%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM586+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012
% 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 01:41:05 PM UTC 2026
% Result : Theorem 0.08s 31.39s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 10 unt; 1 def)
% Number of atoms : 431 ( 91 equ)
% Maximal formula atoms : 47 ( 10 avg)
% Number of connectives : 559 ( 168 ~; 142 |; 216 &)
% ( 13 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 8 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-2 aty)
% Number of variables : 107 ( 95 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p') ).
fof(f87,hypothesis,
aElementOf0(xi,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f88,hypothesis,
( aElementOf0(xx,sdtlcdtrc0(sdtlpdtrp0(xC,xi),szDzozmdt0(sdtlpdtrp0(xC,xi))))
& ? [W0] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W0) = xx
& aElementOf0(W0,szDzozmdt0(sdtlpdtrp0(xC,xi))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f89,conjecture,
? [W0] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W0) = xx
& ( ( ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
=> ( ( ! [W1] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( W1 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(W1,sdtlpdtrp0(xN,xi))
& aElement0(W1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
=> ( aElementOf0(W0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ( sbrdtbr0(W0) = xk
& ( aSubsetOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(W0) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f90,negated_conjecture,
~ ? [W0] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W0) = xx
& ( ( ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
=> ( ( ! [W1] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( W1 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(W1,sdtlpdtrp0(xN,xi))
& aElement0(W1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
=> ( aElementOf0(W0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ( sbrdtbr0(W0) = xk
& ( aSubsetOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(W0) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f437,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(f438,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(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)) )
| 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)],[f437,f438]) ).
fof(f440,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)],[f439]) ).
fof(f441,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)],[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] :
( ( ( 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))],[f441]) ).
fof(f453,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aElementOf0(X1,szDzozmdt0(sdtlpdtrp0(xC,X0)))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f442]) ).
fof(f454,plain,
! [X0,X1,X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,X1)
| ~ aElementOf0(X1,szDzozmdt0(sdtlpdtrp0(xC,X0)))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f442]) ).
fof(f456,plain,
! [X0,X1] :
( sbrdtbr0(X1) = xk
| ~ aElementOf0(X1,szDzozmdt0(sdtlpdtrp0(xC,X0)))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f442]) ).
fof(f468,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f469,plain,
( aElementOf0(xx,sdtlcdtrc0(sdtlpdtrp0(xC,xi),szDzozmdt0(sdtlpdtrp0(xC,xi))))
& sdtlpdtrp0(sdtlpdtrp0(xC,xi),sK25_skl) = xx
& aElementOf0(sK25_skl,szDzozmdt0(sdtlpdtrp0(xC,xi))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25_skl]),skolemize(W0,sK25_skl)],[f88]) ).
fof(f470,plain,
aElementOf0(sK25_skl,szDzozmdt0(sdtlpdtrp0(xC,xi))),
inference(cnf_transformation,[status(thm)],[f469]) ).
fof(f471,plain,
sdtlpdtrp0(sdtlpdtrp0(xC,xi),sK25_skl) = xx,
inference(cnf_transformation,[status(thm)],[f469]) ).
fof(f473,plain,
! [W0] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W0) != xx
| ( ~ aElementOf0(W0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
& ( sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( ? [W1] :
( ~ aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ) ) )
& ! [W1] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( W1 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(W1,sdtlpdtrp0(xN,xi))
& aElement0(W1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W1] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f90]) ).
fof(f474,plain,
! [W0] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W0) != xx
| ( ~ aElementOf0(W0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
& ( sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( ? [W1] :
( ~ aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ) ) )
& ! [W1] :
( ( W1 = szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| ~ aElement0(W1)
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( ( W1 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(W1,sdtlpdtrp0(xN,xi))
& aElement0(W1) )
| ~ aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W1] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ) ),
inference(NNF_transformation,[status(thm)],[f473]) ).
fof(f475,plain,
! [W0] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W0) != xx
| ( ~ aElementOf0(W0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
& ( sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( ? [W1] :
( ~ aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ) ) )
& ! [W1] :
( W1 = szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| ~ aElement0(W1)
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ! [W1] :
( ( W1 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(W1,sdtlpdtrp0(xN,xi))
& aElement0(W1) )
| ~ aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W1] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ) ),
inference(miniscoping,[status(thm)],[f474]) ).
fof(f476,plain,
! [W0] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W0) != xx
| ( ~ aElementOf0(W0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
& ( sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( ( ~ aElementOf0(sK26_skl(W0),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(sK26_skl(W0),W0) )
| ~ aSet0(W0) ) ) )
& ! [W1] :
( W1 = szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xi))
| ~ aElement0(W1)
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ! [W1] :
( ( W1 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(W1,sdtlpdtrp0(xN,xi))
& aElement0(W1) )
| ~ aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W1] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26_skl]),skolemize(W1,sK26_skl(W0))],[f475]) ).
fof(f484,plain,
! [X0] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),X0) != xx
| sbrdtbr0(X0) != xk
| aElementOf0(sK26_skl(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f476]) ).
fof(f485,plain,
! [X0] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),X0) != xx
| sbrdtbr0(X0) != xk
| ~ aElementOf0(sK26_skl(X0),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f476]) ).
fof(f1410,plain,
( aSet0(sK25_skl)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(resolution,[status(thm)],[f470,f453]) ).
fof(f1412,plain,
aSet0(sK25_skl),
inference(forward_subsumption_resolution,[status(thm)],[f1410,f468]) ).
fof(f1414,plain,
( sbrdtbr0(sK25_skl) != xk
| ~ aElementOf0(sK26_skl(sK25_skl),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSet0(sK25_skl) ),
inference(resolution,[status(thm)],[f471,f485]) ).
fof(f1423,plain,
( sbrdtbr0(sK25_skl) != xk
| aElementOf0(sK26_skl(sK25_skl),sK25_skl)
| ~ aSet0(sK25_skl) ),
inference(resolution,[status(thm)],[f471,f484]) ).
fof(f1435,plain,
( sbrdtbr0(sK25_skl) != xk
| ~ aElementOf0(sK26_skl(sK25_skl),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1414,f1412]) ).
fof(f1436,plain,
( sbrdtbr0(sK25_skl) != xk
| aElementOf0(sK26_skl(sK25_skl),sK25_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1423,f1412]) ).
fof(f1693,plain,
( sbrdtbr0(sK25_skl) = xk
| ~ aElementOf0(xi,szNzAzT0) ),
inference(resolution,[status(thm)],[f456,f470]) ).
fof(f1697,plain,
sbrdtbr0(sK25_skl) = xk,
inference(forward_subsumption_resolution,[status(thm)],[f1693,f468]) ).
fof(f1698,plain,
( xk != xk
| ~ aElementOf0(sK26_skl(sK25_skl),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(backward_demodulation,[status(thm)],[f1697,f1435]) ).
fof(f1699,plain,
( xk != xk
| aElementOf0(sK26_skl(sK25_skl),sK25_skl) ),
inference(backward_demodulation,[status(thm)],[f1697,f1436]) ).
fof(f1708,plain,
~ aElementOf0(sK26_skl(sK25_skl),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(trivial_equality_resolution,[status(thm)],[f1698]) ).
fof(f1709,plain,
aElementOf0(sK26_skl(sK25_skl),sK25_skl),
inference(trivial_equality_resolution,[status(thm)],[f1699]) ).
fof(f1792,plain,
! [X0] :
( ~ aElementOf0(sK26_skl(sK25_skl),X0)
| ~ aElementOf0(X0,szDzozmdt0(sdtlpdtrp0(xC,xi)))
| ~ aElementOf0(xi,szNzAzT0) ),
inference(resolution,[status(thm)],[f1708,f454]) ).
fof(f1796,plain,
! [X0] :
( ~ aElementOf0(sK26_skl(sK25_skl),X0)
| ~ aElementOf0(X0,szDzozmdt0(sdtlpdtrp0(xC,xi))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1792,f468]) ).
fof(f1799,plain,
~ aElementOf0(sK26_skl(sK25_skl),sK25_skl),
inference(resolution,[status(thm)],[f1796,f470]) ).
fof(f1804,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1799,f1709]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM586+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/31.17 % Computer : n012
% 0.05/31.17 % Model : x86_64 x86_64
% 0.05/31.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/31.17 % Memory : 8046.5625MB
% 0.05/31.17 % OS : Linux 6.8.0-71-generic
% 0.05/31.17 % CPULimit : 300
% 0.05/31.17 % WCLimit : 300
% 0.05/31.17 % DateTime : Mon Sep 21 02:42:40 UTC 2026
% 0.05/31.17 % CPUTime :
% 0.05/31.18 % Drodi V4.1.1
% 0.08/31.39 % Refutation found
% 0.08/31.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/31.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/31.41 % Elapsed time: 0.224171 seconds
% 0.08/31.41 % CPU time: 1.550126 seconds
% 0.08/31.41 % Total memory used: 154.006 MB
% 0.08/31.41 % Net memory used: 150.511 MB
%------------------------------------------------------------------------------