%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM629+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 : n005.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 01:41:15 PM UTC 2026
% Result : Theorem 21.06s 3.14s
% Output : CNFRefutation 21.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 61 ( 11 unt; 2 def)
% Number of atoms : 358 ( 39 equ)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 434 ( 137 ~; 127 |; 145 &)
% ( 8 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 12 con; 0-2 aty)
% Number of variables : 100 ( 93 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [W0,W1,W2] :
( ( aSet0(W2)
& aSet0(W1)
& aSet0(W0) )
=> ( ( aSubsetOf0(W1,W2)
& aSubsetOf0(W0,W1) )
=> aSubsetOf0(W0,W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f81,hypothesis,
( ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( ( isCountable0(sdtlpdtrp0(xN,W0))
& ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ( ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,W0)) ) ) )
=> ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(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] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) ) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f82,hypothesis,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( isCountable0(sdtlpdtrp0(xN,W0))
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,W0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f91,hypothesis,
( ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0)) ) )
& szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f111,hypothesis,
( sdtlpdtrp0(xe,xn) = xp
& aElementOf0(xn,szNzAzT0)
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xd,xn) = szDzizrdt0(xd)
& aElementOf0(xn,szDzozmdt0(xd)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f113,hypothesis,
( aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f114,hypothesis,
( xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))
& ! [W0] :
( aElementOf0(W0,xD)
<=> ( W0 != szmzizndt0(sdtlpdtrp0(xN,xn))
& aElementOf0(W0,sdtlpdtrp0(xN,xn))
& aElement0(W0) ) )
& aSet0(xD)
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f115,conjecture,
( aElementOf0(xP,slbdtsldtrb0(xD,xk))
| aSubsetOf0(xP,xD)
| ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xD) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f116,negated_conjecture,
~ ( aElementOf0(xP,slbdtsldtrb0(xD,xk))
| aSubsetOf0(xP,xD)
| ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xD) ) ),
inference(negated_conjecture,[status(cth)],[f115]) ).
fof(f141,plain,
! [W0] :
( ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) ) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f142,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)],[f141]) ).
fof(f143,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)],[f142]) ).
fof(f144,plain,
! [W0] :
( ( ! [W1] :
( ( ~ aElementOf0(sK1_skl(W1,W0),W0)
& aElementOf0(sK1_skl(W1,W0),W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f143]) ).
fof(f145,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f155,plain,
! [W0,W1,W2] :
( aSubsetOf0(W0,W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W2)
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f156,plain,
! [X0,X1,X2] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f413,plain,
( ! [W0] :
( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W1] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(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)) )
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& ( ? [W1] :
( ~ aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlpdtrp0(xN,W0)) )
| ~ aSet0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(W0,szNzAzT0) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(pre_NNF_transformation,[status(thm)],[f81]) ).
fof(f414,definition,
! [W0] :
( sP4_prd(W0)
<=> ( ~ isCountable0(sdtlpdtrp0(xN,W0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& ( ? [W1] :
( ~ aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlpdtrp0(xN,W0)) )
| ~ aSet0(sdtlpdtrp0(xN,W0)) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4_prd])],[]) ).
fof(f415,plain,
( ! [W0] :
( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W1] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(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)) )
| sP4_prd(W0)
| ~ aElementOf0(W0,szNzAzT0) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(formula_renaming,[status(thm)],[f413,f414]) ).
fof(f416,plain,
( ! [W0] :
( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W1] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(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)) )
| sP4_prd(W0)
| ~ aElementOf0(W0,szNzAzT0) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(NNF_transformation,[status(thm)],[f415]) ).
fof(f417,plain,
( ! [W0] :
( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W1] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(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)) )
| sP4_prd(W0)
| ~ aElementOf0(W0,szNzAzT0) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(miniscoping,[status(thm)],[f416]) ).
fof(f430,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| sP4_prd(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f432,plain,
! [W0] :
( ( isCountable0(sdtlpdtrp0(xN,W0))
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& ! [W1] :
( aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,W0)) )
& aSet0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f82]) ).
fof(f435,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f432]) ).
fof(f436,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f432]) ).
fof(f548,plain,
( ! [W0] :
( ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0))
& ! [W1] :
( sdtlseqdt0(sdtlpdtrp0(xe,W0),W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,W0)) )
& aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(W0,szNzAzT0) )
& szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe) ),
inference(pre_NNF_transformation,[status(thm)],[f91]) ).
fof(f553,plain,
! [X0] :
( sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f548]) ).
fof(f653,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f654,plain,
sdtlpdtrp0(xe,xn) = xp,
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f656,plain,
( aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(W0,xP) ) ),
inference(pre_NNF_transformation,[status(thm)],[f113]) ).
fof(f658,plain,
aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cnf_transformation,[status(thm)],[f656]) ).
fof(f659,plain,
( xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))
& ! [W0] :
( aElementOf0(W0,xD)
<=> ( W0 != szmzizndt0(sdtlpdtrp0(xN,xn))
& aElementOf0(W0,sdtlpdtrp0(xN,xn))
& aElement0(W0) ) )
& aSet0(xD)
& ! [W0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xn)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f114]) ).
fof(f660,plain,
( xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))
& ! [W0] :
( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xn))
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| ~ aElement0(W0)
| aElementOf0(W0,xD) )
& ( ( W0 != szmzizndt0(sdtlpdtrp0(xN,xn))
& aElementOf0(W0,sdtlpdtrp0(xN,xn))
& aElement0(W0) )
| ~ aElementOf0(W0,xD) ) )
& aSet0(xD)
& ! [W0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xn)) ) ),
inference(NNF_transformation,[status(thm)],[f659]) ).
fof(f661,plain,
( xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))
& ! [W0] :
( W0 = szmzizndt0(sdtlpdtrp0(xN,xn))
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xn))
| ~ aElement0(W0)
| aElementOf0(W0,xD) )
& ! [W0] :
( ( W0 != szmzizndt0(sdtlpdtrp0(xN,xn))
& aElementOf0(W0,sdtlpdtrp0(xN,xn))
& aElement0(W0) )
| ~ aElementOf0(W0,xD) )
& aSet0(xD)
& ! [W0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xn)) ) ),
inference(miniscoping,[status(thm)],[f660]) ).
fof(f663,plain,
aSet0(xD),
inference(cnf_transformation,[status(thm)],[f661]) ).
fof(f668,plain,
xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),
inference(cnf_transformation,[status(thm)],[f661]) ).
fof(f669,plain,
( ~ aElementOf0(xP,slbdtsldtrb0(xD,xk))
& ~ aSubsetOf0(xP,xD)
& ? [W0] :
( ~ aElementOf0(W0,xD)
& aElementOf0(W0,xP) ) ),
inference(pre_NNF_transformation,[status(thm)],[f116]) ).
fof(f670,plain,
( ~ aElementOf0(xP,slbdtsldtrb0(xD,xk))
& ~ aSubsetOf0(xP,xD)
& ~ aElementOf0(sK38_skl,xD)
& aElementOf0(sK38_skl,xP) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38_skl]),skolemize(W0,sK38_skl)],[f669]) ).
fof(f673,plain,
~ aSubsetOf0(xP,xD),
inference(cnf_transformation,[status(thm)],[f670]) ).
fof(f726,plain,
! [W0] :
( ( ( isCountable0(sdtlpdtrp0(xN,W0))
& ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ( ! [W1] :
( aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,W0)) )
& aSet0(sdtlpdtrp0(xN,W0)) ) ) )
| sP4_prd(W0) )
& ( ~ isCountable0(sdtlpdtrp0(xN,W0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& ( ? [W1] :
( ~ aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlpdtrp0(xN,W0)) )
| ~ aSet0(sdtlpdtrp0(xN,W0)) ) )
| ~ sP4_prd(W0) ) ),
inference(NNF_transformation,[status(thm)],[f414]) ).
fof(f727,plain,
( ! [W0] :
( ( isCountable0(sdtlpdtrp0(xN,W0))
& ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ( ! [W1] :
( aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,W0)) )
& aSet0(sdtlpdtrp0(xN,W0)) ) ) )
| sP4_prd(W0) )
& ! [W0] :
( ~ isCountable0(sdtlpdtrp0(xN,W0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& ( ? [W1] :
( ~ aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlpdtrp0(xN,W0)) )
| ~ aSet0(sdtlpdtrp0(xN,W0)) ) )
| ~ sP4_prd(W0) ) ),
inference(miniscoping,[status(thm)],[f726]) ).
fof(f728,plain,
( ! [W0] :
( ( isCountable0(sdtlpdtrp0(xN,W0))
& ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ( ! [W1] :
( aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,W0)) )
& aSet0(sdtlpdtrp0(xN,W0)) ) ) )
| sP4_prd(W0) )
& ! [W0] :
( ~ isCountable0(sdtlpdtrp0(xN,W0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& ( ( ~ aElementOf0(sK50_skl(W0),szNzAzT0)
& aElementOf0(sK50_skl(W0),sdtlpdtrp0(xN,W0)) )
| ~ aSet0(sdtlpdtrp0(xN,W0)) ) )
| ~ sP4_prd(W0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50_skl]),skolemize(W1,sK50_skl(W0))],[f727]) ).
fof(f731,plain,
! [X0] :
( ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ sP4_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f728]) ).
fof(f936,plain,
! [X0,X1,X2] :
( aSubsetOf0(X2,X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X2,X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f156,f145]) ).
fof(f3096,plain,
! [X0] :
( aSubsetOf0(xP,X0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),X0)
| ~ aSet0(X0)
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(resolution,[status(thm)],[f658,f936]) ).
fof(f3098,plain,
! [X0] :
( aSubsetOf0(xP,X0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),X0)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3096,f145]) ).
fof(f7946,plain,
sdtlpdtrp0(xe,xn) = szmzizndt0(sdtlpdtrp0(xN,xn)),
inference(resolution,[status(thm)],[f553,f653]) ).
fof(f7965,plain,
xp = szmzizndt0(sdtlpdtrp0(xN,xn)),
inference(forward_demodulation,[status(thm)],[f654,f7946]) ).
fof(f8189,plain,
xD = sdtmndt0(sdtlpdtrp0(xN,xn),xp),
inference(backward_demodulation,[status(thm)],[f7965,f668]) ).
fof(f10118,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ sP4_prd(X0) ),
inference(resolution,[status(thm)],[f731,f435]) ).
fof(f10120,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ sP4_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f10118,f436]) ).
fof(f10131,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(backward_subsumption_resolution,[status(thm)],[f430,f10120]) ).
fof(f10149,plain,
( aSubsetOf0(xP,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(xn,szNzAzT0) ),
inference(resolution,[status(thm)],[f10131,f3098]) ).
fof(f10179,plain,
( aSubsetOf0(xP,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),xp))
| ~ aElementOf0(xn,szNzAzT0) ),
inference(forward_demodulation,[status(thm)],[f7965,f10149]) ).
fof(f10180,plain,
( aSubsetOf0(xP,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aSet0(xD)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(forward_demodulation,[status(thm)],[f8189,f10179]) ).
fof(f10181,plain,
( aSubsetOf0(xP,sdtmndt0(sdtlpdtrp0(xN,xn),xp))
| ~ aSet0(xD)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(forward_demodulation,[status(thm)],[f7965,f10180]) ).
fof(f10182,plain,
( aSubsetOf0(xP,xD)
| ~ aSet0(xD)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(forward_demodulation,[status(thm)],[f8189,f10181]) ).
fof(f10183,plain,
( aSubsetOf0(xP,xD)
| ~ aSet0(xD) ),
inference(forward_subsumption_resolution,[status(thm)],[f10182,f653]) ).
fof(f10261,plain,
aSubsetOf0(xP,xD),
inference(forward_subsumption_resolution,[status(thm)],[f10183,f663]) ).
fof(f10262,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f673,f10261]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM629+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n005.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Mon Sep 21 02:45:32 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.44 % Drodi V4.1.1
% 21.06/3.14 % Refutation found
% 21.06/3.14 % SZS status Theorem for theBenchmark: Theorem is valid
% 21.06/3.14 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 21.06/3.18 % Elapsed time: 2.751063 seconds
% 21.06/3.18 % CPU time: 21.526450 seconds
% 21.06/3.18 % Total memory used: 273.195 MB
% 21.06/3.18 % Net memory used: 257.846 MB
%------------------------------------------------------------------------------