%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM563+3 : 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 : n006.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 62.82s 11.39s
% Output : CNFRefutation 62.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 98 ( 27 unt; 3 def)
% Number of atoms : 492 ( 118 equ)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 530 ( 169 ~; 151 |; 177 &)
% ( 8 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 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 : 10 ( 8 usr; 3 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-2 aty)
% Number of variables : 159 ( 0 sgn 131 !; 28 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( ~ ? [X1] : aElementOf0(X1,X0)
& aSet0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
fof(f12,axiom,
! [X0] :
( aSet0(X0)
=> aSubsetOf0(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
fof(f42,axiom,
! [X0] :
( aSet0(X0)
=> ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
fof(f52,axiom,
slbdtrb0(sz00) = slcrc0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegZero) ).
fof(f75,axiom,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,szNzAzT0) )
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
fof(f76,axiom,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& ! [X0] :
( aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
=> aElementOf0(X0,xT) )
& ! [X0] :
( aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> ? [X1] :
( sdtlpdtrp0(xc,X1) = X0
& aElementOf0(X1,szDzozmdt0(xc)) ) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& ! [X0] :
( ( ( sbrdtbr0(X0) = xK
& ( aSubsetOf0(X0,xS)
| ( ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
=> aElementOf0(X0,szDzozmdt0(xc)) )
& ( aElementOf0(X0,szDzozmdt0(xc))
=> ( sbrdtbr0(X0) = xK
& aSubsetOf0(X0,xS)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
& aFunction0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3453) ).
fof(f78,conjecture,
( xK = sz00
=> ? [X0] :
( ? [X1] :
( ! [X2] :
( ( aElementOf0(X2,slbdtsldtrb0(X1,xK))
& sbrdtbr0(X2) = xK
& aSubsetOf0(X2,X1)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSet0(X2) )
=> sdtlpdtrp0(xc,X2) = X0 )
& isCountable0(X1)
& ( aSubsetOf0(X1,xS)
| ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xS) )
& aSet0(X1) ) ) )
& aElementOf0(X0,xT) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f79,negated_conjecture,
~ ( xK = sz00
=> ? [X0] :
( ? [X1] :
( ! [X2] :
( ( aElementOf0(X2,slbdtsldtrb0(X1,xK))
& sbrdtbr0(X2) = xK
& aSubsetOf0(X2,X1)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSet0(X2) )
=> sdtlpdtrp0(xc,X2) = X0 )
& isCountable0(X1)
& ( aSubsetOf0(X1,xS)
| ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xS) )
& aSet0(X1) ) ) )
& aElementOf0(X0,xT) ) ),
inference(negated_conjecture,[status(cth)],[f78]) ).
fof(f87,plain,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& ! [X5] :
( aElementOf0(X5,sdtlcdtrc0(xc,szDzozmdt0(xc)))
=> aElementOf0(X5,xT) )
& ! [X3] :
( aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> ? [X4] :
( sdtlpdtrp0(xc,X4) = X3
& aElementOf0(X4,szDzozmdt0(xc)) ) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& ! [X0] :
( ( ( sbrdtbr0(X0) = xK
& ( aSubsetOf0(X0,xS)
| ( ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(X2,xS) )
& aSet0(X0) ) ) )
=> aElementOf0(X0,szDzozmdt0(xc)) )
& ( aElementOf0(X0,szDzozmdt0(xc))
=> ( sbrdtbr0(X0) = xK
& aSubsetOf0(X0,xS)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
& aFunction0(xc) ),
inference(rectify,[],[f76]) ).
fof(f89,plain,
~ ( xK = sz00
=> ? [X0] :
( ? [X1] :
( ! [X3] :
( ( aElementOf0(X3,slbdtsldtrb0(X1,xK))
& sbrdtbr0(X3) = xK
& aSubsetOf0(X3,X1)
& ! [X4] :
( aElementOf0(X4,X3)
=> aElementOf0(X4,X1) )
& aSet0(X3) )
=> sdtlpdtrp0(xc,X3) = X0 )
& isCountable0(X1)
& ( aSubsetOf0(X1,xS)
| ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xS) )
& aSet0(X1) ) ) )
& aElementOf0(X0,xT) ) ),
inference(rectify,[],[f79]) ).
fof(f91,plain,
! [X0] :
( X0 = slcrc0
<=> ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f99,plain,
! [X0] :
( ~ aSet0(X0)
| aSubsetOf0(X0,X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f140,plain,
! [X0] :
( ~ aSet0(X0)
| ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f189,plain,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [X0] :
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,szNzAzT0) )
& aSet0(xS) ),
inference(ennf_transformation,[],[f75]) ).
fof(f190,plain,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& ! [X5] :
( ~ aElementOf0(X5,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(X5,xT) )
& ! [X3] :
( aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> ? [X4] :
( sdtlpdtrp0(xc,X4) = X3
& aElementOf0(X4,szDzozmdt0(xc)) ) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& ! [X0] :
( ( sbrdtbr0(X0) != xK
| ( ~ aSubsetOf0(X0,xS)
& ( ? [X2] :
( aElementOf0(X2,X0)
& ~ aElementOf0(X2,xS) )
| ~ aSet0(X0) ) )
| aElementOf0(X0,szDzozmdt0(xc)) )
& ( ~ aElementOf0(X0,szDzozmdt0(xc))
| ( sbrdtbr0(X0) = xK
& aSubsetOf0(X0,xS)
& ! [X1] :
( ~ aElementOf0(X1,X0)
| aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
& aFunction0(xc) ),
inference(ennf_transformation,[],[f87]) ).
fof(f191,plain,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& ! [X5] :
( ~ aElementOf0(X5,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(X5,xT) )
& ! [X3] :
( aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> ? [X4] :
( sdtlpdtrp0(xc,X4) = X3
& aElementOf0(X4,szDzozmdt0(xc)) ) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& ! [X0] :
( ( sbrdtbr0(X0) != xK
| ( ~ aSubsetOf0(X0,xS)
& ( ? [X2] :
( aElementOf0(X2,X0)
& ~ aElementOf0(X2,xS) )
| ~ aSet0(X0) ) )
| aElementOf0(X0,szDzozmdt0(xc)) )
& ( ~ aElementOf0(X0,szDzozmdt0(xc))
| ( sbrdtbr0(X0) = xK
& aSubsetOf0(X0,xS)
& ! [X1] :
( ~ aElementOf0(X1,X0)
| aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
& aFunction0(xc) ),
inference(flattening,[],[f190]) ).
fof(f194,plain,
( xK = sz00
& ! [X0] :
( ! [X1] :
( ? [X3] :
( aElementOf0(X3,slbdtsldtrb0(X1,xK))
& sbrdtbr0(X3) = xK
& aSubsetOf0(X3,X1)
& ! [X4] :
( ~ aElementOf0(X4,X3)
| aElementOf0(X4,X1) )
& aSet0(X3)
& sdtlpdtrp0(xc,X3) != X0 )
| ~ isCountable0(X1)
| ( ~ aSubsetOf0(X1,xS)
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,xS) )
| ~ aSet0(X1) ) ) )
| ~ aElementOf0(X0,xT) ) ),
inference(ennf_transformation,[],[f89]) ).
fof(f195,plain,
( xK = sz00
& ! [X0] :
( ! [X1] :
( ? [X3] :
( aElementOf0(X3,slbdtsldtrb0(X1,xK))
& sbrdtbr0(X3) = xK
& aSubsetOf0(X3,X1)
& ! [X4] :
( ~ aElementOf0(X4,X3)
| aElementOf0(X4,X1) )
& aSet0(X3)
& sdtlpdtrp0(xc,X3) != X0 )
| ~ isCountable0(X1)
| ( ~ aSubsetOf0(X1,xS)
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,xS) )
| ~ aSet0(X1) ) ) )
| ~ aElementOf0(X0,xT) ) ),
inference(flattening,[],[f194]) ).
fof(f209,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(nnf_transformation,[],[f91]) ).
fof(f210,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(flattening,[],[f209]) ).
fof(f211,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(rectify,[],[f210]) ).
fof(f212,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) ) )
& ( aElementOf0(sK9(X0),X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X1,sK9(X0))],[f211]) ).
fof(f232,plain,
! [X0] :
( ~ aSet0(X0)
| ( ( sz00 != sbrdtbr0(X0)
| X0 = slcrc0 )
& ( slcrc0 != X0
| sbrdtbr0(X0) = sz00 ) ) ),
inference(nnf_transformation,[],[f140]) ).
fof(f268,plain,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& ! [X5] :
( ~ aElementOf0(X5,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(X5,xT) )
& ! [X3] :
( ( ~ aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ? [X4] :
( sdtlpdtrp0(xc,X4) = X3
& aElementOf0(X4,szDzozmdt0(xc)) ) )
& ( ! [X4] :
( sdtlpdtrp0(xc,X4) != X3
| ~ aElementOf0(X4,szDzozmdt0(xc)) )
| aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc))) ) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& ! [X0] :
( ( sbrdtbr0(X0) != xK
| ( ~ aSubsetOf0(X0,xS)
& ( ? [X2] :
( aElementOf0(X2,X0)
& ~ aElementOf0(X2,xS) )
| ~ aSet0(X0) ) )
| aElementOf0(X0,szDzozmdt0(xc)) )
& ( ~ aElementOf0(X0,szDzozmdt0(xc))
| ( sbrdtbr0(X0) = xK
& aSubsetOf0(X0,xS)
& ! [X1] :
( ~ aElementOf0(X1,X0)
| aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
& aFunction0(xc) ),
inference(nnf_transformation,[],[f191]) ).
fof(f269,plain,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& ! [X6] :
( ~ aElementOf0(X6,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(X6,xT) )
& ! [X3] :
( ( ~ aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ? [X5] :
( sdtlpdtrp0(xc,X5) = X3
& aElementOf0(X5,szDzozmdt0(xc)) ) )
& ( ! [X4] :
( sdtlpdtrp0(xc,X4) != X3
| ~ aElementOf0(X4,szDzozmdt0(xc)) )
| aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc))) ) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& ! [X0] :
( ( sbrdtbr0(X0) != xK
| ( ~ aSubsetOf0(X0,xS)
& ( ? [X2] :
( aElementOf0(X2,X0)
& ~ aElementOf0(X2,xS) )
| ~ aSet0(X0) ) )
| aElementOf0(X0,szDzozmdt0(xc)) )
& ( ~ aElementOf0(X0,szDzozmdt0(xc))
| ( sbrdtbr0(X0) = xK
& aSubsetOf0(X0,xS)
& ! [X1] :
( ~ aElementOf0(X1,X0)
| aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
& aFunction0(xc) ),
inference(rectify,[],[f268]) ).
fof(f270,plain,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& ! [X6] :
( ~ aElementOf0(X6,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(X6,xT) )
& ! [X3] :
( ( ~ aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ( sdtlpdtrp0(xc,sK29(X3)) = X3
& aElementOf0(sK29(X3),szDzozmdt0(xc)) ) )
& ( ! [X4] :
( sdtlpdtrp0(xc,X4) != X3
| ~ aElementOf0(X4,szDzozmdt0(xc)) )
| aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc))) ) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& ! [X0] :
( ( sbrdtbr0(X0) != xK
| ( ~ aSubsetOf0(X0,xS)
& ( ( aElementOf0(sK28(X0),X0)
& ~ aElementOf0(sK28(X0),xS) )
| ~ aSet0(X0) ) )
| aElementOf0(X0,szDzozmdt0(xc)) )
& ( ~ aElementOf0(X0,szDzozmdt0(xc))
| ( sbrdtbr0(X0) = xK
& aSubsetOf0(X0,xS)
& ! [X1] :
( ~ aElementOf0(X1,X0)
| aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
& aFunction0(xc) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28,sK29]),skolemize(X2,sK28(X0)),skolemize(X5,sK29(X3))],[f269]) ).
fof(f287,plain,
( xK = sz00
& ! [X0] :
( ! [X1] :
( sP8(X0,X1)
| ~ isCountable0(X1)
| ( ~ aSubsetOf0(X1,xS)
& ( ( aElementOf0(sK39(X1),X1)
& ~ aElementOf0(sK39(X1),xS) )
| ~ aSet0(X1) ) ) )
| ~ aElementOf0(X0,xT) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(X2,sK39(X1))],[f208]) ).
fof(f289,plain,
! [X2,X0] :
( slcrc0 != X0
| ~ aElementOf0(X2,X0) ),
inference(cnf_transformation,[],[f212]) ).
fof(f290,plain,
! [X0] :
( slcrc0 != X0
| aSet0(X0) ),
inference(cnf_transformation,[],[f212]) ).
fof(f300,plain,
! [X0] :
( ~ aSet0(X0)
| aSubsetOf0(X0,X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f355,plain,
! [X0] :
( ~ aSet0(X0)
| sz00 != sbrdtbr0(X0)
| slcrc0 = X0 ),
inference(cnf_transformation,[],[f232]) ).
fof(f356,plain,
! [X0] :
( ~ aSet0(X0)
| slcrc0 != X0
| sz00 = sbrdtbr0(X0) ),
inference(cnf_transformation,[],[f232]) ).
fof(f379,plain,
slcrc0 = slbdtrb0(sz00),
inference(cnf_transformation,[],[f52]) ).
fof(f434,plain,
isCountable0(xS),
inference(cnf_transformation,[],[f189]) ).
fof(f437,plain,
aSet0(xS),
inference(cnf_transformation,[],[f189]) ).
fof(f439,plain,
! [X6] :
( ~ aElementOf0(X6,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(X6,xT) ),
inference(cnf_transformation,[],[f270]) ).
fof(f442,plain,
! [X3,X4] :
( sdtlpdtrp0(xc,X4) != X3
| ~ aElementOf0(X4,szDzozmdt0(xc))
| aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(cnf_transformation,[],[f270]) ).
fof(f446,plain,
! [X0] :
( sbrdtbr0(X0) != xK
| aElementOf0(sK28(X0),X0)
| ~ aSet0(X0)
| aElementOf0(X0,szDzozmdt0(xc)) ),
inference(cnf_transformation,[],[f270]) ).
fof(f490,plain,
sz00 = xK,
inference(cnf_transformation,[],[f287]) ).
fof(f491,plain,
! [X0,X1] :
( sP8(X0,X1)
| ~ isCountable0(X1)
| ~ aSubsetOf0(X1,xS)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[],[f287]) ).
fof(f500,plain,
! [X0] :
( ~ aSet0(X0)
| slcrc0 != X0
| sbrdtbr0(X0) = xK ),
inference(definition_unfolding,[],[f356,f490]) ).
fof(f501,plain,
! [X0] :
( ~ aSet0(X0)
| sbrdtbr0(X0) != xK
| slcrc0 = X0 ),
inference(definition_unfolding,[],[f355,f490]) ).
fof(f502,plain,
slcrc0 = slbdtrb0(xK),
inference(definition_unfolding,[],[f379,f490]) ).
fof(f505,plain,
aSet0(slcrc0),
inference(equality_resolution,[],[f290]) ).
fof(f506,plain,
! [X2] : ~ aElementOf0(X2,slcrc0),
inference(equality_resolution,[],[f289]) ).
fof(f512,plain,
( ~ aSet0(slcrc0)
| xK = sbrdtbr0(slcrc0) ),
inference(equality_resolution,[],[f500]) ).
fof(f542,plain,
! [X4] :
( ~ aElementOf0(X4,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,X4),sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(equality_resolution,[],[f442]) ).
tcf(c_51,plain,
aSet0(slcrc0),
inference(cnf_transformation,[],[f505]) ).
tcf(c_52,plain,
! [X0: $i] : ~ aElementOf0(X0,slcrc0),
inference(cnf_transformation,[],[f506]) ).
tcf(c_61,plain,
! [X0: $i] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f300]) ).
tcf(c_116,negated_conjecture,
( ( sbrdtbr0(slcrc0) = xK )
| ~ aSet0(slcrc0) ),
inference(cnf_transformation,[],[f512]) ).
tcf(c_117,negated_conjecture,
! [X0: $i] :
( ( X0 = slcrc0 )
| ~ aSet0(X0)
| ( sbrdtbr0(X0) != xK ) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_140,negated_conjecture,
slbdtrb0(xK) = slcrc0,
inference(cnf_transformation,[],[f502]) ).
tcf(c_195,plain,
aSet0(xS),
inference(cnf_transformation,[],[f437]) ).
tcf(c_198,plain,
isCountable0(xS),
inference(cnf_transformation,[],[f434]) ).
tcf(c_205,plain,
! [X0: $i] :
( aElementOf0(X0,szDzozmdt0(xc))
| aElementOf0(sK28(X0),X0)
| ~ aSet0(X0)
| ( sbrdtbr0(X0) != xK ) ),
inference(cnf_transformation,[],[f446]) ).
tcf(c_209,plain,
! [X0: $i] :
( aElementOf0(sdtlpdtrp0(xc,X0),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ aElementOf0(X0,szDzozmdt0(xc)) ),
inference(cnf_transformation,[],[f542]) ).
tcf(c_212,plain,
! [X0: $i] :
( aElementOf0(X0,xT)
| ~ aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(cnf_transformation,[],[f439]) ).
tcf(c_253,negated_conjecture,
! [X0: $i,X1: $i] :
( sP8(X0,X1)
| ~ isCountable0(X1)
| ~ aSubsetOf0(X1,xS)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[],[f491]) ).
tcf(c_416,negated_conjecture,
sbrdtbr0(slcrc0) = xK,
inference(global_subsumption_just,[status(thm)],[c_116,c_51,c_116]) ).
tcf(c_15960,definition,
iPr_def_10 = sbrdtbr0(slcrc0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_15961,definition,
iPr_def_11 = slbdtrb0(xK),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_15962,negated_conjecture,
iPr_def_10 = xK,
inference(demodulation,[status(thm)],[c_416,c_15960]) ).
tcf(c_15963,negated_conjecture,
! [X0: $i,X1: $i] :
( sP8(X0,X1)
| ~ isCountable0(X1)
| ~ aSubsetOf0(X1,xS)
| ~ aElementOf0(X0,xT) ),
inference(demodulation,[status(thm)],[c_253]) ).
tcf(c_15968,negated_conjecture,
iPr_def_11 = slcrc0,
inference(demodulation,[status(thm)],[c_140,c_15961]) ).
tcf(c_15969,negated_conjecture,
! [X0: $i] :
( ( X0 = slcrc0 )
| ~ aSet0(X0)
| ( sbrdtbr0(X0) != xK ) ),
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_18679,plain,
! [X0: $i] :
( ( X0 = iPr_def_11 )
| ~ aSet0(X0)
| ( sbrdtbr0(X0) != iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_15969,c_15962,c_15968]) ).
tcf(c_18689,plain,
sbrdtbr0(iPr_def_11) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_15960,c_15968]) ).
tcf(c_18691,plain,
aSet0(iPr_def_11),
inference(light_normalisation,[status(thm)],[c_51,c_15968]) ).
tcf(c_18804,plain,
! [X0: $i] : ~ aElementOf0(X0,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_52,c_15968]) ).
tcf(c_18811,plain,
! [X0: $i] :
( sP8(X0,xS)
| ~ isCountable0(xS)
| ~ aSet0(xS)
| ~ aElementOf0(X0,xT) ),
inference(superposition,[status(thm)],[c_61,c_15963]) ).
tcf(c_18812,plain,
! [X0: $i] :
( sP8(X0,xS)
| ~ aElementOf0(X0,xT) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18811,c_198,c_195]) ).
tcf(c_22775,plain,
! [X0: $i] :
( aElementOf0(sdtlpdtrp0(xc,X0),xT)
| ~ aElementOf0(X0,szDzozmdt0(xc)) ),
inference(superposition,[status(thm)],[c_209,c_212]) ).
tcf(c_28932,plain,
! [X0: $i] :
( sP8(sdtlpdtrp0(xc,X0),xS)
| ~ aElementOf0(X0,szDzozmdt0(xc)) ),
inference(superposition,[status(thm)],[c_22775,c_18812]) ).
tcf(c_33774,plain,
! [X0: $i] :
( aElementOf0(X0,szDzozmdt0(xc))
| aElementOf0(sK28(X0),X0)
| ~ aSet0(X0)
| ( sbrdtbr0(X0) != iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_205,c_15962]) ).
tcf(c_33787,plain,
( aElementOf0(iPr_def_11,szDzozmdt0(xc))
| aElementOf0(sK28(iPr_def_11),iPr_def_11)
| ~ aSet0(iPr_def_11) ),
inference(superposition,[status(thm)],[c_18689,c_33774]) ).
tcf(c_33792,plain,
aElementOf0(iPr_def_11,szDzozmdt0(xc)),
inference(forward_subsumption_resolution,[status(thm)],[c_33787,c_18804,c_18691]) ).
fof(f207,definition,
! [X0,X1] :
( ~ sP8(X0,X1)
| ? [X3] :
( aElementOf0(X3,slbdtsldtrb0(X1,xK))
& sbrdtbr0(X3) = xK
& aSubsetOf0(X3,X1)
& ! [X4] :
( ~ aElementOf0(X4,X3)
| aElementOf0(X4,X1) )
& aSet0(X3)
& sdtlpdtrp0(xc,X3) != X0 ) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f208,plain,
( xK = sz00
& ! [X0] :
( ! [X1] :
( sP8(X0,X1)
| ~ isCountable0(X1)
| ( ~ aSubsetOf0(X1,xS)
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,xS) )
| ~ aSet0(X1) ) ) )
| ~ aElementOf0(X0,xT) ) ),
inference(definition_folding,[],[f195,f207]) ).
fof(f284,plain,
! [X0,X1] :
( ~ sP8(X0,X1)
| ? [X3] :
( aElementOf0(X3,slbdtsldtrb0(X1,xK))
& sbrdtbr0(X3) = xK
& aSubsetOf0(X3,X1)
& ! [X4] :
( ~ aElementOf0(X4,X3)
| aElementOf0(X4,X1) )
& aSet0(X3)
& sdtlpdtrp0(xc,X3) != X0 ) ),
inference(nnf_transformation,[],[f207]) ).
fof(f285,plain,
! [X0,X1] :
( ~ sP8(X0,X1)
| ? [X2] :
( aElementOf0(X2,slbdtsldtrb0(X1,xK))
& sbrdtbr0(X2) = xK
& aSubsetOf0(X2,X1)
& ! [X3] :
( ~ aElementOf0(X3,X2)
| aElementOf0(X3,X1) )
& aSet0(X2)
& sdtlpdtrp0(xc,X2) != X0 ) ),
inference(rectify,[],[f284]) ).
fof(f286,plain,
! [X0,X1] :
( ~ sP8(X0,X1)
| ( aElementOf0(sK38(X0,X1),slbdtsldtrb0(X1,xK))
& xK = sbrdtbr0(sK38(X0,X1))
& aSubsetOf0(sK38(X0,X1),X1)
& ! [X3] :
( ~ aElementOf0(X3,sK38(X0,X1))
| aElementOf0(X3,X1) )
& aSet0(sK38(X0,X1))
& sdtlpdtrp0(xc,sK38(X0,X1)) != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(X2,sK38(X0,X1))],[f285]) ).
fof(f485,plain,
! [X0,X1] :
( ~ sP8(X0,X1)
| xK = sbrdtbr0(sK38(X0,X1)) ),
inference(cnf_transformation,[],[f286]) ).
fof(f488,plain,
! [X0,X1] :
( ~ sP8(X0,X1)
| aSet0(sK38(X0,X1)) ),
inference(cnf_transformation,[],[f286]) ).
fof(f489,plain,
! [X0,X1] :
( ~ sP8(X0,X1)
| sdtlpdtrp0(xc,sK38(X0,X1)) != X0 ),
inference(cnf_transformation,[],[f286]) ).
tcf(c_245,plain,
! [X0: $i,X1: $i] :
( ~ sP8(X0,X1)
| ( sdtlpdtrp0(xc,sK38(X0,X1)) != X0 ) ),
inference(cnf_transformation,[],[f489]) ).
tcf(c_246,plain,
! [X0: $i,X1: $i] :
( aSet0(sK38(X0,X1))
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f488]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i] :
( ( sbrdtbr0(sK38(X0,X1)) = xK )
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f485]) ).
tcf(c_20705,plain,
! [X0: $i,X1: $i] :
( ( sbrdtbr0(sK38(X0,X1)) = iPr_def_10 )
| ~ sP8(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_249,c_15962]) ).
tcf(c_32592,plain,
! [X0: $i] :
( ( sbrdtbr0(sK38(sdtlpdtrp0(xc,X0),xS)) = iPr_def_10 )
| ~ aElementOf0(X0,szDzozmdt0(xc)) ),
inference(superposition,[status(thm)],[c_28932,c_20705]) ).
tcf(c_33817,plain,
sbrdtbr0(sK38(sdtlpdtrp0(xc,iPr_def_11),xS)) = iPr_def_10,
inference(superposition,[status(thm)],[c_33792,c_32592]) ).
tcf(c_34441,plain,
( ( sK38(sdtlpdtrp0(xc,iPr_def_11),xS) = iPr_def_11 )
| ~ aSet0(sK38(sdtlpdtrp0(xc,iPr_def_11),xS)) ),
inference(superposition,[status(thm)],[c_33817,c_18679]) ).
tcf(c_34615,plain,
( ( sK38(sdtlpdtrp0(xc,iPr_def_11),xS) = iPr_def_11 )
| ~ sP8(sdtlpdtrp0(xc,iPr_def_11),xS) ),
inference(superposition,[status(thm)],[c_246,c_34441]) ).
tcf(c_163664,plain,
( ( sK38(sdtlpdtrp0(xc,iPr_def_11),xS) = iPr_def_11 )
| ~ aElementOf0(iPr_def_11,szDzozmdt0(xc)) ),
inference(superposition,[status(thm)],[c_28932,c_34615]) ).
tcf(c_163665,plain,
sK38(sdtlpdtrp0(xc,iPr_def_11),xS) = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_163664,c_33792]) ).
tcf(c_163680,plain,
~ sP8(sdtlpdtrp0(xc,iPr_def_11),xS),
inference(superposition,[status(thm)],[c_163665,c_245]) ).
tcf(c_163696,plain,
~ aElementOf0(iPr_def_11,szDzozmdt0(xc)),
inference(superposition,[status(thm)],[c_28932,c_163680]) ).
tcf(c_163697,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_163696,c_33792]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM563+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 04:38:43 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 62.82/11.39 % SZS status Started for theBenchmark.p
% 62.82/11.39 % SZS status Theorem for theBenchmark.p
% 62.82/11.39
% 62.82/11.39 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 62.82/11.39
% 62.82/11.39 % ------ iProver source info
% 62.82/11.39
% 62.82/11.39 % git: date: 2026-07-19 20:42:38 +0200
% 62.82/11.39 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 62.82/11.39 % git: non_committed_changes: false
% 62.82/11.39
% 62.82/11.39 % ------ Parsing...
% 62.82/11.39 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 62.82/11.39
% 62.82/11.39 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 62.82/11.39
% 62.82/11.39 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 62.82/11.39
% 62.82/11.39 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 62.82/11.39 % ------ Proving...
% 62.82/11.39 % ------ Problem Properties
% 62.82/11.39
% 62.82/11.39 %
% 62.82/11.39 % clauses 172
% 62.82/11.39 % conjectures 14
% 62.82/11.39 % EPR 39
% 62.82/11.39 % Horn 131
% 62.82/11.39 % unary 20
% 62.82/11.39 % binary 30
% 62.82/11.39 % lits 593
% 62.82/11.39 % lits eq 86
% 62.82/11.39 % fd_pure 0
% 62.82/11.39 % fd_pseudo 0
% 62.82/11.39 % fd_cond 10
% 62.82/11.39 % fd_pseudo_cond 24
% 62.82/11.39 % AC symbols 0
% 62.82/11.39
% 62.82/11.39 % ------ Schedule dynamic 5 is on
% 62.82/11.39
% 62.82/11.39 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 62.82/11.39
% 62.82/11.39
% 62.82/11.39 % ------
% 62.82/11.39 % Current options:
% 62.82/11.39 % ------
% 62.82/11.39
% 62.82/11.39
% 62.82/11.39 %
% 62.82/11.39
% 62.82/11.39 % ------ Proving...
% 62.82/11.39 %
% 62.82/11.39
% 62.82/11.39 % SZS status Theorem for theBenchmark.p
% 62.82/11.39
% 62.82/11.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 62.82/11.39
% 62.82/11.39
%------------------------------------------------------------------------------