) )
| aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f30,negated_conjecture,
~ ( ( ! [X0] :
( aElementOf0(X0,xP)
=> sdtlseqdt0(sdtlpdtrp0(xf,xp),X0) )
| aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU) )
& ( ! [X0] :
( aElementOf0(X0,xT)
=> sdtlseqdt0(X0,sdtlpdtrp0(xf,xp)) )
| aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
( aSet0(xU)
& ! [X0] :
( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xU) ) )
| aSubsetOf0(X0,xU) )
=> ? [X2] :
( aElementOf0(X2,xU)
& aElementOf0(X2,xU)
& ! [X3] :
( aElementOf0(X3,X0)
=> sdtlseqdt0(X2,X3) )
& aLowerBoundOfIn0(X2,X0,xU)
& ! [X4] :
( ( ( aElementOf0(X4,xU)
& ! [X5] :
( aElementOf0(X5,X0)
=> sdtlseqdt0(X4,X5) ) )
| aLowerBoundOfIn0(X4,X0,xU) )
=> sdtlseqdt0(X4,X2) )
& aInfimumOfIn0(X2,X0,xU)
& ? [X6] :
( aElementOf0(X6,xU)
& aElementOf0(X6,xU)
& ! [X7] :
( aElementOf0(X7,X0)
=> sdtlseqdt0(X7,X6) )
& aUpperBoundOfIn0(X6,X0,xU)
& ! [X8] :
( ( ( aElementOf0(X8,xU)
& ! [X9] :
( aElementOf0(X9,X0)
=> sdtlseqdt0(X9,X8) ) )
| aUpperBoundOfIn0(X8,X0,xU) )
=> sdtlseqdt0(X6,X8) )
& aSupremumOfIn0(X6,X0,xU) ) ) )
& aCompleteLattice0(xU)
& aFunction0(xf)
& ! [X10,X11] :
( ( aElementOf0(X10,szDzozmdt0(xf))
& aElementOf0(X11,szDzozmdt0(xf)) )
=> ( sdtlseqdt0(X10,X11)
=> sdtlseqdt0(sdtlpdtrp0(xf,X10),sdtlpdtrp0(xf,X11)) ) )
& isMonotone0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& szRzazndt0(xf) = xU
& isOn0(xf,xU) ),
inference(rectify,[],[f24]) ).
fof(f32,plain,
( aSet0(xP)
& ! [X0] :
( ( aElementOf0(X0,xP)
=> ( aElementOf0(X0,xU)
& sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
& ! [X1] :
( aElementOf0(X1,xT)
=> sdtlseqdt0(X1,X0) )
& aUpperBoundOfIn0(X0,xT,xU) ) )
& ( ( aElementOf0(X0,xU)
& sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
& ( ! [X2] :
( aElementOf0(X2,xT)
=> sdtlseqdt0(X2,X0) )
| aUpperBoundOfIn0(X0,xT,xU) ) )
=> aElementOf0(X0,xP) ) )
& xP = cS1241(xU,xf,xT) ),
inference(rectify,[],[f27]) ).
fof(f33,plain,
( aElementOf0(xp,xU)
& aElementOf0(xp,xU)
& ! [X0] :
( aElementOf0(X0,xP)
=> sdtlseqdt0(xp,X0) )
& aLowerBoundOfIn0(xp,xP,xU)
& ! [X1] :
( ( ( aElementOf0(X1,xU)
& ! [X2] :
( aElementOf0(X2,xP)
=> sdtlseqdt0(X1,X2) ) )
| aLowerBoundOfIn0(X1,xP,xU) )
=> sdtlseqdt0(X1,xp) )
& aInfimumOfIn0(xp,xP,xU) ),
inference(rectify,[],[f28]) ).
fof(f34,plain,
~ ( ( ! [X0] :
( aElementOf0(X0,xP)
=> sdtlseqdt0(sdtlpdtrp0(xf,xp),X0) )
| aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU) )
& ( ! [X1] :
( aElementOf0(X1,xT)
=> sdtlseqdt0(X1,sdtlpdtrp0(xf,xp)) )
| aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU) ) ),
inference(rectify,[],[f30]) ).
fof(f40,plain,
( aSet0(xU)
& ! [X0] :
( ? [X2] :
( aElementOf0(X2,xU)
& aElementOf0(X2,xU)
& ! [X3] :
( sdtlseqdt0(X2,X3)
| ~ aElementOf0(X3,X0) )
& aLowerBoundOfIn0(X2,X0,xU)
& ! [X4] :
( sdtlseqdt0(X4,X2)
| ( ( ~ aElementOf0(X4,xU)
| ? [X5] :
( ~ sdtlseqdt0(X4,X5)
& aElementOf0(X5,X0) ) )
& ~ aLowerBoundOfIn0(X4,X0,xU) ) )
& aInfimumOfIn0(X2,X0,xU)
& ? [X6] :
( aElementOf0(X6,xU)
& aElementOf0(X6,xU)
& ! [X7] :
( sdtlseqdt0(X7,X6)
| ~ aElementOf0(X7,X0) )
& aUpperBoundOfIn0(X6,X0,xU)
& ! [X8] :
( sdtlseqdt0(X6,X8)
| ( ( ~ aElementOf0(X8,xU)
| ? [X9] :
( ~ sdtlseqdt0(X9,X8)
& aElementOf0(X9,X0) ) )
& ~ aUpperBoundOfIn0(X8,X0,xU) ) )
& aSupremumOfIn0(X6,X0,xU) ) )
| ( ( ~ aSet0(X0)
| ? [X1] :
( ~ aElementOf0(X1,xU)
& aElementOf0(X1,X0) ) )
& ~ aSubsetOf0(X0,xU) ) )
& aCompleteLattice0(xU)
& aFunction0(xf)
& ! [X10,X11] :
( sdtlseqdt0(sdtlpdtrp0(xf,X10),sdtlpdtrp0(xf,X11))
| ~ sdtlseqdt0(X10,X11)
| ~ aElementOf0(X10,szDzozmdt0(xf))
| ~ aElementOf0(X11,szDzozmdt0(xf)) )
& isMonotone0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& szRzazndt0(xf) = xU
& isOn0(xf,xU) ),
inference(ennf_transformation,[],[f31]) ).
fof(f41,plain,
( aSet0(xU)
& ! [X0] :
( ? [X2] :
( aElementOf0(X2,xU)
& aElementOf0(X2,xU)
& ! [X3] :
( sdtlseqdt0(X2,X3)
| ~ aElementOf0(X3,X0) )
& aLowerBoundOfIn0(X2,X0,xU)
& ! [X4] :
( sdtlseqdt0(X4,X2)
| ( ( ~ aElementOf0(X4,xU)
| ? [X5] :
( ~ sdtlseqdt0(X4,X5)
& aElementOf0(X5,X0) ) )
& ~ aLowerBoundOfIn0(X4,X0,xU) ) )
& aInfimumOfIn0(X2,X0,xU)
& ? [X6] :
( aElementOf0(X6,xU)
& aElementOf0(X6,xU)
& ! [X7] :
( sdtlseqdt0(X7,X6)
| ~ aElementOf0(X7,X0) )
& aUpperBoundOfIn0(X6,X0,xU)
& ! [X8] :
( sdtlseqdt0(X6,X8)
| ( ( ~ aElementOf0(X8,xU)
| ? [X9] :
( ~ sdtlseqdt0(X9,X8)
& aElementOf0(X9,X0) ) )
& ~ aUpperBoundOfIn0(X8,X0,xU) ) )
& aSupremumOfIn0(X6,X0,xU) ) )
| ( ( ~ aSet0(X0)
| ? [X1] :
( ~ aElementOf0(X1,xU)
& aElementOf0(X1,X0) ) )
& ~ aSubsetOf0(X0,xU) ) )
& aCompleteLattice0(xU)
& aFunction0(xf)
& ! [X10,X11] :
( sdtlseqdt0(sdtlpdtrp0(xf,X10),sdtlpdtrp0(xf,X11))
| ~ sdtlseqdt0(X10,X11)
| ~ aElementOf0(X10,szDzozmdt0(xf))
| ~ aElementOf0(X11,szDzozmdt0(xf)) )
& isMonotone0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& szRzazndt0(xf) = xU
& isOn0(xf,xU) ),
inference(flattening,[],[f40]) ).
fof(f42,plain,
( aSet0(xS)
& ! [X0] :
( ( ( aElementOf0(X0,szDzozmdt0(xf))
& sdtlpdtrp0(xf,X0) = X0
& aFixedPointOf0(X0,xf) )
| ~ aElementOf0(X0,xS) )
& ( aElementOf0(X0,xS)
| ( ( ~ aElementOf0(X0,szDzozmdt0(xf))
| sdtlpdtrp0(xf,X0) != X0 )
& ~ aFixedPointOf0(X0,xf) ) ) )
& xS = cS1142(xf) ),
inference(ennf_transformation,[],[f25]) ).
fof(f43,plain,
( aSet0(xT)
& ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xT) )
& aSubsetOf0(xT,xS) ),
inference(ennf_transformation,[],[f26]) ).
fof(f44,plain,
( aSet0(xP)
& ! [X0] :
( ( ( aElementOf0(X0,xU)
& sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
& ! [X1] :
( sdtlseqdt0(X1,X0)
| ~ aElementOf0(X1,xT) )
& aUpperBoundOfIn0(X0,xT,xU) )
| ~ aElementOf0(X0,xP) )
& ( aElementOf0(X0,xP)
| ~ aElementOf0(X0,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
| ( ? [X2] :
( ~ sdtlseqdt0(X2,X0)
& aElementOf0(X2,xT) )
& ~ aUpperBoundOfIn0(X0,xT,xU) ) ) )
& xP = cS1241(xU,xf,xT) ),
inference(ennf_transformation,[],[f32]) ).
fof(f45,plain,
( aSet0(xP)
& ! [X0] :
( ( ( aElementOf0(X0,xU)
& sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
& ! [X1] :
( sdtlseqdt0(X1,X0)
| ~ aElementOf0(X1,xT) )
& aUpperBoundOfIn0(X0,xT,xU) )
| ~ aElementOf0(X0,xP) )
& ( aElementOf0(X0,xP)
| ~ aElementOf0(X0,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
| ( ? [X2] :
( ~ sdtlseqdt0(X2,X0)
& aElementOf0(X2,xT) )
& ~ aUpperBoundOfIn0(X0,xT,xU) ) ) )
& xP = cS1241(xU,xf,xT) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
( aElementOf0(xp,xU)
& aElementOf0(xp,xU)
& ! [X0] :
( sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xP) )
& aLowerBoundOfIn0(xp,xP,xU)
& ! [X1] :
( sdtlseqdt0(X1,xp)
| ( ( ~ aElementOf0(X1,xU)
| ? [X2] :
( ~ sdtlseqdt0(X1,X2)
& aElementOf0(X2,xP) ) )
& ~ aLowerBoundOfIn0(X1,xP,xU) ) )
& aInfimumOfIn0(xp,xP,xU) ),
inference(ennf_transformation,[],[f33]) ).
fof(f47,plain,
( ( ? [X0] :
( ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),X0)
& aElementOf0(X0,xP) )
& ~ aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU) )
| ( ? [X1] :
( ~ sdtlseqdt0(X1,sdtlpdtrp0(xf,xp))
& aElementOf0(X1,xT) )
& ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f57,plain,
! [X0] :
( ( isMonotone0(X0)
<=> ! [X1,X2] :
( sdtlseqdt0(sdtlpdtrp0(X0,X1),sdtlpdtrp0(X0,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X1,szDzozmdt0(X0))
| ~ aElementOf0(X2,szDzozmdt0(X0)) ) )
| ~ aFunction0(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f58,plain,
! [X0] :
( ( isMonotone0(X0)
<=> ! [X1,X2] :
( sdtlseqdt0(sdtlpdtrp0(X0,X1),sdtlpdtrp0(X0,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X1,szDzozmdt0(X0))
| ~ aElementOf0(X2,szDzozmdt0(X0)) ) )
| ~ aFunction0(X0) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( aElementOf0(sdtlpdtrp0(X0,X1),szRzazndt0(X0))
| ~ aElementOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f68,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(ennf_transformation,[],[f9]) ).
fof(f69,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(flattening,[],[f68]) ).
fof(f72,definition,
! [X0] :
( ? [X6] :
( aElementOf0(X6,xU)
& aElementOf0(X6,xU)
& ! [X7] :
( sdtlseqdt0(X7,X6)
| ~ aElementOf0(X7,X0) )
& aUpperBoundOfIn0(X6,X0,xU)
& ! [X8] :
( sdtlseqdt0(X6,X8)
| ( ( ~ aElementOf0(X8,xU)
| ? [X9] :
( ~ sdtlseqdt0(X9,X8)
& aElementOf0(X9,X0) ) )
& ~ aUpperBoundOfIn0(X8,X0,xU) ) )
& aSupremumOfIn0(X6,X0,xU) )
| ~ sP0(X0) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f73,definition,
! [X2,X0] :
( ! [X4] :
( sdtlseqdt0(X4,X2)
| ( ( ~ aElementOf0(X4,xU)
| ? [X5] :
( ~ sdtlseqdt0(X4,X5)
& aElementOf0(X5,X0) ) )
& ~ aLowerBoundOfIn0(X4,X0,xU) ) )
| ~ sP1(X2,X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f74,definition,
! [X0] :
( ? [X2] :
( aElementOf0(X2,xU)
& aElementOf0(X2,xU)
& ! [X3] :
( sdtlseqdt0(X2,X3)
| ~ aElementOf0(X3,X0) )
& aLowerBoundOfIn0(X2,X0,xU)
& sP1(X2,X0)
& aInfimumOfIn0(X2,X0,xU)
& sP0(X0) )
| ~ sP2(X0) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f75,plain,
( aSet0(xU)
& ! [X0] :
( sP2(X0)
| ( ( ~ aSet0(X0)
| ? [X1] :
( ~ aElementOf0(X1,xU)
& aElementOf0(X1,X0) ) )
& ~ aSubsetOf0(X0,xU) ) )
& aCompleteLattice0(xU)
& aFunction0(xf)
& ! [X10,X11] :
( sdtlseqdt0(sdtlpdtrp0(xf,X10),sdtlpdtrp0(xf,X11))
| ~ sdtlseqdt0(X10,X11)
| ~ aElementOf0(X10,szDzozmdt0(xf))
| ~ aElementOf0(X11,szDzozmdt0(xf)) )
& isMonotone0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& szRzazndt0(xf) = xU
& isOn0(xf,xU) ),
inference(definition_folding,[],[f41,f74,f73,f72]) ).
fof(f76,definition,
( ( ? [X1] :
( ~ sdtlseqdt0(X1,sdtlpdtrp0(xf,xp))
& aElementOf0(X1,xT) )
& ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU) )
| ~ sP3 ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f77,plain,
( ( ? [X0] :
( ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),X0)
& aElementOf0(X0,xP) )
& ~ aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU) )
| sP3 ),
inference(definition_folding,[],[f47,f76]) ).
fof(f87,plain,
( aSet0(xU)
& ! [X0] :
( sP2(X0)
| ( ( ~ aSet0(X0)
| ? [X1] :
( ~ aElementOf0(X1,xU)
& aElementOf0(X1,X0) ) )
& ~ aSubsetOf0(X0,xU) ) )
& aCompleteLattice0(xU)
& aFunction0(xf)
& ! [X2,X3] :
( sdtlseqdt0(sdtlpdtrp0(xf,X2),sdtlpdtrp0(xf,X3))
| ~ sdtlseqdt0(X2,X3)
| ~ aElementOf0(X2,szDzozmdt0(xf))
| ~ aElementOf0(X3,szDzozmdt0(xf)) )
& isMonotone0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& szRzazndt0(xf) = xU
& isOn0(xf,xU) ),
inference(rectify,[],[f75]) ).
fof(f88,plain,
( aSet0(xU)
& ! [X0] :
( sP2(X0)
| ( ( ~ aSet0(X0)
| ( ~ aElementOf0(sK8(X0),xU)
& aElementOf0(sK8(X0),X0) ) )
& ~ aSubsetOf0(X0,xU) ) )
& aCompleteLattice0(xU)
& aFunction0(xf)
& ! [X2,X3] :
( sdtlseqdt0(sdtlpdtrp0(xf,X2),sdtlpdtrp0(xf,X3))
| ~ sdtlseqdt0(X2,X3)
| ~ aElementOf0(X2,szDzozmdt0(xf))
| ~ aElementOf0(X3,szDzozmdt0(xf)) )
& isMonotone0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& szRzazndt0(xf) = xU
& isOn0(xf,xU) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X1,sK8(X0))],[f87]) ).
fof(f89,plain,
( aSet0(xP)
& ! [X0] :
( ( ( aElementOf0(X0,xU)
& sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
& ! [X1] :
( sdtlseqdt0(X1,X0)
| ~ aElementOf0(X1,xT) )
& aUpperBoundOfIn0(X0,xT,xU) )
| ~ aElementOf0(X0,xP) )
& ( aElementOf0(X0,xP)
| ~ aElementOf0(X0,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
| ( ~ sdtlseqdt0(sK9(X0),X0)
& aElementOf0(sK9(X0),xT)
& ~ aUpperBoundOfIn0(X0,xT,xU) ) ) )
& xP = cS1241(xU,xf,xT) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X2,sK9(X0))],[f45]) ).
fof(f90,plain,
( aElementOf0(xp,xU)
& aElementOf0(xp,xU)
& ! [X0] :
( sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xP) )
& aLowerBoundOfIn0(xp,xP,xU)
& ! [X1] :
( sdtlseqdt0(X1,xp)
| ( ( ~ aElementOf0(X1,xU)
| ( ~ sdtlseqdt0(X1,sK10(X1))
& aElementOf0(sK10(X1),xP) ) )
& ~ aLowerBoundOfIn0(X1,xP,xU) ) )
& aInfimumOfIn0(xp,xP,xU) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X1))],[f46]) ).
fof(f91,plain,
( ( ? [X1] :
( ~ sdtlseqdt0(X1,sdtlpdtrp0(xf,xp))
& aElementOf0(X1,xT) )
& ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU) )
| ~ sP3 ),
inference(nnf_transformation,[],[f76]) ).
fof(f92,plain,
( ( ? [X0] :
( ~ sdtlseqdt0(X0,sdtlpdtrp0(xf,xp))
& aElementOf0(X0,xT) )
& ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU) )
| ~ sP3 ),
inference(rectify,[],[f91]) ).
fof(f93,plain,
( ( ~ sdtlseqdt0(sK11,sdtlpdtrp0(xf,xp))
& aElementOf0(sK11,xT)
& ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU) )
| ~ sP3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X0,sK11)],[f92]) ).
fof(f94,plain,
( ( ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),sK12)
& aElementOf0(sK12,xP)
& ~ aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU) )
| sP3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X0,sK12)],[f77]) ).
fof(f99,plain,
! [X0] :
( ( ( isMonotone0(X0)
| ? [X1,X2] :
( ~ sdtlseqdt0(sdtlpdtrp0(X0,X1),sdtlpdtrp0(X0,X2))
& sdtlseqdt0(X1,X2)
& aElementOf0(X1,szDzozmdt0(X0))
& aElementOf0(X2,szDzozmdt0(X0)) ) )
& ( ! [X1,X2] :
( sdtlseqdt0(sdtlpdtrp0(X0,X1),sdtlpdtrp0(X0,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X1,szDzozmdt0(X0))
| ~ aElementOf0(X2,szDzozmdt0(X0)) )
| ~ isMonotone0(X0) ) )
| ~ aFunction0(X0) ),
inference(nnf_transformation,[],[f58]) ).
fof(f100,plain,
! [X0] :
( ( ( isMonotone0(X0)
| ? [X1,X2] :
( ~ sdtlseqdt0(sdtlpdtrp0(X0,X1),sdtlpdtrp0(X0,X2))
& sdtlseqdt0(X1,X2)
& aElementOf0(X1,szDzozmdt0(X0))
& aElementOf0(X2,szDzozmdt0(X0)) ) )
& ( ! [X3,X4] :
( sdtlseqdt0(sdtlpdtrp0(X0,X3),sdtlpdtrp0(X0,X4))
| ~ sdtlseqdt0(X3,X4)
| ~ aElementOf0(X3,szDzozmdt0(X0))
| ~ aElementOf0(X4,szDzozmdt0(X0)) )
| ~ isMonotone0(X0) ) )
| ~ aFunction0(X0) ),
inference(rectify,[],[f99]) ).
fof(f101,plain,
! [X0] :
( ( ( isMonotone0(X0)
| ( ~ sdtlseqdt0(sdtlpdtrp0(X0,sK13(X0)),sdtlpdtrp0(X0,sK14(X0)))
& sdtlseqdt0(sK13(X0),sK14(X0))
& aElementOf0(sK13(X0),szDzozmdt0(X0))
& aElementOf0(sK14(X0),szDzozmdt0(X0)) ) )
& ( ! [X3,X4] :
( sdtlseqdt0(sdtlpdtrp0(X0,X3),sdtlpdtrp0(X0,X4))
| ~ sdtlseqdt0(X3,X4)
| ~ aElementOf0(X3,szDzozmdt0(X0))
| ~ aElementOf0(X4,szDzozmdt0(X0)) )
| ~ isMonotone0(X0) ) )
| ~ aFunction0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X1,sK13(X0)),skolemize(X2,sK14(X0))],[f100]) ).
fof(f142,plain,
xU = szRzazndt0(xf),
inference(cnf_transformation,[],[f88]) ).
fof(f143,plain,
szDzozmdt0(xf) = szRzazndt0(xf),
inference(cnf_transformation,[],[f88]) ).
fof(f144,plain,
isMonotone0(xf),
inference(cnf_transformation,[],[f88]) ).
fof(f145,plain,
! [X2,X3] :
( sdtlseqdt0(sdtlpdtrp0(xf,X2),sdtlpdtrp0(xf,X3))
| ~ sdtlseqdt0(X2,X3)
| ~ aElementOf0(X2,szDzozmdt0(xf))
| ~ aElementOf0(X3,szDzozmdt0(xf)) ),
inference(cnf_transformation,[],[f88]) ).
fof(f146,plain,
aFunction0(xf),
inference(cnf_transformation,[],[f88]) ).
fof(f151,plain,
aSet0(xU),
inference(cnf_transformation,[],[f88]) ).
fof(f156,plain,
! [X0] :
( sdtlpdtrp0(xf,X0) = X0
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f42]) ).
fof(f157,plain,
! [X0] :
( aElementOf0(X0,szDzozmdt0(xf))
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f42]) ).
fof(f160,plain,
! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[],[f43]) ).
fof(f167,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| ~ aElementOf0(X1,xT)
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[],[f89]) ).
fof(f168,plain,
! [X0] :
( sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[],[f89]) ).
fof(f169,plain,
! [X0] :
( aElementOf0(X0,xU)
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[],[f89]) ).
fof(f170,plain,
aSet0(xP),
inference(cnf_transformation,[],[f89]) ).
fof(f173,plain,
! [X1] :
( aElementOf0(sK10(X1),xP)
| ~ aElementOf0(X1,xU)
| sdtlseqdt0(X1,xp) ),
inference(cnf_transformation,[],[f90]) ).
fof(f174,plain,
! [X1] :
( ~ sdtlseqdt0(X1,sK10(X1))
| ~ aElementOf0(X1,xU)
| sdtlseqdt0(X1,xp) ),
inference(cnf_transformation,[],[f90]) ).
fof(f176,plain,
! [X0] :
( sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[],[f90]) ).
fof(f177,plain,
aElementOf0(xp,xU),
inference(cnf_transformation,[],[f90]) ).
fof(f180,plain,
( aElementOf0(sK11,xT)
| ~ sP3 ),
inference(cnf_transformation,[],[f93]) ).
fof(f181,plain,
( ~ sdtlseqdt0(sK11,sdtlpdtrp0(xf,xp))
| ~ sP3 ),
inference(cnf_transformation,[],[f93]) ).
fof(f183,plain,
( aElementOf0(sK12,xP)
| sP3 ),
inference(cnf_transformation,[],[f94]) ).
fof(f184,plain,
( ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),sK12)
| sP3 ),
inference(cnf_transformation,[],[f94]) ).
fof(f194,plain,
! [X3,X0,X4] :
( sdtlseqdt0(sdtlpdtrp0(X0,X3),sdtlpdtrp0(X0,X4))
| ~ sdtlseqdt0(X3,X4)
| ~ aElementOf0(X3,szDzozmdt0(X0))
| ~ aElementOf0(X4,szDzozmdt0(X0))
| ~ isMonotone0(X0)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f199,plain,
! [X0,X1] :
( aElementOf0(sdtlpdtrp0(X0,X1),szRzazndt0(X0))
| ~ aElementOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f218,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f225,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f232,definition,
( spl22_1
<=> sP3 ),
introduced(definition,[new_symbols(definition,[spl22_1])],[avatar_definition]) ).
fof(f234,plain,
( sP3
| ~ spl22_1 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f241,definition,
( spl22_3
<=> aElementOf0(sK12,xP) ),
introduced(definition,[new_symbols(definition,[spl22_3])],[avatar_definition]) ).
fof(f243,plain,
( aElementOf0(sK12,xP)
| ~ spl22_3 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f244,plain,
( spl22_1
| spl22_3 ),
inference(avatar_split_clause,[],[f183,f241,f232]) ).
fof(f246,definition,
( spl22_4
<=> sdtlseqdt0(sdtlpdtrp0(xf,xp),sK12) ),
introduced(definition,[new_symbols(definition,[spl22_4])],[avatar_definition]) ).
fof(f248,plain,
( ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),sK12)
| spl22_4 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f249,plain,
( spl22_1
| ~ spl22_4 ),
inference(avatar_split_clause,[],[f184,f246,f232]) ).
fof(f250,plain,
xU = szDzozmdt0(xf),
inference(forward_demodulation,[],[f143,f142]) ).
fof(f251,plain,
( aElement0(sK12)
| ~ aSet0(xP)
| ~ spl22_3 ),
inference(resolution,[],[f243,f218]) ).
fof(f252,plain,
( aElement0(sK12)
| ~ spl22_3 ),
inference(forward_subsumption_resolution,[],[f251,f170]) ).
fof(f253,plain,
( ! [X0] :
( ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),X0)
| ~ sdtlseqdt0(X0,sK12)
| ~ aElement0(sdtlpdtrp0(xf,xp))
| ~ aElement0(X0)
| ~ aElement0(sK12) )
| spl22_4 ),
inference(resolution,[],[f248,f225]) ).
fof(f256,plain,
( ! [X0] :
( ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),X0)
| ~ sdtlseqdt0(X0,sK12)
| ~ aElement0(sdtlpdtrp0(xf,xp))
| ~ aElement0(X0) )
| ~ spl22_3
| spl22_4 ),
inference(forward_subsumption_resolution,[],[f253,f252]) ).
fof(f267,definition,
( spl22_7
<=> aElement0(sdtlpdtrp0(xf,xp)) ),
introduced(definition,[new_symbols(definition,[spl22_7])],[avatar_definition]) ).
fof(f269,plain,
( ~ aElement0(sdtlpdtrp0(xf,xp))
| spl22_7 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f271,definition,
( spl22_8
<=> ! [X0] :
( ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),X0)
| ~ aElement0(X0)
| ~ sdtlseqdt0(X0,sK12) ) ),
introduced(definition,[new_symbols(definition,[spl22_8])],[avatar_definition]) ).
fof(f272,plain,
( ! [X0] :
( ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),X0)
| ~ aElement0(X0)
| ~ sdtlseqdt0(X0,sK12) )
| ~ spl22_8 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f273,plain,
( ~ spl22_7
| spl22_8
| ~ spl22_3
| spl22_4 ),
inference(avatar_split_clause,[],[f256,f246,f241,f271,f267]) ).
fof(f296,plain,
! [X0] :
( aElementOf0(sdtlpdtrp0(xf,X0),xU)
| ~ aElementOf0(X0,szDzozmdt0(xf))
| ~ aFunction0(xf) ),
inference(superposition,[],[f199,f142]) ).
fof(f301,plain,
! [X0] :
( aElementOf0(sdtlpdtrp0(xf,X0),xU)
| ~ aElementOf0(X0,szDzozmdt0(xf)) ),
inference(forward_subsumption_resolution,[],[f296,f146]) ).
fof(f303,plain,
! [X0] :
( aElementOf0(sdtlpdtrp0(xf,X0),xU)
| ~ aElementOf0(X0,xU) ),
inference(forward_demodulation,[],[f301,f250]) ).
fof(f394,plain,
! [X0] :
( aElementOf0(X0,xU)
| ~ aElementOf0(X0,xS) ),
inference(superposition,[],[f157,f250]) ).
fof(f460,plain,
! [X0,X1] :
( sdtlseqdt0(X0,sdtlpdtrp0(xf,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X0,szDzozmdt0(xf))
| ~ aElementOf0(X1,szDzozmdt0(xf))
| ~ isMonotone0(xf)
| ~ aFunction0(xf)
| ~ aElementOf0(X0,xS) ),
inference(superposition,[],[f194,f156]) ).
fof(f465,plain,
! [X0,X1] :
( sdtlseqdt0(X0,sdtlpdtrp0(xf,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X0,szDzozmdt0(xf))
| ~ aElementOf0(X1,szDzozmdt0(xf))
| ~ aFunction0(xf)
| ~ aElementOf0(X0,xS) ),
inference(forward_subsumption_resolution,[],[f460,f144]) ).
fof(f468,plain,
! [X0,X1] :
( sdtlseqdt0(X0,sdtlpdtrp0(xf,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X0,szDzozmdt0(xf))
| ~ aElementOf0(X1,szDzozmdt0(xf))
| ~ aElementOf0(X0,xS) ),
inference(forward_subsumption_resolution,[],[f465,f146]) ).
fof(f471,plain,
! [X0,X1] :
( sdtlseqdt0(X0,sdtlpdtrp0(xf,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szDzozmdt0(xf))
| ~ aElementOf0(X0,xS) ),
inference(forward_subsumption_resolution,[],[f468,f157]) ).
fof(f474,plain,
! [X0,X1] :
( sdtlseqdt0(X0,sdtlpdtrp0(xf,X1))
| ~ aElementOf0(X1,xU)
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X0,xS) ),
inference(forward_demodulation,[],[f471,f250]) ).
fof(f569,plain,
! [X0] :
( ~ aElementOf0(X0,xU)
| sdtlseqdt0(X0,xp)
| ~ aElementOf0(X0,xT)
| ~ aElementOf0(sK10(X0),xP) ),
inference(resolution,[],[f174,f167]) ).
fof(f575,plain,
! [X0] :
( sdtlseqdt0(X0,xp)
| ~ aElementOf0(X0,xU)
| ~ aElementOf0(X0,xT) ),
inference(forward_subsumption_resolution,[],[f569,f173]) ).
fof(f798,plain,
! [X0] :
( ~ aElementOf0(X0,xU)
| aElement0(sdtlpdtrp0(xf,X0))
| ~ aSet0(xU) ),
inference(resolution,[],[f303,f218]) ).
fof(f801,plain,
! [X0] :
( ~ aElementOf0(X0,xU)
| aElement0(sdtlpdtrp0(xf,X0)) ),
inference(forward_subsumption_resolution,[],[f798,f151]) ).
fof(f887,definition,
( spl22_51
<=> aElementOf0(sdtlpdtrp0(xf,xp),xU) ),
introduced(definition,[new_symbols(definition,[spl22_51])],[avatar_definition]) ).
fof(f888,plain,
( aElementOf0(sdtlpdtrp0(xf,xp),xU)
| ~ spl22_51 ),
inference(avatar_component_clause,[],[f887]) ).
fof(f889,plain,
( ~ aElementOf0(sdtlpdtrp0(xf,xp),xU)
| spl22_51 ),
inference(avatar_component_clause,[],[f887]) ).
fof(f1086,plain,
( ~ aElementOf0(xp,xU)
| spl22_51 ),
inference(resolution,[],[f889,f303]) ).
fof(f1091,plain,
( $false
| spl22_51 ),
inference(forward_subsumption_resolution,[],[f1086,f177]) ).
fof(f1092,plain,
spl22_51,
inference(avatar_contradiction_clause,[],[f1091]) ).
fof(f1130,plain,
( ~ aElementOf0(xp,xU)
| ~ sdtlseqdt0(sK11,xp)
| ~ aElementOf0(sK11,xS)
| ~ sP3 ),
inference(resolution,[],[f474,f181]) ).
fof(f1136,plain,
( ~ sdtlseqdt0(sK11,xp)
| ~ aElementOf0(sK11,xS)
| ~ sP3 ),
inference(forward_subsumption_resolution,[],[f1130,f177]) ).
fof(f1142,plain,
( ~ sdtlseqdt0(sK11,xp)
| ~ aElementOf0(sK11,xS)
| ~ spl22_1 ),
inference(forward_subsumption_resolution,[],[f1136,f234]) ).
fof(f1145,definition,
( spl22_63
<=> aElementOf0(sK11,xS) ),
introduced(definition,[new_symbols(definition,[spl22_63])],[avatar_definition]) ).
fof(f1146,plain,
( aElementOf0(sK11,xS)
| ~ spl22_63 ),
inference(avatar_component_clause,[],[f1145]) ).
fof(f1147,plain,
( ~ aElementOf0(sK11,xS)
| spl22_63 ),
inference(avatar_component_clause,[],[f1145]) ).
fof(f1149,definition,
( spl22_64
<=> sdtlseqdt0(sK11,xp) ),
introduced(definition,[new_symbols(definition,[spl22_64])],[avatar_definition]) ).
fof(f1151,plain,
( ~ sdtlseqdt0(sK11,xp)
| spl22_64 ),
inference(avatar_component_clause,[],[f1149]) ).
fof(f1152,plain,
( ~ spl22_63
| ~ spl22_64
| ~ spl22_1 ),
inference(avatar_split_clause,[],[f1142,f232,f1149,f1145]) ).
fof(f1153,plain,
( ~ aElementOf0(sK11,xT)
| spl22_63 ),
inference(resolution,[],[f1147,f160]) ).
fof(f1188,plain,
( ~ aElementOf0(sK11,xU)
| ~ aElementOf0(sK11,xT)
| spl22_64 ),
inference(resolution,[],[f1151,f575]) ).
fof(f1198,definition,
( spl22_66
<=> aElementOf0(sK11,xU) ),
introduced(definition,[new_symbols(definition,[spl22_66])],[avatar_definition]) ).
fof(f1199,plain,
( aElementOf0(sK11,xU)
| ~ spl22_66 ),
inference(avatar_component_clause,[],[f1198]) ).
fof(f1200,plain,
( ~ aElementOf0(sK11,xU)
| spl22_66 ),
inference(avatar_component_clause,[],[f1198]) ).
fof(f1205,plain,
( ~ sP3
| spl22_63 ),
inference(resolution,[],[f1153,f180]) ).
fof(f1206,plain,
( $false
| ~ spl22_1
| spl22_63 ),
inference(forward_subsumption_resolution,[],[f1205,f234]) ).
fof(f1207,plain,
( ~ spl22_1
| spl22_63 ),
inference(avatar_contradiction_clause,[],[f1206]) ).
fof(f1273,plain,
( ~ aElementOf0(sK11,xS)
| spl22_66 ),
inference(resolution,[],[f1200,f394]) ).
fof(f1317,plain,
( aElement0(sdtlpdtrp0(xf,xp))
| ~ aSet0(xU)
| ~ spl22_51 ),
inference(resolution,[],[f888,f218]) ).
fof(f1320,plain,
( ~ aSet0(xU)
| spl22_7
| ~ spl22_51 ),
inference(forward_subsumption_resolution,[],[f1317,f269]) ).
fof(f1321,plain,
( $false
| spl22_7
| ~ spl22_51 ),
inference(forward_subsumption_resolution,[],[f1320,f151]) ).
fof(f1322,plain,
( spl22_7
| ~ spl22_51 ),
inference(avatar_contradiction_clause,[],[f1321]) ).
fof(f1355,plain,
( ! [X0] :
( ~ aElement0(sdtlpdtrp0(xf,X0))
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),sK12)
| ~ sdtlseqdt0(xp,X0)
| ~ aElementOf0(xp,szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf)) )
| ~ spl22_8 ),
inference(resolution,[],[f272,f145]) ).
fof(f1379,plain,
( ! [X0] :
( ~ aElementOf0(xp,xU)
| ~ aElement0(sdtlpdtrp0(xf,X0))
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),sK12)
| ~ sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,szDzozmdt0(xf)) )
| ~ spl22_8 ),
inference(forward_demodulation,[],[f1355,f250]) ).
fof(f1396,plain,
( ! [X0] :
( ~ aElement0(sdtlpdtrp0(xf,X0))
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),sK12)
| ~ sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,szDzozmdt0(xf)) )
| ~ spl22_8 ),
inference(forward_subsumption_resolution,[],[f1379,f177]) ).
fof(f1401,plain,
( ! [X0] :
( ~ aElementOf0(X0,xU)
| ~ aElement0(sdtlpdtrp0(xf,X0))
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),sK12)
| ~ sdtlseqdt0(xp,X0) )
| ~ spl22_8 ),
inference(forward_demodulation,[],[f1396,f250]) ).
fof(f1405,plain,
( ! [X0] :
( ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),sK12)
| ~ aElementOf0(X0,xU)
| ~ sdtlseqdt0(xp,X0) )
| ~ spl22_8 ),
inference(forward_subsumption_resolution,[],[f1401,f801]) ).
fof(f1921,plain,
( ~ aElementOf0(sK12,xU)
| ~ sdtlseqdt0(xp,sK12)
| ~ aElementOf0(sK12,xP)
| ~ spl22_8 ),
inference(resolution,[],[f1405,f168]) ).
fof(f1933,plain,
( ~ sdtlseqdt0(xp,sK12)
| ~ aElementOf0(sK12,xP)
| ~ spl22_8 ),
inference(forward_subsumption_resolution,[],[f1921,f169]) ).
fof(f1936,plain,
( ~ aElementOf0(sK12,xP)
| ~ spl22_8 ),
inference(forward_subsumption_resolution,[],[f1933,f176]) ).
fof(f1937,plain,
( $false
| ~ spl22_3
| ~ spl22_8 ),
inference(forward_subsumption_resolution,[],[f1936,f243]) ).
fof(f1938,plain,
( ~ spl22_3
| ~ spl22_8 ),
inference(avatar_contradiction_clause,[],[f1937]) ).
fof(f1939,plain,
( $false
| ~ spl22_63
| spl22_66 ),
inference(forward_subsumption_resolution,[],[f1273,f1146]) ).
fof(f1940,plain,
( ~ spl22_63
| spl22_66 ),
inference(avatar_contradiction_clause,[],[f1939]) ).
fof(f1961,plain,
( ~ aElementOf0(sK11,xT)
| spl22_64
| ~ spl22_66 ),
inference(forward_subsumption_resolution,[],[f1188,f1199]) ).
fof(f2034,plain,
( ~ sP3
| spl22_64
| ~ spl22_66 ),
inference(resolution,[],[f1961,f180]) ).
fof(f2035,plain,
( $false
| ~ spl22_1
| spl22_64
| ~ spl22_66 ),
inference(forward_subsumption_resolution,[],[f2034,f234]) ).
fof(f2036,plain,
( ~ spl22_1
| spl22_64
| ~ spl22_66 ),
inference(avatar_contradiction_clause,[],[f2035]) ).
cnf(s2,plain,
( spl22_1
| spl22_3 ),
inference(sat_conversion,[],[f244]) ).
cnf(s3,plain,
( spl22_1
| ~ spl22_4 ),
inference(sat_conversion,[],[f249]) ).
cnf(s5,plain,
( ~ spl22_3
| spl22_4
| ~ spl22_7
| spl22_8 ),
inference(sat_conversion,[],[f273]) ).
cnf(s43,plain,
spl22_51,
inference(sat_conversion,[],[f1092]) ).
cnf(s47,plain,
( ~ spl22_1
| ~ spl22_63
| ~ spl22_64 ),
inference(sat_conversion,[],[f1152]) ).
cnf(s49,plain,
( ~ spl22_1
| spl22_63 ),
inference(sat_conversion,[],[f1207]) ).
cnf(s55,plain,
( spl22_7
| ~ spl22_51 ),
inference(sat_conversion,[],[f1322]) ).
cnf(s74,plain,
( ~ spl22_3
| ~ spl22_8 ),
inference(sat_conversion,[],[f1938]) ).
cnf(s75,plain,
( ~ spl22_63
| spl22_66 ),
inference(sat_conversion,[],[f1940]) ).
cnf(s80,plain,
( ~ spl22_1
| spl22_64
| ~ spl22_66 ),
inference(sat_conversion,[],[f2036]) ).
cnf(s81,plain,
spl22_7,
inference(rat,[],[s55,s43]) ).
cnf(s93,plain,
( ~ spl22_3
| spl22_4
| spl22_8 ),
inference(rat,[],[s5,s81]) ).
cnf(s94,plain,
spl22_1,
inference(rat,[],[s93,s74,s2,s3]) ).
cnf(s96,plain,
spl22_63,
inference(rat,[],[s49,s94]) ).
cnf(s97,plain,
spl22_66,
inference(rat,[],[s75,s96]) ).
cnf(s98,plain,
~ spl22_64,
inference(rat,[],[s47,s94,s96]) ).
cnf(s99,plain,
$false,
inference(rat,[],[s80,s94,s97,s98]) ).
fof(f2037,plain,
$false,
inference(avatar_sat_refutation,[],[s99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT386+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 % Computer : n005.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 15:13:17 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 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
% 4.25/1.53 % (4120708)Detected formulas, will run a generic FOF schedule.
% 4.25/1.53 % (4120718)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1685636616:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.25/1.53 % (4120717)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2267026249:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.25/1.53 % (4120714)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=3827338444:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.25/1.53 % (4120716)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=759271806:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.25/1.53 % (4120715)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=1244692566:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.25/1.53 % (4120713)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=124613967:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.25/1.53 % (4120719)dis-21_1_sil=8000:lcm=predicate:random_seed=669711780:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 4.25/1.53 % (4120718)Instruction limit reached!
% 4.25/1.53 % (4120718)------------------------------
% 4.25/1.53 % (4120718)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.25/1.53 % (4120718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.53 % (4120718)CaDiCaL version: 2.1.3
% 4.25/1.53 % (4120718)Termination reason: Instruction limit
% 4.25/1.53 % (4120718)Termination phase: Saturation
% 4.25/1.53 % (4120718)Time elapsed: 0.054 s
% 4.25/1.53 % (4120718)Peak memory usage: 90 MB
% 4.25/1.53 % (4120718)Instructions burned: 140 (million)
% 4.25/1.53 % (4120716)Instruction limit reached!
% 4.25/1.53 % (4120716)------------------------------
% 4.25/1.53 % (4120716)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.25/1.53 % (4120716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.53 % (4120716)CaDiCaL version: 2.1.3
% 4.25/1.53 % (4120716)Termination reason: Instruction limit
% 4.25/1.53 % (4120716)Termination phase: Saturation
% 4.25/1.53 % (4120716)Time elapsed: 0.070 s
% 4.25/1.53 % (4120716)Peak memory usage: 89 MB
% 4.25/1.53 % (4120716)Instructions burned: 109 (million)
% 4.25/1.53 % (4120717)Instruction limit reached!
% 4.25/1.53 % (4120717)------------------------------
% 4.25/1.53 % (4120717)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.25/1.53 % (4120717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.53 % (4120717)CaDiCaL version: 2.1.3
% 4.25/1.53 % (4120717)Termination reason: Instruction limit
% 4.25/1.53 % (4120717)Termination phase: Saturation
% 4.25/1.53 % (4120717)Time elapsed: 0.073 s
% 4.25/1.53 % (4120717)Peak memory usage: 88 MB
% 4.25/1.53 % (4120717)Instructions burned: 121 (million)
% 4.25/1.53 % (4120719)Instruction limit reached!
% 4.25/1.53 % (4120719)------------------------------
% 4.25/1.53 % (4120719)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.25/1.53 % (4120719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.53 % (4120719)CaDiCaL version: 2.1.3
% 4.25/1.53 % (4120719)Termination reason: Instruction limit
% 4.25/1.53 % (4120719)Termination phase: Saturation
% 4.25/1.53 % (4120719)Time elapsed: 0.073 s
% 4.25/1.53 % (4120719)Peak memory usage: 91 MB
% 4.25/1.53 % (4120719)Instructions burned: 129 (million)
% 4.25/1.53 % (4120727)lrs+10_1_sil=8000:sp=occurrence:random_seed=3727213566:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.25/1.53 % (4120730)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=2826300481:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.25/1.53 % (4120729)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2802508465:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.25/1.53 % (4120728)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3581041390:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.25/1.53 % (4120730)Instruction limit reached!
% 4.25/1.53 % (4120730)------------------------------
% 4.25/1.53 % (4120730)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.25/1.53 % (4120730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.53 % (4120730)CaDiCaL version: 2.1.3
% 4.25/1.53 % (4120730)Termination reason: Instruction limit
% 4.25/1.53 % (4120730)Termination phase: Saturation
% 4.25/1.53 % (4120730)Time elapsed: 0.071 s
% 4.25/1.53 % (4120730)Peak memory usage: 89 MB
% 4.25/1.53 % (4120730)Instructions burned: 250 (million)
% 4.25/1.53 % (4120728)Instruction limit reached!
% 4.25/1.53 % (4120728)------------------------------
% 4.25/1.53 % (4120728)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.25/1.53 % (4120728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.53 % (4120728)CaDiCaL version: 2.1.3
% 4.25/1.53 % (4120728)Termination reason: Instruction limit
% 4.25/1.53 % (4120728)Termination phase: Saturation
% 4.25/1.53 % (4120728)Time elapsed: 0.065 s
% 4.25/1.53 % (4120728)Peak memory usage: 89 MB
% 4.25/1.53 % (4120728)Instructions burned: 160 (million)
% 4.25/1.53 % (4120735)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=691399889:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 4.25/1.53 % (4120727)Instruction limit reached!
% 4.25/1.53 % (4120727)------------------------------
% 4.25/1.53 % (4120727)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.25/1.53 % (4120727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.53 % (4120727)CaDiCaL version: 2.1.3
% 4.25/1.53 % (4120727)Termination reason: Instruction limit
% 4.25/1.53 % (4120727)Termination phase: Saturation
% 4.25/1.53 % (4120727)Time elapsed: 0.186 s
% 4.25/1.53 % (4120727)Peak memory usage: 91 MB
% 4.25/1.53 % (4120727)Instructions burned: 285 (million)
% 4.25/1.53 % (4120735)First to succeed.
% 4.25/1.53 % (4120735)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4120708"
% 4.25/1.53 % (4120736)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=286953933:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 4.25/1.53 % (4120729)Instruction limit reached!
% 4.25/1.53 % (4120729)------------------------------
% 4.25/1.53 % (4120729)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.25/1.53 % (4120729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.53 % (4120729)CaDiCaL version: 2.1.3
% 4.25/1.53 % (4120729)Termination reason: Instruction limit
% 4.25/1.53 % (4120729)Termination phase: Saturation
% 4.25/1.53 % (4120729)Time elapsed: 0.230 s
% 4.25/1.53 % (4120729)Peak memory usage: 92 MB
% 4.25/1.53 % (4120729)Instructions burned: 325 (million)
% 4.25/1.53 % (4120738)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3481781627:cts=off:i=113:fsr=off:ss=included:sgt=4_2995 on theBenchmark for (2995ds/113Mi)
% 4.25/1.53 % (4120735)Refutation found. Thanks to Tanya!
% 4.25/1.53 % SZS status Theorem for theBenchmark
% 4.25/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 5.28/1.72 % (4120735)------------------------------
% 5.28/1.72 % (4120735)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.28/1.72 % (4120735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.28/1.72 % (4120735)CaDiCaL version: 2.1.3
% 5.28/1.72 % (4120735)Termination reason: Refutation
% 5.28/1.72 % (4120735)Time elapsed: 0.031 s
% 5.28/1.72 % (4120735)Peak memory usage: 90 MB
% 5.28/1.72 % (4120735)Instructions burned: 87 (million)
% 5.28/1.72 % (4120735)------------------------------
% 5.28/1.72 % (4120735)------------------------------
% 5.28/1.72 % (4120708)Success in time 0.654 s
% 5.28/1.72 % Vampire exiting
%------------------------------------------------------------------------------