%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM534+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 02:25:52 PM UTC 2026
% Result : Theorem 6.23s 1.74s
% Output : CNFRefutation 6.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 8
% Syntax : Number of formulae : 100 ( 21 unt; 2 def)
% Number of atoms : 473 ( 76 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 473 ( 174 ~; 200 |; 75 &)
% ( 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 : 99 ( 0 sgn 96 !; 3 ?; 36 :)
% 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(f17,axiom,
aSet0(xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__617) ).
fof(f18,axiom,
aElementOf0(xx,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__617_02) ).
fof(f19,conjecture,
( ( ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( X0 != xx
& aElementOf0(X0,xS)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( X0 = xx
| aElementOf0(X0,sdtmndt0(xS,xx)) )
& aElement0(X0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> sdtpldt0(sdtmndt0(xS,xx),xx) = xS ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f20,negated_conjecture,
~ ( ( ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( X0 != xx
& aElementOf0(X0,xS)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( X0 = xx
| aElementOf0(X0,sdtmndt0(xS,xx)) )
& aElement0(X0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> sdtpldt0(sdtmndt0(xS,xx),xx) = xS ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f25,plain,
~ ( ( ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( X0 != xx
& aElementOf0(X0,xS)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [X1] :
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( xx = X1
| aElementOf0(X1,sdtmndt0(xS,xx)) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> sdtpldt0(sdtmndt0(xS,xx),xx) = xS ) ),
inference(rectify,[],[f20]) ).
fof(f28,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f30,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f34,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f13]) ).
fof(f35,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f34]) ).
fof(f42,plain,
( ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( X0 != xx
& aElementOf0(X0,xS)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xS,xx))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( xx = X1
| aElementOf0(X1,sdtmndt0(xS,xx)) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& xS != sdtpldt0(sdtmndt0(xS,xx),xx) ),
inference(ennf_transformation,[],[f25]) ).
fof(f43,plain,
( ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( X0 != xx
& aElementOf0(X0,xS)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xS,xx))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( xx = X1
| aElementOf0(X1,sdtmndt0(xS,xx)) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& xS != sdtpldt0(sdtmndt0(xS,xx),xx) ),
inference(flattening,[],[f42]) ).
fof(f54,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,[],[f30]) ).
fof(f55,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,[],[f54]) ).
fof(f56,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,[],[f55]) ).
fof(f57,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))],[f56]) ).
fof(f70,plain,
( ! [X0] :
( ( ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ( X0 != xx
& aElementOf0(X0,xS)
& aElement0(X0) ) )
& ( xx = X0
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(xS,xx)) ) )
& aSet0(sdtmndt0(xS,xx))
& ! [X1] :
( ( ~ aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
| ( ( xx = X1
| aElementOf0(X1,sdtmndt0(xS,xx)) )
& aElement0(X1) ) )
& ( ( xx != X1
& ~ aElementOf0(X1,sdtmndt0(xS,xx)) )
| ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& xS != sdtpldt0(sdtmndt0(xS,xx),xx) ),
inference(nnf_transformation,[],[f43]) ).
fof(f71,plain,
( ! [X0] :
( ( ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ( X0 != xx
& aElementOf0(X0,xS)
& aElement0(X0) ) )
& ( xx = X0
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(xS,xx)) ) )
& aSet0(sdtmndt0(xS,xx))
& ! [X1] :
( ( ~ aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
| ( ( xx = X1
| aElementOf0(X1,sdtmndt0(xS,xx)) )
& aElement0(X1) ) )
& ( ( xx != X1
& ~ aElementOf0(X1,sdtmndt0(xS,xx)) )
| ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& xS != sdtpldt0(sdtmndt0(xS,xx),xx) ),
inference(flattening,[],[f70]) ).
fof(f72,plain,
( ! [X1] :
( ( ~ aElementOf0(X1,sdtmndt0(xS,xx))
| ( xx != X1
& aElementOf0(X1,xS)
& aElement0(X1) ) )
& ( xx = X1
| ~ aElementOf0(X1,xS)
| ~ aElement0(X1)
| aElementOf0(X1,sdtmndt0(xS,xx)) ) )
& aSet0(sdtmndt0(xS,xx))
& ! [X0] :
( ( ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ( ( xx = X0
| aElementOf0(X0,sdtmndt0(xS,xx)) )
& aElement0(X0) ) )
& ( ( xx != X0
& ~ aElementOf0(X0,sdtmndt0(xS,xx)) )
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& xS != sdtpldt0(sdtmndt0(xS,xx),xx) ),
inference(rectify,[],[f71]) ).
fof(f73,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f79,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| aSet0(X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f80,plain,
! [X0,X1] :
( ~ aSet0(X0)
| aElementOf0(sK5(X0,X1),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f81,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(sK5(X0,X1),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f84,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f35]) ).
fof(f110,plain,
aSet0(xS),
inference(cnf_transformation,[],[f17]) ).
fof(f111,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f18]) ).
fof(f113,plain,
! [X1] :
( ~ aElementOf0(X1,sdtmndt0(xS,xx))
| aElementOf0(X1,xS) ),
inference(cnf_transformation,[],[f72]) ).
fof(f114,plain,
! [X1] :
( ~ aElementOf0(X1,sdtmndt0(xS,xx))
| aElement0(X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f115,plain,
! [X1] :
( xx = X1
| ~ aElementOf0(X1,xS)
| ~ aElement0(X1)
| aElementOf0(X1,sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f117,plain,
! [X0] :
( ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| xx = X0
| aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f119,plain,
! [X0] :
( xx != X0
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f120,plain,
! [X0] :
( ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f121,plain,
aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(cnf_transformation,[],[f72]) ).
fof(f122,plain,
xS != sdtpldt0(sdtmndt0(xS,xx),xx),
inference(cnf_transformation,[],[f72]) ).
fof(f129,plain,
( ~ aElement0(xx)
| aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(equality_resolution,[],[f119]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aElementOf0(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(X0,X1)
| aElementOf0(sK5(X1,X0),X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( aSet0(X0)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_86,plain,
aSet0(xS),
inference(cnf_transformation,[],[f110]) ).
tcf(c_87,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f111]) ).
tcf(c_88,negated_conjecture,
sdtpldt0(sdtmndt0(xS,xx),xx) != xS,
inference(cnf_transformation,[],[f122]) ).
tcf(c_89,negated_conjecture,
aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(cnf_transformation,[],[f121]) ).
tcf(c_90,negated_conjecture,
! [X0: $i] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X0)
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_91,negated_conjecture,
( aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(xx) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_93,negated_conjecture,
! [X0: $i] :
( aElementOf0(X0,sdtmndt0(xS,xx))
| ( X0 = xx )
| ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_95,negated_conjecture,
! [X0: $i] :
( aElementOf0(X0,sdtmndt0(xS,xx))
| ( X0 = xx )
| ~ aElement0(X0)
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_96,negated_conjecture,
! [X0: $i] :
( aElement0(X0)
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_97,negated_conjecture,
! [X0: $i] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_124,negated_conjecture,
! [X0: $i] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(global_subsumption_just,[status(thm)],[c_90,c_96,c_90]) ).
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_5676,definition,
iPr_def_10 = sdtmndt0(xS,xx),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_5677,definition,
iPr_def_11 = sdtpldt0(iPr_def_10,xx),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_5678,negated_conjecture,
! [X0: $i] :
( aElementOf0(X0,iPr_def_11)
| ~ aElementOf0(X0,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_124,c_5677,c_5676]) ).
tcf(c_5680,negated_conjecture,
! [X0: $i] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_5682,negated_conjecture,
! [X0: $i] :
( aElementOf0(X0,iPr_def_10)
| ( X0 = xx )
| ~ aElement0(X0)
| ~ aElementOf0(X0,xS) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_5684,negated_conjecture,
! [X0: $i] :
( aElementOf0(X0,iPr_def_10)
| ( X0 = xx )
| ~ aElementOf0(X0,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_5686,negated_conjecture,
( aElementOf0(xx,iPr_def_11)
| ~ aElement0(xx) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_5687,negated_conjecture,
aSet0(iPr_def_11),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_5688,negated_conjecture,
iPr_def_11 != xS,
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_6408,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_87,c_49]) ).
tcf(c_6410,plain,
aElement0(xx),
inference(forward_subsumption_resolution,[status(thm)],[c_6408,c_86]) ).
tcf(c_6411,plain,
aElementOf0(xx,iPr_def_11),
inference(backward_subsumption_resolution,[status(thm)],[c_5686,c_6410]) ).
tcf(c_6641,plain,
! [X0: $i] :
( aSubsetOf0(xS,X0)
| aElementOf0(sK5(X0,xS),iPr_def_10)
| ( sK5(X0,xS) = xx )
| ~ aSet0(xS)
| ~ aSet0(X0)
| ~ aElement0(sK5(X0,xS)) ),
inference(superposition,[status(thm)],[c_55,c_5682]) ).
tcf(c_6645,plain,
! [X0: $i] :
( aSubsetOf0(iPr_def_11,X0)
| aElementOf0(sK5(X0,iPr_def_11),iPr_def_10)
| ( sK5(X0,iPr_def_11) = xx )
| ~ aSet0(iPr_def_11)
| ~ aSet0(X0) ),
inference(superposition,[status(thm)],[c_55,c_5684]) ).
tcf(c_6670,plain,
! [X0: $i] :
( aSubsetOf0(iPr_def_11,X0)
| aElementOf0(sK5(X0,iPr_def_11),iPr_def_10)
| ( sK5(X0,iPr_def_11) = xx )
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6645,c_5687]) ).
tcf(c_6675,plain,
! [X0: $i] :
( aSubsetOf0(xS,X0)
| aElementOf0(sK5(X0,xS),iPr_def_10)
| ( sK5(X0,xS) = xx )
| ~ aSet0(X0)
| ~ aElement0(sK5(X0,xS)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6641,c_86]) ).
tcf(c_6738,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_6670,c_5680]) ).
tcf(c_6973,plain,
( aSubsetOf0(iPr_def_11,xS)
| ( sK5(xS,iPr_def_11) = xx )
| ~ aSet0(iPr_def_11)
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_6738,c_54]) ).
tcf(c_6983,plain,
( aSubsetOf0(iPr_def_11,xS)
| ( sK5(xS,iPr_def_11) = xx ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6973,c_5687,c_86]) ).
tcf(c_7451,plain,
! [X0: $i] :
( aSubsetOf0(xS,X0)
| aElementOf0(sK5(X0,xS),xS)
| ~ aSet0(xS)
| ~ aSet0(X0) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_7603,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_7739,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_6675,c_5680]) ).
tcf(c_7740,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_6675,c_5678]) ).
tcf(c_8979,plain,
! [X0: $i] :
( aSubsetOf0(xS,X0)
| aElementOf0(sK5(X0,xS),xS)
| ~ aSet0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_7739,c_86,c_7451]) ).
tcf(c_8990,plain,
! [X0: $i] :
( aSubsetOf0(xS,X0)
| aElement0(sK5(X0,xS))
| ~ aSet0(xS)
| ~ aSet0(X0) ),
inference(superposition,[status(thm)],[c_8979,c_49]) ).
tcf(c_8994,plain,
! [X0: $i] :
( aSubsetOf0(xS,X0)
| aElement0(sK5(X0,xS))
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8990,c_86]) ).
tcf(c_9004,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_7740,c_7740,c_8994]) ).
tcf(c_9018,plain,
( aSubsetOf0(xS,iPr_def_11)
| ( sK5(iPr_def_11,xS) = xx )
| ~ aSet0(iPr_def_11)
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_9004,c_54]) ).
tcf(c_9021,plain,
( aSubsetOf0(xS,iPr_def_11)
| ( sK5(iPr_def_11,xS) = xx ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9018,c_5687,c_86]) ).
tcf(c_9512,plain,
( ( xS = iPr_def_11 )
| ( sK5(iPr_def_11,xS) = xx )
| ~ aSet0(iPr_def_11)
| ~ aSubsetOf0(iPr_def_11,xS) ),
inference(superposition,[status(thm)],[c_9021,c_127]) ).
tcf(c_9522,plain,
( ( xS = iPr_def_11 )
| ( sK5(iPr_def_11,xS) = xx )
| ~ aSubsetOf0(iPr_def_11,xS) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9512,c_5687]) ).
tcf(c_9539,plain,
( ~ aSubsetOf0(iPr_def_11,xS)
| ( sK5(iPr_def_11,xS) = xx ) ),
inference(global_subsumption_just,[status(thm)],[c_9522,c_86,c_5688,c_7603,c_9021]) ).
tcf(c_9540,plain,
( ( sK5(iPr_def_11,xS) = xx )
| ~ aSubsetOf0(iPr_def_11,xS) ),
inference(renaming,[status(thm)],[c_9539]) ).
tcf(c_9545,plain,
( ( sK5(iPr_def_11,xS) = xx )
| ( sK5(xS,iPr_def_11) = xx ) ),
inference(superposition,[status(thm)],[c_6983,c_9540]) ).
tcf(c_9652,plain,
( aSubsetOf0(iPr_def_11,xS)
| ( sK5(iPr_def_11,xS) = xx )
| ~ aSet0(iPr_def_11)
| ~ aSet0(xS)
| ~ aElementOf0(xx,xS) ),
inference(superposition,[status(thm)],[c_9545,c_54]) ).
tcf(c_9657,plain,
( aSubsetOf0(iPr_def_11,xS)
| ( sK5(iPr_def_11,xS) = xx ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9652,c_5687,c_86,c_87]) ).
tcf(c_9660,plain,
sK5(iPr_def_11,xS) = xx,
inference(global_subsumption_just,[status(thm)],[c_9657,c_9540,c_9657]) ).
tcf(c_9666,plain,
( aSubsetOf0(xS,iPr_def_11)
| ~ aSet0(iPr_def_11)
| ~ aSet0(xS)
| ~ aElementOf0(xx,iPr_def_11) ),
inference(superposition,[status(thm)],[c_9660,c_54]) ).
tcf(c_9671,plain,
aSubsetOf0(xS,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_9666,c_5687,c_86,c_6411]) ).
tcf(c_9672,plain,
( ( xS = iPr_def_11 )
| ~ aSet0(iPr_def_11)
| ~ aSubsetOf0(iPr_def_11,xS) ),
inference(superposition,[status(thm)],[c_9671,c_127]) ).
tcf(c_9675,plain,
( ( xS = iPr_def_11 )
| ~ aSubsetOf0(iPr_def_11,xS) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9672,c_5687]) ).
tcf(c_9745,plain,
~ aSubsetOf0(iPr_def_11,xS),
inference(global_subsumption_just,[status(thm)],[c_9675,c_86,c_5688,c_7603,c_9671]) ).
tcf(c_9747,plain,
sK5(xS,iPr_def_11) = xx,
inference(backward_subsumption_resolution,[status(thm)],[c_6983,c_9745]) ).
tcf(c_9750,plain,
( aSubsetOf0(iPr_def_11,xS)
| ~ aSet0(iPr_def_11)
| ~ aSet0(xS)
| ~ aElementOf0(xx,xS) ),
inference(superposition,[status(thm)],[c_9747,c_54]) ).
tcf(c_9755,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_9750,c_9745,c_5687,c_86,c_87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM534+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n011.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
% 0.02/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Thu Sep 24 04:29:42 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.02/0.40 Running first-order theorem proving
% 0.02/0.40 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
% 0.02/0.41
% 0.02/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.02/0.41
% 0.02/0.42 % Detected problem language: tptp
% 0.02/0.43 % Proving...
% 6.23/1.74 % SZS status Started for theBenchmark.p
% 6.23/1.74 % SZS status Theorem for theBenchmark.p
% 6.23/1.74
% 6.23/1.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.23/1.74
% 6.23/1.74 % ------ iProver source info
% 6.23/1.74
% 6.23/1.74 % git: date: 2026-07-19 20:42:38 +0200
% 6.23/1.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.23/1.74 % git: non_committed_changes: false
% 6.23/1.74
% 6.23/1.74 % ------ Parsing...
% 6.23/1.74 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.23/1.74
% 6.23/1.74 % ------ 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 %
% 6.23/1.74
% 6.23/1.74 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.23/1.74
% 6.23/1.74 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.23/1.74 % ------ Proving...
% 6.23/1.74 % ------ Problem Properties
% 6.23/1.74
% 6.23/1.74 %
% 6.23/1.74 % clauses 48
% 6.23/1.74 % conjectures 11
% 6.23/1.74 % EPR 31
% 6.23/1.74 % Horn 36
% 6.23/1.74 % unary 10
% 6.23/1.74 % binary 9
% 6.23/1.74 % lits 136
% 6.23/1.74 % lits eq 15
% 6.23/1.74 % fd_pure 0
% 6.23/1.74 % fd_pseudo 0
% 6.23/1.74 % fd_cond 3
% 6.23/1.74 % fd_pseudo_cond 5
% 6.23/1.74 % AC symbols 0
% 6.23/1.74
% 6.23/1.74 % ------ Schedule dynamic 5 is on
% 6.23/1.74
% 6.23/1.74 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.23/1.74
% 6.23/1.74
% 6.23/1.74 % ------
% 6.23/1.74 % Current options:
% 6.23/1.74 % ------
% 6.23/1.74
% 6.23/1.74
% 6.23/1.74 %
% 6.23/1.74
% 6.23/1.74 % ------ Proving...
% 6.23/1.74 %
% 6.23/1.74
% 6.23/1.74 % SZS status Theorem for theBenchmark.p
% 6.23/1.74
% 6.23/1.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.23/1.74
% 6.23/1.74
%------------------------------------------------------------------------------