%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LAT386+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 : Thu Sep 24 01:03:04 PM UTC 2026
% Result : Theorem 79.98s 11.06s
% Output : CNFRefutation 79.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 11
% Syntax : Number of formulae : 99 ( 15 unt; 2 def)
% Number of atoms : 580 ( 30 equ)
% Maximal formula atoms : 37 ( 5 avg)
% Number of connectives : 747 ( 266 ~; 235 |; 214 &)
% ( 2 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 2 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 8 con; 0-3 aty)
% Number of variables : 173 ( 149 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [W0,W1,W2] :
( ( aElement0(W2)
& aElement0(W1)
& aElement0(W0) )
=> ( ( sdtlseqdt0(W1,W2)
& sdtlseqdt0(W0,W1) )
=> sdtlseqdt0(W0,W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [W0] :
( aFunction0(W0)
=> ! [W1] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),szRzazndt0(W0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,hypothesis,
( isOn0(xf,xU)
& szRzazndt0(xf) = xU
& szDzozmdt0(xf) = szRzazndt0(xf)
& isMonotone0(xf)
& ! [W0,W1] :
( ( aElementOf0(W1,szDzozmdt0(xf))
& aElementOf0(W0,szDzozmdt0(xf)) )
=> ( sdtlseqdt0(W0,W1)
=> sdtlseqdt0(sdtlpdtrp0(xf,W0),sdtlpdtrp0(xf,W1)) ) )
& aFunction0(xf)
& aCompleteLattice0(xU)
& ! [W0] :
( ( aSubsetOf0(W0,xU)
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xU) )
& aSet0(W0) ) )
=> ? [W1] :
( ? [W2] :
( aSupremumOfIn0(W2,W0,xU)
& ! [W3] :
( ( aUpperBoundOfIn0(W3,W0,xU)
| ( ! [W4] :
( aElementOf0(W4,W0)
=> sdtlseqdt0(W4,W3) )
& aElementOf0(W3,xU) ) )
=> sdtlseqdt0(W2,W3) )
& aUpperBoundOfIn0(W2,W0,xU)
& ! [W3] :
( aElementOf0(W3,W0)
=> sdtlseqdt0(W3,W2) )
& aElementOf0(W2,xU)
& aElementOf0(W2,xU) )
& aInfimumOfIn0(W1,W0,xU)
& ! [W2] :
( ( aLowerBoundOfIn0(W2,W0,xU)
| ( ! [W3] :
( aElementOf0(W3,W0)
=> sdtlseqdt0(W2,W3) )
& aElementOf0(W2,xU) ) )
=> sdtlseqdt0(W2,W1) )
& aLowerBoundOfIn0(W1,W0,xU)
& ! [W2] :
( aElementOf0(W2,W0)
=> sdtlseqdt0(W1,W2) )
& aElementOf0(W1,xU)
& aElementOf0(W1,xU) ) )
& aSet0(xU) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,hypothesis,
( xS = cS1142(xf)
& ! [W0] :
( ( ( aFixedPointOf0(W0,xf)
| ( sdtlpdtrp0(xf,W0) = W0
& aElementOf0(W0,szDzozmdt0(xf)) ) )
=> aElementOf0(W0,xS) )
& ( aElementOf0(W0,xS)
=> ( aFixedPointOf0(W0,xf)
& sdtlpdtrp0(xf,W0) = W0
& aElementOf0(W0,szDzozmdt0(xf)) ) ) )
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,hypothesis,
( aSubsetOf0(xT,xS)
& ! [W0] :
( aElementOf0(W0,xT)
=> aElementOf0(W0,xS) )
& aSet0(xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
( xP = cS1241(xU,xf,xT)
& ! [W0] :
( ( ( ( aUpperBoundOfIn0(W0,xT,xU)
| ! [W1] :
( aElementOf0(W1,xT)
=> sdtlseqdt0(W1,W0) ) )
& sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
& aElementOf0(W0,xU) )
=> aElementOf0(W0,xP) )
& ( aElementOf0(W0,xP)
=> ( aUpperBoundOfIn0(W0,xT,xU)
& ! [W1] :
( aElementOf0(W1,xT)
=> sdtlseqdt0(W1,W0) )
& sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
& aElementOf0(W0,xU) ) ) )
& aSet0(xP) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
( aInfimumOfIn0(xp,xP,xU)
& ! [W0] :
( ( aLowerBoundOfIn0(W0,xP,xU)
| ( ! [W1] :
( aElementOf0(W1,xP)
=> sdtlseqdt0(W0,W1) )
& aElementOf0(W0,xU) ) )
=> sdtlseqdt0(W0,xp) )
& aLowerBoundOfIn0(xp,xP,xU)
& ! [W0] :
( aElementOf0(W0,xP)
=> sdtlseqdt0(xp,W0) )
& aElementOf0(xp,xU)
& aElementOf0(xp,xU) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
( ( aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
| ! [W0] :
( aElementOf0(W0,xT)
=> sdtlseqdt0(W0,sdtlpdtrp0(xf,xp)) ) )
& ( aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
| ! [W0] :
( aElementOf0(W0,xP)
=> sdtlseqdt0(sdtlpdtrp0(xf,xp),W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ( ( aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
| ! [W0] :
( aElementOf0(W0,xT)
=> sdtlseqdt0(W0,sdtlpdtrp0(xf,xp)) ) )
& ( aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
| ! [W0] :
( aElementOf0(W0,xP)
=> sdtlseqdt0(sdtlpdtrp0(xf,xp),W0) ) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f37,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f38,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f58,plain,
! [W0,W1,W2] :
( sdtlseqdt0(W0,W2)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f59,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f119,plain,
! [W0] :
( ! [W1] :
( aElementOf0(sdtlpdtrp0(W0,W1),szRzazndt0(W0))
| ~ aElementOf0(W1,szDzozmdt0(W0)) )
| ~ aFunction0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f120,plain,
! [X0,X1] :
( aElementOf0(sdtlpdtrp0(X0,X1),szRzazndt0(X0))
| ~ aElementOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f135,plain,
( isOn0(xf,xU)
& szRzazndt0(xf) = xU
& szDzozmdt0(xf) = szRzazndt0(xf)
& isMonotone0(xf)
& ! [W0,W1] :
( sdtlseqdt0(sdtlpdtrp0(xf,W0),sdtlpdtrp0(xf,W1))
| ~ sdtlseqdt0(W0,W1)
| ~ aElementOf0(W1,szDzozmdt0(xf))
| ~ aElementOf0(W0,szDzozmdt0(xf)) )
& aFunction0(xf)
& aCompleteLattice0(xU)
& ! [W0] :
( ? [W1] :
( ? [W2] :
( aSupremumOfIn0(W2,W0,xU)
& ! [W3] :
( sdtlseqdt0(W2,W3)
| ( ~ aUpperBoundOfIn0(W3,W0,xU)
& ( ? [W4] :
( ~ sdtlseqdt0(W4,W3)
& aElementOf0(W4,W0) )
| ~ aElementOf0(W3,xU) ) ) )
& aUpperBoundOfIn0(W2,W0,xU)
& ! [W3] :
( sdtlseqdt0(W3,W2)
| ~ aElementOf0(W3,W0) )
& aElementOf0(W2,xU)
& aElementOf0(W2,xU) )
& aInfimumOfIn0(W1,W0,xU)
& ! [W2] :
( sdtlseqdt0(W2,W1)
| ( ~ aLowerBoundOfIn0(W2,W0,xU)
& ( ? [W3] :
( ~ sdtlseqdt0(W2,W3)
& aElementOf0(W3,W0) )
| ~ aElementOf0(W2,xU) ) ) )
& aLowerBoundOfIn0(W1,W0,xU)
& ! [W2] :
( sdtlseqdt0(W1,W2)
| ~ aElementOf0(W2,W0) )
& aElementOf0(W1,xU)
& aElementOf0(W1,xU) )
| ( ~ aSubsetOf0(W0,xU)
& ( ? [W1] :
( ~ aElementOf0(W1,xU)
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ) ) )
& aSet0(xU) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f136,definition,
! [W0] :
( sP0_prd(W0)
<=> ( ~ aSubsetOf0(W0,xU)
& ( ? [W1] :
( ~ aElementOf0(W1,xU)
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f137,plain,
( isOn0(xf,xU)
& szRzazndt0(xf) = xU
& szDzozmdt0(xf) = szRzazndt0(xf)
& isMonotone0(xf)
& ! [W0,W1] :
( sdtlseqdt0(sdtlpdtrp0(xf,W0),sdtlpdtrp0(xf,W1))
| ~ sdtlseqdt0(W0,W1)
| ~ aElementOf0(W1,szDzozmdt0(xf))
| ~ aElementOf0(W0,szDzozmdt0(xf)) )
& aFunction0(xf)
& aCompleteLattice0(xU)
& ! [W0] :
( ? [W1] :
( ? [W2] :
( aSupremumOfIn0(W2,W0,xU)
& ! [W3] :
( sdtlseqdt0(W2,W3)
| ( ~ aUpperBoundOfIn0(W3,W0,xU)
& ( ? [W4] :
( ~ sdtlseqdt0(W4,W3)
& aElementOf0(W4,W0) )
| ~ aElementOf0(W3,xU) ) ) )
& aUpperBoundOfIn0(W2,W0,xU)
& ! [W3] :
( sdtlseqdt0(W3,W2)
| ~ aElementOf0(W3,W0) )
& aElementOf0(W2,xU)
& aElementOf0(W2,xU) )
& aInfimumOfIn0(W1,W0,xU)
& ! [W2] :
( sdtlseqdt0(W2,W1)
| ( ~ aLowerBoundOfIn0(W2,W0,xU)
& ( ? [W3] :
( ~ sdtlseqdt0(W2,W3)
& aElementOf0(W3,W0) )
| ~ aElementOf0(W2,xU) ) ) )
& aLowerBoundOfIn0(W1,W0,xU)
& ! [W2] :
( sdtlseqdt0(W1,W2)
| ~ aElementOf0(W2,W0) )
& aElementOf0(W1,xU)
& aElementOf0(W1,xU) )
| sP0_prd(W0) )
& aSet0(xU) ),
inference(formula_renaming,[status(thm)],[f135,f136]) ).
fof(f138,plain,
( isOn0(xf,xU)
& szRzazndt0(xf) = xU
& szDzozmdt0(xf) = szRzazndt0(xf)
& isMonotone0(xf)
& ! [W0,W1] :
( sdtlseqdt0(sdtlpdtrp0(xf,W0),sdtlpdtrp0(xf,W1))
| ~ sdtlseqdt0(W0,W1)
| ~ aElementOf0(W1,szDzozmdt0(xf))
| ~ aElementOf0(W0,szDzozmdt0(xf)) )
& aFunction0(xf)
& aCompleteLattice0(xU)
& ! [W0] :
( ( ? [W2] :
( aSupremumOfIn0(W2,W0,xU)
& ! [W3] :
( sdtlseqdt0(W2,W3)
| ( ~ aUpperBoundOfIn0(W3,W0,xU)
& ( ? [W4] :
( ~ sdtlseqdt0(W4,W3)
& aElementOf0(W4,W0) )
| ~ aElementOf0(W3,xU) ) ) )
& aUpperBoundOfIn0(W2,W0,xU)
& ! [W3] :
( sdtlseqdt0(W3,W2)
| ~ aElementOf0(W3,W0) )
& aElementOf0(W2,xU)
& aElementOf0(W2,xU) )
& ? [W1] :
( aInfimumOfIn0(W1,W0,xU)
& ! [W2] :
( sdtlseqdt0(W2,W1)
| ( ~ aLowerBoundOfIn0(W2,W0,xU)
& ( ? [W3] :
( ~ sdtlseqdt0(W2,W3)
& aElementOf0(W3,W0) )
| ~ aElementOf0(W2,xU) ) ) )
& aLowerBoundOfIn0(W1,W0,xU)
& ! [W2] :
( sdtlseqdt0(W1,W2)
| ~ aElementOf0(W2,W0) )
& aElementOf0(W1,xU)
& aElementOf0(W1,xU) ) )
| sP0_prd(W0) )
& aSet0(xU) ),
inference(miniscoping,[status(thm)],[f137]) ).
fof(f139,plain,
( isOn0(xf,xU)
& szRzazndt0(xf) = xU
& szDzozmdt0(xf) = szRzazndt0(xf)
& isMonotone0(xf)
& ! [W0,W1] :
( sdtlseqdt0(sdtlpdtrp0(xf,W0),sdtlpdtrp0(xf,W1))
| ~ sdtlseqdt0(W0,W1)
| ~ aElementOf0(W1,szDzozmdt0(xf))
| ~ aElementOf0(W0,szDzozmdt0(xf)) )
& aFunction0(xf)
& aCompleteLattice0(xU)
& ! [W0] :
( ( aSupremumOfIn0(sK13_skl(W0),W0,xU)
& ! [W3] :
( sdtlseqdt0(sK13_skl(W0),W3)
| ( ~ aUpperBoundOfIn0(W3,W0,xU)
& ( ( ~ sdtlseqdt0(sK14_skl(W3,W0),W3)
& aElementOf0(sK14_skl(W3,W0),W0) )
| ~ aElementOf0(W3,xU) ) ) )
& aUpperBoundOfIn0(sK13_skl(W0),W0,xU)
& ! [W3] :
( sdtlseqdt0(W3,sK13_skl(W0))
| ~ aElementOf0(W3,W0) )
& aElementOf0(sK13_skl(W0),xU)
& aElementOf0(sK13_skl(W0),xU)
& aInfimumOfIn0(sK11_skl(W0),W0,xU)
& ! [W2] :
( sdtlseqdt0(W2,sK11_skl(W0))
| ( ~ aLowerBoundOfIn0(W2,W0,xU)
& ( ( ~ sdtlseqdt0(W2,sK12_skl(W2,W0))
& aElementOf0(sK12_skl(W2,W0),W0) )
| ~ aElementOf0(W2,xU) ) ) )
& aLowerBoundOfIn0(sK11_skl(W0),W0,xU)
& ! [W2] :
( sdtlseqdt0(sK11_skl(W0),W2)
| ~ aElementOf0(W2,W0) )
& aElementOf0(sK11_skl(W0),xU)
& aElementOf0(sK11_skl(W0),xU) )
| sP0_prd(W0) )
& aSet0(xU) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl,sK13_skl,sK14_skl]),skolemize(W1,sK11_skl(W0)),skolemize(W3,sK12_skl(W2,W0)),skolemize(W2,sK13_skl(W0)),skolemize(W4,sK14_skl(W3,W0))],[f138]) ).
fof(f140,plain,
aSet0(xU),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f158,plain,
aFunction0(xf),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f159,plain,
! [X0,X1] :
( sdtlseqdt0(sdtlpdtrp0(xf,X0),sdtlpdtrp0(xf,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf)) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f161,plain,
szDzozmdt0(xf) = szRzazndt0(xf),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f162,plain,
szRzazndt0(xf) = xU,
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f164,plain,
( xS = cS1142(xf)
& ! [W0] :
( ( aElementOf0(W0,xS)
| ( ~ aFixedPointOf0(W0,xf)
& ( sdtlpdtrp0(xf,W0) != W0
| ~ aElementOf0(W0,szDzozmdt0(xf)) ) ) )
& ( ( aFixedPointOf0(W0,xf)
& sdtlpdtrp0(xf,W0) = W0
& aElementOf0(W0,szDzozmdt0(xf)) )
| ~ aElementOf0(W0,xS) ) )
& aSet0(xS) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f165,plain,
( xS = cS1142(xf)
& ! [W0] :
( aElementOf0(W0,xS)
| ( ~ aFixedPointOf0(W0,xf)
& ( sdtlpdtrp0(xf,W0) != W0
| ~ aElementOf0(W0,szDzozmdt0(xf)) ) ) )
& ! [W0] :
( ( aFixedPointOf0(W0,xf)
& sdtlpdtrp0(xf,W0) = W0
& aElementOf0(W0,szDzozmdt0(xf)) )
| ~ aElementOf0(W0,xS) )
& aSet0(xS) ),
inference(miniscoping,[status(thm)],[f164]) ).
fof(f167,plain,
! [X0] :
( aElementOf0(X0,szDzozmdt0(xf))
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[status(thm)],[f165]) ).
fof(f168,plain,
! [X0] :
( sdtlpdtrp0(xf,X0) = X0
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[status(thm)],[f165]) ).
fof(f173,plain,
( aSubsetOf0(xT,xS)
& ! [W0] :
( aElementOf0(W0,xS)
| ~ aElementOf0(W0,xT) )
& aSet0(xT) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f175,plain,
! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[status(thm)],[f173]) ).
fof(f177,plain,
( xP = cS1241(xU,xf,xT)
& ! [W0] :
( ( aElementOf0(W0,xP)
| ( ~ aUpperBoundOfIn0(W0,xT,xU)
& ? [W1] :
( ~ sdtlseqdt0(W1,W0)
& aElementOf0(W1,xT) ) )
| ~ sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
| ~ aElementOf0(W0,xU) )
& ( ( aUpperBoundOfIn0(W0,xT,xU)
& ! [W1] :
( sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,xT) )
& sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
& aElementOf0(W0,xU) )
| ~ aElementOf0(W0,xP) ) )
& aSet0(xP) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f178,plain,
( xP = cS1241(xU,xf,xT)
& ! [W0] :
( aElementOf0(W0,xP)
| ( ~ aUpperBoundOfIn0(W0,xT,xU)
& ? [W1] :
( ~ sdtlseqdt0(W1,W0)
& aElementOf0(W1,xT) ) )
| ~ sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
| ~ aElementOf0(W0,xU) )
& ! [W0] :
( ( aUpperBoundOfIn0(W0,xT,xU)
& ! [W1] :
( sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,xT) )
& sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
& aElementOf0(W0,xU) )
| ~ aElementOf0(W0,xP) )
& aSet0(xP) ),
inference(miniscoping,[status(thm)],[f177]) ).
fof(f179,plain,
( xP = cS1241(xU,xf,xT)
& ! [W0] :
( aElementOf0(W0,xP)
| ( ~ aUpperBoundOfIn0(W0,xT,xU)
& ~ sdtlseqdt0(sK15_skl(W0),W0)
& aElementOf0(sK15_skl(W0),xT) )
| ~ sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
| ~ aElementOf0(W0,xU) )
& ! [W0] :
( ( aUpperBoundOfIn0(W0,xT,xU)
& ! [W1] :
( sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,xT) )
& sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
& aElementOf0(W0,xU) )
| ~ aElementOf0(W0,xP) )
& aSet0(xP) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl]),skolemize(W1,sK15_skl(W0))],[f178]) ).
fof(f181,plain,
! [X0] :
( aElementOf0(X0,xU)
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[status(thm)],[f179]) ).
fof(f182,plain,
! [X0] :
( sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[status(thm)],[f179]) ).
fof(f183,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| ~ aElementOf0(X1,xT)
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[status(thm)],[f179]) ).
fof(f189,plain,
( aInfimumOfIn0(xp,xP,xU)
& ! [W0] :
( sdtlseqdt0(W0,xp)
| ( ~ aLowerBoundOfIn0(W0,xP,xU)
& ( ? [W1] :
( ~ sdtlseqdt0(W0,W1)
& aElementOf0(W1,xP) )
| ~ aElementOf0(W0,xU) ) ) )
& aLowerBoundOfIn0(xp,xP,xU)
& ! [W0] :
( sdtlseqdt0(xp,W0)
| ~ aElementOf0(W0,xP) )
& aElementOf0(xp,xU)
& aElementOf0(xp,xU) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f190,plain,
( aInfimumOfIn0(xp,xP,xU)
& ! [W0] :
( sdtlseqdt0(W0,xp)
| ( ~ aLowerBoundOfIn0(W0,xP,xU)
& ( ( ~ sdtlseqdt0(W0,sK16_skl(W0))
& aElementOf0(sK16_skl(W0),xP) )
| ~ aElementOf0(W0,xU) ) ) )
& aLowerBoundOfIn0(xp,xP,xU)
& ! [W0] :
( sdtlseqdt0(xp,W0)
| ~ aElementOf0(W0,xP) )
& aElementOf0(xp,xU)
& aElementOf0(xp,xU) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl]),skolemize(W1,sK16_skl(W0))],[f189]) ).
fof(f191,plain,
aElementOf0(xp,xU),
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f193,plain,
! [X0] :
( sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f195,plain,
! [X0] :
( sdtlseqdt0(X0,xp)
| aElementOf0(sK16_skl(X0),xP)
| ~ aElementOf0(X0,xU) ),
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f196,plain,
! [X0] :
( sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,sK16_skl(X0))
| ~ aElementOf0(X0,xU) ),
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f199,plain,
( ( ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
& ? [W0] :
( ~ sdtlseqdt0(W0,sdtlpdtrp0(xf,xp))
& aElementOf0(W0,xT) ) )
| ( ~ aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
& ? [W0] :
( ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),W0)
& aElementOf0(W0,xP) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f200,definition,
( sP1_prd
<=> ( ~ aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
& ? [W0] :
( ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),W0)
& aElementOf0(W0,xP) ) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f201,plain,
( ( ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
& ? [W0] :
( ~ sdtlseqdt0(W0,sdtlpdtrp0(xf,xp))
& aElementOf0(W0,xT) ) )
| sP1_prd ),
inference(formula_renaming,[status(thm)],[f199,f200]) ).
fof(f202,plain,
( ( ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
& ~ sdtlseqdt0(sK17_skl,sdtlpdtrp0(xf,xp))
& aElementOf0(sK17_skl,xT) )
| sP1_prd ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl]),skolemize(W0,sK17_skl)],[f201]) ).
fof(f203,plain,
( aElementOf0(sK17_skl,xT)
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f204,plain,
( ~ sdtlseqdt0(sK17_skl,sdtlpdtrp0(xf,xp))
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f214,plain,
( ( aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
| ! [W0] :
( sdtlseqdt0(sdtlpdtrp0(xf,xp),W0)
| ~ aElementOf0(W0,xP) )
| sP1_prd )
& ( ( ~ aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
& ? [W0] :
( ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),W0)
& aElementOf0(W0,xP) ) )
| ~ sP1_prd ) ),
inference(NNF_transformation,[status(thm)],[f200]) ).
fof(f215,plain,
( ( aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
| ! [W0] :
( sdtlseqdt0(sdtlpdtrp0(xf,xp),W0)
| ~ aElementOf0(W0,xP) )
| sP1_prd )
& ( ( ~ aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
& ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),sK19_skl)
& aElementOf0(sK19_skl,xP) )
| ~ sP1_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl]),skolemize(W0,sK19_skl)],[f214]) ).
fof(f216,plain,
( aElementOf0(sK19_skl,xP)
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f215]) ).
fof(f217,plain,
( ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),sK19_skl)
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f215]) ).
fof(f232,plain,
szDzozmdt0(xf) = xU,
inference(forward_demodulation,[status(thm)],[f162,f161]) ).
fof(f242,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(X2,X3)
| ~ aSet0(X3)
| sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X0,X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f59,f38]) ).
fof(f291,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f168,f175]) ).
fof(f305,plain,
( sP1_prd
| sdtlpdtrp0(xf,sK17_skl) = sK17_skl ),
inference(resolution,[status(thm)],[f291,f203]) ).
fof(f346,plain,
! [X0] :
( aElementOf0(X0,xU)
| ~ aElementOf0(X0,xS) ),
inference(forward_demodulation,[status(thm)],[f232,f167]) ).
fof(f514,plain,
! [X0] :
( aElementOf0(sdtlpdtrp0(xf,X0),szRzazndt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f120,f158]) ).
fof(f515,plain,
! [X0] :
( aElementOf0(sdtlpdtrp0(xf,X0),szRzazndt0(xf))
| ~ aElementOf0(X0,xU) ),
inference(forward_demodulation,[status(thm)],[f232,f514]) ).
fof(f516,plain,
! [X0] :
( aElementOf0(sdtlpdtrp0(xf,X0),xU)
| ~ aElementOf0(X0,xU) ),
inference(forward_demodulation,[status(thm)],[f162,f515]) ).
fof(f648,plain,
! [X0,X1] :
( sdtlseqdt0(sdtlpdtrp0(xf,X0),sdtlpdtrp0(xf,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szDzozmdt0(xf))
| ~ aElementOf0(X0,xU) ),
inference(forward_demodulation,[status(thm)],[f232,f159]) ).
fof(f649,plain,
! [X0,X1] :
( sdtlseqdt0(sdtlpdtrp0(xf,X0),sdtlpdtrp0(xf,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,xU)
| ~ aElementOf0(X0,xU) ),
inference(forward_demodulation,[status(thm)],[f232,f648]) ).
fof(f721,plain,
! [X0,X1,X2,X3,X4] :
( ~ aElementOf0(X2,X4)
| ~ aSet0(X4)
| ~ aElementOf0(X1,X3)
| ~ aSet0(X3)
| sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f242,f38]) ).
fof(f1531,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ aElementOf0(X0,X5)
| ~ aSet0(X5)
| ~ aElementOf0(X2,X4)
| ~ aSet0(X4)
| ~ aElementOf0(X1,X3)
| ~ aSet0(X3)
| sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1) ),
inference(resolution,[status(thm)],[f721,f38]) ).
fof(f3441,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(X0,xU)
| ~ aElementOf0(X2,xU)
| ~ aElementOf0(X1,X3)
| ~ aSet0(X3)
| sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1) ),
inference(resolution,[status(thm)],[f1531,f140]) ).
fof(f5595,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X0,xU)
| ~ aElementOf0(X2,xU)
| ~ aElementOf0(X1,xU)
| sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1) ),
inference(resolution,[status(thm)],[f3441,f140]) ).
fof(f5708,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X2,xP)
| ~ aElementOf0(X0,xU)
| ~ aElementOf0(X1,xU)
| sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1) ),
inference(resolution,[status(thm)],[f5595,f181]) ).
fof(f5788,plain,
! [X0,X1] :
( ~ sP1_prd
| ~ aElementOf0(X0,xU)
| ~ aElementOf0(X1,xU)
| sdtlseqdt0(X0,sK19_skl)
| ~ sdtlseqdt0(X1,sK19_skl)
| ~ sdtlseqdt0(X0,X1) ),
inference(resolution,[status(thm)],[f5708,f216]) ).
fof(f5813,plain,
! [X0] :
( ~ sP1_prd
| ~ sP1_prd
| ~ aElementOf0(sdtlpdtrp0(xf,xp),xU)
| ~ aElementOf0(X0,xU)
| ~ sdtlseqdt0(X0,sK19_skl)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),X0) ),
inference(resolution,[status(thm)],[f5788,f217]) ).
fof(f5817,plain,
! [X0] :
( ~ sP1_prd
| ~ aElementOf0(sdtlpdtrp0(xf,xp),xU)
| ~ aElementOf0(X0,xU)
| ~ sdtlseqdt0(X0,sK19_skl)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),X0) ),
inference(duplicate_literals_removal,[status(thm)],[f5813]) ).
fof(f6996,plain,
! [X0] :
( ~ aElementOf0(xp,xU)
| ~ sP1_prd
| ~ aElementOf0(X0,xU)
| ~ sdtlseqdt0(X0,sK19_skl)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),X0) ),
inference(resolution,[status(thm)],[f5817,f516]) ).
fof(f7004,plain,
! [X0] :
( ~ sP1_prd
| ~ aElementOf0(X0,xU)
| ~ sdtlseqdt0(X0,sK19_skl)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f6996,f191]) ).
fof(f7012,plain,
! [X0] :
( ~ sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xU)
| ~ aElementOf0(xp,xU)
| ~ sP1_prd
| ~ aElementOf0(sdtlpdtrp0(xf,X0),xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),sK19_skl) ),
inference(resolution,[status(thm)],[f7004,f649]) ).
fof(f7031,plain,
! [X0] :
( ~ sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xU)
| ~ aElementOf0(xp,xU)
| ~ sP1_prd
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),sK19_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f7012,f516]) ).
fof(f7134,plain,
! [X0] :
( ~ sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xU)
| ~ sP1_prd
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),sK19_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f7031,f191]) ).
fof(f7138,plain,
( ~ aElementOf0(sK19_skl,xP)
| ~ sdtlseqdt0(xp,sK19_skl)
| ~ aElementOf0(sK19_skl,xU)
| ~ sP1_prd ),
inference(resolution,[status(thm)],[f7134,f182]) ).
fof(f7149,plain,
( ~ aElementOf0(sK19_skl,xP)
| ~ sdtlseqdt0(xp,sK19_skl)
| ~ sP1_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f7138,f181]) ).
fof(f7153,plain,
~ sP1_prd,
inference(backward_subsumption_resolution,[status(thm)],[f216,f7154]) ).
fof(f7154,plain,
( ~ aElementOf0(sK19_skl,xP)
| ~ sP1_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f7149,f193]) ).
fof(f7174,plain,
~ sdtlseqdt0(sK17_skl,sdtlpdtrp0(xf,xp)),
inference(backward_subsumption_resolution,[status(thm)],[f204,f7153]) ).
fof(f7175,plain,
aElementOf0(sK17_skl,xT),
inference(backward_subsumption_resolution,[status(thm)],[f203,f7153]) ).
fof(f7198,plain,
sdtlpdtrp0(xf,sK17_skl) = sK17_skl,
inference(backward_subsumption_resolution,[status(thm)],[f305,f7153]) ).
fof(f7282,plain,
! [X0] :
( sdtlseqdt0(sK17_skl,sdtlpdtrp0(xf,X0))
| ~ sdtlseqdt0(sK17_skl,X0)
| ~ aElementOf0(X0,xU)
| ~ aElementOf0(sK17_skl,xU) ),
inference(paramodulation,[status(thm)],[f7198,f649]) ).
fof(f7355,plain,
! [X0] :
( ~ aElementOf0(sK17_skl,xS)
| sdtlseqdt0(sK17_skl,sdtlpdtrp0(xf,X0))
| ~ sdtlseqdt0(sK17_skl,X0)
| ~ aElementOf0(X0,xU) ),
inference(resolution,[status(thm)],[f7282,f346]) ).
fof(f8121,plain,
! [X0] :
( ~ aElementOf0(sK17_skl,xT)
| sdtlseqdt0(sK17_skl,sdtlpdtrp0(xf,X0))
| ~ sdtlseqdt0(sK17_skl,X0)
| ~ aElementOf0(X0,xU) ),
inference(resolution,[status(thm)],[f7355,f175]) ).
fof(f8128,plain,
! [X0] :
( sdtlseqdt0(sK17_skl,sdtlpdtrp0(xf,X0))
| ~ sdtlseqdt0(sK17_skl,X0)
| ~ aElementOf0(X0,xU) ),
inference(forward_subsumption_resolution,[status(thm)],[f8121,f7175]) ).
fof(f8132,plain,
( ~ sdtlseqdt0(sK17_skl,xp)
| ~ aElementOf0(xp,xU) ),
inference(resolution,[status(thm)],[f8128,f7174]) ).
fof(f8141,plain,
~ sdtlseqdt0(sK17_skl,xp),
inference(forward_subsumption_resolution,[status(thm)],[f8132,f191]) ).
fof(f8145,plain,
( ~ sdtlseqdt0(sK17_skl,sK16_skl(sK17_skl))
| ~ aElementOf0(sK17_skl,xU) ),
inference(resolution,[status(thm)],[f8141,f196]) ).
fof(f8202,plain,
( ~ aElementOf0(sK17_skl,xT)
| ~ aElementOf0(sK16_skl(sK17_skl),xP)
| ~ aElementOf0(sK17_skl,xU) ),
inference(resolution,[status(thm)],[f8145,f183]) ).
fof(f8203,plain,
( ~ aElementOf0(sK16_skl(sK17_skl),xP)
| ~ aElementOf0(sK17_skl,xU) ),
inference(forward_subsumption_resolution,[status(thm)],[f8202,f7175]) ).
fof(f8204,plain,
( sdtlseqdt0(sK17_skl,xp)
| ~ aElementOf0(sK17_skl,xU)
| ~ aElementOf0(sK17_skl,xU) ),
inference(resolution,[status(thm)],[f8203,f195]) ).
fof(f8210,plain,
( sdtlseqdt0(sK17_skl,xp)
| ~ aElementOf0(sK17_skl,xU) ),
inference(duplicate_literals_removal,[status(thm)],[f8204]) ).
fof(f8211,plain,
~ aElementOf0(sK17_skl,xU),
inference(forward_subsumption_resolution,[status(thm)],[f8210,f8141]) ).
fof(f8217,plain,
~ aElementOf0(sK17_skl,xS),
inference(resolution,[status(thm)],[f8211,f346]) ).
fof(f8236,plain,
~ aElementOf0(sK17_skl,xT),
inference(resolution,[status(thm)],[f8217,f175]) ).
fof(f8243,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f8236,f7175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT386+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n011.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Sun Sep 20 23:57:42 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.50 % Drodi V4.1.1
% 79.98/11.06 % Refutation found
% 79.98/11.06 % SZS status Theorem for theBenchmark: Theorem is valid
% 79.98/11.06 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.18/11.15 % Elapsed time: 10.666671 seconds
% 5.18/11.15 % CPU time: 83.725337 seconds
% 5.18/11.15 % Total memory used: 300.114 MB
% 5.18/11.15 % Net memory used: 276.623 MB
%------------------------------------------------------------------------------