%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM611+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 : n007.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 02:26:13 PM UTC 2026
% Result : Theorem 4.64s 2.10s
% Output : CNFRefutation 4.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 18
% Syntax : Number of formulae : 108 ( 36 unt; 0 def)
% Number of atoms : 401 ( 100 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 485 ( 192 ~; 197 |; 70 &)
% ( 13 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 139 ( 0 sgn 130 !; 9 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
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(f11,axiom,
! [X0] :
( ( isFinite0(X0)
& aSet0(X0) )
=> ! [X1] :
( aSubsetOf0(X1,X0)
=> isFinite0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubFSet) ).
fof(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(f26,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( szszuzczcdt0(X0) = szszuzczcdt0(X1)
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccEquSucc) ).
fof(f33,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlseqdt0(X0,szszuzczcdt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessSucc) ).
fof(f41,axiom,
! [X0] :
( aSet0(X0)
=> ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
<=> isFinite0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardNum) ).
fof(f44,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( ( aElementOf0(X1,X0)
& isFinite0(X0) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardDiff) ).
fof(f47,axiom,
! [X0] :
( ( X0 != slcrc0
& aSubsetOf0(X0,szNzAzT0) )
=> ! [X1] :
( X1 = szmzizndt0(X0)
<=> ( ! [X2] :
( aElementOf0(X2,X0)
=> sdtlseqdt0(X1,X2) )
& aElementOf0(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMin) ).
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(f74,axiom,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).
fof(f80,axiom,
( szszuzczcdt0(xk) = xK
& aElementOf0(xk,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3533) ).
fof(f96,axiom,
( isCountable0(xO)
& aSet0(xO) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4908) ).
fof(f99,axiom,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5078) ).
fof(f100,axiom,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5093) ).
fof(f101,axiom,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5106) ).
fof(f104,axiom,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& aSet0(xP) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).
fof(f107,axiom,
aSubsetOf0(xP,xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5195) ).
fof(f109,conjecture,
sbrdtbr0(xP) = xk,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f110,negated_conjecture,
sbrdtbr0(xP) != xk,
inference(negated_conjecture,[status(cth)],[f109]) ).
fof(f118,plain,
xk != sbrdtbr0(xP),
inference(flattening,[],[f110]) ).
fof(f125,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f126,plain,
! [X0] :
( ~ isFinite0(X0)
| ~ aSet0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,X0)
| isFinite0(X1) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f127,plain,
! [X0] :
( ~ isFinite0(X0)
| ~ aSet0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,X0)
| isFinite0(X1) ) ),
inference(flattening,[],[f126]) ).
fof(f149,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f26]) ).
fof(f150,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| X0 = X1 ),
inference(flattening,[],[f149]) ).
fof(f158,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(X0,szszuzczcdt0(X0)) ),
inference(ennf_transformation,[],[f33]) ).
fof(f168,plain,
! [X0] :
( ~ aSet0(X0)
| ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
<=> isFinite0(X0) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f172,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| ~ isFinite0(X0)
| szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0) ) ),
inference(ennf_transformation,[],[f44]) ).
fof(f173,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| ~ isFinite0(X0)
| szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0) ) ),
inference(flattening,[],[f172]) ).
fof(f178,plain,
! [X0] :
( slcrc0 = X0
| ~ aSubsetOf0(X0,szNzAzT0)
| ! [X1] :
( X1 = szmzizndt0(X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X0)
| sdtlseqdt0(X1,X2) )
& aElementOf0(X1,X0) ) ) ),
inference(ennf_transformation,[],[f47]) ).
fof(f179,plain,
! [X0] :
( slcrc0 = X0
| ~ aSubsetOf0(X0,szNzAzT0)
| ! [X1] :
( X1 = szmzizndt0(X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X0)
| sdtlseqdt0(X1,X2) )
& aElementOf0(X1,X0) ) ) ),
inference(flattening,[],[f178]) ).
fof(f193,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(f194,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,[],[f193]) ).
fof(f252,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,[],[f125]) ).
fof(f253,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,[],[f252]) ).
fof(f254,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,[],[f253]) ).
fof(f255,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))],[f254]) ).
fof(f270,plain,
! [X0] :
( ~ aSet0(X0)
| ( ( ~ aElementOf0(sbrdtbr0(X0),szNzAzT0)
| isFinite0(X0) )
& ( ~ isFinite0(X0)
| aElementOf0(sbrdtbr0(X0),szNzAzT0) ) ) ),
inference(nnf_transformation,[],[f168]) ).
fof(f273,plain,
! [X0] :
( slcrc0 = X0
| ~ aSubsetOf0(X0,szNzAzT0)
| ! [X1] :
( ( szmzizndt0(X0) != X1
| ( ! [X2] :
( ~ aElementOf0(X2,X0)
| sdtlseqdt0(X1,X2) )
& aElementOf0(X1,X0) ) )
& ( ? [X2] :
( aElementOf0(X2,X0)
& ~ sdtlseqdt0(X1,X2) )
| ~ aElementOf0(X1,X0)
| X1 = szmzizndt0(X0) ) ) ),
inference(nnf_transformation,[],[f179]) ).
fof(f274,plain,
! [X0] :
( slcrc0 = X0
| ~ aSubsetOf0(X0,szNzAzT0)
| ! [X1] :
( ( szmzizndt0(X0) != X1
| ( ! [X2] :
( ~ aElementOf0(X2,X0)
| sdtlseqdt0(X1,X2) )
& aElementOf0(X1,X0) ) )
& ( ? [X2] :
( aElementOf0(X2,X0)
& ~ sdtlseqdt0(X1,X2) )
| ~ aElementOf0(X1,X0)
| X1 = szmzizndt0(X0) ) ) ),
inference(flattening,[],[f273]) ).
fof(f275,plain,
! [X0] :
( slcrc0 = X0
| ~ aSubsetOf0(X0,szNzAzT0)
| ! [X1] :
( ( szmzizndt0(X0) != X1
| ( ! [X3] :
( ~ aElementOf0(X3,X0)
| sdtlseqdt0(X1,X3) )
& aElementOf0(X1,X0) ) )
& ( ? [X2] :
( aElementOf0(X2,X0)
& ~ sdtlseqdt0(X1,X2) )
| ~ aElementOf0(X1,X0)
| X1 = szmzizndt0(X0) ) ) ),
inference(rectify,[],[f274]) ).
fof(f276,plain,
! [X0] :
( slcrc0 = X0
| ~ aSubsetOf0(X0,szNzAzT0)
| ! [X1] :
( ( szmzizndt0(X0) != X1
| ( ! [X3] :
( ~ aElementOf0(X3,X0)
| sdtlseqdt0(X1,X3) )
& aElementOf0(X1,X0) ) )
& ( ( aElementOf0(sK10(X0,X1),X0)
& ~ sdtlseqdt0(X1,sK10(X0,X1)) )
| ~ aElementOf0(X1,X0)
| X1 = szmzizndt0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0,X1))],[f275]) ).
fof(f289,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,[],[f194]) ).
fof(f290,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,[],[f289]) ).
fof(f291,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,[],[f290]) ).
fof(f292,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))],[f291]) ).
fof(f319,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| aSet0(X1) ),
inference(cnf_transformation,[],[f255]) ).
fof(f322,plain,
! [X0,X1] :
( ~ isFinite0(X0)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| isFinite0(X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f357,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f361,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f150]) ).
fof(f369,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(X0,szszuzczcdt0(X0)) ),
inference(cnf_transformation,[],[f158]) ).
fof(f376,plain,
! [X0] :
( ~ aSet0(X0)
| ~ aElementOf0(sbrdtbr0(X0),szNzAzT0)
| isFinite0(X0) ),
inference(cnf_transformation,[],[f270]) ).
fof(f377,plain,
! [X0] :
( ~ aSet0(X0)
| ~ isFinite0(X0)
| aElementOf0(sbrdtbr0(X0),szNzAzT0) ),
inference(cnf_transformation,[],[f270]) ).
fof(f381,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| ~ isFinite0(X0)
| sbrdtbr0(X0) = szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) ),
inference(cnf_transformation,[],[f173]) ).
fof(f386,plain,
! [X0,X1] :
( slcrc0 = X0
| ~ aSubsetOf0(X0,szNzAzT0)
| szmzizndt0(X0) != X1
| aElementOf0(X1,X0) ),
inference(cnf_transformation,[],[f276]) ).
fof(f411,plain,
! [X2,X0,X1,X4] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| slbdtsldtrb0(X0,X1) != X2
| ~ aElementOf0(X4,X2)
| sbrdtbr0(X4) = X1 ),
inference(cnf_transformation,[],[f292]) ).
fof(f456,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[],[f74]) ).
fof(f468,plain,
xK = szszuzczcdt0(xk),
inference(cnf_transformation,[],[f80]) ).
fof(f469,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f80]) ).
fof(f505,plain,
aSet0(xO),
inference(cnf_transformation,[],[f96]) ).
fof(f510,plain,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
inference(cnf_transformation,[],[f99]) ).
fof(f511,plain,
slcrc0 != xQ,
inference(cnf_transformation,[],[f100]) ).
fof(f513,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(cnf_transformation,[],[f101]) ).
fof(f516,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(cnf_transformation,[],[f104]) ).
fof(f517,plain,
aSet0(xP),
inference(cnf_transformation,[],[f104]) ).
fof(f520,plain,
aSubsetOf0(xP,xQ),
inference(cnf_transformation,[],[f107]) ).
fof(f522,plain,
xk != sbrdtbr0(xP),
inference(cnf_transformation,[],[f118]) ).
fof(f531,plain,
! [X0] :
( slcrc0 = X0
| ~ aSubsetOf0(X0,szNzAzT0)
| aElementOf0(szmzizndt0(X0),X0) ),
inference(equality_resolution,[],[f386]) ).
fof(f544,plain,
! [X0,X1,X4] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ~ aElementOf0(X4,slbdtsldtrb0(X0,X1))
| sbrdtbr0(X4) = X1 ),
inference(equality_resolution,[],[f411]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( aSet0(X0)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f319]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( isFinite0(X0)
| ~ isFinite0(X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f322]) ).
tcf(c_94,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f357]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ( szszuzczcdt0(X0) != szszuzczcdt0(X1) ) ),
inference(cnf_transformation,[],[f361]) ).
tcf(c_107,plain,
! [X0: $i] :
( sdtlseqdt0(X0,szszuzczcdt0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f369]) ).
tcf(c_114,plain,
! [X0: $i] :
( aElementOf0(sbrdtbr0(X0),szNzAzT0)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f377]) ).
tcf(c_115,plain,
! [X0: $i] :
( isFinite0(X0)
| ~ aSet0(X0)
| ~ aElementOf0(sbrdtbr0(X0),szNzAzT0) ),
inference(cnf_transformation,[],[f376]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i] :
( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X0))) = sbrdtbr0(X1) )
| ~ isFinite0(X1)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f381]) ).
tcf(c_125,plain,
! [X0: $i] :
( aElementOf0(szmzizndt0(X0),X0)
| ( X0 = slcrc0 )
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f531]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sbrdtbr0(X0) = X2 )
| ~ aSet0(X1)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X0,slbdtsldtrb0(X1,X2)) ),
inference(cnf_transformation,[],[f544]) ).
tcf(c_194,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[],[f456]) ).
tcf(c_206,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f469]) ).
tcf(c_207,plain,
szszuzczcdt0(xk) = xK,
inference(cnf_transformation,[],[f468]) ).
tcf(c_242,plain,
aSet0(xO),
inference(cnf_transformation,[],[f505]) ).
tcf(c_248,plain,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
inference(cnf_transformation,[],[f510]) ).
tcf(c_250,plain,
slcrc0 != xQ,
inference(cnf_transformation,[],[f511]) ).
tcf(c_251,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(cnf_transformation,[],[f513]) ).
tcf(c_254,plain,
aSet0(xP),
inference(cnf_transformation,[],[f517]) ).
tcf(c_255,plain,
sdtmndt0(xQ,szmzizndt0(xQ)) = xP,
inference(cnf_transformation,[],[f516]) ).
tcf(c_258,plain,
aSubsetOf0(xP,xQ),
inference(cnf_transformation,[],[f520]) ).
tcf(c_260,negated_conjecture,
sbrdtbr0(xP) != xk,
inference(cnf_transformation,[],[f522]) ).
tcf(c_557,plain,
( aSet0(xQ)
| ~ aSet0(szNzAzT0) ),
inference(superposition,[status(thm)],[c_251,c_58]) ).
tcf(c_653,plain,
( isFinite0(xP)
| ~ isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(superposition,[status(thm)],[c_258,c_60]) ).
tcf(c_779,plain,
( ( sbrdtbr0(xQ) = xK )
| ~ aSet0(xO)
| ~ aElementOf0(xK,szNzAzT0) ),
inference(superposition,[status(thm)],[c_248,c_155]) ).
tcf(c_836,plain,
! [X0: $i] :
( ( X0 = slcrc0 )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,szmzizndt0(X0)))) = sbrdtbr0(X0) )
| ~ isFinite0(X0)
| ~ aSet0(X0)
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(superposition,[status(thm)],[c_125,c_119]) ).
tcf(c_865,plain,
! [X0: $i] :
( ( X0 = xk )
| ~ aElementOf0(xk,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ( szszuzczcdt0(X0) != xK ) ),
inference(superposition,[status(thm)],[c_207,c_99]) ).
tcf(c_1345,plain,
( isFinite0(xP)
| ~ isFinite0(xQ) ),
inference(global_subsumption_just,[status(thm)],[c_653,c_94,c_557,c_653]) ).
tcf(c_1721,plain,
sbrdtbr0(xQ) = xK,
inference(global_subsumption_just,[status(thm)],[c_779,c_242,c_194,c_779]) ).
tcf(c_1729,plain,
( isFinite0(xQ)
| ~ aSet0(xQ)
| ~ aElementOf0(xK,szNzAzT0) ),
inference(superposition,[status(thm)],[c_1721,c_115]) ).
tcf(c_1937,plain,
( ( slcrc0 = xQ )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) )
| ~ isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(superposition,[status(thm)],[c_251,c_836]) ).
tcf(c_1980,plain,
! [X0: $i] :
( ( X0 = xk )
| ( szszuzczcdt0(X0) != xK )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(global_subsumption_just,[status(thm)],[c_865,c_206,c_865]) ).
tcf(c_1981,plain,
! [X0: $i] :
( ( X0 = xk )
| ~ aElementOf0(X0,szNzAzT0)
| ( szszuzczcdt0(X0) != xK ) ),
inference(renaming,[status(thm)],[c_1980]) ).
tcf(c_4635,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ),
inference(global_subsumption_just,[status(thm)],[c_1937,c_94,c_194,c_250,c_557,c_1729,c_1937]) ).
tcf(c_4637,plain,
szszuzczcdt0(sbrdtbr0(xP)) = xK,
inference(light_normalisation,[status(thm)],[c_4635,c_255,c_1721]) ).
tcf(c_4652,plain,
( ( sbrdtbr0(xP) = xk )
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(superposition,[status(thm)],[c_4637,c_1981]) ).
tcf(c_4667,plain,
( sdtlseqdt0(sbrdtbr0(xP),xK)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(superposition,[status(thm)],[c_4637,c_107]) ).
tcf(c_17033,plain,
~ aElementOf0(sbrdtbr0(xP),szNzAzT0),
inference(global_subsumption_just,[status(thm)],[c_4667,c_260,c_4652]) ).
tcf(c_17035,plain,
( ~ isFinite0(xP)
| ~ aSet0(xP) ),
inference(superposition,[status(thm)],[c_114,c_17033]) ).
tcf(c_17037,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_17035,c_1729,c_1345,c_557,c_194,c_94,c_254]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM611+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 04:52:22 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 4.64/2.10 % SZS status Started for theBenchmark.p
% 4.64/2.10 % SZS status Theorem for theBenchmark.p
% 4.64/2.10
% 4.64/2.10 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.64/2.10
% 4.64/2.10 % ------ iProver source info
% 4.64/2.10
% 4.64/2.10 % git: date: 2026-07-19 20:42:38 +0200
% 4.64/2.10 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.64/2.10 % git: non_committed_changes: false
% 4.64/2.10
% 4.64/2.10 % ------ Parsing...
% 4.64/2.10 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.64/2.10 % ------ Proving...
% 4.64/2.10 % ------ Problem Properties
% 4.64/2.10
% 4.64/2.10 %
% 4.64/2.10 % clauses 212
% 4.64/2.10 % conjectures 1
% 4.64/2.10 % EPR 56
% 4.64/2.10 % Horn 173
% 4.64/2.10 % unary 49
% 4.64/2.10 % binary 35
% 4.64/2.10 % lits 683
% 4.64/2.10 % lits eq 104
% 4.64/2.10 % fd_pure 0
% 4.64/2.10 % fd_pseudo 0
% 4.64/2.10 % fd_cond 10
% 4.64/2.10 % fd_pseudo_cond 25
% 4.64/2.10 % AC symbols 0
% 4.64/2.10
% 4.64/2.10 % ------ Input Options Time Limit: Unbounded
% 4.64/2.10
% 4.64/2.10
% 4.64/2.10 % ------
% 4.64/2.10 % Current options:
% 4.64/2.10 % ------
% 4.64/2.10
% 4.64/2.10
% 4.64/2.10 %
% 4.64/2.10
% 4.64/2.10 % ------ Proving...
% 4.64/2.10 %
% 4.64/2.10
% 4.64/2.10 % ------ Proving...
% 4.64/2.10 %
% 4.64/2.10
% 4.64/2.10 % SZS status Theorem for theBenchmark.p
% 4.64/2.10
% 4.64/2.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.64/2.10
% 4.64/2.10
%------------------------------------------------------------------------------