%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM583+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 : n007.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 3.54s 1.19s
% Output : CNFRefutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 39 ( 10 unt; 0 def)
% Number of atoms : 237 ( 31 equ)
% Maximal formula atoms : 18 ( 6 avg)
% Number of connectives : 264 ( 66 ~; 60 |; 113 &)
% ( 8 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 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 : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 48 !; 5 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f86,axiom,
( aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(xQ)
& ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( X0 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(X0,sdtlpdtrp0(xN,xi))
& aElement0(X0) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),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__3989_02) ).
fof(f88,axiom,
( aSubsetOf0(sdtlpdtrp0(xN,xi),xS)
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> aElementOf0(X0,xS) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4037) ).
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)))) )
=> ( 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)))) )
=> ( 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(f102,plain,
( aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X2] :
( aElementOf0(X2,xQ)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(xQ)
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X1
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& aElement0(X1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),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,[],[f86]) ).
fof(f104,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)))) )
=> ( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
| ! [X2] :
( aElementOf0(X2,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
=> aElementOf0(X2,xS) ) ) ) ),
inference(rectify,[],[f90]) ).
fof(f216,plain,
( aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X2] :
( ~ aElementOf0(X2,xQ)
| aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(xQ)
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X1
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& aElement0(X1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),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,[],[f102]) ).
fof(f218,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xi),xS)
& ! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xi))
| aElementOf0(X0,xS) ) ),
inference(ennf_transformation,[],[f88]) ).
fof(f219,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))))
& ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& ? [X2] :
( aElementOf0(X2,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ~ aElementOf0(X2,xS) ) ),
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))))
& ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& ? [X2] :
( aElementOf0(X2,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ~ aElementOf0(X2,xS) ) ),
inference(flattening,[],[f219]) ).
fof(f318,plain,
( aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X2] :
( ~ aElementOf0(X2,xQ)
| aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(xQ)
& ! [X1] :
( ( ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X1
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& aElement0(X1) ) )
& ( szmzizndt0(sdtlpdtrp0(xN,xi)) = X1
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xi))
| ~ aElement0(X1)
| aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),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,[],[f216]) ).
fof(f319,plain,
( aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X2] :
( ~ aElementOf0(X2,xQ)
| aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(xQ)
& ! [X1] :
( ( ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X1
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& aElement0(X1) ) )
& ( szmzizndt0(sdtlpdtrp0(xN,xi)) = X1
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xi))
| ~ aElement0(X1)
| aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),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,[],[f318]) ).
fof(f322,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))))
& ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& ? [X2] :
( aElementOf0(X2,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ~ aElementOf0(X2,xS) ) ),
inference(nnf_transformation,[],[f220]) ).
fof(f323,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))))
& ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& ? [X2] :
( aElementOf0(X2,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ~ aElementOf0(X2,xS) ) ),
inference(flattening,[],[f322]) ).
fof(f324,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))))
& ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& ? [X0] :
( aElementOf0(X0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ~ aElementOf0(X0,xS) ) ),
inference(rectify,[],[f323]) ).
fof(f325,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))))
& ~ 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)],[f324]) ).
fof(f559,plain,
! [X2] :
( ~ aElementOf0(X2,xQ)
| aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(cnf_transformation,[],[f319]) ).
fof(f562,plain,
! [X1] :
( ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| aElementOf0(X1,sdtlpdtrp0(xN,xi)) ),
inference(cnf_transformation,[],[f319]) ).
fof(f577,plain,
! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xi))
| aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f218]) ).
fof(f579,plain,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)),
inference(cnf_transformation,[],[f325]) ).
fof(f580,plain,
! [X1] :
( ~ aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1
| aElementOf0(X1,xQ) ),
inference(cnf_transformation,[],[f325]) ).
fof(f586,plain,
aElementOf0(sK41,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(cnf_transformation,[],[f325]) ).
fof(f587,plain,
~ aElementOf0(sK41,xS),
inference(cnf_transformation,[],[f325]) ).
tcf(c_284,plain,
! [X0: $i] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(cnf_transformation,[],[f562]) ).
tcf(c_287,plain,
! [X0: $i] :
( aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X0,xQ) ),
inference(cnf_transformation,[],[f559]) ).
tcf(c_299,plain,
! [X0: $i] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) ),
inference(cnf_transformation,[],[f577]) ).
tcf(c_301,negated_conjecture,
~ aElementOf0(sK41,xS),
inference(cnf_transformation,[],[f587]) ).
tcf(c_302,negated_conjecture,
aElementOf0(sK41,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(cnf_transformation,[],[f586]) ).
tcf(c_308,negated_conjecture,
! [X0: $i] :
( aElementOf0(X0,xQ)
| ( szmzizndt0(sdtlpdtrp0(xN,xi)) = X0 )
| ~ aElementOf0(X0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(cnf_transformation,[],[f580]) ).
tcf(c_309,negated_conjecture,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)),
inference(cnf_transformation,[],[f579]) ).
tcf(c_562,plain,
! [X0: $i] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X0,xQ) ),
inference(superposition,[status(thm)],[c_287,c_284]) ).
tcf(c_628,plain,
( aElementOf0(sK41,xQ)
| ( szmzizndt0(sdtlpdtrp0(xN,xi)) = sK41 ) ),
inference(superposition,[status(thm)],[c_302,c_308]) ).
tcf(c_715,plain,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xS),
inference(superposition,[status(thm)],[c_309,c_299]) ).
tcf(c_1161,plain,
! [X0: $i] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xQ) ),
inference(superposition,[status(thm)],[c_562,c_299]) ).
tcf(c_1277,plain,
( aElementOf0(sK41,xQ)
| ( szmzizndt0(sdtlpdtrp0(xN,xi)) = sK41 ) ),
inference(superposition,[status(thm)],[c_302,c_308]) ).
tcf(c_2929,plain,
( aElementOf0(sK41,xS)
| ( szmzizndt0(sdtlpdtrp0(xN,xi)) = sK41 ) ),
inference(superposition,[status(thm)],[c_628,c_1161]) ).
tcf(c_3020,plain,
szmzizndt0(sdtlpdtrp0(xN,xi)) = sK41,
inference(global_subsumption_just,[status(thm)],[c_1277,c_301,c_2929]) ).
tcf(c_3037,plain,
aElementOf0(sK41,xS),
inference(superposition,[status(thm)],[c_3020,c_715]) ).
tcf(c_3055,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_301,c_3037]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM583+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 04:43:08 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 3.54/1.19 % SZS status Started for theBenchmark.p
% 3.54/1.19 % SZS status Theorem for theBenchmark.p
% 3.54/1.19
% 3.54/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.54/1.19
% 3.54/1.19 % ------ iProver source info
% 3.54/1.19
% 3.54/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 3.54/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.54/1.19 % git: non_committed_changes: false
% 3.54/1.19
% 3.54/1.19 % ------ Parsing...
% 3.54/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.54/1.19 % ------ Proving...
% 3.54/1.19 % ------ Problem Properties
% 3.54/1.19
% 3.54/1.19 %
% 3.54/1.19 % clauses 262
% 3.54/1.19 % conjectures 10
% 3.54/1.19 % EPR 50
% 3.54/1.19 % Horn 205
% 3.54/1.19 % unary 41
% 3.54/1.19 % binary 63
% 3.54/1.19 % lits 850
% 3.54/1.19 % lits eq 109
% 3.54/1.19 % fd_pure 0
% 3.54/1.19 % fd_pseudo 0
% 3.54/1.19 % fd_cond 13
% 3.54/1.19 % fd_pseudo_cond 35
% 3.54/1.19 % AC symbols 0
% 3.54/1.19
% 3.54/1.19 % ------ Input Options Time Limit: Unbounded
% 3.54/1.19
% 3.54/1.19
% 3.54/1.19 % ------
% 3.54/1.19 % Current options:
% 3.54/1.19 % ------
% 3.54/1.19
% 3.54/1.19
% 3.54/1.19 %
% 3.54/1.19
% 3.54/1.19 % ------ Proving...
% 3.54/1.19 %
% 3.54/1.19
% 3.54/1.19 % SZS status Theorem for theBenchmark.p
% 3.54/1.19
% 3.54/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.54/1.19
% 3.54/1.19
%------------------------------------------------------------------------------