%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LAT383+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:03:56 PM UTC 2026
% Result : CounterSatisfiable 0.14s 0.46s
% Output : Saturation 0.14s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,definition,
! [W0] :
( aSet0(W0)
=> ( isEmpty0(W0)
<=> ~ ? [W1] : aElementOf0(W1,W0) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [W0] :
( aElement0(W0)
=> sdtlseqdt0(W0,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [W0,W1,W2] :
( ( aElement0(W2)
& aElement0(W1)
& aElement0(W0) )
=> ( ( sdtlseqdt0(W1,W2)
& sdtlseqdt0(W0,W1) )
=> sdtlseqdt0(W0,W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [W0] :
( aFunction0(W0)
=> aSet0(szDzozmdt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [W0] :
( aFunction0(W0)
=> aSet0(szRzazndt0(W0)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [W0] :
( aFunction0(W0)
=> ! [W1] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),szRzazndt0(W0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,definition,
! [W0] :
( aFunction0(W0)
=> ! [W1] :
( aFixedPointOf0(W1,W0)
<=> ( sdtlpdtrp0(W0,W1) = W1
& aElementOf0(W1,szDzozmdt0(W0)) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,hypothesis,
( isOn0(xf,xU)
& isMonotone0(xf)
& aFunction0(xf)
& aCompleteLattice0(xU) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,hypothesis,
xS = cS1142(xf),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,conjecture,
aCompleteLattice0(xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
~ aCompleteLattice0(xS),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f34,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f35,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [W0] :
( ( isEmpty0(W0)
<=> ! [W1] : ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f37,plain,
! [W0] :
( ( ( ? [W1] : aElementOf0(W1,W0)
| isEmpty0(W0) )
& ( ! [W1] : ~ aElementOf0(W1,W0)
| ~ isEmpty0(W0) ) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f36]) ).
fof(f38,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))],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| ~ isEmpty0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [X0] :
( aElementOf0(sK0_skl(X0),X0)
| isEmpty0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f41,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(f42,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)],[f41]) ).
fof(f43,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)],[f42]) ).
fof(f44,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))],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f47,plain,
! [X0,X1] :
( aElementOf0(sK1_skl(X1,X0),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f48,plain,
! [X0,X1] :
( ~ aElementOf0(sK1_skl(X1,X0),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f51,plain,
! [W0] :
( sdtlseqdt0(W0,W0)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f52,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
! [W0,W1] :
( W0 = W1
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f54,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f55,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(f56,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f57,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(f58,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)],[f57]) ).
fof(f59,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)],[f58]) ).
fof(f60,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))],[f59]) ).
fof(f61,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aLowerBoundOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f62,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)],[f60]) ).
fof(f63,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)],[f60]) ).
fof(f64,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)],[f60]) ).
fof(f65,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(f66,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)],[f65]) ).
fof(f67,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)],[f66]) ).
fof(f68,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))],[f67]) ).
fof(f69,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aUpperBoundOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,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)],[f68]) ).
fof(f71,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)],[f68]) ).
fof(f72,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)],[f68]) ).
fof(f73,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(f74,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)],[f73]) ).
fof(f75,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)],[f74]) ).
fof(f76,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))],[f75]) ).
fof(f77,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aInfimumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f78,plain,
! [X0,X1,X2] :
( aLowerBoundOfIn0(X2,X1,X0)
| ~ aInfimumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f79,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)],[f76]) ).
fof(f80,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)],[f76]) ).
fof(f81,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)],[f76]) ).
fof(f82,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(f83,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)],[f82]) ).
fof(f84,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)],[f83]) ).
fof(f85,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))],[f84]) ).
fof(f86,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aSupremumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f87,plain,
! [X0,X1,X2] :
( aUpperBoundOfIn0(X2,X1,X0)
| ~ aSupremumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f88,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)],[f85]) ).
fof(f89,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)],[f85]) ).
fof(f90,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)],[f85]) ).
fof(f91,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(f92,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)],[f91]) ).
fof(f93,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(f94,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)],[f93]) ).
fof(f95,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(f96,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)],[f95]) ).
fof(f97,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)],[f96]) ).
fof(f98,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))],[f97]) ).
fof(f99,plain,
! [X0] :
( aSet0(X0)
| ~ aCompleteLattice0(X0) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f100,plain,
! [X0,X1] :
( aInfimumOfIn0(sK6_skl(X1,X0),X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aCompleteLattice0(X0) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f101,plain,
! [X0,X1] :
( aSupremumOfIn0(sK7_skl(X1,X0),X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aCompleteLattice0(X0) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f102,plain,
! [X0] :
( aSubsetOf0(sK8_skl(X0),X0)
| ~ aSet0(X0)
| aCompleteLattice0(X0) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f103,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)],[f98]) ).
fof(f107,plain,
! [W0] :
( aSet0(szDzozmdt0(W0))
| ~ aFunction0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f108,plain,
! [X0] :
( aSet0(szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f109,plain,
! [W0] :
( aSet0(szRzazndt0(W0))
| ~ aFunction0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f110,plain,
! [X0] :
( aSet0(szRzazndt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f111,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(f112,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)],[f111]) ).
fof(f113,plain,
! [X0,X1] :
( szDzozmdt0(X0) = szRzazndt0(X0)
| ~ isOn0(X0,X1)
| ~ aSet0(X1)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f114,plain,
! [X0,X1] :
( szRzazndt0(X0) = X1
| ~ isOn0(X0,X1)
| ~ aSet0(X1)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f115,plain,
! [X0,X1] :
( szRzazndt0(X0) != X1
| szDzozmdt0(X0) != szRzazndt0(X0)
| isOn0(X0,X1)
| ~ aSet0(X1)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f116,plain,
! [W0] :
( ! [W1] :
( aElementOf0(sdtlpdtrp0(W0,W1),szRzazndt0(W0))
| ~ aElementOf0(W1,szDzozmdt0(W0)) )
| ~ aFunction0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f117,plain,
! [X0,X1] :
( aElementOf0(sdtlpdtrp0(X0,X1),szRzazndt0(X0))
| ~ aElementOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f118,plain,
! [W0] :
( ! [W1] :
( aFixedPointOf0(W1,W0)
<=> ( sdtlpdtrp0(W0,W1) = W1
& aElementOf0(W1,szDzozmdt0(W0)) ) )
| ~ aFunction0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f119,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)],[f118]) ).
fof(f120,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)],[f119]) ).
fof(f121,plain,
! [X0,X1] :
( aElementOf0(X1,szDzozmdt0(X0))
| ~ aFixedPointOf0(X1,X0)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f122,plain,
! [X0,X1] :
( sdtlpdtrp0(X0,X1) = X1
| ~ aFixedPointOf0(X1,X0)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f123,plain,
! [X0,X1] :
( sdtlpdtrp0(X0,X1) != X1
| ~ aElementOf0(X1,szDzozmdt0(X0))
| aFixedPointOf0(X1,X0)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f124,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(f125,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)],[f124]) ).
fof(f126,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))],[f125]) ).
fof(f127,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)],[f126]) ).
fof(f128,plain,
! [X0] :
( aElementOf0(sK9_skl(X0),szDzozmdt0(X0))
| isMonotone0(X0)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f129,plain,
! [X0] :
( aElementOf0(sK10_skl(X0),szDzozmdt0(X0))
| isMonotone0(X0)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f130,plain,
! [X0] :
( sdtlseqdt0(sK9_skl(X0),sK10_skl(X0))
| isMonotone0(X0)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f131,plain,
! [X0] :
( ~ sdtlseqdt0(sdtlpdtrp0(X0,sK9_skl(X0)),sdtlpdtrp0(X0,sK10_skl(X0)))
| isMonotone0(X0)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f132,plain,
aCompleteLattice0(xU),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f133,plain,
aFunction0(xf),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f134,plain,
isMonotone0(xf),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f135,plain,
isOn0(xf,xU),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f136,plain,
xS = cS1142(xf),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f137,plain,
~ aCompleteLattice0(xS),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f138,plain,
aSet0(xU),
inference(resolution,[status(thm)],[f132,f99]) ).
fof(f139,plain,
( aElementOf0(sK0_skl(xU),xU)
| isEmpty0(xU) ),
inference(resolution,[status(thm)],[f40,f138]) ).
fof(f140,definition,
( sQ0_spl
<=> isEmpty0(xU) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f141,plain,
( ~ sQ0_spl
| isEmpty0(xU) ),
inference(component_clause,[status(thm)],[f140]) ).
fof(f142,plain,
( sQ0_spl
| ~ isEmpty0(xU) ),
inference(component_clause,[status(thm)],[f140]) ).
fof(f143,definition,
( sQ1_spl
<=> aElementOf0(sK0_skl(xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f144,plain,
( ~ sQ1_spl
| aElementOf0(sK0_skl(xU),xU) ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f145,plain,
( sQ1_spl
| ~ aElementOf0(sK0_skl(xU),xU) ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f146,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f139,f140,f143]) ).
fof(f147,plain,
! [X0] :
( aElementOf0(sK1_skl(X0,xU),X0)
| ~ aSet0(X0)
| aSubsetOf0(X0,xU) ),
inference(resolution,[status(thm)],[f47,f138]) ).
fof(f148,plain,
( aElementOf0(sK1_skl(xU,xU),xU)
| aSubsetOf0(xU,xU) ),
inference(resolution,[status(thm)],[f147,f138]) ).
fof(f149,definition,
( sQ2_spl
<=> aSubsetOf0(xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ2_spl
| aSubsetOf0(xU,xU) ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,definition,
( sQ3_spl
<=> aElementOf0(sK1_skl(xU,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f153,plain,
( ~ sQ3_spl
| aElementOf0(sK1_skl(xU,xU),xU) ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f154,plain,
( sQ3_spl
| ~ aElementOf0(sK1_skl(xU,xU),xU) ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f155,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f148,f149,f152]) ).
fof(f156,plain,
! [X0] :
( ~ sQ2_spl
| aElementOf0(X0,xU)
| ~ aElementOf0(X0,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f150,f46]) ).
fof(f158,definition,
( sQ4_spl
<=> aSet0(xU) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f160,plain,
( sQ4_spl
| ~ aSet0(xU) ),
inference(component_clause,[status(thm)],[f158]) ).
fof(f161,definition,
! [X0] :
( sQ5_spl
<=> ( aElementOf0(X0,xU)
| ~ aElementOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f164,plain,
( ~ sQ2_spl
| sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f156,f158,f161,f149]) ).
fof(f166,plain,
( ~ sQ3_spl
| ~ isEmpty0(xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f153,f39]) ).
fof(f167,plain,
( ~ sQ3_spl
| aElement0(sK1_skl(xU,xU))
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f153,f35]) ).
fof(f168,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f166,f158,f140,f152]) ).
fof(f169,definition,
( sQ6_spl
<=> aElement0(sK1_skl(xU,xU)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( ~ sQ6_spl
| aElement0(sK1_skl(xU,xU)) ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f172,plain,
( ~ sQ3_spl
| sQ6_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f167,f158,f169,f152]) ).
fof(f173,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f160,f138]) ).
fof(f174,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f173]) ).
fof(f175,plain,
( ~ sQ1_spl
| ~ isEmpty0(xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f144,f39]) ).
fof(f176,plain,
( ~ sQ1_spl
| aElement0(sK0_skl(xU))
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f144,f35]) ).
fof(f177,plain,
( ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f175,f158,f140,f143]) ).
fof(f178,definition,
( sQ7_spl
<=> aElement0(sK0_skl(xU)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f179,plain,
( ~ sQ7_spl
| aElement0(sK0_skl(xU)) ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f180,plain,
( sQ7_spl
| ~ aElement0(sK0_skl(xU)) ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f181,plain,
( ~ sQ1_spl
| sQ7_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f176,f158,f178,f143]) ).
fof(f182,plain,
( ~ sQ7_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(resolution,[status(thm)],[f52,f179]) ).
fof(f183,plain,
( ~ sQ6_spl
| sdtlseqdt0(sK1_skl(xU,xU),sK1_skl(xU,xU)) ),
inference(resolution,[status(thm)],[f170,f52]) ).
fof(f184,plain,
( ~ sQ3_spl
| ~ aSet0(xU)
| aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f153,f48]) ).
fof(f187,plain,
( ~ sQ3_spl
| sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f184,f158,f149,f152]) ).
fof(f194,plain,
( ~ sQ7_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)],[f182,f54]) ).
fof(f195,definition,
( sQ8_spl
<=> sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f196,plain,
( ~ sQ8_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(component_clause,[status(thm)],[f195]) ).
fof(f197,plain,
( sQ8_spl
| ~ sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(component_clause,[status(thm)],[f195]) ).
fof(f198,definition,
( sQ9_spl
<=> sK0_skl(xU) = sK0_skl(xU) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f201,plain,
( sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f194,f178,f195,f198]) ).
fof(f202,plain,
( sQ8_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f197,f182]) ).
fof(f203,plain,
( sQ8_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f202]) ).
fof(f204,plain,
! [X0] :
( ~ sQ7_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)],[f56,f182]) ).
fof(f205,definition,
! [X0] :
( sQ10_spl
<=> ( sdtlseqdt0(sK0_skl(xU),X0)
| ~ sdtlseqdt0(sK0_skl(xU),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f208,plain,
( sQ10_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f204,f178,f205]) ).
fof(f209,plain,
aSet0(szDzozmdt0(xf)),
inference(resolution,[status(thm)],[f108,f133]) ).
fof(f210,plain,
( aElementOf0(sK1_skl(szDzozmdt0(xf),xU),szDzozmdt0(xf))
| aSubsetOf0(szDzozmdt0(xf),xU) ),
inference(resolution,[status(thm)],[f209,f147]) ).
fof(f211,plain,
! [X0] :
( aElementOf0(sK1_skl(X0,szDzozmdt0(xf)),X0)
| ~ aSet0(X0)
| aSubsetOf0(X0,szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f209,f47]) ).
fof(f212,plain,
( aElementOf0(sK0_skl(szDzozmdt0(xf)),szDzozmdt0(xf))
| isEmpty0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f209,f40]) ).
fof(f213,definition,
( sQ11_spl
<=> aSubsetOf0(szDzozmdt0(xf),xU) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f214,plain,
( ~ sQ11_spl
| aSubsetOf0(szDzozmdt0(xf),xU) ),
inference(component_clause,[status(thm)],[f213]) ).
fof(f215,plain,
( sQ11_spl
| ~ aSubsetOf0(szDzozmdt0(xf),xU) ),
inference(component_clause,[status(thm)],[f213]) ).
fof(f216,definition,
( sQ12_spl
<=> aElementOf0(sK1_skl(szDzozmdt0(xf),xU),szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f217,plain,
( ~ sQ12_spl
| aElementOf0(sK1_skl(szDzozmdt0(xf),xU),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f216]) ).
fof(f218,plain,
( sQ12_spl
| ~ aElementOf0(sK1_skl(szDzozmdt0(xf),xU),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f216]) ).
fof(f219,plain,
( sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f210,f213,f216]) ).
fof(f220,definition,
( sQ13_spl
<=> isEmpty0(szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f221,plain,
( ~ sQ13_spl
| isEmpty0(szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f222,plain,
( sQ13_spl
| ~ isEmpty0(szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f223,definition,
( sQ14_spl
<=> aElementOf0(sK0_skl(szDzozmdt0(xf)),szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f224,plain,
( ~ sQ14_spl
| aElementOf0(sK0_skl(szDzozmdt0(xf)),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f226,plain,
( sQ14_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f212,f220,f223]) ).
fof(f227,plain,
! [X0] :
( ~ sQ2_spl
| aElementOf0(sK2_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f63,f150]) ).
fof(f228,definition,
! [X0] :
( sQ15_spl
<=> ( aElementOf0(sK2_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f229,plain,
! [X0] :
( ~ sQ15_spl
| aElementOf0(sK2_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(component_clause,[status(thm)],[f228]) ).
fof(f231,plain,
( ~ sQ2_spl
| sQ15_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f227,f158,f228,f149]) ).
fof(f232,plain,
! [X0] :
( ~ sQ11_spl
| aElementOf0(sK2_skl(X0,szDzozmdt0(xf),xU),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,szDzozmdt0(xf),xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f214,f63]) ).
fof(f233,plain,
! [X0] :
( ~ sQ11_spl
| aElementOf0(X0,xU)
| ~ aElementOf0(X0,szDzozmdt0(xf))
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f214,f46]) ).
fof(f235,definition,
! [X0] :
( sQ16_spl
<=> ( aElementOf0(sK2_skl(X0,szDzozmdt0(xf),xU),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,szDzozmdt0(xf),xU) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f236,plain,
! [X0] :
( ~ sQ16_spl
| aElementOf0(sK2_skl(X0,szDzozmdt0(xf),xU),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,szDzozmdt0(xf),xU) ),
inference(component_clause,[status(thm)],[f235]) ).
fof(f238,plain,
( ~ sQ11_spl
| sQ16_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f232,f158,f235,f213]) ).
fof(f239,definition,
! [X0] :
( sQ17_spl
<=> ( aElementOf0(X0,xU)
| ~ aElementOf0(X0,szDzozmdt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f240,plain,
! [X0] :
( ~ sQ17_spl
| aElementOf0(X0,xU)
| ~ aElementOf0(X0,szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f239]) ).
fof(f242,plain,
( ~ sQ11_spl
| sQ17_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f233,f158,f239,f213]) ).
fof(f243,definition,
( sQ18_spl
<=> aSet0(szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f245,plain,
( sQ18_spl
| ~ aSet0(szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f243]) ).
fof(f247,plain,
( ~ sQ12_spl
| ~ isEmpty0(szDzozmdt0(xf))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f217,f39]) ).
fof(f248,plain,
( ~ sQ12_spl
| aElement0(sK1_skl(szDzozmdt0(xf),xU))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f217,f35]) ).
fof(f249,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f247,f243,f220,f216]) ).
fof(f250,definition,
( sQ19_spl
<=> aElement0(sK1_skl(szDzozmdt0(xf),xU)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f251,plain,
( ~ sQ19_spl
| aElement0(sK1_skl(szDzozmdt0(xf),xU)) ),
inference(component_clause,[status(thm)],[f250]) ).
fof(f252,plain,
( sQ19_spl
| ~ aElement0(sK1_skl(szDzozmdt0(xf),xU)) ),
inference(component_clause,[status(thm)],[f250]) ).
fof(f253,plain,
( ~ sQ12_spl
| sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f248,f243,f250,f216]) ).
fof(f254,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f245,f209]) ).
fof(f255,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f254]) ).
fof(f256,plain,
( ~ sQ19_spl
| sdtlseqdt0(sK1_skl(szDzozmdt0(xf),xU),sK1_skl(szDzozmdt0(xf),xU)) ),
inference(resolution,[status(thm)],[f251,f52]) ).
fof(f257,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| aElementOf0(sK2_skl(sK0_skl(xU),xU,xU),xU)
| aLowerBoundOfIn0(sK0_skl(xU),xU,xU) ),
inference(resolution,[status(thm)],[f229,f144]) ).
fof(f258,definition,
( sQ20_spl
<=> aLowerBoundOfIn0(sK0_skl(xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f259,plain,
( ~ sQ20_spl
| aLowerBoundOfIn0(sK0_skl(xU),xU,xU) ),
inference(component_clause,[status(thm)],[f258]) ).
fof(f261,definition,
( sQ21_spl
<=> aElementOf0(sK2_skl(sK0_skl(xU),xU,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f264,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| sQ21_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f257,f258,f261,f228,f143]) ).
fof(f265,plain,
! [X0] :
( ~ sQ19_spl
| sdtlseqdt0(sK1_skl(szDzozmdt0(xf),xU),X0)
| ~ sdtlseqdt0(sK1_skl(szDzozmdt0(xf),xU),X0)
| ~ aElement0(X0)
| ~ aElement0(sK1_skl(szDzozmdt0(xf),xU))
| ~ aElement0(sK1_skl(szDzozmdt0(xf),xU)) ),
inference(resolution,[status(thm)],[f256,f56]) ).
fof(f266,plain,
( ~ sQ19_spl
| sK1_skl(szDzozmdt0(xf),xU) = sK1_skl(szDzozmdt0(xf),xU)
| ~ sdtlseqdt0(sK1_skl(szDzozmdt0(xf),xU),sK1_skl(szDzozmdt0(xf),xU))
| ~ aElement0(sK1_skl(szDzozmdt0(xf),xU))
| ~ aElement0(sK1_skl(szDzozmdt0(xf),xU)) ),
inference(resolution,[status(thm)],[f256,f54]) ).
fof(f267,definition,
! [X0] :
( sQ22_spl
<=> ( sdtlseqdt0(sK1_skl(szDzozmdt0(xf),xU),X0)
| ~ sdtlseqdt0(sK1_skl(szDzozmdt0(xf),xU),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f270,plain,
( sQ22_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f265,f250,f267]) ).
fof(f271,definition,
( sQ23_spl
<=> sdtlseqdt0(sK1_skl(szDzozmdt0(xf),xU),sK1_skl(szDzozmdt0(xf),xU)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f272,plain,
( ~ sQ23_spl
| sdtlseqdt0(sK1_skl(szDzozmdt0(xf),xU),sK1_skl(szDzozmdt0(xf),xU)) ),
inference(component_clause,[status(thm)],[f271]) ).
fof(f273,plain,
( sQ23_spl
| ~ sdtlseqdt0(sK1_skl(szDzozmdt0(xf),xU),sK1_skl(szDzozmdt0(xf),xU)) ),
inference(component_clause,[status(thm)],[f271]) ).
fof(f274,definition,
( sQ24_spl
<=> sK1_skl(szDzozmdt0(xf),xU) = sK1_skl(szDzozmdt0(xf),xU) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f277,plain,
( sQ24_spl
| ~ sQ23_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f266,f250,f271,f274]) ).
fof(f278,plain,
( sQ23_spl
| ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f273,f256]) ).
fof(f279,plain,
( sQ23_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f278]) ).
fof(f280,plain,
! [X0] :
( ~ sQ2_spl
| aElementOf0(sK3_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f71,f150]) ).
fof(f281,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(f282,plain,
! [X0] :
( ~ sQ25_spl
| aElementOf0(sK3_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(component_clause,[status(thm)],[f281]) ).
fof(f284,plain,
( ~ sQ2_spl
| sQ25_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f280,f158,f281,f149]) ).
fof(f285,plain,
aSet0(szRzazndt0(xf)),
inference(resolution,[status(thm)],[f110,f133]) ).
fof(f286,plain,
( aElementOf0(sK1_skl(szRzazndt0(xf),xU),szRzazndt0(xf))
| aSubsetOf0(szRzazndt0(xf),xU) ),
inference(resolution,[status(thm)],[f285,f147]) ).
fof(f287,plain,
! [X0] :
( aElementOf0(sK1_skl(X0,szRzazndt0(xf)),X0)
| ~ aSet0(X0)
| aSubsetOf0(X0,szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f285,f47]) ).
fof(f288,plain,
( aElementOf0(sK0_skl(szRzazndt0(xf)),szRzazndt0(xf))
| isEmpty0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f285,f40]) ).
fof(f289,definition,
( sQ26_spl
<=> aSubsetOf0(szRzazndt0(xf),xU) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f290,plain,
( ~ sQ26_spl
| aSubsetOf0(szRzazndt0(xf),xU) ),
inference(component_clause,[status(thm)],[f289]) ).
fof(f291,plain,
( sQ26_spl
| ~ aSubsetOf0(szRzazndt0(xf),xU) ),
inference(component_clause,[status(thm)],[f289]) ).
fof(f292,definition,
( sQ27_spl
<=> aElementOf0(sK1_skl(szRzazndt0(xf),xU),szRzazndt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f293,plain,
( ~ sQ27_spl
| aElementOf0(sK1_skl(szRzazndt0(xf),xU),szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f292]) ).
fof(f294,plain,
( sQ27_spl
| ~ aElementOf0(sK1_skl(szRzazndt0(xf),xU),szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f292]) ).
fof(f295,plain,
( sQ27_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f286,f289,f292]) ).
fof(f296,definition,
( sQ28_spl
<=> isEmpty0(szRzazndt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f297,plain,
( ~ sQ28_spl
| isEmpty0(szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f296]) ).
fof(f298,plain,
( sQ28_spl
| ~ isEmpty0(szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f296]) ).
fof(f299,definition,
( sQ29_spl
<=> aElementOf0(sK0_skl(szRzazndt0(xf)),szRzazndt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f300,plain,
( ~ sQ29_spl
| aElementOf0(sK0_skl(szRzazndt0(xf)),szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f299]) ).
fof(f302,plain,
( sQ29_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f288,f296,f299]) ).
fof(f303,plain,
! [X0] :
( ~ sQ26_spl
| aElementOf0(sK3_skl(X0,szRzazndt0(xf),xU),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,szRzazndt0(xf),xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f290,f71]) ).
fof(f304,plain,
! [X0] :
( ~ sQ26_spl
| aElementOf0(sK2_skl(X0,szRzazndt0(xf),xU),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,szRzazndt0(xf),xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f290,f63]) ).
fof(f305,plain,
! [X0] :
( ~ sQ26_spl
| aElementOf0(X0,xU)
| ~ aElementOf0(X0,szRzazndt0(xf))
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f290,f46]) ).
fof(f307,definition,
! [X0] :
( sQ30_spl
<=> ( aElementOf0(sK3_skl(X0,szRzazndt0(xf),xU),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,szRzazndt0(xf),xU) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f308,plain,
! [X0] :
( ~ sQ30_spl
| aElementOf0(sK3_skl(X0,szRzazndt0(xf),xU),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,szRzazndt0(xf),xU) ),
inference(component_clause,[status(thm)],[f307]) ).
fof(f310,plain,
( ~ sQ26_spl
| sQ30_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f303,f158,f307,f289]) ).
fof(f311,definition,
! [X0] :
( sQ31_spl
<=> ( aElementOf0(sK2_skl(X0,szRzazndt0(xf),xU),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,szRzazndt0(xf),xU) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f312,plain,
! [X0] :
( ~ sQ31_spl
| aElementOf0(sK2_skl(X0,szRzazndt0(xf),xU),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,szRzazndt0(xf),xU) ),
inference(component_clause,[status(thm)],[f311]) ).
fof(f314,plain,
( ~ sQ26_spl
| sQ31_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f304,f158,f311,f289]) ).
fof(f315,definition,
! [X0] :
( sQ32_spl
<=> ( aElementOf0(X0,xU)
| ~ aElementOf0(X0,szRzazndt0(xf)) ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f316,plain,
! [X0] :
( ~ sQ32_spl
| aElementOf0(X0,xU)
| ~ aElementOf0(X0,szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f315]) ).
fof(f318,plain,
( ~ sQ26_spl
| sQ32_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f305,f158,f315,f289]) ).
fof(f319,definition,
( sQ33_spl
<=> aSet0(szRzazndt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f321,plain,
( sQ33_spl
| ~ aSet0(szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f319]) ).
fof(f323,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)],[f80,f61]) ).
fof(f324,plain,
( ~ sQ27_spl
| ~ isEmpty0(szRzazndt0(xf))
| ~ aSet0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f293,f39]) ).
fof(f325,plain,
( ~ sQ27_spl
| aElement0(sK1_skl(szRzazndt0(xf),xU))
| ~ aSet0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f293,f35]) ).
fof(f326,plain,
( ~ sQ27_spl
| ~ sQ28_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f324,f319,f296,f292]) ).
fof(f327,definition,
( sQ34_spl
<=> aElement0(sK1_skl(szRzazndt0(xf),xU)) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f328,plain,
( ~ sQ34_spl
| aElement0(sK1_skl(szRzazndt0(xf),xU)) ),
inference(component_clause,[status(thm)],[f327]) ).
fof(f329,plain,
( sQ34_spl
| ~ aElement0(sK1_skl(szRzazndt0(xf),xU)) ),
inference(component_clause,[status(thm)],[f327]) ).
fof(f330,plain,
( ~ sQ27_spl
| sQ34_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f325,f319,f327,f292]) ).
fof(f331,plain,
( sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f321,f285]) ).
fof(f332,plain,
sQ33_spl,
inference(contradiction_clause,[status(thm)],[f331]) ).
fof(f333,plain,
( ~ sQ34_spl
| sdtlseqdt0(sK1_skl(szRzazndt0(xf),xU),sK1_skl(szRzazndt0(xf),xU)) ),
inference(resolution,[status(thm)],[f328,f52]) ).
fof(f334,plain,
! [X0] :
( ~ sQ34_spl
| sdtlseqdt0(sK1_skl(szRzazndt0(xf),xU),X0)
| ~ sdtlseqdt0(sK1_skl(szRzazndt0(xf),xU),X0)
| ~ aElement0(X0)
| ~ aElement0(sK1_skl(szRzazndt0(xf),xU))
| ~ aElement0(sK1_skl(szRzazndt0(xf),xU)) ),
inference(resolution,[status(thm)],[f333,f56]) ).
fof(f335,plain,
( ~ sQ34_spl
| sK1_skl(szRzazndt0(xf),xU) = sK1_skl(szRzazndt0(xf),xU)
| ~ sdtlseqdt0(sK1_skl(szRzazndt0(xf),xU),sK1_skl(szRzazndt0(xf),xU))
| ~ aElement0(sK1_skl(szRzazndt0(xf),xU))
| ~ aElement0(sK1_skl(szRzazndt0(xf),xU)) ),
inference(resolution,[status(thm)],[f333,f54]) ).
fof(f336,definition,
! [X0] :
( sQ35_spl
<=> ( sdtlseqdt0(sK1_skl(szRzazndt0(xf),xU),X0)
| ~ sdtlseqdt0(sK1_skl(szRzazndt0(xf),xU),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f339,plain,
( sQ35_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f334,f327,f336]) ).
fof(f340,definition,
( sQ36_spl
<=> sdtlseqdt0(sK1_skl(szRzazndt0(xf),xU),sK1_skl(szRzazndt0(xf),xU)) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f341,plain,
( ~ sQ36_spl
| sdtlseqdt0(sK1_skl(szRzazndt0(xf),xU),sK1_skl(szRzazndt0(xf),xU)) ),
inference(component_clause,[status(thm)],[f340]) ).
fof(f342,plain,
( sQ36_spl
| ~ sdtlseqdt0(sK1_skl(szRzazndt0(xf),xU),sK1_skl(szRzazndt0(xf),xU)) ),
inference(component_clause,[status(thm)],[f340]) ).
fof(f343,definition,
( sQ37_spl
<=> sK1_skl(szRzazndt0(xf),xU) = sK1_skl(szRzazndt0(xf),xU) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f346,plain,
( sQ37_spl
| ~ sQ36_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f335,f327,f340,f343]) ).
fof(f347,plain,
( sQ36_spl
| ~ sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f342,f333]) ).
fof(f348,plain,
( sQ36_spl
| ~ sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f347]) ).
fof(f349,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)],[f81,f61]) ).
fof(f350,plain,
( aSubsetOf0(sK8_skl(szRzazndt0(xf)),szRzazndt0(xf))
| aCompleteLattice0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f102,f285]) ).
fof(f351,plain,
( aSubsetOf0(sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf))
| aCompleteLattice0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f102,f209]) ).
fof(f353,definition,
( sQ38_spl
<=> aCompleteLattice0(szRzazndt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f354,plain,
( ~ sQ38_spl
| aCompleteLattice0(szRzazndt0(xf)) ),
inference(component_clause,[status(thm)],[f353]) ).
fof(f356,definition,
( sQ39_spl
<=> aSubsetOf0(sK8_skl(szRzazndt0(xf)),szRzazndt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f359,plain,
( sQ39_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f350,f353,f356]) ).
fof(f360,definition,
( sQ40_spl
<=> aCompleteLattice0(szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f361,plain,
( ~ sQ40_spl
| aCompleteLattice0(szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f360]) ).
fof(f363,definition,
( sQ41_spl
<=> aSubsetOf0(sK8_skl(szDzozmdt0(xf)),szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f366,plain,
( sQ41_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f351,f360,f363]) ).
fof(f367,definition,
( sQ42_spl
<=> aCompleteLattice0(xU) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f369,plain,
( sQ42_spl
| ~ aCompleteLattice0(xU) ),
inference(component_clause,[status(thm)],[f367]) ).
fof(f370,definition,
( sQ43_spl
<=> aSubsetOf0(sK8_skl(xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f371,plain,
( ~ sQ43_spl
| aSubsetOf0(sK8_skl(xU),xU) ),
inference(component_clause,[status(thm)],[f370]) ).
fof(f375,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)],[f89,f69]) ).
fof(f377,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)],[f90,f69]) ).
fof(f378,plain,
( ~ sQ14_spl
| ~ isEmpty0(szDzozmdt0(xf))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f224,f39]) ).
fof(f379,plain,
( ~ sQ14_spl
| aElement0(sK0_skl(szDzozmdt0(xf)))
| ~ aSet0(szDzozmdt0(xf)) ),
inference(resolution,[status(thm)],[f224,f35]) ).
fof(f380,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f378,f243,f220,f223]) ).
fof(f381,definition,
( sQ44_spl
<=> aElement0(sK0_skl(szDzozmdt0(xf))) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f382,plain,
( ~ sQ44_spl
| aElement0(sK0_skl(szDzozmdt0(xf))) ),
inference(component_clause,[status(thm)],[f381]) ).
fof(f384,plain,
( ~ sQ14_spl
| sQ44_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f379,f243,f381,f223]) ).
fof(f385,plain,
( ~ sQ44_spl
| sdtlseqdt0(sK0_skl(szDzozmdt0(xf)),sK0_skl(szDzozmdt0(xf))) ),
inference(resolution,[status(thm)],[f382,f52]) ).
fof(f386,plain,
( ~ sQ29_spl
| ~ isEmpty0(szRzazndt0(xf))
| ~ aSet0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f300,f39]) ).
fof(f387,plain,
( ~ sQ29_spl
| aElement0(sK0_skl(szRzazndt0(xf)))
| ~ aSet0(szRzazndt0(xf)) ),
inference(resolution,[status(thm)],[f300,f35]) ).
fof(f388,plain,
( ~ sQ29_spl
| ~ sQ28_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f386,f319,f296,f299]) ).
fof(f389,definition,
( sQ45_spl
<=> aElement0(sK0_skl(szRzazndt0(xf))) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f390,plain,
( ~ sQ45_spl
| aElement0(sK0_skl(szRzazndt0(xf))) ),
inference(component_clause,[status(thm)],[f389]) ).
fof(f392,plain,
( ~ sQ29_spl
| sQ45_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f387,f319,f389,f299]) ).
fof(f393,plain,
( ~ sQ45_spl
| sdtlseqdt0(sK0_skl(szRzazndt0(xf)),sK0_skl(szRzazndt0(xf))) ),
inference(resolution,[status(thm)],[f390,f52]) ).
fof(f394,plain,
( ~ sQ2_spl
| aInfimumOfIn0(sK6_skl(xU,xU),xU,xU)
| ~ aCompleteLattice0(xU) ),
inference(resolution,[status(thm)],[f100,f150]) ).
fof(f395,definition,
( sQ46_spl
<=> aInfimumOfIn0(sK6_skl(xU,xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f396,plain,
( ~ sQ46_spl
| aInfimumOfIn0(sK6_skl(xU,xU),xU,xU) ),
inference(component_clause,[status(thm)],[f395]) ).
fof(f398,plain,
( ~ sQ2_spl
| sQ46_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f394,f367,f395,f149]) ).
fof(f399,plain,
( ~ sQ2_spl
| aSupremumOfIn0(sK7_skl(xU,xU),xU,xU)
| ~ aCompleteLattice0(xU) ),
inference(resolution,[status(thm)],[f101,f150]) ).
fof(f400,definition,
( sQ47_spl
<=> aSupremumOfIn0(sK7_skl(xU,xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f401,plain,
( ~ sQ47_spl
| aSupremumOfIn0(sK7_skl(xU,xU),xU,xU) ),
inference(component_clause,[status(thm)],[f400]) ).
fof(f403,plain,
( ~ sQ2_spl
| sQ47_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f399,f367,f400,f149]) ).
fof(f404,plain,
( sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f369,f132]) ).
fof(f405,plain,
sQ42_spl,
inference(contradiction_clause,[status(thm)],[f404]) ).
fof(f406,plain,
! [X0] :
( ~ sQ46_spl
| sK6_skl(xU,xU) = X0
| ~ aInfimumOfIn0(X0,xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f396,f94]) ).
fof(f407,plain,
! [X0] :
( ~ sQ46_spl
| sdtlseqdt0(X0,sK6_skl(xU,xU))
| ~ aLowerBoundOfIn0(X0,xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f396,f79]) ).
fof(f408,plain,
( ~ sQ46_spl
| aLowerBoundOfIn0(sK6_skl(xU,xU),xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f396,f78]) ).
fof(f409,plain,
( ~ sQ46_spl
| aElementOf0(sK6_skl(xU,xU),xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f396,f77]) ).
fof(f410,definition,
! [X0] :
( sQ48_spl
<=> ( sK6_skl(xU,xU) = X0
| ~ aInfimumOfIn0(X0,xU,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f411,plain,
! [X0] :
( ~ sQ48_spl
| sK6_skl(xU,xU) = X0
| ~ aInfimumOfIn0(X0,xU,xU) ),
inference(component_clause,[status(thm)],[f410]) ).
fof(f413,plain,
( ~ sQ46_spl
| sQ48_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f406,f158,f149,f410,f395]) ).
fof(f414,definition,
! [X0] :
( sQ49_spl
<=> ( sdtlseqdt0(X0,sK6_skl(xU,xU))
| ~ aLowerBoundOfIn0(X0,xU,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f415,plain,
! [X0] :
( ~ sQ49_spl
| sdtlseqdt0(X0,sK6_skl(xU,xU))
| ~ aLowerBoundOfIn0(X0,xU,xU) ),
inference(component_clause,[status(thm)],[f414]) ).
fof(f417,plain,
( ~ sQ46_spl
| sQ49_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f407,f158,f149,f414,f395]) ).
fof(f418,definition,
( sQ50_spl
<=> aLowerBoundOfIn0(sK6_skl(xU,xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f419,plain,
( ~ sQ50_spl
| aLowerBoundOfIn0(sK6_skl(xU,xU),xU,xU) ),
inference(component_clause,[status(thm)],[f418]) ).
fof(f421,plain,
( ~ sQ46_spl
| sQ50_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f408,f158,f149,f418,f395]) ).
fof(f422,definition,
( sQ51_spl
<=> aElementOf0(sK6_skl(xU,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f423,plain,
( ~ sQ51_spl
| aElementOf0(sK6_skl(xU,xU),xU) ),
inference(component_clause,[status(thm)],[f422]) ).
fof(f425,plain,
( ~ sQ46_spl
| sQ51_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f409,f158,f149,f422,f395]) ).
fof(f426,plain,
! [X0] :
( ~ sQ47_spl
| sK7_skl(xU,xU) = X0
| ~ aSupremumOfIn0(X0,xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f401,f92]) ).
fof(f427,plain,
! [X0] :
( ~ sQ47_spl
| sdtlseqdt0(sK7_skl(xU,xU),X0)
| ~ aUpperBoundOfIn0(X0,xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f401,f88]) ).
fof(f428,plain,
( ~ sQ47_spl
| aUpperBoundOfIn0(sK7_skl(xU,xU),xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f401,f87]) ).
fof(f429,plain,
( ~ sQ47_spl
| aElementOf0(sK7_skl(xU,xU),xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f401,f86]) ).
fof(f430,definition,
! [X0] :
( sQ52_spl
<=> ( sK7_skl(xU,xU) = X0
| ~ aSupremumOfIn0(X0,xU,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f431,plain,
! [X0] :
( ~ sQ52_spl
| sK7_skl(xU,xU) = X0
| ~ aSupremumOfIn0(X0,xU,xU) ),
inference(component_clause,[status(thm)],[f430]) ).
fof(f433,plain,
( ~ sQ47_spl
| sQ52_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f426,f158,f149,f430,f400]) ).
fof(f434,definition,
! [X0] :
( sQ53_spl
<=> ( sdtlseqdt0(sK7_skl(xU,xU),X0)
| ~ aUpperBoundOfIn0(X0,xU,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f435,plain,
! [X0] :
( ~ sQ53_spl
| sdtlseqdt0(sK7_skl(xU,xU),X0)
| ~ aUpperBoundOfIn0(X0,xU,xU) ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f437,plain,
( ~ sQ47_spl
| sQ53_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f427,f158,f149,f434,f400]) ).
fof(f438,definition,
( sQ54_spl
<=> aUpperBoundOfIn0(sK7_skl(xU,xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f439,plain,
( ~ sQ54_spl
| aUpperBoundOfIn0(sK7_skl(xU,xU),xU,xU) ),
inference(component_clause,[status(thm)],[f438]) ).
fof(f441,plain,
( ~ sQ47_spl
| sQ54_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f428,f158,f149,f438,f400]) ).
fof(f442,definition,
( sQ55_spl
<=> aElementOf0(sK7_skl(xU,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( ~ sQ55_spl
| aElementOf0(sK7_skl(xU,xU),xU) ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,plain,
( ~ sQ47_spl
| sQ55_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f429,f158,f149,f442,f400]) ).
fof(f446,plain,
( ~ sQ25_spl
| ~ sQ51_spl
| aElementOf0(sK3_skl(sK6_skl(xU,xU),xU,xU),xU)
| aUpperBoundOfIn0(sK6_skl(xU,xU),xU,xU) ),
inference(resolution,[status(thm)],[f423,f282]) ).
fof(f447,plain,
( ~ sQ15_spl
| ~ sQ51_spl
| aElementOf0(sK2_skl(sK6_skl(xU,xU),xU,xU),xU)
| aLowerBoundOfIn0(sK6_skl(xU,xU),xU,xU) ),
inference(resolution,[status(thm)],[f423,f229]) ).
fof(f448,plain,
( ~ sQ51_spl
| ~ isEmpty0(xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f423,f39]) ).
fof(f449,plain,
( ~ sQ51_spl
| aElement0(sK6_skl(xU,xU))
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f423,f35]) ).
fof(f450,definition,
( sQ56_spl
<=> aUpperBoundOfIn0(sK6_skl(xU,xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f451,plain,
( ~ sQ56_spl
| aUpperBoundOfIn0(sK6_skl(xU,xU),xU,xU) ),
inference(component_clause,[status(thm)],[f450]) ).
fof(f453,definition,
( sQ57_spl
<=> aElementOf0(sK3_skl(sK6_skl(xU,xU),xU,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f456,plain,
( ~ sQ25_spl
| ~ sQ51_spl
| sQ57_spl
| sQ56_spl ),
inference(split_clause,[status(thm)],[f446,f450,f453,f422,f281]) ).
fof(f457,definition,
( sQ58_spl
<=> aElementOf0(sK2_skl(sK6_skl(xU,xU),xU,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f460,plain,
( ~ sQ15_spl
| ~ sQ51_spl
| sQ58_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f447,f418,f457,f422,f228]) ).
fof(f461,plain,
( ~ sQ51_spl
| ~ sQ0_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f448,f158,f140,f422]) ).
fof(f462,definition,
( sQ59_spl
<=> aElement0(sK6_skl(xU,xU)) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f463,plain,
( ~ sQ59_spl
| aElement0(sK6_skl(xU,xU)) ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f465,plain,
( ~ sQ51_spl
| sQ59_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f449,f158,f462,f422]) ).
fof(f466,plain,
( ~ sQ25_spl
| ~ sQ1_spl
| aElementOf0(sK3_skl(sK0_skl(xU),xU,xU),xU)
| aUpperBoundOfIn0(sK0_skl(xU),xU,xU) ),
inference(resolution,[status(thm)],[f144,f282]) ).
fof(f470,definition,
( sQ60_spl
<=> aUpperBoundOfIn0(sK0_skl(xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f471,plain,
( ~ sQ60_spl
| aUpperBoundOfIn0(sK0_skl(xU),xU,xU) ),
inference(component_clause,[status(thm)],[f470]) ).
fof(f473,definition,
( sQ61_spl
<=> aElementOf0(sK3_skl(sK0_skl(xU),xU,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f476,plain,
( ~ sQ25_spl
| ~ sQ1_spl
| sQ61_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f466,f470,f473,f143,f281]) ).
fof(f481,plain,
( ~ sQ59_spl
| sdtlseqdt0(sK6_skl(xU,xU),sK6_skl(xU,xU)) ),
inference(resolution,[status(thm)],[f463,f52]) ).
fof(f482,plain,
( ~ sQ25_spl
| ~ sQ55_spl
| aElementOf0(sK3_skl(sK7_skl(xU,xU),xU,xU),xU)
| aUpperBoundOfIn0(sK7_skl(xU,xU),xU,xU) ),
inference(resolution,[status(thm)],[f443,f282]) ).
fof(f483,plain,
( ~ sQ15_spl
| ~ sQ55_spl
| aElementOf0(sK2_skl(sK7_skl(xU,xU),xU,xU),xU)
| aLowerBoundOfIn0(sK7_skl(xU,xU),xU,xU) ),
inference(resolution,[status(thm)],[f443,f229]) ).
fof(f484,plain,
( ~ sQ55_spl
| ~ isEmpty0(xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f443,f39]) ).
fof(f485,plain,
( ~ sQ55_spl
| aElement0(sK7_skl(xU,xU))
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f443,f35]) ).
fof(f486,definition,
( sQ62_spl
<=> aElementOf0(sK3_skl(sK7_skl(xU,xU),xU,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f489,plain,
( ~ sQ25_spl
| ~ sQ55_spl
| sQ62_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f482,f438,f486,f442,f281]) ).
fof(f490,definition,
( sQ63_spl
<=> aLowerBoundOfIn0(sK7_skl(xU,xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f491,plain,
( ~ sQ63_spl
| aLowerBoundOfIn0(sK7_skl(xU,xU),xU,xU) ),
inference(component_clause,[status(thm)],[f490]) ).
fof(f493,definition,
( sQ64_spl
<=> aElementOf0(sK2_skl(sK7_skl(xU,xU),xU,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f496,plain,
( ~ sQ15_spl
| ~ sQ55_spl
| sQ64_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f483,f490,f493,f442,f228]) ).
fof(f497,plain,
( ~ sQ55_spl
| ~ sQ0_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f484,f158,f140,f442]) ).
fof(f498,definition,
( sQ65_spl
<=> aElement0(sK7_skl(xU,xU)) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f499,plain,
( ~ sQ65_spl
| aElement0(sK7_skl(xU,xU)) ),
inference(component_clause,[status(thm)],[f498]) ).
fof(f501,plain,
( ~ sQ55_spl
| sQ65_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f485,f158,f498,f442]) ).
fof(f502,plain,
( ~ sQ65_spl
| sdtlseqdt0(sK7_skl(xU,xU),sK7_skl(xU,xU)) ),
inference(resolution,[status(thm)],[f499,f52]) ).
fof(f503,plain,
( szDzozmdt0(xf) = szRzazndt0(xf)
| ~ aSet0(xU)
| ~ aFunction0(xf) ),
inference(resolution,[status(thm)],[f113,f135]) ).
fof(f504,definition,
( sQ66_spl
<=> aFunction0(xf) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f506,plain,
( sQ66_spl
| ~ aFunction0(xf) ),
inference(component_clause,[status(thm)],[f504]) ).
fof(f507,definition,
( sQ67_spl
<=> szDzozmdt0(xf) = szRzazndt0(xf) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f508,plain,
( ~ sQ67_spl
| szDzozmdt0(xf) = szRzazndt0(xf) ),
inference(component_clause,[status(thm)],[f507]) ).
fof(f510,plain,
( sQ67_spl
| ~ sQ4_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f503,f504,f158,f507]) ).
fof(f511,plain,
( sQ66_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f506,f133]) ).
fof(f512,plain,
sQ66_spl,
inference(contradiction_clause,[status(thm)],[f511]) ).
fof(f513,plain,
( szRzazndt0(xf) = xU
| ~ aSet0(xU)
| ~ aFunction0(xf) ),
inference(resolution,[status(thm)],[f114,f135]) ).
fof(f514,definition,
( sQ68_spl
<=> szRzazndt0(xf) = xU ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f515,plain,
( ~ sQ68_spl
| szRzazndt0(xf) = xU ),
inference(component_clause,[status(thm)],[f514]) ).
fof(f517,plain,
( sQ68_spl
| ~ sQ4_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f513,f504,f158,f514]) ).
fof(f518,plain,
! [X0] :
( szRzazndt0(xf) != X0
| szDzozmdt0(xf) != szRzazndt0(xf)
| isOn0(xf,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f115,f133]) ).
fof(f519,definition,
! [X0] :
( sQ69_spl
<=> ( szRzazndt0(xf) != X0
| isOn0(xf,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f520,plain,
! [X0] :
( ~ sQ69_spl
| szRzazndt0(xf) != X0
| isOn0(xf,X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f519]) ).
fof(f522,plain,
( ~ sQ67_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f518,f519,f507]) ).
fof(f523,plain,
( ~ sQ20_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)],[f259,f323]) ).
fof(f524,plain,
! [X0] :
( ~ sQ20_spl
| sdtlseqdt0(sK0_skl(xU),X0)
| ~ aElementOf0(X0,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f259,f62]) ).
fof(f525,plain,
( ~ sQ20_spl
| aElementOf0(sK0_skl(xU),xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f259,f61]) ).
fof(f526,definition,
( sQ70_spl
<=> aInfimumOfIn0(sK0_skl(xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f527,plain,
( ~ sQ70_spl
| aInfimumOfIn0(sK0_skl(xU),xU,xU) ),
inference(component_clause,[status(thm)],[f526]) ).
fof(f529,definition,
( sQ71_spl
<=> aLowerBoundOfIn0(sK4_skl(sK0_skl(xU),xU,xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f532,plain,
( ~ sQ20_spl
| sQ71_spl
| sQ70_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f523,f158,f149,f526,f529,f258]) ).
fof(f533,definition,
! [X0] :
( sQ72_spl
<=> ( sdtlseqdt0(sK0_skl(xU),X0)
| ~ aElementOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f534,plain,
! [X0] :
( ~ sQ72_spl
| sdtlseqdt0(sK0_skl(xU),X0)
| ~ aElementOf0(X0,xU) ),
inference(component_clause,[status(thm)],[f533]) ).
fof(f536,plain,
( ~ sQ20_spl
| sQ72_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f524,f158,f149,f533,f258]) ).
fof(f537,plain,
( ~ sQ20_spl
| sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f525,f158,f149,f143,f258]) ).
fof(f542,plain,
( ~ sQ60_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)],[f471,f375]) ).
fof(f543,plain,
! [X0] :
( ~ sQ60_spl
| sdtlseqdt0(X0,sK0_skl(xU))
| ~ aElementOf0(X0,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f471,f70]) ).
fof(f544,plain,
( ~ sQ60_spl
| aElementOf0(sK0_skl(xU),xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f471,f69]) ).
fof(f545,definition,
( sQ73_spl
<=> aSupremumOfIn0(sK0_skl(xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f546,plain,
( ~ sQ73_spl
| aSupremumOfIn0(sK0_skl(xU),xU,xU) ),
inference(component_clause,[status(thm)],[f545]) ).
fof(f548,definition,
( sQ74_spl
<=> aUpperBoundOfIn0(sK5_skl(sK0_skl(xU),xU,xU),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f551,plain,
( ~ sQ60_spl
| sQ74_spl
| sQ73_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f542,f158,f149,f545,f548,f470]) ).
fof(f552,definition,
! [X0] :
( sQ75_spl
<=> ( sdtlseqdt0(X0,sK0_skl(xU))
| ~ aElementOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f553,plain,
! [X0] :
( ~ sQ75_spl
| sdtlseqdt0(X0,sK0_skl(xU))
| ~ aElementOf0(X0,xU) ),
inference(component_clause,[status(thm)],[f552]) ).
fof(f555,plain,
( ~ sQ60_spl
| sQ75_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f543,f158,f149,f552,f470]) ).
fof(f556,plain,
( ~ sQ60_spl
| sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f544,f158,f149,f143,f470]) ).
fof(f558,plain,
( ~ sQ45_spl
| ~ sQ68_spl
| aElement0(sK0_skl(xU)) ),
inference(backward_demodulation,[status(thm)],[f515,f390]) ).
fof(f559,plain,
( ~ sQ29_spl
| ~ sQ68_spl
| aElementOf0(sK0_skl(szRzazndt0(xf)),xU) ),
inference(backward_demodulation,[status(thm)],[f515,f300]) ).
fof(f561,plain,
( sQ28_spl
| ~ sQ68_spl
| ~ isEmpty0(xU) ),
inference(backward_demodulation,[status(thm)],[f515,f298]) ).
fof(f562,plain,
( ~ sQ34_spl
| ~ sQ68_spl
| sdtlseqdt0(sK1_skl(szRzazndt0(xf),xU),sK1_skl(xU,xU)) ),
inference(backward_demodulation,[status(thm)],[f515,f333]) ).
fof(f563,plain,
( ~ sQ34_spl
| ~ sQ68_spl
| aElement0(sK1_skl(xU,xU)) ),
inference(backward_demodulation,[status(thm)],[f515,f328]) ).
fof(f564,plain,
( ~ sQ27_spl
| ~ sQ68_spl
| aElementOf0(sK1_skl(szRzazndt0(xf),xU),xU) ),
inference(backward_demodulation,[status(thm)],[f515,f293]) ).
fof(f565,plain,
( sQ26_spl
| ~ sQ68_spl
| ~ aSubsetOf0(xU,xU) ),
inference(backward_demodulation,[status(thm)],[f515,f291]) ).
fof(f567,plain,
( ~ sQ29_spl
| ~ sQ68_spl
| aElementOf0(sK0_skl(xU),xU) ),
inference(forward_demodulation,[status(thm)],[f515,f559]) ).
fof(f568,plain,
( ~ sQ34_spl
| ~ sQ68_spl
| sdtlseqdt0(sK1_skl(xU,xU),sK1_skl(xU,xU)) ),
inference(forward_demodulation,[status(thm)],[f515,f562]) ).
fof(f569,plain,
( ~ sQ27_spl
| ~ sQ68_spl
| aElementOf0(sK1_skl(xU,xU),xU) ),
inference(forward_demodulation,[status(thm)],[f515,f564]) ).
fof(f570,plain,
( ~ sQ27_spl
| ~ sQ68_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f569,f154]) ).
fof(f571,plain,
( ~ sQ27_spl
| ~ sQ68_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f570]) ).
fof(f572,plain,
! [X0] :
( ~ sQ30_spl
| ~ sQ68_spl
| aElementOf0(sK3_skl(X0,szRzazndt0(xf),xU),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f515,f308]) ).
fof(f573,plain,
! [X0] :
( ~ sQ30_spl
| ~ sQ68_spl
| aElementOf0(sK3_skl(X0,xU,xU),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f515,f572]) ).
fof(f574,plain,
! [X0] :
( ~ sQ30_spl
| ~ sQ68_spl
| aElementOf0(sK3_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f515,f573]) ).
fof(f575,plain,
! [X0] :
( ~ sQ31_spl
| ~ sQ68_spl
| aElementOf0(sK2_skl(X0,szRzazndt0(xf),xU),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f515,f312]) ).
fof(f576,plain,
! [X0] :
( ~ sQ31_spl
| ~ sQ68_spl
| aElementOf0(sK2_skl(X0,xU,xU),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f515,f575]) ).
fof(f577,plain,
! [X0] :
( ~ sQ31_spl
| ~ sQ68_spl
| aElementOf0(sK2_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f515,f576]) ).
fof(f578,plain,
( ~ sQ26_spl
| ~ sQ68_spl
| aSubsetOf0(xU,xU) ),
inference(forward_demodulation,[status(thm)],[f515,f290]) ).
fof(f579,plain,
( sQ27_spl
| ~ sQ68_spl
| ~ aElementOf0(sK1_skl(xU,xU),szRzazndt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f515,f294]) ).
fof(f580,plain,
( sQ27_spl
| ~ sQ68_spl
| ~ aElementOf0(sK1_skl(xU,xU),xU) ),
inference(forward_demodulation,[status(thm)],[f515,f579]) ).
fof(f581,plain,
( sQ34_spl
| ~ sQ68_spl
| ~ aElement0(sK1_skl(xU,xU)) ),
inference(forward_demodulation,[status(thm)],[f515,f329]) ).
fof(f582,plain,
( ~ sQ44_spl
| ~ sQ67_spl
| ~ sQ68_spl
| aElement0(sK0_skl(xU)) ),
inference(backward_demodulation,[status(thm)],[f591,f382]) ).
fof(f583,plain,
( ~ sQ14_spl
| ~ sQ67_spl
| ~ sQ68_spl
| aElementOf0(sK0_skl(szDzozmdt0(xf)),xU) ),
inference(backward_demodulation,[status(thm)],[f591,f224]) ).
fof(f585,plain,
( ~ sQ19_spl
| ~ sQ67_spl
| ~ sQ68_spl
| sdtlseqdt0(sK1_skl(szDzozmdt0(xf),xU),sK1_skl(xU,xU)) ),
inference(backward_demodulation,[status(thm)],[f591,f256]) ).
fof(f586,plain,
( sQ13_spl
| ~ sQ67_spl
| ~ sQ68_spl
| ~ isEmpty0(xU) ),
inference(backward_demodulation,[status(thm)],[f591,f222]) ).
fof(f587,plain,
( ~ sQ19_spl
| ~ sQ67_spl
| ~ sQ68_spl
| aElement0(sK1_skl(xU,xU)) ),
inference(backward_demodulation,[status(thm)],[f591,f251]) ).
fof(f588,plain,
( sQ11_spl
| ~ sQ67_spl
| ~ sQ68_spl
| ~ aSubsetOf0(xU,xU) ),
inference(backward_demodulation,[status(thm)],[f591,f215]) ).
fof(f589,plain,
( ~ sQ12_spl
| ~ sQ67_spl
| ~ sQ68_spl
| aElementOf0(sK1_skl(szDzozmdt0(xf),xU),xU) ),
inference(backward_demodulation,[status(thm)],[f591,f217]) ).
fof(f591,plain,
( ~ sQ67_spl
| ~ sQ68_spl
| szDzozmdt0(xf) = xU ),
inference(forward_demodulation,[status(thm)],[f515,f508]) ).
fof(f592,plain,
( ~ sQ14_spl
| ~ sQ67_spl
| ~ sQ68_spl
| aElementOf0(sK0_skl(xU),xU) ),
inference(forward_demodulation,[status(thm)],[f591,f583]) ).
fof(f593,plain,
( ~ sQ19_spl
| ~ sQ67_spl
| ~ sQ68_spl
| sdtlseqdt0(sK1_skl(xU,xU),sK1_skl(xU,xU)) ),
inference(forward_demodulation,[status(thm)],[f591,f585]) ).
fof(f594,plain,
( sQ11_spl
| ~ sQ67_spl
| ~ sQ68_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f588,f150]) ).
fof(f595,plain,
( sQ11_spl
| ~ sQ67_spl
| ~ sQ68_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f594]) ).
fof(f596,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ67_spl
| ~ sQ68_spl
| aElementOf0(sK2_skl(X0,szDzozmdt0(xf),xU),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f591,f236]) ).
fof(f597,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ67_spl
| ~ sQ68_spl
| aElementOf0(sK2_skl(X0,xU,xU),szDzozmdt0(xf))
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f591,f596]) ).
fof(f598,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ67_spl
| ~ sQ68_spl
| aElementOf0(sK2_skl(X0,xU,xU),xU)
| ~ aElementOf0(X0,xU)
| aLowerBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f591,f597]) ).
fof(f599,plain,
( ~ sQ11_spl
| ~ sQ67_spl
| ~ sQ68_spl
| aSubsetOf0(xU,xU) ),
inference(forward_demodulation,[status(thm)],[f591,f214]) ).
fof(f600,plain,
( ~ sQ6_spl
| sdtlseqdt0(sK1_skl(xU,xU),sK1_skl(xU,xU)) ),
inference(resolution,[status(thm)],[f170,f52]) ).
fof(f601,plain,
! [X0] :
( ~ sQ67_spl
| ~ sQ68_spl
| aElementOf0(sdtlpdtrp0(xf,X0),szRzazndt0(xf))
| ~ aElementOf0(X0,xU)
| ~ aFunction0(xf) ),
inference(paramodulation,[status(thm)],[f591,f117]) ).
fof(f602,definition,
! [X0] :
( sQ76_spl
<=> ( aElementOf0(sdtlpdtrp0(xf,X0),szRzazndt0(xf))
| ~ aElementOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f603,plain,
! [X0] :
( ~ sQ76_spl
| aElementOf0(sdtlpdtrp0(xf,X0),szRzazndt0(xf))
| ~ aElementOf0(X0,xU) ),
inference(component_clause,[status(thm)],[f602]) ).
fof(f605,plain,
( ~ sQ67_spl
| ~ sQ68_spl
| sQ76_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f601,f504,f602,f514,f507]) ).
fof(f606,plain,
! [X0] :
( ~ sQ76_spl
| ~ sQ68_spl
| aElementOf0(sdtlpdtrp0(xf,X0),xU)
| ~ aElementOf0(X0,xU) ),
inference(forward_demodulation,[status(thm)],[f515,f603]) ).
fof(f607,plain,
! [X0] :
( ~ sQ67_spl
| ~ sQ68_spl
| sdtlpdtrp0(xf,X0) != X0
| ~ aElementOf0(X0,xU)
| aFixedPointOf0(X0,xf)
| ~ aFunction0(xf) ),
inference(paramodulation,[status(thm)],[f591,f123]) ).
fof(f608,definition,
! [X0] :
( sQ77_spl
<=> ( sdtlpdtrp0(xf,X0) != X0
| ~ aElementOf0(X0,xU)
| aFixedPointOf0(X0,xf) ) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f609,plain,
! [X0] :
( ~ sQ77_spl
| sdtlpdtrp0(xf,X0) != X0
| ~ aElementOf0(X0,xU)
| aFixedPointOf0(X0,xf) ),
inference(component_clause,[status(thm)],[f608]) ).
fof(f611,plain,
( ~ sQ67_spl
| ~ sQ68_spl
| sQ77_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f607,f504,f608,f514,f507]) ).
fof(f612,plain,
( sQ34_spl
| ~ sQ68_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f581,f170]) ).
fof(f613,plain,
( sQ34_spl
| ~ sQ68_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f612]) ).
fof(f614,plain,
( ~ sQ36_spl
| ~ sQ68_spl
| sdtlseqdt0(sK1_skl(xU,xU),sK1_skl(szRzazndt0(xf),xU)) ),
inference(forward_demodulation,[status(thm)],[f515,f341]) ).
fof(f615,plain,
( ~ sQ36_spl
| ~ sQ68_spl
| sdtlseqdt0(sK1_skl(xU,xU),sK1_skl(xU,xU)) ),
inference(forward_demodulation,[status(thm)],[f515,f614]) ).
fof(f616,plain,
( ~ sQ19_spl
| ~ sQ67_spl
| ~ sQ68_spl
| sdtlseqdt0(sK1_skl(xU,xU),sK1_skl(xU,xU)) ),
inference(resolution,[status(thm)],[f587,f52]) ).
fof(f617,plain,
( ~ sQ20_spl
| ~ sQ49_spl
| sdtlseqdt0(sK0_skl(xU),sK6_skl(xU,xU)) ),
inference(resolution,[status(thm)],[f415,f259]) ).
fof(f618,plain,
( ~ sQ48_spl
| ~ sQ70_spl
| sK6_skl(xU,xU) = sK0_skl(xU) ),
inference(resolution,[status(thm)],[f527,f411]) ).
fof(f619,plain,
! [X0] :
( ~ sQ70_spl
| sK0_skl(xU) = X0
| ~ aInfimumOfIn0(X0,xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f527,f94]) ).
fof(f620,plain,
! [X0] :
( ~ sQ70_spl
| sdtlseqdt0(X0,sK0_skl(xU))
| ~ aLowerBoundOfIn0(X0,xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f527,f79]) ).
fof(f621,plain,
( ~ sQ70_spl
| aLowerBoundOfIn0(sK0_skl(xU),xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f527,f78]) ).
fof(f622,plain,
( ~ sQ70_spl
| aElementOf0(sK0_skl(xU),xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f527,f77]) ).
fof(f623,definition,
! [X0] :
( sQ78_spl
<=> ( sK0_skl(xU) = X0
| ~ aInfimumOfIn0(X0,xU,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f624,plain,
! [X0] :
( ~ sQ78_spl
| sK0_skl(xU) = X0
| ~ aInfimumOfIn0(X0,xU,xU) ),
inference(component_clause,[status(thm)],[f623]) ).
fof(f626,plain,
( ~ sQ70_spl
| sQ78_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f619,f158,f149,f623,f526]) ).
fof(f627,definition,
! [X0] :
( sQ79_spl
<=> ( sdtlseqdt0(X0,sK0_skl(xU))
| ~ aLowerBoundOfIn0(X0,xU,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f628,plain,
! [X0] :
( ~ sQ79_spl
| sdtlseqdt0(X0,sK0_skl(xU))
| ~ aLowerBoundOfIn0(X0,xU,xU) ),
inference(component_clause,[status(thm)],[f627]) ).
fof(f630,plain,
( ~ sQ70_spl
| sQ79_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f620,f158,f149,f627,f526]) ).
fof(f631,plain,
( ~ sQ70_spl
| sQ20_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f621,f158,f149,f258,f526]) ).
fof(f632,plain,
( ~ sQ70_spl
| sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f622,f158,f149,f143,f526]) ).
fof(f633,plain,
! [X0] :
( ~ sQ73_spl
| sK0_skl(xU) = X0
| ~ aSupremumOfIn0(X0,xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f546,f92]) ).
fof(f634,plain,
! [X0] :
( ~ sQ73_spl
| sdtlseqdt0(sK0_skl(xU),X0)
| ~ aUpperBoundOfIn0(X0,xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f546,f88]) ).
fof(f635,plain,
( ~ sQ73_spl
| aUpperBoundOfIn0(sK0_skl(xU),xU,xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f546,f87]) ).
fof(f636,plain,
( ~ sQ73_spl
| aElementOf0(sK0_skl(xU),xU)
| ~ aSubsetOf0(xU,xU)
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f546,f86]) ).
fof(f637,definition,
! [X0] :
( sQ80_spl
<=> ( sK0_skl(xU) = X0
| ~ aSupremumOfIn0(X0,xU,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f638,plain,
! [X0] :
( ~ sQ80_spl
| sK0_skl(xU) = X0
| ~ aSupremumOfIn0(X0,xU,xU) ),
inference(component_clause,[status(thm)],[f637]) ).
fof(f640,plain,
( ~ sQ73_spl
| sQ80_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f633,f158,f149,f637,f545]) ).
fof(f641,definition,
! [X0] :
( sQ81_spl
<=> ( sdtlseqdt0(sK0_skl(xU),X0)
| ~ aUpperBoundOfIn0(X0,xU,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f642,plain,
! [X0] :
( ~ sQ81_spl
| sdtlseqdt0(sK0_skl(xU),X0)
| ~ aUpperBoundOfIn0(X0,xU,xU) ),
inference(component_clause,[status(thm)],[f641]) ).
fof(f644,plain,
( ~ sQ73_spl
| sQ81_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f634,f158,f149,f641,f545]) ).
fof(f645,plain,
( ~ sQ73_spl
| sQ60_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f635,f158,f149,f470,f545]) ).
fof(f646,plain,
( ~ sQ73_spl
| sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f636,f158,f149,f143,f545]) ).
fof(f647,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ48_spl
| ~ sQ70_spl
| sdtlseqdt0(X0,sK0_skl(xU))
| ~ aLowerBoundOfIn0(X0,xU,xU) ),
inference(backward_demodulation,[status(thm)],[f618,f415]) ).
fof(f648,plain,
! [X0] :
( ~ sQ48_spl
| ~ sQ70_spl
| sK0_skl(xU) = X0
| ~ aInfimumOfIn0(X0,xU,xU) ),
inference(backward_demodulation,[status(thm)],[f618,f411]) ).
fof(f649,plain,
( ~ sQ59_spl
| ~ sQ48_spl
| ~ sQ70_spl
| aElement0(sK0_skl(xU)) ),
inference(backward_demodulation,[status(thm)],[f618,f463]) ).
fof(f650,plain,
( ~ sQ51_spl
| ~ sQ48_spl
| ~ sQ70_spl
| aElementOf0(sK0_skl(xU),xU) ),
inference(backward_demodulation,[status(thm)],[f618,f423]) ).
fof(f652,plain,
! [X0,X1] :
( ~ sQ67_spl
| ~ sQ68_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)],[f591,f127]) ).
fof(f653,definition,
( sQ82_spl
<=> isMonotone0(xf) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f655,plain,
( sQ82_spl
| ~ isMonotone0(xf) ),
inference(component_clause,[status(thm)],[f653]) ).
fof(f656,definition,
! [X0,X1] :
( sQ83_spl
<=> ( sdtlseqdt0(sdtlpdtrp0(xf,X0),sdtlpdtrp0(xf,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szDzozmdt0(xf))
| ~ aElementOf0(X0,xU) ) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f657,plain,
! [X0,X1] :
( ~ sQ83_spl
| sdtlseqdt0(sdtlpdtrp0(xf,X0),sdtlpdtrp0(xf,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szDzozmdt0(xf))
| ~ aElementOf0(X0,xU) ),
inference(component_clause,[status(thm)],[f656]) ).
fof(f659,plain,
( ~ sQ67_spl
| ~ sQ68_spl
| sQ83_spl
| ~ sQ82_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f652,f504,f653,f656,f514,f507]) ).
fof(f660,plain,
( sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f655,f134]) ).
fof(f661,plain,
sQ82_spl,
inference(contradiction_clause,[status(thm)],[f660]) ).
fof(f662,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ sQ67_spl
| ~ sQ68_spl
| sdtlseqdt0(sdtlpdtrp0(xf,X0),sdtlpdtrp0(xf,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,xU)
| ~ aElementOf0(X0,xU) ),
inference(forward_demodulation,[status(thm)],[f591,f657]) ).
fof(f673,plain,
( ~ sQ50_spl
| ~ sQ48_spl
| ~ sQ70_spl
| aLowerBoundOfIn0(sK0_skl(xU),xU,xU) ),
inference(forward_demodulation,[status(thm)],[f618,f419]) ).
fof(f674,plain,
( ~ sQ73_spl
| ~ sQ52_spl
| sK7_skl(xU,xU) = sK0_skl(xU) ),
inference(resolution,[status(thm)],[f431,f546]) ).
fof(f676,plain,
! [X0] :
( ~ sQ52_spl
| ~ sQ73_spl
| sK0_skl(xU) = X0
| ~ aSupremumOfIn0(X0,xU,xU) ),
inference(backward_demodulation,[status(thm)],[f674,f431]) ).
fof(f677,plain,
( ~ sQ65_spl
| ~ sQ73_spl
| ~ sQ52_spl
| aElement0(sK0_skl(xU)) ),
inference(backward_demodulation,[status(thm)],[f674,f499]) ).
fof(f678,plain,
( ~ sQ55_spl
| ~ sQ73_spl
| ~ sQ52_spl
| aElementOf0(sK0_skl(xU),xU) ),
inference(backward_demodulation,[status(thm)],[f674,f443]) ).
fof(f680,plain,
( ~ sQ54_spl
| ~ sQ73_spl
| ~ sQ52_spl
| aUpperBoundOfIn0(sK0_skl(xU),xU,xU) ),
inference(forward_demodulation,[status(thm)],[f674,f439]) ).
fof(f681,plain,
! [X0] :
( ~ sQ53_spl
| ~ sQ73_spl
| ~ sQ52_spl
| sdtlseqdt0(sK0_skl(xU),X0)
| ~ aUpperBoundOfIn0(X0,xU,xU) ),
inference(forward_demodulation,[status(thm)],[f674,f435]) ).
fof(f682,plain,
( ~ sQ60_spl
| ~ sQ53_spl
| ~ sQ73_spl
| ~ sQ52_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(resolution,[status(thm)],[f681,f471]) ).
fof(f683,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ67_spl
| ~ sQ68_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)],[f593,f56]) ).
fof(f684,plain,
( ~ sQ19_spl
| ~ sQ67_spl
| ~ sQ68_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)],[f593,f54]) ).
fof(f685,definition,
! [X0] :
( sQ86_spl
<=> ( sdtlseqdt0(sK1_skl(xU,xU),X0)
| ~ sdtlseqdt0(sK1_skl(xU,xU),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f688,plain,
( ~ sQ19_spl
| ~ sQ67_spl
| ~ sQ68_spl
| sQ86_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f683,f169,f685,f514,f507,f250]) ).
fof(f689,definition,
( sQ87_spl
<=> sdtlseqdt0(sK1_skl(xU,xU),sK1_skl(xU,xU)) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f690,plain,
( ~ sQ87_spl
| sdtlseqdt0(sK1_skl(xU,xU),sK1_skl(xU,xU)) ),
inference(component_clause,[status(thm)],[f689]) ).
fof(f691,plain,
( sQ87_spl
| ~ sdtlseqdt0(sK1_skl(xU,xU),sK1_skl(xU,xU)) ),
inference(component_clause,[status(thm)],[f689]) ).
fof(f692,definition,
( sQ88_spl
<=> sK1_skl(xU,xU) = sK1_skl(xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f695,plain,
( ~ sQ19_spl
| ~ sQ67_spl
| ~ sQ68_spl
| sQ88_spl
| ~ sQ87_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f684,f169,f689,f692,f514,f507,f250]) ).
fof(f696,plain,
( sQ19_spl
| ~ sQ67_spl
| ~ sQ68_spl
| ~ aElement0(sK1_skl(xU,xU)) ),
inference(forward_demodulation,[status(thm)],[f591,f252]) ).
fof(f697,plain,
( sQ12_spl
| ~ sQ67_spl
| ~ sQ68_spl
| ~ aElementOf0(sK1_skl(xU,xU),szDzozmdt0(xf)) ),
inference(forward_demodulation,[status(thm)],[f591,f218]) ).
fof(f698,plain,
( sQ12_spl
| ~ sQ67_spl
| ~ sQ68_spl
| ~ aElementOf0(sK1_skl(xU,xU),xU) ),
inference(forward_demodulation,[status(thm)],[f591,f697]) ).
fof(f700,plain,
( sQ19_spl
| ~ sQ67_spl
| ~ sQ68_spl
| ~ sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f696,f563]) ).
fof(f701,plain,
( sQ19_spl
| ~ sQ67_spl
| ~ sQ68_spl
| ~ sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f700]) ).
fof(f702,plain,
( ~ sQ23_spl
| ~ sQ67_spl
| ~ sQ68_spl
| sdtlseqdt0(sK1_skl(xU,xU),sK1_skl(szDzozmdt0(xf),xU)) ),
inference(forward_demodulation,[status(thm)],[f591,f272]) ).
fof(f703,plain,
( ~ sQ23_spl
| ~ sQ67_spl
| ~ sQ68_spl
| sdtlseqdt0(sK1_skl(xU,xU),sK1_skl(xU,xU)) ),
inference(forward_demodulation,[status(thm)],[f591,f702]) ).
fof(f709,plain,
! [X0] :
( ~ sQ69_spl
| ~ sQ68_spl
| xU != X0
| isOn0(xf,X0)
| ~ aSet0(X0) ),
inference(forward_demodulation,[status(thm)],[f515,f520]) ).
fof(f710,plain,
( ~ sQ69_spl
| ~ sQ68_spl
| xU != xU
| isOn0(xf,xU) ),
inference(resolution,[status(thm)],[f709,f138]) ).
fof(f711,definition,
( sQ90_spl
<=> isOn0(xf,xU) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f714,definition,
( sQ91_spl
<=> xU = xU ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f717,plain,
( ~ sQ69_spl
| ~ sQ68_spl
| ~ sQ91_spl
| sQ90_spl ),
inference(split_clause,[status(thm)],[f710,f711,f714,f514,f519]) ).
fof(f718,plain,
( ~ sQ56_spl
| ~ sQ48_spl
| ~ sQ70_spl
| aUpperBoundOfIn0(sK0_skl(xU),xU,xU) ),
inference(forward_demodulation,[status(thm)],[f618,f451]) ).
fof(f719,plain,
! [X0] :
( ~ sQ34_spl
| ~ sQ68_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)],[f568,f56]) ).
fof(f720,plain,
( ~ sQ34_spl
| ~ sQ68_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)],[f568,f54]) ).
fof(f721,plain,
( ~ sQ34_spl
| ~ sQ68_spl
| sQ86_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f719,f169,f685,f514,f327]) ).
fof(f722,plain,
( ~ sQ34_spl
| ~ sQ68_spl
| sQ88_spl
| ~ sQ87_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f720,f169,f689,f692,f514,f327]) ).
fof(f723,plain,
( ~ sQ63_spl
| ~ sQ73_spl
| ~ sQ52_spl
| aLowerBoundOfIn0(sK0_skl(xU),xU,xU) ),
inference(forward_demodulation,[status(thm)],[f674,f491]) ).
fof(f724,plain,
( ~ sQ1_spl
| ~ sQ72_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(resolution,[status(thm)],[f534,f144]) ).
fof(f725,plain,
( ~ sQ20_spl
| ~ sQ49_spl
| ~ sQ48_spl
| ~ sQ70_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(resolution,[status(thm)],[f647,f259]) ).
fof(f727,plain,
( ~ sQ1_spl
| ~ sQ75_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(resolution,[status(thm)],[f553,f144]) ).
fof(f728,plain,
( ~ sQ20_spl
| ~ sQ49_spl
| ~ sQ48_spl
| ~ sQ70_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(forward_demodulation,[status(thm)],[f618,f617]) ).
fof(f733,plain,
( ~ sQ1_spl
| ~ sQ76_spl
| ~ sQ68_spl
| aElementOf0(sdtlpdtrp0(xf,sK0_skl(xU)),xU) ),
inference(resolution,[status(thm)],[f606,f144]) ).
fof(f735,plain,
( ~ sQ76_spl
| ~ sQ68_spl
| ~ sQ1_spl
| aElementOf0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU))),xU) ),
inference(resolution,[status(thm)],[f733,f606]) ).
fof(f736,plain,
( ~ sQ75_spl
| ~ sQ1_spl
| ~ sQ76_spl
| ~ sQ68_spl
| sdtlseqdt0(sdtlpdtrp0(xf,sK0_skl(xU)),sK0_skl(xU)) ),
inference(resolution,[status(thm)],[f733,f553]) ).
fof(f737,plain,
( ~ sQ72_spl
| ~ sQ1_spl
| ~ sQ76_spl
| ~ sQ68_spl
| sdtlseqdt0(sK0_skl(xU),sdtlpdtrp0(xf,sK0_skl(xU))) ),
inference(resolution,[status(thm)],[f733,f534]) ).
fof(f738,plain,
( ~ sQ25_spl
| ~ sQ1_spl
| ~ sQ76_spl
| ~ sQ68_spl
| aElementOf0(sK3_skl(sdtlpdtrp0(xf,sK0_skl(xU)),xU,xU),xU)
| aUpperBoundOfIn0(sdtlpdtrp0(xf,sK0_skl(xU)),xU,xU) ),
inference(resolution,[status(thm)],[f733,f282]) ).
fof(f739,plain,
( ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ76_spl
| ~ sQ68_spl
| aElementOf0(sK2_skl(sdtlpdtrp0(xf,sK0_skl(xU)),xU,xU),xU)
| aLowerBoundOfIn0(sdtlpdtrp0(xf,sK0_skl(xU)),xU,xU) ),
inference(resolution,[status(thm)],[f733,f229]) ).
fof(f741,plain,
( ~ sQ1_spl
| ~ sQ76_spl
| ~ sQ68_spl
| aElement0(sdtlpdtrp0(xf,sK0_skl(xU)))
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f733,f35]) ).
fof(f742,definition,
( sQ92_spl
<=> aUpperBoundOfIn0(sdtlpdtrp0(xf,sK0_skl(xU)),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f743,plain,
( ~ sQ92_spl
| aUpperBoundOfIn0(sdtlpdtrp0(xf,sK0_skl(xU)),xU,xU) ),
inference(component_clause,[status(thm)],[f742]) ).
fof(f745,definition,
( sQ93_spl
<=> aElementOf0(sK3_skl(sdtlpdtrp0(xf,sK0_skl(xU)),xU,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f748,plain,
( ~ sQ25_spl
| ~ sQ1_spl
| ~ sQ76_spl
| ~ sQ68_spl
| sQ93_spl
| sQ92_spl ),
inference(split_clause,[status(thm)],[f738,f742,f745,f514,f602,f143,f281]) ).
fof(f749,definition,
( sQ94_spl
<=> aLowerBoundOfIn0(sdtlpdtrp0(xf,sK0_skl(xU)),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f750,plain,
( ~ sQ94_spl
| aLowerBoundOfIn0(sdtlpdtrp0(xf,sK0_skl(xU)),xU,xU) ),
inference(component_clause,[status(thm)],[f749]) ).
fof(f752,definition,
( sQ95_spl
<=> aElementOf0(sK2_skl(sdtlpdtrp0(xf,sK0_skl(xU)),xU,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f755,plain,
( ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ76_spl
| ~ sQ68_spl
| sQ95_spl
| sQ94_spl ),
inference(split_clause,[status(thm)],[f739,f749,f752,f514,f602,f143,f228]) ).
fof(f757,definition,
( sQ96_spl
<=> aElement0(sdtlpdtrp0(xf,sK0_skl(xU))) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f758,plain,
( ~ sQ96_spl
| aElement0(sdtlpdtrp0(xf,sK0_skl(xU))) ),
inference(component_clause,[status(thm)],[f757]) ).
fof(f760,plain,
( ~ sQ1_spl
| ~ sQ76_spl
| ~ sQ68_spl
| sQ96_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f741,f158,f757,f514,f602,f143]) ).
fof(f761,plain,
( ~ sQ96_spl
| sdtlseqdt0(sdtlpdtrp0(xf,sK0_skl(xU)),sdtlpdtrp0(xf,sK0_skl(xU))) ),
inference(resolution,[status(thm)],[f758,f52]) ).
fof(f762,plain,
( ~ sQ76_spl
| ~ sQ68_spl
| ~ sQ1_spl
| aElementOf0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU)))),xU) ),
inference(resolution,[status(thm)],[f735,f606]) ).
fof(f763,plain,
( ~ sQ75_spl
| ~ sQ76_spl
| ~ sQ68_spl
| ~ sQ1_spl
| sdtlseqdt0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU))),sK0_skl(xU)) ),
inference(resolution,[status(thm)],[f735,f553]) ).
fof(f764,plain,
( ~ sQ72_spl
| ~ sQ76_spl
| ~ sQ68_spl
| ~ sQ1_spl
| sdtlseqdt0(sK0_skl(xU),sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU)))) ),
inference(resolution,[status(thm)],[f735,f534]) ).
fof(f765,plain,
( ~ sQ25_spl
| ~ sQ76_spl
| ~ sQ68_spl
| ~ sQ1_spl
| aElementOf0(sK3_skl(sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU))),xU,xU),xU)
| aUpperBoundOfIn0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU))),xU,xU) ),
inference(resolution,[status(thm)],[f735,f282]) ).
fof(f766,plain,
( ~ sQ15_spl
| ~ sQ76_spl
| ~ sQ68_spl
| ~ sQ1_spl
| aElementOf0(sK2_skl(sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU))),xU,xU),xU)
| aLowerBoundOfIn0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU))),xU,xU) ),
inference(resolution,[status(thm)],[f735,f229]) ).
fof(f768,plain,
( ~ sQ76_spl
| ~ sQ68_spl
| ~ sQ1_spl
| aElement0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU))))
| ~ aSet0(xU) ),
inference(resolution,[status(thm)],[f735,f35]) ).
fof(f769,definition,
( sQ97_spl
<=> aUpperBoundOfIn0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU))),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f770,plain,
( ~ sQ97_spl
| aUpperBoundOfIn0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU))),xU,xU) ),
inference(component_clause,[status(thm)],[f769]) ).
fof(f772,definition,
( sQ98_spl
<=> aElementOf0(sK3_skl(sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU))),xU,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f775,plain,
( ~ sQ25_spl
| ~ sQ76_spl
| ~ sQ68_spl
| ~ sQ1_spl
| sQ98_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f765,f769,f772,f143,f514,f602,f281]) ).
fof(f776,definition,
( sQ99_spl
<=> aLowerBoundOfIn0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU))),xU,xU) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f777,plain,
( ~ sQ99_spl
| aLowerBoundOfIn0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU))),xU,xU) ),
inference(component_clause,[status(thm)],[f776]) ).
fof(f779,definition,
( sQ100_spl
<=> aElementOf0(sK2_skl(sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU))),xU,xU),xU) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f782,plain,
( ~ sQ15_spl
| ~ sQ76_spl
| ~ sQ68_spl
| ~ sQ1_spl
| sQ100_spl
| sQ99_spl ),
inference(split_clause,[status(thm)],[f766,f776,f779,f143,f514,f602,f228]) ).
fof(f784,definition,
( sQ101_spl
<=> aElement0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU)))) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f785,plain,
( ~ sQ101_spl
| aElement0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU)))) ),
inference(component_clause,[status(thm)],[f784]) ).
fof(f787,plain,
( ~ sQ76_spl
| ~ sQ68_spl
| ~ sQ1_spl
| sQ101_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f768,f158,f784,f143,f514,f602]) ).
fof(f788,plain,
( ~ sQ44_spl
| ~ sQ67_spl
| ~ sQ68_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(szDzozmdt0(xf))) ),
inference(forward_demodulation,[status(thm)],[f591,f385]) ).
fof(f789,plain,
( ~ sQ44_spl
| ~ sQ67_spl
| ~ sQ68_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(forward_demodulation,[status(thm)],[f591,f788]) ).
fof(f790,plain,
( ~ sQ45_spl
| ~ sQ68_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(szRzazndt0(xf))) ),
inference(forward_demodulation,[status(thm)],[f515,f393]) ).
fof(f791,plain,
( ~ sQ45_spl
| ~ sQ68_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(forward_demodulation,[status(thm)],[f515,f790]) ).
fof(f792,plain,
( ~ sQ59_spl
| ~ sQ48_spl
| ~ sQ70_spl
| sdtlseqdt0(sK0_skl(xU),sK6_skl(xU,xU)) ),
inference(forward_demodulation,[status(thm)],[f618,f481]) ).
fof(f793,plain,
( ~ sQ59_spl
| ~ sQ48_spl
| ~ sQ70_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(forward_demodulation,[status(thm)],[f618,f792]) ).
fof(f794,plain,
( ~ sQ76_spl
| ~ sQ68_spl
| ~ sQ1_spl
| ~ sQ77_spl
| sdtlpdtrp0(xf,sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU)))) != sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU)))
| aFixedPointOf0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU))),xf) ),
inference(resolution,[status(thm)],[f609,f735]) ).
fof(f795,plain,
( ~ sQ1_spl
| ~ sQ76_spl
| ~ sQ68_spl
| ~ sQ77_spl
| sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU))) != sdtlpdtrp0(xf,sK0_skl(xU))
| aFixedPointOf0(sdtlpdtrp0(xf,sK0_skl(xU)),xf) ),
inference(resolution,[status(thm)],[f609,f733]) ).
fof(f796,plain,
( ~ sQ1_spl
| ~ sQ77_spl
| sdtlpdtrp0(xf,sK0_skl(xU)) != sK0_skl(xU)
| aFixedPointOf0(sK0_skl(xU),xf) ),
inference(resolution,[status(thm)],[f609,f144]) ).
fof(f797,definition,
( sQ102_spl
<=> aFixedPointOf0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU))),xf) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f798,plain,
( ~ sQ102_spl
| aFixedPointOf0(sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU))),xf) ),
inference(component_clause,[status(thm)],[f797]) ).
fof(f800,definition,
( sQ103_spl
<=> sdtlpdtrp0(xf,sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU)))) = sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU))) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f803,plain,
( ~ sQ76_spl
| ~ sQ68_spl
| ~ sQ1_spl
| ~ sQ77_spl
| ~ sQ103_spl
| sQ102_spl ),
inference(split_clause,[status(thm)],[f794,f797,f800,f608,f143,f514,f602]) ).
fof(f804,definition,
( sQ104_spl
<=> aFixedPointOf0(sdtlpdtrp0(xf,sK0_skl(xU)),xf) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f805,plain,
( ~ sQ104_spl
| aFixedPointOf0(sdtlpdtrp0(xf,sK0_skl(xU)),xf) ),
inference(component_clause,[status(thm)],[f804]) ).
fof(f807,definition,
( sQ105_spl
<=> sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU))) = sdtlpdtrp0(xf,sK0_skl(xU)) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f808,plain,
( ~ sQ105_spl
| sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU))) = sdtlpdtrp0(xf,sK0_skl(xU)) ),
inference(component_clause,[status(thm)],[f807]) ).
fof(f810,plain,
( ~ sQ1_spl
| ~ sQ76_spl
| ~ sQ68_spl
| ~ sQ77_spl
| ~ sQ105_spl
| sQ104_spl ),
inference(split_clause,[status(thm)],[f795,f804,f807,f608,f514,f602,f143]) ).
fof(f811,definition,
( sQ106_spl
<=> aFixedPointOf0(sK0_skl(xU),xf) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f812,plain,
( ~ sQ106_spl
| aFixedPointOf0(sK0_skl(xU),xf) ),
inference(component_clause,[status(thm)],[f811]) ).
fof(f814,definition,
( sQ107_spl
<=> sdtlpdtrp0(xf,sK0_skl(xU)) = sK0_skl(xU) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f815,plain,
( ~ sQ107_spl
| sdtlpdtrp0(xf,sK0_skl(xU)) = sK0_skl(xU) ),
inference(component_clause,[status(thm)],[f814]) ).
fof(f817,plain,
( ~ sQ1_spl
| ~ sQ77_spl
| ~ sQ107_spl
| sQ106_spl ),
inference(split_clause,[status(thm)],[f796,f811,f814,f608,f143]) ).
fof(f818,plain,
( ~ sQ34_spl
| ~ sQ68_spl
| ~ sQ83_spl
| ~ sQ67_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)],[f662,f568]) ).
fof(f819,plain,
( ~ sQ7_spl
| ~ sQ83_spl
| ~ sQ67_spl
| ~ sQ68_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)],[f662,f182]) ).
fof(f820,definition,
( sQ108_spl
<=> sdtlseqdt0(sdtlpdtrp0(xf,sK1_skl(xU,xU)),sdtlpdtrp0(xf,sK1_skl(xU,xU))) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f823,plain,
( ~ sQ34_spl
| ~ sQ68_spl
| ~ sQ83_spl
| ~ sQ67_spl
| sQ108_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f818,f152,f820,f507,f656,f514,f327]) ).
fof(f824,definition,
( sQ109_spl
<=> sdtlseqdt0(sdtlpdtrp0(xf,sK0_skl(xU)),sdtlpdtrp0(xf,sK0_skl(xU))) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f825,plain,
( ~ sQ109_spl
| sdtlseqdt0(sdtlpdtrp0(xf,sK0_skl(xU)),sdtlpdtrp0(xf,sK0_skl(xU))) ),
inference(component_clause,[status(thm)],[f824]) ).
fof(f827,plain,
( ~ sQ7_spl
| ~ sQ83_spl
| ~ sQ67_spl
| ~ sQ68_spl
| sQ109_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f819,f143,f824,f514,f507,f656,f178]) ).
fof(f828,plain,
( ~ sQ106_spl
| aElementOf0(sK0_skl(xU),szDzozmdt0(xf))
| ~ aFunction0(xf) ),
inference(resolution,[status(thm)],[f812,f121]) ).
fof(f829,plain,
( ~ sQ106_spl
| sdtlpdtrp0(xf,sK0_skl(xU)) = sK0_skl(xU)
| ~ aFunction0(xf) ),
inference(resolution,[status(thm)],[f812,f122]) ).
fof(f830,definition,
( sQ110_spl
<=> aElementOf0(sK0_skl(xU),szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f831,plain,
( ~ sQ110_spl
| aElementOf0(sK0_skl(xU),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f830]) ).
fof(f833,plain,
( ~ sQ106_spl
| sQ110_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f828,f504,f830,f811]) ).
fof(f834,plain,
( ~ sQ106_spl
| sQ107_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f829,f504,f814,f811]) ).
fof(f835,plain,
( ~ sQ110_spl
| ~ sQ67_spl
| ~ sQ68_spl
| aElementOf0(sK0_skl(xU),xU) ),
inference(forward_demodulation,[status(thm)],[f591,f831]) ).
fof(f836,plain,
( ~ sQ104_spl
| aElementOf0(sdtlpdtrp0(xf,sK0_skl(xU)),szDzozmdt0(xf))
| ~ aFunction0(xf) ),
inference(resolution,[status(thm)],[f805,f121]) ).
fof(f837,plain,
( ~ sQ104_spl
| sdtlpdtrp0(xf,sdtlpdtrp0(xf,sK0_skl(xU))) = sdtlpdtrp0(xf,sK0_skl(xU))
| ~ aFunction0(xf) ),
inference(resolution,[status(thm)],[f805,f122]) ).
fof(f838,definition,
( sQ111_spl
<=> aElementOf0(sdtlpdtrp0(xf,sK0_skl(xU)),szDzozmdt0(xf)) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f839,plain,
( ~ sQ111_spl
| aElementOf0(sdtlpdtrp0(xf,sK0_skl(xU)),szDzozmdt0(xf)) ),
inference(component_clause,[status(thm)],[f838]) ).
fof(f841,plain,
( ~ sQ104_spl
| sQ111_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f836,f504,f838,f804]) ).
fof(f842,plain,
( ~ sQ104_spl
| sQ105_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f837,f504,f807,f804]) ).
fof(f843,plain,
( ~ sQ111_spl
| ~ sQ67_spl
| ~ sQ68_spl
| aElementOf0(sdtlpdtrp0(xf,sK0_skl(xU)),xU) ),
inference(forward_demodulation,[status(thm)],[f591,f839]) ).
fof(f844,plain,
( ~ sQ104_spl
| ~ sQ107_spl
| aFixedPointOf0(sK0_skl(xU),xf) ),
inference(backward_demodulation,[status(thm)],[f815,f805]) ).
fof(f846,plain,
( ~ sQ96_spl
| ~ sQ107_spl
| aElement0(sK0_skl(xU)) ),
inference(backward_demodulation,[status(thm)],[f815,f758]) ).
fof(f849,plain,
( ~ sQ65_spl
| ~ sQ73_spl
| ~ sQ52_spl
| sdtlseqdt0(sK0_skl(xU),sK7_skl(xU,xU)) ),
inference(forward_demodulation,[status(thm)],[f674,f502]) ).
fof(f850,plain,
( ~ sQ65_spl
| ~ sQ73_spl
| ~ sQ52_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(forward_demodulation,[status(thm)],[f674,f849]) ).
fof(f851,plain,
( ~ sQ92_spl
| ~ sQ107_spl
| aUpperBoundOfIn0(sK0_skl(xU),xU,xU) ),
inference(forward_demodulation,[status(thm)],[f815,f743]) ).
fof(f852,plain,
( sQ87_spl
| ~ sQ34_spl
| ~ sQ68_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f691,f568]) ).
fof(f853,plain,
( sQ87_spl
| ~ sQ34_spl
| ~ sQ68_spl ),
inference(contradiction_clause,[status(thm)],[f852]) ).
fof(f854,plain,
( ~ sQ94_spl
| ~ sQ107_spl
| aLowerBoundOfIn0(sK0_skl(xU),xU,xU) ),
inference(forward_demodulation,[status(thm)],[f815,f750]) ).
fof(f855,plain,
( ~ sQ75_spl
| ~ sQ1_spl
| ~ sQ76_spl
| ~ sQ68_spl
| ~ sQ107_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(forward_demodulation,[status(thm)],[f815,f736]) ).
fof(f856,plain,
( ~ sQ96_spl
| ~ sQ107_spl
| sdtlseqdt0(sK0_skl(xU),sdtlpdtrp0(xf,sK0_skl(xU))) ),
inference(forward_demodulation,[status(thm)],[f815,f761]) ).
fof(f857,plain,
( ~ sQ96_spl
| ~ sQ107_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(forward_demodulation,[status(thm)],[f815,f856]) ).
fof(f861,plain,
( ~ sQ72_spl
| ~ sQ1_spl
| ~ sQ76_spl
| ~ sQ68_spl
| ~ sQ107_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(forward_demodulation,[status(thm)],[f815,f737]) ).
fof(f862,plain,
( ~ sQ101_spl
| ~ sQ107_spl
| aElement0(sdtlpdtrp0(xf,sK0_skl(xU))) ),
inference(forward_demodulation,[status(thm)],[f815,f785]) ).
fof(f863,plain,
( ~ sQ101_spl
| ~ sQ107_spl
| aElement0(sK0_skl(xU)) ),
inference(forward_demodulation,[status(thm)],[f815,f862]) ).
fof(f864,plain,
( ~ sQ102_spl
| ~ sQ107_spl
| aFixedPointOf0(sdtlpdtrp0(xf,sK0_skl(xU)),xf) ),
inference(forward_demodulation,[status(thm)],[f815,f798]) ).
fof(f865,plain,
( ~ sQ102_spl
| ~ sQ107_spl
| aFixedPointOf0(sK0_skl(xU),xf) ),
inference(forward_demodulation,[status(thm)],[f815,f864]) ).
fof(f866,plain,
( ~ sQ97_spl
| ~ sQ107_spl
| aUpperBoundOfIn0(sdtlpdtrp0(xf,sK0_skl(xU)),xU,xU) ),
inference(forward_demodulation,[status(thm)],[f815,f770]) ).
fof(f867,plain,
( ~ sQ97_spl
| ~ sQ107_spl
| aUpperBoundOfIn0(sK0_skl(xU),xU,xU) ),
inference(forward_demodulation,[status(thm)],[f815,f866]) ).
fof(f868,plain,
( ~ sQ99_spl
| ~ sQ107_spl
| aLowerBoundOfIn0(sdtlpdtrp0(xf,sK0_skl(xU)),xU,xU) ),
inference(forward_demodulation,[status(thm)],[f815,f777]) ).
fof(f869,plain,
( ~ sQ99_spl
| ~ sQ107_spl
| aLowerBoundOfIn0(sK0_skl(xU),xU,xU) ),
inference(forward_demodulation,[status(thm)],[f815,f868]) ).
fof(f870,plain,
( ~ sQ109_spl
| ~ sQ107_spl
| sdtlseqdt0(sK0_skl(xU),sdtlpdtrp0(xf,sK0_skl(xU))) ),
inference(forward_demodulation,[status(thm)],[f815,f825]) ).
fof(f871,plain,
( ~ sQ109_spl
| ~ sQ107_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(forward_demodulation,[status(thm)],[f815,f870]) ).
fof(f872,plain,
( ~ sQ75_spl
| ~ sQ76_spl
| ~ sQ68_spl
| ~ sQ1_spl
| ~ sQ107_spl
| sdtlseqdt0(sdtlpdtrp0(xf,sK0_skl(xU)),sK0_skl(xU)) ),
inference(forward_demodulation,[status(thm)],[f815,f763]) ).
fof(f873,plain,
( ~ sQ75_spl
| ~ sQ76_spl
| ~ sQ68_spl
| ~ sQ1_spl
| ~ sQ107_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(forward_demodulation,[status(thm)],[f815,f872]) ).
fof(f874,plain,
( ~ sQ72_spl
| ~ sQ76_spl
| ~ sQ68_spl
| ~ sQ1_spl
| ~ sQ107_spl
| sdtlseqdt0(sK0_skl(xU),sdtlpdtrp0(xf,sK0_skl(xU))) ),
inference(forward_demodulation,[status(thm)],[f815,f764]) ).
fof(f875,plain,
( ~ sQ72_spl
| ~ sQ76_spl
| ~ sQ68_spl
| ~ sQ1_spl
| ~ sQ107_spl
| sdtlseqdt0(sK0_skl(xU),sK0_skl(xU)) ),
inference(forward_demodulation,[status(thm)],[f815,f874]) ).
fof(model,axiom,
( ~ sQ0_spl
| sQ1_spl
| sQ2_spl
| ~ sQ3_spl
| sQ4_spl
| sQ5_spl
| sQ6_spl
| sQ7_spl
| sQ8_spl
| sQ9_spl
| sQ10_spl
| sQ11_spl
| ~ sQ13_spl
| sQ14_spl
| sQ15_spl
| sQ16_spl
| sQ17_spl
| sQ18_spl
| sQ19_spl
| sQ20_spl
| sQ22_spl
| sQ23_spl
| sQ24_spl
| sQ25_spl
| sQ26_spl
| ~ sQ27_spl
| ~ sQ28_spl
| sQ29_spl
| sQ30_spl
| sQ31_spl
| sQ32_spl
| sQ33_spl
| sQ34_spl
| sQ35_spl
| sQ36_spl
| sQ37_spl
| sQ38_spl
| sQ40_spl
| sQ42_spl
| sQ44_spl
| sQ45_spl
| sQ46_spl
| sQ47_spl
| sQ48_spl
| sQ49_spl
| sQ50_spl
| sQ51_spl
| sQ52_spl
| sQ53_spl
| sQ54_spl
| sQ55_spl
| sQ56_spl
| sQ59_spl
| sQ60_spl
| sQ63_spl
| sQ65_spl
| sQ66_spl
| sQ67_spl
| sQ68_spl
| sQ69_spl
| sQ70_spl
| sQ72_spl
| sQ73_spl
| sQ75_spl
| sQ76_spl
| sQ77_spl
| sQ78_spl
| sQ79_spl
| sQ80_spl
| sQ81_spl
| sQ82_spl
| sQ83_spl
| sQ86_spl
| sQ87_spl
| sQ88_spl
| sQ90_spl
| sQ92_spl
| sQ94_spl
| sQ96_spl
| sQ97_spl
| sQ99_spl
| sQ101_spl
| sQ102_spl
| sQ104_spl
| sQ105_spl
| sQ106_spl
| sQ107_spl
| sQ109_spl
| sQ110_spl
| sQ111_spl ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT383+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 23:57:18 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.46 % SZS status CounterSatisfiable for theBenchmark: Theorem is counter-satisfiable, conjecture is false
% 0.14/0.46 % SZS output start Saturation for theBenchmark
% See solution above
% 0.14/0.50 % Elapsed time: 0.113028 seconds
% 0.14/0.50 % CPU time: 0.542358 seconds
% 0.14/0.50 % Total memory used: 110.619 MB
% 0.14/0.50 % Net memory used: 110.047 MB
%------------------------------------------------------------------------------