%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM440+6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:40:32 PM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 117
% Syntax : Number of formulae : 512 ( 21 unt; 112 def)
% Number of atoms : 2524 ( 94 equ)
% Maximal formula atoms : 74 ( 4 avg)
% Number of connectives : 3117 (1105 ~;1229 |; 570 &)
% ( 171 <=>; 40 =>; 0 <=; 2 <~>)
% Maximal formula depth : 38 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 116 ( 114 usr; 106 prp; 0-3 aty)
% Number of functors : 28 ( 28 usr; 12 con; 0-3 aty)
% Number of variables : 512 ( 459 !; 53 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> ( sdtasdt0(W0,W1) = sz00
=> ( W1 = sz00
| W0 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,definition,
! [W0] :
( aInteger0(W0)
=> ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,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(f30,definition,
! [W0,W1] :
( ( aSubsetOf0(W1,cS1395)
& aSubsetOf0(W0,cS1395) )
=> ! [W2] :
( W2 = sdtbsmnsldt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( ( aElementOf0(W3,W1)
| aElementOf0(W3,W0) )
& aInteger0(W3) ) )
& aSet0(W2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,definition,
! [W0] :
( ( ! [W1] :
( aElementOf0(W1,W0)
=> aSubsetOf0(W1,cS1395) )
& aSet0(W0) )
=> ! [W1] :
( W1 = sbsmnsldt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ( ? [W3] :
( aElementOf0(W2,W3)
& aElementOf0(W3,W0) )
& aInteger0(W2) ) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,definition,
! [W0] :
( aSubsetOf0(W0,cS1395)
=> ! [W1] :
( W1 = stldt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ( ~ aElementOf0(W2,W0)
& aInteger0(W2) ) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,definition,
! [W0] :
( aSubsetOf0(W0,cS1395)
=> ( isClosed0(W0)
<=> isOpen0(stldt0(W0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
=> ? [W1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xB))
& ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(xB)) )
& ! [W2] :
( ( ( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) ) )
& aInteger0(W2) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& W1 != sz00
& aInteger0(W1) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
<=> ( ~ aElementOf0(W0,xB)
& aInteger0(W0) ) )
& aSet0(stldt0(xB))
& isClosed0(xA)
& isOpen0(stldt0(xA))
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
=> ? [W1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xA))
& ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(xA)) )
& ! [W2] :
( ( ( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) ) )
& aInteger0(W2) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& W1 != sz00
& aInteger0(W1) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
<=> ( ~ aElementOf0(W0,xA)
& aInteger0(W0) ) )
& aSet0(stldt0(xA))
& aSubsetOf0(xB,cS1395)
& ! [W0] :
( aElementOf0(W0,xB)
=> aElementOf0(W0,cS1395) )
& aSet0(xB)
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(cS1395)
& aSubsetOf0(xA,cS1395)
& ! [W0] :
( aElementOf0(W0,xA)
=> aElementOf0(W0,cS1395) )
& aSet0(xA)
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(cS1395) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,conjecture,
( ( ( ! [W0] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(W0,xB)
| aElementOf0(W0,xA) )
& aInteger0(W0) ) )
& aSet0(sdtbsmnsldt0(xA,xB)) )
=> ( ( ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB))
& aInteger0(W0) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB))) )
=> ( ! [W0] :
( aElementOf0(W0,stldt0(xA))
<=> ( ~ aElementOf0(W0,xA)
& aInteger0(W0) ) )
=> ( ! [W0] :
( aElementOf0(W0,stldt0(xB))
<=> ( ~ aElementOf0(W0,xB)
& aInteger0(W0) ) )
=> ( stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB))
| ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aElementOf0(W0,stldt0(xB))
& aElementOf0(W0,stldt0(xA))
& aInteger0(W0) ) ) ) ) ) ) )
& ( ( ! [W0] :
( aElementOf0(W0,stldt0(xB))
<=> ( ~ aElementOf0(W0,xB)
& aInteger0(W0) ) )
& aSet0(stldt0(xB)) )
=> ( ( ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(cS1395) )
=> ( aSubsetOf0(stldt0(xB),cS1395)
| ! [W0] :
( aElementOf0(W0,stldt0(xB))
=> aElementOf0(W0,cS1395) ) ) ) )
& ( ( ! [W0] :
( aElementOf0(W0,stldt0(xA))
<=> ( ~ aElementOf0(W0,xA)
& aInteger0(W0) ) )
& aSet0(stldt0(xA)) )
=> ( ( ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(cS1395) )
=> ( aSubsetOf0(stldt0(xA),cS1395)
| ! [W0] :
( aElementOf0(W0,stldt0(xA))
=> aElementOf0(W0,cS1395) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
~ ( ( ( ! [W0] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(W0,xB)
| aElementOf0(W0,xA) )
& aInteger0(W0) ) )
& aSet0(sdtbsmnsldt0(xA,xB)) )
=> ( ( ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB))
& aInteger0(W0) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB))) )
=> ( ! [W0] :
( aElementOf0(W0,stldt0(xA))
<=> ( ~ aElementOf0(W0,xA)
& aInteger0(W0) ) )
=> ( ! [W0] :
( aElementOf0(W0,stldt0(xB))
<=> ( ~ aElementOf0(W0,xB)
& aInteger0(W0) ) )
=> ( stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB))
| ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aElementOf0(W0,stldt0(xB))
& aElementOf0(W0,stldt0(xA))
& aInteger0(W0) ) ) ) ) ) ) )
& ( ( ! [W0] :
( aElementOf0(W0,stldt0(xB))
<=> ( ~ aElementOf0(W0,xB)
& aInteger0(W0) ) )
& aSet0(stldt0(xB)) )
=> ( ( ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(cS1395) )
=> ( aSubsetOf0(stldt0(xB),cS1395)
| ! [W0] :
( aElementOf0(W0,stldt0(xB))
=> aElementOf0(W0,cS1395) ) ) ) )
& ( ( ! [W0] :
( aElementOf0(W0,stldt0(xA))
<=> ( ~ aElementOf0(W0,xA)
& aInteger0(W0) ) )
& aSet0(stldt0(xA)) )
=> ( ( ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(cS1395) )
=> ( aSubsetOf0(stldt0(xA),cS1395)
| ! [W0] :
( aElementOf0(W0,stldt0(xA))
=> aElementOf0(W0,cS1395) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f45,plain,
aInteger0(sz00),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f46,plain,
aInteger0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f79,plain,
! [W0,W1] :
( W1 = sz00
| W0 = sz00
| sdtasdt0(W0,W1) != sz00
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f80,plain,
! [X0,X1] :
( X1 = sz00
| X0 = sz00
| sdtasdt0(X0,X1) != sz00
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f81,plain,
! [W0] :
( ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) ) )
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f82,plain,
! [W0] :
( ! [W1] :
( ( ! [W2] :
( sdtasdt0(W1,W2) != W0
| ~ aInteger0(W2) )
| W1 = sz00
| ~ aInteger0(W1)
| aDivisorOf0(W1,W0) )
& ( ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) )
| ~ aDivisorOf0(W1,W0) ) )
| ~ aInteger0(W0) ),
inference(NNF_transformation,[status(thm)],[f81]) ).
fof(f83,plain,
! [W0] :
( ( ! [W1] :
( ! [W2] :
( sdtasdt0(W1,W2) != W0
| ~ aInteger0(W2) )
| W1 = sz00
| ~ aInteger0(W1)
| aDivisorOf0(W1,W0) )
& ! [W1] :
( ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) )
| ~ aDivisorOf0(W1,W0) ) )
| ~ aInteger0(W0) ),
inference(miniscoping,[status(thm)],[f82]) ).
fof(f84,plain,
! [W0] :
( ( ! [W1] :
( ! [W2] :
( sdtasdt0(W1,W2) != W0
| ~ aInteger0(W2) )
| W1 = sz00
| ~ aInteger0(W1)
| aDivisorOf0(W1,W0) )
& ! [W1] :
( ( sdtasdt0(W1,sK0_skl(W1,W0)) = W0
& aInteger0(sK0_skl(W1,W0))
& W1 != sz00
& aInteger0(W1) )
| ~ aDivisorOf0(W1,W0) ) )
| ~ aInteger0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(W2,sK0_skl(W1,W0))],[f83]) ).
fof(f88,plain,
! [X0,X1] :
( sdtasdt0(X1,sK0_skl(X1,X0)) = X0
| ~ aDivisorOf0(X1,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f118,plain,
! [W0] :
( ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) ) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f119,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)],[f118]) ).
fof(f120,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)],[f119]) ).
fof(f121,plain,
! [W0] :
( ( ! [W1] :
( ( ~ aElementOf0(sK2_skl(W1,W0),W0)
& aElementOf0(sK2_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,[sK2_skl]),skolemize(W2,sK2_skl(W1,W0))],[f120]) ).
fof(f122,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f123,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f124,plain,
! [X0,X1] :
( aElementOf0(sK2_skl(X1,X0),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f128,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtbsmnsldt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( ( aElementOf0(W3,W1)
| aElementOf0(W3,W0) )
& aInteger0(W3) ) )
& aSet0(W2) ) )
| ~ aSubsetOf0(W1,cS1395)
| ~ aSubsetOf0(W0,cS1395) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f129,plain,
! [W0,W1] :
( ! [W2] :
( ( ? [W3] :
( ( ( ( aElementOf0(W3,W1)
| aElementOf0(W3,W0) )
& aInteger0(W3) )
| aElementOf0(W3,W2) )
& ( ( ~ aElementOf0(W3,W1)
& ~ aElementOf0(W3,W0) )
| ~ aInteger0(W3)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtbsmnsldt0(W0,W1) )
& ( ( ! [W3] :
( ( ( ~ aElementOf0(W3,W1)
& ~ aElementOf0(W3,W0) )
| ~ aInteger0(W3)
| aElementOf0(W3,W2) )
& ( ( ( aElementOf0(W3,W1)
| aElementOf0(W3,W0) )
& aInteger0(W3) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtbsmnsldt0(W0,W1) ) )
| ~ aSubsetOf0(W1,cS1395)
| ~ aSubsetOf0(W0,cS1395) ),
inference(NNF_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
! [W0,W1] :
( ( ! [W2] :
( ? [W3] :
( ( ( ( aElementOf0(W3,W1)
| aElementOf0(W3,W0) )
& aInteger0(W3) )
| aElementOf0(W3,W2) )
& ( ( ~ aElementOf0(W3,W1)
& ~ aElementOf0(W3,W0) )
| ~ aInteger0(W3)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtbsmnsldt0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ( ~ aElementOf0(W3,W1)
& ~ aElementOf0(W3,W0) )
| ~ aInteger0(W3)
| aElementOf0(W3,W2) )
& ! [W3] :
( ( ( aElementOf0(W3,W1)
| aElementOf0(W3,W0) )
& aInteger0(W3) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtbsmnsldt0(W0,W1) ) )
| ~ aSubsetOf0(W1,cS1395)
| ~ aSubsetOf0(W0,cS1395) ),
inference(miniscoping,[status(thm)],[f129]) ).
fof(f131,plain,
! [W0,W1] :
( ( ! [W2] :
( ( ( ( ( aElementOf0(sK3_skl(W2,W1,W0),W1)
| aElementOf0(sK3_skl(W2,W1,W0),W0) )
& aInteger0(sK3_skl(W2,W1,W0)) )
| aElementOf0(sK3_skl(W2,W1,W0),W2) )
& ( ( ~ aElementOf0(sK3_skl(W2,W1,W0),W1)
& ~ aElementOf0(sK3_skl(W2,W1,W0),W0) )
| ~ aInteger0(sK3_skl(W2,W1,W0))
| ~ aElementOf0(sK3_skl(W2,W1,W0),W2) ) )
| ~ aSet0(W2)
| W2 = sdtbsmnsldt0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ( ~ aElementOf0(W3,W1)
& ~ aElementOf0(W3,W0) )
| ~ aInteger0(W3)
| aElementOf0(W3,W2) )
& ! [W3] :
( ( ( aElementOf0(W3,W1)
| aElementOf0(W3,W0) )
& aInteger0(W3) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtbsmnsldt0(W0,W1) ) )
| ~ aSubsetOf0(W1,cS1395)
| ~ aSubsetOf0(W0,cS1395) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(W3,sK3_skl(W2,W1,W0))],[f130]) ).
fof(f133,plain,
! [X0,X1,X2,X3] :
( aInteger0(X3)
| ~ aElementOf0(X3,X2)
| X2 != sdtbsmnsldt0(X0,X1)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f134,plain,
! [X0,X1,X2,X3] :
( aElementOf0(X3,X1)
| aElementOf0(X3,X0)
| ~ aElementOf0(X3,X2)
| X2 != sdtbsmnsldt0(X0,X1)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f135,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(X3,X0)
| ~ aInteger0(X3)
| aElementOf0(X3,X2)
| X2 != sdtbsmnsldt0(X0,X1)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f136,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(X3,X1)
| ~ aInteger0(X3)
| aElementOf0(X3,X2)
| X2 != sdtbsmnsldt0(X0,X1)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f152,plain,
! [W0] :
( ! [W1] :
( W1 = sbsmnsldt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ( ? [W3] :
( aElementOf0(W2,W3)
& aElementOf0(W3,W0) )
& aInteger0(W2) ) )
& aSet0(W1) ) )
| ? [W1] :
( ~ aSubsetOf0(W1,cS1395)
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f153,definition,
! [W0,W1] :
( sP1_prd(W1,W0)
<=> ( ~ aSubsetOf0(W1,cS1395)
& aElementOf0(W1,W0) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f167,plain,
! [W0] :
( ! [W1] :
( W1 = stldt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ( ~ aElementOf0(W2,W0)
& aInteger0(W2) ) )
& aSet0(W1) ) )
| ~ aSubsetOf0(W0,cS1395) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f168,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ( ( ~ aElementOf0(W2,W0)
& aInteger0(W2) )
| aElementOf0(W2,W1) )
& ( aElementOf0(W2,W0)
| ~ aInteger0(W2)
| ~ aElementOf0(W2,W1) ) )
| ~ aSet0(W1)
| W1 = stldt0(W0) )
& ( ( ! [W2] :
( ( aElementOf0(W2,W0)
| ~ aInteger0(W2)
| aElementOf0(W2,W1) )
& ( ( ~ aElementOf0(W2,W0)
& aInteger0(W2) )
| ~ aElementOf0(W2,W1) ) )
& aSet0(W1) )
| W1 != stldt0(W0) ) )
| ~ aSubsetOf0(W0,cS1395) ),
inference(NNF_transformation,[status(thm)],[f167]) ).
fof(f169,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( ( ( ~ aElementOf0(W2,W0)
& aInteger0(W2) )
| aElementOf0(W2,W1) )
& ( aElementOf0(W2,W0)
| ~ aInteger0(W2)
| ~ aElementOf0(W2,W1) ) )
| ~ aSet0(W1)
| W1 = stldt0(W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aInteger0(W2)
| aElementOf0(W2,W1) )
& ! [W2] :
( ( ~ aElementOf0(W2,W0)
& aInteger0(W2) )
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| W1 != stldt0(W0) ) )
| ~ aSubsetOf0(W0,cS1395) ),
inference(miniscoping,[status(thm)],[f168]) ).
fof(f170,plain,
! [W0] :
( ( ! [W1] :
( ( ( ( ~ aElementOf0(sK9_skl(W1,W0),W0)
& aInteger0(sK9_skl(W1,W0)) )
| aElementOf0(sK9_skl(W1,W0),W1) )
& ( aElementOf0(sK9_skl(W1,W0),W0)
| ~ aInteger0(sK9_skl(W1,W0))
| ~ aElementOf0(sK9_skl(W1,W0),W1) ) )
| ~ aSet0(W1)
| W1 = stldt0(W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aInteger0(W2)
| aElementOf0(W2,W1) )
& ! [W2] :
( ( ~ aElementOf0(W2,W0)
& aInteger0(W2) )
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| W1 != stldt0(W0) ) )
| ~ aSubsetOf0(W0,cS1395) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(W2,sK9_skl(W1,W0))],[f169]) ).
fof(f172,plain,
! [X0,X1,X2] :
( aInteger0(X2)
| ~ aElementOf0(X2,X1)
| X1 != stldt0(X0)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f170]) ).
fof(f173,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1)
| X1 != stldt0(X0)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f170]) ).
fof(f174,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aInteger0(X2)
| aElementOf0(X2,X1)
| X1 != stldt0(X0)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f170]) ).
fof(f197,plain,
! [W0] :
( ( isClosed0(W0)
<=> isOpen0(stldt0(W0)) )
| ~ aSubsetOf0(W0,cS1395) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f198,plain,
! [W0] :
( ( ( ~ isOpen0(stldt0(W0))
| isClosed0(W0) )
& ( isOpen0(stldt0(W0))
| ~ isClosed0(W0) ) )
| ~ aSubsetOf0(W0,cS1395) ),
inference(NNF_transformation,[status(thm)],[f197]) ).
fof(f199,plain,
! [X0] :
( isOpen0(stldt0(X0))
| ~ isClosed0(X0)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f200,plain,
! [X0] :
( ~ isOpen0(stldt0(X0))
| isClosed0(X0)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f207,plain,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [W0] :
( ? [W1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xB))
& ! [W2] :
( aElementOf0(W2,stldt0(xB))
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ! [W2] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
| ( ~ sdteqdtlpzmzozddtrp0(W2,W0,W1)
& ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ! [W3] :
( sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(W0))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& W1 != sz00
& aInteger0(W1) )
| ~ aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
<=> ( ~ aElementOf0(W0,xB)
& aInteger0(W0) ) )
& aSet0(stldt0(xB))
& isClosed0(xA)
& isOpen0(stldt0(xA))
& ! [W0] :
( ? [W1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xA))
& ! [W2] :
( aElementOf0(W2,stldt0(xA))
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ! [W2] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
| ( ~ sdteqdtlpzmzozddtrp0(W2,W0,W1)
& ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ! [W3] :
( sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(W0))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& W1 != sz00
& aInteger0(W1) )
| ~ aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
<=> ( ~ aElementOf0(W0,xA)
& aInteger0(W0) ) )
& aSet0(stldt0(xA))
& aSubsetOf0(xB,cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,xB) )
& aSet0(xB)
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(cS1395)
& aSubsetOf0(xA,cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,xA) )
& aSet0(xA)
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(cS1395) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f208,plain,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [W0] :
( ? [W1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xB))
& ! [W2] :
( aElementOf0(W2,stldt0(xB))
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ! [W2] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
| ( ~ sdteqdtlpzmzozddtrp0(W2,W0,W1)
& ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ! [W3] :
( sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(W0))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& W1 != sz00
& aInteger0(W1) )
| ~ aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( ( aElementOf0(W0,xB)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xB)) )
& ( ( ~ aElementOf0(W0,xB)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xB)) ) )
& aSet0(stldt0(xB))
& isClosed0(xA)
& isOpen0(stldt0(xA))
& ! [W0] :
( ? [W1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xA))
& ! [W2] :
( aElementOf0(W2,stldt0(xA))
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ! [W2] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
| ( ~ sdteqdtlpzmzozddtrp0(W2,W0,W1)
& ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ! [W3] :
( sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(W0))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& W1 != sz00
& aInteger0(W1) )
| ~ aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( ( aElementOf0(W0,xA)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xA)) )
& ( ( ~ aElementOf0(W0,xA)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xA)) ) )
& aSet0(stldt0(xA))
& aSubsetOf0(xB,cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,xB) )
& aSet0(xB)
& ! [W0] :
( ( ~ aInteger0(W0)
| aElementOf0(W0,cS1395) )
& ( aInteger0(W0)
| ~ aElementOf0(W0,cS1395) ) )
& aSet0(cS1395)
& aSubsetOf0(xA,cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,xA) )
& aSet0(xA)
& ! [W0] :
( ( ~ aInteger0(W0)
| aElementOf0(W0,cS1395) )
& ( aInteger0(W0)
| ~ aElementOf0(W0,cS1395) ) )
& aSet0(cS1395) ),
inference(NNF_transformation,[status(thm)],[f207]) ).
fof(f209,plain,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [W0] :
( ? [W1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xB))
& ! [W2] :
( aElementOf0(W2,stldt0(xB))
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
| ( ~ sdteqdtlpzmzozddtrp0(W2,W0,W1)
& ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ! [W3] :
( sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(W0))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ! [W2] :
( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& W1 != sz00
& aInteger0(W1) )
| ~ aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( aElementOf0(W0,xB)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( ( ~ aElementOf0(W0,xB)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xB)) )
& aSet0(stldt0(xB))
& isClosed0(xA)
& isOpen0(stldt0(xA))
& ! [W0] :
( ? [W1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xA))
& ! [W2] :
( aElementOf0(W2,stldt0(xA))
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
| ( ~ sdteqdtlpzmzozddtrp0(W2,W0,W1)
& ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ! [W3] :
( sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(W0))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ! [W2] :
( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& W1 != sz00
& aInteger0(W1) )
| ~ aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( aElementOf0(W0,xA)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( ( ~ aElementOf0(W0,xA)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xA)) )
& aSet0(stldt0(xA))
& aSubsetOf0(xB,cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,xB) )
& aSet0(xB)
& ! [W0] :
( ~ aInteger0(W0)
| aElementOf0(W0,cS1395) )
& ! [W0] :
( aInteger0(W0)
| ~ aElementOf0(W0,cS1395) )
& aSet0(cS1395)
& aSubsetOf0(xA,cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,xA) )
& aSet0(xA)
& ! [W0] :
( ~ aInteger0(W0)
| aElementOf0(W0,cS1395) )
& ! [W0] :
( aInteger0(W0)
| ~ aElementOf0(W0,cS1395) )
& aSet0(cS1395) ),
inference(miniscoping,[status(thm)],[f208]) ).
fof(f210,plain,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [W0] :
( ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,sK16_skl(W0)),stldt0(xB))
& ! [W2] :
( aElementOf0(W2,stldt0(xB))
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,sK16_skl(W0))) )
& ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,sK16_skl(W0)))
| ( ~ sdteqdtlpzmzozddtrp0(W2,W0,sK16_skl(W0))
& ~ aDivisorOf0(sK16_skl(W0),sdtpldt0(W2,smndt0(W0)))
& ! [W3] :
( sdtasdt0(sK16_skl(W0),W3) != sdtpldt0(W2,smndt0(W0))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ! [W2] :
( ( sdteqdtlpzmzozddtrp0(W2,W0,sK16_skl(W0))
& aDivisorOf0(sK16_skl(W0),sdtpldt0(W2,smndt0(W0)))
& sdtasdt0(sK16_skl(W0),sK17_skl(W2,W0)) = sdtpldt0(W2,smndt0(W0))
& aInteger0(sK17_skl(W2,W0))
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,sK16_skl(W0))) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,sK16_skl(W0)))
& sK16_skl(W0) != sz00
& aInteger0(sK16_skl(W0)) )
| ~ aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( aElementOf0(W0,xB)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( ( ~ aElementOf0(W0,xB)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xB)) )
& aSet0(stldt0(xB))
& isClosed0(xA)
& isOpen0(stldt0(xA))
& ! [W0] :
( ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,sK14_skl(W0)),stldt0(xA))
& ! [W2] :
( aElementOf0(W2,stldt0(xA))
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,sK14_skl(W0))) )
& ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,sK14_skl(W0)))
| ( ~ sdteqdtlpzmzozddtrp0(W2,W0,sK14_skl(W0))
& ~ aDivisorOf0(sK14_skl(W0),sdtpldt0(W2,smndt0(W0)))
& ! [W3] :
( sdtasdt0(sK14_skl(W0),W3) != sdtpldt0(W2,smndt0(W0))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ! [W2] :
( ( sdteqdtlpzmzozddtrp0(W2,W0,sK14_skl(W0))
& aDivisorOf0(sK14_skl(W0),sdtpldt0(W2,smndt0(W0)))
& sdtasdt0(sK14_skl(W0),sK15_skl(W2,W0)) = sdtpldt0(W2,smndt0(W0))
& aInteger0(sK15_skl(W2,W0))
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,sK14_skl(W0))) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,sK14_skl(W0)))
& sK14_skl(W0) != sz00
& aInteger0(sK14_skl(W0)) )
| ~ aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( aElementOf0(W0,xA)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( ( ~ aElementOf0(W0,xA)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xA)) )
& aSet0(stldt0(xA))
& aSubsetOf0(xB,cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,xB) )
& aSet0(xB)
& ! [W0] :
( ~ aInteger0(W0)
| aElementOf0(W0,cS1395) )
& ! [W0] :
( aInteger0(W0)
| ~ aElementOf0(W0,cS1395) )
& aSet0(cS1395)
& aSubsetOf0(xA,cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,xA) )
& aSet0(xA)
& ! [W0] :
( ~ aInteger0(W0)
| aElementOf0(W0,cS1395) )
& ! [W0] :
( aInteger0(W0)
| ~ aElementOf0(W0,cS1395) )
& aSet0(cS1395) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl,sK16_skl,sK17_skl]),skolemize(W1,sK14_skl(W0)),skolemize(W3,sK15_skl(W2,W0)),skolemize(W1,sK16_skl(W0)),skolemize(W3,sK17_skl(W2,W0))],[f209]) ).
fof(f211,plain,
aSet0(cS1395),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f212,plain,
! [X0] :
( aInteger0(X0)
| ~ aElementOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f213,plain,
! [X0] :
( ~ aInteger0(X0)
| aElementOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f215,plain,
! [X0] :
( aElementOf0(X0,cS1395)
| ~ aElementOf0(X0,xA) ),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f216,plain,
aSubsetOf0(xA,cS1395),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f221,plain,
! [X0] :
( aElementOf0(X0,cS1395)
| ~ aElementOf0(X0,xB) ),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f222,plain,
aSubsetOf0(xB,cS1395),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f223,plain,
aSet0(stldt0(xA)),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f227,plain,
! [X0] :
( aInteger0(sK14_skl(X0))
| ~ aElementOf0(X0,stldt0(xA)) ),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f241,plain,
isClosed0(xA),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f242,plain,
aSet0(stldt0(xB)),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f243,plain,
! [X0] :
( aInteger0(X0)
| ~ aElementOf0(X0,stldt0(xB)) ),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f246,plain,
! [X0] :
( aInteger0(sK16_skl(X0))
| ~ aElementOf0(X0,stldt0(xB)) ),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f260,plain,
isClosed0(xB),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f261,plain,
( ( stldt0(sdtbsmnsldt0(xA,xB)) != sdtslmnbsdt0(stldt0(xA),stldt0(xB))
& ? [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<~> ( aElementOf0(W0,stldt0(xB))
& aElementOf0(W0,stldt0(xA))
& aInteger0(W0) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
<=> ( ~ aElementOf0(W0,xB)
& aInteger0(W0) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
<=> ( ~ aElementOf0(W0,xA)
& aInteger0(W0) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB))
& aInteger0(W0) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(W0,xB)
| aElementOf0(W0,xA) )
& aInteger0(W0) ) )
& aSet0(sdtbsmnsldt0(xA,xB)) )
| ( ~ aSubsetOf0(stldt0(xB),cS1395)
& ? [W0] :
( ~ aElementOf0(W0,cS1395)
& aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(cS1395)
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
<=> ( ~ aElementOf0(W0,xB)
& aInteger0(W0) ) )
& aSet0(stldt0(xB)) )
| ( ~ aSubsetOf0(stldt0(xA),cS1395)
& ? [W0] :
( ~ aElementOf0(W0,cS1395)
& aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(cS1395)
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
<=> ( ~ aElementOf0(W0,xA)
& aInteger0(W0) ) )
& aSet0(stldt0(xA)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f262,definition,
( sP2_prd
<=> ( ( ~ aSubsetOf0(stldt0(xB),cS1395)
& ? [W0] :
( ~ aElementOf0(W0,cS1395)
& aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(cS1395)
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
<=> ( ~ aElementOf0(W0,xB)
& aInteger0(W0) ) )
& aSet0(stldt0(xB)) )
| ( ~ aSubsetOf0(stldt0(xA),cS1395)
& ? [W0] :
( ~ aElementOf0(W0,cS1395)
& aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(cS1395)
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
<=> ( ~ aElementOf0(W0,xA)
& aInteger0(W0) ) )
& aSet0(stldt0(xA)) ) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f263,plain,
( ( stldt0(sdtbsmnsldt0(xA,xB)) != sdtslmnbsdt0(stldt0(xA),stldt0(xB))
& ? [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<~> ( aElementOf0(W0,stldt0(xB))
& aElementOf0(W0,stldt0(xA))
& aInteger0(W0) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
<=> ( ~ aElementOf0(W0,xB)
& aInteger0(W0) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
<=> ( ~ aElementOf0(W0,xA)
& aInteger0(W0) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB))
& aInteger0(W0) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(W0,xB)
| aElementOf0(W0,xA) )
& aInteger0(W0) ) )
& aSet0(sdtbsmnsldt0(xA,xB)) )
| sP2_prd ),
inference(formula_renaming,[status(thm)],[f261,f262]) ).
fof(f264,plain,
( ( stldt0(sdtbsmnsldt0(xA,xB)) != sdtslmnbsdt0(stldt0(xA),stldt0(xB))
& ? [W0] :
( ( ~ aElementOf0(W0,stldt0(xB))
| ~ aElementOf0(W0,stldt0(xA))
| ~ aInteger0(W0)
| ~ aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ( aElementOf0(W0,stldt0(xB))
& aElementOf0(W0,stldt0(xA))
& aInteger0(W0) )
| aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& ! [W0] :
( ( aElementOf0(W0,xB)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xB)) )
& ( ( ~ aElementOf0(W0,xB)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xB)) ) )
& ! [W0] :
( ( aElementOf0(W0,xA)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xA)) )
& ( ( ~ aElementOf0(W0,xA)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xA)) ) )
& ! [W0] :
( ( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ( ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB))
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0] :
( ( ( ~ aElementOf0(W0,xB)
& ~ aElementOf0(W0,xA) )
| ~ aInteger0(W0)
| aElementOf0(W0,sdtbsmnsldt0(xA,xB)) )
& ( ( ( aElementOf0(W0,xB)
| aElementOf0(W0,xA) )
& aInteger0(W0) )
| ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB)) ) )
& aSet0(sdtbsmnsldt0(xA,xB)) )
| sP2_prd ),
inference(NNF_transformation,[status(thm)],[f263]) ).
fof(f265,plain,
( ( stldt0(sdtbsmnsldt0(xA,xB)) != sdtslmnbsdt0(stldt0(xA),stldt0(xB))
& ? [W0] :
( ( ~ aElementOf0(W0,stldt0(xB))
| ~ aElementOf0(W0,stldt0(xA))
| ~ aInteger0(W0)
| ~ aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ( aElementOf0(W0,stldt0(xB))
& aElementOf0(W0,stldt0(xA))
& aInteger0(W0) )
| aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& ! [W0] :
( aElementOf0(W0,xB)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( ( ~ aElementOf0(W0,xB)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( aElementOf0(W0,xA)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( ( ~ aElementOf0(W0,xA)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB))) )
& ! [W0] :
( ( ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB))
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB))) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0] :
( ( ~ aElementOf0(W0,xB)
& ~ aElementOf0(W0,xA) )
| ~ aInteger0(W0)
| aElementOf0(W0,sdtbsmnsldt0(xA,xB)) )
& ! [W0] :
( ( ( aElementOf0(W0,xB)
| aElementOf0(W0,xA) )
& aInteger0(W0) )
| ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB)) )
& aSet0(sdtbsmnsldt0(xA,xB)) )
| sP2_prd ),
inference(miniscoping,[status(thm)],[f264]) ).
fof(f266,plain,
( ( stldt0(sdtbsmnsldt0(xA,xB)) != sdtslmnbsdt0(stldt0(xA),stldt0(xB))
& ( ~ aElementOf0(sK18_skl,stldt0(xB))
| ~ aElementOf0(sK18_skl,stldt0(xA))
| ~ aInteger0(sK18_skl)
| ~ aElementOf0(sK18_skl,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ( aElementOf0(sK18_skl,stldt0(xB))
& aElementOf0(sK18_skl,stldt0(xA))
& aInteger0(sK18_skl) )
| aElementOf0(sK18_skl,stldt0(sdtbsmnsldt0(xA,xB))) )
& ! [W0] :
( aElementOf0(W0,xB)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( ( ~ aElementOf0(W0,xB)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( aElementOf0(W0,xA)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( ( ~ aElementOf0(W0,xA)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB))) )
& ! [W0] :
( ( ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB))
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB))) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0] :
( ( ~ aElementOf0(W0,xB)
& ~ aElementOf0(W0,xA) )
| ~ aInteger0(W0)
| aElementOf0(W0,sdtbsmnsldt0(xA,xB)) )
& ! [W0] :
( ( ( aElementOf0(W0,xB)
| aElementOf0(W0,xA) )
& aInteger0(W0) )
| ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB)) )
& aSet0(sdtbsmnsldt0(xA,xB)) )
| sP2_prd ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18_skl]),skolemize(W0,sK18_skl)],[f265]) ).
fof(f267,plain,
( aSet0(sdtbsmnsldt0(xA,xB))
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f268,plain,
! [X0] :
( aInteger0(X0)
| ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f269,plain,
! [X0] :
( aElementOf0(X0,xB)
| aElementOf0(X0,xA)
| ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f270,plain,
! [X0] :
( ~ aElementOf0(X0,xA)
| ~ aInteger0(X0)
| aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f271,plain,
! [X0] :
( ~ aElementOf0(X0,xB)
| ~ aInteger0(X0)
| aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f272,plain,
( aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f273,plain,
! [X0] :
( aInteger0(X0)
| ~ aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f274,plain,
! [X0] :
( ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| ~ aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f275,plain,
! [X0] :
( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(X0)
| aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f276,plain,
! [X0] :
( aInteger0(X0)
| ~ aElementOf0(X0,stldt0(xA))
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f277,plain,
! [X0] :
( ~ aElementOf0(X0,xA)
| ~ aElementOf0(X0,stldt0(xA))
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f278,plain,
! [X0] :
( aElementOf0(X0,xA)
| ~ aInteger0(X0)
| aElementOf0(X0,stldt0(xA))
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f279,plain,
! [X0] :
( aInteger0(X0)
| ~ aElementOf0(X0,stldt0(xB))
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f280,plain,
! [X0] :
( ~ aElementOf0(X0,xB)
| ~ aElementOf0(X0,stldt0(xB))
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f281,plain,
! [X0] :
( aElementOf0(X0,xB)
| ~ aInteger0(X0)
| aElementOf0(X0,stldt0(xB))
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f283,plain,
( aElementOf0(sK18_skl,stldt0(xA))
| aElementOf0(sK18_skl,stldt0(sdtbsmnsldt0(xA,xB)))
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f284,plain,
( aElementOf0(sK18_skl,stldt0(xB))
| aElementOf0(sK18_skl,stldt0(sdtbsmnsldt0(xA,xB)))
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f285,plain,
( ~ aElementOf0(sK18_skl,stldt0(xB))
| ~ aElementOf0(sK18_skl,stldt0(xA))
| ~ aInteger0(sK18_skl)
| ~ aElementOf0(sK18_skl,stldt0(sdtbsmnsldt0(xA,xB)))
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f286,plain,
( stldt0(sdtbsmnsldt0(xA,xB)) != sdtslmnbsdt0(stldt0(xA),stldt0(xB))
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f293,plain,
! [W0,W1] :
( ( aSubsetOf0(W1,cS1395)
| ~ aElementOf0(W1,W0)
| sP1_prd(W1,W0) )
& ( ( ~ aSubsetOf0(W1,cS1395)
& aElementOf0(W1,W0) )
| ~ sP1_prd(W1,W0) ) ),
inference(NNF_transformation,[status(thm)],[f153]) ).
fof(f294,plain,
( ! [W0,W1] :
( aSubsetOf0(W1,cS1395)
| ~ aElementOf0(W1,W0)
| sP1_prd(W1,W0) )
& ! [W0,W1] :
( ( ~ aSubsetOf0(W1,cS1395)
& aElementOf0(W1,W0) )
| ~ sP1_prd(W1,W0) ) ),
inference(miniscoping,[status(thm)],[f293]) ).
fof(f295,plain,
! [X0,X1] :
( aElementOf0(X0,X1)
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f294]) ).
fof(f296,plain,
! [X0,X1] :
( ~ aSubsetOf0(X0,cS1395)
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f294]) ).
fof(f297,plain,
! [X0,X1] :
( aSubsetOf0(X0,cS1395)
| ~ aElementOf0(X0,X1)
| sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f294]) ).
fof(f298,definition,
( sP3_prd
<=> ( ~ aSubsetOf0(stldt0(xA),cS1395)
& ? [W0] :
( ~ aElementOf0(W0,cS1395)
& aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(cS1395)
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
<=> ( ~ aElementOf0(W0,xA)
& aInteger0(W0) ) )
& aSet0(stldt0(xA)) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f299,plain,
( sP2_prd
<=> ( ( ~ aSubsetOf0(stldt0(xB),cS1395)
& ? [W0] :
( ~ aElementOf0(W0,cS1395)
& aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(cS1395)
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
<=> ( ~ aElementOf0(W0,xB)
& aInteger0(W0) ) )
& aSet0(stldt0(xB)) )
| sP3_prd ) ),
inference(formula_renaming,[status(thm)],[f262,f298]) ).
fof(f300,plain,
( ( ( ( aSubsetOf0(stldt0(xB),cS1395)
| ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,stldt0(xB)) )
| ? [W0] :
( ( aInteger0(W0)
| aElementOf0(W0,cS1395) )
& ( ~ aInteger0(W0)
| ~ aElementOf0(W0,cS1395) ) )
| ~ aSet0(cS1395)
| ? [W0] :
( ( ( ~ aElementOf0(W0,xB)
& aInteger0(W0) )
| aElementOf0(W0,stldt0(xB)) )
& ( aElementOf0(W0,xB)
| ~ aInteger0(W0)
| ~ aElementOf0(W0,stldt0(xB)) ) )
| ~ aSet0(stldt0(xB)) )
& ~ sP3_prd )
| sP2_prd )
& ( ( ~ aSubsetOf0(stldt0(xB),cS1395)
& ? [W0] :
( ~ aElementOf0(W0,cS1395)
& aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( ( ~ aInteger0(W0)
| aElementOf0(W0,cS1395) )
& ( aInteger0(W0)
| ~ aElementOf0(W0,cS1395) ) )
& aSet0(cS1395)
& ! [W0] :
( ( aElementOf0(W0,xB)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xB)) )
& ( ( ~ aElementOf0(W0,xB)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xB)) ) )
& aSet0(stldt0(xB)) )
| sP3_prd
| ~ sP2_prd ) ),
inference(NNF_transformation,[status(thm)],[f299]) ).
fof(f301,plain,
( ( ( ( aSubsetOf0(stldt0(xB),cS1395)
| ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,stldt0(xB)) )
| ? [W0] :
( ( aInteger0(W0)
| aElementOf0(W0,cS1395) )
& ( ~ aInteger0(W0)
| ~ aElementOf0(W0,cS1395) ) )
| ~ aSet0(cS1395)
| ? [W0] :
( ( ( ~ aElementOf0(W0,xB)
& aInteger0(W0) )
| aElementOf0(W0,stldt0(xB)) )
& ( aElementOf0(W0,xB)
| ~ aInteger0(W0)
| ~ aElementOf0(W0,stldt0(xB)) ) )
| ~ aSet0(stldt0(xB)) )
& ~ sP3_prd )
| sP2_prd )
& ( ( ~ aSubsetOf0(stldt0(xB),cS1395)
& ? [W0] :
( ~ aElementOf0(W0,cS1395)
& aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( ~ aInteger0(W0)
| aElementOf0(W0,cS1395) )
& ! [W0] :
( aInteger0(W0)
| ~ aElementOf0(W0,cS1395) )
& aSet0(cS1395)
& ! [W0] :
( aElementOf0(W0,xB)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( ( ~ aElementOf0(W0,xB)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xB)) )
& aSet0(stldt0(xB)) )
| sP3_prd
| ~ sP2_prd ) ),
inference(miniscoping,[status(thm)],[f300]) ).
fof(f302,plain,
( ( ( ( aSubsetOf0(stldt0(xB),cS1395)
| ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,stldt0(xB)) )
| ( ( aInteger0(sK21_skl)
| aElementOf0(sK21_skl,cS1395) )
& ( ~ aInteger0(sK21_skl)
| ~ aElementOf0(sK21_skl,cS1395) ) )
| ~ aSet0(cS1395)
| ( ( ( ~ aElementOf0(sK20_skl,xB)
& aInteger0(sK20_skl) )
| aElementOf0(sK20_skl,stldt0(xB)) )
& ( aElementOf0(sK20_skl,xB)
| ~ aInteger0(sK20_skl)
| ~ aElementOf0(sK20_skl,stldt0(xB)) ) )
| ~ aSet0(stldt0(xB)) )
& ~ sP3_prd )
| sP2_prd )
& ( ( ~ aSubsetOf0(stldt0(xB),cS1395)
& ~ aElementOf0(sK19_skl,cS1395)
& aElementOf0(sK19_skl,stldt0(xB))
& ! [W0] :
( ~ aInteger0(W0)
| aElementOf0(W0,cS1395) )
& ! [W0] :
( aInteger0(W0)
| ~ aElementOf0(W0,cS1395) )
& aSet0(cS1395)
& ! [W0] :
( aElementOf0(W0,xB)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( ( ~ aElementOf0(W0,xB)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xB)) )
& aSet0(stldt0(xB)) )
| sP3_prd
| ~ sP2_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl,sK20_skl,sK21_skl]),skolemize(W0,sK19_skl),skolemize(W0,sK20_skl),skolemize(W0,sK21_skl)],[f301]) ).
fof(f310,plain,
( aElementOf0(sK19_skl,stldt0(xB))
| sP3_prd
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f302]) ).
fof(f311,plain,
( ~ aElementOf0(sK19_skl,cS1395)
| sP3_prd
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f302]) ).
fof(f312,plain,
( ~ aSubsetOf0(stldt0(xB),cS1395)
| sP3_prd
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f302]) ).
fof(f313,plain,
( ~ sP3_prd
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f302]) ).
fof(f320,plain,
( ( aSubsetOf0(stldt0(xA),cS1395)
| ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,stldt0(xA)) )
| ? [W0] :
( ( aInteger0(W0)
| aElementOf0(W0,cS1395) )
& ( ~ aInteger0(W0)
| ~ aElementOf0(W0,cS1395) ) )
| ~ aSet0(cS1395)
| ? [W0] :
( ( ( ~ aElementOf0(W0,xA)
& aInteger0(W0) )
| aElementOf0(W0,stldt0(xA)) )
& ( aElementOf0(W0,xA)
| ~ aInteger0(W0)
| ~ aElementOf0(W0,stldt0(xA)) ) )
| ~ aSet0(stldt0(xA))
| sP3_prd )
& ( ( ~ aSubsetOf0(stldt0(xA),cS1395)
& ? [W0] :
( ~ aElementOf0(W0,cS1395)
& aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( ( ~ aInteger0(W0)
| aElementOf0(W0,cS1395) )
& ( aInteger0(W0)
| ~ aElementOf0(W0,cS1395) ) )
& aSet0(cS1395)
& ! [W0] :
( ( aElementOf0(W0,xA)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xA)) )
& ( ( ~ aElementOf0(W0,xA)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xA)) ) )
& aSet0(stldt0(xA)) )
| ~ sP3_prd ) ),
inference(NNF_transformation,[status(thm)],[f298]) ).
fof(f321,plain,
( ( aSubsetOf0(stldt0(xA),cS1395)
| ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,stldt0(xA)) )
| ? [W0] :
( ( aInteger0(W0)
| aElementOf0(W0,cS1395) )
& ( ~ aInteger0(W0)
| ~ aElementOf0(W0,cS1395) ) )
| ~ aSet0(cS1395)
| ? [W0] :
( ( ( ~ aElementOf0(W0,xA)
& aInteger0(W0) )
| aElementOf0(W0,stldt0(xA)) )
& ( aElementOf0(W0,xA)
| ~ aInteger0(W0)
| ~ aElementOf0(W0,stldt0(xA)) ) )
| ~ aSet0(stldt0(xA))
| sP3_prd )
& ( ( ~ aSubsetOf0(stldt0(xA),cS1395)
& ? [W0] :
( ~ aElementOf0(W0,cS1395)
& aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( ~ aInteger0(W0)
| aElementOf0(W0,cS1395) )
& ! [W0] :
( aInteger0(W0)
| ~ aElementOf0(W0,cS1395) )
& aSet0(cS1395)
& ! [W0] :
( aElementOf0(W0,xA)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( ( ~ aElementOf0(W0,xA)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xA)) )
& aSet0(stldt0(xA)) )
| ~ sP3_prd ) ),
inference(miniscoping,[status(thm)],[f320]) ).
fof(f322,plain,
( ( aSubsetOf0(stldt0(xA),cS1395)
| ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,stldt0(xA)) )
| ( ( aInteger0(sK24_skl)
| aElementOf0(sK24_skl,cS1395) )
& ( ~ aInteger0(sK24_skl)
| ~ aElementOf0(sK24_skl,cS1395) ) )
| ~ aSet0(cS1395)
| ( ( ( ~ aElementOf0(sK23_skl,xA)
& aInteger0(sK23_skl) )
| aElementOf0(sK23_skl,stldt0(xA)) )
& ( aElementOf0(sK23_skl,xA)
| ~ aInteger0(sK23_skl)
| ~ aElementOf0(sK23_skl,stldt0(xA)) ) )
| ~ aSet0(stldt0(xA))
| sP3_prd )
& ( ( ~ aSubsetOf0(stldt0(xA),cS1395)
& ~ aElementOf0(sK22_skl,cS1395)
& aElementOf0(sK22_skl,stldt0(xA))
& ! [W0] :
( ~ aInteger0(W0)
| aElementOf0(W0,cS1395) )
& ! [W0] :
( aInteger0(W0)
| ~ aElementOf0(W0,cS1395) )
& aSet0(cS1395)
& ! [W0] :
( aElementOf0(W0,xA)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( ( ~ aElementOf0(W0,xA)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xA)) )
& aSet0(stldt0(xA)) )
| ~ sP3_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22_skl,sK23_skl,sK24_skl]),skolemize(W0,sK22_skl),skolemize(W0,sK23_skl),skolemize(W0,sK24_skl)],[f321]) ).
fof(f324,plain,
! [X0] :
( aInteger0(X0)
| ~ aElementOf0(X0,stldt0(xA))
| ~ sP3_prd ),
inference(cnf_transformation,[status(thm)],[f322]) ).
fof(f330,plain,
( aElementOf0(sK22_skl,stldt0(xA))
| ~ sP3_prd ),
inference(cnf_transformation,[status(thm)],[f322]) ).
fof(f331,plain,
( ~ aElementOf0(sK22_skl,cS1395)
| ~ sP3_prd ),
inference(cnf_transformation,[status(thm)],[f322]) ).
fof(f335,plain,
! [X0] :
( aSubsetOf0(stldt0(xA),cS1395)
| aElementOf0(X0,cS1395)
| ~ aElementOf0(X0,stldt0(xA))
| ~ aInteger0(sK24_skl)
| ~ aElementOf0(sK24_skl,cS1395)
| ~ aSet0(cS1395)
| aInteger0(sK23_skl)
| aElementOf0(sK23_skl,stldt0(xA))
| ~ aSet0(stldt0(xA))
| sP3_prd ),
inference(cnf_transformation,[status(thm)],[f322]) ).
fof(f336,plain,
! [X0] :
( aSubsetOf0(stldt0(xA),cS1395)
| aElementOf0(X0,cS1395)
| ~ aElementOf0(X0,stldt0(xA))
| aInteger0(sK24_skl)
| aElementOf0(sK24_skl,cS1395)
| ~ aSet0(cS1395)
| aInteger0(sK23_skl)
| aElementOf0(sK23_skl,stldt0(xA))
| ~ aSet0(stldt0(xA))
| sP3_prd ),
inference(cnf_transformation,[status(thm)],[f322]) ).
fof(f337,plain,
! [X0] :
( aSubsetOf0(stldt0(xA),cS1395)
| aElementOf0(X0,cS1395)
| ~ aElementOf0(X0,stldt0(xA))
| ~ aInteger0(sK24_skl)
| ~ aElementOf0(sK24_skl,cS1395)
| ~ aSet0(cS1395)
| ~ aElementOf0(sK23_skl,xA)
| aElementOf0(sK23_skl,stldt0(xA))
| ~ aSet0(stldt0(xA))
| sP3_prd ),
inference(cnf_transformation,[status(thm)],[f322]) ).
fof(f338,plain,
! [X0] :
( aSubsetOf0(stldt0(xA),cS1395)
| aElementOf0(X0,cS1395)
| ~ aElementOf0(X0,stldt0(xA))
| aInteger0(sK24_skl)
| aElementOf0(sK24_skl,cS1395)
| ~ aSet0(cS1395)
| ~ aElementOf0(sK23_skl,xA)
| aElementOf0(sK23_skl,stldt0(xA))
| ~ aSet0(stldt0(xA))
| sP3_prd ),
inference(cnf_transformation,[status(thm)],[f322]) ).
fof(f339,definition,
( sQ0_spl
<=> sP2_prd ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f342,definition,
( sQ1_spl
<=> aSet0(sdtbsmnsldt0(xA,xB)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f345,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f267,f339,f342]) ).
fof(f346,definition,
! [X0] :
( sQ2_spl
<=> ( aInteger0(X0)
| ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB)) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f347,plain,
! [X0] :
( ~ sQ2_spl
| aInteger0(X0)
| ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB)) ),
inference(component_clause,[status(thm)],[f346]) ).
fof(f349,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f268,f339,f346]) ).
fof(f350,definition,
! [X0] :
( sQ3_spl
<=> ( aElementOf0(X0,xB)
| aElementOf0(X0,xA)
| ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB)) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f351,plain,
! [X0] :
( ~ sQ3_spl
| aElementOf0(X0,xB)
| aElementOf0(X0,xA)
| ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB)) ),
inference(component_clause,[status(thm)],[f350]) ).
fof(f353,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f269,f339,f350]) ).
fof(f354,definition,
! [X0] :
( sQ4_spl
<=> ( ~ aElementOf0(X0,xA)
| ~ aInteger0(X0)
| aElementOf0(X0,sdtbsmnsldt0(xA,xB)) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f355,plain,
! [X0] :
( ~ sQ4_spl
| ~ aElementOf0(X0,xA)
| ~ aInteger0(X0)
| aElementOf0(X0,sdtbsmnsldt0(xA,xB)) ),
inference(component_clause,[status(thm)],[f354]) ).
fof(f357,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f270,f339,f354]) ).
fof(f358,definition,
! [X0] :
( sQ5_spl
<=> ( ~ aElementOf0(X0,xB)
| ~ aInteger0(X0)
| aElementOf0(X0,sdtbsmnsldt0(xA,xB)) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f359,plain,
! [X0] :
( ~ sQ5_spl
| ~ aElementOf0(X0,xB)
| ~ aInteger0(X0)
| aElementOf0(X0,sdtbsmnsldt0(xA,xB)) ),
inference(component_clause,[status(thm)],[f358]) ).
fof(f361,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f271,f339,f358]) ).
fof(f362,definition,
( sQ6_spl
<=> aSet0(stldt0(sdtbsmnsldt0(xA,xB))) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f365,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f272,f339,f362]) ).
fof(f366,definition,
! [X0] :
( sQ7_spl
<=> ( aInteger0(X0)
| ~ aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB))) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f367,plain,
! [X0] :
( ~ sQ7_spl
| aInteger0(X0)
| ~ aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB))) ),
inference(component_clause,[status(thm)],[f366]) ).
fof(f369,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f273,f339,f366]) ).
fof(f370,definition,
! [X0] :
( sQ8_spl
<=> ( ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| ~ aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB))) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f371,plain,
! [X0] :
( ~ sQ8_spl
| ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| ~ aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB))) ),
inference(component_clause,[status(thm)],[f370]) ).
fof(f373,plain,
( sQ8_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f274,f339,f370]) ).
fof(f374,definition,
! [X0] :
( sQ9_spl
<=> ( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(X0)
| aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB))) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f375,plain,
! [X0] :
( ~ sQ9_spl
| aElementOf0(X0,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(X0)
| aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB))) ),
inference(component_clause,[status(thm)],[f374]) ).
fof(f377,plain,
( sQ9_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f275,f339,f374]) ).
fof(f378,definition,
! [X0] :
( sQ10_spl
<=> ( aInteger0(X0)
| ~ aElementOf0(X0,stldt0(xA)) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f379,plain,
! [X0] :
( ~ sQ10_spl
| aInteger0(X0)
| ~ aElementOf0(X0,stldt0(xA)) ),
inference(component_clause,[status(thm)],[f378]) ).
fof(f381,plain,
( sQ10_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f276,f339,f378]) ).
fof(f382,definition,
! [X0] :
( sQ11_spl
<=> ( ~ aElementOf0(X0,xA)
| ~ aElementOf0(X0,stldt0(xA)) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f383,plain,
! [X0] :
( ~ sQ11_spl
| ~ aElementOf0(X0,xA)
| ~ aElementOf0(X0,stldt0(xA)) ),
inference(component_clause,[status(thm)],[f382]) ).
fof(f385,plain,
( sQ11_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f277,f339,f382]) ).
fof(f386,definition,
! [X0] :
( sQ12_spl
<=> ( aElementOf0(X0,xA)
| ~ aInteger0(X0)
| aElementOf0(X0,stldt0(xA)) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f387,plain,
! [X0] :
( ~ sQ12_spl
| aElementOf0(X0,xA)
| ~ aInteger0(X0)
| aElementOf0(X0,stldt0(xA)) ),
inference(component_clause,[status(thm)],[f386]) ).
fof(f389,plain,
( sQ12_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f278,f339,f386]) ).
fof(f390,definition,
! [X0] :
( sQ13_spl
<=> ( aInteger0(X0)
| ~ aElementOf0(X0,stldt0(xB)) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f393,plain,
( sQ13_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f279,f339,f390]) ).
fof(f394,definition,
! [X0] :
( sQ14_spl
<=> ( ~ aElementOf0(X0,xB)
| ~ aElementOf0(X0,stldt0(xB)) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f395,plain,
! [X0] :
( ~ sQ14_spl
| ~ aElementOf0(X0,xB)
| ~ aElementOf0(X0,stldt0(xB)) ),
inference(component_clause,[status(thm)],[f394]) ).
fof(f397,plain,
( sQ14_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f280,f339,f394]) ).
fof(f398,definition,
! [X0] :
( sQ15_spl
<=> ( aElementOf0(X0,xB)
| ~ aInteger0(X0)
| aElementOf0(X0,stldt0(xB)) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f399,plain,
! [X0] :
( ~ sQ15_spl
| aElementOf0(X0,xB)
| ~ aInteger0(X0)
| aElementOf0(X0,stldt0(xB)) ),
inference(component_clause,[status(thm)],[f398]) ).
fof(f401,plain,
( sQ15_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f281,f339,f398]) ).
fof(f402,definition,
( sQ16_spl
<=> aElementOf0(sK18_skl,stldt0(sdtbsmnsldt0(xA,xB))) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f403,plain,
( ~ sQ16_spl
| aElementOf0(sK18_skl,stldt0(sdtbsmnsldt0(xA,xB))) ),
inference(component_clause,[status(thm)],[f402]) ).
fof(f404,plain,
( sQ16_spl
| ~ aElementOf0(sK18_skl,stldt0(sdtbsmnsldt0(xA,xB))) ),
inference(component_clause,[status(thm)],[f402]) ).
fof(f405,definition,
( sQ17_spl
<=> aInteger0(sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f407,plain,
( sQ17_spl
| ~ aInteger0(sK18_skl) ),
inference(component_clause,[status(thm)],[f405]) ).
fof(f409,definition,
( sQ18_spl
<=> aElementOf0(sK18_skl,stldt0(xA)) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f410,plain,
( ~ sQ18_spl
| aElementOf0(sK18_skl,stldt0(xA)) ),
inference(component_clause,[status(thm)],[f409]) ).
fof(f411,plain,
( sQ18_spl
| ~ aElementOf0(sK18_skl,stldt0(xA)) ),
inference(component_clause,[status(thm)],[f409]) ).
fof(f412,plain,
( sQ18_spl
| sQ16_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f283,f339,f402,f409]) ).
fof(f413,definition,
( sQ19_spl
<=> aElementOf0(sK18_skl,stldt0(xB)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f414,plain,
( ~ sQ19_spl
| aElementOf0(sK18_skl,stldt0(xB)) ),
inference(component_clause,[status(thm)],[f413]) ).
fof(f415,plain,
( sQ19_spl
| ~ aElementOf0(sK18_skl,stldt0(xB)) ),
inference(component_clause,[status(thm)],[f413]) ).
fof(f416,plain,
( sQ19_spl
| sQ16_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f284,f339,f402,f413]) ).
fof(f417,plain,
( ~ sQ19_spl
| ~ sQ18_spl
| ~ sQ17_spl
| ~ sQ16_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f285,f339,f402,f405,f409,f413]) ).
fof(f418,definition,
( sQ20_spl
<=> stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f421,plain,
( ~ sQ20_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f286,f339,f418]) ).
fof(f422,definition,
( sQ21_spl
<=> sP3_prd ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f425,definition,
( sQ22_spl
<=> aSet0(stldt0(xB)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f427,plain,
( sQ22_spl
| ~ aSet0(stldt0(xB)) ),
inference(component_clause,[status(thm)],[f425]) ).
fof(f432,definition,
( sQ23_spl
<=> aSet0(cS1395) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f434,plain,
( sQ23_spl
| ~ aSet0(cS1395) ),
inference(component_clause,[status(thm)],[f432]) ).
fof(f444,definition,
( sQ26_spl
<=> aElementOf0(sK19_skl,stldt0(xB)) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f445,plain,
( ~ sQ26_spl
| aElementOf0(sK19_skl,stldt0(xB)) ),
inference(component_clause,[status(thm)],[f444]) ).
fof(f447,plain,
( sQ26_spl
| sQ21_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f310,f339,f422,f444]) ).
fof(f448,definition,
( sQ27_spl
<=> aElementOf0(sK19_skl,cS1395) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f450,plain,
( sQ27_spl
| ~ aElementOf0(sK19_skl,cS1395) ),
inference(component_clause,[status(thm)],[f448]) ).
fof(f451,plain,
( ~ sQ27_spl
| sQ21_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f311,f339,f422,f448]) ).
fof(f452,definition,
( sQ28_spl
<=> aSubsetOf0(stldt0(xB),cS1395) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f453,plain,
( ~ sQ28_spl
| aSubsetOf0(stldt0(xB),cS1395) ),
inference(component_clause,[status(thm)],[f452]) ).
fof(f455,plain,
( ~ sQ28_spl
| sQ21_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f312,f339,f422,f452]) ).
fof(f456,plain,
( ~ sQ21_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f313,f339,f422]) ).
fof(f472,definition,
! [X0] :
( sQ34_spl
<=> ( aElementOf0(X0,cS1395)
| ~ aElementOf0(X0,stldt0(xB)) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f473,plain,
! [X0] :
( ~ sQ34_spl
| aElementOf0(X0,cS1395)
| ~ aElementOf0(X0,stldt0(xB)) ),
inference(component_clause,[status(thm)],[f472]) ).
fof(f481,definition,
( sQ35_spl
<=> aSet0(stldt0(xA)) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f483,plain,
( sQ35_spl
| ~ aSet0(stldt0(xA)) ),
inference(component_clause,[status(thm)],[f481]) ).
fof(f485,plain,
( sQ10_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f324,f422,f378]) ).
fof(f491,definition,
( sQ36_spl
<=> aElementOf0(sK22_skl,stldt0(xA)) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f492,plain,
( ~ sQ36_spl
| aElementOf0(sK22_skl,stldt0(xA)) ),
inference(component_clause,[status(thm)],[f491]) ).
fof(f494,plain,
( sQ36_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f330,f422,f491]) ).
fof(f495,definition,
( sQ37_spl
<=> aElementOf0(sK22_skl,cS1395) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f497,plain,
( sQ37_spl
| ~ aElementOf0(sK22_skl,cS1395) ),
inference(component_clause,[status(thm)],[f495]) ).
fof(f498,plain,
( ~ sQ37_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f331,f422,f495]) ).
fof(f499,definition,
( sQ38_spl
<=> aSubsetOf0(stldt0(xA),cS1395) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f500,plain,
( ~ sQ38_spl
| aSubsetOf0(stldt0(xA),cS1395) ),
inference(component_clause,[status(thm)],[f499]) ).
fof(f503,definition,
( sQ39_spl
<=> aElementOf0(sK23_skl,stldt0(xA)) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f504,plain,
( ~ sQ39_spl
| aElementOf0(sK23_skl,stldt0(xA)) ),
inference(component_clause,[status(thm)],[f503]) ).
fof(f505,plain,
( sQ39_spl
| ~ aElementOf0(sK23_skl,stldt0(xA)) ),
inference(component_clause,[status(thm)],[f503]) ).
fof(f506,definition,
( sQ40_spl
<=> aInteger0(sK23_skl) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f509,definition,
( sQ41_spl
<=> aElementOf0(sK23_skl,xA) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f510,plain,
( ~ sQ41_spl
| aElementOf0(sK23_skl,xA) ),
inference(component_clause,[status(thm)],[f509]) ).
fof(f512,definition,
( sQ42_spl
<=> aElementOf0(sK24_skl,cS1395) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f515,definition,
( sQ43_spl
<=> aInteger0(sK24_skl) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f518,definition,
! [X0] :
( sQ44_spl
<=> ( aElementOf0(X0,cS1395)
| ~ aElementOf0(X0,stldt0(xA)) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f519,plain,
! [X0] :
( ~ sQ44_spl
| aElementOf0(X0,cS1395)
| ~ aElementOf0(X0,stldt0(xA)) ),
inference(component_clause,[status(thm)],[f518]) ).
fof(f523,plain,
( sQ38_spl
| sQ44_spl
| ~ sQ43_spl
| ~ sQ42_spl
| ~ sQ23_spl
| sQ40_spl
| sQ39_spl
| ~ sQ35_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f335,f422,f481,f503,f506,f432,f512,f515,f518,f499]) ).
fof(f524,plain,
( sQ38_spl
| sQ44_spl
| sQ43_spl
| sQ42_spl
| ~ sQ23_spl
| sQ40_spl
| sQ39_spl
| ~ sQ35_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f336,f422,f481,f503,f506,f432,f512,f515,f518,f499]) ).
fof(f525,plain,
( sQ38_spl
| sQ44_spl
| ~ sQ43_spl
| ~ sQ42_spl
| ~ sQ23_spl
| ~ sQ41_spl
| sQ39_spl
| ~ sQ35_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f337,f422,f481,f503,f509,f432,f512,f515,f518,f499]) ).
fof(f526,plain,
( sQ38_spl
| sQ44_spl
| sQ43_spl
| sQ42_spl
| ~ sQ23_spl
| ~ sQ41_spl
| sQ39_spl
| ~ sQ35_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f338,f422,f481,f503,f509,f432,f512,f515,f518,f499]) ).
fof(f532,plain,
! [X0,X1,X2] :
( aInteger0(X2)
| ~ aElementOf0(X2,sdtbsmnsldt0(X0,X1))
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(destructive_equality_resolution,[status(thm)],[f133]) ).
fof(f533,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X1)
| aElementOf0(X2,X0)
| ~ aElementOf0(X2,sdtbsmnsldt0(X0,X1))
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(destructive_equality_resolution,[status(thm)],[f134]) ).
fof(f534,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X2,X0)
| ~ aInteger0(X2)
| aElementOf0(X2,sdtbsmnsldt0(X0,X1))
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(destructive_equality_resolution,[status(thm)],[f135]) ).
fof(f535,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X2,X1)
| ~ aInteger0(X2)
| aElementOf0(X2,sdtbsmnsldt0(X0,X1))
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(destructive_equality_resolution,[status(thm)],[f136]) ).
fof(f545,plain,
! [X0,X1] :
( aInteger0(X1)
| ~ aElementOf0(X1,stldt0(X0))
| ~ aSubsetOf0(X0,cS1395) ),
inference(destructive_equality_resolution,[status(thm)],[f172]) ).
fof(f546,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| ~ aElementOf0(X1,stldt0(X0))
| ~ aSubsetOf0(X0,cS1395) ),
inference(destructive_equality_resolution,[status(thm)],[f173]) ).
fof(f547,plain,
! [X0,X1] :
( aElementOf0(X1,X0)
| ~ aInteger0(X1)
| aElementOf0(X1,stldt0(X0))
| ~ aSubsetOf0(X0,cS1395) ),
inference(destructive_equality_resolution,[status(thm)],[f174]) ).
fof(f552,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f211,f434]) ).
fof(f553,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f552]) ).
fof(f554,plain,
( aSet0(xB)
| ~ aSet0(cS1395) ),
inference(resolution,[status(thm)],[f122,f222]) ).
fof(f555,plain,
( aSet0(xA)
| ~ aSet0(cS1395) ),
inference(resolution,[status(thm)],[f122,f216]) ).
fof(f556,definition,
( sQ45_spl
<=> aSet0(xB) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f559,plain,
( sQ45_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f554,f432,f556]) ).
fof(f560,definition,
( sQ46_spl
<=> aSet0(xA) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f563,plain,
( sQ46_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f555,f432,f560]) ).
fof(f564,plain,
! [X0] :
( aElementOf0(X0,cS1395)
| ~ aElementOf0(X0,xB)
| ~ aSet0(cS1395) ),
inference(resolution,[status(thm)],[f123,f222]) ).
fof(f565,plain,
! [X0] :
( aElementOf0(X0,cS1395)
| ~ aElementOf0(X0,xA)
| ~ aSet0(cS1395) ),
inference(resolution,[status(thm)],[f123,f216]) ).
fof(f566,definition,
! [X0] :
( sQ47_spl
<=> ( aElementOf0(X0,cS1395)
| ~ aElementOf0(X0,xB) ) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f569,plain,
( sQ47_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f564,f432,f566]) ).
fof(f570,definition,
! [X0] :
( sQ48_spl
<=> ( aElementOf0(X0,cS1395)
| ~ aElementOf0(X0,xA) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f573,plain,
( sQ48_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f565,f432,f570]) ).
fof(f574,plain,
( sQ37_spl
| ~ aInteger0(sK22_skl) ),
inference(resolution,[status(thm)],[f213,f497]) ).
fof(f576,plain,
( ~ sQ36_spl
| ~ sQ10_spl
| aInteger0(sK22_skl) ),
inference(resolution,[status(thm)],[f379,f492]) ).
fof(f577,plain,
( ~ sQ36_spl
| ~ sQ10_spl
| sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f576,f574]) ).
fof(f578,plain,
( ~ sQ36_spl
| ~ sQ10_spl
| sQ37_spl ),
inference(contradiction_clause,[status(thm)],[f577]) ).
fof(f579,plain,
( sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f483,f223]) ).
fof(f580,plain,
sQ35_spl,
inference(contradiction_clause,[status(thm)],[f579]) ).
fof(f581,plain,
( sQ27_spl
| ~ aInteger0(sK19_skl) ),
inference(resolution,[status(thm)],[f450,f213]) ).
fof(f583,plain,
! [X0] :
( ~ sQ38_spl
| aElementOf0(X0,cS1395)
| ~ aElementOf0(X0,stldt0(xA))
| ~ aSet0(cS1395) ),
inference(resolution,[status(thm)],[f500,f123]) ).
fof(f585,plain,
( ~ sQ38_spl
| sQ44_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f583,f432,f518,f499]) ).
fof(f587,plain,
( ~ sQ11_spl
| ~ sQ39_spl
| ~ aElementOf0(sK23_skl,xA) ),
inference(resolution,[status(thm)],[f504,f383]) ).
fof(f596,plain,
( ~ sQ26_spl
| aInteger0(sK19_skl) ),
inference(resolution,[status(thm)],[f243,f445]) ).
fof(f597,plain,
( ~ sQ26_spl
| sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f596,f581]) ).
fof(f598,plain,
( ~ sQ26_spl
| sQ27_spl ),
inference(contradiction_clause,[status(thm)],[f597]) ).
fof(f599,plain,
( sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f427,f242]) ).
fof(f600,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f599]) ).
fof(f601,plain,
( ~ sQ41_spl
| ~ sQ11_spl
| ~ sQ39_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f510,f587]) ).
fof(f602,plain,
( ~ sQ41_spl
| ~ sQ11_spl
| ~ sQ39_spl ),
inference(contradiction_clause,[status(thm)],[f601]) ).
fof(f612,plain,
! [X0] :
( ~ sQ28_spl
| aElementOf0(X0,cS1395)
| ~ aElementOf0(X0,stldt0(xB))
| ~ aSet0(cS1395) ),
inference(resolution,[status(thm)],[f453,f123]) ).
fof(f614,plain,
( ~ sQ28_spl
| sQ34_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f612,f432,f472,f452]) ).
fof(f619,plain,
! [X0,X1,X2] :
( aInteger0(X2)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395)
| ~ aElementOf0(X2,X0)
| ~ aInteger0(X2)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(resolution,[status(thm)],[f534,f532]) ).
fof(f620,definition,
! [X0,X2] :
( sQ49_spl
<=> ( aInteger0(X2)
| ~ aSubsetOf0(X0,cS1395)
| ~ aElementOf0(X2,X0)
| ~ aInteger0(X2)
| ~ aSubsetOf0(X0,cS1395) ) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f623,definition,
! [X1] :
( sQ50_spl
<=> ( ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X1,cS1395) ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f624,plain,
! [X0] :
( ~ sQ50_spl
| ~ aSubsetOf0(X0,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(component_clause,[status(thm)],[f623]) ).
fof(f626,plain,
( sQ50_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f619,f620,f623]) ).
fof(f627,plain,
! [X0] :
( ~ sQ50_spl
| ~ aSubsetOf0(X0,cS1395) ),
inference(duplicate_literals_removal,[status(thm)],[f624]) ).
fof(f628,plain,
( ~ sQ28_spl
| ~ sQ50_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f453,f627]) ).
fof(f632,plain,
( ~ sQ28_spl
| ~ sQ50_spl ),
inference(contradiction_clause,[status(thm)],[f628]) ).
fof(f642,plain,
( ~ sQ19_spl
| aInteger0(sK18_skl) ),
inference(resolution,[status(thm)],[f414,f243]) ).
fof(f643,plain,
( ~ sQ19_spl
| sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f642,f407]) ).
fof(f644,plain,
( ~ sQ19_spl
| sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f643]) ).
fof(f645,plain,
( ~ sQ12_spl
| sQ39_spl
| aElementOf0(sK23_skl,xA)
| ~ aInteger0(sK23_skl) ),
inference(resolution,[status(thm)],[f505,f387]) ).
fof(f646,plain,
( ~ sQ12_spl
| sQ39_spl
| sQ41_spl
| ~ sQ40_spl ),
inference(split_clause,[status(thm)],[f645,f506,f509,f503,f386]) ).
fof(f653,plain,
( ~ sQ16_spl
| ~ sQ7_spl
| aInteger0(sK18_skl) ),
inference(resolution,[status(thm)],[f367,f403]) ).
fof(f654,plain,
( sQ19_spl
| ~ sQ15_spl
| aElementOf0(sK18_skl,xB)
| ~ aInteger0(sK18_skl) ),
inference(resolution,[status(thm)],[f399,f415]) ).
fof(f658,definition,
( sQ51_spl
<=> aElementOf0(sK18_skl,xB) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f659,plain,
( ~ sQ51_spl
| aElementOf0(sK18_skl,xB) ),
inference(component_clause,[status(thm)],[f658]) ).
fof(f661,plain,
( sQ19_spl
| ~ sQ15_spl
| sQ51_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f654,f405,f658,f398,f413]) ).
fof(f662,plain,
( ~ sQ51_spl
| aElementOf0(sK18_skl,cS1395) ),
inference(resolution,[status(thm)],[f659,f221]) ).
fof(f664,plain,
( ~ sQ12_spl
| sQ18_spl
| aElementOf0(sK18_skl,xA)
| ~ aInteger0(sK18_skl) ),
inference(resolution,[status(thm)],[f411,f387]) ).
fof(f665,definition,
( sQ52_spl
<=> aElementOf0(sK18_skl,xA) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f666,plain,
( ~ sQ52_spl
| aElementOf0(sK18_skl,xA) ),
inference(component_clause,[status(thm)],[f665]) ).
fof(f668,plain,
( ~ sQ12_spl
| sQ18_spl
| sQ52_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f664,f405,f665,f409,f386]) ).
fof(f673,definition,
( sQ53_spl
<=> aSubsetOf0(sdtbsmnsldt0(xA,xB),cS1395) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f677,definition,
( sQ54_spl
<=> aSubsetOf0(xB,cS1395) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f679,plain,
( sQ54_spl
| ~ aSubsetOf0(xB,cS1395) ),
inference(component_clause,[status(thm)],[f677]) ).
fof(f680,definition,
! [X0] :
( sQ55_spl
<=> ( aElementOf0(X0,xB)
| ~ aInteger0(X0)
| aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f684,definition,
( sQ56_spl
<=> aSubsetOf0(xA,cS1395) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f686,plain,
( sQ56_spl
| ~ aSubsetOf0(xA,cS1395) ),
inference(component_clause,[status(thm)],[f684]) ).
fof(f687,definition,
! [X0] :
( sQ57_spl
<=> ( aElementOf0(X0,xA)
| ~ aInteger0(X0)
| aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f691,plain,
( sQ54_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f679,f222]) ).
fof(f692,plain,
sQ54_spl,
inference(contradiction_clause,[status(thm)],[f691]) ).
fof(f693,plain,
( sQ56_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f686,f216]) ).
fof(f694,plain,
sQ56_spl,
inference(contradiction_clause,[status(thm)],[f693]) ).
fof(f695,plain,
( ~ sQ16_spl
| ~ aElementOf0(sK18_skl,sdtbsmnsldt0(xA,xB))
| ~ aSubsetOf0(sdtbsmnsldt0(xA,xB),cS1395) ),
inference(resolution,[status(thm)],[f546,f403]) ).
fof(f698,definition,
( sQ58_spl
<=> aElementOf0(sK18_skl,sdtbsmnsldt0(xA,xB)) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f699,plain,
( ~ sQ58_spl
| aElementOf0(sK18_skl,sdtbsmnsldt0(xA,xB)) ),
inference(component_clause,[status(thm)],[f698]) ).
fof(f700,plain,
( sQ58_spl
| ~ aElementOf0(sK18_skl,sdtbsmnsldt0(xA,xB)) ),
inference(component_clause,[status(thm)],[f698]) ).
fof(f701,plain,
( ~ sQ16_spl
| ~ sQ58_spl
| ~ sQ53_spl ),
inference(split_clause,[status(thm)],[f695,f673,f698,f402]) ).
fof(f702,definition,
! [X0] :
( sQ59_spl
<=> ( aElementOf0(X0,xB)
| ~ aInteger0(X0)
| ~ aElementOf0(X0,xB) ) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f706,definition,
! [X0] :
( sQ60_spl
<=> ( aElementOf0(X0,xA)
| ~ aInteger0(X0)
| ~ aElementOf0(X0,xA) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f710,plain,
! [X0] :
( ~ sQ2_spl
| aInteger0(X0)
| ~ aElementOf0(X0,xB)
| ~ aInteger0(X0)
| ~ aSubsetOf0(xB,cS1395)
| ~ aSubsetOf0(xA,cS1395) ),
inference(resolution,[status(thm)],[f535,f347]) ).
fof(f711,definition,
! [X0] :
( sQ61_spl
<=> ( aInteger0(X0)
| ~ aElementOf0(X0,xB)
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f714,plain,
( ~ sQ2_spl
| sQ61_spl
| ~ sQ54_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f710,f684,f677,f711,f346]) ).
fof(f717,plain,
( isOpen0(stldt0(xA))
| ~ isClosed0(xA) ),
inference(resolution,[status(thm)],[f199,f216]) ).
fof(f718,plain,
( isOpen0(stldt0(xB))
| ~ isClosed0(xB) ),
inference(resolution,[status(thm)],[f199,f222]) ).
fof(f719,definition,
( sQ62_spl
<=> isClosed0(xA) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f721,plain,
( sQ62_spl
| ~ isClosed0(xA) ),
inference(component_clause,[status(thm)],[f719]) ).
fof(f722,definition,
( sQ63_spl
<=> isOpen0(stldt0(xA)) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f725,plain,
( sQ63_spl
| ~ sQ62_spl ),
inference(split_clause,[status(thm)],[f717,f719,f722]) ).
fof(f726,definition,
( sQ64_spl
<=> isClosed0(xB) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f728,plain,
( sQ64_spl
| ~ isClosed0(xB) ),
inference(component_clause,[status(thm)],[f726]) ).
fof(f729,definition,
( sQ65_spl
<=> isOpen0(stldt0(xB)) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f732,plain,
( sQ65_spl
| ~ sQ64_spl ),
inference(split_clause,[status(thm)],[f718,f726,f729]) ).
fof(f733,plain,
( sQ64_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f728,f260]) ).
fof(f734,plain,
sQ64_spl,
inference(contradiction_clause,[status(thm)],[f733]) ).
fof(f735,plain,
( sQ62_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f721,f241]) ).
fof(f736,plain,
sQ62_spl,
inference(contradiction_clause,[status(thm)],[f735]) ).
fof(f741,plain,
( ~ sQ52_spl
| aSubsetOf0(sK18_skl,cS1395)
| sP1_prd(sK18_skl,xA) ),
inference(resolution,[status(thm)],[f297,f666]) ).
fof(f742,plain,
( ~ sQ51_spl
| aSubsetOf0(sK18_skl,cS1395)
| sP1_prd(sK18_skl,cS1395) ),
inference(resolution,[status(thm)],[f297,f662]) ).
fof(f743,plain,
( ~ sQ51_spl
| aSubsetOf0(sK18_skl,cS1395)
| sP1_prd(sK18_skl,xB) ),
inference(resolution,[status(thm)],[f297,f659]) ).
fof(f751,definition,
( sQ66_spl
<=> sP1_prd(sK18_skl,xA) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f752,plain,
( ~ sQ66_spl
| sP1_prd(sK18_skl,xA) ),
inference(component_clause,[status(thm)],[f751]) ).
fof(f754,definition,
( sQ67_spl
<=> aSubsetOf0(sK18_skl,cS1395) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f755,plain,
( ~ sQ67_spl
| aSubsetOf0(sK18_skl,cS1395) ),
inference(component_clause,[status(thm)],[f754]) ).
fof(f757,plain,
( ~ sQ52_spl
| sQ67_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f741,f751,f754,f665]) ).
fof(f758,definition,
( sQ68_spl
<=> sP1_prd(sK18_skl,cS1395) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f761,plain,
( ~ sQ51_spl
| sQ67_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f742,f758,f754,f658]) ).
fof(f762,definition,
( sQ69_spl
<=> sP1_prd(sK18_skl,xB) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f763,plain,
( ~ sQ69_spl
| sP1_prd(sK18_skl,xB) ),
inference(component_clause,[status(thm)],[f762]) ).
fof(f765,plain,
( ~ sQ51_spl
| sQ67_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f743,f762,f754,f658]) ).
fof(f784,plain,
( ~ sQ67_spl
| isOpen0(stldt0(sK18_skl))
| ~ isClosed0(sK18_skl) ),
inference(resolution,[status(thm)],[f755,f199]) ).
fof(f787,plain,
! [X0] :
( ~ sQ67_spl
| aElementOf0(X0,cS1395)
| ~ aElementOf0(X0,sK18_skl)
| ~ aSet0(cS1395) ),
inference(resolution,[status(thm)],[f755,f123]) ).
fof(f788,plain,
( ~ sQ67_spl
| aSet0(sK18_skl)
| ~ aSet0(cS1395) ),
inference(resolution,[status(thm)],[f755,f122]) ).
fof(f789,definition,
( sQ75_spl
<=> isClosed0(sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f792,definition,
( sQ76_spl
<=> isOpen0(stldt0(sK18_skl)) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f793,plain,
( ~ sQ76_spl
| isOpen0(stldt0(sK18_skl)) ),
inference(component_clause,[status(thm)],[f792]) ).
fof(f795,plain,
( ~ sQ67_spl
| sQ76_spl
| ~ sQ75_spl ),
inference(split_clause,[status(thm)],[f784,f789,f792,f754]) ).
fof(f796,definition,
! [X0] :
( sQ77_spl
<=> ( aElementOf0(X0,cS1395)
| ~ aElementOf0(X0,sK18_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f799,plain,
( ~ sQ67_spl
| sQ77_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f787,f432,f796,f754]) ).
fof(f800,definition,
( sQ78_spl
<=> aSet0(sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f803,plain,
( ~ sQ67_spl
| sQ78_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f788,f432,f800,f754]) ).
fof(f809,plain,
( ~ sQ76_spl
| isClosed0(sK18_skl)
| ~ aSubsetOf0(sK18_skl,cS1395) ),
inference(resolution,[status(thm)],[f793,f200]) ).
fof(f810,plain,
( ~ sQ76_spl
| sQ75_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f809,f754,f789,f792]) ).
fof(f818,definition,
( sQ80_spl
<=> aInteger0(sz00) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f820,plain,
( sQ80_spl
| ~ aInteger0(sz00) ),
inference(component_clause,[status(thm)],[f818]) ).
fof(f825,definition,
( sQ82_spl
<=> aInteger0(sz10) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f827,plain,
( sQ82_spl
| ~ aInteger0(sz10) ),
inference(component_clause,[status(thm)],[f825]) ).
fof(f834,plain,
( sQ80_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f820,f45]) ).
fof(f835,plain,
sQ80_spl,
inference(contradiction_clause,[status(thm)],[f834]) ).
fof(f836,plain,
( sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f827,f46]) ).
fof(f837,plain,
sQ82_spl,
inference(contradiction_clause,[status(thm)],[f836]) ).
fof(f839,plain,
! [X0] :
( sK0_skl(X0,sz00) = sz00
| X0 = sz00
| ~ aInteger0(sK0_skl(X0,sz00))
| ~ aInteger0(X0)
| ~ aDivisorOf0(X0,sz00)
| ~ aInteger0(sz00) ),
inference(resolution,[status(thm)],[f88,f80]) ).
fof(f840,definition,
! [X0] :
( sQ84_spl
<=> ( sK0_skl(X0,sz00) = sz00
| X0 = sz00
| ~ aInteger0(sK0_skl(X0,sz00))
| ~ aInteger0(X0)
| ~ aDivisorOf0(X0,sz00) ) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f843,plain,
( sQ84_spl
| ~ sQ80_spl ),
inference(split_clause,[status(thm)],[f839,f818,f840]) ).
fof(f884,plain,
! [X0] :
( ~ sQ3_spl
| ~ aElementOf0(X0,xB)
| ~ aInteger0(X0)
| ~ aSubsetOf0(xB,cS1395)
| ~ aSubsetOf0(xA,cS1395)
| aElementOf0(X0,xB)
| aElementOf0(X0,xA) ),
inference(resolution,[status(thm)],[f351,f535]) ).
fof(f885,definition,
! [X0] :
( sQ93_spl
<=> ( ~ aElementOf0(X0,xB)
| ~ aInteger0(X0)
| aElementOf0(X0,xB)
| aElementOf0(X0,xA) ) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f888,plain,
( ~ sQ3_spl
| ~ sQ54_spl
| ~ sQ56_spl
| sQ93_spl ),
inference(split_clause,[status(thm)],[f884,f885,f684,f677,f350]) ).
fof(f931,plain,
( sQ18_spl
| aElementOf0(sK18_skl,xA)
| ~ aInteger0(sK18_skl)
| ~ aSubsetOf0(xA,cS1395) ),
inference(resolution,[status(thm)],[f547,f411]) ).
fof(f934,plain,
! [X0] :
( aInteger0(sK16_skl(X0))
| aElementOf0(X0,xB)
| ~ aInteger0(X0)
| ~ aSubsetOf0(xB,cS1395) ),
inference(resolution,[status(thm)],[f547,f246]) ).
fof(f935,plain,
! [X0] :
( ~ sQ14_spl
| ~ aElementOf0(X0,xB)
| aElementOf0(X0,xB)
| ~ aInteger0(X0)
| ~ aSubsetOf0(xB,cS1395) ),
inference(resolution,[status(thm)],[f547,f395]) ).
fof(f936,plain,
! [X0] :
( ~ sQ34_spl
| aElementOf0(X0,cS1395)
| aElementOf0(X0,xB)
| ~ aInteger0(X0)
| ~ aSubsetOf0(xB,cS1395) ),
inference(resolution,[status(thm)],[f547,f473]) ).
fof(f937,plain,
! [X0] :
( aInteger0(X0)
| aElementOf0(X0,xB)
| ~ aInteger0(X0)
| ~ aSubsetOf0(xB,cS1395) ),
inference(resolution,[status(thm)],[f547,f243]) ).
fof(f938,plain,
! [X0] :
( aInteger0(sK14_skl(X0))
| aElementOf0(X0,xA)
| ~ aInteger0(X0)
| ~ aSubsetOf0(xA,cS1395) ),
inference(resolution,[status(thm)],[f547,f227]) ).
fof(f939,plain,
! [X0] :
( ~ sQ44_spl
| aElementOf0(X0,cS1395)
| aElementOf0(X0,xA)
| ~ aInteger0(X0)
| ~ aSubsetOf0(xA,cS1395) ),
inference(resolution,[status(thm)],[f547,f519]) ).
fof(f940,plain,
! [X0] :
( ~ sQ11_spl
| ~ aElementOf0(X0,xA)
| aElementOf0(X0,xA)
| ~ aInteger0(X0)
| ~ aSubsetOf0(xA,cS1395) ),
inference(resolution,[status(thm)],[f547,f383]) ).
fof(f941,plain,
! [X0] :
( ~ sQ10_spl
| aInteger0(X0)
| aElementOf0(X0,xA)
| ~ aInteger0(X0)
| ~ aSubsetOf0(xA,cS1395) ),
inference(resolution,[status(thm)],[f547,f379]) ).
fof(f945,plain,
( sQ18_spl
| sQ52_spl
| ~ sQ17_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f931,f684,f405,f665,f409]) ).
fof(f951,definition,
! [X0] :
( sQ101_spl
<=> ( aInteger0(sK16_skl(X0))
| aElementOf0(X0,xB)
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f954,plain,
( sQ101_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f934,f677,f951]) ).
fof(f955,plain,
( ~ sQ14_spl
| sQ59_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f935,f677,f702,f394]) ).
fof(f956,definition,
! [X0] :
( sQ102_spl
<=> ( aElementOf0(X0,cS1395)
| aElementOf0(X0,xB)
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f959,plain,
( ~ sQ34_spl
| sQ102_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f936,f677,f956,f472]) ).
fof(f960,plain,
( sQ55_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f937,f677,f680]) ).
fof(f961,definition,
! [X0] :
( sQ103_spl
<=> ( aInteger0(sK14_skl(X0))
| aElementOf0(X0,xA)
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f964,plain,
( sQ103_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f938,f684,f961]) ).
fof(f965,definition,
! [X0] :
( sQ104_spl
<=> ( aElementOf0(X0,cS1395)
| aElementOf0(X0,xA)
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f968,plain,
( ~ sQ44_spl
| sQ104_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f939,f684,f965,f518]) ).
fof(f969,plain,
( ~ sQ11_spl
| sQ60_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f940,f684,f706,f382]) ).
fof(f970,plain,
( ~ sQ10_spl
| sQ57_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f941,f684,f687,f378]) ).
fof(f1032,plain,
( ~ sQ41_spl
| aElementOf0(sK23_skl,cS1395) ),
inference(resolution,[status(thm)],[f510,f215]) ).
fof(f1033,plain,
( ~ sQ41_spl
| aSubsetOf0(sK23_skl,cS1395)
| sP1_prd(sK23_skl,xA) ),
inference(resolution,[status(thm)],[f510,f297]) ).
fof(f1034,definition,
( sQ105_spl
<=> sP1_prd(sK23_skl,xA) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f1035,plain,
( ~ sQ105_spl
| sP1_prd(sK23_skl,xA) ),
inference(component_clause,[status(thm)],[f1034]) ).
fof(f1037,definition,
( sQ106_spl
<=> aSubsetOf0(sK23_skl,cS1395) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f1038,plain,
( ~ sQ106_spl
| aSubsetOf0(sK23_skl,cS1395) ),
inference(component_clause,[status(thm)],[f1037]) ).
fof(f1040,plain,
( ~ sQ41_spl
| sQ106_spl
| sQ105_spl ),
inference(split_clause,[status(thm)],[f1033,f1034,f1037,f509]) ).
fof(f1049,plain,
( ~ sQ69_spl
| aElementOf0(sK18_skl,xB) ),
inference(resolution,[status(thm)],[f763,f295]) ).
fof(f1051,plain,
( ~ sQ66_spl
| aElementOf0(sK18_skl,xA) ),
inference(resolution,[status(thm)],[f752,f295]) ).
fof(f1052,plain,
( ~ sQ52_spl
| aElementOf0(sK18_skl,cS1395) ),
inference(resolution,[status(thm)],[f666,f215]) ).
fof(f1061,plain,
( ~ sQ41_spl
| aInteger0(sK23_skl) ),
inference(resolution,[status(thm)],[f1032,f212]) ).
fof(f1062,plain,
( ~ sQ41_spl
| aSubsetOf0(sK23_skl,cS1395)
| sP1_prd(sK23_skl,cS1395) ),
inference(resolution,[status(thm)],[f1032,f297]) ).
fof(f1063,plain,
( ~ sQ41_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f1061,f506,f509]) ).
fof(f1064,definition,
( sQ107_spl
<=> sP1_prd(sK23_skl,cS1395) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f1065,plain,
( ~ sQ107_spl
| sP1_prd(sK23_skl,cS1395) ),
inference(component_clause,[status(thm)],[f1064]) ).
fof(f1067,plain,
( ~ sQ41_spl
| sQ106_spl
| sQ107_spl ),
inference(split_clause,[status(thm)],[f1062,f1064,f1037,f509]) ).
fof(f1068,plain,
( ~ sQ106_spl
| isOpen0(stldt0(sK23_skl))
| ~ isClosed0(sK23_skl) ),
inference(resolution,[status(thm)],[f1038,f199]) ).
fof(f1070,plain,
! [X0] :
( ~ sQ106_spl
| ~ sP1_prd(sK23_skl,X0) ),
inference(resolution,[status(thm)],[f1038,f296]) ).
fof(f1071,plain,
! [X0] :
( ~ sQ106_spl
| aElementOf0(X0,cS1395)
| ~ aElementOf0(X0,sK23_skl)
| ~ aSet0(cS1395) ),
inference(resolution,[status(thm)],[f1038,f123]) ).
fof(f1072,plain,
( ~ sQ106_spl
| aSet0(sK23_skl)
| ~ aSet0(cS1395) ),
inference(resolution,[status(thm)],[f1038,f122]) ).
fof(f1073,definition,
( sQ108_spl
<=> isClosed0(sK23_skl) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f1076,definition,
( sQ109_spl
<=> isOpen0(stldt0(sK23_skl)) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f1077,plain,
( ~ sQ109_spl
| isOpen0(stldt0(sK23_skl)) ),
inference(component_clause,[status(thm)],[f1076]) ).
fof(f1079,plain,
( ~ sQ106_spl
| sQ109_spl
| ~ sQ108_spl ),
inference(split_clause,[status(thm)],[f1068,f1073,f1076,f1037]) ).
fof(f1080,definition,
! [X0] :
( sQ110_spl
<=> ( aElementOf0(X0,cS1395)
| ~ aElementOf0(X0,sK23_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f1081,plain,
! [X0] :
( ~ sQ110_spl
| aElementOf0(X0,cS1395)
| ~ aElementOf0(X0,sK23_skl) ),
inference(component_clause,[status(thm)],[f1080]) ).
fof(f1083,plain,
( ~ sQ106_spl
| sQ110_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f1071,f432,f1080,f1037]) ).
fof(f1084,definition,
( sQ111_spl
<=> aSet0(sK23_skl) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f1087,plain,
( ~ sQ106_spl
| sQ111_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f1072,f432,f1084,f1037]) ).
fof(f1093,plain,
( ~ sQ109_spl
| isClosed0(sK23_skl)
| ~ aSubsetOf0(sK23_skl,cS1395) ),
inference(resolution,[status(thm)],[f1077,f200]) ).
fof(f1094,plain,
( ~ sQ109_spl
| sQ108_spl
| ~ sQ106_spl ),
inference(split_clause,[status(thm)],[f1093,f1037,f1073,f1076]) ).
fof(f1095,plain,
( ~ sQ107_spl
| ~ sQ106_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1065,f1070]) ).
fof(f1096,plain,
( ~ sQ105_spl
| ~ sQ106_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1035,f1070]) ).
fof(f1097,plain,
( ~ sQ107_spl
| ~ sQ106_spl ),
inference(contradiction_clause,[status(thm)],[f1095]) ).
fof(f1098,plain,
( ~ sQ105_spl
| ~ sQ106_spl ),
inference(contradiction_clause,[status(thm)],[f1096]) ).
fof(f1183,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ aElementOf0(sK18_skl,xA) ),
inference(resolution,[status(thm)],[f410,f383]) ).
fof(f1185,plain,
( ~ sQ18_spl
| ~ aElementOf0(sK18_skl,xA)
| ~ aSubsetOf0(xA,cS1395) ),
inference(resolution,[status(thm)],[f410,f546]) ).
fof(f1186,plain,
( ~ sQ18_spl
| aInteger0(sK18_skl)
| ~ aSubsetOf0(xA,cS1395) ),
inference(resolution,[status(thm)],[f410,f545]) ).
fof(f1187,plain,
( ~ sQ18_spl
| aSubsetOf0(sK18_skl,cS1395)
| sP1_prd(sK18_skl,stldt0(xA)) ),
inference(resolution,[status(thm)],[f410,f297]) ).
fof(f1188,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ52_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1183,f666]) ).
fof(f1189,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ52_spl ),
inference(contradiction_clause,[status(thm)],[f1188]) ).
fof(f1190,plain,
( ~ sQ16_spl
| ~ sQ7_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f653,f405,f366,f402]) ).
fof(f1191,plain,
( ~ sQ69_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f1049,f658,f762]) ).
fof(f1194,plain,
( ~ sQ52_spl
| aSubsetOf0(sK18_skl,cS1395)
| sP1_prd(sK18_skl,cS1395) ),
inference(resolution,[status(thm)],[f1052,f297]) ).
fof(f1195,plain,
( ~ sQ52_spl
| sQ67_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f1194,f758,f754,f665]) ).
fof(f1196,plain,
( ~ sQ18_spl
| ~ sQ52_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f1185,f684,f665,f409]) ).
fof(f1197,plain,
( ~ sQ18_spl
| sQ17_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f1186,f684,f405,f409]) ).
fof(f1198,definition,
( sQ120_spl
<=> sP1_prd(sK18_skl,stldt0(xA)) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f1201,plain,
( ~ sQ18_spl
| sQ67_spl
| sQ120_spl ),
inference(split_clause,[status(thm)],[f1187,f1198,f754,f409]) ).
fof(f1237,plain,
! [X0] :
( ~ sQ3_spl
| aElementOf0(X0,xB)
| aElementOf0(X0,xA)
| ~ aElementOf0(X0,xA)
| ~ aInteger0(X0)
| ~ aSubsetOf0(xB,cS1395)
| ~ aSubsetOf0(xA,cS1395) ),
inference(resolution,[status(thm)],[f534,f351]) ).
fof(f1238,plain,
! [X0] :
( ~ sQ2_spl
| aInteger0(X0)
| ~ aElementOf0(X0,xA)
| ~ aInteger0(X0)
| ~ aSubsetOf0(xB,cS1395)
| ~ aSubsetOf0(xA,cS1395) ),
inference(resolution,[status(thm)],[f534,f347]) ).
fof(f1240,definition,
! [X0] :
( sQ121_spl
<=> ( aElementOf0(X0,xB)
| aElementOf0(X0,xA)
| ~ aElementOf0(X0,xA)
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f1243,plain,
( ~ sQ3_spl
| sQ121_spl
| ~ sQ54_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f1237,f684,f677,f1240,f350]) ).
fof(f1244,definition,
! [X0] :
( sQ122_spl
<=> ( aInteger0(X0)
| ~ aElementOf0(X0,xA)
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f1247,plain,
( ~ sQ2_spl
| sQ122_spl
| ~ sQ54_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f1238,f684,f677,f1244,f346]) ).
fof(f1280,plain,
( ~ sQ19_spl
| ~ aElementOf0(sK18_skl,xB)
| ~ aSubsetOf0(xB,cS1395) ),
inference(resolution,[status(thm)],[f414,f546]) ).
fof(f1282,plain,
( ~ sQ19_spl
| aSubsetOf0(sK18_skl,cS1395)
| sP1_prd(sK18_skl,stldt0(xB)) ),
inference(resolution,[status(thm)],[f414,f297]) ).
fof(f1283,plain,
( ~ sQ19_spl
| ~ sQ51_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f1280,f677,f658,f413]) ).
fof(f1285,definition,
( sQ126_spl
<=> sP1_prd(sK18_skl,stldt0(xB)) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f1286,plain,
( ~ sQ126_spl
| sP1_prd(sK18_skl,stldt0(xB)) ),
inference(component_clause,[status(thm)],[f1285]) ).
fof(f1288,plain,
( ~ sQ19_spl
| sQ67_spl
| sQ126_spl ),
inference(split_clause,[status(thm)],[f1282,f1285,f754,f413]) ).
fof(f1310,plain,
( ~ sQ126_spl
| aElementOf0(sK18_skl,stldt0(xB)) ),
inference(resolution,[status(thm)],[f1286,f295]) ).
fof(f1342,plain,
! [X0] :
( ~ sQ3_spl
| aElementOf0(sK2_skl(sdtbsmnsldt0(xA,xB),X0),xB)
| aElementOf0(sK2_skl(sdtbsmnsldt0(xA,xB),X0),xA)
| ~ aSet0(sdtbsmnsldt0(xA,xB))
| aSubsetOf0(sdtbsmnsldt0(xA,xB),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f124,f351]) ).
fof(f1343,plain,
! [X0] :
( ~ sQ2_spl
| aInteger0(sK2_skl(sdtbsmnsldt0(xA,xB),X0))
| ~ aSet0(sdtbsmnsldt0(xA,xB))
| aSubsetOf0(sdtbsmnsldt0(xA,xB),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f124,f347]) ).
fof(f1345,plain,
! [X0] :
( aElementOf0(sK2_skl(xB,X0),cS1395)
| ~ aSet0(xB)
| aSubsetOf0(xB,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f124,f221]) ).
fof(f1346,plain,
! [X0] :
( aElementOf0(sK2_skl(xA,X0),cS1395)
| ~ aSet0(xA)
| aSubsetOf0(xA,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f124,f215]) ).
fof(f1347,plain,
! [X0] :
( ~ sQ8_spl
| ~ aElementOf0(sK2_skl(stldt0(sdtbsmnsldt0(xA,xB)),X0),sdtbsmnsldt0(xA,xB))
| ~ aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
| aSubsetOf0(stldt0(sdtbsmnsldt0(xA,xB)),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f124,f371]) ).
fof(f1348,plain,
! [X0] :
( ~ sQ7_spl
| aInteger0(sK2_skl(stldt0(sdtbsmnsldt0(xA,xB)),X0))
| ~ aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
| aSubsetOf0(stldt0(sdtbsmnsldt0(xA,xB)),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f124,f367]) ).
fof(f1349,plain,
! [X0] :
( aInteger0(sK16_skl(sK2_skl(stldt0(xB),X0)))
| ~ aSet0(stldt0(xB))
| aSubsetOf0(stldt0(xB),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f124,f246]) ).
fof(f1350,plain,
! [X0] :
( ~ sQ14_spl
| ~ aElementOf0(sK2_skl(stldt0(xB),X0),xB)
| ~ aSet0(stldt0(xB))
| aSubsetOf0(stldt0(xB),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f124,f395]) ).
fof(f1351,plain,
! [X0] :
( ~ sQ34_spl
| aElementOf0(sK2_skl(stldt0(xB),X0),cS1395)
| ~ aSet0(stldt0(xB))
| aSubsetOf0(stldt0(xB),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f124,f473]) ).
fof(f1352,plain,
! [X0] :
( aInteger0(sK2_skl(stldt0(xB),X0))
| ~ aSet0(stldt0(xB))
| aSubsetOf0(stldt0(xB),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f124,f243]) ).
fof(f1353,plain,
! [X0] :
( aInteger0(sK14_skl(sK2_skl(stldt0(xA),X0)))
| ~ aSet0(stldt0(xA))
| aSubsetOf0(stldt0(xA),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f124,f227]) ).
fof(f1354,plain,
! [X0] :
( ~ sQ44_spl
| aElementOf0(sK2_skl(stldt0(xA),X0),cS1395)
| ~ aSet0(stldt0(xA))
| aSubsetOf0(stldt0(xA),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f124,f519]) ).
fof(f1355,plain,
! [X0] :
( ~ sQ11_spl
| ~ aElementOf0(sK2_skl(stldt0(xA),X0),xA)
| ~ aSet0(stldt0(xA))
| aSubsetOf0(stldt0(xA),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f124,f383]) ).
fof(f1356,plain,
! [X0] :
( ~ sQ10_spl
| aInteger0(sK2_skl(stldt0(xA),X0))
| ~ aSet0(stldt0(xA))
| aSubsetOf0(stldt0(xA),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f124,f379]) ).
fof(f1359,plain,
! [X0] :
( aInteger0(sK2_skl(cS1395,X0))
| ~ aSet0(cS1395)
| aSubsetOf0(cS1395,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f124,f212]) ).
fof(f1362,definition,
! [X0] :
( sQ134_spl
<=> ( aElementOf0(sK2_skl(sdtbsmnsldt0(xA,xB),X0),xB)
| aElementOf0(sK2_skl(sdtbsmnsldt0(xA,xB),X0),xA)
| aSubsetOf0(sdtbsmnsldt0(xA,xB),X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f1365,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| sQ134_spl ),
inference(split_clause,[status(thm)],[f1342,f1362,f342,f350]) ).
fof(f1366,definition,
! [X0] :
( sQ135_spl
<=> ( aInteger0(sK2_skl(sdtbsmnsldt0(xA,xB),X0))
| aSubsetOf0(sdtbsmnsldt0(xA,xB),X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition]) ).
fof(f1369,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ135_spl ),
inference(split_clause,[status(thm)],[f1343,f1366,f342,f346]) ).
fof(f1370,definition,
! [X0] :
( sQ136_spl
<=> ( aElementOf0(sK2_skl(xB,X0),cS1395)
| aSubsetOf0(xB,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f1373,plain,
( ~ sQ45_spl
| sQ136_spl ),
inference(split_clause,[status(thm)],[f1345,f1370,f556]) ).
fof(f1374,definition,
! [X0] :
( sQ137_spl
<=> ( aElementOf0(sK2_skl(xA,X0),cS1395)
| aSubsetOf0(xA,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f1377,plain,
( ~ sQ46_spl
| sQ137_spl ),
inference(split_clause,[status(thm)],[f1346,f1374,f560]) ).
fof(f1378,definition,
! [X0] :
( sQ138_spl
<=> ( ~ aElementOf0(sK2_skl(stldt0(sdtbsmnsldt0(xA,xB)),X0),sdtbsmnsldt0(xA,xB))
| aSubsetOf0(stldt0(sdtbsmnsldt0(xA,xB)),X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f1381,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| sQ138_spl ),
inference(split_clause,[status(thm)],[f1347,f1378,f362,f370]) ).
fof(f1382,definition,
! [X0] :
( sQ139_spl
<=> ( aInteger0(sK2_skl(stldt0(sdtbsmnsldt0(xA,xB)),X0))
| aSubsetOf0(stldt0(sdtbsmnsldt0(xA,xB)),X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f1385,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| sQ139_spl ),
inference(split_clause,[status(thm)],[f1348,f1382,f362,f366]) ).
fof(f1386,definition,
! [X0] :
( sQ140_spl
<=> ( aInteger0(sK16_skl(sK2_skl(stldt0(xB),X0)))
| aSubsetOf0(stldt0(xB),X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f1389,plain,
( ~ sQ22_spl
| sQ140_spl ),
inference(split_clause,[status(thm)],[f1349,f1386,f425]) ).
fof(f1390,definition,
! [X0] :
( sQ141_spl
<=> ( ~ aElementOf0(sK2_skl(stldt0(xB),X0),xB)
| aSubsetOf0(stldt0(xB),X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f1393,plain,
( ~ sQ14_spl
| ~ sQ22_spl
| sQ141_spl ),
inference(split_clause,[status(thm)],[f1350,f1390,f425,f394]) ).
fof(f1394,definition,
! [X0] :
( sQ142_spl
<=> ( aElementOf0(sK2_skl(stldt0(xB),X0),cS1395)
| aSubsetOf0(stldt0(xB),X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f1397,plain,
( ~ sQ34_spl
| ~ sQ22_spl
| sQ142_spl ),
inference(split_clause,[status(thm)],[f1351,f1394,f425,f472]) ).
fof(f1398,definition,
! [X0] :
( sQ143_spl
<=> ( aInteger0(sK2_skl(stldt0(xB),X0))
| aSubsetOf0(stldt0(xB),X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f1401,plain,
( ~ sQ22_spl
| sQ143_spl ),
inference(split_clause,[status(thm)],[f1352,f1398,f425]) ).
fof(f1402,definition,
! [X0] :
( sQ144_spl
<=> ( aInteger0(sK14_skl(sK2_skl(stldt0(xA),X0)))
| aSubsetOf0(stldt0(xA),X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f1405,plain,
( ~ sQ35_spl
| sQ144_spl ),
inference(split_clause,[status(thm)],[f1353,f1402,f481]) ).
fof(f1406,definition,
! [X0] :
( sQ145_spl
<=> ( aElementOf0(sK2_skl(stldt0(xA),X0),cS1395)
| aSubsetOf0(stldt0(xA),X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f1409,plain,
( ~ sQ44_spl
| ~ sQ35_spl
| sQ145_spl ),
inference(split_clause,[status(thm)],[f1354,f1406,f481,f518]) ).
fof(f1410,definition,
! [X0] :
( sQ146_spl
<=> ( ~ aElementOf0(sK2_skl(stldt0(xA),X0),xA)
| aSubsetOf0(stldt0(xA),X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f1413,plain,
( ~ sQ11_spl
| ~ sQ35_spl
| sQ146_spl ),
inference(split_clause,[status(thm)],[f1355,f1410,f481,f382]) ).
fof(f1414,definition,
! [X0] :
( sQ147_spl
<=> ( aInteger0(sK2_skl(stldt0(xA),X0))
| aSubsetOf0(stldt0(xA),X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f1417,plain,
( ~ sQ10_spl
| ~ sQ35_spl
| sQ147_spl ),
inference(split_clause,[status(thm)],[f1356,f1414,f481,f378]) ).
fof(f1420,definition,
! [X0] :
( sQ148_spl
<=> ( aInteger0(sK2_skl(cS1395,X0))
| aSubsetOf0(cS1395,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f1423,plain,
( ~ sQ23_spl
| sQ148_spl ),
inference(split_clause,[status(thm)],[f1359,f1420,f432]) ).
fof(f1424,plain,
! [X0] :
( ~ sQ110_spl
| ~ aSet0(sK23_skl)
| aSubsetOf0(sK23_skl,X0)
| ~ aSet0(X0)
| aElementOf0(sK2_skl(sK23_skl,X0),cS1395) ),
inference(resolution,[status(thm)],[f1081,f124]) ).
fof(f1425,definition,
! [X0] :
( sQ149_spl
<=> ( aSubsetOf0(sK23_skl,X0)
| ~ aSet0(X0)
| aElementOf0(sK2_skl(sK23_skl,X0),cS1395) ) ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f1428,plain,
( ~ sQ110_spl
| ~ sQ111_spl
| sQ149_spl ),
inference(split_clause,[status(thm)],[f1424,f1425,f1084,f1080]) ).
fof(f1439,plain,
( ~ sQ9_spl
| sQ16_spl
| aElementOf0(sK18_skl,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(sK18_skl) ),
inference(resolution,[status(thm)],[f404,f375]) ).
fof(f1441,plain,
( ~ sQ9_spl
| sQ16_spl
| sQ58_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1439,f405,f698,f402,f374]) ).
fof(f1443,plain,
( ~ sQ3_spl
| ~ sQ58_spl
| aElementOf0(sK18_skl,xB)
| aElementOf0(sK18_skl,xA) ),
inference(resolution,[status(thm)],[f699,f351]) ).
fof(f1445,plain,
( ~ sQ58_spl
| aElementOf0(sK18_skl,xB)
| aElementOf0(sK18_skl,xA)
| ~ aSubsetOf0(xB,cS1395)
| ~ aSubsetOf0(xA,cS1395) ),
inference(resolution,[status(thm)],[f699,f533]) ).
fof(f1446,plain,
( ~ sQ58_spl
| aSubsetOf0(sK18_skl,cS1395)
| sP1_prd(sK18_skl,sdtbsmnsldt0(xA,xB)) ),
inference(resolution,[status(thm)],[f699,f297]) ).
fof(f1447,plain,
( ~ sQ3_spl
| ~ sQ58_spl
| sQ51_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f1443,f665,f658,f698,f350]) ).
fof(f1448,plain,
( ~ sQ58_spl
| sQ51_spl
| sQ52_spl
| ~ sQ54_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f1445,f684,f677,f665,f658,f698]) ).
fof(f1449,definition,
( sQ152_spl
<=> sP1_prd(sK18_skl,sdtbsmnsldt0(xA,xB)) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f1450,plain,
( ~ sQ152_spl
| sP1_prd(sK18_skl,sdtbsmnsldt0(xA,xB)) ),
inference(component_clause,[status(thm)],[f1449]) ).
fof(f1452,plain,
( ~ sQ58_spl
| sQ67_spl
| sQ152_spl ),
inference(split_clause,[status(thm)],[f1446,f1449,f754,f698]) ).
fof(f1453,plain,
( ~ sQ66_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f1051,f665,f751]) ).
fof(f1455,plain,
( ~ sQ126_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f1310,f413,f1285]) ).
fof(f1458,plain,
( sQ19_spl
| aElementOf0(sK18_skl,xB)
| ~ aInteger0(sK18_skl)
| ~ aSubsetOf0(xB,cS1395) ),
inference(resolution,[status(thm)],[f415,f547]) ).
fof(f1460,plain,
( sQ19_spl
| sQ51_spl
| ~ sQ17_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f1458,f677,f405,f658,f413]) ).
fof(f1464,plain,
( ~ sQ152_spl
| aElementOf0(sK18_skl,sdtbsmnsldt0(xA,xB)) ),
inference(resolution,[status(thm)],[f1450,f295]) ).
fof(f1465,plain,
( ~ sQ152_spl
| sQ58_spl ),
inference(split_clause,[status(thm)],[f1464,f698,f1449]) ).
fof(f1466,plain,
( ~ sQ5_spl
| sQ58_spl
| ~ aElementOf0(sK18_skl,xB)
| ~ aInteger0(sK18_skl) ),
inference(resolution,[status(thm)],[f700,f359]) ).
fof(f1467,plain,
( ~ sQ4_spl
| sQ58_spl
| ~ aElementOf0(sK18_skl,xA)
| ~ aInteger0(sK18_skl) ),
inference(resolution,[status(thm)],[f700,f355]) ).
fof(f1469,plain,
( sQ58_spl
| ~ aElementOf0(sK18_skl,xB)
| ~ aInteger0(sK18_skl)
| ~ aSubsetOf0(xB,cS1395)
| ~ aSubsetOf0(xA,cS1395) ),
inference(resolution,[status(thm)],[f700,f535]) ).
fof(f1470,plain,
( ~ sQ5_spl
| sQ58_spl
| ~ sQ51_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1466,f405,f658,f698,f358]) ).
fof(f1471,plain,
( ~ sQ4_spl
| sQ58_spl
| ~ sQ52_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1467,f405,f665,f698,f354]) ).
fof(f1473,plain,
( sQ58_spl
| ~ sQ51_spl
| ~ sQ17_spl
| ~ sQ54_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f1469,f684,f677,f405,f658,f698]) ).
fof(f1483,plain,
( ~ sQ8_spl
| ~ sQ16_spl
| ~ aElementOf0(sK18_skl,sdtbsmnsldt0(xA,xB)) ),
inference(resolution,[status(thm)],[f403,f371]) ).
fof(f1488,plain,
( ~ sQ8_spl
| ~ sQ16_spl
| ~ sQ58_spl ),
inference(split_clause,[status(thm)],[f1483,f698,f402,f370]) ).
fof(f1492,plain,
$false,
inference(sat_refutation,[status(thm)],[f345,f349,f353,f357,f361,f365,f369,f373,f377,f381,f385,f389,f393,f397,f401,f412,f416,f417,f421,f447,f451,f455,f456,f485,f494,f498,f523,f524,f525,f526,f553,f559,f563,f569,f573,f578,f580,f585,f598,f600,f602,f614,f626,f632,f644,f646,f661,f668,f692,f694,f701,f714,f725,f732,f734,f736,f757,f761,f765,f795,f799,f803,f810,f835,f837,f843,f888,f945,f954,f955,f959,f960,f964,f968,f969,f970,f1040,f1063,f1067,f1079,f1083,f1087,f1094,f1097,f1098,f1189,f1190,f1191,f1195,f1196,f1197,f1201,f1243,f1247,f1283,f1288,f1365,f1369,f1373,f1377,f1381,f1385,f1389,f1393,f1397,f1401,f1405,f1409,f1413,f1417,f1423,f1428,f1441,f1447,f1448,f1452,f1453,f1455,f1460,f1465,f1470,f1471,f1473,f1488]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM440+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n003.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 02:31:00 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.42 % Refutation found
% 0.13/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.46 % Elapsed time: 0.086433 seconds
% 0.13/0.46 % CPU time: 0.362694 seconds
% 0.13/0.46 % Total memory used: 94.279 MB
% 0.13/0.46 % Net memory used: 93.792 MB
%------------------------------------------------------------------------------