%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM575+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 : n017.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 01:41:03 PM UTC 2026
% Result : Theorem 66.51s 14.09s
% Output : CNFRefutation 58.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 67 ( 11 unt; 1 def)
% Number of atoms : 346 ( 36 equ)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 431 ( 152 ~; 132 |; 123 &)
% ( 4 <=>; 20 =>; 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 : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 97 ( 91 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( szszuzczcdt0(W0) != sz00
& aElementOf0(szszuzczcdt0(W0),szNzAzT0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( sdtlseqdt0(szszuzczcdt0(W1),W0)
| sdtlseqdt0(W0,W1) ) ),
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(f83,hypothesis,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
& ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f84,conjecture,
! [W0,W1] :
( ( W0 != W1
& aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ~ ( szmzizndt0(sdtlpdtrp0(xN,W0)) = szmzizndt0(sdtlpdtrp0(xN,W1))
& ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W1))
& ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f85,negated_conjecture,
~ ! [W0,W1] :
( ( W0 != W1
& aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ~ ( szmzizndt0(sdtlpdtrp0(xN,W0)) = szmzizndt0(sdtlpdtrp0(xN,W1))
& ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W1))
& ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) ) ),
inference(negated_conjecture,[status(cth)],[f84]) ).
fof(f165,plain,
! [W0] :
( ( szszuzczcdt0(W0) != sz00
& aElementOf0(szszuzczcdt0(W0),szNzAzT0) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f166,plain,
! [X0] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f165]) ).
fof(f190,plain,
! [W0,W1] :
( W0 = W1
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f191,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f194,plain,
! [W0,W1] :
( sdtlseqdt0(szszuzczcdt0(W1),W0)
| sdtlseqdt0(W0,W1)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f195,plain,
! [X0,X1] :
( sdtlseqdt0(szszuzczcdt0(X1),X0)
| sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f382,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(f383,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(f384,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)],[f382,f383]) ).
fof(f385,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)],[f384]) ).
fof(f386,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)],[f385]) ).
fof(f395,plain,
! [X0,X1] :
( X1 != szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| sP4_prd(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f386]) ).
fof(f398,plain,
! [X0,X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| sP4_prd(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f386]) ).
fof(f401,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(f404,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f401]) ).
fof(f405,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f401]) ).
fof(f406,plain,
! [W0,W1] :
( ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
& ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W1))
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0)) ) )
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f83]) ).
fof(f407,plain,
! [X0,X1,X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f406]) ).
fof(f409,plain,
? [W0,W1] :
( szmzizndt0(sdtlpdtrp0(xN,W0)) = szmzizndt0(sdtlpdtrp0(xN,W1))
& ! [W2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W1))
& ! [W2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& W0 != W1
& aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f85]) ).
fof(f410,plain,
( szmzizndt0(sdtlpdtrp0(xN,sK23_skl)) = szmzizndt0(sdtlpdtrp0(xN,sK24_skl))
& ! [W2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK23_skl)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,sK24_skl)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK23_skl)),sdtlpdtrp0(xN,sK24_skl))
& ! [W2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK23_skl)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,sK23_skl)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK23_skl)),sdtlpdtrp0(xN,sK23_skl))
& sK23_skl != sK24_skl
& aElementOf0(sK24_skl,szNzAzT0)
& aElementOf0(sK23_skl,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl,sK24_skl]),skolemize(W0,sK23_skl),skolemize(W1,sK24_skl)],[f409]) ).
fof(f411,plain,
aElementOf0(sK23_skl,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f410]) ).
fof(f412,plain,
aElementOf0(sK24_skl,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f410]) ).
fof(f413,plain,
sK23_skl != sK24_skl,
inference(cnf_transformation,[status(thm)],[f410]) ).
fof(f414,plain,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK23_skl)),sdtlpdtrp0(xN,sK23_skl)),
inference(cnf_transformation,[status(thm)],[f410]) ).
fof(f416,plain,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK23_skl)),sdtlpdtrp0(xN,sK24_skl)),
inference(cnf_transformation,[status(thm)],[f410]) ).
fof(f418,plain,
szmzizndt0(sdtlpdtrp0(xN,sK23_skl)) = szmzizndt0(sdtlpdtrp0(xN,sK24_skl)),
inference(cnf_transformation,[status(thm)],[f410]) ).
fof(f470,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)],[f383]) ).
fof(f471,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)],[f470]) ).
fof(f472,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(sK36_skl(W0),szNzAzT0)
& aElementOf0(sK36_skl(W0),sdtlpdtrp0(xN,W0)) )
| ~ aSet0(sdtlpdtrp0(xN,W0)) ) )
| ~ sP4_prd(W0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36_skl]),skolemize(W1,sK36_skl(W0))],[f471]) ).
fof(f475,plain,
! [X0] :
( ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ sP4_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f472]) ).
fof(f535,plain,
! [X0] :
( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| sP4_prd(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(destructive_equality_resolution,[status(thm)],[f395]) ).
fof(f554,plain,
! [X0] :
( X0 = sK24_skl
| ~ sdtlseqdt0(sK24_skl,X0)
| ~ sdtlseqdt0(X0,sK24_skl)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[status(thm)],[f191,f412]) ).
fof(f599,plain,
! [X0] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK23_skl)),sdtlpdtrp0(xN,X0))
| ~ sdtlseqdt0(X0,sK24_skl)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(sK24_skl,szNzAzT0) ),
inference(resolution,[status(thm)],[f407,f416]) ).
fof(f600,plain,
! [X0] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK23_skl)),sdtlpdtrp0(xN,X0))
| ~ sdtlseqdt0(X0,sK23_skl)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(sK23_skl,szNzAzT0) ),
inference(resolution,[status(thm)],[f407,f414]) ).
fof(f601,plain,
! [X0] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK23_skl)),sdtlpdtrp0(xN,X0))
| ~ sdtlseqdt0(X0,sK24_skl)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f599,f412]) ).
fof(f602,plain,
! [X0] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK23_skl)),sdtlpdtrp0(xN,X0))
| ~ sdtlseqdt0(X0,sK23_skl)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f600,f411]) ).
fof(f4840,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ sP4_prd(X0) ),
inference(resolution,[status(thm)],[f475,f404]) ).
fof(f4844,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ sP4_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f4840,f405]) ).
fof(f13549,plain,
! [X0] :
( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f535,f4844]) ).
fof(f14529,plain,
! [X0,X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f398,f4844]) ).
fof(f14535,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[status(thm)],[f14529,f13549]) ).
fof(f14546,plain,
! [X0] :
( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(duplicate_literals_removal,[status(thm)],[f14535]) ).
fof(f17181,plain,
( ~ sdtlseqdt0(szszuzczcdt0(sK23_skl),sK24_skl)
| ~ aElementOf0(szszuzczcdt0(sK23_skl),szNzAzT0)
| ~ aElementOf0(sK23_skl,szNzAzT0) ),
inference(resolution,[status(thm)],[f14546,f601]) ).
fof(f17184,plain,
( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK23_skl)),sdtlpdtrp0(xN,szszuzczcdt0(sK24_skl)))
| ~ aElementOf0(sK24_skl,szNzAzT0) ),
inference(paramodulation,[status(thm)],[f418,f14546]) ).
fof(f17190,plain,
( ~ sdtlseqdt0(szszuzczcdt0(sK23_skl),sK24_skl)
| ~ aElementOf0(szszuzczcdt0(sK23_skl),szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f17181,f411]) ).
fof(f17192,plain,
~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK23_skl)),sdtlpdtrp0(xN,szszuzczcdt0(sK24_skl))),
inference(forward_subsumption_resolution,[status(thm)],[f17184,f412]) ).
fof(f17204,plain,
( sdtlseqdt0(sK24_skl,sK23_skl)
| ~ aElementOf0(sK23_skl,szNzAzT0)
| ~ aElementOf0(sK24_skl,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(sK23_skl),szNzAzT0) ),
inference(resolution,[status(thm)],[f17190,f195]) ).
fof(f17207,plain,
( sdtlseqdt0(sK24_skl,sK23_skl)
| ~ aElementOf0(sK23_skl,szNzAzT0)
| ~ aElementOf0(sK24_skl,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f17204,f166]) ).
fof(f17214,plain,
( ~ sdtlseqdt0(szszuzczcdt0(sK24_skl),sK23_skl)
| ~ aElementOf0(szszuzczcdt0(sK24_skl),szNzAzT0) ),
inference(resolution,[status(thm)],[f17192,f602]) ).
fof(f17222,plain,
( sdtlseqdt0(sK23_skl,sK24_skl)
| ~ aElementOf0(sK24_skl,szNzAzT0)
| ~ aElementOf0(sK23_skl,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(sK24_skl),szNzAzT0) ),
inference(resolution,[status(thm)],[f17214,f195]) ).
fof(f17225,plain,
( sdtlseqdt0(sK23_skl,sK24_skl)
| ~ aElementOf0(sK24_skl,szNzAzT0)
| ~ aElementOf0(sK23_skl,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f17222,f166]) ).
fof(f17354,plain,
( sdtlseqdt0(sK24_skl,sK23_skl)
| ~ aElementOf0(sK23_skl,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f17207,f412]) ).
fof(f17355,plain,
sdtlseqdt0(sK24_skl,sK23_skl),
inference(resolution,[status(thm)],[f17354,f411]) ).
fof(f17359,plain,
( sK23_skl = sK24_skl
| ~ sdtlseqdt0(sK23_skl,sK24_skl)
| ~ aElementOf0(sK23_skl,szNzAzT0) ),
inference(resolution,[status(thm)],[f17355,f554]) ).
fof(f17381,plain,
( sK23_skl = sK24_skl
| ~ sdtlseqdt0(sK23_skl,sK24_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f17359,f411]) ).
fof(f17415,plain,
~ sdtlseqdt0(sK23_skl,sK24_skl),
inference(forward_subsumption_resolution,[status(thm)],[f17381,f413]) ).
fof(f18068,plain,
( sdtlseqdt0(sK23_skl,sK24_skl)
| ~ aElementOf0(sK24_skl,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f17225,f411]) ).
fof(f18069,plain,
sdtlseqdt0(sK23_skl,sK24_skl),
inference(resolution,[status(thm)],[f18068,f412]) ).
fof(f18070,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f18069,f17415]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM575+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.58 % Computer : n017.cluster.edu
% 0.09/5.58 % Model : x86_64 x86_64
% 0.09/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.58 % Memory : 8046.5625MB
% 0.09/5.58 % OS : Linux 6.8.0-71-generic
% 0.09/5.58 % CPULimit : 300
% 0.09/5.58 % WCLimit : 300
% 0.09/5.58 % DateTime : Mon Sep 21 02:37:03 UTC 2026
% 0.09/5.58 % CPUTime :
% 0.12/5.60 % Drodi V4.1.1
% 66.51/14.09 % Refutation found
% 66.51/14.09 % SZS status Theorem for theBenchmark: Theorem is valid
% 66.51/14.09 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 65.86/14.70 % Elapsed time: 9.100333 seconds
% 65.86/14.70 % CPU time: 68.269868 seconds
% 65.86/14.70 % Total memory used: 395.943 MB
% 65.86/14.70 % Net memory used: 358.451 MB
%------------------------------------------------------------------------------