%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM588+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n011.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 02:26:08 PM UTC 2026
% Result : Theorem 1.36s 1.32s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 20 ( 7 unt; 0 def)
% Number of atoms : 335 ( 35 equ)
% Maximal formula atoms : 40 ( 16 avg)
% Number of connectives : 408 ( 93 ~; 66 |; 209 &)
% ( 10 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 9 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 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 : 90 ( 0 sgn 70 !; 20 ?; 2 :)
% Comments :
%------------------------------------------------------------------------------
fof(f88,conjecture,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( isCountable0(X1)
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(X1)
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( X2 != szmzizndt0(sdtlpdtrp0(xN,X0))
& aElementOf0(X2,sdtlpdtrp0(xN,X0))
& aElement0(X2) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
=> ! [X2] :
( ( aElementOf0(X2,slbdtsldtrb0(X1,xk))
& sbrdtbr0(X2) = xk
& aSubsetOf0(X2,X1)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSet0(X2) )
=> ( ( ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
=> ( ( ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( X3 != szmzizndt0(sdtlpdtrp0(xN,X0))
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
=> ( aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
| aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f89,negated_conjecture,
~ ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( isCountable0(X1)
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(X1)
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( X2 != szmzizndt0(sdtlpdtrp0(xN,X0))
& aElementOf0(X2,sdtlpdtrp0(xN,X0))
& aElement0(X2) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
=> ! [X2] :
( ( aElementOf0(X2,slbdtsldtrb0(X1,xk))
& sbrdtbr0(X2) = xk
& aSubsetOf0(X2,X1)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSet0(X2) )
=> ( ( ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
=> ( ( ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( X3 != szmzizndt0(sdtlpdtrp0(xN,X0))
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
=> ( aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
| aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f88]) ).
fof(f104,plain,
~ ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( isCountable0(X1)
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( aElementOf0(X4,X1)
=> aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(X1)
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
=> ! [X5] :
( ( aElementOf0(X5,slbdtsldtrb0(X1,xk))
& sbrdtbr0(X5) = xk
& aSubsetOf0(X5,X1)
& ! [X6] :
( aElementOf0(X6,X5)
=> aElementOf0(X6,X1) )
& aSet0(X5) )
=> ( ( ! [X7] :
( aElementOf0(X7,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
=> ( ( ! [X8] :
( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X8
& aElementOf0(X8,sdtlpdtrp0(xN,X0))
& aElement0(X8) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
=> ( aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
| aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ! [X9] :
( aElementOf0(X9,X5)
=> aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ) ) ) ) ),
inference(rectify,[],[f89]) ).
fof(f221,plain,
? [X0] :
( aElementOf0(X0,szNzAzT0)
& ? [X1] :
( isCountable0(X1)
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( ~ aElementOf0(X4,X1)
| aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(X1)
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ? [X5] :
( aElementOf0(X5,slbdtsldtrb0(X1,xk))
& sbrdtbr0(X5) = xk
& aSubsetOf0(X5,X1)
& ! [X6] :
( ~ aElementOf0(X6,X5)
| aElementOf0(X6,X1) )
& aSet0(X5)
& ! [X7] :
( ~ aElementOf0(X7,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X8] :
( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X8
& aElementOf0(X8,sdtlpdtrp0(xN,X0))
& aElement0(X8) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ~ aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& ~ aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ? [X9] :
( aElementOf0(X9,X5)
& ~ aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ) ),
inference(ennf_transformation,[],[f104]) ).
fof(f222,plain,
? [X0] :
( aElementOf0(X0,szNzAzT0)
& ? [X1] :
( isCountable0(X1)
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( ~ aElementOf0(X4,X1)
| aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(X1)
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ? [X5] :
( aElementOf0(X5,slbdtsldtrb0(X1,xk))
& sbrdtbr0(X5) = xk
& aSubsetOf0(X5,X1)
& ! [X6] :
( ~ aElementOf0(X6,X5)
| aElementOf0(X6,X1) )
& aSet0(X5)
& ! [X7] :
( ~ aElementOf0(X7,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X8] :
( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X8
& aElementOf0(X8,sdtlpdtrp0(xN,X0))
& aElement0(X8) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ~ aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& ~ aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ? [X9] :
( aElementOf0(X9,X5)
& ~ aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f358,plain,
? [X0] :
( aElementOf0(X0,szNzAzT0)
& ? [X1] :
( isCountable0(X1)
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( ~ aElementOf0(X4,X1)
| aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(X1)
& ! [X3] :
( ( ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X3
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0))
| ~ aElement0(X3)
| aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ? [X5] :
( aElementOf0(X5,slbdtsldtrb0(X1,xk))
& sbrdtbr0(X5) = xk
& aSubsetOf0(X5,X1)
& ! [X6] :
( ~ aElementOf0(X6,X5)
| aElementOf0(X6,X1) )
& aSet0(X5)
& ! [X7] :
( ~ aElementOf0(X7,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X8] :
( ( ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X8
& aElementOf0(X8,sdtlpdtrp0(xN,X0))
& aElement0(X8) ) )
& ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X8
| ~ aElementOf0(X8,sdtlpdtrp0(xN,X0))
| ~ aElement0(X8)
| aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ~ aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& ~ aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ? [X9] :
( aElementOf0(X9,X5)
& ~ aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ) ),
inference(nnf_transformation,[],[f222]) ).
fof(f359,plain,
? [X0] :
( aElementOf0(X0,szNzAzT0)
& ? [X1] :
( isCountable0(X1)
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( ~ aElementOf0(X4,X1)
| aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(X1)
& ! [X3] :
( ( ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X3
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0))
| ~ aElement0(X3)
| aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ? [X5] :
( aElementOf0(X5,slbdtsldtrb0(X1,xk))
& sbrdtbr0(X5) = xk
& aSubsetOf0(X5,X1)
& ! [X6] :
( ~ aElementOf0(X6,X5)
| aElementOf0(X6,X1) )
& aSet0(X5)
& ! [X7] :
( ~ aElementOf0(X7,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X8] :
( ( ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X8
& aElementOf0(X8,sdtlpdtrp0(xN,X0))
& aElement0(X8) ) )
& ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X8
| ~ aElementOf0(X8,sdtlpdtrp0(xN,X0))
| ~ aElement0(X8)
| aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ~ aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& ~ aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ? [X9] :
( aElementOf0(X9,X5)
& ~ aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ) ),
inference(flattening,[],[f358]) ).
fof(f360,plain,
? [X0] :
( aElementOf0(X0,szNzAzT0)
& ? [X1] :
( isCountable0(X1)
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X9] :
( ~ aElementOf0(X9,X1)
| aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(X1)
& ! [X8] :
( ( ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X8
& aElementOf0(X8,sdtlpdtrp0(xN,X0))
& aElement0(X8) ) )
& ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X8
| ~ aElementOf0(X8,sdtlpdtrp0(xN,X0))
| ~ aElement0(X8)
| aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X7] :
( ~ aElementOf0(X7,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ? [X2] :
( aElementOf0(X2,slbdtsldtrb0(X1,xk))
& sbrdtbr0(X2) = xk
& aSubsetOf0(X2,X1)
& ! [X6] :
( ~ aElementOf0(X6,X2)
| aElementOf0(X6,X1) )
& aSet0(X2)
& ! [X5] :
( ~ aElementOf0(X5,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X5) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X4] :
( ( ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X4
& aElementOf0(X4,sdtlpdtrp0(xN,X0))
& aElement0(X4) ) )
& ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X4
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0))
| ~ aElement0(X4)
| aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ~ aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& ~ aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ? [X3] :
( aElementOf0(X3,X2)
& ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ) ),
inference(rectify,[],[f359]) ).
fof(f361,plain,
( aElementOf0(sK53,szNzAzT0)
& isCountable0(sK54)
& aSubsetOf0(sK54,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
& ! [X9] :
( ~ aElementOf0(X9,sK54)
| aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53)))) )
& aSet0(sK54)
& ! [X8] :
( ( ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
| ( szmzizndt0(sdtlpdtrp0(xN,sK53)) != X8
& aElementOf0(X8,sdtlpdtrp0(xN,sK53))
& aElement0(X8) ) )
& ( szmzizndt0(sdtlpdtrp0(xN,sK53)) = X8
| ~ aElementOf0(X8,sdtlpdtrp0(xN,sK53))
| ~ aElement0(X8)
| aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
& ! [X7] :
( ~ aElementOf0(X7,sdtlpdtrp0(xN,sK53))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK53)),X7) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK53)),sdtlpdtrp0(xN,sK53))
& aElementOf0(sK55,slbdtsldtrb0(sK54,xk))
& xk = sbrdtbr0(sK55)
& aSubsetOf0(sK55,sK54)
& ! [X6] :
( ~ aElementOf0(X6,sK55)
| aElementOf0(X6,sK54) )
& aSet0(sK55)
& ! [X5] :
( ~ aElementOf0(X5,sdtlpdtrp0(xN,sK53))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK53)),X5) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK53)),sdtlpdtrp0(xN,sK53))
& ! [X4] :
( ( ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
| ( szmzizndt0(sdtlpdtrp0(xN,sK53)) != X4
& aElementOf0(X4,sdtlpdtrp0(xN,sK53))
& aElement0(X4) ) )
& ( szmzizndt0(sdtlpdtrp0(xN,sK53)) = X4
| ~ aElementOf0(X4,sdtlpdtrp0(xN,sK53))
| ~ aElement0(X4)
| aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
& ~ aElementOf0(sK55,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))),xk))
& ~ aSubsetOf0(sK55,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
& aElementOf0(sK56,sK55)
& ~ aElementOf0(sK56,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56)],[f360]) ).
fof(f664,plain,
! [X9] :
( ~ aElementOf0(X9,sK54)
| aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53)))) ),
inference(cnf_transformation,[],[f361]) ).
fof(f676,plain,
! [X6] :
( ~ aElementOf0(X6,sK55)
| aElementOf0(X6,sK54) ),
inference(cnf_transformation,[],[f361]) ).
fof(f687,plain,
aElementOf0(sK56,sK55),
inference(cnf_transformation,[],[f361]) ).
fof(f688,plain,
~ aElementOf0(sK56,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53)))),
inference(cnf_transformation,[],[f361]) ).
tcf(c_348,negated_conjecture,
~ aElementOf0(sK56,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53)))),
inference(cnf_transformation,[],[f688]) ).
tcf(c_349,negated_conjecture,
aElementOf0(sK56,sK55),
inference(cnf_transformation,[],[f687]) ).
tcf(c_360,negated_conjecture,
! [X0: $i] :
( aElementOf0(X0,sK54)
| ~ aElementOf0(X0,sK55) ),
inference(cnf_transformation,[],[f676]) ).
tcf(c_372,negated_conjecture,
! [X0: $i] :
( aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
| ~ aElementOf0(X0,sK54) ),
inference(cnf_transformation,[],[f664]) ).
tcf(c_473,plain,
aElementOf0(sK56,sK54),
inference(superposition,[status(thm)],[c_349,c_360]) ).
tcf(c_575,plain,
~ aElementOf0(sK56,sK54),
inference(superposition,[status(thm)],[c_372,c_348]) ).
tcf(c_577,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_575,c_473]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM588+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/0.45 % Computer : n011.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Thu Sep 24 04:46:58 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.23/0.51 Running first-order theorem proving
% 0.23/0.51 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.52
% 0.23/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.23/0.52
% 0.23/0.52 % Detected problem language: tptp
% 0.23/0.55 % Proving...
% 1.36/1.32 % SZS status Started for theBenchmark.p
% 1.36/1.32 % SZS status Theorem for theBenchmark.p
% 1.36/1.32
% 1.36/1.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.36/1.32
% 1.36/1.32 % ------ iProver source info
% 1.36/1.32
% 1.36/1.32 % git: date: 2026-07-19 20:42:38 +0200
% 1.36/1.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.36/1.32 % git: non_committed_changes: false
% 1.36/1.32
% 1.36/1.32 % ------ Parsing...
% 1.36/1.32 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.36/1.32 % ------ Proving...
% 1.36/1.32 % ------ Problem Properties
% 1.36/1.32
% 1.36/1.32 %
% 1.36/1.32 % clauses 327
% 1.36/1.32 % conjectures 28
% 1.36/1.32 % EPR 61
% 1.36/1.32 % Horn 251
% 1.36/1.32 % unary 44
% 1.36/1.32 % binary 80
% 1.36/1.32 % lits 1061
% 1.36/1.32 % lits eq 127
% 1.36/1.32 % fd_pure 0
% 1.36/1.32 % fd_pseudo 0
% 1.36/1.32 % fd_cond 12
% 1.36/1.32 % fd_pseudo_cond 40
% 1.36/1.32 % AC symbols 0
% 1.36/1.32
% 1.36/1.32 % ------ Input Options Time Limit: Unbounded
% 1.36/1.32
% 1.36/1.32
% 1.36/1.32 % ------
% 1.36/1.32 % Current options:
% 1.36/1.32 % ------
% 1.36/1.32
% 1.36/1.32
% 1.36/1.32 %
% 1.36/1.32
% 1.36/1.32 % ------ Proving...
% 1.36/1.32 %
% 1.36/1.32
% 1.36/1.32 % SZS status Theorem for theBenchmark.p
% 1.36/1.32
% 1.36/1.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.36/1.33
% 1.36/1.33
%------------------------------------------------------------------------------