%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LAT386+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 01:03:57 PM UTC 2026
% Result : CounterSatisfiable 0.11s 0.41s
% Output : Saturation 0.11s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% 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(f18,axiom,
! [W0] :
( aFunction0(W0)
=> aSet0(szDzozmdt0(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)
& isMonotone0(xf)
& aFunction0(xf)
& aCompleteLattice0(xU) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,hypothesis,
xS = cS1142(xf),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,hypothesis,
aSubsetOf0(xT,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
xP = cS1241(xU,xf,xT),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
aInfimumOfIn0(xp,xP,xU),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
( aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
& aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ( aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
& aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f37,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f38,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
! [W0] :
( ( isEmpty0(W0)
<=> ! [W1] : ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f40,plain,
! [W0] :
( ( ( ? [W1] : aElementOf0(W1,W0)
| isEmpty0(W0) )
& ( ! [W1] : ~ aElementOf0(W1,W0)
| ~ isEmpty0(W0) ) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f39]) ).
fof(f41,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))],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| ~ isEmpty0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0] :
( aElementOf0(sK0_skl(X0),X0)
| isEmpty0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f44,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(f45,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)],[f44]) ).
fof(f46,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)],[f45]) ).
fof(f47,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))],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
! [X0,X1] :
( aElementOf0(sK1_skl(X1,X0),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f51,plain,
! [X0,X1] :
( ~ aElementOf0(sK1_skl(X1,X0),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f54,plain,
! [W0] :
( sdtlseqdt0(W0,W0)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f55,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
! [W0,W1] :
( W0 = W1
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f57,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [W0,W1,W2] :
( sdtlseqdt0(W0,W2)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f59,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f60,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(f61,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)],[f60]) ).
fof(f62,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)],[f61]) ).
fof(f63,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))],[f62]) ).
fof(f64,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aLowerBoundOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f65,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)],[f63]) ).
fof(f66,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)],[f63]) ).
fof(f67,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)],[f63]) ).
fof(f68,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(f69,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)],[f68]) ).
fof(f70,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)],[f69]) ).
fof(f71,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))],[f70]) ).
fof(f72,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aUpperBoundOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f73,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)],[f71]) ).
fof(f74,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)],[f71]) ).
fof(f75,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)],[f71]) ).
fof(f76,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(f77,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)],[f76]) ).
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) )
& ! [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)],[f77]) ).
fof(f79,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))],[f78]) ).
fof(f80,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aInfimumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f81,plain,
! [X0,X1,X2] :
( aLowerBoundOfIn0(X2,X1,X0)
| ~ aInfimumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f82,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)],[f79]) ).
fof(f83,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)],[f79]) ).
fof(f84,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)],[f79]) ).
fof(f85,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(f86,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)],[f85]) ).
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) )
& ! [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)],[f86]) ).
fof(f88,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))],[f87]) ).
fof(f89,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aSupremumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f90,plain,
! [X0,X1,X2] :
( aUpperBoundOfIn0(X2,X1,X0)
| ~ aSupremumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f91,plain,
! [X0,X1,X2,X3] :
( sdtlseqdt0(X2,X3)
| ~ aUpperBoundOfIn0(X3,X1,X0)
| ~ aSupremumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f92,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)],[f88]) ).
fof(f93,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)],[f88]) ).
fof(f94,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(f95,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)],[f94]) ).
fof(f96,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(f97,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)],[f96]) ).
fof(f98,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(f99,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)],[f98]) ).
fof(f100,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)],[f99]) ).
fof(f101,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))],[f100]) ).
fof(f102,plain,
! [X0] :
( aSet0(X0)
| ~ aCompleteLattice0(X0) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f103,plain,
! [X0,X1] :
( aInfimumOfIn0(sK6_skl(X1,X0),X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aCompleteLattice0(X0) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f104,plain,
! [X0,X1] :
( aSupremumOfIn0(sK7_skl(X1,X0),X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aCompleteLattice0(X0) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f105,plain,
! [X0] :
( aSubsetOf0(sK8_skl(X0),X0)
| ~ aSet0(X0)
| aCompleteLattice0(X0) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f106,plain,
! [X0,X1,X2] :
( ~ aSupremumOfIn0(X2,sK8_skl(X0),X0)
| ~ aInfimumOfIn0(X1,sK8_skl(X0),X0)
| ~ aSet0(X0)
| aCompleteLattice0(X0) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f110,plain,
! [W0] :
( aSet0(szDzozmdt0(W0))
| ~ aFunction0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f111,plain,
! [X0] :
( aSet0(szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f112,plain,
! [W0] :
( aSet0(szRzazndt0(W0))
| ~ aFunction0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f113,plain,
! [X0] :
( aSet0(szRzazndt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f114,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(f115,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)],[f114]) ).
fof(f116,plain,
! [X0,X1] :
( szDzozmdt0(X0) = szRzazndt0(X0)
| ~ isOn0(X0,X1)
| ~ aSet0(X1)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
! [X0,X1] :
( szRzazndt0(X0) = X1
| ~ isOn0(X0,X1)
| ~ aSet0(X1)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f118,plain,
! [X0,X1] :
( szRzazndt0(X0) != X1
| szDzozmdt0(X0) != szRzazndt0(X0)
| isOn0(X0,X1)
| ~ aSet0(X1)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f119,plain,
! [W0] :
( ! [W1] :
( aElementOf0(sdtlpdtrp0(W0,W1),szRzazndt0(W0))
| ~ aElementOf0(W1,szDzozmdt0(W0)) )
| ~ aFunction0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f120,plain,
! [X0,X1] :
( aElementOf0(sdtlpdtrp0(X0,X1),szRzazndt0(X0))
| ~ aElementOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f121,plain,
! [W0] :
( ! [W1] :
( aFixedPointOf0(W1,W0)
<=> ( sdtlpdtrp0(W0,W1) = W1
& aElementOf0(W1,szDzozmdt0(W0)) ) )
| ~ aFunction0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f122,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)],[f121]) ).
fof(f123,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)],[f122]) ).
fof(f124,plain,
! [X0,X1] :
( aElementOf0(X1,szDzozmdt0(X0))
| ~ aFixedPointOf0(X1,X0)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f125,plain,
! [X0,X1] :
( sdtlpdtrp0(X0,X1) = X1
| ~ aFixedPointOf0(X1,X0)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f126,plain,
! [X0,X1] :
( sdtlpdtrp0(X0,X1) != X1
| ~ aElementOf0(X1,szDzozmdt0(X0))
| aFixedPointOf0(X1,X0)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f127,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(f128,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)],[f127]) ).
fof(f129,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))],[f128]) ).
fof(f130,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)],[f129]) ).
fof(f131,plain,
! [X0] :
( aElementOf0(sK9_skl(X0),szDzozmdt0(X0))
| isMonotone0(X0)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f132,plain,
! [X0] :
( aElementOf0(sK10_skl(X0),szDzozmdt0(X0))
| isMonotone0(X0)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f133,plain,
! [X0] :
( sdtlseqdt0(sK9_skl(X0),sK10_skl(X0))
| isMonotone0(X0)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f134,plain,
! [X0] :
( ~ sdtlseqdt0(sdtlpdtrp0(X0,sK9_skl(X0)),sdtlpdtrp0(X0,sK10_skl(X0)))
| isMonotone0(X0)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f135,plain,
aCompleteLattice0(xU),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f136,plain,
aFunction0(xf),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f137,plain,
isMonotone0(xf),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f138,plain,
isOn0(xf,xU),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f139,plain,
xS = cS1142(xf),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f140,plain,
aSubsetOf0(xT,xS),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f141,plain,
xP = cS1241(xU,xf,xT),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f142,plain,
aInfimumOfIn0(xp,xP,xU),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f143,plain,
( ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
| ~ aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f144,plain,
( ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
| ~ aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU) ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f145,definition,
( sQ0_spl
<=> aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f147,plain,
( sQ0_spl
| ~ aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU) ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,definition,
( sQ1_spl
<=> aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f151,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f144,f145,f148]) ).
fof(f152,plain,
aSet0(xU),
inference(resolution,[status(thm)],[f102,f135]) ).
fof(f153,plain,
( aElementOf0(sK0_skl(xU),xU)
| isEmpty0(xU) ),
inference(resolution,[status(thm)],[f43,f152]) ).
fof(f154,definition,
( sQ2_spl
<=> isEmpty0(xU) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f155,plain,
( ~ sQ2_spl
| isEmpty0(xU) ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f156,plain,
( sQ2_spl
| ~ isEmpty0(xU) ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,definition,
( sQ3_spl
<=> aElementOf0(sK0_skl(xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f158,plain,
( ~ sQ3_spl
| aElementOf0(sK0_skl(xU),xU) ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f153,f154,f157]) ).
fof(f161,plain,
( aLowerBoundOfIn0(xp,xP,xU)
| ~ aSubsetOf0(xP,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f81,f142]) ).
fof(f162,definition,
( sQ4_spl
<=> aSet0(xU) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f164,plain,
( sQ4_spl
| ~ aSet0(xU) ),
inference(component_clause,[status(thm)],[f162]) ).
fof(f165,definition,
( sQ5_spl
<=> aSubsetOf0(xP,xU) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( sQ5_spl
| ~ aSubsetOf0(xP,xU) ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,definition,
( sQ6_spl
<=> aLowerBoundOfIn0(xp,xP,xU) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f169,plain,
( ~ sQ6_spl
| aLowerBoundOfIn0(xp,xP,xU) ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,plain,
( sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f161,f162,f165,f168]) ).
fof(f172,plain,
! [X0] :
( sdtlseqdt0(X0,xp)
| ~ aLowerBoundOfIn0(X0,xP,xU)
| ~ aSubsetOf0(xP,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f82,f142]) ).
fof(f173,definition,
! [X0] :
( sQ7_spl
<=> ( sdtlseqdt0(X0,xp)
| ~ aLowerBoundOfIn0(X0,xP,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f176,plain,
( sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f172,f162,f165,f173]) ).
fof(f177,plain,
( aSet0(xT)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f48,f140]) ).
fof(f178,definition,
( sQ8_spl
<=> aSet0(xS) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( sQ8_spl
| ~ aSet0(xS) ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f181,definition,
( sQ9_spl
<=> aSet0(xT) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f184,plain,
( sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f177,f178,f181]) ).
fof(f185,plain,
! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xT)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f49,f140]) ).
fof(f186,definition,
! [X0] :
( sQ10_spl
<=> ( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xT) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f189,plain,
( sQ10_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f185,f178,f186]) ).
fof(f190,plain,
! [X0] :
( aElementOf0(sK1_skl(X0,xU),X0)
| ~ aSet0(X0)
| aSubsetOf0(X0,xU) ),
inference(resolution,[status(thm)],[f50,f152]) ).
fof(f191,plain,
( aElementOf0(sK1_skl(xU,xU),xU)
| aSubsetOf0(xU,xU) ),
inference(resolution,[status(thm)],[f190,f152]) ).
fof(f192,definition,
( sQ11_spl
<=> aSubsetOf0(xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f193,plain,
( ~ sQ11_spl
| aSubsetOf0(xU,xU) ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f195,definition,
( sQ12_spl
<=> aElementOf0(sK1_skl(xU,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f196,plain,
( ~ sQ12_spl
| aElementOf0(sK1_skl(xU,xU),xU) ),
inference(component_clause,[status(thm)],[f195]) ).
fof(f197,plain,
( sQ12_spl
| ~ aElementOf0(sK1_skl(xU,xU),xU) ),
inference(component_clause,[status(thm)],[f195]) ).
fof(f198,plain,
( sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f191,f192,f195]) ).
fof(f199,plain,
! [X0] :
( ~ sQ11_spl
| aElementOf0(X0,xU)
| ~ aElementOf0(X0,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f193,f49]) ).
fof(f201,definition,
! [X0] :
( sQ13_spl
<=> ( aElementOf0(X0,xU)
| ~ aElementOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f204,plain,
( ~ sQ11_spl
| sQ13_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f199,f162,f201,f192]) ).
fof(f206,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f164,f152]) ).
fof(f207,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f206]) ).
fof(f208,plain,
( ~ sQ12_spl
| ~ isEmpty0(xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f196,f42]) ).
fof(f209,plain,
( ~ sQ12_spl
| aElement0(sK1_skl(xU,xU))
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f196,f38]) ).
fof(f210,plain,
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f208,f162,f154,f195]) ).
fof(f211,definition,
( sQ14_spl
<=> aElement0(sK1_skl(xU,xU)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f212,plain,
( ~ sQ14_spl
| aElement0(sK1_skl(xU,xU)) ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f213,plain,
( sQ14_spl
| ~ aElement0(sK1_skl(xU,xU)) ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f214,plain,
( ~ sQ12_spl
| sQ14_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f209,f162,f211,f195]) ).
fof(f215,plain,
( ~ sQ3_spl
| ~ isEmpty0(xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f158,f42]) ).
fof(f216,plain,
( ~ sQ3_spl
| aElement0(sK0_skl(xU))
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f158,f38]) ).
fof(f217,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f215,f162,f154,f157]) ).
fof(f218,definition,
( sQ15_spl
<=> aElement0(sK0_skl(xU)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f219,plain,
( ~ sQ15_spl
| aElement0(sK0_skl(xU)) ),
inference(component_clause,[status(thm)],[f218]) ).
fof(f221,plain,
( ~ sQ3_spl
| sQ15_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f216,f162,f218,f157]) ).
fof(f222,plain,
( ~ sQ15_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(resolution,[status(thm)],[f55,f219]) ).
fof(f223,plain,
( ~ sQ14_spl
| sdtlseqdt0(sK1_skl(xU,xU),sK1_skl(xU,xU)) ),
inference(resolution,[status(thm)],[f212,f55]) ).
fof(f224,plain,
( ~ sQ12_spl
| ~ aSet0(xU)
| aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f196,f51]) ).
fof(f227,plain,
( ~ sQ12_spl
| sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f224,f162,f192,f195]) ).
fof(f234,plain,
! [X0] :
( ~ sQ15_spl
| sdtlseqdt0(sK0_skl(xU),X0)
| ~ sdtlseqdt0(sK0_skl(xU),X0)
| ~ aElement0(X0)
| ~ aElement0(sK0_skl(xU))
| ~ aElement0(sK0_skl(xU)) ),
inference(resolution,[status(thm)],[f222,f59]) ).
fof(f235,plain,
( ~ sQ15_spl
| sK0_skl(xU) = sK0_skl(xU)
| ~ sdtlseqdt0(sK0_skl(xU),sK0_skl(xU))
| ~ aElement0(sK0_skl(xU))
| ~ aElement0(sK0_skl(xU)) ),
inference(resolution,[status(thm)],[f222,f57]) ).
fof(f236,definition,
! [X0] :
( sQ16_spl
<=> ( sdtlseqdt0(sK0_skl(xU),X0)
| ~ sdtlseqdt0(sK0_skl(xU),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f239,plain,
( sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f234,f218,f236]) ).
fof(f240,definition,
( sQ17_spl
<=> sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f241,plain,
( ~ sQ17_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(component_clause,[status(thm)],[f240]) ).
fof(f242,plain,
( sQ17_spl
| ~ sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(component_clause,[status(thm)],[f240]) ).
fof(f243,definition,
( sQ18_spl
<=> sK0_skl(xU) = sK0_skl(xU) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f246,plain,
( sQ18_spl
| ~ sQ17_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f235,f218,f240,f243]) ).
fof(f247,plain,
( sQ17_spl
| ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f242,f222]) ).
fof(f248,plain,
( sQ17_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f247]) ).
fof(f249,plain,
! [X0] :
( ~ sQ11_spl
| aElementOf0(sK2_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f66,f193]) ).
fof(f250,plain,
! [X0] :
( aElementOf0(sK2_skl(X0,xT,xS),xT)
| ~ aElementOf0(X0,xS)
| aLowerBoundOfIn0(X0,xT,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f66,f140]) ).
fof(f251,definition,
! [X0] :
( sQ19_spl
<=> ( aElementOf0(sK2_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f252,plain,
! [X0] :
( ~ sQ19_spl
| aElementOf0(sK2_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(component_clause,[status(thm)],[f251]) ).
fof(f254,plain,
( ~ sQ11_spl
| sQ19_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f249,f162,f251,f192]) ).
fof(f255,definition,
! [X0] :
( sQ20_spl
<=> ( aElementOf0(sK2_skl(X0,xT,xS),xT)
| ~ aElementOf0(X0,xS)
| aLowerBoundOfIn0(X0,xT,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f258,plain,
( sQ20_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f250,f178,f255]) ).
fof(f259,plain,
aSet0(szDzozmdt0(xf)),
inference(resolution,[status(thm)],[f111,f136]) ).
fof(f260,plain,
( aElementOf0(sK1_skl(szDzozmdt0(xf),xU),szDzozmdt0(xf))
| aSubsetOf0(szDzozmdt0(xf),xU) ),
inference(resolution,[status(thm)],[f259,f190]) ).
fof(f261,plain,
! [X0] :
( aElementOf0(sK1_skl(X0,szDzozmdt0(xf)),X0)
| ~ aSet0(X0)
| aSubsetOf0(X0,szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f259,f50]) ).
fof(f262,plain,
( aElementOf0(sK0_skl(szDzozmdt0(xf)),szDzozmdt0(xf))
| isEmpty0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f259,f43]) ).
fof(f263,definition,
( sQ21_spl
<=> aSubsetOf0(szDzozmdt0(xf),xU) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f264,plain,
( ~ sQ21_spl
| aSubsetOf0(szDzozmdt0(xf),xU) ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f265,plain,
( sQ21_spl
| ~ aSubsetOf0(szDzozmdt0(xf),xU) ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f266,definition,
( sQ22_spl
<=> aElementOf0(sK1_skl(szDzozmdt0(xf),xU),szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f267,plain,
( ~ sQ22_spl
| aElementOf0(sK1_skl(szDzozmdt0(xf),xU),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f266]) ).
fof(f268,plain,
( sQ22_spl
| ~ aElementOf0(sK1_skl(szDzozmdt0(xf),xU),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f266]) ).
fof(f269,plain,
( sQ22_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f260,f263,f266]) ).
fof(f270,definition,
( sQ23_spl
<=> isEmpty0(szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f271,plain,
( ~ sQ23_spl
| isEmpty0(szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f270]) ).
fof(f272,plain,
( sQ23_spl
| ~ isEmpty0(szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f270]) ).
fof(f273,definition,
( sQ24_spl
<=> aElementOf0(sK0_skl(szDzozmdt0(xf)),szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f274,plain,
( ~ sQ24_spl
| aElementOf0(sK0_skl(szDzozmdt0(xf)),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f273]) ).
fof(f276,plain,
( sQ24_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f262,f270,f273]) ).
fof(f277,plain,
! [X0] :
( ~ sQ11_spl
| aElementOf0(sK3_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f74,f193]) ).
fof(f278,plain,
! [X0] :
( aElementOf0(sK3_skl(X0,xT,xS),xT)
| ~ aElementOf0(X0,xS)
| aUpperBoundOfIn0(X0,xT,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f74,f140]) ).
fof(f279,definition,
! [X0] :
( sQ25_spl
<=> ( aElementOf0(sK3_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f280,plain,
! [X0] :
( ~ sQ25_spl
| aElementOf0(sK3_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(component_clause,[status(thm)],[f279]) ).
fof(f282,plain,
( ~ sQ11_spl
| sQ25_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f277,f162,f279,f192]) ).
fof(f283,definition,
! [X0] :
( sQ26_spl
<=> ( aElementOf0(sK3_skl(X0,xT,xS),xT)
| ~ aElementOf0(X0,xS)
| aUpperBoundOfIn0(X0,xT,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f286,plain,
( sQ26_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f278,f178,f283]) ).
fof(f287,plain,
! [X0] :
( ~ sQ21_spl
| aElementOf0(sK3_skl(X0,szDzozmdt0(xf),xU),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,szDzozmdt0(xf),xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f264,f74]) ).
fof(f288,plain,
! [X0] :
( ~ sQ21_spl
| aElementOf0(sK2_skl(X0,szDzozmdt0(xf),xU),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,szDzozmdt0(xf),xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f264,f66]) ).
fof(f289,plain,
! [X0] :
( ~ sQ21_spl
| aElementOf0(X0,xU)
| ~ aElementOf0(X0,szDzozmdt0(xf))
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f264,f49]) ).
fof(f291,definition,
! [X0] :
( sQ27_spl
<=> ( aElementOf0(sK3_skl(X0,szDzozmdt0(xf),xU),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,szDzozmdt0(xf),xU) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f292,plain,
! [X0] :
( ~ sQ27_spl
| aElementOf0(sK3_skl(X0,szDzozmdt0(xf),xU),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,szDzozmdt0(xf),xU) ),
inference(component_clause,[status(thm)],[f291]) ).
fof(f294,plain,
( ~ sQ21_spl
| sQ27_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f287,f162,f291,f263]) ).
fof(f295,definition,
! [X0] :
( sQ28_spl
<=> ( aElementOf0(sK2_skl(X0,szDzozmdt0(xf),xU),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,szDzozmdt0(xf),xU) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f296,plain,
! [X0] :
( ~ sQ28_spl
| aElementOf0(sK2_skl(X0,szDzozmdt0(xf),xU),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,szDzozmdt0(xf),xU) ),
inference(component_clause,[status(thm)],[f295]) ).
fof(f298,plain,
( ~ sQ21_spl
| sQ28_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f288,f162,f295,f263]) ).
fof(f299,definition,
! [X0] :
( sQ29_spl
<=> ( aElementOf0(X0,xU)
| ~ aElementOf0(X0,szDzozmdt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f300,plain,
! [X0] :
( ~ sQ29_spl
| aElementOf0(X0,xU)
| ~ aElementOf0(X0,szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f299]) ).
fof(f302,plain,
( ~ sQ21_spl
| sQ29_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f289,f162,f299,f263]) ).
fof(f303,definition,
( sQ30_spl
<=> aSet0(szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f305,plain,
( sQ30_spl
| ~ aSet0(szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f303]) ).
fof(f307,plain,
( aElementOf0(sK1_skl(szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| aSubsetOf0(szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f261,f259]) ).
fof(f308,plain,
( aElementOf0(sK1_skl(xU,szDzozmdt0(xf)),xU)
| aSubsetOf0(xU,szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f261,f152]) ).
fof(f309,definition,
( sQ31_spl
<=> aSubsetOf0(szDzozmdt0(xf),szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f310,plain,
( ~ sQ31_spl
| aSubsetOf0(szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f309]) ).
fof(f311,plain,
( sQ31_spl
| ~ aSubsetOf0(szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f309]) ).
fof(f312,definition,
( sQ32_spl
<=> aElementOf0(sK1_skl(szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f313,plain,
( ~ sQ32_spl
| aElementOf0(sK1_skl(szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f312]) ).
fof(f314,plain,
( sQ32_spl
| ~ aElementOf0(sK1_skl(szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f312]) ).
fof(f315,plain,
( sQ32_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f307,f309,f312]) ).
fof(f316,definition,
( sQ33_spl
<=> aSubsetOf0(xU,szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f317,plain,
( ~ sQ33_spl
| aSubsetOf0(xU,szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f316]) ).
fof(f318,plain,
( sQ33_spl
| ~ aSubsetOf0(xU,szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f316]) ).
fof(f319,definition,
( sQ34_spl
<=> aElementOf0(sK1_skl(xU,szDzozmdt0(xf)),xU) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f320,plain,
( ~ sQ34_spl
| aElementOf0(sK1_skl(xU,szDzozmdt0(xf)),xU) ),
inference(component_clause,[status(thm)],[f319]) ).
fof(f321,plain,
( sQ34_spl
| ~ aElementOf0(sK1_skl(xU,szDzozmdt0(xf)),xU) ),
inference(component_clause,[status(thm)],[f319]) ).
fof(f322,plain,
( sQ34_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f308,f316,f319]) ).
fof(f323,plain,
! [X0] :
( ~ sQ33_spl
| aElementOf0(sK3_skl(X0,xU,szDzozmdt0(xf)),xU)
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aUpperBoundOfIn0(X0,xU,szDzozmdt0(xf))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f317,f74]) ).
fof(f324,plain,
! [X0] :
( ~ sQ33_spl
| aElementOf0(sK2_skl(X0,xU,szDzozmdt0(xf)),xU)
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aLowerBoundOfIn0(X0,xU,szDzozmdt0(xf))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f317,f66]) ).
fof(f325,plain,
! [X0] :
( ~ sQ33_spl
| aElementOf0(X0,szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f317,f49]) ).
fof(f326,plain,
( ~ sQ33_spl
| aSet0(xU)
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f317,f48]) ).
fof(f327,definition,
! [X0] :
( sQ35_spl
<=> ( aElementOf0(sK3_skl(X0,xU,szDzozmdt0(xf)),xU)
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aUpperBoundOfIn0(X0,xU,szDzozmdt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f328,plain,
! [X0] :
( ~ sQ35_spl
| aElementOf0(sK3_skl(X0,xU,szDzozmdt0(xf)),xU)
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aUpperBoundOfIn0(X0,xU,szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f327]) ).
fof(f330,plain,
( ~ sQ33_spl
| sQ35_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f323,f303,f327,f316]) ).
fof(f331,definition,
! [X0] :
( sQ36_spl
<=> ( aElementOf0(sK2_skl(X0,xU,szDzozmdt0(xf)),xU)
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aLowerBoundOfIn0(X0,xU,szDzozmdt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f332,plain,
! [X0] :
( ~ sQ36_spl
| aElementOf0(sK2_skl(X0,xU,szDzozmdt0(xf)),xU)
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aLowerBoundOfIn0(X0,xU,szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f331]) ).
fof(f334,plain,
( ~ sQ33_spl
| sQ36_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f324,f303,f331,f316]) ).
fof(f335,definition,
! [X0] :
( sQ37_spl
<=> ( aElementOf0(X0,szDzozmdt0(xf))
| ~ aElementOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f336,plain,
! [X0] :
( ~ sQ37_spl
| aElementOf0(X0,szDzozmdt0(xf))
| ~ aElementOf0(X0,xU) ),
inference(component_clause,[status(thm)],[f335]) ).
fof(f338,plain,
( ~ sQ33_spl
| sQ37_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f325,f303,f335,f316]) ).
fof(f339,plain,
( ~ sQ33_spl
| sQ4_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f326,f303,f162,f316]) ).
fof(f340,plain,
( sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f305,f259]) ).
fof(f341,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f340]) ).
fof(f342,plain,
( ~ sQ22_spl
| ~ isEmpty0(szDzozmdt0(xf))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f267,f42]) ).
fof(f343,plain,
( ~ sQ22_spl
| aElement0(sK1_skl(szDzozmdt0(xf),xU))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f267,f38]) ).
fof(f344,plain,
( ~ sQ22_spl
| ~ sQ23_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f342,f303,f270,f266]) ).
fof(f345,definition,
( sQ38_spl
<=> aElement0(sK1_skl(szDzozmdt0(xf),xU)) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f346,plain,
( ~ sQ38_spl
| aElement0(sK1_skl(szDzozmdt0(xf),xU)) ),
inference(component_clause,[status(thm)],[f345]) ).
fof(f348,plain,
( ~ sQ22_spl
| sQ38_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f343,f303,f345,f266]) ).
fof(f349,plain,
( ~ sQ24_spl
| ~ isEmpty0(szDzozmdt0(xf))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f274,f42]) ).
fof(f350,plain,
( ~ sQ24_spl
| aElement0(sK0_skl(szDzozmdt0(xf)))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f274,f38]) ).
fof(f351,plain,
( ~ sQ24_spl
| ~ sQ23_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f349,f303,f270,f273]) ).
fof(f352,definition,
( sQ39_spl
<=> aElement0(sK0_skl(szDzozmdt0(xf))) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f353,plain,
( ~ sQ39_spl
| aElement0(sK0_skl(szDzozmdt0(xf))) ),
inference(component_clause,[status(thm)],[f352]) ).
fof(f355,plain,
( ~ sQ24_spl
| sQ39_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f350,f303,f352,f273]) ).
fof(f356,plain,
aSet0(szRzazndt0(xf)),
inference(resolution,[status(thm)],[f113,f136]) ).
fof(f357,plain,
( aElementOf0(sK1_skl(szRzazndt0(xf),szDzozmdt0(xf)),szRzazndt0(xf))
| aSubsetOf0(szRzazndt0(xf),szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f356,f261]) ).
fof(f358,plain,
( aElementOf0(sK1_skl(szRzazndt0(xf),xU),szRzazndt0(xf))
| aSubsetOf0(szRzazndt0(xf),xU) ),
inference(resolution,[status(thm)],[f356,f190]) ).
fof(f359,plain,
! [X0] :
( aElementOf0(sK1_skl(X0,szRzazndt0(xf)),X0)
| ~ aSet0(X0)
| aSubsetOf0(X0,szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f356,f50]) ).
fof(f360,plain,
( aElementOf0(sK0_skl(szRzazndt0(xf)),szRzazndt0(xf))
| isEmpty0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f356,f43]) ).
fof(f361,definition,
( sQ40_spl
<=> aSubsetOf0(szRzazndt0(xf),szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f362,plain,
( ~ sQ40_spl
| aSubsetOf0(szRzazndt0(xf),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f361]) ).
fof(f363,plain,
( sQ40_spl
| ~ aSubsetOf0(szRzazndt0(xf),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f361]) ).
fof(f364,definition,
( sQ41_spl
<=> aElementOf0(sK1_skl(szRzazndt0(xf),szDzozmdt0(xf)),szRzazndt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f365,plain,
( ~ sQ41_spl
| aElementOf0(sK1_skl(szRzazndt0(xf),szDzozmdt0(xf)),szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f364]) ).
fof(f366,plain,
( sQ41_spl
| ~ aElementOf0(sK1_skl(szRzazndt0(xf),szDzozmdt0(xf)),szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f364]) ).
fof(f367,plain,
( sQ41_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f357,f361,f364]) ).
fof(f368,definition,
( sQ42_spl
<=> aSubsetOf0(szRzazndt0(xf),xU) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f369,plain,
( ~ sQ42_spl
| aSubsetOf0(szRzazndt0(xf),xU) ),
inference(component_clause,[status(thm)],[f368]) ).
fof(f370,plain,
( sQ42_spl
| ~ aSubsetOf0(szRzazndt0(xf),xU) ),
inference(component_clause,[status(thm)],[f368]) ).
fof(f371,definition,
( sQ43_spl
<=> aElementOf0(sK1_skl(szRzazndt0(xf),xU),szRzazndt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f372,plain,
( ~ sQ43_spl
| aElementOf0(sK1_skl(szRzazndt0(xf),xU),szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f371]) ).
fof(f373,plain,
( sQ43_spl
| ~ aElementOf0(sK1_skl(szRzazndt0(xf),xU),szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f371]) ).
fof(f374,plain,
( sQ43_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f358,f368,f371]) ).
fof(f375,definition,
( sQ44_spl
<=> isEmpty0(szRzazndt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f376,plain,
( ~ sQ44_spl
| isEmpty0(szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f375]) ).
fof(f377,plain,
( sQ44_spl
| ~ isEmpty0(szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f375]) ).
fof(f378,definition,
( sQ45_spl
<=> aElementOf0(sK0_skl(szRzazndt0(xf)),szRzazndt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f379,plain,
( ~ sQ45_spl
| aElementOf0(sK0_skl(szRzazndt0(xf)),szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f378]) ).
fof(f381,plain,
( sQ45_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f360,f375,f378]) ).
fof(f382,plain,
( aElementOf0(xp,xU)
| ~ aSubsetOf0(xP,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f80,f142]) ).
fof(f383,definition,
( sQ46_spl
<=> aElementOf0(xp,xU) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f386,plain,
( sQ46_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f382,f162,f165,f383]) ).
fof(f387,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)],[f83,f64]) ).
fof(f388,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)],[f84,f64]) ).
fof(f389,plain,
( aElementOf0(sK1_skl(szRzazndt0(xf),szRzazndt0(xf)),szRzazndt0(xf))
| aSubsetOf0(szRzazndt0(xf),szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f359,f356]) ).
fof(f390,plain,
( aElementOf0(sK1_skl(szDzozmdt0(xf),szRzazndt0(xf)),szDzozmdt0(xf))
| aSubsetOf0(szDzozmdt0(xf),szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f359,f259]) ).
fof(f391,plain,
( aElementOf0(sK1_skl(xU,szRzazndt0(xf)),xU)
| aSubsetOf0(xU,szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f359,f152]) ).
fof(f392,definition,
( sQ47_spl
<=> aSubsetOf0(szRzazndt0(xf),szRzazndt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f393,plain,
( ~ sQ47_spl
| aSubsetOf0(szRzazndt0(xf),szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f392]) ).
fof(f394,plain,
( sQ47_spl
| ~ aSubsetOf0(szRzazndt0(xf),szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f392]) ).
fof(f395,definition,
( sQ48_spl
<=> aElementOf0(sK1_skl(szRzazndt0(xf),szRzazndt0(xf)),szRzazndt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f396,plain,
( ~ sQ48_spl
| aElementOf0(sK1_skl(szRzazndt0(xf),szRzazndt0(xf)),szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f395]) ).
fof(f397,plain,
( sQ48_spl
| ~ aElementOf0(sK1_skl(szRzazndt0(xf),szRzazndt0(xf)),szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f395]) ).
fof(f398,plain,
( sQ48_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f389,f392,f395]) ).
fof(f399,definition,
( sQ49_spl
<=> aSubsetOf0(szDzozmdt0(xf),szRzazndt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f400,plain,
( ~ sQ49_spl
| aSubsetOf0(szDzozmdt0(xf),szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f399]) ).
fof(f401,plain,
( sQ49_spl
| ~ aSubsetOf0(szDzozmdt0(xf),szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f399]) ).
fof(f402,definition,
( sQ50_spl
<=> aElementOf0(sK1_skl(szDzozmdt0(xf),szRzazndt0(xf)),szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f403,plain,
( ~ sQ50_spl
| aElementOf0(sK1_skl(szDzozmdt0(xf),szRzazndt0(xf)),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f402]) ).
fof(f404,plain,
( sQ50_spl
| ~ aElementOf0(sK1_skl(szDzozmdt0(xf),szRzazndt0(xf)),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f402]) ).
fof(f405,plain,
( sQ50_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f390,f399,f402]) ).
fof(f406,definition,
( sQ51_spl
<=> aSubsetOf0(xU,szRzazndt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f407,plain,
( ~ sQ51_spl
| aSubsetOf0(xU,szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f406]) ).
fof(f408,plain,
( sQ51_spl
| ~ aSubsetOf0(xU,szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f406]) ).
fof(f409,definition,
( sQ52_spl
<=> aElementOf0(sK1_skl(xU,szRzazndt0(xf)),xU) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f410,plain,
( ~ sQ52_spl
| aElementOf0(sK1_skl(xU,szRzazndt0(xf)),xU) ),
inference(component_clause,[status(thm)],[f409]) ).
fof(f411,plain,
( sQ52_spl
| ~ aElementOf0(sK1_skl(xU,szRzazndt0(xf)),xU) ),
inference(component_clause,[status(thm)],[f409]) ).
fof(f412,plain,
( sQ52_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f391,f406,f409]) ).
fof(f413,plain,
( ~ sQ39_spl
| sdtlseqdt0(sK0_skl(szDzozmdt0(xf)),sK0_skl(szDzozmdt0(xf))) ),
inference(resolution,[status(thm)],[f353,f55]) ).
fof(f414,plain,
! [X0] :
( ~ sQ31_spl
| aElementOf0(sK3_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aUpperBoundOfIn0(X0,szDzozmdt0(xf),szDzozmdt0(xf))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f310,f74]) ).
fof(f415,plain,
! [X0] :
( ~ sQ31_spl
| aElementOf0(sK2_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aLowerBoundOfIn0(X0,szDzozmdt0(xf),szDzozmdt0(xf))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f310,f66]) ).
fof(f416,plain,
! [X0] :
( ~ sQ31_spl
| aElementOf0(X0,szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f310,f49]) ).
fof(f418,definition,
! [X0] :
( sQ53_spl
<=> ( aElementOf0(sK3_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aUpperBoundOfIn0(X0,szDzozmdt0(xf),szDzozmdt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f419,plain,
! [X0] :
( ~ sQ53_spl
| aElementOf0(sK3_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aUpperBoundOfIn0(X0,szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f418]) ).
fof(f421,plain,
( ~ sQ31_spl
| sQ53_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f414,f303,f418,f309]) ).
fof(f422,definition,
! [X0] :
( sQ54_spl
<=> ( aElementOf0(sK2_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aLowerBoundOfIn0(X0,szDzozmdt0(xf),szDzozmdt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f423,plain,
! [X0] :
( ~ sQ54_spl
| aElementOf0(sK2_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aLowerBoundOfIn0(X0,szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f422]) ).
fof(f425,plain,
( ~ sQ31_spl
| sQ54_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f415,f303,f422,f309]) ).
fof(f426,definition,
! [X0] :
( sQ55_spl
<=> ( aElementOf0(X0,szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f429,plain,
( ~ sQ31_spl
| sQ55_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f416,f303,f426,f309]) ).
fof(f431,plain,
( ~ sQ34_spl
| ~ isEmpty0(xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f320,f42]) ).
fof(f432,plain,
( ~ sQ34_spl
| aElement0(sK1_skl(xU,szDzozmdt0(xf)))
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f320,f38]) ).
fof(f433,plain,
( ~ sQ34_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f431,f162,f154,f319]) ).
fof(f434,definition,
( sQ56_spl
<=> aElement0(sK1_skl(xU,szDzozmdt0(xf))) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f435,plain,
( ~ sQ56_spl
| aElement0(sK1_skl(xU,szDzozmdt0(xf))) ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f437,plain,
( ~ sQ34_spl
| sQ56_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f432,f162,f434,f319]) ).
fof(f438,plain,
! [X0] :
( ~ sQ42_spl
| aElementOf0(sK3_skl(X0,szRzazndt0(xf),xU),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,szRzazndt0(xf),xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f369,f74]) ).
fof(f439,plain,
! [X0] :
( ~ sQ42_spl
| aElementOf0(sK2_skl(X0,szRzazndt0(xf),xU),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,szRzazndt0(xf),xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f369,f66]) ).
fof(f440,plain,
! [X0] :
( ~ sQ42_spl
| aElementOf0(X0,xU)
| ~ aElementOf0(X0,szRzazndt0(xf))
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f369,f49]) ).
fof(f442,definition,
! [X0] :
( sQ57_spl
<=> ( aElementOf0(sK3_skl(X0,szRzazndt0(xf),xU),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,szRzazndt0(xf),xU) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f443,plain,
! [X0] :
( ~ sQ57_spl
| aElementOf0(sK3_skl(X0,szRzazndt0(xf),xU),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,szRzazndt0(xf),xU) ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,plain,
( ~ sQ42_spl
| sQ57_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f438,f162,f442,f368]) ).
fof(f446,definition,
! [X0] :
( sQ58_spl
<=> ( aElementOf0(sK2_skl(X0,szRzazndt0(xf),xU),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,szRzazndt0(xf),xU) ) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f447,plain,
! [X0] :
( ~ sQ58_spl
| aElementOf0(sK2_skl(X0,szRzazndt0(xf),xU),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,szRzazndt0(xf),xU) ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f449,plain,
( ~ sQ42_spl
| sQ58_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f439,f162,f446,f368]) ).
fof(f450,definition,
! [X0] :
( sQ59_spl
<=> ( aElementOf0(X0,xU)
| ~ aElementOf0(X0,szRzazndt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f451,plain,
! [X0] :
( ~ sQ59_spl
| aElementOf0(X0,xU)
| ~ aElementOf0(X0,szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f450]) ).
fof(f453,plain,
( ~ sQ42_spl
| sQ59_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f440,f162,f450,f368]) ).
fof(f454,definition,
( sQ60_spl
<=> aSet0(szRzazndt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f456,plain,
( sQ60_spl
| ~ aSet0(szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f454]) ).
fof(f458,plain,
! [X0] :
( ~ sQ51_spl
| aElementOf0(sK3_skl(X0,xU,szRzazndt0(xf)),xU)
| ~ aElementOf0(X0,szRzazndt0(xf))
| aUpperBoundOfIn0(X0,xU,szRzazndt0(xf))
| ~ aSet0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f407,f74]) ).
fof(f459,plain,
! [X0] :
( ~ sQ51_spl
| aElementOf0(sK2_skl(X0,xU,szRzazndt0(xf)),xU)
| ~ aElementOf0(X0,szRzazndt0(xf))
| aLowerBoundOfIn0(X0,xU,szRzazndt0(xf))
| ~ aSet0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f407,f66]) ).
fof(f460,plain,
! [X0] :
( ~ sQ51_spl
| aElementOf0(X0,szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| ~ aSet0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f407,f49]) ).
fof(f461,plain,
( ~ sQ51_spl
| aSet0(xU)
| ~ aSet0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f407,f48]) ).
fof(f462,definition,
! [X0] :
( sQ61_spl
<=> ( aElementOf0(sK3_skl(X0,xU,szRzazndt0(xf)),xU)
| ~ aElementOf0(X0,szRzazndt0(xf))
| aUpperBoundOfIn0(X0,xU,szRzazndt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f463,plain,
! [X0] :
( ~ sQ61_spl
| aElementOf0(sK3_skl(X0,xU,szRzazndt0(xf)),xU)
| ~ aElementOf0(X0,szRzazndt0(xf))
| aUpperBoundOfIn0(X0,xU,szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f465,plain,
( ~ sQ51_spl
| sQ61_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f458,f454,f462,f406]) ).
fof(f466,definition,
! [X0] :
( sQ62_spl
<=> ( aElementOf0(sK2_skl(X0,xU,szRzazndt0(xf)),xU)
| ~ aElementOf0(X0,szRzazndt0(xf))
| aLowerBoundOfIn0(X0,xU,szRzazndt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f467,plain,
! [X0] :
( ~ sQ62_spl
| aElementOf0(sK2_skl(X0,xU,szRzazndt0(xf)),xU)
| ~ aElementOf0(X0,szRzazndt0(xf))
| aLowerBoundOfIn0(X0,xU,szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f466]) ).
fof(f469,plain,
( ~ sQ51_spl
| sQ62_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f459,f454,f466,f406]) ).
fof(f470,definition,
! [X0] :
( sQ63_spl
<=> ( aElementOf0(X0,szRzazndt0(xf))
| ~ aElementOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f471,plain,
! [X0] :
( ~ sQ63_spl
| aElementOf0(X0,szRzazndt0(xf))
| ~ aElementOf0(X0,xU) ),
inference(component_clause,[status(thm)],[f470]) ).
fof(f473,plain,
( ~ sQ51_spl
| sQ63_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f460,f454,f470,f406]) ).
fof(f474,plain,
( ~ sQ51_spl
| sQ4_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f461,f454,f162,f406]) ).
fof(f475,plain,
( sQ60_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f456,f356]) ).
fof(f476,plain,
sQ60_spl,
inference(contradiction_clause,[status(thm)],[f475]) ).
fof(f477,plain,
! [X0] :
( ~ sQ40_spl
| aElementOf0(sK3_skl(X0,szRzazndt0(xf),szDzozmdt0(xf)),szRzazndt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aUpperBoundOfIn0(X0,szRzazndt0(xf),szDzozmdt0(xf))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f362,f74]) ).
fof(f478,plain,
! [X0] :
( ~ sQ40_spl
| aElementOf0(sK2_skl(X0,szRzazndt0(xf),szDzozmdt0(xf)),szRzazndt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aLowerBoundOfIn0(X0,szRzazndt0(xf),szDzozmdt0(xf))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f362,f66]) ).
fof(f479,plain,
! [X0] :
( ~ sQ40_spl
| aElementOf0(X0,szDzozmdt0(xf))
| ~ aElementOf0(X0,szRzazndt0(xf))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f362,f49]) ).
fof(f480,plain,
( ~ sQ40_spl
| aSet0(szRzazndt0(xf))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f362,f48]) ).
fof(f481,definition,
! [X0] :
( sQ64_spl
<=> ( aElementOf0(sK3_skl(X0,szRzazndt0(xf),szDzozmdt0(xf)),szRzazndt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aUpperBoundOfIn0(X0,szRzazndt0(xf),szDzozmdt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f482,plain,
! [X0] :
( ~ sQ64_spl
| aElementOf0(sK3_skl(X0,szRzazndt0(xf),szDzozmdt0(xf)),szRzazndt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aUpperBoundOfIn0(X0,szRzazndt0(xf),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f481]) ).
fof(f484,plain,
( ~ sQ40_spl
| sQ64_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f477,f303,f481,f361]) ).
fof(f485,definition,
! [X0] :
( sQ65_spl
<=> ( aElementOf0(sK2_skl(X0,szRzazndt0(xf),szDzozmdt0(xf)),szRzazndt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aLowerBoundOfIn0(X0,szRzazndt0(xf),szDzozmdt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f486,plain,
! [X0] :
( ~ sQ65_spl
| aElementOf0(sK2_skl(X0,szRzazndt0(xf),szDzozmdt0(xf)),szRzazndt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aLowerBoundOfIn0(X0,szRzazndt0(xf),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f485]) ).
fof(f488,plain,
( ~ sQ40_spl
| sQ65_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f478,f303,f485,f361]) ).
fof(f489,definition,
! [X0] :
( sQ66_spl
<=> ( aElementOf0(X0,szDzozmdt0(xf))
| ~ aElementOf0(X0,szRzazndt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f490,plain,
! [X0] :
( ~ sQ66_spl
| aElementOf0(X0,szDzozmdt0(xf))
| ~ aElementOf0(X0,szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f489]) ).
fof(f492,plain,
( ~ sQ40_spl
| sQ66_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f479,f303,f489,f361]) ).
fof(f493,plain,
( ~ sQ40_spl
| sQ60_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f480,f303,f454,f361]) ).
fof(f494,plain,
( ~ sQ38_spl
| sdtlseqdt0(sK1_skl(szDzozmdt0(xf),xU),sK1_skl(szDzozmdt0(xf),xU)) ),
inference(resolution,[status(thm)],[f346,f55]) ).
fof(f495,plain,
! [X0] :
( ~ sQ49_spl
| aElementOf0(sK3_skl(X0,szDzozmdt0(xf),szRzazndt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szRzazndt0(xf))
| aUpperBoundOfIn0(X0,szDzozmdt0(xf),szRzazndt0(xf))
| ~ aSet0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f400,f74]) ).
fof(f496,plain,
! [X0] :
( ~ sQ49_spl
| aElementOf0(sK2_skl(X0,szDzozmdt0(xf),szRzazndt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szRzazndt0(xf))
| aLowerBoundOfIn0(X0,szDzozmdt0(xf),szRzazndt0(xf))
| ~ aSet0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f400,f66]) ).
fof(f497,plain,
! [X0] :
( ~ sQ49_spl
| aElementOf0(X0,szRzazndt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| ~ aSet0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f400,f49]) ).
fof(f498,plain,
( ~ sQ49_spl
| aSet0(szDzozmdt0(xf))
| ~ aSet0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f400,f48]) ).
fof(f499,definition,
! [X0] :
( sQ67_spl
<=> ( aElementOf0(sK3_skl(X0,szDzozmdt0(xf),szRzazndt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szRzazndt0(xf))
| aUpperBoundOfIn0(X0,szDzozmdt0(xf),szRzazndt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f500,plain,
! [X0] :
( ~ sQ67_spl
| aElementOf0(sK3_skl(X0,szDzozmdt0(xf),szRzazndt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szRzazndt0(xf))
| aUpperBoundOfIn0(X0,szDzozmdt0(xf),szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f499]) ).
fof(f502,plain,
( ~ sQ49_spl
| sQ67_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f495,f454,f499,f399]) ).
fof(f503,definition,
! [X0] :
( sQ68_spl
<=> ( aElementOf0(sK2_skl(X0,szDzozmdt0(xf),szRzazndt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szRzazndt0(xf))
| aLowerBoundOfIn0(X0,szDzozmdt0(xf),szRzazndt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f504,plain,
! [X0] :
( ~ sQ68_spl
| aElementOf0(sK2_skl(X0,szDzozmdt0(xf),szRzazndt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szRzazndt0(xf))
| aLowerBoundOfIn0(X0,szDzozmdt0(xf),szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f503]) ).
fof(f506,plain,
( ~ sQ49_spl
| sQ68_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f496,f454,f503,f399]) ).
fof(f507,definition,
! [X0] :
( sQ69_spl
<=> ( aElementOf0(X0,szRzazndt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f508,plain,
! [X0] :
( ~ sQ69_spl
| aElementOf0(X0,szRzazndt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f507]) ).
fof(f510,plain,
( ~ sQ49_spl
| sQ69_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f497,f454,f507,f399]) ).
fof(f511,plain,
( ~ sQ49_spl
| sQ30_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f498,f454,f303,f399]) ).
fof(f512,plain,
! [X0] :
( ~ sQ47_spl
| aElementOf0(sK3_skl(X0,szRzazndt0(xf),szRzazndt0(xf)),szRzazndt0(xf))
| ~ aElementOf0(X0,szRzazndt0(xf))
| aUpperBoundOfIn0(X0,szRzazndt0(xf),szRzazndt0(xf))
| ~ aSet0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f393,f74]) ).
fof(f513,plain,
! [X0] :
( ~ sQ47_spl
| aElementOf0(sK2_skl(X0,szRzazndt0(xf),szRzazndt0(xf)),szRzazndt0(xf))
| ~ aElementOf0(X0,szRzazndt0(xf))
| aLowerBoundOfIn0(X0,szRzazndt0(xf),szRzazndt0(xf))
| ~ aSet0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f393,f66]) ).
fof(f514,plain,
! [X0] :
( ~ sQ47_spl
| aElementOf0(X0,szRzazndt0(xf))
| ~ aElementOf0(X0,szRzazndt0(xf))
| ~ aSet0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f393,f49]) ).
fof(f516,definition,
! [X0] :
( sQ70_spl
<=> ( aElementOf0(sK3_skl(X0,szRzazndt0(xf),szRzazndt0(xf)),szRzazndt0(xf))
| ~ aElementOf0(X0,szRzazndt0(xf))
| aUpperBoundOfIn0(X0,szRzazndt0(xf),szRzazndt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f517,plain,
! [X0] :
( ~ sQ70_spl
| aElementOf0(sK3_skl(X0,szRzazndt0(xf),szRzazndt0(xf)),szRzazndt0(xf))
| ~ aElementOf0(X0,szRzazndt0(xf))
| aUpperBoundOfIn0(X0,szRzazndt0(xf),szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f516]) ).
fof(f519,plain,
( ~ sQ47_spl
| sQ70_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f512,f454,f516,f392]) ).
fof(f520,definition,
! [X0] :
( sQ71_spl
<=> ( aElementOf0(sK2_skl(X0,szRzazndt0(xf),szRzazndt0(xf)),szRzazndt0(xf))
| ~ aElementOf0(X0,szRzazndt0(xf))
| aLowerBoundOfIn0(X0,szRzazndt0(xf),szRzazndt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f521,plain,
! [X0] :
( ~ sQ71_spl
| aElementOf0(sK2_skl(X0,szRzazndt0(xf),szRzazndt0(xf)),szRzazndt0(xf))
| ~ aElementOf0(X0,szRzazndt0(xf))
| aLowerBoundOfIn0(X0,szRzazndt0(xf),szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f520]) ).
fof(f523,plain,
( ~ sQ47_spl
| sQ71_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f513,f454,f520,f392]) ).
fof(f524,definition,
! [X0] :
( sQ72_spl
<=> ( aElementOf0(X0,szRzazndt0(xf))
| ~ aElementOf0(X0,szRzazndt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f527,plain,
( ~ sQ47_spl
| sQ72_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f514,f454,f524,f392]) ).
fof(f529,plain,
( ~ sQ32_spl
| ~ aSet0(szDzozmdt0(xf))
| aSubsetOf0(szDzozmdt0(xf),szDzozmdt0(xf))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f313,f51]) ).
fof(f530,plain,
( ~ sQ32_spl
| ~ isEmpty0(szDzozmdt0(xf))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f313,f42]) ).
fof(f531,plain,
( ~ sQ32_spl
| aElement0(sK1_skl(szDzozmdt0(xf),szDzozmdt0(xf)))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f313,f38]) ).
fof(f532,plain,
( ~ sQ32_spl
| sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f529,f303,f309,f312]) ).
fof(f533,plain,
( ~ sQ32_spl
| ~ sQ23_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f530,f303,f270,f312]) ).
fof(f534,definition,
( sQ73_spl
<=> aElement0(sK1_skl(szDzozmdt0(xf),szDzozmdt0(xf))) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f535,plain,
( ~ sQ73_spl
| aElement0(sK1_skl(szDzozmdt0(xf),szDzozmdt0(xf))) ),
inference(component_clause,[status(thm)],[f534]) ).
fof(f537,plain,
( ~ sQ32_spl
| sQ73_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f531,f303,f534,f312]) ).
fof(f538,plain,
( ~ sQ56_spl
| sdtlseqdt0(sK1_skl(xU,szDzozmdt0(xf)),sK1_skl(xU,szDzozmdt0(xf))) ),
inference(resolution,[status(thm)],[f435,f55]) ).
fof(f539,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)],[f92,f72]) ).
fof(f540,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)],[f93,f72]) ).
fof(f541,plain,
( ~ sQ43_spl
| ~ isEmpty0(szRzazndt0(xf))
| ~ aSet0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f372,f42]) ).
fof(f542,plain,
( ~ sQ43_spl
| aElement0(sK1_skl(szRzazndt0(xf),xU))
| ~ aSet0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f372,f38]) ).
fof(f543,plain,
( ~ sQ43_spl
| ~ sQ44_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f541,f454,f375,f371]) ).
fof(f544,definition,
( sQ74_spl
<=> aElement0(sK1_skl(szRzazndt0(xf),xU)) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f545,plain,
( ~ sQ74_spl
| aElement0(sK1_skl(szRzazndt0(xf),xU)) ),
inference(component_clause,[status(thm)],[f544]) ).
fof(f547,plain,
( ~ sQ43_spl
| sQ74_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f542,f454,f544,f371]) ).
fof(f548,plain,
( ~ sQ45_spl
| ~ isEmpty0(szRzazndt0(xf))
| ~ aSet0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f379,f42]) ).
fof(f549,plain,
( ~ sQ45_spl
| aElement0(sK0_skl(szRzazndt0(xf)))
| ~ aSet0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f379,f38]) ).
fof(f550,plain,
( ~ sQ45_spl
| ~ sQ44_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f548,f454,f375,f378]) ).
fof(f551,definition,
( sQ75_spl
<=> aElement0(sK0_skl(szRzazndt0(xf))) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f552,plain,
( ~ sQ75_spl
| aElement0(sK0_skl(szRzazndt0(xf))) ),
inference(component_clause,[status(thm)],[f551]) ).
fof(f554,plain,
( ~ sQ45_spl
| sQ75_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f549,f454,f551,f378]) ).
fof(f555,plain,
( ~ sQ52_spl
| ~ isEmpty0(xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f410,f42]) ).
fof(f556,plain,
( ~ sQ52_spl
| aElement0(sK1_skl(xU,szRzazndt0(xf)))
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f410,f38]) ).
fof(f557,plain,
( ~ sQ52_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f555,f162,f154,f409]) ).
fof(f558,definition,
( sQ76_spl
<=> aElement0(sK1_skl(xU,szRzazndt0(xf))) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f559,plain,
( ~ sQ76_spl
| aElement0(sK1_skl(xU,szRzazndt0(xf))) ),
inference(component_clause,[status(thm)],[f558]) ).
fof(f561,plain,
( ~ sQ52_spl
| sQ76_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f556,f162,f558,f409]) ).
fof(f562,plain,
( ~ sQ75_spl
| sdtlseqdt0(sK0_skl(szRzazndt0(xf)),sK0_skl(szRzazndt0(xf))) ),
inference(resolution,[status(thm)],[f552,f55]) ).
fof(f571,plain,
( ~ sQ74_spl
| sdtlseqdt0(sK1_skl(szRzazndt0(xf),xU),sK1_skl(szRzazndt0(xf),xU)) ),
inference(resolution,[status(thm)],[f545,f55]) ).
fof(f572,plain,
! [X0] :
( xp = X0
| ~ aInfimumOfIn0(X0,xP,xU)
| ~ aSubsetOf0(xP,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f97,f142]) ).
fof(f573,definition,
! [X0] :
( sQ77_spl
<=> ( xp = X0
| ~ aInfimumOfIn0(X0,xP,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f576,plain,
( sQ77_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f572,f162,f165,f573]) ).
fof(f577,plain,
( ~ sQ31_spl
| aInfimumOfIn0(sK6_skl(szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf),szDzozmdt0(xf))
| ~ aCompleteLattice0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f103,f310]) ).
fof(f578,plain,
( ~ sQ11_spl
| aInfimumOfIn0(sK6_skl(xU,xU),xU,xU)
| ~ aCompleteLattice0(xU) ),
inference(resolution,[status(thm)],[f103,f193]) ).
fof(f579,plain,
( aInfimumOfIn0(sK6_skl(xT,xS),xT,xS)
| ~ aCompleteLattice0(xS) ),
inference(resolution,[status(thm)],[f103,f140]) ).
fof(f580,definition,
( sQ78_spl
<=> aCompleteLattice0(szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f581,plain,
( ~ sQ78_spl
| aCompleteLattice0(szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f580]) ).
fof(f582,plain,
( sQ78_spl
| ~ aCompleteLattice0(szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f580]) ).
fof(f583,definition,
( sQ79_spl
<=> aInfimumOfIn0(sK6_skl(szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf),szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f584,plain,
( ~ sQ79_spl
| aInfimumOfIn0(sK6_skl(szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f583]) ).
fof(f586,plain,
( ~ sQ31_spl
| sQ79_spl
| ~ sQ78_spl ),
inference(split_clause,[status(thm)],[f577,f580,f583,f309]) ).
fof(f587,definition,
( sQ80_spl
<=> aCompleteLattice0(xU) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f589,plain,
( sQ80_spl
| ~ aCompleteLattice0(xU) ),
inference(component_clause,[status(thm)],[f587]) ).
fof(f590,definition,
( sQ81_spl
<=> aInfimumOfIn0(sK6_skl(xU,xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f591,plain,
( ~ sQ81_spl
| aInfimumOfIn0(sK6_skl(xU,xU),xU,xU) ),
inference(component_clause,[status(thm)],[f590]) ).
fof(f593,plain,
( ~ sQ11_spl
| sQ81_spl
| ~ sQ80_spl ),
inference(split_clause,[status(thm)],[f578,f587,f590,f192]) ).
fof(f594,definition,
( sQ82_spl
<=> aCompleteLattice0(xS) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f596,plain,
( sQ82_spl
| ~ aCompleteLattice0(xS) ),
inference(component_clause,[status(thm)],[f594]) ).
fof(f597,definition,
( sQ83_spl
<=> aInfimumOfIn0(sK6_skl(xT,xS),xT,xS) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f600,plain,
( sQ83_spl
| ~ sQ82_spl ),
inference(split_clause,[status(thm)],[f579,f594,f597]) ).
fof(f601,plain,
( sQ80_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f589,f135]) ).
fof(f602,plain,
sQ80_spl,
inference(contradiction_clause,[status(thm)],[f601]) ).
fof(f603,plain,
( ~ sQ31_spl
| aSupremumOfIn0(sK7_skl(szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf),szDzozmdt0(xf))
| ~ aCompleteLattice0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f104,f310]) ).
fof(f604,plain,
( ~ sQ11_spl
| aSupremumOfIn0(sK7_skl(xU,xU),xU,xU)
| ~ aCompleteLattice0(xU) ),
inference(resolution,[status(thm)],[f104,f193]) ).
fof(f605,plain,
( aSupremumOfIn0(sK7_skl(xT,xS),xT,xS)
| ~ aCompleteLattice0(xS) ),
inference(resolution,[status(thm)],[f104,f140]) ).
fof(f606,definition,
( sQ84_spl
<=> aSupremumOfIn0(sK7_skl(szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf),szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f607,plain,
( ~ sQ84_spl
| aSupremumOfIn0(sK7_skl(szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f606]) ).
fof(f609,plain,
( ~ sQ31_spl
| sQ84_spl
| ~ sQ78_spl ),
inference(split_clause,[status(thm)],[f603,f580,f606,f309]) ).
fof(f610,definition,
( sQ85_spl
<=> aSupremumOfIn0(sK7_skl(xU,xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f611,plain,
( ~ sQ85_spl
| aSupremumOfIn0(sK7_skl(xU,xU),xU,xU) ),
inference(component_clause,[status(thm)],[f610]) ).
fof(f613,plain,
( ~ sQ11_spl
| sQ85_spl
| ~ sQ80_spl ),
inference(split_clause,[status(thm)],[f604,f587,f610,f192]) ).
fof(f614,definition,
( sQ86_spl
<=> aSupremumOfIn0(sK7_skl(xT,xS),xT,xS) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f617,plain,
( sQ86_spl
| ~ sQ82_spl ),
inference(split_clause,[status(thm)],[f605,f594,f614]) ).
fof(f618,plain,
( ~ sQ41_spl
| ~ isEmpty0(szRzazndt0(xf))
| ~ aSet0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f365,f42]) ).
fof(f619,plain,
( ~ sQ41_spl
| aElement0(sK1_skl(szRzazndt0(xf),szDzozmdt0(xf)))
| ~ aSet0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f365,f38]) ).
fof(f620,plain,
( ~ sQ41_spl
| ~ sQ44_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f618,f454,f375,f364]) ).
fof(f621,definition,
( sQ87_spl
<=> aElement0(sK1_skl(szRzazndt0(xf),szDzozmdt0(xf))) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f622,plain,
( ~ sQ87_spl
| aElement0(sK1_skl(szRzazndt0(xf),szDzozmdt0(xf))) ),
inference(component_clause,[status(thm)],[f621]) ).
fof(f624,plain,
( ~ sQ41_spl
| sQ87_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f619,f454,f621,f364]) ).
fof(f625,plain,
( ~ sQ76_spl
| sdtlseqdt0(sK1_skl(xU,szRzazndt0(xf)),sK1_skl(xU,szRzazndt0(xf))) ),
inference(resolution,[status(thm)],[f559,f55]) ).
fof(f626,plain,
! [X0] :
( ~ sQ81_spl
| sK6_skl(xU,xU) = X0
| ~ aInfimumOfIn0(X0,xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f591,f97]) ).
fof(f627,plain,
( ~ sQ81_spl
| aElementOf0(sK6_skl(xU,xU),xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f591,f80]) ).
fof(f628,plain,
! [X0] :
( ~ sQ81_spl
| sdtlseqdt0(X0,sK6_skl(xU,xU))
| ~ aLowerBoundOfIn0(X0,xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f591,f82]) ).
fof(f629,plain,
( ~ sQ81_spl
| aLowerBoundOfIn0(sK6_skl(xU,xU),xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f591,f81]) ).
fof(f630,definition,
! [X0] :
( sQ88_spl
<=> ( sK6_skl(xU,xU) = X0
| ~ aInfimumOfIn0(X0,xU,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f631,plain,
! [X0] :
( ~ sQ88_spl
| sK6_skl(xU,xU) = X0
| ~ aInfimumOfIn0(X0,xU,xU) ),
inference(component_clause,[status(thm)],[f630]) ).
fof(f633,plain,
( ~ sQ81_spl
| sQ88_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f626,f162,f192,f630,f590]) ).
fof(f634,definition,
( sQ89_spl
<=> aElementOf0(sK6_skl(xU,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f635,plain,
( ~ sQ89_spl
| aElementOf0(sK6_skl(xU,xU),xU) ),
inference(component_clause,[status(thm)],[f634]) ).
fof(f637,plain,
( ~ sQ81_spl
| sQ89_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f627,f162,f192,f634,f590]) ).
fof(f638,definition,
! [X0] :
( sQ90_spl
<=> ( sdtlseqdt0(X0,sK6_skl(xU,xU))
| ~ aLowerBoundOfIn0(X0,xU,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f639,plain,
! [X0] :
( ~ sQ90_spl
| sdtlseqdt0(X0,sK6_skl(xU,xU))
| ~ aLowerBoundOfIn0(X0,xU,xU) ),
inference(component_clause,[status(thm)],[f638]) ).
fof(f641,plain,
( ~ sQ81_spl
| sQ90_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f628,f162,f192,f638,f590]) ).
fof(f642,definition,
( sQ91_spl
<=> aLowerBoundOfIn0(sK6_skl(xU,xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f643,plain,
( ~ sQ91_spl
| aLowerBoundOfIn0(sK6_skl(xU,xU),xU,xU) ),
inference(component_clause,[status(thm)],[f642]) ).
fof(f645,plain,
( ~ sQ81_spl
| sQ91_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f629,f162,f192,f642,f590]) ).
fof(f646,plain,
( ~ sQ50_spl
| ~ isEmpty0(szDzozmdt0(xf))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f403,f42]) ).
fof(f647,plain,
( ~ sQ50_spl
| aElement0(sK1_skl(szDzozmdt0(xf),szRzazndt0(xf)))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f403,f38]) ).
fof(f648,plain,
( ~ sQ50_spl
| ~ sQ23_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f646,f303,f270,f402]) ).
fof(f649,definition,
( sQ92_spl
<=> aElement0(sK1_skl(szDzozmdt0(xf),szRzazndt0(xf))) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f650,plain,
( ~ sQ92_spl
| aElement0(sK1_skl(szDzozmdt0(xf),szRzazndt0(xf))) ),
inference(component_clause,[status(thm)],[f649]) ).
fof(f652,plain,
( ~ sQ50_spl
| sQ92_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f647,f303,f649,f402]) ).
fof(f653,plain,
( ~ sQ48_spl
| ~ aSet0(szRzazndt0(xf))
| aSubsetOf0(szRzazndt0(xf),szRzazndt0(xf))
| ~ aSet0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f396,f51]) ).
fof(f654,plain,
( ~ sQ48_spl
| ~ isEmpty0(szRzazndt0(xf))
| ~ aSet0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f396,f42]) ).
fof(f655,plain,
( ~ sQ48_spl
| aElement0(sK1_skl(szRzazndt0(xf),szRzazndt0(xf)))
| ~ aSet0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f396,f38]) ).
fof(f656,plain,
( ~ sQ48_spl
| sQ47_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f653,f454,f392,f395]) ).
fof(f657,plain,
( ~ sQ48_spl
| ~ sQ44_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f654,f454,f375,f395]) ).
fof(f658,definition,
( sQ93_spl
<=> aElement0(sK1_skl(szRzazndt0(xf),szRzazndt0(xf))) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f661,plain,
( ~ sQ48_spl
| sQ93_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f655,f454,f658,f395]) ).
fof(f662,plain,
( ~ sQ89_spl
| ~ isEmpty0(xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f635,f42]) ).
fof(f663,plain,
( ~ sQ89_spl
| aElement0(sK6_skl(xU,xU))
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f635,f38]) ).
fof(f664,plain,
( ~ sQ89_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f662,f162,f154,f634]) ).
fof(f665,definition,
( sQ94_spl
<=> aElement0(sK6_skl(xU,xU)) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f666,plain,
( ~ sQ94_spl
| aElement0(sK6_skl(xU,xU)) ),
inference(component_clause,[status(thm)],[f665]) ).
fof(f668,plain,
( ~ sQ89_spl
| sQ94_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f663,f162,f665,f634]) ).
fof(f669,plain,
( ~ sQ94_spl
| sdtlseqdt0(sK6_skl(xU,xU),sK6_skl(xU,xU)) ),
inference(resolution,[status(thm)],[f666,f55]) ).
fof(f670,plain,
( aSubsetOf0(sK8_skl(szRzazndt0(xf)),szRzazndt0(xf))
| aCompleteLattice0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f105,f356]) ).
fof(f671,plain,
( aSubsetOf0(sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf))
| aCompleteLattice0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f105,f259]) ).
fof(f673,definition,
( sQ95_spl
<=> aCompleteLattice0(szRzazndt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f674,plain,
( ~ sQ95_spl
| aCompleteLattice0(szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f673]) ).
fof(f675,plain,
( sQ95_spl
| ~ aCompleteLattice0(szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f673]) ).
fof(f676,definition,
( sQ96_spl
<=> aSubsetOf0(sK8_skl(szRzazndt0(xf)),szRzazndt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f677,plain,
( ~ sQ96_spl
| aSubsetOf0(sK8_skl(szRzazndt0(xf)),szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f676]) ).
fof(f678,plain,
( sQ96_spl
| ~ aSubsetOf0(sK8_skl(szRzazndt0(xf)),szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f676]) ).
fof(f679,plain,
( sQ96_spl
| sQ95_spl ),
inference(split_clause,[status(thm)],[f670,f673,f676]) ).
fof(f680,definition,
( sQ97_spl
<=> aSubsetOf0(sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f681,plain,
( ~ sQ97_spl
| aSubsetOf0(sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f680]) ).
fof(f682,plain,
( sQ97_spl
| ~ aSubsetOf0(sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f680]) ).
fof(f683,plain,
( sQ97_spl
| sQ78_spl ),
inference(split_clause,[status(thm)],[f671,f580,f680]) ).
fof(f688,plain,
( szDzozmdt0(xf) = szRzazndt0(xf)
| ~ aSet0(xU)
| ~ aFunction0(xf) ),
inference(resolution,[status(thm)],[f116,f138]) ).
fof(f689,definition,
( sQ99_spl
<=> aFunction0(xf) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f691,plain,
( sQ99_spl
| ~ aFunction0(xf) ),
inference(component_clause,[status(thm)],[f689]) ).
fof(f692,definition,
( sQ100_spl
<=> szDzozmdt0(xf) = szRzazndt0(xf) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f693,plain,
( ~ sQ100_spl
| szDzozmdt0(xf) = szRzazndt0(xf) ),
inference(component_clause,[status(thm)],[f692]) ).
fof(f695,plain,
( sQ100_spl
| ~ sQ4_spl
| ~ sQ99_spl ),
inference(split_clause,[status(thm)],[f688,f689,f162,f692]) ).
fof(f696,plain,
( sQ99_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f691,f136]) ).
fof(f697,plain,
sQ99_spl,
inference(contradiction_clause,[status(thm)],[f696]) ).
fof(f699,plain,
( ~ sQ97_spl
| aSupremumOfIn0(sK7_skl(sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)),sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aCompleteLattice0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f681,f104]) ).
fof(f700,plain,
( ~ sQ97_spl
| aInfimumOfIn0(sK6_skl(sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)),sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aCompleteLattice0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f681,f103]) ).
fof(f701,plain,
! [X0] :
( ~ sQ97_spl
| aElementOf0(sK3_skl(X0,sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)),sK8_skl(szDzozmdt0(xf)))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aUpperBoundOfIn0(X0,sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f681,f74]) ).
fof(f702,plain,
! [X0] :
( ~ sQ97_spl
| aElementOf0(sK2_skl(X0,sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)),sK8_skl(szDzozmdt0(xf)))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aLowerBoundOfIn0(X0,sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f681,f66]) ).
fof(f703,plain,
! [X0] :
( ~ sQ97_spl
| aElementOf0(X0,szDzozmdt0(xf))
| ~ aElementOf0(X0,sK8_skl(szDzozmdt0(xf)))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f681,f49]) ).
fof(f704,plain,
( ~ sQ97_spl
| aSet0(sK8_skl(szDzozmdt0(xf)))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f681,f48]) ).
fof(f705,definition,
( sQ101_spl
<=> aSupremumOfIn0(sK7_skl(sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)),sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f708,plain,
( ~ sQ97_spl
| sQ101_spl
| ~ sQ78_spl ),
inference(split_clause,[status(thm)],[f699,f580,f705,f680]) ).
fof(f709,definition,
( sQ102_spl
<=> aInfimumOfIn0(sK6_skl(sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)),sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f712,plain,
( ~ sQ97_spl
| sQ102_spl
| ~ sQ78_spl ),
inference(split_clause,[status(thm)],[f700,f580,f709,f680]) ).
fof(f713,definition,
! [X0] :
( sQ103_spl
<=> ( aElementOf0(sK3_skl(X0,sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)),sK8_skl(szDzozmdt0(xf)))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aUpperBoundOfIn0(X0,sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f714,plain,
! [X0] :
( ~ sQ103_spl
| aElementOf0(sK3_skl(X0,sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)),sK8_skl(szDzozmdt0(xf)))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aUpperBoundOfIn0(X0,sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f713]) ).
fof(f716,plain,
( ~ sQ97_spl
| sQ103_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f701,f303,f713,f680]) ).
fof(f717,definition,
! [X0] :
( sQ104_spl
<=> ( aElementOf0(sK2_skl(X0,sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)),sK8_skl(szDzozmdt0(xf)))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aLowerBoundOfIn0(X0,sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f718,plain,
! [X0] :
( ~ sQ104_spl
| aElementOf0(sK2_skl(X0,sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)),sK8_skl(szDzozmdt0(xf)))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aLowerBoundOfIn0(X0,sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f717]) ).
fof(f720,plain,
( ~ sQ97_spl
| sQ104_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f702,f303,f717,f680]) ).
fof(f721,definition,
! [X0] :
( sQ105_spl
<=> ( aElementOf0(X0,szDzozmdt0(xf))
| ~ aElementOf0(X0,sK8_skl(szDzozmdt0(xf))) ) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f722,plain,
! [X0] :
( ~ sQ105_spl
| aElementOf0(X0,szDzozmdt0(xf))
| ~ aElementOf0(X0,sK8_skl(szDzozmdt0(xf))) ),
inference(component_clause,[status(thm)],[f721]) ).
fof(f724,plain,
( ~ sQ97_spl
| sQ105_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f703,f303,f721,f680]) ).
fof(f725,definition,
( sQ106_spl
<=> aSet0(sK8_skl(szDzozmdt0(xf))) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f726,plain,
( ~ sQ106_spl
| aSet0(sK8_skl(szDzozmdt0(xf))) ),
inference(component_clause,[status(thm)],[f725]) ).
fof(f727,plain,
( sQ106_spl
| ~ aSet0(sK8_skl(szDzozmdt0(xf))) ),
inference(component_clause,[status(thm)],[f725]) ).
fof(f728,plain,
( ~ sQ97_spl
| sQ106_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f704,f303,f725,f680]) ).
fof(f729,plain,
( ~ sQ106_spl
| aSubsetOf0(sK8_skl(sK8_skl(szDzozmdt0(xf))),sK8_skl(szDzozmdt0(xf)))
| aCompleteLattice0(sK8_skl(szDzozmdt0(xf))) ),
inference(resolution,[status(thm)],[f726,f105]) ).
fof(f730,plain,
( ~ sQ106_spl
| aElementOf0(sK1_skl(sK8_skl(szDzozmdt0(xf)),szRzazndt0(xf)),sK8_skl(szDzozmdt0(xf)))
| aSubsetOf0(sK8_skl(szDzozmdt0(xf)),szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f726,f359]) ).
fof(f731,plain,
( ~ sQ106_spl
| aElementOf0(sK1_skl(sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)),sK8_skl(szDzozmdt0(xf)))
| aSubsetOf0(sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f726,f261]) ).
fof(f732,plain,
( ~ sQ106_spl
| aElementOf0(sK1_skl(sK8_skl(szDzozmdt0(xf)),xU),sK8_skl(szDzozmdt0(xf)))
| aSubsetOf0(sK8_skl(szDzozmdt0(xf)),xU) ),
inference(resolution,[status(thm)],[f726,f190]) ).
fof(f733,plain,
! [X0] :
( ~ sQ106_spl
| aElementOf0(sK1_skl(X0,sK8_skl(szDzozmdt0(xf))),X0)
| ~ aSet0(X0)
| aSubsetOf0(X0,sK8_skl(szDzozmdt0(xf))) ),
inference(resolution,[status(thm)],[f726,f50]) ).
fof(f734,plain,
( ~ sQ106_spl
| aElementOf0(sK0_skl(sK8_skl(szDzozmdt0(xf))),sK8_skl(szDzozmdt0(xf)))
| isEmpty0(sK8_skl(szDzozmdt0(xf))) ),
inference(resolution,[status(thm)],[f726,f43]) ).
fof(f735,definition,
( sQ107_spl
<=> aCompleteLattice0(sK8_skl(szDzozmdt0(xf))) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f736,plain,
( ~ sQ107_spl
| aCompleteLattice0(sK8_skl(szDzozmdt0(xf))) ),
inference(component_clause,[status(thm)],[f735]) ).
fof(f738,definition,
( sQ108_spl
<=> aSubsetOf0(sK8_skl(sK8_skl(szDzozmdt0(xf))),sK8_skl(szDzozmdt0(xf))) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f741,plain,
( ~ sQ106_spl
| sQ108_spl
| sQ107_spl ),
inference(split_clause,[status(thm)],[f729,f735,f738,f725]) ).
fof(f742,definition,
( sQ109_spl
<=> aSubsetOf0(sK8_skl(szDzozmdt0(xf)),szRzazndt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f743,plain,
( ~ sQ109_spl
| aSubsetOf0(sK8_skl(szDzozmdt0(xf)),szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f742]) ).
fof(f745,definition,
( sQ110_spl
<=> aElementOf0(sK1_skl(sK8_skl(szDzozmdt0(xf)),szRzazndt0(xf)),sK8_skl(szDzozmdt0(xf))) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f748,plain,
( ~ sQ106_spl
| sQ110_spl
| sQ109_spl ),
inference(split_clause,[status(thm)],[f730,f742,f745,f725]) ).
fof(f749,definition,
( sQ111_spl
<=> aElementOf0(sK1_skl(sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)),sK8_skl(szDzozmdt0(xf))) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f752,plain,
( ~ sQ106_spl
| sQ111_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f731,f680,f749,f725]) ).
fof(f753,definition,
( sQ112_spl
<=> aSubsetOf0(sK8_skl(szDzozmdt0(xf)),xU) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f754,plain,
( ~ sQ112_spl
| aSubsetOf0(sK8_skl(szDzozmdt0(xf)),xU) ),
inference(component_clause,[status(thm)],[f753]) ).
fof(f756,definition,
( sQ113_spl
<=> aElementOf0(sK1_skl(sK8_skl(szDzozmdt0(xf)),xU),sK8_skl(szDzozmdt0(xf))) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f759,plain,
( ~ sQ106_spl
| sQ113_spl
| sQ112_spl ),
inference(split_clause,[status(thm)],[f732,f753,f756,f725]) ).
fof(f760,definition,
( sQ114_spl
<=> isEmpty0(sK8_skl(szDzozmdt0(xf))) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f761,plain,
( ~ sQ114_spl
| isEmpty0(sK8_skl(szDzozmdt0(xf))) ),
inference(component_clause,[status(thm)],[f760]) ).
fof(f763,definition,
( sQ115_spl
<=> aElementOf0(sK0_skl(sK8_skl(szDzozmdt0(xf))),sK8_skl(szDzozmdt0(xf))) ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f766,plain,
( ~ sQ106_spl
| sQ115_spl
| sQ114_spl ),
inference(split_clause,[status(thm)],[f734,f760,f763,f725]) ).
fof(f767,plain,
( ~ sQ107_spl
| aSet0(sK8_skl(szDzozmdt0(xf))) ),
inference(resolution,[status(thm)],[f736,f102]) ).
fof(f768,plain,
( sQ48_spl
| ~ sQ100_spl
| ~ aElementOf0(sK1_skl(szRzazndt0(xf),szRzazndt0(xf)),szDzozmdt0(xf)) ),
inference(backward_demodulation,[status(thm)],[f693,f397]) ).
fof(f769,plain,
( ~ sQ95_spl
| ~ sQ100_spl
| aCompleteLattice0(szDzozmdt0(xf)) ),
inference(backward_demodulation,[status(thm)],[f693,f674]) ).
fof(f770,plain,
( ~ sQ50_spl
| ~ sQ100_spl
| aElementOf0(sK1_skl(szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf)) ),
inference(backward_demodulation,[status(thm)],[f693,f403]) ).
fof(f771,plain,
( ~ sQ76_spl
| ~ sQ100_spl
| aElement0(sK1_skl(xU,szDzozmdt0(xf))) ),
inference(backward_demodulation,[status(thm)],[f693,f559]) ).
fof(f772,plain,
( ~ sQ41_spl
| ~ sQ100_spl
| aElementOf0(sK1_skl(szRzazndt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf)) ),
inference(backward_demodulation,[status(thm)],[f693,f365]) ).
fof(f773,plain,
( ~ sQ74_spl
| ~ sQ100_spl
| aElement0(sK1_skl(szDzozmdt0(xf),xU)) ),
inference(backward_demodulation,[status(thm)],[f693,f545]) ).
fof(f774,plain,
( ~ sQ75_spl
| ~ sQ100_spl
| aElement0(sK0_skl(szDzozmdt0(xf))) ),
inference(backward_demodulation,[status(thm)],[f693,f552]) ).
fof(f775,plain,
( ~ sQ52_spl
| ~ sQ100_spl
| aElementOf0(sK1_skl(xU,szDzozmdt0(xf)),xU) ),
inference(backward_demodulation,[status(thm)],[f693,f410]) ).
fof(f776,plain,
( ~ sQ45_spl
| ~ sQ100_spl
| aElementOf0(sK0_skl(szRzazndt0(xf)),szDzozmdt0(xf)) ),
inference(backward_demodulation,[status(thm)],[f693,f379]) ).
fof(f777,plain,
( sQ44_spl
| ~ sQ100_spl
| ~ isEmpty0(szDzozmdt0(xf)) ),
inference(backward_demodulation,[status(thm)],[f693,f377]) ).
fof(f778,plain,
( ~ sQ43_spl
| ~ sQ100_spl
| aElementOf0(sK1_skl(szRzazndt0(xf),xU),szDzozmdt0(xf)) ),
inference(backward_demodulation,[status(thm)],[f693,f372]) ).
fof(f779,plain,
( sQ49_spl
| ~ sQ100_spl
| ~ aSubsetOf0(szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(backward_demodulation,[status(thm)],[f693,f401]) ).
fof(f780,plain,
( sQ40_spl
| ~ sQ100_spl
| ~ aSubsetOf0(szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(backward_demodulation,[status(thm)],[f693,f363]) ).
fof(f781,plain,
( sQ51_spl
| ~ sQ100_spl
| ~ aSubsetOf0(xU,szDzozmdt0(xf)) ),
inference(backward_demodulation,[status(thm)],[f693,f408]) ).
fof(f782,plain,
( sQ42_spl
| ~ sQ100_spl
| ~ aSubsetOf0(szDzozmdt0(xf),xU) ),
inference(backward_demodulation,[status(thm)],[f693,f370]) ).
fof(f785,plain,
( sQ48_spl
| ~ sQ100_spl
| ~ aElementOf0(sK1_skl(szDzozmdt0(xf),szRzazndt0(xf)),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f768]) ).
fof(f786,plain,
( sQ48_spl
| ~ sQ100_spl
| ~ aElementOf0(sK1_skl(szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f785]) ).
fof(f787,plain,
( ~ sQ95_spl
| ~ sQ100_spl
| sQ78_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f769,f582]) ).
fof(f788,plain,
( ~ sQ95_spl
| ~ sQ100_spl
| sQ78_spl ),
inference(contradiction_clause,[status(thm)],[f787]) ).
fof(f789,plain,
( ~ sQ50_spl
| ~ sQ100_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f770,f312,f692,f402]) ).
fof(f790,plain,
( ~ sQ41_spl
| ~ sQ100_spl
| aElementOf0(sK1_skl(szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f772]) ).
fof(f791,plain,
( ~ sQ41_spl
| ~ sQ100_spl
| sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f790,f314]) ).
fof(f792,plain,
( ~ sQ41_spl
| ~ sQ100_spl
| sQ32_spl ),
inference(contradiction_clause,[status(thm)],[f791]) ).
fof(f793,plain,
( ~ sQ45_spl
| ~ sQ100_spl
| aElementOf0(sK0_skl(szDzozmdt0(xf)),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f776]) ).
fof(f794,plain,
( ~ sQ43_spl
| ~ sQ100_spl
| aElementOf0(sK1_skl(szDzozmdt0(xf),xU),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f778]) ).
fof(f796,plain,
( ~ sQ96_spl
| ~ sQ100_spl
| aSubsetOf0(sK8_skl(szDzozmdt0(xf)),szRzazndt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f677]) ).
fof(f797,plain,
( ~ sQ96_spl
| ~ sQ100_spl
| aSubsetOf0(sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f796]) ).
fof(f798,plain,
! [X0] :
( ~ sQ67_spl
| ~ sQ100_spl
| aElementOf0(sK3_skl(X0,szDzozmdt0(xf),szRzazndt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szRzazndt0(xf))
| aUpperBoundOfIn0(X0,szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f500]) ).
fof(f799,plain,
! [X0] :
( ~ sQ67_spl
| ~ sQ100_spl
| aElementOf0(sK3_skl(X0,szDzozmdt0(xf),szRzazndt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aUpperBoundOfIn0(X0,szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f798]) ).
fof(f800,plain,
! [X0] :
( ~ sQ67_spl
| ~ sQ100_spl
| aElementOf0(sK3_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aUpperBoundOfIn0(X0,szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f799]) ).
fof(f801,plain,
! [X0] :
( ~ sQ68_spl
| ~ sQ100_spl
| aElementOf0(sK2_skl(X0,szDzozmdt0(xf),szRzazndt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szRzazndt0(xf))
| aLowerBoundOfIn0(X0,szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f504]) ).
fof(f802,plain,
! [X0] :
( ~ sQ68_spl
| ~ sQ100_spl
| aElementOf0(sK2_skl(X0,szDzozmdt0(xf),szRzazndt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aLowerBoundOfIn0(X0,szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f801]) ).
fof(f803,plain,
! [X0] :
( ~ sQ68_spl
| ~ sQ100_spl
| aElementOf0(sK2_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aLowerBoundOfIn0(X0,szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f802]) ).
fof(f804,plain,
! [X0] :
( ~ sQ64_spl
| ~ sQ100_spl
| aElementOf0(sK3_skl(X0,szRzazndt0(xf),szDzozmdt0(xf)),szRzazndt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aUpperBoundOfIn0(X0,szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f482]) ).
fof(f805,plain,
! [X0] :
( ~ sQ64_spl
| ~ sQ100_spl
| aElementOf0(sK3_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szRzazndt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aUpperBoundOfIn0(X0,szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f804]) ).
fof(f806,plain,
! [X0] :
( ~ sQ64_spl
| ~ sQ100_spl
| aElementOf0(sK3_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aUpperBoundOfIn0(X0,szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f805]) ).
fof(f807,plain,
! [X0] :
( ~ sQ65_spl
| ~ sQ100_spl
| aElementOf0(sK2_skl(X0,szRzazndt0(xf),szDzozmdt0(xf)),szRzazndt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aLowerBoundOfIn0(X0,szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f486]) ).
fof(f808,plain,
! [X0] :
( ~ sQ65_spl
| ~ sQ100_spl
| aElementOf0(sK2_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szRzazndt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aLowerBoundOfIn0(X0,szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f807]) ).
fof(f809,plain,
! [X0] :
( ~ sQ65_spl
| ~ sQ100_spl
| aElementOf0(sK2_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aLowerBoundOfIn0(X0,szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f808]) ).
fof(f810,plain,
( ~ sQ49_spl
| ~ sQ100_spl
| aSubsetOf0(szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f400]) ).
fof(f811,plain,
( ~ sQ40_spl
| ~ sQ100_spl
| aSubsetOf0(szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f362]) ).
fof(f812,plain,
( sQ50_spl
| ~ sQ100_spl
| ~ aElementOf0(sK1_skl(szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f404]) ).
fof(f813,plain,
( sQ41_spl
| ~ sQ100_spl
| ~ aElementOf0(sK1_skl(szDzozmdt0(xf),szDzozmdt0(xf)),szRzazndt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f366]) ).
fof(f814,plain,
( sQ41_spl
| ~ sQ100_spl
| ~ aElementOf0(sK1_skl(szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f813]) ).
fof(f816,plain,
( szRzazndt0(xf) = xU
| ~ aSet0(xU)
| ~ aFunction0(xf) ),
inference(resolution,[status(thm)],[f117,f138]) ).
fof(f817,definition,
( sQ116_spl
<=> szRzazndt0(xf) = xU ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f818,plain,
( ~ sQ116_spl
| szRzazndt0(xf) = xU ),
inference(component_clause,[status(thm)],[f817]) ).
fof(f820,plain,
( sQ116_spl
| ~ sQ4_spl
| ~ sQ99_spl ),
inference(split_clause,[status(thm)],[f816,f689,f162,f817]) ).
fof(f821,plain,
! [X0] :
( szRzazndt0(xf) != X0
| szDzozmdt0(xf) != szRzazndt0(xf)
| isOn0(xf,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f118,f136]) ).
fof(f822,definition,
! [X0] :
( sQ117_spl
<=> ( szRzazndt0(xf) != X0
| isOn0(xf,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f823,plain,
! [X0] :
( ~ sQ117_spl
| szRzazndt0(xf) != X0
| isOn0(xf,X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f822]) ).
fof(f825,plain,
( ~ sQ100_spl
| sQ117_spl ),
inference(split_clause,[status(thm)],[f821,f822,f692]) ).
fof(f826,plain,
! [X0] :
( ~ sQ117_spl
| ~ sQ100_spl
| szDzozmdt0(xf) != X0
| isOn0(xf,X0)
| ~ aSet0(X0) ),
inference(forward_demodulation,[status(thm)],[f693,f823]) ).
fof(f827,plain,
( ~ sQ22_spl
| aElementOf0(sdtlpdtrp0(xf,sK1_skl(szDzozmdt0(xf),xU)),szRzazndt0(xf))
| ~ aFunction0(xf) ),
inference(resolution,[status(thm)],[f120,f267]) ).
fof(f828,plain,
( ~ sQ24_spl
| aElementOf0(sdtlpdtrp0(xf,sK0_skl(szDzozmdt0(xf))),szRzazndt0(xf))
| ~ aFunction0(xf) ),
inference(resolution,[status(thm)],[f120,f274]) ).
fof(f829,definition,
( sQ118_spl
<=> aElementOf0(sdtlpdtrp0(xf,sK1_skl(szDzozmdt0(xf),xU)),szRzazndt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f830,plain,
( ~ sQ118_spl
| aElementOf0(sdtlpdtrp0(xf,sK1_skl(szDzozmdt0(xf),xU)),szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f829]) ).
fof(f831,plain,
( sQ118_spl
| ~ aElementOf0(sdtlpdtrp0(xf,sK1_skl(szDzozmdt0(xf),xU)),szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f829]) ).
fof(f832,plain,
( ~ sQ22_spl
| sQ118_spl
| ~ sQ99_spl ),
inference(split_clause,[status(thm)],[f827,f689,f829,f266]) ).
fof(f833,definition,
( sQ119_spl
<=> aElementOf0(sdtlpdtrp0(xf,sK0_skl(szDzozmdt0(xf))),szRzazndt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f834,plain,
( ~ sQ119_spl
| aElementOf0(sdtlpdtrp0(xf,sK0_skl(szDzozmdt0(xf))),szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f833]) ).
fof(f836,plain,
( ~ sQ24_spl
| sQ119_spl
| ~ sQ99_spl ),
inference(split_clause,[status(thm)],[f828,f689,f833,f273]) ).
fof(f837,plain,
( ~ sQ119_spl
| ~ sQ100_spl
| aElementOf0(sdtlpdtrp0(xf,sK0_skl(szDzozmdt0(xf))),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f834]) ).
fof(f838,plain,
( ~ sQ118_spl
| ~ sQ100_spl
| aElementOf0(sdtlpdtrp0(xf,sK1_skl(szDzozmdt0(xf),xU)),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f830]) ).
fof(f839,plain,
( ~ sQ47_spl
| ~ sQ100_spl
| aSubsetOf0(szDzozmdt0(xf),szRzazndt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f393]) ).
fof(f840,plain,
( ~ sQ47_spl
| ~ sQ100_spl
| aSubsetOf0(szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f839]) ).
fof(f841,plain,
( ~ sQ117_spl
| ~ sQ100_spl
| szDzozmdt0(xf) != szDzozmdt0(xf)
| isOn0(xf,szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f826,f259]) ).
fof(f842,plain,
( ~ sQ117_spl
| ~ sQ100_spl
| szDzozmdt0(xf) != xU
| isOn0(xf,xU) ),
inference(resolution,[status(thm)],[f826,f152]) ).
fof(f843,definition,
( sQ120_spl
<=> isOn0(xf,szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f844,plain,
( ~ sQ120_spl
| isOn0(xf,szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f843]) ).
fof(f846,definition,
( sQ121_spl
<=> szDzozmdt0(xf) = szDzozmdt0(xf) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f848,plain,
( sQ121_spl
| szDzozmdt0(xf) != szDzozmdt0(xf) ),
inference(component_clause,[status(thm)],[f846]) ).
fof(f849,plain,
( ~ sQ117_spl
| ~ sQ100_spl
| ~ sQ121_spl
| sQ120_spl ),
inference(split_clause,[status(thm)],[f841,f843,f846,f692,f822]) ).
fof(f850,definition,
( sQ122_spl
<=> isOn0(xf,xU) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f853,definition,
( sQ123_spl
<=> szDzozmdt0(xf) = xU ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f856,plain,
( ~ sQ117_spl
| ~ sQ100_spl
| ~ sQ123_spl
| sQ122_spl ),
inference(split_clause,[status(thm)],[f842,f850,f853,f692,f822]) ).
fof(f857,plain,
( ~ sQ120_spl
| szRzazndt0(xf) = szDzozmdt0(xf)
| ~ aSet0(szDzozmdt0(xf))
| ~ aFunction0(xf) ),
inference(resolution,[status(thm)],[f844,f117]) ).
fof(f859,plain,
( ~ sQ120_spl
| sQ100_spl
| ~ sQ30_spl
| ~ sQ99_spl ),
inference(split_clause,[status(thm)],[f857,f689,f303,f692,f843]) ).
fof(f861,plain,
( sQ121_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f848]) ).
fof(f862,plain,
sQ121_spl,
inference(contradiction_clause,[status(thm)],[f861]) ).
fof(f867,plain,
( ~ sQ96_spl
| ~ sQ100_spl
| aSupremumOfIn0(sK7_skl(sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)),sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aCompleteLattice0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f797,f104]) ).
fof(f868,plain,
( ~ sQ96_spl
| ~ sQ100_spl
| aInfimumOfIn0(sK6_skl(sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)),sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aCompleteLattice0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f797,f103]) ).
fof(f869,plain,
! [X0] :
( ~ sQ96_spl
| ~ sQ100_spl
| aElementOf0(sK3_skl(X0,sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)),sK8_skl(szDzozmdt0(xf)))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aUpperBoundOfIn0(X0,sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f797,f74]) ).
fof(f870,plain,
! [X0] :
( ~ sQ96_spl
| ~ sQ100_spl
| aElementOf0(sK2_skl(X0,sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)),sK8_skl(szDzozmdt0(xf)))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aLowerBoundOfIn0(X0,sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f797,f66]) ).
fof(f871,plain,
! [X0] :
( ~ sQ96_spl
| ~ sQ100_spl
| aElementOf0(X0,szDzozmdt0(xf))
| ~ aElementOf0(X0,sK8_skl(szDzozmdt0(xf)))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f797,f49]) ).
fof(f872,plain,
( ~ sQ96_spl
| ~ sQ100_spl
| aSet0(sK8_skl(szDzozmdt0(xf)))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f797,f48]) ).
fof(f873,plain,
( ~ sQ96_spl
| ~ sQ100_spl
| sQ101_spl
| ~ sQ78_spl ),
inference(split_clause,[status(thm)],[f867,f580,f705,f692,f676]) ).
fof(f874,plain,
( ~ sQ96_spl
| ~ sQ100_spl
| sQ102_spl
| ~ sQ78_spl ),
inference(split_clause,[status(thm)],[f868,f580,f709,f692,f676]) ).
fof(f875,plain,
( ~ sQ96_spl
| ~ sQ100_spl
| sQ103_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f869,f303,f713,f692,f676]) ).
fof(f876,plain,
( ~ sQ96_spl
| ~ sQ100_spl
| sQ104_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f870,f303,f717,f692,f676]) ).
fof(f877,plain,
( ~ sQ96_spl
| ~ sQ100_spl
| sQ105_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f871,f303,f721,f692,f676]) ).
fof(f878,plain,
( ~ sQ96_spl
| ~ sQ100_spl
| sQ106_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f872,f303,f725,f692,f676]) ).
fof(f879,plain,
( sQ96_spl
| ~ sQ100_spl
| ~ aSubsetOf0(sK8_skl(szDzozmdt0(xf)),szRzazndt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f678]) ).
fof(f880,plain,
( sQ96_spl
| ~ sQ100_spl
| ~ aSubsetOf0(sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f693,f879]) ).
fof(f881,plain,
( ~ sQ100_spl
| ~ sQ116_spl
| szDzozmdt0(xf) = xU ),
inference(backward_demodulation,[status(thm)],[f818,f693]) ).
fof(f882,plain,
( sQ97_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ aSubsetOf0(sK8_skl(szDzozmdt0(xf)),xU) ),
inference(backward_demodulation,[status(thm)],[f881,f682]) ).
fof(f884,plain,
! [X0] :
( ~ sQ117_spl
| ~ sQ100_spl
| ~ sQ116_spl
| xU != X0
| isOn0(xf,X0)
| ~ aSet0(X0) ),
inference(backward_demodulation,[status(thm)],[f881,f826]) ).
fof(f885,plain,
( sQ106_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ aSet0(sK8_skl(xU)) ),
inference(backward_demodulation,[status(thm)],[f881,f727]) ).
fof(f887,plain,
( ~ sQ31_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aSubsetOf0(szDzozmdt0(xf),xU) ),
inference(backward_demodulation,[status(thm)],[f881,f310]) ).
fof(f888,plain,
( ~ sQ56_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElement0(sK1_skl(xU,xU)) ),
inference(backward_demodulation,[status(thm)],[f881,f435]) ).
fof(f889,plain,
( ~ sQ38_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElement0(sK1_skl(xU,xU)) ),
inference(backward_demodulation,[status(thm)],[f881,f346]) ).
fof(f890,plain,
( ~ sQ34_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK1_skl(xU,xU),xU) ),
inference(backward_demodulation,[status(thm)],[f881,f320]) ).
fof(f891,plain,
( ~ sQ39_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElement0(sK0_skl(xU)) ),
inference(backward_demodulation,[status(thm)],[f881,f353]) ).
fof(f892,plain,
( sQ33_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ aSubsetOf0(xU,xU) ),
inference(backward_demodulation,[status(thm)],[f881,f318]) ).
fof(f893,plain,
( sQ23_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ isEmpty0(xU) ),
inference(backward_demodulation,[status(thm)],[f881,f272]) ).
fof(f894,plain,
( ~ sQ24_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK0_skl(szDzozmdt0(xf)),xU) ),
inference(backward_demodulation,[status(thm)],[f881,f274]) ).
fof(f895,plain,
( ~ sQ22_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK1_skl(szDzozmdt0(xf),xU),xU) ),
inference(backward_demodulation,[status(thm)],[f881,f267]) ).
fof(f896,plain,
( sQ21_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ aSubsetOf0(xU,xU) ),
inference(backward_demodulation,[status(thm)],[f881,f265]) ).
fof(f899,plain,
! [X0] :
( ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sdtlpdtrp0(xf,X0),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| ~ aFunction0(xf) ),
inference(paramodulation,[status(thm)],[f881,f120]) ).
fof(f900,plain,
( sQ97_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ aSubsetOf0(sK8_skl(xU),xU) ),
inference(forward_demodulation,[status(thm)],[f881,f882]) ).
fof(f901,plain,
( ~ sQ31_spl
| ~ sQ100_spl
| ~ sQ116_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f887,f263,f817,f692,f309]) ).
fof(f902,plain,
( ~ sQ34_spl
| ~ sQ100_spl
| ~ sQ116_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f890,f195,f817,f692,f319]) ).
fof(f903,plain,
( sQ33_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f892,f193]) ).
fof(f904,plain,
( sQ33_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f903]) ).
fof(f905,plain,
( ~ sQ24_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK0_skl(xU),xU) ),
inference(forward_demodulation,[status(thm)],[f881,f894]) ).
fof(f907,definition,
! [X0] :
( sQ124_spl
<=> ( aElementOf0(sdtlpdtrp0(xf,X0),szRzazndt0(xf))
| ~ aElementOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f908,plain,
! [X0] :
( ~ sQ124_spl
| aElementOf0(sdtlpdtrp0(xf,X0),szRzazndt0(xf))
| ~ aElementOf0(X0,xU) ),
inference(component_clause,[status(thm)],[f907]) ).
fof(f910,plain,
( ~ sQ100_spl
| ~ sQ116_spl
| sQ124_spl
| ~ sQ99_spl ),
inference(split_clause,[status(thm)],[f899,f689,f907,f817,f692]) ).
fof(f911,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)),sK8_skl(szDzozmdt0(xf)))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aUpperBoundOfIn0(X0,sK8_skl(xU),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f881,f714]) ).
fof(f912,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)),sK8_skl(szDzozmdt0(xf)))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aUpperBoundOfIn0(X0,sK8_skl(xU),xU) ),
inference(forward_demodulation,[status(thm)],[f881,f911]) ).
fof(f913,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)),sK8_skl(szDzozmdt0(xf)))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,sK8_skl(xU),xU) ),
inference(forward_demodulation,[status(thm)],[f881,f912]) ).
fof(f914,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,sK8_skl(xU),szDzozmdt0(xf)),sK8_skl(szDzozmdt0(xf)))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,sK8_skl(xU),xU) ),
inference(forward_demodulation,[status(thm)],[f881,f913]) ).
fof(f915,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,sK8_skl(xU),xU),sK8_skl(szDzozmdt0(xf)))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,sK8_skl(xU),xU) ),
inference(forward_demodulation,[status(thm)],[f881,f914]) ).
fof(f916,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,sK8_skl(xU),xU),sK8_skl(xU))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,sK8_skl(xU),xU) ),
inference(forward_demodulation,[status(thm)],[f881,f915]) ).
fof(f917,plain,
! [X0] :
( ~ sQ104_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)),sK8_skl(szDzozmdt0(xf)))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aLowerBoundOfIn0(X0,sK8_skl(xU),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f881,f718]) ).
fof(f918,plain,
! [X0] :
( ~ sQ104_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)),sK8_skl(szDzozmdt0(xf)))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aLowerBoundOfIn0(X0,sK8_skl(xU),xU) ),
inference(forward_demodulation,[status(thm)],[f881,f917]) ).
fof(f919,plain,
! [X0] :
( ~ sQ104_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)),sK8_skl(szDzozmdt0(xf)))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,sK8_skl(xU),xU) ),
inference(forward_demodulation,[status(thm)],[f881,f918]) ).
fof(f920,plain,
! [X0] :
( ~ sQ104_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,sK8_skl(xU),szDzozmdt0(xf)),sK8_skl(szDzozmdt0(xf)))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,sK8_skl(xU),xU) ),
inference(forward_demodulation,[status(thm)],[f881,f919]) ).
fof(f921,plain,
! [X0] :
( ~ sQ104_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,sK8_skl(xU),xU),sK8_skl(szDzozmdt0(xf)))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,sK8_skl(xU),xU) ),
inference(forward_demodulation,[status(thm)],[f881,f920]) ).
fof(f922,plain,
! [X0] :
( ~ sQ104_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,sK8_skl(xU),xU),sK8_skl(xU))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,sK8_skl(xU),xU) ),
inference(forward_demodulation,[status(thm)],[f881,f921]) ).
fof(f923,plain,
! [X0] :
( ~ sQ105_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(X0,szDzozmdt0(xf))
| ~ aElementOf0(X0,sK8_skl(xU)) ),
inference(forward_demodulation,[status(thm)],[f881,f722]) ).
fof(f924,plain,
! [X0] :
( ~ sQ105_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(X0,xU)
| ~ aElementOf0(X0,sK8_skl(xU)) ),
inference(forward_demodulation,[status(thm)],[f881,f923]) ).
fof(f925,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,szDzozmdt0(xf),xU),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f292]) ).
fof(f926,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,xU,xU),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f925]) ).
fof(f927,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f926]) ).
fof(f928,plain,
! [X0] :
( ~ sQ28_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,szDzozmdt0(xf),xU),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f296]) ).
fof(f929,plain,
! [X0] :
( ~ sQ28_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,xU,xU),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f928]) ).
fof(f930,plain,
! [X0] :
( ~ sQ28_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f929]) ).
fof(f931,plain,
( ~ sQ107_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aCompleteLattice0(sK8_skl(xU)) ),
inference(forward_demodulation,[status(thm)],[f881,f736]) ).
fof(f932,plain,
( ~ sQ107_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aSet0(sK8_skl(xU)) ),
inference(forward_demodulation,[status(thm)],[f881,f767]) ).
fof(f933,plain,
( ~ sQ109_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aSubsetOf0(sK8_skl(xU),szRzazndt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f881,f743]) ).
fof(f934,plain,
( ~ sQ109_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aSubsetOf0(sK8_skl(xU),xU) ),
inference(forward_demodulation,[status(thm)],[f818,f933]) ).
fof(f935,plain,
( ~ sQ112_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aSubsetOf0(sK8_skl(xU),xU) ),
inference(forward_demodulation,[status(thm)],[f881,f754]) ).
fof(f936,plain,
( ~ sQ114_spl
| ~ sQ100_spl
| ~ sQ116_spl
| isEmpty0(sK8_skl(xU)) ),
inference(forward_demodulation,[status(thm)],[f881,f761]) ).
fof(f937,plain,
! [X0] :
( ~ sQ35_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,xU,szDzozmdt0(xf)),xU)
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f328]) ).
fof(f938,plain,
! [X0] :
( ~ sQ35_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,xU,szDzozmdt0(xf)),xU)
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f937]) ).
fof(f939,plain,
! [X0] :
( ~ sQ35_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f938]) ).
fof(f940,plain,
! [X0] :
( ~ sQ36_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,xU,szDzozmdt0(xf)),xU)
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f332]) ).
fof(f941,plain,
! [X0] :
( ~ sQ36_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,xU,szDzozmdt0(xf)),xU)
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f940]) ).
fof(f942,plain,
! [X0] :
( ~ sQ36_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f941]) ).
fof(f943,plain,
( ~ sQ74_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElement0(sK1_skl(xU,xU)) ),
inference(forward_demodulation,[status(thm)],[f881,f773]) ).
fof(f944,plain,
( ~ sQ76_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElement0(sK1_skl(xU,xU)) ),
inference(forward_demodulation,[status(thm)],[f881,f771]) ).
fof(f945,plain,
( ~ sQ96_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aSubsetOf0(sK8_skl(xU),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f881,f797]) ).
fof(f946,plain,
( ~ sQ96_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aSubsetOf0(sK8_skl(xU),xU) ),
inference(forward_demodulation,[status(thm)],[f881,f945]) ).
fof(f947,plain,
( sQ78_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ aCompleteLattice0(xU) ),
inference(forward_demodulation,[status(thm)],[f881,f582]) ).
fof(f948,plain,
( sQ78_spl
| ~ sQ100_spl
| ~ sQ116_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f947,f135]) ).
fof(f949,plain,
( sQ78_spl
| ~ sQ100_spl
| ~ sQ116_spl ),
inference(contradiction_clause,[status(thm)],[f948]) ).
fof(f950,plain,
( sQ42_spl
| ~ sQ100_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f782,f263,f692,f368]) ).
fof(f951,plain,
( ~ sQ21_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aSubsetOf0(xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f264]) ).
fof(f952,plain,
( ~ sQ52_spl
| ~ sQ100_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f775,f319,f692,f409]) ).
fof(f953,plain,
( sQ34_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ aElementOf0(sK1_skl(xU,xU),xU) ),
inference(forward_demodulation,[status(thm)],[f881,f321]) ).
fof(f954,plain,
( sQ51_spl
| ~ sQ100_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f781,f316,f692,f406]) ).
fof(f955,plain,
( ~ sQ33_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aSubsetOf0(xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f317]) ).
fof(f956,plain,
( ~ sQ43_spl
| ~ sQ100_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f794,f266,f692,f371]) ).
fof(f957,plain,
( sQ22_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ aElementOf0(sK1_skl(xU,xU),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f881,f268]) ).
fof(f958,plain,
( sQ22_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ aElementOf0(sK1_skl(xU,xU),xU) ),
inference(forward_demodulation,[status(thm)],[f881,f957]) ).
fof(f959,plain,
! [X0] :
( ~ sQ124_spl
| ~ sQ116_spl
| aElementOf0(sdtlpdtrp0(xf,X0),xU)
| ~ aElementOf0(X0,xU) ),
inference(forward_demodulation,[status(thm)],[f818,f908]) ).
fof(f960,plain,
( ~ sQ79_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aInfimumOfIn0(sK6_skl(xU,szDzozmdt0(xf)),szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f881,f584]) ).
fof(f961,plain,
( ~ sQ79_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aInfimumOfIn0(sK6_skl(xU,xU),szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f881,f960]) ).
fof(f962,plain,
( ~ sQ79_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aInfimumOfIn0(sK6_skl(xU,xU),xU,szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f881,f961]) ).
fof(f963,plain,
( ~ sQ79_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aInfimumOfIn0(sK6_skl(xU,xU),xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f962]) ).
fof(f964,plain,
( ~ sQ84_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aSupremumOfIn0(sK7_skl(xU,szDzozmdt0(xf)),szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f881,f607]) ).
fof(f965,plain,
( ~ sQ84_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aSupremumOfIn0(sK7_skl(xU,xU),szDzozmdt0(xf),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f881,f964]) ).
fof(f966,plain,
( ~ sQ84_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aSupremumOfIn0(sK7_skl(xU,xU),xU,szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f881,f965]) ).
fof(f967,plain,
( ~ sQ84_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aSupremumOfIn0(sK7_skl(xU,xU),xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f966]) ).
fof(f968,plain,
( sQ96_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ aSubsetOf0(sK8_skl(xU),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f881,f880]) ).
fof(f969,plain,
( sQ96_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ aSubsetOf0(sK8_skl(xU),xU) ),
inference(forward_demodulation,[status(thm)],[f881,f968]) ).
fof(f971,plain,
! [X0] :
( ~ sQ57_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,szRzazndt0(xf),xU),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f818,f443]) ).
fof(f972,plain,
! [X0] :
( ~ sQ57_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,xU,xU),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f818,f971]) ).
fof(f973,plain,
! [X0] :
( ~ sQ57_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f818,f972]) ).
fof(f974,plain,
! [X0] :
( ~ sQ58_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,szRzazndt0(xf),xU),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f818,f447]) ).
fof(f975,plain,
! [X0] :
( ~ sQ58_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,xU,xU),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f818,f974]) ).
fof(f976,plain,
! [X0] :
( ~ sQ58_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f818,f975]) ).
fof(f977,plain,
! [X0] :
( ~ sQ61_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,xU,szRzazndt0(xf)),xU)
| ~ aElementOf0(X0,szRzazndt0(xf))
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f818,f463]) ).
fof(f978,plain,
! [X0] :
( ~ sQ61_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,xU,szRzazndt0(xf)),xU)
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f818,f977]) ).
fof(f979,plain,
! [X0] :
( ~ sQ61_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f818,f978]) ).
fof(f980,plain,
! [X0] :
( ~ sQ62_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,xU,szRzazndt0(xf)),xU)
| ~ aElementOf0(X0,szRzazndt0(xf))
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f818,f467]) ).
fof(f981,plain,
! [X0] :
( ~ sQ62_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,xU,szRzazndt0(xf)),xU)
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f818,f980]) ).
fof(f982,plain,
! [X0] :
( ~ sQ62_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f818,f981]) ).
fof(f983,plain,
( ~ sQ56_spl
| ~ sQ100_spl
| ~ sQ116_spl
| sdtlseqdt0(sK1_skl(xU,xU),sK1_skl(xU,szDzozmdt0(xf))) ),
inference(forward_demodulation,[status(thm)],[f881,f538]) ).
fof(f984,plain,
( ~ sQ56_spl
| ~ sQ100_spl
| ~ sQ116_spl
| sdtlseqdt0(sK1_skl(xU,xU),sK1_skl(xU,xU)) ),
inference(forward_demodulation,[status(thm)],[f881,f983]) ).
fof(f985,plain,
( ~ sQ38_spl
| ~ sQ100_spl
| ~ sQ116_spl
| sdtlseqdt0(sK1_skl(xU,xU),sK1_skl(szDzozmdt0(xf),xU)) ),
inference(forward_demodulation,[status(thm)],[f881,f494]) ).
fof(f986,plain,
( ~ sQ38_spl
| ~ sQ100_spl
| ~ sQ116_spl
| sdtlseqdt0(sK1_skl(xU,xU),sK1_skl(xU,xU)) ),
inference(forward_demodulation,[status(thm)],[f881,f985]) ).
fof(f987,plain,
( ~ sQ118_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sdtlpdtrp0(xf,sK1_skl(xU,xU)),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f881,f838]) ).
fof(f988,plain,
( ~ sQ118_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sdtlpdtrp0(xf,sK1_skl(xU,xU)),xU) ),
inference(forward_demodulation,[status(thm)],[f881,f987]) ).
fof(f989,plain,
( ~ sQ42_spl
| ~ sQ116_spl
| aSubsetOf0(xU,xU) ),
inference(forward_demodulation,[status(thm)],[f818,f369]) ).
fof(f990,plain,
( ~ sQ51_spl
| ~ sQ116_spl
| aSubsetOf0(xU,xU) ),
inference(forward_demodulation,[status(thm)],[f818,f407]) ).
fof(f991,plain,
( sQ52_spl
| ~ sQ116_spl
| ~ aElementOf0(sK1_skl(xU,xU),xU) ),
inference(forward_demodulation,[status(thm)],[f818,f411]) ).
fof(f992,plain,
( sQ43_spl
| ~ sQ116_spl
| ~ aElementOf0(sK1_skl(xU,xU),szRzazndt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f818,f373]) ).
fof(f993,plain,
( sQ43_spl
| ~ sQ116_spl
| ~ aElementOf0(sK1_skl(xU,xU),xU) ),
inference(forward_demodulation,[status(thm)],[f818,f992]) ).
fof(f994,plain,
! [X0] :
( ~ sQ100_spl
| ~ sQ116_spl
| sdtlpdtrp0(xf,X0) != X0
| ~ aElementOf0(X0,xU)
| aFixedPointOf0(X0,xf)
| ~ aFunction0(xf) ),
inference(paramodulation,[status(thm)],[f881,f126]) ).
fof(f995,definition,
! [X0] :
( sQ125_spl
<=> ( sdtlpdtrp0(xf,X0) != X0
| ~ aElementOf0(X0,xU)
| aFixedPointOf0(X0,xf) ) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f996,plain,
! [X0] :
( ~ sQ125_spl
| sdtlpdtrp0(xf,X0) != X0
| ~ aElementOf0(X0,xU)
| aFixedPointOf0(X0,xf) ),
inference(component_clause,[status(thm)],[f995]) ).
fof(f998,plain,
( ~ sQ100_spl
| ~ sQ116_spl
| sQ125_spl
| ~ sQ99_spl ),
inference(split_clause,[status(thm)],[f994,f689,f995,f817,f692]) ).
fof(f999,plain,
( ~ sQ14_spl
| sdtlseqdt0(sK1_skl(xU,xU),sK1_skl(xU,xU)) ),
inference(resolution,[status(thm)],[f212,f55]) ).
fof(f1000,plain,
( ~ sQ117_spl
| ~ sQ100_spl
| ~ sQ116_spl
| xU != xU
| isOn0(xf,xU) ),
inference(resolution,[status(thm)],[f884,f152]) ).
fof(f1001,definition,
( sQ126_spl
<=> xU = xU ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f1004,plain,
( ~ sQ117_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ sQ126_spl
| sQ122_spl ),
inference(split_clause,[status(thm)],[f1000,f850,f1001,f817,f692,f822]) ).
fof(f1005,plain,
( sQ50_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ aElementOf0(sK1_skl(xU,szDzozmdt0(xf)),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f881,f812]) ).
fof(f1006,plain,
( sQ50_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ aElementOf0(sK1_skl(xU,xU),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f881,f1005]) ).
fof(f1007,plain,
( sQ50_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ aElementOf0(sK1_skl(xU,xU),xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1006]) ).
fof(f1008,plain,
( sQ41_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ aElementOf0(sK1_skl(xU,szDzozmdt0(xf)),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f881,f814]) ).
fof(f1009,plain,
( sQ41_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ aElementOf0(sK1_skl(xU,xU),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f881,f1008]) ).
fof(f1010,plain,
( sQ41_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ aElementOf0(sK1_skl(xU,xU),xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1009]) ).
fof(f1011,plain,
! [X0,X1] :
( ~ sQ100_spl
| ~ sQ116_spl
| sdtlseqdt0(sdtlpdtrp0(xf,X0),sdtlpdtrp0(xf,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| ~ isMonotone0(xf)
| ~ aFunction0(xf) ),
inference(paramodulation,[status(thm)],[f881,f130]) ).
fof(f1012,definition,
( sQ127_spl
<=> isMonotone0(xf) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f1014,plain,
( sQ127_spl
| ~ isMonotone0(xf) ),
inference(component_clause,[status(thm)],[f1012]) ).
fof(f1015,definition,
! [X0,X1] :
( sQ128_spl
<=> ( sdtlseqdt0(sdtlpdtrp0(xf,X0),sdtlpdtrp0(xf,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szDzozmdt0(xf))
| ~ aElementOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f1016,plain,
! [X0,X1] :
( ~ sQ128_spl
| sdtlseqdt0(sdtlpdtrp0(xf,X0),sdtlpdtrp0(xf,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szDzozmdt0(xf))
| ~ aElementOf0(X0,xU) ),
inference(component_clause,[status(thm)],[f1015]) ).
fof(f1018,plain,
( ~ sQ100_spl
| ~ sQ116_spl
| sQ128_spl
| ~ sQ127_spl
| ~ sQ99_spl ),
inference(split_clause,[status(thm)],[f1011,f689,f1012,f1015,f817,f692]) ).
fof(f1019,plain,
( sQ127_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1014,f137]) ).
fof(f1020,plain,
sQ127_spl,
inference(contradiction_clause,[status(thm)],[f1019]) ).
fof(f1021,plain,
! [X0,X1] :
( ~ sQ128_spl
| ~ sQ100_spl
| ~ sQ116_spl
| sdtlseqdt0(sdtlpdtrp0(xf,X0),sdtlpdtrp0(xf,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,xU)
| ~ aElementOf0(X0,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1016]) ).
fof(f1032,plain,
( sQ48_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ aElementOf0(sK1_skl(xU,szDzozmdt0(xf)),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f881,f786]) ).
fof(f1033,plain,
( sQ48_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ aElementOf0(sK1_skl(xU,xU),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f881,f1032]) ).
fof(f1034,plain,
( sQ48_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ aElementOf0(sK1_skl(xU,xU),xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1033]) ).
fof(f1035,plain,
( ~ sQ12_spl
| sQ50_spl
| ~ sQ100_spl
| ~ sQ116_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f196,f1007]) ).
fof(f1036,plain,
( ~ sQ12_spl
| sQ50_spl
| ~ sQ100_spl
| ~ sQ116_spl ),
inference(contradiction_clause,[status(thm)],[f1035]) ).
fof(f1037,plain,
( ~ sQ38_spl
| ~ sQ100_spl
| ~ sQ116_spl
| sdtlseqdt0(sK1_skl(xU,xU),sK1_skl(xU,xU)) ),
inference(resolution,[status(thm)],[f889,f55]) ).
fof(f1038,plain,
( ~ sQ119_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sdtlpdtrp0(xf,sK0_skl(xU)),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f881,f837]) ).
fof(f1039,plain,
( ~ sQ119_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sdtlpdtrp0(xf,sK0_skl(xU)),xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1038]) ).
fof(f1040,plain,
( ~ sQ119_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ isEmpty0(xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1039,f42]) ).
fof(f1041,plain,
( ~ sQ119_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElement0(sdtlpdtrp0(xf,sK0_skl(xU)))
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1039,f38]) ).
fof(f1042,plain,
( ~ sQ119_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1040,f162,f154,f817,f692,f833]) ).
fof(f1043,definition,
( sQ131_spl
<=> aElement0(sdtlpdtrp0(xf,sK0_skl(xU))) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f1044,plain,
( ~ sQ131_spl
| aElement0(sdtlpdtrp0(xf,sK0_skl(xU))) ),
inference(component_clause,[status(thm)],[f1043]) ).
fof(f1046,plain,
( ~ sQ119_spl
| ~ sQ100_spl
| ~ sQ116_spl
| sQ131_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1041,f162,f1043,f817,f692,f833]) ).
fof(f1047,plain,
( ~ sQ119_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ sQ19_spl
| aElementOf0(sK2_skl(sdtlpdtrp0(xf,sK0_skl(xU)),xU,xU),xU)
| aLowerBoundOfIn0(sdtlpdtrp0(xf,sK0_skl(xU)),xU,xU) ),
inference(resolution,[status(thm)],[f252,f1039]) ).
fof(f1048,plain,
( ~ sQ89_spl
| ~ sQ19_spl
| aElementOf0(sK2_skl(sK6_skl(xU,xU),xU,xU),xU)
| aLowerBoundOfIn0(sK6_skl(xU,xU),xU,xU) ),
inference(resolution,[status(thm)],[f252,f635]) ).
fof(f1049,plain,
( ~ sQ3_spl
| ~ sQ19_spl
| aElementOf0(sK2_skl(sK0_skl(xU),xU,xU),xU)
| aLowerBoundOfIn0(sK0_skl(xU),xU,xU) ),
inference(resolution,[status(thm)],[f252,f158]) ).
fof(f1050,definition,
( sQ132_spl
<=> aLowerBoundOfIn0(sdtlpdtrp0(xf,sK0_skl(xU)),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f1051,plain,
( ~ sQ132_spl
| aLowerBoundOfIn0(sdtlpdtrp0(xf,sK0_skl(xU)),xU,xU) ),
inference(component_clause,[status(thm)],[f1050]) ).
fof(f1053,definition,
( sQ133_spl
<=> aElementOf0(sK2_skl(sdtlpdtrp0(xf,sK0_skl(xU)),xU,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f1056,plain,
( ~ sQ119_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ sQ19_spl
| sQ133_spl
| sQ132_spl ),
inference(split_clause,[status(thm)],[f1047,f1050,f1053,f251,f817,f692,f833]) ).
fof(f1057,definition,
( sQ134_spl
<=> aElementOf0(sK2_skl(sK6_skl(xU,xU),xU,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f1060,plain,
( ~ sQ89_spl
| ~ sQ19_spl
| sQ134_spl
| sQ91_spl ),
inference(split_clause,[status(thm)],[f1048,f642,f1057,f251,f634]) ).
fof(f1061,definition,
( sQ135_spl
<=> aLowerBoundOfIn0(sK0_skl(xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition]) ).
fof(f1062,plain,
( ~ sQ135_spl
| aLowerBoundOfIn0(sK0_skl(xU),xU,xU) ),
inference(component_clause,[status(thm)],[f1061]) ).
fof(f1064,definition,
( sQ136_spl
<=> aElementOf0(sK2_skl(sK0_skl(xU),xU,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f1067,plain,
( ~ sQ3_spl
| ~ sQ19_spl
| sQ136_spl
| sQ135_spl ),
inference(split_clause,[status(thm)],[f1049,f1061,f1064,f251,f157]) ).
fof(f1068,plain,
( ~ sQ131_spl
| sdtlseqdt0(sdtlpdtrp0(xf,sK0_skl(xU)),sdtlpdtrp0(xf,sK0_skl(xU))) ),
inference(resolution,[status(thm)],[f1044,f55]) ).
fof(f1069,plain,
( ~ sQ135_spl
| aLowerBoundOfIn0(sK4_skl(sK0_skl(xU),xU,xU),xU,xU)
| aInfimumOfIn0(sK0_skl(xU),xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1062,f387]) ).
fof(f1070,plain,
! [X0] :
( ~ sQ135_spl
| sdtlseqdt0(sK0_skl(xU),X0)
| ~ aElementOf0(X0,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1062,f65]) ).
fof(f1071,plain,
( ~ sQ135_spl
| aElementOf0(sK0_skl(xU),xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1062,f64]) ).
fof(f1072,definition,
( sQ137_spl
<=> aInfimumOfIn0(sK0_skl(xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f1073,plain,
( ~ sQ137_spl
| aInfimumOfIn0(sK0_skl(xU),xU,xU) ),
inference(component_clause,[status(thm)],[f1072]) ).
fof(f1075,definition,
( sQ138_spl
<=> aLowerBoundOfIn0(sK4_skl(sK0_skl(xU),xU,xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f1078,plain,
( ~ sQ135_spl
| sQ138_spl
| sQ137_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1069,f162,f192,f1072,f1075,f1061]) ).
fof(f1079,definition,
! [X0] :
( sQ139_spl
<=> ( sdtlseqdt0(sK0_skl(xU),X0)
| ~ aElementOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f1080,plain,
! [X0] :
( ~ sQ139_spl
| sdtlseqdt0(sK0_skl(xU),X0)
| ~ aElementOf0(X0,xU) ),
inference(component_clause,[status(thm)],[f1079]) ).
fof(f1082,plain,
( ~ sQ135_spl
| sQ139_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1070,f162,f192,f1079,f1061]) ).
fof(f1083,plain,
( ~ sQ135_spl
| sQ3_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1071,f162,f192,f157,f1061]) ).
fof(f1084,plain,
! [X0] :
( ~ sQ137_spl
| sK0_skl(xU) = X0
| ~ aInfimumOfIn0(X0,xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1073,f97]) ).
fof(f1085,plain,
( ~ sQ137_spl
| aElementOf0(sK0_skl(xU),xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1073,f80]) ).
fof(f1086,plain,
! [X0] :
( ~ sQ137_spl
| sdtlseqdt0(X0,sK0_skl(xU))
| ~ aLowerBoundOfIn0(X0,xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1073,f82]) ).
fof(f1087,plain,
( ~ sQ137_spl
| aLowerBoundOfIn0(sK0_skl(xU),xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1073,f81]) ).
fof(f1088,definition,
! [X0] :
( sQ140_spl
<=> ( sK0_skl(xU) = X0
| ~ aInfimumOfIn0(X0,xU,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f1089,plain,
! [X0] :
( ~ sQ140_spl
| sK0_skl(xU) = X0
| ~ aInfimumOfIn0(X0,xU,xU) ),
inference(component_clause,[status(thm)],[f1088]) ).
fof(f1091,plain,
( ~ sQ137_spl
| sQ140_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1084,f162,f192,f1088,f1072]) ).
fof(f1092,plain,
( ~ sQ137_spl
| sQ3_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1085,f162,f192,f157,f1072]) ).
fof(f1093,definition,
! [X0] :
( sQ141_spl
<=> ( sdtlseqdt0(X0,sK0_skl(xU))
| ~ aLowerBoundOfIn0(X0,xU,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f1094,plain,
! [X0] :
( ~ sQ141_spl
| sdtlseqdt0(X0,sK0_skl(xU))
| ~ aLowerBoundOfIn0(X0,xU,xU) ),
inference(component_clause,[status(thm)],[f1093]) ).
fof(f1096,plain,
( ~ sQ137_spl
| sQ141_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1086,f162,f192,f1093,f1072]) ).
fof(f1097,plain,
( ~ sQ137_spl
| sQ135_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1087,f162,f192,f1061,f1072]) ).
fof(f1103,plain,
( ~ sQ119_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ sQ124_spl
| aElementOf0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU))),xU) ),
inference(resolution,[status(thm)],[f959,f1039]) ).
fof(f1104,plain,
( ~ sQ89_spl
| ~ sQ124_spl
| ~ sQ116_spl
| aElementOf0(sdtlpdtrp0(xf,sK6_skl(xU,xU)),xU) ),
inference(resolution,[status(thm)],[f959,f635]) ).
fof(f1105,plain,
( ~ sQ3_spl
| ~ sQ124_spl
| ~ sQ116_spl
| aElementOf0(sdtlpdtrp0(xf,sK0_skl(xU)),xU) ),
inference(resolution,[status(thm)],[f959,f158]) ).
fof(f1106,plain,
! [X0] :
( ~ sQ85_spl
| sK7_skl(xU,xU) = X0
| ~ aSupremumOfIn0(X0,xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f611,f95]) ).
fof(f1107,plain,
! [X0] :
( ~ sQ85_spl
| sdtlseqdt0(sK7_skl(xU,xU),X0)
| ~ aUpperBoundOfIn0(X0,xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f611,f91]) ).
fof(f1108,plain,
( ~ sQ85_spl
| aUpperBoundOfIn0(sK7_skl(xU,xU),xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f611,f90]) ).
fof(f1109,plain,
( ~ sQ85_spl
| aElementOf0(sK7_skl(xU,xU),xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f611,f89]) ).
fof(f1110,definition,
! [X0] :
( sQ143_spl
<=> ( sK7_skl(xU,xU) = X0
| ~ aSupremumOfIn0(X0,xU,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f1111,plain,
! [X0] :
( ~ sQ143_spl
| sK7_skl(xU,xU) = X0
| ~ aSupremumOfIn0(X0,xU,xU) ),
inference(component_clause,[status(thm)],[f1110]) ).
fof(f1113,plain,
( ~ sQ85_spl
| sQ143_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1106,f162,f192,f1110,f610]) ).
fof(f1114,definition,
! [X0] :
( sQ144_spl
<=> ( sdtlseqdt0(sK7_skl(xU,xU),X0)
| ~ aUpperBoundOfIn0(X0,xU,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f1115,plain,
! [X0] :
( ~ sQ144_spl
| sdtlseqdt0(sK7_skl(xU,xU),X0)
| ~ aUpperBoundOfIn0(X0,xU,xU) ),
inference(component_clause,[status(thm)],[f1114]) ).
fof(f1117,plain,
( ~ sQ85_spl
| sQ144_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1107,f162,f192,f1114,f610]) ).
fof(f1118,definition,
( sQ145_spl
<=> aUpperBoundOfIn0(sK7_skl(xU,xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f1119,plain,
( ~ sQ145_spl
| aUpperBoundOfIn0(sK7_skl(xU,xU),xU,xU) ),
inference(component_clause,[status(thm)],[f1118]) ).
fof(f1121,plain,
( ~ sQ85_spl
| sQ145_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1108,f162,f192,f1118,f610]) ).
fof(f1122,definition,
( sQ146_spl
<=> aElementOf0(sK7_skl(xU,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f1123,plain,
( ~ sQ146_spl
| aElementOf0(sK7_skl(xU,xU),xU) ),
inference(component_clause,[status(thm)],[f1122]) ).
fof(f1125,plain,
( ~ sQ85_spl
| sQ146_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1109,f162,f192,f1122,f610]) ).
fof(f1126,plain,
( ~ sQ119_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ sQ25_spl
| aElementOf0(sK3_skl(sdtlpdtrp0(xf,sK0_skl(xU)),xU,xU),xU)
| aUpperBoundOfIn0(sdtlpdtrp0(xf,sK0_skl(xU)),xU,xU) ),
inference(resolution,[status(thm)],[f280,f1039]) ).
fof(f1127,plain,
( ~ sQ89_spl
| ~ sQ25_spl
| aElementOf0(sK3_skl(sK6_skl(xU,xU),xU,xU),xU)
| aUpperBoundOfIn0(sK6_skl(xU,xU),xU,xU) ),
inference(resolution,[status(thm)],[f280,f635]) ).
fof(f1128,plain,
( ~ sQ3_spl
| ~ sQ25_spl
| aElementOf0(sK3_skl(sK0_skl(xU),xU,xU),xU)
| aUpperBoundOfIn0(sK0_skl(xU),xU,xU) ),
inference(resolution,[status(thm)],[f280,f158]) ).
fof(f1129,definition,
( sQ147_spl
<=> aUpperBoundOfIn0(sdtlpdtrp0(xf,sK0_skl(xU)),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f1130,plain,
( ~ sQ147_spl
| aUpperBoundOfIn0(sdtlpdtrp0(xf,sK0_skl(xU)),xU,xU) ),
inference(component_clause,[status(thm)],[f1129]) ).
fof(f1132,definition,
( sQ148_spl
<=> aElementOf0(sK3_skl(sdtlpdtrp0(xf,sK0_skl(xU)),xU,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f1135,plain,
( ~ sQ119_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ sQ25_spl
| sQ148_spl
| sQ147_spl ),
inference(split_clause,[status(thm)],[f1126,f1129,f1132,f279,f817,f692,f833]) ).
fof(f1136,definition,
( sQ149_spl
<=> aUpperBoundOfIn0(sK6_skl(xU,xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f1137,plain,
( ~ sQ149_spl
| aUpperBoundOfIn0(sK6_skl(xU,xU),xU,xU) ),
inference(component_clause,[status(thm)],[f1136]) ).
fof(f1139,definition,
( sQ150_spl
<=> aElementOf0(sK3_skl(sK6_skl(xU,xU),xU,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ150_spl])],[split_symbol_definition]) ).
fof(f1142,plain,
( ~ sQ89_spl
| ~ sQ25_spl
| sQ150_spl
| sQ149_spl ),
inference(split_clause,[status(thm)],[f1127,f1136,f1139,f279,f634]) ).
fof(f1143,definition,
( sQ151_spl
<=> aUpperBoundOfIn0(sK0_skl(xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f1144,plain,
( ~ sQ151_spl
| aUpperBoundOfIn0(sK0_skl(xU),xU,xU) ),
inference(component_clause,[status(thm)],[f1143]) ).
fof(f1146,definition,
( sQ152_spl
<=> aElementOf0(sK3_skl(sK0_skl(xU),xU,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f1149,plain,
( ~ sQ3_spl
| ~ sQ25_spl
| sQ152_spl
| sQ151_spl ),
inference(split_clause,[status(thm)],[f1128,f1143,f1146,f279,f157]) ).
fof(f1150,plain,
( ~ sQ25_spl
| ~ sQ146_spl
| aElementOf0(sK3_skl(sK7_skl(xU,xU),xU,xU),xU)
| aUpperBoundOfIn0(sK7_skl(xU,xU),xU,xU) ),
inference(resolution,[status(thm)],[f1123,f280]) ).
fof(f1151,plain,
( ~ sQ124_spl
| ~ sQ116_spl
| ~ sQ146_spl
| aElementOf0(sdtlpdtrp0(xf,sK7_skl(xU,xU)),xU) ),
inference(resolution,[status(thm)],[f1123,f959]) ).
fof(f1152,plain,
( ~ sQ19_spl
| ~ sQ146_spl
| aElementOf0(sK2_skl(sK7_skl(xU,xU),xU,xU),xU)
| aLowerBoundOfIn0(sK7_skl(xU,xU),xU,xU) ),
inference(resolution,[status(thm)],[f1123,f252]) ).
fof(f1153,plain,
( ~ sQ146_spl
| ~ isEmpty0(xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1123,f42]) ).
fof(f1154,plain,
( ~ sQ146_spl
| aElement0(sK7_skl(xU,xU))
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1123,f38]) ).
fof(f1155,definition,
( sQ153_spl
<=> aElementOf0(sK3_skl(sK7_skl(xU,xU),xU,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ153_spl])],[split_symbol_definition]) ).
fof(f1158,plain,
( ~ sQ25_spl
| ~ sQ146_spl
| sQ153_spl
| sQ145_spl ),
inference(split_clause,[status(thm)],[f1150,f1118,f1155,f1122,f279]) ).
fof(f1159,definition,
( sQ154_spl
<=> aLowerBoundOfIn0(sK7_skl(xU,xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition]) ).
fof(f1160,plain,
( ~ sQ154_spl
| aLowerBoundOfIn0(sK7_skl(xU,xU),xU,xU) ),
inference(component_clause,[status(thm)],[f1159]) ).
fof(f1162,definition,
( sQ155_spl
<=> aElementOf0(sK2_skl(sK7_skl(xU,xU),xU,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition]) ).
fof(f1165,plain,
( ~ sQ19_spl
| ~ sQ146_spl
| sQ155_spl
| sQ154_spl ),
inference(split_clause,[status(thm)],[f1152,f1159,f1162,f1122,f251]) ).
fof(f1166,plain,
( ~ sQ146_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1153,f162,f154,f1122]) ).
fof(f1167,definition,
( sQ156_spl
<=> aElement0(sK7_skl(xU,xU)) ),
introduced(definition,[new_symbols(definition,[sQ156_spl])],[split_symbol_definition]) ).
fof(f1168,plain,
( ~ sQ156_spl
| aElement0(sK7_skl(xU,xU)) ),
inference(component_clause,[status(thm)],[f1167]) ).
fof(f1170,plain,
( ~ sQ146_spl
| sQ156_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1154,f162,f1167,f1122]) ).
fof(f1171,plain,
( ~ sQ156_spl
| sdtlseqdt0(sK7_skl(xU,xU),sK7_skl(xU,xU)) ),
inference(resolution,[status(thm)],[f1168,f55]) ).
fof(f1172,plain,
( ~ sQ39_spl
| ~ sQ100_spl
| ~ sQ116_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(szDzozmdt0(xf))) ),
inference(forward_demodulation,[status(thm)],[f881,f413]) ).
fof(f1173,plain,
( ~ sQ39_spl
| ~ sQ100_spl
| ~ sQ116_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(forward_demodulation,[status(thm)],[f881,f1172]) ).
fof(f1174,plain,
! [X0] :
( ~ sQ53_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aUpperBoundOfIn0(X0,xU,szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f881,f419]) ).
fof(f1175,plain,
! [X0] :
( ~ sQ53_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1174]) ).
fof(f1176,plain,
! [X0] :
( ~ sQ53_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1175]) ).
fof(f1177,plain,
! [X0] :
( ~ sQ53_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,xU,szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1176]) ).
fof(f1178,plain,
! [X0] :
( ~ sQ53_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,xU,xU),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1177]) ).
fof(f1179,plain,
! [X0] :
( ~ sQ53_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1178]) ).
fof(f1180,plain,
( ~ sQ151_spl
| aUpperBoundOfIn0(sK5_skl(sK0_skl(xU),xU,xU),xU,xU)
| aSupremumOfIn0(sK0_skl(xU),xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1144,f539]) ).
fof(f1181,plain,
! [X0] :
( ~ sQ151_spl
| sdtlseqdt0(X0,sK0_skl(xU))
| ~ aElementOf0(X0,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1144,f73]) ).
fof(f1182,plain,
( ~ sQ151_spl
| aElementOf0(sK0_skl(xU),xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1144,f72]) ).
fof(f1183,definition,
( sQ157_spl
<=> aSupremumOfIn0(sK0_skl(xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f1184,plain,
( ~ sQ157_spl
| aSupremumOfIn0(sK0_skl(xU),xU,xU) ),
inference(component_clause,[status(thm)],[f1183]) ).
fof(f1186,definition,
( sQ158_spl
<=> aUpperBoundOfIn0(sK5_skl(sK0_skl(xU),xU,xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ158_spl])],[split_symbol_definition]) ).
fof(f1189,plain,
( ~ sQ151_spl
| sQ158_spl
| sQ157_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1180,f162,f192,f1183,f1186,f1143]) ).
fof(f1190,definition,
! [X0] :
( sQ159_spl
<=> ( sdtlseqdt0(X0,sK0_skl(xU))
| ~ aElementOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f1191,plain,
! [X0] :
( ~ sQ159_spl
| sdtlseqdt0(X0,sK0_skl(xU))
| ~ aElementOf0(X0,xU) ),
inference(component_clause,[status(thm)],[f1190]) ).
fof(f1193,plain,
( ~ sQ151_spl
| sQ159_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1181,f162,f192,f1190,f1143]) ).
fof(f1194,plain,
( ~ sQ151_spl
| sQ3_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1182,f162,f192,f157,f1143]) ).
fof(f1195,plain,
! [X0] :
( ~ sQ157_spl
| sK0_skl(xU) = X0
| ~ aSupremumOfIn0(X0,xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1184,f95]) ).
fof(f1196,plain,
! [X0] :
( ~ sQ157_spl
| sdtlseqdt0(sK0_skl(xU),X0)
| ~ aUpperBoundOfIn0(X0,xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1184,f91]) ).
fof(f1197,plain,
( ~ sQ157_spl
| aUpperBoundOfIn0(sK0_skl(xU),xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1184,f90]) ).
fof(f1198,plain,
( ~ sQ157_spl
| aElementOf0(sK0_skl(xU),xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1184,f89]) ).
fof(f1199,definition,
! [X0] :
( sQ160_spl
<=> ( sK0_skl(xU) = X0
| ~ aSupremumOfIn0(X0,xU,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f1200,plain,
! [X0] :
( ~ sQ160_spl
| sK0_skl(xU) = X0
| ~ aSupremumOfIn0(X0,xU,xU) ),
inference(component_clause,[status(thm)],[f1199]) ).
fof(f1202,plain,
( ~ sQ157_spl
| sQ160_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1195,f162,f192,f1199,f1183]) ).
fof(f1203,definition,
! [X0] :
( sQ161_spl
<=> ( sdtlseqdt0(sK0_skl(xU),X0)
| ~ aUpperBoundOfIn0(X0,xU,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f1204,plain,
! [X0] :
( ~ sQ161_spl
| sdtlseqdt0(sK0_skl(xU),X0)
| ~ aUpperBoundOfIn0(X0,xU,xU) ),
inference(component_clause,[status(thm)],[f1203]) ).
fof(f1206,plain,
( ~ sQ157_spl
| sQ161_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1196,f162,f192,f1203,f1183]) ).
fof(f1207,plain,
( ~ sQ157_spl
| sQ151_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1197,f162,f192,f1143,f1183]) ).
fof(f1208,plain,
( ~ sQ157_spl
| sQ3_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1198,f162,f192,f157,f1183]) ).
fof(f1209,plain,
( ~ sQ91_spl
| aLowerBoundOfIn0(sK4_skl(sK6_skl(xU,xU),xU,xU),xU,xU)
| aInfimumOfIn0(sK6_skl(xU,xU),xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f643,f387]) ).
fof(f1210,plain,
! [X0] :
( ~ sQ91_spl
| sdtlseqdt0(sK6_skl(xU,xU),X0)
| ~ aElementOf0(X0,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f643,f65]) ).
fof(f1211,plain,
( ~ sQ91_spl
| aElementOf0(sK6_skl(xU,xU),xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f643,f64]) ).
fof(f1212,definition,
( sQ162_spl
<=> aLowerBoundOfIn0(sK4_skl(sK6_skl(xU,xU),xU,xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition]) ).
fof(f1215,plain,
( ~ sQ91_spl
| sQ162_spl
| sQ81_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1209,f162,f192,f590,f1212,f642]) ).
fof(f1216,definition,
! [X0] :
( sQ163_spl
<=> ( sdtlseqdt0(sK6_skl(xU,xU),X0)
| ~ aElementOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f1217,plain,
! [X0] :
( ~ sQ163_spl
| sdtlseqdt0(sK6_skl(xU,xU),X0)
| ~ aElementOf0(X0,xU) ),
inference(component_clause,[status(thm)],[f1216]) ).
fof(f1219,plain,
( ~ sQ91_spl
| sQ163_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1210,f162,f192,f1216,f642]) ).
fof(f1220,plain,
( ~ sQ91_spl
| sQ89_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1211,f162,f192,f634,f642]) ).
fof(f1221,plain,
( ~ sQ146_spl
| ~ sQ125_spl
| sdtlpdtrp0(xf,sK7_skl(xU,xU)) != sK7_skl(xU,xU)
| aFixedPointOf0(sK7_skl(xU,xU),xf) ),
inference(resolution,[status(thm)],[f996,f1123]) ).
fof(f1222,plain,
( ~ sQ119_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ sQ125_spl
| sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU))) != sdtlpdtrp0(xf,sK0_skl(xU))
| aFixedPointOf0(sdtlpdtrp0(xf,sK0_skl(xU)),xf) ),
inference(resolution,[status(thm)],[f996,f1039]) ).
fof(f1223,plain,
( ~ sQ89_spl
| ~ sQ125_spl
| sdtlpdtrp0(xf,sK6_skl(xU,xU)) != sK6_skl(xU,xU)
| aFixedPointOf0(sK6_skl(xU,xU),xf) ),
inference(resolution,[status(thm)],[f996,f635]) ).
fof(f1224,plain,
( ~ sQ3_spl
| ~ sQ125_spl
| sdtlpdtrp0(xf,sK0_skl(xU)) != sK0_skl(xU)
| aFixedPointOf0(sK0_skl(xU),xf) ),
inference(resolution,[status(thm)],[f996,f158]) ).
fof(f1225,definition,
( sQ164_spl
<=> aFixedPointOf0(sK7_skl(xU,xU),xf) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f1226,plain,
( ~ sQ164_spl
| aFixedPointOf0(sK7_skl(xU,xU),xf) ),
inference(component_clause,[status(thm)],[f1225]) ).
fof(f1228,definition,
( sQ165_spl
<=> sdtlpdtrp0(xf,sK7_skl(xU,xU)) = sK7_skl(xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ165_spl])],[split_symbol_definition]) ).
fof(f1229,plain,
( ~ sQ165_spl
| sdtlpdtrp0(xf,sK7_skl(xU,xU)) = sK7_skl(xU,xU) ),
inference(component_clause,[status(thm)],[f1228]) ).
fof(f1231,plain,
( ~ sQ146_spl
| ~ sQ125_spl
| ~ sQ165_spl
| sQ164_spl ),
inference(split_clause,[status(thm)],[f1221,f1225,f1228,f995,f1122]) ).
fof(f1232,definition,
( sQ166_spl
<=> aFixedPointOf0(sdtlpdtrp0(xf,sK0_skl(xU)),xf) ),
introduced(definition,[new_symbols(definition,[sQ166_spl])],[split_symbol_definition]) ).
fof(f1233,plain,
( ~ sQ166_spl
| aFixedPointOf0(sdtlpdtrp0(xf,sK0_skl(xU)),xf) ),
inference(component_clause,[status(thm)],[f1232]) ).
fof(f1235,definition,
( sQ167_spl
<=> sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU))) = sdtlpdtrp0(xf,sK0_skl(xU)) ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f1238,plain,
( ~ sQ119_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ sQ125_spl
| ~ sQ167_spl
| sQ166_spl ),
inference(split_clause,[status(thm)],[f1222,f1232,f1235,f995,f817,f692,f833]) ).
fof(f1239,definition,
( sQ168_spl
<=> aFixedPointOf0(sK6_skl(xU,xU),xf) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f1240,plain,
( ~ sQ168_spl
| aFixedPointOf0(sK6_skl(xU,xU),xf) ),
inference(component_clause,[status(thm)],[f1239]) ).
fof(f1242,definition,
( sQ169_spl
<=> sdtlpdtrp0(xf,sK6_skl(xU,xU)) = sK6_skl(xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition]) ).
fof(f1243,plain,
( ~ sQ169_spl
| sdtlpdtrp0(xf,sK6_skl(xU,xU)) = sK6_skl(xU,xU) ),
inference(component_clause,[status(thm)],[f1242]) ).
fof(f1245,plain,
( ~ sQ89_spl
| ~ sQ125_spl
| ~ sQ169_spl
| sQ168_spl ),
inference(split_clause,[status(thm)],[f1223,f1239,f1242,f995,f634]) ).
fof(f1246,definition,
( sQ170_spl
<=> aFixedPointOf0(sK0_skl(xU),xf) ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f1247,plain,
( ~ sQ170_spl
| aFixedPointOf0(sK0_skl(xU),xf) ),
inference(component_clause,[status(thm)],[f1246]) ).
fof(f1249,definition,
( sQ171_spl
<=> sdtlpdtrp0(xf,sK0_skl(xU)) = sK0_skl(xU) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f1250,plain,
( ~ sQ171_spl
| sdtlpdtrp0(xf,sK0_skl(xU)) = sK0_skl(xU) ),
inference(component_clause,[status(thm)],[f1249]) ).
fof(f1252,plain,
( ~ sQ3_spl
| ~ sQ125_spl
| ~ sQ171_spl
| sQ170_spl ),
inference(split_clause,[status(thm)],[f1224,f1246,f1249,f995,f157]) ).
fof(f1253,plain,
( ~ sQ15_spl
| ~ sQ128_spl
| ~ sQ100_spl
| ~ sQ116_spl
| sdtlseqdt0(sdtlpdtrp0(xf,sK0_skl(xU)),sdtlpdtrp0(xf,sK0_skl(xU)))
| ~ aElementOf0(sK0_skl(xU),xU)
| ~ aElementOf0(sK0_skl(xU),xU) ),
inference(resolution,[status(thm)],[f1021,f222]) ).
fof(f1254,definition,
( sQ172_spl
<=> sdtlseqdt0(sdtlpdtrp0(xf,sK0_skl(xU)),sdtlpdtrp0(xf,sK0_skl(xU))) ),
introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition]) ).
fof(f1255,plain,
( ~ sQ172_spl
| sdtlseqdt0(sdtlpdtrp0(xf,sK0_skl(xU)),sdtlpdtrp0(xf,sK0_skl(xU))) ),
inference(component_clause,[status(thm)],[f1254]) ).
fof(f1257,plain,
( ~ sQ15_spl
| ~ sQ128_spl
| ~ sQ100_spl
| ~ sQ116_spl
| sQ172_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1253,f157,f1254,f817,f692,f1015,f218]) ).
fof(f1258,plain,
( ~ sQ170_spl
| sdtlpdtrp0(xf,sK0_skl(xU)) = sK0_skl(xU)
| ~ aFunction0(xf) ),
inference(resolution,[status(thm)],[f1247,f125]) ).
fof(f1259,plain,
( ~ sQ170_spl
| aElementOf0(sK0_skl(xU),szDzozmdt0(xf))
| ~ aFunction0(xf) ),
inference(resolution,[status(thm)],[f1247,f124]) ).
fof(f1260,plain,
( ~ sQ170_spl
| sQ171_spl
| ~ sQ99_spl ),
inference(split_clause,[status(thm)],[f1258,f689,f1249,f1246]) ).
fof(f1261,definition,
( sQ173_spl
<=> aElementOf0(sK0_skl(xU),szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ173_spl])],[split_symbol_definition]) ).
fof(f1262,plain,
( ~ sQ173_spl
| aElementOf0(sK0_skl(xU),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f1261]) ).
fof(f1264,plain,
( ~ sQ170_spl
| sQ173_spl
| ~ sQ99_spl ),
inference(split_clause,[status(thm)],[f1259,f689,f1261,f1246]) ).
fof(f1265,plain,
( ~ sQ173_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK0_skl(xU),xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1262]) ).
fof(f1266,plain,
( ~ sQ164_spl
| sdtlpdtrp0(xf,sK7_skl(xU,xU)) = sK7_skl(xU,xU)
| ~ aFunction0(xf) ),
inference(resolution,[status(thm)],[f1226,f125]) ).
fof(f1267,plain,
( ~ sQ164_spl
| aElementOf0(sK7_skl(xU,xU),szDzozmdt0(xf))
| ~ aFunction0(xf) ),
inference(resolution,[status(thm)],[f1226,f124]) ).
fof(f1268,plain,
( ~ sQ164_spl
| sQ165_spl
| ~ sQ99_spl ),
inference(split_clause,[status(thm)],[f1266,f689,f1228,f1225]) ).
fof(f1269,definition,
( sQ174_spl
<=> aElementOf0(sK7_skl(xU,xU),szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition]) ).
fof(f1270,plain,
( ~ sQ174_spl
| aElementOf0(sK7_skl(xU,xU),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f1269]) ).
fof(f1272,plain,
( ~ sQ164_spl
| sQ174_spl
| ~ sQ99_spl ),
inference(split_clause,[status(thm)],[f1267,f689,f1269,f1225]) ).
fof(f1273,plain,
( ~ sQ174_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK7_skl(xU,xU),xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1270]) ).
fof(f1274,plain,
( ~ sQ131_spl
| ~ sQ171_spl
| aElement0(sK0_skl(xU)) ),
inference(backward_demodulation,[status(thm)],[f1250,f1044]) ).
fof(f1275,plain,
( ~ sQ119_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ sQ171_spl
| aElementOf0(sK0_skl(xU),xU) ),
inference(backward_demodulation,[status(thm)],[f1250,f1039]) ).
fof(f1276,plain,
( ~ sQ168_spl
| sdtlpdtrp0(xf,sK6_skl(xU,xU)) = sK6_skl(xU,xU)
| ~ aFunction0(xf) ),
inference(resolution,[status(thm)],[f1240,f125]) ).
fof(f1277,plain,
( ~ sQ168_spl
| aElementOf0(sK6_skl(xU,xU),szDzozmdt0(xf))
| ~ aFunction0(xf) ),
inference(resolution,[status(thm)],[f1240,f124]) ).
fof(f1278,plain,
( ~ sQ168_spl
| sQ169_spl
| ~ sQ99_spl ),
inference(split_clause,[status(thm)],[f1276,f689,f1242,f1239]) ).
fof(f1279,definition,
( sQ175_spl
<=> aElementOf0(sK6_skl(xU,xU),szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition]) ).
fof(f1280,plain,
( ~ sQ175_spl
| aElementOf0(sK6_skl(xU,xU),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f1279]) ).
fof(f1282,plain,
( ~ sQ168_spl
| sQ175_spl
| ~ sQ99_spl ),
inference(split_clause,[status(thm)],[f1277,f689,f1279,f1239]) ).
fof(f1283,plain,
( ~ sQ175_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK6_skl(xU,xU),xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1280]) ).
fof(f1284,plain,
( ~ sQ73_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElement0(sK1_skl(xU,szDzozmdt0(xf))) ),
inference(forward_demodulation,[status(thm)],[f881,f535]) ).
fof(f1285,plain,
( ~ sQ73_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElement0(sK1_skl(xU,xU)) ),
inference(forward_demodulation,[status(thm)],[f881,f1284]) ).
fof(f1286,plain,
! [X0] :
( ~ sQ54_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aLowerBoundOfIn0(X0,xU,szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f881,f423]) ).
fof(f1287,plain,
! [X0] :
( ~ sQ54_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1286]) ).
fof(f1288,plain,
! [X0] :
( ~ sQ54_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1287]) ).
fof(f1289,plain,
! [X0] :
( ~ sQ54_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,xU,szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1288]) ).
fof(f1290,plain,
! [X0] :
( ~ sQ54_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,xU,xU),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1289]) ).
fof(f1291,plain,
! [X0] :
( ~ sQ54_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1290]) ).
fof(f1292,plain,
( ~ sQ75_spl
| ~ sQ116_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(szRzazndt0(xf))) ),
inference(forward_demodulation,[status(thm)],[f818,f562]) ).
fof(f1293,plain,
( ~ sQ75_spl
| ~ sQ116_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(forward_demodulation,[status(thm)],[f818,f1292]) ).
fof(f1294,plain,
( ~ sQ146_spl
| ~ sQ139_spl
| sdtlseqdt0(sK0_skl(xU),sK7_skl(xU,xU)) ),
inference(resolution,[status(thm)],[f1080,f1123]) ).
fof(f1295,plain,
( ~ sQ89_spl
| ~ sQ139_spl
| sdtlseqdt0(sK0_skl(xU),sK6_skl(xU,xU)) ),
inference(resolution,[status(thm)],[f1080,f635]) ).
fof(f1296,plain,
( ~ sQ3_spl
| ~ sQ139_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(resolution,[status(thm)],[f1080,f158]) ).
fof(f1298,plain,
( ~ sQ81_spl
| ~ sQ140_spl
| sK0_skl(xU) = sK6_skl(xU,xU) ),
inference(resolution,[status(thm)],[f1089,f591]) ).
fof(f1299,plain,
! [X0] :
( ~ sQ70_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,szRzazndt0(xf),szRzazndt0(xf)),szRzazndt0(xf))
| ~ aElementOf0(X0,szRzazndt0(xf))
| aUpperBoundOfIn0(X0,xU,szRzazndt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f818,f517]) ).
fof(f1300,plain,
! [X0] :
( ~ sQ70_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,szRzazndt0(xf),szRzazndt0(xf)),szRzazndt0(xf))
| ~ aElementOf0(X0,szRzazndt0(xf))
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f818,f1299]) ).
fof(f1301,plain,
! [X0] :
( ~ sQ70_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,szRzazndt0(xf),szRzazndt0(xf)),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f818,f1300]) ).
fof(f1302,plain,
! [X0] :
( ~ sQ70_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,xU,szRzazndt0(xf)),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f818,f1301]) ).
fof(f1303,plain,
! [X0] :
( ~ sQ70_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,xU,xU),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f818,f1302]) ).
fof(f1304,plain,
! [X0] :
( ~ sQ70_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f818,f1303]) ).
fof(f1305,plain,
! [X0] :
( ~ sQ71_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,szRzazndt0(xf),szRzazndt0(xf)),szRzazndt0(xf))
| ~ aElementOf0(X0,szRzazndt0(xf))
| aLowerBoundOfIn0(X0,xU,szRzazndt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f818,f521]) ).
fof(f1306,plain,
! [X0] :
( ~ sQ71_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,szRzazndt0(xf),szRzazndt0(xf)),szRzazndt0(xf))
| ~ aElementOf0(X0,szRzazndt0(xf))
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f818,f1305]) ).
fof(f1307,plain,
! [X0] :
( ~ sQ71_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,szRzazndt0(xf),szRzazndt0(xf)),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f818,f1306]) ).
fof(f1308,plain,
! [X0] :
( ~ sQ71_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,xU,szRzazndt0(xf)),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f818,f1307]) ).
fof(f1309,plain,
! [X0] :
( ~ sQ71_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,xU,xU),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f818,f1308]) ).
fof(f1310,plain,
! [X0] :
( ~ sQ71_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f818,f1309]) ).
fof(f1311,plain,
! [X0] :
( ~ sQ67_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aUpperBoundOfIn0(X0,xU,szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f881,f800]) ).
fof(f1312,plain,
! [X0] :
( ~ sQ67_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1311]) ).
fof(f1313,plain,
! [X0] :
( ~ sQ67_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1312]) ).
fof(f1314,plain,
! [X0] :
( ~ sQ67_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,xU,szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1313]) ).
fof(f1315,plain,
! [X0] :
( ~ sQ67_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,xU,xU),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1314]) ).
fof(f1316,plain,
! [X0] :
( ~ sQ67_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1315]) ).
fof(f1317,plain,
( ~ sQ168_spl
| ~ sQ81_spl
| ~ sQ140_spl
| aFixedPointOf0(sK0_skl(xU),xf) ),
inference(backward_demodulation,[status(thm)],[f1298,f1240]) ).
fof(f1318,plain,
( ~ sQ91_spl
| ~ sQ81_spl
| ~ sQ140_spl
| aLowerBoundOfIn0(sK0_skl(xU),xU,xU) ),
inference(backward_demodulation,[status(thm)],[f1298,f643]) ).
fof(f1319,plain,
( ~ sQ94_spl
| ~ sQ81_spl
| ~ sQ140_spl
| aElement0(sK0_skl(xU)) ),
inference(backward_demodulation,[status(thm)],[f1298,f666]) ).
fof(f1320,plain,
( ~ sQ89_spl
| ~ sQ81_spl
| ~ sQ140_spl
| aElementOf0(sK0_skl(xU),xU) ),
inference(backward_demodulation,[status(thm)],[f1298,f635]) ).
fof(f1321,plain,
( ~ sQ81_spl
| ~ sQ140_spl
| aInfimumOfIn0(sK0_skl(xU),xU,xU) ),
inference(backward_demodulation,[status(thm)],[f1298,f591]) ).
fof(f1322,plain,
! [X0] :
( ~ sQ68_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aLowerBoundOfIn0(X0,xU,szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f881,f803]) ).
fof(f1323,plain,
! [X0] :
( ~ sQ68_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1322]) ).
fof(f1324,plain,
! [X0] :
( ~ sQ68_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1323]) ).
fof(f1325,plain,
! [X0] :
( ~ sQ68_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,xU,szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1324]) ).
fof(f1326,plain,
! [X0] :
( ~ sQ68_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,xU,xU),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1325]) ).
fof(f1327,plain,
! [X0] :
( ~ sQ68_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1326]) ).
fof(f1328,plain,
( ~ sQ145_spl
| aUpperBoundOfIn0(sK5_skl(sK7_skl(xU,xU),xU,xU),xU,xU)
| aSupremumOfIn0(sK7_skl(xU,xU),xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1119,f539]) ).
fof(f1329,plain,
! [X0] :
( ~ sQ145_spl
| sdtlseqdt0(X0,sK7_skl(xU,xU))
| ~ aElementOf0(X0,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1119,f73]) ).
fof(f1330,plain,
( ~ sQ145_spl
| aElementOf0(sK7_skl(xU,xU),xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1119,f72]) ).
fof(f1331,definition,
( sQ176_spl
<=> aUpperBoundOfIn0(sK5_skl(sK7_skl(xU,xU),xU,xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ176_spl])],[split_symbol_definition]) ).
fof(f1334,plain,
( ~ sQ145_spl
| sQ176_spl
| sQ85_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1328,f162,f192,f610,f1331,f1118]) ).
fof(f1335,definition,
! [X0] :
( sQ177_spl
<=> ( sdtlseqdt0(X0,sK7_skl(xU,xU))
| ~ aElementOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f1336,plain,
! [X0] :
( ~ sQ177_spl
| sdtlseqdt0(X0,sK7_skl(xU,xU))
| ~ aElementOf0(X0,xU) ),
inference(component_clause,[status(thm)],[f1335]) ).
fof(f1338,plain,
( ~ sQ145_spl
| sQ177_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1329,f162,f192,f1335,f1118]) ).
fof(f1339,plain,
( ~ sQ145_spl
| sQ146_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1330,f162,f192,f1122,f1118]) ).
fof(f1340,plain,
( ~ sQ149_spl
| ~ sQ81_spl
| ~ sQ140_spl
| aUpperBoundOfIn0(sK0_skl(xU),xU,xU) ),
inference(forward_demodulation,[status(thm)],[f1298,f1137]) ).
fof(f1341,plain,
! [X0] :
( ~ sQ64_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aUpperBoundOfIn0(X0,xU,szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f881,f806]) ).
fof(f1342,plain,
! [X0] :
( ~ sQ64_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1341]) ).
fof(f1343,plain,
! [X0] :
( ~ sQ64_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1342]) ).
fof(f1344,plain,
! [X0] :
( ~ sQ64_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,xU,szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1343]) ).
fof(f1345,plain,
! [X0] :
( ~ sQ64_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,xU,xU),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1344]) ).
fof(f1346,plain,
! [X0] :
( ~ sQ64_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1345]) ).
fof(f1347,plain,
! [X0] :
( ~ sQ65_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aLowerBoundOfIn0(X0,xU,szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f881,f809]) ).
fof(f1348,plain,
! [X0] :
( ~ sQ65_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,szDzozmdt0(xf))
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1347]) ).
fof(f1349,plain,
! [X0] :
( ~ sQ65_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,szDzozmdt0(xf),szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1348]) ).
fof(f1350,plain,
! [X0] :
( ~ sQ65_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,xU,szDzozmdt0(xf)),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1349]) ).
fof(f1351,plain,
! [X0] :
( ~ sQ65_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,xU,xU),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1350]) ).
fof(f1352,plain,
! [X0] :
( ~ sQ65_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f881,f1351]) ).
fof(f1353,plain,
( ~ sQ154_spl
| aLowerBoundOfIn0(sK4_skl(sK7_skl(xU,xU),xU,xU),xU,xU)
| aInfimumOfIn0(sK7_skl(xU,xU),xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1160,f387]) ).
fof(f1354,plain,
! [X0] :
( ~ sQ154_spl
| sdtlseqdt0(sK7_skl(xU,xU),X0)
| ~ aElementOf0(X0,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1160,f65]) ).
fof(f1355,plain,
( ~ sQ154_spl
| aElementOf0(sK7_skl(xU,xU),xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f1160,f64]) ).
fof(f1356,definition,
( sQ178_spl
<=> aInfimumOfIn0(sK7_skl(xU,xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f1357,plain,
( ~ sQ178_spl
| aInfimumOfIn0(sK7_skl(xU,xU),xU,xU) ),
inference(component_clause,[status(thm)],[f1356]) ).
fof(f1359,definition,
( sQ179_spl
<=> aLowerBoundOfIn0(sK4_skl(sK7_skl(xU,xU),xU,xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f1362,plain,
( ~ sQ154_spl
| sQ179_spl
| sQ178_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1353,f162,f192,f1356,f1359,f1159]) ).
fof(f1363,definition,
! [X0] :
( sQ180_spl
<=> ( sdtlseqdt0(sK7_skl(xU,xU),X0)
| ~ aElementOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f1364,plain,
! [X0] :
( ~ sQ180_spl
| sdtlseqdt0(sK7_skl(xU,xU),X0)
| ~ aElementOf0(X0,xU) ),
inference(component_clause,[status(thm)],[f1363]) ).
fof(f1366,plain,
( ~ sQ154_spl
| sQ180_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1354,f162,f192,f1363,f1159]) ).
fof(f1367,plain,
( ~ sQ154_spl
| sQ146_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1355,f162,f192,f1122,f1159]) ).
fof(f1368,plain,
( ~ sQ146_spl
| ~ sQ159_spl
| sdtlseqdt0(sK7_skl(xU,xU),sK0_skl(xU)) ),
inference(resolution,[status(thm)],[f1191,f1123]) ).
fof(f1369,plain,
( ~ sQ3_spl
| ~ sQ159_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(resolution,[status(thm)],[f1191,f158]) ).
fof(f1371,plain,
( ~ sQ85_spl
| ~ sQ160_spl
| sK0_skl(xU) = sK7_skl(xU,xU) ),
inference(resolution,[status(thm)],[f1200,f611]) ).
fof(f1372,plain,
( ~ sQ154_spl
| ~ sQ85_spl
| ~ sQ160_spl
| aLowerBoundOfIn0(sK0_skl(xU),xU,xU) ),
inference(backward_demodulation,[status(thm)],[f1371,f1160]) ).
fof(f1373,plain,
( ~ sQ145_spl
| ~ sQ85_spl
| ~ sQ160_spl
| aUpperBoundOfIn0(sK0_skl(xU),xU,xU) ),
inference(backward_demodulation,[status(thm)],[f1371,f1119]) ).
fof(f1374,plain,
( ~ sQ164_spl
| ~ sQ85_spl
| ~ sQ160_spl
| aFixedPointOf0(sK0_skl(xU),xf) ),
inference(backward_demodulation,[status(thm)],[f1371,f1226]) ).
fof(f1375,plain,
( ~ sQ156_spl
| ~ sQ85_spl
| ~ sQ160_spl
| aElement0(sK0_skl(xU)) ),
inference(backward_demodulation,[status(thm)],[f1371,f1168]) ).
fof(f1376,plain,
( ~ sQ146_spl
| ~ sQ85_spl
| ~ sQ160_spl
| aElementOf0(sK0_skl(xU),xU) ),
inference(backward_demodulation,[status(thm)],[f1371,f1123]) ).
fof(f1377,plain,
( ~ sQ85_spl
| ~ sQ160_spl
| aSupremumOfIn0(sK0_skl(xU),xU,xU) ),
inference(backward_demodulation,[status(thm)],[f1371,f611]) ).
fof(f1378,plain,
( ~ sQ166_spl
| ~ sQ171_spl
| aFixedPointOf0(sK0_skl(xU),xf) ),
inference(forward_demodulation,[status(thm)],[f1250,f1233]) ).
fof(f1379,plain,
( ~ sQ146_spl
| ~ sQ139_spl
| ~ sQ85_spl
| ~ sQ160_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(forward_demodulation,[status(thm)],[f1371,f1294]) ).
fof(f1380,plain,
( ~ sQ89_spl
| ~ sQ139_spl
| ~ sQ81_spl
| ~ sQ140_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(forward_demodulation,[status(thm)],[f1298,f1295]) ).
fof(f1381,plain,
( ~ sQ178_spl
| ~ sQ85_spl
| ~ sQ160_spl
| aInfimumOfIn0(sK0_skl(xU),xU,xU) ),
inference(forward_demodulation,[status(thm)],[f1371,f1357]) ).
fof(f1382,plain,
( ~ sQ146_spl
| ~ sQ159_spl
| ~ sQ85_spl
| ~ sQ160_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(forward_demodulation,[status(thm)],[f1371,f1368]) ).
fof(f1383,plain,
( ~ sQ159_spl
| ~ sQ118_spl
| ~ sQ100_spl
| ~ sQ116_spl
| sdtlseqdt0(sdtlpdtrp0(xf,sK1_skl(xU,xU)),sK0_skl(xU)) ),
inference(resolution,[status(thm)],[f988,f1191]) ).
fof(f1384,plain,
( ~ sQ139_spl
| ~ sQ118_spl
| ~ sQ100_spl
| ~ sQ116_spl
| sdtlseqdt0(sK0_skl(xU),sdtlpdtrp0(xf,sK1_skl(xU,xU))) ),
inference(resolution,[status(thm)],[f988,f1080]) ).
fof(f1385,plain,
( ~ sQ125_spl
| ~ sQ118_spl
| ~ sQ100_spl
| ~ sQ116_spl
| sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK1_skl(xU,xU))) != sdtlpdtrp0(xf,sK1_skl(xU,xU))
| aFixedPointOf0(sdtlpdtrp0(xf,sK1_skl(xU,xU)),xf) ),
inference(resolution,[status(thm)],[f988,f996]) ).
fof(f1386,plain,
( ~ sQ25_spl
| ~ sQ118_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK3_skl(sdtlpdtrp0(xf,sK1_skl(xU,xU)),xU,xU),xU)
| aUpperBoundOfIn0(sdtlpdtrp0(xf,sK1_skl(xU,xU)),xU,xU) ),
inference(resolution,[status(thm)],[f988,f280]) ).
fof(f1387,plain,
( ~ sQ124_spl
| ~ sQ116_spl
| ~ sQ118_spl
| ~ sQ100_spl
| aElementOf0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK1_skl(xU,xU))),xU) ),
inference(resolution,[status(thm)],[f988,f959]) ).
fof(f1388,plain,
( ~ sQ19_spl
| ~ sQ118_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElementOf0(sK2_skl(sdtlpdtrp0(xf,sK1_skl(xU,xU)),xU,xU),xU)
| aLowerBoundOfIn0(sdtlpdtrp0(xf,sK1_skl(xU,xU)),xU,xU) ),
inference(resolution,[status(thm)],[f988,f252]) ).
fof(f1389,plain,
( ~ sQ118_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ isEmpty0(xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f988,f42]) ).
fof(f1390,plain,
( ~ sQ118_spl
| ~ sQ100_spl
| ~ sQ116_spl
| aElement0(sdtlpdtrp0(xf,sK1_skl(xU,xU)))
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f988,f38]) ).
fof(f1391,definition,
( sQ181_spl
<=> aFixedPointOf0(sdtlpdtrp0(xf,sK1_skl(xU,xU)),xf) ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f1394,definition,
( sQ182_spl
<=> sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK1_skl(xU,xU))) = sdtlpdtrp0(xf,sK1_skl(xU,xU)) ),
introduced(definition,[new_symbols(definition,[sQ182_spl])],[split_symbol_definition]) ).
fof(f1397,plain,
( ~ sQ125_spl
| ~ sQ118_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ sQ182_spl
| sQ181_spl ),
inference(split_clause,[status(thm)],[f1385,f1391,f1394,f817,f692,f829,f995]) ).
fof(f1398,definition,
( sQ183_spl
<=> aUpperBoundOfIn0(sdtlpdtrp0(xf,sK1_skl(xU,xU)),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f1401,definition,
( sQ184_spl
<=> aElementOf0(sK3_skl(sdtlpdtrp0(xf,sK1_skl(xU,xU)),xU,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ184_spl])],[split_symbol_definition]) ).
fof(f1404,plain,
( ~ sQ25_spl
| ~ sQ118_spl
| ~ sQ100_spl
| ~ sQ116_spl
| sQ184_spl
| sQ183_spl ),
inference(split_clause,[status(thm)],[f1386,f1398,f1401,f817,f692,f829,f279]) ).
fof(f1405,definition,
( sQ185_spl
<=> aLowerBoundOfIn0(sdtlpdtrp0(xf,sK1_skl(xU,xU)),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ185_spl])],[split_symbol_definition]) ).
fof(f1408,definition,
( sQ186_spl
<=> aElementOf0(sK2_skl(sdtlpdtrp0(xf,sK1_skl(xU,xU)),xU,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ186_spl])],[split_symbol_definition]) ).
fof(f1411,plain,
( ~ sQ19_spl
| ~ sQ118_spl
| ~ sQ100_spl
| ~ sQ116_spl
| sQ186_spl
| sQ185_spl ),
inference(split_clause,[status(thm)],[f1388,f1405,f1408,f817,f692,f829,f251]) ).
fof(f1412,plain,
( ~ sQ118_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1389,f162,f154,f817,f692,f829]) ).
fof(f1413,definition,
( sQ187_spl
<=> aElement0(sdtlpdtrp0(xf,sK1_skl(xU,xU))) ),
introduced(definition,[new_symbols(definition,[sQ187_spl])],[split_symbol_definition]) ).
fof(f1416,plain,
( ~ sQ118_spl
| ~ sQ100_spl
| ~ sQ116_spl
| sQ187_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1390,f162,f1413,f817,f692,f829]) ).
fof(f1417,plain,
( sQ118_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ aElementOf0(sdtlpdtrp0(xf,sK1_skl(xU,xU)),szRzazndt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f881,f831]) ).
fof(f1418,plain,
( sQ118_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ aElementOf0(sdtlpdtrp0(xf,sK1_skl(xU,xU)),xU) ),
inference(forward_demodulation,[status(thm)],[f818,f1417]) ).
fof(f1419,plain,
( ~ sQ73_spl
| ~ sQ100_spl
| ~ sQ116_spl
| sdtlseqdt0(sK1_skl(xU,xU),sK1_skl(xU,xU)) ),
inference(resolution,[status(thm)],[f1285,f55]) ).
fof(f1420,plain,
( ~ sQ119_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ sQ124_spl
| ~ sQ171_spl
| aElementOf0(sdtlpdtrp0(xf,sK0_skl(xU)),xU) ),
inference(forward_demodulation,[status(thm)],[f1250,f1103]) ).
fof(f1421,plain,
( ~ sQ119_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ sQ124_spl
| ~ sQ171_spl
| aElementOf0(sK0_skl(xU),xU) ),
inference(forward_demodulation,[status(thm)],[f1250,f1420]) ).
fof(f1423,plain,
( ~ sQ94_spl
| ~ sQ81_spl
| ~ sQ140_spl
| sdtlseqdt0(sK0_skl(xU),sK6_skl(xU,xU)) ),
inference(forward_demodulation,[status(thm)],[f1298,f669]) ).
fof(f1424,plain,
( ~ sQ94_spl
| ~ sQ81_spl
| ~ sQ140_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(forward_demodulation,[status(thm)],[f1298,f1423]) ).
fof(f1425,plain,
! [X0] :
( ~ sQ90_spl
| ~ sQ81_spl
| ~ sQ140_spl
| sdtlseqdt0(X0,sK0_skl(xU))
| ~ aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f1298,f639]) ).
fof(f1426,plain,
( ~ sQ135_spl
| ~ sQ90_spl
| ~ sQ81_spl
| ~ sQ140_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(resolution,[status(thm)],[f1425,f1062]) ).
fof(f1427,plain,
( ~ sQ132_spl
| ~ sQ171_spl
| aLowerBoundOfIn0(sK0_skl(xU),xU,xU) ),
inference(forward_demodulation,[status(thm)],[f1250,f1051]) ).
fof(f1428,plain,
( ~ sQ89_spl
| ~ sQ124_spl
| ~ sQ116_spl
| ~ sQ81_spl
| ~ sQ140_spl
| aElementOf0(sdtlpdtrp0(xf,sK0_skl(xU)),xU) ),
inference(forward_demodulation,[status(thm)],[f1298,f1104]) ).
fof(f1429,plain,
( ~ sQ89_spl
| ~ sQ124_spl
| ~ sQ116_spl
| ~ sQ81_spl
| ~ sQ140_spl
| ~ sQ171_spl
| aElementOf0(sK0_skl(xU),xU) ),
inference(forward_demodulation,[status(thm)],[f1250,f1428]) ).
fof(f1430,plain,
( ~ sQ131_spl
| ~ sQ171_spl
| sdtlseqdt0(sK0_skl(xU),sdtlpdtrp0(xf,sK0_skl(xU))) ),
inference(forward_demodulation,[status(thm)],[f1250,f1068]) ).
fof(f1431,plain,
( ~ sQ131_spl
| ~ sQ171_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(forward_demodulation,[status(thm)],[f1250,f1430]) ).
fof(f1433,plain,
! [X0] :
( ~ sQ144_spl
| ~ sQ85_spl
| ~ sQ160_spl
| sdtlseqdt0(sK0_skl(xU),X0)
| ~ aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f1371,f1115]) ).
fof(f1434,plain,
( ~ sQ151_spl
| ~ sQ144_spl
| ~ sQ85_spl
| ~ sQ160_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(resolution,[status(thm)],[f1433,f1144]) ).
fof(f1435,plain,
( ~ sQ147_spl
| ~ sQ171_spl
| aUpperBoundOfIn0(sK0_skl(xU),xU,xU) ),
inference(forward_demodulation,[status(thm)],[f1250,f1130]) ).
fof(f1436,plain,
( ~ sQ172_spl
| ~ sQ171_spl
| sdtlseqdt0(sK0_skl(xU),sdtlpdtrp0(xf,sK0_skl(xU))) ),
inference(forward_demodulation,[status(thm)],[f1250,f1255]) ).
fof(f1437,plain,
( ~ sQ172_spl
| ~ sQ171_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(forward_demodulation,[status(thm)],[f1250,f1436]) ).
fof(f1438,plain,
( ~ sQ124_spl
| ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ85_spl
| ~ sQ160_spl
| aElementOf0(sdtlpdtrp0(xf,sK0_skl(xU)),xU) ),
inference(forward_demodulation,[status(thm)],[f1371,f1151]) ).
fof(f1439,plain,
( ~ sQ124_spl
| ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ85_spl
| ~ sQ160_spl
| ~ sQ171_spl
| aElementOf0(sK0_skl(xU),xU) ),
inference(forward_demodulation,[status(thm)],[f1250,f1438]) ).
fof(f1440,plain,
( ~ sQ156_spl
| ~ sQ85_spl
| ~ sQ160_spl
| sdtlseqdt0(sK0_skl(xU),sK7_skl(xU,xU)) ),
inference(forward_demodulation,[status(thm)],[f1371,f1171]) ).
fof(f1441,plain,
( ~ sQ156_spl
| ~ sQ85_spl
| ~ sQ160_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(forward_demodulation,[status(thm)],[f1371,f1440]) ).
fof(f1442,plain,
( ~ sQ128_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ sQ73_spl
| sdtlseqdt0(sdtlpdtrp0(xf,sK1_skl(xU,xU)),sdtlpdtrp0(xf,sK1_skl(xU,xU)))
| ~ aElementOf0(sK1_skl(xU,xU),xU)
| ~ aElementOf0(sK1_skl(xU,xU),xU) ),
inference(resolution,[status(thm)],[f1419,f1021]) ).
fof(f1443,plain,
! [X0] :
( ~ sQ73_spl
| ~ sQ100_spl
| ~ sQ116_spl
| sdtlseqdt0(sK1_skl(xU,xU),X0)
| ~ sdtlseqdt0(sK1_skl(xU,xU),X0)
| ~ aElement0(X0)
| ~ aElement0(sK1_skl(xU,xU))
| ~ aElement0(sK1_skl(xU,xU)) ),
inference(resolution,[status(thm)],[f1419,f59]) ).
fof(f1444,plain,
( ~ sQ73_spl
| ~ sQ100_spl
| ~ sQ116_spl
| sK1_skl(xU,xU) = sK1_skl(xU,xU)
| ~ sdtlseqdt0(sK1_skl(xU,xU),sK1_skl(xU,xU))
| ~ aElement0(sK1_skl(xU,xU))
| ~ aElement0(sK1_skl(xU,xU)) ),
inference(resolution,[status(thm)],[f1419,f57]) ).
fof(f1445,definition,
( sQ188_spl
<=> sdtlseqdt0(sdtlpdtrp0(xf,sK1_skl(xU,xU)),sdtlpdtrp0(xf,sK1_skl(xU,xU))) ),
introduced(definition,[new_symbols(definition,[sQ188_spl])],[split_symbol_definition]) ).
fof(f1448,plain,
( ~ sQ128_spl
| ~ sQ100_spl
| ~ sQ116_spl
| ~ sQ73_spl
| sQ188_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1442,f195,f1445,f534,f817,f692,f1015]) ).
fof(f1449,definition,
! [X0] :
( sQ189_spl
<=> ( sdtlseqdt0(sK1_skl(xU,xU),X0)
| ~ sdtlseqdt0(sK1_skl(xU,xU),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition]) ).
fof(f1452,plain,
( ~ sQ73_spl
| ~ sQ100_spl
| ~ sQ116_spl
| sQ189_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f1443,f211,f1449,f817,f692,f534]) ).
fof(f1453,definition,
( sQ190_spl
<=> sdtlseqdt0(sK1_skl(xU,xU),sK1_skl(xU,xU)) ),
introduced(definition,[new_symbols(definition,[sQ190_spl])],[split_symbol_definition]) ).
fof(f1454,plain,
( ~ sQ190_spl
| sdtlseqdt0(sK1_skl(xU,xU),sK1_skl(xU,xU)) ),
inference(component_clause,[status(thm)],[f1453]) ).
fof(f1455,plain,
( sQ190_spl
| ~ sdtlseqdt0(sK1_skl(xU,xU),sK1_skl(xU,xU)) ),
inference(component_clause,[status(thm)],[f1453]) ).
fof(f1456,definition,
( sQ191_spl
<=> sK1_skl(xU,xU) = sK1_skl(xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ191_spl])],[split_symbol_definition]) ).
fof(f1459,plain,
( ~ sQ73_spl
| ~ sQ100_spl
| ~ sQ116_spl
| sQ191_spl
| ~ sQ190_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f1444,f211,f1453,f1456,f817,f692,f534]) ).
fof(f1460,plain,
( sQ14_spl
| ~ sQ73_spl
| ~ sQ100_spl
| ~ sQ116_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f213,f1285]) ).
fof(f1461,plain,
( sQ14_spl
| ~ sQ73_spl
| ~ sQ100_spl
| ~ sQ116_spl ),
inference(contradiction_clause,[status(thm)],[f1460]) ).
fof(f1462,plain,
( sQ190_spl
| ~ sQ73_spl
| ~ sQ100_spl
| ~ sQ116_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1455,f1419]) ).
fof(f1463,plain,
( sQ190_spl
| ~ sQ73_spl
| ~ sQ100_spl
| ~ sQ116_spl ),
inference(contradiction_clause,[status(thm)],[f1462]) ).
fof(f1464,plain,
! [X0] :
( ~ sQ163_spl
| ~ sQ81_spl
| ~ sQ140_spl
| sdtlseqdt0(sK0_skl(xU),X0)
| ~ aElementOf0(X0,xU) ),
inference(forward_demodulation,[status(thm)],[f1298,f1217]) ).
fof(f1465,plain,
! [X0] :
( ~ sQ177_spl
| ~ sQ85_spl
| ~ sQ160_spl
| sdtlseqdt0(X0,sK0_skl(xU))
| ~ aElementOf0(X0,xU) ),
inference(forward_demodulation,[status(thm)],[f1371,f1336]) ).
fof(f1466,plain,
! [X0] :
( ~ sQ180_spl
| ~ sQ85_spl
| ~ sQ160_spl
| sdtlseqdt0(sK0_skl(xU),X0)
| ~ aElementOf0(X0,xU) ),
inference(forward_demodulation,[status(thm)],[f1371,f1364]) ).
fof(f1467,plain,
( ~ sQ165_spl
| ~ sQ85_spl
| ~ sQ160_spl
| sdtlpdtrp0(xf,sK0_skl(xU)) = sK7_skl(xU,xU) ),
inference(forward_demodulation,[status(thm)],[f1371,f1229]) ).
fof(f1469,plain,
( ~ sQ169_spl
| ~ sQ81_spl
| ~ sQ140_spl
| sdtlpdtrp0(xf,sK0_skl(xU)) = sK6_skl(xU,xU) ),
inference(forward_demodulation,[status(thm)],[f1298,f1243]) ).
fof(model,axiom,
( ~ sQ0_spl
| ~ sQ2_spl
| sQ3_spl
| sQ4_spl
| ~ sQ5_spl
| ~ sQ8_spl
| sQ11_spl
| ~ sQ12_spl
| sQ13_spl
| sQ14_spl
| sQ15_spl
| sQ16_spl
| sQ17_spl
| sQ18_spl
| sQ19_spl
| sQ21_spl
| ~ sQ22_spl
| ~ sQ23_spl
| sQ24_spl
| sQ25_spl
| sQ27_spl
| sQ28_spl
| sQ29_spl
| sQ30_spl
| sQ31_spl
| sQ33_spl
| ~ sQ34_spl
| sQ35_spl
| sQ36_spl
| sQ37_spl
| sQ39_spl
| sQ40_spl
| ~ sQ41_spl
| sQ42_spl
| ~ sQ43_spl
| ~ sQ44_spl
| sQ45_spl
| sQ47_spl
| ~ sQ48_spl
| sQ49_spl
| ~ sQ50_spl
| sQ51_spl
| ~ sQ52_spl
| sQ53_spl
| sQ54_spl
| sQ55_spl
| sQ57_spl
| sQ58_spl
| sQ59_spl
| sQ60_spl
| sQ61_spl
| sQ62_spl
| sQ63_spl
| sQ64_spl
| sQ65_spl
| sQ66_spl
| sQ67_spl
| sQ68_spl
| sQ69_spl
| sQ70_spl
| sQ71_spl
| sQ72_spl
| sQ73_spl
| sQ75_spl
| sQ78_spl
| sQ79_spl
| sQ80_spl
| sQ81_spl
| ~ sQ82_spl
| sQ84_spl
| sQ85_spl
| sQ88_spl
| sQ89_spl
| sQ90_spl
| sQ91_spl
| sQ94_spl
| sQ95_spl
| ~ sQ96_spl
| ~ sQ97_spl
| sQ99_spl
| sQ100_spl
| ~ sQ106_spl
| sQ116_spl
| sQ117_spl
| ~ sQ118_spl
| sQ119_spl
| sQ120_spl
| sQ121_spl
| sQ122_spl
| sQ124_spl
| sQ125_spl
| sQ127_spl
| sQ128_spl
| sQ131_spl
| sQ132_spl
| sQ135_spl
| sQ137_spl
| sQ139_spl
| sQ140_spl
| sQ141_spl
| sQ143_spl
| sQ144_spl
| sQ145_spl
| sQ146_spl
| sQ147_spl
| sQ149_spl
| sQ151_spl
| sQ154_spl
| sQ156_spl
| sQ157_spl
| sQ159_spl
| sQ160_spl
| sQ161_spl
| sQ163_spl
| sQ164_spl
| sQ165_spl
| sQ166_spl
| sQ168_spl
| sQ169_spl
| sQ170_spl
| sQ171_spl
| sQ172_spl
| sQ173_spl
| sQ174_spl
| sQ175_spl
| sQ177_spl
| sQ178_spl
| sQ180_spl
| sQ189_spl
| sQ190_spl
| sQ191_spl ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT386+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.33 % Computer : n009.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.33 % CPULimit : 300
% 0.08/0.33 % WCLimit : 300
% 0.08/0.33 % DateTime : Sun Sep 20 23:57:43 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.11/0.41 % SZS status CounterSatisfiable for theBenchmark: Theorem is counter-satisfiable, conjecture is false
% 0.11/0.41 % SZS output start Saturation for theBenchmark
% See solution above
% 0.11/0.44 % Elapsed time: 0.092607 seconds
% 0.11/0.44 % CPU time: 0.388438 seconds
% 0.11/0.44 % Total memory used: 109.103 MB
% 0.11/0.44 % Net memory used: 108.668 MB
%------------------------------------------------------------------------------