%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM537+2 : 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 02:25:55 PM UTC 2026
% Result : Theorem 4.22s 1.18s
% Output : CNFRefutation 4.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 11
% Syntax : Number of formulae : 122 ( 16 unt; 7 def)
% Number of atoms : 554 ( 75 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 630 ( 215 ~; 220 |; 151 &)
% ( 24 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 8 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 95 ( 0 sgn 86 !; 9 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f18,axiom,
( aSet0(xS)
& aElement0(xx) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__679) ).
fof(f19,axiom,
~ aElementOf0(xx,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__679_02) ).
fof(f20,conjecture,
( ( ( ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
<=> ( ( X0 = xx
| aElementOf0(X0,xS) )
& aElement0(X0) ) )
& aSet0(sdtpldt0(xS,xx)) )
=> ( ( ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( X0 != xx
& aElementOf0(X0,sdtpldt0(xS,xx))
& aElement0(X0) ) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) )
=> ( aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
| ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
=> aElementOf0(X0,xS) ) ) ) )
& ( ( ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
<=> ( ( X0 = xx
| aElementOf0(X0,xS) )
& aElement0(X0) ) )
& aSet0(sdtpldt0(xS,xx)) )
=> ( ( ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( X0 != xx
& aElementOf0(X0,sdtpldt0(xS,xx))
& aElement0(X0) ) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) )
=> ( aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f21,negated_conjecture,
~ ( ( ( ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
<=> ( ( X0 = xx
| aElementOf0(X0,xS) )
& aElement0(X0) ) )
& aSet0(sdtpldt0(xS,xx)) )
=> ( ( ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( X0 != xx
& aElementOf0(X0,sdtpldt0(xS,xx))
& aElement0(X0) ) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) )
=> ( aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
| ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
=> aElementOf0(X0,xS) ) ) ) )
& ( ( ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
<=> ( ( X0 = xx
| aElementOf0(X0,xS) )
& aElement0(X0) ) )
& aSet0(sdtpldt0(xS,xx)) )
=> ( ( ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( X0 != xx
& aElementOf0(X0,sdtpldt0(xS,xx))
& aElement0(X0) ) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) )
=> ( aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f26,plain,
~ ( ( ( ! [X3] :
( aElementOf0(X3,sdtpldt0(xS,xx))
<=> ( ( xx = X3
| aElementOf0(X3,xS) )
& aElement0(X3) ) )
& aSet0(sdtpldt0(xS,xx)) )
=> ( ( ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( xx != X4
& aElementOf0(X4,sdtpldt0(xS,xx))
& aElement0(X4) ) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) )
=> ( aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
| ! [X5] :
( aElementOf0(X5,sdtmndt0(sdtpldt0(xS,xx),xx))
=> aElementOf0(X5,xS) ) ) ) )
& ( ( ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
<=> ( ( X0 = xx
| aElementOf0(X0,xS) )
& aElement0(X0) ) )
& aSet0(sdtpldt0(xS,xx)) )
=> ( ( ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( xx != X1
& aElementOf0(X1,sdtpldt0(xS,xx))
& aElement0(X1) ) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) )
=> ( aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| ! [X2] :
( aElementOf0(X2,xS)
=> aElementOf0(X2,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ) ) ) ),
inference(rectify,[],[f21]) ).
fof(f29,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f44,plain,
( ( ! [X3] :
( aElementOf0(X3,sdtpldt0(xS,xx))
<=> ( ( xx = X3
| aElementOf0(X3,xS) )
& aElement0(X3) ) )
& aSet0(sdtpldt0(xS,xx))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( xx != X4
& aElementOf0(X4,sdtpldt0(xS,xx))
& aElement0(X4) ) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
& ? [X5] :
( aElementOf0(X5,sdtmndt0(sdtpldt0(xS,xx),xx))
& ~ aElementOf0(X5,xS) ) )
| ( ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
<=> ( ( X0 = xx
| aElementOf0(X0,xS) )
& aElement0(X0) ) )
& aSet0(sdtpldt0(xS,xx))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( xx != X1
& aElementOf0(X1,sdtpldt0(xS,xx))
& aElement0(X1) ) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
& ? [X2] :
( aElementOf0(X2,xS)
& ~ aElementOf0(X2,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f45,plain,
( ( ! [X3] :
( aElementOf0(X3,sdtpldt0(xS,xx))
<=> ( ( xx = X3
| aElementOf0(X3,xS) )
& aElement0(X3) ) )
& aSet0(sdtpldt0(xS,xx))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( xx != X4
& aElementOf0(X4,sdtpldt0(xS,xx))
& aElement0(X4) ) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
& ? [X5] :
( aElementOf0(X5,sdtmndt0(sdtpldt0(xS,xx),xx))
& ~ aElementOf0(X5,xS) ) )
| ( ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
<=> ( ( X0 = xx
| aElementOf0(X0,xS) )
& aElement0(X0) ) )
& aSet0(sdtpldt0(xS,xx))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( xx != X1
& aElementOf0(X1,sdtpldt0(xS,xx))
& aElement0(X1) ) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
& ? [X2] :
( aElementOf0(X2,xS)
& ~ aElementOf0(X2,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ) ),
inference(flattening,[],[f44]) ).
fof(f78,plain,
( ~ sP8
| ( sP4
& aSet0(sdtpldt0(xS,xx))
& sP5
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
& ? [X5] :
( aElementOf0(X5,sdtmndt0(sdtpldt0(xS,xx),xx))
& ~ aElementOf0(X5,xS) ) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f79,plain,
( ~ sP8
| ( sP4
& aSet0(sdtpldt0(xS,xx))
& sP5
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
& ? [X0] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
& ~ aElementOf0(X0,xS) ) ) ),
inference(rectify,[],[f78]) ).
fof(f80,plain,
( ~ sP8
| ( sP4
& aSet0(sdtpldt0(xS,xx))
& sP5
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
& aElementOf0(sK13,sdtmndt0(sdtpldt0(xS,xx),xx))
& ~ aElementOf0(sK13,xS) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X0,sK13)],[f79]) ).
fof(f81,plain,
( ~ sP7
| ! [X1] :
( ( ~ aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx))
| ( xx != X1
& aElementOf0(X1,sdtpldt0(xS,xx))
& aElement0(X1) ) )
& ( xx = X1
| ~ aElementOf0(X1,sdtpldt0(xS,xx))
| ~ aElement0(X1)
| aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ) ),
inference(nnf_transformation,[],[f55]) ).
fof(f82,plain,
( ~ sP7
| ! [X1] :
( ( ~ aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx))
| ( xx != X1
& aElementOf0(X1,sdtpldt0(xS,xx))
& aElement0(X1) ) )
& ( xx = X1
| ~ aElementOf0(X1,sdtpldt0(xS,xx))
| ~ aElement0(X1)
| aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ) ),
inference(flattening,[],[f81]) ).
fof(f83,plain,
( ~ sP7
| ! [X0] :
( ( ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| ( xx != X0
& aElementOf0(X0,sdtpldt0(xS,xx))
& aElement0(X0) ) )
& ( xx = X0
| ~ aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ) ),
inference(rectify,[],[f82]) ).
fof(f84,plain,
( ~ sP6
| ! [X0] :
( ( ~ aElementOf0(X0,sdtpldt0(xS,xx))
| ( ( X0 = xx
| aElementOf0(X0,xS) )
& aElement0(X0) ) )
& ( ( xx != X0
& ~ aElementOf0(X0,xS) )
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(xS,xx)) ) ) ),
inference(nnf_transformation,[],[f54]) ).
fof(f85,plain,
( ~ sP6
| ! [X0] :
( ( ~ aElementOf0(X0,sdtpldt0(xS,xx))
| ( ( X0 = xx
| aElementOf0(X0,xS) )
& aElement0(X0) ) )
& ( ( xx != X0
& ~ aElementOf0(X0,xS) )
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(xS,xx)) ) ) ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
( ~ sP5
| ! [X4] :
( ( ~ aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
| ( xx != X4
& aElementOf0(X4,sdtpldt0(xS,xx))
& aElement0(X4) ) )
& ( xx = X4
| ~ aElementOf0(X4,sdtpldt0(xS,xx))
| ~ aElement0(X4)
| aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ) ),
inference(nnf_transformation,[],[f53]) ).
fof(f87,plain,
( ~ sP5
| ! [X4] :
( ( ~ aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
| ( xx != X4
& aElementOf0(X4,sdtpldt0(xS,xx))
& aElement0(X4) ) )
& ( xx = X4
| ~ aElementOf0(X4,sdtpldt0(xS,xx))
| ~ aElement0(X4)
| aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ) ),
inference(flattening,[],[f86]) ).
fof(f88,plain,
( ~ sP5
| ! [X0] :
( ( ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| ( xx != X0
& aElementOf0(X0,sdtpldt0(xS,xx))
& aElement0(X0) ) )
& ( xx = X0
| ~ aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ) ),
inference(rectify,[],[f87]) ).
fof(f92,plain,
( sP8
| ( sP6
& aSet0(sdtpldt0(xS,xx))
& sP7
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
& ? [X0] :
( aElementOf0(X0,xS)
& ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ) ),
inference(rectify,[],[f57]) ).
fof(f93,plain,
( sP8
| ( sP6
& aSet0(sdtpldt0(xS,xx))
& sP7
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
& aElementOf0(sK14,xS)
& ~ aElementOf0(sK14,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f92]) ).
fof(f94,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f132,plain,
aSet0(xS),
inference(cnf_transformation,[],[f18]) ).
fof(f134,plain,
~ aElementOf0(xx,xS),
inference(cnf_transformation,[],[f19]) ).
fof(f135,plain,
( ~ sP8
| sP4 ),
inference(cnf_transformation,[],[f80]) ).
fof(f137,plain,
( ~ sP8
| sP5 ),
inference(cnf_transformation,[],[f80]) ).
fof(f140,plain,
( ~ sP8
| aElementOf0(sK13,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(cnf_transformation,[],[f80]) ).
fof(f141,plain,
( ~ sP8
| ~ aElementOf0(sK13,xS) ),
inference(cnf_transformation,[],[f80]) ).
fof(f142,plain,
! [X0] :
( ~ sP7
| ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| xx != X0 ),
inference(cnf_transformation,[],[f83]) ).
fof(f143,plain,
! [X0] :
( ~ sP7
| ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| aElementOf0(X0,sdtpldt0(xS,xx)) ),
inference(cnf_transformation,[],[f83]) ).
fof(f145,plain,
! [X0] :
( ~ sP7
| xx = X0
| ~ aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(cnf_transformation,[],[f83]) ).
fof(f146,plain,
! [X0] :
( ~ sP6
| ~ aElementOf0(X0,sdtpldt0(xS,xx))
| xx = X0
| aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f85]) ).
fof(f147,plain,
! [X0] :
( ~ sP6
| ~ aElementOf0(X0,sdtpldt0(xS,xx))
| aElement0(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f149,plain,
! [X0] :
( ~ sP6
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(xS,xx)) ),
inference(cnf_transformation,[],[f85]) ).
fof(f150,plain,
! [X0] :
( ~ sP5
| ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| xx != X0 ),
inference(cnf_transformation,[],[f88]) ).
fof(f151,plain,
! [X0] :
( ~ sP5
| ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| aElementOf0(X0,sdtpldt0(xS,xx)) ),
inference(cnf_transformation,[],[f88]) ).
fof(f153,plain,
! [X0] :
( ~ sP5
| xx = X0
| ~ aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(cnf_transformation,[],[f88]) ).
fof(f158,plain,
( sP8
| sP6 ),
inference(cnf_transformation,[],[f93]) ).
fof(f160,plain,
( sP8
| sP7 ),
inference(cnf_transformation,[],[f93]) ).
fof(f163,plain,
( sP8
| aElementOf0(sK14,xS) ),
inference(cnf_transformation,[],[f93]) ).
fof(f164,plain,
( sP8
| ~ aElementOf0(sK14,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f171,plain,
( ~ sP7
| ~ aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(equality_resolution,[],[f142]) ).
fof(f173,plain,
( ~ sP5
| ~ aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(equality_resolution,[],[f150]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_88,plain,
aSet0(xS),
inference(cnf_transformation,[],[f132]) ).
tcf(c_89,plain,
~ aElementOf0(xx,xS),
inference(cnf_transformation,[],[f134]) ).
tcf(c_90,plain,
( ~ sP8
| ~ aElementOf0(sK13,xS) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_91,plain,
( aElementOf0(sK13,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ sP8 ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_94,plain,
( sP5
| ~ sP8 ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_96,plain,
( sP4
| ~ sP8 ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_97,plain,
! [X0: $i] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| ( X0 = xx )
| ~ sP7
| ~ aElement0(X0)
| ~ aElementOf0(X0,sdtpldt0(xS,xx)) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_99,plain,
! [X0: $i] :
( aElementOf0(X0,sdtpldt0(xS,xx))
| ~ sP7
| ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_100,plain,
( ~ sP7
| ~ aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_101,plain,
! [X0: $i] :
( aElementOf0(X0,sdtpldt0(xS,xx))
| ~ sP6
| ~ aElement0(X0)
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_103,plain,
! [X0: $i] :
( aElement0(X0)
| ~ sP6
| ~ aElementOf0(X0,sdtpldt0(xS,xx)) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_104,plain,
! [X0: $i] :
( aElementOf0(X0,xS)
| ( X0 = xx )
| ~ sP6
| ~ aElementOf0(X0,sdtpldt0(xS,xx)) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_105,plain,
! [X0: $i] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| ( X0 = xx )
| ~ sP5
| ~ aElement0(X0)
| ~ aElementOf0(X0,sdtpldt0(xS,xx)) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_107,plain,
! [X0: $i] :
( aElementOf0(X0,sdtpldt0(xS,xx))
| ~ sP5
| ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_108,plain,
( ~ sP5
| ~ aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_113,negated_conjecture,
( sP8
| ~ aElementOf0(sK14,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_114,negated_conjecture,
( sP8
| aElementOf0(sK14,xS) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_117,negated_conjecture,
( sP7
| sP8 ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_119,negated_conjecture,
( sP6
| sP8 ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_157,plain,
~ aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx)),
inference(global_subsumption_just,[status(thm)],[c_108,c_117,c_94,c_108,c_100]) ).
tcf(c_163,plain,
~ aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx)),
inference(global_subsumption_just,[status(thm)],[c_100,c_157]) ).
tcf(c_176,plain,
! [X0: $i] :
( aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(global_subsumption_just,[status(thm)],[c_107,c_117,c_94,c_107,c_99]) ).
tcf(c_180,plain,
! [X0: $i] :
( aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(global_subsumption_just,[status(thm)],[c_99,c_176]) ).
tcf(c_6024,definition,
iPr_def_10 = sdtpldt0(xS,xx),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_6025,definition,
iPr_def_11 = sdtmndt0(iPr_def_10,xx),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_6027,negated_conjecture,
( sP8
| aElementOf0(sK14,xS) ),
inference(demodulation,[status(thm)],[c_114]) ).
tcf(c_6028,negated_conjecture,
( sP8
| ~ aElementOf0(sK14,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_113]) ).
tcf(c_6803,plain,
~ aElementOf0(xx,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_163,c_6024,c_6025]) ).
tcf(c_6810,plain,
( sP8
| aElement0(sK14)
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_6027,c_49]) ).
tcf(c_6812,plain,
( sP8
| aElement0(sK14) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6810,c_88]) ).
tcf(c_6830,plain,
( aElementOf0(sK13,iPr_def_11)
| ~ sP8 ),
inference(light_normalisation,[status(thm)],[c_91,c_6024,c_6025]) ).
tcf(c_6845,plain,
! [X0: $i] :
( aElementOf0(X0,iPr_def_10)
| ~ aElementOf0(X0,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_180,c_6024,c_6025]) ).
tcf(c_6852,plain,
( aElementOf0(sK13,iPr_def_10)
| ~ sP8 ),
inference(superposition,[status(thm)],[c_6830,c_6845]) ).
fof(f52,definition,
( ~ sP4
| ! [X3] :
( aElementOf0(X3,sdtpldt0(xS,xx))
<=> ( ( xx = X3
| aElementOf0(X3,xS) )
& aElement0(X3) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f53,definition,
( ~ sP5
| ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( xx != X4
& aElementOf0(X4,sdtpldt0(xS,xx))
& aElement0(X4) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f54,definition,
( ~ sP6
| ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
<=> ( ( X0 = xx
| aElementOf0(X0,xS) )
& aElement0(X0) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f55,definition,
( ~ sP7
| ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( xx != X1
& aElementOf0(X1,sdtpldt0(xS,xx))
& aElement0(X1) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])],[predicate_definition_introduction]) ).
fof(f56,definition,
( ~ sP8
| ( sP4
& aSet0(sdtpldt0(xS,xx))
& sP5
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
& ? [X5] :
( aElementOf0(X5,sdtmndt0(sdtpldt0(xS,xx),xx))
& ~ aElementOf0(X5,xS) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f57,plain,
( sP8
| ( sP6
& aSet0(sdtpldt0(xS,xx))
& sP7
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
& ? [X2] :
( aElementOf0(X2,xS)
& ~ aElementOf0(X2,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ) ),
inference(definition_folding,[],[f45,f56,f55,f54,f53,f52]) ).
fof(f89,plain,
( ~ sP4
| ! [X3] :
( ( ~ aElementOf0(X3,sdtpldt0(xS,xx))
| ( ( xx = X3
| aElementOf0(X3,xS) )
& aElement0(X3) ) )
& ( ( xx != X3
& ~ aElementOf0(X3,xS) )
| ~ aElement0(X3)
| aElementOf0(X3,sdtpldt0(xS,xx)) ) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f90,plain,
( ~ sP4
| ! [X3] :
( ( ~ aElementOf0(X3,sdtpldt0(xS,xx))
| ( ( xx = X3
| aElementOf0(X3,xS) )
& aElement0(X3) ) )
& ( ( xx != X3
& ~ aElementOf0(X3,xS) )
| ~ aElement0(X3)
| aElementOf0(X3,sdtpldt0(xS,xx)) ) ) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
( ~ sP4
| ! [X0] :
( ( ~ aElementOf0(X0,sdtpldt0(xS,xx))
| ( ( xx = X0
| aElementOf0(X0,xS) )
& aElement0(X0) ) )
& ( ( xx != X0
& ~ aElementOf0(X0,xS) )
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(xS,xx)) ) ) ),
inference(rectify,[],[f90]) ).
fof(f154,plain,
! [X0] :
( ~ sP4
| ~ aElementOf0(X0,sdtpldt0(xS,xx))
| xx = X0
| aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f91]) ).
fof(f155,plain,
! [X0] :
( ~ sP4
| ~ aElementOf0(X0,sdtpldt0(xS,xx))
| aElement0(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f157,plain,
! [X0] :
( ~ sP4
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(xS,xx)) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_109,plain,
! [X0: $i] :
( aElementOf0(X0,sdtpldt0(xS,xx))
| ~ sP4
| ~ aElement0(X0)
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_111,plain,
! [X0: $i] :
( aElement0(X0)
| ~ sP4
| ~ aElementOf0(X0,sdtpldt0(xS,xx)) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_112,plain,
! [X0: $i] :
( aElementOf0(X0,xS)
| ( X0 = xx )
| ~ sP4
| ~ aElementOf0(X0,sdtpldt0(xS,xx)) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_153,plain,
! [X0: $i] :
( aElement0(X0)
| ~ aElementOf0(X0,sdtpldt0(xS,xx)) ),
inference(global_subsumption_just,[status(thm)],[c_111,c_119,c_96,c_111,c_103]) ).
tcf(c_169,plain,
! [X0: $i] :
( aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_109,c_119,c_96,c_109,c_101]) ).
tcf(c_170,plain,
! [X0: $i] :
( aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElement0(X0)
| ~ aElementOf0(X0,xS) ),
inference(renaming,[status(thm)],[c_169]) ).
tcf(c_171,plain,
! [X0: $i] :
( aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_101,c_170]) ).
tcf(c_172,plain,
! [X0: $i] :
( aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElement0(X0)
| ~ aElementOf0(X0,xS) ),
inference(renaming,[status(thm)],[c_171]) ).
tcf(c_173,plain,
! [X0: $i] :
( aElementOf0(X0,xS)
| ( X0 = xx )
| ~ aElementOf0(X0,sdtpldt0(xS,xx)) ),
inference(global_subsumption_just,[status(thm)],[c_112,c_119,c_96,c_112,c_104]) ).
tcf(c_178,plain,
! [X0: $i] :
( aElementOf0(X0,xS)
| ( X0 = xx )
| ~ aElementOf0(X0,sdtpldt0(xS,xx)) ),
inference(global_subsumption_just,[status(thm)],[c_104,c_173]) ).
tcf(c_186,plain,
! [X0: $i] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| ( X0 = xx )
| ~ aElementOf0(X0,sdtpldt0(xS,xx)) ),
inference(global_subsumption_just,[status(thm)],[c_105,c_117,c_94,c_105,c_97,c_153]) ).
tcf(c_189,plain,
! [X0: $i] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| ( X0 = xx )
| ~ aElementOf0(X0,sdtpldt0(xS,xx)) ),
inference(global_subsumption_just,[status(thm)],[c_97,c_186]) ).
tcf(c_6944,plain,
! [X0: $i] :
( aElementOf0(X0,iPr_def_10)
| ~ aElement0(X0)
| ~ aElementOf0(X0,xS) ),
inference(light_normalisation,[status(thm)],[c_172,c_6024]) ).
tcf(c_6955,plain,
( sP8
| aElementOf0(sK14,iPr_def_10)
| ~ aElement0(sK14) ),
inference(superposition,[status(thm)],[c_6027,c_6944]) ).
tcf(c_6963,plain,
( sP8
| aElementOf0(sK14,iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_6955,c_6812,c_6955]) ).
tcf(c_6994,plain,
! [X0: $i] :
( aElementOf0(X0,xS)
| ( X0 = xx )
| ~ aElementOf0(X0,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_178,c_6024]) ).
tcf(c_7006,plain,
( aElementOf0(sK13,xS)
| ( xx = sK13 )
| ~ sP8 ),
inference(superposition,[status(thm)],[c_6852,c_6994]) ).
tcf(c_7145,plain,
( ~ sP8
| ( xx = sK13 ) ),
inference(global_subsumption_just,[status(thm)],[c_7006,c_90,c_7006]) ).
tcf(c_7146,plain,
( ( xx = sK13 )
| ~ sP8 ),
inference(renaming,[status(thm)],[c_7145]) ).
tcf(c_7374,plain,
! [X0: $i] :
( aElementOf0(X0,iPr_def_11)
| ( X0 = xx )
| ~ aElementOf0(X0,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_189,c_6024,c_6025]) ).
tcf(c_7389,plain,
( sP8
| aElementOf0(sK14,iPr_def_11)
| ( xx = sK14 ) ),
inference(superposition,[status(thm)],[c_6963,c_7374]) ).
tcf(c_7423,plain,
( sP8
| ( xx = sK14 ) ),
inference(global_subsumption_just,[status(thm)],[c_7389,c_6028,c_7389]) ).
tcf(c_7429,plain,
( ( xx = sK14 )
| ( xx = sK13 ) ),
inference(superposition,[status(thm)],[c_7423,c_7146]) ).
tcf(c_7439,plain,
( sP8
| aElementOf0(xx,xS)
| ( xx = sK13 ) ),
inference(superposition,[status(thm)],[c_7429,c_6027]) ).
tcf(c_7440,plain,
( sP8
| ( xx = sK13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7439,c_89]) ).
tcf(c_7443,plain,
xx = sK13,
inference(global_subsumption_just,[status(thm)],[c_7440,c_7146,c_7440]) ).
tcf(c_7448,plain,
( aElementOf0(xx,iPr_def_11)
| ~ sP8 ),
inference(demodulation,[status(thm)],[c_6830,c_7443]) ).
tcf(c_7450,plain,
~ sP8,
inference(forward_subsumption_resolution,[status(thm)],[c_7448,c_6803]) ).
tcf(c_7451,plain,
xx = sK14,
inference(backward_subsumption_resolution,[status(thm)],[c_7423,c_7450]) ).
tcf(c_7458,plain,
aElementOf0(sK14,xS),
inference(backward_subsumption_resolution,[status(thm)],[c_6027,c_7450]) ).
tcf(c_7467,plain,
aElementOf0(xx,xS),
inference(light_normalisation,[status(thm)],[c_7458,c_7451]) ).
tcf(c_7468,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_7467,c_89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM537+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n011.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 04:30:42 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 4.22/1.18 % SZS status Started for theBenchmark.p
% 4.22/1.18 % SZS status Theorem for theBenchmark.p
% 4.22/1.18
% 4.22/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.22/1.18
% 4.22/1.18 % ------ iProver source info
% 4.22/1.18
% 4.22/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 4.22/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.22/1.18 % git: non_committed_changes: false
% 4.22/1.18
% 4.22/1.18 % ------ Parsing...
% 4.22/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.22/1.18
% 4.22/1.18 % ------ Preprocessing... sup_sim: 0 sf_s rm: 8 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 4.22/1.18
% 4.22/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.22/1.18
% 4.22/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.22/1.18 % ------ Proving...
% 4.22/1.18 % ------ Problem Properties
% 4.22/1.18
% 4.22/1.18 %
% 4.22/1.18 % clauses 55
% 4.22/1.18 % conjectures 3
% 4.22/1.18 % EPR 25
% 4.22/1.18 % Horn 42
% 4.22/1.18 % unary 11
% 4.22/1.18 % binary 13
% 4.22/1.18 % lits 150
% 4.22/1.18 % lits eq 15
% 4.22/1.18 % fd_pure 0
% 4.22/1.18 % fd_pseudo 0
% 4.22/1.18 % fd_cond 3
% 4.22/1.18 % fd_pseudo_cond 5
% 4.22/1.18 % AC symbols 0
% 4.22/1.18
% 4.22/1.18 % ------ Schedule dynamic 5 is on
% 4.22/1.18
% 4.22/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.22/1.18
% 4.22/1.18
% 4.22/1.18 % ------
% 4.22/1.18 % Current options:
% 4.22/1.18 % ------
% 4.22/1.18
% 4.22/1.18
% 4.22/1.18 %
% 4.22/1.18
% 4.22/1.18 % ------ Proving...
% 4.22/1.18 %
% 4.22/1.18
% 4.22/1.18 % SZS status Theorem for theBenchmark.p
% 4.22/1.18
% 4.22/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.22/1.18
% 4.22/1.18
%------------------------------------------------------------------------------