%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM535+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 0.11s 0.43s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 58
% Syntax : Number of formulae : 264 ( 13 unt; 52 def)
% Number of atoms : 1188 ( 163 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 1491 ( 567 ~; 620 |; 207 &)
% ( 76 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 55 ( 53 usr; 49 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 271 ( 251 !; 20 ?)
% 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(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(f17,hypothesis,
aSet0(xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
aElementOf0(xx,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
( ( ( ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
=> aElementOf0(W0,xS) ) ) ) )
& ( ( ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ! [W0] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ( ( ( ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
=> aElementOf0(W0,xS) ) ) ) )
& ( ( ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ! [W0] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f27,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f28,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f31,plain,
! [W0] :
( W0 = slcrc0
<=> ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f32,plain,
! [W0] :
( ( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(NNF_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
( ! [W0] :
( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ! [W0] :
( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f34,plain,
( ! [W0] :
( aElementOf0(sK0_skl(W0),W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ! [W0] :
( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(W1,sK0_skl(W0))],[f33]) ).
fof(f35,plain,
! [X0] :
( aSet0(X0)
| X0 != slcrc0 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| X0 != slcrc0 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f37,plain,
! [X0] :
( aElementOf0(sK0_skl(X0),X0)
| ~ aSet0(X0)
| X0 = slcrc0 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f45,plain,
! [W0] :
( ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) ) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f46,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f48,plain,
! [W0] :
( ( ! [W1] :
( ( ~ aElementOf0(sK1_skl(W1,W0),W0)
& aElementOf0(sK1_skl(W1,W0),W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f51,plain,
! [X0,X1] :
( aElementOf0(sK1_skl(X1,X0),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f52,plain,
! [X0,X1] :
( ~ aElementOf0(sK1_skl(X1,X0),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f57,plain,
! [W0,W1] :
( W0 = W1
| ~ aSubsetOf0(W1,W0)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f58,plain,
! [X0,X1] :
( X0 = X1
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f59,plain,
! [W0,W1,W2] :
( aSubsetOf0(W0,W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W2)
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f60,plain,
! [X0,X1,X2] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtpldt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) ) )
& aSet0(W2) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f62,plain,
! [W0,W1] :
( ! [W2] :
( ( ? [W3] :
( ( ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) )
| aElementOf0(W3,W2) )
& ( ( W3 != W1
& ~ aElementOf0(W3,W0) )
| ~ aElement0(W3)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtpldt0(W0,W1) )
& ( ( ! [W3] :
( ( ( W3 != W1
& ~ aElementOf0(W3,W0) )
| ~ aElement0(W3)
| aElementOf0(W3,W2) )
& ( ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtpldt0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
! [W0,W1] :
( ( ! [W2] :
( ? [W3] :
( ( ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) )
| aElementOf0(W3,W2) )
& ( ( W3 != W1
& ~ aElementOf0(W3,W0) )
| ~ aElement0(W3)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtpldt0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ( W3 != W1
& ~ aElementOf0(W3,W0) )
| ~ aElement0(W3)
| aElementOf0(W3,W2) )
& ! [W3] :
( ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtpldt0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f62]) ).
fof(f64,plain,
! [W0,W1] :
( ( ! [W2] :
( ( ( ( ( sK2_skl(W2,W1,W0) = W1
| aElementOf0(sK2_skl(W2,W1,W0),W0) )
& aElement0(sK2_skl(W2,W1,W0)) )
| aElementOf0(sK2_skl(W2,W1,W0),W2) )
& ( ( sK2_skl(W2,W1,W0) != W1
& ~ aElementOf0(sK2_skl(W2,W1,W0),W0) )
| ~ aElement0(sK2_skl(W2,W1,W0))
| ~ aElementOf0(sK2_skl(W2,W1,W0),W2) ) )
| ~ aSet0(W2)
| W2 = sdtpldt0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ( W3 != W1
& ~ aElementOf0(W3,W0) )
| ~ aElement0(W3)
| aElementOf0(W3,W2) )
& ! [W3] :
( ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtpldt0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(W3,sK2_skl(W2,W1,W0))],[f63]) ).
fof(f65,plain,
! [X0,X1,X2] :
( aSet0(X2)
| X2 != sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f67,plain,
! [X0,X1,X2,X3] :
( X3 = X1
| aElementOf0(X3,X0)
| ~ aElementOf0(X3,X2)
| X2 != sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| aElementOf0(X3,X2)
| X2 != sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( X3 != X1
| ~ aElement0(X3)
| aElementOf0(X3,X2)
| X2 != sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ aElementOf0(sK2_skl(X2,X1,X0),X0)
| ~ aElement0(sK2_skl(X2,X1,X0))
| ~ aElementOf0(sK2_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f71,plain,
! [X0,X1,X2] :
( sK2_skl(X2,X1,X0) != X1
| ~ aElement0(sK2_skl(X2,X1,X0))
| ~ aElementOf0(sK2_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f73,plain,
! [X0,X1,X2] :
( sK2_skl(X2,X1,X0) = X1
| aElementOf0(sK2_skl(X2,X1,X0),X0)
| aElementOf0(sK2_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f85,plain,
aSet0(xS),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f86,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f87,plain,
( ( ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& ? [W0] :
( ~ aElementOf0(W0,xS)
& aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xS,xx)) )
| ( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& ? [W0] :
( ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(W0,xS) )
& ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xS,xx)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f88,definition,
( sP1_prd
<=> ( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& ? [W0] :
( ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(W0,xS) )
& ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f89,plain,
( ( ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& ? [W0] :
( ~ aElementOf0(W0,xS)
& aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xS,xx)) )
| sP1_prd ),
inference(formula_renaming,[status(thm)],[f87,f88]) ).
fof(f90,plain,
( ( ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& ? [W0] :
( ~ aElementOf0(W0,xS)
& aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ! [W0] :
( ( ( W0 != xx
& ~ aElementOf0(W0,sdtmndt0(xS,xx)) )
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( ( W0 = xx
| ~ aElementOf0(W0,xS)
| ~ aElement0(W0)
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& ( ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) )
| ~ aElementOf0(W0,sdtmndt0(xS,xx)) ) )
& aSet0(sdtmndt0(xS,xx)) )
| sP1_prd ),
inference(NNF_transformation,[status(thm)],[f89]) ).
fof(f91,plain,
( ( ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& ? [W0] :
( ~ aElementOf0(W0,xS)
& aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ! [W0] :
( ( W0 != xx
& ~ aElementOf0(W0,sdtmndt0(xS,xx)) )
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ! [W0] :
( ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( W0 = xx
| ~ aElementOf0(W0,xS)
| ~ aElement0(W0)
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& ! [W0] :
( ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) )
| ~ aElementOf0(W0,sdtmndt0(xS,xx)) )
& aSet0(sdtmndt0(xS,xx)) )
| sP1_prd ),
inference(miniscoping,[status(thm)],[f90]) ).
fof(f92,plain,
( ( ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& ~ aElementOf0(sK4_skl,xS)
& aElementOf0(sK4_skl,sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( ( W0 != xx
& ~ aElementOf0(W0,sdtmndt0(xS,xx)) )
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ! [W0] :
( ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( W0 = xx
| ~ aElementOf0(W0,xS)
| ~ aElement0(W0)
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& ! [W0] :
( ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) )
| ~ aElementOf0(W0,sdtmndt0(xS,xx)) )
& aSet0(sdtmndt0(xS,xx)) )
| sP1_prd ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(W0,sK4_skl)],[f91]) ).
fof(f93,plain,
( aSet0(sdtmndt0(xS,xx))
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f95,plain,
! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtmndt0(xS,xx))
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f100,plain,
! [X0] :
( X0 = xx
| aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f103,plain,
( aElementOf0(sK4_skl,sdtpldt0(sdtmndt0(xS,xx),xx))
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f104,plain,
( ~ aElementOf0(sK4_skl,xS)
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f105,plain,
( ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f112,definition,
! [W0] :
( sP2_prd(W0)
<=> ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f113,plain,
( sP1_prd
<=> ( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& ? [W0] :
( ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(W0,xS) )
& ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> sP2_prd(W0) )
& aSet0(sdtmndt0(xS,xx)) ) ),
inference(formula_renaming,[status(thm)],[f88,f112]) ).
fof(f114,plain,
( ( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(W0,xS) )
| ? [W0] :
( ( ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) )
| aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ( W0 != xx
& ~ aElementOf0(W0,sdtmndt0(xS,xx)) )
| ~ aElement0(W0)
| ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ? [W0] :
( ( sP2_prd(W0)
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& ( ~ sP2_prd(W0)
| ~ aElementOf0(W0,sdtmndt0(xS,xx)) ) )
| ~ aSet0(sdtmndt0(xS,xx))
| sP1_prd )
& ( ( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& ? [W0] :
( ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(W0,xS) )
& ! [W0] :
( ( ( W0 != xx
& ~ aElementOf0(W0,sdtmndt0(xS,xx)) )
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( ( ~ sP2_prd(W0)
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& ( sP2_prd(W0)
| ~ aElementOf0(W0,sdtmndt0(xS,xx)) ) )
& aSet0(sdtmndt0(xS,xx)) )
| ~ sP1_prd ) ),
inference(NNF_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
( ( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(W0,xS) )
| ? [W0] :
( ( ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) )
| aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ( W0 != xx
& ~ aElementOf0(W0,sdtmndt0(xS,xx)) )
| ~ aElement0(W0)
| ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ? [W0] :
( ( sP2_prd(W0)
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& ( ~ sP2_prd(W0)
| ~ aElementOf0(W0,sdtmndt0(xS,xx)) ) )
| ~ aSet0(sdtmndt0(xS,xx))
| sP1_prd )
& ( ( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& ? [W0] :
( ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(W0,xS) )
& ! [W0] :
( ( W0 != xx
& ~ aElementOf0(W0,sdtmndt0(xS,xx)) )
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ! [W0] :
( ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( ~ sP2_prd(W0)
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& ! [W0] :
( sP2_prd(W0)
| ~ aElementOf0(W0,sdtmndt0(xS,xx)) )
& aSet0(sdtmndt0(xS,xx)) )
| ~ sP1_prd ) ),
inference(miniscoping,[status(thm)],[f114]) ).
fof(f116,plain,
( ( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(W0,xS) )
| ( ( ( ( sK7_skl = xx
| aElementOf0(sK7_skl,sdtmndt0(xS,xx)) )
& aElement0(sK7_skl) )
| aElementOf0(sK7_skl,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ( sK7_skl != xx
& ~ aElementOf0(sK7_skl,sdtmndt0(xS,xx)) )
| ~ aElement0(sK7_skl)
| ~ aElementOf0(sK7_skl,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ( ( sP2_prd(sK6_skl)
| aElementOf0(sK6_skl,sdtmndt0(xS,xx)) )
& ( ~ sP2_prd(sK6_skl)
| ~ aElementOf0(sK6_skl,sdtmndt0(xS,xx)) ) )
| ~ aSet0(sdtmndt0(xS,xx))
| sP1_prd )
& ( ( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& ~ aElementOf0(sK5_skl,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(sK5_skl,xS)
& ! [W0] :
( ( W0 != xx
& ~ aElementOf0(W0,sdtmndt0(xS,xx)) )
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ! [W0] :
( ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( ~ sP2_prd(W0)
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& ! [W0] :
( sP2_prd(W0)
| ~ aElementOf0(W0,sdtmndt0(xS,xx)) )
& aSet0(sdtmndt0(xS,xx)) )
| ~ sP1_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl,sK7_skl]),skolemize(W0,sK5_skl),skolemize(W0,sK6_skl),skolemize(W0,sK7_skl)],[f115]) ).
fof(f117,plain,
( aSet0(sdtmndt0(xS,xx))
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f118,plain,
! [X0] :
( sP2_prd(X0)
| ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f119,plain,
! [X0] :
( ~ sP2_prd(X0)
| aElementOf0(X0,sdtmndt0(xS,xx))
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f122,plain,
! [X0] :
( X0 = xx
| aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f125,plain,
( aElementOf0(sK5_skl,xS)
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f126,plain,
( ~ aElementOf0(sK5_skl,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f136,plain,
! [W0] :
( ( W0 = xx
| ~ aElementOf0(W0,xS)
| ~ aElement0(W0)
| sP2_prd(W0) )
& ( ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) )
| ~ sP2_prd(W0) ) ),
inference(NNF_transformation,[status(thm)],[f112]) ).
fof(f137,plain,
( ! [W0] :
( W0 = xx
| ~ aElementOf0(W0,xS)
| ~ aElement0(W0)
| sP2_prd(W0) )
& ! [W0] :
( ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) )
| ~ sP2_prd(W0) ) ),
inference(miniscoping,[status(thm)],[f136]) ).
fof(f138,plain,
! [X0] :
( aElement0(X0)
| ~ sP2_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f139,plain,
! [X0] :
( aElementOf0(X0,xS)
| ~ sP2_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f140,plain,
! [X0] :
( X0 != xx
| ~ sP2_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f141,plain,
! [X0] :
( X0 = xx
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| sP2_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f142,definition,
( sQ0_spl
<=> sP1_prd ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f145,definition,
( sQ1_spl
<=> aSet0(sdtmndt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f148,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f93,f142,f145]) ).
fof(f153,definition,
! [X0] :
( sQ3_spl
<=> ( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f154,plain,
! [X0] :
( ~ sQ3_spl
| aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f95,f142,f153]) ).
fof(f173,definition,
! [X0] :
( sQ8_spl
<=> ( X0 = xx
| aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f174,plain,
! [X0] :
( ~ sQ8_spl
| X0 = xx
| aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f176,plain,
( sQ8_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f100,f142,f173]) ).
fof(f185,definition,
( sQ11_spl
<=> aElementOf0(sK4_skl,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f186,plain,
( ~ sQ11_spl
| aElementOf0(sK4_skl,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(component_clause,[status(thm)],[f185]) ).
fof(f188,plain,
( sQ11_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f103,f142,f185]) ).
fof(f189,definition,
( sQ12_spl
<=> aElementOf0(sK4_skl,xS) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f191,plain,
( sQ12_spl
| ~ aElementOf0(sK4_skl,xS) ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,plain,
( ~ sQ12_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f104,f142,f189]) ).
fof(f193,definition,
( sQ13_spl
<=> aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f195,plain,
( sQ13_spl
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,plain,
( ~ sQ13_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f105,f142,f193]) ).
fof(f197,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f117,f142,f145]) ).
fof(f198,definition,
! [X0] :
( sQ14_spl
<=> ( sP2_prd(X0)
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f199,plain,
! [X0] :
( ~ sQ14_spl
| sP2_prd(X0)
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(component_clause,[status(thm)],[f198]) ).
fof(f201,plain,
( sQ14_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f118,f142,f198]) ).
fof(f202,definition,
! [X0] :
( sQ15_spl
<=> ( ~ sP2_prd(X0)
| aElementOf0(X0,sdtmndt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f203,plain,
! [X0] :
( ~ sQ15_spl
| ~ sP2_prd(X0)
| aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f205,plain,
( sQ15_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f119,f142,f202]) ).
fof(f208,plain,
( sQ8_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f122,f142,f173]) ).
fof(f211,definition,
( sQ16_spl
<=> aElementOf0(sK5_skl,xS) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f212,plain,
( ~ sQ16_spl
| aElementOf0(sK5_skl,xS) ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f214,plain,
( sQ16_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f125,f142,f211]) ).
fof(f215,definition,
( sQ17_spl
<=> aElementOf0(sK5_skl,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f217,plain,
( sQ17_spl
| ~ aElementOf0(sK5_skl,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f218,plain,
( ~ sQ17_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f126,f142,f215]) ).
fof(f252,plain,
aSet0(slcrc0),
inference(destructive_equality_resolution,[status(thm)],[f35]) ).
fof(f253,plain,
! [X0] : ~ aElementOf0(X0,slcrc0),
inference(destructive_equality_resolution,[status(thm)],[f36]) ).
fof(f255,plain,
! [X0,X1] :
( aSet0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f65]) ).
fof(f257,plain,
! [X0,X1,X2] :
( X2 = X1
| aElementOf0(X2,X0)
| ~ aElementOf0(X2,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f67]) ).
fof(f258,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X2,X0)
| ~ aElement0(X2)
| aElementOf0(X2,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f68]) ).
fof(f259,plain,
! [X0,X1] :
( ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f69]) ).
fof(f260,plain,
! [X0,X1] :
( aElementOf0(X1,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f259]) ).
fof(f265,plain,
~ sP2_prd(xx),
inference(destructive_equality_resolution,[status(thm)],[f140]) ).
fof(f268,plain,
( xx = xx
| ~ aElement0(xx)
| sP2_prd(xx) ),
inference(resolution,[status(thm)],[f86,f141]) ).
fof(f269,definition,
( sQ26_spl
<=> sP2_prd(xx) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f270,plain,
( ~ sQ26_spl
| sP2_prd(xx) ),
inference(component_clause,[status(thm)],[f269]) ).
fof(f272,definition,
( sQ27_spl
<=> aElement0(xx) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f274,plain,
( sQ27_spl
| ~ aElement0(xx) ),
inference(component_clause,[status(thm)],[f272]) ).
fof(f275,definition,
( sQ28_spl
<=> xx = xx ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f278,plain,
( sQ28_spl
| ~ sQ27_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f268,f269,f272,f275]) ).
fof(f279,plain,
( ~ sQ16_spl
| sK5_skl = xx
| ~ aElement0(sK5_skl)
| sP2_prd(sK5_skl) ),
inference(resolution,[status(thm)],[f212,f141]) ).
fof(f280,definition,
( sQ29_spl
<=> sP2_prd(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f281,plain,
( ~ sQ29_spl
| sP2_prd(sK5_skl) ),
inference(component_clause,[status(thm)],[f280]) ).
fof(f283,definition,
( sQ30_spl
<=> aElement0(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f285,plain,
( sQ30_spl
| ~ aElement0(sK5_skl) ),
inference(component_clause,[status(thm)],[f283]) ).
fof(f286,definition,
( sQ31_spl
<=> sK5_skl = xx ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f287,plain,
( ~ sQ31_spl
| sK5_skl = xx ),
inference(component_clause,[status(thm)],[f286]) ).
fof(f289,plain,
( ~ sQ16_spl
| sQ31_spl
| ~ sQ30_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f279,f280,f283,f286,f211]) ).
fof(f297,plain,
! [X0] :
( sQ30_spl
| ~ aElementOf0(sK5_skl,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f28,f285]) ).
fof(f299,plain,
( ~ sQ16_spl
| sQ30_spl
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f297,f212]) ).
fof(f300,plain,
( ~ sQ16_spl
| sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f299,f85]) ).
fof(f301,plain,
( ~ sQ16_spl
| sQ30_spl ),
inference(contradiction_clause,[status(thm)],[f300]) ).
fof(f302,plain,
( ~ aSet0(slcrc0)
| slcrc0 = slcrc0 ),
inference(resolution,[status(thm)],[f37,f253]) ).
fof(f303,plain,
( sK0_skl(xS) = xx
| ~ aElement0(sK0_skl(xS))
| sP2_prd(sK0_skl(xS))
| ~ aSet0(xS)
| xS = slcrc0 ),
inference(resolution,[status(thm)],[f37,f141]) ).
fof(f304,definition,
( sQ32_spl
<=> slcrc0 = slcrc0 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f307,definition,
( sQ33_spl
<=> aSet0(slcrc0) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f309,plain,
( sQ33_spl
| ~ aSet0(slcrc0) ),
inference(component_clause,[status(thm)],[f307]) ).
fof(f310,plain,
( ~ sQ33_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f302,f304,f307]) ).
fof(f311,definition,
( sQ34_spl
<=> xS = slcrc0 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f312,plain,
( ~ sQ34_spl
| xS = slcrc0 ),
inference(component_clause,[status(thm)],[f311]) ).
fof(f314,definition,
( sQ35_spl
<=> aSet0(xS) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f316,plain,
( sQ35_spl
| ~ aSet0(xS) ),
inference(component_clause,[status(thm)],[f314]) ).
fof(f317,definition,
( sQ36_spl
<=> sP2_prd(sK0_skl(xS)) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f318,plain,
( ~ sQ36_spl
| sP2_prd(sK0_skl(xS)) ),
inference(component_clause,[status(thm)],[f317]) ).
fof(f320,definition,
( sQ37_spl
<=> aElement0(sK0_skl(xS)) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f322,plain,
( sQ37_spl
| ~ aElement0(sK0_skl(xS)) ),
inference(component_clause,[status(thm)],[f320]) ).
fof(f323,definition,
( sQ38_spl
<=> sK0_skl(xS) = xx ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f324,plain,
( ~ sQ38_spl
| sK0_skl(xS) = xx ),
inference(component_clause,[status(thm)],[f323]) ).
fof(f326,plain,
( sQ38_spl
| ~ sQ37_spl
| sQ36_spl
| ~ sQ35_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f303,f311,f314,f317,f320,f323]) ).
fof(f327,plain,
( sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f316,f85]) ).
fof(f328,plain,
sQ35_spl,
inference(contradiction_clause,[status(thm)],[f327]) ).
fof(f329,plain,
( sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f309,f252]) ).
fof(f330,plain,
sQ33_spl,
inference(contradiction_clause,[status(thm)],[f329]) ).
fof(f337,plain,
( ~ sQ34_spl
| aElementOf0(xx,slcrc0) ),
inference(backward_demodulation,[status(thm)],[f312,f86]) ).
fof(f341,plain,
( ~ sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f337,f253]) ).
fof(f342,plain,
~ sQ34_spl,
inference(contradiction_clause,[status(thm)],[f341]) ).
fof(f344,plain,
( ~ sQ38_spl
| aElementOf0(xx,xS)
| ~ aSet0(xS)
| xS = slcrc0 ),
inference(paramodulation,[status(thm)],[f324,f37]) ).
fof(f345,definition,
( sQ39_spl
<=> aElementOf0(xx,xS) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f348,plain,
( ~ sQ38_spl
| sQ39_spl
| ~ sQ35_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f344,f311,f314,f345,f323]) ).
fof(f350,plain,
( ~ sQ36_spl
| aElement0(sK0_skl(xS)) ),
inference(resolution,[status(thm)],[f318,f138]) ).
fof(f351,plain,
( ~ sQ36_spl
| sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f350,f322]) ).
fof(f352,plain,
( ~ sQ36_spl
| sQ37_spl ),
inference(contradiction_clause,[status(thm)],[f351]) ).
fof(f353,plain,
! [X0,X1] :
( X1 = X0
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f58,f49]) ).
fof(f354,plain,
! [X0,X1] :
( aElementOf0(sK1_skl(X1,X0),X1)
| ~ aSet0(X1)
| ~ aSet0(X0)
| X1 = X0
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f353,f51]) ).
fof(f356,plain,
! [X0,X1] :
( aElementOf0(sK1_skl(X1,X0),X1)
| ~ aSet0(X1)
| X1 = X0
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f354]) ).
fof(f357,plain,
! [X0,X1] :
( aElementOf0(sK1_skl(X1,X0),X1)
| ~ aSet0(X1)
| X1 = X0
| ~ aSubsetOf0(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f356,f49]) ).
fof(f358,plain,
! [X0,X1,X2] :
( aSubsetOf0(X2,X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X2,X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f60,f49]) ).
fof(f366,plain,
( ~ sQ14_spl
| ~ aSet0(sdtmndt0(xS,xx))
| sdtmndt0(xS,xx) = slcrc0
| sP2_prd(sK0_skl(sdtmndt0(xS,xx))) ),
inference(resolution,[status(thm)],[f199,f37]) ).
fof(f367,definition,
( sQ40_spl
<=> sP2_prd(sK0_skl(sdtmndt0(xS,xx))) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f370,definition,
( sQ41_spl
<=> sdtmndt0(xS,xx) = slcrc0 ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f371,plain,
( ~ sQ41_spl
| sdtmndt0(xS,xx) = slcrc0 ),
inference(component_clause,[status(thm)],[f370]) ).
fof(f373,plain,
( ~ sQ14_spl
| ~ sQ1_spl
| sQ41_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f366,f367,f370,f145,f198]) ).
fof(f381,plain,
! [X0] :
( sQ27_spl
| ~ aElementOf0(xx,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f274,f28]) ).
fof(f382,plain,
( sQ27_spl
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f381,f86]) ).
fof(f384,plain,
( sQ27_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f382,f314,f272]) ).
fof(f386,plain,
( ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f270,f265]) ).
fof(f387,plain,
~ sQ26_spl,
inference(contradiction_clause,[status(thm)],[f386]) ).
fof(f389,plain,
! [X0] :
( ~ sP2_prd(sK1_skl(X0,xS))
| ~ aSet0(X0)
| aSubsetOf0(X0,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f52,f139]) ).
fof(f390,definition,
! [X0] :
( sQ42_spl
<=> ( ~ sP2_prd(sK1_skl(X0,xS))
| ~ aSet0(X0)
| aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f393,plain,
( sQ42_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f389,f314,f390]) ).
fof(f394,plain,
! [X0] :
( ~ sQ15_spl
| ~ aSet0(X0)
| aSubsetOf0(X0,sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| ~ sP2_prd(sK1_skl(X0,sdtmndt0(xS,xx))) ),
inference(resolution,[status(thm)],[f203,f52]) ).
fof(f395,definition,
! [X0] :
( sQ43_spl
<=> ( ~ aSet0(X0)
| aSubsetOf0(X0,sdtmndt0(xS,xx))
| ~ sP2_prd(sK1_skl(X0,sdtmndt0(xS,xx))) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f398,plain,
( ~ sQ15_spl
| ~ sQ1_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f394,f395,f145,f202]) ).
fof(f418,plain,
! [X0] :
( ~ aSet0(slcrc0)
| slcrc0 = X0
| ~ aSubsetOf0(X0,slcrc0) ),
inference(resolution,[status(thm)],[f357,f253]) ).
fof(f419,definition,
! [X0] :
( sQ46_spl
<=> ( slcrc0 = X0
| ~ aSubsetOf0(X0,slcrc0) ) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f420,plain,
! [X0] :
( ~ sQ46_spl
| slcrc0 = X0
| ~ aSubsetOf0(X0,slcrc0) ),
inference(component_clause,[status(thm)],[f419]) ).
fof(f422,plain,
( ~ sQ33_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f418,f419,f307]) ).
fof(f423,plain,
! [X0,X1] :
( ~ sQ46_spl
| ~ aSubsetOf0(X1,slcrc0)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(slcrc0)
| ~ aSet0(X1)
| slcrc0 = X0 ),
inference(resolution,[status(thm)],[f420,f358]) ).
fof(f424,plain,
! [X0] :
( ~ sQ46_spl
| aElementOf0(sK1_skl(X0,slcrc0),X0)
| ~ aSet0(X0)
| ~ aSet0(slcrc0)
| slcrc0 = X0 ),
inference(resolution,[status(thm)],[f420,f51]) ).
fof(f426,definition,
! [X0,X1] :
( sQ47_spl
<=> ( ~ aSubsetOf0(X1,slcrc0)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| slcrc0 = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f427,plain,
! [X0,X1] :
( ~ sQ47_spl
| ~ aSubsetOf0(X1,slcrc0)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| slcrc0 = X0 ),
inference(component_clause,[status(thm)],[f426]) ).
fof(f429,plain,
( ~ sQ46_spl
| ~ sQ33_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f423,f426,f307,f419]) ).
fof(f430,definition,
! [X0] :
( sQ48_spl
<=> ( aElementOf0(sK1_skl(X0,slcrc0),X0)
| ~ aSet0(X0)
| slcrc0 = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f431,plain,
! [X0] :
( ~ sQ48_spl
| aElementOf0(sK1_skl(X0,slcrc0),X0)
| ~ aSet0(X0)
| slcrc0 = X0 ),
inference(component_clause,[status(thm)],[f430]) ).
fof(f433,plain,
( ~ sQ46_spl
| ~ sQ33_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f424,f430,f307,f419]) ).
fof(f442,plain,
! [X0,X1,X2] :
( ~ sQ47_spl
| ~ aSubsetOf0(X2,slcrc0)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(slcrc0)
| ~ aSet0(X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| slcrc0 = X0 ),
inference(resolution,[status(thm)],[f427,f358]) ).
fof(f443,plain,
! [X0,X1] :
( ~ sQ47_spl
| aElementOf0(sK1_skl(X1,slcrc0),X1)
| ~ aSet0(X1)
| ~ aSet0(slcrc0)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| slcrc0 = X0 ),
inference(resolution,[status(thm)],[f427,f51]) ).
fof(f445,definition,
! [X0,X1,X2] :
( sQ50_spl
<=> ( ~ aSubsetOf0(X2,slcrc0)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| slcrc0 = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f448,plain,
( ~ sQ47_spl
| ~ sQ33_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f442,f445,f307,f426]) ).
fof(f449,definition,
! [X0,X1] :
( sQ51_spl
<=> ( aElementOf0(sK1_skl(X1,slcrc0),X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| slcrc0 = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f452,plain,
( ~ sQ47_spl
| ~ sQ33_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f443,f449,f307,f426]) ).
fof(f470,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X2,X0)
| aElementOf0(X2,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f258,f28]) ).
fof(f471,plain,
( sQ17_spl
| ~ aElementOf0(sK5_skl,sdtmndt0(xS,xx))
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f470,f217]) ).
fof(f474,definition,
( sQ52_spl
<=> aElementOf0(sK5_skl,sdtmndt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f476,plain,
( sQ52_spl
| ~ aElementOf0(sK5_skl,sdtmndt0(xS,xx)) ),
inference(component_clause,[status(thm)],[f474]) ).
fof(f477,plain,
( sQ17_spl
| ~ sQ52_spl
| ~ sQ27_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f471,f145,f272,f474,f215]) ).
fof(f479,plain,
( ~ sQ15_spl
| sQ52_spl
| ~ sP2_prd(sK5_skl) ),
inference(resolution,[status(thm)],[f476,f203]) ).
fof(f480,plain,
( ~ sQ15_spl
| sQ52_spl
| ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f479,f281]) ).
fof(f481,plain,
( ~ sQ15_spl
| sQ52_spl
| ~ sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f480]) ).
fof(f487,plain,
( sQ17_spl
| ~ sQ31_spl
| ~ aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(backward_demodulation,[status(thm)],[f287,f217]) ).
fof(f494,plain,
( sQ17_spl
| ~ sQ31_spl
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f487,f260]) ).
fof(f499,plain,
( sQ17_spl
| ~ sQ31_spl
| ~ sQ27_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f494,f145,f272,f286,f215]) ).
fof(f504,definition,
( sQ55_spl
<=> sK4_skl = xx ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f505,plain,
( ~ sQ55_spl
| sK4_skl = xx ),
inference(component_clause,[status(thm)],[f504]) ).
fof(f512,plain,
! [X0,X1,X2] :
( ~ aElementOf0(sK2_skl(X2,X1,X0),X0)
| ~ aElementOf0(sK2_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f70,f28]) ).
fof(f514,plain,
! [X0,X1] :
( ~ sP2_prd(sK2_skl(xS,X1,X0))
| ~ aElementOf0(sK2_skl(xS,X1,X0),X0)
| ~ aSet0(xS)
| xS = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f512,f139]) ).
fof(f516,definition,
! [X0,X1] :
( sQ56_spl
<=> ( ~ sP2_prd(sK2_skl(xS,X1,X0))
| ~ aElementOf0(sK2_skl(xS,X1,X0),X0)
| xS = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f519,plain,
( ~ sQ35_spl
| sQ56_spl ),
inference(split_clause,[status(thm)],[f514,f516,f314]) ).
fof(f520,plain,
! [X0,X1,X2] :
( sK2_skl(X2,X1,X0) != X1
| ~ aElementOf0(sK2_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f71,f28]) ).
fof(f522,plain,
! [X0,X1] :
( ~ sP2_prd(sK2_skl(xS,X1,X0))
| sK2_skl(xS,X1,X0) != X1
| ~ aSet0(xS)
| xS = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f520,f139]) ).
fof(f524,definition,
! [X0,X1] :
( sQ57_spl
<=> ( ~ sP2_prd(sK2_skl(xS,X1,X0))
| sK2_skl(xS,X1,X0) != X1
| xS = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f527,plain,
( ~ sQ35_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f522,f524,f314]) ).
fof(f552,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ41_spl
| X0 = xx
| aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElementOf0(X0,sdtpldt0(slcrc0,xx)) ),
inference(forward_demodulation,[status(thm)],[f371,f174]) ).
fof(f553,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ41_spl
| X0 = xx
| aElementOf0(X0,slcrc0)
| ~ aElementOf0(X0,sdtpldt0(slcrc0,xx)) ),
inference(forward_demodulation,[status(thm)],[f371,f552]) ).
fof(f554,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ41_spl
| X0 = xx
| ~ aElementOf0(X0,sdtpldt0(slcrc0,xx)) ),
inference(forward_subsumption_resolution,[status(thm)],[f553,f253]) ).
fof(f555,plain,
( ~ sQ48_spl
| ~ sQ8_spl
| ~ sQ41_spl
| ~ aSet0(sdtpldt0(slcrc0,xx))
| slcrc0 = sdtpldt0(slcrc0,xx)
| sK1_skl(sdtpldt0(slcrc0,xx),slcrc0) = xx ),
inference(resolution,[status(thm)],[f554,f431]) ).
fof(f560,definition,
( sQ61_spl
<=> sK1_skl(sdtpldt0(slcrc0,xx),slcrc0) = xx ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f561,plain,
( ~ sQ61_spl
| sK1_skl(sdtpldt0(slcrc0,xx),slcrc0) = xx ),
inference(component_clause,[status(thm)],[f560]) ).
fof(f563,definition,
( sQ62_spl
<=> slcrc0 = sdtpldt0(slcrc0,xx) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f564,plain,
( ~ sQ62_spl
| slcrc0 = sdtpldt0(slcrc0,xx) ),
inference(component_clause,[status(thm)],[f563]) ).
fof(f566,definition,
( sQ63_spl
<=> aSet0(sdtpldt0(slcrc0,xx)) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f568,plain,
( sQ63_spl
| ~ aSet0(sdtpldt0(slcrc0,xx)) ),
inference(component_clause,[status(thm)],[f566]) ).
fof(f569,plain,
( ~ sQ48_spl
| ~ sQ8_spl
| ~ sQ41_spl
| ~ sQ63_spl
| sQ62_spl
| sQ61_spl ),
inference(split_clause,[status(thm)],[f555,f560,f563,f566,f370,f173,f430]) ).
fof(f574,definition,
( sQ65_spl
<=> sK0_skl(sdtpldt0(slcrc0,xx)) = xx ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f575,plain,
( ~ sQ65_spl
| sK0_skl(sdtpldt0(slcrc0,xx)) = xx ),
inference(component_clause,[status(thm)],[f574]) ).
fof(f584,plain,
( ~ sQ11_spl
| sK4_skl = xx
| aElementOf0(sK4_skl,sdtmndt0(xS,xx))
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[f186,f257]) ).
fof(f585,definition,
( sQ67_spl
<=> aElementOf0(sK4_skl,sdtmndt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f586,plain,
( ~ sQ67_spl
| aElementOf0(sK4_skl,sdtmndt0(xS,xx)) ),
inference(component_clause,[status(thm)],[f585]) ).
fof(f588,plain,
( ~ sQ11_spl
| sQ55_spl
| sQ67_spl
| ~ sQ27_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f584,f145,f272,f585,f504,f185]) ).
fof(f608,plain,
( sQ63_spl
| ~ aElement0(xx)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f568,f255]) ).
fof(f610,plain,
( sQ63_spl
| ~ sQ27_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f608,f307,f272,f566]) ).
fof(f613,plain,
( ~ sQ62_spl
| aElementOf0(xx,slcrc0)
| ~ aElement0(xx)
| ~ aSet0(slcrc0) ),
inference(paramodulation,[status(thm)],[f564,f260]) ).
fof(f623,definition,
( sQ73_spl
<=> aElementOf0(xx,slcrc0) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f624,plain,
( ~ sQ73_spl
| aElementOf0(xx,slcrc0) ),
inference(component_clause,[status(thm)],[f623]) ).
fof(f626,plain,
( ~ sQ62_spl
| sQ73_spl
| ~ sQ27_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f613,f307,f272,f623,f563]) ).
fof(f628,plain,
( ~ sQ73_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f624,f253]) ).
fof(f629,plain,
~ sQ73_spl,
inference(contradiction_clause,[status(thm)],[f628]) ).
fof(f631,plain,
( ~ sQ65_spl
| aElementOf0(xx,sdtpldt0(slcrc0,xx))
| ~ aSet0(sdtpldt0(slcrc0,xx))
| sdtpldt0(slcrc0,xx) = slcrc0 ),
inference(paramodulation,[status(thm)],[f575,f37]) ).
fof(f632,definition,
( sQ74_spl
<=> aElementOf0(xx,sdtpldt0(slcrc0,xx)) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f635,plain,
( ~ sQ65_spl
| sQ74_spl
| ~ sQ63_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f631,f563,f566,f632,f574]) ).
fof(f638,plain,
( ~ sQ61_spl
| ~ sQ48_spl
| aElementOf0(xx,sdtpldt0(slcrc0,xx))
| ~ aSet0(sdtpldt0(slcrc0,xx))
| slcrc0 = sdtpldt0(slcrc0,xx) ),
inference(paramodulation,[status(thm)],[f561,f431]) ).
fof(f641,plain,
( ~ sQ61_spl
| ~ sQ48_spl
| sQ74_spl
| ~ sQ63_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f638,f563,f566,f632,f430,f560]) ).
fof(f650,plain,
! [X0] :
( sQ13_spl
| ~ aSubsetOf0(X0,xS)
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aSet0(xS)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f195,f358]) ).
fof(f652,definition,
! [X0] :
( sQ77_spl
<=> ( ~ aSubsetOf0(X0,xS)
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f655,plain,
( sQ13_spl
| ~ sQ35_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f650,f652,f314,f193]) ).
fof(f674,plain,
( ~ sQ67_spl
| ~ sQ3_spl
| aElementOf0(sK4_skl,xS) ),
inference(resolution,[status(thm)],[f154,f586]) ).
fof(f678,plain,
( ~ sQ67_spl
| ~ sQ3_spl
| sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f674,f191]) ).
fof(f679,plain,
( ~ sQ67_spl
| ~ sQ3_spl
| sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f678]) ).
fof(f688,plain,
! [X0,X1] :
( sK2_skl(slcrc0,X1,X0) = X1
| aElementOf0(sK2_skl(slcrc0,X1,X0),X0)
| ~ aSet0(slcrc0)
| slcrc0 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f73,f253]) ).
fof(f698,definition,
! [X0,X1] :
( sQ83_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,[sQ83_spl])],[split_symbol_definition]) ).
fof(f701,plain,
( ~ sQ33_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f688,f698,f307]) ).
fof(f709,plain,
( sQ12_spl
| ~ sQ55_spl
| ~ aElementOf0(xx,xS) ),
inference(backward_demodulation,[status(thm)],[f505,f191]) ).
fof(f711,plain,
( sQ12_spl
| ~ sQ55_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f709,f86]) ).
fof(f712,plain,
( sQ12_spl
| ~ sQ55_spl ),
inference(contradiction_clause,[status(thm)],[f711]) ).
fof(f713,plain,
$false,
inference(sat_refutation,[status(thm)],[f148,f156,f176,f188,f192,f196,f197,f201,f205,f208,f214,f218,f278,f289,f301,f310,f326,f328,f330,f342,f348,f352,f373,f384,f387,f393,f398,f422,f429,f433,f448,f452,f477,f481,f499,f519,f527,f569,f588,f610,f626,f629,f635,f641,f655,f679,f701,f712]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM535+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 02:42:52 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.43 % Refutation found
% 0.11/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.45 % Elapsed time: 0.070717 seconds
% 0.11/0.45 % CPU time: 0.303607 seconds
% 0.11/0.45 % Total memory used: 87.084 MB
% 0.11/0.45 % Net memory used: 86.701 MB
%------------------------------------------------------------------------------