%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM565+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 5.12s 16.67s
% Output : CNFRefutation 5.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 15
% Syntax : Number of formulae : 108 ( 42 unt; 3 def)
% Number of atoms : 449 ( 111 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 518 ( 204 ~; 206 |; 83 &)
% ( 16 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 4 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-3 aty)
% Number of variables : 153 ( 0 sgn 143 !; 10 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(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(f65,axiom,
! [X0] :
( aFunction0(X0)
=> ! [X1] :
( aElementOf0(X1,szDzozmdt0(X0))
=> aElement0(sdtlpdtrp0(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgElm) ).
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/sandbox2/benchmark/theBenchmark.p',mDefPtt) ).
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,axiom,
aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3476) ).
fof(f80,conjecture,
! [X0] :
( aElementOf0(X0,slbdtsldtrb0(xS,sz00))
=> sdtlpdtrp0(xc,X0) = sdtlpdtrp0(xc,slcrc0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f81,negated_conjecture,
~ ! [X0] :
( aElementOf0(X0,slbdtsldtrb0(xS,sz00))
=> sdtlpdtrp0(xc,X0) = sdtlpdtrp0(xc,slcrc0) ),
inference(negated_conjecture,[status(cth)],[f80]) ).
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(f176,plain,
! [X0] :
( ~ aFunction0(X0)
| ! [X1] :
( ~ aElementOf0(X1,szDzozmdt0(X0))
| aElement0(sdtlpdtrp0(X0,X1)) ) ),
inference(ennf_transformation,[],[f65]) ).
fof(f177,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(f178,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,[],[f177]) ).
fof(f190,plain,
? [X0] :
( aElementOf0(X0,slbdtsldtrb0(xS,sz00))
& sdtlpdtrp0(xc,X0) != sdtlpdtrp0(xc,slcrc0) ),
inference(ennf_transformation,[],[f81]) ).
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(nnf_transformation,[],[f95]) ).
fof(f202,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,[],[f201]) ).
fof(f203,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,[],[f202]) ).
fof(f204,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))],[f203]) ).
fof(f220,plain,
! [X0] :
( ~ aSet0(X0)
| ( ( sz00 != sbrdtbr0(X0)
| X0 = slcrc0 )
& ( slcrc0 != X0
| sbrdtbr0(X0) = sz00 ) ) ),
inference(nnf_transformation,[],[f139]) ).
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(nnf_transformation,[],[f164]) ).
fof(f239,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,[],[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) ) )
& ( ? [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,[],[f239]) ).
fof(f241,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))],[f240]) ).
fof(f243,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,[],[f178]) ).
fof(f244,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,[],[f243]) ).
fof(f245,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,[],[f244]) ).
fof(f246,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))],[f245]) ).
fof(f257,plain,
( aElementOf0(sK25,slbdtsldtrb0(xS,sz00))
& sdtlpdtrp0(xc,slcrc0) != sdtlpdtrp0(xc,sK25) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(X0,sK25)],[f190]) ).
fof(f266,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| aSet0(X1) ),
inference(cnf_transformation,[],[f204]) ).
fof(f304,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f325,plain,
! [X0] :
( ~ aSet0(X0)
| sz00 != sbrdtbr0(X0)
| slcrc0 = X0 ),
inference(cnf_transformation,[],[f220]) ).
fof(f358,plain,
! [X2,X0,X1,X4] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| slbdtsldtrb0(X0,X1) != X2
| ~ aElementOf0(X4,X2)
| sbrdtbr0(X4) = X1 ),
inference(cnf_transformation,[],[f241]) ).
fof(f359,plain,
! [X2,X0,X1,X4] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| slbdtsldtrb0(X0,X1) != X2
| ~ aElementOf0(X4,X2)
| aSubsetOf0(X4,X0) ),
inference(cnf_transformation,[],[f241]) ).
fof(f373,plain,
! [X0,X1] :
( ~ aFunction0(X0)
| ~ aElementOf0(X1,szDzozmdt0(X0))
| aElement0(sdtlpdtrp0(X0,X1)) ),
inference(cnf_transformation,[],[f176]) ).
fof(f374,plain,
! [X2,X0,X1,X4] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| sdtlbdtrb0(X0,X1) != X2
| ~ aElementOf0(X4,X2)
| sdtlpdtrp0(X0,X4) = X1 ),
inference(cnf_transformation,[],[f246]) ).
fof(f376,plain,
! [X2,X0,X1,X4] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| sdtlbdtrb0(X0,X1) != X2
| sdtlpdtrp0(X0,X4) != X1
| ~ aElementOf0(X4,szDzozmdt0(X0))
| aElementOf0(X4,X2) ),
inference(cnf_transformation,[],[f246]) ).
fof(f403,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[],[f74]) ).
fof(f405,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f75]) ).
fof(f407,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(cnf_transformation,[],[f76]) ).
fof(f408,plain,
aFunction0(xc),
inference(cnf_transformation,[],[f76]) ).
fof(f413,plain,
sz00 = xK,
inference(cnf_transformation,[],[f78]) ).
fof(f414,plain,
aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(cnf_transformation,[],[f79]) ).
fof(f415,plain,
aElementOf0(sK25,slbdtsldtrb0(xS,sz00)),
inference(cnf_transformation,[],[f257]) ).
fof(f416,plain,
sdtlpdtrp0(xc,slcrc0) != sdtlpdtrp0(xc,sK25),
inference(cnf_transformation,[],[f257]) ).
fof(f424,plain,
! [X0] :
( ~ aSet0(X0)
| sbrdtbr0(X0) != xK
| slcrc0 = X0 ),
inference(definition_unfolding,[],[f325,f413]) ).
fof(f428,plain,
aElementOf0(slcrc0,slbdtsldtrb0(xS,xK)),
inference(definition_unfolding,[],[f414,f413]) ).
fof(f429,plain,
aElementOf0(sK25,slbdtsldtrb0(xS,xK)),
inference(definition_unfolding,[],[f415,f413]) ).
fof(f450,plain,
! [X0,X1,X4] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ~ aElementOf0(X4,slbdtsldtrb0(X0,X1))
| aSubsetOf0(X4,X0) ),
inference(equality_resolution,[],[f359]) ).
fof(f451,plain,
! [X0,X1,X4] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ~ aElementOf0(X4,slbdtsldtrb0(X0,X1))
| sbrdtbr0(X4) = X1 ),
inference(equality_resolution,[],[f358]) ).
fof(f453,plain,
! [X2,X0,X4] :
( ~ aElement0(sdtlpdtrp0(X0,X4))
| ~ aFunction0(X0)
| sdtlbdtrb0(X0,sdtlpdtrp0(X0,X4)) != X2
| ~ aElementOf0(X4,szDzozmdt0(X0))
| aElementOf0(X4,X2) ),
inference(equality_resolution,[],[f376]) ).
fof(f454,plain,
! [X0,X4] :
( ~ aElement0(sdtlpdtrp0(X0,X4))
| ~ aFunction0(X0)
| ~ aElementOf0(X4,szDzozmdt0(X0))
| aElementOf0(X4,sdtlbdtrb0(X0,sdtlpdtrp0(X0,X4))) ),
inference(equality_resolution,[],[f453]) ).
fof(f456,plain,
! [X0,X1,X4] :
( ~ aElement0(X1)
| ~ aFunction0(X0)
| ~ aElementOf0(X4,sdtlbdtrb0(X0,X1))
| sdtlpdtrp0(X0,X4) = X1 ),
inference(equality_resolution,[],[f374]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( aSet0(X0)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f266]) ).
tcf(c_94,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f304]) ).
tcf(c_117,plain,
! [X0: $i] :
( ( X0 = slcrc0 )
| ~ aSet0(X0)
| ( sbrdtbr0(X0) != xK ) ),
inference(cnf_transformation,[],[f424]) ).
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,[],[f450]) ).
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,[],[f451]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] :
( aElement0(sdtlpdtrp0(X1,X0))
| ~ aFunction0(X1)
| ~ aElementOf0(X0,szDzozmdt0(X1)) ),
inference(cnf_transformation,[],[f373]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X1,sdtlbdtrb0(X0,sdtlpdtrp0(X0,X1)))
| ~ aFunction0(X0)
| ~ aElementOf0(X1,szDzozmdt0(X0))
| ~ aElement0(sdtlpdtrp0(X0,X1)) ),
inference(cnf_transformation,[],[f454]) ).
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,[],[f456]) ).
tcf(c_194,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[],[f403]) ).
tcf(c_195,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f405]) ).
tcf(c_197,plain,
aFunction0(xc),
inference(cnf_transformation,[],[f408]) ).
tcf(c_198,plain,
slbdtsldtrb0(xS,xK) = szDzozmdt0(xc),
inference(cnf_transformation,[],[f407]) ).
tcf(c_204,plain,
aElementOf0(slcrc0,slbdtsldtrb0(xS,xK)),
inference(cnf_transformation,[],[f428]) ).
tcf(c_205,negated_conjecture,
sdtlpdtrp0(xc,slcrc0) != sdtlpdtrp0(xc,sK25),
inference(cnf_transformation,[],[f416]) ).
tcf(c_206,negated_conjecture,
aElementOf0(sK25,slbdtsldtrb0(xS,xK)),
inference(cnf_transformation,[],[f429]) ).
tcf(c_580,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,sdtlbdtrb0(X1,sdtlpdtrp0(X1,X0)))
| ~ aFunction0(X1)
| ~ aElementOf0(X0,szDzozmdt0(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_169,c_164]) ).
tcf(c_1498,plain,
aElementOf0(slcrc0,szDzozmdt0(xc)),
inference(demodulation,[status(thm)],[c_204,c_198]) ).
tcf(c_1499,plain,
aElementOf0(sK25,szDzozmdt0(xc)),
inference(demodulation,[status(thm)],[c_206,c_198]) ).
tcf(c_14262,definition,
iPr_def_10 = szDzozmdt0(xc),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_14263,definition,
iPr_def_11 = sdtlpdtrp0(xc,slcrc0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_14264,definition,
iPr_def_12 = sdtlpdtrp0(xc,sK25),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_14265,plain,
aElementOf0(sK25,iPr_def_10),
inference(demodulation,[status(thm)],[c_1499,c_14262]) ).
tcf(c_14266,negated_conjecture,
iPr_def_11 != iPr_def_12,
inference(demodulation,[status(thm)],[c_205,c_14264,c_14263]) ).
tcf(c_16716,plain,
aElementOf0(slcrc0,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_1498,c_14262]) ).
tcf(c_16762,plain,
slbdtsldtrb0(xS,xK) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_198,c_14262]) ).
tcf(c_16858,plain,
( aSet0(xS)
| ~ aSet0(szNzAzT0) ),
inference(superposition,[status(thm)],[c_195,c_58]) ).
tcf(c_16860,plain,
aSet0(xS),
inference(forward_subsumption_resolution,[status(thm)],[c_16858,c_94]) ).
tcf(c_17498,plain,
! [X0: $i] :
( aElement0(sdtlpdtrp0(xc,X0))
| ~ aFunction0(xc)
| ~ aElementOf0(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_14262,c_164]) ).
tcf(c_17499,plain,
! [X0: $i] :
( aElement0(sdtlpdtrp0(xc,X0))
| ~ aElementOf0(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17498,c_197]) ).
tcf(c_17517,plain,
( aElement0(iPr_def_11)
| ~ aElementOf0(slcrc0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_14263,c_17499]) ).
tcf(c_17520,plain,
aElement0(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_17517,c_16716]) ).
tcf(c_19345,plain,
( aElementOf0(slcrc0,sdtlbdtrb0(xc,iPr_def_11))
| ~ aFunction0(xc)
| ~ aElementOf0(slcrc0,szDzozmdt0(xc)) ),
inference(superposition,[status(thm)],[c_14263,c_580]) ).
tcf(c_19352,plain,
( aElementOf0(slcrc0,sdtlbdtrb0(xc,iPr_def_11))
| ~ aFunction0(xc)
| ~ aElementOf0(slcrc0,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_19345,c_14262]) ).
tcf(c_19353,plain,
aElementOf0(slcrc0,sdtlbdtrb0(xc,iPr_def_11)),
inference(forward_subsumption_resolution,[status(thm)],[c_19352,c_197,c_16716]) ).
tcf(c_19420,plain,
! [X0: $i] :
( aSubsetOf0(X0,xS)
| ~ aSet0(xS)
| ~ aElementOf0(xK,szNzAzT0)
| ~ aElementOf0(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_16762,c_154]) ).
tcf(c_19421,plain,
! [X0: $i] :
( aSubsetOf0(X0,xS)
| ~ aElementOf0(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19420,c_16860,c_194]) ).
tcf(c_19487,plain,
aSubsetOf0(sK25,xS),
inference(superposition,[status(thm)],[c_14265,c_19421]) ).
tcf(c_19523,plain,
( aSet0(sK25)
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_19487,c_58]) ).
tcf(c_19524,plain,
aSet0(sK25),
inference(forward_subsumption_resolution,[status(thm)],[c_19523,c_16860]) ).
tcf(c_20803,plain,
! [X0: $i] :
( ( sbrdtbr0(X0) = xK )
| ~ aSet0(xS)
| ~ aElementOf0(xK,szNzAzT0)
| ~ aElementOf0(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_16762,c_155]) ).
tcf(c_20804,plain,
! [X0: $i] :
( ( sbrdtbr0(X0) = xK )
| ~ aElementOf0(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20803,c_16860,c_194]) ).
tcf(c_21189,plain,
( ( sdtlpdtrp0(xc,slcrc0) = iPr_def_11 )
| ~ aFunction0(xc)
| ~ aElement0(iPr_def_11) ),
inference(superposition,[status(thm)],[c_19353,c_171]) ).
tcf(c_21192,plain,
sdtlpdtrp0(xc,slcrc0) = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_21189,c_197,c_17520]) ).
tcf(c_22437,plain,
sbrdtbr0(sK25) = xK,
inference(superposition,[status(thm)],[c_14265,c_20804]) ).
tcf(c_22507,plain,
( ( slcrc0 = sK25 )
| ~ aSet0(sK25) ),
inference(superposition,[status(thm)],[c_22437,c_117]) ).
tcf(c_22516,plain,
slcrc0 = sK25,
inference(forward_subsumption_resolution,[status(thm)],[c_22507,c_19524]) ).
tcf(c_22567,plain,
sdtlpdtrp0(xc,slcrc0) = iPr_def_12,
inference(demodulation,[status(thm)],[c_14264,c_22516]) ).
tcf(c_22569,plain,
iPr_def_11 = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_22567,c_21192]) ).
tcf(c_22570,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_22569,c_14266]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM565+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/15.41 % Computer : n019.cluster.edu
% 0.12/15.41 % Model : x86_64 x86_64
% 0.12/15.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/15.41 % Memory : 8046.5625MB
% 0.12/15.41 % OS : Linux 6.8.0-71-generic
% 0.12/15.41 % CPULimit : 300
% 0.12/15.41 % WCLimit : 300
% 0.12/15.41 % DateTime : Thu Sep 24 04:40:07 UTC 2026
% 0.12/15.41 % CPUTime :
% 0.12/15.41 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/15.45 Running first-order theorem proving
% 0.12/15.45 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
% 0.12/15.46
% 0.12/15.46 % ======== iProver multi-core TPTP/SMT =========
% 0.12/15.46
% 0.12/15.46 % Detected problem language: tptp
% 0.12/15.47 % Proving...
% 5.12/16.67 % SZS status Started for theBenchmark.p
% 5.12/16.67 % SZS status Theorem for theBenchmark.p
% 5.12/16.67
% 5.12/16.67 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 5.12/16.67
% 5.12/16.67 % ------ iProver source info
% 5.12/16.67
% 5.12/16.67 % git: date: 2026-07-19 20:42:38 +0200
% 5.12/16.67 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 5.12/16.67 % git: non_committed_changes: false
% 5.12/16.67
% 5.12/16.67 % ------ Parsing...
% 5.12/16.67 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 5.12/16.67
% 5.12/16.67 % ------ Preprocessing... sup_sim: 2 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 5.12/16.67
% 5.12/16.67 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 5.12/16.67
% 5.12/16.67 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 5.12/16.67 % ------ Proving...
% 5.12/16.67 % ------ Problem Properties
% 5.12/16.67
% 5.12/16.67 %
% 5.12/16.67 % clauses 153
% 5.12/16.67 % conjectures 1
% 5.12/16.67 % EPR 36
% 5.12/16.67 % Horn 114
% 5.12/16.67 % unary 22
% 5.12/16.67 % binary 17
% 5.12/16.67 % lits 538
% 5.12/16.67 % lits eq 81
% 5.12/16.67 % fd_pure 0
% 5.12/16.67 % fd_pseudo 0
% 5.12/16.67 % fd_cond 10
% 5.12/16.67 % fd_pseudo_cond 24
% 5.12/16.67 % AC symbols 0
% 5.12/16.67
% 5.12/16.67 % ------ Schedule dynamic 5 is on
% 5.12/16.67
% 5.12/16.67 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 5.12/16.67
% 5.12/16.67
% 5.12/16.67 % ------
% 5.12/16.67 % Current options:
% 5.12/16.67 % ------
% 5.12/16.67
% 5.12/16.67
% 5.12/16.67 %
% 5.12/16.67
% 5.12/16.67 % ------ Proving...
% 5.12/16.67 %
% 5.12/16.67
% 5.12/16.67 % SZS status Theorem for theBenchmark.p
% 5.12/16.67
% 5.12/16.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 5.12/16.67
% 5.12/16.67
%------------------------------------------------------------------------------