%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM588+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 : n019.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 02:20:27 PM UTC 2026
% Result : Theorem 19.35s 3.40s
% Output : Proof 19.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 5 unt; 0 def)
% Number of atoms : 153 ( 16 equ)
% Maximal formula atoms : 40 ( 13 avg)
% Number of connectives : 180 ( 38 ~; 30 |; 88 &)
% ( 4 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 9 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 28 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f87,conjecture,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( ( isCountable0(W1)
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSet0(W1)
& ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W2,sdtlpdtrp0(xN,W0))
& aElement0(W2) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
=> ! [W2] :
( ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
& sbrdtbr0(W2) = xk
& aSubsetOf0(W2,W1)
& ! [W3] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,W1) )
& aSet0(W2) )
=> ( ( ! [W3] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
=> ( ( ! [W3] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& aElement0(W3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
=> ( aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
| aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ! [W3] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f87_neg,negated_conjecture,
~ ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( ( isCountable0(W1)
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSet0(W1)
& ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W2,sdtlpdtrp0(xN,W0))
& aElement0(W2) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
=> ! [W2] :
( ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
& sbrdtbr0(W2) = xk
& aSubsetOf0(W2,W1)
& ! [W3] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,W1) )
& aSet0(W2) )
=> ( ( ! [W3] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
=> ( ( ! [W3] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& aElement0(W3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
=> ( aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
| aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ! [W3] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f87]) ).
fof(f87_nnf,plain,
? [W0] :
( ? [W1] :
( ? [W2] :
( ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
& ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ? [W3] :
( ~ aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W3,W2) )
& ! [W3] :
( ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0))
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ~ aElement0(W3)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ( ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& aElement0(W3) )
| ~ aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& aElementOf0(W2,slbdtsldtrb0(W1,xk))
& sbrdtbr0(W2) = xk
& aSubsetOf0(W2,W1)
& ! [W3] :
( aElementOf0(W3,W1)
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
& isCountable0(W1)
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,W1) )
& aSet0(W1)
& ! [W2] :
( ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0))
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ~ aElement0(W2)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ( ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W2,sdtlpdtrp0(xN,W0))
& aElement0(W2) )
| ~ aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
& aElementOf0(W0,szNzAzT0) ),
inference(nnf_transformation,[status(thm)],[f87_neg]) ).
fof(f87_sk,plain,
! [W2,W3] :
( ~ aElementOf0(sk37,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sk35),szmzizndt0(sdtlpdtrp0(xN,sk35))),xk))
& ~ aSubsetOf0(sk37,sdtmndt0(sdtlpdtrp0(xN,sk35),szmzizndt0(sdtlpdtrp0(xN,sk35))))
& ~ aElementOf0(sk38,sdtmndt0(sdtlpdtrp0(xN,sk35),szmzizndt0(sdtlpdtrp0(xN,sk35))))
& aElementOf0(sk38,sk37)
& ( W3 = szmzizndt0(sdtlpdtrp0(xN,sk35))
| ~ aElementOf0(W3,sdtlpdtrp0(xN,sk35))
| ~ aElement0(W3)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,sk35),szmzizndt0(sdtlpdtrp0(xN,sk35)))) )
& ( ( W3 != szmzizndt0(sdtlpdtrp0(xN,sk35))
& aElementOf0(W3,sdtlpdtrp0(xN,sk35))
& aElement0(W3) )
| ~ aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,sk35),szmzizndt0(sdtlpdtrp0(xN,sk35)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sk35),szmzizndt0(sdtlpdtrp0(xN,sk35))))
& ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sk35)),W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,sk35)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sk35)),sdtlpdtrp0(xN,sk35))
& aElementOf0(sk37,slbdtsldtrb0(sk36,xk))
& sbrdtbr0(sk37) = xk
& aSubsetOf0(sk37,sk36)
& ( aElementOf0(W3,sk36)
| ~ aElementOf0(W3,sk37) )
& aSet0(sk37)
& isCountable0(sk36)
& aSubsetOf0(sk36,sdtmndt0(sdtlpdtrp0(xN,sk35),szmzizndt0(sdtlpdtrp0(xN,sk35))))
& ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,sk35),szmzizndt0(sdtlpdtrp0(xN,sk35))))
| ~ aElementOf0(W2,sk36) )
& aSet0(sk36)
& ( W2 = szmzizndt0(sdtlpdtrp0(xN,sk35))
| ~ aElementOf0(W2,sdtlpdtrp0(xN,sk35))
| ~ aElement0(W2)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,sk35),szmzizndt0(sdtlpdtrp0(xN,sk35)))) )
& ( ( W2 != szmzizndt0(sdtlpdtrp0(xN,sk35))
& aElementOf0(W2,sdtlpdtrp0(xN,sk35))
& aElement0(W2) )
| ~ aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,sk35),szmzizndt0(sdtlpdtrp0(xN,sk35)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sk35),szmzizndt0(sdtlpdtrp0(xN,sk35))))
& ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sk35)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,sk35)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sk35)),sdtlpdtrp0(xN,sk35))
& aElementOf0(sk35,szNzAzT0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk35,sk36,sk37,sk38])],[f87_nnf]) ).
cnf(c599,plain,
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,sk35),szmzizndt0(sdtlpdtrp0(xN,sk35))))
| ~ aElementOf0(X2,sk36) ),
inference(cnf_transformation,[status(esa)],[f87_sk]) ).
cnf(c603,plain,
( aElementOf0(X3,sk36)
| ~ aElementOf0(X3,sk37) ),
inference(cnf_transformation,[status(esa)],[f87_sk]) ).
cnf(c614,plain,
aElementOf0(sk38,sk37),
inference(cnf_transformation,[status(esa)],[f87_sk]) ).
cnf(p475,plain,
aElementOf0(sk38,sk36),
inference(resolution,[status(thm)],[c603,c614]) ).
cnf(p1066,plain,
aElementOf0(sk38,sdtmndt0(sdtlpdtrp0(xN,sk35),szmzizndt0(sdtlpdtrp0(xN,sk35)))),
inference(resolution,[status(thm)],[c599,p475]) ).
cnf(c615,plain,
~ aElementOf0(sk38,sdtmndt0(sdtlpdtrp0(xN,sk35),szmzizndt0(sdtlpdtrp0(xN,sk35)))),
inference(cnf_transformation,[status(esa)],[f87_sk]) ).
cnf(p1067,plain,
$false,
inference(resolution,[status(thm)],[p1066,c615]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM588+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.78 % Computer : n019.cluster.edu
% 0.08/0.78 % Model : x86_64 x86_64
% 0.08/0.78 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.78 % Memory : 8046.5625MB
% 0.08/0.78 % OS : Linux 6.8.0-71-generic
% 0.08/0.78 % CPULimit : 300
% 0.08/0.78 % WCLimit : 300
% 0.08/0.78 % DateTime : Thu Sep 24 04:47:35 UTC 2026
% 0.08/0.78 % CPUTime :
% 0.08/0.78 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 19.35/3.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.35/3.40 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------