%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM537+1 : 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 : n004.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 6.60s 3.25s
% Output : CNFRefutation 6.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 16
% Syntax : Number of formulae : 196 ( 29 unt; 6 def)
% Number of atoms : 905 ( 135 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 987 ( 398 ~; 437 |; 120 &)
% ( 22 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 3 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 374 ( 0 sgn 361 !; 13 ?; 154 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( ~ ? [X1] : aElementOf0(X1,X0)
& aSet0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
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(f14,axiom,
! [X0,X1,X2] :
( ( aSet0(X2)
& aSet0(X1)
& aSet0(X0) )
=> ( ( aSubsetOf0(X1,X2)
& aSubsetOf0(X0,X1) )
=> aSubsetOf0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubTrans) ).
fof(f15,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aSet0(X0) )
=> ! [X2] :
( X2 = sdtpldt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ( X3 = X1
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefCons) ).
fof(f16,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aSet0(X0) )
=> ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(f17,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> sdtpldt0(sdtmndt0(X0,X1),X1) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mConsDiff) ).
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,
( aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
& aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f21,negated_conjecture,
~ ( aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
& aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f28,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f29,plain,
! [X0] :
( X0 = slcrc0
<=> ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f30,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| aSubsetOf0(X0,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| aSubsetOf0(X0,X2) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| ! [X2] :
( X2 = sdtpldt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ( X3 = X1
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f39,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| ! [X2] :
( X2 = sdtpldt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ( X3 = X1
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
inference(flattening,[],[f38]) ).
fof(f40,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f41,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
inference(flattening,[],[f40]) ).
fof(f42,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| sdtpldt0(sdtmndt0(X0,X1),X1) = X0 ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f43,plain,
( ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
| ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(ennf_transformation,[],[f21]) ).
fof(f50,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f51,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(rectify,[],[f51]) ).
fof(f53,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) ) )
& ( aElementOf0(sK4(X0),X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f52]) ).
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(f58,plain,
! [X1,X0] :
( ~ sP1(X1,X0)
| ! [X2] :
( ( sdtpldt0(X0,X1) != X2
| sP0(X2,X0,X1) )
& ( ~ sP0(X2,X0,X1)
| X2 = sdtpldt0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f59,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| ! [X2] :
( ( sdtpldt0(X1,X0) != X2
| sP0(X2,X1,X0) )
& ( ~ sP0(X2,X1,X0)
| sdtpldt0(X1,X0) = X2 ) ) ),
inference(rectify,[],[f58]) ).
fof(f64,plain,
! [X1,X0] :
( ~ sP3(X1,X0)
| ! [X2] :
( ( sdtmndt0(X0,X1) != X2
| sP2(X2,X0,X1) )
& ( ~ sP2(X2,X0,X1)
| X2 = sdtmndt0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f48]) ).
fof(f65,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| ! [X2] :
( ( sdtmndt0(X1,X0) != X2
| sP2(X2,X1,X0) )
& ( ~ sP2(X2,X1,X0)
| sdtmndt0(X1,X0) = X2 ) ) ),
inference(rectify,[],[f64]) ).
fof(f70,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f71,plain,
! [X2,X0] :
( slcrc0 != X0
| ~ aElementOf0(X2,X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f72,plain,
! [X0] :
( slcrc0 != X0
| aSet0(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f76,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| aSet0(X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f77,plain,
! [X0,X1] :
( ~ aSet0(X0)
| aElementOf0(sK5(X0,X1),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f78,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(sK5(X0,X1),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f82,plain,
! [X2,X0,X1] :
( ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| aSubsetOf0(X0,X2) ),
inference(cnf_transformation,[],[f37]) ).
fof(f83,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1)
| sdtpldt0(X1,X0) != X2
| sP0(X2,X1,X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f84,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1)
| ~ sP0(X2,X1,X0)
| sdtpldt0(X1,X0) = X2 ),
inference(cnf_transformation,[],[f59]) ).
fof(f94,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| sP1(X1,X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f95,plain,
! [X2,X0,X1] :
( ~ sP3(X0,X1)
| sdtmndt0(X1,X0) != X2
| sP2(X2,X1,X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f96,plain,
! [X2,X0,X1] :
( ~ sP3(X0,X1)
| ~ sP2(X2,X1,X0)
| sdtmndt0(X1,X0) = X2 ),
inference(cnf_transformation,[],[f65]) ).
fof(f106,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| sP3(X1,X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f107,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| sdtpldt0(sdtmndt0(X0,X1),X1) = X0 ),
inference(cnf_transformation,[],[f42]) ).
fof(f108,plain,
aSet0(xS),
inference(cnf_transformation,[],[f18]) ).
fof(f109,plain,
aElement0(xx),
inference(cnf_transformation,[],[f18]) ).
fof(f110,plain,
~ aElementOf0(xx,xS),
inference(cnf_transformation,[],[f19]) ).
fof(f111,plain,
( ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
| ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(cnf_transformation,[],[f43]) ).
fof(f112,plain,
aSet0(slcrc0),
inference(equality_resolution,[],[f72]) ).
fof(f113,plain,
! [X2] : ~ aElementOf0(X2,slcrc0),
inference(equality_resolution,[],[f71]) ).
fof(f114,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| sP0(sdtpldt0(X1,X0),X1,X0) ),
inference(equality_resolution,[],[f83]) ).
fof(f116,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| sP2(sdtmndt0(X1,X0),X1,X0) ),
inference(equality_resolution,[],[f95]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_51,plain,
aSet0(slcrc0),
inference(cnf_transformation,[],[f112]) ).
tcf(c_52,plain,
! [X0: $i] : ~ aElementOf0(X0,slcrc0),
inference(cnf_transformation,[],[f113]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aElementOf0(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(X0,X1)
| aElementOf0(sK5(X1,X0),X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( aSet0(X0)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( aSubsetOf0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X2,X0)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(X1,X2) = X0 )
| ~ sP1(X2,X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( sP0(sdtpldt0(X1,X0),X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtmndt0(X1,X2) = X0 )
| ~ sP3(X2,X1)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( sP2(sdtmndt0(X1,X0),X1,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( sP3(X0,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtmndt0(X1,X0),X0) = X1 )
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_87,plain,
aElement0(xx),
inference(cnf_transformation,[],[f109]) ).
tcf(c_88,plain,
aSet0(xS),
inference(cnf_transformation,[],[f108]) ).
tcf(c_89,plain,
~ aElementOf0(xx,xS),
inference(cnf_transformation,[],[f110]) ).
tcf(c_90,negated_conjecture,
( ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i] :
( aSubsetOf0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X2,X0) ),
inference(global_subsumption_just,[status(thm)],[c_61,c_56,c_61]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i,X2: $i] :
( aSubsetOf0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSubsetOf0(X2,X0)
| ~ aSubsetOf0(X0,X1) ),
inference(renaming,[status(thm)],[c_115]) ).
tcf(c_629,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP0(sdtpldt0(X3,X1),X3,X1)
| ~ aSet0(X2)
| ~ aElement0(X0)
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_73,c_63]) ).
tcf(c_630,plain,
! [X0: $i,X1: $i] :
( sP0(sdtpldt0(X1,X0),X1,X0)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(unflattening,[status(thm)],[c_629]) ).
tcf(c_641,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sdtpldt0(X0,X2) = X4 )
| ~ aSet0(X1)
| ~ aElement0(X3)
| ~ sP0(X4,X0,X2)
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_62,c_73]) ).
tcf(c_642,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(X1,X2) = X0 )
| ~ aSet0(X1)
| ~ aElement0(X2)
| ~ sP0(X0,X1,X2) ),
inference(unflattening,[status(thm)],[c_641]) ).
tcf(c_663,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP2(sdtmndt0(X3,X1),X3,X1)
| ~ aSet0(X2)
| ~ aElement0(X0)
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_85,c_75]) ).
tcf(c_664,plain,
! [X0: $i,X1: $i] :
( sP2(sdtmndt0(X1,X0),X1,X0)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(unflattening,[status(thm)],[c_663]) ).
tcf(c_675,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sdtmndt0(X0,X2) = X4 )
| ~ aSet0(X1)
| ~ aElement0(X3)
| ~ sP2(X4,X0,X2)
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_74,c_85]) ).
tcf(c_676,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtmndt0(X1,X2) = X0 )
| ~ aSet0(X1)
| ~ aElement0(X2)
| ~ sP2(X0,X1,X2) ),
inference(unflattening,[status(thm)],[c_675]) ).
tcf(c_4865,definition,
iPr_def_10 = sdtpldt0(xS,xx),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_4866,definition,
iPr_def_11 = sdtmndt0(iPr_def_10,xx),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_4867,negated_conjecture,
( ~ aSubsetOf0(iPr_def_11,xS)
| ~ aSubsetOf0(xS,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_90,c_4865,c_4866]) ).
tcf(c_5580,plain,
( sP0(iPr_def_10,xS,xx)
| ~ aSet0(xS)
| ~ aElement0(xx) ),
inference(superposition,[status(thm)],[c_4865,c_630]) ).
tcf(c_5587,plain,
sP0(iPr_def_10,xS,xx),
inference(forward_subsumption_resolution,[status(thm)],[c_5580,c_88,c_87]) ).
tcf(c_5623,plain,
! [X0: $i] :
( aSubsetOf0(slcrc0,X0)
| ~ aSet0(slcrc0)
| ~ aSet0(X0) ),
inference(superposition,[status(thm)],[c_55,c_52]) ).
tcf(c_5624,plain,
! [X0: $i] :
( aSubsetOf0(slcrc0,X0)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5623,c_51]) ).
tcf(c_5635,plain,
( aSubsetOf0(slcrc0,xS)
| ~ aSet0(xS) ),
inference(instantiation,[status(thm)],[c_5624]) ).
tcf(c_6074,plain,
( sP2(iPr_def_11,iPr_def_10,xx)
| ~ aSet0(iPr_def_10)
| ~ aElement0(xx) ),
inference(superposition,[status(thm)],[c_4866,c_664]) ).
tcf(c_7093,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_8037,plain,
( ( sdtpldt0(xS,xx) = iPr_def_10 )
| ~ aSet0(xS)
| ~ aElement0(xx) ),
inference(superposition,[status(thm)],[c_5587,c_642]) ).
tcf(c_8039,plain,
sdtpldt0(xS,xx) = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_8037,c_88,c_87]) ).
fof(f44,definition,
! [X2,X0,X1] :
( sP0(X2,X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ( X3 = X1
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& aSet0(X2) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f45,definition,
! [X1,X0] :
( ~ sP1(X1,X0)
| ! [X2] :
( X2 = sdtpldt0(X0,X1)
<=> sP0(X2,X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f46,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| sP1(X1,X0) ),
inference(definition_folding,[],[f39,f45,f44]) ).
fof(f47,definition,
! [X2,X0,X1] :
( sP2(X2,X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f48,definition,
! [X1,X0] :
( ~ sP3(X1,X0)
| ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> sP2(X2,X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f49,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| sP3(X1,X0) ),
inference(definition_folding,[],[f41,f48,f47]) ).
fof(f60,plain,
! [X2,X0,X1] :
( ( ~ sP0(X2,X0,X1)
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( ( X3 = X1
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& ( ( X1 != X3
& ~ aElementOf0(X3,X0) )
| ~ aElement0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( ( X3 = X1
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| ( X1 != X3
& ~ aElementOf0(X3,X0) )
| ~ aElement0(X3) ) )
| ~ aSet0(X2)
| sP0(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f44]) ).
fof(f61,plain,
! [X2,X0,X1] :
( ( ~ sP0(X2,X0,X1)
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( ( X3 = X1
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& ( ( X1 != X3
& ~ aElementOf0(X3,X0) )
| ~ aElement0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( ( X3 = X1
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| ( X1 != X3
& ~ aElementOf0(X3,X0) )
| ~ aElement0(X3) ) )
| ~ aSet0(X2)
| sP0(X2,X0,X1) ) ),
inference(flattening,[],[f60]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ( ! [X4] :
( ( ~ aElementOf0(X4,X0)
| ( ( X2 = X4
| aElementOf0(X4,X1) )
& aElement0(X4) ) )
& ( ( X2 != X4
& ~ aElementOf0(X4,X1) )
| ~ aElement0(X4)
| aElementOf0(X4,X0) ) )
& aSet0(X0) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X0)
| ( ( X2 = X3
| aElementOf0(X3,X1) )
& aElement0(X3) ) )
& ( ~ aElementOf0(X3,X0)
| ( X2 != X3
& ~ aElementOf0(X3,X1) )
| ~ aElement0(X3) ) )
| ~ aSet0(X0)
| sP0(X0,X1,X2) ) ),
inference(rectify,[],[f61]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ( ! [X4] :
( ( ~ aElementOf0(X4,X0)
| ( ( X2 = X4
| aElementOf0(X4,X1) )
& aElement0(X4) ) )
& ( ( X2 != X4
& ~ aElementOf0(X4,X1) )
| ~ aElement0(X4)
| aElementOf0(X4,X0) ) )
& aSet0(X0) ) )
& ( ( ( aElementOf0(sK6(X0,X1,X2),X0)
| ( ( sK6(X0,X1,X2) = X2
| aElementOf0(sK6(X0,X1,X2),X1) )
& aElement0(sK6(X0,X1,X2)) ) )
& ( ~ aElementOf0(sK6(X0,X1,X2),X0)
| ( sK6(X0,X1,X2) != X2
& ~ aElementOf0(sK6(X0,X1,X2),X1) )
| ~ aElement0(sK6(X0,X1,X2)) ) )
| ~ aSet0(X0)
| sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X3,sK6(X0,X1,X2))],[f62]) ).
fof(f66,plain,
! [X2,X0,X1] :
( ( ~ sP2(X2,X0,X1)
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& ( X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3) ) )
| ~ aSet0(X2)
| sP2(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f67,plain,
! [X2,X0,X1] :
( ( ~ sP2(X2,X0,X1)
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& ( X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3) ) )
| ~ aSet0(X2)
| sP2(X2,X0,X1) ) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ( ~ sP2(X0,X1,X2)
| ( ! [X4] :
( ( ~ aElementOf0(X4,X0)
| ( X2 != X4
& aElementOf0(X4,X1)
& aElement0(X4) ) )
& ( X2 = X4
| ~ aElementOf0(X4,X1)
| ~ aElement0(X4)
| aElementOf0(X4,X0) ) )
& aSet0(X0) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X0)
| ( X2 != X3
& aElementOf0(X3,X1)
& aElement0(X3) ) )
& ( ~ aElementOf0(X3,X0)
| X2 = X3
| ~ aElementOf0(X3,X1)
| ~ aElement0(X3) ) )
| ~ aSet0(X0)
| sP2(X0,X1,X2) ) ),
inference(rectify,[],[f67]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ( ~ sP2(X0,X1,X2)
| ( ! [X4] :
( ( ~ aElementOf0(X4,X0)
| ( X2 != X4
& aElementOf0(X4,X1)
& aElement0(X4) ) )
& ( X2 = X4
| ~ aElementOf0(X4,X1)
| ~ aElement0(X4)
| aElementOf0(X4,X0) ) )
& aSet0(X0) ) )
& ( ( ( aElementOf0(sK7(X0,X1,X2),X0)
| ( sK7(X0,X1,X2) != X2
& aElementOf0(sK7(X0,X1,X2),X1)
& aElement0(sK7(X0,X1,X2)) ) )
& ( ~ aElementOf0(sK7(X0,X1,X2),X0)
| sK7(X0,X1,X2) = X2
| ~ aElementOf0(sK7(X0,X1,X2),X1)
| ~ aElement0(sK7(X0,X1,X2)) ) )
| ~ aSet0(X0)
| sP2(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f68]) ).
fof(f85,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ aElementOf0(X4,X0)
| X2 = X4
| aElementOf0(X4,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f87,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| X2 != X4
| ~ aElement0(X4)
| aElementOf0(X4,X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f88,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ aElementOf0(X4,X1)
| ~ aElement0(X4)
| aElementOf0(X4,X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f89,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| aSet0(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f97,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ aElementOf0(X4,X0)
| X2 != X4 ),
inference(cnf_transformation,[],[f69]) ).
fof(f98,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ aElementOf0(X4,X0)
| aElementOf0(X4,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f101,plain,
! [X2,X0,X1] :
( ~ sP2(X0,X1,X2)
| aSet0(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f103,plain,
! [X2,X0,X1] :
( aElementOf0(sK7(X0,X1,X2),X0)
| aElementOf0(sK7(X0,X1,X2),X1)
| ~ aSet0(X0)
| sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f104,plain,
! [X2,X0,X1] :
( aElementOf0(sK7(X0,X1,X2),X0)
| aElement0(sK7(X0,X1,X2))
| ~ aSet0(X0)
| sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f115,plain,
! [X0,X1,X4] :
( ~ sP0(X0,X1,X4)
| ~ aElement0(X4)
| aElementOf0(X4,X0) ),
inference(equality_resolution,[],[f87]) ).
fof(f117,plain,
! [X0,X1,X4] :
( ~ sP2(X0,X1,X4)
| ~ aElementOf0(X4,X0) ),
inference(equality_resolution,[],[f97]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( aSet0(X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X3,X0)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X2,X0)
| ~ aElement0(X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X3,X1)
| ( X2 = X3 )
| ~ aElementOf0(X3,X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP2(X0,X1,X2)
| aElement0(sK7(X0,X1,X2))
| aElementOf0(sK7(X0,X1,X2),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP2(X0,X1,X2)
| aElementOf0(sK7(X0,X1,X2),X1)
| aElementOf0(sK7(X0,X1,X2),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( aSet0(X0)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ aElementOf0(X2,X0)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_161,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP2(X0,X1,X2)
| aElement0(sK7(X0,X1,X2))
| ~ aSet0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_77,c_49]) ).
tcf(c_1585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( aElementOf0(X5,X2)
| ~ aSet0(X0)
| ~ aElement0(X5)
| ~ aElement0(X1)
| ~ aElementOf0(X5,X3)
| ( X1 != X4 )
| ( X0 != X3 )
| ( sdtpldt0(X0,X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_69,c_630]) ).
tcf(c_1586,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,sdtpldt0(X1,X2))
| ~ aSet0(X1)
| ~ aElement0(X2)
| ~ aElement0(X0)
| ~ aElementOf0(X0,X1) ),
inference(unflattening,[status(thm)],[c_1585]) ).
tcf(c_1588,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,sdtpldt0(X1,X2))
| ~ aSet0(X1)
| ~ aElement0(X2)
| ~ aElementOf0(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_1586,c_49,c_1586]) ).
tcf(c_5596,plain,
( aElementOf0(xx,iPr_def_10)
| ~ aElement0(xx) ),
inference(superposition,[status(thm)],[c_5587,c_70]) ).
tcf(c_5597,plain,
aSet0(iPr_def_10),
inference(superposition,[status(thm)],[c_5587,c_68]) ).
tcf(c_5598,plain,
aElementOf0(xx,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_5596,c_87]) ).
tcf(c_5675,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,sdtpldt0(X1,X2))
| ~ aSet0(X1)
| ~ aElement0(X2)
| ~ aElement0(X0)
| ~ aElementOf0(X0,X1) ),
inference(superposition,[status(thm)],[c_630,c_69]) ).
tcf(c_5687,plain,
( ( sdtpldt0(sdtmndt0(iPr_def_10,xx),xx) = iPr_def_10 )
| ~ aSet0(iPr_def_10) ),
inference(superposition,[status(thm)],[c_5598,c_86]) ).
tcf(c_5692,plain,
( ( sdtpldt0(iPr_def_11,xx) = iPr_def_10 )
| ~ aSet0(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_5687,c_4866]) ).
tcf(c_5693,plain,
sdtpldt0(iPr_def_11,xx) = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_5692,c_5597]) ).
tcf(c_5715,plain,
( sP0(iPr_def_10,iPr_def_11,xx)
| ~ aSet0(iPr_def_11)
| ~ aElement0(xx) ),
inference(superposition,[status(thm)],[c_5693,c_630]) ).
tcf(c_5716,plain,
( sP0(iPr_def_10,iPr_def_11,xx)
| ~ aSet0(iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5715,c_87]) ).
tcf(c_5838,plain,
! [X0: $i] :
( aElementOf0(X0,xS)
| ( X0 = xx )
| ~ aElementOf0(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_5587,c_72]) ).
tcf(c_5872,plain,
! [X0: $i,X1: $i] :
( sP2(slcrc0,X0,X1)
| aElementOf0(sK7(slcrc0,X0,X1),X0)
| ~ aSet0(slcrc0) ),
inference(superposition,[status(thm)],[c_78,c_52]) ).
tcf(c_5881,plain,
! [X0: $i,X1: $i] :
( sP2(slcrc0,X0,X1)
| aElementOf0(sK7(slcrc0,X0,X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5872,c_51]) ).
tcf(c_5982,plain,
! [X0: $i] : sP2(slcrc0,slcrc0,X0),
inference(superposition,[status(thm)],[c_5881,c_52]) ).
tcf(c_6083,plain,
sP2(iPr_def_11,iPr_def_10,xx),
inference(forward_subsumption_resolution,[status(thm)],[c_6074,c_5597,c_87]) ).
tcf(c_6111,plain,
! [X0: $i] :
( aElementOf0(X0,iPr_def_10)
| ~ aElementOf0(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_6083,c_83]) ).
tcf(c_6113,plain,
~ aElementOf0(xx,iPr_def_11),
inference(superposition,[status(thm)],[c_6083,c_84]) ).
tcf(c_6114,plain,
aSet0(iPr_def_11),
inference(superposition,[status(thm)],[c_6083,c_80]) ).
tcf(c_6123,plain,
sP0(iPr_def_10,iPr_def_11,xx),
inference(backward_subsumption_resolution,[status(thm)],[c_5716,c_6114]) ).
tcf(c_6139,plain,
! [X0: $i] :
( aElementOf0(X0,iPr_def_11)
| ( X0 = xx )
| ~ aElementOf0(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_6123,c_72]) ).
tcf(c_6186,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_6111]) ).
tcf(c_6195,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_6186,c_6114]) ).
tcf(c_6586,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_6195,c_6139]) ).
tcf(c_6587,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_6195,c_5838]) ).
tcf(c_8299,plain,
! [X0: $i] :
( ( sdtmndt0(slcrc0,X0) = slcrc0 )
| ~ aSet0(slcrc0)
| ~ aElement0(X0) ),
inference(superposition,[status(thm)],[c_5982,c_676]) ).
tcf(c_8302,plain,
! [X0: $i] :
( ( sdtmndt0(slcrc0,X0) = slcrc0 )
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8299,c_51]) ).
tcf(c_8639,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP2(X0,X1,X2)
| ( sdtmndt0(slcrc0,sK7(X0,X1,X2)) = slcrc0 )
| ~ aSet0(X0) ),
inference(superposition,[status(thm)],[c_161,c_8302]) ).
tcf(c_11319,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtmndt0(slcrc0,sK7(X1,X2,X0)) = slcrc0 )
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(superposition,[status(thm)],[c_8639,c_84]) ).
tcf(c_16973,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_6586,c_6114,c_7093]) ).
tcf(c_16982,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(iPr_def_11,X0)
| ( sdtmndt0(slcrc0,sK7(iPr_def_11,X1,sK5(X0,iPr_def_11))) = slcrc0 )
| ~ aSet0(iPr_def_11)
| ~ aSet0(X0) ),
inference(superposition,[status(thm)],[c_16973,c_11319]) ).
tcf(c_17010,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(iPr_def_11,X0)
| ( sdtmndt0(slcrc0,sK7(iPr_def_11,X1,sK5(X0,iPr_def_11))) = slcrc0 )
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16982,c_6114]) ).
tcf(c_17055,plain,
( aSubsetOf0(iPr_def_11,xS)
| ( sK5(xS,iPr_def_11) = xx )
| ~ aSet0(iPr_def_11)
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_6587,c_54]) ).
tcf(c_17057,plain,
( aSubsetOf0(iPr_def_11,xS)
| ( sK5(xS,iPr_def_11) = xx ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17055,c_6114,c_88]) ).
tcf(c_17142,plain,
! [X0: $i] :
( aSubsetOf0(X0,xS)
| ( sK5(xS,iPr_def_11) = xx )
| ~ aSet0(xS)
| ~ aSet0(X0)
| ~ aSubsetOf0(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_17057,c_116]) ).
tcf(c_17145,plain,
( ( sK5(xS,iPr_def_11) = xx )
| ~ aSubsetOf0(xS,iPr_def_11) ),
inference(superposition,[status(thm)],[c_17057,c_4867]) ).
tcf(c_17150,plain,
! [X0: $i] :
( aSubsetOf0(X0,xS)
| ( sK5(xS,iPr_def_11) = xx )
| ~ aSet0(X0)
| ~ aSubsetOf0(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17142,c_88]) ).
tcf(c_18353,plain,
( aSubsetOf0(slcrc0,xS)
| ( sK5(xS,iPr_def_11) = xx )
| ~ aSet0(iPr_def_11)
| ~ aSet0(slcrc0) ),
inference(superposition,[status(thm)],[c_5624,c_17150]) ).
tcf(c_18359,plain,
( aSubsetOf0(slcrc0,xS)
| ( sK5(xS,iPr_def_11) = xx ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18353,c_6114,c_51]) ).
tcf(c_18363,plain,
aSubsetOf0(slcrc0,xS),
inference(global_subsumption_just,[status(thm)],[c_18359,c_88,c_5635]) ).
tcf(c_18366,plain,
! [X0: $i] :
( aSubsetOf0(X0,xS)
| ~ aSet0(xS)
| ~ aSet0(X0)
| ~ aSubsetOf0(X0,slcrc0) ),
inference(superposition,[status(thm)],[c_18363,c_116]) ).
tcf(c_18373,plain,
! [X0: $i] :
( aSubsetOf0(X0,xS)
| ~ aSet0(X0)
| ~ aSubsetOf0(X0,slcrc0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18366,c_88]) ).
tcf(c_24876,plain,
! [X0: $i] :
( aSubsetOf0(iPr_def_11,xS)
| ( sdtmndt0(slcrc0,sK7(iPr_def_11,X0,sK5(slcrc0,iPr_def_11))) = slcrc0 )
| ~ aSet0(iPr_def_11)
| ~ aSet0(slcrc0) ),
inference(superposition,[status(thm)],[c_17010,c_18373]) ).
tcf(c_24888,plain,
! [X0: $i] :
( aSubsetOf0(iPr_def_11,xS)
| ( sdtmndt0(slcrc0,sK7(iPr_def_11,X0,sK5(slcrc0,iPr_def_11))) = slcrc0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24876,c_6114,c_51]) ).
tcf(c_25773,plain,
! [X0: $i] :
( ( sdtmndt0(slcrc0,sK7(iPr_def_11,X0,sK5(slcrc0,iPr_def_11))) = slcrc0 )
| ~ aSubsetOf0(xS,iPr_def_11) ),
inference(superposition,[status(thm)],[c_24888,c_4867]) ).
tcf(c_25958,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,sdtpldt0(X1,X2))
| ~ aSet0(X1)
| ~ aElement0(X2)
| ~ aElementOf0(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_5675,c_1588]) ).
tcf(c_25968,plain,
! [X0: $i] :
( aElementOf0(X0,iPr_def_10)
| ~ aSet0(xS)
| ~ aElement0(xx)
| ~ aElementOf0(X0,xS) ),
inference(superposition,[status(thm)],[c_8039,c_25958]) ).
tcf(c_25993,plain,
! [X0: $i] :
( aElementOf0(X0,iPr_def_10)
| ~ aElementOf0(X0,xS) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25968,c_88,c_87]) ).
tcf(c_26362,plain,
! [X0: $i] :
( aSubsetOf0(xS,X0)
| aElementOf0(sK5(X0,xS),iPr_def_10)
| ~ aSet0(xS)
| ~ aSet0(X0) ),
inference(superposition,[status(thm)],[c_55,c_25993]) ).
tcf(c_26405,plain,
! [X0: $i] :
( aSubsetOf0(xS,X0)
| aElementOf0(sK5(X0,xS),iPr_def_10)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26362,c_88]) ).
tcf(c_26882,plain,
! [X0: $i] :
( aSubsetOf0(xS,X0)
| aElementOf0(sK5(X0,xS),iPr_def_11)
| ( sK5(X0,xS) = xx )
| ~ aSet0(X0) ),
inference(superposition,[status(thm)],[c_26405,c_6139]) ).
tcf(c_45731,plain,
( aSubsetOf0(xS,iPr_def_11)
| ( sK5(iPr_def_11,xS) = xx )
| ~ aSet0(iPr_def_11)
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_26882,c_54]) ).
tcf(c_45753,plain,
( aSubsetOf0(xS,iPr_def_11)
| ( sK5(iPr_def_11,xS) = xx ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_45731,c_6114,c_88]) ).
tcf(c_45944,plain,
! [X0: $i] :
( ( sK5(iPr_def_11,xS) = xx )
| ( sdtmndt0(slcrc0,sK7(iPr_def_11,X0,sK5(slcrc0,iPr_def_11))) = slcrc0 ) ),
inference(superposition,[status(thm)],[c_45753,c_25773]) ).
tcf(c_45950,plain,
( ( sK5(iPr_def_11,xS) = xx )
| ( sK5(xS,iPr_def_11) = xx ) ),
inference(superposition,[status(thm)],[c_45753,c_17145]) ).
tcf(c_46016,plain,
( aSubsetOf0(iPr_def_11,xS)
| aElementOf0(xx,iPr_def_11)
| ( sK5(iPr_def_11,xS) = xx )
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_45950,c_16973]) ).
tcf(c_46036,plain,
( aSubsetOf0(iPr_def_11,xS)
| ( sK5(iPr_def_11,xS) = xx ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_46016,c_6113,c_88]) ).
tcf(c_46075,plain,
sK5(iPr_def_11,xS) = xx,
inference(global_subsumption_just,[status(thm)],[c_45944,c_4867,c_45753,c_46036]) ).
tcf(c_46196,plain,
( aSubsetOf0(xS,iPr_def_11)
| aElementOf0(xx,xS)
| ~ aSet0(iPr_def_11)
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_46075,c_55]) ).
tcf(c_46201,plain,
aSubsetOf0(xS,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_46196,c_89,c_6114,c_88]) ).
tcf(c_46208,plain,
sK5(xS,iPr_def_11) = xx,
inference(backward_subsumption_resolution,[status(thm)],[c_17145,c_46201]) ).
tcf(c_46212,plain,
~ aSubsetOf0(iPr_def_11,xS),
inference(backward_subsumption_resolution,[status(thm)],[c_4867,c_46201]) ).
tcf(c_46243,plain,
( aSubsetOf0(iPr_def_11,xS)
| aElementOf0(xx,iPr_def_11)
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_46208,c_16973]) ).
tcf(c_46246,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_46243,c_46212,c_6113,c_88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM537+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n004.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 04:30:05 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 6.60/3.25 % SZS status Started for theBenchmark.p
% 6.60/3.25 % SZS status Theorem for theBenchmark.p
% 6.60/3.25
% 6.60/3.25 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.60/3.25
% 6.60/3.25 % ------ iProver source info
% 6.60/3.25
% 6.60/3.25 % git: date: 2026-07-19 20:42:38 +0200
% 6.60/3.25 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.60/3.25 % git: non_committed_changes: false
% 6.60/3.25
% 6.60/3.25 % ------ Parsing...
% 6.60/3.25 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.60/3.25
% 6.60/3.25 % ------ 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 %
% 6.60/3.25
% 6.60/3.25 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.60/3.25
% 6.60/3.25 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.60/3.25 % ------ Proving...
% 6.60/3.25 % ------ Problem Properties
% 6.60/3.25
% 6.60/3.25 %
% 6.60/3.25 % clauses 40
% 6.60/3.25 % conjectures 1
% 6.60/3.25 % EPR 22
% 6.60/3.25 % Horn 30
% 6.60/3.25 % unary 7
% 6.60/3.25 % binary 5
% 6.60/3.25 % lits 121
% 6.60/3.25 % lits eq 13
% 6.60/3.25 % fd_pure 0
% 6.60/3.25 % fd_pseudo 0
% 6.60/3.25 % fd_cond 1
% 6.60/3.25 % fd_pseudo_cond 5
% 6.60/3.25 % AC symbols 0
% 6.60/3.25
% 6.60/3.25 % ------ Schedule dynamic 5 is on
% 6.60/3.25
% 6.60/3.25 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.60/3.25
% 6.60/3.25
% 6.60/3.25 % ------
% 6.60/3.25 % Current options:
% 6.60/3.25 % ------
% 6.60/3.25
% 6.60/3.25
% 6.60/3.25 %
% 6.60/3.25
% 6.60/3.25 % ------ Proving...
% 6.60/3.25 %
% 6.60/3.25
% 6.60/3.25 % SZS status Theorem for theBenchmark.p
% 6.60/3.25
% 6.60/3.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.60/3.26
% 6.60/3.26
%------------------------------------------------------------------------------