%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM587+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 01:41:06 PM UTC 2026
% Result : Theorem 0.26s 1.04s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 86 ( 19 unt; 11 def)
% Number of atoms : 768 ( 134 equ)
% Maximal formula atoms : 47 ( 8 avg)
% Number of connectives : 941 ( 259 ~; 250 |; 379 &)
% ( 30 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 7 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 19 ( 17 usr; 10 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 12 con; 0-2 aty)
% Number of variables : 192 ( 168 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f69,axiom,
! [W0] :
( aFunction0(W0)
=> ! [W1] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f76,hypothesis,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& ! [W0] :
( aElementOf0(W0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
=> aElementOf0(W0,xT) )
& ! [W0] :
( aElementOf0(W0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> ? [W1] :
( sdtlpdtrp0(xc,W1) = W0
& aElementOf0(W1,szDzozmdt0(xc)) ) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& ! [W0] :
( ( ( sbrdtbr0(W0) = xK
& ( aSubsetOf0(W0,xS)
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) )
=> aElementOf0(W0,szDzozmdt0(xc)) )
& ( aElementOf0(W0,szDzozmdt0(xc))
=> ( sbrdtbr0(W0) = xK
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) )
& aFunction0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f86,hypothesis,
( ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( ! [W1] :
( ( ( ( ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
=> ( ( ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W2,sdtlpdtrp0(xN,W0))
& aElement0(W2) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
=> ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
| ( sbrdtbr0(W1) = xk
& ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ) )
& aSet0(W1) )
=> ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0))
| aElementOf0(W2,W1) )
& aElement0(W2) ) )
& ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) ) )
& szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)
& ! [W1] :
( ( ( sbrdtbr0(W1) = xk
& ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSet0(W1) ) ) )
=> aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) )
& ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
=> ( sbrdtbr0(W1) = xk
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSet0(W1) ) ) )
& ! [W1] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& aElement0(W1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& aFunction0(sdtlpdtrp0(xC,W0)) ) )
& szDzozmdt0(xC) = szNzAzT0
& aFunction0(xC) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f87,hypothesis,
aElementOf0(xi,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f89,hypothesis,
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),xQ) = xx
& aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(xQ)
& ! [W0] :
( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& aElement0(W0) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f90,hypothesis,
( ? [W0] :
( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(W0,szDzozmdt0(xc)) )
& ! [W0] :
( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xQ) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0] :
( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xQ) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f91,conjecture,
aElementOf0(xx,xT),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f92,negated_conjecture,
~ aElementOf0(xx,xT),
inference(negated_conjecture,[status(cth)],[f91]) ).
fof(f329,plain,
! [W0] :
( ! [W1] :
( aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0)))
| ~ aElementOf0(W1,szDzozmdt0(W0)) )
| ~ aFunction0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f69]) ).
fof(f330,plain,
! [X0,X1] :
( aElementOf0(sdtlpdtrp0(X0,X1),sdtlcdtrc0(X0,szDzozmdt0(X0)))
| ~ aElementOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f329]) ).
fof(f357,plain,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& ! [W0] :
( aElementOf0(W0,xT)
| ~ aElementOf0(W0,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& ! [W0] :
( aElementOf0(W0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> ? [W1] :
( sdtlpdtrp0(xc,W1) = W0
& aElementOf0(W1,szDzozmdt0(xc)) ) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& ! [W0] :
( ( aElementOf0(W0,szDzozmdt0(xc))
| sbrdtbr0(W0) != xK
| ( ~ aSubsetOf0(W0,xS)
& ( ? [W1] :
( ~ aElementOf0(W1,xS)
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ) ) )
& ( ( sbrdtbr0(W0) = xK
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,xS)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,szDzozmdt0(xc)) ) )
& aFunction0(xc) ),
inference(pre_NNF_transformation,[status(thm)],[f76]) ).
fof(f358,plain,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& ! [W0] :
( aElementOf0(W0,xT)
| ~ aElementOf0(W0,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& ! [W0] :
( ( ! [W1] :
( sdtlpdtrp0(xc,W1) != W0
| ~ aElementOf0(W1,szDzozmdt0(xc)) )
| aElementOf0(W0,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& ( ? [W1] :
( sdtlpdtrp0(xc,W1) = W0
& aElementOf0(W1,szDzozmdt0(xc)) )
| ~ aElementOf0(W0,sdtlcdtrc0(xc,szDzozmdt0(xc))) ) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& ! [W0] :
( ( aElementOf0(W0,szDzozmdt0(xc))
| sbrdtbr0(W0) != xK
| ( ~ aSubsetOf0(W0,xS)
& ( ? [W1] :
( ~ aElementOf0(W1,xS)
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ) ) )
& ( ( sbrdtbr0(W0) = xK
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,xS)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,szDzozmdt0(xc)) ) )
& aFunction0(xc) ),
inference(NNF_transformation,[status(thm)],[f357]) ).
fof(f359,plain,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& ! [W0] :
( aElementOf0(W0,xT)
| ~ aElementOf0(W0,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& ! [W0] :
( ! [W1] :
( sdtlpdtrp0(xc,W1) != W0
| ~ aElementOf0(W1,szDzozmdt0(xc)) )
| aElementOf0(W0,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& ! [W0] :
( ? [W1] :
( sdtlpdtrp0(xc,W1) = W0
& aElementOf0(W1,szDzozmdt0(xc)) )
| ~ aElementOf0(W0,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& ! [W0] :
( aElementOf0(W0,szDzozmdt0(xc))
| sbrdtbr0(W0) != xK
| ( ~ aSubsetOf0(W0,xS)
& ( ? [W1] :
( ~ aElementOf0(W1,xS)
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ) ) )
& ! [W0] :
( ( sbrdtbr0(W0) = xK
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,xS)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,szDzozmdt0(xc)) )
& aFunction0(xc) ),
inference(miniscoping,[status(thm)],[f358]) ).
fof(f360,plain,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& ! [W0] :
( aElementOf0(W0,xT)
| ~ aElementOf0(W0,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& ! [W0] :
( ! [W1] :
( sdtlpdtrp0(xc,W1) != W0
| ~ aElementOf0(W1,szDzozmdt0(xc)) )
| aElementOf0(W0,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& ! [W0] :
( ( sdtlpdtrp0(xc,sK20_skl(W0)) = W0
& aElementOf0(sK20_skl(W0),szDzozmdt0(xc)) )
| ~ aElementOf0(W0,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& ! [W0] :
( aElementOf0(W0,szDzozmdt0(xc))
| sbrdtbr0(W0) != xK
| ( ~ aSubsetOf0(W0,xS)
& ( ( ~ aElementOf0(sK19_skl(W0),xS)
& aElementOf0(sK19_skl(W0),W0) )
| ~ aSet0(W0) ) ) )
& ! [W0] :
( ( sbrdtbr0(W0) = xK
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,xS)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,szDzozmdt0(xc)) )
& aFunction0(xc) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl,sK20_skl]),skolemize(W1,sK19_skl(W0)),skolemize(W1,sK20_skl(W0))],[f359]) ).
fof(f361,plain,
aFunction0(xc),
inference(cnf_transformation,[status(thm)],[f360]) ).
fof(f374,plain,
! [X0] :
( aElementOf0(X0,xT)
| ~ aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(cnf_transformation,[status(thm)],[f360]) ).
fof(f439,plain,
( ! [W0] :
( ( ! [W1] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0))
| aElementOf0(W2,W1) )
& aElement0(W2) ) )
& ! [W2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
| ( ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
& ( sbrdtbr0(W1) != xk
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ? [W2] :
( ~ aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,W1) ) ) )
& ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W2,sdtlpdtrp0(xN,W0))
& aElement0(W2) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
| ~ aSet0(W1) )
& szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)
& ! [W1] :
( ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| sbrdtbr0(W1) != xk
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( ? [W2] :
( ~ aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,W1) )
| ~ aSet0(W1) ) ) )
& ( ( sbrdtbr0(W1) = xk
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
& ! [W1] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& aElement0(W1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W1] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& aFunction0(sdtlpdtrp0(xC,W0)) )
| ~ aElementOf0(W0,szNzAzT0) )
& szDzozmdt0(xC) = szNzAzT0
& aFunction0(xC) ),
inference(pre_NNF_transformation,[status(thm)],[f86]) ).
fof(f440,definition,
! [W0,W1] :
( sP6_prd(W1,W0)
<=> ( ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
& ( sbrdtbr0(W1) != xk
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ? [W2] :
( ~ aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,W1) ) ) )
& ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W2,sdtlpdtrp0(xN,W0))
& aElement0(W2) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) ) ),
introduced(definition,[new_symbols(definition,[sP6_prd])],[]) ).
fof(f441,plain,
( ! [W0] :
( ( ! [W1] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0))
| aElementOf0(W2,W1) )
& aElement0(W2) ) )
& ! [W2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
| sP6_prd(W1,W0)
| ~ aSet0(W1) )
& szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)
& ! [W1] :
( ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| sbrdtbr0(W1) != xk
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( ? [W2] :
( ~ aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,W1) )
| ~ aSet0(W1) ) ) )
& ( ( sbrdtbr0(W1) = xk
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
& ! [W1] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& aElement0(W1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W1] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& aFunction0(sdtlpdtrp0(xC,W0)) )
| ~ aElementOf0(W0,szNzAzT0) )
& szDzozmdt0(xC) = szNzAzT0
& aFunction0(xC) ),
inference(formula_renaming,[status(thm)],[f439,f440]) ).
fof(f442,plain,
( ! [W0] :
( ( ! [W1] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( ( ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0))
& ~ aElementOf0(W2,W1) )
| ~ aElement0(W2)
| aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ( ( ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0))
| aElementOf0(W2,W1) )
& aElement0(W2) )
| ~ aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
& ! [W2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
| sP6_prd(W1,W0)
| ~ aSet0(W1) )
& szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)
& ! [W1] :
( ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| sbrdtbr0(W1) != xk
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( ? [W2] :
( ~ aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,W1) )
| ~ aSet0(W1) ) ) )
& ( ( sbrdtbr0(W1) = xk
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
& ! [W1] :
( ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0))
| ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| ~ aElement0(W1)
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ( ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& aElement0(W1) )
| ~ aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W1] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& aFunction0(sdtlpdtrp0(xC,W0)) )
| ~ aElementOf0(W0,szNzAzT0) )
& szDzozmdt0(xC) = szNzAzT0
& aFunction0(xC) ),
inference(NNF_transformation,[status(thm)],[f441]) ).
fof(f443,plain,
( ! [W0] :
( ( ! [W1] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0))
& ~ aElementOf0(W2,W1) )
| ~ aElement0(W2)
| aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ! [W2] :
( ( ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0))
| aElementOf0(W2,W1) )
& aElement0(W2) )
| ~ aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ! [W2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
| sP6_prd(W1,W0)
| ~ aSet0(W1) )
& szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)
& ! [W1] :
( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| sbrdtbr0(W1) != xk
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( ? [W2] :
( ~ aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,W1) )
| ~ aSet0(W1) ) ) )
& ! [W1] :
( ( sbrdtbr0(W1) = xk
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) )
& ! [W1] :
( W1 = szmzizndt0(sdtlpdtrp0(xN,W0))
| ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| ~ aElement0(W1)
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ! [W1] :
( ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& aElement0(W1) )
| ~ aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W1] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& aFunction0(sdtlpdtrp0(xC,W0)) )
| ~ aElementOf0(W0,szNzAzT0) )
& szDzozmdt0(xC) = szNzAzT0
& aFunction0(xC) ),
inference(miniscoping,[status(thm)],[f442]) ).
fof(f444,plain,
( ! [W0] :
( ( ! [W1] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0))
& ~ aElementOf0(W2,W1) )
| ~ aElement0(W2)
| aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ! [W2] :
( ( ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0))
| aElementOf0(W2,W1) )
& aElement0(W2) )
| ~ aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ! [W2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
| sP6_prd(W1,W0)
| ~ aSet0(W1) )
& szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)
& ! [W1] :
( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| sbrdtbr0(W1) != xk
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( ( ~ aElementOf0(sK24_skl(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(sK24_skl(W1,W0),W1) )
| ~ aSet0(W1) ) ) )
& ! [W1] :
( ( sbrdtbr0(W1) = xk
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) )
& ! [W1] :
( W1 = szmzizndt0(sdtlpdtrp0(xN,W0))
| ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| ~ aElement0(W1)
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ! [W1] :
( ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& aElement0(W1) )
| ~ aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W1] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& aFunction0(sdtlpdtrp0(xC,W0)) )
| ~ aElementOf0(W0,szNzAzT0) )
& szDzozmdt0(xC) = szNzAzT0
& aFunction0(xC) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24_skl]),skolemize(W2,sK24_skl(W1,W0))],[f443]) ).
fof(f469,plain,
! [X0,X1] :
( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
| sP6_prd(X1,X0)
| ~ aSet0(X1)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f444]) ).
fof(f470,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f475,plain,
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),xQ) = xx
& aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(W0,xQ) )
& aSet0(xQ)
& ! [W0] :
( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& aElement0(W0) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(pre_NNF_transformation,[status(thm)],[f89]) ).
fof(f476,plain,
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),xQ) = xx
& aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(W0,xQ) )
& aSet0(xQ)
& ! [W0] :
( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ~ aElement0(W0)
| aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& aElement0(W0) )
| ~ aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(NNF_transformation,[status(thm)],[f475]) ).
fof(f477,plain,
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),xQ) = xx
& aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(W0,xQ) )
& aSet0(xQ)
& ! [W0] :
( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ~ aElement0(W0)
| aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ! [W0] :
( ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& aElement0(W0) )
| ~ aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(miniscoping,[status(thm)],[f476]) ).
fof(f485,plain,
aSet0(xQ),
inference(cnf_transformation,[status(thm)],[f477]) ).
fof(f487,plain,
aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(cnf_transformation,[status(thm)],[f477]) ).
fof(f488,plain,
sbrdtbr0(xQ) = xk,
inference(cnf_transformation,[status(thm)],[f477]) ).
fof(f490,plain,
sdtlpdtrp0(sdtlpdtrp0(xC,xi),xQ) = xx,
inference(cnf_transformation,[status(thm)],[f477]) ).
fof(f491,plain,
( ? [W0] :
( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(W0,szDzozmdt0(xc)) )
& ! [W0] :
( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xQ) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0] :
( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xQ) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(pre_NNF_transformation,[status(thm)],[f90]) ).
fof(f492,plain,
( ? [W0] :
( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(W0,szDzozmdt0(xc)) )
& ! [W0] :
( ( ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
& ~ aElementOf0(W0,xQ) )
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xQ) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0] :
( ( ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
& ~ aElementOf0(W0,xQ) )
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xQ) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(NNF_transformation,[status(thm)],[f491]) ).
fof(f493,plain,
( ? [W0] :
( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(W0,szDzozmdt0(xc)) )
& ! [W0] :
( ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
& ~ aElementOf0(W0,xQ) )
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ! [W0] :
( ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xQ) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0] :
( ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
& ~ aElementOf0(W0,xQ) )
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ! [W0] :
( ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xQ) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(miniscoping,[status(thm)],[f492]) ).
fof(f494,plain,
( sdtlpdtrp0(xc,sK26_skl) = sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(sK26_skl,szDzozmdt0(xc))
& ! [W0] :
( ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
& ~ aElementOf0(W0,xQ) )
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ! [W0] :
( ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xQ) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0] :
( ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
& ~ aElementOf0(W0,xQ) )
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ! [W0] :
( ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xQ) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26_skl]),skolemize(W0,sK26_skl)],[f493]) ).
fof(f509,plain,
aElementOf0(sK26_skl,szDzozmdt0(xc)),
inference(cnf_transformation,[status(thm)],[f494]) ).
fof(f510,plain,
sdtlpdtrp0(xc,sK26_skl) = sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(cnf_transformation,[status(thm)],[f494]) ).
fof(f511,plain,
~ aElementOf0(xx,xT),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f589,definition,
! [W0,W2] :
( sP10_prd(W2,W0)
<=> ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W2,sdtlpdtrp0(xN,W0))
& aElement0(W2) ) ) ),
introduced(definition,[new_symbols(definition,[sP10_prd])],[]) ).
fof(f590,plain,
! [W0,W1] :
( sP6_prd(W1,W0)
<=> ( ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
& ( sbrdtbr0(W1) != xk
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ? [W2] :
( ~ aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,W1) ) ) )
& ! [W2] : sP10_prd(W2,W0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) ) ),
inference(formula_renaming,[status(thm)],[f440,f589]) ).
fof(f591,plain,
! [W0,W1] :
( ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
| ( sbrdtbr0(W1) = xk
& ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,W1) ) ) )
| ? [W2] : ~ sP10_prd(W2,W0)
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ? [W2] :
( ~ sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2)
& aElementOf0(W2,sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| sP6_prd(W1,W0) )
& ( ( ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
& ( sbrdtbr0(W1) != xk
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ? [W2] :
( ~ aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,W1) ) ) )
& ! [W2] : sP10_prd(W2,W0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
| ~ sP6_prd(W1,W0) ) ),
inference(NNF_transformation,[status(thm)],[f590]) ).
fof(f592,plain,
( ! [W0,W1] :
( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
| ( sbrdtbr0(W1) = xk
& ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,W1) ) ) )
| ? [W2] : ~ sP10_prd(W2,W0)
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ? [W2] :
( ~ sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2)
& aElementOf0(W2,sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| sP6_prd(W1,W0) )
& ! [W0,W1] :
( ( ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
& ( sbrdtbr0(W1) != xk
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ? [W2] :
( ~ aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,W1) ) ) )
& ! [W2] : sP10_prd(W2,W0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
| ~ sP6_prd(W1,W0) ) ),
inference(miniscoping,[status(thm)],[f591]) ).
fof(f593,plain,
( ! [W0,W1] :
( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
| ( sbrdtbr0(W1) = xk
& ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,W1) ) ) )
| ~ sP10_prd(sK44_skl(W1,W0),W0)
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ( ~ sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),sK43_skl(W1,W0))
& aElementOf0(sK43_skl(W1,W0),sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
| sP6_prd(W1,W0) )
& ! [W0,W1] :
( ( ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
& ( sbrdtbr0(W1) != xk
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ~ aElementOf0(sK42_skl(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(sK42_skl(W1,W0),W1) ) )
& ! [W2] : sP10_prd(W2,W0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
| ~ sP6_prd(W1,W0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42_skl,sK43_skl,sK44_skl]),skolemize(W2,sK42_skl(W1,W0)),skolemize(W2,sK43_skl(W1,W0)),skolemize(W2,sK44_skl(W1,W0))],[f592]) ).
fof(f600,plain,
! [X0,X1] :
( sbrdtbr0(X0) != xk
| ~ aSubsetOf0(X0,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
| ~ sP6_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f593]) ).
fof(f1186,definition,
( sQ68_spl
<=> aSet0(xQ) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f1188,plain,
( sQ68_spl
| ~ aSet0(xQ) ),
inference(component_clause,[status(thm)],[f1186]) ).
fof(f1193,plain,
( sQ68_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1188,f485]) ).
fof(f1194,plain,
sQ68_spl,
inference(contradiction_clause,[status(thm)],[f1193]) ).
fof(f1937,definition,
( sQ165_spl
<=> aElementOf0(xi,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ165_spl])],[split_symbol_definition]) ).
fof(f1939,plain,
( sQ165_spl
| ~ aElementOf0(xi,szNzAzT0) ),
inference(component_clause,[status(thm)],[f1937]) ).
fof(f1941,plain,
( sQ165_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1939,f470]) ).
fof(f1942,plain,
sQ165_spl,
inference(contradiction_clause,[status(thm)],[f1941]) ).
fof(f2001,definition,
( sQ171_spl
<=> aElementOf0(xx,xT) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f2002,plain,
( ~ sQ171_spl
| aElementOf0(xx,xT) ),
inference(component_clause,[status(thm)],[f2001]) ).
fof(f2005,plain,
( ~ sQ171_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2002,f511]) ).
fof(f2006,plain,
~ sQ171_spl,
inference(contradiction_clause,[status(thm)],[f2005]) ).
fof(f2021,definition,
( sQ173_spl
<=> aFunction0(xc) ),
introduced(definition,[new_symbols(definition,[sQ173_spl])],[split_symbol_definition]) ).
fof(f2023,plain,
( sQ173_spl
| ~ aFunction0(xc) ),
inference(component_clause,[status(thm)],[f2021]) ).
fof(f2028,plain,
( sQ173_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2023,f361]) ).
fof(f2029,plain,
sQ173_spl,
inference(contradiction_clause,[status(thm)],[f2028]) ).
fof(f2191,definition,
! [X0] :
( sQ200_spl
<=> ( aElementOf0(sdtlpdtrp0(xc,X0),xT)
| ~ aElementOf0(X0,szDzozmdt0(xc)) ) ),
introduced(definition,[new_symbols(definition,[sQ200_spl])],[split_symbol_definition]) ).
fof(f2192,plain,
! [X0] :
( ~ sQ200_spl
| aElementOf0(sdtlpdtrp0(xc,X0),xT)
| ~ aElementOf0(X0,szDzozmdt0(xc)) ),
inference(component_clause,[status(thm)],[f2191]) ).
fof(f3072,plain,
! [X0] :
( ~ aElementOf0(X0,szDzozmdt0(xc))
| ~ aFunction0(xc)
| aElementOf0(sdtlpdtrp0(xc,X0),xT) ),
inference(resolution,[status(thm)],[f374,f330]) ).
fof(f3073,plain,
( ~ sQ173_spl
| sQ200_spl ),
inference(split_clause,[status(thm)],[f3072,f2191,f2021]) ).
fof(f3706,definition,
( sQ420_spl
<=> sbrdtbr0(xQ) = xk ),
introduced(definition,[new_symbols(definition,[sQ420_spl])],[split_symbol_definition]) ).
fof(f3708,plain,
( sQ420_spl
| sbrdtbr0(xQ) != xk ),
inference(component_clause,[status(thm)],[f3706]) ).
fof(f3710,plain,
( sQ420_spl
| xk != xk ),
inference(forward_demodulation,[status(thm)],[f488,f3708]) ).
fof(f3711,plain,
( sQ420_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3710]) ).
fof(f3712,plain,
sQ420_spl,
inference(contradiction_clause,[status(thm)],[f3711]) ).
fof(f5493,plain,
( sbrdtbr0(xQ) != xk
| ~ sP6_prd(xQ,xi) ),
inference(resolution,[status(thm)],[f600,f487]) ).
fof(f5494,definition,
( sQ688_spl
<=> sP6_prd(xQ,xi) ),
introduced(definition,[new_symbols(definition,[sQ688_spl])],[split_symbol_definition]) ).
fof(f5496,plain,
( sQ688_spl
| ~ sP6_prd(xQ,xi) ),
inference(component_clause,[status(thm)],[f5494]) ).
fof(f5497,plain,
( ~ sQ420_spl
| ~ sQ688_spl ),
inference(split_clause,[status(thm)],[f5493,f5494,f3706]) ).
fof(f5647,plain,
( sQ688_spl
| sdtlpdtrp0(sdtlpdtrp0(xC,xi),xQ) = sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSet0(xQ)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(resolution,[status(thm)],[f5496,f469]) ).
fof(f5652,definition,
( sQ718_spl
<=> sdtlpdtrp0(sdtlpdtrp0(xC,xi),xQ) = sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
introduced(definition,[new_symbols(definition,[sQ718_spl])],[split_symbol_definition]) ).
fof(f5653,plain,
( ~ sQ718_spl
| sdtlpdtrp0(sdtlpdtrp0(xC,xi),xQ) = sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(component_clause,[status(thm)],[f5652]) ).
fof(f5655,plain,
( sQ688_spl
| sQ718_spl
| ~ sQ68_spl
| ~ sQ165_spl ),
inference(split_clause,[status(thm)],[f5647,f1937,f1186,f5652,f5494]) ).
fof(f5663,plain,
( ~ sQ718_spl
| xx = sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(forward_demodulation,[status(thm)],[f490,f5653]) ).
fof(f5887,plain,
( ~ sQ718_spl
| sdtlpdtrp0(xc,sK26_skl) = xx ),
inference(backward_demodulation,[status(thm)],[f5663,f510]) ).
fof(f5899,plain,
( ~ sQ718_spl
| ~ sQ200_spl
| aElementOf0(xx,xT)
| ~ aElementOf0(sK26_skl,szDzozmdt0(xc)) ),
inference(paramodulation,[status(thm)],[f5887,f2192]) ).
fof(f5903,definition,
( sQ757_spl
<=> aElementOf0(sK26_skl,szDzozmdt0(xc)) ),
introduced(definition,[new_symbols(definition,[sQ757_spl])],[split_symbol_definition]) ).
fof(f5905,plain,
( sQ757_spl
| ~ aElementOf0(sK26_skl,szDzozmdt0(xc)) ),
inference(component_clause,[status(thm)],[f5903]) ).
fof(f5906,plain,
( ~ sQ718_spl
| ~ sQ200_spl
| sQ171_spl
| ~ sQ757_spl ),
inference(split_clause,[status(thm)],[f5899,f5903,f2001,f2191,f5652]) ).
fof(f5913,plain,
( sQ757_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5905,f509]) ).
fof(f5914,plain,
sQ757_spl,
inference(contradiction_clause,[status(thm)],[f5913]) ).
fof(f5915,plain,
$false,
inference(sat_refutation,[status(thm)],[f1194,f1942,f2006,f2029,f3073,f3712,f5497,f5655,f5906,f5914]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM587+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n009.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 02:42:12 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.49 % Drodi V4.1.1
% 0.26/1.04 % Refutation found
% 0.26/1.04 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.26/1.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.26/1.09 % Elapsed time: 0.635274 seconds
% 0.26/1.09 % CPU time: 4.247985 seconds
% 0.26/1.09 % Total memory used: 153.814 MB
% 0.26/1.09 % Net memory used: 150.481 MB
%------------------------------------------------------------------------------