%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM558+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:26:00 PM UTC 2026
% Result : Theorem 9.95s 2.26s
% Output : CNFRefutation 9.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of formulae : 120 ( 31 unt; 4 def)
% Number of atoms : 581 ( 101 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 742 ( 281 ~; 287 |; 141 &)
% ( 26 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 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 : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 10 con; 0-3 aty)
% Number of variables : 235 ( 0 sgn 223 !; 12 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(f57,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aSet0(X0) )
=> ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
fof(f61,axiom,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202) ).
fof(f62,axiom,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).
fof(f63,axiom,
( slbdtsldtrb0(xS,xk) != slcrc0
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2227) ).
fof(f64,axiom,
aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2256) ).
fof(f66,axiom,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2291) ).
fof(f67,axiom,
( aElementOf0(xy,xQ)
& aElement0(xy) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2304) ).
fof(f70,axiom,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2357) ).
fof(f71,axiom,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2378) ).
fof(f72,conjecture,
aElementOf0(xx,xT),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f73,negated_conjecture,
~ aElementOf0(xx,xT),
inference(negated_conjecture,[status(cth)],[f72]) ).
fof(f80,plain,
~ aElementOf0(xx,xT),
inference(flattening,[],[f73]) ).
fof(f82,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f88,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f96,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(f97,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,[],[f96]) ).
fof(f98,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(f99,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,[],[f98]) ).
fof(f155,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) ) ),
inference(ennf_transformation,[],[f57]) ).
fof(f156,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) ) ),
inference(flattening,[],[f155]) ).
fof(f173,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,[],[f88]) ).
fof(f174,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,[],[f173]) ).
fof(f175,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,[],[f174]) ).
fof(f176,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))],[f175]) ).
fof(f177,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,[],[f164]) ).
fof(f178,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,[],[f177]) ).
fof(f183,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,[],[f167]) ).
fof(f184,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,[],[f183]) ).
fof(f210,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( ( slbdtsldtrb0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& ( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& ( ~ aElementOf0(X3,X2)
| sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0) ) )
| ~ aSet0(X2)
| X2 = slbdtsldtrb0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f156]) ).
fof(f211,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( ( slbdtsldtrb0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& ( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& ( ~ aElementOf0(X3,X2)
| sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0) ) )
| ~ aSet0(X2)
| X2 = slbdtsldtrb0(X0,X1) ) ) ),
inference(flattening,[],[f210]) ).
fof(f212,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( ( slbdtsldtrb0(X0,X1) != X2
| ( ! [X4] :
( ( ~ aElementOf0(X4,X2)
| ( sbrdtbr0(X4) = X1
& aSubsetOf0(X4,X0) ) )
& ( sbrdtbr0(X4) != X1
| ~ aSubsetOf0(X4,X0)
| aElementOf0(X4,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& ( ~ aElementOf0(X3,X2)
| sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0) ) )
| ~ aSet0(X2)
| X2 = slbdtsldtrb0(X0,X1) ) ) ),
inference(rectify,[],[f211]) ).
fof(f213,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( ( slbdtsldtrb0(X0,X1) != X2
| ( ! [X4] :
( ( ~ aElementOf0(X4,X2)
| ( sbrdtbr0(X4) = X1
& aSubsetOf0(X4,X0) ) )
& ( sbrdtbr0(X4) != X1
| ~ aSubsetOf0(X4,X0)
| aElementOf0(X4,X2) ) )
& aSet0(X2) ) )
& ( ( ( aElementOf0(sK14(X0,X1,X2),X2)
| ( sbrdtbr0(sK14(X0,X1,X2)) = X1
& aSubsetOf0(sK14(X0,X1,X2),X0) ) )
& ( ~ aElementOf0(sK14(X0,X1,X2),X2)
| sbrdtbr0(sK14(X0,X1,X2)) != X1
| ~ aSubsetOf0(sK14(X0,X1,X2),X0) ) )
| ~ aSet0(X2)
| X2 = slbdtsldtrb0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X3,sK14(X0,X1,X2))],[f212]) ).
fof(f214,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f221,plain,
! [X3,X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) ),
inference(cnf_transformation,[],[f176]) ).
fof(f229,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1)
| sdtpldt0(X1,X0) != X2
| sP0(X2,X1,X0) ),
inference(cnf_transformation,[],[f178]) ).
fof(f240,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| sP1(X1,X0) ),
inference(cnf_transformation,[],[f165]) ).
fof(f241,plain,
! [X2,X0,X1] :
( ~ sP3(X0,X1)
| sdtmndt0(X1,X0) != X2
| sP2(X2,X1,X0) ),
inference(cnf_transformation,[],[f184]) ).
fof(f252,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| sP3(X1,X0) ),
inference(cnf_transformation,[],[f168]) ).
fof(f314,plain,
! [X2,X0,X1,X4] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| slbdtsldtrb0(X0,X1) != X2
| ~ aElementOf0(X4,X2)
| aSubsetOf0(X4,X0) ),
inference(cnf_transformation,[],[f213]) ).
fof(f316,plain,
! [X2,X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| slbdtsldtrb0(X0,X1) != X2
| aSet0(X2) ),
inference(cnf_transformation,[],[f213]) ).
fof(f323,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f61]) ).
fof(f325,plain,
aSet0(xT),
inference(cnf_transformation,[],[f62]) ).
fof(f326,plain,
aSet0(xS),
inference(cnf_transformation,[],[f62]) ).
fof(f328,plain,
aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)),
inference(cnf_transformation,[],[f63]) ).
fof(f329,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f64]) ).
fof(f333,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f335,plain,
aElement0(xy),
inference(cnf_transformation,[],[f67]) ).
fof(f338,plain,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
inference(cnf_transformation,[],[f70]) ).
fof(f339,plain,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f71]) ).
fof(f340,plain,
~ aElementOf0(xx,xT),
inference(cnf_transformation,[],[f80]) ).
fof(f344,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| sP0(sdtpldt0(X1,X0),X1,X0) ),
inference(equality_resolution,[],[f229]) ).
fof(f346,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| sP2(sdtmndt0(X1,X0),X1,X0) ),
inference(equality_resolution,[],[f241]) ).
fof(f358,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| aSet0(slbdtsldtrb0(X0,X1)) ),
inference(equality_resolution,[],[f316]) ).
fof(f361,plain,
! [X0,X1,X4] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ~ aElementOf0(X4,slbdtsldtrb0(X0,X1))
| aSubsetOf0(X4,X0) ),
inference(equality_resolution,[],[f314]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X2)
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f221]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( sP0(sdtpldt0(X1,X0),X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f344]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f240]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( sP2(sdtmndt0(X1,X0),X1,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f346]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( sP3(X0,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f252]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i] :
( aSet0(slbdtsldtrb0(X1,X0))
| ~ aSet0(X1)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f358]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i,X2: $i] :
( aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X0,slbdtsldtrb0(X1,X2)) ),
inference(cnf_transformation,[],[f361]) ).
tcf(c_158,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f323]) ).
tcf(c_159,plain,
aSet0(xS),
inference(cnf_transformation,[],[f326]) ).
tcf(c_160,plain,
aSet0(xT),
inference(cnf_transformation,[],[f325]) ).
tcf(c_162,plain,
aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)),
inference(cnf_transformation,[],[f328]) ).
tcf(c_164,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f329]) ).
tcf(c_166,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f333]) ).
tcf(c_169,plain,
aElement0(xy),
inference(cnf_transformation,[],[f335]) ).
tcf(c_173,plain,
sdtpldt0(sdtmndt0(xQ,xy),xx) = xP,
inference(cnf_transformation,[],[f338]) ).
tcf(c_174,plain,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f339]) ).
tcf(c_175,negated_conjecture,
~ aElementOf0(xx,xT),
inference(cnf_transformation,[],[f340]) ).
tcf(c_1084,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_75,c_65]) ).
tcf(c_1085,plain,
! [X0: $i,X1: $i] :
( sP0(sdtpldt0(X1,X0),X1,X0)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(unflattening,[status(thm)],[c_1084]) ).
tcf(c_1118,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_87,c_77]) ).
tcf(c_1119,plain,
! [X0: $i,X1: $i] :
( sP2(sdtmndt0(X1,X0),X1,X0)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(unflattening,[status(thm)],[c_1118]) ).
tcf(c_9500,plain,
! [X0: $i] :
( aElement0(xx)
| ~ aSet0(X0)
| ~ aElementOf0(xx,X0) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_9622,plain,
! [X0: $i] :
( aElementOf0(xP,X0)
| ~ aSet0(X0)
| ~ aElementOf0(xP,slbdtsldtrb0(xS,xk))
| ~ aSubsetOf0(slbdtsldtrb0(xS,xk),X0) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_9633,plain,
( aElement0(xx)
| ~ aSet0(xS)
| ~ aElementOf0(xx,xS) ),
inference(instantiation,[status(thm)],[c_9500]) ).
tcf(c_10184,plain,
( aElementOf0(xP,slbdtsldtrb0(xT,xk))
| ~ aSet0(slbdtsldtrb0(xT,xk))
| ~ aElementOf0(xP,slbdtsldtrb0(xS,xk))
| ~ aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)) ),
inference(instantiation,[status(thm)],[c_9622]) ).
tcf(c_11894,plain,
( aSet0(slbdtsldtrb0(xT,xk))
| ~ aSet0(xT)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_151]) ).
tcf(c_12554,plain,
! [X0: $i] :
( aElementOf0(xP,X0)
| ~ aSet0(X0)
| ~ aSubsetOf0(slbdtsldtrb0(xS,xk),X0) ),
inference(superposition,[status(thm)],[c_174,c_59]) ).
tcf(c_13604,plain,
( aElementOf0(xP,slbdtsldtrb0(xT,xk))
| ~ aSet0(slbdtsldtrb0(xT,xk)) ),
inference(superposition,[status(thm)],[c_162,c_12554]) ).
tcf(c_14342,plain,
aElementOf0(xP,slbdtsldtrb0(xT,xk)),
inference(global_subsumption_just,[status(thm)],[c_13604,c_160,c_158,c_174,c_162,c_10184,c_11894]) ).
tcf(c_14987,plain,
( aSubsetOf0(xP,xT)
| ~ aSet0(xT)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(superposition,[status(thm)],[c_14342,c_153]) ).
tcf(c_15568,plain,
aSubsetOf0(xP,xT),
inference(global_subsumption_just,[status(thm)],[c_14987,c_160,c_158,c_14987]) ).
fof(f163,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(f164,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(f165,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| sP1(X1,X0) ),
inference(definition_folding,[],[f97,f164,f163]) ).
fof(f166,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(f167,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(f168,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| sP3(X1,X0) ),
inference(definition_folding,[],[f99,f167,f166]) ).
fof(f179,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,[],[f163]) ).
fof(f180,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,[],[f179]) ).
fof(f181,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,[],[f180]) ).
fof(f182,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))],[f181]) ).
fof(f185,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,[],[f166]) ).
fof(f186,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,[],[f185]) ).
fof(f187,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,[],[f186]) ).
fof(f188,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))],[f187]) ).
fof(f233,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| X2 != X4
| ~ aElement0(X4)
| aElementOf0(X4,X0) ),
inference(cnf_transformation,[],[f182]) ).
fof(f247,plain,
! [X2,X0,X1] :
( ~ sP2(X0,X1,X2)
| aSet0(X0) ),
inference(cnf_transformation,[],[f188]) ).
fof(f345,plain,
! [X0,X1,X4] :
( ~ sP0(X0,X1,X4)
| ~ aElement0(X4)
| aElementOf0(X4,X0) ),
inference(equality_resolution,[],[f233]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X2,X0)
| ~ aElement0(X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f345]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] :
( aSet0(X0)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f247]) ).
tcf(c_11734,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,sdtpldt0(X1,X0))
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(superposition,[status(thm)],[c_1085,c_72]) ).
tcf(c_11793,plain,
( aElementOf0(xx,xP)
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(superposition,[status(thm)],[c_173,c_11734]) ).
tcf(c_11795,plain,
( aElementOf0(xx,xP)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(global_subsumption_just,[status(thm)],[c_11793,c_159,c_164,c_9633,c_11793]) ).
tcf(c_11828,plain,
! [X0: $i,X1: $i] :
( aSet0(sdtmndt0(X1,X0))
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(superposition,[status(thm)],[c_1119,c_82]) ).
tcf(c_11866,plain,
( aElementOf0(xx,xP)
| ~ aSet0(xQ)
| ~ aElement0(xy) ),
inference(superposition,[status(thm)],[c_11828,c_11795]) ).
tcf(c_12111,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,sdtpldt0(X1,X0))
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(superposition,[status(thm)],[c_1085,c_72]) ).
tcf(c_12222,plain,
( aElementOf0(xx,xP)
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(superposition,[status(thm)],[c_173,c_12111]) ).
tcf(c_12224,plain,
aElementOf0(xx,xP),
inference(global_subsumption_just,[status(thm)],[c_12222,c_169,c_166,c_11866]) ).
tcf(c_12556,plain,
! [X0: $i] :
( aElementOf0(xx,X0)
| ~ aSet0(X0)
| ~ aSubsetOf0(xP,X0) ),
inference(superposition,[status(thm)],[c_12224,c_59]) ).
tcf(c_15572,plain,
( aElementOf0(xx,xT)
| ~ aSet0(xT) ),
inference(superposition,[status(thm)],[c_15568,c_12556]) ).
tcf(c_15573,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_15572,c_175,c_160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM558+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 04:37:13 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 9.95/2.26 % SZS status Started for theBenchmark.p
% 9.95/2.26 % SZS status Theorem for theBenchmark.p
% 9.95/2.26
% 9.95/2.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 9.95/2.26
% 9.95/2.26 % ------ iProver source info
% 9.95/2.26
% 9.95/2.26 % git: date: 2026-07-19 20:42:38 +0200
% 9.95/2.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 9.95/2.26 % git: non_committed_changes: false
% 9.95/2.26
% 9.95/2.26 % ------ Parsing...
% 9.95/2.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 9.95/2.26
% 9.95/2.26 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 9.95/2.26
% 9.95/2.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 9.95/2.26
% 9.95/2.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 9.95/2.26 % ------ Proving...
% 9.95/2.26 % ------ Problem Properties
% 9.95/2.26
% 9.95/2.26 %
% 9.95/2.26 % clauses 124
% 9.95/2.26 % conjectures 1
% 9.95/2.26 % EPR 40
% 9.95/2.26 % Horn 94
% 9.95/2.26 % unary 26
% 9.95/2.26 % binary 16
% 9.95/2.26 % lits 394
% 9.95/2.26 % lits eq 59
% 9.95/2.26 % fd_pure 0
% 9.95/2.26 % fd_pseudo 0
% 9.95/2.26 % fd_cond 9
% 9.95/2.26 % fd_pseudo_cond 18
% 9.95/2.26 % AC symbols 0
% 9.95/2.26
% 9.95/2.26 % ------ Input Options Time Limit: Unbounded
% 9.95/2.26
% 9.95/2.26
% 9.95/2.26 % ------
% 9.95/2.26 % Current options:
% 9.95/2.26 % ------
% 9.95/2.26
% 9.95/2.26
% 9.95/2.26 %
% 9.95/2.26
% 9.95/2.26 % ------ Proving...
% 9.95/2.26 %
% 9.95/2.26
% 9.95/2.26 % SZS status Theorem for theBenchmark.p
% 9.95/2.26
% 9.95/2.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 9.95/2.26
% 9.95/2.26
%------------------------------------------------------------------------------