%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM537+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 01:40:54 PM UTC 2026
% Result : Theorem 67.49s 9.04s
% Output : CNFRefutation 67.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 314
% Syntax : Number of formulae : 1244 ( 17 unt; 306 def)
% Number of atoms : 4667 ( 569 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 6246 (2823 ~;3010 |; 84 &)
% ( 316 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 308 ( 306 usr; 302 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 1093 (1084 !; 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(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(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,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
( aSet0(xS)
& aElement0(xx) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
~ aElementOf0(xx,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,conjecture,
( aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
& aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
~ ( aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
& aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f28,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f29,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f32,plain,
! [W0] :
( W0 = slcrc0
<=> ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f33,plain,
! [W0] :
( ( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(NNF_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
( ! [W0] :
( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ! [W0] :
( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(miniscoping,[status(thm)],[f33]) ).
fof(f35,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))],[f34]) ).
fof(f36,plain,
! [X0] :
( aSet0(X0)
| X0 != slcrc0 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| X0 != slcrc0 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f38,plain,
! [X0] :
( aElementOf0(sK0_skl(X0),X0)
| ~ aSet0(X0)
| X0 = slcrc0 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f46,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(f47,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)],[f46]) ).
fof(f48,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)],[f47]) ).
fof(f49,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))],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f52,plain,
! [X0,X1] :
( aElementOf0(sK1_skl(X1,X0),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,plain,
! [X0,X1] :
( ~ aElementOf0(sK1_skl(X1,X0),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f56,plain,
! [W0] :
( aSubsetOf0(W0,W0)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f57,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [W0,W1] :
( W0 = W1
| ~ aSubsetOf0(W1,W0)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f59,plain,
! [X0,X1] :
( X0 = X1
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f60,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(f61,plain,
! [X0,X1,X2] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f62,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(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) )
& ( ( ! [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)],[f62]) ).
fof(f64,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)],[f63]) ).
fof(f65,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))],[f64]) ).
fof(f66,plain,
! [X0,X1,X2] :
( aSet0(X2)
| X2 != sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f68,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)],[f65]) ).
fof(f69,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)],[f65]) ).
fof(f70,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)],[f65]) ).
fof(f71,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)],[f65]) ).
fof(f72,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)],[f65]) ).
fof(f74,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)],[f65]) ).
fof(f75,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(f76,definition,
! [W0,W1,W3] :
( sP0_prd(W3,W1,W0)
<=> ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f77,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)],[f75,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) )
& ( ( ! [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)],[f77]) ).
fof(f79,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)],[f78]) ).
fof(f80,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))],[f79]) ).
fof(f81,plain,
! [X0,X1,X2] :
( aSet0(X2)
| X2 != sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
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)],[f80]) ).
fof(f83,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)],[f80]) ).
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)],[f80]) ).
fof(f85,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)],[f80]) ).
fof(f86,plain,
! [W0] :
( ! [W1] :
( sdtpldt0(sdtmndt0(W0,W1),W1) = W0
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f87,plain,
! [X0,X1] :
( sdtpldt0(sdtmndt0(X0,X1),X1) = X0
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f88,plain,
aElement0(xx),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f89,plain,
aSet0(xS),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f90,plain,
~ aElementOf0(xx,xS),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f91,plain,
( ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
| ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f92,plain,
( ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
| ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f93,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)],[f76]) ).
fof(f94,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)],[f93]) ).
fof(f95,plain,
! [X0,X1,X2] :
( aElement0(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f96,plain,
! [X0,X1,X2] :
( aElementOf0(X0,X2)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f97,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f98,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ aElementOf0(X0,X2)
| ~ aElement0(X0)
| sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f99,definition,
( sQ0_spl
<=> aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f101,plain,
( sQ0_spl
| ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,definition,
( sQ1_spl
<=> aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f103,plain,
( ~ sQ1_spl
| aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS) ),
inference(component_clause,[status(thm)],[f102]) ).
fof(f104,plain,
( sQ1_spl
| ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS) ),
inference(component_clause,[status(thm)],[f102]) ).
fof(f105,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f92,f99,f102]) ).
fof(f106,plain,
aSet0(slcrc0),
inference(destructive_equality_resolution,[status(thm)],[f36]) ).
fof(f107,plain,
! [X0] : ~ aElementOf0(X0,slcrc0),
inference(destructive_equality_resolution,[status(thm)],[f37]) ).
fof(f110,plain,
! [X0,X1] :
( X1 = X0
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f59,f50]) ).
fof(f111,plain,
! [X0,X1,X2] :
( aSubsetOf0(X2,X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X2,X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f61,f50]) ).
fof(f112,plain,
! [X0,X1] :
( aSet0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f66]) ).
fof(f114,plain,
! [X0,X1,X2] :
( X2 = X1
| aElementOf0(X2,X0)
| ~ aElementOf0(X2,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f68]) ).
fof(f115,plain,
! [X0,X1,X3] :
( ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| aElementOf0(X3,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f69]) ).
fof(f116,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X2,X0)
| aElementOf0(X2,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f115,f29]) ).
fof(f117,plain,
! [X0,X1] :
( ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f70]) ).
fof(f118,plain,
! [X0,X1] :
( aElementOf0(X1,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f117]) ).
fof(f119,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)],[f71,f29]) ).
fof(f120,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)],[f72,f29]) ).
fof(f122,plain,
! [X0,X1] :
( aSet0(sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f81]) ).
fof(f123,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(f124,plain,
! [X0,X1,X2] :
( ~ sP0_prd(X2,X1,X0)
| aElementOf0(X2,sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f83]) ).
fof(f125,plain,
! [X0,X1] : ~ sP0_prd(X0,X0,X1),
inference(destructive_equality_resolution,[status(thm)],[f97]) ).
fof(f128,plain,
! [X0,X1] :
( aElementOf0(sK0_skl(X0),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0)
| X0 = slcrc0 ),
inference(resolution,[status(thm)],[f38,f51]) ).
fof(f129,definition,
( sQ2_spl
<=> slcrc0 = slcrc0 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f132,definition,
( sQ3_spl
<=> aSet0(slcrc0) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( sQ3_spl
| ~ aSet0(slcrc0) ),
inference(component_clause,[status(thm)],[f132]) ).
fof(f136,plain,
! [X0,X1] :
( aElementOf0(sK0_skl(X0),X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| X0 = slcrc0 ),
inference(forward_subsumption_resolution,[status(thm)],[f128,f50]) ).
fof(f137,plain,
! [X0,X1,X2] :
( aElementOf0(X1,X2)
| ~ aSubsetOf0(sdtpldt0(X0,X1),X2)
| ~ aSet0(X2)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f118,f51]) ).
fof(f139,plain,
! [X0] :
( ~ aSet0(X0)
| X0 = slcrc0
| sdtpldt0(sdtmndt0(X0,sK0_skl(X0)),sK0_skl(X0)) = X0
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f87,f38]) ).
fof(f141,plain,
! [X0] :
( X0 = slcrc0
| sdtpldt0(sdtmndt0(X0,sK0_skl(X0)),sK0_skl(X0)) = X0
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f139]) ).
fof(f145,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtmndt0(sdtpldt0(X0,X1),X2),X2) = sdtpldt0(X0,X1)
| ~ aSet0(sdtpldt0(X0,X1))
| ~ aElementOf0(X2,X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f116,f87]) ).
fof(f146,plain,
! [X0,X1,X2,X3] :
( aElementOf0(X2,X3)
| ~ aSubsetOf0(sdtpldt0(X0,X1),X3)
| ~ aSet0(X3)
| ~ aElementOf0(X2,X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f116,f51]) ).
fof(f147,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtmndt0(sdtpldt0(X0,X1),X2),X2) = sdtpldt0(X0,X1)
| ~ aElementOf0(X2,X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f145,f112]) ).
fof(f148,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)],[f114,f38]) ).
fof(f151,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)],[f148,f112]) ).
fof(f152,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)],[f123,f38]) ).
fof(f153,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)],[f152,f122]) ).
fof(f156,plain,
( sQ0_spl
| aElementOf0(sK1_skl(xS,sdtmndt0(sdtpldt0(xS,xx),xx)),xS)
| ~ aSet0(xS)
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f52,f101]) ).
fof(f158,plain,
! [X0,X1,X2] :
( aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X2)
| ~ aSet0(X2)
| ~ aSet0(X0)
| aElementOf0(sK1_skl(X1,X0),X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f52,f111]) ).
fof(f159,plain,
! [X0,X1] :
( X1 = X0
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X0)
| aElementOf0(sK1_skl(X1,X0),X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f52,f110]) ).
fof(f160,definition,
( sQ4_spl
<=> aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f161,plain,
( ~ sQ4_spl
| aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f162,plain,
( sQ4_spl
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f163,definition,
( sQ5_spl
<=> aSet0(xS) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f165,plain,
( sQ5_spl
| ~ aSet0(xS) ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f166,definition,
( sQ6_spl
<=> aElementOf0(sK1_skl(xS,sdtmndt0(sdtpldt0(xS,xx),xx)),xS) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( ~ sQ6_spl
| aElementOf0(sK1_skl(xS,sdtmndt0(sdtpldt0(xS,xx),xx)),xS) ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f169,plain,
( sQ0_spl
| sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f156,f160,f163,f166,f99]) ).
fof(f171,plain,
! [X0,X1,X2] :
( aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X2)
| ~ aSet0(X2)
| aElementOf0(sK1_skl(X1,X0),X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f158]) ).
fof(f172,plain,
! [X0,X1,X2] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2)
| aElementOf0(sK1_skl(X0,X1),X0)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f171,f50]) ).
fof(f173,plain,
! [X0,X1] :
( X1 = X0
| ~ aSubsetOf0(X0,X1)
| aElementOf0(sK1_skl(X1,X0),X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f159]) ).
fof(f174,plain,
! [X0,X1] :
( X0 = X1
| ~ aSubsetOf0(X1,X0)
| aElementOf0(sK1_skl(X0,X1),X0)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f173,f50]) ).
fof(f175,plain,
( sQ1_spl
| aElementOf0(sK1_skl(sdtmndt0(sdtpldt0(xS,xx),xx),xS),sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f104,f52]) ).
fof(f176,definition,
( sQ7_spl
<=> aElementOf0(sK1_skl(sdtmndt0(sdtpldt0(xS,xx),xx),xS),sdtmndt0(sdtpldt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f177,plain,
( ~ sQ7_spl
| aElementOf0(sK1_skl(sdtmndt0(sdtpldt0(xS,xx),xx),xS),sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(component_clause,[status(thm)],[f176]) ).
fof(f179,plain,
( sQ1_spl
| sQ7_spl
| ~ sQ4_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f175,f163,f160,f176,f102]) ).
fof(f180,plain,
( sQ4_spl
| ~ aElement0(xx)
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(resolution,[status(thm)],[f162,f122]) ).
fof(f182,definition,
( sQ8_spl
<=> aSet0(sdtpldt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f183,plain,
( ~ sQ8_spl
| aSet0(sdtpldt0(xS,xx)) ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f184,plain,
( sQ8_spl
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f185,definition,
( sQ9_spl
<=> aElement0(xx) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f187,plain,
( sQ9_spl
| ~ aElement0(xx) ),
inference(component_clause,[status(thm)],[f185]) ).
fof(f188,plain,
( sQ4_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f180,f182,f185,f160]) ).
fof(f189,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f165,f89]) ).
fof(f190,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f189]) ).
fof(f191,plain,
! [X0,X1,X2] :
( ~ aElementOf0(sK1_skl(X2,sdtpldt0(X0,X1)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0)
| ~ aSet0(X2)
| aSubsetOf0(X2,sdtpldt0(X0,X1))
| ~ aSet0(sdtpldt0(X0,X1)) ),
inference(resolution,[status(thm)],[f53,f116]) ).
fof(f192,plain,
! [X0,X1,X2] :
( ~ aElementOf0(sK1_skl(X0,sdtpldt0(X1,X2)),X1)
| ~ aElement0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0)
| aSubsetOf0(X0,sdtpldt0(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f191,f112]) ).
fof(f193,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)],[f119,f116]) ).
fof(f194,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)],[f193,f112]) ).
fof(f195,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(sK2_skl(sdtpldt0(X2,X3),X1,X0),X2)
| ~ aElement0(X3)
| ~ aSet0(X2)
| sK2_skl(sdtpldt0(X2,X3),X1,X0) != X1
| ~ aSet0(sdtpldt0(X2,X3))
| sdtpldt0(X2,X3) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f120,f116]) ).
fof(f196,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(sK2_skl(sdtpldt0(X2,X3),X1,X0),X2)
| ~ aElement0(X3)
| ~ aSet0(X2)
| sK2_skl(sdtpldt0(X2,X3),X1,X0) != X1
| sdtpldt0(X2,X3) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f195,f112]) ).
fof(f197,plain,
( sQ8_spl
| ~ aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f184,f112]) ).
fof(f199,plain,
( sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f197,f163,f185,f182]) ).
fof(f200,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f187,f88]) ).
fof(f201,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f200]) ).
fof(f207,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ aElementOf0(X2,X0)
| ~ aElement0(X2)
| aElementOf0(X2,sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f124,f98]) ).
fof(f208,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ aElementOf0(X2,X0)
| aElementOf0(X2,sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f207,f29]) ).
fof(f209,plain,
( ~ sQ4_spl
| sdtmndt0(sdtpldt0(xS,xx),xx) = slcrc0
| sdtpldt0(sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))) = sdtmndt0(sdtpldt0(xS,xx),xx) ),
inference(resolution,[status(thm)],[f141,f161]) ).
fof(f216,definition,
( sQ10_spl
<=> sdtpldt0(sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))) = sdtmndt0(sdtpldt0(xS,xx),xx) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f217,plain,
( ~ sQ10_spl
| sdtpldt0(sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))) = sdtmndt0(sdtpldt0(xS,xx),xx) ),
inference(component_clause,[status(thm)],[f216]) ).
fof(f219,definition,
( sQ11_spl
<=> sdtmndt0(sdtpldt0(xS,xx),xx) = slcrc0 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f220,plain,
( ~ sQ11_spl
| sdtmndt0(sdtpldt0(xS,xx),xx) = slcrc0 ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f221,plain,
( sQ11_spl
| sdtmndt0(sdtpldt0(xS,xx),xx) != slcrc0 ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f222,plain,
( ~ sQ4_spl
| sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f209,f216,f219,f160]) ).
fof(f234,definition,
( sQ15_spl
<=> sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)) = xS ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f235,plain,
( ~ sQ15_spl
| sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)) = xS ),
inference(component_clause,[status(thm)],[f234]) ).
fof(f237,definition,
( sQ16_spl
<=> xS = slcrc0 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f238,plain,
( ~ sQ16_spl
| xS = slcrc0 ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f250,plain,
! [X0] :
( ~ sQ15_spl
| aElementOf0(sK0_skl(xS),X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0)
| ~ aElement0(sK0_skl(xS))
| ~ aSet0(sdtmndt0(xS,sK0_skl(xS))) ),
inference(paramodulation,[status(thm)],[f235,f137]) ).
fof(f251,plain,
! [X0] :
( ~ sQ15_spl
| X0 = sK0_skl(xS)
| aElementOf0(X0,sdtmndt0(xS,sK0_skl(xS)))
| ~ aElementOf0(X0,xS)
| ~ aElement0(sK0_skl(xS))
| ~ aSet0(sdtmndt0(xS,sK0_skl(xS))) ),
inference(paramodulation,[status(thm)],[f235,f114]) ).
fof(f252,plain,
! [X0] :
( ~ sQ15_spl
| ~ aElementOf0(X0,sdtmndt0(xS,sK0_skl(xS)))
| aElementOf0(X0,xS)
| ~ aElement0(sK0_skl(xS))
| ~ aSet0(sdtmndt0(xS,sK0_skl(xS))) ),
inference(paramodulation,[status(thm)],[f235,f116]) ).
fof(f255,definition,
( sQ17_spl
<=> aSet0(sdtmndt0(xS,sK0_skl(xS))) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f256,plain,
( ~ sQ17_spl
| aSet0(sdtmndt0(xS,sK0_skl(xS))) ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f257,plain,
( sQ17_spl
| ~ aSet0(sdtmndt0(xS,sK0_skl(xS))) ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f258,definition,
( sQ18_spl
<=> aElement0(sK0_skl(xS)) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f259,plain,
( ~ sQ18_spl
| aElement0(sK0_skl(xS)) ),
inference(component_clause,[status(thm)],[f258]) ).
fof(f260,plain,
( sQ18_spl
| ~ aElement0(sK0_skl(xS)) ),
inference(component_clause,[status(thm)],[f258]) ).
fof(f261,definition,
! [X0] :
( sQ19_spl
<=> ( aElementOf0(sK0_skl(xS),X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f262,plain,
! [X0] :
( ~ sQ19_spl
| aElementOf0(sK0_skl(xS),X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f261]) ).
fof(f264,plain,
( ~ sQ15_spl
| sQ19_spl
| ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f250,f255,f258,f261,f234]) ).
fof(f265,definition,
! [X0] :
( sQ20_spl
<=> ( X0 = sK0_skl(xS)
| aElementOf0(X0,sdtmndt0(xS,sK0_skl(xS)))
| ~ aElementOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f268,plain,
( ~ sQ15_spl
| sQ20_spl
| ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f251,f255,f258,f265,f234]) ).
fof(f269,definition,
! [X0] :
( sQ21_spl
<=> ( ~ aElementOf0(X0,sdtmndt0(xS,sK0_skl(xS)))
| aElementOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f270,plain,
! [X0] :
( ~ sQ21_spl
| ~ aElementOf0(X0,sdtmndt0(xS,sK0_skl(xS)))
| aElementOf0(X0,xS) ),
inference(component_clause,[status(thm)],[f269]) ).
fof(f272,plain,
( ~ sQ15_spl
| sQ21_spl
| ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f252,f255,f258,f269,f234]) ).
fof(f273,definition,
( sQ22_spl
<=> aElementOf0(sK0_skl(xS),xS) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f274,plain,
( ~ sQ22_spl
| aElementOf0(sK0_skl(xS),xS) ),
inference(component_clause,[status(thm)],[f273]) ).
fof(f280,plain,
! [X0,X1] :
( sQ18_spl
| ~ sP0_prd(sK0_skl(xS),X0,X1) ),
inference(resolution,[status(thm)],[f260,f95]) ).
fof(f298,plain,
( sQ17_spl
| ~ aElement0(sK0_skl(xS))
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f257,f122]) ).
fof(f300,plain,
( sQ17_spl
| ~ sQ18_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f298,f163,f258,f255]) ).
fof(f304,plain,
! [X0] :
( ~ sQ16_spl
| ~ aElementOf0(X0,xS) ),
inference(backward_demodulation,[status(thm)],[f238,f107]) ).
fof(f314,plain,
( ~ sQ6_spl
| ~ sQ16_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f167,f304]) ).
fof(f315,plain,
( ~ sQ6_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f314]) ).
fof(f318,plain,
! [X0,X1,X2,X3] :
( ~ aElement0(X3)
| ~ aSet0(X2)
| sK2_skl(sdtmndt0(X2,X3),X1,X0) = X1
| aElementOf0(sK2_skl(sdtmndt0(X2,X3),X1,X0),X0)
| aElementOf0(sK2_skl(sdtmndt0(X2,X3),X1,X0),sdtmndt0(X2,X3))
| sdtmndt0(X2,X3) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f74,f122]) ).
fof(f320,plain,
! [X0,X1,X2,X3] :
( ~ aElement0(X3)
| ~ aSet0(X2)
| sK2_skl(sdtpldt0(X2,X3),X1,X0) = X1
| aElementOf0(sK2_skl(sdtpldt0(X2,X3),X1,X0),X0)
| aElementOf0(sK2_skl(sdtpldt0(X2,X3),X1,X0),sdtpldt0(X2,X3))
| sdtpldt0(X2,X3) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f74,f112]) ).
fof(f321,plain,
! [X0,X1] :
( sK2_skl(xS,X1,X0) = X1
| aElementOf0(sK2_skl(xS,X1,X0),X0)
| aElementOf0(sK2_skl(xS,X1,X0),xS)
| xS = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f74,f89]) ).
fof(f323,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(sK3_skl(sdtpldt0(X2,X3),X1,X0),X2)
| ~ aElement0(X3)
| ~ aSet0(X2)
| ~ sP0_prd(sK3_skl(sdtpldt0(X2,X3),X1,X0),X1,X0)
| ~ aSet0(sdtpldt0(X2,X3))
| sdtpldt0(X2,X3) = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f84,f116]) ).
fof(f324,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(sK3_skl(sdtpldt0(X2,X3),X1,X0),X2)
| ~ aElement0(X3)
| ~ aSet0(X2)
| ~ sP0_prd(sK3_skl(sdtpldt0(X2,X3),X1,X0),X1,X0)
| sdtpldt0(X2,X3) = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f323,f112]) ).
fof(f339,plain,
( ~ sQ7_spl
| sP0_prd(sK1_skl(sdtmndt0(sdtpldt0(xS,xx),xx),xS),xx,sdtpldt0(xS,xx))
| ~ aElement0(xx)
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(resolution,[status(thm)],[f177,f123]) ).
fof(f342,definition,
( sQ28_spl
<=> sP0_prd(sK1_skl(sdtmndt0(sdtpldt0(xS,xx),xx),xS),xx,sdtpldt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f343,plain,
( ~ sQ28_spl
| sP0_prd(sK1_skl(sdtmndt0(sdtpldt0(xS,xx),xx),xS),xx,sdtpldt0(xS,xx)) ),
inference(component_clause,[status(thm)],[f342]) ).
fof(f345,plain,
( ~ sQ7_spl
| sQ28_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f339,f182,f185,f342,f176]) ).
fof(f350,plain,
( ~ sQ22_spl
| sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)) = xS
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f274,f87]) ).
fof(f351,plain,
! [X0] :
( ~ sQ22_spl
| aElementOf0(sK0_skl(xS),X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f274,f51]) ).
fof(f352,plain,
( ~ sQ22_spl
| sQ15_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f350,f163,f234,f273]) ).
fof(f354,plain,
! [X0] :
( ~ sQ22_spl
| sdtpldt0(sdtmndt0(sdtpldt0(xS,X0),sK0_skl(xS)),sK0_skl(xS)) = sdtpldt0(xS,X0)
| ~ aElement0(X0)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f147,f274]) ).
fof(f359,definition,
! [X0] :
( sQ30_spl
<=> ( sdtpldt0(sdtmndt0(sdtpldt0(xS,X0),sK0_skl(xS)),sK0_skl(xS)) = sdtpldt0(xS,X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f362,plain,
( ~ sQ22_spl
| sQ30_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f354,f163,f359,f273]) ).
fof(f378,plain,
! [X0,X1] :
( sK2_skl(slcrc0,X1,X0) = X1
| aElementOf0(sK2_skl(slcrc0,X1,X0),X0)
| aElementOf0(sK2_skl(slcrc0,X1,X0),slcrc0)
| slcrc0 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f106,f74]) ).
fof(f379,plain,
! [X0,X1] :
( sK2_skl(slcrc0,X1,X0) = X1
| aElementOf0(sK2_skl(slcrc0,X1,X0),X0)
| slcrc0 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f378,f107]) ).
fof(f389,plain,
! [X0] :
( ~ sQ19_spl
| aElementOf0(sK1_skl(xS,X0),xS)
| ~ aSet0(xS)
| ~ aSet0(X0)
| aElementOf0(sK0_skl(xS),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f262,f52]) ).
fof(f391,definition,
! [X0] :
( sQ33_spl
<=> ( aElementOf0(sK1_skl(xS,X0),xS)
| ~ aSet0(X0)
| aElementOf0(sK0_skl(xS),X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f394,plain,
( ~ sQ19_spl
| ~ sQ5_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f389,f391,f163,f261]) ).
fof(f397,plain,
! [X0,X1,X2] :
( aElementOf0(sK3_skl(X2,X1,X0),sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0)
| aElementOf0(sK3_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f85,f124]) ).
fof(f398,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)],[f85,f96]) ).
fof(f399,plain,
! [X0,X1,X2] :
( aElementOf0(sK3_skl(X2,X1,X0),sdtmndt0(X0,X1))
| aElementOf0(sK3_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f397]) ).
fof(f407,plain,
( ~ sQ28_spl
| aElementOf0(sK1_skl(sdtmndt0(sdtpldt0(xS,xx),xx),xS),sdtpldt0(xS,xx)) ),
inference(resolution,[status(thm)],[f343,f96]) ).
fof(f409,plain,
( ~ sQ28_spl
| sK1_skl(sdtmndt0(sdtpldt0(xS,xx),xx),xS) = xx
| aElementOf0(sK1_skl(sdtmndt0(sdtpldt0(xS,xx),xx),xS),xS)
| ~ aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f407,f114]) ).
fof(f413,definition,
( sQ34_spl
<=> aElementOf0(sK1_skl(sdtmndt0(sdtpldt0(xS,xx),xx),xS),xS) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f414,plain,
( ~ sQ34_spl
| aElementOf0(sK1_skl(sdtmndt0(sdtpldt0(xS,xx),xx),xS),xS) ),
inference(component_clause,[status(thm)],[f413]) ).
fof(f416,definition,
( sQ35_spl
<=> sK1_skl(sdtmndt0(sdtpldt0(xS,xx),xx),xS) = xx ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f417,plain,
( ~ sQ35_spl
| sK1_skl(sdtmndt0(sdtpldt0(xS,xx),xx),xS) = xx ),
inference(component_clause,[status(thm)],[f416]) ).
fof(f419,plain,
( ~ sQ28_spl
| sQ35_spl
| sQ34_spl
| ~ sQ9_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f409,f163,f185,f413,f416,f342]) ).
fof(f428,plain,
! [X0] :
( ~ sQ10_spl
| ~ aElementOf0(sK1_skl(X0,sdtmndt0(sdtpldt0(xS,xx),xx)),sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))))
| ~ aElement0(sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)))
| ~ aSet0(sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))))
| ~ aSet0(X0)
| aSubsetOf0(X0,sdtpldt0(sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)))) ),
inference(paramodulation,[status(thm)],[f217,f192]) ).
fof(f429,plain,
! [X0,X1] :
( ~ sQ10_spl
| aElementOf0(X0,X1)
| ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),X1)
| ~ aSet0(X1)
| ~ aElementOf0(X0,sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))))
| ~ aElement0(sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)))
| ~ aSet0(sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)))) ),
inference(paramodulation,[status(thm)],[f217,f146]) ).
fof(f430,plain,
! [X0] :
( ~ sQ10_spl
| aElementOf0(sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)),X0)
| ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),X0)
| ~ aSet0(X0)
| ~ aElement0(sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)))
| ~ aSet0(sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)))) ),
inference(paramodulation,[status(thm)],[f217,f137]) ).
fof(f431,plain,
! [X0] :
( ~ sQ10_spl
| X0 = sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))
| aElementOf0(X0,sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))))
| ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aElement0(sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)))
| ~ aSet0(sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)))) ),
inference(paramodulation,[status(thm)],[f217,f114]) ).
fof(f432,plain,
! [X0] :
( ~ sQ10_spl
| ~ aElementOf0(X0,sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))))
| aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aElement0(sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)))
| ~ aSet0(sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)))) ),
inference(paramodulation,[status(thm)],[f217,f116]) ).
fof(f433,plain,
( ~ sQ10_spl
| aElementOf0(sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)),sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aElement0(sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)))
| ~ aSet0(sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)))) ),
inference(paramodulation,[status(thm)],[f217,f118]) ).
fof(f435,definition,
! [X0] :
( sQ38_spl
<=> ( ~ aElementOf0(sK1_skl(X0,sdtmndt0(sdtpldt0(xS,xx),xx)),sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))))
| ~ aSet0(X0)
| aSubsetOf0(X0,sdtpldt0(sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)))) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f438,definition,
( sQ39_spl
<=> aSet0(sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)))) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f441,definition,
( sQ40_spl
<=> aElement0(sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( sQ40_spl
| ~ aElement0(sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))) ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,plain,
( ~ sQ10_spl
| ~ sQ40_spl
| ~ sQ39_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f428,f435,f438,f441,f216]) ).
fof(f445,definition,
! [X0,X1] :
( sQ41_spl
<=> ( aElementOf0(X0,X1)
| ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),X1)
| ~ aSet0(X1)
| ~ aElementOf0(X0,sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)))) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f448,plain,
( ~ sQ10_spl
| sQ41_spl
| ~ sQ40_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f429,f438,f441,f445,f216]) ).
fof(f449,definition,
! [X0] :
( sQ42_spl
<=> ( aElementOf0(sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)),X0)
| ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f452,plain,
( ~ sQ10_spl
| sQ42_spl
| ~ sQ40_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f430,f438,f441,f449,f216]) ).
fof(f453,definition,
! [X0] :
( sQ43_spl
<=> ( X0 = sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))
| aElementOf0(X0,sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))))
| ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f456,plain,
( ~ sQ10_spl
| sQ43_spl
| ~ sQ40_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f431,f438,f441,f453,f216]) ).
fof(f457,definition,
! [X0] :
( sQ44_spl
<=> ( ~ aElementOf0(X0,sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))))
| aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f460,plain,
( ~ sQ10_spl
| sQ44_spl
| ~ sQ40_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f432,f438,f441,f457,f216]) ).
fof(f461,definition,
( sQ45_spl
<=> aElementOf0(sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)),sdtmndt0(sdtpldt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f462,plain,
( ~ sQ45_spl
| aElementOf0(sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)),sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(component_clause,[status(thm)],[f461]) ).
fof(f464,plain,
( ~ sQ10_spl
| sQ45_spl
| ~ sQ40_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f433,f438,f441,f461,f216]) ).
fof(f468,plain,
! [X0,X1] :
( sQ40_spl
| ~ sP0_prd(sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)),X0,X1) ),
inference(resolution,[status(thm)],[f443,f95]) ).
fof(f469,plain,
( ~ sQ21_spl
| ~ aSet0(sdtmndt0(xS,sK0_skl(xS)))
| sdtmndt0(xS,sK0_skl(xS)) = slcrc0
| aElementOf0(sK0_skl(sdtmndt0(xS,sK0_skl(xS))),xS) ),
inference(resolution,[status(thm)],[f270,f38]) ).
fof(f470,definition,
( sQ46_spl
<=> aElementOf0(sK0_skl(sdtmndt0(xS,sK0_skl(xS))),xS) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f471,plain,
( ~ sQ46_spl
| aElementOf0(sK0_skl(sdtmndt0(xS,sK0_skl(xS))),xS) ),
inference(component_clause,[status(thm)],[f470]) ).
fof(f473,definition,
( sQ47_spl
<=> sdtmndt0(xS,sK0_skl(xS)) = slcrc0 ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f474,plain,
( ~ sQ47_spl
| sdtmndt0(xS,sK0_skl(xS)) = slcrc0 ),
inference(component_clause,[status(thm)],[f473]) ).
fof(f476,plain,
( ~ sQ21_spl
| ~ sQ17_spl
| sQ47_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f469,f470,f473,f255,f269]) ).
fof(f477,plain,
! [X0] :
( ~ sQ46_spl
| sdtpldt0(sdtmndt0(sdtpldt0(xS,X0),sK0_skl(sdtmndt0(xS,sK0_skl(xS)))),sK0_skl(sdtmndt0(xS,sK0_skl(xS)))) = sdtpldt0(xS,X0)
| ~ aElement0(X0)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f471,f147]) ).
fof(f478,plain,
( ~ sQ46_spl
| sdtpldt0(sdtmndt0(xS,sK0_skl(sdtmndt0(xS,sK0_skl(xS)))),sK0_skl(sdtmndt0(xS,sK0_skl(xS)))) = xS
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f471,f87]) ).
fof(f480,definition,
! [X0] :
( sQ48_spl
<=> ( sdtpldt0(sdtmndt0(sdtpldt0(xS,X0),sK0_skl(sdtmndt0(xS,sK0_skl(xS)))),sK0_skl(sdtmndt0(xS,sK0_skl(xS)))) = sdtpldt0(xS,X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f483,plain,
( ~ sQ46_spl
| sQ48_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f477,f163,f480,f470]) ).
fof(f484,definition,
( sQ49_spl
<=> sdtpldt0(sdtmndt0(xS,sK0_skl(sdtmndt0(xS,sK0_skl(xS)))),sK0_skl(sdtmndt0(xS,sK0_skl(xS)))) = xS ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f487,plain,
( ~ sQ46_spl
| sQ49_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f478,f163,f484,f470]) ).
fof(f488,plain,
! [X0] :
( ~ sQ15_spl
| ~ aElementOf0(sK1_skl(X0,xS),sdtmndt0(xS,sK0_skl(xS)))
| ~ aElement0(sK0_skl(xS))
| ~ aSet0(sdtmndt0(xS,sK0_skl(xS)))
| ~ aSet0(X0)
| aSubsetOf0(X0,sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS))) ),
inference(paramodulation,[status(thm)],[f235,f192]) ).
fof(f489,plain,
! [X0,X1] :
( ~ sQ15_spl
| aElementOf0(X0,X1)
| ~ aSubsetOf0(xS,X1)
| ~ aSet0(X1)
| ~ aElementOf0(X0,sdtmndt0(xS,sK0_skl(xS)))
| ~ aElement0(sK0_skl(xS))
| ~ aSet0(sdtmndt0(xS,sK0_skl(xS))) ),
inference(paramodulation,[status(thm)],[f235,f146]) ).
fof(f495,definition,
! [X0] :
( sQ50_spl
<=> ( ~ aElementOf0(sK1_skl(X0,xS),sdtmndt0(xS,sK0_skl(xS)))
| ~ aSet0(X0)
| aSubsetOf0(X0,sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS))) ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f498,plain,
( ~ sQ15_spl
| ~ sQ18_spl
| ~ sQ17_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f488,f495,f255,f258,f234]) ).
fof(f499,definition,
! [X0,X1] :
( sQ51_spl
<=> ( aElementOf0(X0,X1)
| ~ aSubsetOf0(xS,X1)
| ~ aSet0(X1)
| ~ aElementOf0(X0,sdtmndt0(xS,sK0_skl(xS))) ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f502,plain,
( ~ sQ15_spl
| sQ51_spl
| ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f489,f255,f258,f499,f234]) ).
fof(f510,plain,
! [X0,X1] :
( ~ sQ15_spl
| ~ aElementOf0(sK2_skl(xS,X1,X0),sdtmndt0(xS,sK0_skl(xS)))
| ~ aElement0(sK0_skl(xS))
| ~ aSet0(sdtmndt0(xS,sK0_skl(xS)))
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)),X1,X0),X0)
| sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(paramodulation,[status(thm)],[f235,f194]) ).
fof(f511,plain,
! [X0,X1] :
( ~ sQ10_spl
| ~ aElementOf0(sK2_skl(sdtmndt0(sdtpldt0(xS,xx),xx),X1,X0),sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))))
| ~ aElement0(sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)))
| ~ aSet0(sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))))
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))),X1,X0),X0)
| sdtpldt0(sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(paramodulation,[status(thm)],[f217,f194]) ).
fof(f513,definition,
! [X0,X1] :
( sQ52_spl
<=> ( ~ aElementOf0(sK2_skl(xS,X1,X0),sdtmndt0(xS,sK0_skl(xS)))
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)),X1,X0),X0)
| sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f516,plain,
( ~ sQ15_spl
| ~ sQ18_spl
| ~ sQ17_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f510,f513,f255,f258,f234]) ).
fof(f517,definition,
! [X0,X1] :
( sQ53_spl
<=> ( ~ aElementOf0(sK2_skl(sdtmndt0(sdtpldt0(xS,xx),xx),X1,X0),sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))))
| ~ aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))),X1,X0),X0)
| sdtpldt0(sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f520,plain,
( ~ sQ10_spl
| ~ sQ40_spl
| ~ sQ39_spl
| sQ53_spl ),
inference(split_clause,[status(thm)],[f511,f517,f438,f441,f216]) ).
fof(f524,plain,
! [X0,X1] :
( ~ sQ15_spl
| ~ aElementOf0(sK2_skl(xS,X1,X0),sdtmndt0(xS,sK0_skl(xS)))
| ~ aElement0(sK0_skl(xS))
| ~ aSet0(sdtmndt0(xS,sK0_skl(xS)))
| sK2_skl(sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)),X1,X0) != X1
| sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(paramodulation,[status(thm)],[f235,f196]) ).
fof(f525,plain,
! [X0,X1] :
( ~ sQ10_spl
| ~ aElementOf0(sK2_skl(sdtmndt0(sdtpldt0(xS,xx),xx),X1,X0),sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))))
| ~ aElement0(sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)))
| ~ aSet0(sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))))
| sK2_skl(sdtpldt0(sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))),X1,X0) != X1
| sdtpldt0(sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(paramodulation,[status(thm)],[f217,f196]) ).
fof(f527,definition,
! [X0,X1] :
( sQ54_spl
<=> ( ~ aElementOf0(sK2_skl(xS,X1,X0),sdtmndt0(xS,sK0_skl(xS)))
| sK2_skl(sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)),X1,X0) != X1
| sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f530,plain,
( ~ sQ15_spl
| ~ sQ18_spl
| ~ sQ17_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f524,f527,f255,f258,f234]) ).
fof(f531,definition,
! [X0,X1] :
( sQ55_spl
<=> ( ~ aElementOf0(sK2_skl(sdtmndt0(sdtpldt0(xS,xx),xx),X1,X0),sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))))
| sK2_skl(sdtpldt0(sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))),X1,X0) != X1
| sdtpldt0(sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f534,plain,
( ~ sQ10_spl
| ~ sQ40_spl
| ~ sQ39_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f525,f531,f438,f441,f216]) ).
fof(f550,plain,
( ~ sQ17_spl
| sdtmndt0(xS,sK0_skl(xS)) = slcrc0
| sdtpldt0(sdtmndt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(sdtmndt0(xS,sK0_skl(xS)))),sK0_skl(sdtmndt0(xS,sK0_skl(xS)))) = sdtmndt0(xS,sK0_skl(xS)) ),
inference(resolution,[status(thm)],[f141,f256]) ).
fof(f558,definition,
( sQ58_spl
<=> sdtpldt0(sdtmndt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(sdtmndt0(xS,sK0_skl(xS)))),sK0_skl(sdtmndt0(xS,sK0_skl(xS)))) = sdtmndt0(xS,sK0_skl(xS)) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f559,plain,
( ~ sQ58_spl
| sdtpldt0(sdtmndt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(sdtmndt0(xS,sK0_skl(xS)))),sK0_skl(sdtmndt0(xS,sK0_skl(xS)))) = sdtmndt0(xS,sK0_skl(xS)) ),
inference(component_clause,[status(thm)],[f558]) ).
fof(f561,plain,
( ~ sQ17_spl
| sQ47_spl
| sQ58_spl ),
inference(split_clause,[status(thm)],[f550,f558,f473,f255]) ).
fof(f583,plain,
! [X0] :
( ~ sQ47_spl
| sP0_prd(X0,sK0_skl(xS),xS)
| ~ aElementOf0(X0,slcrc0)
| ~ aElement0(sK0_skl(xS))
| ~ aSet0(xS) ),
inference(paramodulation,[status(thm)],[f474,f123]) ).
fof(f585,definition,
! [X0] :
( sQ59_spl
<=> ( sP0_prd(X0,sK0_skl(xS),xS)
| ~ aElementOf0(X0,slcrc0) ) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f588,plain,
( ~ sQ47_spl
| sQ59_spl
| ~ sQ18_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f583,f163,f258,f585,f473]) ).
fof(f600,plain,
! [X0,X1] :
( X1 = xx
| ~ aElementOf0(X1,X0)
| aElementOf0(X1,sdtmndt0(X0,xx))
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f208,f88]) ).
fof(f604,plain,
( sQ40_spl
| sdtmndt0(sdtpldt0(xS,xx),xx) = slcrc0
| ~ aElement0(xx)
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(resolution,[status(thm)],[f153,f468]) ).
fof(f607,plain,
( sQ40_spl
| sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f604,f182,f185,f219,f441]) ).
fof(f618,plain,
( ~ sQ34_spl
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
| aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f414,f53]) ).
fof(f622,plain,
( ~ sQ34_spl
| ~ sQ4_spl
| sQ1_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f618,f163,f102,f160,f413]) ).
fof(f631,plain,
( ~ sQ1_spl
| aElementOf0(sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)),xS)
| ~ aSet0(xS)
| sdtmndt0(sdtpldt0(xS,xx),xx) = slcrc0 ),
inference(resolution,[status(thm)],[f103,f136]) ).
fof(f636,definition,
( sQ62_spl
<=> aElementOf0(sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)),xS) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f637,plain,
( ~ sQ62_spl
| aElementOf0(sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)),xS) ),
inference(component_clause,[status(thm)],[f636]) ).
fof(f639,plain,
( ~ sQ1_spl
| sQ62_spl
| ~ sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f631,f219,f163,f636,f102]) ).
fof(f644,definition,
( sQ64_spl
<=> xS = sdtmndt0(sdtpldt0(xS,xx),xx) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f645,plain,
( ~ sQ64_spl
| xS = sdtmndt0(sdtpldt0(xS,xx),xx) ),
inference(component_clause,[status(thm)],[f644]) ).
fof(f657,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| aElementOf0(sK1_skl(sdtmndt0(sdtpldt0(xS,xx),xx),xS),slcrc0) ),
inference(backward_demodulation,[status(thm)],[f220,f177]) ).
fof(f678,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| aElementOf0(sK1_skl(slcrc0,xS),slcrc0) ),
inference(forward_demodulation,[status(thm)],[f220,f657]) ).
fof(f679,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f678,f107]) ).
fof(f680,plain,
( ~ sQ7_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f679]) ).
fof(f697,definition,
( sQ66_spl
<=> aElementOf0(sK0_skl(slcrc0),xS) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f698,plain,
( ~ sQ66_spl
| aElementOf0(sK0_skl(slcrc0),xS) ),
inference(component_clause,[status(thm)],[f697]) ).
fof(f699,plain,
( sQ66_spl
| ~ aElementOf0(sK0_skl(slcrc0),xS) ),
inference(component_clause,[status(thm)],[f697]) ).
fof(f701,definition,
! [X0] :
( sQ67_spl
<=> ( aSubsetOf0(X0,xS)
| aElementOf0(sK1_skl(X0,slcrc0),X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f702,plain,
! [X0] :
( ~ sQ67_spl
| aSubsetOf0(X0,xS)
| aElementOf0(sK1_skl(X0,slcrc0),X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f701]) ).
fof(f705,definition,
( sQ68_spl
<=> aElementOf0(sK1_skl(xS,slcrc0),xS) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f706,plain,
( ~ sQ68_spl
| aElementOf0(sK1_skl(xS,slcrc0),xS) ),
inference(component_clause,[status(thm)],[f705]) ).
fof(f713,definition,
( sQ70_spl
<=> aSubsetOf0(xS,slcrc0) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f715,plain,
( sQ70_spl
| ~ aSubsetOf0(xS,slcrc0) ),
inference(component_clause,[status(thm)],[f713]) ).
fof(f757,plain,
! [X0] :
( ~ sQ62_spl
| sdtpldt0(sdtmndt0(sdtpldt0(xS,X0),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))) = sdtpldt0(xS,X0)
| ~ aElement0(X0)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f637,f147]) ).
fof(f758,plain,
( ~ sQ62_spl
| sdtpldt0(sdtmndt0(xS,sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))) = xS
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f637,f87]) ).
fof(f760,definition,
! [X0] :
( sQ71_spl
<=> ( sdtpldt0(sdtmndt0(sdtpldt0(xS,X0),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))) = sdtpldt0(xS,X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f763,plain,
( ~ sQ62_spl
| sQ71_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f757,f163,f760,f636]) ).
fof(f764,definition,
( sQ72_spl
<=> sdtpldt0(sdtmndt0(xS,sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))) = xS ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f767,plain,
( ~ sQ62_spl
| sQ72_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f758,f163,f764,f636]) ).
fof(f768,plain,
( ~ sQ62_spl
| sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)) = xx
| aElementOf0(sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)),sdtmndt0(xS,xx))
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f600,f637]) ).
fof(f769,plain,
( ~ sQ46_spl
| sK0_skl(sdtmndt0(xS,sK0_skl(xS))) = xx
| aElementOf0(sK0_skl(sdtmndt0(xS,sK0_skl(xS))),sdtmndt0(xS,xx))
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f600,f471]) ).
fof(f770,plain,
( ~ sQ22_spl
| sK0_skl(xS) = xx
| aElementOf0(sK0_skl(xS),sdtmndt0(xS,xx))
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f600,f274]) ).
fof(f774,definition,
( sQ73_spl
<=> aElementOf0(sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)),sdtmndt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f777,definition,
( sQ74_spl
<=> sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)) = xx ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f778,plain,
( ~ sQ74_spl
| sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)) = xx ),
inference(component_clause,[status(thm)],[f777]) ).
fof(f780,plain,
( ~ sQ62_spl
| sQ74_spl
| sQ73_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f768,f163,f774,f777,f636]) ).
fof(f781,definition,
( sQ75_spl
<=> aElementOf0(sK0_skl(sdtmndt0(xS,sK0_skl(xS))),sdtmndt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f784,definition,
( sQ76_spl
<=> sK0_skl(sdtmndt0(xS,sK0_skl(xS))) = xx ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f785,plain,
( ~ sQ76_spl
| sK0_skl(sdtmndt0(xS,sK0_skl(xS))) = xx ),
inference(component_clause,[status(thm)],[f784]) ).
fof(f787,plain,
( ~ sQ46_spl
| sQ76_spl
| sQ75_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f769,f163,f781,f784,f470]) ).
fof(f788,definition,
( sQ77_spl
<=> aElementOf0(sK0_skl(xS),sdtmndt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f789,plain,
( ~ sQ77_spl
| aElementOf0(sK0_skl(xS),sdtmndt0(xS,xx)) ),
inference(component_clause,[status(thm)],[f788]) ).
fof(f791,definition,
( sQ78_spl
<=> sK0_skl(xS) = xx ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f792,plain,
( ~ sQ78_spl
| sK0_skl(xS) = xx ),
inference(component_clause,[status(thm)],[f791]) ).
fof(f794,plain,
( ~ sQ22_spl
| sQ78_spl
| sQ77_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f770,f163,f788,f791,f273]) ).
fof(f798,plain,
( ~ sQ77_spl
| sP0_prd(sK0_skl(xS),xx,xS)
| ~ aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f789,f123]) ).
fof(f799,plain,
( ~ sQ77_spl
| sK0_skl(xS) = xx
| aElementOf0(sK0_skl(xS),sdtmndt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f789,f600]) ).
fof(f800,plain,
! [X0] :
( ~ sQ77_spl
| sdtpldt0(sdtmndt0(sdtpldt0(sdtmndt0(xS,xx),X0),sK0_skl(xS)),sK0_skl(xS)) = sdtpldt0(sdtmndt0(xS,xx),X0)
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f789,f147]) ).
fof(f801,plain,
( ~ sQ77_spl
| sdtpldt0(sdtmndt0(sdtmndt0(xS,xx),sK0_skl(xS)),sK0_skl(xS)) = sdtmndt0(xS,xx)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f789,f87]) ).
fof(f802,plain,
! [X0] :
( ~ sQ77_spl
| aElementOf0(sK0_skl(xS),X0)
| ~ aSubsetOf0(sdtmndt0(xS,xx),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f789,f51]) ).
fof(f803,definition,
( sQ79_spl
<=> sP0_prd(sK0_skl(xS),xx,xS) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f804,plain,
( ~ sQ79_spl
| sP0_prd(sK0_skl(xS),xx,xS) ),
inference(component_clause,[status(thm)],[f803]) ).
fof(f806,plain,
( ~ sQ77_spl
| sQ79_spl
| ~ sQ9_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f798,f163,f185,f803,f788]) ).
fof(f807,definition,
( sQ80_spl
<=> aSet0(sdtmndt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f808,plain,
( ~ sQ80_spl
| aSet0(sdtmndt0(xS,xx)) ),
inference(component_clause,[status(thm)],[f807]) ).
fof(f809,plain,
( sQ80_spl
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(component_clause,[status(thm)],[f807]) ).
fof(f810,definition,
( sQ81_spl
<=> aElementOf0(sK0_skl(xS),sdtmndt0(sdtmndt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f811,plain,
( ~ sQ81_spl
| aElementOf0(sK0_skl(xS),sdtmndt0(sdtmndt0(xS,xx),xx)) ),
inference(component_clause,[status(thm)],[f810]) ).
fof(f813,plain,
( ~ sQ77_spl
| sQ78_spl
| sQ81_spl
| ~ sQ80_spl ),
inference(split_clause,[status(thm)],[f799,f807,f810,f791,f788]) ).
fof(f814,definition,
! [X0] :
( sQ82_spl
<=> ( sdtpldt0(sdtmndt0(sdtpldt0(sdtmndt0(xS,xx),X0),sK0_skl(xS)),sK0_skl(xS)) = sdtpldt0(sdtmndt0(xS,xx),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f817,plain,
( ~ sQ77_spl
| sQ82_spl
| ~ sQ80_spl ),
inference(split_clause,[status(thm)],[f800,f807,f814,f788]) ).
fof(f818,definition,
( sQ83_spl
<=> sdtpldt0(sdtmndt0(sdtmndt0(xS,xx),sK0_skl(xS)),sK0_skl(xS)) = sdtmndt0(xS,xx) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f821,plain,
( ~ sQ77_spl
| sQ83_spl
| ~ sQ80_spl ),
inference(split_clause,[status(thm)],[f801,f807,f818,f788]) ).
fof(f836,plain,
! [X0,X1] :
( sK2_skl(xS,X1,X0) != X1
| ~ aSet0(xS)
| xS = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0)
| sK2_skl(xS,X1,X0) = X1
| aElementOf0(sK2_skl(xS,X1,X0),X0)
| xS = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f321,f120]) ).
fof(f837,plain,
! [X0,X1] :
( ~ aElementOf0(sK2_skl(xS,X1,X0),X0)
| ~ aSet0(xS)
| xS = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0)
| sK2_skl(xS,X1,X0) = X1
| aElementOf0(sK2_skl(xS,X1,X0),X0)
| xS = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f321,f119]) ).
fof(f838,plain,
! [X0,X1] :
( sK2_skl(xS,X1,X0) = xx
| aElementOf0(sK2_skl(xS,X1,X0),sdtmndt0(xS,xx))
| ~ aSet0(xS)
| sK2_skl(xS,X1,X0) = X1
| aElementOf0(sK2_skl(xS,X1,X0),X0)
| xS = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f321,f600]) ).
fof(f839,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtmndt0(sdtpldt0(xS,X2),sK2_skl(xS,X1,X0)),sK2_skl(xS,X1,X0)) = sdtpldt0(xS,X2)
| ~ aElement0(X2)
| ~ aSet0(xS)
| sK2_skl(xS,X1,X0) = X1
| aElementOf0(sK2_skl(xS,X1,X0),X0)
| xS = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f321,f147]) ).
fof(f840,plain,
! [X0,X1] :
( sdtpldt0(sdtmndt0(xS,sK2_skl(xS,X1,X0)),sK2_skl(xS,X1,X0)) = xS
| ~ aSet0(xS)
| sK2_skl(xS,X1,X0) = X1
| aElementOf0(sK2_skl(xS,X1,X0),X0)
| xS = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f321,f87]) ).
fof(f842,definition,
! [X0,X1] :
( sQ84_spl
<=> ( sK2_skl(xS,X1,X0) != X1
| xS = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0)
| sK2_skl(xS,X1,X0) = X1
| aElementOf0(sK2_skl(xS,X1,X0),X0)
| xS = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f845,plain,
( ~ sQ5_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f836,f842,f163]) ).
fof(f846,definition,
! [X0,X1] :
( sQ85_spl
<=> ( ~ aElementOf0(sK2_skl(xS,X1,X0),X0)
| xS = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0)
| sK2_skl(xS,X1,X0) = X1
| aElementOf0(sK2_skl(xS,X1,X0),X0)
| xS = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f849,plain,
( ~ sQ5_spl
| sQ85_spl ),
inference(split_clause,[status(thm)],[f837,f846,f163]) ).
fof(f850,definition,
! [X0,X1] :
( sQ86_spl
<=> ( sK2_skl(xS,X1,X0) = xx
| aElementOf0(sK2_skl(xS,X1,X0),sdtmndt0(xS,xx))
| sK2_skl(xS,X1,X0) = X1
| aElementOf0(sK2_skl(xS,X1,X0),X0)
| xS = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f853,plain,
( ~ sQ5_spl
| sQ86_spl ),
inference(split_clause,[status(thm)],[f838,f850,f163]) ).
fof(f854,definition,
! [X0,X1,X2] :
( sQ87_spl
<=> ( sdtpldt0(sdtmndt0(sdtpldt0(xS,X2),sK2_skl(xS,X1,X0)),sK2_skl(xS,X1,X0)) = sdtpldt0(xS,X2)
| ~ aElement0(X2)
| sK2_skl(xS,X1,X0) = X1
| aElementOf0(sK2_skl(xS,X1,X0),X0)
| xS = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f857,plain,
( ~ sQ5_spl
| sQ87_spl ),
inference(split_clause,[status(thm)],[f839,f854,f163]) ).
fof(f858,definition,
! [X0,X1] :
( sQ88_spl
<=> ( sdtpldt0(sdtmndt0(xS,sK2_skl(xS,X1,X0)),sK2_skl(xS,X1,X0)) = xS
| sK2_skl(xS,X1,X0) = X1
| aElementOf0(sK2_skl(xS,X1,X0),X0)
| xS = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f861,plain,
( ~ sQ5_spl
| sQ88_spl ),
inference(split_clause,[status(thm)],[f840,f858,f163]) ).
fof(f869,definition,
( sQ90_spl
<=> sK1_skl(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) = xx ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f870,plain,
( ~ sQ90_spl
| sK1_skl(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) = xx ),
inference(component_clause,[status(thm)],[f869]) ).
fof(f875,plain,
( sQ80_spl
| ~ aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f809,f122]) ).
fof(f877,plain,
( sQ80_spl
| ~ sQ9_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f875,f163,f185,f807]) ).
fof(f883,plain,
( ~ sQ22_spl
| ~ sQ78_spl
| aElementOf0(xx,xS) ),
inference(backward_demodulation,[status(thm)],[f792,f274]) ).
fof(f905,plain,
( ~ sQ22_spl
| ~ sQ78_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f883,f90]) ).
fof(f906,plain,
( ~ sQ22_spl
| ~ sQ78_spl ),
inference(contradiction_clause,[status(thm)],[f905]) ).
fof(f909,plain,
( sQ11_spl
| ~ sQ64_spl
| xS != slcrc0 ),
inference(backward_demodulation,[status(thm)],[f645,f221]) ).
fof(f951,plain,
( ~ sQ74_spl
| ~ sQ64_spl
| sK0_skl(xS) = xx ),
inference(forward_demodulation,[status(thm)],[f645,f778]) ).
fof(f976,plain,
( ~ sQ45_spl
| ~ sQ64_spl
| aElementOf0(sK0_skl(xS),sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(forward_demodulation,[status(thm)],[f645,f462]) ).
fof(f977,plain,
( ~ sQ45_spl
| ~ sQ64_spl
| ~ sQ74_spl
| aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(forward_demodulation,[status(thm)],[f951,f976]) ).
fof(f978,plain,
( ~ sQ45_spl
| ~ sQ64_spl
| ~ sQ74_spl
| aElementOf0(xx,xS) ),
inference(forward_demodulation,[status(thm)],[f645,f977]) ).
fof(f979,plain,
( ~ sQ45_spl
| ~ sQ64_spl
| ~ sQ74_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f978,f90]) ).
fof(f980,plain,
( ~ sQ45_spl
| ~ sQ64_spl
| ~ sQ74_spl ),
inference(contradiction_clause,[status(thm)],[f979]) ).
fof(f1047,plain,
( sQ11_spl
| ~ sQ64_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f909,f237,f644,f219]) ).
fof(f1062,plain,
( ~ sQ79_spl
| sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f804,f280]) ).
fof(f1063,plain,
( ~ sQ79_spl
| sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f1062]) ).
fof(f1072,plain,
( ~ sQ28_spl
| ~ sQ35_spl
| sP0_prd(xx,xx,sdtpldt0(xS,xx)) ),
inference(backward_demodulation,[status(thm)],[f417,f343]) ).
fof(f1081,plain,
( ~ sQ28_spl
| ~ sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1072,f125]) ).
fof(f1082,plain,
( ~ sQ28_spl
| ~ sQ35_spl ),
inference(contradiction_clause,[status(thm)],[f1081]) ).
fof(f1096,plain,
( ~ sQ6_spl
| ~ sQ90_spl
| aElementOf0(xx,xS) ),
inference(forward_demodulation,[status(thm)],[f870,f167]) ).
fof(f1131,plain,
( ~ sQ46_spl
| ~ sQ76_spl
| aElementOf0(xx,xS) ),
inference(forward_demodulation,[status(thm)],[f785,f471]) ).
fof(f1134,plain,
( ~ sQ6_spl
| ~ sQ90_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f90,f1096]) ).
fof(f1135,plain,
( ~ sQ6_spl
| ~ sQ90_spl ),
inference(contradiction_clause,[status(thm)],[f1134]) ).
fof(f1210,plain,
( ~ sQ46_spl
| ~ sQ76_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1131,f90]) ).
fof(f1211,plain,
( ~ sQ46_spl
| ~ sQ76_spl ),
inference(contradiction_clause,[status(thm)],[f1210]) ).
fof(f1256,plain,
( aElementOf0(sK0_skl(slcrc0),slcrc0)
| slcrc0 = slcrc0 ),
inference(resolution,[status(thm)],[f38,f106]) ).
fof(f1258,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| aElementOf0(sK0_skl(sdtpldt0(X0,X1)),sdtpldt0(X0,X1))
| sdtpldt0(X0,X1) = slcrc0 ),
inference(resolution,[status(thm)],[f38,f112]) ).
fof(f1259,plain,
( aElementOf0(sK0_skl(xS),xS)
| xS = slcrc0 ),
inference(resolution,[status(thm)],[f38,f89]) ).
fof(f1261,definition,
( sQ91_spl
<=> aElementOf0(sK0_skl(slcrc0),slcrc0) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f1262,plain,
( ~ sQ91_spl
| aElementOf0(sK0_skl(slcrc0),slcrc0) ),
inference(component_clause,[status(thm)],[f1261]) ).
fof(f1264,plain,
( sQ91_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1256,f129,f1261]) ).
fof(f1265,plain,
( sQ22_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f1259,f237,f273]) ).
fof(f1266,plain,
( ~ sQ91_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1262,f107]) ).
fof(f1267,plain,
~ sQ91_spl,
inference(contradiction_clause,[status(thm)],[f1266]) ).
fof(f1315,definition,
! [X0] :
( sQ94_spl
<=> ( aElementOf0(sK1_skl(slcrc0,X0),slcrc0)
| ~ aSet0(X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f1316,plain,
! [X0] :
( ~ sQ94_spl
| aElementOf0(sK1_skl(slcrc0,X0),slcrc0)
| ~ aSet0(X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f1315]) ).
fof(f1320,plain,
! [X0] :
( ~ sQ94_spl
| aElementOf0(sK1_skl(slcrc0,X0),slcrc0)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1316]) ).
fof(f1321,plain,
( ~ sQ94_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f106,f1325]) ).
fof(f1325,plain,
! [X0] :
( ~ sQ94_spl
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1320,f107]) ).
fof(f1368,plain,
~ sQ94_spl,
inference(contradiction_clause,[status(thm)],[f1321]) ).
fof(f1369,plain,
! [X0,X1,X2] :
( aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X2,X0)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f111,f50]) ).
fof(f1370,plain,
! [X0,X1] :
( sP0_prd(X1,X0,xS)
| ~ aElementOf0(X1,sdtmndt0(xS,X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f123,f89]) ).
fof(f1371,plain,
! [X0,X1] :
( sP0_prd(X1,X0,slcrc0)
| ~ aElementOf0(X1,sdtmndt0(slcrc0,X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f106,f123]) ).
fof(f1378,plain,
! [X0,X1] :
( sP0_prd(sK3_skl(slcrc0,X1,X0),X1,X0)
| ~ aSet0(slcrc0)
| slcrc0 = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f85,f107]) ).
fof(f1379,definition,
! [X0,X1] :
( sQ96_spl
<=> ( sP0_prd(sK3_skl(slcrc0,X1,X0),X1,X0)
| slcrc0 = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f1382,plain,
( ~ sQ3_spl
| sQ96_spl ),
inference(split_clause,[status(thm)],[f1378,f1379,f132]) ).
fof(f1385,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)],[f74,f107]) ).
fof(f1386,definition,
! [X0,X1] :
( sQ97_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,[sQ97_spl])],[split_symbol_definition]) ).
fof(f1389,plain,
( ~ sQ3_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f1385,f1386,f132]) ).
fof(f1397,definition,
! [X0,X1] :
( sQ98_spl
<=> ( sK2_skl(sdtmndt0(slcrc0,sK0_skl(slcrc0)),X1,X0) = X1
| aElementOf0(sK2_skl(sdtmndt0(slcrc0,sK0_skl(slcrc0)),X1,X0),X0)
| sdtmndt0(slcrc0,sK0_skl(slcrc0)) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f1400,definition,
( sQ99_spl
<=> aSet0(sdtmndt0(slcrc0,sK0_skl(slcrc0))) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f1401,plain,
( ~ sQ99_spl
| aSet0(sdtmndt0(slcrc0,sK0_skl(slcrc0))) ),
inference(component_clause,[status(thm)],[f1400]) ).
fof(f1402,plain,
( sQ99_spl
| ~ aSet0(sdtmndt0(slcrc0,sK0_skl(slcrc0))) ),
inference(component_clause,[status(thm)],[f1400]) ).
fof(f1408,definition,
( sQ101_spl
<=> aElement0(sK0_skl(slcrc0)) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f1409,plain,
( ~ sQ101_spl
| aElement0(sK0_skl(slcrc0)) ),
inference(component_clause,[status(thm)],[f1408]) ).
fof(f1410,plain,
( sQ101_spl
| ~ aElement0(sK0_skl(slcrc0)) ),
inference(component_clause,[status(thm)],[f1408]) ).
fof(f1466,definition,
( sQ104_spl
<=> aSet0(sdtmndt0(xS,sK1_skl(xS,slcrc0))) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f1467,plain,
( ~ sQ104_spl
| aSet0(sdtmndt0(xS,sK1_skl(xS,slcrc0))) ),
inference(component_clause,[status(thm)],[f1466]) ).
fof(f1468,plain,
( sQ104_spl
| ~ aSet0(sdtmndt0(xS,sK1_skl(xS,slcrc0))) ),
inference(component_clause,[status(thm)],[f1466]) ).
fof(f1469,definition,
( sQ105_spl
<=> aElement0(sK1_skl(xS,slcrc0)) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f1470,plain,
( ~ sQ105_spl
| aElement0(sK1_skl(xS,slcrc0)) ),
inference(component_clause,[status(thm)],[f1469]) ).
fof(f1471,plain,
( sQ105_spl
| ~ aElement0(sK1_skl(xS,slcrc0)) ),
inference(component_clause,[status(thm)],[f1469]) ).
fof(f1480,plain,
! [X0] :
( sQ105_spl
| ~ aElementOf0(sK1_skl(xS,slcrc0),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f1471,f29]) ).
fof(f1581,plain,
( ~ sQ68_spl
| sdtpldt0(sdtmndt0(xS,sK1_skl(xS,slcrc0)),sK1_skl(xS,slcrc0)) = xS
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f706,f87]) ).
fof(f1582,definition,
( sQ108_spl
<=> sdtpldt0(sdtmndt0(xS,sK1_skl(xS,slcrc0)),sK1_skl(xS,slcrc0)) = xS ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f1585,plain,
( ~ sQ68_spl
| sQ108_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1581,f163,f1582,f705]) ).
fof(f1588,plain,
( sQ99_spl
| ~ aElement0(sK0_skl(slcrc0))
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f122,f1402]) ).
fof(f1590,plain,
( sQ99_spl
| ~ sQ101_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1588,f132,f1408,f1400]) ).
fof(f1591,plain,
( sQ70_spl
| ~ aElementOf0(sK1_skl(xS,slcrc0),slcrc0)
| ~ aSet0(xS)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f53,f715]) ).
fof(f1592,definition,
( sQ109_spl
<=> aElementOf0(sK1_skl(xS,slcrc0),slcrc0) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f1595,plain,
( sQ70_spl
| ~ sQ109_spl
| ~ sQ5_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1591,f132,f163,f1592,f713]) ).
fof(f1597,plain,
! [X0] :
( sQ101_spl
| ~ aElementOf0(sK0_skl(slcrc0),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f1410,f29]) ).
fof(f1610,plain,
( sQ104_spl
| ~ aElement0(sK1_skl(xS,slcrc0))
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f1468,f122]) ).
fof(f1612,plain,
( sQ104_spl
| ~ sQ105_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1610,f163,f1469,f1466]) ).
fof(f1619,definition,
! [X0] :
( sQ112_spl
<=> ( ~ aSet0(sdtpldt0(X0,sK0_skl(slcrc0)))
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f1620,plain,
! [X0] :
( ~ sQ112_spl
| ~ aSet0(sdtpldt0(X0,sK0_skl(slcrc0)))
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f1619]) ).
fof(f1654,plain,
! [X0] :
( ~ sQ1_spl
| aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f51,f103]) ).
fof(f1658,definition,
! [X0] :
( sQ116_spl
<=> ( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f1659,plain,
! [X0] :
( ~ sQ116_spl
| aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(component_clause,[status(thm)],[f1658]) ).
fof(f1661,plain,
( ~ sQ1_spl
| sQ116_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1654,f163,f1658,f102]) ).
fof(f1664,plain,
! [X0,X1,X2,X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X2,X0)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f1369,f51]) ).
fof(f1665,plain,
! [X0,X1,X2] :
( X1 = X0
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X2,X0)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f1369,f110]) ).
fof(f1666,plain,
! [X0,X1,X2,X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aSubsetOf0(X2,X0)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1664]) ).
fof(f1667,plain,
! [X0,X1,X2] :
( X1 = X0
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X2,X0)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1665]) ).
fof(f1670,plain,
( sQ0_spl
| ~ aElementOf0(sK1_skl(xS,sdtmndt0(sdtpldt0(xS,xx),xx)),sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSet0(xS)
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f101,f53]) ).
fof(f1676,definition,
( sQ118_spl
<=> aElementOf0(sK1_skl(xS,sdtmndt0(sdtpldt0(xS,xx),xx)),sdtmndt0(sdtpldt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f1678,plain,
( sQ118_spl
| ~ aElementOf0(sK1_skl(xS,sdtmndt0(sdtpldt0(xS,xx),xx)),sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(component_clause,[status(thm)],[f1676]) ).
fof(f1679,plain,
( sQ0_spl
| ~ sQ118_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1670,f160,f163,f1676,f99]) ).
fof(f1689,plain,
( ~ sQ22_spl
| ~ aSubsetOf0(xS,slcrc0)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f351,f107]) ).
fof(f1692,plain,
( ~ sQ22_spl
| ~ sQ70_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1689,f132,f713,f273]) ).
fof(f1694,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f134,f106]) ).
fof(f1695,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f1694]) ).
fof(f1696,plain,
! [X0] :
( sQ70_spl
| ~ aSubsetOf0(X0,slcrc0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f715,f1369]) ).
fof(f1697,plain,
( sQ70_spl
| aElementOf0(sK1_skl(xS,slcrc0),xS)
| ~ aSet0(xS)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f715,f52]) ).
fof(f1699,definition,
! [X0] :
( sQ119_spl
<=> ( ~ aSubsetOf0(X0,slcrc0)
| ~ aSubsetOf0(xS,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f1700,plain,
! [X0] :
( ~ sQ119_spl
| ~ aSubsetOf0(X0,slcrc0)
| ~ aSubsetOf0(xS,X0) ),
inference(component_clause,[status(thm)],[f1699]) ).
fof(f1702,plain,
( sQ70_spl
| sQ119_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1696,f132,f1699,f713]) ).
fof(f1703,plain,
( sQ70_spl
| sQ68_spl
| ~ sQ5_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1697,f132,f163,f705,f713]) ).
fof(f1715,definition,
! [X2] :
( sQ120_spl
<=> ( ~ aSubsetOf0(slcrc0,X2)
| ~ aSet0(X2) ) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f1716,plain,
! [X0] :
( ~ sQ120_spl
| ~ aSubsetOf0(slcrc0,X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f1715]) ).
fof(f1725,plain,
( ~ sQ120_spl
| ~ aSet0(slcrc0)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f1716,f57]) ).
fof(f1732,plain,
( ~ sQ120_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1725,f132,f1715]) ).
fof(f1741,plain,
! [X0] :
( ~ sQ119_spl
| aElementOf0(sK1_skl(xS,X0),xS)
| ~ aSet0(xS)
| ~ aSet0(X0)
| ~ aSubsetOf0(X0,slcrc0) ),
inference(resolution,[status(thm)],[f1700,f52]) ).
fof(f1742,plain,
! [X0] :
( ~ sQ119_spl
| ~ aElementOf0(sK1_skl(xS,X0),X0)
| ~ aSet0(xS)
| ~ aSet0(X0)
| ~ aSubsetOf0(X0,slcrc0) ),
inference(resolution,[status(thm)],[f1700,f53]) ).
fof(f1744,definition,
! [X0] :
( sQ122_spl
<=> ( aElementOf0(sK1_skl(xS,X0),xS)
| ~ aSet0(X0)
| ~ aSubsetOf0(X0,slcrc0) ) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f1747,plain,
( ~ sQ119_spl
| ~ sQ5_spl
| sQ122_spl ),
inference(split_clause,[status(thm)],[f1741,f1744,f163,f1699]) ).
fof(f1748,definition,
! [X0] :
( sQ123_spl
<=> ( ~ aElementOf0(sK1_skl(xS,X0),X0)
| ~ aSet0(X0)
| ~ aSubsetOf0(X0,slcrc0) ) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f1751,plain,
( ~ sQ119_spl
| ~ sQ5_spl
| sQ123_spl ),
inference(split_clause,[status(thm)],[f1742,f1748,f163,f1699]) ).
fof(f1753,plain,
( sQ105_spl
| ~ sQ68_spl
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f706,f1480]) ).
fof(f1755,plain,
( sQ105_spl
| ~ sQ68_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1753,f163,f705,f1469]) ).
fof(f1790,plain,
! [X0,X1] :
( ~ sQ15_spl
| ~ aElement0(sK0_skl(xS))
| ~ aSet0(sdtmndt0(xS,sK0_skl(xS)))
| sK2_skl(sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)),X1,X0) = X1
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)),X1,X0),X0)
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)),X1,X0),xS)
| sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(paramodulation,[status(thm)],[f235,f320]) ).
fof(f1791,plain,
! [X0,X1] :
( ~ sQ15_spl
| ~ aElement0(sK0_skl(xS))
| ~ aSet0(sdtmndt0(xS,sK0_skl(xS)))
| sK2_skl(sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)),X1,X0) = X1
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)),X1,X0),X0)
| aElementOf0(sK2_skl(xS,X1,X0),sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)))
| sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(paramodulation,[status(thm)],[f235,f320]) ).
fof(f1792,plain,
! [X0,X1] :
( ~ sQ15_spl
| ~ aElementOf0(sK3_skl(sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)),X1,X0),sdtmndt0(xS,sK0_skl(xS)))
| ~ aElement0(sK0_skl(xS))
| ~ aSet0(sdtmndt0(xS,sK0_skl(xS)))
| ~ sP0_prd(sK3_skl(xS,X1,X0),X1,X0)
| sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)) = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(paramodulation,[status(thm)],[f235,f324]) ).
fof(f1797,definition,
! [X0,X1] :
( sQ124_spl
<=> ( sK2_skl(sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)),X1,X0) = X1
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)),X1,X0),X0)
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)),X1,X0),xS)
| sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f1800,plain,
( ~ sQ15_spl
| ~ sQ18_spl
| ~ sQ17_spl
| sQ124_spl ),
inference(split_clause,[status(thm)],[f1790,f1797,f255,f258,f234]) ).
fof(f1801,definition,
! [X0,X1] :
( sQ125_spl
<=> ( sK2_skl(sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)),X1,X0) = X1
| aElementOf0(sK2_skl(sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)),X1,X0),X0)
| aElementOf0(sK2_skl(xS,X1,X0),sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)))
| sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f1804,plain,
( ~ sQ15_spl
| ~ sQ18_spl
| ~ sQ17_spl
| sQ125_spl ),
inference(split_clause,[status(thm)],[f1791,f1801,f255,f258,f234]) ).
fof(f1805,definition,
! [X0,X1] :
( sQ126_spl
<=> ( ~ aElementOf0(sK3_skl(sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)),X1,X0),sdtmndt0(xS,sK0_skl(xS)))
| ~ sP0_prd(sK3_skl(xS,X1,X0),X1,X0)
| sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS)) = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f1808,plain,
( ~ sQ15_spl
| ~ sQ18_spl
| ~ sQ17_spl
| sQ126_spl ),
inference(split_clause,[status(thm)],[f1792,f1805,f255,f258,f234]) ).
fof(f1823,plain,
( ~ sQ81_spl
| sdtpldt0(sdtmndt0(sdtmndt0(sdtmndt0(xS,xx),xx),sK0_skl(xS)),sK0_skl(xS)) = sdtmndt0(sdtmndt0(xS,xx),xx)
| ~ aSet0(sdtmndt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f811,f87]) ).
fof(f1824,definition,
( sQ127_spl
<=> aSet0(sdtmndt0(sdtmndt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f1825,plain,
( ~ sQ127_spl
| aSet0(sdtmndt0(sdtmndt0(xS,xx),xx)) ),
inference(component_clause,[status(thm)],[f1824]) ).
fof(f1826,plain,
( sQ127_spl
| ~ aSet0(sdtmndt0(sdtmndt0(xS,xx),xx)) ),
inference(component_clause,[status(thm)],[f1824]) ).
fof(f1827,definition,
( sQ128_spl
<=> sdtpldt0(sdtmndt0(sdtmndt0(sdtmndt0(xS,xx),xx),sK0_skl(xS)),sK0_skl(xS)) = sdtmndt0(sdtmndt0(xS,xx),xx) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f1830,plain,
( ~ sQ81_spl
| sQ128_spl
| ~ sQ127_spl ),
inference(split_clause,[status(thm)],[f1823,f1824,f1827,f810]) ).
fof(f1845,plain,
( sQ127_spl
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f1826,f122]) ).
fof(f1847,plain,
( sQ127_spl
| ~ sQ9_spl
| ~ sQ80_spl ),
inference(split_clause,[status(thm)],[f1845,f807,f185,f1824]) ).
fof(f1849,plain,
! [X0,X1] :
( ~ sQ21_spl
| ~ aElement0(sK0_skl(xS))
| ~ aSet0(xS)
| sK2_skl(sdtmndt0(xS,sK0_skl(xS)),X0,X1) = X0
| aElementOf0(sK2_skl(sdtmndt0(xS,sK0_skl(xS)),X0,X1),X1)
| sdtmndt0(xS,sK0_skl(xS)) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| aElementOf0(sK2_skl(sdtmndt0(xS,sK0_skl(xS)),X0,X1),xS) ),
inference(resolution,[status(thm)],[f270,f318]) ).
fof(f1852,plain,
! [X0,X1] :
( ~ sQ21_spl
| sP0_prd(sK3_skl(sdtmndt0(xS,sK0_skl(xS)),X0,X1),X0,X1)
| ~ aSet0(sdtmndt0(xS,sK0_skl(xS)))
| sdtmndt0(xS,sK0_skl(xS)) = sdtmndt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| aElementOf0(sK3_skl(sdtmndt0(xS,sK0_skl(xS)),X0,X1),xS) ),
inference(resolution,[status(thm)],[f270,f85]) ).
fof(f1855,plain,
! [X0] :
( ~ sQ21_spl
| X0 = sK0_skl(xS)
| ~ aElementOf0(X0,xS)
| ~ aElement0(sK0_skl(xS))
| ~ aSet0(xS)
| aElementOf0(X0,xS) ),
inference(resolution,[status(thm)],[f270,f208]) ).
fof(f1856,plain,
! [X0] :
( ~ sQ21_spl
| ~ sP0_prd(X0,sK0_skl(xS),xS)
| ~ aElement0(sK0_skl(xS))
| ~ aSet0(xS)
| aElementOf0(X0,xS) ),
inference(resolution,[status(thm)],[f270,f124]) ).
fof(f1857,definition,
! [X0,X1] :
( sQ129_spl
<=> ( sK2_skl(sdtmndt0(xS,sK0_skl(xS)),X0,X1) = X0
| aElementOf0(sK2_skl(sdtmndt0(xS,sK0_skl(xS)),X0,X1),X1)
| sdtmndt0(xS,sK0_skl(xS)) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| aElementOf0(sK2_skl(sdtmndt0(xS,sK0_skl(xS)),X0,X1),xS) ) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f1860,plain,
( ~ sQ21_spl
| ~ sQ18_spl
| ~ sQ5_spl
| sQ129_spl ),
inference(split_clause,[status(thm)],[f1849,f1857,f163,f258,f269]) ).
fof(f1861,definition,
! [X2] :
( sQ130_spl
<=> ( ~ aSubsetOf0(sdtmndt0(xS,sK0_skl(xS)),X2)
| ~ aSet0(X2) ) ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f1862,plain,
! [X0] :
( ~ sQ130_spl
| ~ aSubsetOf0(sdtmndt0(xS,sK0_skl(xS)),X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f1861]) ).
fof(f1866,definition,
! [X0,X1] :
( sQ131_spl
<=> ( sP0_prd(sK3_skl(sdtmndt0(xS,sK0_skl(xS)),X0,X1),X0,X1)
| sdtmndt0(xS,sK0_skl(xS)) = sdtmndt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| aElementOf0(sK3_skl(sdtmndt0(xS,sK0_skl(xS)),X0,X1),xS) ) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f1869,plain,
( ~ sQ21_spl
| ~ sQ17_spl
| sQ131_spl ),
inference(split_clause,[status(thm)],[f1852,f1866,f255,f269]) ).
fof(f1870,definition,
( sQ132_spl
<=> aSubsetOf0(xS,sdtmndt0(xS,sK0_skl(xS))) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f1872,plain,
( sQ132_spl
| ~ aSubsetOf0(xS,sdtmndt0(xS,sK0_skl(xS))) ),
inference(component_clause,[status(thm)],[f1870]) ).
fof(f1875,definition,
! [X0] :
( sQ133_spl
<=> ( X0 = sK0_skl(xS)
| ~ aElementOf0(X0,xS)
| aElementOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f1878,plain,
( ~ sQ21_spl
| ~ sQ18_spl
| ~ sQ5_spl
| sQ133_spl ),
inference(split_clause,[status(thm)],[f1855,f1875,f163,f258,f269]) ).
fof(f1879,definition,
! [X0] :
( sQ134_spl
<=> ( ~ sP0_prd(X0,sK0_skl(xS),xS)
| aElementOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f1882,plain,
( ~ sQ21_spl
| ~ sQ18_spl
| ~ sQ5_spl
| sQ134_spl ),
inference(split_clause,[status(thm)],[f1856,f1879,f163,f258,f269]) ).
fof(f1886,plain,
( ~ sQ130_spl
| ~ aSet0(sdtmndt0(xS,sK0_skl(xS)))
| ~ aSet0(sdtmndt0(xS,sK0_skl(xS))) ),
inference(resolution,[status(thm)],[f1862,f57]) ).
fof(f1896,plain,
( ~ sQ130_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1886,f255,f1861]) ).
fof(f1900,plain,
! [X0] :
( ~ sQ21_spl
| aElementOf0(sK1_skl(sdtmndt0(xS,sK0_skl(xS)),X0),xS)
| sdtmndt0(xS,sK0_skl(xS)) = X0
| ~ aSubsetOf0(X0,sdtmndt0(xS,sK0_skl(xS)))
| ~ aSet0(sdtmndt0(xS,sK0_skl(xS))) ),
inference(resolution,[status(thm)],[f174,f270]) ).
fof(f1902,plain,
! [X0] :
( slcrc0 = X0
| ~ aSubsetOf0(X0,slcrc0)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f174,f107]) ).
fof(f1904,definition,
( sQ137_spl
<=> aSubsetOf0(slcrc0,slcrc0) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f1905,plain,
( ~ sQ137_spl
| aSubsetOf0(slcrc0,slcrc0) ),
inference(component_clause,[status(thm)],[f1904]) ).
fof(f1908,definition,
! [X0] :
( sQ138_spl
<=> ( aElementOf0(sK1_skl(sdtmndt0(xS,sK0_skl(xS)),X0),xS)
| sdtmndt0(xS,sK0_skl(xS)) = X0
| ~ aSubsetOf0(X0,sdtmndt0(xS,sK0_skl(xS))) ) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f1911,plain,
( ~ sQ21_spl
| sQ138_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1900,f255,f1908,f269]) ).
fof(f1913,definition,
! [X0] :
( sQ139_spl
<=> ( slcrc0 = X0
| ~ aSubsetOf0(X0,slcrc0) ) ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f1914,plain,
! [X0] :
( ~ sQ139_spl
| slcrc0 = X0
| ~ aSubsetOf0(X0,slcrc0) ),
inference(component_clause,[status(thm)],[f1913]) ).
fof(f1916,plain,
( sQ139_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1902,f132,f1913]) ).
fof(f1919,plain,
! [X0,X1] :
( ~ sQ139_spl
| ~ aSubsetOf0(X1,slcrc0)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(slcrc0)
| slcrc0 = X0 ),
inference(resolution,[status(thm)],[f1914,f1369]) ).
fof(f1920,plain,
! [X0] :
( ~ sQ139_spl
| aElementOf0(sK1_skl(X0,slcrc0),X0)
| ~ aSet0(X0)
| ~ aSet0(slcrc0)
| slcrc0 = X0 ),
inference(resolution,[status(thm)],[f1914,f52]) ).
fof(f1921,plain,
! [X0] :
( ~ sQ139_spl
| ~ aElementOf0(sK1_skl(X0,slcrc0),slcrc0)
| ~ aSet0(X0)
| ~ aSet0(slcrc0)
| slcrc0 = X0 ),
inference(resolution,[status(thm)],[f1914,f53]) ).
fof(f1924,definition,
! [X0,X1] :
( sQ140_spl
<=> ( ~ aSubsetOf0(X1,slcrc0)
| ~ aSubsetOf0(X0,X1)
| slcrc0 = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f1925,plain,
! [X0,X1] :
( ~ sQ140_spl
| ~ aSubsetOf0(X1,slcrc0)
| ~ aSubsetOf0(X0,X1)
| slcrc0 = X0 ),
inference(component_clause,[status(thm)],[f1924]) ).
fof(f1927,plain,
( ~ sQ139_spl
| ~ sQ3_spl
| sQ140_spl ),
inference(split_clause,[status(thm)],[f1919,f1924,f132,f1913]) ).
fof(f1928,definition,
! [X0] :
( sQ141_spl
<=> ( aElementOf0(sK1_skl(X0,slcrc0),X0)
| ~ aSet0(X0)
| slcrc0 = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f1929,plain,
! [X0] :
( ~ sQ141_spl
| aElementOf0(sK1_skl(X0,slcrc0),X0)
| ~ aSet0(X0)
| slcrc0 = X0 ),
inference(component_clause,[status(thm)],[f1928]) ).
fof(f1931,plain,
( ~ sQ139_spl
| ~ sQ3_spl
| sQ141_spl ),
inference(split_clause,[status(thm)],[f1920,f1928,f132,f1913]) ).
fof(f1932,definition,
! [X0] :
( sQ142_spl
<=> ( ~ aElementOf0(sK1_skl(X0,slcrc0),slcrc0)
| ~ aSet0(X0)
| slcrc0 = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f1935,plain,
( ~ sQ139_spl
| ~ sQ3_spl
| sQ142_spl ),
inference(split_clause,[status(thm)],[f1921,f1932,f132,f1913]) ).
fof(f1937,plain,
! [X0,X1] :
( ~ sQ119_spl
| ~ aSubsetOf0(sdtpldt0(X0,X1),slcrc0)
| ~ aElementOf0(sK1_skl(xS,sdtpldt0(X0,X1)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f192,f1700]) ).
fof(f1940,plain,
! [X0] :
( ~ sQ15_spl
| ~ aElementOf0(sK1_skl(X0,sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS))),sdtmndt0(xS,sK0_skl(xS)))
| ~ aElement0(sK0_skl(xS))
| ~ aSet0(sdtmndt0(xS,sK0_skl(xS)))
| ~ aSet0(X0)
| aSubsetOf0(X0,xS) ),
inference(paramodulation,[status(thm)],[f235,f192]) ).
fof(f1941,definition,
! [X0,X1] :
( sQ143_spl
<=> ( ~ aSubsetOf0(sdtpldt0(X0,X1),slcrc0)
| ~ aElementOf0(sK1_skl(xS,sdtpldt0(X0,X1)),X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f1944,plain,
( ~ sQ119_spl
| sQ143_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1937,f163,f1941,f1699]) ).
fof(f1947,definition,
! [X0] :
( sQ144_spl
<=> ( ~ aElementOf0(sK1_skl(X0,sdtpldt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(xS))),sdtmndt0(xS,sK0_skl(xS)))
| ~ aSet0(X0)
| aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f1950,plain,
( ~ sQ15_spl
| ~ sQ18_spl
| ~ sQ17_spl
| sQ144_spl ),
inference(split_clause,[status(thm)],[f1940,f1947,f255,f258,f234]) ).
fof(f1953,plain,
! [X0,X1] :
( ~ sQ21_spl
| aElementOf0(sK1_skl(sdtmndt0(xS,sK0_skl(xS)),X1),xS)
| aSubsetOf0(sdtmndt0(xS,sK0_skl(xS)),X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0)
| ~ aSet0(sdtmndt0(xS,sK0_skl(xS))) ),
inference(resolution,[status(thm)],[f172,f270]) ).
fof(f1955,plain,
! [X0,X1] :
( aSubsetOf0(slcrc0,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f172,f107]) ).
fof(f1961,definition,
! [X0,X1] :
( sQ146_spl
<=> ( aElementOf0(sK1_skl(sdtmndt0(xS,sK0_skl(xS)),X1),xS)
| aSubsetOf0(sdtmndt0(xS,sK0_skl(xS)),X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f1964,plain,
( ~ sQ21_spl
| sQ146_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1953,f255,f1961,f269]) ).
fof(f1966,definition,
! [X0,X1] :
( sQ147_spl
<=> ( aSubsetOf0(slcrc0,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f1967,plain,
! [X0,X1] :
( ~ sQ147_spl
| aSubsetOf0(slcrc0,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f1966]) ).
fof(f1969,plain,
( sQ147_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1955,f132,f1966]) ).
fof(f1984,plain,
( ~ sQ21_spl
| ~ sQ67_spl
| aElementOf0(sK1_skl(sdtmndt0(xS,sK0_skl(xS)),slcrc0),xS)
| aSubsetOf0(sdtmndt0(xS,sK0_skl(xS)),xS)
| ~ aSet0(sdtmndt0(xS,sK0_skl(xS))) ),
inference(resolution,[status(thm)],[f702,f270]) ).
fof(f1988,definition,
( sQ148_spl
<=> aSubsetOf0(sdtmndt0(xS,sK0_skl(xS)),xS) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f1991,definition,
( sQ149_spl
<=> aElementOf0(sK1_skl(sdtmndt0(xS,sK0_skl(xS)),slcrc0),xS) ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f1994,plain,
( ~ sQ21_spl
| ~ sQ67_spl
| sQ149_spl
| sQ148_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1984,f255,f1988,f1991,f701,f269]) ).
fof(f1996,definition,
( sQ150_spl
<=> aSubsetOf0(slcrc0,xS) ),
introduced(definition,[new_symbols(definition,[sQ150_spl])],[split_symbol_definition]) ).
fof(f1997,plain,
( ~ sQ150_spl
| aSubsetOf0(slcrc0,xS) ),
inference(component_clause,[status(thm)],[f1996]) ).
fof(f1998,plain,
( sQ150_spl
| ~ aSubsetOf0(slcrc0,xS) ),
inference(component_clause,[status(thm)],[f1996]) ).
fof(f2001,plain,
! [X0] :
( ~ sQ150_spl
| aElementOf0(X0,xS)
| ~ aElementOf0(X0,slcrc0)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f1997,f51]) ).
fof(f2003,definition,
! [X0] :
( sQ151_spl
<=> ( aElementOf0(X0,xS)
| ~ aElementOf0(X0,slcrc0) ) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f2006,plain,
( ~ sQ150_spl
| sQ151_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2001,f163,f2003,f1996]) ).
fof(f2008,plain,
( sQ101_spl
| ~ sQ116_spl
| ~ aSet0(xS)
| ~ aElementOf0(sK0_skl(slcrc0),sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f1659,f1597]) ).
fof(f2009,plain,
! [X0,X1,X2] :
( ~ sQ116_spl
| ~ aElement0(X0)
| ~ aSet0(xS)
| ~ aElementOf0(sK2_skl(sdtpldt0(xS,X0),X1,X2),X2)
| sdtpldt0(xS,X0) = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(sK2_skl(sdtpldt0(xS,X0),X1,X2),sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f1659,f194]) ).
fof(f2010,plain,
! [X0,X1,X2] :
( ~ sQ116_spl
| ~ aElement0(X0)
| ~ aSet0(xS)
| sK2_skl(sdtpldt0(xS,X0),X1,X2) != X1
| sdtpldt0(xS,X0) = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(sK2_skl(sdtpldt0(xS,X0),X1,X2),sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f1659,f196]) ).
fof(f2011,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ aElementOf0(sK2_skl(xS,X0,X1),X1)
| ~ aSet0(xS)
| xS = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(sK2_skl(xS,X0,X1),sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f1659,f119]) ).
fof(f2012,plain,
! [X0,X1] :
( ~ sQ116_spl
| sK2_skl(xS,X0,X1) != X0
| ~ aSet0(xS)
| xS = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(sK2_skl(xS,X0,X1),sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f1659,f120]) ).
fof(f2013,plain,
( ~ sQ116_spl
| ~ aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f1659,f90]) ).
fof(f2014,plain,
! [X0] :
( ~ sQ116_spl
| sdtpldt0(sdtmndt0(xS,X0),X0) = xS
| ~ aSet0(xS)
| ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f1659,f87]) ).
fof(f2015,definition,
( sQ152_spl
<=> aElementOf0(sK0_skl(slcrc0),sdtmndt0(sdtpldt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f2018,plain,
( sQ101_spl
| ~ sQ116_spl
| ~ sQ5_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f2008,f2015,f163,f1658,f1408]) ).
fof(f2019,definition,
! [X0,X1,X2] :
( sQ153_spl
<=> ( ~ aElement0(X0)
| ~ aElementOf0(sK2_skl(sdtpldt0(xS,X0),X1,X2),X2)
| sdtpldt0(xS,X0) = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(sK2_skl(sdtpldt0(xS,X0),X1,X2),sdtmndt0(sdtpldt0(xS,xx),xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ153_spl])],[split_symbol_definition]) ).
fof(f2022,plain,
( ~ sQ116_spl
| ~ sQ5_spl
| sQ153_spl ),
inference(split_clause,[status(thm)],[f2009,f2019,f163,f1658]) ).
fof(f2023,definition,
! [X0,X1,X2] :
( sQ154_spl
<=> ( ~ aElement0(X0)
| sK2_skl(sdtpldt0(xS,X0),X1,X2) != X1
| sdtpldt0(xS,X0) = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(sK2_skl(sdtpldt0(xS,X0),X1,X2),sdtmndt0(sdtpldt0(xS,xx),xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition]) ).
fof(f2026,plain,
( ~ sQ116_spl
| ~ sQ5_spl
| sQ154_spl ),
inference(split_clause,[status(thm)],[f2010,f2023,f163,f1658]) ).
fof(f2027,definition,
! [X0,X1] :
( sQ155_spl
<=> ( ~ aElementOf0(sK2_skl(xS,X0,X1),X1)
| xS = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(sK2_skl(xS,X0,X1),sdtmndt0(sdtpldt0(xS,xx),xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition]) ).
fof(f2030,plain,
( ~ sQ116_spl
| ~ sQ5_spl
| sQ155_spl ),
inference(split_clause,[status(thm)],[f2011,f2027,f163,f1658]) ).
fof(f2031,definition,
! [X0,X1] :
( sQ156_spl
<=> ( sK2_skl(xS,X0,X1) != X0
| xS = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(sK2_skl(xS,X0,X1),sdtmndt0(sdtpldt0(xS,xx),xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ156_spl])],[split_symbol_definition]) ).
fof(f2034,plain,
( ~ sQ116_spl
| ~ sQ5_spl
| sQ156_spl ),
inference(split_clause,[status(thm)],[f2012,f2031,f163,f1658]) ).
fof(f2035,definition,
! [X0] :
( sQ157_spl
<=> ( sdtpldt0(sdtmndt0(xS,X0),X0) = xS
| ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f2036,plain,
! [X0] :
( ~ sQ157_spl
| sdtpldt0(sdtmndt0(xS,X0),X0) = xS
| ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(component_clause,[status(thm)],[f2035]) ).
fof(f2038,plain,
( ~ sQ116_spl
| ~ sQ5_spl
| sQ157_spl ),
inference(split_clause,[status(thm)],[f2014,f2035,f163,f1658]) ).
fof(f2040,plain,
! [X0,X1,X2] :
( ~ sQ140_spl
| ~ aSubsetOf0(X2,slcrc0)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(slcrc0)
| ~ aSubsetOf0(X0,X1)
| slcrc0 = X0 ),
inference(resolution,[status(thm)],[f1925,f1369]) ).
fof(f2041,plain,
! [X0,X1] :
( ~ sQ140_spl
| aElementOf0(sK1_skl(X1,slcrc0),X1)
| ~ aSet0(X1)
| ~ aSet0(slcrc0)
| ~ aSubsetOf0(X0,X1)
| slcrc0 = X0 ),
inference(resolution,[status(thm)],[f1925,f52]) ).
fof(f2042,plain,
! [X0,X1] :
( ~ sQ140_spl
| ~ aElementOf0(sK1_skl(X1,slcrc0),slcrc0)
| ~ aSet0(X1)
| ~ aSet0(slcrc0)
| ~ aSubsetOf0(X0,X1)
| slcrc0 = X0 ),
inference(resolution,[status(thm)],[f1925,f53]) ).
fof(f2044,definition,
! [X0,X1,X2] :
( sQ158_spl
<=> ( ~ aSubsetOf0(X2,slcrc0)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| slcrc0 = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ158_spl])],[split_symbol_definition]) ).
fof(f2047,plain,
( ~ sQ140_spl
| ~ sQ3_spl
| sQ158_spl ),
inference(split_clause,[status(thm)],[f2040,f2044,f132,f1924]) ).
fof(f2048,definition,
! [X0,X1] :
( sQ159_spl
<=> ( aElementOf0(sK1_skl(X1,slcrc0),X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1)
| slcrc0 = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f2051,plain,
( ~ sQ140_spl
| ~ sQ3_spl
| sQ159_spl ),
inference(split_clause,[status(thm)],[f2041,f2048,f132,f1924]) ).
fof(f2052,definition,
! [X0,X1] :
( sQ160_spl
<=> ( ~ aElementOf0(sK1_skl(X1,slcrc0),slcrc0)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1)
| slcrc0 = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f2055,plain,
( ~ sQ140_spl
| ~ sQ3_spl
| sQ160_spl ),
inference(split_clause,[status(thm)],[f2042,f2052,f132,f1924]) ).
fof(f2071,definition,
( sQ162_spl
<=> sdtmndt0(xS,sK0_skl(xS)) = xS ),
introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition]) ).
fof(f2072,plain,
( ~ sQ162_spl
| sdtmndt0(xS,sK0_skl(xS)) = xS ),
inference(component_clause,[status(thm)],[f2071]) ).
fof(f2100,plain,
( sQ132_spl
| ~ sQ162_spl
| ~ aSubsetOf0(xS,xS) ),
inference(forward_demodulation,[status(thm)],[f2072,f1872]) ).
fof(f2141,plain,
( sQ132_spl
| ~ sQ162_spl
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f2100,f57]) ).
fof(f2142,definition,
! [X0] :
( sQ163_spl
<=> ( ~ aSubsetOf0(X0,xS)
| ~ aSubsetOf0(xS,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f2143,plain,
! [X0] :
( ~ sQ163_spl
| ~ aSubsetOf0(X0,xS)
| ~ aSubsetOf0(xS,X0) ),
inference(component_clause,[status(thm)],[f2142]) ).
fof(f2151,plain,
( sQ132_spl
| ~ sQ162_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2141,f163,f2071,f1870]) ).
fof(f2156,plain,
( ~ sQ163_spl
| ~ aSet0(xS)
| ~ aSubsetOf0(xS,xS) ),
inference(resolution,[status(thm)],[f2143,f57]) ).
fof(f2169,definition,
( sQ168_spl
<=> aSubsetOf0(xS,xS) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f2170,plain,
( ~ sQ168_spl
| aSubsetOf0(xS,xS) ),
inference(component_clause,[status(thm)],[f2169]) ).
fof(f2171,plain,
( sQ168_spl
| ~ aSubsetOf0(xS,xS) ),
inference(component_clause,[status(thm)],[f2169]) ).
fof(f2172,plain,
( ~ sQ163_spl
| ~ sQ5_spl
| ~ sQ168_spl ),
inference(split_clause,[status(thm)],[f2156,f2169,f163,f2142]) ).
fof(f2176,plain,
( sQ168_spl
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f2171,f57]) ).
fof(f2180,plain,
( sQ168_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2176,f163,f2169]) ).
fof(f2182,plain,
! [X0] :
( ~ sQ168_spl
| aElementOf0(X0,xS)
| ~ aElementOf0(X0,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f2170,f51]) ).
fof(f2184,definition,
! [X0] :
( sQ169_spl
<=> ( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition]) ).
fof(f2187,plain,
( ~ sQ168_spl
| sQ169_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2182,f163,f2184,f2169]) ).
fof(f2188,definition,
( sQ170_spl
<=> xS = xS ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f2212,plain,
( ~ sQ116_spl
| ~ sP0_prd(xx,xx,sdtpldt0(xS,xx))
| ~ aElement0(xx)
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(resolution,[status(thm)],[f2013,f124]) ).
fof(f2213,definition,
( sQ171_spl
<=> aElementOf0(xx,sdtpldt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f2214,plain,
( ~ sQ171_spl
| aElementOf0(xx,sdtpldt0(xS,xx)) ),
inference(component_clause,[status(thm)],[f2213]) ).
fof(f2215,plain,
( sQ171_spl
| ~ aElementOf0(xx,sdtpldt0(xS,xx)) ),
inference(component_clause,[status(thm)],[f2213]) ).
fof(f2216,definition,
( sQ172_spl
<=> xx = xx ),
introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition]) ).
fof(f2220,definition,
( sQ173_spl
<=> sP0_prd(xx,xx,sdtpldt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[sQ173_spl])],[split_symbol_definition]) ).
fof(f2223,plain,
( ~ sQ116_spl
| ~ sQ173_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2212,f182,f185,f2220,f1658]) ).
fof(f2224,plain,
( sQ171_spl
| ~ aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f2215,f118]) ).
fof(f2226,plain,
( sQ171_spl
| ~ sQ9_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2224,f163,f185,f2213]) ).
fof(f2227,definition,
( sQ174_spl
<=> aElementOf0(xx,xS) ),
introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition]) ).
fof(f2228,plain,
( ~ sQ174_spl
| aElementOf0(xx,xS) ),
inference(component_clause,[status(thm)],[f2227]) ).
fof(f2236,definition,
! [X0] :
( sQ175_spl
<=> ~ aSubsetOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition]) ).
fof(f2237,plain,
! [X0] :
( ~ sQ175_spl
| ~ aSubsetOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(component_clause,[status(thm)],[f2236]) ).
fof(f2254,plain,
( ~ sQ171_spl
| xx = xx
| aElementOf0(xx,xS)
| ~ aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f2214,f114]) ).
fof(f2255,plain,
( ~ sQ171_spl
| sdtpldt0(sdtmndt0(sdtpldt0(xS,xx),xx),xx) = sdtpldt0(xS,xx)
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(resolution,[status(thm)],[f2214,f87]) ).
fof(f2256,plain,
( ~ sQ171_spl
| sQ172_spl
| sQ174_spl
| ~ sQ9_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2254,f163,f185,f2227,f2216,f2213]) ).
fof(f2257,definition,
( sQ179_spl
<=> sdtpldt0(sdtmndt0(sdtpldt0(xS,xx),xx),xx) = sdtpldt0(xS,xx) ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f2260,plain,
( ~ sQ171_spl
| sQ179_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2255,f182,f2257,f2213]) ).
fof(f2261,plain,
( ~ sQ174_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2228,f90]) ).
fof(f2262,plain,
~ sQ174_spl,
inference(contradiction_clause,[status(thm)],[f2261]) ).
fof(f2263,plain,
! [X0] :
( sQ132_spl
| ~ aSubsetOf0(X0,sdtmndt0(xS,sK0_skl(xS)))
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(sdtmndt0(xS,sK0_skl(xS))) ),
inference(resolution,[status(thm)],[f1872,f1369]) ).
fof(f2264,plain,
( sQ132_spl
| aElementOf0(sK1_skl(xS,sdtmndt0(xS,sK0_skl(xS))),xS)
| ~ aSet0(xS)
| ~ aSet0(sdtmndt0(xS,sK0_skl(xS))) ),
inference(resolution,[status(thm)],[f1872,f52]) ).
fof(f2265,plain,
( sQ132_spl
| ~ aElementOf0(sK1_skl(xS,sdtmndt0(xS,sK0_skl(xS))),sdtmndt0(xS,sK0_skl(xS)))
| ~ aSet0(xS)
| ~ aSet0(sdtmndt0(xS,sK0_skl(xS))) ),
inference(resolution,[status(thm)],[f1872,f53]) ).
fof(f2266,definition,
! [X0] :
( sQ180_spl
<=> ( ~ aSubsetOf0(X0,sdtmndt0(xS,sK0_skl(xS)))
| ~ aSubsetOf0(xS,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f2269,plain,
( sQ132_spl
| sQ180_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f2263,f255,f2266,f1870]) ).
fof(f2270,definition,
( sQ181_spl
<=> aElementOf0(sK1_skl(xS,sdtmndt0(xS,sK0_skl(xS))),xS) ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f2273,plain,
( sQ132_spl
| sQ181_spl
| ~ sQ5_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f2264,f255,f163,f2270,f1870]) ).
fof(f2274,definition,
( sQ182_spl
<=> aElementOf0(sK1_skl(xS,sdtmndt0(xS,sK0_skl(xS))),sdtmndt0(xS,sK0_skl(xS))) ),
introduced(definition,[new_symbols(definition,[sQ182_spl])],[split_symbol_definition]) ).
fof(f2277,plain,
( sQ132_spl
| ~ sQ182_spl
| ~ sQ5_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f2265,f255,f163,f2274,f1870]) ).
fof(f2334,plain,
( ~ sQ175_spl
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[f2237,f57]) ).
fof(f2348,plain,
( ~ sQ175_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f2334,f160,f2236]) ).
fof(f2435,definition,
( sQ188_spl
<=> aElementOf0(sK0_skl(xS),sdtpldt0(xS,sK0_skl(xS))) ),
introduced(definition,[new_symbols(definition,[sQ188_spl])],[split_symbol_definition]) ).
fof(f2436,plain,
( ~ sQ188_spl
| aElementOf0(sK0_skl(xS),sdtpldt0(xS,sK0_skl(xS))) ),
inference(component_clause,[status(thm)],[f2435]) ).
fof(f2516,plain,
! [X0] :
( ~ 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)],[f379,f119]) ).
fof(f2517,plain,
! [X0] :
( sK2_skl(slcrc0,X0,slcrc0) != X0
| ~ 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)],[f379,f120]) ).
fof(f2519,plain,
! [X0] :
( sK2_skl(slcrc0,X0,slcrc0) = X0
| slcrc0 = sdtpldt0(slcrc0,X0)
| ~ aElement0(X0)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f379,f107]) ).
fof(f2521,definition,
! [X0] :
( sQ197_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,[sQ197_spl])],[split_symbol_definition]) ).
fof(f2524,plain,
( sQ197_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2516,f132,f2521]) ).
fof(f2525,definition,
! [X0] :
( sQ198_spl
<=> ( sK2_skl(slcrc0,X0,slcrc0) != X0
| slcrc0 = sdtpldt0(slcrc0,X0)
| ~ aElement0(X0)
| sK2_skl(slcrc0,X0,slcrc0) = X0
| slcrc0 = sdtpldt0(slcrc0,X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ198_spl])],[split_symbol_definition]) ).
fof(f2528,plain,
( sQ198_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2517,f132,f2525]) ).
fof(f2530,definition,
! [X0] :
( sQ199_spl
<=> ( sK2_skl(slcrc0,X0,slcrc0) = X0
| slcrc0 = sdtpldt0(slcrc0,X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ199_spl])],[split_symbol_definition]) ).
fof(f2533,plain,
( sQ199_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2519,f132,f2530]) ).
fof(f2538,plain,
( ~ sQ99_spl
| sdtmndt0(slcrc0,sK0_skl(slcrc0)) = slcrc0
| sdtpldt0(sdtmndt0(sdtmndt0(slcrc0,sK0_skl(slcrc0)),sK0_skl(sdtmndt0(slcrc0,sK0_skl(slcrc0)))),sK0_skl(sdtmndt0(slcrc0,sK0_skl(slcrc0)))) = sdtmndt0(slcrc0,sK0_skl(slcrc0)) ),
inference(resolution,[status(thm)],[f141,f1401]) ).
fof(f2539,plain,
( ~ sQ127_spl
| sdtmndt0(sdtmndt0(xS,xx),xx) = slcrc0
| sdtpldt0(sdtmndt0(sdtmndt0(sdtmndt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtmndt0(xS,xx),xx))),sK0_skl(sdtmndt0(sdtmndt0(xS,xx),xx))) = sdtmndt0(sdtmndt0(xS,xx),xx) ),
inference(resolution,[status(thm)],[f141,f1825]) ).
fof(f2541,plain,
( ~ sQ104_spl
| sdtmndt0(xS,sK1_skl(xS,slcrc0)) = slcrc0
| sdtpldt0(sdtmndt0(sdtmndt0(xS,sK1_skl(xS,slcrc0)),sK0_skl(sdtmndt0(xS,sK1_skl(xS,slcrc0)))),sK0_skl(sdtmndt0(xS,sK1_skl(xS,slcrc0)))) = sdtmndt0(xS,sK1_skl(xS,slcrc0)) ),
inference(resolution,[status(thm)],[f141,f1467]) ).
fof(f2542,plain,
( ~ sQ80_spl
| sdtmndt0(xS,xx) = slcrc0
| sdtpldt0(sdtmndt0(sdtmndt0(xS,xx),sK0_skl(sdtmndt0(xS,xx))),sK0_skl(sdtmndt0(xS,xx))) = sdtmndt0(xS,xx) ),
inference(resolution,[status(thm)],[f141,f808]) ).
fof(f2548,definition,
( sQ200_spl
<=> sdtpldt0(sdtmndt0(sdtmndt0(slcrc0,sK0_skl(slcrc0)),sK0_skl(sdtmndt0(slcrc0,sK0_skl(slcrc0)))),sK0_skl(sdtmndt0(slcrc0,sK0_skl(slcrc0)))) = sdtmndt0(slcrc0,sK0_skl(slcrc0)) ),
introduced(definition,[new_symbols(definition,[sQ200_spl])],[split_symbol_definition]) ).
fof(f2549,plain,
( ~ sQ200_spl
| sdtpldt0(sdtmndt0(sdtmndt0(slcrc0,sK0_skl(slcrc0)),sK0_skl(sdtmndt0(slcrc0,sK0_skl(slcrc0)))),sK0_skl(sdtmndt0(slcrc0,sK0_skl(slcrc0)))) = sdtmndt0(slcrc0,sK0_skl(slcrc0)) ),
inference(component_clause,[status(thm)],[f2548]) ).
fof(f2551,definition,
( sQ201_spl
<=> sdtmndt0(slcrc0,sK0_skl(slcrc0)) = slcrc0 ),
introduced(definition,[new_symbols(definition,[sQ201_spl])],[split_symbol_definition]) ).
fof(f2552,plain,
( ~ sQ201_spl
| sdtmndt0(slcrc0,sK0_skl(slcrc0)) = slcrc0 ),
inference(component_clause,[status(thm)],[f2551]) ).
fof(f2554,plain,
( ~ sQ99_spl
| sQ201_spl
| sQ200_spl ),
inference(split_clause,[status(thm)],[f2538,f2548,f2551,f1400]) ).
fof(f2555,definition,
( sQ202_spl
<=> sdtpldt0(sdtmndt0(sdtmndt0(sdtmndt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtmndt0(xS,xx),xx))),sK0_skl(sdtmndt0(sdtmndt0(xS,xx),xx))) = sdtmndt0(sdtmndt0(xS,xx),xx) ),
introduced(definition,[new_symbols(definition,[sQ202_spl])],[split_symbol_definition]) ).
fof(f2558,definition,
( sQ203_spl
<=> sdtmndt0(sdtmndt0(xS,xx),xx) = slcrc0 ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f2559,plain,
( ~ sQ203_spl
| sdtmndt0(sdtmndt0(xS,xx),xx) = slcrc0 ),
inference(component_clause,[status(thm)],[f2558]) ).
fof(f2561,plain,
( ~ sQ127_spl
| sQ203_spl
| sQ202_spl ),
inference(split_clause,[status(thm)],[f2539,f2555,f2558,f1824]) ).
fof(f2563,definition,
( sQ204_spl
<=> sdtpldt0(sdtmndt0(sdtmndt0(xS,sK1_skl(xS,slcrc0)),sK0_skl(sdtmndt0(xS,sK1_skl(xS,slcrc0)))),sK0_skl(sdtmndt0(xS,sK1_skl(xS,slcrc0)))) = sdtmndt0(xS,sK1_skl(xS,slcrc0)) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f2564,plain,
( ~ sQ204_spl
| sdtpldt0(sdtmndt0(sdtmndt0(xS,sK1_skl(xS,slcrc0)),sK0_skl(sdtmndt0(xS,sK1_skl(xS,slcrc0)))),sK0_skl(sdtmndt0(xS,sK1_skl(xS,slcrc0)))) = sdtmndt0(xS,sK1_skl(xS,slcrc0)) ),
inference(component_clause,[status(thm)],[f2563]) ).
fof(f2566,definition,
( sQ205_spl
<=> sdtmndt0(xS,sK1_skl(xS,slcrc0)) = slcrc0 ),
introduced(definition,[new_symbols(definition,[sQ205_spl])],[split_symbol_definition]) ).
fof(f2567,plain,
( ~ sQ205_spl
| sdtmndt0(xS,sK1_skl(xS,slcrc0)) = slcrc0 ),
inference(component_clause,[status(thm)],[f2566]) ).
fof(f2569,plain,
( ~ sQ104_spl
| sQ205_spl
| sQ204_spl ),
inference(split_clause,[status(thm)],[f2541,f2563,f2566,f1466]) ).
fof(f2570,definition,
( sQ206_spl
<=> sdtpldt0(sdtmndt0(sdtmndt0(xS,xx),sK0_skl(sdtmndt0(xS,xx))),sK0_skl(sdtmndt0(xS,xx))) = sdtmndt0(xS,xx) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f2573,definition,
( sQ207_spl
<=> sdtmndt0(xS,xx) = slcrc0 ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f2574,plain,
( ~ sQ207_spl
| sdtmndt0(xS,xx) = slcrc0 ),
inference(component_clause,[status(thm)],[f2573]) ).
fof(f2576,plain,
( ~ sQ80_spl
| sQ207_spl
| sQ206_spl ),
inference(split_clause,[status(thm)],[f2542,f2570,f2573,f807]) ).
fof(f2580,plain,
( ~ sQ81_spl
| ~ sQ207_spl
| aElementOf0(sK0_skl(xS),sdtmndt0(slcrc0,xx)) ),
inference(backward_demodulation,[status(thm)],[f2574,f811]) ).
fof(f2595,plain,
( ~ sQ204_spl
| ~ sQ205_spl
| sdtpldt0(sdtmndt0(sdtmndt0(xS,sK1_skl(xS,slcrc0)),sK0_skl(sdtmndt0(xS,sK1_skl(xS,slcrc0)))),sK0_skl(sdtmndt0(xS,sK1_skl(xS,slcrc0)))) = slcrc0 ),
inference(backward_demodulation,[status(thm)],[f2567,f2564]) ).
fof(f2600,plain,
( ~ sQ203_spl
| ~ sQ207_spl
| sdtmndt0(slcrc0,xx) = slcrc0 ),
inference(forward_demodulation,[status(thm)],[f2574,f2559]) ).
fof(f2602,plain,
( ~ sQ200_spl
| ~ sQ201_spl
| sdtpldt0(sdtmndt0(sdtmndt0(slcrc0,sK0_skl(slcrc0)),sK0_skl(sdtmndt0(slcrc0,sK0_skl(slcrc0)))),sK0_skl(sdtmndt0(slcrc0,sK0_skl(slcrc0)))) = slcrc0 ),
inference(backward_demodulation,[status(thm)],[f2552,f2549]) ).
fof(f2607,plain,
( ~ sQ81_spl
| ~ sQ207_spl
| ~ sQ203_spl
| aElementOf0(sK0_skl(xS),slcrc0) ),
inference(forward_demodulation,[status(thm)],[f2600,f2580]) ).
fof(f2608,plain,
( ~ sQ81_spl
| ~ sQ207_spl
| ~ sQ203_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2607,f107]) ).
fof(f2609,plain,
( ~ sQ81_spl
| ~ sQ207_spl
| ~ sQ203_spl ),
inference(contradiction_clause,[status(thm)],[f2608]) ).
fof(f2610,plain,
( ~ sQ204_spl
| ~ sQ205_spl
| sdtpldt0(sdtmndt0(slcrc0,sK0_skl(sdtmndt0(xS,sK1_skl(xS,slcrc0)))),sK0_skl(sdtmndt0(xS,sK1_skl(xS,slcrc0)))) = slcrc0 ),
inference(forward_demodulation,[status(thm)],[f2567,f2595]) ).
fof(f2611,plain,
( ~ sQ204_spl
| ~ sQ205_spl
| sdtpldt0(sdtmndt0(slcrc0,sK0_skl(slcrc0)),sK0_skl(sdtmndt0(xS,sK1_skl(xS,slcrc0)))) = slcrc0 ),
inference(forward_demodulation,[status(thm)],[f2567,f2610]) ).
fof(f2612,plain,
( ~ sQ204_spl
| ~ sQ205_spl
| ~ sQ201_spl
| sdtpldt0(slcrc0,sK0_skl(sdtmndt0(xS,sK1_skl(xS,slcrc0)))) = slcrc0 ),
inference(forward_demodulation,[status(thm)],[f2552,f2611]) ).
fof(f2613,plain,
( ~ sQ204_spl
| ~ sQ205_spl
| ~ sQ201_spl
| sdtpldt0(slcrc0,sK0_skl(slcrc0)) = slcrc0 ),
inference(forward_demodulation,[status(thm)],[f2567,f2612]) ).
fof(f2616,plain,
( ~ sQ200_spl
| ~ sQ201_spl
| sdtpldt0(sdtmndt0(slcrc0,sK0_skl(sdtmndt0(slcrc0,sK0_skl(slcrc0)))),sK0_skl(sdtmndt0(slcrc0,sK0_skl(slcrc0)))) = slcrc0 ),
inference(forward_demodulation,[status(thm)],[f2552,f2602]) ).
fof(f2617,plain,
( ~ sQ200_spl
| ~ sQ201_spl
| sdtpldt0(sdtmndt0(slcrc0,sK0_skl(slcrc0)),sK0_skl(sdtmndt0(slcrc0,sK0_skl(slcrc0)))) = slcrc0 ),
inference(forward_demodulation,[status(thm)],[f2552,f2616]) ).
fof(f2618,plain,
( ~ sQ200_spl
| ~ sQ201_spl
| sdtpldt0(slcrc0,sK0_skl(sdtmndt0(slcrc0,sK0_skl(slcrc0)))) = slcrc0 ),
inference(forward_demodulation,[status(thm)],[f2552,f2617]) ).
fof(f2619,plain,
( ~ sQ200_spl
| ~ sQ201_spl
| sdtpldt0(slcrc0,sK0_skl(slcrc0)) = slcrc0 ),
inference(forward_demodulation,[status(thm)],[f2552,f2618]) ).
fof(f2632,plain,
! [X0] :
( ~ sQ201_spl
| X0 = sK0_skl(slcrc0)
| ~ aElementOf0(X0,slcrc0)
| aElementOf0(X0,slcrc0)
| ~ aElement0(sK0_skl(slcrc0))
| ~ aSet0(slcrc0) ),
inference(paramodulation,[status(thm)],[f2552,f208]) ).
fof(f2633,plain,
! [X0,X1] :
( ~ sQ201_spl
| ~ aElement0(sK0_skl(slcrc0))
| ~ aSet0(slcrc0)
| sK2_skl(sdtmndt0(slcrc0,sK0_skl(slcrc0)),X1,X0) = X1
| aElementOf0(sK2_skl(sdtmndt0(slcrc0,sK0_skl(slcrc0)),X1,X0),X0)
| aElementOf0(sK2_skl(sdtmndt0(slcrc0,sK0_skl(slcrc0)),X1,X0),slcrc0)
| sdtmndt0(slcrc0,sK0_skl(slcrc0)) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(paramodulation,[status(thm)],[f2552,f318]) ).
fof(f2634,plain,
! [X0,X1] :
( ~ sQ201_spl
| ~ aElement0(sK0_skl(slcrc0))
| ~ aSet0(slcrc0)
| sK2_skl(sdtmndt0(slcrc0,sK0_skl(slcrc0)),X1,X0) = X1
| aElementOf0(sK2_skl(sdtmndt0(slcrc0,sK0_skl(slcrc0)),X1,X0),X0)
| aElementOf0(sK2_skl(slcrc0,X1,X0),sdtmndt0(slcrc0,sK0_skl(slcrc0)))
| sdtmndt0(slcrc0,sK0_skl(slcrc0)) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(paramodulation,[status(thm)],[f2552,f318]) ).
fof(f2636,plain,
! [X0] :
( ~ sQ201_spl
| ~ sP0_prd(X0,sK0_skl(slcrc0),slcrc0)
| aElementOf0(X0,slcrc0)
| ~ aElement0(sK0_skl(slcrc0))
| ~ aSet0(slcrc0) ),
inference(paramodulation,[status(thm)],[f2552,f124]) ).
fof(f2637,definition,
! [X0] :
( sQ209_spl
<=> ( X0 = sK0_skl(slcrc0)
| ~ aElementOf0(X0,slcrc0)
| aElementOf0(X0,slcrc0) ) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f2640,plain,
( ~ sQ201_spl
| sQ209_spl
| ~ sQ101_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2632,f132,f1408,f2637,f2551]) ).
fof(f2641,definition,
! [X0,X1] :
( sQ210_spl
<=> ( sK2_skl(sdtmndt0(slcrc0,sK0_skl(slcrc0)),X1,X0) = X1
| aElementOf0(sK2_skl(sdtmndt0(slcrc0,sK0_skl(slcrc0)),X1,X0),X0)
| aElementOf0(sK2_skl(sdtmndt0(slcrc0,sK0_skl(slcrc0)),X1,X0),slcrc0)
| sdtmndt0(slcrc0,sK0_skl(slcrc0)) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f2644,plain,
( ~ sQ201_spl
| ~ sQ101_spl
| ~ sQ3_spl
| sQ210_spl ),
inference(split_clause,[status(thm)],[f2633,f2641,f132,f1408,f2551]) ).
fof(f2645,definition,
! [X0,X1] :
( sQ211_spl
<=> ( sK2_skl(sdtmndt0(slcrc0,sK0_skl(slcrc0)),X1,X0) = X1
| aElementOf0(sK2_skl(sdtmndt0(slcrc0,sK0_skl(slcrc0)),X1,X0),X0)
| aElementOf0(sK2_skl(slcrc0,X1,X0),sdtmndt0(slcrc0,sK0_skl(slcrc0)))
| sdtmndt0(slcrc0,sK0_skl(slcrc0)) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ211_spl])],[split_symbol_definition]) ).
fof(f2648,plain,
( ~ sQ201_spl
| ~ sQ101_spl
| ~ sQ3_spl
| sQ211_spl ),
inference(split_clause,[status(thm)],[f2634,f2645,f132,f1408,f2551]) ).
fof(f2650,definition,
! [X0] :
( sQ212_spl
<=> ( ~ sP0_prd(X0,sK0_skl(slcrc0),slcrc0)
| aElementOf0(X0,slcrc0) ) ),
introduced(definition,[new_symbols(definition,[sQ212_spl])],[split_symbol_definition]) ).
fof(f2653,plain,
( ~ sQ201_spl
| sQ212_spl
| ~ sQ101_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2636,f132,f1408,f2650,f2551]) ).
fof(f2662,plain,
( sQ118_spl
| sK1_skl(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) = xx
| ~ aElementOf0(sK1_skl(xS,sdtmndt0(sdtpldt0(xS,xx),xx)),sdtpldt0(xS,xx))
| ~ aElement0(xx)
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(resolution,[status(thm)],[f1678,f208]) ).
fof(f2664,definition,
( sQ213_spl
<=> aElementOf0(sK1_skl(xS,sdtmndt0(sdtpldt0(xS,xx),xx)),sdtpldt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[sQ213_spl])],[split_symbol_definition]) ).
fof(f2666,plain,
( sQ213_spl
| ~ aElementOf0(sK1_skl(xS,sdtmndt0(sdtpldt0(xS,xx),xx)),sdtpldt0(xS,xx)) ),
inference(component_clause,[status(thm)],[f2664]) ).
fof(f2667,plain,
( sQ118_spl
| sQ90_spl
| ~ sQ213_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2662,f182,f185,f2664,f869,f1676]) ).
fof(f2677,plain,
( ~ sQ204_spl
| ~ sQ205_spl
| ~ sQ201_spl
| ~ aElement0(sK0_skl(slcrc0))
| ~ aSet0(slcrc0)
| aElementOf0(sK0_skl(sdtpldt0(slcrc0,sK0_skl(slcrc0))),slcrc0)
| sdtpldt0(slcrc0,sK0_skl(slcrc0)) = slcrc0 ),
inference(paramodulation,[status(thm)],[f2613,f1258]) ).
fof(f2691,definition,
( sQ215_spl
<=> sdtpldt0(slcrc0,sK0_skl(slcrc0)) = slcrc0 ),
introduced(definition,[new_symbols(definition,[sQ215_spl])],[split_symbol_definition]) ).
fof(f2692,plain,
( ~ sQ215_spl
| sdtpldt0(slcrc0,sK0_skl(slcrc0)) = slcrc0 ),
inference(component_clause,[status(thm)],[f2691]) ).
fof(f2693,plain,
( sQ215_spl
| sdtpldt0(slcrc0,sK0_skl(slcrc0)) != slcrc0 ),
inference(component_clause,[status(thm)],[f2691]) ).
fof(f2694,definition,
( sQ216_spl
<=> aElementOf0(sK0_skl(sdtpldt0(slcrc0,sK0_skl(slcrc0))),slcrc0) ),
introduced(definition,[new_symbols(definition,[sQ216_spl])],[split_symbol_definition]) ).
fof(f2695,plain,
( ~ sQ216_spl
| aElementOf0(sK0_skl(sdtpldt0(slcrc0,sK0_skl(slcrc0))),slcrc0) ),
inference(component_clause,[status(thm)],[f2694]) ).
fof(f2697,plain,
( ~ sQ204_spl
| ~ sQ205_spl
| ~ sQ201_spl
| ~ sQ101_spl
| ~ sQ3_spl
| sQ216_spl
| sQ215_spl ),
inference(split_clause,[status(thm)],[f2677,f2691,f2694,f132,f1408,f2551,f2566,f2563]) ).
fof(f2698,definition,
( sQ217_spl
<=> aElementOf0(sK0_skl(slcrc0),sdtpldt0(slcrc0,sK0_skl(slcrc0))) ),
introduced(definition,[new_symbols(definition,[sQ217_spl])],[split_symbol_definition]) ).
fof(f2699,plain,
( ~ sQ217_spl
| aElementOf0(sK0_skl(slcrc0),sdtpldt0(slcrc0,sK0_skl(slcrc0))) ),
inference(component_clause,[status(thm)],[f2698]) ).
fof(f2702,definition,
! [X0] :
( sQ218_spl
<=> ( aElementOf0(sK0_skl(slcrc0),X0)
| ~ aSubsetOf0(slcrc0,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f2703,plain,
! [X0] :
( ~ sQ218_spl
| aElementOf0(sK0_skl(slcrc0),X0)
| ~ aSubsetOf0(slcrc0,X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f2702]) ).
fof(f2736,definition,
! [X0] :
( sQ226_spl
<=> ( ~ aElementOf0(X0,slcrc0)
| aElementOf0(X0,slcrc0) ) ),
introduced(definition,[new_symbols(definition,[sQ226_spl])],[split_symbol_definition]) ).
fof(f2756,plain,
( ~ sQ217_spl
| ~ sQ215_spl
| aElementOf0(sK0_skl(slcrc0),slcrc0) ),
inference(forward_demodulation,[status(thm)],[f2692,f2699]) ).
fof(f2757,plain,
( ~ sQ217_spl
| ~ sQ215_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2756,f107]) ).
fof(f2758,plain,
( ~ sQ217_spl
| ~ sQ215_spl ),
inference(contradiction_clause,[status(thm)],[f2757]) ).
fof(f2759,plain,
( ~ sQ216_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2695,f107]) ).
fof(f2760,plain,
~ sQ216_spl,
inference(contradiction_clause,[status(thm)],[f2759]) ).
fof(f2761,plain,
( ~ sQ200_spl
| ~ sQ201_spl
| sQ215_spl ),
inference(split_clause,[status(thm)],[f2619,f2691,f2551,f2548]) ).
fof(f2769,plain,
! [X0] :
( ~ sQ215_spl
| aElementOf0(sK0_skl(slcrc0),X0)
| ~ aSubsetOf0(slcrc0,X0)
| ~ aSet0(X0)
| ~ aElement0(sK0_skl(slcrc0))
| ~ aSet0(slcrc0) ),
inference(paramodulation,[status(thm)],[f2692,f137]) ).
fof(f2783,plain,
( ~ sQ215_spl
| sQ218_spl
| ~ sQ101_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2769,f132,f1408,f2702,f2691]) ).
fof(f2800,definition,
( sQ227_spl
<=> sP0_prd(sK0_skl(xS),sK0_skl(xS),xS) ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f2801,plain,
( ~ sQ227_spl
| sP0_prd(sK0_skl(xS),sK0_skl(xS),xS) ),
inference(component_clause,[status(thm)],[f2800]) ).
fof(f2804,plain,
( ~ sQ227_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2801,f125]) ).
fof(f2805,plain,
~ sQ227_spl,
inference(contradiction_clause,[status(thm)],[f2804]) ).
fof(f2810,plain,
! [X0] :
( sdtpldt0(slcrc0,X0) = slcrc0
| sK0_skl(sdtpldt0(slcrc0,X0)) = X0
| ~ aElement0(X0)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f151,f107]) ).
fof(f2813,definition,
! [X0] :
( sQ228_spl
<=> ( sdtpldt0(slcrc0,X0) = slcrc0
| sK0_skl(sdtpldt0(slcrc0,X0)) = X0
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f2816,plain,
( sQ228_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2810,f132,f2813]) ).
fof(f2825,plain,
! [X0,X1] :
( aElementOf0(sK3_skl(slcrc0,X1,X0),X0)
| ~ aSet0(slcrc0)
| slcrc0 = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f398,f107]) ).
fof(f2828,definition,
! [X0,X1] :
( sQ229_spl
<=> ( aElementOf0(sK3_skl(slcrc0,X1,X0),X0)
| slcrc0 = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ229_spl])],[split_symbol_definition]) ).
fof(f2831,plain,
( ~ sQ3_spl
| sQ229_spl ),
inference(split_clause,[status(thm)],[f2825,f2828,f132]) ).
fof(f2835,plain,
! [X0,X1,X2] :
( ~ aElementOf0(sK3_skl(sdtpldt0(X1,X2),X0,xS),X1)
| ~ aElement0(X2)
| ~ aSet0(X1)
| sdtpldt0(X1,X2) = sdtmndt0(xS,X0)
| ~ aElement0(X0)
| ~ aSet0(xS)
| ~ aElementOf0(sK3_skl(sdtpldt0(X1,X2),X0,xS),sdtmndt0(xS,X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f1370,f324]) ).
fof(f2836,plain,
! [X0,X1] :
( ~ aElementOf0(sK3_skl(X1,X0,xS),X1)
| ~ aSet0(X1)
| X1 = sdtmndt0(xS,X0)
| ~ aElement0(X0)
| ~ aSet0(xS)
| ~ aElementOf0(sK3_skl(X1,X0,xS),sdtmndt0(xS,X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f1370,f84]) ).
fof(f2838,plain,
! [X0] :
( ~ aElementOf0(X0,sdtmndt0(xS,X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f1370,f125]) ).
fof(f2839,definition,
! [X0,X1,X2] :
( sQ230_spl
<=> ( ~ aElementOf0(sK3_skl(sdtpldt0(X1,X2),X0,xS),X1)
| ~ aElement0(X2)
| ~ aSet0(X1)
| sdtpldt0(X1,X2) = sdtmndt0(xS,X0)
| ~ aElement0(X0)
| ~ aElementOf0(sK3_skl(sdtpldt0(X1,X2),X0,xS),sdtmndt0(xS,X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ230_spl])],[split_symbol_definition]) ).
fof(f2842,plain,
( ~ sQ5_spl
| sQ230_spl ),
inference(split_clause,[status(thm)],[f2835,f2839,f163]) ).
fof(f2843,definition,
! [X0,X1] :
( sQ231_spl
<=> ( ~ aElementOf0(sK3_skl(X1,X0,xS),X1)
| ~ aSet0(X1)
| X1 = sdtmndt0(xS,X0)
| ~ aElement0(X0)
| ~ aElementOf0(sK3_skl(X1,X0,xS),sdtmndt0(xS,X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ231_spl])],[split_symbol_definition]) ).
fof(f2846,plain,
( ~ sQ5_spl
| sQ231_spl ),
inference(split_clause,[status(thm)],[f2836,f2843,f163]) ).
fof(f2863,plain,
( ~ sQ22_spl
| ~ aSubsetOf0(xS,sdtmndt0(xS,sK0_skl(xS)))
| ~ aSet0(sdtmndt0(xS,sK0_skl(xS)))
| ~ aElement0(sK0_skl(xS)) ),
inference(resolution,[status(thm)],[f2838,f351]) ).
fof(f2865,plain,
! [X0] :
( X0 = X0
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| ~ aSet0(xS)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f2838,f208]) ).
fof(f2866,plain,
! [X0] :
( ~ sP0_prd(X0,X0,xS)
| ~ aElement0(X0)
| ~ aSet0(xS)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f2838,f124]) ).
fof(f2867,plain,
( ~ sQ22_spl
| ~ sQ132_spl
| ~ sQ17_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f2863,f258,f255,f1870,f273]) ).
fof(f2868,definition,
! [X0] :
( sQ233_spl
<=> ( X0 = X0
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ233_spl])],[split_symbol_definition]) ).
fof(f2871,plain,
( ~ sQ5_spl
| sQ233_spl ),
inference(split_clause,[status(thm)],[f2865,f2868,f163]) ).
fof(f2872,definition,
! [X0] :
( sQ234_spl
<=> ( ~ sP0_prd(X0,X0,xS)
| ~ aElement0(X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f2875,plain,
( ~ sQ5_spl
| sQ234_spl ),
inference(split_clause,[status(thm)],[f2866,f2872,f163]) ).
fof(f2882,plain,
! [X0,X1,X2] :
( ~ aElementOf0(sK3_skl(sdtpldt0(X1,X2),X0,slcrc0),X1)
| ~ aElement0(X2)
| ~ aSet0(X1)
| sdtpldt0(X1,X2) = sdtmndt0(slcrc0,X0)
| ~ aElement0(X0)
| ~ aSet0(slcrc0)
| ~ aElementOf0(sK3_skl(sdtpldt0(X1,X2),X0,slcrc0),sdtmndt0(slcrc0,X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f1371,f324]) ).
fof(f2883,plain,
! [X0,X1] :
( ~ aElementOf0(sK3_skl(X1,X0,slcrc0),X1)
| ~ aSet0(X1)
| X1 = sdtmndt0(slcrc0,X0)
| ~ aElement0(X0)
| ~ aSet0(slcrc0)
| ~ aElementOf0(sK3_skl(X1,X0,slcrc0),sdtmndt0(slcrc0,X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f1371,f84]) ).
fof(f2884,plain,
! [X0,X1] :
( aElementOf0(X1,slcrc0)
| ~ aElementOf0(X1,sdtmndt0(slcrc0,X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f1371,f96]) ).
fof(f2886,definition,
! [X0,X1,X2] :
( sQ235_spl
<=> ( ~ aElementOf0(sK3_skl(sdtpldt0(X1,X2),X0,slcrc0),X1)
| ~ aElement0(X2)
| ~ aSet0(X1)
| sdtpldt0(X1,X2) = sdtmndt0(slcrc0,X0)
| ~ aElement0(X0)
| ~ aElementOf0(sK3_skl(sdtpldt0(X1,X2),X0,slcrc0),sdtmndt0(slcrc0,X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f2889,plain,
( ~ sQ3_spl
| sQ235_spl ),
inference(split_clause,[status(thm)],[f2882,f2886,f132]) ).
fof(f2890,definition,
! [X0,X1] :
( sQ236_spl
<=> ( ~ aElementOf0(sK3_skl(X1,X0,slcrc0),X1)
| ~ aSet0(X1)
| X1 = sdtmndt0(slcrc0,X0)
| ~ aElement0(X0)
| ~ aElementOf0(sK3_skl(X1,X0,slcrc0),sdtmndt0(slcrc0,X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ236_spl])],[split_symbol_definition]) ).
fof(f2893,plain,
( ~ sQ3_spl
| sQ236_spl ),
inference(split_clause,[status(thm)],[f2883,f2890,f132]) ).
fof(f2894,plain,
! [X0,X1] :
( ~ aElementOf0(X1,sdtmndt0(slcrc0,X0))
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2884,f107]) ).
fof(f2905,plain,
! [X0] :
( ~ sQ105_spl
| ~ aElementOf0(X0,sdtmndt0(slcrc0,sK1_skl(xS,slcrc0))) ),
inference(resolution,[status(thm)],[f2894,f1470]) ).
fof(f2907,plain,
! [X0] :
( ~ sQ101_spl
| ~ aElementOf0(X0,sdtmndt0(slcrc0,sK0_skl(slcrc0))) ),
inference(resolution,[status(thm)],[f2894,f1409]) ).
fof(f2909,plain,
! [X0] :
( ~ sQ18_spl
| ~ aElementOf0(X0,sdtmndt0(slcrc0,sK0_skl(xS))) ),
inference(resolution,[status(thm)],[f2894,f259]) ).
fof(f2910,plain,
! [X0] : ~ aElementOf0(X0,sdtmndt0(slcrc0,xx)),
inference(resolution,[status(thm)],[f2894,f88]) ).
fof(f2914,plain,
! [X0,X1] :
( aSubsetOf0(sdtmndt0(slcrc0,xx),X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0)
| ~ aSet0(sdtmndt0(slcrc0,xx)) ),
inference(resolution,[status(thm)],[f2910,f172]) ).
fof(f2915,plain,
! [X0] :
( sdtmndt0(slcrc0,xx) = X0
| ~ aSubsetOf0(X0,sdtmndt0(slcrc0,xx))
| ~ aSet0(sdtmndt0(slcrc0,xx)) ),
inference(resolution,[status(thm)],[f2910,f174]) ).
fof(f2916,plain,
! [X0] :
( sK2_skl(slcrc0,X0,sdtmndt0(slcrc0,xx)) = X0
| slcrc0 = sdtpldt0(sdtmndt0(slcrc0,xx),X0)
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(slcrc0,xx)) ),
inference(resolution,[status(thm)],[f2910,f379]) ).
fof(f2917,plain,
! [X0,X1] :
( ~ aElement0(xx)
| ~ aSet0(slcrc0)
| sK2_skl(sdtmndt0(slcrc0,xx),X1,X0) = X1
| aElementOf0(sK2_skl(sdtmndt0(slcrc0,xx),X1,X0),X0)
| sdtmndt0(slcrc0,xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f2910,f318]) ).
fof(f2920,plain,
! [X0] :
( aElementOf0(sK3_skl(X0,xx,slcrc0),X0)
| ~ aSet0(X0)
| X0 = sdtmndt0(slcrc0,xx)
| ~ aElement0(xx)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f2910,f399]) ).
fof(f2921,plain,
! [X0,X1] :
( aElementOf0(sK3_skl(sdtmndt0(slcrc0,xx),X1,X0),X0)
| ~ aSet0(sdtmndt0(slcrc0,xx))
| sdtmndt0(slcrc0,xx) = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f2910,f398]) ).
fof(f2922,plain,
! [X0,X1] :
( sP0_prd(sK3_skl(sdtmndt0(slcrc0,xx),X1,X0),X1,X0)
| ~ aSet0(sdtmndt0(slcrc0,xx))
| sdtmndt0(slcrc0,xx) = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f2910,f85]) ).
fof(f2923,plain,
! [X0] :
( sdtpldt0(sdtmndt0(slcrc0,xx),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtmndt0(slcrc0,xx),X0)) = X0
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(slcrc0,xx)) ),
inference(resolution,[status(thm)],[f2910,f151]) ).
fof(f2924,plain,
( ~ sQ22_spl
| ~ aSubsetOf0(xS,sdtmndt0(slcrc0,xx))
| ~ aSet0(sdtmndt0(slcrc0,xx)) ),
inference(resolution,[status(thm)],[f2910,f351]) ).
fof(f2925,plain,
! [X0] :
( ~ aSubsetOf0(X0,sdtmndt0(slcrc0,xx))
| ~ aSet0(sdtmndt0(slcrc0,xx))
| X0 = slcrc0 ),
inference(resolution,[status(thm)],[f2910,f136]) ).
fof(f2927,plain,
( ~ aSet0(sdtmndt0(slcrc0,xx))
| sdtmndt0(slcrc0,xx) = slcrc0 ),
inference(resolution,[status(thm)],[f2910,f38]) ).
fof(f2928,plain,
! [X0] :
( X0 = xx
| ~ aElementOf0(X0,slcrc0)
| ~ aElement0(xx)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f2910,f208]) ).
fof(f2929,plain,
! [X0] :
( ~ sP0_prd(X0,xx,slcrc0)
| ~ aElement0(xx)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f2910,f124]) ).
fof(f2930,definition,
( sQ237_spl
<=> aSet0(sdtmndt0(slcrc0,xx)) ),
introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition]) ).
fof(f2932,plain,
( sQ237_spl
| ~ aSet0(sdtmndt0(slcrc0,xx)) ),
inference(component_clause,[status(thm)],[f2930]) ).
fof(f2933,definition,
! [X0,X1] :
( sQ238_spl
<=> ( aSubsetOf0(sdtmndt0(slcrc0,xx),X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f2936,plain,
( sQ238_spl
| ~ sQ237_spl ),
inference(split_clause,[status(thm)],[f2914,f2930,f2933]) ).
fof(f2937,definition,
! [X0] :
( sQ239_spl
<=> ( sdtmndt0(slcrc0,xx) = X0
| ~ aSubsetOf0(X0,sdtmndt0(slcrc0,xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ239_spl])],[split_symbol_definition]) ).
fof(f2940,plain,
( sQ239_spl
| ~ sQ237_spl ),
inference(split_clause,[status(thm)],[f2915,f2930,f2937]) ).
fof(f2941,definition,
! [X0] :
( sQ240_spl
<=> ( sK2_skl(slcrc0,X0,sdtmndt0(slcrc0,xx)) = X0
| slcrc0 = sdtpldt0(sdtmndt0(slcrc0,xx),X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ240_spl])],[split_symbol_definition]) ).
fof(f2944,plain,
( sQ240_spl
| ~ sQ237_spl ),
inference(split_clause,[status(thm)],[f2916,f2930,f2941]) ).
fof(f2945,definition,
! [X0,X1] :
( sQ241_spl
<=> ( sK2_skl(sdtmndt0(slcrc0,xx),X1,X0) = X1
| aElementOf0(sK2_skl(sdtmndt0(slcrc0,xx),X1,X0),X0)
| sdtmndt0(slcrc0,xx) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ241_spl])],[split_symbol_definition]) ).
fof(f2948,plain,
( ~ sQ9_spl
| ~ sQ3_spl
| sQ241_spl ),
inference(split_clause,[status(thm)],[f2917,f2945,f132,f185]) ).
fof(f2949,definition,
! [X2] :
( sQ242_spl
<=> ( ~ aSubsetOf0(sdtmndt0(slcrc0,xx),X2)
| ~ aSet0(X2) ) ),
introduced(definition,[new_symbols(definition,[sQ242_spl])],[split_symbol_definition]) ).
fof(f2950,plain,
! [X0] :
( ~ sQ242_spl
| ~ aSubsetOf0(sdtmndt0(slcrc0,xx),X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f2949]) ).
fof(f2954,definition,
! [X0] :
( sQ243_spl
<=> ( aElementOf0(sK3_skl(X0,xx,slcrc0),X0)
| ~ aSet0(X0)
| X0 = sdtmndt0(slcrc0,xx) ) ),
introduced(definition,[new_symbols(definition,[sQ243_spl])],[split_symbol_definition]) ).
fof(f2957,plain,
( sQ243_spl
| ~ sQ9_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2920,f132,f185,f2954]) ).
fof(f2958,definition,
! [X0,X1] :
( sQ244_spl
<=> ( aElementOf0(sK3_skl(sdtmndt0(slcrc0,xx),X1,X0),X0)
| sdtmndt0(slcrc0,xx) = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ244_spl])],[split_symbol_definition]) ).
fof(f2961,plain,
( ~ sQ237_spl
| sQ244_spl ),
inference(split_clause,[status(thm)],[f2921,f2958,f2930]) ).
fof(f2962,definition,
! [X0,X1] :
( sQ245_spl
<=> ( sP0_prd(sK3_skl(sdtmndt0(slcrc0,xx),X1,X0),X1,X0)
| sdtmndt0(slcrc0,xx) = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition]) ).
fof(f2965,plain,
( ~ sQ237_spl
| sQ245_spl ),
inference(split_clause,[status(thm)],[f2922,f2962,f2930]) ).
fof(f2966,definition,
! [X0] :
( sQ246_spl
<=> ( sdtpldt0(sdtmndt0(slcrc0,xx),X0) = slcrc0
| sK0_skl(sdtpldt0(sdtmndt0(slcrc0,xx),X0)) = X0
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ246_spl])],[split_symbol_definition]) ).
fof(f2969,plain,
( sQ246_spl
| ~ sQ237_spl ),
inference(split_clause,[status(thm)],[f2923,f2930,f2966]) ).
fof(f2970,definition,
( sQ247_spl
<=> aSubsetOf0(xS,sdtmndt0(slcrc0,xx)) ),
introduced(definition,[new_symbols(definition,[sQ247_spl])],[split_symbol_definition]) ).
fof(f2973,plain,
( ~ sQ22_spl
| ~ sQ247_spl
| ~ sQ237_spl ),
inference(split_clause,[status(thm)],[f2924,f2930,f2970,f273]) ).
fof(f2974,definition,
! [X0] :
( sQ248_spl
<=> ( ~ aSubsetOf0(X0,sdtmndt0(slcrc0,xx))
| X0 = slcrc0 ) ),
introduced(definition,[new_symbols(definition,[sQ248_spl])],[split_symbol_definition]) ).
fof(f2977,plain,
( ~ sQ237_spl
| sQ248_spl ),
inference(split_clause,[status(thm)],[f2925,f2974,f2930]) ).
fof(f2978,definition,
( sQ249_spl
<=> sdtmndt0(slcrc0,xx) = slcrc0 ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f2979,plain,
( ~ sQ249_spl
| sdtmndt0(slcrc0,xx) = slcrc0 ),
inference(component_clause,[status(thm)],[f2978]) ).
fof(f2982,plain,
( ~ sQ237_spl
| sQ249_spl ),
inference(split_clause,[status(thm)],[f2927,f2978,f2930]) ).
fof(f2983,definition,
! [X0] :
( sQ250_spl
<=> ( X0 = xx
| ~ aElementOf0(X0,slcrc0) ) ),
introduced(definition,[new_symbols(definition,[sQ250_spl])],[split_symbol_definition]) ).
fof(f2986,plain,
( sQ250_spl
| ~ sQ9_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2928,f132,f185,f2983]) ).
fof(f2987,definition,
! [X0] :
( sQ251_spl
<=> ~ sP0_prd(X0,xx,slcrc0) ),
introduced(definition,[new_symbols(definition,[sQ251_spl])],[split_symbol_definition]) ).
fof(f2988,plain,
! [X0] :
( ~ sQ251_spl
| ~ sP0_prd(X0,xx,slcrc0) ),
inference(component_clause,[status(thm)],[f2987]) ).
fof(f2990,plain,
( sQ251_spl
| ~ sQ9_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2929,f132,f185,f2987]) ).
fof(f2994,plain,
! [X0,X1] :
( ~ sQ147_spl
| ~ sQ242_spl
| ~ sQ249_spl
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f1967,f2995]) ).
fof(f2995,plain,
! [X0] :
( ~ sQ242_spl
| ~ sQ249_spl
| ~ aSubsetOf0(slcrc0,X0)
| ~ aSet0(X0) ),
inference(forward_demodulation,[status(thm)],[f2979,f2950]) ).
fof(f3015,plain,
! [X0] :
( ~ sQ147_spl
| ~ sQ242_spl
| ~ sQ249_spl
| ~ aSet0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f57,f2994]) ).
fof(f3017,plain,
( ~ sQ8_spl
| ~ sQ147_spl
| ~ sQ242_spl
| ~ sQ249_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f183,f3015]) ).
fof(f3026,plain,
( ~ sQ8_spl
| ~ sQ147_spl
| ~ sQ242_spl
| ~ sQ249_spl ),
inference(contradiction_clause,[status(thm)],[f3017]) ).
fof(f3033,plain,
! [X0,X1] :
( aSubsetOf0(X0,xS)
| ~ aSubsetOf0(X1,xS)
| ~ aSubsetOf0(X0,X1) ),
inference(resolution,[status(thm)],[f1369,f89]) ).
fof(f3035,plain,
! [X0,X1] :
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0)
| ~ aSubsetOf0(X0,xS) ),
inference(resolution,[status(thm)],[f51,f89]) ).
fof(f3043,plain,
( ~ sQ8_spl
| aSubsetOf0(sdtpldt0(xS,xx),sdtpldt0(xS,xx)) ),
inference(resolution,[status(thm)],[f183,f57]) ).
fof(f3056,plain,
( ~ sQ80_spl
| aSubsetOf0(sdtmndt0(xS,xx),sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f808,f57]) ).
fof(f3058,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X2,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f50,f110]) ).
fof(f3059,plain,
! [X0,X1,X2,X3] :
( aElementOf0(X3,X1)
| ~ aElementOf0(X3,X2)
| ~ aSubsetOf0(X2,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f50,f51]) ).
fof(f3060,plain,
! [X0,X1,X2,X3] :
( aSubsetOf0(X2,X1)
| ~ aSubsetOf0(X3,X1)
| ~ aSubsetOf0(X2,X3)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f50,f1369]) ).
fof(f3061,plain,
! [X0,X1] :
( aSubsetOf0(X1,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f50,f57]) ).
fof(f3109,plain,
! [X0,X1] :
( aSubsetOf0(X0,slcrc0)
| ~ aSubsetOf0(X1,slcrc0)
| ~ aSubsetOf0(X0,X1) ),
inference(resolution,[status(thm)],[f106,f1369]) ).
fof(f3111,plain,
! [X0,X1] :
( aElementOf0(X1,slcrc0)
| ~ aElementOf0(X1,X0)
| ~ aSubsetOf0(X0,slcrc0) ),
inference(resolution,[status(thm)],[f106,f51]) ).
fof(f3113,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| ~ aSubsetOf0(X0,slcrc0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3111,f107]) ).
fof(f3120,plain,
! [X0] :
( ~ sQ116_spl
| ~ aElementOf0(sK1_skl(X0,xS),sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSet0(X0)
| aSubsetOf0(X0,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f53,f1659]) ).
fof(f3121,definition,
! [X0] :
( sQ253_spl
<=> ( ~ aElementOf0(sK1_skl(X0,xS),sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSet0(X0)
| aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ253_spl])],[split_symbol_definition]) ).
fof(f3124,plain,
( ~ sQ116_spl
| sQ253_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3120,f163,f3121,f1658]) ).
fof(f3126,plain,
! [X0] :
( aElementOf0(sK1_skl(slcrc0,X0),slcrc0)
| aSubsetOf0(slcrc0,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f52,f106]) ).
fof(f3130,plain,
! [X0] :
( ~ sQ218_spl
| aElementOf0(sK0_skl(slcrc0),X0)
| ~ aSet0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f2703,f3131]) ).
fof(f3131,plain,
! [X0] :
( aSubsetOf0(slcrc0,X0)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3126,f107]) ).
fof(f3142,plain,
( ~ sQ218_spl
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f3130,f107]) ).
fof(f3144,definition,
( sQ254_spl
<=> aSet0(sdtmndt0(xS,sK0_skl(slcrc0))) ),
introduced(definition,[new_symbols(definition,[sQ254_spl])],[split_symbol_definition]) ).
fof(f3146,plain,
( sQ254_spl
| ~ aSet0(sdtmndt0(xS,sK0_skl(slcrc0))) ),
inference(component_clause,[status(thm)],[f3144]) ).
fof(f3148,plain,
( ~ sQ218_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3142,f132,f2702]) ).
fof(f3168,plain,
! [X0,X1] :
( ~ aElementOf0(X1,sdtmndt0(xS,X0))
| ~ aElement0(X0)
| aElementOf0(X1,sdtmndt0(xS,X0))
| ~ aElement0(X0)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f124,f1370]) ).
fof(f3171,definition,
! [X0,X1] :
( sQ255_spl
<=> ( ~ aElementOf0(X1,sdtmndt0(xS,X0))
| ~ aElement0(X0)
| aElementOf0(X1,sdtmndt0(xS,X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ255_spl])],[split_symbol_definition]) ).
fof(f3174,plain,
( sQ255_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3168,f163,f3171]) ).
fof(f3175,plain,
( sQ150_spl
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f3131,f1998]) ).
fof(f3179,plain,
( sQ150_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3175,f163,f1996]) ).
fof(f3180,definition,
! [X0] :
( sQ256_spl
<=> ~ aElementOf0(X0,slcrc0) ),
introduced(definition,[new_symbols(definition,[sQ256_spl])],[split_symbol_definition]) ).
fof(f3199,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ aElementOf0(sK3_skl(xS,X1,X0),sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ sP0_prd(sK3_skl(xS,X1,X0),X1,X0)
| ~ aSet0(xS)
| xS = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f84,f1659]) ).
fof(f3200,definition,
! [X0,X1] :
( sQ257_spl
<=> ( ~ aElementOf0(sK3_skl(xS,X1,X0),sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ sP0_prd(sK3_skl(xS,X1,X0),X1,X0)
| xS = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ257_spl])],[split_symbol_definition]) ).
fof(f3203,plain,
( ~ sQ116_spl
| ~ sQ5_spl
| sQ257_spl ),
inference(split_clause,[status(thm)],[f3199,f3200,f163,f1658]) ).
fof(f3205,plain,
! [X0,X1] :
( ~ sQ18_spl
| sK2_skl(sdtmndt0(slcrc0,sK0_skl(xS)),X1,X0) = X1
| aElementOf0(sK2_skl(sdtmndt0(slcrc0,sK0_skl(xS)),X1,X0),X0)
| ~ aSet0(sdtmndt0(slcrc0,sK0_skl(xS)))
| sdtmndt0(slcrc0,sK0_skl(xS)) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f74,f2909]) ).
fof(f3209,definition,
! [X0,X1] :
( sQ258_spl
<=> ( sK2_skl(sdtmndt0(slcrc0,sK0_skl(xS)),X1,X0) = X1
| aElementOf0(sK2_skl(sdtmndt0(slcrc0,sK0_skl(xS)),X1,X0),X0)
| sdtmndt0(slcrc0,sK0_skl(xS)) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ258_spl])],[split_symbol_definition]) ).
fof(f3212,definition,
( sQ259_spl
<=> aSet0(sdtmndt0(slcrc0,sK0_skl(xS))) ),
introduced(definition,[new_symbols(definition,[sQ259_spl])],[split_symbol_definition]) ).
fof(f3214,plain,
( sQ259_spl
| ~ aSet0(sdtmndt0(slcrc0,sK0_skl(xS))) ),
inference(component_clause,[status(thm)],[f3212]) ).
fof(f3215,plain,
( ~ sQ18_spl
| ~ sQ259_spl
| sQ258_spl ),
inference(split_clause,[status(thm)],[f3205,f3209,f3212,f258]) ).
fof(f3223,plain,
! [X0,X1] :
( ~ sQ105_spl
| sK2_skl(sdtmndt0(slcrc0,sK1_skl(xS,slcrc0)),X1,X0) = X1
| aElementOf0(sK2_skl(sdtmndt0(slcrc0,sK1_skl(xS,slcrc0)),X1,X0),X0)
| ~ aSet0(sdtmndt0(slcrc0,sK1_skl(xS,slcrc0)))
| sdtmndt0(slcrc0,sK1_skl(xS,slcrc0)) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f2905,f74]) ).
fof(f3224,definition,
! [X0,X1] :
( sQ260_spl
<=> ( sK2_skl(sdtmndt0(slcrc0,sK1_skl(xS,slcrc0)),X1,X0) = X1
| aElementOf0(sK2_skl(sdtmndt0(slcrc0,sK1_skl(xS,slcrc0)),X1,X0),X0)
| sdtmndt0(slcrc0,sK1_skl(xS,slcrc0)) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ260_spl])],[split_symbol_definition]) ).
fof(f3227,definition,
( sQ261_spl
<=> aSet0(sdtmndt0(slcrc0,sK1_skl(xS,slcrc0))) ),
introduced(definition,[new_symbols(definition,[sQ261_spl])],[split_symbol_definition]) ).
fof(f3229,plain,
( sQ261_spl
| ~ aSet0(sdtmndt0(slcrc0,sK1_skl(xS,slcrc0))) ),
inference(component_clause,[status(thm)],[f3227]) ).
fof(f3230,plain,
( ~ sQ105_spl
| ~ sQ261_spl
| sQ260_spl ),
inference(split_clause,[status(thm)],[f3223,f3224,f3227,f1469]) ).
fof(f3242,plain,
! [X0,X1] :
( ~ aElementOf0(X1,slcrc0)
| ~ aSubsetOf0(slcrc0,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f3061,f3113]) ).
fof(f3245,definition,
! [X0] :
( sQ264_spl
<=> ( ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ264_spl])],[split_symbol_definition]) ).
fof(f3246,plain,
! [X0] :
( ~ sQ264_spl
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f3245]) ).
fof(f3250,plain,
( sQ256_spl
| sQ120_spl ),
inference(split_clause,[status(thm)],[f3242,f1715,f3180]) ).
fof(f3254,plain,
( ~ sQ168_spl
| ~ sQ264_spl
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f3246,f2170]) ).
fof(f3256,plain,
( ~ sQ168_spl
| ~ sQ264_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3254,f163,f3245,f2169]) ).
fof(f3284,plain,
! [X0] :
( ~ sQ18_spl
| aSet0(sdtmndt0(X0,sK0_skl(xS)))
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f122,f259]) ).
fof(f3285,plain,
! [X0] :
( aSet0(sdtmndt0(X0,xx))
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f122,f88]) ).
fof(f3288,plain,
( sQ237_spl
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f3285,f2932]) ).
fof(f3291,plain,
! [X0] :
( aSubsetOf0(sdtmndt0(X0,xx),sdtmndt0(X0,xx))
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f3285,f57]) ).
fof(f3294,plain,
( sQ237_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3288,f132,f2930]) ).
fof(f3314,plain,
! [X0] :
( ~ sQ101_spl
| aSet0(sdtmndt0(X0,sK0_skl(slcrc0)))
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f1409,f122]) ).
fof(f3317,plain,
! [X0] :
( ~ sQ249_spl
| sP0_prd(X0,xx,slcrc0)
| ~ aElementOf0(X0,slcrc0)
| ~ aElement0(xx)
| ~ aSet0(slcrc0) ),
inference(paramodulation,[status(thm)],[f2979,f123]) ).
fof(f3319,definition,
! [X0] :
( sQ267_spl
<=> ( sP0_prd(X0,xx,slcrc0)
| ~ aElementOf0(X0,slcrc0) ) ),
introduced(definition,[new_symbols(definition,[sQ267_spl])],[split_symbol_definition]) ).
fof(f3322,plain,
( ~ sQ249_spl
| sQ267_spl
| ~ sQ9_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3317,f132,f185,f3319,f2978]) ).
fof(f3338,plain,
! [X0,X1] :
( ~ sQ101_spl
| sK2_skl(sdtmndt0(slcrc0,sK0_skl(slcrc0)),X1,X0) = X1
| aElementOf0(sK2_skl(sdtmndt0(slcrc0,sK0_skl(slcrc0)),X1,X0),X0)
| ~ aSet0(sdtmndt0(slcrc0,sK0_skl(slcrc0)))
| sdtmndt0(slcrc0,sK0_skl(slcrc0)) = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f2907,f74]) ).
fof(f3339,plain,
( ~ sQ101_spl
| ~ sQ99_spl
| sQ98_spl ),
inference(split_clause,[status(thm)],[f3338,f1397,f1400,f1408]) ).
fof(f3357,plain,
( sQ259_spl
| ~ sQ18_spl
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f3284,f3214]) ).
fof(f3363,plain,
( sQ259_spl
| ~ sQ18_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3357,f132,f258,f3212]) ).
fof(f3392,plain,
( ~ sQ105_spl
| ~ aSet0(sdtmndt0(slcrc0,sK1_skl(xS,slcrc0)))
| sdtmndt0(slcrc0,sK1_skl(xS,slcrc0)) = slcrc0 ),
inference(resolution,[status(thm)],[f38,f2905]) ).
fof(f3393,plain,
( ~ sQ101_spl
| ~ aSet0(sdtmndt0(slcrc0,sK0_skl(slcrc0)))
| sdtmndt0(slcrc0,sK0_skl(slcrc0)) = slcrc0 ),
inference(resolution,[status(thm)],[f38,f2907]) ).
fof(f3394,plain,
( ~ sQ18_spl
| ~ aSet0(sdtmndt0(slcrc0,sK0_skl(xS)))
| sdtmndt0(slcrc0,sK0_skl(xS)) = slcrc0 ),
inference(resolution,[status(thm)],[f38,f2909]) ).
fof(f3398,definition,
( sQ268_spl
<=> sdtmndt0(slcrc0,sK1_skl(xS,slcrc0)) = slcrc0 ),
introduced(definition,[new_symbols(definition,[sQ268_spl])],[split_symbol_definition]) ).
fof(f3399,plain,
( ~ sQ268_spl
| sdtmndt0(slcrc0,sK1_skl(xS,slcrc0)) = slcrc0 ),
inference(component_clause,[status(thm)],[f3398]) ).
fof(f3401,plain,
( ~ sQ105_spl
| ~ sQ261_spl
| sQ268_spl ),
inference(split_clause,[status(thm)],[f3392,f3398,f3227,f1469]) ).
fof(f3402,plain,
( ~ sQ101_spl
| ~ sQ99_spl
| sQ201_spl ),
inference(split_clause,[status(thm)],[f3393,f2551,f1400,f1408]) ).
fof(f3403,definition,
( sQ269_spl
<=> sdtmndt0(slcrc0,sK0_skl(xS)) = slcrc0 ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f3404,plain,
( ~ sQ269_spl
| sdtmndt0(slcrc0,sK0_skl(xS)) = slcrc0 ),
inference(component_clause,[status(thm)],[f3403]) ).
fof(f3406,plain,
( ~ sQ18_spl
| ~ sQ259_spl
| sQ269_spl ),
inference(split_clause,[status(thm)],[f3394,f3403,f3212,f258]) ).
fof(f3417,plain,
( sQ261_spl
| ~ sQ268_spl
| ~ aSet0(slcrc0) ),
inference(backward_demodulation,[status(thm)],[f3399,f3229]) ).
fof(f3442,plain,
( sQ261_spl
| ~ sQ268_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3417,f132,f3398,f3227]) ).
fof(f3456,plain,
! [X0] :
( ~ sQ269_spl
| sP0_prd(X0,sK0_skl(xS),slcrc0)
| ~ aElementOf0(X0,slcrc0)
| ~ aElement0(sK0_skl(xS))
| ~ aSet0(slcrc0) ),
inference(paramodulation,[status(thm)],[f3404,f123]) ).
fof(f3458,definition,
! [X0] :
( sQ270_spl
<=> ( sP0_prd(X0,sK0_skl(xS),slcrc0)
| ~ aElementOf0(X0,slcrc0) ) ),
introduced(definition,[new_symbols(definition,[sQ270_spl])],[split_symbol_definition]) ).
fof(f3461,plain,
( ~ sQ269_spl
| sQ270_spl
| ~ sQ18_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3456,f132,f258,f3458,f3403]) ).
fof(f3462,plain,
! [X0] :
( ~ sQ201_spl
| sP0_prd(X0,sK0_skl(slcrc0),slcrc0)
| ~ aElementOf0(X0,slcrc0)
| ~ aElement0(sK0_skl(slcrc0))
| ~ aSet0(slcrc0) ),
inference(paramodulation,[status(thm)],[f2552,f123]) ).
fof(f3463,definition,
! [X0] :
( sQ271_spl
<=> ( sP0_prd(X0,sK0_skl(slcrc0),slcrc0)
| ~ aElementOf0(X0,slcrc0) ) ),
introduced(definition,[new_symbols(definition,[sQ271_spl])],[split_symbol_definition]) ).
fof(f3466,plain,
( ~ sQ201_spl
| sQ271_spl
| ~ sQ101_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3462,f132,f1408,f3463,f2551]) ).
fof(f3467,plain,
( sQ254_spl
| ~ sQ101_spl
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f3314,f3146]) ).
fof(f3474,plain,
( sQ254_spl
| ~ sQ101_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3467,f163,f1408,f3144]) ).
fof(f3485,plain,
! [X0,X1,X2] :
( ~ aElementOf0(sK2_skl(xS,X1,X2),X2)
| ~ aSet0(xS)
| xS = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(sK2_skl(xS,X1,X2),X0)
| ~ aSubsetOf0(X0,xS) ),
inference(resolution,[status(thm)],[f3035,f119]) ).
fof(f3486,plain,
! [X0,X1,X2] :
( sK2_skl(xS,X1,X2) != X1
| ~ aSet0(xS)
| xS = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(sK2_skl(xS,X1,X2),X0)
| ~ aSubsetOf0(X0,xS) ),
inference(resolution,[status(thm)],[f3035,f120]) ).
fof(f3487,plain,
! [X0,X1,X2] :
( ~ sP0_prd(sK3_skl(xS,X1,X2),X1,X2)
| ~ aSet0(xS)
| xS = sdtmndt0(X2,X1)
| ~ aElement0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(sK3_skl(xS,X1,X2),X0)
| ~ aSubsetOf0(X0,xS) ),
inference(resolution,[status(thm)],[f3035,f84]) ).
fof(f3488,plain,
! [X0,X1] :
( ~ aSet0(X1)
| aSubsetOf0(X1,xS)
| ~ aSet0(xS)
| ~ aElementOf0(sK1_skl(X1,xS),X0)
| ~ aSubsetOf0(X0,xS) ),
inference(resolution,[status(thm)],[f3035,f53]) ).
fof(f3489,plain,
! [X0] :
( ~ aElementOf0(xx,X0)
| ~ aSubsetOf0(X0,xS) ),
inference(resolution,[status(thm)],[f3035,f90]) ).
fof(f3490,plain,
! [X0,X1] :
( sdtpldt0(sdtmndt0(xS,X1),X1) = xS
| ~ aSet0(xS)
| ~ aElementOf0(X1,X0)
| ~ aSubsetOf0(X0,xS) ),
inference(resolution,[status(thm)],[f3035,f87]) ).
fof(f3491,definition,
! [X0,X1,X2] :
( sQ272_spl
<=> ( ~ aElementOf0(sK2_skl(xS,X1,X2),X2)
| xS = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(sK2_skl(xS,X1,X2),X0)
| ~ aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ272_spl])],[split_symbol_definition]) ).
fof(f3494,plain,
( ~ sQ5_spl
| sQ272_spl ),
inference(split_clause,[status(thm)],[f3485,f3491,f163]) ).
fof(f3495,definition,
! [X0,X1,X2] :
( sQ273_spl
<=> ( sK2_skl(xS,X1,X2) != X1
| xS = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(sK2_skl(xS,X1,X2),X0)
| ~ aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ273_spl])],[split_symbol_definition]) ).
fof(f3498,plain,
( ~ sQ5_spl
| sQ273_spl ),
inference(split_clause,[status(thm)],[f3486,f3495,f163]) ).
fof(f3499,definition,
! [X0,X1,X2] :
( sQ274_spl
<=> ( ~ sP0_prd(sK3_skl(xS,X1,X2),X1,X2)
| xS = sdtmndt0(X2,X1)
| ~ aElement0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(sK3_skl(xS,X1,X2),X0)
| ~ aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ274_spl])],[split_symbol_definition]) ).
fof(f3502,plain,
( ~ sQ5_spl
| sQ274_spl ),
inference(split_clause,[status(thm)],[f3487,f3499,f163]) ).
fof(f3503,definition,
! [X0,X1] :
( sQ275_spl
<=> ( ~ aSet0(X1)
| aSubsetOf0(X1,xS)
| ~ aElementOf0(sK1_skl(X1,xS),X0)
| ~ aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ275_spl])],[split_symbol_definition]) ).
fof(f3506,plain,
( ~ sQ5_spl
| sQ275_spl ),
inference(split_clause,[status(thm)],[f3488,f3503,f163]) ).
fof(f3507,definition,
! [X0,X1] :
( sQ276_spl
<=> ( sdtpldt0(sdtmndt0(xS,X1),X1) = xS
| ~ aElementOf0(X1,X0)
| ~ aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ276_spl])],[split_symbol_definition]) ).
fof(f3510,plain,
( ~ sQ5_spl
| sQ276_spl ),
inference(split_clause,[status(thm)],[f3490,f3507,f163]) ).
fof(f3517,plain,
! [X0] :
( ~ sQ268_spl
| sP0_prd(X0,sK1_skl(xS,slcrc0),slcrc0)
| ~ aElementOf0(X0,slcrc0)
| ~ aElement0(sK1_skl(xS,slcrc0))
| ~ aSet0(slcrc0) ),
inference(paramodulation,[status(thm)],[f3399,f123]) ).
fof(f3518,definition,
! [X0] :
( sQ277_spl
<=> ( sP0_prd(X0,sK1_skl(xS,slcrc0),slcrc0)
| ~ aElementOf0(X0,slcrc0) ) ),
introduced(definition,[new_symbols(definition,[sQ277_spl])],[split_symbol_definition]) ).
fof(f3521,plain,
( ~ sQ268_spl
| sQ277_spl
| ~ sQ105_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3517,f132,f1469,f3518,f3398]) ).
fof(f3527,plain,
( ~ sQ171_spl
| ~ aSubsetOf0(sdtpldt0(xS,xx),xS) ),
inference(resolution,[status(thm)],[f3489,f2214]) ).
fof(f3529,plain,
! [X0] :
( ~ aElement0(xx)
| ~ aSet0(X0)
| ~ aSubsetOf0(sdtpldt0(X0,xx),xS) ),
inference(resolution,[status(thm)],[f3489,f118]) ).
fof(f3530,plain,
! [X0] :
( ~ aElementOf0(xx,X0)
| ~ aSubsetOf0(X0,xS)
| ~ aSubsetOf0(xS,xS) ),
inference(resolution,[status(thm)],[f3489,f3035]) ).
fof(f3531,plain,
( ~ sQ116_spl
| ~ aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSubsetOf0(xS,xS) ),
inference(resolution,[status(thm)],[f3489,f1659]) ).
fof(f3532,definition,
! [X0] :
( sQ279_spl
<=> ( ~ aSet0(X0)
| ~ aSubsetOf0(sdtpldt0(X0,xx),xS) ) ),
introduced(definition,[new_symbols(definition,[sQ279_spl])],[split_symbol_definition]) ).
fof(f3535,plain,
( ~ sQ9_spl
| sQ279_spl ),
inference(split_clause,[status(thm)],[f3529,f3532,f185]) ).
fof(f3536,definition,
! [X0] :
( sQ280_spl
<=> ( ~ aElementOf0(xx,X0)
| ~ aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ280_spl])],[split_symbol_definition]) ).
fof(f3539,plain,
( sQ280_spl
| ~ sQ168_spl ),
inference(split_clause,[status(thm)],[f3530,f2169,f3536]) ).
fof(f3540,definition,
( sQ281_spl
<=> aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[sQ281_spl])],[split_symbol_definition]) ).
fof(f3543,plain,
( ~ sQ116_spl
| ~ sQ281_spl
| ~ sQ168_spl ),
inference(split_clause,[status(thm)],[f3531,f2169,f3540,f1658]) ).
fof(f3544,plain,
! [X0] :
( ~ sQ171_spl
| ~ aSubsetOf0(X0,xS)
| ~ aSubsetOf0(sdtpldt0(xS,xx),X0) ),
inference(resolution,[status(thm)],[f3527,f3033]) ).
fof(f3564,plain,
! [X0,X1] :
( ~ sQ150_spl
| aSubsetOf0(X1,xS)
| ~ aSubsetOf0(X1,slcrc0)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f3060,f1997]) ).
fof(f3567,plain,
! [X0,X1] :
( ~ sQ168_spl
| aSubsetOf0(X1,xS)
| ~ aSubsetOf0(X1,xS)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f3060,f2170]) ).
fof(f3569,plain,
! [X0,X1,X2,X3] :
( ~ aSubsetOf0(X3,xS)
| ~ aSubsetOf0(X2,X3)
| aSubsetOf0(X1,xS)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f3060,f3033]) ).
fof(f3575,definition,
! [X1] :
( sQ282_spl
<=> ( aSubsetOf0(X1,xS)
| ~ aSubsetOf0(X1,slcrc0) ) ),
introduced(definition,[new_symbols(definition,[sQ282_spl])],[split_symbol_definition]) ).
fof(f3578,plain,
( ~ sQ150_spl
| sQ282_spl
| sQ264_spl ),
inference(split_clause,[status(thm)],[f3564,f3245,f3575,f1996]) ).
fof(f3579,definition,
! [X1] :
( sQ283_spl
<=> ( aSubsetOf0(X1,slcrc0)
| ~ aSubsetOf0(X1,slcrc0) ) ),
introduced(definition,[new_symbols(definition,[sQ283_spl])],[split_symbol_definition]) ).
fof(f3584,definition,
! [X1] :
( sQ284_spl
<=> ( aSubsetOf0(X1,xS)
| ~ aSubsetOf0(X1,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ284_spl])],[split_symbol_definition]) ).
fof(f3587,plain,
( ~ sQ168_spl
| sQ284_spl
| sQ264_spl ),
inference(split_clause,[status(thm)],[f3567,f3245,f3584,f2169]) ).
fof(f3592,definition,
! [X1,X2,X3] :
( sQ286_spl
<=> ( ~ aSubsetOf0(X3,xS)
| ~ aSubsetOf0(X2,X3)
| aSubsetOf0(X1,xS)
| ~ aSubsetOf0(X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ286_spl])],[split_symbol_definition]) ).
fof(f3595,plain,
( sQ286_spl
| sQ264_spl ),
inference(split_clause,[status(thm)],[f3569,f3245,f3592]) ).
fof(f3597,plain,
! [X0,X1] :
( ~ sQ137_spl
| aElementOf0(X1,slcrc0)
| ~ aElementOf0(X1,slcrc0)
| ~ aSubsetOf0(slcrc0,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f3059,f1905]) ).
fof(f3601,plain,
! [X0,X1,X2,X3] :
( ~ aSubsetOf0(X3,xS)
| ~ aSubsetOf0(X2,X3)
| aElementOf0(X1,xS)
| ~ aElementOf0(X1,X2)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f3059,f3033]) ).
fof(f3604,plain,
( ~ sQ137_spl
| sQ226_spl
| sQ120_spl ),
inference(split_clause,[status(thm)],[f3597,f1715,f2736,f1904]) ).
fof(f3607,definition,
! [X1,X2,X3] :
( sQ287_spl
<=> ( ~ aSubsetOf0(X3,xS)
| ~ aSubsetOf0(X2,X3)
| aElementOf0(X1,xS)
| ~ aElementOf0(X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ287_spl])],[split_symbol_definition]) ).
fof(f3610,plain,
( sQ287_spl
| sQ264_spl ),
inference(split_clause,[status(thm)],[f3601,f3245,f3607]) ).
fof(f3617,plain,
( ~ sQ188_spl
| sdtpldt0(sdtmndt0(sdtpldt0(xS,sK0_skl(xS)),sK0_skl(xS)),sK0_skl(xS)) = sdtpldt0(xS,sK0_skl(xS))
| ~ aSet0(sdtpldt0(xS,sK0_skl(xS))) ),
inference(resolution,[status(thm)],[f2436,f87]) ).
fof(f3622,definition,
( sQ289_spl
<=> aSet0(sdtpldt0(xS,sK0_skl(xS))) ),
introduced(definition,[new_symbols(definition,[sQ289_spl])],[split_symbol_definition]) ).
fof(f3623,plain,
( ~ sQ289_spl
| aSet0(sdtpldt0(xS,sK0_skl(xS))) ),
inference(component_clause,[status(thm)],[f3622]) ).
fof(f3624,plain,
( sQ289_spl
| ~ aSet0(sdtpldt0(xS,sK0_skl(xS))) ),
inference(component_clause,[status(thm)],[f3622]) ).
fof(f3625,definition,
( sQ290_spl
<=> sdtpldt0(sdtmndt0(sdtpldt0(xS,sK0_skl(xS)),sK0_skl(xS)),sK0_skl(xS)) = sdtpldt0(xS,sK0_skl(xS)) ),
introduced(definition,[new_symbols(definition,[sQ290_spl])],[split_symbol_definition]) ).
fof(f3628,plain,
( ~ sQ188_spl
| sQ290_spl
| ~ sQ289_spl ),
inference(split_clause,[status(thm)],[f3617,f3622,f3625,f2435]) ).
fof(f3629,plain,
( sQ289_spl
| ~ aElement0(sK0_skl(xS))
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f3624,f112]) ).
fof(f3631,plain,
( sQ289_spl
| ~ sQ18_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3629,f163,f258,f3622]) ).
fof(f3639,plain,
! [X0,X1] :
( ~ sQ8_spl
| aElementOf0(X1,sdtpldt0(xS,xx))
| ~ aElementOf0(X1,sdtpldt0(xS,xx))
| ~ aSubsetOf0(sdtpldt0(xS,xx),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f3043,f3059]) ).
fof(f3641,plain,
! [X0,X1] :
( ~ sQ8_spl
| aSubsetOf0(X1,sdtpldt0(xS,xx))
| ~ aSubsetOf0(X1,sdtpldt0(xS,xx))
| ~ aSubsetOf0(sdtpldt0(xS,xx),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f3043,f3060]) ).
fof(f3644,definition,
! [X0] :
( sQ291_spl
<=> ( ~ aSubsetOf0(sdtpldt0(xS,xx),X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ291_spl])],[split_symbol_definition]) ).
fof(f3645,plain,
! [X0] :
( ~ sQ291_spl
| ~ aSubsetOf0(sdtpldt0(xS,xx),X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f3644]) ).
fof(f3647,definition,
! [X1] :
( sQ292_spl
<=> ( aElementOf0(X1,sdtpldt0(xS,xx))
| ~ aElementOf0(X1,sdtpldt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ292_spl])],[split_symbol_definition]) ).
fof(f3650,plain,
( ~ sQ8_spl
| sQ292_spl
| sQ291_spl ),
inference(split_clause,[status(thm)],[f3639,f3644,f3647,f182]) ).
fof(f3651,definition,
( sQ293_spl
<=> aSubsetOf0(sdtpldt0(xS,xx),sdtpldt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[sQ293_spl])],[split_symbol_definition]) ).
fof(f3655,definition,
! [X1] :
( sQ294_spl
<=> ( aSubsetOf0(X1,sdtpldt0(xS,xx))
| ~ aSubsetOf0(X1,sdtpldt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ294_spl])],[split_symbol_definition]) ).
fof(f3658,plain,
( ~ sQ8_spl
| sQ294_spl
| sQ291_spl ),
inference(split_clause,[status(thm)],[f3641,f3644,f3655,f182]) ).
fof(f3661,plain,
! [X0] :
( ~ sQ8_spl
| sdtpldt0(xS,xx) = sdtpldt0(xS,xx)
| ~ aSubsetOf0(sdtpldt0(xS,xx),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f3058,f3043]) ).
fof(f3668,plain,
! [X0] :
( ~ sQ168_spl
| xS = xS
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f3058,f2170]) ).
fof(f3672,plain,
! [X0,X1,X2] :
( ~ aSubsetOf0(X2,xS)
| ~ aSubsetOf0(X1,X2)
| X1 = xS
| ~ aSubsetOf0(xS,X1)
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f3058,f3033]) ).
fof(f3678,plain,
! [X0,X1] :
( ~ aSet0(X1)
| X1 = slcrc0
| ~ aSubsetOf0(X1,slcrc0)
| ~ aSubsetOf0(slcrc0,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f3058,f3131]) ).
fof(f3683,definition,
( sQ295_spl
<=> sdtpldt0(xS,xx) = sdtpldt0(xS,xx) ),
introduced(definition,[new_symbols(definition,[sQ295_spl])],[split_symbol_definition]) ).
fof(f3686,plain,
( ~ sQ8_spl
| sQ295_spl
| sQ291_spl ),
inference(split_clause,[status(thm)],[f3661,f3644,f3683,f182]) ).
fof(f3692,plain,
( ~ sQ168_spl
| sQ170_spl
| sQ264_spl ),
inference(split_clause,[status(thm)],[f3668,f3245,f2188,f2169]) ).
fof(f3696,definition,
! [X1,X2] :
( sQ296_spl
<=> ( ~ aSubsetOf0(X2,xS)
| ~ aSubsetOf0(X1,X2)
| X1 = xS
| ~ aSubsetOf0(xS,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ296_spl])],[split_symbol_definition]) ).
fof(f3699,plain,
( sQ296_spl
| sQ264_spl ),
inference(split_clause,[status(thm)],[f3672,f3245,f3696]) ).
fof(f3703,definition,
! [X1] :
( sQ297_spl
<=> ( ~ aSet0(X1)
| X1 = slcrc0
| ~ aSubsetOf0(X1,slcrc0) ) ),
introduced(definition,[new_symbols(definition,[sQ297_spl])],[split_symbol_definition]) ).
fof(f3706,plain,
( sQ297_spl
| sQ120_spl ),
inference(split_clause,[status(thm)],[f3678,f1715,f3703]) ).
fof(f3718,plain,
! [X0,X1] :
( ~ sQ8_spl
| aElementOf0(X1,sdtpldt0(xS,xx))
| ~ aElementOf0(X1,X0)
| ~ aSubsetOf0(X0,sdtpldt0(xS,xx))
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(resolution,[status(thm)],[f1666,f3043]) ).
fof(f3719,plain,
! [X0,X1] :
( ~ sQ150_spl
| aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0)
| ~ aSubsetOf0(X0,slcrc0)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f1666,f1997]) ).
fof(f3720,plain,
! [X0,X1] :
( ~ sQ137_spl
| aElementOf0(X1,slcrc0)
| ~ aElementOf0(X1,X0)
| ~ aSubsetOf0(X0,slcrc0)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f1666,f1905]) ).
fof(f3722,plain,
! [X0,X1] :
( ~ sQ168_spl
| aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0)
| ~ aSubsetOf0(X0,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f1666,f2170]) ).
fof(f3724,plain,
! [X0,X1,X2,X3] :
( ~ aSubsetOf0(X3,xS)
| ~ aSubsetOf0(X1,X3)
| aElementOf0(X2,xS)
| ~ aElementOf0(X2,X0)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f1666,f3033]) ).
fof(f3726,definition,
! [X0,X1] :
( sQ299_spl
<=> ( aElementOf0(X1,sdtpldt0(xS,xx))
| ~ aElementOf0(X1,X0)
| ~ aSubsetOf0(X0,sdtpldt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ299_spl])],[split_symbol_definition]) ).
fof(f3729,plain,
( sQ299_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3718,f182,f3726]) ).
fof(f3730,definition,
! [X0,X1] :
( sQ300_spl
<=> ( aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0)
| ~ aSubsetOf0(X0,slcrc0) ) ),
introduced(definition,[new_symbols(definition,[sQ300_spl])],[split_symbol_definition]) ).
fof(f3733,plain,
( ~ sQ150_spl
| sQ300_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3719,f163,f3730,f1996]) ).
fof(f3734,definition,
! [X0,X1] :
( sQ301_spl
<=> ( aElementOf0(X1,slcrc0)
| ~ aElementOf0(X1,X0)
| ~ aSubsetOf0(X0,slcrc0) ) ),
introduced(definition,[new_symbols(definition,[sQ301_spl])],[split_symbol_definition]) ).
fof(f3737,plain,
( ~ sQ137_spl
| sQ301_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3720,f132,f3734,f1904]) ).
fof(f3739,definition,
! [X0,X1] :
( sQ302_spl
<=> ( aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0)
| ~ aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ302_spl])],[split_symbol_definition]) ).
fof(f3742,plain,
( ~ sQ168_spl
| sQ302_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3722,f163,f3739,f2169]) ).
fof(f3747,definition,
! [X0,X1,X2,X3] :
( sQ304_spl
<=> ( ~ aSubsetOf0(X3,xS)
| ~ aSubsetOf0(X1,X3)
| aElementOf0(X2,xS)
| ~ aElementOf0(X2,X0)
| ~ aSubsetOf0(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ304_spl])],[split_symbol_definition]) ).
fof(f3750,plain,
( sQ304_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3724,f163,f3747]) ).
fof(f3751,plain,
( ~ sQ8_spl
| ~ sQ291_spl
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(resolution,[status(thm)],[f3645,f3043]) ).
fof(f3754,plain,
( ~ sQ291_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3751,f182,f3644]) ).
fof(f3755,definition,
! [X0] :
( sQ305_spl
<=> ( ~ aSubsetOf0(X0,xS)
| ~ aSubsetOf0(sdtpldt0(xS,xx),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ305_spl])],[split_symbol_definition]) ).
fof(f3773,plain,
! [X0,X1] :
( ~ sQ80_spl
| aElementOf0(X1,sdtmndt0(xS,xx))
| ~ aElementOf0(X1,X0)
| ~ aSubsetOf0(X0,sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f3056,f1666]) ).
fof(f3774,plain,
! [X0] :
( ~ sQ80_spl
| sdtmndt0(xS,xx) = sdtmndt0(xS,xx)
| ~ aSubsetOf0(sdtmndt0(xS,xx),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f3056,f3058]) ).
fof(f3778,plain,
! [X0,X1] :
( ~ sQ80_spl
| aElementOf0(X1,sdtmndt0(xS,xx))
| ~ aElementOf0(X1,sdtmndt0(xS,xx))
| ~ aSubsetOf0(sdtmndt0(xS,xx),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f3056,f3059]) ).
fof(f3780,plain,
! [X0,X1] :
( ~ sQ80_spl
| aSubsetOf0(X1,sdtmndt0(xS,xx))
| ~ aSubsetOf0(X1,sdtmndt0(xS,xx))
| ~ aSubsetOf0(sdtmndt0(xS,xx),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f3056,f3060]) ).
fof(f3783,definition,
! [X0,X1] :
( sQ306_spl
<=> ( aElementOf0(X1,sdtmndt0(xS,xx))
| ~ aElementOf0(X1,X0)
| ~ aSubsetOf0(X0,sdtmndt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ306_spl])],[split_symbol_definition]) ).
fof(f3786,plain,
( sQ306_spl
| ~ sQ80_spl ),
inference(split_clause,[status(thm)],[f3773,f807,f3783]) ).
fof(f3787,definition,
! [X0] :
( sQ307_spl
<=> ( ~ aSubsetOf0(sdtmndt0(xS,xx),X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ307_spl])],[split_symbol_definition]) ).
fof(f3788,plain,
! [X0] :
( ~ sQ307_spl
| ~ aSubsetOf0(sdtmndt0(xS,xx),X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f3787]) ).
fof(f3790,definition,
( sQ308_spl
<=> sdtmndt0(xS,xx) = sdtmndt0(xS,xx) ),
introduced(definition,[new_symbols(definition,[sQ308_spl])],[split_symbol_definition]) ).
fof(f3793,plain,
( ~ sQ80_spl
| sQ308_spl
| sQ307_spl ),
inference(split_clause,[status(thm)],[f3774,f3787,f3790,f807]) ).
fof(f3794,definition,
( sQ309_spl
<=> aSubsetOf0(sdtmndt0(xS,xx),sdtmndt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[sQ309_spl])],[split_symbol_definition]) ).
fof(f3800,definition,
! [X1] :
( sQ310_spl
<=> ( aElementOf0(X1,sdtmndt0(xS,xx))
| ~ aElementOf0(X1,sdtmndt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ310_spl])],[split_symbol_definition]) ).
fof(f3803,plain,
( ~ sQ80_spl
| sQ310_spl
| sQ307_spl ),
inference(split_clause,[status(thm)],[f3778,f3787,f3800,f807]) ).
fof(f3805,definition,
! [X1] :
( sQ311_spl
<=> ( aSubsetOf0(X1,sdtmndt0(xS,xx))
| ~ aSubsetOf0(X1,sdtmndt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ311_spl])],[split_symbol_definition]) ).
fof(f3808,plain,
( ~ sQ80_spl
| sQ311_spl
| sQ307_spl ),
inference(split_clause,[status(thm)],[f3780,f3787,f3805,f807]) ).
fof(f3811,plain,
( ~ sQ80_spl
| ~ sQ307_spl
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f3788,f3056]) ).
fof(f3814,plain,
( ~ sQ307_spl
| ~ sQ80_spl ),
inference(split_clause,[status(thm)],[f3811,f807,f3787]) ).
fof(f3834,plain,
! [X0,X1] :
( ~ aSubsetOf0(slcrc0,X1)
| ~ aSet0(X1)
| aSubsetOf0(X0,slcrc0)
| ~ aSubsetOf0(X0,slcrc0) ),
inference(resolution,[status(thm)],[f3109,f3061]) ).
fof(f3836,plain,
( sQ120_spl
| sQ283_spl ),
inference(split_clause,[status(thm)],[f3834,f3579,f1715]) ).
fof(f3837,plain,
! [X0] :
( ~ sQ8_spl
| X0 = sdtpldt0(xS,xx)
| ~ aSubsetOf0(sdtpldt0(xS,xx),X0)
| ~ aSubsetOf0(X0,sdtpldt0(xS,xx))
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(resolution,[status(thm)],[f1667,f3043]) ).
fof(f3838,plain,
! [X0] :
( ~ sQ150_spl
| X0 = xS
| ~ aSubsetOf0(xS,X0)
| ~ aSubsetOf0(X0,slcrc0)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f1667,f1997]) ).
fof(f3839,plain,
! [X0] :
( ~ sQ137_spl
| X0 = slcrc0
| ~ aSubsetOf0(slcrc0,X0)
| ~ aSubsetOf0(X0,slcrc0)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f1667,f1905]) ).
fof(f3841,plain,
! [X0] :
( ~ sQ168_spl
| X0 = xS
| ~ aSubsetOf0(xS,X0)
| ~ aSubsetOf0(X0,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f1667,f2170]) ).
fof(f3842,plain,
! [X0] :
( ~ sQ80_spl
| X0 = sdtmndt0(xS,xx)
| ~ aSubsetOf0(sdtmndt0(xS,xx),X0)
| ~ aSubsetOf0(X0,sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f1667,f3056]) ).
fof(f3844,plain,
! [X0,X1,X2] :
( ~ aSubsetOf0(X2,xS)
| ~ aSubsetOf0(X1,X2)
| X0 = xS
| ~ aSubsetOf0(xS,X0)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f1667,f3033]) ).
fof(f3846,definition,
! [X0] :
( sQ313_spl
<=> ( X0 = sdtpldt0(xS,xx)
| ~ aSubsetOf0(sdtpldt0(xS,xx),X0)
| ~ aSubsetOf0(X0,sdtpldt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ313_spl])],[split_symbol_definition]) ).
fof(f3849,plain,
( sQ313_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3837,f182,f3846]) ).
fof(f3850,definition,
! [X0] :
( sQ314_spl
<=> ( X0 = xS
| ~ aSubsetOf0(xS,X0)
| ~ aSubsetOf0(X0,slcrc0) ) ),
introduced(definition,[new_symbols(definition,[sQ314_spl])],[split_symbol_definition]) ).
fof(f3853,plain,
( ~ sQ150_spl
| sQ314_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3838,f163,f3850,f1996]) ).
fof(f3854,definition,
! [X0] :
( sQ315_spl
<=> ( X0 = slcrc0
| ~ aSubsetOf0(slcrc0,X0)
| ~ aSubsetOf0(X0,slcrc0) ) ),
introduced(definition,[new_symbols(definition,[sQ315_spl])],[split_symbol_definition]) ).
fof(f3857,plain,
( ~ sQ137_spl
| sQ315_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3839,f132,f3854,f1904]) ).
fof(f3859,definition,
! [X0] :
( sQ316_spl
<=> ( X0 = xS
| ~ aSubsetOf0(xS,X0)
| ~ aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ316_spl])],[split_symbol_definition]) ).
fof(f3862,plain,
( ~ sQ168_spl
| sQ316_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3841,f163,f3859,f2169]) ).
fof(f3863,definition,
! [X0] :
( sQ317_spl
<=> ( X0 = sdtmndt0(xS,xx)
| ~ aSubsetOf0(sdtmndt0(xS,xx),X0)
| ~ aSubsetOf0(X0,sdtmndt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ317_spl])],[split_symbol_definition]) ).
fof(f3866,plain,
( sQ317_spl
| ~ sQ80_spl ),
inference(split_clause,[status(thm)],[f3842,f807,f3863]) ).
fof(f3871,definition,
! [X0,X1,X2] :
( sQ319_spl
<=> ( ~ aSubsetOf0(X2,xS)
| ~ aSubsetOf0(X1,X2)
| X0 = xS
| ~ aSubsetOf0(xS,X0)
| ~ aSubsetOf0(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ319_spl])],[split_symbol_definition]) ).
fof(f3874,plain,
( sQ319_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3844,f163,f3871]) ).
fof(f3888,plain,
! [X0] :
( ~ sQ171_spl
| ~ aSubsetOf0(X0,xS)
| ~ aSubsetOf0(sdtpldt0(xS,xx),X0)
| ~ aSubsetOf0(xS,xS) ),
inference(resolution,[status(thm)],[f3544,f3033]) ).
fof(f3889,plain,
! [X0] :
( ~ sQ171_spl
| ~ aSubsetOf0(sdtpldt0(xS,xx),X0)
| ~ aSet0(X0)
| ~ aSubsetOf0(sdtpldt0(xS,xx),xS) ),
inference(resolution,[status(thm)],[f3544,f3061]) ).
fof(f3890,plain,
( ~ sQ171_spl
| sQ305_spl
| ~ sQ168_spl ),
inference(split_clause,[status(thm)],[f3888,f2169,f3755,f2213]) ).
fof(f3891,definition,
( sQ320_spl
<=> aSubsetOf0(sdtpldt0(xS,xx),xS) ),
introduced(definition,[new_symbols(definition,[sQ320_spl])],[split_symbol_definition]) ).
fof(f3894,plain,
( ~ sQ171_spl
| sQ291_spl
| ~ sQ320_spl ),
inference(split_clause,[status(thm)],[f3889,f3891,f3644,f2213]) ).
fof(f3932,plain,
! [X0] :
( ~ sQ8_spl
| aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aSet0(sdtpldt0(xS,xx))
| ~ aElementOf0(X0,xS)
| ~ aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f146,f3043]) ).
fof(f3933,plain,
! [X0,X1,X2,X3] :
( ~ aSubsetOf0(X3,xS)
| ~ aSubsetOf0(sdtpldt0(X0,X1),X3)
| aElementOf0(X2,xS)
| ~ aSet0(xS)
| ~ aElementOf0(X2,X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f146,f3033]) ).
fof(f3936,definition,
! [X0] :
( sQ322_spl
<=> ( aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElementOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ322_spl])],[split_symbol_definition]) ).
fof(f3937,plain,
! [X0] :
( ~ sQ322_spl
| aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElementOf0(X0,xS) ),
inference(component_clause,[status(thm)],[f3936]) ).
fof(f3939,plain,
( ~ sQ8_spl
| sQ322_spl
| ~ sQ9_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3932,f163,f185,f3936,f182]) ).
fof(f3940,definition,
! [X0,X1,X2,X3] :
( sQ323_spl
<=> ( ~ aSubsetOf0(X3,xS)
| ~ aSubsetOf0(sdtpldt0(X0,X1),X3)
| aElementOf0(X2,xS)
| ~ aElementOf0(X2,X0)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ323_spl])],[split_symbol_definition]) ).
fof(f3943,plain,
( ~ sQ5_spl
| sQ323_spl ),
inference(split_clause,[status(thm)],[f3933,f3940,f163]) ).
fof(f3948,plain,
! [X0,X1] :
( ~ sQ322_spl
| ~ aElementOf0(sK2_skl(sdtpldt0(xS,xx),X0,X1),X1)
| ~ aSet0(sdtpldt0(xS,xx))
| sdtpldt0(xS,xx) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(sK2_skl(sdtpldt0(xS,xx),X0,X1),xS) ),
inference(resolution,[status(thm)],[f3937,f119]) ).
fof(f3949,plain,
! [X0,X1] :
( ~ sQ322_spl
| sK2_skl(sdtpldt0(xS,xx),X0,X1) != X0
| ~ aSet0(sdtpldt0(xS,xx))
| sdtpldt0(xS,xx) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(sK2_skl(sdtpldt0(xS,xx),X0,X1),xS) ),
inference(resolution,[status(thm)],[f3937,f120]) ).
fof(f3950,plain,
! [X0,X1] :
( ~ sQ322_spl
| ~ sP0_prd(sK3_skl(sdtpldt0(xS,xx),X0,X1),X0,X1)
| ~ aSet0(sdtpldt0(xS,xx))
| sdtpldt0(xS,xx) = sdtmndt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(sK3_skl(sdtpldt0(xS,xx),X0,X1),xS) ),
inference(resolution,[status(thm)],[f3937,f84]) ).
fof(f3952,plain,
! [X0] :
( ~ sQ322_spl
| ~ aSet0(X0)
| aSubsetOf0(X0,sdtpldt0(xS,xx))
| ~ aSet0(sdtpldt0(xS,xx))
| ~ aElementOf0(sK1_skl(X0,sdtpldt0(xS,xx)),xS) ),
inference(resolution,[status(thm)],[f3937,f53]) ).
fof(f3954,plain,
! [X0] :
( ~ sQ322_spl
| X0 = xx
| aElementOf0(X0,xS)
| ~ aElement0(xx)
| ~ aSet0(xS)
| ~ aElementOf0(X0,xS) ),
inference(resolution,[status(thm)],[f3937,f114]) ).
fof(f3955,plain,
! [X0] :
( ~ sQ322_spl
| sdtpldt0(sdtmndt0(sdtpldt0(xS,xx),X0),X0) = sdtpldt0(xS,xx)
| ~ aSet0(sdtpldt0(xS,xx))
| ~ aElementOf0(X0,xS) ),
inference(resolution,[status(thm)],[f3937,f87]) ).
fof(f3956,definition,
! [X0,X1] :
( sQ325_spl
<=> ( ~ aElementOf0(sK2_skl(sdtpldt0(xS,xx),X0,X1),X1)
| sdtpldt0(xS,xx) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(sK2_skl(sdtpldt0(xS,xx),X0,X1),xS) ) ),
introduced(definition,[new_symbols(definition,[sQ325_spl])],[split_symbol_definition]) ).
fof(f3959,plain,
( ~ sQ322_spl
| ~ sQ8_spl
| sQ325_spl ),
inference(split_clause,[status(thm)],[f3948,f3956,f182,f3936]) ).
fof(f3960,definition,
! [X0,X1] :
( sQ326_spl
<=> ( sK2_skl(sdtpldt0(xS,xx),X0,X1) != X0
| sdtpldt0(xS,xx) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(sK2_skl(sdtpldt0(xS,xx),X0,X1),xS) ) ),
introduced(definition,[new_symbols(definition,[sQ326_spl])],[split_symbol_definition]) ).
fof(f3963,plain,
( ~ sQ322_spl
| ~ sQ8_spl
| sQ326_spl ),
inference(split_clause,[status(thm)],[f3949,f3960,f182,f3936]) ).
fof(f3964,definition,
! [X0,X1] :
( sQ327_spl
<=> ( ~ sP0_prd(sK3_skl(sdtpldt0(xS,xx),X0,X1),X0,X1)
| sdtpldt0(xS,xx) = sdtmndt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(sK3_skl(sdtpldt0(xS,xx),X0,X1),xS) ) ),
introduced(definition,[new_symbols(definition,[sQ327_spl])],[split_symbol_definition]) ).
fof(f3967,plain,
( ~ sQ322_spl
| ~ sQ8_spl
| sQ327_spl ),
inference(split_clause,[status(thm)],[f3950,f3964,f182,f3936]) ).
fof(f3968,definition,
! [X0] :
( sQ328_spl
<=> ( ~ aSet0(X0)
| aSubsetOf0(X0,sdtpldt0(xS,xx))
| ~ aElementOf0(sK1_skl(X0,sdtpldt0(xS,xx)),xS) ) ),
introduced(definition,[new_symbols(definition,[sQ328_spl])],[split_symbol_definition]) ).
fof(f3971,plain,
( ~ sQ322_spl
| ~ sQ8_spl
| sQ328_spl ),
inference(split_clause,[status(thm)],[f3952,f3968,f182,f3936]) ).
fof(f3973,definition,
! [X0] :
( sQ329_spl
<=> ( X0 = xx
| aElementOf0(X0,xS)
| ~ aElementOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ329_spl])],[split_symbol_definition]) ).
fof(f3976,plain,
( ~ sQ322_spl
| ~ sQ9_spl
| ~ sQ5_spl
| sQ329_spl ),
inference(split_clause,[status(thm)],[f3954,f3973,f163,f185,f3936]) ).
fof(f3977,definition,
! [X0] :
( sQ330_spl
<=> ( sdtpldt0(sdtmndt0(sdtpldt0(xS,xx),X0),X0) = sdtpldt0(xS,xx)
| ~ aElementOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ330_spl])],[split_symbol_definition]) ).
fof(f3980,plain,
( ~ sQ322_spl
| ~ sQ8_spl
| sQ330_spl ),
inference(split_clause,[status(thm)],[f3955,f3977,f182,f3936]) ).
fof(f4000,definition,
! [X1] :
( sQ331_spl
<=> ( ~ aElementOf0(sK1_skl(xS,slcrc0),X1)
| ~ aSet0(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ331_spl])],[split_symbol_definition]) ).
fof(f4001,plain,
! [X0] :
( ~ sQ331_spl
| ~ aElementOf0(sK1_skl(xS,slcrc0),X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f4000]) ).
fof(f4004,definition,
! [X1] :
( sQ332_spl
<=> ( ~ aElementOf0(sK0_skl(slcrc0),X1)
| ~ aSet0(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ332_spl])],[split_symbol_definition]) ).
fof(f4005,plain,
! [X0] :
( ~ sQ332_spl
| ~ aElementOf0(sK0_skl(slcrc0),X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f4004]) ).
fof(f4008,definition,
! [X1] :
( sQ333_spl
<=> ( ~ aElementOf0(sK0_skl(xS),X1)
| ~ aSet0(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ333_spl])],[split_symbol_definition]) ).
fof(f4009,plain,
! [X0] :
( ~ sQ333_spl
| ~ aElementOf0(sK0_skl(xS),X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f4008]) ).
fof(f4012,definition,
! [X1] :
( sQ334_spl
<=> ( ~ aElementOf0(xx,X1)
| ~ aSet0(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ334_spl])],[split_symbol_definition]) ).
fof(f4013,plain,
! [X0] :
( ~ sQ334_spl
| ~ aElementOf0(xx,X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f4012]) ).
fof(f4016,plain,
! [X0] :
( ~ sQ77_spl
| ~ sQ333_spl
| ~ aSubsetOf0(sdtmndt0(xS,xx),X0)
| ~ aSet0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f802,f4009]) ).
fof(f4020,plain,
( ~ sQ77_spl
| ~ sQ333_spl
| sQ307_spl ),
inference(split_clause,[status(thm)],[f4016,f3787,f4008,f788]) ).
fof(f4025,plain,
! [X0] :
( ~ sQ334_spl
| ~ aElement0(xx)
| ~ aSet0(X0)
| ~ aSet0(sdtpldt0(X0,xx)) ),
inference(resolution,[status(thm)],[f4013,f118]) ).
fof(f4030,definition,
! [X0] :
( sQ335_spl
<=> ( ~ aSet0(X0)
| ~ aSet0(sdtpldt0(X0,xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ335_spl])],[split_symbol_definition]) ).
fof(f4031,plain,
! [X0] :
( ~ sQ335_spl
| ~ aSet0(X0)
| ~ aSet0(sdtpldt0(X0,xx)) ),
inference(component_clause,[status(thm)],[f4030]) ).
fof(f4033,plain,
( ~ sQ334_spl
| ~ sQ9_spl
| sQ335_spl ),
inference(split_clause,[status(thm)],[f4025,f4030,f185,f4012]) ).
fof(f4039,plain,
! [X0] :
( ~ sQ332_spl
| ~ aElement0(sK0_skl(slcrc0))
| ~ aSet0(X0)
| ~ aSet0(sdtpldt0(X0,sK0_skl(slcrc0))) ),
inference(resolution,[status(thm)],[f4005,f118]) ).
fof(f4044,plain,
( ~ sQ332_spl
| ~ sQ101_spl
| sQ112_spl ),
inference(split_clause,[status(thm)],[f4039,f1619,f1408,f4004]) ).
fof(f4045,definition,
! [X0] :
( sQ336_spl
<=> ( ~ aElementOf0(sK0_skl(slcrc0),X0)
| ~ aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ336_spl])],[split_symbol_definition]) ).
fof(f4046,plain,
! [X0] :
( ~ sQ336_spl
| ~ aElementOf0(sK0_skl(slcrc0),X0)
| ~ aSubsetOf0(X0,xS) ),
inference(component_clause,[status(thm)],[f4045]) ).
fof(f4050,plain,
! [X0] :
( sQ66_spl
| ~ aElementOf0(sK0_skl(slcrc0),X0)
| ~ aSubsetOf0(X0,xS) ),
inference(resolution,[status(thm)],[f699,f3035]) ).
fof(f4053,plain,
! [X0,X1,X2] :
( ~ aSubsetOf0(X2,xS)
| ~ aSubsetOf0(sdtpldt0(X0,X1),X2)
| aElementOf0(X1,xS)
| ~ aSet0(xS)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f137,f3033]) ).
fof(f4057,definition,
! [X0,X1,X2] :
( sQ337_spl
<=> ( ~ aSubsetOf0(X2,xS)
| ~ aSubsetOf0(sdtpldt0(X0,X1),X2)
| aElementOf0(X1,xS)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ337_spl])],[split_symbol_definition]) ).
fof(f4060,plain,
( ~ sQ5_spl
| sQ337_spl ),
inference(split_clause,[status(thm)],[f4053,f4057,f163]) ).
fof(f4071,plain,
( ~ sQ8_spl
| ~ sQ335_spl
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f4031,f183]) ).
fof(f4074,plain,
( ~ sQ8_spl
| ~ sQ335_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f4071,f163,f4030,f182]) ).
fof(f4075,definition,
! [X0] :
( sQ339_spl
<=> ( ~ aSet0(X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ339_spl])],[split_symbol_definition]) ).
fof(f4076,plain,
! [X0] :
( ~ sQ339_spl
| ~ aSet0(X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f4075]) ).
fof(f4079,plain,
( ~ sQ127_spl
| ~ sQ339_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1825,f4089]) ).
fof(f4089,plain,
! [X0] :
( ~ sQ339_spl
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f4076]) ).
fof(f4090,plain,
( ~ sQ127_spl
| ~ sQ339_spl ),
inference(contradiction_clause,[status(thm)],[f4079]) ).
fof(f4100,plain,
! [X0] :
( sdtpldt0(sdtmndt0(xS,X0),X0) = xS
| ~ aElementOf0(X0,xS) ),
inference(resolution,[status(thm)],[f87,f89]) ).
fof(f4120,plain,
! [X0,X1] :
( aSubsetOf0(slcrc0,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f50,f3131]) ).
fof(f4129,plain,
! [X0,X1] :
( aSubsetOf0(slcrc0,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f112,f3131]) ).
fof(f4135,plain,
! [X0,X1] :
( aSubsetOf0(sdtmndt0(X0,X1),sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f122,f57]) ).
fof(f4146,plain,
( ~ sQ8_spl
| aSubsetOf0(sdtpldt0(xS,xx),sdtpldt0(xS,xx))
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(resolution,[status(thm)],[f3061,f3043]) ).
fof(f4152,plain,
( ~ sQ80_spl
| aSubsetOf0(sdtmndt0(xS,xx),sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f3061,f3056]) ).
fof(f4154,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,xS)
| ~ aSubsetOf0(X0,X1)
| aSubsetOf0(X0,X0)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f3061,f3033]) ).
fof(f4155,plain,
( sQ293_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f4146,f182,f3651]) ).
fof(f4161,plain,
( sQ309_spl
| ~ sQ80_spl ),
inference(split_clause,[status(thm)],[f4152,f807,f3794]) ).
fof(f4163,definition,
! [X0,X1] :
( sQ340_spl
<=> ( ~ aSubsetOf0(X1,xS)
| ~ aSubsetOf0(X0,X1)
| aSubsetOf0(X0,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ340_spl])],[split_symbol_definition]) ).
fof(f4164,plain,
! [X0,X1] :
( ~ sQ340_spl
| ~ aSubsetOf0(X1,xS)
| ~ aSubsetOf0(X0,X1)
| aSubsetOf0(X0,X0) ),
inference(component_clause,[status(thm)],[f4163]) ).
fof(f4166,plain,
( sQ340_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f4154,f163,f4163]) ).
fof(f4170,plain,
( ~ sQ116_spl
| ~ sQ336_spl
| ~ aElementOf0(sK0_skl(slcrc0),sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSubsetOf0(xS,xS) ),
inference(resolution,[status(thm)],[f4046,f1659]) ).
fof(f4174,plain,
( ~ sQ116_spl
| ~ sQ336_spl
| ~ sQ152_spl
| ~ sQ168_spl ),
inference(split_clause,[status(thm)],[f4170,f2169,f2015,f4045,f1658]) ).
fof(f4175,plain,
( sQ66_spl
| sQ336_spl ),
inference(split_clause,[status(thm)],[f4050,f4045,f697]) ).
fof(f4195,plain,
! [X0] :
( ~ sQ112_spl
| ~ aElement0(sK0_skl(slcrc0))
| ~ aSet0(X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f1620,f112]) ).
fof(f4197,plain,
( ~ sQ112_spl
| ~ sQ101_spl
| sQ339_spl ),
inference(split_clause,[status(thm)],[f4195,f4075,f1408,f1619]) ).
fof(f4207,plain,
( ~ sQ68_spl
| ~ sQ331_spl
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f4001,f706]) ).
fof(f4211,plain,
( ~ sQ68_spl
| ~ sQ331_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f4207,f163,f4000,f705]) ).
fof(f4213,definition,
! [X0] :
( sQ341_spl
<=> ( ~ aElementOf0(sK1_skl(xS,slcrc0),X0)
| ~ aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ341_spl])],[split_symbol_definition]) ).
fof(f4214,plain,
! [X0] :
( ~ sQ341_spl
| ~ aElementOf0(sK1_skl(xS,slcrc0),X0)
| ~ aSubsetOf0(X0,xS) ),
inference(component_clause,[status(thm)],[f4213]) ).
fof(f4244,definition,
! [X0] :
( sQ343_spl
<=> ( ~ aSet0(sdtmndt0(X0,xx))
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ343_spl])],[split_symbol_definition]) ).
fof(f4245,plain,
! [X0] :
( ~ sQ343_spl
| ~ aSet0(sdtmndt0(X0,xx))
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f4244]) ).
fof(f4249,plain,
( ~ sQ289_spl
| ~ sQ343_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f3623,f4259]) ).
fof(f4259,plain,
! [X0] :
( ~ sQ343_spl
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f4245,f3285]) ).
fof(f4260,plain,
( ~ sQ289_spl
| ~ sQ343_spl ),
inference(contradiction_clause,[status(thm)],[f4249]) ).
fof(f4263,plain,
! [X0,X1] :
( X1 = X0
| aElementOf0(X1,slcrc0)
| ~ aElementOf0(X1,sdtpldt0(slcrc0,X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f114,f106]) ).
fof(f4264,plain,
! [X0,X1] :
( X1 = X0
| aElementOf0(X1,xS)
| ~ aElementOf0(X1,sdtpldt0(xS,X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f114,f89]) ).
fof(f4265,plain,
! [X0,X1] :
( X1 = X0
| ~ aElementOf0(X1,sdtpldt0(slcrc0,X0))
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f4263,f107]) ).
fof(f4440,plain,
! [X0,X1] :
( ~ sQ340_spl
| ~ aSubsetOf0(xS,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,slcrc0)
| aSubsetOf0(X0,X0) ),
inference(resolution,[status(thm)],[f4164,f4120]) ).
fof(f4445,plain,
! [X0,X1] :
( ~ sQ340_spl
| ~ aSubsetOf0(xS,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,xS)
| aSubsetOf0(X0,X0) ),
inference(resolution,[status(thm)],[f4164,f3061]) ).
fof(f4446,definition,
! [X0] :
( sQ344_spl
<=> ( ~ aSubsetOf0(X0,slcrc0)
| aSubsetOf0(X0,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ344_spl])],[split_symbol_definition]) ).
fof(f4449,plain,
( ~ sQ340_spl
| sQ264_spl
| sQ344_spl ),
inference(split_clause,[status(thm)],[f4440,f4446,f3245,f4163]) ).
fof(f4455,definition,
! [X0] :
( sQ345_spl
<=> ( ~ aSubsetOf0(X0,xS)
| aSubsetOf0(X0,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ345_spl])],[split_symbol_definition]) ).
fof(f4458,plain,
( ~ sQ340_spl
| sQ264_spl
| sQ345_spl ),
inference(split_clause,[status(thm)],[f4445,f4455,f3245,f4163]) ).
fof(f4494,plain,
! [X0] :
( ~ sQ336_spl
| ~ aSubsetOf0(sdtpldt0(X0,sK0_skl(slcrc0)),xS)
| ~ aElement0(sK0_skl(slcrc0))
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f118,f4046]) ).
fof(f4499,definition,
! [X0] :
( sQ346_spl
<=> ( ~ aSubsetOf0(sdtpldt0(X0,sK0_skl(slcrc0)),xS)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ346_spl])],[split_symbol_definition]) ).
fof(f4502,plain,
( ~ sQ336_spl
| ~ sQ101_spl
| sQ346_spl ),
inference(split_clause,[status(thm)],[f4494,f4499,f1408,f4045]) ).
fof(f4506,plain,
( ~ sQ66_spl
| sdtpldt0(sdtmndt0(xS,sK0_skl(slcrc0)),sK0_skl(slcrc0)) = xS
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f698,f87]) ).
fof(f4507,definition,
( sQ347_spl
<=> sdtpldt0(sdtmndt0(xS,sK0_skl(slcrc0)),sK0_skl(slcrc0)) = xS ),
introduced(definition,[new_symbols(definition,[sQ347_spl])],[split_symbol_definition]) ).
fof(f4510,plain,
( ~ sQ66_spl
| sQ347_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f4506,f163,f4507,f697]) ).
fof(f4522,plain,
! [X0] :
( ~ aElement0(X0)
| ~ aSet0(slcrc0)
| X0 = X0
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f4265,f118]) ).
fof(f4523,definition,
! [X0] :
( sQ348_spl
<=> ( ~ aElement0(X0)
| X0 = X0
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ348_spl])],[split_symbol_definition]) ).
fof(f4526,plain,
( ~ sQ3_spl
| sQ348_spl ),
inference(split_clause,[status(thm)],[f4522,f4523,f132]) ).
fof(f4527,plain,
( ~ sQ68_spl
| ~ sQ341_spl
| ~ aSubsetOf0(xS,xS) ),
inference(resolution,[status(thm)],[f4214,f706]) ).
fof(f4532,plain,
( ~ sQ68_spl
| ~ sQ341_spl
| ~ sQ168_spl ),
inference(split_clause,[status(thm)],[f4527,f2169,f4213,f705]) ).
fof(f4540,plain,
! [X0] :
( ~ sQ251_spl
| ~ aElementOf0(X0,sdtmndt0(slcrc0,xx))
| ~ aElement0(xx)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f123,f2988]) ).
fof(f4543,plain,
! [X0,X1] :
( ~ aElementOf0(X1,sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f123,f125]) ).
fof(f4544,definition,
! [X0] :
( sQ350_spl
<=> ~ aElementOf0(X0,sdtmndt0(slcrc0,xx)) ),
introduced(definition,[new_symbols(definition,[sQ350_spl])],[split_symbol_definition]) ).
fof(f4547,plain,
( ~ sQ251_spl
| sQ350_spl
| ~ sQ9_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4540,f132,f185,f4544,f2987]) ).
fof(f4557,plain,
( ~ sQ269_spl
| ~ aElementOf0(sK0_skl(xS),slcrc0)
| ~ aElement0(sK0_skl(xS))
| ~ aSet0(slcrc0) ),
inference(paramodulation,[status(thm)],[f3404,f4543]) ).
fof(f4558,plain,
( ~ sQ249_spl
| ~ aElementOf0(xx,slcrc0)
| ~ aElement0(xx)
| ~ aSet0(slcrc0) ),
inference(paramodulation,[status(thm)],[f2979,f4543]) ).
fof(f4561,definition,
( sQ351_spl
<=> aElementOf0(sK0_skl(xS),slcrc0) ),
introduced(definition,[new_symbols(definition,[sQ351_spl])],[split_symbol_definition]) ).
fof(f4564,plain,
( ~ sQ269_spl
| ~ sQ351_spl
| ~ sQ18_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4557,f132,f258,f4561,f3403]) ).
fof(f4565,definition,
( sQ352_spl
<=> aElementOf0(xx,slcrc0) ),
introduced(definition,[new_symbols(definition,[sQ352_spl])],[split_symbol_definition]) ).
fof(f4568,plain,
( ~ sQ249_spl
| ~ sQ352_spl
| ~ sQ9_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4558,f132,f185,f4565,f2978]) ).
fof(f4582,definition,
( sQ353_spl
<=> aSubsetOf0(slcrc0,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[sQ353_spl])],[split_symbol_definition]) ).
fof(f4594,plain,
! [X0] :
( ~ aSet0(slcrc0)
| aSubsetOf0(slcrc0,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f52,f107]) ).
fof(f4595,plain,
! [X0,X1,X2] :
( aElementOf0(sK1_skl(X1,X0),X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f52,f51]) ).
fof(f4598,definition,
! [X0] :
( sQ354_spl
<=> ( aSubsetOf0(slcrc0,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ354_spl])],[split_symbol_definition]) ).
fof(f4601,plain,
( ~ sQ3_spl
| sQ354_spl ),
inference(split_clause,[status(thm)],[f4594,f4598,f132]) ).
fof(f4602,plain,
! [X0,X1,X2] :
( aElementOf0(sK1_skl(X1,X0),X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f4595,f50]) ).
fof(f4606,plain,
! [X0,X1,X2,X3] :
( aElementOf0(sK3_skl(X2,X1,X0),X3)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3)
| sP0_prd(sK3_skl(X2,X1,X0),X1,X0)
| ~ aSet0(X2)
| X2 = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f85,f51]) ).
fof(f4609,plain,
! [X0,X1,X2,X3] :
( aElementOf0(sK3_skl(X2,X1,X0),X3)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3)
| sP0_prd(sK3_skl(X2,X1,X0),X1,X0)
| X2 = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f4606,f50]) ).
fof(f4644,plain,
! [X0,X1] :
( sP0_prd(sK3_skl(xS,X0,X1),X0,X1)
| ~ aSet0(xS)
| xS = sdtmndt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| sdtpldt0(sdtmndt0(xS,sK3_skl(xS,X0,X1)),sK3_skl(xS,X0,X1)) = xS ),
inference(resolution,[status(thm)],[f4100,f85]) ).
fof(f4648,plain,
! [X0] :
( ~ aSet0(xS)
| aSubsetOf0(xS,X0)
| ~ aSet0(X0)
| sdtpldt0(sdtmndt0(xS,sK1_skl(xS,X0)),sK1_skl(xS,X0)) = xS ),
inference(resolution,[status(thm)],[f4100,f52]) ).
fof(f4655,definition,
! [X0,X1] :
( sQ355_spl
<=> ( sP0_prd(sK3_skl(xS,X0,X1),X0,X1)
| xS = sdtmndt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| sdtpldt0(sdtmndt0(xS,sK3_skl(xS,X0,X1)),sK3_skl(xS,X0,X1)) = xS ) ),
introduced(definition,[new_symbols(definition,[sQ355_spl])],[split_symbol_definition]) ).
fof(f4658,plain,
( ~ sQ5_spl
| sQ355_spl ),
inference(split_clause,[status(thm)],[f4644,f4655,f163]) ).
fof(f4660,definition,
! [X0] :
( sQ356_spl
<=> ( aSubsetOf0(xS,X0)
| ~ aSet0(X0)
| sdtpldt0(sdtmndt0(xS,sK1_skl(xS,X0)),sK1_skl(xS,X0)) = xS ) ),
introduced(definition,[new_symbols(definition,[sQ356_spl])],[split_symbol_definition]) ).
fof(f4663,plain,
( ~ sQ5_spl
| sQ356_spl ),
inference(split_clause,[status(thm)],[f4648,f4660,f163]) ).
fof(f4666,plain,
( ~ sQ268_spl
| aSubsetOf0(slcrc0,sdtmndt0(slcrc0,sK1_skl(xS,slcrc0)))
| ~ aElement0(sK1_skl(xS,slcrc0))
| ~ aSet0(slcrc0) ),
inference(paramodulation,[status(thm)],[f3399,f4135]) ).
fof(f4667,plain,
( ~ sQ201_spl
| aSubsetOf0(slcrc0,sdtmndt0(slcrc0,sK0_skl(slcrc0)))
| ~ aElement0(sK0_skl(slcrc0))
| ~ aSet0(slcrc0) ),
inference(paramodulation,[status(thm)],[f2552,f4135]) ).
fof(f4668,plain,
( ~ sQ269_spl
| aSubsetOf0(slcrc0,sdtmndt0(slcrc0,sK0_skl(xS)))
| ~ aElement0(sK0_skl(xS))
| ~ aSet0(slcrc0) ),
inference(paramodulation,[status(thm)],[f3404,f4135]) ).
fof(f4670,plain,
( ~ sQ268_spl
| aSubsetOf0(sdtmndt0(slcrc0,sK1_skl(xS,slcrc0)),slcrc0)
| ~ aElement0(sK1_skl(xS,slcrc0))
| ~ aSet0(slcrc0) ),
inference(paramodulation,[status(thm)],[f3399,f4135]) ).
fof(f4671,plain,
( ~ sQ201_spl
| aSubsetOf0(sdtmndt0(slcrc0,sK0_skl(slcrc0)),slcrc0)
| ~ aElement0(sK0_skl(slcrc0))
| ~ aSet0(slcrc0) ),
inference(paramodulation,[status(thm)],[f2552,f4135]) ).
fof(f4672,plain,
( ~ sQ269_spl
| aSubsetOf0(sdtmndt0(slcrc0,sK0_skl(xS)),slcrc0)
| ~ aElement0(sK0_skl(xS))
| ~ aSet0(slcrc0) ),
inference(paramodulation,[status(thm)],[f3404,f4135]) ).
fof(f4675,definition,
( sQ357_spl
<=> aSubsetOf0(slcrc0,sdtmndt0(slcrc0,sK1_skl(xS,slcrc0))) ),
introduced(definition,[new_symbols(definition,[sQ357_spl])],[split_symbol_definition]) ).
fof(f4678,plain,
( ~ sQ268_spl
| sQ357_spl
| ~ sQ105_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4666,f132,f1469,f4675,f3398]) ).
fof(f4679,definition,
( sQ358_spl
<=> aSubsetOf0(slcrc0,sdtmndt0(slcrc0,sK0_skl(slcrc0))) ),
introduced(definition,[new_symbols(definition,[sQ358_spl])],[split_symbol_definition]) ).
fof(f4682,plain,
( ~ sQ201_spl
| sQ358_spl
| ~ sQ101_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4667,f132,f1408,f4679,f2551]) ).
fof(f4683,definition,
( sQ359_spl
<=> aSubsetOf0(slcrc0,sdtmndt0(slcrc0,sK0_skl(xS))) ),
introduced(definition,[new_symbols(definition,[sQ359_spl])],[split_symbol_definition]) ).
fof(f4686,plain,
( ~ sQ269_spl
| sQ359_spl
| ~ sQ18_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4668,f132,f258,f4683,f3403]) ).
fof(f4687,definition,
( sQ360_spl
<=> aSubsetOf0(slcrc0,sdtmndt0(slcrc0,xx)) ),
introduced(definition,[new_symbols(definition,[sQ360_spl])],[split_symbol_definition]) ).
fof(f4691,definition,
( sQ361_spl
<=> aSubsetOf0(sdtmndt0(slcrc0,sK1_skl(xS,slcrc0)),slcrc0) ),
introduced(definition,[new_symbols(definition,[sQ361_spl])],[split_symbol_definition]) ).
fof(f4694,plain,
( ~ sQ268_spl
| sQ361_spl
| ~ sQ105_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4670,f132,f1469,f4691,f3398]) ).
fof(f4695,definition,
( sQ362_spl
<=> aSubsetOf0(sdtmndt0(slcrc0,sK0_skl(slcrc0)),slcrc0) ),
introduced(definition,[new_symbols(definition,[sQ362_spl])],[split_symbol_definition]) ).
fof(f4698,plain,
( ~ sQ201_spl
| sQ362_spl
| ~ sQ101_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4671,f132,f1408,f4695,f2551]) ).
fof(f4699,definition,
( sQ363_spl
<=> aSubsetOf0(sdtmndt0(slcrc0,sK0_skl(xS)),slcrc0) ),
introduced(definition,[new_symbols(definition,[sQ363_spl])],[split_symbol_definition]) ).
fof(f4702,plain,
( ~ sQ269_spl
| sQ363_spl
| ~ sQ18_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4672,f132,f258,f4699,f3403]) ).
fof(f4703,definition,
( sQ364_spl
<=> aSubsetOf0(sdtmndt0(slcrc0,xx),slcrc0) ),
introduced(definition,[new_symbols(definition,[sQ364_spl])],[split_symbol_definition]) ).
fof(f4716,plain,
( ~ sQ249_spl
| aSubsetOf0(slcrc0,sdtmndt0(slcrc0,xx))
| ~ aSet0(slcrc0) ),
inference(paramodulation,[status(thm)],[f2979,f3291]) ).
fof(f4717,plain,
( ~ sQ249_spl
| aSubsetOf0(sdtmndt0(slcrc0,xx),slcrc0)
| ~ aSet0(slcrc0) ),
inference(paramodulation,[status(thm)],[f2979,f3291]) ).
fof(f4719,plain,
( ~ sQ249_spl
| sQ360_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4716,f132,f4687,f2978]) ).
fof(f4720,plain,
( ~ sQ249_spl
| sQ364_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4717,f132,f4703,f2978]) ).
fof(f4750,plain,
! [X0,X1,X2] :
( ~ aElementOf0(sK3_skl(X2,X1,X0),sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0)
| ~ aElementOf0(sK3_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f84,f123]) ).
fof(f4753,plain,
! [X0,X1,X2] :
( ~ aElementOf0(sK3_skl(X2,X1,X0),sdtmndt0(X0,X1))
| ~ aElementOf0(sK3_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f4750]) ).
fof(f4760,plain,
! [X0,X1,X2,X3] :
( aElementOf0(sK2_skl(X2,X1,X0),X3)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3)
| sK2_skl(X2,X1,X0) = X1
| aElementOf0(sK2_skl(X2,X1,X0),X0)
| ~ aSet0(X2)
| X2 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f74,f51]) ).
fof(f4764,plain,
! [X0,X1,X2,X3] :
( aElementOf0(sK2_skl(X2,X1,X0),X3)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3)
| sK2_skl(X2,X1,X0) = X1
| aElementOf0(sK2_skl(X2,X1,X0),X0)
| X2 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f4760,f50]) ).
fof(f4802,plain,
( ~ sQ141_spl
| ~ sQ21_spl
| ~ aSet0(sdtmndt0(xS,sK0_skl(xS)))
| slcrc0 = sdtmndt0(xS,sK0_skl(xS))
| aElementOf0(sK1_skl(sdtmndt0(xS,sK0_skl(xS)),slcrc0),xS) ),
inference(resolution,[status(thm)],[f270,f1929]) ).
fof(f4803,plain,
! [X0] :
( ~ sQ21_spl
| ~ aSet0(sdtmndt0(xS,sK0_skl(xS)))
| aSubsetOf0(sdtmndt0(xS,sK0_skl(xS)),X0)
| ~ aSet0(X0)
| aElementOf0(sK1_skl(sdtmndt0(xS,sK0_skl(xS)),X0),xS) ),
inference(resolution,[status(thm)],[f270,f52]) ).
fof(f4807,plain,
( ~ sQ141_spl
| ~ sQ21_spl
| ~ sQ17_spl
| sQ47_spl
| sQ149_spl ),
inference(split_clause,[status(thm)],[f4802,f1991,f473,f255,f269,f1928]) ).
fof(f4808,definition,
! [X0] :
( sQ367_spl
<=> ( aSubsetOf0(sdtmndt0(xS,sK0_skl(xS)),X0)
| ~ aSet0(X0)
| aElementOf0(sK1_skl(sdtmndt0(xS,sK0_skl(xS)),X0),xS) ) ),
introduced(definition,[new_symbols(definition,[sQ367_spl])],[split_symbol_definition]) ).
fof(f4811,plain,
( ~ sQ21_spl
| ~ sQ17_spl
| sQ367_spl ),
inference(split_clause,[status(thm)],[f4803,f4808,f255,f269]) ).
fof(f4851,plain,
( ~ sQ58_spl
| ~ sQ47_spl
| sdtpldt0(sdtmndt0(sdtmndt0(xS,sK0_skl(xS)),sK0_skl(sdtmndt0(xS,sK0_skl(xS)))),sK0_skl(sdtmndt0(xS,sK0_skl(xS)))) = slcrc0 ),
inference(backward_demodulation,[status(thm)],[f474,f559]) ).
fof(f4892,plain,
( ~ sQ58_spl
| ~ sQ47_spl
| sdtpldt0(sdtmndt0(slcrc0,sK0_skl(sdtmndt0(xS,sK0_skl(xS)))),sK0_skl(sdtmndt0(xS,sK0_skl(xS)))) = slcrc0 ),
inference(forward_demodulation,[status(thm)],[f474,f4851]) ).
fof(f4893,plain,
( ~ sQ58_spl
| ~ sQ47_spl
| sdtpldt0(sdtmndt0(slcrc0,sK0_skl(slcrc0)),sK0_skl(sdtmndt0(xS,sK0_skl(xS)))) = slcrc0 ),
inference(forward_demodulation,[status(thm)],[f474,f4892]) ).
fof(f4894,plain,
( ~ sQ58_spl
| ~ sQ47_spl
| ~ sQ201_spl
| sdtpldt0(slcrc0,sK0_skl(sdtmndt0(xS,sK0_skl(xS)))) = slcrc0 ),
inference(forward_demodulation,[status(thm)],[f2552,f4893]) ).
fof(f4895,plain,
( ~ sQ58_spl
| ~ sQ47_spl
| ~ sQ201_spl
| sdtpldt0(slcrc0,sK0_skl(slcrc0)) = slcrc0 ),
inference(forward_demodulation,[status(thm)],[f474,f4894]) ).
fof(f4896,plain,
( ~ sQ58_spl
| ~ sQ47_spl
| ~ sQ201_spl
| sQ215_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4895,f2693]) ).
fof(f4897,plain,
( ~ sQ58_spl
| ~ sQ47_spl
| ~ sQ201_spl
| sQ215_spl ),
inference(contradiction_clause,[status(thm)],[f4896]) ).
fof(f4975,plain,
! [X0] :
( ~ sQ8_spl
| aSubsetOf0(X0,X0)
| ~ aSubsetOf0(X0,sdtpldt0(xS,xx)) ),
inference(resolution,[status(thm)],[f3061,f183]) ).
fof(f5212,plain,
! [X0,X1,X2] :
( sK2_skl(xS,X1,X2) != X1
| ~ aSet0(xS)
| xS = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aSet0(X2)
| sK2_skl(xS,X1,X2) = X0
| ~ aElementOf0(sK2_skl(xS,X1,X2),sdtpldt0(xS,X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f4264,f120]) ).
fof(f5213,plain,
! [X0,X1,X2] :
( ~ aElementOf0(sK2_skl(xS,X1,X2),X2)
| ~ aSet0(xS)
| xS = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aSet0(X2)
| sK2_skl(xS,X1,X2) = X0
| ~ aElementOf0(sK2_skl(xS,X1,X2),sdtpldt0(xS,X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f4264,f119]) ).
fof(f5214,plain,
! [X0,X1] :
( ~ aSet0(X1)
| aSubsetOf0(X1,xS)
| ~ aSet0(xS)
| sK1_skl(X1,xS) = X0
| ~ aElementOf0(sK1_skl(X1,xS),sdtpldt0(xS,X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f4264,f53]) ).
fof(f5216,plain,
! [X0] :
( ~ aSubsetOf0(xS,xS)
| xx = X0
| ~ aElementOf0(xx,sdtpldt0(xS,X0))
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f4264,f3489]) ).
fof(f5218,definition,
! [X0,X1,X2] :
( sQ368_spl
<=> ( sK2_skl(xS,X1,X2) != X1
| xS = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aSet0(X2)
| sK2_skl(xS,X1,X2) = X0
| ~ aElementOf0(sK2_skl(xS,X1,X2),sdtpldt0(xS,X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ368_spl])],[split_symbol_definition]) ).
fof(f5221,plain,
( ~ sQ5_spl
| sQ368_spl ),
inference(split_clause,[status(thm)],[f5212,f5218,f163]) ).
fof(f5222,definition,
! [X0,X1,X2] :
( sQ369_spl
<=> ( ~ aElementOf0(sK2_skl(xS,X1,X2),X2)
| xS = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aSet0(X2)
| sK2_skl(xS,X1,X2) = X0
| ~ aElementOf0(sK2_skl(xS,X1,X2),sdtpldt0(xS,X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ369_spl])],[split_symbol_definition]) ).
fof(f5225,plain,
( ~ sQ5_spl
| sQ369_spl ),
inference(split_clause,[status(thm)],[f5213,f5222,f163]) ).
fof(f5226,definition,
! [X0,X1] :
( sQ370_spl
<=> ( ~ aSet0(X1)
| aSubsetOf0(X1,xS)
| sK1_skl(X1,xS) = X0
| ~ aElementOf0(sK1_skl(X1,xS),sdtpldt0(xS,X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ370_spl])],[split_symbol_definition]) ).
fof(f5229,plain,
( ~ sQ5_spl
| sQ370_spl ),
inference(split_clause,[status(thm)],[f5214,f5226,f163]) ).
fof(f5230,definition,
! [X0] :
( sQ371_spl
<=> ( xx = X0
| ~ aElementOf0(xx,sdtpldt0(xS,X0))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ371_spl])],[split_symbol_definition]) ).
fof(f5233,plain,
( ~ sQ168_spl
| sQ371_spl ),
inference(split_clause,[status(thm)],[f5216,f5230,f2169]) ).
fof(f5270,plain,
( ~ sQ10_spl
| aSubsetOf0(slcrc0,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aElement0(sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)))
| ~ aSet0(sdtmndt0(sdtmndt0(sdtpldt0(xS,xx),xx),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx)))) ),
inference(paramodulation,[status(thm)],[f217,f4129]) ).
fof(f5274,plain,
( ~ sQ10_spl
| sQ353_spl
| ~ sQ40_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f5270,f438,f441,f4582,f216]) ).
fof(f5325,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtmndt0(xS,sK2_skl(X1,X0,xS)),sK2_skl(X1,X0,xS)) = xS
| aElementOf0(sK2_skl(X1,X0,xS),X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2)
| sK2_skl(X1,X0,xS) = X0
| X1 = sdtpldt0(xS,X0)
| ~ aElement0(X0)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f4764,f4100]) ).
fof(f5328,plain,
! [X0,X1,X2] :
( aElementOf0(sK2_skl(X1,X0,slcrc0),X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2)
| sK2_skl(X1,X0,slcrc0) = X0
| X1 = sdtpldt0(slcrc0,X0)
| ~ aElement0(X0)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f4764,f107]) ).
fof(f5330,definition,
! [X0,X1,X2] :
( sQ373_spl
<=> ( sdtpldt0(sdtmndt0(xS,sK2_skl(X1,X0,xS)),sK2_skl(X1,X0,xS)) = xS
| aElementOf0(sK2_skl(X1,X0,xS),X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2)
| sK2_skl(X1,X0,xS) = X0
| X1 = sdtpldt0(xS,X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ373_spl])],[split_symbol_definition]) ).
fof(f5333,plain,
( sQ373_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f5325,f163,f5330]) ).
fof(f5334,definition,
! [X0,X1,X2] :
( sQ374_spl
<=> ( aElementOf0(sK2_skl(X1,X0,slcrc0),X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2)
| sK2_skl(X1,X0,slcrc0) = X0
| X1 = sdtpldt0(slcrc0,X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ374_spl])],[split_symbol_definition]) ).
fof(f5337,plain,
( sQ374_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f5328,f132,f5334]) ).
fof(f5339,plain,
! [X0] :
( ~ sQ268_spl
| ~ aElementOf0(sK3_skl(X0,sK1_skl(xS,slcrc0),slcrc0),slcrc0)
| ~ aElementOf0(sK3_skl(X0,sK1_skl(xS,slcrc0),slcrc0),X0)
| ~ aSet0(X0)
| X0 = sdtmndt0(slcrc0,sK1_skl(xS,slcrc0))
| ~ aElement0(sK1_skl(xS,slcrc0))
| ~ aSet0(slcrc0) ),
inference(paramodulation,[status(thm)],[f3399,f4753]) ).
fof(f5340,plain,
! [X0] :
( ~ sQ201_spl
| ~ aElementOf0(sK3_skl(X0,sK0_skl(slcrc0),slcrc0),slcrc0)
| ~ aElementOf0(sK3_skl(X0,sK0_skl(slcrc0),slcrc0),X0)
| ~ aSet0(X0)
| X0 = sdtmndt0(slcrc0,sK0_skl(slcrc0))
| ~ aElement0(sK0_skl(slcrc0))
| ~ aSet0(slcrc0) ),
inference(paramodulation,[status(thm)],[f2552,f4753]) ).
fof(f5341,plain,
! [X0] :
( ~ sQ269_spl
| ~ aElementOf0(sK3_skl(X0,sK0_skl(xS),slcrc0),slcrc0)
| ~ aElementOf0(sK3_skl(X0,sK0_skl(xS),slcrc0),X0)
| ~ aSet0(X0)
| X0 = sdtmndt0(slcrc0,sK0_skl(xS))
| ~ aElement0(sK0_skl(xS))
| ~ aSet0(slcrc0) ),
inference(paramodulation,[status(thm)],[f3404,f4753]) ).
fof(f5342,plain,
! [X0] :
( ~ sQ249_spl
| ~ aElementOf0(sK3_skl(X0,xx,slcrc0),slcrc0)
| ~ aElementOf0(sK3_skl(X0,xx,slcrc0),X0)
| ~ aSet0(X0)
| X0 = sdtmndt0(slcrc0,xx)
| ~ aElement0(xx)
| ~ aSet0(slcrc0) ),
inference(paramodulation,[status(thm)],[f2979,f4753]) ).
fof(f5343,definition,
! [X0] :
( sQ375_spl
<=> ( ~ aElementOf0(sK3_skl(X0,sK1_skl(xS,slcrc0),slcrc0),slcrc0)
| ~ aElementOf0(sK3_skl(X0,sK1_skl(xS,slcrc0),slcrc0),X0)
| ~ aSet0(X0)
| X0 = sdtmndt0(slcrc0,sK1_skl(xS,slcrc0)) ) ),
introduced(definition,[new_symbols(definition,[sQ375_spl])],[split_symbol_definition]) ).
fof(f5346,plain,
( ~ sQ268_spl
| sQ375_spl
| ~ sQ105_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f5339,f132,f1469,f5343,f3398]) ).
fof(f5347,definition,
! [X0] :
( sQ376_spl
<=> ( ~ aElementOf0(sK3_skl(X0,sK0_skl(slcrc0),slcrc0),slcrc0)
| ~ aElementOf0(sK3_skl(X0,sK0_skl(slcrc0),slcrc0),X0)
| ~ aSet0(X0)
| X0 = sdtmndt0(slcrc0,sK0_skl(slcrc0)) ) ),
introduced(definition,[new_symbols(definition,[sQ376_spl])],[split_symbol_definition]) ).
fof(f5350,plain,
( ~ sQ201_spl
| sQ376_spl
| ~ sQ101_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f5340,f132,f1408,f5347,f2551]) ).
fof(f5351,definition,
! [X0] :
( sQ377_spl
<=> ( ~ aElementOf0(sK3_skl(X0,sK0_skl(xS),slcrc0),slcrc0)
| ~ aElementOf0(sK3_skl(X0,sK0_skl(xS),slcrc0),X0)
| ~ aSet0(X0)
| X0 = sdtmndt0(slcrc0,sK0_skl(xS)) ) ),
introduced(definition,[new_symbols(definition,[sQ377_spl])],[split_symbol_definition]) ).
fof(f5354,plain,
( ~ sQ269_spl
| sQ377_spl
| ~ sQ18_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f5341,f132,f258,f5351,f3403]) ).
fof(f5355,definition,
! [X0] :
( sQ378_spl
<=> ( ~ aElementOf0(sK3_skl(X0,xx,slcrc0),slcrc0)
| ~ aElementOf0(sK3_skl(X0,xx,slcrc0),X0)
| ~ aSet0(X0)
| X0 = sdtmndt0(slcrc0,xx) ) ),
introduced(definition,[new_symbols(definition,[sQ378_spl])],[split_symbol_definition]) ).
fof(f5358,plain,
( ~ sQ249_spl
| sQ378_spl
| ~ sQ9_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f5342,f132,f185,f5355,f2978]) ).
fof(f5364,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtmndt0(xS,sK3_skl(X2,X1,X0)),sK3_skl(X2,X1,X0)) = xS
| ~ aSubsetOf0(X2,xS)
| ~ aSet0(xS)
| sP0_prd(sK3_skl(X2,X1,X0),X1,X0)
| X2 = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f4609,f4100]) ).
fof(f5369,plain,
! [X0,X1,X2] :
( ~ aSubsetOf0(X2,slcrc0)
| ~ aSet0(slcrc0)
| sP0_prd(sK3_skl(X2,X1,X0),X1,X0)
| X2 = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f4609,f107]) ).
fof(f5372,definition,
! [X0,X1,X2] :
( sQ379_spl
<=> ( sdtpldt0(sdtmndt0(xS,sK3_skl(X2,X1,X0)),sK3_skl(X2,X1,X0)) = xS
| ~ aSubsetOf0(X2,xS)
| sP0_prd(sK3_skl(X2,X1,X0),X1,X0)
| X2 = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ379_spl])],[split_symbol_definition]) ).
fof(f5375,plain,
( ~ sQ5_spl
| sQ379_spl ),
inference(split_clause,[status(thm)],[f5364,f5372,f163]) ).
fof(f5377,definition,
! [X0,X1,X2] :
( sQ380_spl
<=> ( ~ aSubsetOf0(X2,slcrc0)
| sP0_prd(sK3_skl(X2,X1,X0),X1,X0)
| X2 = sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ380_spl])],[split_symbol_definition]) ).
fof(f5380,plain,
( ~ sQ3_spl
| sQ380_spl ),
inference(split_clause,[status(thm)],[f5369,f5377,f132]) ).
fof(f5397,plain,
! [X0,X1,X2] :
( ~ sQ157_spl
| ~ aSubsetOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
| sP0_prd(sK3_skl(X0,X1,X2),X1,X2)
| X0 = sdtmndt0(X2,X1)
| ~ aElement0(X1)
| ~ aSet0(X2)
| sdtpldt0(sdtmndt0(xS,sK3_skl(X0,X1,X2)),sK3_skl(X0,X1,X2)) = xS ),
inference(resolution,[status(thm)],[f2036,f4609]) ).
fof(f5398,plain,
! [X0,X1] :
( ~ sQ157_spl
| sP0_prd(sK3_skl(sdtmndt0(sdtpldt0(xS,xx),xx),X0,X1),X0,X1)
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
| sdtmndt0(sdtpldt0(xS,xx),xx) = sdtmndt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| sdtpldt0(sdtmndt0(xS,sK3_skl(sdtmndt0(sdtpldt0(xS,xx),xx),X0,X1)),sK3_skl(sdtmndt0(sdtpldt0(xS,xx),xx),X0,X1)) = xS ),
inference(resolution,[status(thm)],[f2036,f85]) ).
fof(f5399,plain,
! [X0,X1,X2] :
( ~ sQ157_spl
| aElementOf0(sK2_skl(X0,X1,sdtmndt0(sdtpldt0(xS,xx),xx)),X2)
| ~ aSubsetOf0(X0,X2)
| ~ aSet0(X2)
| sK2_skl(X0,X1,sdtmndt0(sdtpldt0(xS,xx),xx)) = X1
| X0 = sdtpldt0(sdtmndt0(sdtpldt0(xS,xx),xx),X1)
| ~ aElement0(X1)
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
| sdtpldt0(sdtmndt0(xS,sK2_skl(X0,X1,sdtmndt0(sdtpldt0(xS,xx),xx))),sK2_skl(X0,X1,sdtmndt0(sdtpldt0(xS,xx),xx))) = xS ),
inference(resolution,[status(thm)],[f2036,f4764]) ).
fof(f5400,plain,
! [X0,X1] :
( ~ sQ157_spl
| sK2_skl(sdtmndt0(sdtpldt0(xS,xx),xx),X0,X1) = X0
| aElementOf0(sK2_skl(sdtmndt0(sdtpldt0(xS,xx),xx),X0,X1),X1)
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
| sdtmndt0(sdtpldt0(xS,xx),xx) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| sdtpldt0(sdtmndt0(xS,sK2_skl(sdtmndt0(sdtpldt0(xS,xx),xx),X0,X1)),sK2_skl(sdtmndt0(sdtpldt0(xS,xx),xx),X0,X1)) = xS ),
inference(resolution,[status(thm)],[f2036,f74]) ).
fof(f5402,plain,
( ~ sQ141_spl
| ~ sQ157_spl
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
| slcrc0 = sdtmndt0(sdtpldt0(xS,xx),xx)
| sdtpldt0(sdtmndt0(xS,sK1_skl(sdtmndt0(sdtpldt0(xS,xx),xx),slcrc0)),sK1_skl(sdtmndt0(sdtpldt0(xS,xx),xx),slcrc0)) = xS ),
inference(resolution,[status(thm)],[f2036,f1929]) ).
fof(f5403,plain,
! [X0] :
( ~ sQ157_spl
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
| aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),X0)
| ~ aSet0(X0)
| sdtpldt0(sdtmndt0(xS,sK1_skl(sdtmndt0(sdtpldt0(xS,xx),xx),X0)),sK1_skl(sdtmndt0(sdtpldt0(xS,xx),xx),X0)) = xS ),
inference(resolution,[status(thm)],[f2036,f52]) ).
fof(f5404,plain,
( ~ sQ157_spl
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
| sdtmndt0(sdtpldt0(xS,xx),xx) = slcrc0
| sdtpldt0(sdtmndt0(xS,sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))),sK0_skl(sdtmndt0(sdtpldt0(xS,xx),xx))) = xS ),
inference(resolution,[status(thm)],[f2036,f38]) ).
fof(f5405,definition,
! [X0,X1,X2] :
( sQ383_spl
<=> ( ~ aSubsetOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| sP0_prd(sK3_skl(X0,X1,X2),X1,X2)
| X0 = sdtmndt0(X2,X1)
| ~ aElement0(X1)
| ~ aSet0(X2)
| sdtpldt0(sdtmndt0(xS,sK3_skl(X0,X1,X2)),sK3_skl(X0,X1,X2)) = xS ) ),
introduced(definition,[new_symbols(definition,[sQ383_spl])],[split_symbol_definition]) ).
fof(f5408,plain,
( ~ sQ157_spl
| ~ sQ4_spl
| sQ383_spl ),
inference(split_clause,[status(thm)],[f5397,f5405,f160,f2035]) ).
fof(f5409,definition,
! [X0,X1] :
( sQ384_spl
<=> ( sP0_prd(sK3_skl(sdtmndt0(sdtpldt0(xS,xx),xx),X0,X1),X0,X1)
| sdtmndt0(sdtpldt0(xS,xx),xx) = sdtmndt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| sdtpldt0(sdtmndt0(xS,sK3_skl(sdtmndt0(sdtpldt0(xS,xx),xx),X0,X1)),sK3_skl(sdtmndt0(sdtpldt0(xS,xx),xx),X0,X1)) = xS ) ),
introduced(definition,[new_symbols(definition,[sQ384_spl])],[split_symbol_definition]) ).
fof(f5412,plain,
( ~ sQ157_spl
| ~ sQ4_spl
| sQ384_spl ),
inference(split_clause,[status(thm)],[f5398,f5409,f160,f2035]) ).
fof(f5413,definition,
! [X0,X1,X2] :
( sQ385_spl
<=> ( aElementOf0(sK2_skl(X0,X1,sdtmndt0(sdtpldt0(xS,xx),xx)),X2)
| ~ aSubsetOf0(X0,X2)
| ~ aSet0(X2)
| sK2_skl(X0,X1,sdtmndt0(sdtpldt0(xS,xx),xx)) = X1
| X0 = sdtpldt0(sdtmndt0(sdtpldt0(xS,xx),xx),X1)
| ~ aElement0(X1)
| sdtpldt0(sdtmndt0(xS,sK2_skl(X0,X1,sdtmndt0(sdtpldt0(xS,xx),xx))),sK2_skl(X0,X1,sdtmndt0(sdtpldt0(xS,xx),xx))) = xS ) ),
introduced(definition,[new_symbols(definition,[sQ385_spl])],[split_symbol_definition]) ).
fof(f5416,plain,
( ~ sQ157_spl
| ~ sQ4_spl
| sQ385_spl ),
inference(split_clause,[status(thm)],[f5399,f5413,f160,f2035]) ).
fof(f5417,definition,
! [X0,X1] :
( sQ386_spl
<=> ( sK2_skl(sdtmndt0(sdtpldt0(xS,xx),xx),X0,X1) = X0
| aElementOf0(sK2_skl(sdtmndt0(sdtpldt0(xS,xx),xx),X0,X1),X1)
| sdtmndt0(sdtpldt0(xS,xx),xx) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| sdtpldt0(sdtmndt0(xS,sK2_skl(sdtmndt0(sdtpldt0(xS,xx),xx),X0,X1)),sK2_skl(sdtmndt0(sdtpldt0(xS,xx),xx),X0,X1)) = xS ) ),
introduced(definition,[new_symbols(definition,[sQ386_spl])],[split_symbol_definition]) ).
fof(f5420,plain,
( ~ sQ157_spl
| ~ sQ4_spl
| sQ386_spl ),
inference(split_clause,[status(thm)],[f5400,f5417,f160,f2035]) ).
fof(f5421,definition,
( sQ387_spl
<=> sdtpldt0(sdtmndt0(xS,sK1_skl(sdtmndt0(sdtpldt0(xS,xx),xx),slcrc0)),sK1_skl(sdtmndt0(sdtpldt0(xS,xx),xx),slcrc0)) = xS ),
introduced(definition,[new_symbols(definition,[sQ387_spl])],[split_symbol_definition]) ).
fof(f5424,plain,
( ~ sQ141_spl
| ~ sQ157_spl
| ~ sQ4_spl
| sQ11_spl
| sQ387_spl ),
inference(split_clause,[status(thm)],[f5402,f5421,f219,f160,f2035,f1928]) ).
fof(f5425,definition,
! [X0] :
( sQ388_spl
<=> ( aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),X0)
| ~ aSet0(X0)
| sdtpldt0(sdtmndt0(xS,sK1_skl(sdtmndt0(sdtpldt0(xS,xx),xx),X0)),sK1_skl(sdtmndt0(sdtpldt0(xS,xx),xx),X0)) = xS ) ),
introduced(definition,[new_symbols(definition,[sQ388_spl])],[split_symbol_definition]) ).
fof(f5428,plain,
( ~ sQ157_spl
| ~ sQ4_spl
| sQ388_spl ),
inference(split_clause,[status(thm)],[f5403,f5425,f160,f2035]) ).
fof(f5429,plain,
( ~ sQ157_spl
| ~ sQ4_spl
| sQ11_spl
| sQ72_spl ),
inference(split_clause,[status(thm)],[f5404,f764,f219,f160,f2035]) ).
fof(f5485,plain,
! [X0,X1] :
( sdtpldt0(sdtmndt0(xS,sK1_skl(X1,X0)),sK1_skl(X1,X0)) = xS
| ~ aSubsetOf0(X1,xS)
| ~ aSet0(xS)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f4602,f4100]) ).
fof(f5488,plain,
! [X0,X1] :
( ~ sQ157_spl
| sdtpldt0(sdtmndt0(xS,sK1_skl(X1,X0)),sK1_skl(X1,X0)) = xS
| ~ aSubsetOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f4602,f2036]) ).
fof(f5492,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,slcrc0)
| ~ aSet0(slcrc0)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f4602,f107]) ).
fof(f5494,definition,
! [X0,X1] :
( sQ389_spl
<=> ( sdtpldt0(sdtmndt0(xS,sK1_skl(X1,X0)),sK1_skl(X1,X0)) = xS
| ~ aSubsetOf0(X1,xS)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ389_spl])],[split_symbol_definition]) ).
fof(f5497,plain,
( ~ sQ5_spl
| sQ389_spl ),
inference(split_clause,[status(thm)],[f5485,f5494,f163]) ).
fof(f5498,definition,
! [X0,X1] :
( sQ390_spl
<=> ( sdtpldt0(sdtmndt0(xS,sK1_skl(X1,X0)),sK1_skl(X1,X0)) = xS
| ~ aSubsetOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx))
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ390_spl])],[split_symbol_definition]) ).
fof(f5501,plain,
( ~ sQ157_spl
| ~ sQ4_spl
| sQ390_spl ),
inference(split_clause,[status(thm)],[f5488,f5498,f160,f2035]) ).
fof(f5503,definition,
! [X0,X1] :
( sQ391_spl
<=> ( ~ aSubsetOf0(X1,slcrc0)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ391_spl])],[split_symbol_definition]) ).
fof(f5506,plain,
( ~ sQ3_spl
| sQ391_spl ),
inference(split_clause,[status(thm)],[f5492,f5503,f132]) ).
fof(f5534,definition,
! [X0,X1] :
( sQ393_spl
<=> ( ~ aSubsetOf0(sdtmndt0(X0,xx),X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ393_spl])],[split_symbol_definition]) ).
fof(f5535,plain,
! [X0,X1] :
( ~ sQ393_spl
| ~ aSubsetOf0(sdtmndt0(X0,xx),X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f5534]) ).
fof(f5543,plain,
( ~ sQ80_spl
| ~ sQ393_spl
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f5535,f3056]) ).
fof(f5548,plain,
( ~ sQ393_spl
| ~ sQ80_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f5543,f163,f807,f5534]) ).
fof(f5732,plain,
! [X0] :
( ~ sQ8_spl
| aSubsetOf0(slcrc0,slcrc0)
| ~ aSubsetOf0(sdtpldt0(xS,xx),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f4120,f4975]) ).
fof(f5747,plain,
( ~ sQ8_spl
| sQ137_spl
| sQ291_spl ),
inference(split_clause,[status(thm)],[f5732,f3644,f1904,f182]) ).
fof(f5792,plain,
( ~ sQ322_spl
| sQ213_spl
| ~ aElementOf0(sK1_skl(xS,sdtmndt0(sdtpldt0(xS,xx),xx)),xS) ),
inference(resolution,[status(thm)],[f2666,f3937]) ).
fof(f5794,plain,
( ~ sQ322_spl
| sQ213_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f5792,f166,f2664,f3936]) ).
fof(f5796,plain,
$false,
inference(sat_refutation,[status(thm)],[f105,f169,f179,f188,f190,f199,f201,f222,f264,f268,f272,f300,f315,f345,f352,f362,f394,f419,f444,f448,f452,f456,f460,f464,f476,f483,f487,f498,f502,f516,f520,f530,f534,f561,f588,f607,f622,f639,f680,f763,f767,f780,f787,f794,f806,f813,f817,f821,f845,f849,f853,f857,f861,f877,f906,f980,f1047,f1063,f1082,f1135,f1211,f1264,f1265,f1267,f1368,f1382,f1389,f1585,f1590,f1595,f1612,f1661,f1679,f1692,f1695,f1702,f1703,f1732,f1747,f1751,f1755,f1800,f1804,f1808,f1830,f1847,f1860,f1869,f1878,f1882,f1896,f1911,f1916,f1927,f1931,f1935,f1944,f1950,f1964,f1969,f1994,f2006,f2018,f2022,f2026,f2030,f2034,f2038,f2047,f2051,f2055,f2151,f2172,f2180,f2187,f2223,f2226,f2256,f2260,f2262,f2269,f2273,f2277,f2348,f2524,f2528,f2533,f2554,f2561,f2569,f2576,f2609,f2640,f2644,f2648,f2653,f2667,f2697,f2758,f2760,f2761,f2783,f2805,f2816,f2831,f2842,f2846,f2867,f2871,f2875,f2889,f2893,f2936,f2940,f2944,f2948,f2957,f2961,f2965,f2969,f2973,f2977,f2982,f2986,f2990,f3026,f3124,f3148,f3174,f3179,f3203,f3215,f3230,f3250,f3256,f3294,f3322,f3339,f3363,f3401,f3402,f3406,f3442,f3461,f3466,f3474,f3494,f3498,f3502,f3506,f3510,f3521,f3535,f3539,f3543,f3578,f3587,f3595,f3604,f3610,f3628,f3631,f3650,f3658,f3686,f3692,f3699,f3706,f3729,f3733,f3737,f3742,f3750,f3754,f3786,f3793,f3803,f3808,f3814,f3836,f3849,f3853,f3857,f3862,f3866,f3874,f3890,f3894,f3939,f3943,f3959,f3963,f3967,f3971,f3976,f3980,f4020,f4033,f4044,f4060,f4074,f4090,f4155,f4161,f4166,f4174,f4175,f4197,f4211,f4260,f4449,f4458,f4502,f4510,f4526,f4532,f4547,f4564,f4568,f4601,f4658,f4663,f4678,f4682,f4686,f4694,f4698,f4702,f4719,f4720,f4807,f4811,f4897,f5221,f5225,f5229,f5233,f5274,f5333,f5337,f5346,f5350,f5354,f5358,f5375,f5380,f5408,f5412,f5416,f5420,f5424,f5428,f5429,f5497,f5501,f5506,f5548,f5747,f5794]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM537+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n020.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 02:39:17 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 67.49/9.04 % Refutation found
% 67.49/9.04 % SZS status Theorem for theBenchmark: Theorem is valid
% 67.49/9.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 25.02/9.10 % Elapsed time: 8.644696 seconds
% 25.02/9.10 % CPU time: 68.077996 seconds
% 25.02/9.10 % Total memory used: 347.444 MB
% 25.02/9.10 % Net memory used: 307.715 MB
%------------------------------------------------------------------------------