%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM597+1 : 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 : n012.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 02:26:10 PM UTC 2026
% Result : Theorem 93.94s 14.13s
% Output : CNFRefutation 93.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 118 ( 31 unt; 0 def)
% Number of atoms : 460 ( 93 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 595 ( 253 ~; 248 |; 71 &)
% ( 10 <=>; 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 : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-3 aty)
% Number of variables : 176 ( 0 sgn 166 !; 10 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( ~ ? [X1] : aElementOf0(X1,X0)
& aSet0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(f11,axiom,
! [X0] :
( ( isFinite0(X0)
& aSet0(X0) )
=> ! [X1] :
( aSubsetOf0(X1,X0)
=> isFinite0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubFSet) ).
fof(f13,axiom,
! [X0,X1] :
( ( aSet0(X1)
& aSet0(X0) )
=> ( ( aSubsetOf0(X1,X0)
& aSubsetOf0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubASymm) ).
fof(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
fof(f66,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aFunction0(X0) )
=> ! [X2] :
( X2 = sdtlbdtrb0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPtt) ).
fof(f69,axiom,
! [X0] :
( aFunction0(X0)
=> ! [X1] :
( aElementOf0(X1,szDzozmdt0(X0))
=> aElementOf0(sdtlpdtrp0(X0,X1),sdtlcdtrc0(X0,szDzozmdt0(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mImgRng) ).
fof(f72,axiom,
! [X0] :
( aFunction0(X0)
=> ( ( isFinite0(sdtlcdtrc0(X0,szDzozmdt0(X0)))
& isCountable0(szDzozmdt0(X0)) )
=> ( isCountable0(sdtlbdtrb0(X0,szDzizrdt0(X0)))
& aElement0(szDzizrdt0(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDirichlet) ).
fof(f73,axiom,
( isFinite0(xT)
& aSet0(xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3291) ).
fof(f92,axiom,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk))
& aSet0(X1) )
=> sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) ) )
& szDzozmdt0(xd) = szNzAzT0
& aFunction0(xd) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4730) ).
fof(f93,axiom,
aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4758) ).
fof(f94,axiom,
sdtlbdtrb0(xd,szDzizrdt0(xd)) != slcrc0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4868) ).
fof(f95,conjecture,
aElementOf0(szDzizrdt0(xd),xT),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f96,negated_conjecture,
~ aElementOf0(szDzizrdt0(xd),xT),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f104,plain,
~ aElementOf0(szDzizrdt0(xd),xT),
inference(flattening,[],[f96]) ).
fof(f106,plain,
! [X0] :
( X0 = slcrc0
<=> ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f111,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f112,plain,
! [X0] :
( ~ isFinite0(X0)
| ~ aSet0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,X0)
| isFinite0(X1) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f113,plain,
! [X0] :
( ~ isFinite0(X0)
| ~ aSet0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,X0)
| isFinite0(X1) ) ),
inference(flattening,[],[f112]) ).
fof(f115,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f13]) ).
fof(f116,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f115]) ).
fof(f193,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| ! [X2] :
( X2 = sdtlbdtrb0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& aSet0(X2) ) ) ),
inference(ennf_transformation,[],[f66]) ).
fof(f194,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| ! [X2] :
( X2 = sdtlbdtrb0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& aSet0(X2) ) ) ),
inference(flattening,[],[f193]) ).
fof(f198,plain,
! [X0] :
( ~ aFunction0(X0)
| ! [X1] :
( ~ aElementOf0(X1,szDzozmdt0(X0))
| aElementOf0(sdtlpdtrp0(X0,X1),sdtlcdtrc0(X0,szDzozmdt0(X0))) ) ),
inference(ennf_transformation,[],[f69]) ).
fof(f202,plain,
! [X0] :
( ~ aFunction0(X0)
| ~ isFinite0(sdtlcdtrc0(X0,szDzozmdt0(X0)))
| ~ isCountable0(szDzozmdt0(X0))
| ( isCountable0(sdtlbdtrb0(X0,szDzizrdt0(X0)))
& aElement0(szDzizrdt0(X0)) ) ),
inference(ennf_transformation,[],[f72]) ).
fof(f203,plain,
! [X0] :
( ~ aFunction0(X0)
| ~ isFinite0(sdtlcdtrc0(X0,szDzozmdt0(X0)))
| ~ isCountable0(szDzozmdt0(X0))
| ( isCountable0(sdtlbdtrb0(X0,szDzizrdt0(X0)))
& aElement0(szDzizrdt0(X0)) ) ),
inference(flattening,[],[f202]) ).
fof(f225,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ! [X1] :
( ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk))
| ~ aSet0(X1)
| sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) ) )
& szDzozmdt0(xd) = szNzAzT0
& aFunction0(xd) ),
inference(ennf_transformation,[],[f92]) ).
fof(f226,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ! [X1] :
( ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk))
| ~ aSet0(X1)
| sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) ) )
& szDzozmdt0(xd) = szNzAzT0
& aFunction0(xd) ),
inference(flattening,[],[f225]) ).
fof(f233,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(nnf_transformation,[],[f106]) ).
fof(f234,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(flattening,[],[f233]) ).
fof(f235,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(rectify,[],[f234]) ).
fof(f236,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))],[f235]) ).
fof(f237,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,[],[f111]) ).
fof(f238,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,[],[f237]) ).
fof(f239,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,[],[f238]) ).
fof(f240,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))],[f239]) ).
fof(f279,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| ! [X2] :
( ( sdtlbdtrb0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& ( sdtlpdtrp0(X0,X3) != X1
| ~ aElementOf0(X3,szDzozmdt0(X0))
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& ( ~ aElementOf0(X3,X2)
| sdtlpdtrp0(X0,X3) != X1
| ~ aElementOf0(X3,szDzozmdt0(X0)) ) )
| ~ aSet0(X2)
| X2 = sdtlbdtrb0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f194]) ).
fof(f280,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| ! [X2] :
( ( sdtlbdtrb0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& ( sdtlpdtrp0(X0,X3) != X1
| ~ aElementOf0(X3,szDzozmdt0(X0))
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& ( ~ aElementOf0(X3,X2)
| sdtlpdtrp0(X0,X3) != X1
| ~ aElementOf0(X3,szDzozmdt0(X0)) ) )
| ~ aSet0(X2)
| X2 = sdtlbdtrb0(X0,X1) ) ) ),
inference(flattening,[],[f279]) ).
fof(f281,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| ! [X2] :
( ( sdtlbdtrb0(X0,X1) != X2
| ( ! [X4] :
( ( ~ aElementOf0(X4,X2)
| ( sdtlpdtrp0(X0,X4) = X1
& aElementOf0(X4,szDzozmdt0(X0)) ) )
& ( sdtlpdtrp0(X0,X4) != X1
| ~ aElementOf0(X4,szDzozmdt0(X0))
| aElementOf0(X4,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& ( ~ aElementOf0(X3,X2)
| sdtlpdtrp0(X0,X3) != X1
| ~ aElementOf0(X3,szDzozmdt0(X0)) ) )
| ~ aSet0(X2)
| X2 = sdtlbdtrb0(X0,X1) ) ) ),
inference(rectify,[],[f280]) ).
fof(f282,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| ! [X2] :
( ( sdtlbdtrb0(X0,X1) != X2
| ( ! [X4] :
( ( ~ aElementOf0(X4,X2)
| ( sdtlpdtrp0(X0,X4) = X1
& aElementOf0(X4,szDzozmdt0(X0)) ) )
& ( sdtlpdtrp0(X0,X4) != X1
| ~ aElementOf0(X4,szDzozmdt0(X0))
| aElementOf0(X4,X2) ) )
& aSet0(X2) ) )
& ( ( ( aElementOf0(sK16(X0,X1,X2),X2)
| ( sdtlpdtrp0(X0,sK16(X0,X1,X2)) = X1
& aElementOf0(sK16(X0,X1,X2),szDzozmdt0(X0)) ) )
& ( ~ aElementOf0(sK16(X0,X1,X2),X2)
| sdtlpdtrp0(X0,sK16(X0,X1,X2)) != X1
| ~ aElementOf0(sK16(X0,X1,X2),szDzozmdt0(X0)) ) )
| ~ aSet0(X2)
| X2 = sdtlbdtrb0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X3,sK16(X0,X1,X2))],[f281]) ).
fof(f296,plain,
! [X2,X0] :
( slcrc0 != X0
| ~ aElementOf0(X2,X0) ),
inference(cnf_transformation,[],[f236]) ).
fof(f297,plain,
! [X0] :
( slcrc0 != X0
| aSet0(X0) ),
inference(cnf_transformation,[],[f236]) ).
fof(f302,plain,
! [X3,X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) ),
inference(cnf_transformation,[],[f240]) ).
fof(f303,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| aSet0(X1) ),
inference(cnf_transformation,[],[f240]) ).
fof(f304,plain,
! [X0,X1] :
( ~ aSet0(X0)
| aElementOf0(sK5(X0,X1),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ),
inference(cnf_transformation,[],[f240]) ).
fof(f306,plain,
! [X0,X1] :
( ~ isFinite0(X0)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| isFinite0(X1) ),
inference(cnf_transformation,[],[f113]) ).
fof(f308,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f116]) ).
fof(f340,plain,
isCountable0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f411,plain,
! [X2,X0,X1,X4] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| sdtlbdtrb0(X0,X1) != X2
| ~ aElementOf0(X4,X2)
| sdtlpdtrp0(X0,X4) = X1 ),
inference(cnf_transformation,[],[f282]) ).
fof(f412,plain,
! [X2,X0,X1,X4] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| sdtlbdtrb0(X0,X1) != X2
| ~ aElementOf0(X4,X2)
| aElementOf0(X4,szDzozmdt0(X0)) ),
inference(cnf_transformation,[],[f282]) ).
fof(f414,plain,
! [X2,X0,X1] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| sdtlbdtrb0(X0,X1) != X2
| aSet0(X2) ),
inference(cnf_transformation,[],[f282]) ).
fof(f426,plain,
! [X0,X1] :
( ~ aFunction0(X0)
| ~ aElementOf0(X1,szDzozmdt0(X0))
| aElementOf0(sdtlpdtrp0(X0,X1),sdtlcdtrc0(X0,szDzozmdt0(X0))) ),
inference(cnf_transformation,[],[f198]) ).
fof(f437,plain,
! [X0] :
( ~ aFunction0(X0)
| ~ isFinite0(sdtlcdtrc0(X0,szDzozmdt0(X0)))
| ~ isCountable0(szDzozmdt0(X0))
| aElement0(szDzizrdt0(X0)) ),
inference(cnf_transformation,[],[f203]) ).
fof(f438,plain,
isFinite0(xT),
inference(cnf_transformation,[],[f73]) ).
fof(f439,plain,
aSet0(xT),
inference(cnf_transformation,[],[f73]) ).
fof(f481,plain,
szNzAzT0 = szDzozmdt0(xd),
inference(cnf_transformation,[],[f226]) ).
fof(f482,plain,
aFunction0(xd),
inference(cnf_transformation,[],[f226]) ).
fof(f483,plain,
aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),
inference(cnf_transformation,[],[f93]) ).
fof(f484,plain,
slcrc0 != sdtlbdtrb0(xd,szDzizrdt0(xd)),
inference(cnf_transformation,[],[f94]) ).
fof(f485,plain,
~ aElementOf0(szDzizrdt0(xd),xT),
inference(cnf_transformation,[],[f104]) ).
fof(f486,plain,
aSet0(slcrc0),
inference(equality_resolution,[],[f297]) ).
fof(f487,plain,
! [X2] : ~ aElementOf0(X2,slcrc0),
inference(equality_resolution,[],[f296]) ).
fof(f508,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| aSet0(sdtlbdtrb0(X0,X1)) ),
inference(equality_resolution,[],[f414]) ).
fof(f511,plain,
! [X0,X1,X4] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| ~ aElementOf0(X4,sdtlbdtrb0(X0,X1))
| aElementOf0(X4,szDzozmdt0(X0)) ),
inference(equality_resolution,[],[f412]) ).
fof(f512,plain,
! [X0,X1,X4] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| ~ aElementOf0(X4,sdtlbdtrb0(X0,X1))
| sdtlpdtrp0(X0,X4) = X1 ),
inference(equality_resolution,[],[f411]) ).
tcf(c_51,plain,
aSet0(slcrc0),
inference(cnf_transformation,[],[f486]) ).
tcf(c_52,plain,
! [X0: $i] : ~ aElementOf0(X0,slcrc0),
inference(cnf_transformation,[],[f487]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(X0,X1)
| aElementOf0(sK5(X1,X0),X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f304]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( aSet0(X0)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f303]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X2)
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f302]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( isFinite0(X0)
| ~ isFinite0(X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f306]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f308]) ).
tcf(c_95,plain,
isCountable0(szNzAzT0),
inference(cnf_transformation,[],[f340]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i] :
( aSet0(sdtlbdtrb0(X1,X0))
| ~ aFunction0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f508]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,szDzozmdt0(X1))
| ~ aFunction0(X1)
| ~ aElement0(X2)
| ~ aElementOf0(X0,sdtlbdtrb0(X1,X2)) ),
inference(cnf_transformation,[],[f511]) ).
tcf(c_171,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtlpdtrp0(X1,X0) = X2 )
| ~ aFunction0(X1)
| ~ aElement0(X2)
| ~ aElementOf0(X0,sdtlbdtrb0(X1,X2)) ),
inference(cnf_transformation,[],[f512]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtlpdtrp0(X1,X0),sdtlcdtrc0(X1,szDzozmdt0(X1)))
| ~ aFunction0(X1)
| ~ aElementOf0(X0,szDzozmdt0(X1)) ),
inference(cnf_transformation,[],[f426]) ).
tcf(c_190,plain,
! [X0: $i] :
( aElement0(szDzizrdt0(X0))
| ~ aFunction0(X0)
| ~ isCountable0(szDzozmdt0(X0))
| ~ isFinite0(sdtlcdtrc0(X0,szDzozmdt0(X0))) ),
inference(cnf_transformation,[],[f437]) ).
tcf(c_192,plain,
aSet0(xT),
inference(cnf_transformation,[],[f439]) ).
tcf(c_193,plain,
isFinite0(xT),
inference(cnf_transformation,[],[f438]) ).
tcf(c_234,plain,
aFunction0(xd),
inference(cnf_transformation,[],[f482]) ).
tcf(c_235,plain,
szDzozmdt0(xd) = szNzAzT0,
inference(cnf_transformation,[],[f481]) ).
tcf(c_237,plain,
aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),
inference(cnf_transformation,[],[f483]) ).
tcf(c_238,plain,
sdtlbdtrb0(xd,szDzizrdt0(xd)) != slcrc0,
inference(cnf_transformation,[],[f484]) ).
tcf(c_239,negated_conjecture,
~ aElementOf0(szDzizrdt0(xd),xT),
inference(cnf_transformation,[],[f485]) ).
tcf(c_381,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_62,c_58,c_62]) ).
tcf(c_382,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1) ),
inference(renaming,[status(thm)],[c_381]) ).
tcf(c_447,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_449,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_451,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X0,X2)
| ~ aElementOf0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_571,plain,
aSubsetOf0(sdtlcdtrc0(xd,szNzAzT0),xT),
inference(demodulation,[status(thm)],[c_237,c_235]) ).
tcf(c_593,plain,
( aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd)
| ~ isCountable0(szDzozmdt0(xd))
| ~ isFinite0(sdtlcdtrc0(xd,szNzAzT0)) ),
inference(superposition,[status(thm)],[c_235,c_190]) ).
tcf(c_594,plain,
( aElement0(szDzizrdt0(xd))
| ~ isFinite0(sdtlcdtrc0(xd,szNzAzT0))
| ~ isCountable0(szDzozmdt0(xd)) ),
inference(global_subsumption_just,[status(thm)],[c_593,c_234,c_593]) ).
tcf(c_595,plain,
( aElement0(szDzizrdt0(xd))
| ~ isCountable0(szDzozmdt0(xd))
| ~ isFinite0(sdtlcdtrc0(xd,szNzAzT0)) ),
inference(renaming,[status(thm)],[c_594]) ).
tcf(c_599,plain,
( aElement0(szDzizrdt0(xd))
| ~ isCountable0(szNzAzT0)
| ~ isFinite0(sdtlcdtrc0(xd,szNzAzT0)) ),
inference(light_normalisation,[status(thm)],[c_595,c_235]) ).
tcf(c_1115,plain,
( isFinite0(sdtlcdtrc0(xd,szNzAzT0))
| ~ isFinite0(xT)
| ~ aSet0(xT) ),
inference(superposition,[status(thm)],[c_571,c_60]) ).
tcf(c_1277,plain,
( ( sdtlbdtrb0(xd,szDzizrdt0(xd)) = slcrc0 )
| ~ aSet0(slcrc0)
| ~ aSubsetOf0(slcrc0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),slcrc0) ),
inference(instantiation,[status(thm)],[c_382]) ).
tcf(c_2914,plain,
( aSubsetOf0(slcrc0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(sK5(sdtlbdtrb0(xd,szDzizrdt0(xd)),slcrc0),slcrc0)
| ~ aSet0(slcrc0)
| ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_4606,plain,
! [X0: $i] :
( aSet0(sdtlbdtrb0(xd,X0))
| ~ aFunction0(xd)
| ~ aElement0(X0) ),
inference(instantiation,[status(thm)],[c_168]) ).
tcf(c_5001,plain,
! [X0: $i] :
( aElementOf0(szDzizrdt0(xd),xT)
| ~ aSet0(xT)
| ~ aSubsetOf0(X0,xT)
| ~ aElementOf0(szDzizrdt0(xd),X0) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_17145,plain,
( aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aFunction0(xd)
| ~ aElement0(szDzizrdt0(xd)) ),
inference(instantiation,[status(thm)],[c_4606]) ).
tcf(c_18337,plain,
szDzizrdt0(xd) = szDzizrdt0(xd),
inference(instantiation,[status(thm)],[c_447]) ).
tcf(c_18398,plain,
( aElementOf0(szDzizrdt0(xd),xT)
| ~ aSet0(xT)
| ~ aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT)
| ~ aElementOf0(szDzizrdt0(xd),sdtlcdtrc0(xd,szDzozmdt0(xd))) ),
inference(instantiation,[status(thm)],[c_5001]) ).
tcf(c_33838,plain,
! [X0: $i] :
( aElementOf0(sdtlpdtrp0(xd,X0),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ aFunction0(xd)
| ~ aElementOf0(X0,szDzozmdt0(xd)) ),
inference(instantiation,[status(thm)],[c_180]) ).
tcf(c_35084,plain,
( aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),slcrc0)
| aElementOf0(sK5(slcrc0,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSet0(slcrc0)
| ~ aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_40421,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(szDzizrdt0(xd),X1)
| ~ aElementOf0(X0,X2)
| ( X1 != X2 )
| ( szDzizrdt0(xd) != X0 ) ),
inference(instantiation,[status(thm)],[c_451]) ).
tcf(c_40441,plain,
! [X0: $i,X1: $i] :
( ( szDzizrdt0(xd) = X1 )
| ( X1 != X0 )
| ( szDzizrdt0(xd) != X0 ) ),
inference(instantiation,[status(thm)],[c_449]) ).
tcf(c_40462,plain,
~ aElementOf0(sK5(sdtlbdtrb0(xd,szDzizrdt0(xd)),slcrc0),slcrc0),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_42498,plain,
( ( sdtlpdtrp0(xd,sK5(slcrc0,sdtlbdtrb0(xd,szDzizrdt0(xd)))) = szDzizrdt0(xd) )
| ~ aFunction0(xd)
| ~ aElement0(szDzizrdt0(xd))
| ~ aElementOf0(sK5(slcrc0,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(instantiation,[status(thm)],[c_171]) ).
tcf(c_42499,plain,
( aElementOf0(sK5(slcrc0,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzozmdt0(xd))
| ~ aFunction0(xd)
| ~ aElement0(szDzizrdt0(xd))
| ~ aElementOf0(sK5(slcrc0,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(instantiation,[status(thm)],[c_170]) ).
tcf(c_44472,plain,
! [X0: $i] :
( ( szDzizrdt0(xd) = X0 )
| ( X0 != szDzizrdt0(xd) )
| ( szDzizrdt0(xd) != szDzizrdt0(xd) ) ),
inference(instantiation,[status(thm)],[c_40441]) ).
tcf(c_48247,plain,
( ( szDzizrdt0(xd) = sdtlpdtrp0(xd,sK5(slcrc0,sdtlbdtrb0(xd,szDzizrdt0(xd)))) )
| ( szDzizrdt0(xd) != szDzizrdt0(xd) )
| ( sdtlpdtrp0(xd,sK5(slcrc0,sdtlbdtrb0(xd,szDzizrdt0(xd)))) != szDzizrdt0(xd) ) ),
inference(instantiation,[status(thm)],[c_44472]) ).
tcf(c_52584,plain,
! [X0: $i,X1: $i] :
( aElementOf0(szDzizrdt0(xd),X0)
| ~ aElementOf0(sdtlpdtrp0(xd,sK5(slcrc0,sdtlbdtrb0(xd,szDzizrdt0(xd)))),X1)
| ( X0 != X1 )
| ( szDzizrdt0(xd) != sdtlpdtrp0(xd,sK5(slcrc0,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ),
inference(instantiation,[status(thm)],[c_40421]) ).
tcf(c_56823,plain,
( aElementOf0(sdtlpdtrp0(xd,sK5(slcrc0,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ aFunction0(xd)
| ~ aElementOf0(sK5(slcrc0,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzozmdt0(xd)) ),
inference(instantiation,[status(thm)],[c_33838]) ).
tcf(c_63462,plain,
! [X0: $i] :
( aElementOf0(szDzizrdt0(xd),X0)
| ~ aElementOf0(sdtlpdtrp0(xd,sK5(slcrc0,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ( X0 != sdtlcdtrc0(xd,szDzozmdt0(xd)) )
| ( szDzizrdt0(xd) != sdtlpdtrp0(xd,sK5(slcrc0,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ),
inference(instantiation,[status(thm)],[c_52584]) ).
tcf(c_73919,plain,
( aElementOf0(szDzizrdt0(xd),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ aElementOf0(sdtlpdtrp0(xd,sK5(slcrc0,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ( szDzizrdt0(xd) != sdtlpdtrp0(xd,sK5(slcrc0,sdtlbdtrb0(xd,szDzizrdt0(xd)))) )
| ( sdtlcdtrc0(xd,szDzozmdt0(xd)) != sdtlcdtrc0(xd,szDzozmdt0(xd)) ) ),
inference(instantiation,[status(thm)],[c_63462]) ).
tcf(c_73920,plain,
sdtlcdtrc0(xd,szDzozmdt0(xd)) = sdtlcdtrc0(xd,szDzozmdt0(xd)),
inference(instantiation,[status(thm)],[c_447]) ).
tcf(c_73921,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_73920,c_73919,c_56823,c_48247,c_42498,c_42499,c_40462,c_35084,c_18398,c_18337,c_17145,c_2914,c_1277,c_1115,c_599,c_238,c_237,c_239,c_51,c_95,c_192,c_193,c_234]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM597+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.02/0.30 % Computer : n012.cluster.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.30 % Memory : 8046.5625MB
% 0.02/0.30 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Thu Sep 24 04:49:51 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.02/0.32 Running first-order theorem proving
% 0.02/0.32 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
% 0.07/0.33
% 0.07/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.33
% 0.07/0.33 % Detected problem language: tptp
% 0.07/0.33 % Proving...
% 93.94/14.13 % SZS status Started for theBenchmark.p
% 93.94/14.13 % SZS status Theorem for theBenchmark.p
% 93.94/14.13
% 93.94/14.13 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 93.94/14.13
% 93.94/14.13 % ------ iProver source info
% 93.94/14.13
% 93.94/14.13 % git: date: 2026-07-19 20:42:38 +0200
% 93.94/14.13 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 93.94/14.13 % git: non_committed_changes: false
% 93.94/14.13
% 93.94/14.13 % ------ Parsing...
% 93.94/14.13 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 93.94/14.13
% 93.94/14.13 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 1 0s sf_e %
% 93.94/14.13
% 93.94/14.13 % ------ Preprocessing...%
% 93.94/14.13
% 93.94/14.13 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 93.94/14.13 % ------ Proving...
% 93.94/14.13 % ------ Problem Properties
% 93.94/14.13
% 93.94/14.13 %
% 93.94/14.13 % clauses 190
% 93.94/14.13 % conjectures 1
% 93.94/14.13 % EPR 43
% 93.94/14.13 % Horn 151
% 93.94/14.13 % unary 32
% 93.94/14.13 % binary 32
% 93.94/14.13 % lits 649
% 93.94/14.13 % lits eq 98
% 93.94/14.13 % fd_pure 0
% 93.94/14.13 % fd_pseudo 0
% 93.94/14.13 % fd_cond 10
% 93.94/14.13 % fd_pseudo_cond 25
% 93.94/14.13 % AC symbols 0
% 93.94/14.13
% 93.94/14.13 % ------ Input Options Time Limit: Unbounded
% 93.94/14.13
% 93.94/14.13
% 93.94/14.13 % ------
% 93.94/14.13 % Current options:
% 93.94/14.13 % ------
% 93.94/14.13
% 93.94/14.13
% 93.94/14.13 %
% 93.94/14.13
% 93.94/14.13 % ------ Proving...
% 93.94/14.13 %
% 93.94/14.13
% 93.94/14.13 % SZS status Theorem for theBenchmark.p
% 93.94/14.13
% 93.94/14.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 93.94/14.13
% 93.94/14.13
%------------------------------------------------------------------------------