%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM584+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 : n013.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 02:26:07 PM UTC 2026
% Result : Theorem 1.85s 1.27s
% Output : CNFRefutation 1.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 5 unt; 0 def)
% Number of atoms : 258 ( 45 equ)
% Maximal formula atoms : 17 ( 9 avg)
% Number of connectives : 309 ( 77 ~; 72 |; 131 &)
% ( 11 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 8 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 46 !; 5 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
fof(f87,axiom,
( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK
& ! [X0] :
( aElementOf0(X0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ( X0 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X0,xQ) )
& aElement0(X0) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4007) ).
fof(f88,axiom,
( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& ! [X0] :
( aElementOf0(X0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
=> aElementOf0(X0,xS) )
& ! [X0] :
( aElementOf0(X0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ( X0 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X0,xQ) )
& aElement0(X0) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4024) ).
fof(f89,conjecture,
( ( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
=> ( ( ! [X0] :
( aElementOf0(X0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ( X0 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X0,xQ) )
& aElement0(X0) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
=> ( aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK))
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK
& ( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
| ! [X0] :
( aElementOf0(X0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
=> aElementOf0(X0,xS) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f90,negated_conjecture,
~ ( ( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
=> ( ( ! [X0] :
( aElementOf0(X0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ( X0 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X0,xQ) )
& aElement0(X0) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
=> ( aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK))
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK
& ( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
| ! [X0] :
( aElementOf0(X0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
=> aElementOf0(X0,xS) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f103,plain,
( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = X1
| aElementOf0(X1,xQ) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(rectify,[],[f87]) ).
fof(f104,plain,
( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& ! [X2] :
( aElementOf0(X2,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
=> aElementOf0(X2,xS) )
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = X1
| aElementOf0(X1,xQ) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(rectify,[],[f88]) ).
fof(f105,plain,
~ ( ( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
=> ( ( ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = X1
| aElementOf0(X1,xQ) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
=> ( aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK))
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK
& ( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
| ! [X2] :
( aElementOf0(X2,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
=> aElementOf0(X2,xS) ) ) ) ) ) ),
inference(rectify,[],[f90]) ).
fof(f218,plain,
( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = X1
| aElementOf0(X1,xQ) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(ennf_transformation,[],[f103]) ).
fof(f219,plain,
( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& ! [X2] :
( ~ aElementOf0(X2,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| aElementOf0(X2,xS) )
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = X1
| aElementOf0(X1,xQ) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(ennf_transformation,[],[f104]) ).
fof(f220,plain,
( ! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = X1
| aElementOf0(X1,xQ) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK))
& ( xK != sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& ? [X2] :
( aElementOf0(X2,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ~ aElementOf0(X2,xS) ) ) ) ),
inference(ennf_transformation,[],[f105]) ).
fof(f221,plain,
( ! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = X1
| aElementOf0(X1,xQ) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK))
& ( xK != sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& ? [X2] :
( aElementOf0(X2,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ~ aElementOf0(X2,xS) ) ) ) ),
inference(flattening,[],[f220]) ).
fof(f321,plain,
( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK
& ! [X1] :
( ( ~ aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = X1
| aElementOf0(X1,xQ) )
& aElement0(X1) ) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X1
& ~ aElementOf0(X1,xQ) )
| ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(nnf_transformation,[],[f218]) ).
fof(f322,plain,
( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK
& ! [X1] :
( ( ~ aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = X1
| aElementOf0(X1,xQ) )
& aElement0(X1) ) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X1
& ~ aElementOf0(X1,xQ) )
| ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(flattening,[],[f321]) ).
fof(f323,plain,
( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& ! [X2] :
( ~ aElementOf0(X2,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| aElementOf0(X2,xS) )
& ! [X1] :
( ( ~ aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = X1
| aElementOf0(X1,xQ) )
& aElement0(X1) ) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X1
& ~ aElementOf0(X1,xQ) )
| ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(nnf_transformation,[],[f219]) ).
fof(f324,plain,
( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& ! [X2] :
( ~ aElementOf0(X2,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| aElementOf0(X2,xS) )
& ! [X1] :
( ( ~ aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = X1
| aElementOf0(X1,xQ) )
& aElement0(X1) ) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X1
& ~ aElementOf0(X1,xQ) )
| ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(flattening,[],[f323]) ).
fof(f325,plain,
( ! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( ( ~ aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = X1
| aElementOf0(X1,xQ) )
& aElement0(X1) ) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X1
& ~ aElementOf0(X1,xQ) )
| ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK))
& ( xK != sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& ? [X2] :
( aElementOf0(X2,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ~ aElementOf0(X2,xS) ) ) ) ),
inference(nnf_transformation,[],[f221]) ).
fof(f326,plain,
( ! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( ( ~ aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = X1
| aElementOf0(X1,xQ) )
& aElement0(X1) ) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X1
& ~ aElementOf0(X1,xQ) )
| ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK))
& ( xK != sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& ? [X2] :
( aElementOf0(X2,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ~ aElementOf0(X2,xS) ) ) ) ),
inference(flattening,[],[f325]) ).
fof(f327,plain,
( ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( ( ~ aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = X1
| aElementOf0(X1,xQ) )
& aElement0(X1) ) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X1
& ~ aElementOf0(X1,xQ) )
| ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK))
& ( xK != sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& ? [X0] :
( aElementOf0(X0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ~ aElementOf0(X0,xS) ) ) ) ),
inference(rectify,[],[f326]) ).
fof(f328,plain,
( ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( ( ~ aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = X1
| aElementOf0(X1,xQ) )
& aElement0(X1) ) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X1
& ~ aElementOf0(X1,xQ) )
| ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK))
& ( xK != sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& aElementOf0(sK41,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ~ aElementOf0(sK41,xS) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(X0,sK41)],[f327]) ).
fof(f571,plain,
xK = sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(cnf_transformation,[],[f322]) ).
fof(f579,plain,
aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
inference(cnf_transformation,[],[f324]) ).
fof(f596,plain,
( xK != sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) ),
inference(cnf_transformation,[],[f328]) ).
tcf(c_298,plain,
sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK,
inference(cnf_transformation,[],[f571]) ).
tcf(c_307,plain,
aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
inference(cnf_transformation,[],[f579]) ).
tcf(c_310,negated_conjecture,
( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
| ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK ) ),
inference(cnf_transformation,[],[f596]) ).
tcf(c_447,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_310,c_298,c_307]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM584+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 04:45:06 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 1.85/1.27 % SZS status Started for theBenchmark.p
% 1.85/1.27 % SZS status Theorem for theBenchmark.p
% 1.85/1.27
% 1.85/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.85/1.27
% 1.85/1.27 % ------ iProver source info
% 1.85/1.27
% 1.85/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.85/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.85/1.27 % git: non_committed_changes: false
% 1.85/1.27
% 1.85/1.27 % ------ Parsing...
% 1.85/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.85/1.27
% 1.85/1.27 % ------ Preprocessing...%
% 1.85/1.27
% 1.85/1.27 % SZS status Theorem for theBenchmark.p
% 1.85/1.27
% 1.85/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.85/1.27
% 1.85/1.27
%------------------------------------------------------------------------------