%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LAT387+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 38.28s 5.37s
% Output : CNFRefutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 359
% Syntax : Number of formulae : 1527 ( 30 unt; 344 def)
% Number of atoms : 5960 ( 300 equ)
% Maximal formula atoms : 37 ( 3 avg)
% Number of connectives : 8065 (3632 ~;3650 |; 364 &)
% ( 354 <=>; 65 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 351 ( 349 usr; 334 prp; 0-3 aty)
% Number of functors : 31 ( 31 usr; 8 con; 0-3 aty)
% Number of variables : 1259 (1207 !; 52 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,definition,
! [W0] :
( aSet0(W0)
=> ( isEmpty0(W0)
<=> ~ ? [W1] : aElementOf0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [W0] :
( aElement0(W0)
=> sdtlseqdt0(W0,W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f10,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
=> ! [W2] :
( aLowerBoundOfIn0(W2,W1,W0)
<=> ( ! [W3] :
( aElementOf0(W3,W1)
=> sdtlseqdt0(W2,W3) )
& aElementOf0(W2,W0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
=> ! [W2] :
( aUpperBoundOfIn0(W2,W1,W0)
<=> ( ! [W3] :
( aElementOf0(W3,W1)
=> sdtlseqdt0(W3,W2) )
& aElementOf0(W2,W0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
=> ! [W2] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( ! [W3] :
( aLowerBoundOfIn0(W3,W1,W0)
=> sdtlseqdt0(W3,W2) )
& aLowerBoundOfIn0(W2,W1,W0)
& aElementOf0(W2,W0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
=> ! [W2] :
( aSupremumOfIn0(W2,W1,W0)
<=> ( ! [W3] :
( aUpperBoundOfIn0(W3,W1,W0)
=> sdtlseqdt0(W2,W3) )
& aUpperBoundOfIn0(W2,W1,W0)
& aElementOf0(W2,W0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
=> ! [W2,W3] :
( ( aSupremumOfIn0(W3,W1,W0)
& aSupremumOfIn0(W2,W1,W0) )
=> W2 = W3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
=> ! [W2,W3] :
( ( aInfimumOfIn0(W3,W1,W0)
& aInfimumOfIn0(W2,W1,W0) )
=> W2 = W3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,definition,
! [W0] :
( aCompleteLattice0(W0)
<=> ( ! [W1] :
( aSubsetOf0(W1,W0)
=> ? [W2] :
( ? [W3] : aSupremumOfIn0(W3,W1,W0)
& aInfimumOfIn0(W2,W1,W0) ) )
& aSet0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [W0] :
( aFunction0(W0)
=> aSet0(szRzazndt0(W0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,definition,
! [W0,W1] :
( ( aSet0(W1)
& aFunction0(W0) )
=> ( isOn0(W0,W1)
<=> ( szRzazndt0(W0) = W1
& szDzozmdt0(W0) = szRzazndt0(W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [W0] :
( aFunction0(W0)
=> ! [W1] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),szRzazndt0(W0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,definition,
! [W0] :
( aFunction0(W0)
=> ! [W1] :
( aFixedPointOf0(W1,W0)
<=> ( sdtlpdtrp0(W0,W1) = W1
& aElementOf0(W1,szDzozmdt0(W0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,definition,
! [W0] :
( aFunction0(W0)
=> ( isMonotone0(W0)
<=> ! [W1,W2] :
( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W1,szDzozmdt0(W0)) )
=> ( sdtlseqdt0(W1,W2)
=> sdtlseqdt0(sdtlpdtrp0(W0,W1),sdtlpdtrp0(W0,W2)) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f26,hypothesis,
( aSubsetOf0(xT,xS)
& ! [W0] :
( aElementOf0(W0,xT)
=> aElementOf0(W0,xS) )
& aSet0(xT) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f29,hypothesis,
( 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/sandbox/benchmark/theBenchmark.p') ).
fof(f30,conjecture,
( ( aSupremumOfIn0(xp,xT,xS)
| ( ! [W0] :
( ( aUpperBoundOfIn0(W0,xT,xS)
& ! [W1] :
( aElementOf0(W1,xT)
=> sdtlseqdt0(W1,W0) )
& aElementOf0(W0,xS) )
=> sdtlseqdt0(xp,W0) )
& ( aUpperBoundOfIn0(xp,xT,xS)
| ! [W0] :
( aElementOf0(W0,xT)
=> sdtlseqdt0(W0,xp) ) ) ) )
& ( aFixedPointOf0(xp,xf)
| ( sdtlpdtrp0(xf,xp) = xp
& aElementOf0(xp,szDzozmdt0(xf)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ ( ( aSupremumOfIn0(xp,xT,xS)
| ( ! [W0] :
( ( aUpperBoundOfIn0(W0,xT,xS)
& ! [W1] :
( aElementOf0(W1,xT)
=> sdtlseqdt0(W1,W0) )
& aElementOf0(W0,xS) )
=> sdtlseqdt0(xp,W0) )
& ( aUpperBoundOfIn0(xp,xT,xS)
| ! [W0] :
( aElementOf0(W0,xT)
=> sdtlseqdt0(W0,xp) ) ) ) )
& ( aFixedPointOf0(xp,xf)
| ( sdtlpdtrp0(xf,xp) = xp
& aElementOf0(xp,szDzozmdt0(xf)) ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f38,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f39,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [W0] :
( ( isEmpty0(W0)
<=> ! [W1] : ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f41,plain,
! [W0] :
( ( ( ? [W1] : aElementOf0(W1,W0)
| isEmpty0(W0) )
& ( ! [W1] : ~ aElementOf0(W1,W0)
| ~ isEmpty0(W0) ) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [W0] :
( ( ( aElementOf0(sK0_skl(W0),W0)
| isEmpty0(W0) )
& ( ! [W1] : ~ aElementOf0(W1,W0)
| ~ isEmpty0(W0) ) )
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(W1,sK0_skl(W0))],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| ~ isEmpty0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [X0] :
( aElementOf0(sK0_skl(X0),X0)
| isEmpty0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f45,plain,
! [W0] :
( ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) ) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f46,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f48,plain,
! [W0] :
( ( ! [W1] :
( ( ~ aElementOf0(sK1_skl(W1,W0),W0)
& aElementOf0(sK1_skl(W1,W0),W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f51,plain,
! [X0,X1] :
( aElementOf0(sK1_skl(X1,X0),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f52,plain,
! [X0,X1] :
( ~ aElementOf0(sK1_skl(X1,X0),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f55,plain,
! [W0] :
( sdtlseqdt0(W0,W0)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f56,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
! [W0,W1] :
( W0 = W1
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f58,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f59,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(f60,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [W0] :
( ! [W1] :
( ! [W2] :
( aLowerBoundOfIn0(W2,W1,W0)
<=> ( ! [W3] :
( sdtlseqdt0(W2,W3)
| ~ aElementOf0(W3,W1) )
& aElementOf0(W2,W0) ) )
| ~ aSubsetOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f62,plain,
! [W0] :
( ! [W1] :
( ! [W2] :
( ( ? [W3] :
( ~ sdtlseqdt0(W2,W3)
& aElementOf0(W3,W1) )
| ~ aElementOf0(W2,W0)
| aLowerBoundOfIn0(W2,W1,W0) )
& ( ( ! [W3] :
( sdtlseqdt0(W2,W3)
| ~ aElementOf0(W3,W1) )
& aElementOf0(W2,W0) )
| ~ aLowerBoundOfIn0(W2,W1,W0) ) )
| ~ aSubsetOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
! [W0] :
( ! [W1] :
( ( ! [W2] :
( ? [W3] :
( ~ sdtlseqdt0(W2,W3)
& aElementOf0(W3,W1) )
| ~ aElementOf0(W2,W0)
| aLowerBoundOfIn0(W2,W1,W0) )
& ! [W2] :
( ( ! [W3] :
( sdtlseqdt0(W2,W3)
| ~ aElementOf0(W3,W1) )
& aElementOf0(W2,W0) )
| ~ aLowerBoundOfIn0(W2,W1,W0) ) )
| ~ aSubsetOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f62]) ).
fof(f64,plain,
! [W0] :
( ! [W1] :
( ( ! [W2] :
( ( ~ sdtlseqdt0(W2,sK2_skl(W2,W1,W0))
& aElementOf0(sK2_skl(W2,W1,W0),W1) )
| ~ aElementOf0(W2,W0)
| aLowerBoundOfIn0(W2,W1,W0) )
& ! [W2] :
( ( ! [W3] :
( sdtlseqdt0(W2,W3)
| ~ aElementOf0(W3,W1) )
& aElementOf0(W2,W0) )
| ~ aLowerBoundOfIn0(W2,W1,W0) ) )
| ~ aSubsetOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(W3,sK2_skl(W2,W1,W0))],[f63]) ).
fof(f65,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aLowerBoundOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [X0,X1,X2,X3] :
( sdtlseqdt0(X2,X3)
| ~ aElementOf0(X3,X1)
| ~ aLowerBoundOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f67,plain,
! [X0,X1,X2] :
( aElementOf0(sK2_skl(X2,X1,X0),X1)
| ~ aElementOf0(X2,X0)
| aLowerBoundOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ~ sdtlseqdt0(X2,sK2_skl(X2,X1,X0))
| ~ aElementOf0(X2,X0)
| aLowerBoundOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f69,plain,
! [W0] :
( ! [W1] :
( ! [W2] :
( aUpperBoundOfIn0(W2,W1,W0)
<=> ( ! [W3] :
( sdtlseqdt0(W3,W2)
| ~ aElementOf0(W3,W1) )
& aElementOf0(W2,W0) ) )
| ~ aSubsetOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f70,plain,
! [W0] :
( ! [W1] :
( ! [W2] :
( ( ? [W3] :
( ~ sdtlseqdt0(W3,W2)
& aElementOf0(W3,W1) )
| ~ aElementOf0(W2,W0)
| aUpperBoundOfIn0(W2,W1,W0) )
& ( ( ! [W3] :
( sdtlseqdt0(W3,W2)
| ~ aElementOf0(W3,W1) )
& aElementOf0(W2,W0) )
| ~ aUpperBoundOfIn0(W2,W1,W0) ) )
| ~ aSubsetOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
! [W0] :
( ! [W1] :
( ( ! [W2] :
( ? [W3] :
( ~ sdtlseqdt0(W3,W2)
& aElementOf0(W3,W1) )
| ~ aElementOf0(W2,W0)
| aUpperBoundOfIn0(W2,W1,W0) )
& ! [W2] :
( ( ! [W3] :
( sdtlseqdt0(W3,W2)
| ~ aElementOf0(W3,W1) )
& aElementOf0(W2,W0) )
| ~ aUpperBoundOfIn0(W2,W1,W0) ) )
| ~ aSubsetOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f70]) ).
fof(f72,plain,
! [W0] :
( ! [W1] :
( ( ! [W2] :
( ( ~ sdtlseqdt0(sK3_skl(W2,W1,W0),W2)
& aElementOf0(sK3_skl(W2,W1,W0),W1) )
| ~ aElementOf0(W2,W0)
| aUpperBoundOfIn0(W2,W1,W0) )
& ! [W2] :
( ( ! [W3] :
( sdtlseqdt0(W3,W2)
| ~ aElementOf0(W3,W1) )
& aElementOf0(W2,W0) )
| ~ aUpperBoundOfIn0(W2,W1,W0) ) )
| ~ aSubsetOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(W3,sK3_skl(W2,W1,W0))],[f71]) ).
fof(f73,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aUpperBoundOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f74,plain,
! [X0,X1,X2,X3] :
( sdtlseqdt0(X3,X2)
| ~ aElementOf0(X3,X1)
| ~ aUpperBoundOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f75,plain,
! [X0,X1,X2] :
( aElementOf0(sK3_skl(X2,X1,X0),X1)
| ~ aElementOf0(X2,X0)
| aUpperBoundOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ~ sdtlseqdt0(sK3_skl(X2,X1,X0),X2)
| ~ aElementOf0(X2,X0)
| aUpperBoundOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f77,plain,
! [W0] :
( ! [W1] :
( ! [W2] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( ! [W3] :
( sdtlseqdt0(W3,W2)
| ~ aLowerBoundOfIn0(W3,W1,W0) )
& aLowerBoundOfIn0(W2,W1,W0)
& aElementOf0(W2,W0) ) )
| ~ aSubsetOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f78,plain,
! [W0] :
( ! [W1] :
( ! [W2] :
( ( ? [W3] :
( ~ sdtlseqdt0(W3,W2)
& aLowerBoundOfIn0(W3,W1,W0) )
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| aInfimumOfIn0(W2,W1,W0) )
& ( ( ! [W3] :
( sdtlseqdt0(W3,W2)
| ~ aLowerBoundOfIn0(W3,W1,W0) )
& aLowerBoundOfIn0(W2,W1,W0)
& aElementOf0(W2,W0) )
| ~ aInfimumOfIn0(W2,W1,W0) ) )
| ~ aSubsetOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f77]) ).
fof(f79,plain,
! [W0] :
( ! [W1] :
( ( ! [W2] :
( ? [W3] :
( ~ sdtlseqdt0(W3,W2)
& aLowerBoundOfIn0(W3,W1,W0) )
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| aInfimumOfIn0(W2,W1,W0) )
& ! [W2] :
( ( ! [W3] :
( sdtlseqdt0(W3,W2)
| ~ aLowerBoundOfIn0(W3,W1,W0) )
& aLowerBoundOfIn0(W2,W1,W0)
& aElementOf0(W2,W0) )
| ~ aInfimumOfIn0(W2,W1,W0) ) )
| ~ aSubsetOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f78]) ).
fof(f80,plain,
! [W0] :
( ! [W1] :
( ( ! [W2] :
( ( ~ sdtlseqdt0(sK4_skl(W2,W1,W0),W2)
& aLowerBoundOfIn0(sK4_skl(W2,W1,W0),W1,W0) )
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| aInfimumOfIn0(W2,W1,W0) )
& ! [W2] :
( ( ! [W3] :
( sdtlseqdt0(W3,W2)
| ~ aLowerBoundOfIn0(W3,W1,W0) )
& aLowerBoundOfIn0(W2,W1,W0)
& aElementOf0(W2,W0) )
| ~ aInfimumOfIn0(W2,W1,W0) ) )
| ~ aSubsetOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(W3,sK4_skl(W2,W1,W0))],[f79]) ).
fof(f81,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aInfimumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f82,plain,
! [X0,X1,X2] :
( aLowerBoundOfIn0(X2,X1,X0)
| ~ aInfimumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f83,plain,
! [X0,X1,X2,X3] :
( sdtlseqdt0(X3,X2)
| ~ aLowerBoundOfIn0(X3,X1,X0)
| ~ aInfimumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f84,plain,
! [X0,X1,X2] :
( aLowerBoundOfIn0(sK4_skl(X2,X1,X0),X1,X0)
| ~ aLowerBoundOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| aInfimumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ~ sdtlseqdt0(sK4_skl(X2,X1,X0),X2)
| ~ aLowerBoundOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| aInfimumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f86,plain,
! [W0] :
( ! [W1] :
( ! [W2] :
( aSupremumOfIn0(W2,W1,W0)
<=> ( ! [W3] :
( sdtlseqdt0(W2,W3)
| ~ aUpperBoundOfIn0(W3,W1,W0) )
& aUpperBoundOfIn0(W2,W1,W0)
& aElementOf0(W2,W0) ) )
| ~ aSubsetOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f87,plain,
! [W0] :
( ! [W1] :
( ! [W2] :
( ( ? [W3] :
( ~ sdtlseqdt0(W2,W3)
& aUpperBoundOfIn0(W3,W1,W0) )
| ~ aUpperBoundOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| aSupremumOfIn0(W2,W1,W0) )
& ( ( ! [W3] :
( sdtlseqdt0(W2,W3)
| ~ aUpperBoundOfIn0(W3,W1,W0) )
& aUpperBoundOfIn0(W2,W1,W0)
& aElementOf0(W2,W0) )
| ~ aSupremumOfIn0(W2,W1,W0) ) )
| ~ aSubsetOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f86]) ).
fof(f88,plain,
! [W0] :
( ! [W1] :
( ( ! [W2] :
( ? [W3] :
( ~ sdtlseqdt0(W2,W3)
& aUpperBoundOfIn0(W3,W1,W0) )
| ~ aUpperBoundOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| aSupremumOfIn0(W2,W1,W0) )
& ! [W2] :
( ( ! [W3] :
( sdtlseqdt0(W2,W3)
| ~ aUpperBoundOfIn0(W3,W1,W0) )
& aUpperBoundOfIn0(W2,W1,W0)
& aElementOf0(W2,W0) )
| ~ aSupremumOfIn0(W2,W1,W0) ) )
| ~ aSubsetOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f87]) ).
fof(f89,plain,
! [W0] :
( ! [W1] :
( ( ! [W2] :
( ( ~ sdtlseqdt0(W2,sK5_skl(W2,W1,W0))
& aUpperBoundOfIn0(sK5_skl(W2,W1,W0),W1,W0) )
| ~ aUpperBoundOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| aSupremumOfIn0(W2,W1,W0) )
& ! [W2] :
( ( ! [W3] :
( sdtlseqdt0(W2,W3)
| ~ aUpperBoundOfIn0(W3,W1,W0) )
& aUpperBoundOfIn0(W2,W1,W0)
& aElementOf0(W2,W0) )
| ~ aSupremumOfIn0(W2,W1,W0) ) )
| ~ aSubsetOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W3,sK5_skl(W2,W1,W0))],[f88]) ).
fof(f90,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aSupremumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f91,plain,
! [X0,X1,X2] :
( aUpperBoundOfIn0(X2,X1,X0)
| ~ aSupremumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f93,plain,
! [X0,X1,X2] :
( aUpperBoundOfIn0(sK5_skl(X2,X1,X0),X1,X0)
| ~ aUpperBoundOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| aSupremumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ~ sdtlseqdt0(X2,sK5_skl(X2,X1,X0))
| ~ aUpperBoundOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| aSupremumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f95,plain,
! [W0] :
( ! [W1] :
( ! [W2,W3] :
( W2 = W3
| ~ aSupremumOfIn0(W3,W1,W0)
| ~ aSupremumOfIn0(W2,W1,W0) )
| ~ aSubsetOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f96,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ aSupremumOfIn0(X3,X1,X0)
| ~ aSupremumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f97,plain,
! [W0] :
( ! [W1] :
( ! [W2,W3] :
( W2 = W3
| ~ aInfimumOfIn0(W3,W1,W0)
| ~ aInfimumOfIn0(W2,W1,W0) )
| ~ aSubsetOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f98,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ aInfimumOfIn0(X3,X1,X0)
| ~ aInfimumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f99,plain,
! [W0] :
( aCompleteLattice0(W0)
<=> ( ! [W1] :
( ? [W2] :
( ? [W3] : aSupremumOfIn0(W3,W1,W0)
& aInfimumOfIn0(W2,W1,W0) )
| ~ aSubsetOf0(W1,W0) )
& aSet0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f100,plain,
! [W0] :
( ( ? [W1] :
( ! [W2] :
( ! [W3] : ~ aSupremumOfIn0(W3,W1,W0)
| ~ aInfimumOfIn0(W2,W1,W0) )
& aSubsetOf0(W1,W0) )
| ~ aSet0(W0)
| aCompleteLattice0(W0) )
& ( ( ! [W1] :
( ? [W2] :
( ? [W3] : aSupremumOfIn0(W3,W1,W0)
& aInfimumOfIn0(W2,W1,W0) )
| ~ aSubsetOf0(W1,W0) )
& aSet0(W0) )
| ~ aCompleteLattice0(W0) ) ),
inference(NNF_transformation,[status(thm)],[f99]) ).
fof(f101,plain,
( ! [W0] :
( ? [W1] :
( ( ! [W3] : ~ aSupremumOfIn0(W3,W1,W0)
| ! [W2] : ~ aInfimumOfIn0(W2,W1,W0) )
& aSubsetOf0(W1,W0) )
| ~ aSet0(W0)
| aCompleteLattice0(W0) )
& ! [W0] :
( ( ! [W1] :
( ( ? [W3] : aSupremumOfIn0(W3,W1,W0)
& ? [W2] : aInfimumOfIn0(W2,W1,W0) )
| ~ aSubsetOf0(W1,W0) )
& aSet0(W0) )
| ~ aCompleteLattice0(W0) ) ),
inference(miniscoping,[status(thm)],[f100]) ).
fof(f102,plain,
( ! [W0] :
( ( ( ! [W3] : ~ aSupremumOfIn0(W3,sK8_skl(W0),W0)
| ! [W2] : ~ aInfimumOfIn0(W2,sK8_skl(W0),W0) )
& aSubsetOf0(sK8_skl(W0),W0) )
| ~ aSet0(W0)
| aCompleteLattice0(W0) )
& ! [W0] :
( ( ! [W1] :
( ( aSupremumOfIn0(sK7_skl(W1,W0),W1,W0)
& aInfimumOfIn0(sK6_skl(W1,W0),W1,W0) )
| ~ aSubsetOf0(W1,W0) )
& aSet0(W0) )
| ~ aCompleteLattice0(W0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl,sK8_skl]),skolemize(W2,sK6_skl(W1,W0)),skolemize(W3,sK7_skl(W1,W0)),skolemize(W1,sK8_skl(W0))],[f101]) ).
fof(f104,plain,
! [X0,X1] :
( aInfimumOfIn0(sK6_skl(X1,X0),X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aCompleteLattice0(X0) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f105,plain,
! [X0,X1] :
( aSupremumOfIn0(sK7_skl(X1,X0),X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aCompleteLattice0(X0) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f113,plain,
! [W0] :
( aSet0(szRzazndt0(W0))
| ~ aFunction0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f114,plain,
! [X0] :
( aSet0(szRzazndt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [W0,W1] :
( ( isOn0(W0,W1)
<=> ( szRzazndt0(W0) = W1
& szDzozmdt0(W0) = szRzazndt0(W0) ) )
| ~ aSet0(W1)
| ~ aFunction0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f116,plain,
! [W0,W1] :
( ( ( szRzazndt0(W0) != W1
| szDzozmdt0(W0) != szRzazndt0(W0)
| isOn0(W0,W1) )
& ( ( szRzazndt0(W0) = W1
& szDzozmdt0(W0) = szRzazndt0(W0) )
| ~ isOn0(W0,W1) ) )
| ~ aSet0(W1)
| ~ aFunction0(W0) ),
inference(NNF_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
! [X0,X1] :
( szDzozmdt0(X0) = szRzazndt0(X0)
| ~ isOn0(X0,X1)
| ~ aSet0(X1)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f118,plain,
! [X0,X1] :
( szRzazndt0(X0) = X1
| ~ isOn0(X0,X1)
| ~ aSet0(X1)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f119,plain,
! [X0,X1] :
( szRzazndt0(X0) != X1
| szDzozmdt0(X0) != szRzazndt0(X0)
| isOn0(X0,X1)
| ~ aSet0(X1)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f120,plain,
! [W0] :
( ! [W1] :
( aElementOf0(sdtlpdtrp0(W0,W1),szRzazndt0(W0))
| ~ aElementOf0(W1,szDzozmdt0(W0)) )
| ~ aFunction0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f121,plain,
! [X0,X1] :
( aElementOf0(sdtlpdtrp0(X0,X1),szRzazndt0(X0))
| ~ aElementOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f122,plain,
! [W0] :
( ! [W1] :
( aFixedPointOf0(W1,W0)
<=> ( sdtlpdtrp0(W0,W1) = W1
& aElementOf0(W1,szDzozmdt0(W0)) ) )
| ~ aFunction0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f123,plain,
! [W0] :
( ! [W1] :
( ( sdtlpdtrp0(W0,W1) != W1
| ~ aElementOf0(W1,szDzozmdt0(W0))
| aFixedPointOf0(W1,W0) )
& ( ( sdtlpdtrp0(W0,W1) = W1
& aElementOf0(W1,szDzozmdt0(W0)) )
| ~ aFixedPointOf0(W1,W0) ) )
| ~ aFunction0(W0) ),
inference(NNF_transformation,[status(thm)],[f122]) ).
fof(f124,plain,
! [W0] :
( ( ! [W1] :
( sdtlpdtrp0(W0,W1) != W1
| ~ aElementOf0(W1,szDzozmdt0(W0))
| aFixedPointOf0(W1,W0) )
& ! [W1] :
( ( sdtlpdtrp0(W0,W1) = W1
& aElementOf0(W1,szDzozmdt0(W0)) )
| ~ aFixedPointOf0(W1,W0) ) )
| ~ aFunction0(W0) ),
inference(miniscoping,[status(thm)],[f123]) ).
fof(f126,plain,
! [X0,X1] :
( sdtlpdtrp0(X0,X1) = X1
| ~ aFixedPointOf0(X1,X0)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f127,plain,
! [X0,X1] :
( sdtlpdtrp0(X0,X1) != X1
| ~ aElementOf0(X1,szDzozmdt0(X0))
| aFixedPointOf0(X1,X0)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f128,plain,
! [W0] :
( ( isMonotone0(W0)
<=> ! [W1,W2] :
( sdtlseqdt0(sdtlpdtrp0(W0,W1),sdtlpdtrp0(W0,W2))
| ~ sdtlseqdt0(W1,W2)
| ~ aElementOf0(W2,szDzozmdt0(W0))
| ~ aElementOf0(W1,szDzozmdt0(W0)) ) )
| ~ aFunction0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f129,plain,
! [W0] :
( ( ( ? [W1,W2] :
( ~ sdtlseqdt0(sdtlpdtrp0(W0,W1),sdtlpdtrp0(W0,W2))
& sdtlseqdt0(W1,W2)
& aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W1,szDzozmdt0(W0)) )
| isMonotone0(W0) )
& ( ! [W1,W2] :
( sdtlseqdt0(sdtlpdtrp0(W0,W1),sdtlpdtrp0(W0,W2))
| ~ sdtlseqdt0(W1,W2)
| ~ aElementOf0(W2,szDzozmdt0(W0))
| ~ aElementOf0(W1,szDzozmdt0(W0)) )
| ~ isMonotone0(W0) ) )
| ~ aFunction0(W0) ),
inference(NNF_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
! [W0] :
( ( ( ( ~ sdtlseqdt0(sdtlpdtrp0(W0,sK9_skl(W0)),sdtlpdtrp0(W0,sK10_skl(W0)))
& sdtlseqdt0(sK9_skl(W0),sK10_skl(W0))
& aElementOf0(sK10_skl(W0),szDzozmdt0(W0))
& aElementOf0(sK9_skl(W0),szDzozmdt0(W0)) )
| isMonotone0(W0) )
& ( ! [W1,W2] :
( sdtlseqdt0(sdtlpdtrp0(W0,W1),sdtlpdtrp0(W0,W2))
| ~ sdtlseqdt0(W1,W2)
| ~ aElementOf0(W2,szDzozmdt0(W0))
| ~ aElementOf0(W1,szDzozmdt0(W0)) )
| ~ isMonotone0(W0) ) )
| ~ aFunction0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl]),skolemize(W1,sK9_skl(W0)),skolemize(W2,sK10_skl(W0))],[f129]) ).
fof(f131,plain,
! [X0,X1,X2] :
( sdtlseqdt0(sdtlpdtrp0(X0,X1),sdtlpdtrp0(X0,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,szDzozmdt0(X0))
| ~ aElementOf0(X1,szDzozmdt0(X0))
| ~ isMonotone0(X0)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f136,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(f137,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(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] :
( ? [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)],[f136,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] :
( ( ? [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)],[f138]) ).
fof(f140,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))],[f139]) ).
fof(f141,plain,
aSet0(xU),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f144,plain,
! [X0,X1] :
( sdtlseqdt0(sK11_skl(X0),X1)
| ~ aElementOf0(X1,X0)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f145,plain,
! [X0] :
( aLowerBoundOfIn0(sK11_skl(X0),X0,xU)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f146,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sK11_skl(X0))
| aElementOf0(sK12_skl(X1,X0),X0)
| ~ aElementOf0(X1,xU)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f147,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sK11_skl(X0))
| ~ sdtlseqdt0(X1,sK12_skl(X1,X0))
| ~ aElementOf0(X1,xU)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f148,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sK11_skl(X0))
| ~ aLowerBoundOfIn0(X1,X0,xU)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f149,plain,
! [X0] :
( aInfimumOfIn0(sK11_skl(X0),X0,xU)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f152,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sK13_skl(X0))
| ~ aElementOf0(X1,X0)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f153,plain,
! [X0] :
( aUpperBoundOfIn0(sK13_skl(X0),X0,xU)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f154,plain,
! [X0,X1] :
( sdtlseqdt0(sK13_skl(X0),X1)
| aElementOf0(sK14_skl(X1,X0),X0)
| ~ aElementOf0(X1,xU)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f155,plain,
! [X0,X1] :
( sdtlseqdt0(sK13_skl(X0),X1)
| ~ sdtlseqdt0(sK14_skl(X1,X0),X1)
| ~ aElementOf0(X1,xU)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f157,plain,
! [X0] :
( aSupremumOfIn0(sK13_skl(X0),X0,xU)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f158,plain,
aCompleteLattice0(xU),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f159,plain,
aFunction0(xf),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f160,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)],[f140]) ).
fof(f161,plain,
isMonotone0(xf),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f162,plain,
szDzozmdt0(xf) = szRzazndt0(xf),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f163,plain,
szRzazndt0(xf) = xU,
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f164,plain,
isOn0(xf,xU),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f165,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(f166,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)],[f165]) ).
fof(f167,plain,
aSet0(xS),
inference(cnf_transformation,[status(thm)],[f166]) ).
fof(f168,plain,
! [X0] :
( aElementOf0(X0,szDzozmdt0(xf))
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[status(thm)],[f166]) ).
fof(f169,plain,
! [X0] :
( sdtlpdtrp0(xf,X0) = X0
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[status(thm)],[f166]) ).
fof(f170,plain,
! [X0] :
( aFixedPointOf0(X0,xf)
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[status(thm)],[f166]) ).
fof(f171,plain,
! [X0] :
( aElementOf0(X0,xS)
| sdtlpdtrp0(xf,X0) != X0
| ~ aElementOf0(X0,szDzozmdt0(xf)) ),
inference(cnf_transformation,[status(thm)],[f166]) ).
fof(f172,plain,
! [X0] :
( aElementOf0(X0,xS)
| ~ aFixedPointOf0(X0,xf) ),
inference(cnf_transformation,[status(thm)],[f166]) ).
fof(f174,plain,
( aSubsetOf0(xT,xS)
& ! [W0] :
( aElementOf0(W0,xS)
| ~ aElementOf0(W0,xT) )
& aSet0(xT) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f175,plain,
aSet0(xT),
inference(cnf_transformation,[status(thm)],[f174]) ).
fof(f176,plain,
! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[status(thm)],[f174]) ).
fof(f177,plain,
aSubsetOf0(xT,xS),
inference(cnf_transformation,[status(thm)],[f174]) ).
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) )
& ( ( 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(f179,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)],[f178]) ).
fof(f180,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))],[f179]) ).
fof(f181,plain,
aSet0(xP),
inference(cnf_transformation,[status(thm)],[f180]) ).
fof(f182,plain,
! [X0] :
( aElementOf0(X0,xU)
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[status(thm)],[f180]) ).
fof(f184,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| ~ aElementOf0(X1,xT)
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[status(thm)],[f180]) ).
fof(f185,plain,
! [X0] :
( aUpperBoundOfIn0(X0,xT,xU)
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[status(thm)],[f180]) ).
fof(f186,plain,
! [X0] :
( aElementOf0(X0,xP)
| aElementOf0(sK15_skl(X0),xT)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
| ~ aElementOf0(X0,xU) ),
inference(cnf_transformation,[status(thm)],[f180]) ).
fof(f187,plain,
! [X0] :
( aElementOf0(X0,xP)
| ~ sdtlseqdt0(sK15_skl(X0),X0)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
| ~ aElementOf0(X0,xU) ),
inference(cnf_transformation,[status(thm)],[f180]) ).
fof(f188,plain,
! [X0] :
( aElementOf0(X0,xP)
| ~ aUpperBoundOfIn0(X0,xT,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
| ~ aElementOf0(X0,xU) ),
inference(cnf_transformation,[status(thm)],[f180]) ).
fof(f190,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(f191,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))],[f190]) ).
fof(f192,plain,
aElementOf0(xp,xU),
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f194,plain,
! [X0] :
( sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f195,plain,
aLowerBoundOfIn0(xp,xP,xU),
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f196,plain,
! [X0] :
( sdtlseqdt0(X0,xp)
| aElementOf0(sK16_skl(X0),xP)
| ~ aElementOf0(X0,xU) ),
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f197,plain,
! [X0] :
( sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,sK16_skl(X0))
| ~ aElementOf0(X0,xU) ),
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f198,plain,
! [X0] :
( sdtlseqdt0(X0,xp)
| ~ aLowerBoundOfIn0(X0,xP,xU) ),
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f199,plain,
aInfimumOfIn0(xp,xP,xU),
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f200,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)],[f29]) ).
fof(f202,plain,
aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f203,plain,
! [X0] :
( sdtlseqdt0(X0,sdtlpdtrp0(xf,xp))
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f204,plain,
aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f205,plain,
( ( ~ aSupremumOfIn0(xp,xT,xS)
& ( ? [W0] :
( ~ sdtlseqdt0(xp,W0)
& aUpperBoundOfIn0(W0,xT,xS)
& ! [W1] :
( sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,xT) )
& aElementOf0(W0,xS) )
| ( ~ aUpperBoundOfIn0(xp,xT,xS)
& ? [W0] :
( ~ sdtlseqdt0(W0,xp)
& aElementOf0(W0,xT) ) ) ) )
| ( ~ aFixedPointOf0(xp,xf)
& ( sdtlpdtrp0(xf,xp) != xp
| ~ aElementOf0(xp,szDzozmdt0(xf)) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f206,definition,
( sP1_prd
<=> ( ~ aFixedPointOf0(xp,xf)
& ( sdtlpdtrp0(xf,xp) != xp
| ~ aElementOf0(xp,szDzozmdt0(xf)) ) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f207,plain,
( ( ~ aSupremumOfIn0(xp,xT,xS)
& ( ? [W0] :
( ~ sdtlseqdt0(xp,W0)
& aUpperBoundOfIn0(W0,xT,xS)
& ! [W1] :
( sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,xT) )
& aElementOf0(W0,xS) )
| ( ~ aUpperBoundOfIn0(xp,xT,xS)
& ? [W0] :
( ~ sdtlseqdt0(W0,xp)
& aElementOf0(W0,xT) ) ) ) )
| sP1_prd ),
inference(formula_renaming,[status(thm)],[f205,f206]) ).
fof(f208,definition,
( sP2_prd
<=> ( ~ aUpperBoundOfIn0(xp,xT,xS)
& ? [W0] :
( ~ sdtlseqdt0(W0,xp)
& aElementOf0(W0,xT) ) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f209,plain,
( ( ~ aSupremumOfIn0(xp,xT,xS)
& ( ? [W0] :
( ~ sdtlseqdt0(xp,W0)
& aUpperBoundOfIn0(W0,xT,xS)
& ! [W1] :
( sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,xT) )
& aElementOf0(W0,xS) )
| sP2_prd ) )
| sP1_prd ),
inference(formula_renaming,[status(thm)],[f207,f208]) ).
fof(f210,plain,
( ( ~ aSupremumOfIn0(xp,xT,xS)
& ( ( ~ sdtlseqdt0(xp,sK17_skl)
& aUpperBoundOfIn0(sK17_skl,xT,xS)
& ! [W1] :
( sdtlseqdt0(W1,sK17_skl)
| ~ aElementOf0(W1,xT) )
& aElementOf0(sK17_skl,xS) )
| sP2_prd ) )
| sP1_prd ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl]),skolemize(W0,sK17_skl)],[f209]) ).
fof(f211,plain,
( aElementOf0(sK17_skl,xS)
| sP2_prd
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f212,plain,
! [X0] :
( sdtlseqdt0(X0,sK17_skl)
| ~ aElementOf0(X0,xT)
| sP2_prd
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f213,plain,
( aUpperBoundOfIn0(sK17_skl,xT,xS)
| sP2_prd
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f214,plain,
( ~ sdtlseqdt0(xp,sK17_skl)
| sP2_prd
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f215,plain,
( ~ aSupremumOfIn0(xp,xT,xS)
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f216,plain,
! [W0] :
( ( aSubsetOf0(W0,xU)
| ( ! [W1] :
( aElementOf0(W1,xU)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| sP0_prd(W0) )
& ( ( ~ aSubsetOf0(W0,xU)
& ( ? [W1] :
( ~ aElementOf0(W1,xU)
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ) )
| ~ sP0_prd(W0) ) ),
inference(NNF_transformation,[status(thm)],[f137]) ).
fof(f217,plain,
( ! [W0] :
( aSubsetOf0(W0,xU)
| ( ! [W1] :
( aElementOf0(W1,xU)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| sP0_prd(W0) )
& ! [W0] :
( ( ~ aSubsetOf0(W0,xU)
& ( ? [W1] :
( ~ aElementOf0(W1,xU)
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ) )
| ~ sP0_prd(W0) ) ),
inference(miniscoping,[status(thm)],[f216]) ).
fof(f218,plain,
( ! [W0] :
( aSubsetOf0(W0,xU)
| ( ! [W1] :
( aElementOf0(W1,xU)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| sP0_prd(W0) )
& ! [W0] :
( ( ~ aSubsetOf0(W0,xU)
& ( ( ~ aElementOf0(sK18_skl(W0),xU)
& aElementOf0(sK18_skl(W0),W0) )
| ~ aSet0(W0) ) )
| ~ sP0_prd(W0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18_skl]),skolemize(W1,sK18_skl(W0))],[f217]) ).
fof(f219,plain,
! [X0] :
( aElementOf0(sK18_skl(X0),X0)
| ~ aSet0(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f220,plain,
! [X0] :
( ~ aElementOf0(sK18_skl(X0),xU)
| ~ aSet0(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f221,plain,
! [X0] :
( ~ aSubsetOf0(X0,xU)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f223,plain,
! [X0,X1] :
( aSubsetOf0(X0,xU)
| aElementOf0(X1,xU)
| ~ aElementOf0(X1,X0)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f224,plain,
( ( aFixedPointOf0(xp,xf)
| ( sdtlpdtrp0(xf,xp) = xp
& aElementOf0(xp,szDzozmdt0(xf)) )
| sP1_prd )
& ( ( ~ aFixedPointOf0(xp,xf)
& ( sdtlpdtrp0(xf,xp) != xp
| ~ aElementOf0(xp,szDzozmdt0(xf)) ) )
| ~ sP1_prd ) ),
inference(NNF_transformation,[status(thm)],[f206]) ).
fof(f225,plain,
( sdtlpdtrp0(xf,xp) != xp
| ~ aElementOf0(xp,szDzozmdt0(xf))
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f224]) ).
fof(f226,plain,
( ~ aFixedPointOf0(xp,xf)
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f224]) ).
fof(f229,plain,
( ( aUpperBoundOfIn0(xp,xT,xS)
| ! [W0] :
( sdtlseqdt0(W0,xp)
| ~ aElementOf0(W0,xT) )
| sP2_prd )
& ( ( ~ aUpperBoundOfIn0(xp,xT,xS)
& ? [W0] :
( ~ sdtlseqdt0(W0,xp)
& aElementOf0(W0,xT) ) )
| ~ sP2_prd ) ),
inference(NNF_transformation,[status(thm)],[f208]) ).
fof(f230,plain,
( ( aUpperBoundOfIn0(xp,xT,xS)
| ! [W0] :
( sdtlseqdt0(W0,xp)
| ~ aElementOf0(W0,xT) )
| sP2_prd )
& ( ( ~ aUpperBoundOfIn0(xp,xT,xS)
& ~ sdtlseqdt0(sK19_skl,xp)
& aElementOf0(sK19_skl,xT) )
| ~ sP2_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl]),skolemize(W0,sK19_skl)],[f229]) ).
fof(f231,plain,
( aElementOf0(sK19_skl,xT)
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f232,plain,
( ~ sdtlseqdt0(sK19_skl,xp)
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f233,plain,
( ~ aUpperBoundOfIn0(xp,xT,xS)
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f234,plain,
! [X0] :
( aUpperBoundOfIn0(xp,xT,xS)
| sdtlseqdt0(X0,xp)
| ~ aElementOf0(X0,xT)
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f235,definition,
( sQ0_spl
<=> sP1_prd ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f238,definition,
( sQ1_spl
<=> sP2_prd ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f241,definition,
( sQ2_spl
<=> aElementOf0(sK17_skl,xS) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f242,plain,
( ~ sQ2_spl
| aElementOf0(sK17_skl,xS) ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f243,plain,
( sQ2_spl
| ~ aElementOf0(sK17_skl,xS) ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f244,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f211,f235,f238,f241]) ).
fof(f245,definition,
! [X0] :
( sQ3_spl
<=> ( sdtlseqdt0(X0,sK17_skl)
| ~ aElementOf0(X0,xT) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f246,plain,
! [X0] :
( ~ sQ3_spl
| sdtlseqdt0(X0,sK17_skl)
| ~ aElementOf0(X0,xT) ),
inference(component_clause,[status(thm)],[f245]) ).
fof(f248,plain,
( sQ3_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f212,f235,f238,f245]) ).
fof(f249,definition,
( sQ4_spl
<=> aUpperBoundOfIn0(sK17_skl,xT,xS) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f250,plain,
( ~ sQ4_spl
| aUpperBoundOfIn0(sK17_skl,xT,xS) ),
inference(component_clause,[status(thm)],[f249]) ).
fof(f252,plain,
( sQ4_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f213,f235,f238,f249]) ).
fof(f253,definition,
( sQ5_spl
<=> sdtlseqdt0(xp,sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f255,plain,
( sQ5_spl
| ~ sdtlseqdt0(xp,sK17_skl) ),
inference(component_clause,[status(thm)],[f253]) ).
fof(f256,plain,
( ~ sQ5_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f214,f235,f238,f253]) ).
fof(f257,definition,
( sQ6_spl
<=> aSupremumOfIn0(xp,xT,xS) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f260,plain,
( ~ sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f215,f235,f257]) ).
fof(f261,definition,
( sQ7_spl
<=> aElementOf0(xp,szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f263,plain,
( sQ7_spl
| ~ aElementOf0(xp,szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f261]) ).
fof(f264,definition,
( sQ8_spl
<=> sdtlpdtrp0(xf,xp) = xp ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f265,plain,
( ~ sQ8_spl
| sdtlpdtrp0(xf,xp) = xp ),
inference(component_clause,[status(thm)],[f264]) ).
fof(f266,plain,
( sQ8_spl
| sdtlpdtrp0(xf,xp) != xp ),
inference(component_clause,[status(thm)],[f264]) ).
fof(f267,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f225,f235,f261,f264]) ).
fof(f268,definition,
( sQ9_spl
<=> aFixedPointOf0(xp,xf) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f269,plain,
( ~ sQ9_spl
| aFixedPointOf0(xp,xf) ),
inference(component_clause,[status(thm)],[f268]) ).
fof(f270,plain,
( sQ9_spl
| ~ aFixedPointOf0(xp,xf) ),
inference(component_clause,[status(thm)],[f268]) ).
fof(f271,plain,
( ~ sQ9_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f226,f235,f268]) ).
fof(f274,definition,
( sQ10_spl
<=> aElementOf0(sK19_skl,xT) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f275,plain,
( ~ sQ10_spl
| aElementOf0(sK19_skl,xT) ),
inference(component_clause,[status(thm)],[f274]) ).
fof(f277,plain,
( sQ10_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f231,f238,f274]) ).
fof(f278,definition,
( sQ11_spl
<=> sdtlseqdt0(sK19_skl,xp) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f280,plain,
( sQ11_spl
| ~ sdtlseqdt0(sK19_skl,xp) ),
inference(component_clause,[status(thm)],[f278]) ).
fof(f281,plain,
( ~ sQ11_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f232,f238,f278]) ).
fof(f282,definition,
( sQ12_spl
<=> aUpperBoundOfIn0(xp,xT,xS) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f283,plain,
( ~ sQ12_spl
| aUpperBoundOfIn0(xp,xT,xS) ),
inference(component_clause,[status(thm)],[f282]) ).
fof(f284,plain,
( sQ12_spl
| ~ aUpperBoundOfIn0(xp,xT,xS) ),
inference(component_clause,[status(thm)],[f282]) ).
fof(f285,plain,
( ~ sQ12_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f233,f238,f282]) ).
fof(f286,definition,
! [X0] :
( sQ13_spl
<=> ( sdtlseqdt0(X0,xp)
| ~ aElementOf0(X0,xT) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f287,plain,
! [X0] :
( ~ sQ13_spl
| sdtlseqdt0(X0,xp)
| ~ aElementOf0(X0,xT) ),
inference(component_clause,[status(thm)],[f286]) ).
fof(f289,plain,
( sQ12_spl
| sQ13_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f234,f238,f286,f282]) ).
fof(f290,plain,
! [X0] :
( szDzozmdt0(X0) != szRzazndt0(X0)
| isOn0(X0,szRzazndt0(X0))
| ~ aSet0(szRzazndt0(X0))
| ~ aFunction0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f119]) ).
fof(f291,plain,
( sQ9_spl
| ~ aElementOf0(xp,xS) ),
inference(resolution,[status(thm)],[f170,f270]) ).
fof(f293,plain,
( isEmpty0(xT)
| ~ aSet0(xT)
| aElementOf0(sK0_skl(xT),xS) ),
inference(resolution,[status(thm)],[f176,f44]) ).
fof(f294,definition,
( sQ14_spl
<=> aElementOf0(sK0_skl(xT),xS) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f295,plain,
( ~ sQ14_spl
| aElementOf0(sK0_skl(xT),xS) ),
inference(component_clause,[status(thm)],[f294]) ).
fof(f297,definition,
( sQ15_spl
<=> aSet0(xT) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f299,plain,
( sQ15_spl
| ~ aSet0(xT) ),
inference(component_clause,[status(thm)],[f297]) ).
fof(f300,definition,
( sQ16_spl
<=> isEmpty0(xT) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f301,plain,
( ~ sQ16_spl
| isEmpty0(xT) ),
inference(component_clause,[status(thm)],[f300]) ).
fof(f303,plain,
( sQ16_spl
| ~ sQ15_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f293,f294,f297,f300]) ).
fof(f304,plain,
! [X0] :
( ~ sQ16_spl
| ~ aElementOf0(X0,xT)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[f301,f43]) ).
fof(f305,definition,
! [X0] :
( sQ17_spl
<=> ~ aElementOf0(X0,xT) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f306,plain,
! [X0] :
( ~ sQ17_spl
| ~ aElementOf0(X0,xT) ),
inference(component_clause,[status(thm)],[f305]) ).
fof(f308,plain,
( ~ sQ16_spl
| sQ17_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f304,f297,f305,f300]) ).
fof(f309,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f299,f175]) ).
fof(f310,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f309]) ).
fof(f311,plain,
( ~ sQ17_spl
| isEmpty0(xT)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[f306,f44]) ).
fof(f312,plain,
( ~ sQ17_spl
| sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f311,f297,f300,f305]) ).
fof(f313,plain,
( aSet0(xU)
| ~ aFunction0(xf) ),
inference(paramodulation,[status(thm)],[f163,f114]) ).
fof(f314,definition,
( sQ18_spl
<=> aFunction0(xf) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f316,plain,
( sQ18_spl
| ~ aFunction0(xf) ),
inference(component_clause,[status(thm)],[f314]) ).
fof(f317,definition,
( sQ19_spl
<=> aSet0(xU) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f320,plain,
( sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f313,f314,f317]) ).
fof(f321,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f316,f159]) ).
fof(f322,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f321]) ).
fof(f323,plain,
( sQ7_spl
| ~ aElementOf0(xp,xU) ),
inference(backward_demodulation,[status(thm)],[f324,f263]) ).
fof(f324,plain,
szDzozmdt0(xf) = xU,
inference(forward_demodulation,[status(thm)],[f163,f162]) ).
fof(f326,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f323,f192]) ).
fof(f327,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f326]) ).
fof(f331,plain,
! [X0,X1] :
( sQ11_spl
| ~ aElementOf0(sK19_skl,X1)
| ~ aUpperBoundOfIn0(xp,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f280,f74]) ).
fof(f332,plain,
( ~ sQ9_spl
| aElementOf0(xp,xS) ),
inference(resolution,[status(thm)],[f269,f172]) ).
fof(f333,plain,
! [X0] :
( ~ aSet0(xS)
| aSubsetOf0(xS,X0)
| ~ aSet0(X0)
| sdtlpdtrp0(xf,sK1_skl(xS,X0)) = sK1_skl(xS,X0) ),
inference(resolution,[status(thm)],[f169,f51]) ).
fof(f334,plain,
( ~ sQ14_spl
| sdtlpdtrp0(xf,sK0_skl(xT)) = sK0_skl(xT) ),
inference(resolution,[status(thm)],[f169,f295]) ).
fof(f335,plain,
( isEmpty0(xS)
| ~ aSet0(xS)
| sdtlpdtrp0(xf,sK0_skl(xS)) = sK0_skl(xS) ),
inference(resolution,[status(thm)],[f169,f44]) ).
fof(f336,plain,
( ~ sQ9_spl
| sdtlpdtrp0(xf,xp) = xp ),
inference(resolution,[status(thm)],[f169,f332]) ).
fof(f337,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f169,f176]) ).
fof(f338,plain,
! [X0,X1] :
( ~ aElementOf0(X0,X1)
| ~ aSubsetOf0(X1,xS)
| ~ aSet0(xS)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f169,f50]) ).
fof(f339,definition,
! [X0] :
( sQ20_spl
<=> ( aSubsetOf0(xS,X0)
| ~ aSet0(X0)
| sdtlpdtrp0(xf,sK1_skl(xS,X0)) = sK1_skl(xS,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f342,definition,
( sQ21_spl
<=> aSet0(xS) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f344,plain,
( sQ21_spl
| ~ aSet0(xS) ),
inference(component_clause,[status(thm)],[f342]) ).
fof(f345,plain,
( ~ sQ21_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f333,f339,f342]) ).
fof(f346,definition,
( sQ22_spl
<=> sdtlpdtrp0(xf,sK0_skl(xS)) = sK0_skl(xS) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f347,plain,
( ~ sQ22_spl
| sdtlpdtrp0(xf,sK0_skl(xS)) = sK0_skl(xS) ),
inference(component_clause,[status(thm)],[f346]) ).
fof(f349,definition,
( sQ23_spl
<=> isEmpty0(xS) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f350,plain,
( ~ sQ23_spl
| isEmpty0(xS) ),
inference(component_clause,[status(thm)],[f349]) ).
fof(f352,plain,
( sQ23_spl
| ~ sQ21_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f335,f346,f342,f349]) ).
fof(f353,definition,
! [X0,X1] :
( sQ24_spl
<=> ( ~ aElementOf0(X0,X1)
| ~ aSubsetOf0(X1,xS)
| sdtlpdtrp0(xf,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f354,plain,
! [X0,X1] :
( ~ sQ24_spl
| ~ aElementOf0(X0,X1)
| ~ aSubsetOf0(X1,xS)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(component_clause,[status(thm)],[f353]) ).
fof(f356,plain,
( ~ sQ21_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f338,f353,f342]) ).
fof(f357,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f344,f167]) ).
fof(f358,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f357]) ).
fof(f359,plain,
! [X0] :
( ~ aSet0(xT)
| aSubsetOf0(xT,X0)
| ~ aSet0(X0)
| sdtlpdtrp0(xf,sK1_skl(xT,X0)) = sK1_skl(xT,X0) ),
inference(resolution,[status(thm)],[f337,f51]) ).
fof(f361,plain,
( isEmpty0(xT)
| ~ aSet0(xT)
| sdtlpdtrp0(xf,sK0_skl(xT)) = sK0_skl(xT) ),
inference(resolution,[status(thm)],[f337,f44]) ).
fof(f362,plain,
! [X0,X1] :
( ~ aElementOf0(X0,X1)
| ~ aSubsetOf0(X1,xT)
| ~ aSet0(xT)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f337,f50]) ).
fof(f363,definition,
! [X0] :
( sQ25_spl
<=> ( aSubsetOf0(xT,X0)
| ~ aSet0(X0)
| sdtlpdtrp0(xf,sK1_skl(xT,X0)) = sK1_skl(xT,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f366,plain,
( ~ sQ15_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f359,f363,f297]) ).
fof(f367,definition,
( sQ26_spl
<=> sdtlpdtrp0(xf,sK0_skl(xT)) = sK0_skl(xT) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f370,plain,
( sQ16_spl
| ~ sQ15_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f361,f367,f297,f300]) ).
fof(f371,definition,
! [X0,X1] :
( sQ27_spl
<=> ( ~ aElementOf0(X0,X1)
| ~ aSubsetOf0(X1,xT)
| sdtlpdtrp0(xf,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f372,plain,
! [X0,X1] :
( ~ sQ27_spl
| ~ aElementOf0(X0,X1)
| ~ aSubsetOf0(X1,xT)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(component_clause,[status(thm)],[f371]) ).
fof(f374,plain,
( ~ sQ15_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f362,f371,f297]) ).
fof(f377,plain,
( ~ sQ10_spl
| ~ sQ17_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f275,f306]) ).
fof(f378,plain,
! [X0] :
( ~ sQ17_spl
| ~ aSet0(xT)
| aSubsetOf0(xT,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f306,f51]) ).
fof(f381,plain,
( ~ sQ10_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f377]) ).
fof(f382,definition,
! [X0] :
( sQ28_spl
<=> ( aSubsetOf0(xT,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f383,plain,
! [X0] :
( ~ sQ28_spl
| aSubsetOf0(xT,X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f382]) ).
fof(f385,plain,
( ~ sQ17_spl
| ~ sQ15_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f378,f382,f297,f305]) ).
fof(f394,plain,
! [X0] :
( sQ9_spl
| ~ aElementOf0(xp,X0)
| ~ aSubsetOf0(X0,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f291,f50]) ).
fof(f395,definition,
! [X0] :
( sQ30_spl
<=> ( ~ aElementOf0(xp,X0)
| ~ aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f396,plain,
! [X0] :
( ~ sQ30_spl
| ~ aElementOf0(xp,X0)
| ~ aSubsetOf0(X0,xS) ),
inference(component_clause,[status(thm)],[f395]) ).
fof(f398,plain,
( sQ9_spl
| sQ30_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f394,f342,f395,f268]) ).
fof(f399,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X1,X2)
| ~ aSet0(X2)
| X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f58,f39]) ).
fof(f400,plain,
( ~ sQ30_spl
| ~ aElementOf0(xp,xT) ),
inference(resolution,[status(thm)],[f396,f177]) ).
fof(f401,plain,
! [X0] :
( ~ sQ30_spl
| ~ aElementOf0(sK1_skl(X0,xS),xS)
| ~ aSet0(X0)
| ~ aSet0(xS)
| ~ aElementOf0(xp,X0) ),
inference(resolution,[status(thm)],[f396,f52]) ).
fof(f402,definition,
! [X0] :
( sQ31_spl
<=> ( ~ aElementOf0(sK1_skl(X0,xS),xS)
| ~ aSet0(X0)
| ~ aElementOf0(xp,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f403,plain,
! [X0] :
( ~ sQ31_spl
| ~ aElementOf0(sK1_skl(X0,xS),xS)
| ~ aSet0(X0)
| ~ aElementOf0(xp,X0) ),
inference(component_clause,[status(thm)],[f402]) ).
fof(f405,plain,
( ~ sQ30_spl
| ~ sQ21_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f401,f402,f342,f395]) ).
fof(f407,plain,
! [X0,X1] :
( ~ sQ31_spl
| ~ aElementOf0(sK1_skl(X0,xS),X1)
| ~ aSubsetOf0(X1,xS)
| ~ aSet0(xS)
| ~ aSet0(X0)
| ~ aElementOf0(xp,X0) ),
inference(resolution,[status(thm)],[f403,f50]) ).
fof(f408,definition,
( sQ32_spl
<=> aElementOf0(xp,xS) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f409,plain,
( ~ sQ32_spl
| aElementOf0(xp,xS) ),
inference(component_clause,[status(thm)],[f408]) ).
fof(f410,plain,
( sQ32_spl
| ~ aElementOf0(xp,xS) ),
inference(component_clause,[status(thm)],[f408]) ).
fof(f415,definition,
! [X0,X1] :
( sQ34_spl
<=> ( ~ aElementOf0(sK1_skl(X0,xS),X1)
| ~ aSubsetOf0(X1,xS)
| ~ aSet0(X0)
| ~ aElementOf0(xp,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f416,plain,
! [X0,X1] :
( ~ sQ34_spl
| ~ aElementOf0(sK1_skl(X0,xS),X1)
| ~ aSubsetOf0(X1,xS)
| ~ aSet0(X0)
| ~ aElementOf0(xp,X0) ),
inference(component_clause,[status(thm)],[f415]) ).
fof(f418,plain,
( ~ sQ31_spl
| ~ sQ21_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f407,f415,f342,f402]) ).
fof(f420,plain,
! [X0,X1] :
( ~ sQ34_spl
| ~ aElementOf0(sK1_skl(X1,xS),xS)
| ~ aSet0(X1)
| ~ aSet0(xS)
| ~ aElementOf0(sK1_skl(X0,xS),X1)
| ~ aSet0(X0)
| ~ aElementOf0(xp,X0) ),
inference(resolution,[status(thm)],[f416,f52]) ).
fof(f421,definition,
! [X0,X1] :
( sQ35_spl
<=> ( ~ aElementOf0(sK1_skl(X1,xS),xS)
| ~ aSet0(X1)
| ~ aElementOf0(sK1_skl(X0,xS),X1)
| ~ aSet0(X0)
| ~ aElementOf0(xp,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f422,plain,
! [X0,X1] :
( ~ sQ35_spl
| ~ aElementOf0(sK1_skl(X1,xS),xS)
| ~ aSet0(X1)
| ~ aElementOf0(sK1_skl(X0,xS),X1)
| ~ aSet0(X0)
| ~ aElementOf0(xp,X0) ),
inference(component_clause,[status(thm)],[f421]) ).
fof(f424,plain,
( ~ sQ34_spl
| ~ sQ21_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f420,f421,f342,f415]) ).
fof(f426,plain,
! [X0,X1,X2] :
( ~ sQ35_spl
| ~ aElementOf0(sK1_skl(X1,xS),X2)
| ~ aSubsetOf0(X2,xS)
| ~ aSet0(xS)
| ~ aSet0(X1)
| ~ aElementOf0(sK1_skl(X0,xS),X1)
| ~ aSet0(X0)
| ~ aElementOf0(xp,X0) ),
inference(resolution,[status(thm)],[f422,f50]) ).
fof(f428,definition,
! [X0,X1,X2] :
( sQ36_spl
<=> ( ~ aElementOf0(sK1_skl(X1,xS),X2)
| ~ aSubsetOf0(X2,xS)
| ~ aSet0(X1)
| ~ aElementOf0(sK1_skl(X0,xS),X1)
| ~ aSet0(X0)
| ~ aElementOf0(xp,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f429,plain,
! [X0,X1,X2] :
( ~ sQ36_spl
| ~ aElementOf0(sK1_skl(X1,xS),X2)
| ~ aSubsetOf0(X2,xS)
| ~ aSet0(X1)
| ~ aElementOf0(sK1_skl(X0,xS),X1)
| ~ aSet0(X0)
| ~ aElementOf0(xp,X0) ),
inference(component_clause,[status(thm)],[f428]) ).
fof(f431,plain,
( ~ sQ35_spl
| ~ sQ21_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f426,f428,f342,f421]) ).
fof(f440,definition,
( sQ38_spl
<=> aElementOf0(xp,xT) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f442,plain,
( sQ38_spl
| ~ aElementOf0(xp,xT) ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f451,plain,
! [X0] :
( sdtlpdtrp0(xf,X0) = X0
| ~ aFixedPointOf0(X0,xf) ),
inference(resolution,[status(thm)],[f126,f159]) ).
fof(f453,plain,
! [X0] :
( sdtlpdtrp0(xf,X0) != X0
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aFixedPointOf0(X0,xf) ),
inference(resolution,[status(thm)],[f127,f159]) ).
fof(f454,plain,
! [X0] :
( sdtlpdtrp0(xf,X0) != X0
| ~ aElementOf0(X0,xU)
| aFixedPointOf0(X0,xf) ),
inference(forward_demodulation,[status(thm)],[f324,f453]) ).
fof(f455,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)],[f324,f160]) ).
fof(f456,plain,
! [X0,X1] :
( sdtlseqdt0(sdtlpdtrp0(xf,X0),sdtlpdtrp0(xf,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,xU)
| ~ aElementOf0(X0,xU) ),
inference(forward_demodulation,[status(thm)],[f324,f455]) ).
fof(f457,plain,
! [X0] :
( sP0_prd(X0)
| aElementOf0(sK11_skl(X0),xU)
| ~ aSubsetOf0(X0,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f65,f145]) ).
fof(f458,plain,
( aElementOf0(xp,xU)
| ~ aSubsetOf0(xP,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f65,f195]) ).
fof(f459,definition,
! [X0] :
( sQ40_spl
<=> ( sP0_prd(X0)
| aElementOf0(sK11_skl(X0),xU)
| ~ aSubsetOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f462,plain,
( sQ40_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f457,f317,f459]) ).
fof(f463,definition,
( sQ41_spl
<=> aSubsetOf0(xP,xU) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f464,plain,
( ~ sQ41_spl
| aSubsetOf0(xP,xU) ),
inference(component_clause,[status(thm)],[f463]) ).
fof(f465,plain,
( sQ41_spl
| ~ aSubsetOf0(xP,xU) ),
inference(component_clause,[status(thm)],[f463]) ).
fof(f466,definition,
( sQ42_spl
<=> aElementOf0(xp,xU) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f469,plain,
( sQ42_spl
| ~ sQ41_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f458,f317,f463,f466]) ).
fof(f474,plain,
! [X0,X1,X2] :
( ~ sQ36_spl
| ~ aElementOf0(sK1_skl(X2,xS),xS)
| ~ aSet0(X2)
| ~ aSet0(xS)
| ~ aElementOf0(sK1_skl(X1,xS),X2)
| ~ aSet0(X1)
| ~ aElementOf0(sK1_skl(X0,xS),X1)
| ~ aSet0(X0)
| ~ aElementOf0(xp,X0) ),
inference(resolution,[status(thm)],[f429,f52]) ).
fof(f479,definition,
! [X0,X1,X2] :
( sQ44_spl
<=> ( ~ aElementOf0(sK1_skl(X2,xS),xS)
| ~ aSet0(X2)
| ~ aElementOf0(sK1_skl(X1,xS),X2)
| ~ aSet0(X1)
| ~ aElementOf0(sK1_skl(X0,xS),X1)
| ~ aSet0(X0)
| ~ aElementOf0(xp,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f480,plain,
! [X0,X1,X2] :
( ~ sQ44_spl
| ~ aElementOf0(sK1_skl(X2,xS),xS)
| ~ aSet0(X2)
| ~ aElementOf0(sK1_skl(X1,xS),X2)
| ~ aSet0(X1)
| ~ aElementOf0(sK1_skl(X0,xS),X1)
| ~ aSet0(X0)
| ~ aElementOf0(xp,X0) ),
inference(component_clause,[status(thm)],[f479]) ).
fof(f482,plain,
( ~ sQ36_spl
| ~ sQ21_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f474,f479,f342,f428]) ).
fof(f484,plain,
! [X0,X1,X2,X3] :
( ~ sQ44_spl
| ~ aElementOf0(sK1_skl(X2,xS),X3)
| ~ aSubsetOf0(X3,xS)
| ~ aSet0(xS)
| ~ aSet0(X2)
| ~ aElementOf0(sK1_skl(X1,xS),X2)
| ~ aSet0(X1)
| ~ aElementOf0(sK1_skl(X0,xS),X1)
| ~ aSet0(X0)
| ~ aElementOf0(xp,X0) ),
inference(resolution,[status(thm)],[f480,f50]) ).
fof(f486,definition,
! [X0,X1,X2,X3] :
( sQ45_spl
<=> ( ~ aElementOf0(sK1_skl(X2,xS),X3)
| ~ aSubsetOf0(X3,xS)
| ~ aSet0(X2)
| ~ aElementOf0(sK1_skl(X1,xS),X2)
| ~ aSet0(X1)
| ~ aElementOf0(sK1_skl(X0,xS),X1)
| ~ aSet0(X0)
| ~ aElementOf0(xp,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f487,plain,
! [X0,X1,X2,X3] :
( ~ sQ45_spl
| ~ aElementOf0(sK1_skl(X2,xS),X3)
| ~ aSubsetOf0(X3,xS)
| ~ aSet0(X2)
| ~ aElementOf0(sK1_skl(X1,xS),X2)
| ~ aSet0(X1)
| ~ aElementOf0(sK1_skl(X0,xS),X1)
| ~ aSet0(X0)
| ~ aElementOf0(xp,X0) ),
inference(component_clause,[status(thm)],[f486]) ).
fof(f489,plain,
( ~ sQ44_spl
| ~ sQ21_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f484,f486,f342,f479]) ).
fof(f493,plain,
! [X0,X1,X2,X3] :
( ~ sQ45_spl
| ~ aElementOf0(sK1_skl(X3,xS),xS)
| ~ aSet0(X3)
| ~ aSet0(xS)
| ~ aElementOf0(sK1_skl(X2,xS),X3)
| ~ aSet0(X2)
| ~ aElementOf0(sK1_skl(X1,xS),X2)
| ~ aSet0(X1)
| ~ aElementOf0(sK1_skl(X0,xS),X1)
| ~ aSet0(X0)
| ~ aElementOf0(xp,X0) ),
inference(resolution,[status(thm)],[f487,f52]) ).
fof(f498,definition,
! [X0,X1,X2,X3] :
( sQ47_spl
<=> ( ~ aElementOf0(sK1_skl(X3,xS),xS)
| ~ aSet0(X3)
| ~ aElementOf0(sK1_skl(X2,xS),X3)
| ~ aSet0(X2)
| ~ aElementOf0(sK1_skl(X1,xS),X2)
| ~ aSet0(X1)
| ~ aElementOf0(sK1_skl(X0,xS),X1)
| ~ aSet0(X0)
| ~ aElementOf0(xp,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f499,plain,
! [X0,X1,X2,X3] :
( ~ sQ47_spl
| ~ aElementOf0(sK1_skl(X3,xS),xS)
| ~ aSet0(X3)
| ~ aElementOf0(sK1_skl(X2,xS),X3)
| ~ aSet0(X2)
| ~ aElementOf0(sK1_skl(X1,xS),X2)
| ~ aSet0(X1)
| ~ aElementOf0(sK1_skl(X0,xS),X1)
| ~ aSet0(X0)
| ~ aElementOf0(xp,X0) ),
inference(component_clause,[status(thm)],[f498]) ).
fof(f501,plain,
( ~ sQ45_spl
| ~ sQ21_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f493,f498,f342,f486]) ).
fof(f503,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ47_spl
| ~ aElementOf0(sK1_skl(X3,xS),X4)
| ~ aSubsetOf0(X4,xS)
| ~ aSet0(xS)
| ~ aSet0(X3)
| ~ aElementOf0(sK1_skl(X2,xS),X3)
| ~ aSet0(X2)
| ~ aElementOf0(sK1_skl(X1,xS),X2)
| ~ aSet0(X1)
| ~ aElementOf0(sK1_skl(X0,xS),X1)
| ~ aSet0(X0)
| ~ aElementOf0(xp,X0) ),
inference(resolution,[status(thm)],[f499,f50]) ).
fof(f505,definition,
! [X0,X1,X2,X3,X4] :
( sQ48_spl
<=> ( ~ aElementOf0(sK1_skl(X3,xS),X4)
| ~ aSubsetOf0(X4,xS)
| ~ aSet0(X3)
| ~ aElementOf0(sK1_skl(X2,xS),X3)
| ~ aSet0(X2)
| ~ aElementOf0(sK1_skl(X1,xS),X2)
| ~ aSet0(X1)
| ~ aElementOf0(sK1_skl(X0,xS),X1)
| ~ aSet0(X0)
| ~ aElementOf0(xp,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f508,plain,
( ~ sQ47_spl
| ~ sQ21_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f503,f505,f342,f498]) ).
fof(f509,plain,
! [X0] :
( aElementOf0(X0,xU)
| ~ aElementOf0(X0,xS) ),
inference(forward_demodulation,[status(thm)],[f324,f168]) ).
fof(f510,plain,
( aElementOf0(sdtlpdtrp0(xf,xp),xU)
| ~ aSubsetOf0(xT,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f204,f73]) ).
fof(f511,definition,
( sQ49_spl
<=> aSubsetOf0(xT,xU) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f513,plain,
( sQ49_spl
| ~ aSubsetOf0(xT,xU) ),
inference(component_clause,[status(thm)],[f511]) ).
fof(f514,definition,
( sQ50_spl
<=> aElementOf0(sdtlpdtrp0(xf,xp),xU) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f515,plain,
( ~ sQ50_spl
| aElementOf0(sdtlpdtrp0(xf,xp),xU) ),
inference(component_clause,[status(thm)],[f514]) ).
fof(f517,plain,
( sQ50_spl
| ~ sQ49_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f510,f317,f511,f514]) ).
fof(f518,plain,
( ~ sQ28_spl
| sQ49_spl
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f513,f383]) ).
fof(f519,plain,
( sQ49_spl
| ~ aElementOf0(sK1_skl(xT,xU),xU)
| ~ aSet0(xT)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f513,f52]) ).
fof(f520,plain,
( ~ sQ28_spl
| sQ49_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f518,f141]) ).
fof(f521,plain,
( ~ sQ28_spl
| sQ49_spl ),
inference(contradiction_clause,[status(thm)],[f520]) ).
fof(f522,plain,
! [X0] :
( ~ sQ22_spl
| sdtlseqdt0(sdtlpdtrp0(xf,X0),sK0_skl(xS))
| ~ sdtlseqdt0(X0,sK0_skl(xS))
| ~ aElementOf0(sK0_skl(xS),xU)
| ~ aElementOf0(X0,xU) ),
inference(paramodulation,[status(thm)],[f347,f456]) ).
fof(f523,plain,
! [X0] :
( ~ sQ22_spl
| sdtlseqdt0(sK0_skl(xS),sdtlpdtrp0(xf,X0))
| ~ sdtlseqdt0(sK0_skl(xS),X0)
| ~ aElementOf0(X0,xU)
| ~ aElementOf0(sK0_skl(xS),xU) ),
inference(paramodulation,[status(thm)],[f347,f456]) ).
fof(f524,definition,
! [X0] :
( sQ51_spl
<=> ( sdtlseqdt0(sdtlpdtrp0(xf,X0),sK0_skl(xS))
| ~ sdtlseqdt0(X0,sK0_skl(xS))
| ~ aElementOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f527,definition,
( sQ52_spl
<=> aElementOf0(sK0_skl(xS),xU) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f528,plain,
( ~ sQ52_spl
| aElementOf0(sK0_skl(xS),xU) ),
inference(component_clause,[status(thm)],[f527]) ).
fof(f529,plain,
( sQ52_spl
| ~ aElementOf0(sK0_skl(xS),xU) ),
inference(component_clause,[status(thm)],[f527]) ).
fof(f530,plain,
( ~ sQ22_spl
| ~ sQ52_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f522,f524,f527,f346]) ).
fof(f531,definition,
! [X0] :
( sQ53_spl
<=> ( sdtlseqdt0(sK0_skl(xS),sdtlpdtrp0(xf,X0))
| ~ sdtlseqdt0(sK0_skl(xS),X0)
| ~ aElementOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f534,plain,
( ~ sQ22_spl
| sQ53_spl
| ~ sQ52_spl ),
inference(split_clause,[status(thm)],[f523,f527,f531,f346]) ).
fof(f535,plain,
! [X0] :
( aElementOf0(X0,xS)
| sdtlpdtrp0(xf,X0) != X0
| ~ aElementOf0(X0,xU) ),
inference(forward_demodulation,[status(thm)],[f324,f171]) ).
fof(f540,plain,
( sQ9_spl
| sdtlpdtrp0(xf,xp) != xp
| ~ aElementOf0(xp,xU) ),
inference(resolution,[status(thm)],[f535,f291]) ).
fof(f542,plain,
( sQ9_spl
| ~ sQ8_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f540,f466,f264,f268]) ).
fof(f543,plain,
( sQ41_spl
| ~ aElementOf0(sK1_skl(xP,xU),xU)
| ~ aSet0(xP)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f465,f52]) ).
fof(f544,definition,
( sQ54_spl
<=> aSet0(xP) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f546,plain,
( sQ54_spl
| ~ aSet0(xP) ),
inference(component_clause,[status(thm)],[f544]) ).
fof(f547,definition,
( sQ55_spl
<=> aElementOf0(sK1_skl(xP,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f549,plain,
( sQ55_spl
| ~ aElementOf0(sK1_skl(xP,xU),xU) ),
inference(component_clause,[status(thm)],[f547]) ).
fof(f550,plain,
( sQ41_spl
| ~ sQ55_spl
| ~ sQ54_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f543,f317,f544,f547,f463]) ).
fof(f551,plain,
( sQ54_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f546,f181]) ).
fof(f552,plain,
sQ54_spl,
inference(contradiction_clause,[status(thm)],[f551]) ).
fof(f553,plain,
( sQ52_spl
| ~ aElementOf0(sK0_skl(xS),xS) ),
inference(resolution,[status(thm)],[f529,f509]) ).
fof(f561,plain,
( sQ52_spl
| isEmpty0(xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f553,f44]) ).
fof(f564,plain,
( sQ52_spl
| sQ23_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f561,f342,f349,f527]) ).
fof(f570,plain,
! [X0] :
( ~ sQ23_spl
| ~ aElementOf0(X0,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f350,f43]) ).
fof(f571,definition,
! [X0] :
( sQ58_spl
<=> ~ aElementOf0(X0,xS) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f572,plain,
! [X0] :
( ~ sQ58_spl
| ~ aElementOf0(X0,xS) ),
inference(component_clause,[status(thm)],[f571]) ).
fof(f574,plain,
( ~ sQ23_spl
| sQ58_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f570,f342,f571,f349]) ).
fof(f585,definition,
! [X0,X1] :
( sQ60_spl
<=> ( ~ aElementOf0(X1,X0)
| ~ aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f586,plain,
! [X0,X1] :
( ~ sQ60_spl
| ~ aElementOf0(X1,X0)
| ~ aSubsetOf0(X0,xS) ),
inference(component_clause,[status(thm)],[f585]) ).
fof(f605,plain,
! [X0] :
( sQ5_spl
| ~ sdtlseqdt0(X0,sK17_skl)
| ~ sdtlseqdt0(xp,X0)
| ~ aElement0(sK17_skl)
| ~ aElement0(X0)
| ~ aElement0(xp) ),
inference(resolution,[status(thm)],[f255,f60]) ).
fof(f607,plain,
! [X0,X1] :
( sQ5_spl
| ~ aElementOf0(xp,X1)
| ~ aUpperBoundOfIn0(sK17_skl,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f255,f74]) ).
fof(f608,definition,
( sQ61_spl
<=> aElement0(xp) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f609,plain,
( ~ sQ61_spl
| aElement0(xp) ),
inference(component_clause,[status(thm)],[f608]) ).
fof(f610,plain,
( sQ61_spl
| ~ aElement0(xp) ),
inference(component_clause,[status(thm)],[f608]) ).
fof(f611,definition,
! [X0] :
( sQ62_spl
<=> ( ~ sdtlseqdt0(X0,sK17_skl)
| ~ sdtlseqdt0(xp,X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f612,plain,
! [X0] :
( ~ sQ62_spl
| ~ sdtlseqdt0(X0,sK17_skl)
| ~ sdtlseqdt0(xp,X0)
| ~ aElement0(X0) ),
inference(component_clause,[status(thm)],[f611]) ).
fof(f614,definition,
( sQ63_spl
<=> aElement0(sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f615,plain,
( ~ sQ63_spl
| aElement0(sK17_skl) ),
inference(component_clause,[status(thm)],[f614]) ).
fof(f616,plain,
( sQ63_spl
| ~ aElement0(sK17_skl) ),
inference(component_clause,[status(thm)],[f614]) ).
fof(f617,plain,
( sQ5_spl
| ~ sQ63_spl
| sQ62_spl
| ~ sQ61_spl ),
inference(split_clause,[status(thm)],[f605,f608,f611,f614,f253]) ).
fof(f618,plain,
! [X0] :
( sQ63_spl
| ~ aElementOf0(sK17_skl,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f616,f39]) ).
fof(f619,plain,
( ~ sQ4_spl
| aElementOf0(sK17_skl,xS)
| ~ aSubsetOf0(xT,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f250,f73]) ).
fof(f620,definition,
( sQ64_spl
<=> aSubsetOf0(xT,xS) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f622,plain,
( sQ64_spl
| ~ aSubsetOf0(xT,xS) ),
inference(component_clause,[status(thm)],[f620]) ).
fof(f623,plain,
( ~ sQ4_spl
| sQ2_spl
| ~ sQ64_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f619,f342,f620,f241,f249]) ).
fof(f624,plain,
( sQ64_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f622,f177]) ).
fof(f625,plain,
sQ64_spl,
inference(contradiction_clause,[status(thm)],[f624]) ).
fof(f627,definition,
! [X0] :
( sQ65_spl
<=> ( ~ aElementOf0(sK17_skl,X0)
| ~ aSubsetOf0(X0,xP) ) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f628,plain,
! [X0] :
( ~ sQ65_spl
| ~ aElementOf0(sK17_skl,X0)
| ~ aSubsetOf0(X0,xP) ),
inference(component_clause,[status(thm)],[f627]) ).
fof(f631,plain,
( sQ32_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f410,f332]) ).
fof(f632,plain,
( sQ32_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f631]) ).
fof(f634,plain,
( ~ sQ9_spl
| aUpperBoundOfIn0(xp,xT,xU) ),
inference(backward_demodulation,[status(thm)],[f336,f204]) ).
fof(f637,definition,
! [X0] :
( sQ66_spl
<=> ( sdtlseqdt0(sdtlpdtrp0(xf,X0),xp)
| ~ sdtlseqdt0(X0,xp)
| ~ aElementOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f641,definition,
! [X0] :
( sQ67_spl
<=> ( sdtlseqdt0(xp,sdtlpdtrp0(xf,X0))
| ~ sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f647,plain,
! [X0] :
( ~ sQ30_spl
| ~ aElementOf0(xp,X0)
| ~ aSubsetOf0(X0,xT)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[f400,f50]) ).
fof(f648,definition,
! [X0] :
( sQ68_spl
<=> ( ~ aElementOf0(xp,X0)
| ~ aSubsetOf0(X0,xT) ) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f649,plain,
! [X0] :
( ~ sQ68_spl
| ~ aElementOf0(xp,X0)
| ~ aSubsetOf0(X0,xT) ),
inference(component_clause,[status(thm)],[f648]) ).
fof(f651,plain,
( ~ sQ30_spl
| sQ68_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f647,f297,f648,f395]) ).
fof(f653,plain,
( ~ sQ2_spl
| sQ63_spl
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f618,f242]) ).
fof(f657,plain,
( ~ sQ2_spl
| sQ63_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f653,f342,f614,f241]) ).
fof(f659,definition,
( sQ69_spl
<=> aElementOf0(sK17_skl,xP) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f661,plain,
( sQ69_spl
| ~ aElementOf0(sK17_skl,xP) ),
inference(component_clause,[status(thm)],[f659]) ).
fof(f664,plain,
! [X0] :
( ~ sQ63_spl
| X0 = sK17_skl
| ~ sdtlseqdt0(sK17_skl,X0)
| ~ sdtlseqdt0(X0,sK17_skl)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f615,f58]) ).
fof(f665,plain,
! [X0] :
( ~ sQ30_spl
| ~ aInfimumOfIn0(xp,X0,xT)
| ~ aSubsetOf0(X0,xT)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[f81,f400]) ).
fof(f667,definition,
! [X0] :
( sQ70_spl
<=> ( ~ aInfimumOfIn0(xp,X0,xT)
| ~ aSubsetOf0(X0,xT) ) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f668,plain,
! [X0] :
( ~ sQ70_spl
| ~ aInfimumOfIn0(xp,X0,xT)
| ~ aSubsetOf0(X0,xT) ),
inference(component_clause,[status(thm)],[f667]) ).
fof(f670,plain,
( ~ sQ30_spl
| sQ70_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f665,f297,f667,f395]) ).
fof(f671,definition,
! [X0] :
( sQ71_spl
<=> ( ~ aInfimumOfIn0(xp,X0,xS)
| ~ aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f672,plain,
! [X0] :
( ~ sQ71_spl
| ~ aInfimumOfIn0(xp,X0,xS)
| ~ aSubsetOf0(X0,xS) ),
inference(component_clause,[status(thm)],[f671]) ).
fof(f677,plain,
! [X0] :
( sQ69_spl
| ~ aInfimumOfIn0(sK17_skl,X0,xP)
| ~ aSubsetOf0(X0,xP)
| ~ aSet0(xP) ),
inference(resolution,[status(thm)],[f661,f81]) ).
fof(f678,plain,
! [X0] :
( sQ69_spl
| ~ aElementOf0(sK17_skl,X0)
| ~ aSubsetOf0(X0,xP)
| ~ aSet0(xP) ),
inference(resolution,[status(thm)],[f661,f50]) ).
fof(f679,definition,
! [X0] :
( sQ72_spl
<=> ( ~ aInfimumOfIn0(sK17_skl,X0,xP)
| ~ aSubsetOf0(X0,xP) ) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f680,plain,
! [X0] :
( ~ sQ72_spl
| ~ aInfimumOfIn0(sK17_skl,X0,xP)
| ~ aSubsetOf0(X0,xP) ),
inference(component_clause,[status(thm)],[f679]) ).
fof(f682,plain,
( sQ69_spl
| sQ72_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f677,f544,f679,f659]) ).
fof(f683,plain,
( sQ69_spl
| sQ65_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f678,f544,f627,f659]) ).
fof(f684,plain,
! [X0] :
( ~ sQ65_spl
| ~ aElementOf0(sK1_skl(X0,xP),xP)
| ~ aSet0(X0)
| ~ aSet0(xP)
| ~ aElementOf0(sK17_skl,X0) ),
inference(resolution,[status(thm)],[f628,f52]) ).
fof(f685,definition,
! [X0] :
( sQ73_spl
<=> ( ~ aElementOf0(sK1_skl(X0,xP),xP)
| ~ aSet0(X0)
| ~ aElementOf0(sK17_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f686,plain,
! [X0] :
( ~ sQ73_spl
| ~ aElementOf0(sK1_skl(X0,xP),xP)
| ~ aSet0(X0)
| ~ aElementOf0(sK17_skl,X0) ),
inference(component_clause,[status(thm)],[f685]) ).
fof(f688,plain,
( ~ sQ65_spl
| ~ sQ54_spl
| sQ73_spl ),
inference(split_clause,[status(thm)],[f684,f685,f544,f627]) ).
fof(f695,plain,
( ~ sQ2_spl
| sdtlpdtrp0(xf,sK17_skl) = sK17_skl ),
inference(resolution,[status(thm)],[f169,f242]) ).
fof(f696,plain,
! [X0,X1] :
( ~ aElementOf0(X0,X1)
| aUpperBoundOfIn0(X0,xS,X1)
| ~ aSubsetOf0(xS,X1)
| ~ aSet0(X1)
| sdtlpdtrp0(xf,sK3_skl(X0,xS,X1)) = sK3_skl(X0,xS,X1) ),
inference(resolution,[status(thm)],[f169,f75]) ).
fof(f701,plain,
! [X0,X1] :
( ~ aInfimumOfIn0(X0,X1,xS)
| ~ aSubsetOf0(X1,xS)
| ~ aSet0(xS)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f169,f81]) ).
fof(f705,definition,
! [X0,X1] :
( sQ74_spl
<=> ( ~ aInfimumOfIn0(X0,X1,xS)
| ~ aSubsetOf0(X1,xS)
| sdtlpdtrp0(xf,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f706,plain,
! [X0,X1] :
( ~ sQ74_spl
| ~ aInfimumOfIn0(X0,X1,xS)
| ~ aSubsetOf0(X1,xS)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(component_clause,[status(thm)],[f705]) ).
fof(f708,plain,
( ~ sQ21_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f701,f705,f342]) ).
fof(f713,plain,
! [X0] :
( ~ sQ2_spl
| sdtlseqdt0(sdtlpdtrp0(xf,X0),sK17_skl)
| ~ sdtlseqdt0(X0,sK17_skl)
| ~ aElementOf0(sK17_skl,xU)
| ~ aElementOf0(X0,xU) ),
inference(paramodulation,[status(thm)],[f695,f456]) ).
fof(f714,plain,
! [X0] :
( ~ sQ2_spl
| sdtlseqdt0(sK17_skl,sdtlpdtrp0(xf,X0))
| ~ sdtlseqdt0(sK17_skl,X0)
| ~ aElementOf0(X0,xU)
| ~ aElementOf0(sK17_skl,xU) ),
inference(paramodulation,[status(thm)],[f695,f456]) ).
fof(f715,definition,
! [X0] :
( sQ75_spl
<=> ( sdtlseqdt0(sdtlpdtrp0(xf,X0),sK17_skl)
| ~ sdtlseqdt0(X0,sK17_skl)
| ~ aElementOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f718,definition,
( sQ76_spl
<=> aElementOf0(sK17_skl,xU) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f719,plain,
( ~ sQ76_spl
| aElementOf0(sK17_skl,xU) ),
inference(component_clause,[status(thm)],[f718]) ).
fof(f720,plain,
( sQ76_spl
| ~ aElementOf0(sK17_skl,xU) ),
inference(component_clause,[status(thm)],[f718]) ).
fof(f721,plain,
( ~ sQ2_spl
| ~ sQ76_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f713,f715,f718,f241]) ).
fof(f722,definition,
! [X0] :
( sQ77_spl
<=> ( sdtlseqdt0(sK17_skl,sdtlpdtrp0(xf,X0))
| ~ sdtlseqdt0(sK17_skl,X0)
| ~ aElementOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f725,plain,
( ~ sQ2_spl
| sQ77_spl
| ~ sQ76_spl ),
inference(split_clause,[status(thm)],[f714,f718,f722,f241]) ).
fof(f727,plain,
( sQ76_spl
| ~ aElementOf0(sK17_skl,xS) ),
inference(resolution,[status(thm)],[f720,f509]) ).
fof(f740,plain,
( sQ2_spl
| ~ aElementOf0(sK17_skl,xT) ),
inference(resolution,[status(thm)],[f243,f176]) ).
fof(f741,plain,
! [X0] :
( sQ2_spl
| ~ aInfimumOfIn0(sK17_skl,X0,xS)
| ~ aSubsetOf0(X0,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f243,f81]) ).
fof(f742,plain,
! [X0] :
( sQ2_spl
| ~ aElementOf0(sK17_skl,X0)
| ~ aSubsetOf0(X0,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f243,f50]) ).
fof(f743,definition,
( sQ80_spl
<=> sdtlpdtrp0(xf,sK17_skl) = sK17_skl ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f745,plain,
( sQ80_spl
| sdtlpdtrp0(xf,sK17_skl) != sK17_skl ),
inference(component_clause,[status(thm)],[f743]) ).
fof(f747,definition,
! [X0] :
( sQ81_spl
<=> ( ~ aInfimumOfIn0(sK17_skl,X0,xS)
| ~ aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f748,plain,
! [X0] :
( ~ sQ81_spl
| ~ aInfimumOfIn0(sK17_skl,X0,xS)
| ~ aSubsetOf0(X0,xS) ),
inference(component_clause,[status(thm)],[f747]) ).
fof(f750,plain,
( sQ2_spl
| sQ81_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f741,f342,f747,f241]) ).
fof(f751,definition,
! [X0] :
( sQ82_spl
<=> ( ~ aElementOf0(sK17_skl,X0)
| ~ aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f752,plain,
! [X0] :
( ~ sQ82_spl
| ~ aElementOf0(sK17_skl,X0)
| ~ aSubsetOf0(X0,xS) ),
inference(component_clause,[status(thm)],[f751]) ).
fof(f754,plain,
( sQ2_spl
| sQ82_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f742,f342,f751,f241]) ).
fof(f755,plain,
( sQ76_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f727,f241,f718]) ).
fof(f756,plain,
( ~ sQ2_spl
| sdtlpdtrp0(xf,sK17_skl) = sK17_skl ),
inference(resolution,[status(thm)],[f242,f169]) ).
fof(f757,plain,
( ~ sQ2_spl
| sQ80_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f695,f745]) ).
fof(f758,plain,
( ~ sQ2_spl
| sQ80_spl ),
inference(contradiction_clause,[status(thm)],[f757]) ).
fof(f763,plain,
! [X0,X1,X2] :
( aLowerBoundOfIn0(sK4_skl(X2,X1,X0),X1,X0)
| ~ aLowerBoundOfIn0(X2,X1,X0)
| aInfimumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f84,f65]) ).
fof(f764,plain,
! [X0,X1,X2] :
( ~ sdtlseqdt0(sK4_skl(X2,X1,X0),X2)
| ~ aLowerBoundOfIn0(X2,X1,X0)
| aInfimumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f85,f65]) ).
fof(f765,plain,
! [X0,X1,X2] :
( aUpperBoundOfIn0(sK5_skl(X2,X1,X0),X1,X0)
| ~ aUpperBoundOfIn0(X2,X1,X0)
| aSupremumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f93,f73]) ).
fof(f766,plain,
! [X0,X1,X2] :
( aElementOf0(sK5_skl(X2,X1,X0),X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0)
| ~ aUpperBoundOfIn0(X2,X1,X0)
| aSupremumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f765,f73]) ).
fof(f767,plain,
! [X0,X1,X2] :
( aElementOf0(sK5_skl(X2,X1,X0),X0)
| ~ aUpperBoundOfIn0(X2,X1,X0)
| aSupremumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f766]) ).
fof(f768,plain,
! [X0] :
( ~ sQ68_spl
| ~ aElementOf0(sK1_skl(X0,xT),xT)
| ~ aSet0(X0)
| ~ aSet0(xT)
| ~ aElementOf0(xp,X0) ),
inference(resolution,[status(thm)],[f649,f52]) ).
fof(f769,definition,
! [X0] :
( sQ83_spl
<=> ( ~ aElementOf0(sK1_skl(X0,xT),xT)
| ~ aSet0(X0)
| ~ aElementOf0(xp,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f772,plain,
( ~ sQ68_spl
| ~ sQ15_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f768,f769,f297,f648]) ).
fof(f778,plain,
( ~ sQ63_spl
| ~ sQ62_spl
| ~ sdtlseqdt0(sK17_skl,sK17_skl)
| ~ sdtlseqdt0(xp,sK17_skl) ),
inference(resolution,[status(thm)],[f612,f615]) ).
fof(f779,plain,
! [X0,X1] :
( ~ sQ62_spl
| ~ aElementOf0(X0,X1)
| ~ aSet0(X1)
| ~ sdtlseqdt0(X0,sK17_skl)
| ~ sdtlseqdt0(xp,X0) ),
inference(resolution,[status(thm)],[f612,f39]) ).
fof(f780,definition,
( sQ85_spl
<=> sdtlseqdt0(sK17_skl,sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f781,plain,
( ~ sQ85_spl
| sdtlseqdt0(sK17_skl,sK17_skl) ),
inference(component_clause,[status(thm)],[f780]) ).
fof(f782,plain,
( sQ85_spl
| ~ sdtlseqdt0(sK17_skl,sK17_skl) ),
inference(component_clause,[status(thm)],[f780]) ).
fof(f783,plain,
( ~ sQ63_spl
| ~ sQ62_spl
| ~ sQ85_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f778,f253,f780,f611,f614]) ).
fof(f784,plain,
! [X0] :
( sQ61_spl
| ~ aElementOf0(xp,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f610,f39]) ).
fof(f789,plain,
( sQ85_spl
| ~ aElement0(sK17_skl) ),
inference(resolution,[status(thm)],[f782,f56]) ).
fof(f806,plain,
! [X0] :
( sQ2_spl
| ~ aInfimumOfIn0(sK17_skl,X0,xT)
| ~ aSubsetOf0(X0,xT)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[f740,f81]) ).
fof(f807,plain,
! [X0] :
( sQ2_spl
| ~ aElementOf0(sK17_skl,X0)
| ~ aSubsetOf0(X0,xT)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[f740,f50]) ).
fof(f808,definition,
! [X0] :
( sQ87_spl
<=> ( ~ aInfimumOfIn0(sK17_skl,X0,xT)
| ~ aSubsetOf0(X0,xT) ) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f809,plain,
! [X0] :
( ~ sQ87_spl
| ~ aInfimumOfIn0(sK17_skl,X0,xT)
| ~ aSubsetOf0(X0,xT) ),
inference(component_clause,[status(thm)],[f808]) ).
fof(f811,plain,
( sQ2_spl
| sQ87_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f806,f297,f808,f241]) ).
fof(f812,definition,
! [X0] :
( sQ88_spl
<=> ( ~ aElementOf0(sK17_skl,X0)
| ~ aSubsetOf0(X0,xT) ) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f813,plain,
! [X0] :
( ~ sQ88_spl
| ~ aElementOf0(sK17_skl,X0)
| ~ aSubsetOf0(X0,xT) ),
inference(component_clause,[status(thm)],[f812]) ).
fof(f815,plain,
( sQ2_spl
| sQ88_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f807,f297,f812,f241]) ).
fof(f831,plain,
! [X0,X1] :
( sQ11_spl
| ~ aLowerBoundOfIn0(sK19_skl,X1,X0)
| ~ aInfimumOfIn0(xp,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f280,f83]) ).
fof(f833,plain,
! [X0] :
( sQ11_spl
| ~ sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(sK19_skl,X0)
| ~ aElement0(xp)
| ~ aElement0(X0)
| ~ aElement0(sK19_skl) ),
inference(resolution,[status(thm)],[f280,f60]) ).
fof(f836,definition,
( sQ89_spl
<=> aElement0(sK19_skl) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f838,plain,
( sQ89_spl
| ~ aElement0(sK19_skl) ),
inference(component_clause,[status(thm)],[f836]) ).
fof(f839,definition,
! [X0] :
( sQ90_spl
<=> ( ~ sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(sK19_skl,X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f840,plain,
! [X0] :
( ~ sQ90_spl
| ~ sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(sK19_skl,X0)
| ~ aElement0(X0) ),
inference(component_clause,[status(thm)],[f839]) ).
fof(f842,plain,
( sQ11_spl
| ~ sQ61_spl
| sQ90_spl
| ~ sQ89_spl ),
inference(split_clause,[status(thm)],[f833,f836,f839,f608,f278]) ).
fof(f843,plain,
! [X0] :
( sQ89_spl
| ~ aElementOf0(sK19_skl,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f838,f39]) ).
fof(f847,plain,
! [X0,X1] :
( sQ5_spl
| ~ aElementOf0(sK17_skl,X1)
| ~ aLowerBoundOfIn0(xp,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f255,f66]) ).
fof(f850,plain,
! [X0,X1] :
( sQ5_spl
| ~ aElementOf0(xp,X1)
| ~ aUpperBoundOfIn0(sK17_skl,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f255,f74]) ).
fof(f852,plain,
! [X0,X1,X2] :
( ~ sdtlseqdt0(X2,sK5_skl(X2,X1,X0))
| ~ aUpperBoundOfIn0(X2,X1,X0)
| aSupremumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f94,f73]) ).
fof(f854,plain,
! [X0] :
( ~ sdtlseqdt0(X0,sK5_skl(X0,xT,xS))
| ~ aUpperBoundOfIn0(X0,xT,xS)
| aSupremumOfIn0(X0,xT,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f852,f177]) ).
fof(f860,definition,
! [X0] :
( sQ92_spl
<=> ( ~ sdtlseqdt0(X0,sK5_skl(X0,xT,xS))
| ~ aUpperBoundOfIn0(X0,xT,xS)
| aSupremumOfIn0(X0,xT,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f861,plain,
! [X0] :
( ~ sQ92_spl
| ~ sdtlseqdt0(X0,sK5_skl(X0,xT,xS))
| ~ aUpperBoundOfIn0(X0,xT,xS)
| aSupremumOfIn0(X0,xT,xS) ),
inference(component_clause,[status(thm)],[f860]) ).
fof(f863,plain,
( sQ92_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f854,f342,f860]) ).
fof(f866,plain,
! [X0,X1] :
( X0 = X1
| ~ aInfimumOfIn0(X1,xT,xS)
| ~ aInfimumOfIn0(X0,xT,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f98,f177]) ).
fof(f867,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(sK1_skl(X2,X0),X0)
| ~ aSet0(X2)
| ~ aSet0(X0)
| X1 = X3
| ~ aInfimumOfIn0(X3,X2,X0)
| ~ aInfimumOfIn0(X1,X2,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f98,f52]) ).
fof(f872,definition,
! [X0,X1] :
( sQ94_spl
<=> ( X0 = X1
| ~ aInfimumOfIn0(X1,xT,xS)
| ~ aInfimumOfIn0(X0,xT,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f873,plain,
! [X0,X1] :
( ~ sQ94_spl
| X0 = X1
| ~ aInfimumOfIn0(X1,xT,xS)
| ~ aInfimumOfIn0(X0,xT,xS) ),
inference(component_clause,[status(thm)],[f872]) ).
fof(f875,plain,
( sQ94_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f866,f342,f872]) ).
fof(f876,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(sK1_skl(X2,X0),X0)
| ~ aSet0(X2)
| X1 = X3
| ~ aInfimumOfIn0(X3,X2,X0)
| ~ aInfimumOfIn0(X1,X2,X0)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f867]) ).
fof(f884,plain,
! [X0] :
( ~ sQ82_spl
| ~ aElementOf0(sK1_skl(X0,xS),xS)
| ~ aSet0(X0)
| ~ aSet0(xS)
| ~ aElementOf0(sK17_skl,X0) ),
inference(resolution,[status(thm)],[f752,f52]) ).
fof(f885,definition,
! [X0] :
( sQ96_spl
<=> ( ~ aElementOf0(sK1_skl(X0,xS),xS)
| ~ aSet0(X0)
| ~ aElementOf0(sK17_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f886,plain,
! [X0] :
( ~ sQ96_spl
| ~ aElementOf0(sK1_skl(X0,xS),xS)
| ~ aSet0(X0)
| ~ aElementOf0(sK17_skl,X0) ),
inference(component_clause,[status(thm)],[f885]) ).
fof(f888,plain,
( ~ sQ82_spl
| ~ sQ21_spl
| sQ96_spl ),
inference(split_clause,[status(thm)],[f884,f885,f342,f751]) ).
fof(f892,plain,
( ~ sQ14_spl
| ~ sQ58_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f295,f572]) ).
fof(f900,plain,
( ~ sQ14_spl
| ~ sQ58_spl ),
inference(contradiction_clause,[status(thm)],[f892]) ).
fof(f909,plain,
( sQ61_spl
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f784,f192]) ).
fof(f914,plain,
( sQ61_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f909,f141]) ).
fof(f915,plain,
sQ61_spl,
inference(contradiction_clause,[status(thm)],[f914]) ).
fof(f917,plain,
( sQ9_spl
| ~ aElementOf0(xp,xS) ),
inference(resolution,[status(thm)],[f170,f270]) ).
fof(f919,plain,
! [X0] :
( ~ sQ61_spl
| X0 = xp
| ~ sdtlseqdt0(xp,X0)
| ~ sdtlseqdt0(X0,xp)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f609,f58]) ).
fof(f920,plain,
( sQ89_spl
| ~ aElementOf0(sK19_skl,xS)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f843,f509]) ).
fof(f922,plain,
( sQ89_spl
| ~ aElementOf0(sK19_skl,xP)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f843,f182]) ).
fof(f925,definition,
( sQ97_spl
<=> aElementOf0(sK19_skl,xS) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f927,plain,
( sQ97_spl
| ~ aElementOf0(sK19_skl,xS) ),
inference(component_clause,[status(thm)],[f925]) ).
fof(f928,plain,
( sQ89_spl
| ~ sQ97_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f920,f317,f925,f836]) ).
fof(f929,definition,
( sQ98_spl
<=> aFixedPointOf0(sK19_skl,xf) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f930,plain,
( ~ sQ98_spl
| aFixedPointOf0(sK19_skl,xf) ),
inference(component_clause,[status(thm)],[f929]) ).
fof(f933,definition,
( sQ99_spl
<=> aElementOf0(sK19_skl,xP) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f935,plain,
( sQ99_spl
| ~ aElementOf0(sK19_skl,xP) ),
inference(component_clause,[status(thm)],[f933]) ).
fof(f936,plain,
( sQ89_spl
| ~ sQ99_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f922,f317,f933,f836]) ).
fof(f940,plain,
! [X0] :
( sQ99_spl
| ~ aInfimumOfIn0(sK19_skl,X0,xP)
| ~ aSubsetOf0(X0,xP)
| ~ aSet0(xP) ),
inference(resolution,[status(thm)],[f935,f81]) ).
fof(f941,plain,
! [X0] :
( sQ99_spl
| ~ aElementOf0(sK19_skl,X0)
| ~ aSubsetOf0(X0,xP)
| ~ aSet0(xP) ),
inference(resolution,[status(thm)],[f935,f50]) ).
fof(f942,definition,
! [X0] :
( sQ100_spl
<=> ( ~ aInfimumOfIn0(sK19_skl,X0,xP)
| ~ aSubsetOf0(X0,xP) ) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f943,plain,
! [X0] :
( ~ sQ100_spl
| ~ aInfimumOfIn0(sK19_skl,X0,xP)
| ~ aSubsetOf0(X0,xP) ),
inference(component_clause,[status(thm)],[f942]) ).
fof(f945,plain,
( sQ99_spl
| sQ100_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f940,f544,f942,f933]) ).
fof(f946,definition,
! [X0] :
( sQ101_spl
<=> ( ~ aElementOf0(sK19_skl,X0)
| ~ aSubsetOf0(X0,xP) ) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f947,plain,
! [X0] :
( ~ sQ101_spl
| ~ aElementOf0(sK19_skl,X0)
| ~ aSubsetOf0(X0,xP) ),
inference(component_clause,[status(thm)],[f946]) ).
fof(f949,plain,
( sQ99_spl
| sQ101_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f941,f544,f946,f933]) ).
fof(f951,plain,
! [X0] :
( sQ97_spl
| ~ aInfimumOfIn0(sK19_skl,X0,xS)
| ~ aSubsetOf0(X0,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f927,f81]) ).
fof(f952,plain,
! [X0] :
( sQ97_spl
| ~ aElementOf0(sK19_skl,X0)
| ~ aSubsetOf0(X0,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f927,f50]) ).
fof(f953,definition,
! [X0] :
( sQ102_spl
<=> ( ~ aInfimumOfIn0(sK19_skl,X0,xS)
| ~ aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f954,plain,
! [X0] :
( ~ sQ102_spl
| ~ aInfimumOfIn0(sK19_skl,X0,xS)
| ~ aSubsetOf0(X0,xS) ),
inference(component_clause,[status(thm)],[f953]) ).
fof(f956,plain,
( sQ97_spl
| sQ102_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f951,f342,f953,f925]) ).
fof(f957,definition,
! [X0] :
( sQ103_spl
<=> ( ~ aElementOf0(sK19_skl,X0)
| ~ aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f958,plain,
! [X0] :
( ~ sQ103_spl
| ~ aElementOf0(sK19_skl,X0)
| ~ aSubsetOf0(X0,xS) ),
inference(component_clause,[status(thm)],[f957]) ).
fof(f960,plain,
( sQ97_spl
| sQ103_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f952,f342,f957,f925]) ).
fof(f965,plain,
! [X0] :
( aSupremumOfIn0(sK7_skl(X0,xU),X0,xU)
| ~ aSubsetOf0(X0,xU) ),
inference(resolution,[status(thm)],[f105,f158]) ).
fof(f967,plain,
! [X0] :
( ~ sQ88_spl
| ~ aElementOf0(sK1_skl(X0,xT),xT)
| ~ aSet0(X0)
| ~ aSet0(xT)
| ~ aElementOf0(sK17_skl,X0) ),
inference(resolution,[status(thm)],[f813,f52]) ).
fof(f968,definition,
! [X0] :
( sQ104_spl
<=> ( ~ aElementOf0(sK1_skl(X0,xT),xT)
| ~ aSet0(X0)
| ~ aElementOf0(sK17_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f969,plain,
! [X0] :
( ~ sQ104_spl
| ~ aElementOf0(sK1_skl(X0,xT),xT)
| ~ aSet0(X0)
| ~ aElementOf0(sK17_skl,X0) ),
inference(component_clause,[status(thm)],[f968]) ).
fof(f971,plain,
( ~ sQ88_spl
| ~ sQ15_spl
| sQ104_spl ),
inference(split_clause,[status(thm)],[f967,f968,f297,f812]) ).
fof(f972,plain,
! [X0] :
( ~ sQ101_spl
| ~ aElementOf0(sK1_skl(X0,xP),xP)
| ~ aSet0(X0)
| ~ aSet0(xP)
| ~ aElementOf0(sK19_skl,X0) ),
inference(resolution,[status(thm)],[f947,f52]) ).
fof(f973,definition,
! [X0] :
( sQ105_spl
<=> ( ~ aElementOf0(sK1_skl(X0,xP),xP)
| ~ aSet0(X0)
| ~ aElementOf0(sK19_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f976,plain,
( ~ sQ101_spl
| ~ sQ54_spl
| sQ105_spl ),
inference(split_clause,[status(thm)],[f972,f973,f544,f946]) ).
fof(f977,plain,
! [X0] :
( ~ sQ81_spl
| ~ sdtlseqdt0(sK4_skl(sK17_skl,X0,xS),sK17_skl)
| ~ aLowerBoundOfIn0(sK17_skl,X0,xS)
| ~ aSubsetOf0(X0,xS)
| ~ aSet0(xS)
| ~ aSubsetOf0(X0,xS) ),
inference(resolution,[status(thm)],[f748,f764]) ).
fof(f978,plain,
! [X0] :
( ~ sQ81_spl
| aLowerBoundOfIn0(sK4_skl(sK17_skl,X0,xS),X0,xS)
| ~ aLowerBoundOfIn0(sK17_skl,X0,xS)
| ~ aSubsetOf0(X0,xS)
| ~ aSet0(xS)
| ~ aSubsetOf0(X0,xS) ),
inference(resolution,[status(thm)],[f748,f763]) ).
fof(f979,definition,
! [X0] :
( sQ106_spl
<=> ( ~ sdtlseqdt0(sK4_skl(sK17_skl,X0,xS),sK17_skl)
| ~ aLowerBoundOfIn0(sK17_skl,X0,xS)
| ~ aSubsetOf0(X0,xS)
| ~ aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f980,plain,
! [X0] :
( ~ sQ106_spl
| ~ sdtlseqdt0(sK4_skl(sK17_skl,X0,xS),sK17_skl)
| ~ aLowerBoundOfIn0(sK17_skl,X0,xS)
| ~ aSubsetOf0(X0,xS)
| ~ aSubsetOf0(X0,xS) ),
inference(component_clause,[status(thm)],[f979]) ).
fof(f982,plain,
( ~ sQ81_spl
| ~ sQ21_spl
| sQ106_spl ),
inference(split_clause,[status(thm)],[f977,f979,f342,f747]) ).
fof(f983,definition,
! [X0] :
( sQ107_spl
<=> ( aLowerBoundOfIn0(sK4_skl(sK17_skl,X0,xS),X0,xS)
| ~ aLowerBoundOfIn0(sK17_skl,X0,xS)
| ~ aSubsetOf0(X0,xS)
| ~ aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f984,plain,
! [X0] :
( ~ sQ107_spl
| aLowerBoundOfIn0(sK4_skl(sK17_skl,X0,xS),X0,xS)
| ~ aLowerBoundOfIn0(sK17_skl,X0,xS)
| ~ aSubsetOf0(X0,xS)
| ~ aSubsetOf0(X0,xS) ),
inference(component_clause,[status(thm)],[f983]) ).
fof(f986,plain,
( ~ sQ81_spl
| ~ sQ21_spl
| sQ107_spl ),
inference(split_clause,[status(thm)],[f978,f983,f342,f747]) ).
fof(f987,plain,
! [X0] :
( ~ sQ106_spl
| ~ sdtlseqdt0(sK4_skl(sK17_skl,X0,xS),sK17_skl)
| ~ aLowerBoundOfIn0(sK17_skl,X0,xS)
| ~ aSubsetOf0(X0,xS) ),
inference(duplicate_literals_removal,[status(thm)],[f980]) ).
fof(f988,plain,
! [X0] :
( ~ sQ107_spl
| aLowerBoundOfIn0(sK4_skl(sK17_skl,X0,xS),X0,xS)
| ~ aLowerBoundOfIn0(sK17_skl,X0,xS)
| ~ aSubsetOf0(X0,xS) ),
inference(duplicate_literals_removal,[status(thm)],[f984]) ).
fof(f990,plain,
! [X0] :
( ~ sQ60_spl
| ~ aElementOf0(X0,xT) ),
inference(resolution,[status(thm)],[f586,f177]) ).
fof(f993,plain,
( ~ sQ60_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f990,f305,f585]) ).
fof(f998,plain,
! [X0] :
( sQ9_spl
| ~ aInfimumOfIn0(xp,X0,xS)
| ~ aSubsetOf0(X0,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f917,f81]) ).
fof(f1000,plain,
( sQ9_spl
| sQ71_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f998,f342,f671,f268]) ).
fof(f1013,plain,
( ~ sQ98_spl
| aElementOf0(sK19_skl,xS) ),
inference(resolution,[status(thm)],[f172,f930]) ).
fof(f1037,plain,
( ~ sQ98_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f1013,f925,f929]) ).
fof(f1062,plain,
( sQ55_spl
| ~ aElementOf0(sK1_skl(xP,xU),xP) ),
inference(resolution,[status(thm)],[f549,f182]) ).
fof(f1073,plain,
! [X0] :
( szDzozmdt0(xf) = szRzazndt0(xf)
| ~ isOn0(xf,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f117,f159]) ).
fof(f1074,definition,
! [X0] :
( sQ117_spl
<=> ( ~ isOn0(xf,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f1075,plain,
! [X0] :
( ~ sQ117_spl
| ~ isOn0(xf,X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f1074]) ).
fof(f1077,definition,
( sQ118_spl
<=> szDzozmdt0(xf) = szRzazndt0(xf) ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f1080,plain,
( sQ118_spl
| sQ117_spl ),
inference(split_clause,[status(thm)],[f1073,f1074,f1077]) ).
fof(f1082,plain,
! [X0] :
( szRzazndt0(xf) = X0
| ~ isOn0(xf,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f118,f159]) ).
fof(f1083,plain,
! [X0] :
( xU = X0
| ~ isOn0(xf,X0)
| ~ aSet0(X0) ),
inference(forward_demodulation,[status(thm)],[f163,f1082]) ).
fof(f1084,plain,
! [X0] :
( szDzozmdt0(X0) != szRzazndt0(X0)
| isOn0(X0,szRzazndt0(X0))
| ~ aFunction0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f290,f114]) ).
fof(f1085,plain,
( szDzozmdt0(xf) != szRzazndt0(xf)
| isOn0(xf,xU)
| ~ aFunction0(xf) ),
inference(paramodulation,[status(thm)],[f163,f1084]) ).
fof(f1086,definition,
( sQ119_spl
<=> isOn0(xf,xU) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f1089,plain,
( ~ sQ118_spl
| sQ119_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f1085,f314,f1086,f1077]) ).
fof(f1091,plain,
( ~ sQ103_spl
| ~ aElementOf0(sK19_skl,xT) ),
inference(resolution,[status(thm)],[f958,f177]) ).
fof(f1092,plain,
! [X0] :
( ~ sQ103_spl
| ~ aElementOf0(sK1_skl(X0,xS),xS)
| ~ aSet0(X0)
| ~ aSet0(xS)
| ~ aElementOf0(sK19_skl,X0) ),
inference(resolution,[status(thm)],[f958,f52]) ).
fof(f1093,definition,
! [X0] :
( sQ120_spl
<=> ( ~ aElementOf0(sK1_skl(X0,xS),xS)
| ~ aSet0(X0)
| ~ aElementOf0(sK19_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f1096,plain,
( ~ sQ103_spl
| ~ sQ21_spl
| sQ120_spl ),
inference(split_clause,[status(thm)],[f1092,f1093,f342,f957]) ).
fof(f1097,plain,
! [X0] :
( ~ sQ103_spl
| ~ aInfimumOfIn0(sK19_skl,X0,xT)
| ~ aSubsetOf0(X0,xT)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[f1091,f81]) ).
fof(f1098,plain,
! [X0] :
( ~ sQ103_spl
| ~ aElementOf0(sK19_skl,X0)
| ~ aSubsetOf0(X0,xT)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[f1091,f50]) ).
fof(f1099,definition,
! [X0] :
( sQ121_spl
<=> ( ~ aInfimumOfIn0(sK19_skl,X0,xT)
| ~ aSubsetOf0(X0,xT) ) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f1100,plain,
! [X0] :
( ~ sQ121_spl
| ~ aInfimumOfIn0(sK19_skl,X0,xT)
| ~ aSubsetOf0(X0,xT) ),
inference(component_clause,[status(thm)],[f1099]) ).
fof(f1102,plain,
( ~ sQ103_spl
| sQ121_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f1097,f297,f1099,f957]) ).
fof(f1103,definition,
! [X0] :
( sQ122_spl
<=> ( ~ aElementOf0(sK19_skl,X0)
| ~ aSubsetOf0(X0,xT) ) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f1104,plain,
! [X0] :
( ~ sQ122_spl
| ~ aElementOf0(sK19_skl,X0)
| ~ aSubsetOf0(X0,xT) ),
inference(component_clause,[status(thm)],[f1103]) ).
fof(f1106,plain,
( ~ sQ103_spl
| sQ122_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f1098,f297,f1103,f957]) ).
fof(f1118,definition,
( sQ124_spl
<=> aLowerBoundOfIn0(xp,xT,xS) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f1119,plain,
( ~ sQ124_spl
| aLowerBoundOfIn0(xp,xT,xS) ),
inference(component_clause,[status(thm)],[f1118]) ).
fof(f1120,plain,
( sQ124_spl
| ~ aLowerBoundOfIn0(xp,xT,xS) ),
inference(component_clause,[status(thm)],[f1118]) ).
fof(f1121,definition,
( sQ125_spl
<=> aElementOf0(sK17_skl,xT) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f1123,plain,
( sQ125_spl
| ~ aElementOf0(sK17_skl,xT) ),
inference(component_clause,[status(thm)],[f1121]) ).
fof(f1128,plain,
( sQ124_spl
| ~ aInfimumOfIn0(xp,xT,xS)
| ~ aSubsetOf0(xT,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f1120,f82]) ).
fof(f1131,definition,
( sQ126_spl
<=> aInfimumOfIn0(xp,xT,xS) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f1134,plain,
( sQ124_spl
| ~ sQ126_spl
| ~ sQ64_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f1128,f342,f620,f1131,f1118]) ).
fof(f1168,plain,
( ~ sQ124_spl
| aElementOf0(xp,xS)
| ~ aSubsetOf0(xT,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f1119,f65]) ).
fof(f1169,plain,
( ~ sQ124_spl
| sQ32_spl
| ~ sQ64_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f1168,f342,f620,f408,f1118]) ).
fof(f1185,plain,
( ~ sQ117_spl
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1075,f164]) ).
fof(f1187,plain,
( ~ sQ117_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1185,f141]) ).
fof(f1188,plain,
~ sQ117_spl,
inference(contradiction_clause,[status(thm)],[f1187]) ).
fof(f1221,plain,
! [X0] :
( aElementOf0(sdtlpdtrp0(xf,X0),xU)
| ~ aElementOf0(X0,szDzozmdt0(xf))
| ~ aFunction0(xf) ),
inference(paramodulation,[status(thm)],[f163,f121]) ).
fof(f1222,definition,
! [X0] :
( sQ137_spl
<=> ( aElementOf0(sdtlpdtrp0(xf,X0),xU)
| ~ aElementOf0(X0,szDzozmdt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f1225,plain,
( sQ137_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f1221,f314,f1222]) ).
fof(f1232,plain,
( ~ sQ61_spl
| ~ sQ90_spl
| ~ sdtlseqdt0(xp,xp)
| ~ sdtlseqdt0(sK19_skl,xp) ),
inference(resolution,[status(thm)],[f840,f609]) ).
fof(f1238,definition,
( sQ139_spl
<=> sdtlseqdt0(xp,xp) ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f1240,plain,
( sQ139_spl
| ~ sdtlseqdt0(xp,xp) ),
inference(component_clause,[status(thm)],[f1238]) ).
fof(f1241,plain,
( ~ sQ61_spl
| ~ sQ90_spl
| ~ sQ139_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1232,f278,f1238,f839,f608]) ).
fof(f1248,plain,
( sQ139_spl
| ~ aElement0(xp) ),
inference(resolution,[status(thm)],[f1240,f56]) ).
fof(f1256,plain,
( sQ139_spl
| ~ sQ61_spl ),
inference(split_clause,[status(thm)],[f1248,f608,f1238]) ).
fof(f1280,plain,
! [X0,X1] :
( ~ sQ24_spl
| ~ aElementOf0(sK1_skl(X1,xS),xS)
| ~ aSet0(X1)
| ~ aSet0(xS)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f354,f52]) ).
fof(f1281,definition,
! [X0,X1] :
( sQ142_spl
<=> ( ~ aElementOf0(sK1_skl(X1,xS),xS)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f1282,plain,
! [X0,X1] :
( ~ sQ142_spl
| ~ aElementOf0(sK1_skl(X1,xS),xS)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(component_clause,[status(thm)],[f1281]) ).
fof(f1284,plain,
( ~ sQ24_spl
| ~ sQ21_spl
| sQ142_spl ),
inference(split_clause,[status(thm)],[f1280,f1281,f342,f353]) ).
fof(f1329,plain,
! [X0] :
( ~ sQ122_spl
| ~ aElementOf0(sK1_skl(X0,xT),xT)
| ~ aSet0(X0)
| ~ aSet0(xT)
| ~ aElementOf0(sK19_skl,X0) ),
inference(resolution,[status(thm)],[f1104,f52]) ).
fof(f1330,definition,
! [X0] :
( sQ148_spl
<=> ( ~ aElementOf0(sK1_skl(X0,xT),xT)
| ~ aSet0(X0)
| ~ aElementOf0(sK19_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f1333,plain,
( ~ sQ122_spl
| ~ sQ15_spl
| sQ148_spl ),
inference(split_clause,[status(thm)],[f1329,f1330,f297,f1103]) ).
fof(f1372,definition,
( sQ153_spl
<=> aFixedPointOf0(sK17_skl,xf) ),
introduced(definition,[new_symbols(definition,[sQ153_spl])],[split_symbol_definition]) ).
fof(f1373,plain,
( ~ sQ153_spl
| aFixedPointOf0(sK17_skl,xf) ),
inference(component_clause,[status(thm)],[f1372]) ).
fof(f1374,plain,
( sQ153_spl
| ~ aFixedPointOf0(sK17_skl,xf) ),
inference(component_clause,[status(thm)],[f1372]) ).
fof(f1379,plain,
( sQ85_spl
| ~ sQ63_spl ),
inference(split_clause,[status(thm)],[f789,f614,f780]) ).
fof(f1389,plain,
( sQ153_spl
| sdtlpdtrp0(xf,sK17_skl) != sK17_skl
| ~ aElementOf0(sK17_skl,xU) ),
inference(resolution,[status(thm)],[f454,f1374]) ).
fof(f1393,plain,
( sQ153_spl
| ~ sQ80_spl
| ~ sQ76_spl ),
inference(split_clause,[status(thm)],[f1389,f718,f743,f1372]) ).
fof(f1396,plain,
( sQ5_spl
| ~ aElementOf0(sK17_skl,xP) ),
inference(resolution,[status(thm)],[f255,f194]) ).
fof(f1449,plain,
! [X0,X1] :
( ~ aElementOf0(X0,X1)
| aUpperBoundOfIn0(X0,xT,X1)
| ~ aSubsetOf0(xT,X1)
| ~ aSet0(X1)
| sdtlpdtrp0(xf,sK3_skl(X0,xT,X1)) = sK3_skl(X0,xT,X1) ),
inference(resolution,[status(thm)],[f337,f75]) ).
fof(f1452,plain,
! [X0,X1] :
( ~ aInfimumOfIn0(X0,X1,xT)
| ~ aSubsetOf0(X1,xT)
| ~ aSet0(xT)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f337,f81]) ).
fof(f1456,definition,
! [X0,X1] :
( sQ159_spl
<=> ( ~ aInfimumOfIn0(X0,X1,xT)
| ~ aSubsetOf0(X1,xT)
| sdtlpdtrp0(xf,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f1457,plain,
! [X0,X1] :
( ~ sQ159_spl
| ~ aInfimumOfIn0(X0,X1,xT)
| ~ aSubsetOf0(X1,xT)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(component_clause,[status(thm)],[f1456]) ).
fof(f1459,plain,
( ~ sQ15_spl
| sQ159_spl ),
inference(split_clause,[status(thm)],[f1452,f1456,f297]) ).
fof(f1462,plain,
! [X0,X1] :
( ~ aElementOf0(sK1_skl(xS,X1),X1)
| ~ aSet0(xS)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| aUpperBoundOfIn0(X0,xS,X1)
| ~ aSet0(X1)
| sdtlpdtrp0(xf,sK3_skl(X0,xS,X1)) = sK3_skl(X0,xS,X1) ),
inference(resolution,[status(thm)],[f696,f52]) ).
fof(f1467,definition,
! [X0,X1] :
( sQ161_spl
<=> ( ~ aElementOf0(sK1_skl(xS,X1),X1)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| aUpperBoundOfIn0(X0,xS,X1)
| ~ aSet0(X1)
| sdtlpdtrp0(xf,sK3_skl(X0,xS,X1)) = sK3_skl(X0,xS,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f1470,plain,
( ~ sQ21_spl
| sQ161_spl ),
inference(split_clause,[status(thm)],[f1462,f1467,f342]) ).
fof(f1472,plain,
( sQ55_spl
| ~ aSet0(xP)
| aSubsetOf0(xP,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1062,f51]) ).
fof(f1475,plain,
( sQ55_spl
| ~ sQ54_spl
| sQ41_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1472,f317,f463,f544,f547]) ).
fof(f1485,plain,
! [X0,X1] :
( ~ sQ41_spl
| X0 = X1
| ~ aInfimumOfIn0(X1,xP,xU)
| ~ aInfimumOfIn0(X0,xP,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f464,f98]) ).
fof(f1486,plain,
! [X0] :
( ~ sQ41_spl
| ~ sdtlseqdt0(X0,sK5_skl(X0,xP,xU))
| ~ aUpperBoundOfIn0(X0,xP,xU)
| aSupremumOfIn0(X0,xP,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f464,f852]) ).
fof(f1487,definition,
! [X0,X1] :
( sQ164_spl
<=> ( X0 = X1
| ~ aInfimumOfIn0(X1,xP,xU)
| ~ aInfimumOfIn0(X0,xP,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f1488,plain,
! [X0,X1] :
( ~ sQ164_spl
| X0 = X1
| ~ aInfimumOfIn0(X1,xP,xU)
| ~ aInfimumOfIn0(X0,xP,xU) ),
inference(component_clause,[status(thm)],[f1487]) ).
fof(f1490,plain,
( ~ sQ41_spl
| sQ164_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1485,f317,f1487,f463]) ).
fof(f1491,definition,
! [X0] :
( sQ165_spl
<=> ( ~ sdtlseqdt0(X0,sK5_skl(X0,xP,xU))
| ~ aUpperBoundOfIn0(X0,xP,xU)
| aSupremumOfIn0(X0,xP,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ165_spl])],[split_symbol_definition]) ).
fof(f1492,plain,
! [X0] :
( ~ sQ165_spl
| ~ sdtlseqdt0(X0,sK5_skl(X0,xP,xU))
| ~ aUpperBoundOfIn0(X0,xP,xU)
| aSupremumOfIn0(X0,xP,xU) ),
inference(component_clause,[status(thm)],[f1491]) ).
fof(f1494,plain,
( ~ sQ41_spl
| sQ165_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1486,f317,f1491,f463]) ).
fof(f1495,plain,
! [X0] :
( ~ aSubsetOf0(X0,xU)
| aUpperBoundOfIn0(sK13_skl(X0),X0,xU) ),
inference(resolution,[status(thm)],[f153,f221]) ).
fof(f1496,plain,
! [X0] :
( ~ aSubsetOf0(X0,xU)
| aSupremumOfIn0(sK13_skl(X0),X0,xU) ),
inference(resolution,[status(thm)],[f157,f221]) ).
fof(f1497,plain,
( xU = xU
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1083,f164]) ).
fof(f1498,plain,
( szDzozmdt0(xf) != szRzazndt0(xf)
| ~ aFunction0(xf)
| xU = szRzazndt0(xf)
| ~ aSet0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f1083,f1084]) ).
fof(f1499,definition,
( sQ166_spl
<=> xU = xU ),
introduced(definition,[new_symbols(definition,[sQ166_spl])],[split_symbol_definition]) ).
fof(f1502,plain,
( sQ166_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1497,f317,f1499]) ).
fof(f1503,definition,
( sQ167_spl
<=> aSet0(szRzazndt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f1505,plain,
( sQ167_spl
| ~ aSet0(szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f1503]) ).
fof(f1506,definition,
( sQ168_spl
<=> xU = szRzazndt0(xf) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f1509,plain,
( ~ sQ118_spl
| ~ sQ18_spl
| sQ168_spl
| ~ sQ167_spl ),
inference(split_clause,[status(thm)],[f1498,f1503,f1506,f314,f1077]) ).
fof(f1510,plain,
( sQ167_spl
| ~ aSet0(xU) ),
inference(forward_demodulation,[status(thm)],[f163,f1505]) ).
fof(f1511,plain,
( sQ167_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1510,f141]) ).
fof(f1512,plain,
sQ167_spl,
inference(contradiction_clause,[status(thm)],[f1511]) ).
fof(f1514,plain,
! [X0] :
( ~ sQ70_spl
| ~ aElementOf0(sK1_skl(X0,xT),xT)
| ~ aSet0(X0)
| ~ aSet0(xT)
| ~ aInfimumOfIn0(xp,X0,xT) ),
inference(resolution,[status(thm)],[f668,f52]) ).
fof(f1515,definition,
! [X0] :
( sQ169_spl
<=> ( ~ aElementOf0(sK1_skl(X0,xT),xT)
| ~ aSet0(X0)
| ~ aInfimumOfIn0(xp,X0,xT) ) ),
introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition]) ).
fof(f1518,plain,
( ~ sQ70_spl
| ~ sQ15_spl
| sQ169_spl ),
inference(split_clause,[status(thm)],[f1514,f1515,f297,f667]) ).
fof(f1519,plain,
! [X0] :
( ~ sQ71_spl
| ~ sdtlseqdt0(sK4_skl(xp,X0,xS),xp)
| ~ aLowerBoundOfIn0(xp,X0,xS)
| ~ aSubsetOf0(X0,xS)
| ~ aSet0(xS)
| ~ aSubsetOf0(X0,xS) ),
inference(resolution,[status(thm)],[f672,f764]) ).
fof(f1520,plain,
! [X0] :
( ~ sQ71_spl
| aLowerBoundOfIn0(sK4_skl(xp,X0,xS),X0,xS)
| ~ aLowerBoundOfIn0(xp,X0,xS)
| ~ aSubsetOf0(X0,xS)
| ~ aSet0(xS)
| ~ aSubsetOf0(X0,xS) ),
inference(resolution,[status(thm)],[f672,f763]) ).
fof(f1521,definition,
! [X0] :
( sQ170_spl
<=> ( ~ sdtlseqdt0(sK4_skl(xp,X0,xS),xp)
| ~ aLowerBoundOfIn0(xp,X0,xS)
| ~ aSubsetOf0(X0,xS)
| ~ aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f1524,plain,
( ~ sQ71_spl
| ~ sQ21_spl
| sQ170_spl ),
inference(split_clause,[status(thm)],[f1519,f1521,f342,f671]) ).
fof(f1525,definition,
! [X0] :
( sQ171_spl
<=> ( aLowerBoundOfIn0(sK4_skl(xp,X0,xS),X0,xS)
| ~ aLowerBoundOfIn0(xp,X0,xS)
| ~ aSubsetOf0(X0,xS)
| ~ aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f1528,plain,
( ~ sQ71_spl
| ~ sQ21_spl
| sQ171_spl ),
inference(split_clause,[status(thm)],[f1520,f1525,f342,f671]) ).
fof(f1531,plain,
! [X0] :
( ~ sQ72_spl
| ~ aElementOf0(sK1_skl(X0,xP),xP)
| ~ aSet0(X0)
| ~ aSet0(xP)
| ~ aInfimumOfIn0(sK17_skl,X0,xP) ),
inference(resolution,[status(thm)],[f680,f52]) ).
fof(f1532,definition,
! [X0] :
( sQ172_spl
<=> ( ~ aElementOf0(sK1_skl(X0,xP),xP)
| ~ aSet0(X0)
| ~ aInfimumOfIn0(sK17_skl,X0,xP) ) ),
introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition]) ).
fof(f1535,plain,
( ~ sQ72_spl
| ~ sQ54_spl
| sQ172_spl ),
inference(split_clause,[status(thm)],[f1531,f1532,f544,f679]) ).
fof(f1536,plain,
! [X0] :
( ~ sQ14_spl
| sdtlseqdt0(sdtlpdtrp0(xf,X0),sK0_skl(xT))
| ~ sdtlseqdt0(X0,sK0_skl(xT))
| ~ aElementOf0(sK0_skl(xT),xU)
| ~ aElementOf0(X0,xU) ),
inference(paramodulation,[status(thm)],[f334,f456]) ).
fof(f1537,plain,
! [X0] :
( ~ sQ14_spl
| sdtlseqdt0(sK0_skl(xT),sdtlpdtrp0(xf,X0))
| ~ sdtlseqdt0(sK0_skl(xT),X0)
| ~ aElementOf0(X0,xU)
| ~ aElementOf0(sK0_skl(xT),xU) ),
inference(paramodulation,[status(thm)],[f334,f456]) ).
fof(f1538,plain,
! [X0] :
( ~ sQ14_spl
| sdtlseqdt0(sdtlpdtrp0(xf,X0),sK0_skl(xT))
| ~ sdtlseqdt0(X0,sK0_skl(xT))
| ~ aElementOf0(sK0_skl(xT),szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| ~ isMonotone0(xf)
| ~ aFunction0(xf) ),
inference(paramodulation,[status(thm)],[f334,f131]) ).
fof(f1539,plain,
! [X0] :
( ~ sQ14_spl
| sdtlseqdt0(sK0_skl(xT),sdtlpdtrp0(xf,X0))
| ~ sdtlseqdt0(sK0_skl(xT),X0)
| ~ aElementOf0(X0,szDzozmdt0(xf))
| ~ aElementOf0(sK0_skl(xT),szDzozmdt0(xf))
| ~ isMonotone0(xf)
| ~ aFunction0(xf) ),
inference(paramodulation,[status(thm)],[f334,f131]) ).
fof(f1540,plain,
( ~ sQ14_spl
| aElementOf0(sK0_skl(xT),szRzazndt0(xf))
| ~ aElementOf0(sK0_skl(xT),szDzozmdt0(xf))
| ~ aFunction0(xf) ),
inference(paramodulation,[status(thm)],[f334,f121]) ).
fof(f1541,definition,
! [X0] :
( sQ173_spl
<=> ( sdtlseqdt0(sdtlpdtrp0(xf,X0),sK0_skl(xT))
| ~ sdtlseqdt0(X0,sK0_skl(xT))
| ~ aElementOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ173_spl])],[split_symbol_definition]) ).
fof(f1544,definition,
( sQ174_spl
<=> aElementOf0(sK0_skl(xT),xU) ),
introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition]) ).
fof(f1546,plain,
( sQ174_spl
| ~ aElementOf0(sK0_skl(xT),xU) ),
inference(component_clause,[status(thm)],[f1544]) ).
fof(f1547,plain,
( ~ sQ14_spl
| ~ sQ174_spl
| sQ173_spl ),
inference(split_clause,[status(thm)],[f1536,f1541,f1544,f294]) ).
fof(f1548,definition,
! [X0] :
( sQ175_spl
<=> ( sdtlseqdt0(sK0_skl(xT),sdtlpdtrp0(xf,X0))
| ~ sdtlseqdt0(sK0_skl(xT),X0)
| ~ aElementOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition]) ).
fof(f1551,plain,
( ~ sQ14_spl
| sQ175_spl
| ~ sQ174_spl ),
inference(split_clause,[status(thm)],[f1537,f1544,f1548,f294]) ).
fof(f1552,definition,
( sQ176_spl
<=> isMonotone0(xf) ),
introduced(definition,[new_symbols(definition,[sQ176_spl])],[split_symbol_definition]) ).
fof(f1554,plain,
( sQ176_spl
| ~ isMonotone0(xf) ),
inference(component_clause,[status(thm)],[f1552]) ).
fof(f1555,definition,
! [X0] :
( sQ177_spl
<=> ( sdtlseqdt0(sdtlpdtrp0(xf,X0),sK0_skl(xT))
| ~ sdtlseqdt0(X0,sK0_skl(xT))
| ~ aElementOf0(X0,szDzozmdt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f1558,definition,
( sQ178_spl
<=> aElementOf0(sK0_skl(xT),szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f1560,plain,
( sQ178_spl
| ~ aElementOf0(sK0_skl(xT),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f1558]) ).
fof(f1561,plain,
( ~ sQ14_spl
| ~ sQ178_spl
| sQ177_spl
| ~ sQ176_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f1538,f314,f1552,f1555,f1558,f294]) ).
fof(f1562,definition,
! [X0] :
( sQ179_spl
<=> ( sdtlseqdt0(sK0_skl(xT),sdtlpdtrp0(xf,X0))
| ~ sdtlseqdt0(sK0_skl(xT),X0)
| ~ aElementOf0(X0,szDzozmdt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f1565,plain,
( ~ sQ14_spl
| sQ179_spl
| ~ sQ178_spl
| ~ sQ176_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f1539,f314,f1552,f1558,f1562,f294]) ).
fof(f1566,definition,
( sQ180_spl
<=> aElementOf0(sK0_skl(xT),szRzazndt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f1567,plain,
( ~ sQ180_spl
| aElementOf0(sK0_skl(xT),szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f1566]) ).
fof(f1569,plain,
( ~ sQ14_spl
| sQ180_spl
| ~ sQ178_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f1540,f314,f1558,f1566,f294]) ).
fof(f1570,plain,
( sQ178_spl
| ~ aElementOf0(sK0_skl(xT),xU) ),
inference(forward_demodulation,[status(thm)],[f324,f1560]) ).
fof(f1571,plain,
( sQ176_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1554,f161]) ).
fof(f1572,plain,
sQ176_spl,
inference(contradiction_clause,[status(thm)],[f1571]) ).
fof(f1573,plain,
( ~ sQ180_spl
| aElementOf0(sK0_skl(xT),xU) ),
inference(forward_demodulation,[status(thm)],[f163,f1567]) ).
fof(f1576,plain,
( sQ178_spl
| ~ aElementOf0(sK0_skl(xT),xS) ),
inference(resolution,[status(thm)],[f1570,f509]) ).
fof(f1581,plain,
( sQ178_spl
| ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1576,f295]) ).
fof(f1582,plain,
( sQ178_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f1581]) ).
fof(f1592,plain,
! [X0] :
( ~ sQ74_spl
| ~ aInfimumOfIn0(X0,xT,xS)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f706,f177]) ).
fof(f1593,plain,
! [X0,X1] :
( ~ sQ74_spl
| ~ aElementOf0(sK1_skl(X1,xS),xS)
| ~ aSet0(X1)
| ~ aSet0(xS)
| ~ aInfimumOfIn0(X0,X1,xS)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f706,f52]) ).
fof(f1594,definition,
! [X0,X1] :
( sQ181_spl
<=> ( ~ aElementOf0(sK1_skl(X1,xS),xS)
| ~ aSet0(X1)
| ~ aInfimumOfIn0(X0,X1,xS)
| sdtlpdtrp0(xf,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f1595,plain,
! [X0,X1] :
( ~ sQ181_spl
| ~ aElementOf0(sK1_skl(X1,xS),xS)
| ~ aSet0(X1)
| ~ aInfimumOfIn0(X0,X1,xS)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(component_clause,[status(thm)],[f1594]) ).
fof(f1597,plain,
( ~ sQ74_spl
| ~ sQ21_spl
| sQ181_spl ),
inference(split_clause,[status(thm)],[f1593,f1594,f342,f705]) ).
fof(f1598,plain,
! [X0,X1] :
( sdtlpdtrp0(xf,sK5_skl(X1,X0,xT)) = sK5_skl(X1,X0,xT)
| ~ aUpperBoundOfIn0(X1,X0,xT)
| aSupremumOfIn0(X1,X0,xT)
| ~ aSubsetOf0(X0,xT)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[f767,f337]) ).
fof(f1599,plain,
! [X0,X1] :
( sdtlpdtrp0(xf,sK5_skl(X1,X0,xS)) = sK5_skl(X1,X0,xS)
| ~ aUpperBoundOfIn0(X1,X0,xS)
| aSupremumOfIn0(X1,X0,xS)
| ~ aSubsetOf0(X0,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f767,f169]) ).
fof(f1600,definition,
! [X0,X1] :
( sQ182_spl
<=> ( sdtlpdtrp0(xf,sK5_skl(X1,X0,xT)) = sK5_skl(X1,X0,xT)
| ~ aUpperBoundOfIn0(X1,X0,xT)
| aSupremumOfIn0(X1,X0,xT)
| ~ aSubsetOf0(X0,xT) ) ),
introduced(definition,[new_symbols(definition,[sQ182_spl])],[split_symbol_definition]) ).
fof(f1601,plain,
! [X0,X1] :
( ~ sQ182_spl
| sdtlpdtrp0(xf,sK5_skl(X1,X0,xT)) = sK5_skl(X1,X0,xT)
| ~ aUpperBoundOfIn0(X1,X0,xT)
| aSupremumOfIn0(X1,X0,xT)
| ~ aSubsetOf0(X0,xT) ),
inference(component_clause,[status(thm)],[f1600]) ).
fof(f1603,plain,
( sQ182_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f1598,f297,f1600]) ).
fof(f1604,definition,
! [X0,X1] :
( sQ183_spl
<=> ( sdtlpdtrp0(xf,sK5_skl(X1,X0,xS)) = sK5_skl(X1,X0,xS)
| ~ aUpperBoundOfIn0(X1,X0,xS)
| aSupremumOfIn0(X1,X0,xS)
| ~ aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f1605,plain,
! [X0,X1] :
( ~ sQ183_spl
| sdtlpdtrp0(xf,sK5_skl(X1,X0,xS)) = sK5_skl(X1,X0,xS)
| ~ aUpperBoundOfIn0(X1,X0,xS)
| aSupremumOfIn0(X1,X0,xS)
| ~ aSubsetOf0(X0,xS) ),
inference(component_clause,[status(thm)],[f1604]) ).
fof(f1607,plain,
( sQ183_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f1599,f342,f1604]) ).
fof(f1608,plain,
( sQ11_spl
| ~ aElementOf0(sK19_skl,xT)
| ~ aSubsetOf0(xT,xU)
| ~ aSet0(xU)
| ~ aElementOf0(xp,xP) ),
inference(resolution,[status(thm)],[f185,f331]) ).
fof(f1610,definition,
( sQ184_spl
<=> aElementOf0(xp,xP) ),
introduced(definition,[new_symbols(definition,[sQ184_spl])],[split_symbol_definition]) ).
fof(f1612,plain,
( sQ184_spl
| ~ aElementOf0(xp,xP) ),
inference(component_clause,[status(thm)],[f1610]) ).
fof(f1613,plain,
( sQ11_spl
| ~ sQ10_spl
| ~ sQ49_spl
| ~ sQ19_spl
| ~ sQ184_spl ),
inference(split_clause,[status(thm)],[f1608,f1610,f317,f511,f274,f278]) ).
fof(f1618,definition,
( sQ186_spl
<=> aElementOf0(sK1_skl(xT,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ186_spl])],[split_symbol_definition]) ).
fof(f1620,plain,
( sQ186_spl
| ~ aElementOf0(sK1_skl(xT,xU),xU) ),
inference(component_clause,[status(thm)],[f1618]) ).
fof(f1621,plain,
( sQ49_spl
| ~ sQ186_spl
| ~ sQ15_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f519,f317,f297,f1618,f511]) ).
fof(f1622,plain,
! [X0] :
( sQ184_spl
| ~ aInfimumOfIn0(xp,X0,xP)
| ~ aSubsetOf0(X0,xP)
| ~ aSet0(xP) ),
inference(resolution,[status(thm)],[f1612,f81]) ).
fof(f1623,plain,
! [X0] :
( sQ184_spl
| ~ aElementOf0(xp,X0)
| ~ aSubsetOf0(X0,xP)
| ~ aSet0(xP) ),
inference(resolution,[status(thm)],[f1612,f50]) ).
fof(f1624,definition,
! [X0] :
( sQ187_spl
<=> ( ~ aInfimumOfIn0(xp,X0,xP)
| ~ aSubsetOf0(X0,xP) ) ),
introduced(definition,[new_symbols(definition,[sQ187_spl])],[split_symbol_definition]) ).
fof(f1625,plain,
! [X0] :
( ~ sQ187_spl
| ~ aInfimumOfIn0(xp,X0,xP)
| ~ aSubsetOf0(X0,xP) ),
inference(component_clause,[status(thm)],[f1624]) ).
fof(f1627,plain,
( sQ184_spl
| sQ187_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f1622,f544,f1624,f1610]) ).
fof(f1628,definition,
! [X0] :
( sQ188_spl
<=> ( ~ aElementOf0(xp,X0)
| ~ aSubsetOf0(X0,xP) ) ),
introduced(definition,[new_symbols(definition,[sQ188_spl])],[split_symbol_definition]) ).
fof(f1629,plain,
! [X0] :
( ~ sQ188_spl
| ~ aElementOf0(xp,X0)
| ~ aSubsetOf0(X0,xP) ),
inference(component_clause,[status(thm)],[f1628]) ).
fof(f1631,plain,
( sQ184_spl
| sQ188_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f1623,f544,f1628,f1610]) ).
fof(f1634,plain,
( sQ186_spl
| ~ aElementOf0(sK1_skl(xT,xU),xS) ),
inference(resolution,[status(thm)],[f1620,f509]) ).
fof(f1647,plain,
! [X0] :
( ~ sQ188_spl
| ~ aElementOf0(sK1_skl(X0,xP),xP)
| ~ aSet0(X0)
| ~ aSet0(xP)
| ~ aElementOf0(xp,X0) ),
inference(resolution,[status(thm)],[f1629,f52]) ).
fof(f1648,definition,
! [X0] :
( sQ191_spl
<=> ( ~ aElementOf0(sK1_skl(X0,xP),xP)
| ~ aSet0(X0)
| ~ aElementOf0(xp,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ191_spl])],[split_symbol_definition]) ).
fof(f1651,plain,
( ~ sQ188_spl
| ~ sQ54_spl
| sQ191_spl ),
inference(split_clause,[status(thm)],[f1647,f1648,f544,f1628]) ).
fof(f1652,plain,
( sQ186_spl
| ~ aElementOf0(sK1_skl(xT,xU),xT) ),
inference(resolution,[status(thm)],[f1634,f176]) ).
fof(f1682,definition,
( sQ197_spl
<=> aElementOf0(sK0_skl(xT),xP) ),
introduced(definition,[new_symbols(definition,[sQ197_spl])],[split_symbol_definition]) ).
fof(f1685,definition,
( sQ198_spl
<=> sdtlseqdt0(sK0_skl(xT),sK0_skl(xT)) ),
introduced(definition,[new_symbols(definition,[sQ198_spl])],[split_symbol_definition]) ).
fof(f1686,plain,
( ~ sQ198_spl
| sdtlseqdt0(sK0_skl(xT),sK0_skl(xT)) ),
inference(component_clause,[status(thm)],[f1685]) ).
fof(f1687,plain,
( sQ198_spl
| ~ sdtlseqdt0(sK0_skl(xT),sK0_skl(xT)) ),
inference(component_clause,[status(thm)],[f1685]) ).
fof(f1701,plain,
! [X0] :
( ~ sQ87_spl
| ~ aElementOf0(sK1_skl(X0,xT),xT)
| ~ aSet0(X0)
| ~ aSet0(xT)
| ~ aInfimumOfIn0(sK17_skl,X0,xT) ),
inference(resolution,[status(thm)],[f809,f52]) ).
fof(f1702,definition,
! [X0] :
( sQ201_spl
<=> ( ~ aElementOf0(sK1_skl(X0,xT),xT)
| ~ aSet0(X0)
| ~ aInfimumOfIn0(sK17_skl,X0,xT) ) ),
introduced(definition,[new_symbols(definition,[sQ201_spl])],[split_symbol_definition]) ).
fof(f1703,plain,
! [X0] :
( ~ sQ201_spl
| ~ aElementOf0(sK1_skl(X0,xT),xT)
| ~ aSet0(X0)
| ~ aInfimumOfIn0(sK17_skl,X0,xT) ),
inference(component_clause,[status(thm)],[f1702]) ).
fof(f1705,plain,
( ~ sQ87_spl
| ~ sQ15_spl
| sQ201_spl ),
inference(split_clause,[status(thm)],[f1701,f1702,f297,f808]) ).
fof(f1706,plain,
! [X0] :
( ~ sQ100_spl
| ~ aElementOf0(sK1_skl(X0,xP),xP)
| ~ aSet0(X0)
| ~ aSet0(xP)
| ~ aInfimumOfIn0(sK19_skl,X0,xP) ),
inference(resolution,[status(thm)],[f943,f52]) ).
fof(f1707,definition,
! [X0] :
( sQ202_spl
<=> ( ~ aElementOf0(sK1_skl(X0,xP),xP)
| ~ aSet0(X0)
| ~ aInfimumOfIn0(sK19_skl,X0,xP) ) ),
introduced(definition,[new_symbols(definition,[sQ202_spl])],[split_symbol_definition]) ).
fof(f1710,plain,
( ~ sQ100_spl
| ~ sQ54_spl
| sQ202_spl ),
inference(split_clause,[status(thm)],[f1706,f1707,f544,f942]) ).
fof(f1711,plain,
( sQ11_spl
| ~ aLowerBoundOfIn0(sK19_skl,xP,xU)
| ~ aSubsetOf0(xP,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f831,f199]) ).
fof(f1714,definition,
( sQ203_spl
<=> aLowerBoundOfIn0(sK19_skl,xP,xU) ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f1716,plain,
( sQ203_spl
| ~ aLowerBoundOfIn0(sK19_skl,xP,xU) ),
inference(component_clause,[status(thm)],[f1714]) ).
fof(f1717,plain,
( sQ11_spl
| ~ sQ203_spl
| ~ sQ41_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1711,f317,f463,f1714,f278]) ).
fof(f1723,definition,
! [X0] :
( sQ204_spl
<=> ( ~ aInfimumOfIn0(sK0_skl(xT),X0,xP)
| ~ aSubsetOf0(X0,xP) ) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f1727,definition,
! [X0] :
( sQ205_spl
<=> ( ~ aElementOf0(sK0_skl(xT),X0)
| ~ aSubsetOf0(X0,xP) ) ),
introduced(definition,[new_symbols(definition,[sQ205_spl])],[split_symbol_definition]) ).
fof(f1728,plain,
! [X0] :
( ~ sQ205_spl
| ~ aElementOf0(sK0_skl(xT),X0)
| ~ aSubsetOf0(X0,xP) ),
inference(component_clause,[status(thm)],[f1727]) ).
fof(f1731,plain,
( sQ203_spl
| ~ aInfimumOfIn0(sK19_skl,xP,xU)
| ~ aSubsetOf0(xP,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1716,f82]) ).
fof(f1734,definition,
( sQ206_spl
<=> aInfimumOfIn0(sK19_skl,xP,xU) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f1737,plain,
( sQ203_spl
| ~ sQ206_spl
| ~ sQ41_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1731,f317,f463,f1734,f1714]) ).
fof(f1753,plain,
( sQ89_spl
| ~ aElementOf0(sK19_skl,xT)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f843,f176]) ).
fof(f1760,plain,
( sQ89_spl
| ~ sQ10_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f1753,f342,f274,f836]) ).
fof(f1775,plain,
! [X0] :
( ~ sQ92_spl
| ~ aUpperBoundOfIn0(X0,xT,xS)
| aSupremumOfIn0(X0,xT,xS)
| ~ aSubsetOf0(xT,xS)
| ~ aSet0(xS)
| ~ sdtlseqdt0(sK5_skl(X0,xT,xS),sK5_skl(sK5_skl(X0,xT,xS),xT,xS))
| aSupremumOfIn0(sK5_skl(X0,xT,xS),xT,xS) ),
inference(resolution,[status(thm)],[f861,f765]) ).
fof(f1776,plain,
! [X0] :
( ~ sQ92_spl
| ~ sdtlseqdt0(sK3_skl(X0,xT,xS),X0)
| ~ aElementOf0(X0,xS)
| ~ aSubsetOf0(xT,xS)
| ~ aSet0(xS)
| ~ sdtlseqdt0(X0,sK5_skl(X0,xT,xS))
| aSupremumOfIn0(X0,xT,xS) ),
inference(resolution,[status(thm)],[f861,f76]) ).
fof(f1777,definition,
! [X0] :
( sQ209_spl
<=> ( ~ aUpperBoundOfIn0(X0,xT,xS)
| aSupremumOfIn0(X0,xT,xS)
| ~ sdtlseqdt0(sK5_skl(X0,xT,xS),sK5_skl(sK5_skl(X0,xT,xS),xT,xS))
| aSupremumOfIn0(sK5_skl(X0,xT,xS),xT,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f1778,plain,
! [X0] :
( ~ sQ209_spl
| ~ aUpperBoundOfIn0(X0,xT,xS)
| aSupremumOfIn0(X0,xT,xS)
| ~ sdtlseqdt0(sK5_skl(X0,xT,xS),sK5_skl(sK5_skl(X0,xT,xS),xT,xS))
| aSupremumOfIn0(sK5_skl(X0,xT,xS),xT,xS) ),
inference(component_clause,[status(thm)],[f1777]) ).
fof(f1780,plain,
( ~ sQ92_spl
| ~ sQ64_spl
| ~ sQ21_spl
| sQ209_spl ),
inference(split_clause,[status(thm)],[f1775,f1777,f342,f620,f860]) ).
fof(f1781,definition,
! [X0] :
( sQ210_spl
<=> ( ~ sdtlseqdt0(sK3_skl(X0,xT,xS),X0)
| ~ aElementOf0(X0,xS)
| ~ sdtlseqdt0(X0,sK5_skl(X0,xT,xS))
| aSupremumOfIn0(X0,xT,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f1782,plain,
! [X0] :
( ~ sQ210_spl
| ~ sdtlseqdt0(sK3_skl(X0,xT,xS),X0)
| ~ aElementOf0(X0,xS)
| ~ sdtlseqdt0(X0,sK5_skl(X0,xT,xS))
| aSupremumOfIn0(X0,xT,xS) ),
inference(component_clause,[status(thm)],[f1781]) ).
fof(f1784,plain,
( ~ sQ92_spl
| ~ sQ64_spl
| ~ sQ21_spl
| sQ210_spl ),
inference(split_clause,[status(thm)],[f1776,f1781,f342,f620,f860]) ).
fof(f1795,plain,
( sQ186_spl
| ~ aSet0(xT)
| aSubsetOf0(xT,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1652,f51]) ).
fof(f1798,plain,
( sQ186_spl
| ~ sQ15_spl
| sQ49_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1795,f317,f511,f297,f1618]) ).
fof(f1824,plain,
! [X0] :
( sdtlpdtrp0(xf,sK15_skl(X0)) = sK15_skl(X0)
| aElementOf0(X0,xP)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
| ~ aElementOf0(X0,xU) ),
inference(resolution,[status(thm)],[f186,f337]) ).
fof(f1828,definition,
( sQ217_spl
<=> sdtlseqdt0(sdtlpdtrp0(xf,sK0_skl(xT)),sK0_skl(xT)) ),
introduced(definition,[new_symbols(definition,[sQ217_spl])],[split_symbol_definition]) ).
fof(f1830,plain,
( sQ217_spl
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sK0_skl(xT)),sK0_skl(xT)) ),
inference(component_clause,[status(thm)],[f1828]) ).
fof(f1831,definition,
( sQ218_spl
<=> sdtlseqdt0(sK15_skl(sK0_skl(xT)),sK0_skl(xT)) ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f1843,plain,
( sQ217_spl
| ~ sQ14_spl
| ~ sdtlseqdt0(sK0_skl(xT),sK0_skl(xT)) ),
inference(forward_demodulation,[status(thm)],[f334,f1830]) ).
fof(f1844,plain,
( sQ217_spl
| ~ sQ14_spl
| ~ sQ198_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1843,f1686]) ).
fof(f1845,plain,
( sQ217_spl
| ~ sQ14_spl
| ~ sQ198_spl ),
inference(contradiction_clause,[status(thm)],[f1844]) ).
fof(f1849,definition,
( sQ221_spl
<=> sdtlseqdt0(sdtlpdtrp0(xf,sK17_skl),sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ221_spl])],[split_symbol_definition]) ).
fof(f1851,plain,
( sQ221_spl
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sK17_skl),sK17_skl) ),
inference(component_clause,[status(thm)],[f1849]) ).
fof(f1852,definition,
( sQ222_spl
<=> sdtlseqdt0(sK15_skl(sK17_skl),sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ222_spl])],[split_symbol_definition]) ).
fof(f1854,plain,
( sQ222_spl
| ~ sdtlseqdt0(sK15_skl(sK17_skl),sK17_skl) ),
inference(component_clause,[status(thm)],[f1852]) ).
fof(f1858,plain,
( sQ5_spl
| ~ sdtlseqdt0(sK15_skl(sK17_skl),sK17_skl)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sK17_skl),sK17_skl)
| ~ aElementOf0(sK17_skl,xU) ),
inference(resolution,[status(thm)],[f1396,f187]) ).
fof(f1861,plain,
( sQ5_spl
| ~ sQ222_spl
| ~ sQ221_spl
| ~ sQ76_spl ),
inference(split_clause,[status(thm)],[f1858,f718,f1849,f1852,f253]) ).
fof(f1895,plain,
! [X0,X1] :
( ~ sQ94_spl
| ~ sdtlseqdt0(sK4_skl(X1,xT,xS),X1)
| ~ aLowerBoundOfIn0(X1,xT,xS)
| ~ aSubsetOf0(xT,xS)
| ~ aSet0(xS)
| X0 = X1
| ~ aInfimumOfIn0(X0,xT,xS) ),
inference(resolution,[status(thm)],[f873,f764]) ).
fof(f1896,plain,
! [X0,X1] :
( ~ sQ94_spl
| aLowerBoundOfIn0(sK4_skl(X1,xT,xS),xT,xS)
| ~ aLowerBoundOfIn0(X1,xT,xS)
| ~ aSubsetOf0(xT,xS)
| ~ aSet0(xS)
| X0 = X1
| ~ aInfimumOfIn0(X0,xT,xS) ),
inference(resolution,[status(thm)],[f873,f763]) ).
fof(f1904,definition,
! [X0,X1] :
( sQ228_spl
<=> ( ~ sdtlseqdt0(sK4_skl(X1,xT,xS),X1)
| ~ aLowerBoundOfIn0(X1,xT,xS)
| X0 = X1
| ~ aInfimumOfIn0(X0,xT,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f1905,plain,
! [X0,X1] :
( ~ sQ228_spl
| ~ sdtlseqdt0(sK4_skl(X1,xT,xS),X1)
| ~ aLowerBoundOfIn0(X1,xT,xS)
| X0 = X1
| ~ aInfimumOfIn0(X0,xT,xS) ),
inference(component_clause,[status(thm)],[f1904]) ).
fof(f1907,plain,
( ~ sQ94_spl
| ~ sQ64_spl
| ~ sQ21_spl
| sQ228_spl ),
inference(split_clause,[status(thm)],[f1895,f1904,f342,f620,f872]) ).
fof(f1908,definition,
! [X0,X1] :
( sQ229_spl
<=> ( aLowerBoundOfIn0(sK4_skl(X1,xT,xS),xT,xS)
| ~ aLowerBoundOfIn0(X1,xT,xS)
| X0 = X1
| ~ aInfimumOfIn0(X0,xT,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ229_spl])],[split_symbol_definition]) ).
fof(f1909,plain,
! [X0,X1] :
( ~ sQ229_spl
| aLowerBoundOfIn0(sK4_skl(X1,xT,xS),xT,xS)
| ~ aLowerBoundOfIn0(X1,xT,xS)
| X0 = X1
| ~ aInfimumOfIn0(X0,xT,xS) ),
inference(component_clause,[status(thm)],[f1908]) ).
fof(f1911,plain,
( ~ sQ94_spl
| ~ sQ64_spl
| ~ sQ21_spl
| sQ229_spl ),
inference(split_clause,[status(thm)],[f1896,f1908,f342,f620,f872]) ).
fof(f1915,plain,
! [X0] :
( ~ sQ22_spl
| sdtlseqdt0(sdtlpdtrp0(xf,X0),sK0_skl(xS))
| ~ sdtlseqdt0(X0,sK0_skl(xS))
| ~ aElementOf0(sK0_skl(xS),szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| ~ isMonotone0(xf)
| ~ aFunction0(xf) ),
inference(paramodulation,[status(thm)],[f347,f131]) ).
fof(f1916,plain,
! [X0] :
( ~ sQ22_spl
| sdtlseqdt0(sK0_skl(xS),sdtlpdtrp0(xf,X0))
| ~ sdtlseqdt0(sK0_skl(xS),X0)
| ~ aElementOf0(X0,szDzozmdt0(xf))
| ~ aElementOf0(sK0_skl(xS),szDzozmdt0(xf))
| ~ isMonotone0(xf)
| ~ aFunction0(xf) ),
inference(paramodulation,[status(thm)],[f347,f131]) ).
fof(f1917,plain,
( ~ sQ22_spl
| aElementOf0(sK0_skl(xS),szRzazndt0(xf))
| ~ aElementOf0(sK0_skl(xS),szDzozmdt0(xf))
| ~ aFunction0(xf) ),
inference(paramodulation,[status(thm)],[f347,f121]) ).
fof(f1921,definition,
( sQ231_spl
<=> sdtlseqdt0(sK0_skl(xS),sK0_skl(xS)) ),
introduced(definition,[new_symbols(definition,[sQ231_spl])],[split_symbol_definition]) ).
fof(f1922,plain,
( ~ sQ231_spl
| sdtlseqdt0(sK0_skl(xS),sK0_skl(xS)) ),
inference(component_clause,[status(thm)],[f1921]) ).
fof(f1923,plain,
( sQ231_spl
| ~ sdtlseqdt0(sK0_skl(xS),sK0_skl(xS)) ),
inference(component_clause,[status(thm)],[f1921]) ).
fof(f1927,definition,
! [X0] :
( sQ232_spl
<=> ( sdtlseqdt0(sdtlpdtrp0(xf,X0),sK0_skl(xS))
| ~ sdtlseqdt0(X0,sK0_skl(xS))
| ~ aElementOf0(X0,szDzozmdt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ232_spl])],[split_symbol_definition]) ).
fof(f1930,definition,
( sQ233_spl
<=> aElementOf0(sK0_skl(xS),szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ233_spl])],[split_symbol_definition]) ).
fof(f1932,plain,
( sQ233_spl
| ~ aElementOf0(sK0_skl(xS),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f1930]) ).
fof(f1933,plain,
( ~ sQ22_spl
| ~ sQ233_spl
| sQ232_spl
| ~ sQ176_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f1915,f314,f1552,f1927,f1930,f346]) ).
fof(f1934,definition,
! [X0] :
( sQ234_spl
<=> ( sdtlseqdt0(sK0_skl(xS),sdtlpdtrp0(xf,X0))
| ~ sdtlseqdt0(sK0_skl(xS),X0)
| ~ aElementOf0(X0,szDzozmdt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f1937,plain,
( ~ sQ22_spl
| sQ234_spl
| ~ sQ233_spl
| ~ sQ176_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f1916,f314,f1552,f1930,f1934,f346]) ).
fof(f1938,definition,
( sQ235_spl
<=> aElementOf0(sK0_skl(xS),szRzazndt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f1941,plain,
( ~ sQ22_spl
| sQ235_spl
| ~ sQ233_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f1917,f314,f1930,f1938,f346]) ).
fof(f1942,plain,
( sQ233_spl
| ~ aElementOf0(sK0_skl(xS),xU) ),
inference(forward_demodulation,[status(thm)],[f324,f1932]) ).
fof(f1943,plain,
( sQ233_spl
| ~ sQ52_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1942,f528]) ).
fof(f1944,plain,
( sQ233_spl
| ~ sQ52_spl ),
inference(contradiction_clause,[status(thm)],[f1943]) ).
fof(f1958,plain,
! [X0] :
( sQ222_spl
| ~ sdtlseqdt0(X0,sK17_skl)
| ~ sdtlseqdt0(sK15_skl(sK17_skl),X0)
| ~ aElement0(sK17_skl)
| ~ aElement0(X0)
| ~ aElement0(sK15_skl(sK17_skl)) ),
inference(resolution,[status(thm)],[f1854,f60]) ).
fof(f1961,definition,
( sQ237_spl
<=> aElementOf0(sK15_skl(sK17_skl),xT) ),
introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition]) ).
fof(f1963,plain,
( sQ237_spl
| ~ aElementOf0(sK15_skl(sK17_skl),xT) ),
inference(component_clause,[status(thm)],[f1961]) ).
fof(f1965,definition,
( sQ238_spl
<=> aElement0(sK15_skl(sK17_skl)) ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f1966,plain,
( ~ sQ238_spl
| aElement0(sK15_skl(sK17_skl)) ),
inference(component_clause,[status(thm)],[f1965]) ).
fof(f1967,plain,
( sQ238_spl
| ~ aElement0(sK15_skl(sK17_skl)) ),
inference(component_clause,[status(thm)],[f1965]) ).
fof(f1968,definition,
! [X0] :
( sQ239_spl
<=> ( ~ sdtlseqdt0(X0,sK17_skl)
| ~ sdtlseqdt0(sK15_skl(sK17_skl),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ239_spl])],[split_symbol_definition]) ).
fof(f1971,plain,
( sQ222_spl
| ~ sQ63_spl
| sQ239_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f1958,f1965,f1968,f614,f1852]) ).
fof(f1972,plain,
! [X0] :
( sQ238_spl
| ~ aElementOf0(sK15_skl(sK17_skl),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f1967,f39]) ).
fof(f1979,plain,
( aElementOf0(sdtlpdtrp0(xf,xp),xP)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,xp)),sdtlpdtrp0(xf,xp))
| ~ aElementOf0(sdtlpdtrp0(xf,xp),xU) ),
inference(resolution,[status(thm)],[f188,f204]) ).
fof(f1983,definition,
( sQ240_spl
<=> sdtlseqdt0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,xp)),sdtlpdtrp0(xf,xp)) ),
introduced(definition,[new_symbols(definition,[sQ240_spl])],[split_symbol_definition]) ).
fof(f1985,plain,
( sQ240_spl
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,xp)),sdtlpdtrp0(xf,xp)) ),
inference(component_clause,[status(thm)],[f1983]) ).
fof(f1986,definition,
( sQ241_spl
<=> aElementOf0(sdtlpdtrp0(xf,xp),xP) ),
introduced(definition,[new_symbols(definition,[sQ241_spl])],[split_symbol_definition]) ).
fof(f1987,plain,
( ~ sQ241_spl
| aElementOf0(sdtlpdtrp0(xf,xp),xP) ),
inference(component_clause,[status(thm)],[f1986]) ).
fof(f1989,plain,
( sQ241_spl
| ~ sQ240_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f1979,f514,f1983,f1986]) ).
fof(f2014,definition,
( sQ246_spl
<=> sdtlseqdt0(sdtlpdtrp0(xf,sK0_skl(xS)),sK0_skl(xS)) ),
introduced(definition,[new_symbols(definition,[sQ246_spl])],[split_symbol_definition]) ).
fof(f2016,plain,
( sQ246_spl
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sK0_skl(xS)),sK0_skl(xS)) ),
inference(component_clause,[status(thm)],[f2014]) ).
fof(f2029,plain,
( sQ246_spl
| ~ sQ22_spl
| ~ sdtlseqdt0(sK0_skl(xS),sK0_skl(xS)) ),
inference(forward_demodulation,[status(thm)],[f347,f2016]) ).
fof(f2045,plain,
( sQ237_spl
| aElementOf0(sK17_skl,xP)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sK17_skl),sK17_skl)
| ~ aElementOf0(sK17_skl,xU) ),
inference(resolution,[status(thm)],[f1963,f186]) ).
fof(f2048,plain,
( sQ237_spl
| sQ69_spl
| ~ sQ221_spl
| ~ sQ76_spl ),
inference(split_clause,[status(thm)],[f2045,f718,f1849,f659,f1961]) ).
fof(f2137,plain,
( aElementOf0(sdtlpdtrp0(xf,xp),xU)
| ~ aSubsetOf0(xP,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f202,f65]) ).
fof(f2138,plain,
( sQ50_spl
| ~ sQ41_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f2137,f317,f463,f514]) ).
fof(f2140,plain,
! [X0] :
( aUpperBoundOfIn0(sK13_skl(X0),X0,xU)
| aElementOf0(sK18_skl(X0),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f219,f153]) ).
fof(f2168,definition,
( sQ272_spl
<=> aElementOf0(sdtlpdtrp0(xf,sK17_skl),xT) ),
introduced(definition,[new_symbols(definition,[sQ272_spl])],[split_symbol_definition]) ).
fof(f2169,plain,
( ~ sQ272_spl
| aElementOf0(sdtlpdtrp0(xf,sK17_skl),xT) ),
inference(component_clause,[status(thm)],[f2168]) ).
fof(f2170,plain,
( sQ272_spl
| ~ aElementOf0(sdtlpdtrp0(xf,sK17_skl),xT) ),
inference(component_clause,[status(thm)],[f2168]) ).
fof(f2172,definition,
( sQ273_spl
<=> aElement0(sdtlpdtrp0(xf,sK17_skl)) ),
introduced(definition,[new_symbols(definition,[sQ273_spl])],[split_symbol_definition]) ).
fof(f2174,plain,
( sQ273_spl
| ~ aElement0(sdtlpdtrp0(xf,sK17_skl)) ),
inference(component_clause,[status(thm)],[f2172]) ).
fof(f2179,plain,
( sQ5_spl
| ~ aElementOf0(sK17_skl,xP) ),
inference(resolution,[status(thm)],[f255,f194]) ).
fof(f2194,plain,
( sQ198_spl
| ~ aElement0(sK0_skl(xT)) ),
inference(resolution,[status(thm)],[f1687,f56]) ).
fof(f2197,definition,
( sQ275_spl
<=> aElementOf0(sK0_skl(xT),xT) ),
introduced(definition,[new_symbols(definition,[sQ275_spl])],[split_symbol_definition]) ).
fof(f2198,plain,
( ~ sQ275_spl
| aElementOf0(sK0_skl(xT),xT) ),
inference(component_clause,[status(thm)],[f2197]) ).
fof(f2199,plain,
( sQ275_spl
| ~ aElementOf0(sK0_skl(xT),xT) ),
inference(component_clause,[status(thm)],[f2197]) ).
fof(f2202,definition,
( sQ276_spl
<=> aElement0(sK0_skl(xT)) ),
introduced(definition,[new_symbols(definition,[sQ276_spl])],[split_symbol_definition]) ).
fof(f2203,plain,
( ~ sQ276_spl
| aElement0(sK0_skl(xT)) ),
inference(component_clause,[status(thm)],[f2202]) ).
fof(f2204,plain,
( sQ276_spl
| ~ aElement0(sK0_skl(xT)) ),
inference(component_clause,[status(thm)],[f2202]) ).
fof(f2211,plain,
! [X0] :
( sQ276_spl
| ~ aElementOf0(sK0_skl(xT),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f2204,f39]) ).
fof(f2212,plain,
( sQ275_spl
| isEmpty0(xT)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[f2199,f44]) ).
fof(f2215,plain,
( sQ275_spl
| sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2212,f297,f300,f2197]) ).
fof(f2225,plain,
( sQ240_spl
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),xp)
| ~ aElementOf0(xp,xU)
| ~ aElementOf0(sdtlpdtrp0(xf,xp),xU) ),
inference(resolution,[status(thm)],[f1985,f456]) ).
fof(f2235,definition,
( sQ280_spl
<=> sdtlseqdt0(sdtlpdtrp0(xf,xp),xp) ),
introduced(definition,[new_symbols(definition,[sQ280_spl])],[split_symbol_definition]) ).
fof(f2237,plain,
( sQ280_spl
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),xp) ),
inference(component_clause,[status(thm)],[f2235]) ).
fof(f2238,plain,
( sQ240_spl
| ~ sQ280_spl
| ~ sQ42_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f2225,f514,f466,f2235,f1983]) ).
fof(f2239,definition,
( sQ281_spl
<=> aElementOf0(sdtlpdtrp0(xf,xp),szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ281_spl])],[split_symbol_definition]) ).
fof(f2241,plain,
( sQ281_spl
| ~ aElementOf0(sdtlpdtrp0(xf,xp),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f2239]) ).
fof(f2253,definition,
( sQ285_spl
<=> aElement0(sdtlpdtrp0(xf,xp)) ),
introduced(definition,[new_symbols(definition,[sQ285_spl])],[split_symbol_definition]) ).
fof(f2255,plain,
( sQ285_spl
| ~ aElement0(sdtlpdtrp0(xf,xp)) ),
inference(component_clause,[status(thm)],[f2253]) ).
fof(f2257,plain,
( sQ281_spl
| ~ aElementOf0(sdtlpdtrp0(xf,xp),xU) ),
inference(forward_demodulation,[status(thm)],[f324,f2241]) ).
fof(f2258,plain,
( sQ281_spl
| ~ sQ50_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2257,f515]) ).
fof(f2259,plain,
( sQ281_spl
| ~ sQ50_spl ),
inference(contradiction_clause,[status(thm)],[f2258]) ).
fof(f2262,plain,
! [X0,X1] :
( sQ5_spl
| ~ sdtlseqdt0(sK3_skl(sK17_skl,X1,X0),sK17_skl)
| ~ aElementOf0(sK17_skl,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0)
| ~ aElementOf0(xp,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f607,f76]) ).
fof(f2264,plain,
! [X0,X1] :
( sQ5_spl
| ~ sdtlseqdt0(sK3_skl(sK17_skl,X1,X0),sK17_skl)
| ~ aElementOf0(sK17_skl,X0)
| ~ aElementOf0(xp,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2262]) ).
fof(f2291,plain,
( sQ238_spl
| ~ aElementOf0(sK15_skl(sK17_skl),xT) ),
inference(resolution,[status(thm)],[f1972,f175]) ).
fof(f2296,plain,
( sQ238_spl
| ~ sQ237_spl ),
inference(split_clause,[status(thm)],[f2291,f1961,f1965]) ).
fof(f2303,plain,
( sQ246_spl
| ~ sQ22_spl
| ~ sQ231_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2029,f1922]) ).
fof(f2304,plain,
( sQ246_spl
| ~ sQ22_spl
| ~ sQ231_spl ),
inference(contradiction_clause,[status(thm)],[f2303]) ).
fof(f2324,plain,
! [X0] :
( aSupremumOfIn0(sK13_skl(X0),X0,xU)
| ~ aElementOf0(sK18_skl(X0),xU)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f220,f157]) ).
fof(f2326,plain,
! [X0,X1] :
( ~ aElementOf0(sK18_skl(X1),xU)
| ~ aSet0(X1)
| aSubsetOf0(X1,xU)
| aElementOf0(X0,xU)
| ~ aElementOf0(X0,X1) ),
inference(resolution,[status(thm)],[f223,f220]) ).
fof(f2330,plain,
! [X0,X1] :
( ~ sQ61_spl
| ~ aElementOf0(X0,X1)
| ~ aSet0(X1)
| xp = X0
| ~ sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(xp,X0) ),
inference(resolution,[status(thm)],[f399,f609]) ).
fof(f2371,plain,
! [X0,X1] :
( sQ5_spl
| ~ sdtlseqdt0(xp,sK2_skl(xp,X1,X0))
| ~ aElementOf0(xp,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0)
| ~ aElementOf0(sK17_skl,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f847,f68]) ).
fof(f2372,plain,
! [X0,X1] :
( sQ5_spl
| aElementOf0(sK2_skl(xp,X1,X0),X1)
| ~ aElementOf0(xp,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0)
| ~ aElementOf0(sK17_skl,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f847,f67]) ).
fof(f2375,plain,
! [X0,X1] :
( sQ5_spl
| ~ sdtlseqdt0(xp,sK2_skl(xp,X1,X0))
| ~ aElementOf0(xp,X0)
| ~ aElementOf0(sK17_skl,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2371]) ).
fof(f2376,plain,
! [X0,X1] :
( sQ5_spl
| aElementOf0(sK2_skl(xp,X1,X0),X1)
| ~ aElementOf0(xp,X0)
| ~ aElementOf0(sK17_skl,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2372]) ).
fof(f2387,plain,
! [X0] :
( sQ272_spl
| ~ aInfimumOfIn0(sdtlpdtrp0(xf,sK17_skl),X0,xT)
| ~ aSubsetOf0(X0,xT)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[f2170,f81]) ).
fof(f2388,plain,
! [X0] :
( sQ272_spl
| ~ aElementOf0(sdtlpdtrp0(xf,sK17_skl),X0)
| ~ aSubsetOf0(X0,xT)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[f2170,f50]) ).
fof(f2389,definition,
! [X0] :
( sQ293_spl
<=> ( ~ aInfimumOfIn0(sdtlpdtrp0(xf,sK17_skl),X0,xT)
| ~ aSubsetOf0(X0,xT) ) ),
introduced(definition,[new_symbols(definition,[sQ293_spl])],[split_symbol_definition]) ).
fof(f2392,plain,
( sQ272_spl
| sQ293_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2387,f297,f2389,f2168]) ).
fof(f2393,definition,
! [X0] :
( sQ294_spl
<=> ( ~ aElementOf0(sdtlpdtrp0(xf,sK17_skl),X0)
| ~ aSubsetOf0(X0,xT) ) ),
introduced(definition,[new_symbols(definition,[sQ294_spl])],[split_symbol_definition]) ).
fof(f2396,plain,
( sQ272_spl
| sQ294_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2388,f297,f2393,f2168]) ).
fof(f2401,plain,
( sQ276_spl
| ~ aElementOf0(sK0_skl(xT),xU) ),
inference(resolution,[status(thm)],[f2211,f141]) ).
fof(f2402,plain,
( sQ276_spl
| ~ aElementOf0(sK0_skl(xT),xT) ),
inference(resolution,[status(thm)],[f2211,f175]) ).
fof(f2407,plain,
( sQ276_spl
| ~ sQ174_spl ),
inference(split_clause,[status(thm)],[f2401,f1544,f2202]) ).
fof(f2408,plain,
( sQ276_spl
| ~ sQ275_spl ),
inference(split_clause,[status(thm)],[f2402,f2197,f2202]) ).
fof(f2416,plain,
( sQ280_spl
| ~ aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU) ),
inference(resolution,[status(thm)],[f2237,f198]) ).
fof(f2430,plain,
( sQ280_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2416,f202]) ).
fof(f2431,plain,
sQ280_spl,
inference(contradiction_clause,[status(thm)],[f2430]) ).
fof(f2433,plain,
! [X0,X1] :
( sP0_prd(X1)
| ~ aElementOf0(sK1_skl(X1,xU),xU)
| ~ aSet0(X1)
| X0 = sK11_skl(X1)
| ~ aInfimumOfIn0(X0,X1,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f876,f149]) ).
fof(f2435,plain,
! [X0,X1,X2,X3] :
( ~ sdtlseqdt0(sK4_skl(X3,X2,X0),X3)
| ~ aLowerBoundOfIn0(X3,X2,X0)
| ~ aSubsetOf0(X2,X0)
| ~ aSet0(X0)
| ~ aElementOf0(sK1_skl(X2,X0),X0)
| ~ aSet0(X2)
| X1 = X3
| ~ aInfimumOfIn0(X1,X2,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f876,f764]) ).
fof(f2438,definition,
! [X0,X1] :
( sQ296_spl
<=> ( sP0_prd(X1)
| ~ aElementOf0(sK1_skl(X1,xU),xU)
| ~ aSet0(X1)
| X0 = sK11_skl(X1)
| ~ aInfimumOfIn0(X0,X1,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ296_spl])],[split_symbol_definition]) ).
fof(f2441,plain,
( sQ296_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f2433,f317,f2438]) ).
fof(f2442,definition,
! [X0] :
( sQ297_spl
<=> ( X0 = xp
| ~ aInfimumOfIn0(X0,xP,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ297_spl])],[split_symbol_definition]) ).
fof(f2443,plain,
! [X0] :
( ~ sQ297_spl
| X0 = xp
| ~ aInfimumOfIn0(X0,xP,xU) ),
inference(component_clause,[status(thm)],[f2442]) ).
fof(f2446,plain,
! [X0,X1,X2,X3] :
( ~ sdtlseqdt0(sK4_skl(X3,X2,X0),X3)
| ~ aLowerBoundOfIn0(X3,X2,X0)
| ~ aSubsetOf0(X2,X0)
| ~ aElementOf0(sK1_skl(X2,X0),X0)
| ~ aSet0(X2)
| X1 = X3
| ~ aInfimumOfIn0(X1,X2,X0)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2435]) ).
fof(f2447,plain,
! [X0,X1,X2,X3] :
( ~ sdtlseqdt0(sK4_skl(X3,X2,X0),X3)
| ~ aLowerBoundOfIn0(X3,X2,X0)
| ~ aSubsetOf0(X2,X0)
| ~ aElementOf0(sK1_skl(X2,X0),X0)
| X1 = X3
| ~ aInfimumOfIn0(X1,X2,X0)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2446,f49]) ).
fof(f2450,plain,
( ~ sQ41_spl
| aSupremumOfIn0(sK7_skl(xP,xU),xP,xU) ),
inference(resolution,[status(thm)],[f965,f464]) ).
fof(f2452,plain,
! [X0] :
( ~ aElementOf0(sK1_skl(X0,xU),xU)
| ~ aSet0(X0)
| ~ aSet0(xU)
| aSupremumOfIn0(sK7_skl(X0,xU),X0,xU) ),
inference(resolution,[status(thm)],[f965,f52]) ).
fof(f2453,definition,
! [X0] :
( sQ298_spl
<=> ( ~ aElementOf0(sK1_skl(X0,xU),xU)
| ~ aSet0(X0)
| aSupremumOfIn0(sK7_skl(X0,xU),X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ298_spl])],[split_symbol_definition]) ).
fof(f2454,plain,
! [X0] :
( ~ sQ298_spl
| ~ aElementOf0(sK1_skl(X0,xU),xU)
| ~ aSet0(X0)
| aSupremumOfIn0(sK7_skl(X0,xU),X0,xU) ),
inference(component_clause,[status(thm)],[f2453]) ).
fof(f2456,plain,
( ~ sQ19_spl
| sQ298_spl ),
inference(split_clause,[status(thm)],[f2452,f2453,f317]) ).
fof(f2486,definition,
( sQ302_spl
<=> sdtlseqdt0(sK17_skl,sK0_skl(xT)) ),
introduced(definition,[new_symbols(definition,[sQ302_spl])],[split_symbol_definition]) ).
fof(f2488,plain,
( sQ302_spl
| ~ sdtlseqdt0(sK17_skl,sK0_skl(xT)) ),
inference(component_clause,[status(thm)],[f2486]) ).
fof(f2494,plain,
( sQ231_spl
| ~ aElement0(sK0_skl(xS)) ),
inference(resolution,[status(thm)],[f1923,f56]) ).
fof(f2502,definition,
( sQ304_spl
<=> aElement0(sK0_skl(xS)) ),
introduced(definition,[new_symbols(definition,[sQ304_spl])],[split_symbol_definition]) ).
fof(f2504,plain,
( sQ304_spl
| ~ aElement0(sK0_skl(xS)) ),
inference(component_clause,[status(thm)],[f2502]) ).
fof(f2511,plain,
! [X0] :
( sQ304_spl
| ~ aElementOf0(sK0_skl(xS),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f2504,f39]) ).
fof(f2550,definition,
( sQ313_spl
<=> aSubsetOf0(xT,xT) ),
introduced(definition,[new_symbols(definition,[sQ313_spl])],[split_symbol_definition]) ).
fof(f2551,plain,
( ~ sQ313_spl
| aSubsetOf0(xT,xT) ),
inference(component_clause,[status(thm)],[f2550]) ).
fof(f2558,plain,
( ~ sQ88_spl
| ~ sQ313_spl
| ~ aElementOf0(sK17_skl,xT) ),
inference(resolution,[status(thm)],[f2551,f813]) ).
fof(f2595,plain,
( ~ sQ297_spl
| ~ aSubsetOf0(xP,xU)
| ~ aCompleteLattice0(xU)
| sK6_skl(xP,xU) = xp ),
inference(resolution,[status(thm)],[f2443,f104]) ).
fof(f2596,plain,
( ~ sQ297_spl
| sP0_prd(xP)
| sK11_skl(xP) = xp ),
inference(resolution,[status(thm)],[f2443,f149]) ).
fof(f2598,plain,
! [X0] :
( ~ sQ297_spl
| ~ sdtlseqdt0(sK4_skl(X0,xP,xU),X0)
| ~ aLowerBoundOfIn0(X0,xP,xU)
| ~ aSubsetOf0(xP,xU)
| ~ aSet0(xU)
| X0 = xp ),
inference(resolution,[status(thm)],[f2443,f764]) ).
fof(f2599,plain,
! [X0] :
( ~ sQ297_spl
| aLowerBoundOfIn0(sK4_skl(X0,xP,xU),xP,xU)
| ~ aLowerBoundOfIn0(X0,xP,xU)
| ~ aSubsetOf0(xP,xU)
| ~ aSet0(xU)
| X0 = xp ),
inference(resolution,[status(thm)],[f2443,f763]) ).
fof(f2600,definition,
( sQ320_spl
<=> sK6_skl(xP,xU) = xp ),
introduced(definition,[new_symbols(definition,[sQ320_spl])],[split_symbol_definition]) ).
fof(f2601,plain,
( ~ sQ320_spl
| sK6_skl(xP,xU) = xp ),
inference(component_clause,[status(thm)],[f2600]) ).
fof(f2603,definition,
( sQ321_spl
<=> aCompleteLattice0(xU) ),
introduced(definition,[new_symbols(definition,[sQ321_spl])],[split_symbol_definition]) ).
fof(f2605,plain,
( sQ321_spl
| ~ aCompleteLattice0(xU) ),
inference(component_clause,[status(thm)],[f2603]) ).
fof(f2606,plain,
( ~ sQ297_spl
| ~ sQ41_spl
| ~ sQ321_spl
| sQ320_spl ),
inference(split_clause,[status(thm)],[f2595,f2600,f2603,f463,f2442]) ).
fof(f2607,definition,
( sQ322_spl
<=> sK11_skl(xP) = xp ),
introduced(definition,[new_symbols(definition,[sQ322_spl])],[split_symbol_definition]) ).
fof(f2608,plain,
( ~ sQ322_spl
| sK11_skl(xP) = xp ),
inference(component_clause,[status(thm)],[f2607]) ).
fof(f2610,definition,
( sQ323_spl
<=> sP0_prd(xP) ),
introduced(definition,[new_symbols(definition,[sQ323_spl])],[split_symbol_definition]) ).
fof(f2611,plain,
( ~ sQ323_spl
| sP0_prd(xP) ),
inference(component_clause,[status(thm)],[f2610]) ).
fof(f2612,plain,
( sQ323_spl
| ~ sP0_prd(xP) ),
inference(component_clause,[status(thm)],[f2610]) ).
fof(f2613,plain,
( ~ sQ297_spl
| sQ323_spl
| sQ322_spl ),
inference(split_clause,[status(thm)],[f2596,f2607,f2610,f2442]) ).
fof(f2614,definition,
! [X0] :
( sQ324_spl
<=> ( ~ sdtlseqdt0(sK4_skl(X0,xP,xU),X0)
| ~ aLowerBoundOfIn0(X0,xP,xU)
| X0 = xp ) ),
introduced(definition,[new_symbols(definition,[sQ324_spl])],[split_symbol_definition]) ).
fof(f2617,plain,
( ~ sQ297_spl
| ~ sQ41_spl
| ~ sQ19_spl
| sQ324_spl ),
inference(split_clause,[status(thm)],[f2598,f2614,f317,f463,f2442]) ).
fof(f2618,definition,
! [X0] :
( sQ325_spl
<=> ( aLowerBoundOfIn0(sK4_skl(X0,xP,xU),xP,xU)
| ~ aLowerBoundOfIn0(X0,xP,xU)
| X0 = xp ) ),
introduced(definition,[new_symbols(definition,[sQ325_spl])],[split_symbol_definition]) ).
fof(f2621,plain,
( ~ sQ297_spl
| ~ sQ41_spl
| ~ sQ19_spl
| sQ325_spl ),
inference(split_clause,[status(thm)],[f2599,f2618,f317,f463,f2442]) ).
fof(f2622,plain,
( sQ321_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2605,f158]) ).
fof(f2623,plain,
sQ321_spl,
inference(contradiction_clause,[status(thm)],[f2622]) ).
fof(f2626,plain,
( ~ sQ323_spl
| ~ aSubsetOf0(xP,xU) ),
inference(resolution,[status(thm)],[f2611,f221]) ).
fof(f2635,plain,
( ~ sQ323_spl
| ~ sQ41_spl ),
inference(split_clause,[status(thm)],[f2626,f463,f2610]) ).
fof(f2637,plain,
( sQ323_spl
| aSupremumOfIn0(sK13_skl(xP),xP,xU) ),
inference(resolution,[status(thm)],[f2612,f157]) ).
fof(f2640,plain,
! [X0] :
( ~ sQ322_spl
| sdtlseqdt0(X0,xp)
| ~ aLowerBoundOfIn0(X0,xP,xU)
| sP0_prd(xP) ),
inference(paramodulation,[status(thm)],[f2608,f148]) ).
fof(f2641,plain,
! [X0] :
( ~ sQ322_spl
| sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,sK12_skl(X0,xP))
| ~ aElementOf0(X0,xU)
| sP0_prd(xP) ),
inference(paramodulation,[status(thm)],[f2608,f147]) ).
fof(f2642,plain,
! [X0] :
( ~ sQ322_spl
| sdtlseqdt0(X0,xp)
| aElementOf0(sK12_skl(X0,xP),xP)
| ~ aElementOf0(X0,xU)
| sP0_prd(xP) ),
inference(paramodulation,[status(thm)],[f2608,f146]) ).
fof(f2643,plain,
! [X0] :
( ~ sQ322_spl
| sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xP)
| sP0_prd(xP) ),
inference(paramodulation,[status(thm)],[f2608,f144]) ).
fof(f2645,plain,
( ~ sQ322_spl
| aLowerBoundOfIn0(xp,xP,xU)
| sP0_prd(xP) ),
inference(paramodulation,[status(thm)],[f2608,f145]) ).
fof(f2647,definition,
! [X0] :
( sQ328_spl
<=> ( sdtlseqdt0(X0,xp)
| ~ aLowerBoundOfIn0(X0,xP,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ328_spl])],[split_symbol_definition]) ).
fof(f2650,plain,
( ~ sQ322_spl
| sQ328_spl
| sQ323_spl ),
inference(split_clause,[status(thm)],[f2640,f2610,f2647,f2607]) ).
fof(f2651,definition,
! [X0] :
( sQ329_spl
<=> ( sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(X0,sK12_skl(X0,xP))
| ~ aElementOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ329_spl])],[split_symbol_definition]) ).
fof(f2654,plain,
( ~ sQ322_spl
| sQ329_spl
| sQ323_spl ),
inference(split_clause,[status(thm)],[f2641,f2610,f2651,f2607]) ).
fof(f2655,definition,
! [X0] :
( sQ330_spl
<=> ( sdtlseqdt0(X0,xp)
| aElementOf0(sK12_skl(X0,xP),xP)
| ~ aElementOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ330_spl])],[split_symbol_definition]) ).
fof(f2658,plain,
( ~ sQ322_spl
| sQ330_spl
| sQ323_spl ),
inference(split_clause,[status(thm)],[f2642,f2610,f2655,f2607]) ).
fof(f2659,definition,
! [X0] :
( sQ331_spl
<=> ( sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xP) ) ),
introduced(definition,[new_symbols(definition,[sQ331_spl])],[split_symbol_definition]) ).
fof(f2662,plain,
( ~ sQ322_spl
| sQ331_spl
| sQ323_spl ),
inference(split_clause,[status(thm)],[f2643,f2610,f2659,f2607]) ).
fof(f2663,definition,
( sQ332_spl
<=> aInfimumOfIn0(xp,xP,xU) ),
introduced(definition,[new_symbols(definition,[sQ332_spl])],[split_symbol_definition]) ).
fof(f2667,definition,
( sQ333_spl
<=> aLowerBoundOfIn0(xp,xP,xU) ),
introduced(definition,[new_symbols(definition,[sQ333_spl])],[split_symbol_definition]) ).
fof(f2670,plain,
( ~ sQ322_spl
| sQ333_spl
| sQ323_spl ),
inference(split_clause,[status(thm)],[f2645,f2610,f2667,f2607]) ).
fof(f2672,plain,
( ~ sQ320_spl
| aInfimumOfIn0(xp,xP,xU)
| ~ aSubsetOf0(xP,xU)
| ~ aCompleteLattice0(xU) ),
inference(paramodulation,[status(thm)],[f2601,f104]) ).
fof(f2673,plain,
( ~ sQ320_spl
| sQ332_spl
| ~ sQ41_spl
| ~ sQ321_spl ),
inference(split_clause,[status(thm)],[f2672,f2603,f463,f2663,f2600]) ).
fof(f2679,plain,
! [X0] :
( aElementOf0(sK13_skl(X0),xU)
| ~ aSubsetOf0(X0,xU)
| ~ aSet0(xU)
| ~ aSubsetOf0(X0,xU) ),
inference(resolution,[status(thm)],[f1495,f73]) ).
fof(f2690,definition,
! [X0] :
( sQ337_spl
<=> ( aElementOf0(sK13_skl(X0),xU)
| ~ aSubsetOf0(X0,xU)
| ~ aSubsetOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ337_spl])],[split_symbol_definition]) ).
fof(f2693,plain,
( ~ sQ19_spl
| sQ337_spl ),
inference(split_clause,[status(thm)],[f2679,f2690,f317]) ).
fof(f2697,plain,
! [X0] :
( ~ aElementOf0(sK1_skl(X0,xU),xU)
| ~ aSet0(X0)
| ~ aSet0(xU)
| aSupremumOfIn0(sK13_skl(X0),X0,xU) ),
inference(resolution,[status(thm)],[f1496,f52]) ).
fof(f2698,definition,
! [X0] :
( sQ338_spl
<=> ( ~ aElementOf0(sK1_skl(X0,xU),xU)
| ~ aSet0(X0)
| aSupremumOfIn0(sK13_skl(X0),X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ338_spl])],[split_symbol_definition]) ).
fof(f2699,plain,
! [X0] :
( ~ sQ338_spl
| ~ aElementOf0(sK1_skl(X0,xU),xU)
| ~ aSet0(X0)
| aSupremumOfIn0(sK13_skl(X0),X0,xU) ),
inference(component_clause,[status(thm)],[f2698]) ).
fof(f2701,plain,
( ~ sQ19_spl
| sQ338_spl ),
inference(split_clause,[status(thm)],[f2697,f2698,f317]) ).
fof(f2703,plain,
! [X0] :
( ~ sQ102_spl
| ~ sdtlseqdt0(sK4_skl(sK19_skl,X0,xS),sK19_skl)
| ~ aLowerBoundOfIn0(sK19_skl,X0,xS)
| ~ aSubsetOf0(X0,xS)
| ~ aSet0(xS)
| ~ aSubsetOf0(X0,xS) ),
inference(resolution,[status(thm)],[f954,f764]) ).
fof(f2704,plain,
! [X0] :
( ~ sQ102_spl
| aLowerBoundOfIn0(sK4_skl(sK19_skl,X0,xS),X0,xS)
| ~ aLowerBoundOfIn0(sK19_skl,X0,xS)
| ~ aSubsetOf0(X0,xS)
| ~ aSet0(xS)
| ~ aSubsetOf0(X0,xS) ),
inference(resolution,[status(thm)],[f954,f763]) ).
fof(f2705,definition,
! [X0] :
( sQ339_spl
<=> ( ~ sdtlseqdt0(sK4_skl(sK19_skl,X0,xS),sK19_skl)
| ~ aLowerBoundOfIn0(sK19_skl,X0,xS)
| ~ aSubsetOf0(X0,xS)
| ~ aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ339_spl])],[split_symbol_definition]) ).
fof(f2708,plain,
( ~ sQ102_spl
| ~ sQ21_spl
| sQ339_spl ),
inference(split_clause,[status(thm)],[f2703,f2705,f342,f953]) ).
fof(f2709,definition,
! [X0] :
( sQ340_spl
<=> ( aLowerBoundOfIn0(sK4_skl(sK19_skl,X0,xS),X0,xS)
| ~ aLowerBoundOfIn0(sK19_skl,X0,xS)
| ~ aSubsetOf0(X0,xS)
| ~ aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ340_spl])],[split_symbol_definition]) ).
fof(f2712,plain,
( ~ sQ102_spl
| ~ sQ21_spl
| sQ340_spl ),
inference(split_clause,[status(thm)],[f2704,f2709,f342,f953]) ).
fof(f2733,definition,
( sQ344_spl
<=> sdtlseqdt0(sK0_skl(xT),sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ344_spl])],[split_symbol_definition]) ).
fof(f2735,plain,
( sQ344_spl
| ~ sdtlseqdt0(sK0_skl(xT),sK17_skl) ),
inference(component_clause,[status(thm)],[f2733]) ).
fof(f2737,plain,
( ~ sQ52_spl
| sQ304_spl
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f2511,f528]) ).
fof(f2747,plain,
( ~ sQ52_spl
| sQ304_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2737,f141]) ).
fof(f2748,plain,
( ~ sQ52_spl
| sQ304_spl ),
inference(contradiction_clause,[status(thm)],[f2747]) ).
fof(f2765,plain,
! [X0,X1] :
( ~ sQ27_spl
| ~ aElementOf0(sK1_skl(X1,xT),xT)
| ~ aSet0(X1)
| ~ aSet0(xT)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f372,f52]) ).
fof(f2766,definition,
! [X0,X1] :
( sQ345_spl
<=> ( ~ aElementOf0(sK1_skl(X1,xT),xT)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ345_spl])],[split_symbol_definition]) ).
fof(f2767,plain,
! [X0,X1] :
( ~ sQ345_spl
| ~ aElementOf0(sK1_skl(X1,xT),xT)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(component_clause,[status(thm)],[f2766]) ).
fof(f2769,plain,
( ~ sQ27_spl
| ~ sQ15_spl
| sQ345_spl ),
inference(split_clause,[status(thm)],[f2765,f2766,f297,f371]) ).
fof(f2854,plain,
! [X0] :
( aElementOf0(sK13_skl(X0),xU)
| ~ aSubsetOf0(X0,xU)
| ~ aSet0(xU)
| aElementOf0(sK18_skl(X0),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f2140,f73]) ).
fof(f2859,definition,
! [X0] :
( sQ361_spl
<=> ( aElementOf0(sK13_skl(X0),xU)
| ~ aSubsetOf0(X0,xU)
| aElementOf0(sK18_skl(X0),X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ361_spl])],[split_symbol_definition]) ).
fof(f2862,plain,
( ~ sQ19_spl
| sQ361_spl ),
inference(split_clause,[status(thm)],[f2854,f2859,f317]) ).
fof(f2863,plain,
! [X0] :
( ~ sQ121_spl
| ~ aElementOf0(sK1_skl(X0,xT),xT)
| ~ aSet0(X0)
| ~ aSet0(xT)
| ~ aInfimumOfIn0(sK19_skl,X0,xT) ),
inference(resolution,[status(thm)],[f1100,f52]) ).
fof(f2864,definition,
! [X0] :
( sQ362_spl
<=> ( ~ aElementOf0(sK1_skl(X0,xT),xT)
| ~ aSet0(X0)
| ~ aInfimumOfIn0(sK19_skl,X0,xT) ) ),
introduced(definition,[new_symbols(definition,[sQ362_spl])],[split_symbol_definition]) ).
fof(f2867,plain,
( ~ sQ121_spl
| ~ sQ15_spl
| sQ362_spl ),
inference(split_clause,[status(thm)],[f2863,f2864,f297,f1099]) ).
fof(f2868,plain,
! [X0] :
( ~ sQ187_spl
| ~ aElementOf0(sK1_skl(X0,xP),xP)
| ~ aSet0(X0)
| ~ aSet0(xP)
| ~ aInfimumOfIn0(xp,X0,xP) ),
inference(resolution,[status(thm)],[f1625,f52]) ).
fof(f2869,definition,
! [X0] :
( sQ363_spl
<=> ( ~ aElementOf0(sK1_skl(X0,xP),xP)
| ~ aSet0(X0)
| ~ aInfimumOfIn0(xp,X0,xP) ) ),
introduced(definition,[new_symbols(definition,[sQ363_spl])],[split_symbol_definition]) ).
fof(f2872,plain,
( ~ sQ187_spl
| ~ sQ54_spl
| sQ363_spl ),
inference(split_clause,[status(thm)],[f2868,f2869,f544,f1624]) ).
fof(f2893,plain,
! [X0,X1] :
( ~ sQ96_spl
| ~ aInfimumOfIn0(sK1_skl(X0,xS),X1,xS)
| ~ aSubsetOf0(X1,xS)
| ~ aSet0(xS)
| ~ aSet0(X0)
| ~ aElementOf0(sK17_skl,X0) ),
inference(resolution,[status(thm)],[f886,f81]) ).
fof(f2894,plain,
! [X0,X1] :
( ~ sQ96_spl
| ~ aElementOf0(sK1_skl(X0,xS),X1)
| ~ aSubsetOf0(X1,xS)
| ~ aSet0(xS)
| ~ aSet0(X0)
| ~ aElementOf0(sK17_skl,X0) ),
inference(resolution,[status(thm)],[f886,f50]) ).
fof(f2898,definition,
! [X0,X1] :
( sQ365_spl
<=> ( ~ aInfimumOfIn0(sK1_skl(X0,xS),X1,xS)
| ~ aSubsetOf0(X1,xS)
| ~ aSet0(X0)
| ~ aElementOf0(sK17_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ365_spl])],[split_symbol_definition]) ).
fof(f2901,plain,
( ~ sQ96_spl
| ~ sQ21_spl
| sQ365_spl ),
inference(split_clause,[status(thm)],[f2893,f2898,f342,f885]) ).
fof(f2902,definition,
! [X0,X1] :
( sQ366_spl
<=> ( ~ aElementOf0(sK1_skl(X0,xS),X1)
| ~ aSubsetOf0(X1,xS)
| ~ aSet0(X0)
| ~ aElementOf0(sK17_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ366_spl])],[split_symbol_definition]) ).
fof(f2905,plain,
( ~ sQ96_spl
| ~ sQ21_spl
| sQ366_spl ),
inference(split_clause,[status(thm)],[f2894,f2902,f342,f885]) ).
fof(f2969,plain,
! [X0] :
( sQ323_spl
| X0 = sK13_skl(xP)
| ~ aSupremumOfIn0(X0,xP,xU)
| ~ aSubsetOf0(xP,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f2637,f96]) ).
fof(f2970,plain,
( sQ323_spl
| aUpperBoundOfIn0(sK13_skl(xP),xP,xU)
| ~ aSubsetOf0(xP,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f2637,f91]) ).
fof(f2972,definition,
! [X0] :
( sQ374_spl
<=> ( X0 = sK13_skl(xP)
| ~ aSupremumOfIn0(X0,xP,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ374_spl])],[split_symbol_definition]) ).
fof(f2975,plain,
( sQ323_spl
| sQ374_spl
| ~ sQ41_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f2969,f317,f463,f2972,f2610]) ).
fof(f2976,definition,
( sQ375_spl
<=> aUpperBoundOfIn0(sK13_skl(xP),xP,xU) ),
introduced(definition,[new_symbols(definition,[sQ375_spl])],[split_symbol_definition]) ).
fof(f2977,plain,
( ~ sQ375_spl
| aUpperBoundOfIn0(sK13_skl(xP),xP,xU) ),
inference(component_clause,[status(thm)],[f2976]) ).
fof(f2979,plain,
( sQ323_spl
| sQ375_spl
| ~ sQ41_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f2970,f317,f463,f2976,f2610]) ).
fof(f2980,definition,
( sQ376_spl
<=> aElementOf0(sK13_skl(xP),xU) ),
introduced(definition,[new_symbols(definition,[sQ376_spl])],[split_symbol_definition]) ).
fof(f2985,plain,
! [X0,X1] :
( X1 = sK13_skl(X0)
| ~ aSupremumOfIn0(X1,X0,xU)
| ~ aSubsetOf0(X0,xU)
| ~ aSet0(xU)
| ~ aElementOf0(sK18_skl(X0),xU)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f2324,f96]) ).
fof(f2986,plain,
! [X0] :
( aUpperBoundOfIn0(sK13_skl(X0),X0,xU)
| ~ aSubsetOf0(X0,xU)
| ~ aSet0(xU)
| ~ aElementOf0(sK18_skl(X0),xU)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f2324,f91]) ).
fof(f2987,plain,
! [X0] :
( aElementOf0(sK13_skl(X0),xU)
| ~ aSubsetOf0(X0,xU)
| ~ aSet0(xU)
| ~ aElementOf0(sK18_skl(X0),xU)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f2324,f90]) ).
fof(f2998,definition,
! [X0,X1] :
( sQ380_spl
<=> ( X1 = sK13_skl(X0)
| ~ aSupremumOfIn0(X1,X0,xU)
| ~ aSubsetOf0(X0,xU)
| ~ aElementOf0(sK18_skl(X0),xU)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ380_spl])],[split_symbol_definition]) ).
fof(f2999,plain,
! [X0,X1] :
( ~ sQ380_spl
| X1 = sK13_skl(X0)
| ~ aSupremumOfIn0(X1,X0,xU)
| ~ aSubsetOf0(X0,xU)
| ~ aElementOf0(sK18_skl(X0),xU)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f2998]) ).
fof(f3001,plain,
( ~ sQ19_spl
| sQ380_spl ),
inference(split_clause,[status(thm)],[f2985,f2998,f317]) ).
fof(f3002,definition,
! [X0] :
( sQ381_spl
<=> ( aUpperBoundOfIn0(sK13_skl(X0),X0,xU)
| ~ aSubsetOf0(X0,xU)
| ~ aElementOf0(sK18_skl(X0),xU)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ381_spl])],[split_symbol_definition]) ).
fof(f3005,plain,
( ~ sQ19_spl
| sQ381_spl ),
inference(split_clause,[status(thm)],[f2986,f3002,f317]) ).
fof(f3006,definition,
! [X0] :
( sQ382_spl
<=> ( aElementOf0(sK13_skl(X0),xU)
| ~ aSubsetOf0(X0,xU)
| ~ aElementOf0(sK18_skl(X0),xU)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ382_spl])],[split_symbol_definition]) ).
fof(f3009,plain,
( ~ sQ19_spl
| sQ382_spl ),
inference(split_clause,[status(thm)],[f2987,f3006,f317]) ).
fof(f3019,plain,
! [X0] :
( sQ89_spl
| ~ aSet0(xU)
| ~ aElementOf0(sK18_skl(X0),xU)
| ~ aSet0(X0)
| aSubsetOf0(X0,xU)
| ~ aElementOf0(sK19_skl,X0) ),
inference(resolution,[status(thm)],[f2326,f843]) ).
fof(f3021,definition,
! [X0] :
( sQ384_spl
<=> ( ~ aElementOf0(sK18_skl(X0),xU)
| ~ aSet0(X0)
| aSubsetOf0(X0,xU)
| ~ aElementOf0(sK19_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ384_spl])],[split_symbol_definition]) ).
fof(f3024,plain,
( sQ89_spl
| ~ sQ19_spl
| sQ384_spl ),
inference(split_clause,[status(thm)],[f3019,f3021,f317,f836]) ).
fof(f3043,plain,
( ~ sQ276_spl
| ~ sQ61_spl
| sK0_skl(xT) = xp
| ~ sdtlseqdt0(xp,sK0_skl(xT))
| ~ sdtlseqdt0(sK0_skl(xT),xp) ),
inference(resolution,[status(thm)],[f919,f2203]) ).
fof(f3044,plain,
( ~ sQ63_spl
| ~ sQ61_spl
| sK17_skl = xp
| ~ sdtlseqdt0(xp,sK17_skl)
| ~ sdtlseqdt0(sK17_skl,xp) ),
inference(resolution,[status(thm)],[f919,f615]) ).
fof(f3045,plain,
( ~ sQ61_spl
| xp = xp
| ~ sdtlseqdt0(xp,xp)
| ~ sdtlseqdt0(xp,xp) ),
inference(resolution,[status(thm)],[f919,f609]) ).
fof(f3053,definition,
( sQ389_spl
<=> sK0_skl(xS) = xp ),
introduced(definition,[new_symbols(definition,[sQ389_spl])],[split_symbol_definition]) ).
fof(f3054,plain,
( ~ sQ389_spl
| sK0_skl(xS) = xp ),
inference(component_clause,[status(thm)],[f3053]) ).
fof(f3057,definition,
( sQ390_spl
<=> sdtlseqdt0(sK0_skl(xT),xp) ),
introduced(definition,[new_symbols(definition,[sQ390_spl])],[split_symbol_definition]) ).
fof(f3059,plain,
( sQ390_spl
| ~ sdtlseqdt0(sK0_skl(xT),xp) ),
inference(component_clause,[status(thm)],[f3057]) ).
fof(f3060,definition,
( sQ391_spl
<=> sdtlseqdt0(xp,sK0_skl(xT)) ),
introduced(definition,[new_symbols(definition,[sQ391_spl])],[split_symbol_definition]) ).
fof(f3062,plain,
( sQ391_spl
| ~ sdtlseqdt0(xp,sK0_skl(xT)) ),
inference(component_clause,[status(thm)],[f3060]) ).
fof(f3063,definition,
( sQ392_spl
<=> sK0_skl(xT) = xp ),
introduced(definition,[new_symbols(definition,[sQ392_spl])],[split_symbol_definition]) ).
fof(f3064,plain,
( ~ sQ392_spl
| sK0_skl(xT) = xp ),
inference(component_clause,[status(thm)],[f3063]) ).
fof(f3066,plain,
( ~ sQ276_spl
| ~ sQ61_spl
| sQ392_spl
| ~ sQ391_spl
| ~ sQ390_spl ),
inference(split_clause,[status(thm)],[f3043,f3057,f3060,f3063,f608,f2202]) ).
fof(f3067,definition,
( sQ393_spl
<=> sdtlseqdt0(sK17_skl,xp) ),
introduced(definition,[new_symbols(definition,[sQ393_spl])],[split_symbol_definition]) ).
fof(f3069,plain,
( sQ393_spl
| ~ sdtlseqdt0(sK17_skl,xp) ),
inference(component_clause,[status(thm)],[f3067]) ).
fof(f3070,definition,
( sQ394_spl
<=> sK17_skl = xp ),
introduced(definition,[new_symbols(definition,[sQ394_spl])],[split_symbol_definition]) ).
fof(f3071,plain,
( ~ sQ394_spl
| sK17_skl = xp ),
inference(component_clause,[status(thm)],[f3070]) ).
fof(f3073,plain,
( ~ sQ63_spl
| ~ sQ61_spl
| sQ394_spl
| ~ sQ5_spl
| ~ sQ393_spl ),
inference(split_clause,[status(thm)],[f3044,f3067,f253,f3070,f608,f614]) ).
fof(f3074,definition,
( sQ395_spl
<=> xp = xp ),
introduced(definition,[new_symbols(definition,[sQ395_spl])],[split_symbol_definition]) ).
fof(f3077,plain,
( ~ sQ61_spl
| sQ395_spl
| ~ sQ139_spl ),
inference(split_clause,[status(thm)],[f3045,f1238,f3074,f608]) ).
fof(f3104,plain,
( sQ393_spl
| ~ sdtlseqdt0(sK17_skl,sK16_skl(sK17_skl))
| ~ aElementOf0(sK17_skl,xU) ),
inference(resolution,[status(thm)],[f3069,f197]) ).
fof(f3110,plain,
! [X0] :
( sQ393_spl
| ~ sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(sK17_skl,X0)
| ~ aElement0(xp)
| ~ aElement0(X0)
| ~ aElement0(sK17_skl) ),
inference(resolution,[status(thm)],[f3069,f60]) ).
fof(f3113,definition,
( sQ396_spl
<=> sdtlseqdt0(sK17_skl,sK16_skl(sK17_skl)) ),
introduced(definition,[new_symbols(definition,[sQ396_spl])],[split_symbol_definition]) ).
fof(f3115,plain,
( sQ396_spl
| ~ sdtlseqdt0(sK17_skl,sK16_skl(sK17_skl)) ),
inference(component_clause,[status(thm)],[f3113]) ).
fof(f3116,plain,
( sQ393_spl
| ~ sQ396_spl
| ~ sQ76_spl ),
inference(split_clause,[status(thm)],[f3104,f718,f3113,f3067]) ).
fof(f3118,definition,
! [X0] :
( sQ397_spl
<=> ( ~ sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(sK17_skl,X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ397_spl])],[split_symbol_definition]) ).
fof(f3121,plain,
( sQ393_spl
| ~ sQ61_spl
| sQ397_spl
| ~ sQ63_spl ),
inference(split_clause,[status(thm)],[f3110,f614,f3118,f608,f3067]) ).
fof(f3124,plain,
( ~ sQ275_spl
| ~ sQ392_spl
| aElementOf0(xp,xT) ),
inference(backward_demodulation,[status(thm)],[f3064,f2198]) ).
fof(f3130,plain,
( ~ sQ275_spl
| ~ sQ392_spl
| ~ sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3124,f400]) ).
fof(f3131,plain,
( ~ sQ275_spl
| ~ sQ392_spl
| ~ sQ30_spl ),
inference(contradiction_clause,[status(thm)],[f3130]) ).
fof(f3136,plain,
( ~ sQ22_spl
| ~ sQ389_spl
| sdtlpdtrp0(xf,sK0_skl(xS)) = xp ),
inference(backward_demodulation,[status(thm)],[f3054,f347]) ).
fof(f3142,plain,
( ~ sQ22_spl
| ~ sQ389_spl
| sdtlpdtrp0(xf,xp) = xp ),
inference(forward_demodulation,[status(thm)],[f3054,f3136]) ).
fof(f3143,plain,
( ~ sQ22_spl
| ~ sQ389_spl
| sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3142,f266]) ).
fof(f3144,plain,
( ~ sQ22_spl
| ~ sQ389_spl
| sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f3143]) ).
fof(f3212,plain,
( sQ391_spl
| ~ aElementOf0(sK0_skl(xT),xP) ),
inference(resolution,[status(thm)],[f3062,f194]) ).
fof(f3213,plain,
( sQ391_spl
| ~ aElementOf0(xp,xT)
| ~ aElementOf0(sK0_skl(xT),xP) ),
inference(resolution,[status(thm)],[f3062,f184]) ).
fof(f3216,plain,
! [X0] :
( sQ391_spl
| ~ sdtlseqdt0(X0,sK0_skl(xT))
| ~ sdtlseqdt0(xp,X0)
| ~ aElement0(sK0_skl(xT))
| ~ aElement0(X0)
| ~ aElement0(xp) ),
inference(resolution,[status(thm)],[f3062,f60]) ).
fof(f3219,plain,
( sQ391_spl
| ~ sQ38_spl
| ~ sQ197_spl ),
inference(split_clause,[status(thm)],[f3213,f1682,f440,f3060]) ).
fof(f3220,definition,
! [X0] :
( sQ403_spl
<=> ( ~ sdtlseqdt0(X0,sK0_skl(xT))
| ~ sdtlseqdt0(xp,X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ403_spl])],[split_symbol_definition]) ).
fof(f3223,plain,
( sQ391_spl
| ~ sQ276_spl
| sQ403_spl
| ~ sQ61_spl ),
inference(split_clause,[status(thm)],[f3216,f608,f3220,f2202,f3060]) ).
fof(f3255,plain,
( ~ sQ13_spl
| sQ390_spl
| ~ aElementOf0(sK0_skl(xT),xT) ),
inference(resolution,[status(thm)],[f3059,f287]) ).
fof(f3266,plain,
( ~ sQ13_spl
| sQ390_spl
| ~ sQ275_spl ),
inference(split_clause,[status(thm)],[f3255,f2197,f3057,f286]) ).
fof(f3273,plain,
( sQ184_spl
| ~ sdtlseqdt0(sK15_skl(xp),xp)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),xp)
| ~ aElementOf0(xp,xU) ),
inference(resolution,[status(thm)],[f1612,f187]) ).
fof(f3280,definition,
( sQ411_spl
<=> sdtlseqdt0(sK15_skl(xp),xp) ),
introduced(definition,[new_symbols(definition,[sQ411_spl])],[split_symbol_definition]) ).
fof(f3282,plain,
( sQ411_spl
| ~ sdtlseqdt0(sK15_skl(xp),xp) ),
inference(component_clause,[status(thm)],[f3280]) ).
fof(f3283,plain,
( sQ184_spl
| ~ sQ411_spl
| ~ sQ280_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f3273,f466,f2235,f3280,f1610]) ).
fof(f3316,plain,
( ~ sQ12_spl
| aElementOf0(xp,xS)
| ~ aSubsetOf0(xT,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f283,f73]) ).
fof(f3318,plain,
( ~ sQ12_spl
| sQ32_spl
| ~ sQ64_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3316,f342,f620,f408,f282]) ).
fof(f3319,plain,
( ~ sQ32_spl
| sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f409,f917]) ).
fof(f3320,plain,
( ~ sQ32_spl
| sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f3319]) ).
fof(f3321,plain,
( sQ12_spl
| ~ sdtlseqdt0(sK3_skl(xp,xT,xS),xp)
| ~ aElementOf0(xp,xS)
| ~ aSubsetOf0(xT,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f284,f76]) ).
fof(f3322,definition,
( sQ415_spl
<=> sdtlseqdt0(sK3_skl(xp,xT,xS),xp) ),
introduced(definition,[new_symbols(definition,[sQ415_spl])],[split_symbol_definition]) ).
fof(f3324,plain,
( sQ415_spl
| ~ sdtlseqdt0(sK3_skl(xp,xT,xS),xp) ),
inference(component_clause,[status(thm)],[f3322]) ).
fof(f3325,plain,
( sQ12_spl
| ~ sQ415_spl
| ~ sQ32_spl
| ~ sQ64_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3321,f342,f620,f408,f3322,f282]) ).
fof(f3359,plain,
( sQ415_spl
| ~ sdtlseqdt0(sK3_skl(xp,xT,xS),sK16_skl(sK3_skl(xp,xT,xS)))
| ~ aElementOf0(sK3_skl(xp,xT,xS),xU) ),
inference(resolution,[status(thm)],[f3324,f197]) ).
fof(f3361,plain,
( sQ415_spl
| ~ aElementOf0(sK3_skl(xp,xT,xS),xT)
| ~ aElementOf0(xp,xP) ),
inference(resolution,[status(thm)],[f3324,f184]) ).
fof(f3364,plain,
! [X0] :
( sQ415_spl
| ~ sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(sK3_skl(xp,xT,xS),X0)
| ~ aElement0(xp)
| ~ aElement0(X0)
| ~ aElement0(sK3_skl(xp,xT,xS)) ),
inference(resolution,[status(thm)],[f3324,f60]) ).
fof(f3367,definition,
( sQ416_spl
<=> aElementOf0(sK3_skl(xp,xT,xS),xU) ),
introduced(definition,[new_symbols(definition,[sQ416_spl])],[split_symbol_definition]) ).
fof(f3369,plain,
( sQ416_spl
| ~ aElementOf0(sK3_skl(xp,xT,xS),xU) ),
inference(component_clause,[status(thm)],[f3367]) ).
fof(f3370,definition,
( sQ417_spl
<=> sdtlseqdt0(sK3_skl(xp,xT,xS),sK16_skl(sK3_skl(xp,xT,xS))) ),
introduced(definition,[new_symbols(definition,[sQ417_spl])],[split_symbol_definition]) ).
fof(f3372,plain,
( sQ417_spl
| ~ sdtlseqdt0(sK3_skl(xp,xT,xS),sK16_skl(sK3_skl(xp,xT,xS))) ),
inference(component_clause,[status(thm)],[f3370]) ).
fof(f3373,plain,
( sQ415_spl
| ~ sQ417_spl
| ~ sQ416_spl ),
inference(split_clause,[status(thm)],[f3359,f3367,f3370,f3322]) ).
fof(f3374,definition,
( sQ418_spl
<=> aElementOf0(sK3_skl(xp,xT,xS),xT) ),
introduced(definition,[new_symbols(definition,[sQ418_spl])],[split_symbol_definition]) ).
fof(f3376,plain,
( sQ418_spl
| ~ aElementOf0(sK3_skl(xp,xT,xS),xT) ),
inference(component_clause,[status(thm)],[f3374]) ).
fof(f3377,plain,
( sQ415_spl
| ~ sQ418_spl
| ~ sQ184_spl ),
inference(split_clause,[status(thm)],[f3361,f1610,f3374,f3322]) ).
fof(f3378,definition,
( sQ419_spl
<=> aElement0(sK3_skl(xp,xT,xS)) ),
introduced(definition,[new_symbols(definition,[sQ419_spl])],[split_symbol_definition]) ).
fof(f3381,definition,
! [X0] :
( sQ420_spl
<=> ( ~ sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(sK3_skl(xp,xT,xS),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ420_spl])],[split_symbol_definition]) ).
fof(f3382,plain,
! [X0] :
( ~ sQ420_spl
| ~ sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(sK3_skl(xp,xT,xS),X0)
| ~ aElement0(X0) ),
inference(component_clause,[status(thm)],[f3381]) ).
fof(f3384,plain,
( sQ415_spl
| ~ sQ61_spl
| sQ420_spl
| ~ sQ419_spl ),
inference(split_clause,[status(thm)],[f3364,f3378,f3381,f608,f3322]) ).
fof(f3385,plain,
( ~ sQ13_spl
| sQ411_spl
| ~ aElementOf0(sK15_skl(xp),xT) ),
inference(resolution,[status(thm)],[f3282,f287]) ).
fof(f3401,definition,
( sQ423_spl
<=> aElementOf0(sK15_skl(xp),xT) ),
introduced(definition,[new_symbols(definition,[sQ423_spl])],[split_symbol_definition]) ).
fof(f3403,plain,
( sQ423_spl
| ~ aElementOf0(sK15_skl(xp),xT) ),
inference(component_clause,[status(thm)],[f3401]) ).
fof(f3413,plain,
! [X0] :
( ~ sQ106_spl
| ~ aInfimumOfIn0(sK17_skl,X0,xS)
| ~ aSubsetOf0(X0,xS)
| ~ aSet0(xS)
| ~ sdtlseqdt0(sK4_skl(sK17_skl,X0,xS),sK17_skl)
| ~ aSubsetOf0(X0,xS) ),
inference(resolution,[status(thm)],[f987,f82]) ).
fof(f3416,definition,
! [X0] :
( sQ426_spl
<=> ( ~ aInfimumOfIn0(sK17_skl,X0,xS)
| ~ aSubsetOf0(X0,xS)
| ~ sdtlseqdt0(sK4_skl(sK17_skl,X0,xS),sK17_skl)
| ~ aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ426_spl])],[split_symbol_definition]) ).
fof(f3419,plain,
( ~ sQ106_spl
| ~ sQ21_spl
| sQ426_spl ),
inference(split_clause,[status(thm)],[f3413,f3416,f342,f979]) ).
fof(f3458,plain,
( sQ391_spl
| ~ sdtlseqdt0(sK15_skl(sK0_skl(xT)),sK0_skl(xT))
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sK0_skl(xT)),sK0_skl(xT))
| ~ aElementOf0(sK0_skl(xT),xU) ),
inference(resolution,[status(thm)],[f3212,f187]) ).
fof(f3459,plain,
! [X0] :
( sQ391_spl
| ~ aInfimumOfIn0(sK0_skl(xT),X0,xP)
| ~ aSubsetOf0(X0,xP)
| ~ aSet0(xP) ),
inference(resolution,[status(thm)],[f3212,f81]) ).
fof(f3460,plain,
! [X0] :
( sQ391_spl
| ~ aElementOf0(sK0_skl(xT),X0)
| ~ aSubsetOf0(X0,xP)
| ~ aSet0(xP) ),
inference(resolution,[status(thm)],[f3212,f50]) ).
fof(f3465,plain,
( sQ391_spl
| ~ sQ218_spl
| ~ sQ217_spl
| ~ sQ174_spl ),
inference(split_clause,[status(thm)],[f3458,f1544,f1828,f1831,f3060]) ).
fof(f3466,plain,
( sQ391_spl
| sQ204_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f3459,f544,f1723,f3060]) ).
fof(f3467,plain,
( sQ391_spl
| sQ205_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f3460,f544,f1727,f3060]) ).
fof(f3468,plain,
( sQ198_spl
| ~ sQ276_spl ),
inference(split_clause,[status(thm)],[f2194,f2202,f1685]) ).
fof(f3537,plain,
( sQ231_spl
| ~ sQ304_spl ),
inference(split_clause,[status(thm)],[f2494,f2502,f1921]) ).
fof(f3538,plain,
! [X0] :
( ~ sQ107_spl
| aElementOf0(sK4_skl(sK17_skl,X0,xS),xS)
| ~ aSubsetOf0(X0,xS)
| ~ aSet0(xS)
| ~ aLowerBoundOfIn0(sK17_skl,X0,xS)
| ~ aSubsetOf0(X0,xS) ),
inference(resolution,[status(thm)],[f988,f65]) ).
fof(f3539,definition,
! [X0] :
( sQ435_spl
<=> ( aElementOf0(sK4_skl(sK17_skl,X0,xS),xS)
| ~ aSubsetOf0(X0,xS)
| ~ aLowerBoundOfIn0(sK17_skl,X0,xS)
| ~ aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ435_spl])],[split_symbol_definition]) ).
fof(f3542,plain,
( ~ sQ107_spl
| ~ sQ21_spl
| sQ435_spl ),
inference(split_clause,[status(thm)],[f3538,f3539,f342,f983]) ).
fof(f3545,plain,
! [X0,X1] :
( ~ sQ142_spl
| ~ aElementOf0(sK1_skl(X1,xS),xT)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f1282,f176]) ).
fof(f3546,plain,
! [X0,X1] :
( ~ sQ142_spl
| sdtlpdtrp0(xf,sK1_skl(X1,xS)) != sK1_skl(X1,xS)
| ~ aElementOf0(sK1_skl(X1,xS),xU)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f1282,f535]) ).
fof(f3547,plain,
! [X0,X1,X2] :
( ~ sQ142_spl
| ~ aInfimumOfIn0(sK1_skl(X1,xS),X2,xS)
| ~ aSubsetOf0(X2,xS)
| ~ aSet0(xS)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f1282,f81]) ).
fof(f3548,plain,
! [X0,X1,X2] :
( ~ sQ142_spl
| ~ aElementOf0(sK1_skl(X1,xS),X2)
| ~ aSubsetOf0(X2,xS)
| ~ aSet0(xS)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f1282,f50]) ).
fof(f3553,definition,
! [X0,X1,X2] :
( sQ437_spl
<=> ( ~ aInfimumOfIn0(sK1_skl(X1,xS),X2,xS)
| ~ aSubsetOf0(X2,xS)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ437_spl])],[split_symbol_definition]) ).
fof(f3554,plain,
! [X0,X1,X2] :
( ~ sQ437_spl
| ~ aInfimumOfIn0(sK1_skl(X1,xS),X2,xS)
| ~ aSubsetOf0(X2,xS)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(component_clause,[status(thm)],[f3553]) ).
fof(f3556,plain,
( ~ sQ142_spl
| ~ sQ21_spl
| sQ437_spl ),
inference(split_clause,[status(thm)],[f3547,f3553,f342,f1281]) ).
fof(f3557,definition,
! [X0,X1,X2] :
( sQ438_spl
<=> ( ~ aElementOf0(sK1_skl(X1,xS),X2)
| ~ aSubsetOf0(X2,xS)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ438_spl])],[split_symbol_definition]) ).
fof(f3558,plain,
! [X0,X1,X2] :
( ~ sQ438_spl
| ~ aElementOf0(sK1_skl(X1,xS),X2)
| ~ aSubsetOf0(X2,xS)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(component_clause,[status(thm)],[f3557]) ).
fof(f3560,plain,
( ~ sQ142_spl
| ~ sQ21_spl
| sQ438_spl ),
inference(split_clause,[status(thm)],[f3548,f3557,f342,f1281]) ).
fof(f3586,plain,
! [X0] :
( ~ sQ61_spl
| ~ aElementOf0(X0,xP)
| xp = X0
| ~ sdtlseqdt0(X0,xp)
| ~ sdtlseqdt0(xp,X0) ),
inference(resolution,[status(thm)],[f2330,f181]) ).
fof(f3593,plain,
! [X0] :
( ~ sQ61_spl
| ~ aElementOf0(X0,xP)
| xp = X0
| ~ sdtlseqdt0(X0,xp) ),
inference(forward_subsumption_resolution,[status(thm)],[f3586,f194]) ).
fof(f3695,plain,
! [X0] :
( sQ125_spl
| ~ aInfimumOfIn0(sK17_skl,X0,xT)
| ~ aSubsetOf0(X0,xT)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[f1123,f81]) ).
fof(f3696,plain,
! [X0] :
( sQ125_spl
| ~ aElementOf0(sK17_skl,X0)
| ~ aSubsetOf0(X0,xT)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[f1123,f50]) ).
fof(f3697,plain,
( sQ125_spl
| sQ87_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f3695,f297,f808,f1121]) ).
fof(f3698,plain,
( sQ125_spl
| sQ88_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f3696,f297,f812,f1121]) ).
fof(f3720,definition,
( sQ451_spl
<=> aSupremumOfIn0(sK17_skl,xT,xS) ),
introduced(definition,[new_symbols(definition,[sQ451_spl])],[split_symbol_definition]) ).
fof(f3721,plain,
( ~ sQ451_spl
| aSupremumOfIn0(sK17_skl,xT,xS) ),
inference(component_clause,[status(thm)],[f3720]) ).
fof(f3732,plain,
! [X0] :
( ~ sQ2_spl
| sdtlseqdt0(sdtlpdtrp0(xf,X0),sK17_skl)
| ~ sdtlseqdt0(X0,sK17_skl)
| ~ aElementOf0(sK17_skl,szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| ~ isMonotone0(xf)
| ~ aFunction0(xf) ),
inference(paramodulation,[status(thm)],[f756,f131]) ).
fof(f3733,plain,
! [X0] :
( ~ sQ2_spl
| sdtlseqdt0(sK17_skl,sdtlpdtrp0(xf,X0))
| ~ sdtlseqdt0(sK17_skl,X0)
| ~ aElementOf0(X0,szDzozmdt0(xf))
| ~ aElementOf0(sK17_skl,szDzozmdt0(xf))
| ~ isMonotone0(xf)
| ~ aFunction0(xf) ),
inference(paramodulation,[status(thm)],[f756,f131]) ).
fof(f3734,plain,
( ~ sQ2_spl
| aElementOf0(sK17_skl,szRzazndt0(xf))
| ~ aElementOf0(sK17_skl,szDzozmdt0(xf))
| ~ aFunction0(xf) ),
inference(paramodulation,[status(thm)],[f756,f121]) ).
fof(f3739,definition,
! [X0] :
( sQ453_spl
<=> ( sdtlseqdt0(sdtlpdtrp0(xf,X0),sK17_skl)
| ~ sdtlseqdt0(X0,sK17_skl)
| ~ aElementOf0(X0,szDzozmdt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ453_spl])],[split_symbol_definition]) ).
fof(f3742,definition,
( sQ454_spl
<=> aElementOf0(sK17_skl,szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ454_spl])],[split_symbol_definition]) ).
fof(f3744,plain,
( sQ454_spl
| ~ aElementOf0(sK17_skl,szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f3742]) ).
fof(f3745,plain,
( ~ sQ2_spl
| ~ sQ454_spl
| sQ453_spl
| ~ sQ176_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f3732,f314,f1552,f3739,f3742,f241]) ).
fof(f3746,definition,
! [X0] :
( sQ455_spl
<=> ( sdtlseqdt0(sK17_skl,sdtlpdtrp0(xf,X0))
| ~ sdtlseqdt0(sK17_skl,X0)
| ~ aElementOf0(X0,szDzozmdt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ455_spl])],[split_symbol_definition]) ).
fof(f3749,plain,
( ~ sQ2_spl
| sQ455_spl
| ~ sQ454_spl
| ~ sQ176_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f3733,f314,f1552,f3742,f3746,f241]) ).
fof(f3750,definition,
( sQ456_spl
<=> aElementOf0(sK17_skl,szRzazndt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ456_spl])],[split_symbol_definition]) ).
fof(f3753,plain,
( ~ sQ2_spl
| sQ456_spl
| ~ sQ454_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f3734,f314,f3742,f3750,f241]) ).
fof(f3754,plain,
( sQ454_spl
| ~ aElementOf0(sK17_skl,xU) ),
inference(forward_demodulation,[status(thm)],[f324,f3744]) ).
fof(f3761,plain,
( ~ sQ4_spl
| sQ5_spl
| ~ aElementOf0(xp,xT)
| ~ aSubsetOf0(xT,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f850,f250]) ).
fof(f3764,plain,
( ~ sQ4_spl
| sQ5_spl
| ~ sQ38_spl
| ~ sQ64_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3761,f342,f620,f440,f253,f249]) ).
fof(f3787,plain,
( sQ454_spl
| ~ sQ76_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3754,f719]) ).
fof(f3788,plain,
( sQ454_spl
| ~ sQ76_spl ),
inference(contradiction_clause,[status(thm)],[f3787]) ).
fof(f3824,plain,
( sQ273_spl
| ~ sQ2_spl
| ~ aElement0(sK17_skl) ),
inference(forward_demodulation,[status(thm)],[f756,f2174]) ).
fof(f3825,plain,
( sQ273_spl
| ~ sQ2_spl
| ~ sQ63_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3824,f615]) ).
fof(f3826,plain,
( sQ273_spl
| ~ sQ2_spl
| ~ sQ63_spl ),
inference(contradiction_clause,[status(thm)],[f3825]) ).
fof(f3865,plain,
( sQ423_spl
| aElementOf0(xp,xP)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),xp)
| ~ aElementOf0(xp,xU) ),
inference(resolution,[status(thm)],[f3403,f186]) ).
fof(f3868,plain,
( sQ423_spl
| sQ184_spl
| ~ sQ280_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f3865,f466,f2235,f1610,f3401]) ).
fof(f3877,plain,
( sQ396_spl
| ~ aElementOf0(sK17_skl,xT)
| ~ aElementOf0(sK16_skl(sK17_skl),xP) ),
inference(resolution,[status(thm)],[f3115,f184]) ).
fof(f3883,definition,
( sQ472_spl
<=> aElementOf0(sK16_skl(sK17_skl),xP) ),
introduced(definition,[new_symbols(definition,[sQ472_spl])],[split_symbol_definition]) ).
fof(f3885,plain,
( sQ472_spl
| ~ aElementOf0(sK16_skl(sK17_skl),xP) ),
inference(component_clause,[status(thm)],[f3883]) ).
fof(f3886,plain,
( sQ396_spl
| ~ sQ125_spl
| ~ sQ472_spl ),
inference(split_clause,[status(thm)],[f3877,f3883,f1121,f3113]) ).
fof(f3913,plain,
( ~ sQ451_spl
| aUpperBoundOfIn0(sK17_skl,xT,xS)
| ~ aSubsetOf0(xT,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f3721,f91]) ).
fof(f3919,plain,
( ~ sQ451_spl
| sQ4_spl
| ~ sQ64_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3913,f342,f620,f249,f3720]) ).
fof(f3939,plain,
( sQ472_spl
| sdtlseqdt0(sK17_skl,xp)
| ~ aElementOf0(sK17_skl,xU) ),
inference(resolution,[status(thm)],[f3885,f196]) ).
fof(f3944,plain,
( sQ472_spl
| sQ393_spl
| ~ sQ76_spl ),
inference(split_clause,[status(thm)],[f3939,f718,f3067,f3883]) ).
fof(f3999,plain,
( ~ sQ375_spl
| aElementOf0(sK13_skl(xP),xU)
| ~ aSubsetOf0(xP,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f2977,f73]) ).
fof(f4000,plain,
( ~ sQ375_spl
| sQ376_spl
| ~ sQ41_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f3999,f317,f463,f2980,f2976]) ).
fof(f4042,plain,
( ~ sQ276_spl
| ~ sQ62_spl
| ~ sdtlseqdt0(sK0_skl(xT),sK17_skl)
| ~ sdtlseqdt0(xp,sK0_skl(xT)) ),
inference(resolution,[status(thm)],[f612,f2203]) ).
fof(f4047,plain,
( ~ sQ276_spl
| ~ sQ62_spl
| ~ sQ344_spl
| ~ sQ391_spl ),
inference(split_clause,[status(thm)],[f4042,f3060,f2733,f611,f2202]) ).
fof(f4049,plain,
( ~ sQ3_spl
| sQ344_spl
| ~ aElementOf0(sK0_skl(xT),xT) ),
inference(resolution,[status(thm)],[f2735,f246]) ).
fof(f4050,plain,
( sQ344_spl
| ~ aElementOf0(sK0_skl(xT),xT)
| ~ aElementOf0(sK17_skl,xP) ),
inference(resolution,[status(thm)],[f2735,f184]) ).
fof(f4053,plain,
! [X0] :
( sQ344_spl
| ~ sdtlseqdt0(X0,sK17_skl)
| ~ sdtlseqdt0(sK0_skl(xT),X0)
| ~ aElement0(sK17_skl)
| ~ aElement0(X0)
| ~ aElement0(sK0_skl(xT)) ),
inference(resolution,[status(thm)],[f2735,f60]) ).
fof(f4056,plain,
( ~ sQ3_spl
| sQ344_spl
| ~ sQ275_spl ),
inference(split_clause,[status(thm)],[f4049,f2197,f2733,f245]) ).
fof(f4057,plain,
( sQ344_spl
| ~ sQ275_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f4050,f659,f2197,f2733]) ).
fof(f4058,definition,
! [X0] :
( sQ493_spl
<=> ( ~ sdtlseqdt0(X0,sK17_skl)
| ~ sdtlseqdt0(sK0_skl(xT),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ493_spl])],[split_symbol_definition]) ).
fof(f4061,plain,
( sQ344_spl
| ~ sQ63_spl
| sQ493_spl
| ~ sQ276_spl ),
inference(split_clause,[status(thm)],[f4053,f2202,f4058,f614,f2733]) ).
fof(f4063,plain,
( sQ174_spl
| ~ sQ180_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1546,f1573]) ).
fof(f4064,plain,
( sQ174_spl
| ~ sQ180_spl ),
inference(contradiction_clause,[status(thm)],[f4063]) ).
fof(f4065,plain,
( ~ sQ13_spl
| sQ411_spl
| ~ sQ423_spl ),
inference(split_clause,[status(thm)],[f3385,f3401,f3280,f286]) ).
fof(f4091,plain,
( ~ sQ9_spl
| aElementOf0(xp,xP)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),xp)
| ~ aElementOf0(xp,xU) ),
inference(resolution,[status(thm)],[f634,f188]) ).
fof(f4093,plain,
( ~ sQ9_spl
| sQ184_spl
| ~ sQ280_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f4091,f466,f2235,f1610,f268]) ).
fof(f4097,plain,
( ~ sQ32_spl
| sdtlpdtrp0(xf,xp) = xp ),
inference(resolution,[status(thm)],[f409,f169]) ).
fof(f4120,plain,
( sQ285_spl
| ~ sQ8_spl
| ~ aElement0(xp) ),
inference(backward_demodulation,[status(thm)],[f265,f2255]) ).
fof(f4136,plain,
( sQ285_spl
| ~ sQ8_spl
| ~ sQ61_spl ),
inference(split_clause,[status(thm)],[f4120,f608,f264,f2253]) ).
fof(f4143,definition,
! [X0] :
( sQ495_spl
<=> ( sdtlseqdt0(sdtlpdtrp0(xf,X0),xp)
| ~ sdtlseqdt0(X0,xp)
| ~ aElementOf0(X0,szDzozmdt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ495_spl])],[split_symbol_definition]) ).
fof(f4147,definition,
! [X0] :
( sQ496_spl
<=> ( sdtlseqdt0(xp,sdtlpdtrp0(xf,X0))
| ~ sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,szDzozmdt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ496_spl])],[split_symbol_definition]) ).
fof(f4151,definition,
( sQ497_spl
<=> aElementOf0(xp,szRzazndt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ497_spl])],[split_symbol_definition]) ).
fof(f4311,plain,
( ~ sQ272_spl
| ~ sQ2_spl
| aElementOf0(sK17_skl,xT) ),
inference(forward_demodulation,[status(thm)],[f756,f2169]) ).
fof(f4312,plain,
( ~ sQ272_spl
| ~ sQ2_spl
| sQ125_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4311,f1123]) ).
fof(f4313,plain,
( ~ sQ272_spl
| ~ sQ2_spl
| sQ125_spl ),
inference(contradiction_clause,[status(thm)],[f4312]) ).
fof(f4337,plain,
! [X0,X1] :
( ~ sQ159_spl
| ~ aElementOf0(sK1_skl(X1,xT),xT)
| ~ aSet0(X1)
| ~ aSet0(xT)
| ~ aInfimumOfIn0(X0,X1,xT)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f1457,f52]) ).
fof(f4338,definition,
! [X0,X1] :
( sQ514_spl
<=> ( ~ aElementOf0(sK1_skl(X1,xT),xT)
| ~ aSet0(X1)
| ~ aInfimumOfIn0(X0,X1,xT)
| sdtlpdtrp0(xf,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ514_spl])],[split_symbol_definition]) ).
fof(f4341,plain,
( ~ sQ159_spl
| ~ sQ15_spl
| sQ514_spl ),
inference(split_clause,[status(thm)],[f4337,f4338,f297,f1456]) ).
fof(f4381,plain,
! [X0] :
( ~ sQ164_spl
| ~ aSubsetOf0(xP,xU)
| ~ aCompleteLattice0(xU)
| X0 = sK6_skl(xP,xU)
| ~ aInfimumOfIn0(X0,xP,xU) ),
inference(resolution,[status(thm)],[f1488,f104]) ).
fof(f4382,plain,
! [X0] :
( ~ sQ164_spl
| sP0_prd(xP)
| X0 = sK11_skl(xP)
| ~ aInfimumOfIn0(X0,xP,xU) ),
inference(resolution,[status(thm)],[f1488,f149]) ).
fof(f4383,plain,
! [X0] :
( ~ sQ164_spl
| X0 = xp
| ~ aInfimumOfIn0(X0,xP,xU) ),
inference(resolution,[status(thm)],[f1488,f199]) ).
fof(f4384,plain,
! [X0,X1] :
( ~ sQ164_spl
| ~ sdtlseqdt0(sK4_skl(X1,xP,xU),X1)
| ~ aLowerBoundOfIn0(X1,xP,xU)
| ~ aSubsetOf0(xP,xU)
| ~ aSet0(xU)
| X0 = X1
| ~ aInfimumOfIn0(X0,xP,xU) ),
inference(resolution,[status(thm)],[f1488,f764]) ).
fof(f4385,plain,
! [X0,X1] :
( ~ sQ164_spl
| aLowerBoundOfIn0(sK4_skl(X1,xP,xU),xP,xU)
| ~ aLowerBoundOfIn0(X1,xP,xU)
| ~ aSubsetOf0(xP,xU)
| ~ aSet0(xU)
| X0 = X1
| ~ aInfimumOfIn0(X0,xP,xU) ),
inference(resolution,[status(thm)],[f1488,f763]) ).
fof(f4386,definition,
! [X0] :
( sQ517_spl
<=> ( X0 = sK6_skl(xP,xU)
| ~ aInfimumOfIn0(X0,xP,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ517_spl])],[split_symbol_definition]) ).
fof(f4389,plain,
( ~ sQ164_spl
| ~ sQ41_spl
| ~ sQ321_spl
| sQ517_spl ),
inference(split_clause,[status(thm)],[f4381,f4386,f2603,f463,f1487]) ).
fof(f4390,definition,
! [X0] :
( sQ518_spl
<=> ( X0 = sK11_skl(xP)
| ~ aInfimumOfIn0(X0,xP,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ518_spl])],[split_symbol_definition]) ).
fof(f4393,plain,
( ~ sQ164_spl
| sQ323_spl
| sQ518_spl ),
inference(split_clause,[status(thm)],[f4382,f4390,f2610,f1487]) ).
fof(f4394,plain,
( ~ sQ164_spl
| sQ297_spl ),
inference(split_clause,[status(thm)],[f4383,f2442,f1487]) ).
fof(f4395,definition,
! [X0,X1] :
( sQ519_spl
<=> ( ~ sdtlseqdt0(sK4_skl(X1,xP,xU),X1)
| ~ aLowerBoundOfIn0(X1,xP,xU)
| X0 = X1
| ~ aInfimumOfIn0(X0,xP,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ519_spl])],[split_symbol_definition]) ).
fof(f4398,plain,
( ~ sQ164_spl
| ~ sQ41_spl
| ~ sQ19_spl
| sQ519_spl ),
inference(split_clause,[status(thm)],[f4384,f4395,f317,f463,f1487]) ).
fof(f4399,definition,
! [X0,X1] :
( sQ520_spl
<=> ( aLowerBoundOfIn0(sK4_skl(X1,xP,xU),xP,xU)
| ~ aLowerBoundOfIn0(X1,xP,xU)
| X0 = X1
| ~ aInfimumOfIn0(X0,xP,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ520_spl])],[split_symbol_definition]) ).
fof(f4402,plain,
( ~ sQ164_spl
| ~ sQ41_spl
| ~ sQ19_spl
| sQ520_spl ),
inference(split_clause,[status(thm)],[f4385,f4399,f317,f463,f1487]) ).
fof(f4405,plain,
! [X0,X1] :
( ~ sQ165_spl
| X1 = X0
| ~ aSupremumOfIn0(X1,xP,xU)
| ~ aSubsetOf0(xP,xU)
| ~ aSet0(xU)
| ~ sdtlseqdt0(X0,sK5_skl(X0,xP,xU))
| ~ aUpperBoundOfIn0(X0,xP,xU) ),
inference(resolution,[status(thm)],[f1492,f96]) ).
fof(f4406,plain,
! [X0] :
( ~ sQ165_spl
| aUpperBoundOfIn0(X0,xP,xU)
| ~ aSubsetOf0(xP,xU)
| ~ aSet0(xU)
| ~ sdtlseqdt0(X0,sK5_skl(X0,xP,xU))
| ~ aUpperBoundOfIn0(X0,xP,xU) ),
inference(resolution,[status(thm)],[f1492,f91]) ).
fof(f4407,plain,
! [X0] :
( ~ sQ165_spl
| aElementOf0(X0,xU)
| ~ aSubsetOf0(xP,xU)
| ~ aSet0(xU)
| ~ sdtlseqdt0(X0,sK5_skl(X0,xP,xU))
| ~ aUpperBoundOfIn0(X0,xP,xU) ),
inference(resolution,[status(thm)],[f1492,f90]) ).
fof(f4418,definition,
! [X0,X1] :
( sQ524_spl
<=> ( X1 = X0
| ~ aSupremumOfIn0(X1,xP,xU)
| ~ sdtlseqdt0(X0,sK5_skl(X0,xP,xU))
| ~ aUpperBoundOfIn0(X0,xP,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ524_spl])],[split_symbol_definition]) ).
fof(f4421,plain,
( ~ sQ165_spl
| ~ sQ41_spl
| ~ sQ19_spl
| sQ524_spl ),
inference(split_clause,[status(thm)],[f4405,f4418,f317,f463,f1491]) ).
fof(f4422,definition,
! [X0] :
( sQ525_spl
<=> ( aUpperBoundOfIn0(X0,xP,xU)
| ~ sdtlseqdt0(X0,sK5_skl(X0,xP,xU))
| ~ aUpperBoundOfIn0(X0,xP,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ525_spl])],[split_symbol_definition]) ).
fof(f4425,plain,
( ~ sQ165_spl
| ~ sQ41_spl
| ~ sQ19_spl
| sQ525_spl ),
inference(split_clause,[status(thm)],[f4406,f4422,f317,f463,f1491]) ).
fof(f4426,definition,
! [X0] :
( sQ526_spl
<=> ( aElementOf0(X0,xU)
| ~ sdtlseqdt0(X0,sK5_skl(X0,xP,xU))
| ~ aUpperBoundOfIn0(X0,xP,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ526_spl])],[split_symbol_definition]) ).
fof(f4429,plain,
( ~ sQ165_spl
| ~ sQ41_spl
| ~ sQ19_spl
| sQ526_spl ),
inference(split_clause,[status(thm)],[f4407,f4426,f317,f463,f1491]) ).
fof(f4474,plain,
! [X0] :
( ~ sQ74_spl
| ~ sdtlseqdt0(sK4_skl(X0,xT,xS),X0)
| ~ aLowerBoundOfIn0(X0,xT,xS)
| ~ aSubsetOf0(xT,xS)
| ~ aSet0(xS)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f1592,f764]) ).
fof(f4475,plain,
! [X0] :
( ~ sQ74_spl
| aLowerBoundOfIn0(sK4_skl(X0,xT,xS),xT,xS)
| ~ aLowerBoundOfIn0(X0,xT,xS)
| ~ aSubsetOf0(xT,xS)
| ~ aSet0(xS)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f1592,f763]) ).
fof(f4480,definition,
! [X0] :
( sQ533_spl
<=> ( ~ sdtlseqdt0(sK4_skl(X0,xT,xS),X0)
| ~ aLowerBoundOfIn0(X0,xT,xS)
| sdtlpdtrp0(xf,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ533_spl])],[split_symbol_definition]) ).
fof(f4483,plain,
( ~ sQ74_spl
| ~ sQ64_spl
| ~ sQ21_spl
| sQ533_spl ),
inference(split_clause,[status(thm)],[f4474,f4480,f342,f620,f705]) ).
fof(f4484,definition,
! [X0] :
( sQ534_spl
<=> ( aLowerBoundOfIn0(sK4_skl(X0,xT,xS),xT,xS)
| ~ aLowerBoundOfIn0(X0,xT,xS)
| sdtlpdtrp0(xf,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ534_spl])],[split_symbol_definition]) ).
fof(f4487,plain,
( ~ sQ74_spl
| ~ sQ64_spl
| ~ sQ21_spl
| sQ534_spl ),
inference(split_clause,[status(thm)],[f4475,f4484,f342,f620,f705]) ).
fof(f4489,plain,
! [X0,X1] :
( ~ sQ181_spl
| ~ sdtlseqdt0(sK4_skl(X0,X1,xS),X0)
| ~ aLowerBoundOfIn0(X0,X1,xS)
| ~ aSubsetOf0(X1,xS)
| ~ aSet0(xS)
| ~ aElementOf0(sK1_skl(X1,xS),xS)
| ~ aSet0(X1)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f1595,f764]) ).
fof(f4490,plain,
! [X0,X1] :
( ~ sQ181_spl
| aLowerBoundOfIn0(sK4_skl(X0,X1,xS),X1,xS)
| ~ aLowerBoundOfIn0(X0,X1,xS)
| ~ aSubsetOf0(X1,xS)
| ~ aSet0(xS)
| ~ aElementOf0(sK1_skl(X1,xS),xS)
| ~ aSet0(X1)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f1595,f763]) ).
fof(f4495,definition,
! [X0,X1] :
( sQ536_spl
<=> ( ~ sdtlseqdt0(sK4_skl(X0,X1,xS),X0)
| ~ aLowerBoundOfIn0(X0,X1,xS)
| ~ aSubsetOf0(X1,xS)
| ~ aElementOf0(sK1_skl(X1,xS),xS)
| ~ aSet0(X1)
| sdtlpdtrp0(xf,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ536_spl])],[split_symbol_definition]) ).
fof(f4498,plain,
( ~ sQ181_spl
| ~ sQ21_spl
| sQ536_spl ),
inference(split_clause,[status(thm)],[f4489,f4495,f342,f1594]) ).
fof(f4499,definition,
! [X0,X1] :
( sQ537_spl
<=> ( aLowerBoundOfIn0(sK4_skl(X0,X1,xS),X1,xS)
| ~ aLowerBoundOfIn0(X0,X1,xS)
| ~ aSubsetOf0(X1,xS)
| ~ aElementOf0(sK1_skl(X1,xS),xS)
| ~ aSet0(X1)
| sdtlpdtrp0(xf,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ537_spl])],[split_symbol_definition]) ).
fof(f4502,plain,
( ~ sQ181_spl
| ~ sQ21_spl
| sQ537_spl ),
inference(split_clause,[status(thm)],[f4490,f4499,f342,f1594]) ).
fof(f4528,plain,
( sQ221_spl
| ~ sQ2_spl
| ~ sdtlseqdt0(sK17_skl,sK17_skl) ),
inference(forward_demodulation,[status(thm)],[f756,f1851]) ).
fof(f4529,plain,
( sQ221_spl
| ~ sQ2_spl
| ~ sQ85_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4528,f781]) ).
fof(f4530,plain,
( sQ221_spl
| ~ sQ2_spl
| ~ sQ85_spl ),
inference(contradiction_clause,[status(thm)],[f4529]) ).
fof(f4549,plain,
( ~ sQ153_spl
| ~ sQ394_spl
| aFixedPointOf0(xp,xf) ),
inference(backward_demodulation,[status(thm)],[f3071,f1373]) ).
fof(f4561,plain,
( ~ sQ153_spl
| ~ sQ394_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f4549,f268,f3070,f1372]) ).
fof(f4580,plain,
! [X0] :
( sQ38_spl
| ~ aInfimumOfIn0(xp,X0,xT)
| ~ aSubsetOf0(X0,xT)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[f442,f81]) ).
fof(f4581,plain,
! [X0] :
( sQ38_spl
| ~ aElementOf0(xp,X0)
| ~ aSubsetOf0(X0,xT)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[f442,f50]) ).
fof(f4582,plain,
( sQ38_spl
| sQ70_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f4580,f297,f667,f440]) ).
fof(f4583,plain,
( sQ38_spl
| sQ68_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f4581,f297,f648,f440]) ).
fof(f4644,plain,
( ~ sQ61_spl
| ~ sQ238_spl
| sK15_skl(sK17_skl) = xp
| ~ sdtlseqdt0(xp,sK15_skl(sK17_skl))
| ~ sdtlseqdt0(sK15_skl(sK17_skl),xp) ),
inference(resolution,[status(thm)],[f1966,f919]) ).
fof(f4647,definition,
( sQ543_spl
<=> sdtlseqdt0(sK15_skl(sK17_skl),xp) ),
introduced(definition,[new_symbols(definition,[sQ543_spl])],[split_symbol_definition]) ).
fof(f4649,plain,
( sQ543_spl
| ~ sdtlseqdt0(sK15_skl(sK17_skl),xp) ),
inference(component_clause,[status(thm)],[f4647]) ).
fof(f4650,definition,
( sQ544_spl
<=> sdtlseqdt0(xp,sK15_skl(sK17_skl)) ),
introduced(definition,[new_symbols(definition,[sQ544_spl])],[split_symbol_definition]) ).
fof(f4652,plain,
( sQ544_spl
| ~ sdtlseqdt0(xp,sK15_skl(sK17_skl)) ),
inference(component_clause,[status(thm)],[f4650]) ).
fof(f4653,definition,
( sQ545_spl
<=> sK15_skl(sK17_skl) = xp ),
introduced(definition,[new_symbols(definition,[sQ545_spl])],[split_symbol_definition]) ).
fof(f4654,plain,
( ~ sQ545_spl
| sK15_skl(sK17_skl) = xp ),
inference(component_clause,[status(thm)],[f4653]) ).
fof(f4656,plain,
( ~ sQ61_spl
| ~ sQ238_spl
| sQ545_spl
| ~ sQ544_spl
| ~ sQ543_spl ),
inference(split_clause,[status(thm)],[f4644,f4647,f4650,f4653,f1965,f608]) ).
fof(f4658,plain,
( ~ sQ545_spl
| aElementOf0(sK17_skl,xP)
| aElementOf0(xp,xT)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sK17_skl),sK17_skl)
| ~ aElementOf0(sK17_skl,xU) ),
inference(paramodulation,[status(thm)],[f4654,f186]) ).
fof(f4659,plain,
( ~ sQ545_spl
| sQ69_spl
| sQ38_spl
| ~ sQ221_spl
| ~ sQ76_spl ),
inference(split_clause,[status(thm)],[f4658,f718,f1849,f440,f659,f4653]) ).
fof(f4660,plain,
( ~ sQ30_spl
| ~ sQ38_spl ),
inference(split_clause,[status(thm)],[f400,f440,f395]) ).
fof(f4669,plain,
! [X0] :
( ~ sQ17_spl
| aElementOf0(X0,xP)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X0),X0)
| ~ aElementOf0(X0,xU) ),
inference(backward_subsumption_resolution,[status(thm)],[f186,f306]) ).
fof(f4726,plain,
( sQ5_spl
| ~ sQ17_spl
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sK17_skl),sK17_skl)
| ~ aElementOf0(sK17_skl,xU) ),
inference(resolution,[status(thm)],[f4669,f2179]) ).
fof(f4730,plain,
( sQ5_spl
| ~ sQ17_spl
| ~ sQ221_spl
| ~ sQ76_spl ),
inference(split_clause,[status(thm)],[f4726,f718,f1849,f305,f253]) ).
fof(f4770,plain,
( ~ sQ9_spl
| sdtlpdtrp0(xf,xp) = xp ),
inference(resolution,[status(thm)],[f269,f451]) ).
fof(f4774,plain,
( sQ5_spl
| ~ aUpperBoundOfIn0(sK17_skl,xT,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sK17_skl),sK17_skl)
| ~ aElementOf0(sK17_skl,xU) ),
inference(resolution,[status(thm)],[f188,f2179]) ).
fof(f4778,definition,
( sQ548_spl
<=> aUpperBoundOfIn0(sK17_skl,xT,xU) ),
introduced(definition,[new_symbols(definition,[sQ548_spl])],[split_symbol_definition]) ).
fof(f4781,plain,
( sQ5_spl
| ~ sQ548_spl
| ~ sQ221_spl
| ~ sQ76_spl ),
inference(split_clause,[status(thm)],[f4774,f718,f1849,f4778,f253]) ).
fof(f4819,plain,
! [X0] :
( ~ sQ8_spl
| sdtlseqdt0(X0,xp)
| ~ aElementOf0(X0,xT) ),
inference(forward_demodulation,[status(thm)],[f265,f203]) ).
fof(f4826,plain,
( sQ544_spl
| ~ aElementOf0(sK15_skl(sK17_skl),xP) ),
inference(resolution,[status(thm)],[f4652,f194]) ).
fof(f4829,plain,
! [X0] :
( sQ544_spl
| ~ sdtlseqdt0(X0,sK15_skl(sK17_skl))
| ~ sdtlseqdt0(xp,X0)
| ~ aElement0(sK15_skl(sK17_skl))
| ~ aElement0(X0)
| ~ aElement0(xp) ),
inference(resolution,[status(thm)],[f4652,f60]) ).
fof(f4832,definition,
! [X0] :
( sQ551_spl
<=> ( ~ sdtlseqdt0(X0,sK15_skl(sK17_skl))
| ~ sdtlseqdt0(xp,X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ551_spl])],[split_symbol_definition]) ).
fof(f4835,plain,
( sQ544_spl
| ~ sQ238_spl
| sQ551_spl
| ~ sQ61_spl ),
inference(split_clause,[status(thm)],[f4829,f608,f4832,f1965,f4650]) ).
fof(f4836,plain,
( ~ sQ13_spl
| sQ543_spl
| ~ aElementOf0(sK15_skl(sK17_skl),xT) ),
inference(resolution,[status(thm)],[f4649,f287]) ).
fof(f4844,plain,
( ~ sQ13_spl
| sQ543_spl
| ~ sQ237_spl ),
inference(split_clause,[status(thm)],[f4836,f1961,f4647,f286]) ).
fof(f4856,plain,
( ~ sQ8_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f4819,f286,f264]) ).
fof(f4859,plain,
( ~ sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f4770,f264,f268]) ).
fof(f4874,plain,
! [X0] :
( ~ sQ32_spl
| sdtlseqdt0(sdtlpdtrp0(xf,X0),xp)
| ~ sdtlseqdt0(X0,xp)
| ~ aElementOf0(xp,xU)
| ~ aElementOf0(X0,xU) ),
inference(paramodulation,[status(thm)],[f4097,f456]) ).
fof(f4875,plain,
! [X0] :
( ~ sQ32_spl
| sdtlseqdt0(xp,sdtlpdtrp0(xf,X0))
| ~ sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xU)
| ~ aElementOf0(xp,xU) ),
inference(paramodulation,[status(thm)],[f4097,f456]) ).
fof(f4876,plain,
! [X0] :
( ~ sQ32_spl
| sdtlseqdt0(sdtlpdtrp0(xf,X0),xp)
| ~ sdtlseqdt0(X0,xp)
| ~ aElementOf0(xp,szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| ~ isMonotone0(xf)
| ~ aFunction0(xf) ),
inference(paramodulation,[status(thm)],[f4097,f131]) ).
fof(f4877,plain,
! [X0] :
( ~ sQ32_spl
| sdtlseqdt0(xp,sdtlpdtrp0(xf,X0))
| ~ sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,szDzozmdt0(xf))
| ~ aElementOf0(xp,szDzozmdt0(xf))
| ~ isMonotone0(xf)
| ~ aFunction0(xf) ),
inference(paramodulation,[status(thm)],[f4097,f131]) ).
fof(f4878,plain,
( ~ sQ32_spl
| aElementOf0(xp,szRzazndt0(xf))
| ~ aElementOf0(xp,szDzozmdt0(xf))
| ~ aFunction0(xf) ),
inference(paramodulation,[status(thm)],[f4097,f121]) ).
fof(f4883,plain,
( ~ sQ32_spl
| ~ sQ42_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f4874,f637,f466,f408]) ).
fof(f4884,plain,
( ~ sQ32_spl
| sQ67_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f4875,f466,f641,f408]) ).
fof(f4885,plain,
( ~ sQ32_spl
| ~ sQ7_spl
| sQ495_spl
| ~ sQ176_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f4876,f314,f1552,f4143,f261,f408]) ).
fof(f4886,plain,
( ~ sQ32_spl
| sQ496_spl
| ~ sQ7_spl
| ~ sQ176_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f4877,f314,f1552,f261,f4147,f408]) ).
fof(f4887,plain,
( ~ sQ32_spl
| sQ497_spl
| ~ sQ7_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f4878,f314,f261,f4151,f408]) ).
fof(f4914,plain,
( sQ391_spl
| ~ aUpperBoundOfIn0(sK0_skl(xT),xT,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sK0_skl(xT)),sK0_skl(xT))
| ~ aElementOf0(sK0_skl(xT),xU) ),
inference(resolution,[status(thm)],[f3212,f188]) ).
fof(f4918,definition,
( sQ555_spl
<=> aUpperBoundOfIn0(sK0_skl(xT),xT,xU) ),
introduced(definition,[new_symbols(definition,[sQ555_spl])],[split_symbol_definition]) ).
fof(f4921,plain,
( sQ391_spl
| ~ sQ555_spl
| ~ sQ217_spl
| ~ sQ174_spl ),
inference(split_clause,[status(thm)],[f4914,f1544,f1828,f4918,f3060]) ).
fof(f4926,plain,
( sQ222_spl
| ~ sQ3_spl
| ~ aElementOf0(sK15_skl(sK17_skl),xT) ),
inference(resolution,[status(thm)],[f246,f1854]) ).
fof(f4928,plain,
( sQ222_spl
| ~ sQ3_spl
| ~ sQ237_spl ),
inference(split_clause,[status(thm)],[f4926,f1961,f245,f1852]) ).
fof(f4977,plain,
! [X0] :
( sQ544_spl
| ~ aInfimumOfIn0(sK15_skl(sK17_skl),X0,xP)
| ~ aSubsetOf0(X0,xP)
| ~ aSet0(xP) ),
inference(resolution,[status(thm)],[f4826,f81]) ).
fof(f4978,plain,
! [X0] :
( sQ544_spl
| ~ aElementOf0(sK15_skl(sK17_skl),X0)
| ~ aSubsetOf0(X0,xP)
| ~ aSet0(xP) ),
inference(resolution,[status(thm)],[f4826,f50]) ).
fof(f4990,definition,
! [X0] :
( sQ562_spl
<=> ( ~ aInfimumOfIn0(sK15_skl(sK17_skl),X0,xP)
| ~ aSubsetOf0(X0,xP) ) ),
introduced(definition,[new_symbols(definition,[sQ562_spl])],[split_symbol_definition]) ).
fof(f4993,plain,
( sQ544_spl
| sQ562_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f4977,f544,f4990,f4650]) ).
fof(f4994,definition,
! [X0] :
( sQ563_spl
<=> ( ~ aElementOf0(sK15_skl(sK17_skl),X0)
| ~ aSubsetOf0(X0,xP) ) ),
introduced(definition,[new_symbols(definition,[sQ563_spl])],[split_symbol_definition]) ).
fof(f4997,plain,
( sQ544_spl
| sQ563_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f4978,f544,f4994,f4650]) ).
fof(f5166,plain,
( ~ sQ88_spl
| ~ sQ313_spl
| ~ sQ125_spl ),
inference(split_clause,[status(thm)],[f2558,f1121,f2550,f812]) ).
fof(f5364,plain,
! [X0,X1] :
( ~ sQ182_spl
| ~ aElementOf0(sK1_skl(X1,xT),xT)
| ~ aSet0(X1)
| ~ aSet0(xT)
| sdtlpdtrp0(xf,sK5_skl(X0,X1,xT)) = sK5_skl(X0,X1,xT)
| ~ aUpperBoundOfIn0(X0,X1,xT)
| aSupremumOfIn0(X0,X1,xT) ),
inference(resolution,[status(thm)],[f1601,f52]) ).
fof(f5365,definition,
! [X0,X1] :
( sQ595_spl
<=> ( ~ aElementOf0(sK1_skl(X1,xT),xT)
| ~ aSet0(X1)
| sdtlpdtrp0(xf,sK5_skl(X0,X1,xT)) = sK5_skl(X0,X1,xT)
| ~ aUpperBoundOfIn0(X0,X1,xT)
| aSupremumOfIn0(X0,X1,xT) ) ),
introduced(definition,[new_symbols(definition,[sQ595_spl])],[split_symbol_definition]) ).
fof(f5368,plain,
( ~ sQ182_spl
| ~ sQ15_spl
| sQ595_spl ),
inference(split_clause,[status(thm)],[f5364,f5365,f297,f1600]) ).
fof(f5409,plain,
! [X0,X1] :
( ~ sQ183_spl
| ~ aElementOf0(sK1_skl(X1,xS),xS)
| ~ aSet0(X1)
| ~ aSet0(xS)
| sdtlpdtrp0(xf,sK5_skl(X0,X1,xS)) = sK5_skl(X0,X1,xS)
| ~ aUpperBoundOfIn0(X0,X1,xS)
| aSupremumOfIn0(X0,X1,xS) ),
inference(resolution,[status(thm)],[f1605,f52]) ).
fof(f5410,definition,
! [X0,X1] :
( sQ600_spl
<=> ( ~ aElementOf0(sK1_skl(X1,xS),xS)
| ~ aSet0(X1)
| sdtlpdtrp0(xf,sK5_skl(X0,X1,xS)) = sK5_skl(X0,X1,xS)
| ~ aUpperBoundOfIn0(X0,X1,xS)
| aSupremumOfIn0(X0,X1,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ600_spl])],[split_symbol_definition]) ).
fof(f5413,plain,
( ~ sQ183_spl
| ~ sQ21_spl
| sQ600_spl ),
inference(split_clause,[status(thm)],[f5409,f5410,f342,f1604]) ).
fof(f5523,plain,
! [X0,X1] :
( ~ sQ209_spl
| X1 = sK5_skl(X0,xT,xS)
| ~ aSupremumOfIn0(X1,xT,xS)
| ~ aSubsetOf0(xT,xS)
| ~ aSet0(xS)
| ~ aUpperBoundOfIn0(X0,xT,xS)
| aSupremumOfIn0(X0,xT,xS)
| ~ sdtlseqdt0(sK5_skl(X0,xT,xS),sK5_skl(sK5_skl(X0,xT,xS),xT,xS)) ),
inference(resolution,[status(thm)],[f1778,f96]) ).
fof(f5524,plain,
! [X0] :
( ~ sQ209_spl
| aUpperBoundOfIn0(sK5_skl(X0,xT,xS),xT,xS)
| ~ aSubsetOf0(xT,xS)
| ~ aSet0(xS)
| ~ aUpperBoundOfIn0(X0,xT,xS)
| aSupremumOfIn0(X0,xT,xS)
| ~ sdtlseqdt0(sK5_skl(X0,xT,xS),sK5_skl(sK5_skl(X0,xT,xS),xT,xS)) ),
inference(resolution,[status(thm)],[f1778,f91]) ).
fof(f5525,plain,
! [X0] :
( ~ sQ209_spl
| aElementOf0(sK5_skl(X0,xT,xS),xS)
| ~ aSubsetOf0(xT,xS)
| ~ aSet0(xS)
| ~ aUpperBoundOfIn0(X0,xT,xS)
| aSupremumOfIn0(X0,xT,xS)
| ~ sdtlseqdt0(sK5_skl(X0,xT,xS),sK5_skl(sK5_skl(X0,xT,xS),xT,xS)) ),
inference(resolution,[status(thm)],[f1778,f90]) ).
fof(f5526,definition,
! [X0,X1] :
( sQ612_spl
<=> ( X1 = sK5_skl(X0,xT,xS)
| ~ aSupremumOfIn0(X1,xT,xS)
| ~ aUpperBoundOfIn0(X0,xT,xS)
| aSupremumOfIn0(X0,xT,xS)
| ~ sdtlseqdt0(sK5_skl(X0,xT,xS),sK5_skl(sK5_skl(X0,xT,xS),xT,xS)) ) ),
introduced(definition,[new_symbols(definition,[sQ612_spl])],[split_symbol_definition]) ).
fof(f5529,plain,
( ~ sQ209_spl
| ~ sQ64_spl
| ~ sQ21_spl
| sQ612_spl ),
inference(split_clause,[status(thm)],[f5523,f5526,f342,f620,f1777]) ).
fof(f5530,definition,
! [X0] :
( sQ613_spl
<=> ( aUpperBoundOfIn0(sK5_skl(X0,xT,xS),xT,xS)
| ~ aUpperBoundOfIn0(X0,xT,xS)
| aSupremumOfIn0(X0,xT,xS)
| ~ sdtlseqdt0(sK5_skl(X0,xT,xS),sK5_skl(sK5_skl(X0,xT,xS),xT,xS)) ) ),
introduced(definition,[new_symbols(definition,[sQ613_spl])],[split_symbol_definition]) ).
fof(f5533,plain,
( ~ sQ209_spl
| ~ sQ64_spl
| ~ sQ21_spl
| sQ613_spl ),
inference(split_clause,[status(thm)],[f5524,f5530,f342,f620,f1777]) ).
fof(f5534,definition,
! [X0] :
( sQ614_spl
<=> ( aElementOf0(sK5_skl(X0,xT,xS),xS)
| ~ aUpperBoundOfIn0(X0,xT,xS)
| aSupremumOfIn0(X0,xT,xS)
| ~ sdtlseqdt0(sK5_skl(X0,xT,xS),sK5_skl(sK5_skl(X0,xT,xS),xT,xS)) ) ),
introduced(definition,[new_symbols(definition,[sQ614_spl])],[split_symbol_definition]) ).
fof(f5537,plain,
( ~ sQ209_spl
| ~ sQ64_spl
| ~ sQ21_spl
| sQ614_spl ),
inference(split_clause,[status(thm)],[f5525,f5534,f342,f620,f1777]) ).
fof(f5540,plain,
! [X0,X1] :
( ~ sQ210_spl
| X1 = X0
| ~ aSupremumOfIn0(X1,xT,xS)
| ~ aSubsetOf0(xT,xS)
| ~ aSet0(xS)
| ~ sdtlseqdt0(sK3_skl(X0,xT,xS),X0)
| ~ aElementOf0(X0,xS)
| ~ sdtlseqdt0(X0,sK5_skl(X0,xT,xS)) ),
inference(resolution,[status(thm)],[f1782,f96]) ).
fof(f5541,plain,
! [X0] :
( ~ sQ210_spl
| aUpperBoundOfIn0(X0,xT,xS)
| ~ aSubsetOf0(xT,xS)
| ~ aSet0(xS)
| ~ sdtlseqdt0(sK3_skl(X0,xT,xS),X0)
| ~ aElementOf0(X0,xS)
| ~ sdtlseqdt0(X0,sK5_skl(X0,xT,xS)) ),
inference(resolution,[status(thm)],[f1782,f91]) ).
fof(f5542,plain,
! [X0] :
( ~ sQ210_spl
| aElementOf0(X0,xS)
| ~ aSubsetOf0(xT,xS)
| ~ aSet0(xS)
| ~ sdtlseqdt0(sK3_skl(X0,xT,xS),X0)
| ~ aElementOf0(X0,xS)
| ~ sdtlseqdt0(X0,sK5_skl(X0,xT,xS)) ),
inference(resolution,[status(thm)],[f1782,f90]) ).
fof(f5545,definition,
! [X0,X1] :
( sQ615_spl
<=> ( X1 = X0
| ~ aSupremumOfIn0(X1,xT,xS)
| ~ sdtlseqdt0(sK3_skl(X0,xT,xS),X0)
| ~ aElementOf0(X0,xS)
| ~ sdtlseqdt0(X0,sK5_skl(X0,xT,xS)) ) ),
introduced(definition,[new_symbols(definition,[sQ615_spl])],[split_symbol_definition]) ).
fof(f5548,plain,
( ~ sQ210_spl
| ~ sQ64_spl
| ~ sQ21_spl
| sQ615_spl ),
inference(split_clause,[status(thm)],[f5540,f5545,f342,f620,f1781]) ).
fof(f5549,definition,
! [X0] :
( sQ616_spl
<=> ( aUpperBoundOfIn0(X0,xT,xS)
| ~ sdtlseqdt0(sK3_skl(X0,xT,xS),X0)
| ~ aElementOf0(X0,xS)
| ~ sdtlseqdt0(X0,sK5_skl(X0,xT,xS)) ) ),
introduced(definition,[new_symbols(definition,[sQ616_spl])],[split_symbol_definition]) ).
fof(f5552,plain,
( ~ sQ210_spl
| ~ sQ64_spl
| ~ sQ21_spl
| sQ616_spl ),
inference(split_clause,[status(thm)],[f5541,f5549,f342,f620,f1781]) ).
fof(f5553,definition,
! [X0] :
( sQ617_spl
<=> ( aElementOf0(X0,xS)
| ~ sdtlseqdt0(sK3_skl(X0,xT,xS),X0)
| ~ aElementOf0(X0,xS)
| ~ sdtlseqdt0(X0,sK5_skl(X0,xT,xS)) ) ),
introduced(definition,[new_symbols(definition,[sQ617_spl])],[split_symbol_definition]) ).
fof(f5556,plain,
( ~ sQ210_spl
| ~ sQ64_spl
| ~ sQ21_spl
| sQ617_spl ),
inference(split_clause,[status(thm)],[f5542,f5553,f342,f620,f1781]) ).
fof(f5615,definition,
( sQ626_spl
<=> sP0_prd(xT) ),
introduced(definition,[new_symbols(definition,[sQ626_spl])],[split_symbol_definition]) ).
fof(f5616,plain,
( ~ sQ626_spl
| sP0_prd(xT) ),
inference(component_clause,[status(thm)],[f5615]) ).
fof(f5631,definition,
( sQ629_spl
<=> aUpperBoundOfIn0(xp,xT,xU) ),
introduced(definition,[new_symbols(definition,[sQ629_spl])],[split_symbol_definition]) ).
fof(f5632,plain,
( ~ sQ629_spl
| aUpperBoundOfIn0(xp,xT,xU) ),
inference(component_clause,[status(thm)],[f5631]) ).
fof(f5633,plain,
( sQ629_spl
| ~ aUpperBoundOfIn0(xp,xT,xU) ),
inference(component_clause,[status(thm)],[f5631]) ).
fof(f5649,plain,
( sQ391_spl
| sdtlpdtrp0(xf,sK15_skl(sK0_skl(xT))) = sK15_skl(sK0_skl(xT))
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sK0_skl(xT)),sK0_skl(xT))
| ~ aElementOf0(sK0_skl(xT),xU) ),
inference(resolution,[status(thm)],[f1824,f3212]) ).
fof(f5650,plain,
( sQ5_spl
| sdtlpdtrp0(xf,sK15_skl(sK17_skl)) = sK15_skl(sK17_skl)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sK17_skl),sK17_skl)
| ~ aElementOf0(sK17_skl,xU) ),
inference(resolution,[status(thm)],[f1824,f2179]) ).
fof(f5665,definition,
( sQ635_spl
<=> sdtlpdtrp0(xf,sK15_skl(sK0_skl(xT))) = sK15_skl(sK0_skl(xT)) ),
introduced(definition,[new_symbols(definition,[sQ635_spl])],[split_symbol_definition]) ).
fof(f5668,plain,
( sQ391_spl
| sQ635_spl
| ~ sQ217_spl
| ~ sQ174_spl ),
inference(split_clause,[status(thm)],[f5649,f1544,f1828,f5665,f3060]) ).
fof(f5669,definition,
( sQ636_spl
<=> sdtlpdtrp0(xf,sK15_skl(sK17_skl)) = sK15_skl(sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ636_spl])],[split_symbol_definition]) ).
fof(f5672,plain,
( sQ5_spl
| sQ636_spl
| ~ sQ221_spl
| ~ sQ76_spl ),
inference(split_clause,[status(thm)],[f5650,f718,f1849,f5669,f253]) ).
fof(f5694,plain,
( sQ629_spl
| ~ aElementOf0(xp,xP) ),
inference(resolution,[status(thm)],[f5633,f185]) ).
fof(f5696,plain,
( sQ629_spl
| ~ sQ184_spl ),
inference(split_clause,[status(thm)],[f5694,f1610,f5631]) ).
fof(f5698,plain,
( ~ sQ629_spl
| aElementOf0(xp,xU)
| ~ aSubsetOf0(xT,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f5632,f73]) ).
fof(f5699,plain,
( ~ sQ629_spl
| sQ42_spl
| ~ sQ49_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f5698,f317,f511,f466,f5631]) ).
fof(f5700,plain,
( sQ418_spl
| ~ aElementOf0(xp,xS)
| aUpperBoundOfIn0(xp,xT,xS)
| ~ aSubsetOf0(xT,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f3376,f75]) ).
fof(f5701,plain,
! [X0] :
( sQ418_spl
| ~ aInfimumOfIn0(sK3_skl(xp,xT,xS),X0,xT)
| ~ aSubsetOf0(X0,xT)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[f3376,f81]) ).
fof(f5702,plain,
! [X0] :
( sQ418_spl
| ~ aElementOf0(sK3_skl(xp,xT,xS),X0)
| ~ aSubsetOf0(X0,xT)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[f3376,f50]) ).
fof(f5703,plain,
( sQ418_spl
| ~ sQ32_spl
| sQ12_spl
| ~ sQ64_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f5700,f342,f620,f282,f408,f3374]) ).
fof(f5704,definition,
! [X0] :
( sQ642_spl
<=> ( ~ aInfimumOfIn0(sK3_skl(xp,xT,xS),X0,xT)
| ~ aSubsetOf0(X0,xT) ) ),
introduced(definition,[new_symbols(definition,[sQ642_spl])],[split_symbol_definition]) ).
fof(f5707,plain,
( sQ418_spl
| sQ642_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f5701,f297,f5704,f3374]) ).
fof(f5708,definition,
! [X0] :
( sQ643_spl
<=> ( ~ aElementOf0(sK3_skl(xp,xT,xS),X0)
| ~ aSubsetOf0(X0,xT) ) ),
introduced(definition,[new_symbols(definition,[sQ643_spl])],[split_symbol_definition]) ).
fof(f5711,plain,
( sQ418_spl
| sQ643_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f5702,f297,f5708,f3374]) ).
fof(f5714,plain,
( ~ sQ626_spl
| ~ aSubsetOf0(xT,xU) ),
inference(resolution,[status(thm)],[f5616,f221]) ).
fof(f5717,plain,
( ~ sQ626_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f5714,f511,f5615]) ).
fof(f5736,plain,
! [X0,X1] :
( ~ sQ228_spl
| ~ sdtlseqdt0(sK4_skl(X0,xT,xS),X0)
| ~ aLowerBoundOfIn0(X0,xT,xS)
| ~ aSubsetOf0(xT,xS)
| ~ aSet0(xS)
| ~ sdtlseqdt0(sK4_skl(X1,xT,xS),X1)
| ~ aLowerBoundOfIn0(X1,xT,xS)
| X0 = X1 ),
inference(resolution,[status(thm)],[f1905,f764]) ).
fof(f5737,plain,
! [X0,X1] :
( ~ sQ228_spl
| aLowerBoundOfIn0(sK4_skl(X0,xT,xS),xT,xS)
| ~ aLowerBoundOfIn0(X0,xT,xS)
| ~ aSubsetOf0(xT,xS)
| ~ aSet0(xS)
| ~ sdtlseqdt0(sK4_skl(X1,xT,xS),X1)
| ~ aLowerBoundOfIn0(X1,xT,xS)
| X0 = X1 ),
inference(resolution,[status(thm)],[f1905,f763]) ).
fof(f5742,definition,
! [X0,X1] :
( sQ647_spl
<=> ( ~ sdtlseqdt0(sK4_skl(X0,xT,xS),X0)
| ~ aLowerBoundOfIn0(X0,xT,xS)
| ~ sdtlseqdt0(sK4_skl(X1,xT,xS),X1)
| ~ aLowerBoundOfIn0(X1,xT,xS)
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ647_spl])],[split_symbol_definition]) ).
fof(f5745,plain,
( ~ sQ228_spl
| ~ sQ64_spl
| ~ sQ21_spl
| sQ647_spl ),
inference(split_clause,[status(thm)],[f5736,f5742,f342,f620,f1904]) ).
fof(f5746,definition,
! [X0,X1] :
( sQ648_spl
<=> ( aLowerBoundOfIn0(sK4_skl(X0,xT,xS),xT,xS)
| ~ aLowerBoundOfIn0(X0,xT,xS)
| ~ sdtlseqdt0(sK4_skl(X1,xT,xS),X1)
| ~ aLowerBoundOfIn0(X1,xT,xS)
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ648_spl])],[split_symbol_definition]) ).
fof(f5749,plain,
( ~ sQ228_spl
| ~ sQ64_spl
| ~ sQ21_spl
| sQ648_spl ),
inference(split_clause,[status(thm)],[f5737,f5746,f342,f620,f1904]) ).
fof(f5750,plain,
! [X0,X1] :
( ~ sQ229_spl
| aElementOf0(sK4_skl(X1,xT,xS),xS)
| ~ aSubsetOf0(xT,xS)
| ~ aSet0(xS)
| ~ aLowerBoundOfIn0(X1,xT,xS)
| X0 = X1
| ~ aInfimumOfIn0(X0,xT,xS) ),
inference(resolution,[status(thm)],[f1909,f65]) ).
fof(f5751,definition,
! [X0,X1] :
( sQ649_spl
<=> ( aElementOf0(sK4_skl(X1,xT,xS),xS)
| ~ aLowerBoundOfIn0(X1,xT,xS)
| X0 = X1
| ~ aInfimumOfIn0(X0,xT,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ649_spl])],[split_symbol_definition]) ).
fof(f5754,plain,
( ~ sQ229_spl
| ~ sQ64_spl
| ~ sQ21_spl
| sQ649_spl ),
inference(split_clause,[status(thm)],[f5750,f5751,f342,f620,f1908]) ).
fof(f5762,plain,
! [X0] :
( ~ sQ205_spl
| ~ aElementOf0(sK1_skl(X0,xP),xP)
| ~ aSet0(X0)
| ~ aSet0(xP)
| ~ aElementOf0(sK0_skl(xT),X0) ),
inference(resolution,[status(thm)],[f1728,f52]) ).
fof(f5763,definition,
! [X0] :
( sQ651_spl
<=> ( ~ aElementOf0(sK1_skl(X0,xP),xP)
| ~ aSet0(X0)
| ~ aElementOf0(sK0_skl(xT),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ651_spl])],[split_symbol_definition]) ).
fof(f5766,plain,
( ~ sQ205_spl
| ~ sQ54_spl
| sQ651_spl ),
inference(split_clause,[status(thm)],[f5762,f5763,f544,f1727]) ).
fof(f5815,plain,
! [X0] :
( sQ416_spl
| ~ aInfimumOfIn0(sK3_skl(xp,xT,xS),X0,xU)
| ~ aSubsetOf0(X0,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f3369,f81]) ).
fof(f5816,plain,
! [X0] :
( sQ416_spl
| ~ aElementOf0(sK3_skl(xp,xT,xS),X0)
| ~ aSubsetOf0(X0,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f3369,f50]) ).
fof(f5817,definition,
! [X0] :
( sQ659_spl
<=> ( ~ aInfimumOfIn0(sK3_skl(xp,xT,xS),X0,xU)
| ~ aSubsetOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ659_spl])],[split_symbol_definition]) ).
fof(f5820,plain,
( sQ416_spl
| sQ659_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f5815,f317,f5817,f3367]) ).
fof(f5821,definition,
! [X0] :
( sQ660_spl
<=> ( ~ aElementOf0(sK3_skl(xp,xT,xS),X0)
| ~ aSubsetOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ660_spl])],[split_symbol_definition]) ).
fof(f5824,plain,
( sQ416_spl
| sQ660_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f5816,f317,f5821,f3367]) ).
fof(f5905,definition,
! [X0] :
( sQ670_spl
<=> ( X0 = sK7_skl(xP,xU)
| ~ aSupremumOfIn0(X0,xP,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ670_spl])],[split_symbol_definition]) ).
fof(f6065,plain,
! [X0,X1] :
( sP0_prd(X0)
| ~ sdtlseqdt0(sK4_skl(X1,X0,xU),X1)
| ~ aLowerBoundOfIn0(X1,X0,xU)
| ~ aSubsetOf0(X0,xU)
| ~ aElementOf0(sK1_skl(X0,xU),xU)
| sK11_skl(X0) = X1
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f2447,f149]) ).
fof(f6071,definition,
! [X0,X1] :
( sQ694_spl
<=> ( sP0_prd(X0)
| ~ sdtlseqdt0(sK4_skl(X1,X0,xU),X1)
| ~ aLowerBoundOfIn0(X1,X0,xU)
| ~ aSubsetOf0(X0,xU)
| ~ aElementOf0(sK1_skl(X0,xU),xU)
| sK11_skl(X0) = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ694_spl])],[split_symbol_definition]) ).
fof(f6074,plain,
( sQ694_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f6065,f317,f6071]) ).
fof(f6088,plain,
( ~ sQ238_spl
| ~ sQ63_spl
| sK15_skl(sK17_skl) = sK17_skl
| ~ sdtlseqdt0(sK17_skl,sK15_skl(sK17_skl))
| ~ sdtlseqdt0(sK15_skl(sK17_skl),sK17_skl) ),
inference(resolution,[status(thm)],[f664,f1966]) ).
fof(f6089,plain,
( ~ sQ63_spl
| sK17_skl = sK17_skl
| ~ sdtlseqdt0(sK17_skl,sK17_skl)
| ~ sdtlseqdt0(sK17_skl,sK17_skl) ),
inference(resolution,[status(thm)],[f664,f615]) ).
fof(f6090,plain,
( ~ sQ276_spl
| ~ sQ63_spl
| sK0_skl(xT) = sK17_skl
| ~ sdtlseqdt0(sK17_skl,sK0_skl(xT))
| ~ sdtlseqdt0(sK0_skl(xT),sK17_skl) ),
inference(resolution,[status(thm)],[f664,f2203]) ).
fof(f6101,definition,
( sQ697_spl
<=> sdtlseqdt0(sK17_skl,sK15_skl(sK17_skl)) ),
introduced(definition,[new_symbols(definition,[sQ697_spl])],[split_symbol_definition]) ).
fof(f6103,plain,
( sQ697_spl
| ~ sdtlseqdt0(sK17_skl,sK15_skl(sK17_skl)) ),
inference(component_clause,[status(thm)],[f6101]) ).
fof(f6104,definition,
( sQ698_spl
<=> sK15_skl(sK17_skl) = sK17_skl ),
introduced(definition,[new_symbols(definition,[sQ698_spl])],[split_symbol_definition]) ).
fof(f6105,plain,
( ~ sQ698_spl
| sK15_skl(sK17_skl) = sK17_skl ),
inference(component_clause,[status(thm)],[f6104]) ).
fof(f6107,plain,
( ~ sQ238_spl
| ~ sQ63_spl
| sQ698_spl
| ~ sQ697_spl
| ~ sQ222_spl ),
inference(split_clause,[status(thm)],[f6088,f1852,f6101,f6104,f614,f1965]) ).
fof(f6108,definition,
( sQ699_spl
<=> sK17_skl = sK17_skl ),
introduced(definition,[new_symbols(definition,[sQ699_spl])],[split_symbol_definition]) ).
fof(f6111,plain,
( ~ sQ63_spl
| sQ699_spl
| ~ sQ85_spl ),
inference(split_clause,[status(thm)],[f6089,f780,f6108,f614]) ).
fof(f6112,definition,
( sQ700_spl
<=> sK0_skl(xT) = sK17_skl ),
introduced(definition,[new_symbols(definition,[sQ700_spl])],[split_symbol_definition]) ).
fof(f6113,plain,
( ~ sQ700_spl
| sK0_skl(xT) = sK17_skl ),
inference(component_clause,[status(thm)],[f6112]) ).
fof(f6115,plain,
( ~ sQ276_spl
| ~ sQ63_spl
| sQ700_spl
| ~ sQ302_spl
| ~ sQ344_spl ),
inference(split_clause,[status(thm)],[f6090,f2733,f2486,f6112,f614,f2202]) ).
fof(f6116,definition,
( sQ701_spl
<=> sK0_skl(xS) = sK17_skl ),
introduced(definition,[new_symbols(definition,[sQ701_spl])],[split_symbol_definition]) ).
fof(f6117,plain,
( ~ sQ701_spl
| sK0_skl(xS) = sK17_skl ),
inference(component_clause,[status(thm)],[f6116]) ).
fof(f6132,plain,
( ~ sQ701_spl
| aElementOf0(sK17_skl,xS)
| isEmpty0(xS)
| ~ aSet0(xS) ),
inference(paramodulation,[status(thm)],[f6117,f44]) ).
fof(f6137,plain,
( ~ sQ701_spl
| sQ2_spl
| sQ23_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f6132,f342,f349,f241,f6116]) ).
fof(f6149,plain,
( ~ sQ700_spl
| aElementOf0(sK17_skl,xT)
| isEmpty0(xT)
| ~ aSet0(xT) ),
inference(paramodulation,[status(thm)],[f6113,f44]) ).
fof(f6151,plain,
( ~ sQ700_spl
| sQ125_spl
| sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6149,f297,f300,f1121,f6112]) ).
fof(f6156,plain,
( sQ222_spl
| ~ sQ698_spl
| ~ sdtlseqdt0(sK17_skl,sK17_skl) ),
inference(backward_demodulation,[status(thm)],[f6105,f1854]) ).
fof(f6160,plain,
( ~ sQ698_spl
| aElementOf0(sK17_skl,xP)
| aElementOf0(sK17_skl,xT)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,sK17_skl),sK17_skl)
| ~ aElementOf0(sK17_skl,xU) ),
inference(paramodulation,[status(thm)],[f6105,f186]) ).
fof(f6161,plain,
( sQ222_spl
| ~ sQ698_spl
| ~ sQ85_spl ),
inference(split_clause,[status(thm)],[f6156,f780,f6104,f1852]) ).
fof(f6162,plain,
( ~ sQ698_spl
| sQ69_spl
| sQ125_spl
| ~ sQ221_spl
| ~ sQ76_spl ),
inference(split_clause,[status(thm)],[f6160,f718,f1849,f1121,f659,f6104]) ).
fof(f6267,plain,
! [X0] :
( ~ sQ41_spl
| X0 = sK7_skl(xP,xU)
| ~ aSupremumOfIn0(X0,xP,xU)
| ~ aSubsetOf0(xP,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f2450,f96]) ).
fof(f6268,plain,
( ~ sQ41_spl
| aUpperBoundOfIn0(sK7_skl(xP,xU),xP,xU)
| ~ aSubsetOf0(xP,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f2450,f91]) ).
fof(f6269,plain,
( ~ sQ41_spl
| aElementOf0(sK7_skl(xP,xU),xU)
| ~ aSubsetOf0(xP,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f2450,f90]) ).
fof(f6270,plain,
( sQ670_spl
| ~ sQ41_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f6267,f317,f463,f5905]) ).
fof(f6271,definition,
( sQ704_spl
<=> aUpperBoundOfIn0(sK7_skl(xP,xU),xP,xU) ),
introduced(definition,[new_symbols(definition,[sQ704_spl])],[split_symbol_definition]) ).
fof(f6274,plain,
( sQ704_spl
| ~ sQ41_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f6268,f317,f463,f6271]) ).
fof(f6275,definition,
( sQ705_spl
<=> aElementOf0(sK7_skl(xP,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ705_spl])],[split_symbol_definition]) ).
fof(f6278,plain,
( sQ705_spl
| ~ sQ41_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f6269,f317,f463,f6275]) ).
fof(f6342,plain,
! [X0] :
( sQ302_spl
| ~ sdtlseqdt0(X0,sK0_skl(xT))
| ~ sdtlseqdt0(sK17_skl,X0)
| ~ aElement0(sK0_skl(xT))
| ~ aElement0(X0)
| ~ aElement0(sK17_skl) ),
inference(resolution,[status(thm)],[f2488,f60]) ).
fof(f6346,definition,
! [X0] :
( sQ717_spl
<=> ( ~ sdtlseqdt0(X0,sK0_skl(xT))
| ~ sdtlseqdt0(sK17_skl,X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ717_spl])],[split_symbol_definition]) ).
fof(f6349,plain,
( sQ302_spl
| ~ sQ276_spl
| sQ717_spl
| ~ sQ63_spl ),
inference(split_clause,[status(thm)],[f6342,f614,f6346,f2202,f2486]) ).
fof(f6353,plain,
! [X0] :
( sQ697_spl
| ~ sdtlseqdt0(X0,sK15_skl(sK17_skl))
| ~ sdtlseqdt0(sK17_skl,X0)
| ~ aElement0(sK15_skl(sK17_skl))
| ~ aElement0(X0)
| ~ aElement0(sK17_skl) ),
inference(resolution,[status(thm)],[f6103,f60]) ).
fof(f6357,definition,
! [X0] :
( sQ718_spl
<=> ( ~ sdtlseqdt0(X0,sK15_skl(sK17_skl))
| ~ sdtlseqdt0(sK17_skl,X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ718_spl])],[split_symbol_definition]) ).
fof(f6360,plain,
( sQ697_spl
| ~ sQ238_spl
| sQ718_spl
| ~ sQ63_spl ),
inference(split_clause,[status(thm)],[f6353,f614,f6357,f1965,f6101]) ).
fof(f6436,plain,
! [X0,X1] :
( ~ sQ298_spl
| X1 = sK7_skl(X0,xU)
| ~ aSupremumOfIn0(X1,X0,xU)
| ~ aSubsetOf0(X0,xU)
| ~ aSet0(xU)
| ~ aElementOf0(sK1_skl(X0,xU),xU)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f2454,f96]) ).
fof(f6437,plain,
! [X0] :
( ~ sQ298_spl
| aUpperBoundOfIn0(sK7_skl(X0,xU),X0,xU)
| ~ aSubsetOf0(X0,xU)
| ~ aSet0(xU)
| ~ aElementOf0(sK1_skl(X0,xU),xU)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f2454,f91]) ).
fof(f6438,plain,
! [X0] :
( ~ sQ298_spl
| aElementOf0(sK7_skl(X0,xU),xU)
| ~ aSubsetOf0(X0,xU)
| ~ aSet0(xU)
| ~ aElementOf0(sK1_skl(X0,xU),xU)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f2454,f90]) ).
fof(f6440,definition,
! [X0,X1] :
( sQ724_spl
<=> ( X1 = sK7_skl(X0,xU)
| ~ aSupremumOfIn0(X1,X0,xU)
| ~ aSubsetOf0(X0,xU)
| ~ aElementOf0(sK1_skl(X0,xU),xU)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ724_spl])],[split_symbol_definition]) ).
fof(f6443,plain,
( ~ sQ298_spl
| ~ sQ19_spl
| sQ724_spl ),
inference(split_clause,[status(thm)],[f6436,f6440,f317,f2453]) ).
fof(f6444,definition,
! [X0] :
( sQ725_spl
<=> ( aUpperBoundOfIn0(sK7_skl(X0,xU),X0,xU)
| ~ aSubsetOf0(X0,xU)
| ~ aElementOf0(sK1_skl(X0,xU),xU)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ725_spl])],[split_symbol_definition]) ).
fof(f6447,plain,
( ~ sQ298_spl
| ~ sQ19_spl
| sQ725_spl ),
inference(split_clause,[status(thm)],[f6437,f6444,f317,f2453]) ).
fof(f6448,definition,
! [X0] :
( sQ726_spl
<=> ( aElementOf0(sK7_skl(X0,xU),xU)
| ~ aSubsetOf0(X0,xU)
| ~ aElementOf0(sK1_skl(X0,xU),xU)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ726_spl])],[split_symbol_definition]) ).
fof(f6451,plain,
( ~ sQ298_spl
| ~ sQ19_spl
| sQ726_spl ),
inference(split_clause,[status(thm)],[f6438,f6448,f317,f2453]) ).
fof(f6453,plain,
! [X0,X1] :
( ~ sQ338_spl
| X1 = sK13_skl(X0)
| ~ aSupremumOfIn0(X1,X0,xU)
| ~ aSubsetOf0(X0,xU)
| ~ aSet0(xU)
| ~ aElementOf0(sK1_skl(X0,xU),xU)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f2699,f96]) ).
fof(f6454,plain,
! [X0] :
( ~ sQ338_spl
| aUpperBoundOfIn0(sK13_skl(X0),X0,xU)
| ~ aSubsetOf0(X0,xU)
| ~ aSet0(xU)
| ~ aElementOf0(sK1_skl(X0,xU),xU)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f2699,f91]) ).
fof(f6455,plain,
! [X0] :
( ~ sQ338_spl
| aElementOf0(sK13_skl(X0),xU)
| ~ aSubsetOf0(X0,xU)
| ~ aSet0(xU)
| ~ aElementOf0(sK1_skl(X0,xU),xU)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f2699,f90]) ).
fof(f6457,definition,
! [X0,X1] :
( sQ727_spl
<=> ( X1 = sK13_skl(X0)
| ~ aSupremumOfIn0(X1,X0,xU)
| ~ aSubsetOf0(X0,xU)
| ~ aElementOf0(sK1_skl(X0,xU),xU)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ727_spl])],[split_symbol_definition]) ).
fof(f6460,plain,
( ~ sQ338_spl
| ~ sQ19_spl
| sQ727_spl ),
inference(split_clause,[status(thm)],[f6453,f6457,f317,f2698]) ).
fof(f6461,definition,
! [X0] :
( sQ728_spl
<=> ( aUpperBoundOfIn0(sK13_skl(X0),X0,xU)
| ~ aSubsetOf0(X0,xU)
| ~ aElementOf0(sK1_skl(X0,xU),xU)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ728_spl])],[split_symbol_definition]) ).
fof(f6464,plain,
( ~ sQ338_spl
| ~ sQ19_spl
| sQ728_spl ),
inference(split_clause,[status(thm)],[f6454,f6461,f317,f2698]) ).
fof(f6465,definition,
! [X0] :
( sQ729_spl
<=> ( aElementOf0(sK13_skl(X0),xU)
| ~ aSubsetOf0(X0,xU)
| ~ aElementOf0(sK1_skl(X0,xU),xU)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ729_spl])],[split_symbol_definition]) ).
fof(f6468,plain,
( ~ sQ338_spl
| ~ sQ19_spl
| sQ729_spl ),
inference(split_clause,[status(thm)],[f6455,f6465,f317,f2698]) ).
fof(f6712,plain,
! [X0,X1] :
( ~ sQ380_spl
| ~ aElementOf0(sK1_skl(X0,xU),xU)
| ~ aSet0(X0)
| ~ aSet0(xU)
| X1 = sK13_skl(X0)
| ~ aSupremumOfIn0(X1,X0,xU)
| ~ aElementOf0(sK18_skl(X0),xU)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f2999,f52]) ).
fof(f6716,definition,
! [X0,X1] :
( sQ766_spl
<=> ( ~ aElementOf0(sK1_skl(X0,xU),xU)
| ~ aSet0(X0)
| X1 = sK13_skl(X0)
| ~ aSupremumOfIn0(X1,X0,xU)
| ~ aElementOf0(sK18_skl(X0),xU)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ766_spl])],[split_symbol_definition]) ).
fof(f6719,plain,
( ~ sQ380_spl
| ~ sQ19_spl
| sQ766_spl ),
inference(split_clause,[status(thm)],[f6712,f6716,f317,f2998]) ).
fof(f6895,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| aUpperBoundOfIn0(X0,xT,xS)
| ~ aSet0(xS)
| sdtlpdtrp0(xf,sK3_skl(X0,xT,xS)) = sK3_skl(X0,xT,xS) ),
inference(resolution,[status(thm)],[f1449,f177]) ).
fof(f6896,plain,
! [X0,X1] :
( ~ aElementOf0(sK1_skl(xT,X1),X1)
| ~ aSet0(xT)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| aUpperBoundOfIn0(X0,xT,X1)
| ~ aSet0(X1)
| sdtlpdtrp0(xf,sK3_skl(X0,xT,X1)) = sK3_skl(X0,xT,X1) ),
inference(resolution,[status(thm)],[f1449,f52]) ).
fof(f6909,definition,
! [X0] :
( sQ792_spl
<=> ( ~ aElementOf0(X0,xS)
| aUpperBoundOfIn0(X0,xT,xS)
| sdtlpdtrp0(xf,sK3_skl(X0,xT,xS)) = sK3_skl(X0,xT,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ792_spl])],[split_symbol_definition]) ).
fof(f6912,plain,
( ~ sQ21_spl
| sQ792_spl ),
inference(split_clause,[status(thm)],[f6895,f6909,f342]) ).
fof(f6913,definition,
! [X0,X1] :
( sQ793_spl
<=> ( ~ aElementOf0(sK1_skl(xT,X1),X1)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| aUpperBoundOfIn0(X0,xT,X1)
| ~ aSet0(X1)
| sdtlpdtrp0(xf,sK3_skl(X0,xT,X1)) = sK3_skl(X0,xT,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ793_spl])],[split_symbol_definition]) ).
fof(f6916,plain,
( ~ sQ15_spl
| sQ793_spl ),
inference(split_clause,[status(thm)],[f6896,f6913,f297]) ).
fof(f7164,plain,
! [X0,X1,X2] :
( sQ5_spl
| ~ sdtlseqdt0(X2,sK17_skl)
| ~ sdtlseqdt0(sK3_skl(sK17_skl,X1,X0),X2)
| ~ aElement0(sK17_skl)
| ~ aElement0(X2)
| ~ aElement0(sK3_skl(sK17_skl,X1,X0))
| ~ aElementOf0(sK17_skl,X0)
| ~ aElementOf0(xp,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f2264,f60]) ).
fof(f7171,definition,
! [X0,X1,X2] :
( sQ824_spl
<=> ( ~ sdtlseqdt0(X2,sK17_skl)
| ~ sdtlseqdt0(sK3_skl(sK17_skl,X1,X0),X2)
| ~ aElement0(X2)
| ~ aElement0(sK3_skl(sK17_skl,X1,X0))
| ~ aElementOf0(sK17_skl,X0)
| ~ aElementOf0(xp,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ824_spl])],[split_symbol_definition]) ).
fof(f7174,plain,
( sQ5_spl
| ~ sQ63_spl
| sQ824_spl ),
inference(split_clause,[status(thm)],[f7164,f7171,f614,f253]) ).
fof(f7308,plain,
! [X0,X1,X2] :
( sQ5_spl
| ~ sdtlseqdt0(X2,sK2_skl(xp,X1,X0))
| ~ sdtlseqdt0(xp,X2)
| ~ aElement0(sK2_skl(xp,X1,X0))
| ~ aElement0(X2)
| ~ aElement0(xp)
| ~ aElementOf0(xp,X0)
| ~ aElementOf0(sK17_skl,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f2375,f60]) ).
fof(f7315,definition,
! [X0,X1,X2] :
( sQ844_spl
<=> ( ~ sdtlseqdt0(X2,sK2_skl(xp,X1,X0))
| ~ sdtlseqdt0(xp,X2)
| ~ aElement0(sK2_skl(xp,X1,X0))
| ~ aElement0(X2)
| ~ aElementOf0(xp,X0)
| ~ aElementOf0(sK17_skl,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ844_spl])],[split_symbol_definition]) ).
fof(f7318,plain,
( sQ5_spl
| ~ sQ61_spl
| sQ844_spl ),
inference(split_clause,[status(thm)],[f7308,f7315,f608,f253]) ).
fof(f7367,plain,
! [X0] :
( sQ5_spl
| sdtlpdtrp0(xf,sK2_skl(xp,xS,X0)) = sK2_skl(xp,xS,X0)
| ~ aElementOf0(xp,X0)
| ~ aElementOf0(sK17_skl,xS)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f2376,f169]) ).
fof(f7372,definition,
! [X0] :
( sQ852_spl
<=> ( sdtlpdtrp0(xf,sK2_skl(xp,xS,X0)) = sK2_skl(xp,xS,X0)
| ~ aElementOf0(xp,X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ852_spl])],[split_symbol_definition]) ).
fof(f7375,plain,
( sQ5_spl
| ~ sQ2_spl
| sQ852_spl ),
inference(split_clause,[status(thm)],[f7367,f7372,f241,f253]) ).
fof(f7458,plain,
! [X0] :
( ~ sQ62_spl
| ~ aElementOf0(X0,xP)
| ~ sdtlseqdt0(X0,sK17_skl)
| ~ sdtlseqdt0(xp,X0) ),
inference(resolution,[status(thm)],[f779,f181]) ).
fof(f7465,plain,
! [X0] :
( ~ sQ62_spl
| ~ aElementOf0(X0,xP)
| ~ sdtlseqdt0(X0,sK17_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f7458,f194]) ).
fof(f7571,definition,
( sQ866_spl
<=> sK13_skl(xT) = sK17_skl ),
introduced(definition,[new_symbols(definition,[sQ866_spl])],[split_symbol_definition]) ).
fof(f7572,plain,
( ~ sQ866_spl
| sK13_skl(xT) = sK17_skl ),
inference(component_clause,[status(thm)],[f7571]) ).
fof(f7635,plain,
! [X0] :
( ~ sQ866_spl
| sdtlseqdt0(X0,sK17_skl)
| ~ aElementOf0(X0,xT)
| sP0_prd(xT) ),
inference(paramodulation,[status(thm)],[f7572,f152]) ).
fof(f7658,plain,
( ~ sQ866_spl
| sQ3_spl
| sQ626_spl ),
inference(split_clause,[status(thm)],[f7635,f5615,f245,f7571]) ).
fof(f8064,plain,
( ~ sQ238_spl
| ~ sQ420_spl
| ~ sdtlseqdt0(sK15_skl(sK17_skl),xp)
| ~ sdtlseqdt0(sK3_skl(xp,xT,xS),sK15_skl(sK17_skl)) ),
inference(resolution,[status(thm)],[f3382,f1966]) ).
fof(f8065,plain,
( ~ sQ276_spl
| ~ sQ420_spl
| ~ sdtlseqdt0(sK0_skl(xT),xp)
| ~ sdtlseqdt0(sK3_skl(xp,xT,xS),sK0_skl(xT)) ),
inference(resolution,[status(thm)],[f3382,f2203]) ).
fof(f8068,plain,
( ~ sQ61_spl
| ~ sQ420_spl
| ~ sdtlseqdt0(xp,xp)
| ~ sdtlseqdt0(sK3_skl(xp,xT,xS),xp) ),
inference(resolution,[status(thm)],[f3382,f609]) ).
fof(f8078,definition,
( sQ912_spl
<=> sdtlseqdt0(sK3_skl(xp,xT,xS),sK15_skl(sK17_skl)) ),
introduced(definition,[new_symbols(definition,[sQ912_spl])],[split_symbol_definition]) ).
fof(f8081,plain,
( ~ sQ238_spl
| ~ sQ420_spl
| ~ sQ543_spl
| ~ sQ912_spl ),
inference(split_clause,[status(thm)],[f8064,f8078,f4647,f3381,f1965]) ).
fof(f8082,definition,
( sQ913_spl
<=> sdtlseqdt0(sK3_skl(xp,xT,xS),sK0_skl(xT)) ),
introduced(definition,[new_symbols(definition,[sQ913_spl])],[split_symbol_definition]) ).
fof(f8085,plain,
( ~ sQ276_spl
| ~ sQ420_spl
| ~ sQ390_spl
| ~ sQ913_spl ),
inference(split_clause,[status(thm)],[f8065,f8082,f3057,f3381,f2202]) ).
fof(f8094,plain,
( ~ sQ61_spl
| ~ sQ420_spl
| ~ sQ139_spl
| ~ sQ415_spl ),
inference(split_clause,[status(thm)],[f8068,f3322,f1238,f3381,f608]) ).
fof(f8098,plain,
( sQ417_spl
| ~ aElementOf0(sK3_skl(xp,xT,xS),xT)
| ~ aElementOf0(sK16_skl(sK3_skl(xp,xT,xS)),xP) ),
inference(resolution,[status(thm)],[f3372,f184]) ).
fof(f8104,definition,
( sQ916_spl
<=> aElementOf0(sK16_skl(sK3_skl(xp,xT,xS)),xP) ),
introduced(definition,[new_symbols(definition,[sQ916_spl])],[split_symbol_definition]) ).
fof(f8107,plain,
( sQ417_spl
| ~ sQ418_spl
| ~ sQ916_spl ),
inference(split_clause,[status(thm)],[f8098,f8104,f3374,f3370]) ).
fof(f8356,definition,
( sQ947_spl
<=> sdtlseqdt0(xp,sdtlpdtrp0(xf,xp)) ),
introduced(definition,[new_symbols(definition,[sQ947_spl])],[split_symbol_definition]) ).
fof(f8358,plain,
( sQ947_spl
| ~ sdtlseqdt0(xp,sdtlpdtrp0(xf,xp)) ),
inference(component_clause,[status(thm)],[f8356]) ).
fof(f8373,plain,
! [X0] :
( ~ sQ87_spl
| ~ sdtlseqdt0(sK4_skl(sK17_skl,X0,xT),sK17_skl)
| ~ aLowerBoundOfIn0(sK17_skl,X0,xT)
| ~ aSubsetOf0(X0,xT)
| ~ aSet0(xT)
| ~ aSubsetOf0(X0,xT) ),
inference(resolution,[status(thm)],[f809,f764]) ).
fof(f8374,plain,
! [X0] :
( ~ sQ87_spl
| aLowerBoundOfIn0(sK4_skl(sK17_skl,X0,xT),X0,xT)
| ~ aLowerBoundOfIn0(sK17_skl,X0,xT)
| ~ aSubsetOf0(X0,xT)
| ~ aSet0(xT)
| ~ aSubsetOf0(X0,xT) ),
inference(resolution,[status(thm)],[f809,f763]) ).
fof(f8375,definition,
! [X0] :
( sQ951_spl
<=> ( ~ sdtlseqdt0(sK4_skl(sK17_skl,X0,xT),sK17_skl)
| ~ aLowerBoundOfIn0(sK17_skl,X0,xT)
| ~ aSubsetOf0(X0,xT)
| ~ aSubsetOf0(X0,xT) ) ),
introduced(definition,[new_symbols(definition,[sQ951_spl])],[split_symbol_definition]) ).
fof(f8378,plain,
( ~ sQ87_spl
| ~ sQ15_spl
| sQ951_spl ),
inference(split_clause,[status(thm)],[f8373,f8375,f297,f808]) ).
fof(f8379,definition,
! [X0] :
( sQ952_spl
<=> ( aLowerBoundOfIn0(sK4_skl(sK17_skl,X0,xT),X0,xT)
| ~ aLowerBoundOfIn0(sK17_skl,X0,xT)
| ~ aSubsetOf0(X0,xT)
| ~ aSubsetOf0(X0,xT) ) ),
introduced(definition,[new_symbols(definition,[sQ952_spl])],[split_symbol_definition]) ).
fof(f8382,plain,
( ~ sQ87_spl
| ~ sQ15_spl
| sQ952_spl ),
inference(split_clause,[status(thm)],[f8374,f8379,f297,f808]) ).
fof(f8449,plain,
! [X0] :
( ~ sQ62_spl
| ~ sdtlseqdt0(sK14_skl(sK17_skl,X0),sK17_skl)
| ~ aElementOf0(sK17_skl,xU)
| sP0_prd(X0)
| ~ aElementOf0(sK13_skl(X0),xP) ),
inference(resolution,[status(thm)],[f7465,f155]) ).
fof(f8450,plain,
! [X0] :
( ~ sQ62_spl
| aElementOf0(sK14_skl(sK17_skl,X0),X0)
| ~ aElementOf0(sK17_skl,xU)
| sP0_prd(X0)
| ~ aElementOf0(sK13_skl(X0),xP) ),
inference(resolution,[status(thm)],[f7465,f154]) ).
fof(f8452,plain,
( ~ sQ62_spl
| ~ aElementOf0(sK17_skl,xP)
| ~ aElementOf0(xp,xP) ),
inference(resolution,[status(thm)],[f7465,f194]) ).
fof(f8459,plain,
! [X0,X1] :
( ~ sQ62_spl
| ~ sdtlseqdt0(X1,sK17_skl)
| ~ sdtlseqdt0(X0,X1)
| ~ aElement0(sK17_skl)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ aElementOf0(X0,xP) ),
inference(resolution,[status(thm)],[f7465,f60]) ).
fof(f8460,plain,
( ~ sQ62_spl
| ~ aElement0(sK17_skl)
| ~ aElementOf0(sK17_skl,xP) ),
inference(resolution,[status(thm)],[f7465,f56]) ).
fof(f8463,definition,
! [X0] :
( sQ965_spl
<=> ( ~ sdtlseqdt0(sK14_skl(sK17_skl,X0),sK17_skl)
| sP0_prd(X0)
| ~ aElementOf0(sK13_skl(X0),xP) ) ),
introduced(definition,[new_symbols(definition,[sQ965_spl])],[split_symbol_definition]) ).
fof(f8466,plain,
( ~ sQ62_spl
| ~ sQ76_spl
| sQ965_spl ),
inference(split_clause,[status(thm)],[f8449,f8463,f718,f611]) ).
fof(f8467,definition,
! [X0] :
( sQ966_spl
<=> ( aElementOf0(sK14_skl(sK17_skl,X0),X0)
| sP0_prd(X0)
| ~ aElementOf0(sK13_skl(X0),xP) ) ),
introduced(definition,[new_symbols(definition,[sQ966_spl])],[split_symbol_definition]) ).
fof(f8470,plain,
( ~ sQ62_spl
| ~ sQ76_spl
| sQ966_spl ),
inference(split_clause,[status(thm)],[f8450,f8467,f718,f611]) ).
fof(f8471,plain,
( ~ sQ62_spl
| ~ sQ69_spl
| ~ sQ184_spl ),
inference(split_clause,[status(thm)],[f8452,f1610,f659,f611]) ).
fof(f8481,definition,
! [X0,X1] :
( sQ969_spl
<=> ( ~ sdtlseqdt0(X1,sK17_skl)
| ~ sdtlseqdt0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ aElementOf0(X0,xP) ) ),
introduced(definition,[new_symbols(definition,[sQ969_spl])],[split_symbol_definition]) ).
fof(f8484,plain,
( ~ sQ62_spl
| ~ sQ63_spl
| sQ969_spl ),
inference(split_clause,[status(thm)],[f8459,f8481,f614,f611]) ).
fof(f8485,plain,
( ~ sQ62_spl
| ~ sQ63_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f8460,f659,f614,f611]) ).
fof(f8879,plain,
! [X0,X1] :
( ~ sQ73_spl
| ~ aInfimumOfIn0(sK1_skl(X0,xP),X1,xP)
| ~ aSubsetOf0(X1,xP)
| ~ aSet0(xP)
| ~ aSet0(X0)
| ~ aElementOf0(sK17_skl,X0) ),
inference(resolution,[status(thm)],[f686,f81]) ).
fof(f8880,plain,
! [X0,X1] :
( ~ sQ73_spl
| ~ aElementOf0(sK1_skl(X0,xP),X1)
| ~ aSubsetOf0(X1,xP)
| ~ aSet0(xP)
| ~ aSet0(X0)
| ~ aElementOf0(sK17_skl,X0) ),
inference(resolution,[status(thm)],[f686,f50]) ).
fof(f8885,definition,
! [X0,X1] :
( sQ1002_spl
<=> ( ~ aInfimumOfIn0(sK1_skl(X0,xP),X1,xP)
| ~ aSubsetOf0(X1,xP)
| ~ aSet0(X0)
| ~ aElementOf0(sK17_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1002_spl])],[split_symbol_definition]) ).
fof(f8888,plain,
( ~ sQ73_spl
| ~ sQ54_spl
| sQ1002_spl ),
inference(split_clause,[status(thm)],[f8879,f8885,f544,f685]) ).
fof(f8889,definition,
! [X0,X1] :
( sQ1003_spl
<=> ( ~ aElementOf0(sK1_skl(X0,xP),X1)
| ~ aSubsetOf0(X1,xP)
| ~ aSet0(X0)
| ~ aElementOf0(sK17_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1003_spl])],[split_symbol_definition]) ).
fof(f8892,plain,
( ~ sQ73_spl
| ~ sQ54_spl
| sQ1003_spl ),
inference(split_clause,[status(thm)],[f8880,f8889,f544,f685]) ).
fof(f8952,plain,
( ~ sQ104_spl
| ~ aSet0(xT)
| aSubsetOf0(xT,xT)
| ~ aSet0(xT)
| ~ aSet0(xT)
| ~ aElementOf0(sK17_skl,xT) ),
inference(resolution,[status(thm)],[f969,f51]) ).
fof(f8953,plain,
! [X0,X1] :
( ~ sQ104_spl
| ~ aInfimumOfIn0(sK1_skl(X0,xT),X1,xT)
| ~ aSubsetOf0(X1,xT)
| ~ aSet0(xT)
| ~ aSet0(X0)
| ~ aElementOf0(sK17_skl,X0) ),
inference(resolution,[status(thm)],[f969,f81]) ).
fof(f8954,plain,
! [X0,X1] :
( ~ sQ104_spl
| ~ aElementOf0(sK1_skl(X0,xT),X1)
| ~ aSubsetOf0(X1,xT)
| ~ aSet0(xT)
| ~ aSet0(X0)
| ~ aElementOf0(sK17_skl,X0) ),
inference(resolution,[status(thm)],[f969,f50]) ).
fof(f8956,plain,
( ~ sQ104_spl
| sQ313_spl
| ~ sQ15_spl
| ~ sQ125_spl ),
inference(split_clause,[status(thm)],[f8952,f1121,f297,f2550,f968]) ).
fof(f8957,definition,
! [X0,X1] :
( sQ1009_spl
<=> ( ~ aInfimumOfIn0(sK1_skl(X0,xT),X1,xT)
| ~ aSubsetOf0(X1,xT)
| ~ aSet0(X0)
| ~ aElementOf0(sK17_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1009_spl])],[split_symbol_definition]) ).
fof(f8960,plain,
( ~ sQ104_spl
| ~ sQ15_spl
| sQ1009_spl ),
inference(split_clause,[status(thm)],[f8953,f8957,f297,f968]) ).
fof(f8961,definition,
! [X0,X1] :
( sQ1010_spl
<=> ( ~ aElementOf0(sK1_skl(X0,xT),X1)
| ~ aSubsetOf0(X1,xT)
| ~ aSet0(X0)
| ~ aElementOf0(sK17_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1010_spl])],[split_symbol_definition]) ).
fof(f8964,plain,
( ~ sQ104_spl
| ~ sQ15_spl
| sQ1010_spl ),
inference(split_clause,[status(thm)],[f8954,f8961,f297,f968]) ).
fof(f9052,plain,
! [X0] :
( ~ sQ201_spl
| ~ sdtlseqdt0(sK4_skl(sK17_skl,X0,xT),sK17_skl)
| ~ aLowerBoundOfIn0(sK17_skl,X0,xT)
| ~ aSubsetOf0(X0,xT)
| ~ aSet0(xT)
| ~ aElementOf0(sK1_skl(X0,xT),xT)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f1703,f764]) ).
fof(f9053,plain,
! [X0] :
( ~ sQ201_spl
| aLowerBoundOfIn0(sK4_skl(sK17_skl,X0,xT),X0,xT)
| ~ aLowerBoundOfIn0(sK17_skl,X0,xT)
| ~ aSubsetOf0(X0,xT)
| ~ aSet0(xT)
| ~ aElementOf0(sK1_skl(X0,xT),xT)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f1703,f763]) ).
fof(f9054,definition,
! [X0] :
( sQ1016_spl
<=> ( ~ sdtlseqdt0(sK4_skl(sK17_skl,X0,xT),sK17_skl)
| ~ aLowerBoundOfIn0(sK17_skl,X0,xT)
| ~ aSubsetOf0(X0,xT)
| ~ aElementOf0(sK1_skl(X0,xT),xT)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1016_spl])],[split_symbol_definition]) ).
fof(f9057,plain,
( ~ sQ201_spl
| ~ sQ15_spl
| sQ1016_spl ),
inference(split_clause,[status(thm)],[f9052,f9054,f297,f1702]) ).
fof(f9058,definition,
! [X0] :
( sQ1017_spl
<=> ( aLowerBoundOfIn0(sK4_skl(sK17_skl,X0,xT),X0,xT)
| ~ aLowerBoundOfIn0(sK17_skl,X0,xT)
| ~ aSubsetOf0(X0,xT)
| ~ aElementOf0(sK1_skl(X0,xT),xT)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1017_spl])],[split_symbol_definition]) ).
fof(f9061,plain,
( ~ sQ201_spl
| ~ sQ15_spl
| sQ1017_spl ),
inference(split_clause,[status(thm)],[f9053,f9058,f297,f1702]) ).
fof(f9837,plain,
! [X0,X1,X2] :
( ~ sQ345_spl
| ~ aInfimumOfIn0(sK1_skl(X1,xT),X2,xT)
| ~ aSubsetOf0(X2,xT)
| ~ aSet0(xT)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f2767,f81]) ).
fof(f9838,plain,
! [X0,X1,X2] :
( ~ sQ345_spl
| ~ aElementOf0(sK1_skl(X1,xT),X2)
| ~ aSubsetOf0(X2,xT)
| ~ aSet0(xT)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f2767,f50]) ).
fof(f9840,definition,
! [X0,X1,X2] :
( sQ1068_spl
<=> ( ~ aInfimumOfIn0(sK1_skl(X1,xT),X2,xT)
| ~ aSubsetOf0(X2,xT)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ1068_spl])],[split_symbol_definition]) ).
fof(f9843,plain,
( ~ sQ345_spl
| ~ sQ15_spl
| sQ1068_spl ),
inference(split_clause,[status(thm)],[f9837,f9840,f297,f2766]) ).
fof(f9844,definition,
! [X0,X1,X2] :
( sQ1069_spl
<=> ( ~ aElementOf0(sK1_skl(X1,xT),X2)
| ~ aSubsetOf0(X2,xT)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ1069_spl])],[split_symbol_definition]) ).
fof(f9847,plain,
( ~ sQ345_spl
| ~ sQ15_spl
| sQ1069_spl ),
inference(split_clause,[status(thm)],[f9838,f9844,f297,f2766]) ).
fof(f9889,plain,
( sQ947_spl
| ~ aElementOf0(sdtlpdtrp0(xf,xp),xP) ),
inference(resolution,[status(thm)],[f8358,f194]) ).
fof(f9898,plain,
( sQ947_spl
| ~ sQ241_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9889,f1987]) ).
fof(f9899,plain,
( sQ947_spl
| ~ sQ241_spl ),
inference(contradiction_clause,[status(thm)],[f9898]) ).
fof(f10059,plain,
! [X0,X1,X2] :
( ~ sQ142_spl
| ~ aInfimumOfIn0(sK1_skl(X1,xS),X2,xT)
| ~ aSubsetOf0(X2,xT)
| ~ aSet0(xT)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f3545,f81]) ).
fof(f10060,plain,
! [X0,X1,X2] :
( ~ sQ142_spl
| ~ aElementOf0(sK1_skl(X1,xS),X2)
| ~ aSubsetOf0(X2,xT)
| ~ aSet0(xT)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f3545,f50]) ).
fof(f10062,definition,
! [X0,X1,X2] :
( sQ1094_spl
<=> ( ~ aInfimumOfIn0(sK1_skl(X1,xS),X2,xT)
| ~ aSubsetOf0(X2,xT)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ1094_spl])],[split_symbol_definition]) ).
fof(f10065,plain,
( ~ sQ142_spl
| ~ sQ15_spl
| sQ1094_spl ),
inference(split_clause,[status(thm)],[f10059,f10062,f297,f1281]) ).
fof(f10066,definition,
! [X0,X1,X2] :
( sQ1095_spl
<=> ( ~ aElementOf0(sK1_skl(X1,xS),X2)
| ~ aSubsetOf0(X2,xT)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ1095_spl])],[split_symbol_definition]) ).
fof(f10069,plain,
( ~ sQ142_spl
| ~ sQ15_spl
| sQ1095_spl ),
inference(split_clause,[status(thm)],[f10060,f10066,f297,f1281]) ).
fof(f10185,plain,
! [X0,X1,X2] :
( ~ sQ142_spl
| ~ aInfimumOfIn0(sK1_skl(X1,xS),X2,xU)
| ~ aSubsetOf0(X2,xU)
| ~ aSet0(xU)
| sdtlpdtrp0(xf,sK1_skl(X1,xS)) != sK1_skl(X1,xS)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f3546,f81]) ).
fof(f10186,plain,
! [X0,X1,X2] :
( ~ sQ142_spl
| ~ aElementOf0(sK1_skl(X1,xS),X2)
| ~ aSubsetOf0(X2,xU)
| ~ aSet0(xU)
| sdtlpdtrp0(xf,sK1_skl(X1,xS)) != sK1_skl(X1,xS)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f3546,f50]) ).
fof(f10194,definition,
( sQ1111_spl
<=> aSubsetOf0(xU,xS) ),
introduced(definition,[new_symbols(definition,[sQ1111_spl])],[split_symbol_definition]) ).
fof(f10195,plain,
( ~ sQ1111_spl
| aSubsetOf0(xU,xS) ),
inference(component_clause,[status(thm)],[f10194]) ).
fof(f10196,plain,
( sQ1111_spl
| ~ aSubsetOf0(xU,xS) ),
inference(component_clause,[status(thm)],[f10194]) ).
fof(f10199,definition,
! [X0,X1,X2] :
( sQ1112_spl
<=> ( ~ aInfimumOfIn0(sK1_skl(X1,xS),X2,xU)
| ~ aSubsetOf0(X2,xU)
| sdtlpdtrp0(xf,sK1_skl(X1,xS)) != sK1_skl(X1,xS)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ1112_spl])],[split_symbol_definition]) ).
fof(f10202,plain,
( ~ sQ142_spl
| ~ sQ19_spl
| sQ1112_spl ),
inference(split_clause,[status(thm)],[f10185,f10199,f317,f1281]) ).
fof(f10203,definition,
! [X0,X1,X2] :
( sQ1113_spl
<=> ( ~ aElementOf0(sK1_skl(X1,xS),X2)
| ~ aSubsetOf0(X2,xU)
| sdtlpdtrp0(xf,sK1_skl(X1,xS)) != sK1_skl(X1,xS)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ1113_spl])],[split_symbol_definition]) ).
fof(f10206,plain,
( ~ sQ142_spl
| ~ sQ19_spl
| sQ1113_spl ),
inference(split_clause,[status(thm)],[f10186,f10203,f317,f1281]) ).
fof(f10209,plain,
( ~ sQ30_spl
| ~ sQ1111_spl
| ~ aElementOf0(xp,xU) ),
inference(resolution,[status(thm)],[f10195,f396]) ).
fof(f10218,plain,
( ~ sQ30_spl
| ~ sQ1111_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10209,f192]) ).
fof(f10219,plain,
( ~ sQ30_spl
| ~ sQ1111_spl ),
inference(contradiction_clause,[status(thm)],[f10218]) ).
fof(f10220,plain,
( sQ1111_spl
| ~ aElementOf0(sK1_skl(xU,xS),xS)
| ~ aSet0(xU)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f10196,f52]) ).
fof(f10221,definition,
( sQ1114_spl
<=> aElementOf0(sK1_skl(xU,xS),xS) ),
introduced(definition,[new_symbols(definition,[sQ1114_spl])],[split_symbol_definition]) ).
fof(f10224,plain,
( sQ1111_spl
| ~ sQ1114_spl
| ~ sQ19_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f10220,f342,f317,f10221,f10194]) ).
fof(f10256,plain,
! [X0,X1,X2] :
( ~ sQ437_spl
| ~ sdtlseqdt0(sK4_skl(sK1_skl(X1,xS),X2,xS),sK1_skl(X1,xS))
| ~ aLowerBoundOfIn0(sK1_skl(X1,xS),X2,xS)
| ~ aSubsetOf0(X2,xS)
| ~ aSet0(xS)
| ~ aSubsetOf0(X2,xS)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f3554,f764]) ).
fof(f10257,plain,
! [X0,X1,X2] :
( ~ sQ437_spl
| aLowerBoundOfIn0(sK4_skl(sK1_skl(X1,xS),X2,xS),X2,xS)
| ~ aLowerBoundOfIn0(sK1_skl(X1,xS),X2,xS)
| ~ aSubsetOf0(X2,xS)
| ~ aSet0(xS)
| ~ aSubsetOf0(X2,xS)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f3554,f763]) ).
fof(f10258,definition,
! [X0,X1,X2] :
( sQ1116_spl
<=> ( ~ sdtlseqdt0(sK4_skl(sK1_skl(X1,xS),X2,xS),sK1_skl(X1,xS))
| ~ aLowerBoundOfIn0(sK1_skl(X1,xS),X2,xS)
| ~ aSubsetOf0(X2,xS)
| ~ aSubsetOf0(X2,xS)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ1116_spl])],[split_symbol_definition]) ).
fof(f10261,plain,
( ~ sQ437_spl
| ~ sQ21_spl
| sQ1116_spl ),
inference(split_clause,[status(thm)],[f10256,f10258,f342,f3553]) ).
fof(f10262,definition,
! [X0,X1,X2] :
( sQ1117_spl
<=> ( aLowerBoundOfIn0(sK4_skl(sK1_skl(X1,xS),X2,xS),X2,xS)
| ~ aLowerBoundOfIn0(sK1_skl(X1,xS),X2,xS)
| ~ aSubsetOf0(X2,xS)
| ~ aSubsetOf0(X2,xS)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ1117_spl])],[split_symbol_definition]) ).
fof(f10265,plain,
( ~ sQ437_spl
| ~ sQ21_spl
| sQ1117_spl ),
inference(split_clause,[status(thm)],[f10257,f10262,f342,f3553]) ).
fof(f10271,plain,
! [X0,X1,X2] :
( ~ sQ438_spl
| ~ aElementOf0(sK1_skl(X2,xS),xS)
| ~ aSet0(X2)
| ~ aSet0(xS)
| ~ aElementOf0(sK1_skl(X1,xS),X2)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ),
inference(resolution,[status(thm)],[f3558,f52]) ).
fof(f10272,definition,
! [X0,X1,X2] :
( sQ1118_spl
<=> ( ~ aElementOf0(sK1_skl(X2,xS),xS)
| ~ aSet0(X2)
| ~ aElementOf0(sK1_skl(X1,xS),X2)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1)
| sdtlpdtrp0(xf,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ1118_spl])],[split_symbol_definition]) ).
fof(f10275,plain,
( ~ sQ438_spl
| ~ sQ21_spl
| sQ1118_spl ),
inference(split_clause,[status(thm)],[f10271,f10272,f342,f3557]) ).
fof(f10352,plain,
! [X0,X1] :
( ~ sQ61_spl
| ~ aUpperBoundOfIn0(X0,X1,xP)
| aSupremumOfIn0(X0,X1,xP)
| ~ aSubsetOf0(X1,xP)
| ~ aSet0(xP)
| xp = sK5_skl(X0,X1,xP)
| ~ sdtlseqdt0(sK5_skl(X0,X1,xP),xp) ),
inference(resolution,[status(thm)],[f3593,f767]) ).
fof(f10353,plain,
( ~ sQ241_spl
| ~ sQ61_spl
| xp = sdtlpdtrp0(xf,xp)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),xp) ),
inference(resolution,[status(thm)],[f3593,f1987]) ).
fof(f10355,plain,
! [X0] :
( ~ sQ61_spl
| ~ aSet0(xP)
| aSubsetOf0(xP,X0)
| ~ aSet0(X0)
| xp = sK1_skl(xP,X0)
| ~ sdtlseqdt0(sK1_skl(xP,X0),xp) ),
inference(resolution,[status(thm)],[f3593,f51]) ).
fof(f10362,plain,
! [X0,X1] :
( ~ sQ61_spl
| ~ aInfimumOfIn0(X0,X1,xP)
| ~ aSubsetOf0(X1,xP)
| ~ aSet0(xP)
| xp = X0
| ~ sdtlseqdt0(X0,xp) ),
inference(resolution,[status(thm)],[f3593,f81]) ).
fof(f10363,plain,
! [X0,X1] :
( ~ sQ61_spl
| ~ aElementOf0(X0,X1)
| ~ aSubsetOf0(X1,xP)
| ~ aSet0(xP)
| xp = X0
| ~ sdtlseqdt0(X0,xp) ),
inference(resolution,[status(thm)],[f3593,f50]) ).
fof(f10395,definition,
! [X0,X1] :
( sQ1138_spl
<=> ( ~ aUpperBoundOfIn0(X0,X1,xP)
| aSupremumOfIn0(X0,X1,xP)
| ~ aSubsetOf0(X1,xP)
| xp = sK5_skl(X0,X1,xP)
| ~ sdtlseqdt0(sK5_skl(X0,X1,xP),xp) ) ),
introduced(definition,[new_symbols(definition,[sQ1138_spl])],[split_symbol_definition]) ).
fof(f10398,plain,
( ~ sQ61_spl
| ~ sQ54_spl
| sQ1138_spl ),
inference(split_clause,[status(thm)],[f10352,f10395,f544,f608]) ).
fof(f10399,plain,
( ~ sQ241_spl
| ~ sQ61_spl
| sQ8_spl
| ~ sQ280_spl ),
inference(split_clause,[status(thm)],[f10353,f2235,f264,f608,f1986]) ).
fof(f10400,definition,
! [X0] :
( sQ1139_spl
<=> ( aSubsetOf0(xP,X0)
| ~ aSet0(X0)
| xp = sK1_skl(xP,X0)
| ~ sdtlseqdt0(sK1_skl(xP,X0),xp) ) ),
introduced(definition,[new_symbols(definition,[sQ1139_spl])],[split_symbol_definition]) ).
fof(f10403,plain,
( ~ sQ61_spl
| ~ sQ54_spl
| sQ1139_spl ),
inference(split_clause,[status(thm)],[f10355,f10400,f544,f608]) ).
fof(f10415,definition,
! [X0,X1] :
( sQ1143_spl
<=> ( ~ aInfimumOfIn0(X0,X1,xP)
| ~ aSubsetOf0(X1,xP)
| xp = X0
| ~ sdtlseqdt0(X0,xp) ) ),
introduced(definition,[new_symbols(definition,[sQ1143_spl])],[split_symbol_definition]) ).
fof(f10418,plain,
( ~ sQ61_spl
| ~ sQ54_spl
| sQ1143_spl ),
inference(split_clause,[status(thm)],[f10362,f10415,f544,f608]) ).
fof(f10419,definition,
! [X0,X1] :
( sQ1144_spl
<=> ( ~ aElementOf0(X0,X1)
| ~ aSubsetOf0(X1,xP)
| xp = X0
| ~ sdtlseqdt0(X0,xp) ) ),
introduced(definition,[new_symbols(definition,[sQ1144_spl])],[split_symbol_definition]) ).
fof(f10422,plain,
( ~ sQ61_spl
| ~ sQ54_spl
| sQ1144_spl ),
inference(split_clause,[status(thm)],[f10363,f10419,f544,f608]) ).
fof(f10423,plain,
$false,
inference(sat_refutation,[status(thm)],[f244,f248,f252,f256,f260,f267,f271,f277,f281,f285,f289,f303,f308,f310,f312,f320,f322,f327,f345,f352,f356,f358,f366,f370,f374,f381,f385,f398,f405,f418,f424,f431,f462,f469,f482,f489,f501,f508,f517,f521,f530,f534,f542,f550,f552,f564,f574,f617,f623,f625,f632,f651,f657,f670,f682,f683,f688,f708,f721,f725,f750,f754,f755,f758,f772,f783,f811,f815,f842,f863,f875,f888,f900,f915,f928,f936,f945,f949,f956,f960,f971,f976,f982,f986,f993,f1000,f1037,f1080,f1089,f1096,f1102,f1106,f1134,f1169,f1188,f1225,f1241,f1256,f1284,f1333,f1379,f1393,f1459,f1470,f1475,f1490,f1494,f1502,f1509,f1512,f1518,f1524,f1528,f1535,f1547,f1551,f1561,f1565,f1569,f1572,f1582,f1597,f1603,f1607,f1613,f1621,f1627,f1631,f1651,f1705,f1710,f1717,f1737,f1760,f1780,f1784,f1798,f1845,f1861,f1907,f1911,f1933,f1937,f1941,f1944,f1971,f1989,f2048,f2138,f2215,f2238,f2259,f2296,f2304,f2392,f2396,f2407,f2408,f2431,f2441,f2456,f2606,f2613,f2617,f2621,f2623,f2635,f2650,f2654,f2658,f2662,f2670,f2673,f2693,f2701,f2708,f2712,f2748,f2769,f2862,f2867,f2872,f2901,f2905,f2975,f2979,f3001,f3005,f3009,f3024,f3066,f3073,f3077,f3116,f3121,f3131,f3144,f3219,f3223,f3266,f3283,f3318,f3320,f3325,f3373,f3377,f3384,f3419,f3465,f3466,f3467,f3468,f3537,f3542,f3556,f3560,f3697,f3698,f3745,f3749,f3753,f3764,f3788,f3826,f3868,f3886,f3919,f3944,f4000,f4047,f4056,f4057,f4061,f4064,f4065,f4093,f4136,f4313,f4341,f4389,f4393,f4394,f4398,f4402,f4421,f4425,f4429,f4483,f4487,f4498,f4502,f4530,f4561,f4582,f4583,f4656,f4659,f4660,f4730,f4781,f4835,f4844,f4856,f4859,f4883,f4884,f4885,f4886,f4887,f4921,f4928,f4993,f4997,f5166,f5368,f5413,f5529,f5533,f5537,f5548,f5552,f5556,f5668,f5672,f5696,f5699,f5703,f5707,f5711,f5717,f5745,f5749,f5754,f5766,f5820,f5824,f6074,f6107,f6111,f6115,f6137,f6151,f6161,f6162,f6270,f6274,f6278,f6349,f6360,f6443,f6447,f6451,f6460,f6464,f6468,f6719,f6912,f6916,f7174,f7318,f7375,f7658,f8081,f8085,f8094,f8107,f8378,f8382,f8466,f8470,f8471,f8484,f8485,f8888,f8892,f8956,f8960,f8964,f9057,f9061,f9843,f9847,f9899,f10065,f10069,f10202,f10206,f10219,f10224,f10261,f10265,f10275,f10398,f10399,f10403,f10418,f10422]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT387+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n007.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sun Sep 20 23:55:50 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.45 % Drodi V4.1.1
% 38.28/5.37 % Refutation found
% 38.28/5.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 38.28/5.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.53/5.45 % Elapsed time: 5.001917 seconds
% 3.53/5.45 % CPU time: 39.006539 seconds
% 3.53/5.45 % Total memory used: 251.163 MB
% 3.53/5.45 % Net memory used: 234.442 MB
%------------------------------------------------------------------------------