%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM566+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n011.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 17.20s 3.21s
% Output : CNFRefutation 17.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 80 ( 17 unt; 1 def)
% Number of atoms : 432 ( 80 equ)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 513 ( 161 ~; 147 |; 175 &)
% ( 6 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 150 ( 0 sgn 124 !; 26 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0] :
( aSet0(X0)
=> aSubsetOf0(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubRefl) ).
fof(f42,axiom,
! [X0] :
( aSet0(X0)
=> ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardEmpty) ).
fof(f75,axiom,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,szNzAzT0) )
& aSet0(xS) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',m__3453) ).
fof(f78,axiom,
xK = sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3462) ).
fof(f79,axiom,
( aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00))
& aSubsetOf0(slcrc0,xS)
& ! [X0] :
( aElementOf0(X0,slcrc0)
=> aElementOf0(X0,xS) )
& ~ ? [X0] : aElementOf0(X0,slcrc0)
& aSet0(slcrc0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3476) ).
fof(f81,conjecture,
? [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/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f82,negated_conjecture,
~ ? [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)],[f81]) ).
fof(f83,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(f85,plain,
( aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00))
& aSubsetOf0(slcrc0,xS)
& ! [X1] :
( aElementOf0(X1,slcrc0)
=> aElementOf0(X1,xS) )
& ~ ? [X0] : aElementOf0(X0,slcrc0)
& aSet0(slcrc0) ),
inference(rectify,[],[f79]) ).
fof(f87,plain,
~ ? [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,[],[f82]) ).
fof(f98,plain,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [X0] :
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,szNzAzT0) )
& aSet0(xS) ),
inference(ennf_transformation,[],[f75]) ).
fof(f99,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,[],[f83]) ).
fof(f100,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,[],[f99]) ).
fof(f103,plain,
( aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00))
& aSubsetOf0(slcrc0,xS)
& ! [X1] :
( ~ aElementOf0(X1,slcrc0)
| aElementOf0(X1,xS) )
& ! [X0] : ~ aElementOf0(X0,slcrc0)
& aSet0(slcrc0) ),
inference(ennf_transformation,[],[f85]) ).
fof(f105,plain,
! [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,[],[f87]) ).
fof(f106,plain,
! [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,[],[f105]) ).
fof(f124,plain,
! [X0] :
( ~ aSet0(X0)
| aSubsetOf0(X0,X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f128,plain,
! [X0] :
( ~ aSet0(X0)
| ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f171,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,[],[f100]) ).
fof(f172,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,[],[f171]) ).
fof(f173,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,sK7(X3)) = X3
& aElementOf0(sK7(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(sK6(X0),X0)
& ~ aElementOf0(sK6(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,[sK6,sK7]),skolemize(X2,sK6(X0)),skolemize(X5,sK7(X3))],[f172]) ).
fof(f193,plain,
! [X0] :
( ! [X1] :
( sP5(X0,X1)
| ~ isCountable0(X1)
| ( ~ aSubsetOf0(X1,xS)
& ( ( aElementOf0(sK18(X1),X1)
& ~ aElementOf0(sK18(X1),xS) )
| ~ aSet0(X1) ) ) )
| ~ aElementOf0(X0,xT) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(X2,sK18(X1))],[f170]) ).
fof(f204,plain,
! [X0] :
( ~ aSet0(X0)
| ( ( sz00 != sbrdtbr0(X0)
| X0 = slcrc0 )
& ( slcrc0 != X0
| sbrdtbr0(X0) = sz00 ) ) ),
inference(nnf_transformation,[],[f128]) ).
fof(f220,plain,
isCountable0(xS),
inference(cnf_transformation,[],[f98]) ).
fof(f223,plain,
aSet0(xS),
inference(cnf_transformation,[],[f98]) ).
fof(f225,plain,
! [X6] :
( ~ aElementOf0(X6,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(X6,xT) ),
inference(cnf_transformation,[],[f173]) ).
fof(f228,plain,
! [X3,X4] :
( sdtlpdtrp0(xc,X4) != X3
| ~ aElementOf0(X4,szDzozmdt0(xc))
| aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(cnf_transformation,[],[f173]) ).
fof(f230,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(cnf_transformation,[],[f173]) ).
fof(f270,plain,
sz00 = xK,
inference(cnf_transformation,[],[f78]) ).
fof(f271,plain,
aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(cnf_transformation,[],[f103]) ).
fof(f289,plain,
! [X0,X1] :
( sP5(X0,X1)
| ~ isCountable0(X1)
| ~ aSubsetOf0(X1,xS)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[],[f193]) ).
fof(f290,plain,
! [X0,X1] :
( sP5(X0,X1)
| ~ isCountable0(X1)
| aElementOf0(sK18(X1),X1)
| ~ aSet0(X1)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[],[f193]) ).
fof(f291,plain,
! [X0,X1] :
( sP5(X0,X1)
| ~ isCountable0(X1)
| ~ aElementOf0(sK18(X1),xS)
| ~ aSet0(X1)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[],[f193]) ).
fof(f305,plain,
! [X0] :
( ~ aSet0(X0)
| aSubsetOf0(X0,X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f317,plain,
! [X0] :
( ~ aSet0(X0)
| sz00 != sbrdtbr0(X0)
| slcrc0 = X0 ),
inference(cnf_transformation,[],[f204]) ).
fof(f359,plain,
aElementOf0(slcrc0,slbdtsldtrb0(xS,xK)),
inference(definition_unfolding,[],[f271,f270]) ).
fof(f366,plain,
! [X0] :
( ~ aSet0(X0)
| sbrdtbr0(X0) != xK
| slcrc0 = X0 ),
inference(definition_unfolding,[],[f317,f270]) ).
fof(f374,plain,
! [X4] :
( ~ aElementOf0(X4,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,X4),sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(equality_resolution,[],[f228]) ).
tcf(c_52,plain,
aSet0(xS),
inference(cnf_transformation,[],[f223]) ).
tcf(c_55,plain,
isCountable0(xS),
inference(cnf_transformation,[],[f220]) ).
tcf(c_64,plain,
slbdtsldtrb0(xS,xK) = szDzozmdt0(xc),
inference(cnf_transformation,[],[f230]) ).
tcf(c_66,plain,
! [X0: $i] :
( aElementOf0(sdtlpdtrp0(xc,X0),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ aElementOf0(X0,szDzozmdt0(xc)) ),
inference(cnf_transformation,[],[f374]) ).
tcf(c_69,plain,
! [X0: $i] :
( aElementOf0(X0,xT)
| ~ aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(cnf_transformation,[],[f225]) ).
tcf(c_106,plain,
aElementOf0(slcrc0,slbdtsldtrb0(xS,xK)),
inference(cnf_transformation,[],[f359]) ).
tcf(c_120,negated_conjecture,
! [X0: $i,X1: $i] :
( sP5(X1,X0)
| ~ isCountable0(X0)
| ~ aSet0(X0)
| ~ aElementOf0(X1,xT)
| ~ aElementOf0(sK18(X0),xS) ),
inference(cnf_transformation,[],[f291]) ).
tcf(c_121,negated_conjecture,
! [X0: $i,X1: $i] :
( sP5(X0,X1)
| aElementOf0(sK18(X1),X1)
| ~ isCountable0(X1)
| ~ aSet0(X1)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[],[f290]) ).
tcf(c_122,negated_conjecture,
! [X0: $i,X1: $i] :
( sP5(X0,X1)
| ~ isCountable0(X1)
| ~ aSubsetOf0(X1,xS)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[],[f289]) ).
tcf(c_136,plain,
! [X0: $i] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f305]) ).
tcf(c_149,plain,
! [X0: $i] :
( ( X0 = slcrc0 )
| ~ aSet0(X0)
| ( sbrdtbr0(X0) != xK ) ),
inference(cnf_transformation,[],[f366]) ).
tcf(c_1218,plain,
aElementOf0(slcrc0,szDzozmdt0(xc)),
inference(demodulation,[status(thm)],[c_106,c_64]) ).
tcf(c_5863,plain,
! [X0: $i,X1: $i] :
( sP5(X1,xS)
| sP5(X0,xS)
| ~ isCountable0(xS)
| ~ aSet0(xS)
| ~ aElementOf0(X1,xT)
| ~ aElementOf0(X0,xT) ),
inference(superposition,[status(thm)],[c_121,c_120]) ).
tcf(c_5871,plain,
! [X0: $i,X1: $i] :
( sP5(X1,xS)
| sP5(X0,xS)
| ~ aElementOf0(X1,xT)
| ~ aElementOf0(X0,xT) ),
inference(global_subsumption_just,[status(thm)],[c_5863,c_55,c_52,c_5863]) ).
tcf(c_7506,plain,
! [X0: $i] :
( aElementOf0(sdtlpdtrp0(xc,X0),xT)
| ~ aElementOf0(X0,szDzozmdt0(xc)) ),
inference(superposition,[status(thm)],[c_66,c_69]) ).
tcf(c_7783,plain,
! [X0: $i,X1: $i] :
( sP5(X1,xS)
| sP5(sdtlpdtrp0(xc,X0),xS)
| ~ aElementOf0(X1,xT)
| ~ aElementOf0(X0,szDzozmdt0(xc)) ),
inference(superposition,[status(thm)],[c_7506,c_5871]) ).
tcf(c_7784,plain,
! [X0: $i,X1: $i] :
( sP5(sdtlpdtrp0(xc,X0),X1)
| ~ isCountable0(X1)
| ~ aSubsetOf0(X1,xS)
| ~ aElementOf0(X0,szDzozmdt0(xc)) ),
inference(superposition,[status(thm)],[c_7506,c_122]) ).
tcf(c_8161,plain,
! [X0: $i] :
( sP5(sdtlpdtrp0(xc,X0),xS)
| ~ aElementOf0(X0,szDzozmdt0(xc))
| ~ aElementOf0(sdtlpdtrp0(xc,X0),xT) ),
inference(equality_factoring,[status(thm)],[c_7783]) ).
tcf(c_18902,plain,
! [X0: $i] :
( sP5(sdtlpdtrp0(xc,X0),xS)
| ~ aElementOf0(X0,szDzozmdt0(xc)) ),
inference(global_subsumption_just,[status(thm)],[c_8161,c_7506,c_8161]) ).
fof(f169,definition,
! [X0,X1] :
( ~ sP5(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,[sP5])],[predicate_definition_introduction]) ).
fof(f170,plain,
! [X0] :
( ! [X1] :
( sP5(X0,X1)
| ~ isCountable0(X1)
| ( ~ aSubsetOf0(X1,xS)
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,xS) )
| ~ aSet0(X1) ) ) )
| ~ aElementOf0(X0,xT) ),
inference(definition_folding,[],[f106,f169]) ).
fof(f190,plain,
! [X0,X1] :
( ~ sP5(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,[],[f169]) ).
fof(f191,plain,
! [X0,X1] :
( ~ sP5(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,[],[f190]) ).
fof(f192,plain,
! [X0,X1] :
( ~ sP5(X0,X1)
| ( aElementOf0(sK17(X0,X1),slbdtsldtrb0(X1,xK))
& xK = sbrdtbr0(sK17(X0,X1))
& aSubsetOf0(sK17(X0,X1),X1)
& ! [X3] :
( ~ aElementOf0(X3,sK17(X0,X1))
| aElementOf0(X3,X1) )
& aSet0(sK17(X0,X1))
& sdtlpdtrp0(xc,sK17(X0,X1)) != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X2,sK17(X0,X1))],[f191]) ).
fof(f284,plain,
! [X0,X1] :
( ~ sP5(X0,X1)
| xK = sbrdtbr0(sK17(X0,X1)) ),
inference(cnf_transformation,[],[f192]) ).
fof(f287,plain,
! [X0,X1] :
( ~ sP5(X0,X1)
| aSet0(sK17(X0,X1)) ),
inference(cnf_transformation,[],[f192]) ).
fof(f288,plain,
! [X0,X1] :
( ~ sP5(X0,X1)
| sdtlpdtrp0(xc,sK17(X0,X1)) != X0 ),
inference(cnf_transformation,[],[f192]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i] :
( ~ sP5(X0,X1)
| ( sdtlpdtrp0(xc,sK17(X0,X1)) != X0 ) ),
inference(cnf_transformation,[],[f288]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i] :
( aSet0(sK17(X0,X1))
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f287]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i] :
( ( sbrdtbr0(sK17(X0,X1)) = xK )
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f284]) ).
tcf(c_7835,plain,
! [X0: $i,X1: $i] :
( ( sbrdtbr0(sK17(sdtlpdtrp0(xc,X0),X1)) = xK )
| ~ isCountable0(X1)
| ~ aSubsetOf0(X1,xS)
| ~ aElementOf0(X0,szDzozmdt0(xc)) ),
inference(superposition,[status(thm)],[c_7784,c_118]) ).
tcf(c_8223,plain,
! [X0: $i] :
( ( sbrdtbr0(sK17(sdtlpdtrp0(xc,slcrc0),X0)) = xK )
| ~ isCountable0(X0)
| ~ aSubsetOf0(X0,xS) ),
inference(superposition,[status(thm)],[c_1218,c_7835]) ).
tcf(c_19590,plain,
( ( sbrdtbr0(sK17(sdtlpdtrp0(xc,slcrc0),xS)) = xK )
| ~ isCountable0(xS)
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_136,c_8223]) ).
tcf(c_19608,plain,
sbrdtbr0(sK17(sdtlpdtrp0(xc,slcrc0),xS)) = xK,
inference(forward_subsumption_resolution,[status(thm)],[c_19590,c_55,c_52]) ).
tcf(c_20372,plain,
( ( sK17(sdtlpdtrp0(xc,slcrc0),xS) = slcrc0 )
| ~ aSet0(sK17(sdtlpdtrp0(xc,slcrc0),xS)) ),
inference(superposition,[status(thm)],[c_19608,c_149]) ).
tcf(c_29450,plain,
( ( sK17(sdtlpdtrp0(xc,slcrc0),xS) = slcrc0 )
| ~ sP5(sdtlpdtrp0(xc,slcrc0),xS) ),
inference(superposition,[status(thm)],[c_115,c_20372]) ).
tcf(c_29462,plain,
( ( sK17(sdtlpdtrp0(xc,slcrc0),xS) = slcrc0 )
| ~ aElementOf0(slcrc0,szDzozmdt0(xc)) ),
inference(superposition,[status(thm)],[c_18902,c_29450]) ).
tcf(c_29469,plain,
sK17(sdtlpdtrp0(xc,slcrc0),xS) = slcrc0,
inference(forward_subsumption_resolution,[status(thm)],[c_29462,c_1218]) ).
tcf(c_29481,plain,
~ sP5(sdtlpdtrp0(xc,slcrc0),xS),
inference(superposition,[status(thm)],[c_29469,c_114]) ).
tcf(c_29501,plain,
~ aElementOf0(slcrc0,szDzozmdt0(xc)),
inference(superposition,[status(thm)],[c_18902,c_29481]) ).
tcf(c_29508,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_29501,c_1218]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM566+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.43 % Computer : n011.cluster.edu
% 0.08/0.43 % Model : x86_64 x86_64
% 0.08/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.43 % Memory : 8046.5625MB
% 0.08/0.43 % OS : Linux 6.8.0-71-generic
% 0.08/0.43 % CPULimit : 300
% 0.08/0.43 % WCLimit : 300
% 0.08/0.43 % DateTime : Thu Sep 24 04:40:12 UTC 2026
% 0.08/0.43 % CPUTime :
% 0.08/0.43 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.46 Running first-order theorem proving
% 0.14/0.46 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.47
% 0.14/0.47 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.47
% 0.14/0.48 % Detected problem language: tptp
% 0.14/0.49 % Proving...
% 17.20/3.21 % SZS status Started for theBenchmark.p
% 17.20/3.21 % SZS status Theorem for theBenchmark.p
% 17.20/3.21
% 17.20/3.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 17.20/3.21
% 17.20/3.21 % ------ iProver source info
% 17.20/3.21
% 17.20/3.21 % git: date: 2026-07-19 20:42:38 +0200
% 17.20/3.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 17.20/3.21 % git: non_committed_changes: false
% 17.20/3.21
% 17.20/3.21 % ------ Parsing...
% 17.20/3.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 17.20/3.21
% 17.20/3.21 % ------ Preprocessing... sup_sim: 2 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: 5 0s sf_e pe_s pe_e %
% 17.20/3.21
% 17.20/3.21 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 17.20/3.21
% 17.20/3.21 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 17.20/3.21 % ------ Proving...
% 17.20/3.21 % ------ Problem Properties
% 17.20/3.21
% 17.20/3.21 %
% 17.20/3.21 % clauses 100
% 17.20/3.21 % conjectures 3
% 17.20/3.21 % EPR 26
% 17.20/3.21 % Horn 83
% 17.20/3.21 % unary 19
% 17.20/3.21 % binary 23
% 17.20/3.21 % lits 306
% 17.20/3.21 % lits eq 47
% 17.20/3.21 % fd_pure 0
% 17.20/3.21 % fd_pseudo 0
% 17.20/3.21 % fd_cond 5
% 17.20/3.21 % fd_pseudo_cond 9
% 17.20/3.21 % AC symbols 0
% 17.20/3.21
% 17.20/3.21 % ------ Schedule dynamic 5 is on
% 17.20/3.21
% 17.20/3.21 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 17.20/3.21
% 17.20/3.21
% 17.20/3.21 % ------
% 17.20/3.21 % Current options:
% 17.20/3.21 % ------
% 17.20/3.21
% 17.20/3.21
% 17.20/3.21 %
% 17.20/3.21
% 17.20/3.21 % ------ Proving...
% 17.20/3.21 %
% 17.20/3.21
% 17.20/3.21 % SZS status Theorem for theBenchmark.p
% 17.20/3.21
% 17.20/3.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.20/3.21
% 17.20/3.21
%------------------------------------------------------------------------------