%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM536+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 3.32s 1.18s
% Output : CNFRefutation 3.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 8
% Syntax : Number of formulae : 98 ( 21 unt; 2 def)
% Number of atoms : 467 ( 72 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 464 ( 170 ~; 194 |; 76 &)
% ( 12 <=>; 12 =>; 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 : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 102 ( 0 sgn 99 !; 3 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(f13,axiom,
! [X0,X1] :
( ( aSet0(X1)
& aSet0(X0) )
=> ( ( aSubsetOf0(X1,X0)
& aSubsetOf0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubASymm) ).
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)) )
=> sdtmndt0(sdtpldt0(xS,xx),xx) = xS ) ),
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)) )
=> sdtmndt0(sdtpldt0(xS,xx),xx) = xS ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f26,plain,
~ ( ( ! [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)) )
=> sdtmndt0(sdtpldt0(xS,xx),xx) = xS ) ),
inference(rectify,[],[f21]) ).
fof(f29,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f31,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f35,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f13]) ).
fof(f36,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f35]) ).
fof(f44,plain,
( ! [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))
& xS != sdtmndt0(sdtpldt0(xS,xx),xx) ),
inference(ennf_transformation,[],[f26]) ).
fof(f45,plain,
( ! [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))
& xS != sdtmndt0(sdtpldt0(xS,xx),xx) ),
inference(flattening,[],[f44]) ).
fof(f56,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f57,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(rectify,[],[f57]) ).
fof(f59,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ( aElementOf0(sK5(X0,X1),X1)
& ~ aElementOf0(sK5(X0,X1),X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f58]) ).
fof(f72,plain,
( ! [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)) ) )
& aSet0(sdtpldt0(xS,xx))
& ! [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)) ) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& xS != sdtmndt0(sdtpldt0(xS,xx),xx) ),
inference(nnf_transformation,[],[f45]) ).
fof(f73,plain,
( ! [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)) ) )
& aSet0(sdtpldt0(xS,xx))
& ! [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)) ) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& xS != sdtmndt0(sdtpldt0(xS,xx),xx) ),
inference(flattening,[],[f72]) ).
fof(f74,plain,
( ! [X1] :
( ( ~ aElementOf0(X1,sdtpldt0(xS,xx))
| ( ( xx = X1
| aElementOf0(X1,xS) )
& aElement0(X1) ) )
& ( ( xx != X1
& ~ aElementOf0(X1,xS) )
| ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(xS,xx)) ) )
& aSet0(sdtpldt0(xS,xx))
& ! [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)) ) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& xS != sdtmndt0(sdtpldt0(xS,xx),xx) ),
inference(rectify,[],[f73]) ).
fof(f75,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f81,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| aSet0(X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f82,plain,
! [X0,X1] :
( ~ aSet0(X0)
| aElementOf0(sK5(X0,X1),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f83,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(sK5(X0,X1),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f86,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f36]) ).
fof(f113,plain,
aSet0(xS),
inference(cnf_transformation,[],[f18]) ).
fof(f115,plain,
~ aElementOf0(xx,xS),
inference(cnf_transformation,[],[f19]) ).
fof(f116,plain,
! [X1] :
( ~ aElementOf0(X1,sdtpldt0(xS,xx))
| xx = X1
| aElementOf0(X1,xS) ),
inference(cnf_transformation,[],[f74]) ).
fof(f117,plain,
! [X1] :
( ~ aElementOf0(X1,sdtpldt0(xS,xx))
| aElement0(X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f119,plain,
! [X1] :
( ~ aElementOf0(X1,xS)
| ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(xS,xx)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f121,plain,
! [X0] :
( ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| xx != X0 ),
inference(cnf_transformation,[],[f74]) ).
fof(f122,plain,
! [X0] :
( ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| aElementOf0(X0,sdtpldt0(xS,xx)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f124,plain,
! [X0] :
( xx = X0
| ~ aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f125,plain,
aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)),
inference(cnf_transformation,[],[f74]) ).
fof(f126,plain,
xS != sdtmndt0(sdtpldt0(xS,xx),xx),
inference(cnf_transformation,[],[f74]) ).
fof(f133,plain,
~ aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx)),
inference(equality_resolution,[],[f121]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aElementOf0(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(X0,X1)
| aElementOf0(sK5(X1,X0),X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( aSet0(X0)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_88,plain,
aSet0(xS),
inference(cnf_transformation,[],[f113]) ).
tcf(c_89,plain,
~ aElementOf0(xx,xS),
inference(cnf_transformation,[],[f115]) ).
tcf(c_90,negated_conjecture,
sdtmndt0(sdtpldt0(xS,xx),xx) != xS,
inference(cnf_transformation,[],[f126]) ).
tcf(c_91,negated_conjecture,
aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)),
inference(cnf_transformation,[],[f125]) ).
tcf(c_92,negated_conjecture,
! [X0: $i] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| ( X0 = xx )
| ~ aElement0(X0)
| ~ aElementOf0(X0,sdtpldt0(xS,xx)) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_94,negated_conjecture,
! [X0: $i] :
( aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_95,negated_conjecture,
~ aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx)),
inference(cnf_transformation,[],[f133]) ).
tcf(c_97,negated_conjecture,
! [X0: $i] :
( aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElement0(X0)
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_99,negated_conjecture,
! [X0: $i] :
( aElement0(X0)
| ~ aElementOf0(X0,sdtpldt0(xS,xx)) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_100,negated_conjecture,
! [X0: $i] :
( aElementOf0(X0,xS)
| ( X0 = xx )
| ~ aElementOf0(X0,sdtpldt0(xS,xx)) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_60,c_56,c_60]) ).
tcf(c_127,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1) ),
inference(renaming,[status(thm)],[c_126]) ).
tcf(c_128,negated_conjecture,
! [X0: $i] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| ( X0 = xx )
| ~ aElementOf0(X0,sdtpldt0(xS,xx)) ),
inference(global_subsumption_just,[status(thm)],[c_92,c_99,c_92]) ).
tcf(c_5678,definition,
iPr_def_10 = sdtpldt0(xS,xx),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_5679,definition,
iPr_def_11 = sdtmndt0(iPr_def_10,xx),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_5680,negated_conjecture,
! [X0: $i] :
( aElementOf0(X0,iPr_def_11)
| ( X0 = xx )
| ~ aElementOf0(X0,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_128,c_5679,c_5678]) ).
tcf(c_5682,negated_conjecture,
! [X0: $i] :
( aElementOf0(X0,xS)
| ( X0 = xx )
| ~ aElementOf0(X0,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_5684,negated_conjecture,
! [X0: $i] :
( aElementOf0(X0,iPr_def_10)
| ~ aElement0(X0)
| ~ aElementOf0(X0,xS) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_5686,negated_conjecture,
~ aElementOf0(xx,iPr_def_11),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_5687,negated_conjecture,
! [X0: $i] :
( aElementOf0(X0,iPr_def_10)
| ~ aElementOf0(X0,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_5689,negated_conjecture,
aSet0(iPr_def_11),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_5690,negated_conjecture,
iPr_def_11 != xS,
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_6633,plain,
! [X0: $i] :
( aSubsetOf0(xS,X0)
| aElementOf0(sK5(X0,xS),iPr_def_10)
| ~ aSet0(xS)
| ~ aSet0(X0)
| ~ aElement0(sK5(X0,xS)) ),
inference(superposition,[status(thm)],[c_55,c_5684]) ).
tcf(c_6637,plain,
! [X0: $i] :
( aSubsetOf0(iPr_def_11,X0)
| aElementOf0(sK5(X0,iPr_def_11),iPr_def_10)
| ~ aSet0(iPr_def_11)
| ~ aSet0(X0) ),
inference(superposition,[status(thm)],[c_55,c_5687]) ).
tcf(c_6654,plain,
! [X0: $i] :
( aSubsetOf0(iPr_def_11,X0)
| aElementOf0(sK5(X0,iPr_def_11),iPr_def_10)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6637,c_5689]) ).
tcf(c_6658,plain,
! [X0: $i] :
( aSubsetOf0(xS,X0)
| aElementOf0(sK5(X0,xS),iPr_def_10)
| ~ aSet0(X0)
| ~ aElement0(sK5(X0,xS)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6633,c_88]) ).
tcf(c_6813,plain,
! [X0: $i] :
( aSubsetOf0(iPr_def_11,X0)
| aElementOf0(sK5(X0,iPr_def_11),xS)
| ( sK5(X0,iPr_def_11) = xx )
| ~ aSet0(X0) ),
inference(superposition,[status(thm)],[c_6654,c_5682]) ).
tcf(c_6814,plain,
! [X0: $i] :
( aSubsetOf0(iPr_def_11,X0)
| aElementOf0(sK5(X0,iPr_def_11),iPr_def_11)
| ( sK5(X0,iPr_def_11) = xx )
| ~ aSet0(X0) ),
inference(superposition,[status(thm)],[c_6654,c_5680]) ).
tcf(c_7339,plain,
! [X0: $i] :
( aSubsetOf0(xS,X0)
| aElementOf0(sK5(X0,xS),xS)
| ~ aSet0(xS)
| ~ aSet0(X0) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_7343,plain,
! [X0: $i] :
( aSubsetOf0(iPr_def_11,X0)
| aElementOf0(sK5(X0,iPr_def_11),iPr_def_11)
| ~ aSet0(iPr_def_11)
| ~ aSet0(X0) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_7516,plain,
( ( iPr_def_11 = xS )
| ~ aSet0(xS)
| ~ aSubsetOf0(iPr_def_11,xS)
| ~ aSubsetOf0(xS,iPr_def_11) ),
inference(instantiation,[status(thm)],[c_127]) ).
tcf(c_7728,plain,
( aSubsetOf0(iPr_def_11,xS)
| ( sK5(xS,iPr_def_11) = xx )
| ~ aSet0(iPr_def_11)
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_6813,c_54]) ).
tcf(c_7730,plain,
( aSubsetOf0(iPr_def_11,xS)
| ( sK5(xS,iPr_def_11) = xx ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7728,c_5689,c_88]) ).
tcf(c_7770,plain,
! [X0: $i] :
( aSubsetOf0(iPr_def_11,X0)
| aElementOf0(sK5(X0,iPr_def_11),iPr_def_11)
| ~ aSet0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_6814,c_5689,c_7343]) ).
tcf(c_9606,plain,
( ( xS = iPr_def_11 )
| ( sK5(xS,iPr_def_11) = xx )
| ~ aSet0(xS)
| ~ aSubsetOf0(xS,iPr_def_11) ),
inference(superposition,[status(thm)],[c_7730,c_127]) ).
tcf(c_9613,plain,
( ( xS = iPr_def_11 )
| ( sK5(xS,iPr_def_11) = xx )
| ~ aSubsetOf0(xS,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9606,c_88]) ).
tcf(c_9638,plain,
( ~ aSubsetOf0(xS,iPr_def_11)
| ( sK5(xS,iPr_def_11) = xx ) ),
inference(global_subsumption_just,[status(thm)],[c_9613,c_88,c_5690,c_7516,c_7730]) ).
tcf(c_9639,plain,
( ( sK5(xS,iPr_def_11) = xx )
| ~ aSubsetOf0(xS,iPr_def_11) ),
inference(renaming,[status(thm)],[c_9638]) ).
tcf(c_10054,plain,
! [X0: $i] :
( aSubsetOf0(xS,X0)
| aElementOf0(sK5(X0,xS),xS)
| ( sK5(X0,xS) = xx )
| ~ aSet0(X0)
| ~ aElement0(sK5(X0,xS)) ),
inference(superposition,[status(thm)],[c_6658,c_5682]) ).
tcf(c_10055,plain,
! [X0: $i] :
( aSubsetOf0(xS,X0)
| aElementOf0(sK5(X0,xS),iPr_def_11)
| ( sK5(X0,xS) = xx )
| ~ aSet0(X0)
| ~ aElement0(sK5(X0,xS)) ),
inference(superposition,[status(thm)],[c_6658,c_5680]) ).
tcf(c_10852,plain,
! [X0: $i] :
( aSubsetOf0(xS,X0)
| aElementOf0(sK5(X0,xS),xS)
| ~ aSet0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_10054,c_88,c_7339]) ).
tcf(c_10863,plain,
! [X0: $i] :
( aSubsetOf0(xS,X0)
| aElement0(sK5(X0,xS))
| ~ aSet0(xS)
| ~ aSet0(X0) ),
inference(superposition,[status(thm)],[c_10852,c_49]) ).
tcf(c_10867,plain,
! [X0: $i] :
( aSubsetOf0(xS,X0)
| aElement0(sK5(X0,xS))
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10863,c_88]) ).
tcf(c_10892,plain,
! [X0: $i] :
( aSubsetOf0(xS,X0)
| aElementOf0(sK5(X0,xS),iPr_def_11)
| ( sK5(X0,xS) = xx )
| ~ aSet0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_10055,c_10055,c_10867]) ).
tcf(c_10906,plain,
( aSubsetOf0(xS,iPr_def_11)
| ( sK5(iPr_def_11,xS) = xx )
| ~ aSet0(iPr_def_11)
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_10892,c_54]) ).
tcf(c_10909,plain,
( aSubsetOf0(xS,iPr_def_11)
| ( sK5(iPr_def_11,xS) = xx ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10906,c_5689,c_88]) ).
tcf(c_10979,plain,
( ( sK5(iPr_def_11,xS) = xx )
| ( sK5(xS,iPr_def_11) = xx ) ),
inference(superposition,[status(thm)],[c_10909,c_9639]) ).
tcf(c_11033,plain,
( aSubsetOf0(iPr_def_11,xS)
| aElementOf0(xx,iPr_def_11)
| ( sK5(iPr_def_11,xS) = xx )
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_10979,c_7770]) ).
tcf(c_11037,plain,
( aSubsetOf0(iPr_def_11,xS)
| ( sK5(iPr_def_11,xS) = xx ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11033,c_5686,c_88]) ).
tcf(c_11041,plain,
sK5(iPr_def_11,xS) = xx,
inference(global_subsumption_just,[status(thm)],[c_11037,c_88,c_5690,c_7516,c_10909,c_11037]) ).
tcf(c_11050,plain,
( aSubsetOf0(xS,iPr_def_11)
| aElementOf0(xx,xS)
| ~ aSet0(iPr_def_11) ),
inference(superposition,[status(thm)],[c_11041,c_10852]) ).
tcf(c_11051,plain,
aSubsetOf0(xS,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_11050,c_89,c_5689]) ).
tcf(c_11052,plain,
sK5(xS,iPr_def_11) = xx,
inference(backward_subsumption_resolution,[status(thm)],[c_9639,c_11051]) ).
tcf(c_11061,plain,
( aSubsetOf0(iPr_def_11,xS)
| aElementOf0(xx,iPr_def_11)
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_11052,c_7770]) ).
tcf(c_11065,plain,
aSubsetOf0(iPr_def_11,xS),
inference(forward_subsumption_resolution,[status(thm)],[c_11061,c_5686,c_88]) ).
tcf(c_11066,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11065,c_11051,c_7516,c_5690,c_88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM536+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 04:30:28 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.38 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
% 0.12/0.41 % Proving...
% 3.32/1.18 % SZS status Started for theBenchmark.p
% 3.32/1.18 % SZS status Theorem for theBenchmark.p
% 3.32/1.18
% 3.32/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.32/1.18
% 3.32/1.18 % ------ iProver source info
% 3.32/1.18
% 3.32/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 3.32/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.32/1.18 % git: non_committed_changes: false
% 3.32/1.18
% 3.32/1.18 % ------ Parsing...
% 3.32/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.32/1.18
% 3.32/1.18 % ------ Preprocessing... sup_sim: 0 sf_s rm: 4 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 %
% 3.32/1.18
% 3.32/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.32/1.18
% 3.32/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.32/1.18 % ------ Proving...
% 3.32/1.18 % ------ Problem Properties
% 3.32/1.18
% 3.32/1.18 %
% 3.32/1.18 % clauses 50
% 3.32/1.18 % conjectures 11
% 3.32/1.18 % EPR 32
% 3.32/1.18 % Horn 38
% 3.32/1.18 % unary 12
% 3.32/1.18 % binary 7
% 3.32/1.18 % lits 139
% 3.32/1.18 % lits eq 16
% 3.32/1.18 % fd_pure 0
% 3.32/1.18 % fd_pseudo 0
% 3.32/1.18 % fd_cond 3
% 3.32/1.18 % fd_pseudo_cond 5
% 3.32/1.18 % AC symbols 0
% 3.32/1.18
% 3.32/1.18 % ------ Schedule dynamic 5 is on
% 3.32/1.18
% 3.32/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.32/1.18
% 3.32/1.18
% 3.32/1.18 % ------
% 3.32/1.18 % Current options:
% 3.32/1.18 % ------
% 3.32/1.18
% 3.32/1.18
% 3.32/1.18 %
% 3.32/1.18
% 3.32/1.18 % ------ Proving...
% 3.32/1.18 %
% 3.32/1.18
% 3.32/1.18 % SZS status Theorem for theBenchmark.p
% 3.32/1.18
% 3.32/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.32/1.19
% 3.32/1.19
%------------------------------------------------------------------------------