%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM558+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 : n014.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 01:40:59 PM UTC 2026
% Result : Theorem 0.17s 0.53s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 31 ( 11 unt; 0 def)
% Number of atoms : 271 ( 45 equ)
% Maximal formula atoms : 43 ( 8 avg)
% Number of connectives : 337 ( 97 ~; 84 |; 137 &)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-2 aty)
% Number of variables : 69 ( 60 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f62,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f63,hypothesis,
( ~ ( ! [W0] :
( ( ( sbrdtbr0(W0) = xk
& ( aSubsetOf0(W0,xS)
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) )
=> ( slbdtsldtrb0(xS,xk) = slcrc0
| ~ ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& ! [W0] :
( ( ( sbrdtbr0(W0) = xk
& ( aSubsetOf0(W0,xT)
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSet0(W0) ) ) )
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
=> ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xT)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSet0(W0) ) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [W0] :
( ( ( sbrdtbr0(W0) = xk
& ( aSubsetOf0(W0,xS)
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f64,hypothesis,
aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f70,hypothesis,
( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
& ! [W0] :
( aElementOf0(W0,xP)
<=> ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xQ,xy)) )
& aElement0(W0) ) )
& aSet0(xP)
& ! [W0] :
( aElementOf0(W0,sdtmndt0(xQ,xy))
<=> ( W0 != xy
& aElementOf0(W0,xQ)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xQ,xy)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f71,hypothesis,
( aElementOf0(xP,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xP) = xk
& aSubsetOf0(xP,xS)
& ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xS) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f72,conjecture,
aElementOf0(xx,xT),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f73,negated_conjecture,
~ aElementOf0(xx,xT),
inference(negated_conjecture,[status(cth)],[f72]) ).
fof(f80,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f81,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f273,plain,
aSet0(xS),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f276,plain,
( slbdtsldtrb0(xS,xk) != slcrc0
& ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk))
& ! [W0] :
( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,xS)
& ( ? [W1] :
( ~ aElementOf0(W1,xS)
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ) ) )
& ( ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,xS)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& ! [W0] :
( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,xT)
& ( ? [W1] :
( ~ aElementOf0(W1,xT)
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ) ) )
& ( ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xT)
& ! [W1] :
( aElementOf0(W1,xT)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [W0] :
( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,xS)
& ( ? [W1] :
( ~ aElementOf0(W1,xS)
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ) ) )
& ( ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,xS)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(pre_NNF_transformation,[status(thm)],[f63]) ).
fof(f277,plain,
( slbdtsldtrb0(xS,xk) != slcrc0
& ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk))
& ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,xS)
& ( ? [W1] :
( ~ aElementOf0(W1,xS)
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ) ) )
& ! [W0] :
( ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,xS)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,xT)
& ( ? [W1] :
( ~ aElementOf0(W1,xT)
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ) ) )
& ! [W0] :
( ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xT)
& ! [W1] :
( aElementOf0(W1,xT)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,xS)
& ( ? [W1] :
( ~ aElementOf0(W1,xS)
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ) ) )
& ! [W0] :
( ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,xS)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(miniscoping,[status(thm)],[f276]) ).
fof(f278,plain,
( slbdtsldtrb0(xS,xk) != slcrc0
& aElementOf0(sK14_skl,slbdtsldtrb0(xS,xk))
& ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,xS)
& ( ( ~ aElementOf0(sK13_skl(W0),xS)
& aElementOf0(sK13_skl(W0),W0) )
| ~ aSet0(W0) ) ) )
& ! [W0] :
( ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,xS)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,xT)
& ( ( ~ aElementOf0(sK12_skl(W0),xT)
& aElementOf0(sK12_skl(W0),W0) )
| ~ aSet0(W0) ) ) )
& ! [W0] :
( ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xT)
& ! [W1] :
( aElementOf0(W1,xT)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,xS)
& ( ( ~ aElementOf0(sK11_skl(W0),xS)
& aElementOf0(sK11_skl(W0),W0) )
| ~ aSet0(W0) ) ) )
& ! [W0] :
( ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,xS)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl,sK13_skl,sK14_skl]),skolemize(W1,sK11_skl(W0)),skolemize(W1,sK12_skl(W0)),skolemize(W1,sK13_skl(W0)),skolemize(W0,sK14_skl)],[f277]) ).
fof(f289,plain,
! [X0,X1] :
( aElementOf0(X1,xT)
| ~ aElementOf0(X1,X0)
| ~ aElementOf0(X0,slbdtsldtrb0(xT,xk)) ),
inference(cnf_transformation,[status(thm)],[f278]) ).
fof(f295,plain,
! [X0] :
( aElementOf0(X0,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) ),
inference(cnf_transformation,[status(thm)],[f278]) ).
fof(f306,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f320,plain,
( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
& ! [W0] :
( ( ( W0 != xx
& ~ aElementOf0(W0,sdtmndt0(xQ,xy)) )
| ~ aElement0(W0)
| aElementOf0(W0,xP) )
& ( ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xQ,xy)) )
& aElement0(W0) )
| ~ aElementOf0(W0,xP) ) )
& aSet0(xP)
& ! [W0] :
( ( W0 = xy
| ~ aElementOf0(W0,xQ)
| ~ aElement0(W0)
| aElementOf0(W0,sdtmndt0(xQ,xy)) )
& ( ( W0 != xy
& aElementOf0(W0,xQ)
& aElement0(W0) )
| ~ aElementOf0(W0,sdtmndt0(xQ,xy)) ) )
& aSet0(sdtmndt0(xQ,xy)) ),
inference(NNF_transformation,[status(thm)],[f70]) ).
fof(f321,plain,
( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
& ! [W0] :
( ( W0 != xx
& ~ aElementOf0(W0,sdtmndt0(xQ,xy)) )
| ~ aElement0(W0)
| aElementOf0(W0,xP) )
& ! [W0] :
( ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xQ,xy)) )
& aElement0(W0) )
| ~ aElementOf0(W0,xP) )
& aSet0(xP)
& ! [W0] :
( W0 = xy
| ~ aElementOf0(W0,xQ)
| ~ aElement0(W0)
| aElementOf0(W0,sdtmndt0(xQ,xy)) )
& ! [W0] :
( ( W0 != xy
& aElementOf0(W0,xQ)
& aElement0(W0) )
| ~ aElementOf0(W0,sdtmndt0(xQ,xy)) )
& aSet0(sdtmndt0(xQ,xy)) ),
inference(miniscoping,[status(thm)],[f320]) ).
fof(f331,plain,
! [X0] :
( X0 != xx
| ~ aElement0(X0)
| aElementOf0(X0,xP) ),
inference(cnf_transformation,[status(thm)],[f321]) ).
fof(f333,plain,
( aElementOf0(xP,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xP) = xk
& aSubsetOf0(xP,xS)
& ! [W0] :
( aElementOf0(W0,xS)
| ~ aElementOf0(W0,xP) ) ),
inference(pre_NNF_transformation,[status(thm)],[f71]) ).
fof(f337,plain,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[status(thm)],[f333]) ).
fof(f338,plain,
~ aElementOf0(xx,xT),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f373,plain,
( ~ aElement0(xx)
| aElementOf0(xx,xP) ),
inference(destructive_equality_resolution,[status(thm)],[f331]) ).
fof(f376,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f81,f306]) ).
fof(f377,plain,
aElement0(xx),
inference(forward_subsumption_resolution,[status(thm)],[f376,f273]) ).
fof(f389,plain,
aElementOf0(xx,xP),
inference(backward_subsumption_resolution,[status(thm)],[f373,f377]) ).
fof(f399,plain,
! [X0,X1] :
( aElementOf0(X1,xT)
| ~ aElementOf0(X1,X0)
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) ),
inference(resolution,[status(thm)],[f295,f289]) ).
fof(f802,plain,
! [X0] :
( aElementOf0(X0,xT)
| ~ aElementOf0(X0,xP) ),
inference(resolution,[status(thm)],[f337,f399]) ).
fof(f913,plain,
aElementOf0(xx,xT),
inference(resolution,[status(thm)],[f802,f389]) ).
fof(f917,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f913,f338]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM558+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n014.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 02:39:49 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.46 % Drodi V4.1.1
% 0.17/0.53 % Refutation found
% 0.17/0.53 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.56 % Elapsed time: 0.108255 seconds
% 0.17/0.56 % CPU time: 0.522174 seconds
% 0.17/0.56 % Total memory used: 103.779 MB
% 0.17/0.56 % Net memory used: 103.382 MB
%------------------------------------------------------------------------------