%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LAT381+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 11:48:44 AM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of formulae : 110 ( 13 unt; 0 def)
% Number of atoms : 584 ( 9 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 806 ( 332 ~; 349 |; 91 &)
% ( 12 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 304 ( 286 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f4,axiom,
! [X0] :
( aSet0(X0)
=> ( isEmpty0(X0)
<=> ~ ? [X1] : aElementOf0(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmpty) ).
fof(f5,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(f7,axiom,
! [X0] :
( aElement0(X0)
=> sdtlseqdt0(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mARefl) ).
fof(f8,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X0) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mASymm) ).
fof(f9,axiom,
! [X0,X1,X2] :
( ( aElement0(X0)
& aElement0(X1)
& aElement0(X2) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTrans) ).
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
=> ! [X2] :
( aLowerBoundOfIn0(X2,X1,X0)
<=> ( aElementOf0(X2,X0)
& ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLB) ).
fof(f11,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
=> ! [X2] :
( aUpperBoundOfIn0(X2,X1,X0)
<=> ( aElementOf0(X2,X0)
& ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefUB) ).
fof(f12,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
=> ! [X2] :
( aInfimumOfIn0(X2,X1,X0)
<=> ( aElementOf0(X2,X0)
& aLowerBoundOfIn0(X2,X1,X0)
& ! [X3] :
( aLowerBoundOfIn0(X3,X1,X0)
=> sdtlseqdt0(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefInf) ).
fof(f13,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
=> ! [X2] :
( aSupremumOfIn0(X2,X1,X0)
<=> ( aElementOf0(X2,X0)
& aUpperBoundOfIn0(X2,X1,X0)
& ! [X3] :
( aUpperBoundOfIn0(X3,X1,X0)
=> sdtlseqdt0(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSup) ).
fof(f14,axiom,
aSet0(xT),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__725) ).
fof(f15,axiom,
aSubsetOf0(xS,xT),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__725_01) ).
fof(f16,axiom,
( aSupremumOfIn0(xu,xS,xT)
& aSupremumOfIn0(xv,xS,xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__744) ).
fof(f17,conjecture,
xu = xv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f18,negated_conjecture,
xu != xv,
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f22,plain,
xu != xv,
inference(flattening,[],[f18]) ).
fof(f23,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f24,plain,
! [X0] :
( ( isEmpty0(X0)
<=> ! [X1] : ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f25,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f26,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f27,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f28,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(ennf_transformation,[],[f9]) ).
fof(f30,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( aLowerBoundOfIn0(X2,X1,X0)
<=> ( aElementOf0(X2,X0)
& ! [X3] :
( sdtlseqdt0(X2,X3)
| ~ aElementOf0(X3,X1) ) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f32,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( aUpperBoundOfIn0(X2,X1,X0)
<=> ( aElementOf0(X2,X0)
& ! [X3] :
( sdtlseqdt0(X3,X2)
| ~ aElementOf0(X3,X1) ) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f33,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( aInfimumOfIn0(X2,X1,X0)
<=> ( aElementOf0(X2,X0)
& aLowerBoundOfIn0(X2,X1,X0)
& ! [X3] :
( sdtlseqdt0(X3,X2)
| ~ aLowerBoundOfIn0(X3,X1,X0) ) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f34,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( aSupremumOfIn0(X2,X1,X0)
<=> ( aElementOf0(X2,X0)
& aUpperBoundOfIn0(X2,X1,X0)
& ! [X3] :
( sdtlseqdt0(X2,X3)
| ~ aUpperBoundOfIn0(X3,X1,X0) ) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f35,plain,
! [X0] :
( ( ( isEmpty0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ! [X1] : ~ aElementOf0(X1,X0)
| ~ isEmpty0(X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f24]) ).
fof(f36,plain,
! [X0] :
( ( ( isEmpty0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ! [X2] : ~ aElementOf0(X2,X0)
| ~ isEmpty0(X0) ) )
| ~ aSet0(X0) ),
inference(rectify,[],[f35]) ).
fof(f37,plain,
! [X0] :
( ( ( isEmpty0(X0)
| aElementOf0(sK0(X0),X0) )
& ( ! [X2] : ~ aElementOf0(X2,X0)
| ~ isEmpty0(X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f36]) ).
fof(f38,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f25]) ).
fof(f39,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(flattening,[],[f38]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(rectify,[],[f39]) ).
fof(f41,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK1(X0,X1),X0)
& aElementOf0(sK1(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f40]) ).
fof(f42,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aLowerBoundOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| ? [X3] :
( ~ sdtlseqdt0(X2,X3)
& aElementOf0(X3,X1) ) )
& ( ( aElementOf0(X2,X0)
& ! [X3] :
( sdtlseqdt0(X2,X3)
| ~ aElementOf0(X3,X1) ) )
| ~ aLowerBoundOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f31]) ).
fof(f43,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aLowerBoundOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| ? [X3] :
( ~ sdtlseqdt0(X2,X3)
& aElementOf0(X3,X1) ) )
& ( ( aElementOf0(X2,X0)
& ! [X3] :
( sdtlseqdt0(X2,X3)
| ~ aElementOf0(X3,X1) ) )
| ~ aLowerBoundOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aLowerBoundOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| ? [X3] :
( ~ sdtlseqdt0(X2,X3)
& aElementOf0(X3,X1) ) )
& ( ( aElementOf0(X2,X0)
& ! [X4] :
( sdtlseqdt0(X2,X4)
| ~ aElementOf0(X4,X1) ) )
| ~ aLowerBoundOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(rectify,[],[f43]) ).
fof(f45,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aLowerBoundOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| ( ~ sdtlseqdt0(X2,sK2(X1,X2))
& aElementOf0(sK2(X1,X2),X1) ) )
& ( ( aElementOf0(X2,X0)
& ! [X4] :
( sdtlseqdt0(X2,X4)
| ~ aElementOf0(X4,X1) ) )
| ~ aLowerBoundOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X1,X2))],[f44]) ).
fof(f46,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aUpperBoundOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| ? [X3] :
( ~ sdtlseqdt0(X3,X2)
& aElementOf0(X3,X1) ) )
& ( ( aElementOf0(X2,X0)
& ! [X3] :
( sdtlseqdt0(X3,X2)
| ~ aElementOf0(X3,X1) ) )
| ~ aUpperBoundOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f32]) ).
fof(f47,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aUpperBoundOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| ? [X3] :
( ~ sdtlseqdt0(X3,X2)
& aElementOf0(X3,X1) ) )
& ( ( aElementOf0(X2,X0)
& ! [X3] :
( sdtlseqdt0(X3,X2)
| ~ aElementOf0(X3,X1) ) )
| ~ aUpperBoundOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aUpperBoundOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| ? [X3] :
( ~ sdtlseqdt0(X3,X2)
& aElementOf0(X3,X1) ) )
& ( ( aElementOf0(X2,X0)
& ! [X4] :
( sdtlseqdt0(X4,X2)
| ~ aElementOf0(X4,X1) ) )
| ~ aUpperBoundOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(rectify,[],[f47]) ).
fof(f49,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aUpperBoundOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| ( ~ sdtlseqdt0(sK3(X1,X2),X2)
& aElementOf0(sK3(X1,X2),X1) ) )
& ( ( aElementOf0(X2,X0)
& ! [X4] :
( sdtlseqdt0(X4,X2)
| ~ aElementOf0(X4,X1) ) )
| ~ aUpperBoundOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X1,X2))],[f48]) ).
fof(f50,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aInfimumOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| ~ aLowerBoundOfIn0(X2,X1,X0)
| ? [X3] :
( ~ sdtlseqdt0(X3,X2)
& aLowerBoundOfIn0(X3,X1,X0) ) )
& ( ( aElementOf0(X2,X0)
& aLowerBoundOfIn0(X2,X1,X0)
& ! [X3] :
( sdtlseqdt0(X3,X2)
| ~ aLowerBoundOfIn0(X3,X1,X0) ) )
| ~ aInfimumOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f33]) ).
fof(f51,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aInfimumOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| ~ aLowerBoundOfIn0(X2,X1,X0)
| ? [X3] :
( ~ sdtlseqdt0(X3,X2)
& aLowerBoundOfIn0(X3,X1,X0) ) )
& ( ( aElementOf0(X2,X0)
& aLowerBoundOfIn0(X2,X1,X0)
& ! [X3] :
( sdtlseqdt0(X3,X2)
| ~ aLowerBoundOfIn0(X3,X1,X0) ) )
| ~ aInfimumOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aInfimumOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| ~ aLowerBoundOfIn0(X2,X1,X0)
| ? [X3] :
( ~ sdtlseqdt0(X3,X2)
& aLowerBoundOfIn0(X3,X1,X0) ) )
& ( ( aElementOf0(X2,X0)
& aLowerBoundOfIn0(X2,X1,X0)
& ! [X4] :
( sdtlseqdt0(X4,X2)
| ~ aLowerBoundOfIn0(X4,X1,X0) ) )
| ~ aInfimumOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(rectify,[],[f51]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aInfimumOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| ~ aLowerBoundOfIn0(X2,X1,X0)
| ( ~ sdtlseqdt0(sK4(X0,X1,X2),X2)
& aLowerBoundOfIn0(sK4(X0,X1,X2),X1,X0) ) )
& ( ( aElementOf0(X2,X0)
& aLowerBoundOfIn0(X2,X1,X0)
& ! [X4] :
( sdtlseqdt0(X4,X2)
| ~ aLowerBoundOfIn0(X4,X1,X0) ) )
| ~ aInfimumOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f52]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aSupremumOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| ~ aUpperBoundOfIn0(X2,X1,X0)
| ? [X3] :
( ~ sdtlseqdt0(X2,X3)
& aUpperBoundOfIn0(X3,X1,X0) ) )
& ( ( aElementOf0(X2,X0)
& aUpperBoundOfIn0(X2,X1,X0)
& ! [X3] :
( sdtlseqdt0(X2,X3)
| ~ aUpperBoundOfIn0(X3,X1,X0) ) )
| ~ aSupremumOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f34]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aSupremumOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| ~ aUpperBoundOfIn0(X2,X1,X0)
| ? [X3] :
( ~ sdtlseqdt0(X2,X3)
& aUpperBoundOfIn0(X3,X1,X0) ) )
& ( ( aElementOf0(X2,X0)
& aUpperBoundOfIn0(X2,X1,X0)
& ! [X3] :
( sdtlseqdt0(X2,X3)
| ~ aUpperBoundOfIn0(X3,X1,X0) ) )
| ~ aSupremumOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aSupremumOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| ~ aUpperBoundOfIn0(X2,X1,X0)
| ? [X3] :
( ~ sdtlseqdt0(X2,X3)
& aUpperBoundOfIn0(X3,X1,X0) ) )
& ( ( aElementOf0(X2,X0)
& aUpperBoundOfIn0(X2,X1,X0)
& ! [X4] :
( sdtlseqdt0(X2,X4)
| ~ aUpperBoundOfIn0(X4,X1,X0) ) )
| ~ aSupremumOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(rectify,[],[f55]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aSupremumOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| ~ aUpperBoundOfIn0(X2,X1,X0)
| ( ~ sdtlseqdt0(X2,sK5(X0,X1,X2))
& aUpperBoundOfIn0(sK5(X0,X1,X2),X1,X0) ) )
& ( ( aElementOf0(X2,X0)
& aUpperBoundOfIn0(X2,X1,X0)
& ! [X4] :
( sdtlseqdt0(X2,X4)
| ~ aUpperBoundOfIn0(X4,X1,X0) ) )
| ~ aSupremumOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f59,plain,
! [X2,X0] :
( ~ aElementOf0(X2,X0)
| ~ isEmpty0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f60,plain,
! [X0] :
( isEmpty0(X0)
| aElementOf0(sK0(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f61,plain,
! [X3,X0,X1] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f62,plain,
! [X0,X1] :
( aSet0(X0)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f63,plain,
! [X0,X1] :
( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| aElementOf0(sK1(X0,X1),X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f64,plain,
! [X0,X1] :
( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ~ aElementOf0(sK1(X0,X1),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f65,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f66,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f67,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f68,plain,
! [X2,X0,X1,X4] :
( sdtlseqdt0(X2,X4)
| ~ aElementOf0(X4,X1)
| ~ aLowerBoundOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f69,plain,
! [X2,X0,X1] :
( aElementOf0(X2,X0)
| ~ aLowerBoundOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f70,plain,
! [X2,X0,X1] :
( aLowerBoundOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| aElementOf0(sK2(X1,X2),X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f71,plain,
! [X2,X0,X1] :
( aLowerBoundOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| ~ sdtlseqdt0(X2,sK2(X1,X2))
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f72,plain,
! [X2,X0,X1,X4] :
( sdtlseqdt0(X4,X2)
| ~ aElementOf0(X4,X1)
| ~ aUpperBoundOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f73,plain,
! [X2,X0,X1] :
( aElementOf0(X2,X0)
| ~ aUpperBoundOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f74,plain,
! [X2,X0,X1] :
( aUpperBoundOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| aElementOf0(sK3(X1,X2),X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f75,plain,
! [X2,X0,X1] :
( aUpperBoundOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| ~ sdtlseqdt0(sK3(X1,X2),X2)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f76,plain,
! [X2,X0,X1,X4] :
( sdtlseqdt0(X4,X2)
| ~ aLowerBoundOfIn0(X4,X1,X0)
| ~ aInfimumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f79,plain,
! [X2,X0,X1] :
( aInfimumOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| ~ aLowerBoundOfIn0(X2,X1,X0)
| aLowerBoundOfIn0(sK4(X0,X1,X2),X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f80,plain,
! [X2,X0,X1] :
( aInfimumOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| ~ aLowerBoundOfIn0(X2,X1,X0)
| ~ sdtlseqdt0(sK4(X0,X1,X2),X2)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f81,plain,
! [X2,X0,X1,X4] :
( sdtlseqdt0(X2,X4)
| ~ aUpperBoundOfIn0(X4,X1,X0)
| ~ aSupremumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f82,plain,
! [X2,X0,X1] :
( aUpperBoundOfIn0(X2,X1,X0)
| ~ aSupremumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f83,plain,
! [X2,X0,X1] :
( aElementOf0(X2,X0)
| ~ aSupremumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f84,plain,
! [X2,X0,X1] :
( aSupremumOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| ~ aUpperBoundOfIn0(X2,X1,X0)
| aUpperBoundOfIn0(sK5(X0,X1,X2),X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f85,plain,
! [X2,X0,X1] :
( aSupremumOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| ~ aUpperBoundOfIn0(X2,X1,X0)
| ~ sdtlseqdt0(X2,sK5(X0,X1,X2))
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f86,plain,
aSet0(xT),
inference(cnf_transformation,[],[f14]) ).
fof(f87,plain,
aSubsetOf0(xS,xT),
inference(cnf_transformation,[],[f15]) ).
fof(f88,plain,
aSupremumOfIn0(xv,xS,xT),
inference(cnf_transformation,[],[f16]) ).
fof(f89,plain,
aSupremumOfIn0(xu,xS,xT),
inference(cnf_transformation,[],[f16]) ).
fof(f90,plain,
xu != xv,
inference(cnf_transformation,[],[f22]) ).
fof(f91,plain,
! [X0,X1] :
( ~ aElement0(X0)
| aElementOf0(X0,X1)
| ~ aSet0(X1) ),
inference(consistent_polarity_flipping,[],[f58]) ).
fof(f92,plain,
! [X0] :
( isEmpty0(X0)
| ~ aElementOf0(sK0(X0),X0)
| ~ aSet0(X0) ),
inference(consistent_polarity_flipping,[],[f60]) ).
fof(f93,plain,
! [X0,X1] :
( aElementOf0(X0,X1)
| ~ isEmpty0(X1)
| ~ aSet0(X1) ),
inference(consistent_polarity_flipping,[],[f59]) ).
fof(f94,plain,
! [X0,X1] :
( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| aElementOf0(sK1(X0,X1),X0)
| ~ aSet0(X0) ),
inference(consistent_polarity_flipping,[],[f64]) ).
fof(f95,plain,
! [X0,X1] :
( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ~ aElementOf0(sK1(X0,X1),X1)
| ~ aSet0(X0) ),
inference(consistent_polarity_flipping,[],[f63]) ).
fof(f96,plain,
! [X2,X0,X1] :
( ~ aElementOf0(X0,X1)
| aElementOf0(X0,X2)
| ~ aSubsetOf0(X2,X1)
| ~ aSet0(X1) ),
inference(consistent_polarity_flipping,[],[f61]) ).
fof(f97,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| aElement0(X0) ),
inference(consistent_polarity_flipping,[],[f65]) ).
fof(f98,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| aElement0(X0)
| aElement0(X1) ),
inference(consistent_polarity_flipping,[],[f66]) ).
fof(f99,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X2,X1)
| aElement0(X0)
| aElement0(X2)
| aElement0(X1) ),
inference(consistent_polarity_flipping,[],[f67]) ).
fof(f100,plain,
! [X2,X0,X1] :
( ~ aLowerBoundOfIn0(X2,X1,X0)
| aElementOf0(X2,X0)
| ~ sdtlseqdt0(X2,sK2(X1,X2))
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(consistent_polarity_flipping,[],[f71]) ).
fof(f101,plain,
! [X2,X0,X1] :
( ~ aLowerBoundOfIn0(X2,X1,X0)
| aElementOf0(X2,X0)
| ~ aElementOf0(sK2(X1,X2),X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(consistent_polarity_flipping,[],[f70]) ).
fof(f102,plain,
! [X2,X0,X1] :
( ~ aElementOf0(X0,X1)
| aLowerBoundOfIn0(X0,X2,X1)
| ~ aSubsetOf0(X2,X1)
| ~ aSet0(X1) ),
inference(consistent_polarity_flipping,[],[f69]) ).
fof(f103,plain,
! [X2,X0,X1,X4] :
( sdtlseqdt0(X2,X4)
| aElementOf0(X4,X1)
| aLowerBoundOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(consistent_polarity_flipping,[],[f68]) ).
fof(f104,plain,
! [X2,X0,X1] :
( ~ aUpperBoundOfIn0(X2,X1,X0)
| aElementOf0(X2,X0)
| ~ sdtlseqdt0(sK3(X1,X2),X2)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(consistent_polarity_flipping,[],[f75]) ).
fof(f105,plain,
! [X2,X0,X1] :
( ~ aUpperBoundOfIn0(X2,X1,X0)
| aElementOf0(X2,X0)
| ~ aElementOf0(sK3(X1,X2),X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(consistent_polarity_flipping,[],[f74]) ).
fof(f106,plain,
! [X2,X0,X1] :
( ~ aElementOf0(X0,X1)
| aUpperBoundOfIn0(X0,X2,X1)
| ~ aSubsetOf0(X2,X1)
| ~ aSet0(X1) ),
inference(consistent_polarity_flipping,[],[f73]) ).
fof(f107,plain,
! [X2,X0,X1,X4] :
( sdtlseqdt0(X4,X2)
| aElementOf0(X4,X1)
| aUpperBoundOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(consistent_polarity_flipping,[],[f72]) ).
fof(f108,plain,
! [X2,X0,X1] :
( ~ aInfimumOfIn0(X2,X1,X0)
| aElementOf0(X2,X0)
| aLowerBoundOfIn0(X2,X1,X0)
| ~ sdtlseqdt0(sK4(X0,X1,X2),X2)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(consistent_polarity_flipping,[],[f80]) ).
fof(f109,plain,
! [X2,X0,X1] :
( ~ aInfimumOfIn0(X2,X1,X0)
| aElementOf0(X2,X0)
| aLowerBoundOfIn0(X2,X1,X0)
| ~ aLowerBoundOfIn0(sK4(X0,X1,X2),X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(consistent_polarity_flipping,[],[f79]) ).
fof(f110,plain,
! [X2,X3,X0,X1] :
( sdtlseqdt0(X0,X1)
| aLowerBoundOfIn0(X0,X2,X3)
| aInfimumOfIn0(X1,X2,X3)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3) ),
inference(consistent_polarity_flipping,[],[f76]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ aSupremumOfIn0(X2,X1,X0)
| aElementOf0(X2,X0)
| aUpperBoundOfIn0(X2,X1,X0)
| ~ sdtlseqdt0(X2,sK5(X0,X1,X2))
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(consistent_polarity_flipping,[],[f85]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ aSupremumOfIn0(X2,X1,X0)
| aElementOf0(X2,X0)
| aUpperBoundOfIn0(X2,X1,X0)
| ~ aUpperBoundOfIn0(sK5(X0,X1,X2),X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(consistent_polarity_flipping,[],[f84]) ).
fof(f113,plain,
! [X2,X0,X1] :
( ~ aElementOf0(X0,X1)
| aSupremumOfIn0(X0,X2,X1)
| ~ aSubsetOf0(X2,X1)
| ~ aSet0(X1) ),
inference(consistent_polarity_flipping,[],[f83]) ).
fof(f114,plain,
! [X2,X0,X1] :
( ~ aUpperBoundOfIn0(X0,X1,X2)
| aSupremumOfIn0(X0,X1,X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2) ),
inference(consistent_polarity_flipping,[],[f82]) ).
fof(f115,plain,
! [X2,X3,X0,X1] :
( sdtlseqdt0(X0,X1)
| aUpperBoundOfIn0(X1,X2,X3)
| aSupremumOfIn0(X0,X2,X3)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3) ),
inference(consistent_polarity_flipping,[],[f81]) ).
fof(f116,plain,
~ aSupremumOfIn0(xu,xS,xT),
inference(consistent_polarity_flipping,[],[f89]) ).
fof(f117,plain,
~ aSupremumOfIn0(xv,xS,xT),
inference(consistent_polarity_flipping,[],[f88]) ).
fof(f146,plain,
$false,
inference(finite_model_not_found_(exhaustively_excluded_all_possible_domain_size_assignments),[],[f91,f92,f93,f94,f95,f62,f96,f97,f98,f99,f100,f101,f102,f103,f104,f105,f106,f107,f108,f109,f110,f111,f112,f113,f114,f115,f86,f87,f116,f117,f90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT381+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 15:12:02 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.45 % (921976)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (921981)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2676598389_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.45 % TRYING [1]
% 0.11/0.45 % TRYING [2]
% 0.11/0.45 % (921981) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-921976-921981"...
% 0.11/0.45 % (921982)% WARNING: option uhcvi not known.
% 0.11/0.45 % (921981)...printing done.
% 0.11/0.45 % (921981)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Theorem for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (921981)------------------------------
% 0.11/0.45 % (921981)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (921981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (921981)CaDiCaL version: 2.1.3
% 0.11/0.45 % (921981)Termination reason: Refutation
% 0.11/0.45 % (921981)Time elapsed: 0.003 s
% 0.11/0.45 % (921981)Peak memory usage: 11 MB
% 0.11/0.45 % (921981)Instructions burned: 9 (million)
% 0.11/0.45 % (921976)Success in time 0.029 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------