%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM558+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 : Fri Sep 25 02:20:22 PM UTC 2026
% Result : Theorem 23.53s 3.82s
% Output : Proof 23.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 15 unt; 0 def)
% Number of atoms : 243 ( 41 equ)
% Maximal formula atoms : 43 ( 6 avg)
% Number of connectives : 288 ( 82 ~; 69 |; 118 &)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 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 : 46 ( 0 sgn 33 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f62,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/sandbox/benchmark/theBenchmark.p',m__2227) ).
fof(f62_nnf,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(nnf_transformation,[status(thm)],[f62]) ).
fof(f62_sk,plain,
! [W0,W1] :
( slbdtsldtrb0(xS,xk) != slcrc0
& aElementOf0(sk14,slbdtsldtrb0(xS,xk))
& ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,xS)
& ( ( ~ aElementOf0(sk13(W0),xS)
& aElementOf0(sk13(W0),W0) )
| ~ aSet0(W0) ) ) )
& ( ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xS)
& ( aElementOf0(W1,xS)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,xT)
& ( ( ~ aElementOf0(sk12(W0),xT)
& aElementOf0(sk12(W0),W0) )
| ~ aSet0(W0) ) ) )
& ( ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xT)
& ( aElementOf0(W1,xT)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& aSet0(slbdtsldtrb0(xT,xk))
& ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,xS)
& ( ( ~ aElementOf0(sk11(W0),xS)
& aElementOf0(sk11(W0),W0) )
| ~ aSet0(W0) ) ) )
& ( ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xS)
& ( aElementOf0(W1,xS)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11,sk12,sk13,sk14])],[f62_nnf]) ).
cnf(c139,plain,
( aElementOf0(X1,xT)
| ~ aElementOf0(X1,X0)
| ~ aElementOf0(X0,slbdtsldtrb0(xT,xk)) ),
inference(cnf_transformation,[status(esa)],[f62_sk]) ).
cnf(c145,plain,
( aElementOf0(X0,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) ),
inference(cnf_transformation,[status(esa)],[f62_sk]) ).
fof(f70,hypothesis,
( aElementOf0(xP,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xP) = xk
& aSubsetOf0(xP,xS)
& ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xS) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2378) ).
fof(f70_nnf,plain,
( aElementOf0(xP,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xP) = xk
& aSubsetOf0(xP,xS)
& ! [W0] :
( aElementOf0(W0,xS)
| ~ aElementOf0(W0,xP) ) ),
inference(nnf_transformation,[status(thm)],[f70]) ).
fof(f70_sk,plain,
! [W0] :
( aElementOf0(xP,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xP) = xk
& aSubsetOf0(xP,xS)
& ( aElementOf0(W0,xS)
| ~ aElementOf0(W0,xP) ) ),
inference(skolemisation,[status(esa)],[f70_nnf]) ).
cnf(c183,plain,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[status(esa)],[f70_sk]) ).
cnf(p757,plain,
aElementOf0(xP,slbdtsldtrb0(xT,xk)),
inference(resolution,[status(thm)],[c145,c183]) ).
cnf(p5235,plain,
( aElementOf0(X0,xT)
| ~ aElementOf0(X0,xP) ),
inference(resolution,[status(thm)],[c139,p757]) ).
fof(f69,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/sandbox/benchmark/theBenchmark.p',m__2357) ).
fof(f69_nnf,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)],[f69]) ).
fof(f69_sk,plain,
! [W0] :
( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
& ( ( 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 = 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(skolemisation,[status(esa)],[f69_nnf]) ).
cnf(c178,plain,
( X0 != xx
| ~ aElement0(X0)
| aElementOf0(X0,xP) ),
inference(cnf_transformation,[status(esa)],[f69_sk]) ).
cnf(p423,plain,
( ~ aElement0(xx)
| aElementOf0(xx,xP) ),
inference(equality_resolution,[status(thm)],[c178]) ).
fof(f2,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f2_nnf,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [W0,W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0)
| ~ aSet0(W0) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f61,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).
fof(f61_nnf,plain,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
inference(nnf_transformation,[status(thm)],[f61]) ).
fof(f61_sk,plain,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
inference(skolemisation,[status(esa)],[f61_nnf]) ).
cnf(c126,plain,
aSet0(xS),
inference(cnf_transformation,[status(esa)],[f61_sk]) ).
cnf(p326,plain,
( aElement0(X0)
| ~ aElementOf0(X0,xS) ),
inference(resolution,[status(thm)],[c2,c126]) ).
fof(f63,hypothesis,
aElementOf0(xx,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2256) ).
fof(f63_nnf,plain,
aElementOf0(xx,xS),
inference(nnf_transformation,[status(thm)],[f63]) ).
cnf(c156,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[status(esa)],[f63_nnf]) ).
cnf(p343,plain,
aElement0(xx),
inference(resolution,[status(thm)],[p326,c156]) ).
cnf(p449,plain,
aElementOf0(xx,xP),
inference(resolution,[status(thm)],[p423,p343]) ).
cnf(p5239,plain,
aElementOf0(xx,xT),
inference(resolution,[status(thm)],[p5235,p449]) ).
fof(f71,conjecture,
aElementOf0(xx,xT),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f71_neg,negated_conjecture,
~ aElementOf0(xx,xT),
inference(negated_conjecture,[status(cth)],[f71]) ).
fof(f71_nnf,plain,
~ aElementOf0(xx,xT),
inference(nnf_transformation,[status(thm)],[f71_neg]) ).
fof(f71_sk,plain,
~ aElementOf0(xx,xT),
inference(skolemisation,[status(esa)],[f71_nnf]) ).
cnf(c184,plain,
~ aElementOf0(xx,xT),
inference(cnf_transformation,[status(esa)],[f71_sk]) ).
cnf(p5241,plain,
$false,
inference(resolution,[status(thm)],[p5239,c184]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM558+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 04:39:19 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 23.53/3.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.53/3.82 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------