%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM630+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 : n007.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 02:26:18 PM UTC 2026
% Result : Theorem 131.62s 19.43s
% Output : CNFRefutation 131.62s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f303ERROR: Could not build tree for root c_37085ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
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(f14,axiom,
! [X0,X1,X2] :
( ( aSet0(X2)
& aSet0(X1)
& aSet0(X0) )
=> ( ( aSubsetOf0(X1,X2)
& aSubsetOf0(X0,X1) )
=> aSubsetOf0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubTrans) ).
fof(f82,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( isCountable0(sdtlpdtrp0(xN,X0))
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
fof(f104,axiom,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X0] :
( aElementOf0(X0,xP)
<=> ( X0 != szmzizndt0(xQ)
& aElementOf0(X0,xQ)
& aElement0(X0) ) )
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),X0) )
& aSet0(xP) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5164) ).
fof(f109,axiom,
sbrdtbr0(xP) = xk,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5217) ).
fof(f111,axiom,
( sdtlpdtrp0(xe,xn) = xp
& aElementOf0(xn,szNzAzT0)
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xd,xn) = szDzizrdt0(xd)
& aElementOf0(xn,szDzozmdt0(xd)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5309) ).
fof(f113,axiom,
( aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5334) ).
fof(f116,conjecture,
( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0) )
=> ( ( ! [X0] :
( aElementOf0(X0,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( ( X0 = szmzizndt0(sdtlpdtrp0(xN,xn))
| aElementOf0(X0,xP) )
& aElement0(X0) ) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
=> sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f117,negated_conjecture,
~ ( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0) )
=> ( ( ! [X0] :
( aElementOf0(X0,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( ( X0 = szmzizndt0(sdtlpdtrp0(xN,xn))
| aElementOf0(X0,xP) )
& aElement0(X0) ) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
=> sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ) ),
inference(negated_conjecture,[status(cth)],[f116]) ).
fof(f139,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( szmzizndt0(xQ) != X1
& aElementOf0(X1,xQ)
& aElement0(X1) ) )
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),X0) )
& aSet0(xP) ),
inference(rectify,[],[f104]) ).
fof(f141,plain,
~ ( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0) )
=> ( ( ! [X1] :
( aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,xn)) = X1
| aElementOf0(X1,xP) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
=> sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ) ),
inference(rectify,[],[f117]) ).
fof(f148,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f154,plain,
! [X0,X1,X2] :
( ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| aSubsetOf0(X0,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f155,plain,
! [X0,X1,X2] :
( ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| aSubsetOf0(X0,X2) ),
inference(flattening,[],[f154]) ).
fof(f248,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ( isCountable0(sdtlpdtrp0(xN,X0))
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ! [X1] :
( ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| aElementOf0(X1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X0)) ) ),
inference(ennf_transformation,[],[f82]) ).
fof(f276,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( szmzizndt0(xQ) != X1
& aElementOf0(X1,xQ)
& aElement0(X1) ) )
& ! [X0] :
( ~ aElementOf0(X0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),X0) )
& aSet0(xP) ),
inference(ennf_transformation,[],[f139]) ).
fof(f279,plain,
( aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& ! [X0] :
( ~ aElementOf0(X0,xP)
| aElementOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
inference(ennf_transformation,[],[f113]) ).
fof(f282,plain,
( ! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0) )
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,xn)) = X1
| aElementOf0(X1,xP) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ),
inference(ennf_transformation,[],[f141]) ).
fof(f283,plain,
( ! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0) )
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,xn)) = X1
| aElementOf0(X1,xP) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ),
inference(flattening,[],[f282]) ).
fof(f321,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,[],[f148]) ).
fof(f322,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,[],[f321]) ).
fof(f323,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,[],[f322]) ).
fof(f324,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ( aElementOf0(sK26(X0,X1),X1)
& ~ aElementOf0(sK26(X0,X1),X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(X2,sK26(X0,X1))],[f323]) ).
fof(f392,plain,
! [X0] :
( ~ sP9(X0)
| ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& sP8(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) ),
inference(nnf_transformation,[],[f296]) ).
fof(f393,plain,
! [X0] :
( ~ sP9(X0)
| ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& sP8(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X1] :
( ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) ),
inference(rectify,[],[f392]) ).
fof(f397,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ( aElementOf0(sK54(X0),sdtlpdtrp0(xN,X0))
& ~ aElementOf0(sK54(X0),szNzAzT0) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) )
| sP9(X0) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(X1,sK54(X0))],[f297]) ).
fof(f416,plain,
! [X0] :
( ~ sP15(X0)
| ! [X6] :
( sP14(X0,X6)
| ~ aSet0(X6)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X6) = sdtlpdtrp0(xc,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X11] :
( ( ~ aElementOf0(X11,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X11
| aElementOf0(X11,X6) )
& aElement0(X11) ) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X11
& ~ aElementOf0(X11,X6) )
| ~ aElement0(X11)
| aElementOf0(X11,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& ! [X10] :
( ~ aElementOf0(X10,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X10) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) ) ),
inference(nnf_transformation,[],[f304]) ).
fof(f417,plain,
! [X0] :
( ~ sP15(X0)
| ! [X6] :
( sP14(X0,X6)
| ~ aSet0(X6)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X6) = sdtlpdtrp0(xc,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X11] :
( ( ~ aElementOf0(X11,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X11
| aElementOf0(X11,X6) )
& aElement0(X11) ) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X11
& ~ aElementOf0(X11,X6) )
| ~ aElement0(X11)
| aElementOf0(X11,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& ! [X10] :
( ~ aElementOf0(X10,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X10) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) ) ),
inference(flattening,[],[f416]) ).
fof(f418,plain,
! [X0] :
( ~ sP15(X0)
| ! [X1] :
( sP14(X0,X1)
| ~ aSet0(X1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( ( ~ aElementOf0(X3,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X3
| aElementOf0(X3,X1) )
& aElement0(X3) ) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& ~ aElementOf0(X3,X1) )
| ~ aElement0(X3)
| aElementOf0(X3,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) ) ),
inference(rectify,[],[f417]) ).
fof(f419,plain,
! [X0,X6] :
( ~ sP14(X0,X6)
| ( ! [X7] :
( ~ aElementOf0(X7,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& sP13(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ~ aElementOf0(X6,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& ( xk != sbrdtbr0(X6)
| ( ~ aSubsetOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ? [X9] :
( aElementOf0(X9,X6)
& ~ aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ) ) ),
inference(nnf_transformation,[],[f303]) ).
fof(f420,plain,
! [X0,X1] :
( ~ sP14(X0,X1)
| ( ! [X3] :
( ~ aElementOf0(X3,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& sP13(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ~ aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& ( sbrdtbr0(X1) != xk
| ( ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ) ) ),
inference(rectify,[],[f419]) ).
fof(f421,plain,
! [X0,X1] :
( ~ sP14(X0,X1)
| ( ! [X3] :
( ~ aElementOf0(X3,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& sP13(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ~ aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& ( sbrdtbr0(X1) != xk
| ( ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(sK58(X0,X1),X1)
& ~ aElementOf0(sK58(X0,X1),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(X2,sK58(X0,X1))],[f420]) ).
fof(f465,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X1] :
( ( ~ aElementOf0(X1,xP)
| ( szmzizndt0(xQ) != X1
& aElementOf0(X1,xQ)
& aElement0(X1) ) )
& ( szmzizndt0(xQ) = X1
| ~ aElementOf0(X1,xQ)
| ~ aElement0(X1)
| aElementOf0(X1,xP) ) )
& ! [X0] :
( ~ aElementOf0(X0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),X0) )
& aSet0(xP) ),
inference(nnf_transformation,[],[f276]) ).
fof(f466,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X1] :
( ( ~ aElementOf0(X1,xP)
| ( szmzizndt0(xQ) != X1
& aElementOf0(X1,xQ)
& aElement0(X1) ) )
& ( szmzizndt0(xQ) = X1
| ~ aElementOf0(X1,xQ)
| ~ aElement0(X1)
| aElementOf0(X1,xP) ) )
& ! [X0] :
( ~ aElementOf0(X0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),X0) )
& aSet0(xP) ),
inference(flattening,[],[f465]) ).
fof(f470,plain,
( ! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0) )
& ! [X1] :
( ( ~ aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
| ( ( szmzizndt0(sdtlpdtrp0(xN,xn)) = X1
| aElementOf0(X1,xP) )
& aElement0(X1) ) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,xn)) != X1
& ~ aElementOf0(X1,xP) )
| ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ),
inference(nnf_transformation,[],[f283]) ).
fof(f471,plain,
( ! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0) )
& ! [X1] :
( ( ~ aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
| ( ( szmzizndt0(sdtlpdtrp0(xN,xn)) = X1
| aElementOf0(X1,xP) )
& aElement0(X1) ) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,xn)) != X1
& ~ aElementOf0(X1,xP) )
| ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ),
inference(flattening,[],[f470]) ).
fof(f472,plain,
( ! [X1] :
( ~ aElementOf0(X1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X1) )
& ! [X0] :
( ( ~ aElementOf0(X0,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
| ( ( szmzizndt0(sdtlpdtrp0(xN,xn)) = X0
| aElementOf0(X0,xP) )
& aElement0(X0) ) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,xn)) != X0
& ~ aElementOf0(X0,xP) )
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ),
inference(rectify,[],[f471]) ).
fof(f481,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| aSet0(X1) ),
inference(cnf_transformation,[],[f324]) ).
fof(f487,plain,
! [X2,X0,X1] :
( ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| aSubsetOf0(X0,X2) ),
inference(cnf_transformation,[],[f155]) ).
fof(f674,plain,
! [X0] :
( ~ sP9(X0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ),
inference(cnf_transformation,[],[f393]) ).
fof(f685,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| sP9(X0) ),
inference(cnf_transformation,[],[f397]) ).
fof(f686,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| aElementOf0(sK54(X0),sdtlpdtrp0(xN,X0))
| ~ aSet0(sdtlpdtrp0(xN,X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f397]) ).
fof(f691,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,X0)) ),
inference(cnf_transformation,[],[f248]) ).
fof(f692,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) ),
inference(cnf_transformation,[],[f248]) ).
fof(f737,plain,
! [X0,X1] :
( ~ sP15(X0)
| sP14(X0,X1)
| ~ aSet0(X1)
| sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) ),
inference(cnf_transformation,[],[f418]) ).
fof(f749,plain,
! [X0,X1] :
( ~ sP14(X0,X1)
| sbrdtbr0(X1) != xk
| ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ),
inference(cnf_transformation,[],[f421]) ).
fof(f756,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sP15(X0) ),
inference(cnf_transformation,[],[f307]) ).
fof(f760,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ),
inference(cnf_transformation,[],[f307]) ).
fof(f889,plain,
aSet0(xP),
inference(cnf_transformation,[],[f466]) ).
fof(f897,plain,
xk = sbrdtbr0(xP),
inference(cnf_transformation,[],[f109]) ).
fof(f900,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f111]) ).
fof(f905,plain,
aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cnf_transformation,[],[f279]) ).
fof(f923,plain,
sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
inference(cnf_transformation,[],[f472]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( aSet0(X0)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f481]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( aSubsetOf0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X2,X0)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f487]) ).
tcf(c_255,plain,
! [X0: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f674]) ).
tcf(c_265,plain,
! [X0: $i] :
( sP9(X0)
| aElementOf0(sK54(X0),sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aSet0(sdtlpdtrp0(xN,X0)) ),
inference(cnf_transformation,[],[f686]) ).
tcf(c_266,plain,
! [X0: $i] :
( sP9(X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) ),
inference(cnf_transformation,[],[f685]) ).
tcf(c_269,plain,
! [X0: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f692]) ).
tcf(c_270,plain,
! [X0: $i] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f691]) ).
tcf(c_319,plain,
! [X0: $i,X1: $i] :
( sP14(X1,X0)
| ( sdtlpdtrp0(xc,sdtpldt0(X0,szmzizndt0(sdtlpdtrp0(xN,X1)))) = sdtlpdtrp0(sdtlpdtrp0(xC,X1),X0) )
| ~ sP15(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f737]) ).
tcf(c_322,plain,
! [X0: $i,X1: $i] :
( ~ sP14(X1,X0)
| ~ aSubsetOf0(X0,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
| ( sbrdtbr0(X0) != xk ) ),
inference(cnf_transformation,[],[f749]) ).
tcf(c_337,plain,
! [X0: $i] :
( aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f760]) ).
tcf(c_341,plain,
! [X0: $i] :
( sP15(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f756]) ).
tcf(c_459,plain,
aSet0(xP),
inference(cnf_transformation,[],[f889]) ).
tcf(c_473,plain,
sbrdtbr0(xP) = xk,
inference(cnf_transformation,[],[f897]) ).
tcf(c_478,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f900]) ).
tcf(c_482,plain,
aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cnf_transformation,[],[f905]) ).
tcf(c_493,negated_conjecture,
sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
inference(cnf_transformation,[],[f923]) ).
tcf(c_856,plain,
! [X0: $i,X1: $i,X2: $i] :
( aSubsetOf0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X2,X0) ),
inference(global_subsumption_just,[status(thm)],[c_63,c_58,c_63]) ).
tcf(c_857,plain,
! [X0: $i,X1: $i,X2: $i] :
( aSubsetOf0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSubsetOf0(X2,X0)
| ~ aSubsetOf0(X0,X1) ),
inference(renaming,[status(thm)],[c_856]) ).
tcf(c_865,plain,
! [X0: $i] :
( sP9(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(global_subsumption_just,[status(thm)],[c_265,c_270,c_269,c_266]) ).
tcf(c_4363,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
| ~ aElementOf0(X0,szNzAzT0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_865,c_255]) ).
tcf(c_4364,plain,
! [X0: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(unflattening,[status(thm)],[c_4363]) ).
tcf(c_4442,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP14(X0,X2)
| ( sdtlpdtrp0(xc,sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X0)))) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X2) )
| ~ aSet0(X2)
| ~ aElementOf0(X1,szNzAzT0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_319,c_341]) ).
tcf(c_4443,plain,
! [X0: $i,X1: $i] :
( sP14(X0,X1)
| ( sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) )
| ~ aSet0(X1)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(unflattening,[status(thm)],[c_4442]) ).
tcf(c_27295,plain,
( aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(xn,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_27373,plain,
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElementOf0(xn,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_4364]) ).
tcf(c_27848,plain,
! [X0: $i] :
( aSubsetOf0(xP,X0)
| ~ aSet0(xP)
| ~ aSet0(X0)
| ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),X0) ),
inference(instantiation,[status(thm)],[c_857]) ).
tcf(c_27857,plain,
! [X0: $i] :
( sP14(xn,X0)
| ( sdtlpdtrp0(xc,sdtpldt0(X0,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),X0) )
| ~ aSet0(X0)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_4443]) ).
tcf(c_29776,plain,
( aSubsetOf0(xP,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aSet0(xP)
| ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ),
inference(instantiation,[status(thm)],[c_27848]) ).
tcf(c_29904,plain,
( sP14(xn,xP)
| ( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) )
| ~ aSet0(xP)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_27857]) ).
tcf(c_37084,plain,
( ~ sP14(xn,xP)
| ~ aSubsetOf0(xP,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ( sbrdtbr0(xP) != xk ) ),
inference(instantiation,[status(thm)],[c_322]) ).
tcf(c_37085,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_37084,c_29904,c_29776,c_27373,c_27295,c_493,c_482,c_473,c_478,c_459]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM630+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n007.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 04:58:22 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 131.62/19.43 % SZS status Started for theBenchmark.p
% 131.62/19.43 % SZS status Theorem for theBenchmark.p
% 131.62/19.43
% 131.62/19.43 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 131.62/19.43
% 131.62/19.43 % ------ iProver source info
% 131.62/19.43
% 131.62/19.43 % git: date: 2026-07-19 20:42:38 +0200
% 131.62/19.43 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 131.62/19.43 % git: non_committed_changes: false
% 131.62/19.43
% 131.62/19.43 % ------ Parsing...
% 131.62/19.43 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 131.62/19.43
% 131.62/19.43 % ------ Preprocessing... sup_sim: 11 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 131.62/19.43
% 131.62/19.43 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 131.62/19.43
% 131.62/19.43 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 131.62/19.43 % ------ Proving...
% 131.62/19.43 % ------ Problem Properties
% 131.62/19.43
% 131.62/19.43 %
% 131.62/19.43 % clauses 404
% 131.62/19.43 % conjectures 7
% 131.62/19.43 % EPR 78
% 131.62/19.43 % Horn 327
% 131.62/19.43 % unary 72
% 131.62/19.43 % binary 111
% 131.62/19.43 % lits 1219
% 131.62/19.43 % lits eq 177
% 131.62/19.43 % fd_pure 0
% 131.62/19.43 % fd_pseudo 0
% 131.62/19.43 % fd_cond 13
% 131.62/19.43 % fd_pseudo_cond 39
% 131.62/19.43 % AC symbols 0
% 131.62/19.43
% 131.62/19.43 % ------ Input Options Time Limit: Unbounded
% 131.62/19.43
% 131.62/19.43
% 131.62/19.43 % ------
% 131.62/19.43 % Current options:
% 131.62/19.43 % ------
% 131.62/19.43
% 131.62/19.43
% 131.62/19.43 %
% 131.62/19.43
% 131.62/19.43 % ------ Proving...
% 131.62/19.43 %
% 131.62/19.43
% 131.62/19.43 % SZS status Theorem for theBenchmark.p
% 131.62/19.43
% 131.62/19.43 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 131.62/19.43
% 131.62/19.43
%------------------------------------------------------------------------------