%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM534+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 01:40:53 PM UTC 2026
% Result : Theorem 5.56s 1.15s
% Output : CNFRefutation 5.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 274
% Syntax : Number of formulae : 1068 ( 22 unt; 264 def)
% Number of atoms : 5558 ( 868 equ)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 7762 (3272 ~;4072 |; 120 &)
% ( 280 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 268 ( 266 usr; 260 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 1551 (1542 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,definition,
! [W0] :
( W0 = slcrc0
<=> ( ~ ? [W1] : aElementOf0(W1,W0)
& aSet0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
isFinite0(slcrc0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> ~ isFinite0(W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W0] :
( ( isFinite0(W0)
& aSet0(W0) )
=> ! [W1] :
( aSubsetOf0(W1,W0)
=> isFinite0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [W0] :
( aSet0(W0)
=> aSubsetOf0(W0,W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [W0,W1] :
( ( aSet0(W1)
& aSet0(W0) )
=> ( ( aSubsetOf0(W1,W0)
& aSubsetOf0(W0,W1) )
=> W0 = W1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [W0,W1,W2] :
( ( aSet0(W2)
& aSet0(W1)
& aSet0(W0) )
=> ( ( aSubsetOf0(W1,W2)
& aSubsetOf0(W0,W1) )
=> aSubsetOf0(W0,W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,definition,
! [W0,W1] :
( ( aElement0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtpldt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) ) )
& aSet0(W2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,definition,
! [W0,W1] :
( ( aElement0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtmndt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) ) )
& aSet0(W2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
aSet0(xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
aElementOf0(xx,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
( ( ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> sdtpldt0(sdtmndt0(xS,xx),xx) = xS ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ( ( ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> sdtpldt0(sdtmndt0(xS,xx),xx) = xS ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f27,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f28,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f31,plain,
! [W0] :
( W0 = slcrc0
<=> ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f32,plain,
! [W0] :
( ( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(NNF_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
( ! [W0] :
( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ! [W0] :
( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f34,plain,
( ! [W0] :
( aElementOf0(sK0_skl(W0),W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ! [W0] :
( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(W1,sK0_skl(W0))],[f33]) ).
fof(f35,plain,
! [X0] :
( aSet0(X0)
| X0 != slcrc0 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| X0 != slcrc0 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f37,plain,
! [X0] :
( aElementOf0(sK0_skl(X0),X0)
| ~ aSet0(X0)
| X0 = slcrc0 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f38,plain,
isFinite0(slcrc0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
! [W0] :
( ~ isFinite0(W0)
| ~ isCountable0(W0)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f42,plain,
! [X0] :
( ~ isFinite0(X0)
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f45,plain,
! [W0] :
( ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) ) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f46,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f48,plain,
! [W0] :
( ( ! [W1] :
( ( ~ aElementOf0(sK1_skl(W1,W0),W0)
& aElementOf0(sK1_skl(W1,W0),W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f51,plain,
! [X0,X1] :
( aElementOf0(sK1_skl(X1,X0),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f52,plain,
! [X0,X1] :
( ~ aElementOf0(sK1_skl(X1,X0),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f53,plain,
! [W0] :
( ! [W1] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) )
| ~ isFinite0(W0)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f54,plain,
! [X0,X1] :
( isFinite0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f55,plain,
! [W0] :
( aSubsetOf0(W0,W0)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f56,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
! [W0,W1] :
( W0 = W1
| ~ aSubsetOf0(W1,W0)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f58,plain,
! [X0,X1] :
( X0 = X1
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f59,plain,
! [W0,W1,W2] :
( aSubsetOf0(W0,W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W2)
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f60,plain,
! [X0,X1,X2] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtpldt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) ) )
& aSet0(W2) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f62,plain,
! [W0,W1] :
( ! [W2] :
( ( ? [W3] :
( ( ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) )
| aElementOf0(W3,W2) )
& ( ( W3 != W1
& ~ aElementOf0(W3,W0) )
| ~ aElement0(W3)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtpldt0(W0,W1) )
& ( ( ! [W3] :
( ( ( W3 != W1
& ~ aElementOf0(W3,W0) )
| ~ aElement0(W3)
| aElementOf0(W3,W2) )
& ( ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtpldt0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
! [W0,W1] :
( ( ! [W2] :
( ? [W3] :
( ( ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) )
| aElementOf0(W3,W2) )
& ( ( W3 != W1
& ~ aElementOf0(W3,W0) )
| ~ aElement0(W3)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtpldt0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ( W3 != W1
& ~ aElementOf0(W3,W0) )
| ~ aElement0(W3)
| aElementOf0(W3,W2) )
& ! [W3] :
( ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtpldt0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f62]) ).
fof(f64,plain,
! [W0,W1] :
( ( ! [W2] :
( ( ( ( ( sK2_skl(W2,W1,W0) = W1
| aElementOf0(sK2_skl(W2,W1,W0),W0) )
& aElement0(sK2_skl(W2,W1,W0)) )
| aElementOf0(sK2_skl(W2,W1,W0),W2) )
& ( ( sK2_skl(W2,W1,W0) != W1
& ~ aElementOf0(sK2_skl(W2,W1,W0),W0) )
| ~ aElement0(sK2_skl(W2,W1,W0))
| ~ aElementOf0(sK2_skl(W2,W1,W0),W2) ) )
| ~ aSet0(W2)
| W2 = sdtpldt0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ( W3 != W1
& ~ aElementOf0(W3,W0) )
| ~ aElement0(W3)
| aElementOf0(W3,W2) )
& ! [W3] :
( ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtpldt0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(W3,sK2_skl(W2,W1,W0))],[f63]) ).
fof(f65,plain,
! [X0,X1,X2] :
( aSet0(X2)
| X2 != sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [X0,X1,X2,X3] :
( aElement0(X3)
| ~ aElementOf0(X3,X2)
| X2 != sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f67,plain,
! [X0,X1,X2,X3] :
( X3 = X1
| aElementOf0(X3,X0)
| ~ aElementOf0(X3,X2)
| X2 != sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| aElementOf0(X3,X2)
| X2 != sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( X3 != X1
| ~ aElement0(X3)
| aElementOf0(X3,X2)
| X2 != sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ aElementOf0(sK2_skl(X2,X1,X0),X0)
| ~ aElement0(sK2_skl(X2,X1,X0))
| ~ aElementOf0(sK2_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f71,plain,
! [X0,X1,X2] :
( sK2_skl(X2,X1,X0) != X1
| ~ aElement0(sK2_skl(X2,X1,X0))
| ~ aElementOf0(sK2_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f73,plain,
! [X0,X1,X2] :
( sK2_skl(X2,X1,X0) = X1
| aElementOf0(sK2_skl(X2,X1,X0),X0)
| aElementOf0(sK2_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f74,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtmndt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) ) )
& aSet0(W2) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f75,definition,
! [W0,W1,W3] :
( sP0_prd(W3,W1,W0)
<=> ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f76,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtmndt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> sP0_prd(W3,W1,W0) )
& aSet0(W2) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(formula_renaming,[status(thm)],[f74,f75]) ).
fof(f77,plain,
! [W0,W1] :
( ! [W2] :
( ( ? [W3] :
( ( sP0_prd(W3,W1,W0)
| aElementOf0(W3,W2) )
& ( ~ sP0_prd(W3,W1,W0)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtmndt0(W0,W1) )
& ( ( ! [W3] :
( ( ~ sP0_prd(W3,W1,W0)
| aElementOf0(W3,W2) )
& ( sP0_prd(W3,W1,W0)
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtmndt0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f76]) ).
fof(f78,plain,
! [W0,W1] :
( ( ! [W2] :
( ? [W3] :
( ( sP0_prd(W3,W1,W0)
| aElementOf0(W3,W2) )
& ( ~ sP0_prd(W3,W1,W0)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtmndt0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ~ sP0_prd(W3,W1,W0)
| aElementOf0(W3,W2) )
& ! [W3] :
( sP0_prd(W3,W1,W0)
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtmndt0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f77]) ).
fof(f79,plain,
! [W0,W1] :
( ( ! [W2] :
( ( ( sP0_prd(sK3_skl(W2,W1,W0),W1,W0)
| aElementOf0(sK3_skl(W2,W1,W0),W2) )
& ( ~ sP0_prd(sK3_skl(W2,W1,W0),W1,W0)
| ~ aElementOf0(sK3_skl(W2,W1,W0),W2) ) )
| ~ aSet0(W2)
| W2 = sdtmndt0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ~ sP0_prd(W3,W1,W0)
| aElementOf0(W3,W2) )
& ! [W3] :
( sP0_prd(W3,W1,W0)
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtmndt0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(W3,sK3_skl(W2,W1,W0))],[f78]) ).
fof(f80,plain,
! [X0,X1,X2] :
( aSet0(X2)
| X2 != sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f81,plain,
! [X0,X1,X2,X3] :
( sP0_prd(X3,X1,X0)
| ~ aElementOf0(X3,X2)
| X2 != sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f82,plain,
! [X0,X1,X2,X3] :
( ~ sP0_prd(X3,X1,X0)
| aElementOf0(X3,X2)
| X2 != sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ~ sP0_prd(sK3_skl(X2,X1,X0),X1,X0)
| ~ aElementOf0(sK3_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f84,plain,
! [X0,X1,X2] :
( sP0_prd(sK3_skl(X2,X1,X0),X1,X0)
| aElementOf0(sK3_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f85,plain,
aSet0(xS),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f86,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f87,plain,
( sdtpldt0(sdtmndt0(xS,xx),xx) != xS
& ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xS,xx)) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f88,plain,
( sdtpldt0(sdtmndt0(xS,xx),xx) != xS
& ! [W0] :
( ( ( W0 != xx
& ~ aElementOf0(W0,sdtmndt0(xS,xx)) )
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( ( W0 = xx
| ~ aElementOf0(W0,xS)
| ~ aElement0(W0)
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& ( ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) )
| ~ aElementOf0(W0,sdtmndt0(xS,xx)) ) )
& aSet0(sdtmndt0(xS,xx)) ),
inference(NNF_transformation,[status(thm)],[f87]) ).
fof(f89,plain,
( sdtpldt0(sdtmndt0(xS,xx),xx) != xS
& ! [W0] :
( ( W0 != xx
& ~ aElementOf0(W0,sdtmndt0(xS,xx)) )
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ! [W0] :
( ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( W0 = xx
| ~ aElementOf0(W0,xS)
| ~ aElement0(W0)
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& ! [W0] :
( ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) )
| ~ aElementOf0(W0,sdtmndt0(xS,xx)) )
& aSet0(sdtmndt0(xS,xx)) ),
inference(miniscoping,[status(thm)],[f88]) ).
fof(f90,plain,
aSet0(sdtmndt0(xS,xx)),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f91,plain,
! [X0] :
( aElement0(X0)
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f92,plain,
! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f93,plain,
! [X0] :
( X0 != xx
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f94,plain,
! [X0] :
( X0 = xx
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f95,plain,
aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f96,plain,
! [X0] :
( aElement0(X0)
| ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f97,plain,
! [X0] :
( X0 = xx
| aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f98,plain,
! [X0] :
( ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f99,plain,
! [X0] :
( X0 != xx
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f100,plain,
sdtpldt0(sdtmndt0(xS,xx),xx) != xS,
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f101,plain,
! [W0,W1,W3] :
( ( W3 = W1
| ~ aElementOf0(W3,W0)
| ~ aElement0(W3)
| sP0_prd(W3,W1,W0) )
& ( ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) )
| ~ sP0_prd(W3,W1,W0) ) ),
inference(NNF_transformation,[status(thm)],[f75]) ).
fof(f102,plain,
( ! [W0,W1,W3] :
( W3 = W1
| ~ aElementOf0(W3,W0)
| ~ aElement0(W3)
| sP0_prd(W3,W1,W0) )
& ! [W0,W1,W3] :
( ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) )
| ~ sP0_prd(W3,W1,W0) ) ),
inference(miniscoping,[status(thm)],[f101]) ).
fof(f104,plain,
! [X0,X1,X2] :
( aElementOf0(X0,X2)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f105,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f106,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ aElementOf0(X0,X2)
| ~ aElement0(X0)
| sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f107,plain,
aSet0(slcrc0),
inference(destructive_equality_resolution,[status(thm)],[f35]) ).
fof(f108,plain,
! [X0] : ~ aElementOf0(X0,slcrc0),
inference(destructive_equality_resolution,[status(thm)],[f36]) ).
fof(f110,plain,
! [X0,X1] :
( aSet0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f65]) ).
fof(f111,plain,
! [X0,X1,X2] :
( aElement0(X2)
| ~ aElementOf0(X2,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f66]) ).
fof(f112,plain,
! [X0,X1,X2] :
( X2 = X1
| aElementOf0(X2,X0)
| ~ aElementOf0(X2,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f67]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X2,X0)
| ~ aElement0(X2)
| aElementOf0(X2,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f68]) ).
fof(f114,plain,
! [X0,X1] :
( ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f69]) ).
fof(f115,plain,
! [X0,X1] :
( aElementOf0(X1,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f114]) ).
fof(f116,plain,
! [X0,X1] :
( aSet0(sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f80]) ).
fof(f117,plain,
! [X0,X1,X2] :
( sP0_prd(X2,X1,X0)
| ~ aElementOf0(X2,sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f81]) ).
fof(f118,plain,
! [X0,X1,X2] :
( ~ sP0_prd(X2,X1,X0)
| aElementOf0(X2,sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f82]) ).
fof(f119,plain,
~ aElementOf0(xx,sdtmndt0(xS,xx)),
inference(destructive_equality_resolution,[status(thm)],[f93]) ).
fof(f120,plain,
( ~ aElement0(xx)
| aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(destructive_equality_resolution,[status(thm)],[f99]) ).
fof(f121,plain,
! [X0,X1] : ~ sP0_prd(X0,X0,X1),
inference(destructive_equality_resolution,[status(thm)],[f105]) ).
fof(f122,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f28,f86]) ).
fof(f123,definition,
( sQ0_spl
<=> aSet0(xS) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f125,plain,
( sQ0_spl
| ~ aSet0(xS) ),
inference(component_clause,[status(thm)],[f123]) ).
fof(f126,definition,
( sQ1_spl
<=> aElement0(xx) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f127,plain,
( ~ sQ1_spl
| aElement0(xx) ),
inference(component_clause,[status(thm)],[f126]) ).
fof(f129,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f122,f123,f126]) ).
fof(f130,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f125,f85]) ).
fof(f131,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f130]) ).
fof(f133,plain,
( ~ aSet0(slcrc0)
| slcrc0 = slcrc0 ),
inference(resolution,[status(thm)],[f37,f108]) ).
fof(f137,definition,
( sQ2_spl
<=> slcrc0 = slcrc0 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f140,definition,
( sQ3_spl
<=> aSet0(slcrc0) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( sQ3_spl
| ~ aSet0(slcrc0) ),
inference(component_clause,[status(thm)],[f140]) ).
fof(f143,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f133,f137,f140]) ).
fof(f148,definition,
( sQ5_spl
<=> aSet0(sdtmndt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( sQ5_spl
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(component_clause,[status(thm)],[f148]) ).
fof(f156,plain,
( ~ isCountable0(slcrc0)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f42,f38]) ).
fof(f157,definition,
( sQ7_spl
<=> isCountable0(slcrc0) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f160,plain,
( ~ sQ7_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f156,f140,f157]) ).
fof(f161,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f142,f107]) ).
fof(f162,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f161]) ).
fof(f169,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f150,f90]) ).
fof(f170,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f169]) ).
fof(f178,plain,
! [X0,X1] :
( ~ aSet0(sdtpldt0(X0,X1))
| sdtpldt0(X0,X1) = slcrc0
| sK0_skl(sdtpldt0(X0,X1)) = X1
| aElementOf0(sK0_skl(sdtpldt0(X0,X1)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f112,f37]) ).
fof(f179,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = slcrc0
| sK0_skl(sdtpldt0(X0,X1)) = X1
| aElementOf0(sK0_skl(sdtpldt0(X0,X1)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f178,f110]) ).
fof(f180,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X2,X0)
| aElementOf0(X2,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f113,f28]) ).
fof(f195,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElement0(X1)
| ~ aSet0(X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f115,f111]) ).
fof(f197,definition,
! [X0] :
( sQ11_spl
<=> ( ~ aSet0(X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f198,plain,
! [X0] :
( ~ sQ11_spl
| ~ aSet0(X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f197]) ).
fof(f200,definition,
! [X1] :
( sQ12_spl
<=> ( aElement0(X1)
| ~ aElement0(X1)
| ~ aElement0(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f203,plain,
( sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f195,f197,f200]) ).
fof(f204,plain,
! [X0] :
( ~ sQ11_spl
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f198]) ).
fof(f205,plain,
( ~ sQ11_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f107,f204]) ).
fof(f208,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f205]) ).
fof(f209,plain,
! [X0] :
( ~ aSet0(slcrc0)
| aSubsetOf0(slcrc0,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f51,f108]) ).
fof(f210,definition,
! [X0] :
( sQ13_spl
<=> ( aSubsetOf0(slcrc0,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f211,plain,
! [X0] :
( ~ sQ13_spl
| aSubsetOf0(slcrc0,X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f210]) ).
fof(f213,plain,
( ~ sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f209,f210,f140]) ).
fof(f221,definition,
( sQ15_spl
<=> aSet0(sdtpldt0(slcrc0,xx)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f223,plain,
( sQ15_spl
| ~ aSet0(sdtpldt0(slcrc0,xx)) ),
inference(component_clause,[status(thm)],[f221]) ).
fof(f225,plain,
! [X0] :
( ~ aSet0(X0)
| aSubsetOf0(X0,sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| sK1_skl(X0,sdtmndt0(xS,xx)) = xx
| ~ aElementOf0(sK1_skl(X0,sdtmndt0(xS,xx)),xS)
| ~ aElement0(sK1_skl(X0,sdtmndt0(xS,xx))) ),
inference(resolution,[status(thm)],[f94,f52]) ).
fof(f226,definition,
! [X0] :
( sQ16_spl
<=> ( ~ aSet0(X0)
| aSubsetOf0(X0,sdtmndt0(xS,xx))
| sK1_skl(X0,sdtmndt0(xS,xx)) = xx
| ~ aElementOf0(sK1_skl(X0,sdtmndt0(xS,xx)),xS)
| ~ aElement0(sK1_skl(X0,sdtmndt0(xS,xx))) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f227,plain,
! [X0] :
( ~ sQ16_spl
| ~ aSet0(X0)
| aSubsetOf0(X0,sdtmndt0(xS,xx))
| sK1_skl(X0,sdtmndt0(xS,xx)) = xx
| ~ aElementOf0(sK1_skl(X0,sdtmndt0(xS,xx)),xS)
| ~ aElement0(sK1_skl(X0,sdtmndt0(xS,xx))) ),
inference(component_clause,[status(thm)],[f226]) ).
fof(f229,plain,
( ~ sQ5_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f225,f226,f148]) ).
fof(f230,plain,
! [X0,X1] :
( ~ aSet0(X0)
| aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| aElement0(sK1_skl(X0,X1))
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f28,f51]) ).
fof(f232,plain,
! [X0] :
( X0 = xx
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f28,f94]) ).
fof(f233,plain,
! [X0,X1] :
( aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| aElement0(sK1_skl(X0,X1))
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f230]) ).
fof(f235,definition,
! [X0] :
( sQ17_spl
<=> ( X0 = xx
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f238,plain,
( sQ17_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f232,f148,f235]) ).
fof(f239,plain,
! [X0] :
( ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aSet0(X0)
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0) = xx
| aElementOf0(sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0),sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f97,f51]) ).
fof(f240,definition,
! [X0] :
( sQ18_spl
<=> ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aSet0(X0)
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0) = xx
| aElementOf0(sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0),sdtmndt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f241,plain,
! [X0] :
( ~ sQ18_spl
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aSet0(X0)
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0) = xx
| aElementOf0(sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0),sdtmndt0(xS,xx)) ),
inference(component_clause,[status(thm)],[f240]) ).
fof(f243,definition,
( sQ19_spl
<=> aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f245,plain,
( sQ19_spl
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(component_clause,[status(thm)],[f243]) ).
fof(f246,plain,
( ~ sQ19_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f239,f240,f243]) ).
fof(f247,plain,
! [X0] :
( ~ aSet0(X0)
| aSubsetOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(sK1_skl(X0,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx))
| ~ aElement0(sK1_skl(X0,sdtpldt0(sdtmndt0(xS,xx),xx))) ),
inference(resolution,[status(thm)],[f98,f52]) ).
fof(f249,plain,
! [X0] :
( aElement0(X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f98,f28]) ).
fof(f250,definition,
! [X0] :
( sQ20_spl
<=> ( ~ aSet0(X0)
| aSubsetOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(sK1_skl(X0,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx))
| ~ aElement0(sK1_skl(X0,sdtpldt0(sdtmndt0(xS,xx),xx))) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f251,plain,
! [X0] :
( ~ sQ20_spl
| ~ aSet0(X0)
| aSubsetOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(sK1_skl(X0,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx))
| ~ aElement0(sK1_skl(X0,sdtpldt0(sdtmndt0(xS,xx),xx))) ),
inference(component_clause,[status(thm)],[f250]) ).
fof(f253,plain,
( ~ sQ19_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f247,f250,f243]) ).
fof(f254,definition,
! [X0] :
( sQ21_spl
<=> ( aElement0(X0)
| ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f257,plain,
( ~ sQ19_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f249,f254,f243]) ).
fof(f266,plain,
! [X0,X1] :
( X1 = X0
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f58,f49]) ).
fof(f267,plain,
! [X0] :
( ~ sQ13_spl
| ~ aSet0(X0)
| slcrc0 = X0
| ~ aSubsetOf0(X0,slcrc0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f266,f211]) ).
fof(f269,plain,
! [X0] :
( ~ sQ13_spl
| slcrc0 = X0
| ~ aSubsetOf0(X0,slcrc0)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f267]) ).
fof(f270,plain,
! [X0,X1,X2] :
( aSubsetOf0(X2,X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X2,X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f60,f49]) ).
fof(f274,plain,
! [X0,X1,X2] :
( ~ aElementOf0(sK2_skl(X2,X1,X0),X0)
| ~ aElementOf0(sK2_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f70,f28]) ).
fof(f275,plain,
! [X0,X1] :
( ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),sdtmndt0(xS,xx))
| ~ aElement0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0))
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f274,f98]) ).
fof(f276,plain,
! [X0,X1] :
( sK2_skl(sdtmndt0(xS,xx),X1,X0) = xx
| ~ aElementOf0(sK2_skl(sdtmndt0(xS,xx),X1,X0),xS)
| ~ aElement0(sK2_skl(sdtmndt0(xS,xx),X1,X0))
| ~ aElementOf0(sK2_skl(sdtmndt0(xS,xx),X1,X0),X0)
| ~ aSet0(sdtmndt0(xS,xx))
| sdtmndt0(xS,xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f274,f94]) ).
fof(f277,definition,
! [X0,X1] :
( sQ22_spl
<=> ( ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),sdtmndt0(xS,xx))
| ~ aElement0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0))
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),X0)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f278,plain,
! [X0,X1] :
( ~ sQ22_spl
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),sdtmndt0(xS,xx))
| ~ aElement0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0))
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),X0)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f277]) ).
fof(f280,plain,
( ~ sQ19_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f275,f277,f243]) ).
fof(f281,definition,
! [X0,X1] :
( sQ23_spl
<=> ( sK2_skl(sdtmndt0(xS,xx),X1,X0) = xx
| ~ aElementOf0(sK2_skl(sdtmndt0(xS,xx),X1,X0),xS)
| ~ aElement0(sK2_skl(sdtmndt0(xS,xx),X1,X0))
| ~ aElementOf0(sK2_skl(sdtmndt0(xS,xx),X1,X0),X0)
| sdtmndt0(xS,xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f284,plain,
( ~ sQ5_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f276,f281,f148]) ).
fof(f286,plain,
! [X0,X1] :
( ~ sQ22_spl
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),sdtmndt0(xS,xx))
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),X0)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f278,f28]) ).
fof(f287,plain,
( xx = xx
| ~ aElementOf0(xx,xS)
| ~ aElement0(xx) ),
inference(resolution,[status(thm)],[f119,f94]) ).
fof(f288,definition,
( sQ24_spl
<=> aElementOf0(xx,xS) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f290,plain,
( sQ24_spl
| ~ aElementOf0(xx,xS) ),
inference(component_clause,[status(thm)],[f288]) ).
fof(f291,definition,
( sQ25_spl
<=> xx = xx ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f294,plain,
( sQ25_spl
| ~ sQ24_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f287,f126,f288,f291]) ).
fof(f295,plain,
( sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f290,f86]) ).
fof(f296,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f295]) ).
fof(f297,plain,
( ~ sQ1_spl
| aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(forward_subsumption_resolution,[status(thm)],[f120,f127]) ).
fof(f300,definition,
( sQ26_spl
<=> aElementOf0(xx,sdtmndt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f301,plain,
( ~ sQ26_spl
| aElementOf0(xx,sdtmndt0(xS,xx)) ),
inference(component_clause,[status(thm)],[f300]) ).
fof(f305,plain,
( ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f301,f119]) ).
fof(f306,plain,
~ sQ26_spl,
inference(contradiction_clause,[status(thm)],[f305]) ).
fof(f307,plain,
( sQ15_spl
| ~ aElement0(xx)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f110,f223]) ).
fof(f308,plain,
( sQ15_spl
| ~ sQ1_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f307,f140,f126,f221]) ).
fof(f312,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,X3),X3)
| ~ aSet0(sdtpldt0(X0,X1))
| sdtpldt0(X0,X1) = sdtpldt0(X3,X2)
| ~ aElement0(X2)
| ~ aSet0(X3)
| ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,X3),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f180,f274]) ).
fof(f313,plain,
! [X0,X1,X2] :
( ~ aSet0(X2)
| aSubsetOf0(X2,sdtpldt0(X0,X1))
| ~ aSet0(sdtpldt0(X0,X1))
| ~ aElementOf0(sK1_skl(X2,sdtpldt0(X0,X1)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f180,f52]) ).
fof(f314,plain,
! [X0] :
( X0 = xx
| aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f180,f97]) ).
fof(f316,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,X3),X3)
| sdtpldt0(X0,X1) = sdtpldt0(X3,X2)
| ~ aElement0(X2)
| ~ aSet0(X3)
| ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,X3),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f312,f110]) ).
fof(f317,plain,
! [X0,X1,X2] :
( ~ aSet0(X2)
| aSubsetOf0(X2,sdtpldt0(X0,X1))
| ~ aElementOf0(sK1_skl(X2,sdtpldt0(X0,X1)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f313,f110]) ).
fof(f318,definition,
! [X0] :
( sQ27_spl
<=> ( X0 = xx
| aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f321,plain,
( sQ27_spl
| ~ sQ1_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f314,f148,f126,f318]) ).
fof(f329,definition,
( sQ28_spl
<=> sdtpldt0(sdtmndt0(xS,xx),xx) = slcrc0 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f330,plain,
( ~ sQ28_spl
| sdtpldt0(sdtmndt0(xS,xx),xx) = slcrc0 ),
inference(component_clause,[status(thm)],[f329]) ).
fof(f343,plain,
! [X0] :
( ~ aElementOf0(X0,sdtmndt0(xS,xx))
| aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(backward_subsumption_resolution,[status(thm)],[f98,f91]) ).
fof(f345,plain,
! [X0] :
( ~ aSet0(sdtmndt0(xS,xx))
| aSubsetOf0(sdtmndt0(xS,xx),X0)
| ~ aSet0(X0)
| aElement0(sK1_skl(sdtmndt0(xS,xx),X0)) ),
inference(resolution,[status(thm)],[f91,f51]) ).
fof(f348,definition,
! [X0] :
( sQ31_spl
<=> ( aSubsetOf0(sdtmndt0(xS,xx),X0)
| ~ aSet0(X0)
| aElement0(sK1_skl(sdtmndt0(xS,xx),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f351,plain,
( ~ sQ5_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f345,f348,f148]) ).
fof(f352,plain,
! [X0,X1,X2] :
( sK2_skl(X2,X1,X0) != X1
| ~ aElementOf0(sK2_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f71,f28]) ).
fof(f355,plain,
! [X0,X1] :
( aElement0(sK2_skl(sdtmndt0(xS,xx),X1,X0))
| sK2_skl(sdtmndt0(xS,xx),X1,X0) = X1
| aElementOf0(sK2_skl(sdtmndt0(xS,xx),X1,X0),X0)
| ~ aSet0(sdtmndt0(xS,xx))
| sdtmndt0(xS,xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f73,f91]) ).
fof(f356,plain,
! [X0,X1] :
( sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0) = xx
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),sdtmndt0(xS,xx))
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0) = X1
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f73,f97]) ).
fof(f357,plain,
! [X0,X1] :
( sK2_skl(slcrc0,X1,X0) = X1
| aElementOf0(sK2_skl(slcrc0,X1,X0),X0)
| ~ aSet0(slcrc0)
| slcrc0 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f73,f108]) ).
fof(f359,definition,
! [X0,X1] :
( sQ32_spl
<=> ( aElement0(sK2_skl(sdtmndt0(xS,xx),X1,X0))
| sK2_skl(sdtmndt0(xS,xx),X1,X0) = X1
| aElementOf0(sK2_skl(sdtmndt0(xS,xx),X1,X0),X0)
| sdtmndt0(xS,xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f360,plain,
! [X0,X1] :
( ~ sQ32_spl
| aElement0(sK2_skl(sdtmndt0(xS,xx),X1,X0))
| sK2_skl(sdtmndt0(xS,xx),X1,X0) = X1
| aElementOf0(sK2_skl(sdtmndt0(xS,xx),X1,X0),X0)
| sdtmndt0(xS,xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f359]) ).
fof(f362,plain,
( ~ sQ5_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f355,f359,f148]) ).
fof(f363,definition,
! [X0,X1] :
( sQ33_spl
<=> ( sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0) = xx
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),sdtmndt0(xS,xx))
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0) = X1
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),X0)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f364,plain,
! [X0,X1] :
( ~ sQ33_spl
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0) = xx
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),sdtmndt0(xS,xx))
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0) = X1
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),X0)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f363]) ).
fof(f366,plain,
( ~ sQ19_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f356,f363,f243]) ).
fof(f367,definition,
! [X0,X1] :
( sQ34_spl
<=> ( sK2_skl(slcrc0,X1,X0) = X1
| aElementOf0(sK2_skl(slcrc0,X1,X0),X0)
| slcrc0 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f368,plain,
! [X0,X1] :
( ~ sQ34_spl
| sK2_skl(slcrc0,X1,X0) = X1
| aElementOf0(sK2_skl(slcrc0,X1,X0),X0)
| slcrc0 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f367]) ).
fof(f370,plain,
( ~ sQ3_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f357,f367,f140]) ).
fof(f372,plain,
! [X0,X1] :
( ~ sQ32_spl
| aElement0(sK2_skl(sdtmndt0(xS,xx),X1,X0))
| sK2_skl(sdtmndt0(xS,xx),X1,X0) = X1
| sdtmndt0(xS,xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f360,f28]) ).
fof(f373,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f245,f95]) ).
fof(f374,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f373]) ).
fof(f375,plain,
! [X0] :
( ~ sQ20_spl
| ~ aSet0(X0)
| aSubsetOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(sK1_skl(X0,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx)) ),
inference(forward_subsumption_resolution,[status(thm)],[f251,f91]) ).
fof(f376,plain,
! [X0,X1] :
( sK2_skl(sdtmndt0(xS,xx),X0,X1) = X0
| aElementOf0(sK2_skl(sdtmndt0(xS,xx),X0,X1),X1)
| ~ aSet0(sdtmndt0(xS,xx))
| sdtmndt0(xS,xx) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| aElementOf0(sK2_skl(sdtmndt0(xS,xx),X0,X1),xS) ),
inference(resolution,[status(thm)],[f92,f73]) ).
fof(f378,plain,
! [X0] :
( ~ aSet0(sdtmndt0(xS,xx))
| aSubsetOf0(sdtmndt0(xS,xx),X0)
| ~ aSet0(X0)
| aElementOf0(sK1_skl(sdtmndt0(xS,xx),X0),xS) ),
inference(resolution,[status(thm)],[f92,f51]) ).
fof(f380,definition,
! [X0,X1] :
( sQ35_spl
<=> ( sK2_skl(sdtmndt0(xS,xx),X0,X1) = X0
| aElementOf0(sK2_skl(sdtmndt0(xS,xx),X0,X1),X1)
| sdtmndt0(xS,xx) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| aElementOf0(sK2_skl(sdtmndt0(xS,xx),X0,X1),xS) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f383,plain,
( ~ sQ5_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f376,f380,f148]) ).
fof(f385,definition,
! [X0] :
( sQ36_spl
<=> ( aSubsetOf0(sdtmndt0(xS,xx),X0)
| ~ aSet0(X0)
| aElementOf0(sK1_skl(sdtmndt0(xS,xx),X0),xS) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f386,plain,
! [X0] :
( ~ sQ36_spl
| aSubsetOf0(sdtmndt0(xS,xx),X0)
| ~ aSet0(X0)
| aElementOf0(sK1_skl(sdtmndt0(xS,xx),X0),xS) ),
inference(component_clause,[status(thm)],[f385]) ).
fof(f388,plain,
( ~ sQ5_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f378,f385,f148]) ).
fof(f389,plain,
! [X0,X1] :
( sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,X1) = X0
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,X1),X1)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| aElement0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,X1)) ),
inference(resolution,[status(thm)],[f96,f73]) ).
fof(f390,plain,
( ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| sdtpldt0(sdtmndt0(xS,xx),xx) = slcrc0
| aElement0(sK0_skl(sdtpldt0(sdtmndt0(xS,xx),xx))) ),
inference(resolution,[status(thm)],[f96,f37]) ).
fof(f391,plain,
! [X0] :
( ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aSet0(X0)
| aElement0(sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0)) ),
inference(resolution,[status(thm)],[f96,f51]) ).
fof(f393,plain,
! [X0] :
( ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xS,xx))
| aElement0(X0) ),
inference(resolution,[status(thm)],[f96,f180]) ).
fof(f395,definition,
! [X0,X1] :
( sQ37_spl
<=> ( sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,X1) = X0
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,X1),X1)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| aElement0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f396,plain,
! [X0,X1] :
( ~ sQ37_spl
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,X1) = X0
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,X1),X1)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| aElement0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,X1)) ),
inference(component_clause,[status(thm)],[f395]) ).
fof(f398,plain,
( ~ sQ19_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f389,f395,f243]) ).
fof(f399,definition,
( sQ38_spl
<=> aElement0(sK0_skl(sdtpldt0(sdtmndt0(xS,xx),xx))) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f402,plain,
( ~ sQ19_spl
| sQ28_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f390,f399,f329,f243]) ).
fof(f403,definition,
! [X0] :
( sQ39_spl
<=> ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aSet0(X0)
| aElement0(sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f406,plain,
( ~ sQ19_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f391,f403,f243]) ).
fof(f407,definition,
! [X0] :
( sQ40_spl
<=> ( ~ aElementOf0(X0,sdtmndt0(xS,xx))
| aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f410,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f393,f407,f148,f126]) ).
fof(f412,plain,
! [X0,X1] :
( ~ sQ37_spl
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,X1) = X0
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| aElement0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f396,f28]) ).
fof(f416,plain,
( ~ sQ1_spl
| ~ sQ28_spl
| aElementOf0(xx,slcrc0) ),
inference(backward_demodulation,[status(thm)],[f330,f297]) ).
fof(f421,plain,
( ~ sQ1_spl
| ~ sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f416,f108]) ).
fof(f422,plain,
( ~ sQ1_spl
| ~ sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f421]) ).
fof(f423,plain,
! [X0,X1,X2,X3] :
( sK2_skl(sdtpldt0(X0,X1),X2,X3) = X2
| aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,X3),X3)
| ~ aSet0(sdtpldt0(X0,X1))
| sdtpldt0(X0,X1) = sdtpldt0(X3,X2)
| ~ aElement0(X2)
| ~ aSet0(X3)
| sK2_skl(sdtpldt0(X0,X1),X2,X3) = X1
| aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,X3),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f112,f73]) ).
fof(f425,plain,
! [X0,X1,X2] :
( ~ aSet0(sdtpldt0(X0,X1))
| aSubsetOf0(sdtpldt0(X0,X1),X2)
| ~ aSet0(X2)
| sK1_skl(sdtpldt0(X0,X1),X2) = X1
| aElementOf0(sK1_skl(sdtpldt0(X0,X1),X2),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f112,f51]) ).
fof(f428,plain,
! [X0,X1,X2,X3] :
( sK2_skl(sdtpldt0(X0,X1),X2,X3) = X2
| aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,X3),X3)
| sdtpldt0(X0,X1) = sdtpldt0(X3,X2)
| ~ aElement0(X2)
| ~ aSet0(X3)
| sK2_skl(sdtpldt0(X0,X1),X2,X3) = X1
| aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,X3),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f423,f110]) ).
fof(f430,plain,
! [X0,X1,X2] :
( aSubsetOf0(sdtpldt0(X0,X1),X2)
| ~ aSet0(X2)
| sK1_skl(sdtpldt0(X0,X1),X2) = X1
| aElementOf0(sK1_skl(sdtpldt0(X0,X1),X2),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f425,f110]) ).
fof(f439,plain,
! [X0] :
( ~ sQ13_spl
| ~ aSet0(X0)
| isFinite0(slcrc0)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f54,f211]) ).
fof(f441,definition,
! [X0] :
( sQ41_spl
<=> ( ~ aSet0(X0)
| ~ isFinite0(X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f442,plain,
! [X0] :
( ~ sQ41_spl
| ~ aSet0(X0)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,definition,
( sQ42_spl
<=> isFinite0(slcrc0) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f447,plain,
( ~ sQ13_spl
| sQ42_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f439,f441,f444,f210]) ).
fof(f448,plain,
! [X0] :
( ~ sQ41_spl
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f442]) ).
fof(f449,plain,
( ~ sQ41_spl
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f448,f38]) ).
fof(f450,plain,
( ~ sQ41_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f449,f140,f441]) ).
fof(f459,plain,
! [X0,X1,X2,X3] :
( sK2_skl(sdtmndt0(X0,X1),X2,X3) = X2
| aElementOf0(sK2_skl(sdtmndt0(X0,X1),X2,X3),X3)
| ~ aSet0(sdtmndt0(X0,X1))
| sdtmndt0(X0,X1) = sdtpldt0(X3,X2)
| ~ aElement0(X2)
| ~ aSet0(X3)
| sP0_prd(sK2_skl(sdtmndt0(X0,X1),X2,X3),X1,X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f117,f73]) ).
fof(f460,plain,
! [X0,X1] :
( ~ aSet0(sdtmndt0(X0,X1))
| sdtmndt0(X0,X1) = slcrc0
| sP0_prd(sK0_skl(sdtmndt0(X0,X1)),X1,X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f117,f37]) ).
fof(f461,plain,
! [X0,X1,X2] :
( ~ aSet0(sdtmndt0(X0,X1))
| aSubsetOf0(sdtmndt0(X0,X1),X2)
| ~ aSet0(X2)
| sP0_prd(sK1_skl(sdtmndt0(X0,X1),X2),X1,X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f117,f51]) ).
fof(f462,plain,
! [X0] :
( X0 = xx
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| sP0_prd(X0,xx,xS)
| ~ aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f117,f94]) ).
fof(f463,plain,
! [X0,X1,X2,X3] :
( sK2_skl(sdtmndt0(X0,X1),X2,X3) = X2
| aElementOf0(sK2_skl(sdtmndt0(X0,X1),X2,X3),X3)
| sdtmndt0(X0,X1) = sdtpldt0(X3,X2)
| ~ aElement0(X2)
| ~ aSet0(X3)
| sP0_prd(sK2_skl(sdtmndt0(X0,X1),X2,X3),X1,X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f459,f116]) ).
fof(f464,plain,
! [X0,X1] :
( sdtmndt0(X0,X1) = slcrc0
| sP0_prd(sK0_skl(sdtmndt0(X0,X1)),X1,X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f460,f116]) ).
fof(f465,plain,
! [X0,X1,X2] :
( aSubsetOf0(sdtmndt0(X0,X1),X2)
| ~ aSet0(X2)
| sP0_prd(sK1_skl(sdtmndt0(X0,X1),X2),X1,X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f461,f116]) ).
fof(f466,definition,
! [X0] :
( sQ43_spl
<=> ( X0 = xx
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| sP0_prd(X0,xx,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f469,plain,
( sQ43_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f462,f123,f126,f466]) ).
fof(f470,plain,
( ~ sP0_prd(xx,xx,xS)
| ~ aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f118,f119]) ).
fof(f473,plain,
! [X0] :
( aElementOf0(X0,xS)
| ~ sP0_prd(X0,xx,xS)
| ~ aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f118,f92]) ).
fof(f474,plain,
! [X0] :
( aElement0(X0)
| ~ sP0_prd(X0,xx,xS)
| ~ aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f118,f91]) ).
fof(f477,definition,
( sQ44_spl
<=> sP0_prd(xx,xx,xS) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f480,plain,
( ~ sQ44_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f470,f123,f126,f477]) ).
fof(f483,definition,
! [X0] :
( sQ45_spl
<=> ( aElementOf0(X0,xS)
| ~ sP0_prd(X0,xx,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f486,plain,
( sQ45_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f473,f123,f126,f483]) ).
fof(f487,definition,
! [X0] :
( sQ46_spl
<=> ( aElement0(X0)
| ~ sP0_prd(X0,xx,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f490,plain,
( sQ46_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f474,f123,f126,f487]) ).
fof(f491,plain,
! [X0,X1,X2] :
( sK3_skl(X2,X1,X0) = X1
| ~ aElementOf0(sK3_skl(X2,X1,X0),X0)
| ~ aElement0(sK3_skl(X2,X1,X0))
| ~ aElementOf0(sK3_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f83,f106]) ).
fof(f492,plain,
! [X0,X1,X2] :
( sK3_skl(X2,X1,X0) = X1
| ~ aElementOf0(sK3_skl(X2,X1,X0),X0)
| ~ aElementOf0(sK3_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f491,f28]) ).
fof(f510,plain,
! [X0,X1] :
( ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,X1),X1)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,X1),sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f343,f274]) ).
fof(f511,plain,
! [X0] :
( ~ aSet0(X0)
| aSubsetOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(sK1_skl(X0,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f343,f52]) ).
fof(f516,definition,
! [X0,X1] :
( sQ47_spl
<=> ( ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,X1),X1)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,X1),sdtmndt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f519,plain,
( ~ sQ19_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f510,f516,f243]) ).
fof(f520,definition,
! [X0] :
( sQ48_spl
<=> ( ~ aSet0(X0)
| aSubsetOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(sK1_skl(X0,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f521,plain,
! [X0] :
( ~ sQ48_spl
| ~ aSet0(X0)
| aSubsetOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(sK1_skl(X0,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx)) ),
inference(component_clause,[status(thm)],[f520]) ).
fof(f523,plain,
( ~ sQ19_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f511,f520,f243]) ).
fof(f551,plain,
! [X0] :
( sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)) = xx
| aElementOf0(sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)),sdtmndt0(xS,xx))
| sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)) = X0
| ~ aElement0(X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f179,f97]) ).
fof(f552,plain,
! [X0] :
( aElement0(sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)))
| sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)) = X0
| ~ aElement0(X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f179,f96]) ).
fof(f554,plain,
! [X0,X1,X2] :
( sK0_skl(sdtpldt0(sdtpldt0(X0,X1),X2)) = X1
| aElementOf0(sK0_skl(sdtpldt0(sdtpldt0(X0,X1),X2)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0)
| sdtpldt0(sdtpldt0(X0,X1),X2) = slcrc0
| sK0_skl(sdtpldt0(sdtpldt0(X0,X1),X2)) = X2
| ~ aElement0(X2)
| ~ aSet0(sdtpldt0(X0,X1)) ),
inference(resolution,[status(thm)],[f179,f112]) ).
fof(f555,plain,
! [X0] :
( aElementOf0(sK0_skl(sdtpldt0(sdtmndt0(xS,xx),X0)),xS)
| sdtpldt0(sdtmndt0(xS,xx),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtmndt0(xS,xx),X0)) = X0
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f179,f92]) ).
fof(f558,plain,
! [X0] :
( sdtpldt0(slcrc0,X0) = slcrc0
| sK0_skl(sdtpldt0(slcrc0,X0)) = X0
| ~ aElement0(X0)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f179,f108]) ).
fof(f560,definition,
! [X0] :
( sQ50_spl
<=> ( sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)) = xx
| aElementOf0(sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)),sdtmndt0(xS,xx))
| sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)) = X0
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f561,plain,
! [X0] :
( ~ sQ50_spl
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)) = xx
| aElementOf0(sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)),sdtmndt0(xS,xx))
| sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)) = X0
| ~ aElement0(X0) ),
inference(component_clause,[status(thm)],[f560]) ).
fof(f563,plain,
( sQ50_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f551,f243,f560]) ).
fof(f564,definition,
! [X0] :
( sQ51_spl
<=> ( aElement0(sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)))
| sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)) = X0
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f567,plain,
( sQ51_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f552,f243,f564]) ).
fof(f568,plain,
! [X0,X1,X2] :
( sK0_skl(sdtpldt0(sdtpldt0(X1,X2),X0)) = X2
| aElementOf0(sK0_skl(sdtpldt0(sdtpldt0(X1,X2),X0)),X1)
| ~ aElement0(X2)
| ~ aSet0(X1)
| sdtpldt0(sdtpldt0(X1,X2),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtpldt0(X1,X2),X0)) = X0
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f554,f110]) ).
fof(f569,definition,
! [X0] :
( sQ52_spl
<=> ( aElementOf0(sK0_skl(sdtpldt0(sdtmndt0(xS,xx),X0)),xS)
| sdtpldt0(sdtmndt0(xS,xx),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtmndt0(xS,xx),X0)) = X0
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f570,plain,
! [X0] :
( ~ sQ52_spl
| aElementOf0(sK0_skl(sdtpldt0(sdtmndt0(xS,xx),X0)),xS)
| sdtpldt0(sdtmndt0(xS,xx),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtmndt0(xS,xx),X0)) = X0
| ~ aElement0(X0) ),
inference(component_clause,[status(thm)],[f569]) ).
fof(f572,plain,
( sQ52_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f555,f148,f569]) ).
fof(f573,definition,
! [X0] :
( sQ53_spl
<=> ( aElement0(sK0_skl(sdtpldt0(sdtmndt0(xS,xx),X0)))
| sdtpldt0(sdtmndt0(xS,xx),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtmndt0(xS,xx),X0)) = X0
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f578,definition,
! [X0] :
( sQ54_spl
<=> ( sdtpldt0(slcrc0,X0) = slcrc0
| sK0_skl(sdtpldt0(slcrc0,X0)) = X0
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f581,plain,
( sQ54_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f558,f140,f578]) ).
fof(f585,plain,
! [X0,X1] :
( aElementOf0(sK0_skl(sdtmndt0(X0,X1)),X0)
| sdtmndt0(X0,X1) = slcrc0
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f464,f104]) ).
fof(f587,plain,
! [X0] :
( sK0_skl(sdtmndt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)) = xx
| aElementOf0(sK0_skl(sdtmndt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)),sdtmndt0(xS,xx))
| sdtmndt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0) = slcrc0
| ~ aElement0(X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f585,f97]) ).
fof(f588,plain,
! [X0] :
( aElement0(sK0_skl(sdtmndt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)))
| sdtmndt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0) = slcrc0
| ~ aElement0(X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f585,f96]) ).
fof(f591,plain,
! [X0] :
( aElementOf0(sK0_skl(sdtmndt0(sdtmndt0(xS,xx),X0)),xS)
| sdtmndt0(sdtmndt0(xS,xx),X0) = slcrc0
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f585,f92]) ).
fof(f592,plain,
! [X0] :
( aElement0(sK0_skl(sdtmndt0(sdtmndt0(xS,xx),X0)))
| sdtmndt0(sdtmndt0(xS,xx),X0) = slcrc0
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f585,f91]) ).
fof(f594,plain,
! [X0] :
( sdtmndt0(slcrc0,X0) = slcrc0
| ~ aElement0(X0)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f585,f108]) ).
fof(f596,definition,
! [X0] :
( sQ55_spl
<=> ( sK0_skl(sdtmndt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)) = xx
| aElementOf0(sK0_skl(sdtmndt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)),sdtmndt0(xS,xx))
| sdtmndt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0) = slcrc0
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f599,plain,
( sQ55_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f587,f243,f596]) ).
fof(f600,definition,
! [X0] :
( sQ56_spl
<=> ( aElement0(sK0_skl(sdtmndt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)))
| sdtmndt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0) = slcrc0
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f603,plain,
( sQ56_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f588,f243,f600]) ).
fof(f605,definition,
! [X0] :
( sQ57_spl
<=> ( aElementOf0(sK0_skl(sdtmndt0(sdtmndt0(xS,xx),X0)),xS)
| sdtmndt0(sdtmndt0(xS,xx),X0) = slcrc0
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f608,plain,
( sQ57_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f591,f148,f605]) ).
fof(f609,definition,
! [X0] :
( sQ58_spl
<=> ( aElement0(sK0_skl(sdtmndt0(sdtmndt0(xS,xx),X0)))
| sdtmndt0(sdtmndt0(xS,xx),X0) = slcrc0
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f612,plain,
( sQ58_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f592,f148,f609]) ).
fof(f614,definition,
! [X0] :
( sQ59_spl
<=> ( sdtmndt0(slcrc0,X0) = slcrc0
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f617,plain,
( sQ59_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f594,f140,f614]) ).
fof(f620,plain,
! [X0,X1,X2] :
( aElementOf0(sK3_skl(X2,X1,X0),X0)
| aElementOf0(sK3_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f84,f104]) ).
fof(f623,plain,
( ~ sQ16_spl
| ~ aSet0(xS)
| aSubsetOf0(xS,sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aSet0(xS)
| aSubsetOf0(xS,sdtmndt0(xS,xx))
| sK1_skl(xS,sdtmndt0(xS,xx)) = xx
| ~ aElement0(sK1_skl(xS,sdtmndt0(xS,xx))) ),
inference(resolution,[status(thm)],[f227,f51]) ).
fof(f624,definition,
( sQ60_spl
<=> aElement0(sK1_skl(xS,sdtmndt0(xS,xx))) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f626,plain,
( sQ60_spl
| ~ aElement0(sK1_skl(xS,sdtmndt0(xS,xx))) ),
inference(component_clause,[status(thm)],[f624]) ).
fof(f627,definition,
( sQ61_spl
<=> sK1_skl(xS,sdtmndt0(xS,xx)) = xx ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f630,definition,
( sQ62_spl
<=> aSubsetOf0(xS,sdtmndt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f631,plain,
( ~ sQ62_spl
| aSubsetOf0(xS,sdtmndt0(xS,xx)) ),
inference(component_clause,[status(thm)],[f630]) ).
fof(f633,plain,
( ~ sQ16_spl
| ~ sQ5_spl
| ~ sQ0_spl
| sQ62_spl
| sQ61_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f623,f624,f627,f630,f123,f148,f226]) ).
fof(f638,plain,
! [X0] :
( ~ sQ62_spl
| aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElementOf0(X0,xS)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f631,f50]) ).
fof(f650,definition,
( sQ66_spl
<=> aSubsetOf0(sdtmndt0(xS,xx),xS) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f651,plain,
( ~ sQ66_spl
| aSubsetOf0(sdtmndt0(xS,xx),xS) ),
inference(component_clause,[status(thm)],[f650]) ).
fof(f653,definition,
( sQ67_spl
<=> xS = sdtmndt0(xS,xx) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f654,plain,
( ~ sQ67_spl
| xS = sdtmndt0(xS,xx) ),
inference(component_clause,[status(thm)],[f653]) ).
fof(f658,definition,
! [X0] :
( sQ68_spl
<=> ( aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElementOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f659,plain,
! [X0] :
( ~ sQ68_spl
| aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElementOf0(X0,xS) ),
inference(component_clause,[status(thm)],[f658]) ).
fof(f661,plain,
( ~ sQ62_spl
| sQ68_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f638,f148,f658,f630]) ).
fof(f662,plain,
( sQ60_spl
| aSubsetOf0(xS,sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f626,f233]) ).
fof(f663,plain,
( sQ60_spl
| sQ62_spl
| ~ sQ5_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f662,f123,f148,f630,f624]) ).
fof(f675,plain,
! [X0,X1,X2] :
( ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx))
| sdtpldt0(X0,X1) = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X2)
| ~ aElement0(X2)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f316,f343]) ).
fof(f676,plain,
! [X0,X1,X2,X3,X4] :
( ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(X3,X4)),X3)
| ~ aElement0(X4)
| ~ aSet0(X3)
| sdtpldt0(X0,X1) = sdtpldt0(sdtpldt0(X3,X4),X2)
| ~ aElement0(X2)
| ~ aSet0(sdtpldt0(X3,X4))
| ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(X3,X4)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f316,f180]) ).
fof(f677,plain,
! [X0,X1,X2] :
( sK2_skl(sdtpldt0(X0,X1),X2,sdtmndt0(xS,xx)) = xx
| ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtmndt0(xS,xx)),xS)
| ~ aElement0(sK2_skl(sdtpldt0(X0,X1),X2,sdtmndt0(xS,xx)))
| sdtpldt0(X0,X1) = sdtpldt0(sdtmndt0(xS,xx),X2)
| ~ aElement0(X2)
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtmndt0(xS,xx)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f316,f94]) ).
fof(f680,definition,
! [X0,X1,X2] :
( sQ69_spl
<=> ( ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx))
| sdtpldt0(X0,X1) = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X2)
| ~ aElement0(X2)
| ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f681,plain,
! [X0,X1,X2] :
( ~ sQ69_spl
| ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx))
| sdtpldt0(X0,X1) = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X2)
| ~ aElement0(X2)
| ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f680]) ).
fof(f683,plain,
( ~ sQ19_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f675,f680,f243]) ).
fof(f684,plain,
! [X0,X1,X2,X3,X4] :
( ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(X3,X4)),X3)
| ~ aElement0(X4)
| ~ aSet0(X3)
| sdtpldt0(X0,X1) = sdtpldt0(sdtpldt0(X3,X4),X2)
| ~ aElement0(X2)
| ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(X3,X4)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f676,f110]) ).
fof(f685,definition,
! [X0,X1,X2] :
( sQ70_spl
<=> ( sK2_skl(sdtpldt0(X0,X1),X2,sdtmndt0(xS,xx)) = xx
| ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtmndt0(xS,xx)),xS)
| ~ aElement0(sK2_skl(sdtpldt0(X0,X1),X2,sdtmndt0(xS,xx)))
| sdtpldt0(X0,X1) = sdtpldt0(sdtmndt0(xS,xx),X2)
| ~ aElement0(X2)
| ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtmndt0(xS,xx)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f688,plain,
( ~ sQ5_spl
| sQ70_spl ),
inference(split_clause,[status(thm)],[f677,f685,f148]) ).
fof(f691,plain,
! [X0,X1] :
( ~ aSet0(X0)
| aSubsetOf0(X0,sdtpldt0(X0,X1))
| ~ aSet0(sdtpldt0(X0,X1))
| ~ aSet0(X0)
| aSubsetOf0(X0,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f317,f51]) ).
fof(f692,plain,
! [X0,X1] :
( ~ aElementOf0(sK1_skl(X1,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)),sdtmndt0(xS,xx))
| ~ aSet0(X1)
| aSubsetOf0(X1,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| ~ aElement0(X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f317,f343]) ).
fof(f693,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(sK1_skl(X3,sdtpldt0(sdtpldt0(X0,X1),X2)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0)
| ~ aSet0(X3)
| aSubsetOf0(X3,sdtpldt0(sdtpldt0(X0,X1),X2))
| ~ aElement0(X2)
| ~ aSet0(sdtpldt0(X0,X1)) ),
inference(resolution,[status(thm)],[f317,f180]) ).
fof(f694,plain,
! [X0,X1] :
( sK1_skl(X1,sdtpldt0(sdtmndt0(xS,xx),X0)) = xx
| ~ aElementOf0(sK1_skl(X1,sdtpldt0(sdtmndt0(xS,xx),X0)),xS)
| ~ aElement0(sK1_skl(X1,sdtpldt0(sdtmndt0(xS,xx),X0)))
| ~ aSet0(X1)
| aSubsetOf0(X1,sdtpldt0(sdtmndt0(xS,xx),X0))
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f317,f94]) ).
fof(f696,plain,
! [X0,X1] :
( ~ aSet0(sdtpldt0(X0,X1))
| aSubsetOf0(X0,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f691]) ).
fof(f697,plain,
! [X0,X1] :
( aSubsetOf0(X0,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f696,f110]) ).
fof(f698,definition,
! [X0,X1] :
( sQ71_spl
<=> ( ~ aElementOf0(sK1_skl(X1,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)),sdtmndt0(xS,xx))
| ~ aSet0(X1)
| aSubsetOf0(X1,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f699,plain,
! [X0,X1] :
( ~ sQ71_spl
| ~ aElementOf0(sK1_skl(X1,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)),sdtmndt0(xS,xx))
| ~ aSet0(X1)
| aSubsetOf0(X1,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| ~ aElement0(X0) ),
inference(component_clause,[status(thm)],[f698]) ).
fof(f701,plain,
( sQ71_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f692,f243,f698]) ).
fof(f702,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(sK1_skl(X1,sdtpldt0(sdtpldt0(X2,X3),X0)),X2)
| ~ aElement0(X3)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aSubsetOf0(X1,sdtpldt0(sdtpldt0(X2,X3),X0))
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f693,f110]) ).
fof(f703,definition,
! [X0,X1] :
( sQ72_spl
<=> ( sK1_skl(X1,sdtpldt0(sdtmndt0(xS,xx),X0)) = xx
| ~ aElementOf0(sK1_skl(X1,sdtpldt0(sdtmndt0(xS,xx),X0)),xS)
| ~ aElement0(sK1_skl(X1,sdtpldt0(sdtmndt0(xS,xx),X0)))
| ~ aSet0(X1)
| aSubsetOf0(X1,sdtpldt0(sdtmndt0(xS,xx),X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f704,plain,
! [X0,X1] :
( ~ sQ72_spl
| sK1_skl(X1,sdtpldt0(sdtmndt0(xS,xx),X0)) = xx
| ~ aElementOf0(sK1_skl(X1,sdtpldt0(sdtmndt0(xS,xx),X0)),xS)
| ~ aElement0(sK1_skl(X1,sdtpldt0(sdtmndt0(xS,xx),X0)))
| ~ aSet0(X1)
| aSubsetOf0(X1,sdtpldt0(sdtmndt0(xS,xx),X0))
| ~ aElement0(X0) ),
inference(component_clause,[status(thm)],[f703]) ).
fof(f706,plain,
( sQ72_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f694,f148,f703]) ).
fof(f709,plain,
! [X0,X1,X2] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(sdtpldt0(X0,X1),X2)
| ~ aSet0(X2)
| ~ aSet0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f697,f270]) ).
fof(f714,plain,
! [X0,X1,X2] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(sdtpldt0(X0,X1),X2)
| ~ aSet0(X2)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f709,f49]) ).
fof(f716,plain,
( ~ sQ68_spl
| ~ aElementOf0(xx,xS) ),
inference(resolution,[status(thm)],[f659,f119]) ).
fof(f725,plain,
( ~ sQ68_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f716,f288,f658]) ).
fof(f742,definition,
! [X0] :
( sQ77_spl
<=> ( sP0_prd(X0,xx,xS)
| ~ aElementOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f743,plain,
! [X0] :
( ~ sQ77_spl
| sP0_prd(X0,xx,xS)
| ~ aElementOf0(X0,xS) ),
inference(component_clause,[status(thm)],[f742]) ).
fof(f775,plain,
! [X0] :
( ~ sQ34_spl
| ~ aElementOf0(sK2_skl(slcrc0,X0,slcrc0),slcrc0)
| ~ aSet0(slcrc0)
| slcrc0 = sdtpldt0(slcrc0,X0)
| ~ aElement0(X0)
| ~ aSet0(slcrc0)
| sK2_skl(slcrc0,X0,slcrc0) = X0
| slcrc0 = sdtpldt0(slcrc0,X0)
| ~ aElement0(X0)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f368,f274]) ).
fof(f776,plain,
! [X0] :
( ~ sQ34_spl
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| aElementOf0(sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx))
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aElement0(X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f368,f97]) ).
fof(f777,plain,
! [X0] :
( ~ sQ34_spl
| aElement0(sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)))
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aElement0(X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f368,f96]) ).
fof(f778,plain,
! [X0,X1,X2] :
( ~ sQ34_spl
| aElement0(sK2_skl(slcrc0,X2,sdtpldt0(X0,X1)))
| ~ aElement0(X1)
| ~ aSet0(X0)
| sK2_skl(slcrc0,X2,sdtpldt0(X0,X1)) = X2
| slcrc0 = sdtpldt0(sdtpldt0(X0,X1),X2)
| ~ aElement0(X2)
| ~ aSet0(sdtpldt0(X0,X1)) ),
inference(resolution,[status(thm)],[f368,f111]) ).
fof(f779,plain,
! [X0,X1,X2] :
( ~ sQ34_spl
| sK2_skl(slcrc0,X2,sdtpldt0(X0,X1)) = X1
| aElementOf0(sK2_skl(slcrc0,X2,sdtpldt0(X0,X1)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0)
| sK2_skl(slcrc0,X2,sdtpldt0(X0,X1)) = X2
| slcrc0 = sdtpldt0(sdtpldt0(X0,X1),X2)
| ~ aElement0(X2)
| ~ aSet0(sdtpldt0(X0,X1)) ),
inference(resolution,[status(thm)],[f368,f112]) ).
fof(f780,plain,
! [X0] :
( ~ sQ34_spl
| aElementOf0(sK2_skl(slcrc0,X0,sdtmndt0(xS,xx)),xS)
| sK2_skl(slcrc0,X0,sdtmndt0(xS,xx)) = X0
| slcrc0 = sdtpldt0(sdtmndt0(xS,xx),X0)
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f368,f92]) ).
fof(f782,plain,
! [X0,X1,X2] :
( ~ sQ34_spl
| sP0_prd(sK2_skl(slcrc0,X2,sdtmndt0(X0,X1)),X1,X0)
| ~ aElement0(X1)
| ~ aSet0(X0)
| sK2_skl(slcrc0,X2,sdtmndt0(X0,X1)) = X2
| slcrc0 = sdtpldt0(sdtmndt0(X0,X1),X2)
| ~ aElement0(X2)
| ~ aSet0(sdtmndt0(X0,X1)) ),
inference(resolution,[status(thm)],[f368,f117]) ).
fof(f783,plain,
! [X0] :
( ~ sQ34_spl
| sK2_skl(slcrc0,X0,slcrc0) = X0
| slcrc0 = sdtpldt0(slcrc0,X0)
| ~ aElement0(X0)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f368,f108]) ).
fof(f784,plain,
! [X0,X1] :
( ~ sQ34_spl
| aElement0(sK2_skl(slcrc0,X1,X0))
| ~ aSet0(X0)
| sK2_skl(slcrc0,X1,X0) = X1
| slcrc0 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f368,f28]) ).
fof(f785,definition,
! [X0] :
( sQ79_spl
<=> ( ~ aElementOf0(sK2_skl(slcrc0,X0,slcrc0),slcrc0)
| slcrc0 = sdtpldt0(slcrc0,X0)
| ~ aElement0(X0)
| sK2_skl(slcrc0,X0,slcrc0) = X0
| slcrc0 = sdtpldt0(slcrc0,X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f788,plain,
( ~ sQ34_spl
| sQ79_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f775,f140,f785,f367]) ).
fof(f789,definition,
! [X0] :
( sQ80_spl
<=> ( sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| aElementOf0(sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx))
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f790,plain,
! [X0] :
( ~ sQ80_spl
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| aElementOf0(sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx))
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aElement0(X0) ),
inference(component_clause,[status(thm)],[f789]) ).
fof(f792,plain,
( ~ sQ34_spl
| sQ80_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f776,f243,f789,f367]) ).
fof(f793,definition,
! [X0] :
( sQ81_spl
<=> ( aElement0(sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)))
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f794,plain,
! [X0] :
( ~ sQ81_spl
| aElement0(sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)))
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aElement0(X0) ),
inference(component_clause,[status(thm)],[f793]) ).
fof(f796,plain,
( ~ sQ34_spl
| sQ81_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f777,f243,f793,f367]) ).
fof(f797,plain,
! [X0,X1,X2] :
( ~ sQ34_spl
| aElement0(sK2_skl(slcrc0,X0,sdtpldt0(X1,X2)))
| ~ aElement0(X2)
| ~ aSet0(X1)
| sK2_skl(slcrc0,X0,sdtpldt0(X1,X2)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(X1,X2),X0)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f778,f110]) ).
fof(f798,plain,
! [X0,X1,X2] :
( ~ sQ34_spl
| sK2_skl(slcrc0,X0,sdtpldt0(X1,X2)) = X2
| aElementOf0(sK2_skl(slcrc0,X0,sdtpldt0(X1,X2)),X1)
| ~ aElement0(X2)
| ~ aSet0(X1)
| sK2_skl(slcrc0,X0,sdtpldt0(X1,X2)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(X1,X2),X0)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f779,f110]) ).
fof(f799,definition,
! [X0] :
( sQ82_spl
<=> ( aElementOf0(sK2_skl(slcrc0,X0,sdtmndt0(xS,xx)),xS)
| sK2_skl(slcrc0,X0,sdtmndt0(xS,xx)) = X0
| slcrc0 = sdtpldt0(sdtmndt0(xS,xx),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f800,plain,
! [X0] :
( ~ sQ82_spl
| aElementOf0(sK2_skl(slcrc0,X0,sdtmndt0(xS,xx)),xS)
| sK2_skl(slcrc0,X0,sdtmndt0(xS,xx)) = X0
| slcrc0 = sdtpldt0(sdtmndt0(xS,xx),X0)
| ~ aElement0(X0) ),
inference(component_clause,[status(thm)],[f799]) ).
fof(f802,plain,
( ~ sQ34_spl
| sQ82_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f780,f148,f799,f367]) ).
fof(f803,definition,
! [X0] :
( sQ83_spl
<=> ( aElement0(sK2_skl(slcrc0,X0,sdtmndt0(xS,xx)))
| sK2_skl(slcrc0,X0,sdtmndt0(xS,xx)) = X0
| slcrc0 = sdtpldt0(sdtmndt0(xS,xx),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f804,plain,
! [X0] :
( ~ sQ83_spl
| aElement0(sK2_skl(slcrc0,X0,sdtmndt0(xS,xx)))
| sK2_skl(slcrc0,X0,sdtmndt0(xS,xx)) = X0
| slcrc0 = sdtpldt0(sdtmndt0(xS,xx),X0)
| ~ aElement0(X0) ),
inference(component_clause,[status(thm)],[f803]) ).
fof(f807,plain,
! [X0,X1,X2] :
( ~ sQ34_spl
| sP0_prd(sK2_skl(slcrc0,X0,sdtmndt0(X1,X2)),X2,X1)
| ~ aElement0(X2)
| ~ aSet0(X1)
| sK2_skl(slcrc0,X0,sdtmndt0(X1,X2)) = X0
| slcrc0 = sdtpldt0(sdtmndt0(X1,X2),X0)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f782,f116]) ).
fof(f808,definition,
! [X0] :
( sQ84_spl
<=> ( sK2_skl(slcrc0,X0,slcrc0) = X0
| slcrc0 = sdtpldt0(slcrc0,X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f809,plain,
! [X0] :
( ~ sQ84_spl
| sK2_skl(slcrc0,X0,slcrc0) = X0
| slcrc0 = sdtpldt0(slcrc0,X0)
| ~ aElement0(X0) ),
inference(component_clause,[status(thm)],[f808]) ).
fof(f811,plain,
( ~ sQ34_spl
| sQ84_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f783,f140,f808,f367]) ).
fof(f812,plain,
! [X0,X1] :
( ~ sQ34_spl
| aElement0(sK2_skl(slcrc0,X1,X0))
| sK2_skl(slcrc0,X1,X0) = X1
| slcrc0 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f784]) ).
fof(f814,plain,
! [X0] :
( ~ sQ36_spl
| ~ aSet0(sdtmndt0(xS,xx))
| aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(xS,X0))
| ~ aElement0(X0)
| ~ aSet0(xS)
| aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(xS,X0))
| ~ aSet0(sdtpldt0(xS,X0)) ),
inference(resolution,[status(thm)],[f386,f317]) ).
fof(f816,plain,
( ~ sQ36_spl
| ~ aSet0(sdtmndt0(xS,xx))
| aSubsetOf0(sdtmndt0(xS,xx),xS)
| ~ aSet0(xS)
| aSubsetOf0(sdtmndt0(xS,xx),xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f386,f52]) ).
fof(f818,definition,
! [X0] :
( sQ85_spl
<=> ( aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(xS,X0))
| ~ aElement0(X0)
| aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(xS,X0))
| ~ aSet0(sdtpldt0(xS,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f821,plain,
( ~ sQ36_spl
| ~ sQ5_spl
| ~ sQ0_spl
| sQ85_spl ),
inference(split_clause,[status(thm)],[f814,f818,f123,f148,f385]) ).
fof(f832,plain,
( ~ sQ36_spl
| ~ sQ5_spl
| sQ66_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f816,f123,f650,f148,f385]) ).
fof(f836,plain,
! [X0] :
( ~ sQ66_spl
| aSubsetOf0(sdtmndt0(xS,xx),X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f651,f270]) ).
fof(f839,plain,
! [X0] :
( ~ sQ66_spl
| aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f651,f50]) ).
fof(f841,definition,
! [X0] :
( sQ89_spl
<=> ( aSubsetOf0(sdtmndt0(xS,xx),X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f842,plain,
! [X0] :
( ~ sQ89_spl
| aSubsetOf0(sdtmndt0(xS,xx),X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f841]) ).
fof(f844,plain,
( ~ sQ66_spl
| sQ89_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f836,f123,f841,f650]) ).
fof(f847,definition,
! [X0] :
( sQ90_spl
<=> ( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f850,plain,
( ~ sQ66_spl
| sQ90_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f839,f123,f847,f650]) ).
fof(f851,plain,
! [X0,X1] :
( ~ sQ32_spl
| ~ aElementOf0(sK2_skl(sdtmndt0(xS,xx),X1,X0),sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| sdtmndt0(xS,xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0)
| aElement0(sK2_skl(sdtmndt0(xS,xx),X1,X0))
| sdtmndt0(xS,xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f372,f352]) ).
fof(f852,definition,
! [X0,X1] :
( sQ91_spl
<=> ( ~ aElementOf0(sK2_skl(sdtmndt0(xS,xx),X1,X0),sdtmndt0(xS,xx))
| sdtmndt0(xS,xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0)
| aElement0(sK2_skl(sdtmndt0(xS,xx),X1,X0))
| sdtmndt0(xS,xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f855,plain,
( ~ sQ32_spl
| ~ sQ5_spl
| sQ91_spl ),
inference(split_clause,[status(thm)],[f851,f852,f148,f359]) ).
fof(f880,plain,
( ~ sQ67_spl
| ~ aElementOf0(xx,xS) ),
inference(backward_demodulation,[status(thm)],[f654,f119]) ).
fof(f902,plain,
( ~ sQ67_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f880,f288,f653]) ).
fof(f1010,plain,
( ~ sQ77_spl
| ~ aElementOf0(xx,xS) ),
inference(resolution,[status(thm)],[f743,f121]) ).
fof(f1015,plain,
( ~ sQ77_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f1010,f288,f742]) ).
fof(f1079,plain,
! [X0] :
( ~ sQ18_spl
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtmndt0(xS,xx),X0))
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtmndt0(xS,xx),X0))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),X0))
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtmndt0(xS,xx),X0)) = xx ),
inference(resolution,[status(thm)],[f241,f317]) ).
fof(f1080,plain,
( ~ sQ18_spl
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),sdtmndt0(xS,xx)) = xx ),
inference(resolution,[status(thm)],[f241,f52]) ).
fof(f1082,plain,
! [X0] :
( ~ sQ18_spl
| aElementOf0(sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0),xS)
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aSet0(X0)
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0) = xx ),
inference(resolution,[status(thm)],[f241,f92]) ).
fof(f1083,plain,
! [X0] :
( ~ sQ18_spl
| sP0_prd(sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0),xx,xS)
| ~ aElement0(xx)
| ~ aSet0(xS)
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aSet0(X0)
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0) = xx ),
inference(resolution,[status(thm)],[f241,f117]) ).
fof(f1084,plain,
! [X0] :
( ~ sQ18_spl
| aElement0(sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| ~ aSet0(sdtmndt0(xS,xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aSet0(X0)
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0) = xx ),
inference(resolution,[status(thm)],[f241,f28]) ).
fof(f1085,definition,
! [X0] :
( sQ99_spl
<=> ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtmndt0(xS,xx),X0))
| ~ aElement0(X0)
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtmndt0(xS,xx),X0))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),X0))
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtmndt0(xS,xx),X0)) = xx ) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f1088,plain,
( ~ sQ18_spl
| ~ sQ19_spl
| ~ sQ5_spl
| sQ99_spl ),
inference(split_clause,[status(thm)],[f1079,f1085,f148,f243,f240]) ).
fof(f1089,definition,
( sQ100_spl
<=> sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),sdtmndt0(xS,xx)) = xx ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f1090,plain,
( ~ sQ100_spl
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),sdtmndt0(xS,xx)) = xx ),
inference(component_clause,[status(thm)],[f1089]) ).
fof(f1092,definition,
( sQ101_spl
<=> aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtmndt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f1095,plain,
( ~ sQ18_spl
| ~ sQ19_spl
| sQ101_spl
| ~ sQ5_spl
| sQ100_spl ),
inference(split_clause,[status(thm)],[f1080,f1089,f148,f1092,f243,f240]) ).
fof(f1096,definition,
! [X0] :
( sQ102_spl
<=> ( sP0_prd(sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0),xx,xS)
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aSet0(X0)
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0) = xx ) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f1097,plain,
! [X0] :
( ~ sQ102_spl
| sP0_prd(sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0),xx,xS)
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aSet0(X0)
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0) = xx ),
inference(component_clause,[status(thm)],[f1096]) ).
fof(f1099,plain,
( ~ sQ18_spl
| ~ sQ1_spl
| ~ sQ0_spl
| sQ102_spl ),
inference(split_clause,[status(thm)],[f1083,f1096,f123,f126,f240]) ).
fof(f1100,definition,
! [X0] :
( sQ103_spl
<=> ( aElement0(sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aSet0(X0)
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0) = xx ) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f1103,plain,
( ~ sQ18_spl
| ~ sQ5_spl
| sQ103_spl ),
inference(split_clause,[status(thm)],[f1084,f1100,f148,f240]) ).
fof(f1106,plain,
( ~ sQ20_spl
| ~ aSet0(sdtmndt0(xS,xx))
| aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtmndt0(xS,xx))
| aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f375,f51]) ).
fof(f1107,plain,
! [X0] :
( ~ sQ20_spl
| sK1_skl(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| ~ aElementOf0(sK1_skl(X0,sdtpldt0(sdtmndt0(xS,xx),xx)),xS)
| ~ aElement0(sK1_skl(X0,sdtpldt0(sdtmndt0(xS,xx),xx)))
| ~ aSet0(X0)
| aSubsetOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f375,f94]) ).
fof(f1108,plain,
! [X0] :
( ~ sQ20_spl
| ~ sP0_prd(sK1_skl(X0,sdtpldt0(sdtmndt0(xS,xx),xx)),xx,xS)
| ~ aElement0(xx)
| ~ aSet0(xS)
| ~ aSet0(X0)
| aSubsetOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f375,f118]) ).
fof(f1109,definition,
( sQ104_spl
<=> aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtmndt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f1110,plain,
( ~ sQ104_spl
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(component_clause,[status(thm)],[f1109]) ).
fof(f1111,plain,
( sQ104_spl
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(component_clause,[status(thm)],[f1109]) ).
fof(f1116,definition,
( sQ106_spl
<=> aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(sdtmndt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f1117,plain,
( ~ sQ106_spl
| aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(component_clause,[status(thm)],[f1116]) ).
fof(f1119,plain,
( ~ sQ20_spl
| ~ sQ19_spl
| ~ sQ5_spl
| sQ106_spl ),
inference(split_clause,[status(thm)],[f1106,f1116,f148,f243,f250]) ).
fof(f1120,definition,
! [X0] :
( sQ107_spl
<=> ( ~ sP0_prd(sK1_skl(X0,sdtpldt0(sdtmndt0(xS,xx),xx)),xx,xS)
| ~ aSet0(X0)
| aSubsetOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f1123,plain,
( ~ sQ20_spl
| ~ sQ1_spl
| ~ sQ0_spl
| sQ107_spl ),
inference(split_clause,[status(thm)],[f1108,f1120,f123,f126,f250]) ).
fof(f1125,plain,
! [X0,X1] :
( ~ sQ22_spl
| ~ sP0_prd(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),xx,xS)
| ~ aElement0(xx)
| ~ aSet0(xS)
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),X0)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f286,f118]) ).
fof(f1127,definition,
! [X0,X1] :
( sQ108_spl
<=> ( ~ sP0_prd(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),xx,xS)
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),X0)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f1130,plain,
( ~ sQ22_spl
| ~ sQ1_spl
| ~ sQ0_spl
| sQ108_spl ),
inference(split_clause,[status(thm)],[f1125,f1127,f123,f126,f277]) ).
fof(f1134,plain,
! [X0] :
( ~ sQ33_spl
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(sdtmndt0(xS,xx),X0)
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,sdtmndt0(xS,xx)),sdtmndt0(xS,xx))
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xS,xx))
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,sdtmndt0(xS,xx)) = xx
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,sdtmndt0(xS,xx)) = X0
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,sdtmndt0(xS,xx)),sdtmndt0(xS,xx))
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(sdtmndt0(xS,xx),X0)
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f364,f316]) ).
fof(f1137,plain,
! [X0,X1] :
( ~ sQ33_spl
| sP0_prd(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),xx,xS)
| ~ aElement0(xx)
| ~ aSet0(xS)
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0) = xx
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0) = X1
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),X0)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f364,f117]) ).
fof(f1138,plain,
! [X0,X1] :
( ~ sQ33_spl
| aElement0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0))
| ~ aSet0(sdtmndt0(xS,xx))
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0) = xx
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0) = X1
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),X0)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f364,f28]) ).
fof(f1139,definition,
! [X0] :
( sQ109_spl
<=> ( sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(sdtmndt0(xS,xx),X0)
| ~ aElement0(X0)
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,sdtmndt0(xS,xx)),sdtmndt0(xS,xx))
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,sdtmndt0(xS,xx)) = xx
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,sdtmndt0(xS,xx)) = X0
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,sdtmndt0(xS,xx)),sdtmndt0(xS,xx))
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(sdtmndt0(xS,xx),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f1142,plain,
( ~ sQ33_spl
| ~ sQ1_spl
| sQ109_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1134,f148,f1139,f126,f363]) ).
fof(f1144,definition,
! [X0,X1] :
( sQ110_spl
<=> ( sP0_prd(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),xx,xS)
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0) = xx
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0) = X1
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),X0)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f1147,plain,
( ~ sQ33_spl
| ~ sQ1_spl
| ~ sQ0_spl
| sQ110_spl ),
inference(split_clause,[status(thm)],[f1137,f1144,f123,f126,f363]) ).
fof(f1148,definition,
! [X0,X1] :
( sQ111_spl
<=> ( aElement0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0))
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0) = xx
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0) = X1
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),X0)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f1151,plain,
( ~ sQ33_spl
| ~ sQ5_spl
| sQ111_spl ),
inference(split_clause,[status(thm)],[f1138,f1148,f148,f363]) ).
fof(f1155,plain,
! [X0,X1] :
( ~ sQ89_spl
| aSubsetOf0(sdtmndt0(xS,xx),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f842,f270]) ).
fof(f1158,plain,
! [X0,X1] :
( ~ sQ89_spl
| aElementOf0(X1,X0)
| ~ aElementOf0(X1,sdtmndt0(xS,xx))
| ~ aSet0(X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f842,f50]) ).
fof(f1167,plain,
! [X0,X1] :
( ~ sQ89_spl
| aSubsetOf0(sdtmndt0(xS,xx),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1155]) ).
fof(f1168,plain,
! [X0,X1] :
( ~ sQ89_spl
| aSubsetOf0(sdtmndt0(xS,xx),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1167,f49]) ).
fof(f1170,definition,
! [X0] :
( sQ114_spl
<=> ( ~ aSet0(X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f1171,plain,
! [X0] :
( ~ sQ114_spl
| ~ aSet0(X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f1170]) ).
fof(f1174,plain,
! [X0,X1] :
( ~ sQ89_spl
| aElementOf0(X1,X0)
| ~ aElementOf0(X1,sdtmndt0(xS,xx))
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1158]) ).
fof(f1559,plain,
! [X0,X1] :
( ~ sQ37_spl
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,X1),sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| aElement0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,X1)) ),
inference(resolution,[status(thm)],[f412,f352]) ).
fof(f1560,definition,
! [X0,X1] :
( sQ136_spl
<=> ( ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,X1),sdtpldt0(sdtmndt0(xS,xx),xx))
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| aElement0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f1563,plain,
( ~ sQ37_spl
| ~ sQ19_spl
| sQ136_spl ),
inference(split_clause,[status(thm)],[f1559,f1560,f243,f395]) ).
fof(f1572,plain,
! [X0,X1] :
( ~ sQ89_spl
| aElementOf0(X1,X0)
| ~ aElementOf0(X1,sdtmndt0(xS,xx))
| ~ aSet0(X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f842,f50]) ).
fof(f1579,plain,
! [X0,X1] :
( ~ sQ89_spl
| aElementOf0(X1,X0)
| ~ aElementOf0(X1,sdtmndt0(xS,xx))
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1572]) ).
fof(f1582,plain,
! [X0,X1,X2] :
( aElement0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)))
| sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)) = X2
| sdtpldt0(X0,X1) = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X2)
| ~ aElement0(X2)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)) = X1
| aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f428,f96]) ).
fof(f1583,plain,
! [X0,X1,X2] :
( sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx))
| sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)) = X2
| sdtpldt0(X0,X1) = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X2)
| ~ aElement0(X2)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)) = X1
| aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f428,f97]) ).
fof(f1586,plain,
! [X0,X1,X2] :
( aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtmndt0(xS,xx)),xS)
| sK2_skl(sdtpldt0(X0,X1),X2,sdtmndt0(xS,xx)) = X2
| sdtpldt0(X0,X1) = sdtpldt0(sdtmndt0(xS,xx),X2)
| ~ aElement0(X2)
| ~ aSet0(sdtmndt0(xS,xx))
| sK2_skl(sdtpldt0(X0,X1),X2,sdtmndt0(xS,xx)) = X1
| aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtmndt0(xS,xx)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f428,f92]) ).
fof(f1587,plain,
! [X0,X1,X2] :
( aElement0(sK2_skl(sdtpldt0(X0,X1),X2,sdtmndt0(xS,xx)))
| sK2_skl(sdtpldt0(X0,X1),X2,sdtmndt0(xS,xx)) = X2
| sdtpldt0(X0,X1) = sdtpldt0(sdtmndt0(xS,xx),X2)
| ~ aElement0(X2)
| ~ aSet0(sdtmndt0(xS,xx))
| sK2_skl(sdtpldt0(X0,X1),X2,sdtmndt0(xS,xx)) = X1
| aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtmndt0(xS,xx)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f428,f91]) ).
fof(f1589,plain,
! [X0,X1,X2] :
( sK2_skl(sdtpldt0(X0,X1),X2,slcrc0) = X2
| sdtpldt0(X0,X1) = sdtpldt0(slcrc0,X2)
| ~ aElement0(X2)
| ~ aSet0(slcrc0)
| sK2_skl(sdtpldt0(X0,X1),X2,slcrc0) = X1
| aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,slcrc0),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f428,f108]) ).
fof(f1592,definition,
! [X0,X1,X2] :
( sQ137_spl
<=> ( aElement0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)))
| sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)) = X2
| sdtpldt0(X0,X1) = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X2)
| ~ aElement0(X2)
| sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)) = X1
| aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f1595,plain,
( ~ sQ19_spl
| sQ137_spl ),
inference(split_clause,[status(thm)],[f1582,f1592,f243]) ).
fof(f1596,definition,
! [X0,X1,X2] :
( sQ138_spl
<=> ( sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx))
| sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)) = X2
| sdtpldt0(X0,X1) = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X2)
| ~ aElement0(X2)
| sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)) = X1
| aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f1599,plain,
( ~ sQ19_spl
| sQ138_spl ),
inference(split_clause,[status(thm)],[f1583,f1596,f243]) ).
fof(f1602,definition,
! [X0,X1,X2] :
( sQ139_spl
<=> ( aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtmndt0(xS,xx)),xS)
| sK2_skl(sdtpldt0(X0,X1),X2,sdtmndt0(xS,xx)) = X2
| sdtpldt0(X0,X1) = sdtpldt0(sdtmndt0(xS,xx),X2)
| ~ aElement0(X2)
| sK2_skl(sdtpldt0(X0,X1),X2,sdtmndt0(xS,xx)) = X1
| aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtmndt0(xS,xx)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f1605,plain,
( ~ sQ5_spl
| sQ139_spl ),
inference(split_clause,[status(thm)],[f1586,f1602,f148]) ).
fof(f1606,definition,
! [X0,X1,X2] :
( sQ140_spl
<=> ( aElement0(sK2_skl(sdtpldt0(X0,X1),X2,sdtmndt0(xS,xx)))
| sK2_skl(sdtpldt0(X0,X1),X2,sdtmndt0(xS,xx)) = X2
| sdtpldt0(X0,X1) = sdtpldt0(sdtmndt0(xS,xx),X2)
| ~ aElement0(X2)
| sK2_skl(sdtpldt0(X0,X1),X2,sdtmndt0(xS,xx)) = X1
| aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtmndt0(xS,xx)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f1609,plain,
( ~ sQ5_spl
| sQ140_spl ),
inference(split_clause,[status(thm)],[f1587,f1606,f148]) ).
fof(f1611,definition,
! [X0,X1,X2] :
( sQ141_spl
<=> ( sK2_skl(sdtpldt0(X0,X1),X2,slcrc0) = X2
| sdtpldt0(X0,X1) = sdtpldt0(slcrc0,X2)
| ~ aElement0(X2)
| sK2_skl(sdtpldt0(X0,X1),X2,slcrc0) = X1
| aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,slcrc0),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f1614,plain,
( ~ sQ3_spl
| sQ141_spl ),
inference(split_clause,[status(thm)],[f1589,f1611,f140]) ).
fof(f1619,plain,
! [X0] :
( ~ sQ84_spl
| ~ aElementOf0(sK2_skl(slcrc0,X0,slcrc0),slcrc0)
| ~ aSet0(slcrc0)
| slcrc0 = sdtpldt0(slcrc0,X0)
| ~ aElement0(X0)
| ~ aSet0(slcrc0)
| slcrc0 = sdtpldt0(slcrc0,X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f809,f352]) ).
fof(f1620,definition,
! [X0] :
( sQ142_spl
<=> ( ~ aElementOf0(sK2_skl(slcrc0,X0,slcrc0),slcrc0)
| slcrc0 = sdtpldt0(slcrc0,X0)
| ~ aElement0(X0)
| slcrc0 = sdtpldt0(slcrc0,X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f1623,plain,
( ~ sQ84_spl
| ~ sQ3_spl
| sQ142_spl ),
inference(split_clause,[status(thm)],[f1619,f1620,f140,f808]) ).
fof(f1628,plain,
! [X0] :
( ~ sQ106_spl
| aSubsetOf0(sdtmndt0(xS,xx),X0)
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aSet0(X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f1117,f270]) ).
fof(f1629,plain,
( ~ sQ106_spl
| sdtmndt0(xS,xx) = sdtpldt0(sdtmndt0(xS,xx),xx)
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtmndt0(xS,xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f1117,f266]) ).
fof(f1631,plain,
! [X0] :
( ~ sQ106_spl
| aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f1117,f50]) ).
fof(f1636,definition,
! [X0] :
( sQ144_spl
<=> ( aSubsetOf0(sdtmndt0(xS,xx),X0)
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f1637,plain,
! [X0] :
( ~ sQ144_spl
| aSubsetOf0(sdtmndt0(xS,xx),X0)
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f1636]) ).
fof(f1639,plain,
( ~ sQ106_spl
| sQ144_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1628,f243,f1636,f1116]) ).
fof(f1640,definition,
( sQ145_spl
<=> sdtmndt0(xS,xx) = sdtpldt0(sdtmndt0(xS,xx),xx) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f1641,plain,
( ~ sQ145_spl
| sdtmndt0(xS,xx) = sdtpldt0(sdtmndt0(xS,xx),xx) ),
inference(component_clause,[status(thm)],[f1640]) ).
fof(f1643,plain,
( ~ sQ106_spl
| sQ145_spl
| ~ sQ101_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1629,f243,f1092,f1640,f1116]) ).
fof(f1645,definition,
! [X0] :
( sQ146_spl
<=> ( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f1648,plain,
( ~ sQ106_spl
| sQ146_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1631,f243,f1645,f1116]) ).
fof(f1660,plain,
! [X0,X1] :
( aElement0(sK1_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1))
| aSubsetOf0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1)
| ~ aSet0(X1)
| sK1_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1) = X0
| ~ aElement0(X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f430,f96]) ).
fof(f1661,plain,
! [X0,X1] :
( sK1_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1) = xx
| aElementOf0(sK1_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1),sdtmndt0(xS,xx))
| aSubsetOf0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1)
| ~ aSet0(X1)
| sK1_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1) = X0
| ~ aElement0(X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f430,f97]) ).
fof(f1664,plain,
! [X0,X1] :
( aElementOf0(sK1_skl(sdtpldt0(sdtmndt0(xS,xx),X0),X1),xS)
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),X0),X1)
| ~ aSet0(X1)
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),X0),X1) = X0
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f430,f92]) ).
fof(f1665,plain,
! [X0,X1] :
( aElement0(sK1_skl(sdtpldt0(sdtmndt0(xS,xx),X0),X1))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),X0),X1)
| ~ aSet0(X1)
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),X0),X1) = X0
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f430,f91]) ).
fof(f1667,plain,
! [X0,X1] :
( aSubsetOf0(sdtpldt0(slcrc0,X0),X1)
| ~ aSet0(X1)
| sK1_skl(sdtpldt0(slcrc0,X0),X1) = X0
| ~ aElement0(X0)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f430,f108]) ).
fof(f1673,definition,
! [X0,X1] :
( sQ148_spl
<=> ( aElement0(sK1_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1))
| aSubsetOf0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1)
| ~ aSet0(X1)
| sK1_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1) = X0
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f1676,plain,
( sQ148_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1660,f243,f1673]) ).
fof(f1677,definition,
! [X0,X1] :
( sQ149_spl
<=> ( sK1_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1) = xx
| aElementOf0(sK1_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1),sdtmndt0(xS,xx))
| aSubsetOf0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1)
| ~ aSet0(X1)
| sK1_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1) = X0
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f1680,plain,
( sQ149_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1661,f243,f1677]) ).
fof(f1683,definition,
! [X0,X1] :
( sQ150_spl
<=> ( aElementOf0(sK1_skl(sdtpldt0(sdtmndt0(xS,xx),X0),X1),xS)
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),X0),X1)
| ~ aSet0(X1)
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),X0),X1) = X0
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ150_spl])],[split_symbol_definition]) ).
fof(f1686,plain,
( sQ150_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1664,f148,f1683]) ).
fof(f1687,definition,
! [X0,X1] :
( sQ151_spl
<=> ( aElement0(sK1_skl(sdtpldt0(sdtmndt0(xS,xx),X0),X1))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),X0),X1)
| ~ aSet0(X1)
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),X0),X1) = X0
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f1690,plain,
( sQ151_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1665,f148,f1687]) ).
fof(f1692,definition,
! [X0,X1] :
( sQ152_spl
<=> ( aSubsetOf0(sdtpldt0(slcrc0,X0),X1)
| ~ aSet0(X1)
| sK1_skl(sdtpldt0(slcrc0,X0),X1) = X0
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f1695,plain,
( sQ152_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1667,f140,f1692]) ).
fof(f1709,plain,
( ~ sQ1_spl
| ~ sQ145_spl
| aElementOf0(xx,sdtmndt0(xS,xx)) ),
inference(backward_demodulation,[status(thm)],[f1641,f297]) ).
fof(f1732,plain,
( ~ sQ1_spl
| ~ sQ145_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f1709,f300,f1640,f126]) ).
fof(f1857,plain,
! [X0,X1,X2] :
( aElementOf0(sK1_skl(sdtmndt0(X0,X1),X2),X0)
| aSubsetOf0(sdtmndt0(X0,X1),X2)
| ~ aSet0(X2)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f465,f104]) ).
fof(f1871,plain,
! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aSet0(sdtpldt0(X0,X1))
| aSubsetOf0(X0,sdtpldt0(sdtpldt0(X0,X1),X2))
| ~ aSet0(sdtpldt0(sdtpldt0(X0,X1),X2))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f714,f697]) ).
fof(f1873,plain,
! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aSet0(sdtpldt0(X0,X1))
| aSubsetOf0(X0,sdtpldt0(sdtpldt0(X0,X1),X2))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1871,f110]) ).
fof(f1879,plain,
( ~ sQ100_spl
| aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(paramodulation,[status(thm)],[f1090,f51]) ).
fof(f1884,definition,
( sQ159_spl
<=> aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f1887,plain,
( ~ sQ100_spl
| sQ159_spl
| ~ sQ19_spl
| sQ101_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1879,f148,f1092,f243,f1884,f1089]) ).
fof(f1890,plain,
! [X0,X1,X2] :
( ~ sQ89_spl
| aSubsetOf0(sdtmndt0(xS,xx),X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ),
inference(resolution,[status(thm)],[f1168,f270]) ).
fof(f1893,plain,
! [X0,X1,X2] :
( ~ sQ89_spl
| aElementOf0(X2,X1)
| ~ aElementOf0(X2,sdtmndt0(xS,xx))
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ),
inference(resolution,[status(thm)],[f1168,f50]) ).
fof(f1902,plain,
! [X0,X1,X2] :
( ~ sQ89_spl
| aSubsetOf0(sdtmndt0(xS,xx),X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1890]) ).
fof(f1903,plain,
! [X0,X1,X2] :
( ~ sQ89_spl
| aSubsetOf0(sdtmndt0(xS,xx),X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(xS,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1902,f49]) ).
fof(f1905,definition,
! [X0,X1] :
( sQ162_spl
<=> ( ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition]) ).
fof(f1906,plain,
! [X0,X1] :
( ~ sQ162_spl
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ),
inference(component_clause,[status(thm)],[f1905]) ).
fof(f1909,plain,
! [X0,X1,X2] :
( ~ sQ89_spl
| aElementOf0(X2,X1)
| ~ aElementOf0(X2,sdtmndt0(xS,xx))
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1893]) ).
fof(f1930,plain,
! [X0,X1,X2,X3] :
( ~ sQ89_spl
| sK2_skl(sdtpldt0(X1,X2),X3,sdtmndt0(xS,xx)) = X3
| sdtpldt0(X1,X2) = sdtpldt0(sdtmndt0(xS,xx),X3)
| ~ aElement0(X3)
| ~ aSet0(sdtmndt0(xS,xx))
| sK2_skl(sdtpldt0(X1,X2),X3,sdtmndt0(xS,xx)) = X2
| aElementOf0(sK2_skl(sdtpldt0(X1,X2),X3,sdtmndt0(xS,xx)),X1)
| ~ aElement0(X2)
| ~ aSet0(X1)
| aElementOf0(sK2_skl(sdtpldt0(X1,X2),X3,sdtmndt0(xS,xx)),X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f1174,f428]) ).
fof(f1931,plain,
! [X0,X1] :
( ~ sQ34_spl
| ~ sQ89_spl
| sK2_skl(slcrc0,X1,sdtmndt0(xS,xx)) = X1
| slcrc0 = sdtpldt0(sdtmndt0(xS,xx),X1)
| ~ aElement0(X1)
| ~ aSet0(sdtmndt0(xS,xx))
| aElementOf0(sK2_skl(slcrc0,X1,sdtmndt0(xS,xx)),X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f1174,f368]) ).
fof(f1932,plain,
! [X0,X1,X2] :
( ~ sQ89_spl
| sK2_skl(sdtmndt0(xS,xx),X1,X2) = X1
| aElementOf0(sK2_skl(sdtmndt0(xS,xx),X1,X2),X2)
| ~ aSet0(sdtmndt0(xS,xx))
| sdtmndt0(xS,xx) = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aSet0(X2)
| aElementOf0(sK2_skl(sdtmndt0(xS,xx),X1,X2),X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f1174,f73]) ).
fof(f1934,plain,
! [X0,X1] :
( ~ sQ89_spl
| sdtpldt0(sdtmndt0(xS,xx),X1) = slcrc0
| sK0_skl(sdtpldt0(sdtmndt0(xS,xx),X1)) = X1
| ~ aElement0(X1)
| ~ aSet0(sdtmndt0(xS,xx))
| aElementOf0(sK0_skl(sdtpldt0(sdtmndt0(xS,xx),X1)),X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f1174,f179]) ).
fof(f1935,plain,
! [X0,X1] :
( ~ sQ89_spl
| sdtmndt0(sdtmndt0(xS,xx),X1) = slcrc0
| ~ aElement0(X1)
| ~ aSet0(sdtmndt0(xS,xx))
| aElementOf0(sK0_skl(sdtmndt0(sdtmndt0(xS,xx),X1)),X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f1174,f585]) ).
fof(f1937,plain,
! [X0,X1,X2] :
( ~ sQ89_spl
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),X1),X2)
| ~ aSet0(X2)
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),X1),X2) = X1
| ~ aElement0(X1)
| ~ aSet0(sdtmndt0(xS,xx))
| aElementOf0(sK1_skl(sdtpldt0(sdtmndt0(xS,xx),X1),X2),X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f1174,f430]) ).
fof(f1938,plain,
! [X0,X1] :
( ~ sQ89_spl
| ~ aSet0(sdtmndt0(xS,xx))
| aSubsetOf0(sdtmndt0(xS,xx),X1)
| ~ aSet0(X1)
| aElementOf0(sK1_skl(sdtmndt0(xS,xx),X1),X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f1174,f51]) ).
fof(f1940,plain,
! [X0,X1] :
( ~ sQ89_spl
| ~ sP0_prd(X1,xx,xS)
| ~ aElement0(xx)
| ~ aSet0(xS)
| aElementOf0(X1,X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f1174,f118]) ).
fof(f1941,definition,
! [X0,X1,X2,X3] :
( sQ164_spl
<=> ( sK2_skl(sdtpldt0(X1,X2),X3,sdtmndt0(xS,xx)) = X3
| sdtpldt0(X1,X2) = sdtpldt0(sdtmndt0(xS,xx),X3)
| ~ aElement0(X3)
| sK2_skl(sdtpldt0(X1,X2),X3,sdtmndt0(xS,xx)) = X2
| aElementOf0(sK2_skl(sdtpldt0(X1,X2),X3,sdtmndt0(xS,xx)),X1)
| ~ aElement0(X2)
| ~ aSet0(X1)
| aElementOf0(sK2_skl(sdtpldt0(X1,X2),X3,sdtmndt0(xS,xx)),X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f1944,plain,
( ~ sQ89_spl
| ~ sQ5_spl
| sQ164_spl ),
inference(split_clause,[status(thm)],[f1930,f1941,f148,f841]) ).
fof(f1945,definition,
! [X0,X1] :
( sQ165_spl
<=> ( sK2_skl(slcrc0,X1,sdtmndt0(xS,xx)) = X1
| slcrc0 = sdtpldt0(sdtmndt0(xS,xx),X1)
| ~ aElement0(X1)
| aElementOf0(sK2_skl(slcrc0,X1,sdtmndt0(xS,xx)),X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ165_spl])],[split_symbol_definition]) ).
fof(f1948,plain,
( ~ sQ34_spl
| ~ sQ89_spl
| ~ sQ5_spl
| sQ165_spl ),
inference(split_clause,[status(thm)],[f1931,f1945,f148,f841,f367]) ).
fof(f1949,definition,
! [X0,X1,X2] :
( sQ166_spl
<=> ( sK2_skl(sdtmndt0(xS,xx),X1,X2) = X1
| aElementOf0(sK2_skl(sdtmndt0(xS,xx),X1,X2),X2)
| sdtmndt0(xS,xx) = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aSet0(X2)
| aElementOf0(sK2_skl(sdtmndt0(xS,xx),X1,X2),X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ166_spl])],[split_symbol_definition]) ).
fof(f1952,plain,
( ~ sQ89_spl
| ~ sQ5_spl
| sQ166_spl ),
inference(split_clause,[status(thm)],[f1932,f1949,f148,f841]) ).
fof(f1953,definition,
! [X0,X1] :
( sQ167_spl
<=> ( sdtpldt0(sdtmndt0(xS,xx),X1) = slcrc0
| sK0_skl(sdtpldt0(sdtmndt0(xS,xx),X1)) = X1
| ~ aElement0(X1)
| aElementOf0(sK0_skl(sdtpldt0(sdtmndt0(xS,xx),X1)),X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f1956,plain,
( ~ sQ89_spl
| ~ sQ5_spl
| sQ167_spl ),
inference(split_clause,[status(thm)],[f1934,f1953,f148,f841]) ).
fof(f1957,definition,
! [X0,X1] :
( sQ168_spl
<=> ( sdtmndt0(sdtmndt0(xS,xx),X1) = slcrc0
| ~ aElement0(X1)
| aElementOf0(sK0_skl(sdtmndt0(sdtmndt0(xS,xx),X1)),X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f1960,plain,
( ~ sQ89_spl
| ~ sQ5_spl
| sQ168_spl ),
inference(split_clause,[status(thm)],[f1935,f1957,f148,f841]) ).
fof(f1965,definition,
! [X0,X1,X2] :
( sQ170_spl
<=> ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),X1),X2)
| ~ aSet0(X2)
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),X1),X2) = X1
| ~ aElement0(X1)
| aElementOf0(sK1_skl(sdtpldt0(sdtmndt0(xS,xx),X1),X2),X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f1968,plain,
( ~ sQ89_spl
| ~ sQ5_spl
| sQ170_spl ),
inference(split_clause,[status(thm)],[f1937,f1965,f148,f841]) ).
fof(f1969,definition,
! [X0,X1] :
( sQ171_spl
<=> ( aSubsetOf0(sdtmndt0(xS,xx),X1)
| ~ aSet0(X1)
| aElementOf0(sK1_skl(sdtmndt0(xS,xx),X1),X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f1972,plain,
( ~ sQ89_spl
| ~ sQ5_spl
| sQ171_spl ),
inference(split_clause,[status(thm)],[f1938,f1969,f148,f841]) ).
fof(f1973,definition,
! [X0,X1] :
( sQ172_spl
<=> ( ~ sP0_prd(X1,xx,xS)
| aElementOf0(X1,X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition]) ).
fof(f1974,plain,
! [X0,X1] :
( ~ sQ172_spl
| ~ sP0_prd(X1,xx,xS)
| aElementOf0(X1,X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f1973]) ).
fof(f1976,plain,
( ~ sQ89_spl
| ~ sQ1_spl
| ~ sQ0_spl
| sQ172_spl ),
inference(split_clause,[status(thm)],[f1940,f1973,f123,f126,f841]) ).
fof(f1979,plain,
! [X0,X1] :
( ~ sQ172_spl
| aElementOf0(sK3_skl(X1,xx,xS),X1)
| ~ aSet0(X1)
| X1 = sdtmndt0(xS,xx)
| ~ aElement0(xx)
| ~ aSet0(xS)
| aElementOf0(sK3_skl(X1,xx,xS),X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f1974,f84]) ).
fof(f1985,definition,
! [X0,X1] :
( sQ173_spl
<=> ( aElementOf0(sK3_skl(X1,xx,xS),X1)
| ~ aSet0(X1)
| X1 = sdtmndt0(xS,xx)
| aElementOf0(sK3_skl(X1,xx,xS),X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ173_spl])],[split_symbol_definition]) ).
fof(f1988,plain,
( ~ sQ172_spl
| ~ sQ1_spl
| ~ sQ0_spl
| sQ173_spl ),
inference(split_clause,[status(thm)],[f1979,f1985,f123,f126,f1973]) ).
fof(f2000,definition,
( sQ174_spl
<=> aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition]) ).
fof(f2019,plain,
! [X0] :
( ~ sQ114_spl
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1171]) ).
fof(f2020,plain,
! [X0,X1] :
( ~ aElementOf0(sK3_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),sdtmndt0(xS,xx))
| sK3_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0) = X1
| ~ aElementOf0(sK3_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f492,f343]) ).
fof(f2022,plain,
! [X0,X1] :
( sK3_skl(sdtmndt0(xS,xx),X1,X0) = xx
| ~ aElementOf0(sK3_skl(sdtmndt0(xS,xx),X1,X0),xS)
| ~ aElement0(sK3_skl(sdtmndt0(xS,xx),X1,X0))
| sK3_skl(sdtmndt0(xS,xx),X1,X0) = X1
| ~ aElementOf0(sK3_skl(sdtmndt0(xS,xx),X1,X0),X0)
| ~ aSet0(sdtmndt0(xS,xx))
| sdtmndt0(xS,xx) = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f492,f94]) ).
fof(f2024,definition,
! [X0,X1] :
( sQ177_spl
<=> ( ~ aElementOf0(sK3_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),sdtmndt0(xS,xx))
| sK3_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0) = X1
| ~ aElementOf0(sK3_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),X0)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f2027,plain,
( ~ sQ19_spl
| sQ177_spl ),
inference(split_clause,[status(thm)],[f2020,f2024,f243]) ).
fof(f2029,definition,
! [X0,X1] :
( sQ178_spl
<=> ( sK3_skl(sdtmndt0(xS,xx),X1,X0) = xx
| ~ aElementOf0(sK3_skl(sdtmndt0(xS,xx),X1,X0),xS)
| ~ aElement0(sK3_skl(sdtmndt0(xS,xx),X1,X0))
| sK3_skl(sdtmndt0(xS,xx),X1,X0) = X1
| ~ aElementOf0(sK3_skl(sdtmndt0(xS,xx),X1,X0),X0)
| sdtmndt0(xS,xx) = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f2032,plain,
( ~ sQ5_spl
| sQ178_spl ),
inference(split_clause,[status(thm)],[f2022,f2029,f148]) ).
fof(f2035,plain,
! [X0] :
( ~ sQ48_spl
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),X0),sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),X0),sdtpldt0(sdtmndt0(xS,xx),xx)) = X0
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),X0))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),X0),sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f521,f430]) ).
fof(f2039,definition,
! [X0] :
( sQ179_spl
<=> ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),X0),sdtpldt0(sdtmndt0(xS,xx),xx))
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),X0),sdtpldt0(sdtmndt0(xS,xx),xx)) = X0
| ~ aElement0(X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),X0))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),X0),sdtpldt0(sdtmndt0(xS,xx),xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f2042,plain,
( ~ sQ48_spl
| ~ sQ19_spl
| ~ sQ5_spl
| sQ179_spl ),
inference(split_clause,[status(thm)],[f2035,f2039,f148,f243,f520]) ).
fof(f2047,plain,
! [X0,X1] :
( sK3_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0) = xx
| aElementOf0(sK3_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),sdtmndt0(xS,xx))
| aElementOf0(sK3_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f620,f97]) ).
fof(f2048,plain,
! [X0,X1] :
( aElement0(sK3_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0))
| aElementOf0(sK3_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f620,f96]) ).
fof(f2051,plain,
! [X0,X1,X2] :
( ~ sQ89_spl
| aElementOf0(sK3_skl(sdtmndt0(xS,xx),X1,X0),X2)
| ~ aSubsetOf0(xS,X2)
| ~ aSet0(X2)
| aElementOf0(sK3_skl(sdtmndt0(xS,xx),X1,X0),X0)
| ~ aSet0(sdtmndt0(xS,xx))
| sdtmndt0(xS,xx) = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f620,f1174]) ).
fof(f2052,plain,
! [X0,X1] :
( aElementOf0(sK3_skl(sdtmndt0(xS,xx),X1,X0),xS)
| aElementOf0(sK3_skl(sdtmndt0(xS,xx),X1,X0),X0)
| ~ aSet0(sdtmndt0(xS,xx))
| sdtmndt0(xS,xx) = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f620,f92]) ).
fof(f2053,plain,
! [X0,X1] :
( aElement0(sK3_skl(sdtmndt0(xS,xx),X1,X0))
| aElementOf0(sK3_skl(sdtmndt0(xS,xx),X1,X0),X0)
| ~ aSet0(sdtmndt0(xS,xx))
| sdtmndt0(xS,xx) = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f620,f91]) ).
fof(f2055,plain,
! [X0,X1] :
( aElementOf0(sK3_skl(slcrc0,X1,X0),X0)
| ~ aSet0(slcrc0)
| slcrc0 = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f620,f108]) ).
fof(f2057,definition,
! [X0,X1] :
( sQ180_spl
<=> ( sK3_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0) = xx
| aElementOf0(sK3_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),sdtmndt0(xS,xx))
| aElementOf0(sK3_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),X0)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f2060,plain,
( ~ sQ19_spl
| sQ180_spl ),
inference(split_clause,[status(thm)],[f2047,f2057,f243]) ).
fof(f2061,definition,
! [X0,X1] :
( sQ181_spl
<=> ( aElement0(sK3_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0))
| aElementOf0(sK3_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),X0)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f2064,plain,
( ~ sQ19_spl
| sQ181_spl ),
inference(split_clause,[status(thm)],[f2048,f2061,f243]) ).
fof(f2066,definition,
! [X0,X1,X2] :
( sQ182_spl
<=> ( aElementOf0(sK3_skl(sdtmndt0(xS,xx),X1,X0),X2)
| ~ aSubsetOf0(xS,X2)
| ~ aSet0(X2)
| aElementOf0(sK3_skl(sdtmndt0(xS,xx),X1,X0),X0)
| sdtmndt0(xS,xx) = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ182_spl])],[split_symbol_definition]) ).
fof(f2069,plain,
( ~ sQ89_spl
| ~ sQ5_spl
| sQ182_spl ),
inference(split_clause,[status(thm)],[f2051,f2066,f148,f841]) ).
fof(f2070,definition,
! [X0,X1] :
( sQ183_spl
<=> ( aElementOf0(sK3_skl(sdtmndt0(xS,xx),X1,X0),xS)
| aElementOf0(sK3_skl(sdtmndt0(xS,xx),X1,X0),X0)
| sdtmndt0(xS,xx) = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f2073,plain,
( ~ sQ5_spl
| sQ183_spl ),
inference(split_clause,[status(thm)],[f2052,f2070,f148]) ).
fof(f2074,definition,
! [X0,X1] :
( sQ184_spl
<=> ( aElement0(sK3_skl(sdtmndt0(xS,xx),X1,X0))
| aElementOf0(sK3_skl(sdtmndt0(xS,xx),X1,X0),X0)
| sdtmndt0(xS,xx) = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ184_spl])],[split_symbol_definition]) ).
fof(f2077,plain,
( ~ sQ5_spl
| sQ184_spl ),
inference(split_clause,[status(thm)],[f2053,f2074,f148]) ).
fof(f2079,definition,
! [X0,X1] :
( sQ185_spl
<=> ( aElementOf0(sK3_skl(slcrc0,X1,X0),X0)
| slcrc0 = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ185_spl])],[split_symbol_definition]) ).
fof(f2080,plain,
! [X0,X1] :
( ~ sQ185_spl
| aElementOf0(sK3_skl(slcrc0,X1,X0),X0)
| slcrc0 = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f2079]) ).
fof(f2082,plain,
( ~ sQ3_spl
| sQ185_spl ),
inference(split_clause,[status(thm)],[f2055,f2079,f140]) ).
fof(f2087,plain,
( ~ sQ114_spl
| ~ aSet0(xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f2019,f56]) ).
fof(f2092,plain,
( ~ sQ114_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f2087,f123,f1170]) ).
fof(f2167,plain,
! [X0] :
( ~ sQ185_spl
| sK3_skl(slcrc0,X0,slcrc0) = X0
| ~ aElementOf0(sK3_skl(slcrc0,X0,slcrc0),slcrc0)
| ~ aSet0(slcrc0)
| slcrc0 = sdtmndt0(slcrc0,X0)
| ~ aElement0(X0)
| ~ aSet0(slcrc0)
| slcrc0 = sdtmndt0(slcrc0,X0)
| ~ aElement0(X0)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f2080,f492]) ).
fof(f2168,plain,
! [X0] :
( ~ sQ185_spl
| sK3_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| aElementOf0(sK3_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx))
| slcrc0 = sdtmndt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aElement0(X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f2080,f97]) ).
fof(f2169,plain,
! [X0] :
( ~ sQ185_spl
| aElement0(sK3_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)))
| slcrc0 = sdtmndt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aElement0(X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f2080,f96]) ).
fof(f2172,plain,
! [X0,X1] :
( ~ sQ89_spl
| ~ sQ185_spl
| aElementOf0(sK3_skl(slcrc0,X0,sdtmndt0(xS,xx)),X1)
| ~ aSubsetOf0(xS,X1)
| ~ aSet0(X1)
| slcrc0 = sdtmndt0(sdtmndt0(xS,xx),X0)
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f2080,f1579]) ).
fof(f2173,plain,
! [X0] :
( ~ sQ185_spl
| aElementOf0(sK3_skl(slcrc0,X0,sdtmndt0(xS,xx)),xS)
| slcrc0 = sdtmndt0(sdtmndt0(xS,xx),X0)
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f2080,f92]) ).
fof(f2174,plain,
! [X0] :
( ~ sQ185_spl
| aElement0(sK3_skl(slcrc0,X0,sdtmndt0(xS,xx)))
| slcrc0 = sdtmndt0(sdtmndt0(xS,xx),X0)
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f2080,f91]) ).
fof(f2178,definition,
! [X0] :
( sQ187_spl
<=> ( sK3_skl(slcrc0,X0,slcrc0) = X0
| ~ aElementOf0(sK3_skl(slcrc0,X0,slcrc0),slcrc0)
| slcrc0 = sdtmndt0(slcrc0,X0)
| ~ aElement0(X0)
| slcrc0 = sdtmndt0(slcrc0,X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ187_spl])],[split_symbol_definition]) ).
fof(f2181,plain,
( ~ sQ185_spl
| sQ187_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2167,f140,f2178,f2079]) ).
fof(f2182,definition,
! [X0] :
( sQ188_spl
<=> ( sK3_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| aElementOf0(sK3_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx))
| slcrc0 = sdtmndt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ188_spl])],[split_symbol_definition]) ).
fof(f2185,plain,
( ~ sQ185_spl
| sQ188_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f2168,f243,f2182,f2079]) ).
fof(f2186,definition,
! [X0] :
( sQ189_spl
<=> ( aElement0(sK3_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)))
| slcrc0 = sdtmndt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition]) ).
fof(f2189,plain,
( ~ sQ185_spl
| sQ189_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f2169,f243,f2186,f2079]) ).
fof(f2192,definition,
! [X0,X1] :
( sQ190_spl
<=> ( aElementOf0(sK3_skl(slcrc0,X0,sdtmndt0(xS,xx)),X1)
| ~ aSubsetOf0(xS,X1)
| ~ aSet0(X1)
| slcrc0 = sdtmndt0(sdtmndt0(xS,xx),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ190_spl])],[split_symbol_definition]) ).
fof(f2195,plain,
( ~ sQ89_spl
| ~ sQ185_spl
| sQ190_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2172,f148,f2192,f2079,f841]) ).
fof(f2196,definition,
! [X0] :
( sQ191_spl
<=> ( aElementOf0(sK3_skl(slcrc0,X0,sdtmndt0(xS,xx)),xS)
| slcrc0 = sdtmndt0(sdtmndt0(xS,xx),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ191_spl])],[split_symbol_definition]) ).
fof(f2199,plain,
( ~ sQ185_spl
| sQ191_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2173,f148,f2196,f2079]) ).
fof(f2200,definition,
! [X0] :
( sQ192_spl
<=> ( aElement0(sK3_skl(slcrc0,X0,sdtmndt0(xS,xx)))
| slcrc0 = sdtmndt0(sdtmndt0(xS,xx),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ192_spl])],[split_symbol_definition]) ).
fof(f2203,plain,
( ~ sQ185_spl
| sQ192_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2174,f148,f2200,f2079]) ).
fof(f2210,plain,
! [X0] :
( ~ sQ16_spl
| aSubsetOf0(sdtpldt0(xS,X0),sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| sK1_skl(sdtpldt0(xS,X0),sdtmndt0(xS,xx)) = X0
| ~ aElement0(X0)
| ~ aSet0(xS)
| ~ aSet0(sdtpldt0(xS,X0))
| aSubsetOf0(sdtpldt0(xS,X0),sdtmndt0(xS,xx))
| sK1_skl(sdtpldt0(xS,X0),sdtmndt0(xS,xx)) = xx
| ~ aElement0(sK1_skl(sdtpldt0(xS,X0),sdtmndt0(xS,xx))) ),
inference(resolution,[status(thm)],[f227,f430]) ).
fof(f2215,definition,
! [X0] :
( sQ193_spl
<=> ( aSubsetOf0(sdtpldt0(xS,X0),sdtmndt0(xS,xx))
| sK1_skl(sdtpldt0(xS,X0),sdtmndt0(xS,xx)) = X0
| ~ aElement0(X0)
| ~ aSet0(sdtpldt0(xS,X0))
| aSubsetOf0(sdtpldt0(xS,X0),sdtmndt0(xS,xx))
| sK1_skl(sdtpldt0(xS,X0),sdtmndt0(xS,xx)) = xx
| ~ aElement0(sK1_skl(sdtpldt0(xS,X0),sdtmndt0(xS,xx))) ) ),
introduced(definition,[new_symbols(definition,[sQ193_spl])],[split_symbol_definition]) ).
fof(f2218,plain,
( ~ sQ16_spl
| ~ sQ5_spl
| ~ sQ0_spl
| sQ193_spl ),
inference(split_clause,[status(thm)],[f2210,f2215,f123,f148,f226]) ).
fof(f2239,plain,
! [X0] :
( ~ sQ104_spl
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aSet0(X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f1110,f270]) ).
fof(f2240,plain,
( ~ sQ104_spl
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(sdtmndt0(xS,xx),xx)
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f1110,f266]) ).
fof(f2242,plain,
! [X0] :
( ~ sQ104_spl
| aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f1110,f50]) ).
fof(f2245,definition,
! [X0] :
( sQ195_spl
<=> ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ195_spl])],[split_symbol_definition]) ).
fof(f2248,plain,
( ~ sQ104_spl
| sQ195_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f2239,f243,f2245,f1109]) ).
fof(f2249,definition,
( sQ196_spl
<=> sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(sdtmndt0(xS,xx),xx) ),
introduced(definition,[new_symbols(definition,[sQ196_spl])],[split_symbol_definition]) ).
fof(f2252,plain,
( sQ196_spl
| ~ sQ104_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f2240,f243,f1109,f2249]) ).
fof(f2254,definition,
! [X0] :
( sQ197_spl
<=> ( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ197_spl])],[split_symbol_definition]) ).
fof(f2257,plain,
( ~ sQ104_spl
| sQ197_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f2242,f243,f2254,f1109]) ).
fof(f2316,plain,
( sQ104_spl
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f1111,f56]) ).
fof(f2317,plain,
( sQ104_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f2316,f243,f1109]) ).
fof(f2351,plain,
! [X0,X1] :
( sK0_skl(sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1),X0)) = xx
| aElementOf0(sK0_skl(sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1),X0)),sdtmndt0(xS,xx))
| sK0_skl(sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1),X0)) = X1
| ~ aElement0(X1)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1),X0)) = X0
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f568,f97]) ).
fof(f2352,plain,
! [X0,X1] :
( aElement0(sK0_skl(sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1),X0)))
| sK0_skl(sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1),X0)) = X1
| ~ aElement0(X1)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1),X0)) = X0
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f568,f96]) ).
fof(f2355,plain,
! [X0,X1,X2] :
( ~ sQ89_spl
| aElementOf0(sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)),X2)
| ~ aSubsetOf0(xS,X2)
| ~ aSet0(X2)
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)) = X1
| ~ aElement0(X1)
| ~ aSet0(sdtmndt0(xS,xx))
| sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)) = X0
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f568,f1579]) ).
fof(f2356,plain,
! [X0,X1] :
( aElementOf0(sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)),xS)
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)) = X1
| ~ aElement0(X1)
| ~ aSet0(sdtmndt0(xS,xx))
| sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)) = X0
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f568,f92]) ).
fof(f2357,plain,
! [X0,X1] :
( aElement0(sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)))
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)) = X1
| ~ aElement0(X1)
| ~ aSet0(sdtmndt0(xS,xx))
| sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)) = X0
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f568,f91]) ).
fof(f2359,plain,
! [X0,X1] :
( sK0_skl(sdtpldt0(sdtpldt0(slcrc0,X1),X0)) = X1
| ~ aElement0(X1)
| ~ aSet0(slcrc0)
| sdtpldt0(sdtpldt0(slcrc0,X1),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtpldt0(slcrc0,X1),X0)) = X0
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f568,f108]) ).
fof(f2361,definition,
! [X0,X1] :
( sQ203_spl
<=> ( sK0_skl(sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1),X0)) = xx
| aElementOf0(sK0_skl(sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1),X0)),sdtmndt0(xS,xx))
| sK0_skl(sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1),X0)) = X1
| ~ aElement0(X1)
| sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1),X0)) = X0
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f2364,plain,
( ~ sQ19_spl
| sQ203_spl ),
inference(split_clause,[status(thm)],[f2351,f2361,f243]) ).
fof(f2365,definition,
! [X0,X1] :
( sQ204_spl
<=> ( aElement0(sK0_skl(sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1),X0)))
| sK0_skl(sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1),X0)) = X1
| ~ aElement0(X1)
| sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1),X0)) = X0
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f2368,plain,
( ~ sQ19_spl
| sQ204_spl ),
inference(split_clause,[status(thm)],[f2352,f2365,f243]) ).
fof(f2371,definition,
! [X0,X1,X2] :
( sQ205_spl
<=> ( aElementOf0(sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)),X2)
| ~ aSubsetOf0(xS,X2)
| ~ aSet0(X2)
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)) = X1
| ~ aElement0(X1)
| sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)) = X0
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ205_spl])],[split_symbol_definition]) ).
fof(f2374,plain,
( ~ sQ89_spl
| ~ sQ5_spl
| sQ205_spl ),
inference(split_clause,[status(thm)],[f2355,f2371,f148,f841]) ).
fof(f2375,definition,
! [X0,X1] :
( sQ206_spl
<=> ( aElementOf0(sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)),xS)
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)) = X1
| ~ aElement0(X1)
| sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)) = X0
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f2378,plain,
( ~ sQ5_spl
| sQ206_spl ),
inference(split_clause,[status(thm)],[f2356,f2375,f148]) ).
fof(f2379,definition,
! [X0,X1] :
( sQ207_spl
<=> ( aElement0(sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)))
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)) = X1
| ~ aElement0(X1)
| sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)) = X0
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f2382,plain,
( ~ sQ5_spl
| sQ207_spl ),
inference(split_clause,[status(thm)],[f2357,f2379,f148]) ).
fof(f2384,definition,
! [X0,X1] :
( sQ208_spl
<=> ( sK0_skl(sdtpldt0(sdtpldt0(slcrc0,X1),X0)) = X1
| ~ aElement0(X1)
| sdtpldt0(sdtpldt0(slcrc0,X1),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtpldt0(slcrc0,X1),X0)) = X0
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ208_spl])],[split_symbol_definition]) ).
fof(f2387,plain,
( ~ sQ3_spl
| sQ208_spl ),
inference(split_clause,[status(thm)],[f2359,f2384,f140]) ).
fof(f2390,plain,
! [X0] :
( ~ sQ144_spl
| ~ aElement0(X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| ~ aSet0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)) ),
inference(resolution,[status(thm)],[f1637,f697]) ).
fof(f2393,definition,
! [X0] :
( sQ209_spl
<=> ( ~ aElement0(X0)
| aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| ~ aSet0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f2396,plain,
( ~ sQ144_spl
| ~ sQ19_spl
| sQ209_spl ),
inference(split_clause,[status(thm)],[f2390,f2393,f243,f1636]) ).
fof(f2398,plain,
! [X0] :
( ~ sQ52_spl
| aElement0(sK0_skl(sdtpldt0(sdtmndt0(xS,xx),X0)))
| ~ aSet0(xS)
| sdtpldt0(sdtmndt0(xS,xx),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtmndt0(xS,xx),X0)) = X0
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f570,f28]) ).
fof(f2399,plain,
( ~ sQ52_spl
| ~ sQ0_spl
| sQ53_spl ),
inference(split_clause,[status(thm)],[f2398,f573,f123,f569]) ).
fof(f2400,plain,
! [X0,X1,X2] :
( ~ aElement0(X2)
| aSubsetOf0(X0,sdtpldt0(sdtpldt0(X0,X1),X2))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1873,f110]) ).
fof(f2402,plain,
! [X0,X1] :
( ~ sQ144_spl
| aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1))
| ~ aSet0(sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1))
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f2400,f1637]) ).
fof(f2410,definition,
! [X0,X1] :
( sQ210_spl
<=> ( aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1))
| ~ aSet0(sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f2413,plain,
( ~ sQ144_spl
| sQ210_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f2402,f243,f2410,f1636]) ).
fof(f2470,plain,
! [X0,X1,X2] :
( ~ sQ185_spl
| ~ sQ89_spl
| slcrc0 = sdtmndt0(sdtmndt0(xS,xx),X2)
| ~ aElement0(X2)
| ~ aSet0(sdtmndt0(xS,xx))
| aElementOf0(sK3_skl(slcrc0,X2,sdtmndt0(xS,xx)),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ),
inference(resolution,[status(thm)],[f1909,f2080]) ).
fof(f2471,plain,
! [X0,X1,X2,X3] :
( ~ sQ89_spl
| aElementOf0(sK3_skl(sdtmndt0(xS,xx),X2,X3),X3)
| ~ aSet0(sdtmndt0(xS,xx))
| sdtmndt0(xS,xx) = sdtmndt0(X3,X2)
| ~ aElement0(X2)
| ~ aSet0(X3)
| aElementOf0(sK3_skl(sdtmndt0(xS,xx),X2,X3),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ),
inference(resolution,[status(thm)],[f1909,f620]) ).
fof(f2473,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ89_spl
| sK2_skl(sdtpldt0(X2,X3),X4,sdtmndt0(xS,xx)) = X4
| sdtpldt0(X2,X3) = sdtpldt0(sdtmndt0(xS,xx),X4)
| ~ aElement0(X4)
| ~ aSet0(sdtmndt0(xS,xx))
| sK2_skl(sdtpldt0(X2,X3),X4,sdtmndt0(xS,xx)) = X3
| aElementOf0(sK2_skl(sdtpldt0(X2,X3),X4,sdtmndt0(xS,xx)),X2)
| ~ aElement0(X3)
| ~ aSet0(X2)
| aElementOf0(sK2_skl(sdtpldt0(X2,X3),X4,sdtmndt0(xS,xx)),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ),
inference(resolution,[status(thm)],[f1909,f428]) ).
fof(f2474,plain,
! [X0,X1,X2] :
( ~ sQ34_spl
| ~ sQ89_spl
| sK2_skl(slcrc0,X2,sdtmndt0(xS,xx)) = X2
| slcrc0 = sdtpldt0(sdtmndt0(xS,xx),X2)
| ~ aElement0(X2)
| ~ aSet0(sdtmndt0(xS,xx))
| aElementOf0(sK2_skl(slcrc0,X2,sdtmndt0(xS,xx)),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ),
inference(resolution,[status(thm)],[f1909,f368]) ).
fof(f2475,plain,
! [X0,X1,X2,X3] :
( ~ sQ89_spl
| sK2_skl(sdtmndt0(xS,xx),X2,X3) = X2
| aElementOf0(sK2_skl(sdtmndt0(xS,xx),X2,X3),X3)
| ~ aSet0(sdtmndt0(xS,xx))
| sdtmndt0(xS,xx) = sdtpldt0(X3,X2)
| ~ aElement0(X2)
| ~ aSet0(X3)
| aElementOf0(sK2_skl(sdtmndt0(xS,xx),X2,X3),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ),
inference(resolution,[status(thm)],[f1909,f73]) ).
fof(f2476,plain,
! [X0,X1,X2,X3] :
( ~ sQ89_spl
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X2),X3)) = X2
| ~ aElement0(X2)
| ~ aSet0(sdtmndt0(xS,xx))
| sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X2),X3) = slcrc0
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X2),X3)) = X3
| ~ aElement0(X3)
| aElementOf0(sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X2),X3)),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ),
inference(resolution,[status(thm)],[f1909,f568]) ).
fof(f2479,plain,
! [X0,X1,X2] :
( ~ sQ89_spl
| sdtpldt0(sdtmndt0(xS,xx),X2) = slcrc0
| sK0_skl(sdtpldt0(sdtmndt0(xS,xx),X2)) = X2
| ~ aElement0(X2)
| ~ aSet0(sdtmndt0(xS,xx))
| aElementOf0(sK0_skl(sdtpldt0(sdtmndt0(xS,xx),X2)),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ),
inference(resolution,[status(thm)],[f1909,f179]) ).
fof(f2481,plain,
! [X0,X1,X2] :
( ~ sQ89_spl
| sdtmndt0(sdtmndt0(xS,xx),X2) = slcrc0
| ~ aElement0(X2)
| ~ aSet0(sdtmndt0(xS,xx))
| aElementOf0(sK0_skl(sdtmndt0(sdtmndt0(xS,xx),X2)),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ),
inference(resolution,[status(thm)],[f1909,f585]) ).
fof(f2484,plain,
! [X0,X1,X2,X3] :
( ~ sQ89_spl
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),X2),X3)
| ~ aSet0(X3)
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),X2),X3) = X2
| ~ aElement0(X2)
| ~ aSet0(sdtmndt0(xS,xx))
| aElementOf0(sK1_skl(sdtpldt0(sdtmndt0(xS,xx),X2),X3),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ),
inference(resolution,[status(thm)],[f1909,f430]) ).
fof(f2485,plain,
! [X0,X1,X2] :
( ~ sQ89_spl
| ~ aSet0(sdtmndt0(xS,xx))
| aSubsetOf0(sdtmndt0(xS,xx),X2)
| ~ aSet0(X2)
| aElementOf0(sK1_skl(sdtmndt0(xS,xx),X2),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ),
inference(resolution,[status(thm)],[f1909,f51]) ).
fof(f2487,plain,
! [X0,X1,X2] :
( ~ sQ89_spl
| ~ sP0_prd(X2,xx,xS)
| ~ aElement0(xx)
| ~ aSet0(xS)
| aElementOf0(X2,X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ),
inference(resolution,[status(thm)],[f1909,f118]) ).
fof(f2488,definition,
! [X0,X1,X2] :
( sQ218_spl
<=> ( slcrc0 = sdtmndt0(sdtmndt0(xS,xx),X2)
| ~ aElement0(X2)
| aElementOf0(sK3_skl(slcrc0,X2,sdtmndt0(xS,xx)),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f2491,plain,
( ~ sQ185_spl
| ~ sQ89_spl
| ~ sQ5_spl
| sQ218_spl ),
inference(split_clause,[status(thm)],[f2470,f2488,f148,f841,f2079]) ).
fof(f2492,definition,
! [X0,X1,X2,X3] :
( sQ219_spl
<=> ( aElementOf0(sK3_skl(sdtmndt0(xS,xx),X2,X3),X3)
| sdtmndt0(xS,xx) = sdtmndt0(X3,X2)
| ~ aElement0(X2)
| ~ aSet0(X3)
| aElementOf0(sK3_skl(sdtmndt0(xS,xx),X2,X3),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ219_spl])],[split_symbol_definition]) ).
fof(f2495,plain,
( ~ sQ89_spl
| ~ sQ5_spl
| sQ219_spl ),
inference(split_clause,[status(thm)],[f2471,f2492,f148,f841]) ).
fof(f2496,definition,
! [X0,X1,X2,X3,X4] :
( sQ220_spl
<=> ( sK2_skl(sdtpldt0(X2,X3),X4,sdtmndt0(xS,xx)) = X4
| sdtpldt0(X2,X3) = sdtpldt0(sdtmndt0(xS,xx),X4)
| ~ aElement0(X4)
| sK2_skl(sdtpldt0(X2,X3),X4,sdtmndt0(xS,xx)) = X3
| aElementOf0(sK2_skl(sdtpldt0(X2,X3),X4,sdtmndt0(xS,xx)),X2)
| ~ aElement0(X3)
| ~ aSet0(X2)
| aElementOf0(sK2_skl(sdtpldt0(X2,X3),X4,sdtmndt0(xS,xx)),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ220_spl])],[split_symbol_definition]) ).
fof(f2499,plain,
( ~ sQ89_spl
| ~ sQ5_spl
| sQ220_spl ),
inference(split_clause,[status(thm)],[f2473,f2496,f148,f841]) ).
fof(f2500,definition,
! [X0,X1,X2] :
( sQ221_spl
<=> ( sK2_skl(slcrc0,X2,sdtmndt0(xS,xx)) = X2
| slcrc0 = sdtpldt0(sdtmndt0(xS,xx),X2)
| ~ aElement0(X2)
| aElementOf0(sK2_skl(slcrc0,X2,sdtmndt0(xS,xx)),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ221_spl])],[split_symbol_definition]) ).
fof(f2503,plain,
( ~ sQ34_spl
| ~ sQ89_spl
| ~ sQ5_spl
| sQ221_spl ),
inference(split_clause,[status(thm)],[f2474,f2500,f148,f841,f367]) ).
fof(f2504,definition,
! [X0,X1,X2,X3] :
( sQ222_spl
<=> ( sK2_skl(sdtmndt0(xS,xx),X2,X3) = X2
| aElementOf0(sK2_skl(sdtmndt0(xS,xx),X2,X3),X3)
| sdtmndt0(xS,xx) = sdtpldt0(X3,X2)
| ~ aElement0(X2)
| ~ aSet0(X3)
| aElementOf0(sK2_skl(sdtmndt0(xS,xx),X2,X3),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ222_spl])],[split_symbol_definition]) ).
fof(f2507,plain,
( ~ sQ89_spl
| ~ sQ5_spl
| sQ222_spl ),
inference(split_clause,[status(thm)],[f2475,f2504,f148,f841]) ).
fof(f2508,definition,
! [X0,X1,X2,X3] :
( sQ223_spl
<=> ( sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X2),X3)) = X2
| ~ aElement0(X2)
| sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X2),X3) = slcrc0
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X2),X3)) = X3
| ~ aElement0(X3)
| aElementOf0(sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X2),X3)),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ223_spl])],[split_symbol_definition]) ).
fof(f2511,plain,
( ~ sQ89_spl
| ~ sQ5_spl
| sQ223_spl ),
inference(split_clause,[status(thm)],[f2476,f2508,f148,f841]) ).
fof(f2516,definition,
! [X0,X1,X2] :
( sQ225_spl
<=> ( sdtpldt0(sdtmndt0(xS,xx),X2) = slcrc0
| sK0_skl(sdtpldt0(sdtmndt0(xS,xx),X2)) = X2
| ~ aElement0(X2)
| aElementOf0(sK0_skl(sdtpldt0(sdtmndt0(xS,xx),X2)),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition]) ).
fof(f2519,plain,
( ~ sQ89_spl
| ~ sQ5_spl
| sQ225_spl ),
inference(split_clause,[status(thm)],[f2479,f2516,f148,f841]) ).
fof(f2524,definition,
! [X0,X1,X2] :
( sQ227_spl
<=> ( sdtmndt0(sdtmndt0(xS,xx),X2) = slcrc0
| ~ aElement0(X2)
| aElementOf0(sK0_skl(sdtmndt0(sdtmndt0(xS,xx),X2)),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f2527,plain,
( ~ sQ89_spl
| ~ sQ5_spl
| sQ227_spl ),
inference(split_clause,[status(thm)],[f2481,f2524,f148,f841]) ).
fof(f2529,definition,
! [X0,X1,X2,X3] :
( sQ228_spl
<=> ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),X2),X3)
| ~ aSet0(X3)
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),X2),X3) = X2
| ~ aElement0(X2)
| aElementOf0(sK1_skl(sdtpldt0(sdtmndt0(xS,xx),X2),X3),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f2532,plain,
( ~ sQ89_spl
| ~ sQ5_spl
| sQ228_spl ),
inference(split_clause,[status(thm)],[f2484,f2529,f148,f841]) ).
fof(f2533,definition,
! [X0,X1,X2] :
( sQ229_spl
<=> ( aSubsetOf0(sdtmndt0(xS,xx),X2)
| ~ aSet0(X2)
| aElementOf0(sK1_skl(sdtmndt0(xS,xx),X2),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ229_spl])],[split_symbol_definition]) ).
fof(f2536,plain,
( ~ sQ89_spl
| ~ sQ5_spl
| sQ229_spl ),
inference(split_clause,[status(thm)],[f2485,f2533,f148,f841]) ).
fof(f2537,definition,
! [X0,X1,X2] :
( sQ230_spl
<=> ( ~ sP0_prd(X2,xx,xS)
| aElementOf0(X2,X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ230_spl])],[split_symbol_definition]) ).
fof(f2538,plain,
! [X0,X1,X2] :
( ~ sQ230_spl
| ~ sP0_prd(X2,xx,xS)
| aElementOf0(X2,X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ),
inference(component_clause,[status(thm)],[f2537]) ).
fof(f2540,plain,
( ~ sQ89_spl
| ~ sQ1_spl
| ~ sQ0_spl
| sQ230_spl ),
inference(split_clause,[status(thm)],[f2487,f2537,f123,f126,f841]) ).
fof(f2584,plain,
! [X0] :
( ~ sQ50_spl
| sP0_prd(sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)),xx,xS)
| ~ aElement0(xx)
| ~ aSet0(xS)
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)) = xx
| sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)) = X0
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f561,f117]) ).
fof(f2585,plain,
! [X0] :
( ~ sQ50_spl
| aElement0(sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)))
| ~ aSet0(sdtmndt0(xS,xx))
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)) = xx
| sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)) = X0
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f561,f28]) ).
fof(f2586,definition,
! [X0] :
( sQ233_spl
<=> ( sP0_prd(sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)),xx,xS)
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)) = xx
| sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)) = X0
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ233_spl])],[split_symbol_definition]) ).
fof(f2589,plain,
( ~ sQ50_spl
| ~ sQ1_spl
| ~ sQ0_spl
| sQ233_spl ),
inference(split_clause,[status(thm)],[f2584,f2586,f123,f126,f560]) ).
fof(f2590,definition,
! [X0] :
( sQ234_spl
<=> ( aElement0(sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)))
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)) = xx
| sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)) = X0
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f2593,plain,
( ~ sQ50_spl
| ~ sQ5_spl
| sQ234_spl ),
inference(split_clause,[status(thm)],[f2585,f2590,f148,f560]) ).
fof(f2594,plain,
! [X0,X1] :
( ~ sQ33_spl
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,sdtpldt0(sdtmndt0(xS,xx),X1)) = xx
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,sdtpldt0(sdtmndt0(xS,xx),X1)) = X0
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,sdtpldt0(sdtmndt0(xS,xx),X1)),sdtpldt0(sdtmndt0(xS,xx),X1))
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)
| ~ aElement0(X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),X1))
| ~ aElement0(X1)
| ~ aSet0(sdtmndt0(xS,xx))
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)
| ~ aElement0(X0)
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,sdtpldt0(sdtmndt0(xS,xx),X1)),sdtmndt0(xS,xx))
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f684,f364]) ).
fof(f2596,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X3)),sdtmndt0(xS,xx))
| ~ aElement0(X3)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| sdtpldt0(X0,X1) = sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X3),X2)
| ~ aElement0(X2)
| ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X3)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f684,f343]) ).
fof(f2598,plain,
! [X0,X1,X2,X3] :
( sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),X3)) = xx
| ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),X3)),xS)
| ~ aElement0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),X3)))
| ~ aElement0(X3)
| ~ aSet0(sdtmndt0(xS,xx))
| sdtpldt0(X0,X1) = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X3),X2)
| ~ aElement0(X2)
| ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),X3)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f684,f94]) ).
fof(f2600,definition,
! [X0,X1] :
( sQ235_spl
<=> ( sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,sdtpldt0(sdtmndt0(xS,xx),X1)) = xx
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,sdtpldt0(sdtmndt0(xS,xx),X1)) = X0
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,sdtpldt0(sdtmndt0(xS,xx),X1)),sdtpldt0(sdtmndt0(xS,xx),X1))
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)
| ~ aElement0(X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),X1))
| ~ aElement0(X1)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)
| ~ aElement0(X0)
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,sdtpldt0(sdtmndt0(xS,xx),X1)),sdtmndt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f2603,plain,
( ~ sQ33_spl
| sQ235_spl
| ~ sQ1_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2594,f148,f126,f2600,f363]) ).
fof(f2606,definition,
! [X0,X1,X2,X3] :
( sQ236_spl
<=> ( ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X3)),sdtmndt0(xS,xx))
| ~ aElement0(X3)
| sdtpldt0(X0,X1) = sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X3),X2)
| ~ aElement0(X2)
| ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X3)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ236_spl])],[split_symbol_definition]) ).
fof(f2609,plain,
( ~ sQ19_spl
| sQ236_spl ),
inference(split_clause,[status(thm)],[f2596,f2606,f243]) ).
fof(f2611,definition,
! [X0,X1,X2,X3] :
( sQ237_spl
<=> ( sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),X3)) = xx
| ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),X3)),xS)
| ~ aElement0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),X3)))
| ~ aElement0(X3)
| sdtpldt0(X0,X1) = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X3),X2)
| ~ aElement0(X2)
| ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),X3)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition]) ).
fof(f2614,plain,
( ~ sQ5_spl
| sQ237_spl ),
inference(split_clause,[status(thm)],[f2598,f2611,f148]) ).
fof(f2630,plain,
! [X0,X1] :
( ~ sQ162_spl
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1906]) ).
fof(f2633,plain,
! [X0] :
( ~ sQ162_spl
| ~ aSet0(xS)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f2630,f56]) ).
fof(f2642,definition,
! [X0] :
( sQ241_spl
<=> ( ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ241_spl])],[split_symbol_definition]) ).
fof(f2643,plain,
! [X0] :
( ~ sQ241_spl
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f2642]) ).
fof(f2645,plain,
( ~ sQ162_spl
| ~ sQ0_spl
| sQ241_spl ),
inference(split_clause,[status(thm)],[f2633,f2642,f123,f1905]) ).
fof(f2648,plain,
( ~ sQ241_spl
| ~ aSet0(xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f2643,f56]) ).
fof(f2654,plain,
( ~ sQ241_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f2648,f123,f2642]) ).
fof(f2827,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(sK2_skl(sdtpldt0(X2,X3),X1,X0),X2)
| ~ aElement0(X3)
| ~ aSet0(X2)
| ~ aElementOf0(sK2_skl(sdtpldt0(X2,X3),X1,X0),X0)
| ~ aSet0(sdtpldt0(X2,X3))
| sdtpldt0(X2,X3) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f274,f180]) ).
fof(f2831,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(sK2_skl(sdtpldt0(X2,X3),X1,X0),X2)
| ~ aElement0(X3)
| ~ aSet0(X2)
| ~ aElementOf0(sK2_skl(sdtpldt0(X2,X3),X1,X0),X0)
| sdtpldt0(X2,X3) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2827,f110]) ).
fof(f2835,plain,
! [X0] :
( ~ sQ89_spl
| sdtmndt0(xS,xx) = X0
| ~ aSubsetOf0(X0,sdtmndt0(xS,xx))
| ~ aSet0(X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f842,f266]) ).
fof(f2842,plain,
! [X0] :
( ~ sQ89_spl
| sdtmndt0(xS,xx) = X0
| ~ aSubsetOf0(X0,sdtmndt0(xS,xx))
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2835]) ).
fof(f3001,plain,
! [X0,X1,X2] :
( aElementOf0(sK1_skl(sdtmndt0(X0,X1),X2),X0)
| aSubsetOf0(sdtmndt0(X0,X1),X2)
| ~ aSet0(X2)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f465,f104]) ).
fof(f3180,plain,
! [X0,X1,X2] :
( ~ sQ230_spl
| aElementOf0(sK3_skl(X2,xx,xS),X2)
| ~ aSet0(X2)
| X2 = sdtmndt0(xS,xx)
| ~ aElement0(xx)
| ~ aSet0(xS)
| aElementOf0(sK3_skl(X2,xx,xS),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ),
inference(resolution,[status(thm)],[f2538,f84]) ).
fof(f3187,definition,
! [X0,X1,X2] :
( sQ244_spl
<=> ( aElementOf0(sK3_skl(X2,xx,xS),X2)
| ~ aSet0(X2)
| X2 = sdtmndt0(xS,xx)
| aElementOf0(sK3_skl(X2,xx,xS),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ244_spl])],[split_symbol_definition]) ).
fof(f3190,plain,
( ~ sQ230_spl
| ~ sQ1_spl
| ~ sQ0_spl
| sQ244_spl ),
inference(split_clause,[status(thm)],[f3180,f3187,f123,f126,f2537]) ).
fof(f3324,plain,
! [X0] :
( ~ sQ33_spl
| ~ sQ69_spl
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = X0
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtpldt0(sdtmndt0(xS,xx),xx))
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aElement0(X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aElement0(X0)
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx))
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f681,f364]) ).
fof(f3326,plain,
! [X0,X1,X2] :
( ~ sQ69_spl
| ~ sP0_prd(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)),xx,xS)
| ~ aElement0(xx)
| ~ aSet0(xS)
| sdtpldt0(X0,X1) = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X2)
| ~ aElement0(X2)
| ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f681,f118]) ).
fof(f3327,definition,
! [X0] :
( sQ245_spl
<=> ( sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = X0
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtpldt0(sdtmndt0(xS,xx),xx))
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aElement0(X0)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aElement0(X0)
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition]) ).
fof(f3330,plain,
( ~ sQ33_spl
| ~ sQ69_spl
| ~ sQ19_spl
| sQ245_spl
| ~ sQ1_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3324,f148,f126,f3327,f243,f680,f363]) ).
fof(f3332,definition,
! [X0,X1,X2] :
( sQ246_spl
<=> ( ~ sP0_prd(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)),xx,xS)
| sdtpldt0(X0,X1) = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X2)
| ~ aElement0(X2)
| ~ aElementOf0(sK2_skl(sdtpldt0(X0,X1),X2,sdtpldt0(sdtmndt0(xS,xx),xx)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ246_spl])],[split_symbol_definition]) ).
fof(f3335,plain,
( ~ sQ69_spl
| ~ sQ1_spl
| ~ sQ0_spl
| sQ246_spl ),
inference(split_clause,[status(thm)],[f3326,f3332,f123,f126,f680]) ).
fof(f3337,plain,
! [X0] :
( ~ sQ16_spl
| ~ aSet0(sdtmndt0(xS,X0))
| aSubsetOf0(sdtmndt0(xS,X0),sdtmndt0(xS,xx))
| sK1_skl(sdtmndt0(xS,X0),sdtmndt0(xS,xx)) = xx
| ~ aElement0(sK1_skl(sdtmndt0(xS,X0),sdtmndt0(xS,xx)))
| aSubsetOf0(sdtmndt0(xS,X0),sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aElement0(X0)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f1857,f227]) ).
fof(f3338,plain,
! [X0] :
( ~ sQ48_spl
| ~ aSet0(sdtmndt0(sdtmndt0(xS,xx),X0))
| aSubsetOf0(sdtmndt0(sdtmndt0(xS,xx),X0),sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(sdtmndt0(sdtmndt0(xS,xx),X0),sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f1857,f521]) ).
fof(f3339,plain,
! [X0,X1,X2] :
( ~ aSet0(sdtmndt0(X0,X1))
| aSubsetOf0(sdtmndt0(X0,X1),sdtpldt0(X0,X2))
| ~ aElement0(X2)
| ~ aSet0(X0)
| aSubsetOf0(sdtmndt0(X0,X1),sdtpldt0(X0,X2))
| ~ aSet0(sdtpldt0(X0,X2))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f1857,f317]) ).
fof(f3340,plain,
! [X0,X1] :
( ~ aSet0(sdtmndt0(X0,X1))
| aSubsetOf0(sdtmndt0(X0,X1),X0)
| ~ aSet0(X0)
| aSubsetOf0(sdtmndt0(X0,X1),X0)
| ~ aSet0(X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f1857,f52]) ).
fof(f3341,plain,
! [X0,X1] :
( aElement0(sK1_skl(sdtmndt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1))
| aSubsetOf0(sdtmndt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1)
| ~ aSet0(X1)
| ~ aElement0(X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f1857,f96]) ).
fof(f3342,plain,
! [X0,X1] :
( sK1_skl(sdtmndt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1) = xx
| aElementOf0(sK1_skl(sdtmndt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1),sdtmndt0(xS,xx))
| aSubsetOf0(sdtmndt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1)
| ~ aSet0(X1)
| ~ aElement0(X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f1857,f97]) ).
fof(f3345,plain,
! [X0,X1,X2,X3] :
( ~ sQ89_spl
| aElementOf0(sK1_skl(sdtmndt0(sdtmndt0(xS,xx),X0),X1),X3)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3)
| ~ aSubsetOf0(xS,X2)
| aSubsetOf0(sdtmndt0(sdtmndt0(xS,xx),X0),X1)
| ~ aSet0(X1)
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f1857,f1909]) ).
fof(f3346,plain,
! [X0,X1,X2] :
( ~ sQ89_spl
| aElementOf0(sK1_skl(sdtmndt0(sdtmndt0(xS,xx),X0),X1),X2)
| ~ aSubsetOf0(xS,X2)
| ~ aSet0(X2)
| aSubsetOf0(sdtmndt0(sdtmndt0(xS,xx),X0),X1)
| ~ aSet0(X1)
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f1857,f1579]) ).
fof(f3347,plain,
! [X0,X1] :
( aElement0(sK1_skl(sdtmndt0(sdtmndt0(xS,xx),X0),X1))
| aSubsetOf0(sdtmndt0(sdtmndt0(xS,xx),X0),X1)
| ~ aSet0(X1)
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f1857,f91]) ).
fof(f3348,plain,
! [X0,X1] :
( aElementOf0(sK1_skl(sdtmndt0(sdtmndt0(xS,xx),X0),X1),xS)
| aSubsetOf0(sdtmndt0(sdtmndt0(xS,xx),X0),X1)
| ~ aSet0(X1)
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f1857,f92]) ).
fof(f3350,plain,
! [X0,X1] :
( aSubsetOf0(sdtmndt0(slcrc0,X0),X1)
| ~ aSet0(X1)
| ~ aElement0(X0)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f1857,f108]) ).
fof(f3352,definition,
! [X0] :
( sQ247_spl
<=> ( ~ aSet0(sdtmndt0(xS,X0))
| aSubsetOf0(sdtmndt0(xS,X0),sdtmndt0(xS,xx))
| sK1_skl(sdtmndt0(xS,X0),sdtmndt0(xS,xx)) = xx
| ~ aElement0(sK1_skl(sdtmndt0(xS,X0),sdtmndt0(xS,xx)))
| aSubsetOf0(sdtmndt0(xS,X0),sdtmndt0(xS,xx))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ247_spl])],[split_symbol_definition]) ).
fof(f3355,plain,
( ~ sQ16_spl
| ~ sQ5_spl
| sQ247_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f3337,f123,f3352,f148,f226]) ).
fof(f3356,definition,
! [X0] :
( sQ248_spl
<=> ( ~ aSet0(sdtmndt0(sdtmndt0(xS,xx),X0))
| aSubsetOf0(sdtmndt0(sdtmndt0(xS,xx),X0),sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(sdtmndt0(sdtmndt0(xS,xx),X0),sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ248_spl])],[split_symbol_definition]) ).
fof(f3359,plain,
( ~ sQ48_spl
| ~ sQ19_spl
| sQ248_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3338,f148,f3356,f243,f520]) ).
fof(f3360,plain,
! [X0,X1,X2] :
( ~ aSet0(sdtmndt0(X0,X1))
| ~ aElement0(X2)
| aSubsetOf0(sdtmndt0(X0,X1),sdtpldt0(X0,X2))
| ~ aSet0(sdtpldt0(X0,X2))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f3339]) ).
fof(f3361,plain,
! [X0,X1,X2] :
( ~ aSet0(sdtmndt0(X0,X1))
| ~ aElement0(X2)
| aSubsetOf0(sdtmndt0(X0,X1),sdtpldt0(X0,X2))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3360,f110]) ).
fof(f3362,plain,
! [X0,X1] :
( ~ aSet0(sdtmndt0(X0,X1))
| aSubsetOf0(sdtmndt0(X0,X1),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f3340]) ).
fof(f3363,plain,
! [X0,X1] :
( aSubsetOf0(sdtmndt0(X0,X1),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3362,f116]) ).
fof(f3364,definition,
! [X0,X1] :
( sQ249_spl
<=> ( aElement0(sK1_skl(sdtmndt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1))
| aSubsetOf0(sdtmndt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f3367,plain,
( sQ249_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f3341,f243,f3364]) ).
fof(f3368,definition,
! [X0,X1] :
( sQ250_spl
<=> ( sK1_skl(sdtmndt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1) = xx
| aElementOf0(sK1_skl(sdtmndt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1),sdtmndt0(xS,xx))
| aSubsetOf0(sdtmndt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ250_spl])],[split_symbol_definition]) ).
fof(f3371,plain,
( sQ250_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f3342,f243,f3368]) ).
fof(f3373,definition,
! [X0,X1,X2,X3] :
( sQ251_spl
<=> ( aElementOf0(sK1_skl(sdtmndt0(sdtmndt0(xS,xx),X0),X1),X3)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3)
| ~ aSubsetOf0(xS,X2)
| aSubsetOf0(sdtmndt0(sdtmndt0(xS,xx),X0),X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ251_spl])],[split_symbol_definition]) ).
fof(f3376,plain,
( ~ sQ89_spl
| sQ251_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3345,f148,f3373,f841]) ).
fof(f3377,definition,
! [X0,X1,X2] :
( sQ252_spl
<=> ( aElementOf0(sK1_skl(sdtmndt0(sdtmndt0(xS,xx),X0),X1),X2)
| ~ aSubsetOf0(xS,X2)
| ~ aSet0(X2)
| aSubsetOf0(sdtmndt0(sdtmndt0(xS,xx),X0),X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ252_spl])],[split_symbol_definition]) ).
fof(f3380,plain,
( ~ sQ89_spl
| sQ252_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3346,f148,f3377,f841]) ).
fof(f3381,definition,
! [X0,X1] :
( sQ253_spl
<=> ( aElement0(sK1_skl(sdtmndt0(sdtmndt0(xS,xx),X0),X1))
| aSubsetOf0(sdtmndt0(sdtmndt0(xS,xx),X0),X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ253_spl])],[split_symbol_definition]) ).
fof(f3384,plain,
( sQ253_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3347,f148,f3381]) ).
fof(f3385,definition,
! [X0,X1] :
( sQ254_spl
<=> ( aElementOf0(sK1_skl(sdtmndt0(sdtmndt0(xS,xx),X0),X1),xS)
| aSubsetOf0(sdtmndt0(sdtmndt0(xS,xx),X0),X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ254_spl])],[split_symbol_definition]) ).
fof(f3388,plain,
( sQ254_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3348,f148,f3385]) ).
fof(f3390,definition,
! [X0,X1] :
( sQ255_spl
<=> ( aSubsetOf0(sdtmndt0(slcrc0,X0),X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ255_spl])],[split_symbol_definition]) ).
fof(f3391,plain,
! [X0,X1] :
( ~ sQ255_spl
| aSubsetOf0(sdtmndt0(slcrc0,X0),X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(component_clause,[status(thm)],[f3390]) ).
fof(f3393,plain,
( sQ255_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3350,f140,f3390]) ).
fof(f3398,plain,
! [X0] :
( ~ sQ13_spl
| slcrc0 = sdtmndt0(slcrc0,X0)
| ~ aSet0(sdtmndt0(slcrc0,X0))
| ~ aElement0(X0)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f3363,f269]) ).
fof(f3400,plain,
! [X0,X1,X2] :
( aSubsetOf0(sdtmndt0(X0,X1),X2)
| ~ aSubsetOf0(X0,X2)
| ~ aSet0(X2)
| ~ aSet0(X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f3363,f270]) ).
fof(f3401,plain,
! [X0,X1] :
( sdtmndt0(X0,X1) = X0
| ~ aSubsetOf0(X0,sdtmndt0(X0,X1))
| ~ aSet0(X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f3363,f266]) ).
fof(f3403,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,sdtmndt0(X0,X1))
| ~ aSet0(X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f3363,f50]) ).
fof(f3408,definition,
! [X0] :
( sQ257_spl
<=> ( slcrc0 = sdtmndt0(slcrc0,X0)
| ~ aSet0(sdtmndt0(slcrc0,X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ257_spl])],[split_symbol_definition]) ).
fof(f3411,plain,
( ~ sQ13_spl
| sQ257_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3398,f140,f3408,f210]) ).
fof(f3413,plain,
! [X0,X1,X2] :
( aSubsetOf0(sdtmndt0(X0,X1),X2)
| ~ aSubsetOf0(X0,X2)
| ~ aSet0(X2)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f3400]) ).
fof(f3414,plain,
! [X0,X1,X2] :
( aSubsetOf0(sdtmndt0(X2,X0),X1)
| ~ aSubsetOf0(X2,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3413,f49]) ).
fof(f3415,plain,
! [X0,X1] :
( sdtmndt0(X0,X1) = X0
| ~ aSubsetOf0(X0,sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f3401]) ).
fof(f3417,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f3403]) ).
fof(f3419,plain,
! [X0,X1] :
( ~ sQ255_spl
| isFinite0(sdtmndt0(slcrc0,X0))
| ~ isFinite0(X1)
| ~ aSet0(X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f3391,f54]) ).
fof(f3421,plain,
! [X0,X1] :
( ~ sQ255_spl
| sdtmndt0(slcrc0,X0) = X1
| ~ aSubsetOf0(X1,sdtmndt0(slcrc0,X0))
| ~ aSet0(X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f3391,f266]) ).
fof(f3422,plain,
! [X0,X1] :
( ~ sQ255_spl
| aSet0(sdtmndt0(slcrc0,X0))
| ~ aSet0(X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f3391,f49]) ).
fof(f3423,plain,
! [X0,X1,X2] :
( ~ sQ255_spl
| aElementOf0(X2,X1)
| ~ aElementOf0(X2,sdtmndt0(slcrc0,X0))
| ~ aSet0(X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f3391,f50]) ).
fof(f3425,definition,
! [X0] :
( sQ258_spl
<=> ( isFinite0(sdtmndt0(slcrc0,X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ258_spl])],[split_symbol_definition]) ).
fof(f3428,plain,
( ~ sQ255_spl
| sQ41_spl
| sQ258_spl ),
inference(split_clause,[status(thm)],[f3419,f3425,f441,f3390]) ).
fof(f3430,plain,
! [X0,X1] :
( ~ sQ255_spl
| sdtmndt0(slcrc0,X0) = X1
| ~ aSubsetOf0(X1,sdtmndt0(slcrc0,X0))
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f3421]) ).
fof(f3431,definition,
! [X0] :
( sQ259_spl
<=> ( aSet0(sdtmndt0(slcrc0,X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ259_spl])],[split_symbol_definition]) ).
fof(f3434,plain,
( ~ sQ255_spl
| sQ11_spl
| sQ259_spl ),
inference(split_clause,[status(thm)],[f3422,f3431,f197,f3390]) ).
fof(f3435,plain,
! [X0,X1,X2] :
( ~ sQ255_spl
| aElementOf0(X2,X1)
| ~ aElementOf0(X2,sdtmndt0(slcrc0,X0))
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f3423]) ).
fof(f3439,plain,
! [X0,X1] :
( ~ sQ13_spl
| slcrc0 = sdtmndt0(X1,X0)
| ~ aSet0(sdtmndt0(X1,X0))
| ~ aSubsetOf0(X1,slcrc0)
| ~ aSet0(slcrc0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f3414,f269]) ).
fof(f3441,plain,
! [X0,X1,X2,X3] :
( aSubsetOf0(sdtmndt0(X2,X0),X3)
| ~ aSubsetOf0(X1,X3)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aSubsetOf0(X2,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f3414,f270]) ).
fof(f3442,plain,
! [X0,X1,X2] :
( sdtmndt0(X2,X0) = X1
| ~ aSubsetOf0(X1,sdtmndt0(X2,X0))
| ~ aSet0(X1)
| ~ aSubsetOf0(X2,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f3414,f266]) ).
fof(f3443,plain,
! [X0,X1,X2] :
( aSet0(sdtmndt0(X2,X0))
| ~ aSet0(X1)
| ~ aSubsetOf0(X2,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f3414,f49]) ).
fof(f3444,plain,
! [X0,X1,X2,X3] :
( aElementOf0(X3,X1)
| ~ aElementOf0(X3,sdtmndt0(X2,X0))
| ~ aSet0(X1)
| ~ aSubsetOf0(X2,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f3414,f50]) ).
fof(f3445,definition,
! [X0,X1] :
( sQ260_spl
<=> ( slcrc0 = sdtmndt0(X1,X0)
| ~ aSet0(sdtmndt0(X1,X0))
| ~ aSubsetOf0(X1,slcrc0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ260_spl])],[split_symbol_definition]) ).
fof(f3448,plain,
( ~ sQ13_spl
| ~ sQ3_spl
| sQ260_spl ),
inference(split_clause,[status(thm)],[f3439,f3445,f140,f210]) ).
fof(f3450,plain,
! [X0,X1,X2,X3] :
( aSubsetOf0(sdtmndt0(X2,X0),X3)
| ~ aSubsetOf0(X1,X3)
| ~ aSet0(X3)
| ~ aSubsetOf0(X2,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f3441]) ).
fof(f3451,plain,
! [X0,X1,X2,X3] :
( aSubsetOf0(sdtmndt0(X1,X0),X3)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3)
| ~ aSubsetOf0(X1,X2)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3450,f49]) ).
fof(f3452,plain,
! [X0,X1,X2] :
( sdtmndt0(X2,X0) = X1
| ~ aSubsetOf0(X1,sdtmndt0(X2,X0))
| ~ aSubsetOf0(X2,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f3442]) ).
fof(f3453,plain,
! [X0,X1,X2] :
( aSet0(sdtmndt0(X2,X0))
| ~ aSubsetOf0(X2,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f3443]) ).
fof(f3454,plain,
! [X0,X1,X2,X3] :
( aElementOf0(X3,X1)
| ~ aElementOf0(X3,sdtmndt0(X2,X0))
| ~ aSubsetOf0(X2,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f3444]) ).
fof(f3455,plain,
! [X0] :
( ~ sQ255_spl
| ~ sQ89_spl
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aElement0(X0)
| sdtmndt0(xS,xx) = sdtmndt0(slcrc0,X0)
| ~ aSubsetOf0(xS,sdtmndt0(slcrc0,X0))
| ~ aSet0(sdtmndt0(slcrc0,X0)) ),
inference(resolution,[status(thm)],[f2842,f3391]) ).
fof(f3460,plain,
! [X0,X1] :
( ~ sQ89_spl
| ~ aSubsetOf0(X0,sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aElement0(X1)
| sdtmndt0(xS,xx) = sdtmndt0(X0,X1)
| ~ aSubsetOf0(xS,sdtmndt0(X0,X1))
| ~ aSet0(sdtmndt0(X0,X1)) ),
inference(resolution,[status(thm)],[f2842,f3414]) ).
fof(f3461,plain,
! [X0] :
( ~ sQ89_spl
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx))
| sdtmndt0(xS,xx) = sdtmndt0(sdtmndt0(xS,xx),X0)
| ~ aSubsetOf0(xS,sdtmndt0(sdtmndt0(xS,xx),X0))
| ~ aSet0(sdtmndt0(sdtmndt0(xS,xx),X0)) ),
inference(resolution,[status(thm)],[f2842,f3363]) ).
fof(f3464,definition,
! [X0] :
( sQ261_spl
<=> ( ~ aElement0(X0)
| sdtmndt0(xS,xx) = sdtmndt0(slcrc0,X0)
| ~ aSubsetOf0(xS,sdtmndt0(slcrc0,X0))
| ~ aSet0(sdtmndt0(slcrc0,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ261_spl])],[split_symbol_definition]) ).
fof(f3467,plain,
( ~ sQ255_spl
| ~ sQ89_spl
| ~ sQ5_spl
| sQ261_spl ),
inference(split_clause,[status(thm)],[f3455,f3464,f148,f841,f3390]) ).
fof(f3472,definition,
! [X0,X1] :
( sQ262_spl
<=> ( ~ aSubsetOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X1)
| sdtmndt0(xS,xx) = sdtmndt0(X0,X1)
| ~ aSubsetOf0(xS,sdtmndt0(X0,X1))
| ~ aSet0(sdtmndt0(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ262_spl])],[split_symbol_definition]) ).
fof(f3475,plain,
( ~ sQ89_spl
| ~ sQ5_spl
| sQ262_spl ),
inference(split_clause,[status(thm)],[f3460,f3472,f148,f841]) ).
fof(f3476,definition,
! [X0] :
( sQ263_spl
<=> ( ~ aElement0(X0)
| sdtmndt0(xS,xx) = sdtmndt0(sdtmndt0(xS,xx),X0)
| ~ aSubsetOf0(xS,sdtmndt0(sdtmndt0(xS,xx),X0))
| ~ aSet0(sdtmndt0(sdtmndt0(xS,xx),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ263_spl])],[split_symbol_definition]) ).
fof(f3479,plain,
( ~ sQ89_spl
| ~ sQ5_spl
| sQ263_spl ),
inference(split_clause,[status(thm)],[f3461,f3476,f148,f841]) ).
fof(f3483,plain,
! [X0] :
( ~ sQ36_spl
| ~ sQ72_spl
| aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(sdtmndt0(xS,xx),X0))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),X0))
| sK1_skl(sdtmndt0(xS,xx),sdtpldt0(sdtmndt0(xS,xx),X0)) = xx
| ~ aElement0(sK1_skl(sdtmndt0(xS,xx),sdtpldt0(sdtmndt0(xS,xx),X0)))
| ~ aSet0(sdtmndt0(xS,xx))
| aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(sdtmndt0(xS,xx),X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f704,f386]) ).
fof(f3484,plain,
! [X0,X1] :
( ~ sQ72_spl
| aSubsetOf0(sdtmndt0(xS,X1),sdtpldt0(sdtmndt0(xS,xx),X0))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),X0))
| ~ aElement0(X1)
| ~ aSet0(xS)
| sK1_skl(sdtmndt0(xS,X1),sdtpldt0(sdtmndt0(xS,xx),X0)) = xx
| ~ aElement0(sK1_skl(sdtmndt0(xS,X1),sdtpldt0(sdtmndt0(xS,xx),X0)))
| ~ aSet0(sdtmndt0(xS,X1))
| aSubsetOf0(sdtmndt0(xS,X1),sdtpldt0(sdtmndt0(xS,xx),X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f704,f1857]) ).
fof(f3485,plain,
! [X0,X1] :
( ~ sQ72_spl
| aSubsetOf0(sdtpldt0(xS,X1),sdtpldt0(sdtmndt0(xS,xx),X0))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),X0))
| sK1_skl(sdtpldt0(xS,X1),sdtpldt0(sdtmndt0(xS,xx),X0)) = X1
| ~ aElement0(X1)
| ~ aSet0(xS)
| sK1_skl(sdtpldt0(xS,X1),sdtpldt0(sdtmndt0(xS,xx),X0)) = xx
| ~ aElement0(sK1_skl(sdtpldt0(xS,X1),sdtpldt0(sdtmndt0(xS,xx),X0)))
| ~ aSet0(sdtpldt0(xS,X1))
| aSubsetOf0(sdtpldt0(xS,X1),sdtpldt0(sdtmndt0(xS,xx),X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f704,f430]) ).
fof(f3486,plain,
! [X0] :
( ~ sQ72_spl
| ~ aSet0(xS)
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),X0))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),X0))
| sK1_skl(xS,sdtpldt0(sdtmndt0(xS,xx),X0)) = xx
| ~ aElement0(sK1_skl(xS,sdtpldt0(sdtmndt0(xS,xx),X0)))
| ~ aSet0(xS)
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f704,f51]) ).
fof(f3487,definition,
! [X0] :
( sQ264_spl
<=> ( aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(sdtmndt0(xS,xx),X0))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),X0))
| sK1_skl(sdtmndt0(xS,xx),sdtpldt0(sdtmndt0(xS,xx),X0)) = xx
| ~ aElement0(sK1_skl(sdtmndt0(xS,xx),sdtpldt0(sdtmndt0(xS,xx),X0)))
| aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(sdtmndt0(xS,xx),X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ264_spl])],[split_symbol_definition]) ).
fof(f3490,plain,
( ~ sQ36_spl
| ~ sQ72_spl
| ~ sQ5_spl
| sQ264_spl ),
inference(split_clause,[status(thm)],[f3483,f3487,f148,f703,f385]) ).
fof(f3491,definition,
! [X0,X1] :
( sQ265_spl
<=> ( aSubsetOf0(sdtmndt0(xS,X1),sdtpldt0(sdtmndt0(xS,xx),X0))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),X0))
| ~ aElement0(X1)
| sK1_skl(sdtmndt0(xS,X1),sdtpldt0(sdtmndt0(xS,xx),X0)) = xx
| ~ aElement0(sK1_skl(sdtmndt0(xS,X1),sdtpldt0(sdtmndt0(xS,xx),X0)))
| ~ aSet0(sdtmndt0(xS,X1))
| aSubsetOf0(sdtmndt0(xS,X1),sdtpldt0(sdtmndt0(xS,xx),X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ265_spl])],[split_symbol_definition]) ).
fof(f3494,plain,
( ~ sQ72_spl
| ~ sQ0_spl
| sQ265_spl ),
inference(split_clause,[status(thm)],[f3484,f3491,f123,f703]) ).
fof(f3495,definition,
! [X0,X1] :
( sQ266_spl
<=> ( aSubsetOf0(sdtpldt0(xS,X1),sdtpldt0(sdtmndt0(xS,xx),X0))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),X0))
| sK1_skl(sdtpldt0(xS,X1),sdtpldt0(sdtmndt0(xS,xx),X0)) = X1
| ~ aElement0(X1)
| sK1_skl(sdtpldt0(xS,X1),sdtpldt0(sdtmndt0(xS,xx),X0)) = xx
| ~ aElement0(sK1_skl(sdtpldt0(xS,X1),sdtpldt0(sdtmndt0(xS,xx),X0)))
| ~ aSet0(sdtpldt0(xS,X1))
| aSubsetOf0(sdtpldt0(xS,X1),sdtpldt0(sdtmndt0(xS,xx),X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ266_spl])],[split_symbol_definition]) ).
fof(f3498,plain,
( ~ sQ72_spl
| ~ sQ0_spl
| sQ266_spl ),
inference(split_clause,[status(thm)],[f3485,f3495,f123,f703]) ).
fof(f3499,definition,
! [X0] :
( sQ267_spl
<=> ( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),X0))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),X0))
| sK1_skl(xS,sdtpldt0(sdtmndt0(xS,xx),X0)) = xx
| ~ aElement0(sK1_skl(xS,sdtpldt0(sdtmndt0(xS,xx),X0)))
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ267_spl])],[split_symbol_definition]) ).
fof(f3502,plain,
( ~ sQ72_spl
| ~ sQ0_spl
| sQ267_spl ),
inference(split_clause,[status(thm)],[f3486,f3499,f123,f703]) ).
fof(f3513,plain,
! [X0,X1] :
( ~ sQ33_spl
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,X1) = xx
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,X1) = X0
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,X1),X1)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,X1),xS)
| ~ aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f3417,f364]) ).
fof(f3525,plain,
! [X0] :
( ~ sQ18_spl
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aSet0(X0)
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0) = xx
| aElementOf0(sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0),xS)
| ~ aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f3417,f241]) ).
fof(f3528,plain,
! [X0] :
( X0 = xx
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| aElementOf0(X0,xS)
| ~ aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f3417,f94]) ).
fof(f3533,definition,
! [X0,X1] :
( sQ268_spl
<=> ( sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,X1) = xx
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,X1) = X0
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,X1),X1)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0,X1),xS) ) ),
introduced(definition,[new_symbols(definition,[sQ268_spl])],[split_symbol_definition]) ).
fof(f3536,plain,
( ~ sQ33_spl
| sQ268_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f3513,f123,f126,f3533,f363]) ).
fof(f3547,definition,
! [X0] :
( sQ269_spl
<=> ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aSet0(X0)
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0) = xx
| aElementOf0(sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0),xS) ) ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f3550,plain,
( ~ sQ18_spl
| sQ269_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f3525,f123,f126,f3547,f240]) ).
fof(f3552,definition,
! [X0] :
( sQ270_spl
<=> ( X0 = xx
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| aElementOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ270_spl])],[split_symbol_definition]) ).
fof(f3555,plain,
( sQ270_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f3528,f123,f126,f3552]) ).
fof(f3559,plain,
! [X0,X1] :
( ~ sQ89_spl
| ~ aSubsetOf0(X1,sdtmndt0(sdtmndt0(xS,xx),X0))
| ~ aSet0(sdtmndt0(sdtmndt0(xS,xx),X0))
| ~ aSubsetOf0(xS,X1)
| sdtmndt0(sdtmndt0(xS,xx),X0) = sdtmndt0(xS,xx)
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f3415,f1168]) ).
fof(f3561,plain,
! [X0,X1,X2] :
( ~ sQ89_spl
| ~ aSubsetOf0(X2,sdtmndt0(sdtmndt0(xS,xx),X0))
| ~ aSet0(sdtmndt0(sdtmndt0(xS,xx),X0))
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(xS,X1)
| sdtmndt0(sdtmndt0(xS,xx),X0) = sdtmndt0(xS,xx)
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f3415,f1903]) ).
fof(f3565,definition,
! [X0,X1] :
( sQ271_spl
<=> ( ~ aSubsetOf0(X1,sdtmndt0(sdtmndt0(xS,xx),X0))
| ~ aSet0(sdtmndt0(sdtmndt0(xS,xx),X0))
| ~ aSubsetOf0(xS,X1)
| sdtmndt0(sdtmndt0(xS,xx),X0) = sdtmndt0(xS,xx)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ271_spl])],[split_symbol_definition]) ).
fof(f3568,plain,
( ~ sQ89_spl
| sQ271_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3559,f148,f3565,f841]) ).
fof(f3570,definition,
! [X0,X1,X2] :
( sQ272_spl
<=> ( ~ aSubsetOf0(X2,sdtmndt0(sdtmndt0(xS,xx),X0))
| ~ aSet0(sdtmndt0(sdtmndt0(xS,xx),X0))
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(xS,X1)
| sdtmndt0(sdtmndt0(xS,xx),X0) = sdtmndt0(xS,xx)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ272_spl])],[split_symbol_definition]) ).
fof(f3573,plain,
( ~ sQ89_spl
| sQ272_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3561,f148,f3570,f841]) ).
fof(f3590,plain,
! [X0,X1,X2] :
( ~ sQ255_spl
| ~ sP0_prd(X2,X0,slcrc0)
| ~ aElement0(X0)
| ~ aSet0(slcrc0)
| aElementOf0(X2,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f3435,f118]) ).
fof(f3599,definition,
! [X1] :
( sQ274_spl
<=> ( aElementOf0(sK0_skl(sdtmndt0(xS,xx)),X1)
| ~ aSet0(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ274_spl])],[split_symbol_definition]) ).
fof(f3600,plain,
! [X0] :
( ~ sQ274_spl
| aElementOf0(sK0_skl(sdtmndt0(xS,xx)),X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f3599]) ).
fof(f3615,definition,
! [X0,X1,X2] :
( sQ277_spl
<=> ( ~ sP0_prd(X2,X0,slcrc0)
| ~ aElement0(X0)
| aElementOf0(X2,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ277_spl])],[split_symbol_definition]) ).
fof(f3616,plain,
! [X0,X1,X2] :
( ~ sQ277_spl
| ~ sP0_prd(X2,X0,slcrc0)
| ~ aElement0(X0)
| aElementOf0(X2,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(component_clause,[status(thm)],[f3615]) ).
fof(f3618,plain,
( ~ sQ255_spl
| ~ sQ3_spl
| sQ277_spl ),
inference(split_clause,[status(thm)],[f3590,f3615,f140,f3390]) ).
fof(f3620,plain,
! [X0,X1,X2] :
( ~ sQ277_spl
| ~ sP0_prd(X2,X0,slcrc0)
| aElementOf0(X2,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f3616]) ).
fof(f3632,plain,
( ~ sQ274_spl
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f3600,f108]) ).
fof(f3649,plain,
( ~ sQ274_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3632,f140,f3599]) ).
fof(f3652,plain,
! [X0,X1,X2,X3] :
( ~ sQ277_spl
| sK2_skl(sdtmndt0(slcrc0,X0),X2,X3) = X2
| aElementOf0(sK2_skl(sdtmndt0(slcrc0,X0),X2,X3),X3)
| sdtmndt0(slcrc0,X0) = sdtpldt0(X3,X2)
| ~ aElement0(X2)
| ~ aSet0(X3)
| ~ aElement0(X0)
| ~ aSet0(slcrc0)
| aElementOf0(sK2_skl(sdtmndt0(slcrc0,X0),X2,X3),X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f3620,f463]) ).
fof(f3653,plain,
! [X0,X1,X2] :
( ~ sQ277_spl
| aSubsetOf0(sdtmndt0(slcrc0,X0),X2)
| ~ aSet0(X2)
| ~ aElement0(X0)
| ~ aSet0(slcrc0)
| aElementOf0(sK1_skl(sdtmndt0(slcrc0,X0),X2),X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f3620,f465]) ).
fof(f3654,plain,
! [X0,X1,X2] :
( ~ sQ277_spl
| aElementOf0(sK3_skl(X2,X0,slcrc0),X2)
| ~ aSet0(X2)
| X2 = sdtmndt0(slcrc0,X0)
| ~ aElement0(X0)
| ~ aSet0(slcrc0)
| aElementOf0(sK3_skl(X2,X0,slcrc0),X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f3620,f84]) ).
fof(f3655,plain,
! [X0,X1] :
( ~ sQ277_spl
| sdtmndt0(slcrc0,X0) = slcrc0
| ~ aElement0(X0)
| ~ aSet0(slcrc0)
| aElementOf0(sK0_skl(sdtmndt0(slcrc0,X0)),X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f3620,f464]) ).
fof(f3657,definition,
! [X0,X1,X2,X3] :
( sQ280_spl
<=> ( sK2_skl(sdtmndt0(slcrc0,X0),X2,X3) = X2
| aElementOf0(sK2_skl(sdtmndt0(slcrc0,X0),X2,X3),X3)
| sdtmndt0(slcrc0,X0) = sdtpldt0(X3,X2)
| ~ aElement0(X2)
| ~ aSet0(X3)
| ~ aElement0(X0)
| aElementOf0(sK2_skl(sdtmndt0(slcrc0,X0),X2,X3),X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ280_spl])],[split_symbol_definition]) ).
fof(f3660,plain,
( ~ sQ277_spl
| ~ sQ3_spl
| sQ280_spl ),
inference(split_clause,[status(thm)],[f3652,f3657,f140,f3615]) ).
fof(f3661,definition,
! [X0,X1,X2] :
( sQ281_spl
<=> ( aSubsetOf0(sdtmndt0(slcrc0,X0),X2)
| ~ aSet0(X2)
| ~ aElement0(X0)
| aElementOf0(sK1_skl(sdtmndt0(slcrc0,X0),X2),X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ281_spl])],[split_symbol_definition]) ).
fof(f3664,plain,
( ~ sQ277_spl
| ~ sQ3_spl
| sQ281_spl ),
inference(split_clause,[status(thm)],[f3653,f3661,f140,f3615]) ).
fof(f3665,definition,
! [X0,X1,X2] :
( sQ282_spl
<=> ( aElementOf0(sK3_skl(X2,X0,slcrc0),X2)
| ~ aSet0(X2)
| X2 = sdtmndt0(slcrc0,X0)
| ~ aElement0(X0)
| aElementOf0(sK3_skl(X2,X0,slcrc0),X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ282_spl])],[split_symbol_definition]) ).
fof(f3668,plain,
( ~ sQ277_spl
| ~ sQ3_spl
| sQ282_spl ),
inference(split_clause,[status(thm)],[f3654,f3665,f140,f3615]) ).
fof(f3669,definition,
! [X0,X1] :
( sQ283_spl
<=> ( sdtmndt0(slcrc0,X0) = slcrc0
| ~ aElement0(X0)
| aElementOf0(sK0_skl(sdtmndt0(slcrc0,X0)),X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ283_spl])],[split_symbol_definition]) ).
fof(f3672,plain,
( ~ sQ277_spl
| ~ sQ3_spl
| sQ283_spl ),
inference(split_clause,[status(thm)],[f3655,f3669,f140,f3615]) ).
fof(f3938,plain,
! [X0,X1,X2] :
( sK2_skl(sdtpldt0(sdtmndt0(xS,xx),X2),X1,X0) = xx
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),X2),X1,X0),xS)
| ~ aElement0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),X2),X1,X0))
| ~ aElement0(X2)
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),X2),X1,X0),X0)
| sdtpldt0(sdtmndt0(xS,xx),X2) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f2831,f94]) ).
fof(f3940,plain,
! [X0,X1,X2] :
( ~ aElementOf0(sK2_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X2),X1,X0),sdtmndt0(xS,xx))
| ~ aElement0(X2)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X2),X1,X0),X0)
| sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X2) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f2831,f343]) ).
fof(f3942,definition,
! [X0,X1,X2] :
( sQ286_spl
<=> ( sK2_skl(sdtpldt0(sdtmndt0(xS,xx),X2),X1,X0) = xx
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),X2),X1,X0),xS)
| ~ aElement0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),X2),X1,X0))
| ~ aElement0(X2)
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),X2),X1,X0),X0)
| sdtpldt0(sdtmndt0(xS,xx),X2) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ286_spl])],[split_symbol_definition]) ).
fof(f3945,plain,
( ~ sQ5_spl
| sQ286_spl ),
inference(split_clause,[status(thm)],[f3938,f3942,f148]) ).
fof(f3947,definition,
! [X0,X1,X2] :
( sQ287_spl
<=> ( ~ aElementOf0(sK2_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X2),X1,X0),sdtmndt0(xS,xx))
| ~ aElement0(X2)
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X2),X1,X0),X0)
| sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X2) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ287_spl])],[split_symbol_definition]) ).
fof(f3950,plain,
( ~ sQ19_spl
| sQ287_spl ),
inference(split_clause,[status(thm)],[f3940,f3947,f243]) ).
fof(f4233,plain,
! [X0,X1] :
( ~ sQ89_spl
| ~ sQ255_spl
| ~ aSubsetOf0(X1,sdtmndt0(slcrc0,X0))
| ~ aSet0(sdtmndt0(slcrc0,X0))
| ~ aSubsetOf0(xS,X1)
| sdtmndt0(slcrc0,X0) = sdtmndt0(xS,xx)
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f3430,f1168]) ).
fof(f4235,plain,
! [X0,X1,X2] :
( ~ sQ89_spl
| ~ sQ255_spl
| ~ aSubsetOf0(X2,sdtmndt0(slcrc0,X0))
| ~ aSet0(sdtmndt0(slcrc0,X0))
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(xS,X1)
| sdtmndt0(slcrc0,X0) = sdtmndt0(xS,xx)
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f3430,f1903]) ).
fof(f4241,definition,
! [X0,X1] :
( sQ288_spl
<=> ( ~ aSubsetOf0(X1,sdtmndt0(slcrc0,X0))
| ~ aSet0(sdtmndt0(slcrc0,X0))
| ~ aSubsetOf0(xS,X1)
| sdtmndt0(slcrc0,X0) = sdtmndt0(xS,xx)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ288_spl])],[split_symbol_definition]) ).
fof(f4244,plain,
( ~ sQ89_spl
| ~ sQ255_spl
| ~ sQ5_spl
| sQ288_spl ),
inference(split_clause,[status(thm)],[f4233,f4241,f148,f3390,f841]) ).
fof(f4246,definition,
! [X0,X1,X2] :
( sQ289_spl
<=> ( ~ aSubsetOf0(X2,sdtmndt0(slcrc0,X0))
| ~ aSet0(sdtmndt0(slcrc0,X0))
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(xS,X1)
| sdtmndt0(slcrc0,X0) = sdtmndt0(xS,xx)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ289_spl])],[split_symbol_definition]) ).
fof(f4249,plain,
( ~ sQ89_spl
| ~ sQ255_spl
| ~ sQ5_spl
| sQ289_spl ),
inference(split_clause,[status(thm)],[f4235,f4246,f148,f3390,f841]) ).
fof(f4327,plain,
! [X0,X1,X2] :
( ~ sQ89_spl
| sdtmndt0(xS,xx) = sdtmndt0(X1,X0)
| ~ aSubsetOf0(xS,sdtmndt0(X1,X0))
| ~ aSet0(sdtmndt0(X1,X0))
| ~ aSubsetOf0(X2,sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aSubsetOf0(X1,X2)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f3451,f2842]) ).
fof(f4329,plain,
! [X0,X1,X2] :
( ~ sQ13_spl
| slcrc0 = sdtmndt0(X1,X0)
| ~ aSet0(sdtmndt0(X1,X0))
| ~ aSubsetOf0(X2,slcrc0)
| ~ aSet0(slcrc0)
| ~ aSubsetOf0(X1,X2)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f3451,f269]) ).
fof(f4331,plain,
! [X0,X1,X2,X3,X4] :
( aSubsetOf0(sdtmndt0(X1,X0),X4)
| ~ aSubsetOf0(X3,X4)
| ~ aSet0(X4)
| ~ aSet0(X3)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3)
| ~ aSubsetOf0(X1,X2)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f3451,f270]) ).
fof(f4332,plain,
! [X0,X1,X2,X3] :
( sdtmndt0(X1,X0) = X3
| ~ aSubsetOf0(X3,sdtmndt0(X1,X0))
| ~ aSet0(X3)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3)
| ~ aSubsetOf0(X1,X2)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f3451,f266]) ).
fof(f4334,plain,
! [X0,X1,X2,X3,X4] :
( aElementOf0(X4,X3)
| ~ aElementOf0(X4,sdtmndt0(X1,X0))
| ~ aSet0(X3)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3)
| ~ aSubsetOf0(X1,X2)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f3451,f50]) ).
fof(f4337,definition,
! [X0,X1,X2] :
( sQ291_spl
<=> ( sdtmndt0(xS,xx) = sdtmndt0(X1,X0)
| ~ aSubsetOf0(xS,sdtmndt0(X1,X0))
| ~ aSet0(sdtmndt0(X1,X0))
| ~ aSubsetOf0(X2,sdtmndt0(xS,xx))
| ~ aSubsetOf0(X1,X2)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ291_spl])],[split_symbol_definition]) ).
fof(f4340,plain,
( ~ sQ89_spl
| ~ sQ5_spl
| sQ291_spl ),
inference(split_clause,[status(thm)],[f4327,f4337,f148,f841]) ).
fof(f4342,definition,
! [X0,X1,X2] :
( sQ292_spl
<=> ( slcrc0 = sdtmndt0(X1,X0)
| ~ aSet0(sdtmndt0(X1,X0))
| ~ aSubsetOf0(X2,slcrc0)
| ~ aSubsetOf0(X1,X2)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ292_spl])],[split_symbol_definition]) ).
fof(f4345,plain,
( ~ sQ13_spl
| ~ sQ3_spl
| sQ292_spl ),
inference(split_clause,[status(thm)],[f4329,f4342,f140,f210]) ).
fof(f4347,plain,
! [X0,X1,X2,X3,X4] :
( aSubsetOf0(sdtmndt0(X1,X0),X4)
| ~ aSubsetOf0(X3,X4)
| ~ aSet0(X4)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3)
| ~ aSubsetOf0(X1,X2)
| ~ aElement0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f4331]) ).
fof(f4348,plain,
! [X0,X1,X2,X3,X4] :
( aSubsetOf0(sdtmndt0(X1,X0),X4)
| ~ aSubsetOf0(X3,X4)
| ~ aSet0(X4)
| ~ aSubsetOf0(X2,X3)
| ~ aSubsetOf0(X1,X2)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f4347,f49]) ).
fof(f4349,plain,
! [X0,X1,X2,X3] :
( sdtmndt0(X1,X0) = X3
| ~ aSubsetOf0(X3,sdtmndt0(X1,X0))
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3)
| ~ aSubsetOf0(X1,X2)
| ~ aElement0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f4332]) ).
fof(f4351,plain,
! [X0,X1,X2,X3,X4] :
( aElementOf0(X4,X3)
| ~ aElementOf0(X4,sdtmndt0(X1,X0))
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3)
| ~ aSubsetOf0(X1,X2)
| ~ aElement0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f4334]) ).
fof(f4363,plain,
! [X0,X1,X2] :
( ~ aSet0(sdtmndt0(X2,X0))
| sdtmndt0(X2,X0) = slcrc0
| aElementOf0(sK0_skl(sdtmndt0(X2,X0)),X1)
| ~ aSubsetOf0(X2,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f3454,f37]) ).
fof(f4367,plain,
! [X0,X1] :
( X1 = xx
| ~ aElementOf0(X1,xS)
| ~ aElement0(X1)
| aElementOf0(X1,X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0)
| ~ aElement0(xx) ),
inference(resolution,[status(thm)],[f3454,f94]) ).
fof(f4368,plain,
! [X0,X1,X2,X3] :
( ~ sP0_prd(X3,X0,X2)
| ~ aElement0(X0)
| ~ aSet0(X2)
| aElementOf0(X3,X1)
| ~ aSubsetOf0(X2,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f3454,f118]) ).
fof(f4378,plain,
! [X0,X1,X2] :
( sdtmndt0(X2,X0) = slcrc0
| aElementOf0(sK0_skl(sdtmndt0(X2,X0)),X1)
| ~ aSubsetOf0(X2,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f4363,f3453]) ).
fof(f4379,definition,
! [X0,X1] :
( sQ293_spl
<=> ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X1)
| ~ aSet0(X1)
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1) = xx
| aElementOf0(sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1),X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ293_spl])],[split_symbol_definition]) ).
fof(f4385,definition,
! [X0,X1] :
( sQ294_spl
<=> ( X1 = xx
| ~ aElementOf0(X1,xS)
| ~ aElement0(X1)
| aElementOf0(X1,X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ294_spl])],[split_symbol_definition]) ).
fof(f4388,plain,
( sQ294_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f4367,f126,f4385]) ).
fof(f4389,plain,
! [X0,X1,X2,X3] :
( ~ sP0_prd(X3,X0,X2)
| ~ aSet0(X2)
| aElementOf0(X3,X1)
| ~ aSubsetOf0(X2,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f4368]) ).
fof(f4390,plain,
! [X0,X1,X2,X3] :
( ~ sP0_prd(X3,X0,X2)
| aElementOf0(X3,X1)
| ~ aSubsetOf0(X2,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f4389,f49]) ).
fof(f4410,plain,
! [X0,X1] :
( ~ sQ33_spl
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),X0)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0)
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0) = xx
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0) = X1
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),X0)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f364,f2831]) ).
fof(f4415,plain,
! [X0,X1,X2] :
( ~ sQ33_spl
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),X2)
| ~ aSubsetOf0(xS,X2)
| ~ aSet0(X2)
| ~ aElement0(xx)
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0) = xx
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0) = X1
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),X0)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f364,f3454]) ).
fof(f4419,definition,
! [X0,X1] :
( sQ295_spl
<=> ( ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),X0)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0)
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0) = xx
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0) = X1
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),X0)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ295_spl])],[split_symbol_definition]) ).
fof(f4422,plain,
( ~ sQ33_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sQ295_spl ),
inference(split_clause,[status(thm)],[f4410,f4419,f148,f126,f363]) ).
fof(f4424,definition,
! [X0,X1,X2] :
( sQ296_spl
<=> ( aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),X2)
| ~ aSubsetOf0(xS,X2)
| ~ aSet0(X2)
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0) = xx
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0) = X1
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X0),X0)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ296_spl])],[split_symbol_definition]) ).
fof(f4427,plain,
( ~ sQ33_spl
| ~ sQ1_spl
| sQ296_spl ),
inference(split_clause,[status(thm)],[f4415,f4424,f126,f363]) ).
fof(f4538,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ71_spl
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| ~ aSet0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)) = xx
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f699,f241]) ).
fof(f4539,plain,
! [X0,X1] :
( ~ sQ71_spl
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),X1),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| ~ aSet0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),X1),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)) = X1
| ~ aElement0(X1)
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),X1))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),X1),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f699,f430]) ).
fof(f4540,plain,
! [X0] :
( ~ sQ71_spl
| ~ aSet0(sdtmndt0(xS,xx))
| aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| ~ aSet0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| ~ aSet0(sdtmndt0(xS,xx))
| aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f699,f51]) ).
fof(f4542,plain,
! [X0,X1] :
( ~ sQ71_spl
| ~ sP0_prd(sK1_skl(X1,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)),xx,xS)
| ~ aElement0(xx)
| ~ aSet0(xS)
| ~ aSet0(X1)
| aSubsetOf0(X1,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f699,f118]) ).
fof(f4543,definition,
! [X0] :
( sQ297_spl
<=> ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| ~ aSet0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)) = xx
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ297_spl])],[split_symbol_definition]) ).
fof(f4546,plain,
( ~ sQ18_spl
| ~ sQ71_spl
| ~ sQ19_spl
| sQ297_spl ),
inference(split_clause,[status(thm)],[f4538,f4543,f243,f698,f240]) ).
fof(f4547,definition,
! [X0,X1] :
( sQ298_spl
<=> ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),X1),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| ~ aSet0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),X1),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)) = X1
| ~ aElement0(X1)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),X1))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),X1),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ298_spl])],[split_symbol_definition]) ).
fof(f4550,plain,
( ~ sQ71_spl
| ~ sQ5_spl
| sQ298_spl ),
inference(split_clause,[status(thm)],[f4539,f4547,f148,f698]) ).
fof(f4551,definition,
! [X0] :
( sQ299_spl
<=> ( aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| ~ aSet0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ299_spl])],[split_symbol_definition]) ).
fof(f4554,plain,
( ~ sQ71_spl
| ~ sQ5_spl
| sQ299_spl ),
inference(split_clause,[status(thm)],[f4540,f4551,f148,f698]) ).
fof(f4555,definition,
! [X0,X1] :
( sQ300_spl
<=> ( ~ sP0_prd(sK1_skl(X1,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)),xx,xS)
| ~ aSet0(X1)
| aSubsetOf0(X1,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ300_spl])],[split_symbol_definition]) ).
fof(f4558,plain,
( ~ sQ71_spl
| ~ sQ1_spl
| ~ sQ0_spl
| sQ300_spl ),
inference(split_clause,[status(thm)],[f4542,f4555,f123,f126,f698]) ).
fof(f4564,plain,
! [X0,X1,X2] :
( ~ sQ89_spl
| ~ aSubsetOf0(X2,sdtmndt0(X1,X0))
| ~ aSet0(sdtmndt0(X1,X0))
| ~ aSubsetOf0(xS,X2)
| sdtmndt0(X1,X0) = sdtmndt0(xS,xx)
| ~ aSubsetOf0(X1,sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f3452,f1168]) ).
fof(f4566,plain,
! [X0,X1,X2,X3] :
( ~ sQ89_spl
| ~ aSubsetOf0(X3,sdtmndt0(X1,X0))
| ~ aSet0(sdtmndt0(X1,X0))
| ~ aSubsetOf0(X2,X3)
| ~ aSubsetOf0(xS,X2)
| sdtmndt0(X1,X0) = sdtmndt0(xS,xx)
| ~ aSubsetOf0(X1,sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f3452,f1903]) ).
fof(f4574,definition,
! [X0,X1,X2] :
( sQ301_spl
<=> ( ~ aSubsetOf0(X2,sdtmndt0(X1,X0))
| ~ aSet0(sdtmndt0(X1,X0))
| ~ aSubsetOf0(xS,X2)
| sdtmndt0(X1,X0) = sdtmndt0(xS,xx)
| ~ aSubsetOf0(X1,sdtmndt0(xS,xx))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ301_spl])],[split_symbol_definition]) ).
fof(f4577,plain,
( ~ sQ89_spl
| ~ sQ5_spl
| sQ301_spl ),
inference(split_clause,[status(thm)],[f4564,f4574,f148,f841]) ).
fof(f4579,definition,
! [X0,X1,X2,X3] :
( sQ302_spl
<=> ( ~ aSubsetOf0(X3,sdtmndt0(X1,X0))
| ~ aSet0(sdtmndt0(X1,X0))
| ~ aSubsetOf0(X2,X3)
| ~ aSubsetOf0(xS,X2)
| sdtmndt0(X1,X0) = sdtmndt0(xS,xx)
| ~ aSubsetOf0(X1,sdtmndt0(xS,xx))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ302_spl])],[split_symbol_definition]) ).
fof(f4582,plain,
( ~ sQ89_spl
| ~ sQ5_spl
| sQ302_spl ),
inference(split_clause,[status(thm)],[f4566,f4579,f148,f841]) ).
fof(f4649,plain,
! [X0,X1] :
( ~ sQ80_spl
| aElementOf0(sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)),X1)
| ~ aSubsetOf0(xS,X1)
| ~ aSet0(X1)
| ~ aElement0(xx)
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f790,f3454]) ).
fof(f4650,plain,
! [X0] :
( ~ sQ80_spl
| aElementOf0(sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)),xS)
| ~ aElement0(xx)
| ~ aSet0(xS)
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f790,f3417]) ).
fof(f4651,plain,
! [X0] :
( ~ sQ80_spl
| sP0_prd(sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)),xx,xS)
| ~ aElement0(xx)
| ~ aSet0(xS)
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f790,f117]) ).
fof(f4652,plain,
! [X0] :
( ~ sQ80_spl
| aElement0(sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)))
| ~ aSet0(sdtmndt0(xS,xx))
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f790,f28]) ).
fof(f4653,definition,
! [X0,X1] :
( sQ308_spl
<=> ( aElementOf0(sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)),X1)
| ~ aSubsetOf0(xS,X1)
| ~ aSet0(X1)
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ308_spl])],[split_symbol_definition]) ).
fof(f4656,plain,
( ~ sQ80_spl
| ~ sQ1_spl
| sQ308_spl ),
inference(split_clause,[status(thm)],[f4649,f4653,f126,f789]) ).
fof(f4657,definition,
! [X0] :
( sQ309_spl
<=> ( aElementOf0(sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)),xS)
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ309_spl])],[split_symbol_definition]) ).
fof(f4660,plain,
( ~ sQ80_spl
| ~ sQ1_spl
| ~ sQ0_spl
| sQ309_spl ),
inference(split_clause,[status(thm)],[f4650,f4657,f123,f126,f789]) ).
fof(f4661,definition,
! [X0] :
( sQ310_spl
<=> ( sP0_prd(sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)),xx,xS)
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ310_spl])],[split_symbol_definition]) ).
fof(f4664,plain,
( ~ sQ80_spl
| ~ sQ1_spl
| ~ sQ0_spl
| sQ310_spl ),
inference(split_clause,[status(thm)],[f4651,f4661,f123,f126,f789]) ).
fof(f4665,definition,
! [X0] :
( sQ311_spl
<=> ( aElement0(sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)))
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ311_spl])],[split_symbol_definition]) ).
fof(f4668,plain,
( ~ sQ80_spl
| ~ sQ5_spl
| sQ311_spl ),
inference(split_clause,[status(thm)],[f4652,f4665,f148,f789]) ).
fof(f4669,plain,
! [X0,X1,X2] :
( ~ aElement0(X2)
| aSubsetOf0(sdtmndt0(X0,X1),sdtpldt0(X0,X2))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3361,f116]) ).
fof(f4674,plain,
! [X0,X1,X2,X3] :
( aElementOf0(X3,sdtpldt0(X0,X2))
| ~ aElementOf0(X3,sdtmndt0(X0,X1))
| ~ aSet0(sdtpldt0(X0,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f4669,f50]) ).
fof(f4678,plain,
! [X0,X1,X2,X3] :
( aElementOf0(X3,sdtpldt0(X0,X2))
| ~ aElementOf0(X3,sdtmndt0(X0,X1))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f4674,f110]) ).
fof(f4681,plain,
! [X0,X1,X2] :
( ~ sQ33_spl
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X2) = xx
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X2) = X1
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X2),X2)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aSet0(X2)
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X2),sdtpldt0(xS,X0))
| ~ aElement0(X0)
| ~ aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f4678,f364]) ).
fof(f4683,plain,
! [X0,X1] :
( ~ sQ80_spl
| sK2_skl(slcrc0,X1,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| sK2_skl(slcrc0,X1,sdtpldt0(sdtmndt0(xS,xx),xx)) = X1
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1)
| ~ aElement0(X1)
| aElementOf0(sK2_skl(slcrc0,X1,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtpldt0(xS,X0))
| ~ aElement0(X0)
| ~ aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f4678,f790]) ).
fof(f4695,plain,
! [X0,X1] :
( ~ sQ18_spl
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X1)
| ~ aSet0(X1)
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1) = xx
| aElementOf0(sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1),sdtpldt0(xS,X0))
| ~ aElement0(X0)
| ~ aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f4678,f241]) ).
fof(f4698,plain,
! [X0,X1] :
( X1 = xx
| ~ aElementOf0(X1,xS)
| ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(xS,X0))
| ~ aElement0(X0)
| ~ aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f4678,f94]) ).
fof(f4699,plain,
! [X0,X1,X2,X3] :
( ~ sP0_prd(X3,X1,X0)
| ~ aElement0(X1)
| ~ aSet0(X0)
| aElementOf0(X3,sdtpldt0(X0,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f4678,f118]) ).
fof(f4702,definition,
! [X0,X1,X2] :
( sQ312_spl
<=> ( sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X2) = xx
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X2) = X1
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X2),X2)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aSet0(X2)
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1,X2),sdtpldt0(xS,X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ312_spl])],[split_symbol_definition]) ).
fof(f4705,plain,
( ~ sQ33_spl
| sQ312_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f4681,f123,f126,f4702,f363]) ).
fof(f4707,definition,
! [X0,X1] :
( sQ313_spl
<=> ( sK2_skl(slcrc0,X1,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| sK2_skl(slcrc0,X1,sdtpldt0(sdtmndt0(xS,xx),xx)) = X1
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1)
| ~ aElement0(X1)
| aElementOf0(sK2_skl(slcrc0,X1,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtpldt0(xS,X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ313_spl])],[split_symbol_definition]) ).
fof(f4710,plain,
( ~ sQ80_spl
| sQ313_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f4683,f123,f126,f4707,f789]) ).
fof(f4728,definition,
! [X0,X1] :
( sQ316_spl
<=> ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X1)
| ~ aSet0(X1)
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1) = xx
| aElementOf0(sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X1),sdtpldt0(xS,X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ316_spl])],[split_symbol_definition]) ).
fof(f4731,plain,
( ~ sQ18_spl
| sQ316_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f4695,f123,f126,f4728,f240]) ).
fof(f4734,definition,
! [X0,X1] :
( sQ317_spl
<=> ( X1 = xx
| ~ aElementOf0(X1,xS)
| ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(xS,X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ317_spl])],[split_symbol_definition]) ).
fof(f4735,plain,
! [X0,X1] :
( ~ sQ317_spl
| X1 = xx
| ~ aElementOf0(X1,xS)
| ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(xS,X0))
| ~ aElement0(X0) ),
inference(component_clause,[status(thm)],[f4734]) ).
fof(f4737,plain,
( sQ317_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f4698,f123,f126,f4734]) ).
fof(f4738,plain,
! [X0,X1,X2,X3] :
( ~ sP0_prd(X3,X1,X0)
| aElementOf0(X3,sdtpldt0(X0,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f4699]) ).
fof(f4753,plain,
! [X0,X1] :
( aElement0(X1)
| ~ sP0_prd(X1,X0,sdtmndt0(xS,xx))
| ~ aElement0(xx)
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f4738,f96]) ).
fof(f4754,plain,
! [X0,X1] :
( X1 = xx
| aElementOf0(X1,sdtmndt0(xS,xx))
| ~ sP0_prd(X1,X0,sdtmndt0(xS,xx))
| ~ aElement0(xx)
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f4738,f97]) ).
fof(f4763,definition,
! [X0,X1] :
( sQ319_spl
<=> ( aElement0(X1)
| ~ sP0_prd(X1,X0,sdtmndt0(xS,xx))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ319_spl])],[split_symbol_definition]) ).
fof(f4766,plain,
( ~ sQ1_spl
| sQ319_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f4753,f148,f4763,f126]) ).
fof(f4767,definition,
! [X0,X1] :
( sQ320_spl
<=> ( X1 = xx
| aElementOf0(X1,sdtmndt0(xS,xx))
| ~ sP0_prd(X1,X0,sdtmndt0(xS,xx))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ320_spl])],[split_symbol_definition]) ).
fof(f4770,plain,
( ~ sQ1_spl
| sQ320_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f4754,f148,f4767,f126]) ).
fof(f4783,plain,
! [X0,X1] :
( ~ sQ317_spl
| X1 = X0
| aElementOf0(X1,xS)
| ~ aElement0(X0)
| ~ aSet0(xS)
| X1 = xx
| ~ aElementOf0(X1,xS)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f4735,f112]) ).
fof(f4790,definition,
! [X0,X1] :
( sQ322_spl
<=> ( X1 = X0
| aElementOf0(X1,xS)
| ~ aElement0(X0)
| X1 = xx
| ~ aElementOf0(X1,xS)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ322_spl])],[split_symbol_definition]) ).
fof(f4793,plain,
( ~ sQ317_spl
| ~ sQ0_spl
| sQ322_spl ),
inference(split_clause,[status(thm)],[f4783,f4790,f123,f4734]) ).
fof(f4830,plain,
! [X0] :
( ~ sQ81_spl
| ~ aElementOf0(sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)),slcrc0)
| ~ aSet0(slcrc0)
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aElement0(X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)))
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f794,f352]) ).
fof(f4831,definition,
! [X0] :
( sQ327_spl
<=> ( ~ aElementOf0(sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)),slcrc0)
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aElement0(X0)
| aElement0(sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),xx)))
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ327_spl])],[split_symbol_definition]) ).
fof(f4834,plain,
( ~ sQ81_spl
| ~ sQ3_spl
| ~ sQ19_spl
| sQ327_spl ),
inference(split_clause,[status(thm)],[f4830,f4831,f243,f140,f793]) ).
fof(f4838,plain,
! [X0,X1,X2,X3] :
( ~ sQ89_spl
| sdtmndt0(xS,xx) = sdtmndt0(X1,X0)
| ~ aSubsetOf0(xS,sdtmndt0(X1,X0))
| ~ aSet0(sdtmndt0(X1,X0))
| ~ aSubsetOf0(X3,sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aSubsetOf0(X2,X3)
| ~ aSubsetOf0(X1,X2)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f4348,f2842]) ).
fof(f4841,plain,
! [X0,X1,X2,X3] :
( ~ sQ13_spl
| slcrc0 = sdtmndt0(X1,X0)
| ~ aSet0(sdtmndt0(X1,X0))
| ~ aSubsetOf0(X3,slcrc0)
| ~ aSet0(slcrc0)
| ~ aSubsetOf0(X2,X3)
| ~ aSubsetOf0(X1,X2)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f4348,f269]) ).
fof(f4849,definition,
! [X0,X1,X2,X3] :
( sQ328_spl
<=> ( sdtmndt0(xS,xx) = sdtmndt0(X1,X0)
| ~ aSubsetOf0(xS,sdtmndt0(X1,X0))
| ~ aSet0(sdtmndt0(X1,X0))
| ~ aSubsetOf0(X3,sdtmndt0(xS,xx))
| ~ aSubsetOf0(X2,X3)
| ~ aSubsetOf0(X1,X2)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ328_spl])],[split_symbol_definition]) ).
fof(f4852,plain,
( ~ sQ89_spl
| ~ sQ5_spl
| sQ328_spl ),
inference(split_clause,[status(thm)],[f4838,f4849,f148,f841]) ).
fof(f4855,definition,
! [X0,X1,X2,X3] :
( sQ329_spl
<=> ( slcrc0 = sdtmndt0(X1,X0)
| ~ aSet0(sdtmndt0(X1,X0))
| ~ aSubsetOf0(X3,slcrc0)
| ~ aSubsetOf0(X2,X3)
| ~ aSubsetOf0(X1,X2)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ329_spl])],[split_symbol_definition]) ).
fof(f4858,plain,
( ~ sQ13_spl
| ~ sQ3_spl
| sQ329_spl ),
inference(split_clause,[status(thm)],[f4841,f4855,f140,f210]) ).
fof(f4871,plain,
! [X0,X1,X2,X3] :
( ~ sQ33_spl
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X2,X3) = xx
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X2,X3) = X2
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X2,X3),X3)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X3,X2)
| ~ aElement0(X2)
| ~ aSet0(X3)
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X2,X3),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0)
| ~ aElement0(xx) ),
inference(resolution,[status(thm)],[f4351,f364]) ).
fof(f4873,plain,
! [X0,X1,X2] :
( ~ sQ80_spl
| sK2_skl(slcrc0,X2,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| sK2_skl(slcrc0,X2,sdtpldt0(sdtmndt0(xS,xx),xx)) = X2
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X2)
| ~ aElement0(X2)
| aElementOf0(sK2_skl(slcrc0,X2,sdtpldt0(sdtmndt0(xS,xx),xx)),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0)
| ~ aElement0(xx) ),
inference(resolution,[status(thm)],[f4351,f790]) ).
fof(f4885,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X2)
| ~ aSet0(X2)
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X2) = xx
| aElementOf0(sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X2),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0)
| ~ aElement0(xx) ),
inference(resolution,[status(thm)],[f4351,f241]) ).
fof(f4888,plain,
! [X0,X1,X2] :
( X2 = xx
| ~ aElementOf0(X2,xS)
| ~ aElement0(X2)
| aElementOf0(X2,X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0)
| ~ aElement0(xx) ),
inference(resolution,[status(thm)],[f4351,f94]) ).
fof(f4892,definition,
! [X0,X1,X2,X3] :
( sQ330_spl
<=> ( sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X2,X3) = xx
| sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X2,X3) = X2
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X2,X3),X3)
| sdtpldt0(sdtmndt0(xS,xx),xx) = sdtpldt0(X3,X2)
| ~ aElement0(X2)
| ~ aSet0(X3)
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X2,X3),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ330_spl])],[split_symbol_definition]) ).
fof(f4895,plain,
( ~ sQ33_spl
| sQ330_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f4871,f126,f4892,f363]) ).
fof(f4897,definition,
! [X0,X1,X2] :
( sQ331_spl
<=> ( sK2_skl(slcrc0,X2,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| sK2_skl(slcrc0,X2,sdtpldt0(sdtmndt0(xS,xx),xx)) = X2
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X2)
| ~ aElement0(X2)
| aElementOf0(sK2_skl(slcrc0,X2,sdtpldt0(sdtmndt0(xS,xx),xx)),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ331_spl])],[split_symbol_definition]) ).
fof(f4900,plain,
( ~ sQ80_spl
| sQ331_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f4873,f126,f4897,f789]) ).
fof(f4912,definition,
! [X0,X1,X2] :
( sQ332_spl
<=> ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X2)
| ~ aSet0(X2)
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X2) = xx
| aElementOf0(sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X2),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ332_spl])],[split_symbol_definition]) ).
fof(f4915,plain,
( ~ sQ18_spl
| sQ332_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f4885,f126,f4912,f240]) ).
fof(f4918,definition,
! [X0,X1,X2] :
( sQ333_spl
<=> ( X2 = xx
| ~ aElementOf0(X2,xS)
| ~ aElement0(X2)
| aElementOf0(X2,X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ333_spl])],[split_symbol_definition]) ).
fof(f4921,plain,
( sQ333_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f4888,f126,f4918]) ).
fof(f4928,plain,
! [X0,X1] :
( ~ sQ36_spl
| aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(sdtpldt0(xS,X1),X0))
| ~ aSet0(sdtpldt0(sdtpldt0(xS,X1),X0))
| ~ aElement0(X1)
| ~ aSet0(xS)
| ~ aSet0(sdtmndt0(xS,xx))
| aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(sdtpldt0(xS,X1),X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f702,f386]) ).
fof(f4929,plain,
! [X0,X1] :
( ~ sQ18_spl
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0))
| ~ aSet0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0))
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)) = xx
| ~ aElement0(X1)
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f702,f241]) ).
fof(f4932,plain,
! [X0,X1,X2] :
( sK1_skl(X1,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X2),X0)) = xx
| ~ aElementOf0(sK1_skl(X1,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X2),X0)),xS)
| ~ aElement0(sK1_skl(X1,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X2),X0)))
| ~ aElement0(X2)
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aSet0(X1)
| aSubsetOf0(X1,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X2),X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f702,f94]) ).
fof(f4935,plain,
! [X0,X1,X2] :
( ~ aElementOf0(sK1_skl(X1,sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X2),X0)),sdtmndt0(xS,xx))
| ~ aElement0(X2)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(X1)
| aSubsetOf0(X1,sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X2),X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f702,f343]) ).
fof(f4938,definition,
! [X0,X1] :
( sQ335_spl
<=> ( aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(sdtpldt0(xS,X1),X0))
| ~ aSet0(sdtpldt0(sdtpldt0(xS,X1),X0))
| ~ aElement0(X1)
| aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(sdtpldt0(xS,X1),X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ335_spl])],[split_symbol_definition]) ).
fof(f4941,plain,
( ~ sQ36_spl
| ~ sQ0_spl
| ~ sQ5_spl
| sQ335_spl ),
inference(split_clause,[status(thm)],[f4928,f4938,f148,f123,f385]) ).
fof(f4942,definition,
! [X0,X1] :
( sQ336_spl
<=> ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0))
| ~ aSet0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0))
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)) = xx
| ~ aElement0(X1)
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ336_spl])],[split_symbol_definition]) ).
fof(f4945,plain,
( ~ sQ18_spl
| ~ sQ5_spl
| ~ sQ19_spl
| sQ336_spl ),
inference(split_clause,[status(thm)],[f4929,f4942,f243,f148,f240]) ).
fof(f4949,definition,
! [X0,X1,X2] :
( sQ337_spl
<=> ( sK1_skl(X1,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X2),X0)) = xx
| ~ aElementOf0(sK1_skl(X1,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X2),X0)),xS)
| ~ aElement0(sK1_skl(X1,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X2),X0)))
| ~ aElement0(X2)
| ~ aSet0(X1)
| aSubsetOf0(X1,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X2),X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ337_spl])],[split_symbol_definition]) ).
fof(f4952,plain,
( ~ sQ5_spl
| sQ337_spl ),
inference(split_clause,[status(thm)],[f4932,f4949,f148]) ).
fof(f4954,definition,
! [X0,X1,X2] :
( sQ338_spl
<=> ( ~ aElementOf0(sK1_skl(X1,sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X2),X0)),sdtmndt0(xS,xx))
| ~ aElement0(X2)
| ~ aSet0(X1)
| aSubsetOf0(X1,sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X2),X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ338_spl])],[split_symbol_definition]) ).
fof(f4957,plain,
( ~ sQ19_spl
| sQ338_spl ),
inference(split_clause,[status(thm)],[f4935,f4954,f243]) ).
fof(f4966,plain,
! [X0,X1] :
( aElement0(sK0_skl(sdtmndt0(X1,X0)))
| sdtmndt0(X1,X0) = slcrc0
| ~ aSubsetOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f4378,f96]) ).
fof(f4967,plain,
! [X0,X1] :
( sK0_skl(sdtmndt0(X1,X0)) = xx
| aElementOf0(sK0_skl(sdtmndt0(X1,X0)),sdtmndt0(xS,xx))
| sdtmndt0(X1,X0) = slcrc0
| ~ aSubsetOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f4378,f97]) ).
fof(f4971,plain,
! [X0,X1] :
( aElement0(sK0_skl(sdtmndt0(X1,X0)))
| sdtmndt0(X1,X0) = slcrc0
| ~ aSubsetOf0(X1,sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f4378,f91]) ).
fof(f4972,plain,
! [X0,X1,X2,X3] :
( ~ sQ89_spl
| aElementOf0(sK0_skl(sdtmndt0(X1,X0)),X3)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3)
| ~ aSubsetOf0(xS,X2)
| sdtmndt0(X1,X0) = slcrc0
| ~ aSubsetOf0(X1,sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f4378,f1909]) ).
fof(f4973,plain,
! [X0,X1,X2] :
( ~ sQ89_spl
| aElementOf0(sK0_skl(sdtmndt0(X1,X0)),X2)
| ~ aSubsetOf0(xS,X2)
| ~ aSet0(X2)
| sdtmndt0(X1,X0) = slcrc0
| ~ aSubsetOf0(X1,sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f4378,f1579]) ).
fof(f4974,plain,
! [X0,X1] :
( aElementOf0(sK0_skl(sdtmndt0(X1,X0)),xS)
| sdtmndt0(X1,X0) = slcrc0
| ~ aSubsetOf0(X1,sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f4378,f92]) ).
fof(f4980,plain,
! [X0,X1] :
( sdtmndt0(X1,X0) = slcrc0
| ~ aSubsetOf0(X1,slcrc0)
| ~ aSet0(slcrc0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f4378,f108]) ).
fof(f4982,definition,
! [X0,X1] :
( sQ339_spl
<=> ( aElement0(sK0_skl(sdtmndt0(X1,X0)))
| sdtmndt0(X1,X0) = slcrc0
| ~ aSubsetOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ339_spl])],[split_symbol_definition]) ).
fof(f4985,plain,
( ~ sQ19_spl
| sQ339_spl ),
inference(split_clause,[status(thm)],[f4966,f4982,f243]) ).
fof(f4986,definition,
! [X0,X1] :
( sQ340_spl
<=> ( sK0_skl(sdtmndt0(X1,X0)) = xx
| aElementOf0(sK0_skl(sdtmndt0(X1,X0)),sdtmndt0(xS,xx))
| sdtmndt0(X1,X0) = slcrc0
| ~ aSubsetOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ340_spl])],[split_symbol_definition]) ).
fof(f4989,plain,
( ~ sQ19_spl
| sQ340_spl ),
inference(split_clause,[status(thm)],[f4967,f4986,f243]) ).
fof(f4993,definition,
! [X0,X1] :
( sQ341_spl
<=> ( aElement0(sK0_skl(sdtmndt0(X1,X0)))
| sdtmndt0(X1,X0) = slcrc0
| ~ aSubsetOf0(X1,sdtmndt0(xS,xx))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ341_spl])],[split_symbol_definition]) ).
fof(f4996,plain,
( ~ sQ5_spl
| sQ341_spl ),
inference(split_clause,[status(thm)],[f4971,f4993,f148]) ).
fof(f4997,definition,
! [X0,X1,X2,X3] :
( sQ342_spl
<=> ( aElementOf0(sK0_skl(sdtmndt0(X1,X0)),X3)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3)
| ~ aSubsetOf0(xS,X2)
| sdtmndt0(X1,X0) = slcrc0
| ~ aSubsetOf0(X1,sdtmndt0(xS,xx))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ342_spl])],[split_symbol_definition]) ).
fof(f5000,plain,
( ~ sQ89_spl
| ~ sQ5_spl
| sQ342_spl ),
inference(split_clause,[status(thm)],[f4972,f4997,f148,f841]) ).
fof(f5001,definition,
! [X0,X1,X2] :
( sQ343_spl
<=> ( aElementOf0(sK0_skl(sdtmndt0(X1,X0)),X2)
| ~ aSubsetOf0(xS,X2)
| ~ aSet0(X2)
| sdtmndt0(X1,X0) = slcrc0
| ~ aSubsetOf0(X1,sdtmndt0(xS,xx))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ343_spl])],[split_symbol_definition]) ).
fof(f5004,plain,
( ~ sQ89_spl
| ~ sQ5_spl
| sQ343_spl ),
inference(split_clause,[status(thm)],[f4973,f5001,f148,f841]) ).
fof(f5005,definition,
! [X0,X1] :
( sQ344_spl
<=> ( aElementOf0(sK0_skl(sdtmndt0(X1,X0)),xS)
| sdtmndt0(X1,X0) = slcrc0
| ~ aSubsetOf0(X1,sdtmndt0(xS,xx))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ344_spl])],[split_symbol_definition]) ).
fof(f5008,plain,
( ~ sQ5_spl
| sQ344_spl ),
inference(split_clause,[status(thm)],[f4974,f5005,f148]) ).
fof(f5014,definition,
! [X0,X1] :
( sQ345_spl
<=> ( sdtmndt0(X1,X0) = slcrc0
| ~ aSubsetOf0(X1,slcrc0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ345_spl])],[split_symbol_definition]) ).
fof(f5017,plain,
( ~ sQ3_spl
| sQ345_spl ),
inference(split_clause,[status(thm)],[f4980,f5014,f140]) ).
fof(f5023,plain,
! [X0,X1,X2] :
( ~ sQ34_spl
| ~ aElementOf0(sK2_skl(slcrc0,X0,sdtpldt0(X1,X2)),slcrc0)
| ~ aSet0(slcrc0)
| slcrc0 = sdtpldt0(sdtpldt0(X1,X2),X0)
| ~ aElement0(X0)
| ~ aSet0(sdtpldt0(X1,X2))
| aElement0(sK2_skl(slcrc0,X0,sdtpldt0(X1,X2)))
| ~ aElement0(X2)
| ~ aSet0(X1)
| slcrc0 = sdtpldt0(sdtpldt0(X1,X2),X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f797,f352]) ).
fof(f5024,definition,
! [X0,X1,X2] :
( sQ346_spl
<=> ( ~ aElementOf0(sK2_skl(slcrc0,X0,sdtpldt0(X1,X2)),slcrc0)
| slcrc0 = sdtpldt0(sdtpldt0(X1,X2),X0)
| ~ aElement0(X0)
| ~ aSet0(sdtpldt0(X1,X2))
| aElement0(sK2_skl(slcrc0,X0,sdtpldt0(X1,X2)))
| ~ aElement0(X2)
| ~ aSet0(X1)
| slcrc0 = sdtpldt0(sdtpldt0(X1,X2),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ346_spl])],[split_symbol_definition]) ).
fof(f5027,plain,
( ~ sQ34_spl
| ~ sQ3_spl
| sQ346_spl ),
inference(split_clause,[status(thm)],[f5023,f5024,f140,f367]) ).
fof(f5029,plain,
! [X0,X1] :
( ~ sQ34_spl
| ~ aElementOf0(sK2_skl(slcrc0,X0,sdtpldt0(slcrc0,X1)),sdtpldt0(slcrc0,X1))
| ~ aSet0(slcrc0)
| slcrc0 = sdtpldt0(sdtpldt0(slcrc0,X1),X0)
| ~ aElement0(X0)
| ~ aSet0(sdtpldt0(slcrc0,X1))
| sK2_skl(slcrc0,X0,sdtpldt0(slcrc0,X1)) = X1
| ~ aElement0(X1)
| ~ aSet0(slcrc0)
| sK2_skl(slcrc0,X0,sdtpldt0(slcrc0,X1)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(slcrc0,X1),X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f798,f274]) ).
fof(f5030,plain,
! [X0,X1] :
( ~ sQ34_spl
| aElement0(sK2_skl(slcrc0,X0,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1)))
| sK2_skl(slcrc0,X0,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1)) = X1
| ~ aElement0(X1)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| sK2_skl(slcrc0,X0,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1),X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f798,f96]) ).
fof(f5031,plain,
! [X0,X1] :
( ~ sQ34_spl
| sK2_skl(slcrc0,X0,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1)) = xx
| aElementOf0(sK2_skl(slcrc0,X0,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1)),sdtmndt0(xS,xx))
| sK2_skl(slcrc0,X0,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1)) = X1
| ~ aElement0(X1)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| sK2_skl(slcrc0,X0,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1),X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f798,f97]) ).
fof(f5035,plain,
! [X0,X1] :
( ~ sQ34_spl
| aElement0(sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),X1)))
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),X1)) = X1
| ~ aElement0(X1)
| ~ aSet0(sdtmndt0(xS,xx))
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),X1)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f798,f91]) ).
fof(f5036,plain,
! [X0,X1,X2,X3] :
( ~ sQ89_spl
| ~ sQ34_spl
| aElementOf0(sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),X1)),X3)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3)
| ~ aSubsetOf0(xS,X2)
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),X1)) = X1
| ~ aElement0(X1)
| ~ aSet0(sdtmndt0(xS,xx))
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),X1)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f798,f1909]) ).
fof(f5037,plain,
! [X0,X1,X2] :
( ~ sQ89_spl
| ~ sQ34_spl
| aElementOf0(sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),X1)),X2)
| ~ aSubsetOf0(xS,X2)
| ~ aSet0(X2)
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),X1)) = X1
| ~ aElement0(X1)
| ~ aSet0(sdtmndt0(xS,xx))
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),X1)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f798,f1579]) ).
fof(f5038,plain,
! [X0,X1] :
( ~ sQ34_spl
| aElementOf0(sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),X1)),xS)
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),X1)) = X1
| ~ aElement0(X1)
| ~ aSet0(sdtmndt0(xS,xx))
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),X1)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f798,f92]) ).
fof(f5044,plain,
! [X0,X1] :
( ~ sQ34_spl
| sK2_skl(slcrc0,X0,sdtpldt0(slcrc0,X1)) = X1
| ~ aElement0(X1)
| ~ aSet0(slcrc0)
| sK2_skl(slcrc0,X0,sdtpldt0(slcrc0,X1)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(slcrc0,X1),X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f798,f108]) ).
fof(f5046,definition,
! [X0,X1] :
( sQ347_spl
<=> ( ~ aElementOf0(sK2_skl(slcrc0,X0,sdtpldt0(slcrc0,X1)),sdtpldt0(slcrc0,X1))
| slcrc0 = sdtpldt0(sdtpldt0(slcrc0,X1),X0)
| ~ aElement0(X0)
| ~ aSet0(sdtpldt0(slcrc0,X1))
| sK2_skl(slcrc0,X0,sdtpldt0(slcrc0,X1)) = X1
| ~ aElement0(X1)
| sK2_skl(slcrc0,X0,sdtpldt0(slcrc0,X1)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(slcrc0,X1),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ347_spl])],[split_symbol_definition]) ).
fof(f5049,plain,
( ~ sQ34_spl
| ~ sQ3_spl
| sQ347_spl ),
inference(split_clause,[status(thm)],[f5029,f5046,f140,f367]) ).
fof(f5050,definition,
! [X0,X1] :
( sQ348_spl
<=> ( aElement0(sK2_skl(slcrc0,X0,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1)))
| sK2_skl(slcrc0,X0,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1)) = X1
| ~ aElement0(X1)
| sK2_skl(slcrc0,X0,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ348_spl])],[split_symbol_definition]) ).
fof(f5053,plain,
( ~ sQ34_spl
| ~ sQ19_spl
| sQ348_spl ),
inference(split_clause,[status(thm)],[f5030,f5050,f243,f367]) ).
fof(f5054,definition,
! [X0,X1] :
( sQ349_spl
<=> ( sK2_skl(slcrc0,X0,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1)) = xx
| aElementOf0(sK2_skl(slcrc0,X0,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1)),sdtmndt0(xS,xx))
| sK2_skl(slcrc0,X0,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1)) = X1
| ~ aElement0(X1)
| sK2_skl(slcrc0,X0,sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ349_spl])],[split_symbol_definition]) ).
fof(f5057,plain,
( ~ sQ34_spl
| ~ sQ19_spl
| sQ349_spl ),
inference(split_clause,[status(thm)],[f5031,f5054,f243,f367]) ).
fof(f5060,definition,
! [X0,X1] :
( sQ350_spl
<=> ( aElement0(sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),X1)))
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),X1)) = X1
| ~ aElement0(X1)
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),X1)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ350_spl])],[split_symbol_definition]) ).
fof(f5063,plain,
( ~ sQ34_spl
| ~ sQ5_spl
| sQ350_spl ),
inference(split_clause,[status(thm)],[f5035,f5060,f148,f367]) ).
fof(f5064,definition,
! [X0,X1,X2,X3] :
( sQ351_spl
<=> ( aElementOf0(sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),X1)),X3)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3)
| ~ aSubsetOf0(xS,X2)
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),X1)) = X1
| ~ aElement0(X1)
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),X1)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ351_spl])],[split_symbol_definition]) ).
fof(f5067,plain,
( ~ sQ89_spl
| ~ sQ34_spl
| ~ sQ5_spl
| sQ351_spl ),
inference(split_clause,[status(thm)],[f5036,f5064,f148,f367,f841]) ).
fof(f5068,definition,
! [X0,X1,X2] :
( sQ352_spl
<=> ( aElementOf0(sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),X1)),X2)
| ~ aSubsetOf0(xS,X2)
| ~ aSet0(X2)
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),X1)) = X1
| ~ aElement0(X1)
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),X1)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ352_spl])],[split_symbol_definition]) ).
fof(f5071,plain,
( ~ sQ89_spl
| ~ sQ34_spl
| ~ sQ5_spl
| sQ352_spl ),
inference(split_clause,[status(thm)],[f5037,f5068,f148,f367,f841]) ).
fof(f5072,definition,
! [X0,X1] :
( sQ353_spl
<=> ( aElementOf0(sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),X1)),xS)
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),X1)) = X1
| ~ aElement0(X1)
| sK2_skl(slcrc0,X0,sdtpldt0(sdtmndt0(xS,xx),X1)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),X1),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ353_spl])],[split_symbol_definition]) ).
fof(f5075,plain,
( ~ sQ34_spl
| ~ sQ5_spl
| sQ353_spl ),
inference(split_clause,[status(thm)],[f5038,f5072,f148,f367]) ).
fof(f5081,definition,
! [X0,X1] :
( sQ354_spl
<=> ( sK2_skl(slcrc0,X0,sdtpldt0(slcrc0,X1)) = X1
| ~ aElement0(X1)
| sK2_skl(slcrc0,X0,sdtpldt0(slcrc0,X1)) = X0
| slcrc0 = sdtpldt0(sdtpldt0(slcrc0,X1),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ354_spl])],[split_symbol_definition]) ).
fof(f5084,plain,
( ~ sQ34_spl
| ~ sQ3_spl
| sQ354_spl ),
inference(split_clause,[status(thm)],[f5044,f5081,f140,f367]) ).
fof(f5090,plain,
! [X0,X1,X2] :
( ~ sQ277_spl
| ~ sQ34_spl
| aElementOf0(sK2_skl(slcrc0,X0,sdtmndt0(slcrc0,X1)),X2)
| ~ aSet0(X2)
| ~ aElement0(X1)
| ~ aElement0(X1)
| ~ aSet0(slcrc0)
| sK2_skl(slcrc0,X0,sdtmndt0(slcrc0,X1)) = X0
| slcrc0 = sdtpldt0(sdtmndt0(slcrc0,X1),X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f807,f3620]) ).
fof(f5096,definition,
! [X0,X1,X2] :
( sQ355_spl
<=> ( aElementOf0(sK2_skl(slcrc0,X0,sdtmndt0(slcrc0,X1)),X2)
| ~ aSet0(X2)
| ~ aElement0(X1)
| ~ aElement0(X1)
| sK2_skl(slcrc0,X0,sdtmndt0(slcrc0,X1)) = X0
| slcrc0 = sdtpldt0(sdtmndt0(slcrc0,X1),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ355_spl])],[split_symbol_definition]) ).
fof(f5099,plain,
( ~ sQ277_spl
| ~ sQ34_spl
| ~ sQ3_spl
| sQ355_spl ),
inference(split_clause,[status(thm)],[f5090,f5096,f140,f367,f3615]) ).
fof(f5103,plain,
! [X0] :
( ~ sQ82_spl
| aElement0(sK2_skl(slcrc0,X0,sdtmndt0(xS,xx)))
| ~ aSet0(xS)
| sK2_skl(slcrc0,X0,sdtmndt0(xS,xx)) = X0
| slcrc0 = sdtpldt0(sdtmndt0(xS,xx),X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f800,f28]) ).
fof(f5104,plain,
( ~ sQ82_spl
| ~ sQ0_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f5103,f803,f123,f799]) ).
fof(f5111,plain,
! [X0,X1] :
( ~ sQ71_spl
| ~ aSet0(sdtmndt0(sdtmndt0(xS,xx),X0))
| aSubsetOf0(sdtmndt0(sdtmndt0(xS,xx),X0),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1))
| ~ aElement0(X1)
| aSubsetOf0(sdtmndt0(sdtmndt0(xS,xx),X0),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1))
| ~ aSet0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1))
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f3001,f699]) ).
fof(f5133,definition,
! [X0,X1] :
( sQ356_spl
<=> ( ~ aSet0(sdtmndt0(sdtmndt0(xS,xx),X0))
| aSubsetOf0(sdtmndt0(sdtmndt0(xS,xx),X0),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1))
| ~ aElement0(X1)
| aSubsetOf0(sdtmndt0(sdtmndt0(xS,xx),X0),sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1))
| ~ aSet0(sdtpldt0(sdtpldt0(sdtmndt0(xS,xx),xx),X1))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ356_spl])],[split_symbol_definition]) ).
fof(f5136,plain,
( ~ sQ71_spl
| sQ356_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f5111,f148,f5133,f698]) ).
fof(f5158,plain,
! [X0,X1] :
( ~ sQ34_spl
| ~ aElementOf0(sK2_skl(slcrc0,X1,X0),slcrc0)
| ~ aSet0(slcrc0)
| slcrc0 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0)
| aElement0(sK2_skl(slcrc0,X1,X0))
| slcrc0 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f812,f352]) ).
fof(f5159,definition,
! [X0,X1] :
( sQ357_spl
<=> ( ~ aElementOf0(sK2_skl(slcrc0,X1,X0),slcrc0)
| slcrc0 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0)
| aElement0(sK2_skl(slcrc0,X1,X0))
| slcrc0 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ357_spl])],[split_symbol_definition]) ).
fof(f5162,plain,
( ~ sQ34_spl
| ~ sQ3_spl
| sQ357_spl ),
inference(split_clause,[status(thm)],[f5158,f5159,f140,f367]) ).
fof(f5164,plain,
! [X0] :
( ~ sQ83_spl
| ~ aElementOf0(sK2_skl(slcrc0,X0,sdtmndt0(xS,xx)),slcrc0)
| ~ aSet0(slcrc0)
| slcrc0 = sdtpldt0(sdtmndt0(xS,xx),X0)
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx))
| aElement0(sK2_skl(slcrc0,X0,sdtmndt0(xS,xx)))
| slcrc0 = sdtpldt0(sdtmndt0(xS,xx),X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f804,f352]) ).
fof(f5165,definition,
! [X0] :
( sQ358_spl
<=> ( ~ aElementOf0(sK2_skl(slcrc0,X0,sdtmndt0(xS,xx)),slcrc0)
| slcrc0 = sdtpldt0(sdtmndt0(xS,xx),X0)
| ~ aElement0(X0)
| aElement0(sK2_skl(slcrc0,X0,sdtmndt0(xS,xx)))
| slcrc0 = sdtpldt0(sdtmndt0(xS,xx),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ358_spl])],[split_symbol_definition]) ).
fof(f5168,plain,
( ~ sQ83_spl
| ~ sQ3_spl
| ~ sQ5_spl
| sQ358_spl ),
inference(split_clause,[status(thm)],[f5164,f5165,f148,f140,f803]) ).
fof(f5173,plain,
! [X0,X1,X2,X3] :
( ~ sQ89_spl
| ~ aSubsetOf0(X3,sdtmndt0(X1,X0))
| ~ aSet0(sdtmndt0(X1,X0))
| ~ aSubsetOf0(xS,X3)
| sdtmndt0(X1,X0) = sdtmndt0(xS,xx)
| ~ aSubsetOf0(X2,sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aSubsetOf0(X1,X2)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f4349,f1168]) ).
fof(f5175,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ89_spl
| ~ aSubsetOf0(X4,sdtmndt0(X1,X0))
| ~ aSet0(sdtmndt0(X1,X0))
| ~ aSubsetOf0(X3,X4)
| ~ aSubsetOf0(xS,X3)
| sdtmndt0(X1,X0) = sdtmndt0(xS,xx)
| ~ aSubsetOf0(X2,sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aSubsetOf0(X1,X2)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f4349,f1903]) ).
fof(f5184,definition,
! [X0,X1,X2,X3] :
( sQ359_spl
<=> ( ~ aSubsetOf0(X3,sdtmndt0(X1,X0))
| ~ aSet0(sdtmndt0(X1,X0))
| ~ aSubsetOf0(xS,X3)
| sdtmndt0(X1,X0) = sdtmndt0(xS,xx)
| ~ aSubsetOf0(X2,sdtmndt0(xS,xx))
| ~ aSubsetOf0(X1,X2)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ359_spl])],[split_symbol_definition]) ).
fof(f5187,plain,
( ~ sQ89_spl
| ~ sQ5_spl
| sQ359_spl ),
inference(split_clause,[status(thm)],[f5173,f5184,f148,f841]) ).
fof(f5189,definition,
! [X0,X1,X2,X3,X4] :
( sQ360_spl
<=> ( ~ aSubsetOf0(X4,sdtmndt0(X1,X0))
| ~ aSet0(sdtmndt0(X1,X0))
| ~ aSubsetOf0(X3,X4)
| ~ aSubsetOf0(xS,X3)
| sdtmndt0(X1,X0) = sdtmndt0(xS,xx)
| ~ aSubsetOf0(X2,sdtmndt0(xS,xx))
| ~ aSubsetOf0(X1,X2)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ360_spl])],[split_symbol_definition]) ).
fof(f5192,plain,
( ~ sQ89_spl
| ~ sQ5_spl
| sQ360_spl ),
inference(split_clause,[status(thm)],[f5175,f5189,f148,f841]) ).
fof(f5199,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ aElement0(X0)
| ~ aSet0(xS)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtpldt0(xS,X0),X1))
| ~ aElement0(X1)
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtpldt0(xS,X0),X1))
| ~ aSet0(sdtpldt0(sdtpldt0(xS,X0),X1))
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtpldt0(xS,X0),X1)) = xx ),
inference(resolution,[status(thm)],[f1082,f702]) ).
fof(f5200,plain,
! [X0] :
( ~ sQ18_spl
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(xS,X0))
| ~ aElement0(X0)
| ~ aSet0(xS)
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(xS,X0))
| ~ aSet0(sdtpldt0(xS,X0))
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(xS,X0)) = xx ),
inference(resolution,[status(thm)],[f1082,f317]) ).
fof(f5201,plain,
( ~ sQ18_spl
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSet0(xS)
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSet0(xS)
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),xS) = xx ),
inference(resolution,[status(thm)],[f1082,f52]) ).
fof(f5205,definition,
! [X0,X1] :
( sQ361_spl
<=> ( ~ aElement0(X0)
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtpldt0(xS,X0),X1))
| ~ aElement0(X1)
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtpldt0(xS,X0),X1))
| ~ aSet0(sdtpldt0(sdtpldt0(xS,X0),X1))
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtpldt0(xS,X0),X1)) = xx ) ),
introduced(definition,[new_symbols(definition,[sQ361_spl])],[split_symbol_definition]) ).
fof(f5208,plain,
( ~ sQ18_spl
| ~ sQ0_spl
| ~ sQ19_spl
| sQ361_spl ),
inference(split_clause,[status(thm)],[f5199,f5205,f243,f123,f240]) ).
fof(f5209,definition,
! [X0] :
( sQ362_spl
<=> ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(xS,X0))
| ~ aElement0(X0)
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(xS,X0))
| ~ aSet0(sdtpldt0(xS,X0))
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(xS,X0)) = xx ) ),
introduced(definition,[new_symbols(definition,[sQ362_spl])],[split_symbol_definition]) ).
fof(f5212,plain,
( ~ sQ18_spl
| ~ sQ19_spl
| ~ sQ0_spl
| sQ362_spl ),
inference(split_clause,[status(thm)],[f5200,f5209,f123,f243,f240]) ).
fof(f5213,definition,
( sQ363_spl
<=> sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),xS) = xx ),
introduced(definition,[new_symbols(definition,[sQ363_spl])],[split_symbol_definition]) ).
fof(f5214,plain,
( ~ sQ363_spl
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),xS) = xx ),
inference(component_clause,[status(thm)],[f5213]) ).
fof(f5216,definition,
( sQ364_spl
<=> aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) ),
introduced(definition,[new_symbols(definition,[sQ364_spl])],[split_symbol_definition]) ).
fof(f5217,plain,
( ~ sQ364_spl
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) ),
inference(component_clause,[status(thm)],[f5216]) ).
fof(f5219,plain,
( ~ sQ18_spl
| ~ sQ19_spl
| sQ364_spl
| ~ sQ0_spl
| sQ363_spl ),
inference(split_clause,[status(thm)],[f5201,f5213,f123,f5216,f243,f240]) ).
fof(f5260,plain,
( ~ sQ363_spl
| ~ aElementOf0(xx,xS)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSet0(xS) ),
inference(paramodulation,[status(thm)],[f5214,f52]) ).
fof(f5268,plain,
( ~ sQ363_spl
| ~ sQ24_spl
| ~ sQ19_spl
| sQ364_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f5260,f123,f5216,f243,f288,f5213]) ).
fof(f5274,plain,
! [X0,X1] :
( ~ sQ102_spl
| aElementOf0(sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0),X1)
| ~ aSubsetOf0(xS,X1)
| ~ aSet0(X1)
| ~ aElement0(xx)
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aSet0(X0)
| sK1_skl(sdtpldt0(sdtmndt0(xS,xx),xx),X0) = xx ),
inference(resolution,[status(thm)],[f1097,f4390]) ).
fof(f5280,plain,
( ~ sQ102_spl
| ~ sQ1_spl
| sQ293_spl ),
inference(split_clause,[status(thm)],[f5274,f4379,f126,f1096]) ).
fof(f5286,plain,
( ~ sQ364_spl
| sdtpldt0(sdtmndt0(xS,xx),xx) = xS
| ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f5217,f266]) ).
fof(f5296,definition,
( sQ369_spl
<=> sdtpldt0(sdtmndt0(xS,xx),xx) = xS ),
introduced(definition,[new_symbols(definition,[sQ369_spl])],[split_symbol_definition]) ).
fof(f5297,plain,
( ~ sQ369_spl
| sdtpldt0(sdtmndt0(xS,xx),xx) = xS ),
inference(component_clause,[status(thm)],[f5296]) ).
fof(f5299,plain,
( ~ sQ364_spl
| sQ369_spl
| ~ sQ174_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f5286,f123,f2000,f5296,f5216]) ).
fof(f5423,plain,
! [X0] :
( ~ sQ20_spl
| aSubsetOf0(sdtmndt0(xS,X0),sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X0)
| ~ aSet0(xS)
| sK1_skl(sdtmndt0(xS,X0),sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| ~ aElement0(sK1_skl(sdtmndt0(xS,X0),sdtpldt0(sdtmndt0(xS,xx),xx)))
| ~ aSet0(sdtmndt0(xS,X0))
| aSubsetOf0(sdtmndt0(xS,X0),sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f1107,f3001]) ).
fof(f5425,plain,
! [X0] :
( ~ sQ20_spl
| aSubsetOf0(sdtpldt0(xS,X0),sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| sK1_skl(sdtpldt0(xS,X0),sdtpldt0(sdtmndt0(xS,xx),xx)) = X0
| ~ aElement0(X0)
| ~ aSet0(xS)
| sK1_skl(sdtpldt0(xS,X0),sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| ~ aElement0(sK1_skl(sdtpldt0(xS,X0),sdtpldt0(sdtmndt0(xS,xx),xx)))
| ~ aSet0(sdtpldt0(xS,X0))
| aSubsetOf0(sdtpldt0(xS,X0),sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f1107,f430]) ).
fof(f5426,plain,
( ~ sQ20_spl
| ~ aSet0(xS)
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| sK1_skl(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| ~ aElement0(sK1_skl(xS,sdtpldt0(sdtmndt0(xS,xx),xx)))
| ~ aSet0(xS)
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f1107,f51]) ).
fof(f5434,definition,
! [X0] :
( sQ392_spl
<=> ( aSubsetOf0(sdtmndt0(xS,X0),sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X0)
| sK1_skl(sdtmndt0(xS,X0),sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| ~ aElement0(sK1_skl(sdtmndt0(xS,X0),sdtpldt0(sdtmndt0(xS,xx),xx)))
| ~ aSet0(sdtmndt0(xS,X0))
| aSubsetOf0(sdtmndt0(xS,X0),sdtpldt0(sdtmndt0(xS,xx),xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ392_spl])],[split_symbol_definition]) ).
fof(f5437,plain,
( ~ sQ20_spl
| ~ sQ19_spl
| ~ sQ0_spl
| sQ392_spl ),
inference(split_clause,[status(thm)],[f5423,f5434,f123,f243,f250]) ).
fof(f5442,definition,
! [X0] :
( sQ394_spl
<=> ( aSubsetOf0(sdtpldt0(xS,X0),sdtpldt0(sdtmndt0(xS,xx),xx))
| sK1_skl(sdtpldt0(xS,X0),sdtpldt0(sdtmndt0(xS,xx),xx)) = X0
| ~ aElement0(X0)
| sK1_skl(sdtpldt0(xS,X0),sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| ~ aElement0(sK1_skl(sdtpldt0(xS,X0),sdtpldt0(sdtmndt0(xS,xx),xx)))
| ~ aSet0(sdtpldt0(xS,X0))
| aSubsetOf0(sdtpldt0(xS,X0),sdtpldt0(sdtmndt0(xS,xx),xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ394_spl])],[split_symbol_definition]) ).
fof(f5445,plain,
( ~ sQ20_spl
| ~ sQ19_spl
| ~ sQ0_spl
| sQ394_spl ),
inference(split_clause,[status(thm)],[f5425,f5442,f123,f243,f250]) ).
fof(f5446,definition,
( sQ395_spl
<=> aElement0(sK1_skl(xS,sdtpldt0(sdtmndt0(xS,xx),xx))) ),
introduced(definition,[new_symbols(definition,[sQ395_spl])],[split_symbol_definition]) ).
fof(f5448,plain,
( sQ395_spl
| ~ aElement0(sK1_skl(xS,sdtpldt0(sdtmndt0(xS,xx),xx))) ),
inference(component_clause,[status(thm)],[f5446]) ).
fof(f5449,definition,
( sQ396_spl
<=> sK1_skl(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx ),
introduced(definition,[new_symbols(definition,[sQ396_spl])],[split_symbol_definition]) ).
fof(f5450,plain,
( ~ sQ396_spl
| sK1_skl(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx ),
inference(component_clause,[status(thm)],[f5449]) ).
fof(f5452,plain,
( ~ sQ20_spl
| ~ sQ19_spl
| sQ396_spl
| ~ sQ395_spl
| ~ sQ0_spl
| sQ174_spl ),
inference(split_clause,[status(thm)],[f5426,f2000,f123,f5446,f5449,f243,f250]) ).
fof(f5455,plain,
( sQ395_spl
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f5448,f233]) ).
fof(f5456,plain,
( sQ395_spl
| sQ174_spl
| ~ sQ19_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f5455,f123,f243,f2000,f5446]) ).
fof(f5462,plain,
( ~ sQ396_spl
| ~ aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(xS)
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(paramodulation,[status(thm)],[f5450,f52]) ).
fof(f5469,plain,
( ~ sQ396_spl
| ~ sQ159_spl
| ~ sQ0_spl
| sQ174_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f5462,f243,f2000,f123,f1884,f5449]) ).
fof(f5471,plain,
( ~ sQ369_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5297,f100]) ).
fof(f5472,plain,
~ sQ369_spl,
inference(contradiction_clause,[status(thm)],[f5471]) ).
fof(f5473,plain,
$false,
inference(sat_refutation,[status(thm)],[f129,f131,f143,f160,f162,f170,f203,f208,f213,f229,f238,f246,f253,f257,f280,f284,f294,f296,f306,f308,f321,f351,f362,f366,f370,f374,f383,f388,f398,f402,f406,f410,f422,f447,f450,f469,f480,f486,f490,f519,f523,f563,f567,f572,f581,f599,f603,f608,f612,f617,f633,f661,f663,f683,f688,f701,f706,f725,f788,f792,f796,f802,f811,f821,f832,f844,f850,f855,f902,f1015,f1088,f1095,f1099,f1103,f1119,f1123,f1130,f1142,f1147,f1151,f1563,f1595,f1599,f1605,f1609,f1614,f1623,f1639,f1643,f1648,f1676,f1680,f1686,f1690,f1695,f1732,f1887,f1944,f1948,f1952,f1956,f1960,f1968,f1972,f1976,f1988,f2027,f2032,f2042,f2060,f2064,f2069,f2073,f2077,f2082,f2092,f2181,f2185,f2189,f2195,f2199,f2203,f2218,f2248,f2252,f2257,f2317,f2364,f2368,f2374,f2378,f2382,f2387,f2396,f2399,f2413,f2491,f2495,f2499,f2503,f2507,f2511,f2519,f2527,f2532,f2536,f2540,f2589,f2593,f2603,f2609,f2614,f2645,f2654,f3190,f3330,f3335,f3355,f3359,f3367,f3371,f3376,f3380,f3384,f3388,f3393,f3411,f3428,f3434,f3448,f3467,f3475,f3479,f3490,f3494,f3498,f3502,f3536,f3550,f3555,f3568,f3573,f3618,f3649,f3660,f3664,f3668,f3672,f3945,f3950,f4244,f4249,f4340,f4345,f4388,f4422,f4427,f4546,f4550,f4554,f4558,f4577,f4582,f4656,f4660,f4664,f4668,f4705,f4710,f4731,f4737,f4766,f4770,f4793,f4834,f4852,f4858,f4895,f4900,f4915,f4921,f4941,f4945,f4952,f4957,f4985,f4989,f4996,f5000,f5004,f5008,f5017,f5027,f5049,f5053,f5057,f5063,f5067,f5071,f5075,f5084,f5099,f5104,f5136,f5162,f5168,f5187,f5192,f5208,f5212,f5219,f5268,f5280,f5299,f5437,f5445,f5452,f5456,f5469,f5472]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM534+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 02:39:45 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 5.56/1.15 % Refutation found
% 5.56/1.15 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.56/1.15 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.56/1.17 % Elapsed time: 0.815451 seconds
% 5.56/1.17 % CPU time: 6.074703 seconds
% 5.56/1.17 % Total memory used: 156.857 MB
% 5.56/1.17 % Net memory used: 146.863 MB
%------------------------------------------------------------------------------