%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM603+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 : n016.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 01:41:09 PM UTC 2026
% Result : Theorem 7.57s 1.45s
% Output : CNFRefutation 7.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 8 unt; 1 def)
% Number of atoms : 172 ( 19 equ)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 200 ( 58 ~; 51 |; 76 &)
% ( 4 <=>; 11 =>; 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 : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 42 ( 39 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f24,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(sz00,W0) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f99,hypothesis,
( sdtlpdtrp0(xe,xi) = xx
& aElementOf0(xi,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f100,conjecture,
( aSubsetOf0(sdtlpdtrp0(xN,xi),xS)
| ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> aElementOf0(W0,xS) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f101,negated_conjecture,
~ ( aSubsetOf0(sdtlpdtrp0(xN,xi),xS)
| ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> aElementOf0(W0,xS) ) ),
inference(negated_conjecture,[status(cth)],[f100]) ).
fof(f180,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f194,plain,
! [W0] :
( sdtlseqdt0(sz00,W0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f195,plain,
! [X0] :
( sdtlseqdt0(sz00,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f398,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(f399,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(f400,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)],[f398,f399]) ).
fof(f401,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)],[f400]) ).
fof(f402,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)],[f401]) ).
fof(f405,plain,
sdtlpdtrp0(xN,sz00) = xS,
inference(cnf_transformation,[status(thm)],[f402]) ).
fof(f422,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(f423,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)],[f422]) ).
fof(f590,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f592,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS)
& ? [W0] :
( ~ aElementOf0(W0,xS)
& aElementOf0(W0,sdtlpdtrp0(xN,xi)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f101]) ).
fof(f593,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS)
& ~ aElementOf0(sK37_skl,xS)
& aElementOf0(sK37_skl,sdtlpdtrp0(xN,xi)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37_skl]),skolemize(W0,sK37_skl)],[f592]) ).
fof(f594,plain,
aElementOf0(sK37_skl,sdtlpdtrp0(xN,xi)),
inference(cnf_transformation,[status(thm)],[f593]) ).
fof(f595,plain,
~ aElementOf0(sK37_skl,xS),
inference(cnf_transformation,[status(thm)],[f593]) ).
fof(f4829,plain,
! [X0] :
( aElementOf0(sK37_skl,sdtlpdtrp0(xN,X0))
| ~ sdtlseqdt0(X0,xi)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(resolution,[status(thm)],[f423,f594]) ).
fof(f4836,plain,
! [X0] :
( aElementOf0(sK37_skl,sdtlpdtrp0(xN,X0))
| ~ sdtlseqdt0(X0,xi)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f4829,f590]) ).
fof(f4864,plain,
( ~ aElementOf0(xi,szNzAzT0)
| aElementOf0(sK37_skl,sdtlpdtrp0(xN,sz00))
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(resolution,[status(thm)],[f4836,f195]) ).
fof(f4870,plain,
( ~ aElementOf0(xi,szNzAzT0)
| aElementOf0(sK37_skl,xS)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(forward_demodulation,[status(thm)],[f405,f4864]) ).
fof(f4871,plain,
( ~ aElementOf0(xi,szNzAzT0)
| aElementOf0(sK37_skl,xS) ),
inference(forward_subsumption_resolution,[status(thm)],[f4870,f180]) ).
fof(f5198,plain,
~ aElementOf0(xi,szNzAzT0),
inference(forward_subsumption_resolution,[status(thm)],[f4871,f595]) ).
fof(f5199,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f590,f5198]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM603+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n016.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 02:48:25 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.03/0.41 % Drodi V4.1.1
% 7.57/1.45 % Refutation found
% 7.57/1.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 7.57/1.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.65/1.53 % Elapsed time: 1.145889 seconds
% 0.65/1.53 % CPU time: 8.221208 seconds
% 0.65/1.53 % Total memory used: 202.823 MB
% 0.65/1.53 % Net memory used: 192.886 MB
%------------------------------------------------------------------------------