%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM592+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 : n006.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 01:41:07 PM UTC 2026
% Result : Theorem 19.63s 8.41s
% Output : CNFRefutation 19.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 9 unt; 2 def)
% Number of atoms : 307 ( 45 equ)
% Maximal formula atoms : 22 ( 7 avg)
% Number of connectives : 378 ( 110 ~; 96 |; 146 &)
% ( 10 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-2 aty)
% Number of variables : 89 ( 73 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f91,hypothesis,
( xd = sdtlpdtrp0(xC,xi)
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& ! [W0] :
( aElementOf0(W0,xY)
<=> ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& aElement0(W0) ) )
& aSet0(xY)
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f93,hypothesis,
( ! [W0] :
( ( ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ( sbrdtbr0(W0) = xk
& ( aSubsetOf0(W0,xX)
| ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xX) ) ) ) )
& aSet0(W0) )
=> sdtlpdtrp0(xd,W0) = xu )
& isCountable0(xX)
& aSubsetOf0(xX,xY)
& ! [W0] :
( aElementOf0(W0,xX)
=> aElementOf0(W0,xY) )
& aSet0(xX)
& aElementOf0(xu,xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f94,conjecture,
? [W0] :
( ? [W1] :
( ! [W2] :
( ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
& sbrdtbr0(W2) = xk
& aSubsetOf0(W2,W1)
& ! [W3] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,W1) )
& aSet0(W2) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 )
& isCountable0(W1)
& ( ( ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
=> ( ( ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& aElement0(W2) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
=> ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(W1) ) ) ) ) )
& aElementOf0(W0,xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f95,negated_conjecture,
~ ? [W0] :
( ? [W1] :
( ! [W2] :
( ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
& sbrdtbr0(W2) = xk
& aSubsetOf0(W2,W1)
& ! [W3] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,W1) )
& aSet0(W2) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 )
& isCountable0(W1)
& ( ( ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
=> ( ( ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& aElement0(W2) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
=> ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(W1) ) ) ) ) )
& aElementOf0(W0,xT) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f502,plain,
( xd = sdtlpdtrp0(xC,xi)
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& ! [W0] :
( aElementOf0(W0,xY)
<=> ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& aElement0(W0) ) )
& aSet0(xY)
& ! [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)],[f91]) ).
fof(f503,plain,
( xd = sdtlpdtrp0(xC,xi)
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& ! [W0] :
( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ~ aElement0(W0)
| aElementOf0(W0,xY) )
& ( ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& aElement0(W0) )
| ~ aElementOf0(W0,xY) ) )
& aSet0(xY)
& ! [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)],[f502]) ).
fof(f504,plain,
( xd = sdtlpdtrp0(xC,xi)
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& ! [W0] :
( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ~ aElement0(W0)
| aElementOf0(W0,xY) )
& ! [W0] :
( ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& aElement0(W0) )
| ~ aElementOf0(W0,xY) )
& aSet0(xY)
& ! [W0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(miniscoping,[status(thm)],[f503]) ).
fof(f512,plain,
xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),
inference(cnf_transformation,[status(thm)],[f504]) ).
fof(f513,plain,
xd = sdtlpdtrp0(xC,xi),
inference(cnf_transformation,[status(thm)],[f504]) ).
fof(f533,plain,
( ! [W0] :
( sdtlpdtrp0(xd,W0) = xu
| ( ~ aElementOf0(W0,slbdtsldtrb0(xX,xk))
& ( sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,xX)
& ? [W1] :
( ~ aElementOf0(W1,xX)
& aElementOf0(W1,W0) ) ) ) )
| ~ aSet0(W0) )
& isCountable0(xX)
& aSubsetOf0(xX,xY)
& ! [W0] :
( aElementOf0(W0,xY)
| ~ aElementOf0(W0,xX) )
& aSet0(xX)
& aElementOf0(xu,xT) ),
inference(pre_NNF_transformation,[status(thm)],[f93]) ).
fof(f534,plain,
( ! [W0] :
( sdtlpdtrp0(xd,W0) = xu
| ( ~ aElementOf0(W0,slbdtsldtrb0(xX,xk))
& ( sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,xX)
& ~ aElementOf0(sK29_skl(W0),xX)
& aElementOf0(sK29_skl(W0),W0) ) ) )
| ~ aSet0(W0) )
& isCountable0(xX)
& aSubsetOf0(xX,xY)
& ! [W0] :
( aElementOf0(W0,xY)
| ~ aElementOf0(W0,xX) )
& aSet0(xX)
& aElementOf0(xu,xT) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29_skl]),skolemize(W1,sK29_skl(W0))],[f533]) ).
fof(f535,plain,
aElementOf0(xu,xT),
inference(cnf_transformation,[status(thm)],[f534]) ).
fof(f538,plain,
aSubsetOf0(xX,xY),
inference(cnf_transformation,[status(thm)],[f534]) ).
fof(f539,plain,
isCountable0(xX),
inference(cnf_transformation,[status(thm)],[f534]) ).
fof(f543,plain,
! [X0] :
( sdtlpdtrp0(xd,X0) = xu
| ~ aElementOf0(X0,slbdtsldtrb0(xX,xk))
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f534]) ).
fof(f544,plain,
! [W0] :
( ! [W1] :
( ? [W2] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) != W0
& aElementOf0(W2,slbdtsldtrb0(W1,xk))
& sbrdtbr0(W2) = xk
& aSubsetOf0(W2,W1)
& ! [W3] :
( aElementOf0(W3,W1)
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( ? [W2] :
( ~ aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(W2,W1) )
| ~ aSet0(W1) )
& ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& aElement0(W2) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ) )
| ~ aElementOf0(W0,xT) ),
inference(pre_NNF_transformation,[status(thm)],[f95]) ).
fof(f545,definition,
! [W1] :
( sP9_prd(W1)
<=> ( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( ? [W2] :
( ~ aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(W2,W1) )
| ~ aSet0(W1) )
& ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& aElement0(W2) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ) ) ),
introduced(definition,[new_symbols(definition,[sP9_prd])],[]) ).
fof(f546,plain,
! [W0] :
( ! [W1] :
( ? [W2] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) != W0
& aElementOf0(W2,slbdtsldtrb0(W1,xk))
& sbrdtbr0(W2) = xk
& aSubsetOf0(W2,W1)
& ! [W3] :
( aElementOf0(W3,W1)
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| sP9_prd(W1) )
| ~ aElementOf0(W0,xT) ),
inference(formula_renaming,[status(thm)],[f544,f545]) ).
fof(f547,plain,
! [W0] :
( ! [W1] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),sK30_skl(W1,W0)) != W0
& aElementOf0(sK30_skl(W1,W0),slbdtsldtrb0(W1,xk))
& sbrdtbr0(sK30_skl(W1,W0)) = xk
& aSubsetOf0(sK30_skl(W1,W0),W1)
& ! [W3] :
( aElementOf0(W3,W1)
| ~ aElementOf0(W3,sK30_skl(W1,W0)) )
& aSet0(sK30_skl(W1,W0)) )
| sP9_prd(W1) )
| ~ aElementOf0(W0,xT) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30_skl]),skolemize(W2,sK30_skl(W1,W0))],[f546]) ).
fof(f548,plain,
! [X0,X1] :
( aSet0(sK30_skl(X1,X0))
| sP9_prd(X1)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[status(thm)],[f547]) ).
fof(f552,plain,
! [X0,X1] :
( aElementOf0(sK30_skl(X1,X0),slbdtsldtrb0(X1,xk))
| sP9_prd(X1)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[status(thm)],[f547]) ).
fof(f553,plain,
! [X0,X1] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),sK30_skl(X1,X0)) != X0
| sP9_prd(X1)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[status(thm)],[f547]) ).
fof(f675,definition,
! [W2] :
( sP16_prd(W2)
<=> ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( W2 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(W2,sdtlpdtrp0(xN,xi))
& aElement0(W2) ) ) ),
introduced(definition,[new_symbols(definition,[sP16_prd])],[]) ).
fof(f676,plain,
! [W1] :
( sP9_prd(W1)
<=> ( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( ? [W2] :
( ~ aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(W2,W1) )
| ~ aSet0(W1) )
& ! [W2] : sP16_prd(W2)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ) ) ),
inference(formula_renaming,[status(thm)],[f545,f675]) ).
fof(f677,plain,
! [W1] :
( ( ( isCountable0(W1)
& ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ? [W2] : ~ sP16_prd(W2)
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ? [W2] :
( ~ sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ) )
| sP9_prd(W1) )
& ( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( ? [W2] :
( ~ aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(W2,W1) )
| ~ aSet0(W1) )
& ! [W2] : sP16_prd(W2)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
| ~ sP9_prd(W1) ) ),
inference(NNF_transformation,[status(thm)],[f676]) ).
fof(f678,plain,
( ! [W1] :
( ( isCountable0(W1)
& ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ? [W2] : ~ sP16_prd(W2)
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ? [W2] :
( ~ sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2)
& aElementOf0(W2,sdtlpdtrp0(xN,xi)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ) )
| sP9_prd(W1) )
& ! [W1] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( ? [W2] :
( ~ aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(W2,W1) )
| ~ aSet0(W1) )
& ! [W2] : sP16_prd(W2)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
| ~ sP9_prd(W1) ) ),
inference(miniscoping,[status(thm)],[f677]) ).
fof(f679,plain,
( ! [W1] :
( ( isCountable0(W1)
& ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ sP16_prd(sK55_skl(W1))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( ~ sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),sK54_skl(W1))
& aElementOf0(sK54_skl(W1),sdtlpdtrp0(xN,xi)) )
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ) )
| sP9_prd(W1) )
& ! [W1] :
( ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( ( ~ aElementOf0(sK53_skl(W1),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(sK53_skl(W1),W1) )
| ~ aSet0(W1) )
& ! [W2] : sP16_prd(W2)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
| ~ sP9_prd(W1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53_skl,sK54_skl,sK55_skl]),skolemize(W2,sK53_skl(W1)),skolemize(W2,sK54_skl(W1)),skolemize(W2,sK55_skl(W1))],[f678]) ).
fof(f686,plain,
! [X0] :
( ~ isCountable0(X0)
| ~ aSubsetOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ sP9_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f679]) ).
fof(f953,plain,
! [X0,X1] :
( sdtlpdtrp0(xd,sK30_skl(X1,X0)) != X0
| sP9_prd(X1)
| ~ aElementOf0(X0,xT) ),
inference(backward_demodulation,[status(thm)],[f513,f553]) ).
fof(f1063,plain,
! [X0] :
( sdtlpdtrp0(xd,sK30_skl(X0,xu)) != xu
| sP9_prd(X0) ),
inference(resolution,[status(thm)],[f953,f535]) ).
fof(f5700,plain,
! [X0] :
( ~ isCountable0(X0)
| ~ aSubsetOf0(X0,xY)
| ~ sP9_prd(X0) ),
inference(backward_demodulation,[status(thm)],[f512,f686]) ).
fof(f5872,plain,
( ~ isCountable0(xX)
| ~ sP9_prd(xX) ),
inference(resolution,[status(thm)],[f5700,f538]) ).
fof(f5879,plain,
~ sP9_prd(xX),
inference(forward_subsumption_resolution,[status(thm)],[f5872,f539]) ).
fof(f6365,plain,
! [X0] :
( sP9_prd(xX)
| ~ aElementOf0(X0,xT)
| sdtlpdtrp0(xd,sK30_skl(xX,X0)) = xu
| ~ aSet0(sK30_skl(xX,X0)) ),
inference(resolution,[status(thm)],[f543,f552]) ).
fof(f6367,plain,
! [X0] :
( sP9_prd(xX)
| ~ aElementOf0(X0,xT)
| sdtlpdtrp0(xd,sK30_skl(xX,X0)) = xu ),
inference(forward_subsumption_resolution,[status(thm)],[f6365,f548]) ).
fof(f9874,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| sdtlpdtrp0(xd,sK30_skl(xX,X0)) = xu ),
inference(forward_subsumption_resolution,[status(thm)],[f6367,f5879]) ).
fof(f9875,plain,
sdtlpdtrp0(xd,sK30_skl(xX,xu)) = xu,
inference(resolution,[status(thm)],[f9874,f535]) ).
fof(f9976,plain,
sP9_prd(xX),
inference(resolution,[status(thm)],[f9875,f1063]) ).
fof(f9979,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f9976,f5879]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM592+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.78 % Computer : n006.cluster.edu
% 0.11/5.78 % Model : x86_64 x86_64
% 0.11/5.78 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.78 % Memory : 8046.5625MB
% 0.11/5.78 % OS : Linux 6.8.0-71-generic
% 0.11/5.78 % CPULimit : 300
% 0.11/5.78 % WCLimit : 300
% 0.11/5.78 % DateTime : Mon Sep 21 02:42:48 UTC 2026
% 0.11/5.79 % CPUTime :
% 0.15/5.81 % Drodi V4.1.1
% 19.63/8.41 % Refutation found
% 19.63/8.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 19.63/8.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 19.63/8.49 % Elapsed time: 2.683758 seconds
% 19.63/8.49 % CPU time: 20.794270 seconds
% 19.63/8.49 % Total memory used: 251.668 MB
% 19.63/8.49 % Net memory used: 240.318 MB
%------------------------------------------------------------------------------