%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM564+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 : n019.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 02:26:02 PM UTC 2026
% Result : Theorem 3.54s 1.20s
% Output : CNFRefutation 4.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 117 ( 29 unt; 0 def)
% Number of atoms : 434 ( 100 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 555 ( 238 ~; 236 |; 62 &)
% ( 12 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 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 : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-3 aty)
% Number of variables : 161 ( 0 sgn 151 !; 10 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( ~ ? [X1] : aElementOf0(X1,X0)
& aSet0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
fof(f8,axiom,
! [X0] :
( ( isCountable0(X0)
& aSet0(X0) )
=> ~ isFinite0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin) ).
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(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(f42,axiom,
! [X0] :
( aSet0(X0)
=> ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
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(f59,axiom,
! [X0] :
( ( ~ isFinite0(X0)
& aSet0(X0) )
=> ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> slbdtsldtrb0(X0,X1) != slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSelNSet) ).
fof(f74,axiom,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).
fof(f75,axiom,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
fof(f76,axiom,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aFunction0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3453) ).
fof(f78,axiom,
xK = sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3462) ).
fof(f79,conjecture,
aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f80,negated_conjecture,
~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(negated_conjecture,[status(cth)],[f79]) ).
fof(f88,plain,
~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(flattening,[],[f80]) ).
fof(f90,plain,
! [X0] :
( X0 = slcrc0
<=> ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f91,plain,
! [X0] :
( ~ isCountable0(X0)
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f92,plain,
! [X0] :
( ~ isCountable0(X0)
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(flattening,[],[f91]) ).
fof(f95,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f139,plain,
! [X0] :
( ~ aSet0(X0)
| ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f163,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(f164,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,[],[f163]) ).
fof(f167,plain,
! [X0] :
( isFinite0(X0)
| ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,szNzAzT0)
| slbdtsldtrb0(X0,X1) != slcrc0 ) ),
inference(ennf_transformation,[],[f59]) ).
fof(f168,plain,
! [X0] :
( isFinite0(X0)
| ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,szNzAzT0)
| slbdtsldtrb0(X0,X1) != slcrc0 ) ),
inference(flattening,[],[f167]) ).
fof(f196,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(nnf_transformation,[],[f90]) ).
fof(f197,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(flattening,[],[f196]) ).
fof(f198,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(rectify,[],[f197]) ).
fof(f199,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))],[f198]) ).
fof(f200,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,[],[f95]) ).
fof(f201,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,[],[f200]) ).
fof(f202,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,[],[f201]) ).
fof(f203,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))],[f202]) ).
fof(f219,plain,
! [X0] :
( ~ aSet0(X0)
| ( ( sz00 != sbrdtbr0(X0)
| X0 = slcrc0 )
& ( slcrc0 != X0
| sbrdtbr0(X0) = sz00 ) ) ),
inference(nnf_transformation,[],[f139]) ).
fof(f237,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,[],[f164]) ).
fof(f238,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,[],[f237]) ).
fof(f239,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,[],[f238]) ).
fof(f240,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))],[f239]) ).
fof(f258,plain,
! [X0] :
( slcrc0 != X0
| aSet0(X0) ),
inference(cnf_transformation,[],[f199]) ).
fof(f259,plain,
! [X0] :
( aElementOf0(sK4(X0),X0)
| ~ aSet0(X0)
| slcrc0 = X0 ),
inference(cnf_transformation,[],[f199]) ).
fof(f261,plain,
! [X0] :
( ~ isCountable0(X0)
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f263,plain,
! [X3,X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) ),
inference(cnf_transformation,[],[f203]) ).
fof(f264,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| aSet0(X1) ),
inference(cnf_transformation,[],[f203]) ).
fof(f302,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f323,plain,
! [X0] :
( ~ aSet0(X0)
| sz00 != sbrdtbr0(X0)
| slcrc0 = X0 ),
inference(cnf_transformation,[],[f219]) ).
fof(f324,plain,
! [X0] :
( ~ aSet0(X0)
| slcrc0 != X0
| sz00 = sbrdtbr0(X0) ),
inference(cnf_transformation,[],[f219]) ).
fof(f356,plain,
! [X2,X0,X1,X4] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| slbdtsldtrb0(X0,X1) != X2
| ~ aElementOf0(X4,X2)
| sbrdtbr0(X4) = X1 ),
inference(cnf_transformation,[],[f240]) ).
fof(f357,plain,
! [X2,X0,X1,X4] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| slbdtsldtrb0(X0,X1) != X2
| ~ aElementOf0(X4,X2)
| aSubsetOf0(X4,X0) ),
inference(cnf_transformation,[],[f240]) ).
fof(f358,plain,
! [X2,X0,X1,X4] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| slbdtsldtrb0(X0,X1) != X2
| sbrdtbr0(X4) != X1
| ~ aSubsetOf0(X4,X0)
| aElementOf0(X4,X2) ),
inference(cnf_transformation,[],[f240]) ).
fof(f359,plain,
! [X2,X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| slbdtsldtrb0(X0,X1) != X2
| aSet0(X2) ),
inference(cnf_transformation,[],[f240]) ).
fof(f364,plain,
! [X0,X1] :
( isFinite0(X0)
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0)
| slcrc0 != slbdtsldtrb0(X0,X1) ),
inference(cnf_transformation,[],[f168]) ).
fof(f401,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[],[f74]) ).
fof(f402,plain,
isCountable0(xS),
inference(cnf_transformation,[],[f75]) ).
fof(f403,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f75]) ).
fof(f405,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(cnf_transformation,[],[f76]) ).
fof(f411,plain,
sz00 = xK,
inference(cnf_transformation,[],[f78]) ).
fof(f412,plain,
~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(cnf_transformation,[],[f88]) ).
fof(f419,plain,
! [X0] :
( ~ aSet0(X0)
| slcrc0 != X0
| sbrdtbr0(X0) = xK ),
inference(definition_unfolding,[],[f324,f411]) ).
fof(f420,plain,
! [X0] :
( ~ aSet0(X0)
| sbrdtbr0(X0) != xK
| slcrc0 = X0 ),
inference(definition_unfolding,[],[f323,f411]) ).
fof(f424,plain,
~ aElementOf0(slcrc0,slbdtsldtrb0(xS,xK)),
inference(definition_unfolding,[],[f412,f411]) ).
fof(f425,plain,
aSet0(slcrc0),
inference(equality_resolution,[],[f258]) ).
fof(f432,plain,
( ~ aSet0(slcrc0)
| xK = sbrdtbr0(slcrc0) ),
inference(equality_resolution,[],[f419]) ).
fof(f442,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| aSet0(slbdtsldtrb0(X0,X1)) ),
inference(equality_resolution,[],[f359]) ).
fof(f443,plain,
! [X2,X0,X4] :
( ~ aElementOf0(sbrdtbr0(X4),szNzAzT0)
| ~ aSet0(X0)
| slbdtsldtrb0(X0,sbrdtbr0(X4)) != X2
| ~ aSubsetOf0(X4,X0)
| aElementOf0(X4,X2) ),
inference(equality_resolution,[],[f358]) ).
fof(f444,plain,
! [X0,X4] :
( ~ aElementOf0(sbrdtbr0(X4),szNzAzT0)
| ~ aSet0(X0)
| ~ aSubsetOf0(X4,X0)
| aElementOf0(X4,slbdtsldtrb0(X0,sbrdtbr0(X4))) ),
inference(equality_resolution,[],[f443]) ).
fof(f445,plain,
! [X0,X1,X4] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ~ aElementOf0(X4,slbdtsldtrb0(X0,X1))
| aSubsetOf0(X4,X0) ),
inference(equality_resolution,[],[f357]) ).
fof(f446,plain,
! [X0,X1,X4] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ~ aElementOf0(X4,slbdtsldtrb0(X0,X1))
| sbrdtbr0(X4) = X1 ),
inference(equality_resolution,[],[f356]) ).
tcf(c_50,plain,
! [X0: $i] :
( aElementOf0(sK4(X0),X0)
| ( X0 = slcrc0 )
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f259]) ).
tcf(c_51,plain,
aSet0(slcrc0),
inference(cnf_transformation,[],[f425]) ).
tcf(c_54,plain,
! [X0: $i] :
( ~ isCountable0(X0)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f261]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( aSet0(X0)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f264]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X2)
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f263]) ).
tcf(c_94,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f302]) ).
tcf(c_116,plain,
( ( sbrdtbr0(slcrc0) = xK )
| ~ aSet0(slcrc0) ),
inference(cnf_transformation,[],[f432]) ).
tcf(c_117,plain,
! [X0: $i] :
( ( X0 = slcrc0 )
| ~ aSet0(X0)
| ( sbrdtbr0(X0) != xK ) ),
inference(cnf_transformation,[],[f420]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i] :
( aSet0(slbdtsldtrb0(X1,X0))
| ~ aSet0(X1)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f442]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,slbdtsldtrb0(X1,sbrdtbr0(X0)))
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1)
| ~ aElementOf0(sbrdtbr0(X0),szNzAzT0) ),
inference(cnf_transformation,[],[f444]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i,X2: $i] :
( aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X0,slbdtsldtrb0(X1,X2)) ),
inference(cnf_transformation,[],[f445]) ).
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,[],[f446]) ).
tcf(c_157,plain,
! [X0: $i,X1: $i] :
( isFinite0(X0)
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0)
| ( slbdtsldtrb0(X0,X1) != slcrc0 ) ),
inference(cnf_transformation,[],[f364]) ).
tcf(c_194,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[],[f401]) ).
tcf(c_195,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f403]) ).
tcf(c_196,plain,
isCountable0(xS),
inference(cnf_transformation,[],[f402]) ).
tcf(c_198,plain,
slbdtsldtrb0(xS,xK) = szDzozmdt0(xc),
inference(cnf_transformation,[],[f405]) ).
tcf(c_204,negated_conjecture,
~ aElementOf0(slcrc0,slbdtsldtrb0(xS,xK)),
inference(cnf_transformation,[],[f424]) ).
tcf(c_265,plain,
( aSet0(szDzozmdt0(xc))
| ~ aSet0(xS)
| ~ aElementOf0(xK,szNzAzT0) ),
inference(superposition,[status(thm)],[c_198,c_152]) ).
tcf(c_298,plain,
( isFinite0(xS)
| ~ aSet0(xS)
| ~ aElementOf0(xK,szNzAzT0)
| ( szDzozmdt0(xc) != slcrc0 ) ),
inference(superposition,[status(thm)],[c_198,c_157]) ).
tcf(c_308,plain,
! [X0: $i] :
( aSubsetOf0(X0,xS)
| ~ aSet0(xS)
| ~ aElementOf0(xK,szNzAzT0)
| ~ aElementOf0(X0,szDzozmdt0(xc)) ),
inference(superposition,[status(thm)],[c_198,c_154]) ).
tcf(c_358,plain,
( isFinite0(xS)
| ~ aSet0(xS)
| ( szDzozmdt0(xc) != slcrc0 ) ),
inference(global_subsumption_just,[status(thm)],[c_298,c_194,c_298]) ).
tcf(c_366,plain,
! [X0: $i] :
( aSubsetOf0(X0,xS)
| ~ aSet0(xS)
| ~ aElementOf0(X0,szDzozmdt0(xc)) ),
inference(global_subsumption_just,[status(thm)],[c_308,c_194,c_308]) ).
tcf(c_375,plain,
( aSubsetOf0(sK4(szDzozmdt0(xc)),xS)
| ( szDzozmdt0(xc) = slcrc0 )
| ~ aSet0(xS)
| ~ aSet0(szDzozmdt0(xc)) ),
inference(superposition,[status(thm)],[c_50,c_366]) ).
tcf(c_395,plain,
( aSubsetOf0(sK4(szDzozmdt0(xc)),xS)
| ( szDzozmdt0(xc) = slcrc0 )
| ~ aSet0(xS) ),
inference(global_subsumption_just,[status(thm)],[c_375,c_194,c_265,c_375]) ).
tcf(c_475,plain,
sbrdtbr0(slcrc0) = xK,
inference(global_subsumption_just,[status(thm)],[c_116,c_51,c_116]) ).
tcf(c_501,plain,
( aSet0(xS)
| ~ aSet0(szNzAzT0) ),
inference(superposition,[status(thm)],[c_195,c_58]) ).
tcf(c_603,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sK4(X0),X1)
| ( X0 = slcrc0 )
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X0,X1) ),
inference(superposition,[status(thm)],[c_50,c_59]) ).
tcf(c_647,plain,
! [X0: $i] :
( aSubsetOf0(X0,xS)
| ~ aSet0(xS)
| ~ aElementOf0(xK,szNzAzT0)
| ~ aElementOf0(X0,szDzozmdt0(xc)) ),
inference(superposition,[status(thm)],[c_198,c_154]) ).
tcf(c_687,plain,
! [X0: $i] :
( ( sbrdtbr0(X0) = xK )
| ~ aSet0(xS)
| ~ aElementOf0(xK,szNzAzT0)
| ~ aElementOf0(X0,szDzozmdt0(xc)) ),
inference(superposition,[status(thm)],[c_198,c_155]) ).
tcf(c_698,plain,
! [X0: $i] :
( aElementOf0(slcrc0,slbdtsldtrb0(X0,xK))
| ~ aSet0(X0)
| ~ aSubsetOf0(slcrc0,X0)
| ~ aElementOf0(sbrdtbr0(slcrc0),szNzAzT0) ),
inference(superposition,[status(thm)],[c_475,c_153]) ).
tcf(c_820,plain,
aSet0(xS),
inference(global_subsumption_just,[status(thm)],[c_501,c_94,c_501]) ).
tcf(c_822,plain,
( ~ isCountable0(xS)
| ~ isFinite0(xS) ),
inference(superposition,[status(thm)],[c_820,c_54]) ).
tcf(c_1102,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sK4(X0),X1)
| ( X0 = slcrc0 )
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_603,c_58,c_603]) ).
tcf(c_1112,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sK4(X0),X2)
| ( X0 = slcrc0 )
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1) ),
inference(superposition,[status(thm)],[c_1102,c_59]) ).
tcf(c_1183,plain,
! [X0: $i] :
( aSubsetOf0(X0,xS)
| ~ aElementOf0(X0,szDzozmdt0(xc)) ),
inference(global_subsumption_just,[status(thm)],[c_647,c_366,c_94,c_501]) ).
tcf(c_1190,plain,
( aSubsetOf0(sK4(szDzozmdt0(xc)),xS)
| ( szDzozmdt0(xc) = slcrc0 )
| ~ aSet0(szDzozmdt0(xc)) ),
inference(superposition,[status(thm)],[c_50,c_1183]) ).
tcf(c_1284,plain,
! [X0: $i] :
( ( sbrdtbr0(X0) = xK )
| ~ aElementOf0(X0,szDzozmdt0(xc)) ),
inference(global_subsumption_just,[status(thm)],[c_687,c_194,c_94,c_501,c_687]) ).
tcf(c_1291,plain,
( ( szDzozmdt0(xc) = slcrc0 )
| ( sbrdtbr0(sK4(szDzozmdt0(xc))) = xK )
| ~ aSet0(szDzozmdt0(xc)) ),
inference(superposition,[status(thm)],[c_50,c_1284]) ).
tcf(c_1367,plain,
! [X0: $i] :
( aElementOf0(slcrc0,slbdtsldtrb0(X0,xK))
| ~ aSet0(X0)
| ~ aElementOf0(xK,szNzAzT0)
| ~ aSubsetOf0(slcrc0,X0) ),
inference(light_normalisation,[status(thm)],[c_698,c_475]) ).
tcf(c_1372,plain,
! [X0: $i] :
( aElementOf0(slcrc0,slbdtsldtrb0(X0,xK))
| ~ aSet0(X0)
| ~ aSubsetOf0(slcrc0,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1367,c_194]) ).
tcf(c_1383,plain,
( ~ aSet0(xS)
| ~ aSubsetOf0(slcrc0,xS) ),
inference(superposition,[status(thm)],[c_1372,c_204]) ).
tcf(c_2318,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sK4(X0),X2)
| ( X0 = slcrc0 )
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1112,c_58]) ).
tcf(c_2469,plain,
aSubsetOf0(sK4(szDzozmdt0(xc)),xS),
inference(global_subsumption_just,[status(thm)],[c_1190,c_196,c_358,c_395,c_94,c_501,c_822]) ).
tcf(c_2471,plain,
! [X0: $i] :
( aElementOf0(sK4(sK4(szDzozmdt0(xc))),X0)
| ( sK4(szDzozmdt0(xc)) = slcrc0 )
| ~ aSet0(X0)
| ~ aSubsetOf0(xS,X0) ),
inference(superposition,[status(thm)],[c_2469,c_2318]) ).
tcf(c_2477,plain,
( aSet0(sK4(szDzozmdt0(xc)))
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_2469,c_58]) ).
tcf(c_2601,plain,
sbrdtbr0(sK4(szDzozmdt0(xc))) = xK,
inference(global_subsumption_just,[status(thm)],[c_1291,c_196,c_194,c_265,c_358,c_94,c_501,c_822,c_1291]) ).
tcf(c_2616,plain,
( ( sK4(szDzozmdt0(xc)) = slcrc0 )
| ~ aSet0(sK4(szDzozmdt0(xc))) ),
inference(superposition,[status(thm)],[c_2601,c_117]) ).
tcf(c_2881,plain,
~ aSubsetOf0(slcrc0,xS),
inference(global_subsumption_just,[status(thm)],[c_1383,c_94,c_501,c_1383]) ).
tcf(c_6208,plain,
sK4(szDzozmdt0(xc)) = slcrc0,
inference(global_subsumption_just,[status(thm)],[c_2471,c_94,c_501,c_2477,c_2616]) ).
tcf(c_6225,plain,
aSubsetOf0(slcrc0,xS),
inference(superposition,[status(thm)],[c_6208,c_2469]) ).
tcf(c_6226,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_2881,c_6225]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM564+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 04:39:39 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 3.54/1.20 % SZS status Started for theBenchmark.p
% 3.54/1.20 % SZS status Theorem for theBenchmark.p
% 3.54/1.20
% 3.54/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.54/1.20
% 3.54/1.20 % ------ iProver source info
% 3.54/1.20
% 3.54/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 3.54/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.54/1.20 % git: non_committed_changes: false
% 3.54/1.20
% 3.54/1.20 % ------ Parsing...
% 3.54/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.54/1.20 % ------ Proving...
% 3.54/1.20 % ------ Problem Properties
% 3.54/1.20
% 3.54/1.20 %
% 3.54/1.20 % clauses 156
% 3.54/1.20 % conjectures 1
% 3.54/1.20 % EPR 37
% 3.54/1.20 % Horn 117
% 3.54/1.20 % unary 16
% 3.54/1.20 % binary 22
% 3.54/1.20 % lits 582
% 3.54/1.20 % lits eq 82
% 3.54/1.20 % fd_pure 0
% 3.54/1.20 % fd_pseudo 0
% 3.54/1.20 % fd_cond 10
% 3.54/1.20 % fd_pseudo_cond 24
% 3.54/1.20 % AC symbols 0
% 3.54/1.20
% 3.54/1.20 % ------ Input Options Time Limit: Unbounded
% 3.54/1.20
% 3.54/1.20
% 3.54/1.20 % ------
% 3.54/1.20 % Current options:
% 3.54/1.20 % ------
% 3.54/1.20
% 3.54/1.20
% 3.54/1.20 %
% 3.54/1.20
% 3.54/1.20 % ------ Proving...
% 3.54/1.20 %
% 3.54/1.20
% 3.54/1.20 % ------ Proving...
% 3.54/1.20 %
% 3.54/1.20
% 3.54/1.20 % SZS status Theorem for theBenchmark.p
% 3.54/1.20
% 3.54/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.40/1.20
% 4.40/1.20
%------------------------------------------------------------------------------