%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM573+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:49:37 PM UTC 2026
% Result : Theorem 94.72s 12.40s
% Output : CNFRefutation 94.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 11 unt; 0 def)
% Number of atoms : 370 ( 23 equ)
% Maximal formula atoms : 181 ( 8 avg)
% Number of connectives : 522 ( 197 ~; 211 |; 86 &)
% ( 2 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 45 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 37 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__3623,hypothesis,
( ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( ( isCountable0(sdtlpdtrp0(xN,X1))
& ( aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
| ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> aElementOf0(X2,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X1)) ) ) )
=> ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X1)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X1)))
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X1)))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
<=> ( X2 != szmzizndt0(sdtlpdtrp0(xN,X1))
& aElementOf0(X2,sdtlpdtrp0(xN,X1))
& aElement0(X2) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1)) ) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3623) ).
fof(m__3671,hypothesis,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( isCountable0(sdtlpdtrp0(xN,X1))
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> aElementOf0(X2,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3671) ).
fof(m__,conjecture,
( ( ? [X1] :
( szszuzczcdt0(X1) = xi
& aElementOf0(X1,szNzAzT0) )
& sdtlseqdt0(xj,xi) )
=> ( sdtlseqdt0(xj,xi)
=> ( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
| ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> aElementOf0(X1,sdtlpdtrp0(xN,xj)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mIH,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> iLess0(X1,szszuzczcdt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
fof(m__3754,hypothesis,
! [X1,X2] :
( ( aElementOf0(X2,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( sdtlseqdt0(X2,X1)
=> ( iLess0(X1,xi)
=> ( aSubsetOf0(sdtlpdtrp0(xN,X1),sdtlpdtrp0(xN,X2))
& ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X1))
=> aElementOf0(X3,sdtlpdtrp0(xN,X2)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3754) ).
fof(mLessTotal,axiom,
! [X1,X2] :
( ( aElementOf0(X2,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( sdtlseqdt0(szszuzczcdt0(X2),X1)
| sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessTotal) ).
fof(mLessASymm,axiom,
! [X1,X2] :
( ( aElementOf0(X2,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( ( sdtlseqdt0(X2,X1)
& sdtlseqdt0(X1,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessASymm) ).
fof(m__3786,hypothesis,
( aElementOf0(xi,szNzAzT0)
& aElementOf0(xj,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3786) ).
fof(c_0_8,hypothesis,
( ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( ( isCountable0(sdtlpdtrp0(xN,X1))
& ( aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
| ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> aElementOf0(X2,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X1)) ) ) )
=> ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X1)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X1)))
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X1)))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
<=> ( X2 != szmzizndt0(sdtlpdtrp0(xN,X1))
& aElementOf0(X2,sdtlpdtrp0(xN,X1))
& aElement0(X2) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1)) ) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(fof_simplification,[status(thm)],[m__3623]) ).
fof(c_0_9,hypothesis,
! [X90,X92,X93,X94,X95] :
( ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X90),szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X90))) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X90),szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X90)),sdtmndt0(sdtlpdtrp0(xN,X90),szmzizndt0(sdtlpdtrp0(xN,X90)))) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X90),szNzAzT0)
| aElementOf0(X95,sdtmndt0(sdtlpdtrp0(xN,X90),szmzizndt0(sdtlpdtrp0(xN,X90))))
| ~ aElementOf0(X95,sdtlpdtrp0(xN,szszuzczcdt0(X90))) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X90),szNzAzT0)
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X90))) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X90),szNzAzT0)
| aElementOf0(X94,sdtmndt0(sdtlpdtrp0(xN,X90),szmzizndt0(sdtlpdtrp0(xN,X90))))
| X94 = szmzizndt0(sdtlpdtrp0(xN,X90))
| ~ aElementOf0(X94,sdtlpdtrp0(xN,X90))
| ~ aElement0(X94) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X90),szNzAzT0)
| ~ aElementOf0(X93,sdtmndt0(sdtlpdtrp0(xN,X90),szmzizndt0(sdtlpdtrp0(xN,X90))))
| X93 != szmzizndt0(sdtlpdtrp0(xN,X90)) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X90),szNzAzT0)
| ~ aElementOf0(X93,sdtmndt0(sdtlpdtrp0(xN,X90),szmzizndt0(sdtlpdtrp0(xN,X90))))
| aElementOf0(X93,sdtlpdtrp0(xN,X90)) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X90),szNzAzT0)
| ~ aElementOf0(X93,sdtmndt0(sdtlpdtrp0(xN,X90),szmzizndt0(sdtlpdtrp0(xN,X90))))
| aElement0(X93) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X90),szNzAzT0)
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X90),szmzizndt0(sdtlpdtrp0(xN,X90)))) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X90),szNzAzT0)
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X90)),X92)
| ~ aElementOf0(X92,sdtlpdtrp0(xN,X90)) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X90),szNzAzT0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X90)),sdtlpdtrp0(xN,X90)) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSet0(sdtlpdtrp0(xN,X90))
| ~ aElementOf0(esk23_1(X90),szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X90))) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSet0(sdtlpdtrp0(xN,X90))
| ~ aElementOf0(esk23_1(X90),szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X90)),sdtmndt0(sdtlpdtrp0(xN,X90),szmzizndt0(sdtlpdtrp0(xN,X90)))) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSet0(sdtlpdtrp0(xN,X90))
| ~ aElementOf0(esk23_1(X90),szNzAzT0)
| aElementOf0(X95,sdtmndt0(sdtlpdtrp0(xN,X90),szmzizndt0(sdtlpdtrp0(xN,X90))))
| ~ aElementOf0(X95,sdtlpdtrp0(xN,szszuzczcdt0(X90))) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSet0(sdtlpdtrp0(xN,X90))
| ~ aElementOf0(esk23_1(X90),szNzAzT0)
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X90))) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSet0(sdtlpdtrp0(xN,X90))
| ~ aElementOf0(esk23_1(X90),szNzAzT0)
| aElementOf0(X94,sdtmndt0(sdtlpdtrp0(xN,X90),szmzizndt0(sdtlpdtrp0(xN,X90))))
| X94 = szmzizndt0(sdtlpdtrp0(xN,X90))
| ~ aElementOf0(X94,sdtlpdtrp0(xN,X90))
| ~ aElement0(X94) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSet0(sdtlpdtrp0(xN,X90))
| ~ aElementOf0(esk23_1(X90),szNzAzT0)
| ~ aElementOf0(X93,sdtmndt0(sdtlpdtrp0(xN,X90),szmzizndt0(sdtlpdtrp0(xN,X90))))
| X93 != szmzizndt0(sdtlpdtrp0(xN,X90)) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSet0(sdtlpdtrp0(xN,X90))
| ~ aElementOf0(esk23_1(X90),szNzAzT0)
| ~ aElementOf0(X93,sdtmndt0(sdtlpdtrp0(xN,X90),szmzizndt0(sdtlpdtrp0(xN,X90))))
| aElementOf0(X93,sdtlpdtrp0(xN,X90)) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSet0(sdtlpdtrp0(xN,X90))
| ~ aElementOf0(esk23_1(X90),szNzAzT0)
| ~ aElementOf0(X93,sdtmndt0(sdtlpdtrp0(xN,X90),szmzizndt0(sdtlpdtrp0(xN,X90))))
| aElement0(X93) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSet0(sdtlpdtrp0(xN,X90))
| ~ aElementOf0(esk23_1(X90),szNzAzT0)
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X90),szmzizndt0(sdtlpdtrp0(xN,X90)))) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSet0(sdtlpdtrp0(xN,X90))
| ~ aElementOf0(esk23_1(X90),szNzAzT0)
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X90)),X92)
| ~ aElementOf0(X92,sdtlpdtrp0(xN,X90)) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSet0(sdtlpdtrp0(xN,X90))
| ~ aElementOf0(esk23_1(X90),szNzAzT0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X90)),sdtlpdtrp0(xN,X90)) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSet0(sdtlpdtrp0(xN,X90))
| aElementOf0(esk23_1(X90),sdtlpdtrp0(xN,X90))
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X90))) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSet0(sdtlpdtrp0(xN,X90))
| aElementOf0(esk23_1(X90),sdtlpdtrp0(xN,X90))
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X90)),sdtmndt0(sdtlpdtrp0(xN,X90),szmzizndt0(sdtlpdtrp0(xN,X90)))) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSet0(sdtlpdtrp0(xN,X90))
| aElementOf0(esk23_1(X90),sdtlpdtrp0(xN,X90))
| aElementOf0(X95,sdtmndt0(sdtlpdtrp0(xN,X90),szmzizndt0(sdtlpdtrp0(xN,X90))))
| ~ aElementOf0(X95,sdtlpdtrp0(xN,szszuzczcdt0(X90))) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSet0(sdtlpdtrp0(xN,X90))
| aElementOf0(esk23_1(X90),sdtlpdtrp0(xN,X90))
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X90))) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSet0(sdtlpdtrp0(xN,X90))
| aElementOf0(esk23_1(X90),sdtlpdtrp0(xN,X90))
| aElementOf0(X94,sdtmndt0(sdtlpdtrp0(xN,X90),szmzizndt0(sdtlpdtrp0(xN,X90))))
| X94 = szmzizndt0(sdtlpdtrp0(xN,X90))
| ~ aElementOf0(X94,sdtlpdtrp0(xN,X90))
| ~ aElement0(X94) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSet0(sdtlpdtrp0(xN,X90))
| aElementOf0(esk23_1(X90),sdtlpdtrp0(xN,X90))
| ~ aElementOf0(X93,sdtmndt0(sdtlpdtrp0(xN,X90),szmzizndt0(sdtlpdtrp0(xN,X90))))
| X93 != szmzizndt0(sdtlpdtrp0(xN,X90)) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSet0(sdtlpdtrp0(xN,X90))
| aElementOf0(esk23_1(X90),sdtlpdtrp0(xN,X90))
| ~ aElementOf0(X93,sdtmndt0(sdtlpdtrp0(xN,X90),szmzizndt0(sdtlpdtrp0(xN,X90))))
| aElementOf0(X93,sdtlpdtrp0(xN,X90)) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSet0(sdtlpdtrp0(xN,X90))
| aElementOf0(esk23_1(X90),sdtlpdtrp0(xN,X90))
| ~ aElementOf0(X93,sdtmndt0(sdtlpdtrp0(xN,X90),szmzizndt0(sdtlpdtrp0(xN,X90))))
| aElement0(X93) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSet0(sdtlpdtrp0(xN,X90))
| aElementOf0(esk23_1(X90),sdtlpdtrp0(xN,X90))
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X90),szmzizndt0(sdtlpdtrp0(xN,X90)))) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSet0(sdtlpdtrp0(xN,X90))
| aElementOf0(esk23_1(X90),sdtlpdtrp0(xN,X90))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X90)),X92)
| ~ aElementOf0(X92,sdtlpdtrp0(xN,X90)) )
& ( ~ aElementOf0(X90,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X90))
| ~ aSet0(sdtlpdtrp0(xN,X90))
| aElementOf0(esk23_1(X90),sdtlpdtrp0(xN,X90))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X90)),sdtlpdtrp0(xN,X90)) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])])])]) ).
fof(c_0_10,hypothesis,
! [X96,X97] :
( ( ~ aElementOf0(X96,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,X96)) )
& ( ~ aElementOf0(X96,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X96),szNzAzT0) )
& ( ~ aElementOf0(X96,szNzAzT0)
| aElementOf0(X97,szNzAzT0)
| ~ aElementOf0(X97,sdtlpdtrp0(xN,X96)) )
& ( ~ aElementOf0(X96,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,X96)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3671])])])])]) ).
cnf(c_0_11,hypothesis,
( ~ aElementOf0(X2,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X2))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X2),szNzAzT0)
| ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X2),szmzizndt0(sdtlpdtrp0(xN,X2))))
| aElementOf0(X1,sdtlpdtrp0(xN,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,hypothesis,
( ~ aElementOf0(X2,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X2))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X2),szNzAzT0)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X2)))
| aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X2),szmzizndt0(sdtlpdtrp0(xN,X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_15,negated_conjecture,
~ ( ( ? [X1] :
( szszuzczcdt0(X1) = xi
& aElementOf0(X1,szNzAzT0) )
& sdtlseqdt0(xj,xi) )
=> ( sdtlseqdt0(xj,xi)
=> ( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
| ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> aElementOf0(X1,sdtlpdtrp0(xN,xj)) ) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_16,hypothesis,
( ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X2),szmzizndt0(sdtlpdtrp0(xN,X2))))
| aElementOf0(X1,sdtlpdtrp0(xN,X2)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_17,hypothesis,
( ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X2)))
| aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X2),szmzizndt0(sdtlpdtrp0(xN,X2)))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_14,c_0_12]),c_0_13]) ).
fof(c_0_18,negated_conjecture,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
& ~ aElementOf0(esk2_0,sdtlpdtrp0(xN,xj))
& aElementOf0(esk2_0,sdtlpdtrp0(xN,xi))
& sdtlseqdt0(xj,xi)
& szszuzczcdt0(esk1_0) = xi
& aElementOf0(esk1_0,szNzAzT0)
& sdtlseqdt0(xj,xi) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
fof(c_0_19,plain,
! [X130] :
( iLess0(X130,szszuzczcdt0(X130))
| ~ aElementOf0(X130,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIH])])]) ).
fof(c_0_20,hypothesis,
! [X98,X99,X100] :
( ( ~ aElementOf0(X99,szNzAzT0)
| ~ aElementOf0(X98,szNzAzT0)
| ~ sdtlseqdt0(X99,X98)
| ~ iLess0(X98,xi)
| aSubsetOf0(sdtlpdtrp0(xN,X98),sdtlpdtrp0(xN,X99)) )
& ( ~ aElementOf0(X99,szNzAzT0)
| ~ aElementOf0(X98,szNzAzT0)
| ~ sdtlseqdt0(X99,X98)
| ~ iLess0(X98,xi)
| aElementOf0(X100,sdtlpdtrp0(xN,X99))
| ~ aElementOf0(X100,sdtlpdtrp0(xN,X98)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3754])])])])]) ).
cnf(c_0_21,hypothesis,
( ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X2)))
| aElementOf0(X1,sdtlpdtrp0(xN,X2)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,negated_conjecture,
szszuzczcdt0(esk1_0) = xi,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
aElementOf0(esk1_0,szNzAzT0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( ~ aElementOf0(X1,szNzAzT0)
| iLess0(X1,szszuzczcdt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_25,plain,
! [X122,X123] :
( sdtlseqdt0(szszuzczcdt0(X123),X122)
| sdtlseqdt0(X122,X123)
| ~ aElementOf0(X123,szNzAzT0)
| ~ aElementOf0(X122,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessTotal])])]) ).
cnf(c_0_26,hypothesis,
( ~ aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(X3,X2)
| ~ iLess0(X2,xi)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X2))
| aElementOf0(X1,sdtlpdtrp0(xN,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,negated_conjecture,
( ~ aElementOf0(X1,sdtlpdtrp0(xN,xi))
| aElementOf0(X1,sdtlpdtrp0(xN,esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_28,negated_conjecture,
iLess0(esk1_0,xi),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_22]),c_0_23])]) ).
cnf(c_0_29,plain,
( ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| sdtlseqdt0(szszuzczcdt0(X2),X1)
| sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_30,plain,
! [X117,X118] :
( X117 = X118
| ~ sdtlseqdt0(X118,X117)
| ~ sdtlseqdt0(X117,X118)
| ~ aElementOf0(X118,szNzAzT0)
| ~ aElementOf0(X117,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessASymm])])]) ).
cnf(c_0_31,hypothesis,
( ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xi))
| ~ sdtlseqdt0(X2,esk1_0)
| aElementOf0(X1,sdtlpdtrp0(xN,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_23])]) ).
cnf(c_0_32,negated_conjecture,
aElementOf0(esk2_0,sdtlpdtrp0(xN,xi)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_33,negated_conjecture,
( ~ aElementOf0(X1,szNzAzT0)
| sdtlseqdt0(xi,X1)
| sdtlseqdt0(X1,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_22]),c_0_23])]) ).
cnf(c_0_34,hypothesis,
aElementOf0(xj,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3786]) ).
cnf(c_0_35,plain,
( ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,negated_conjecture,
sdtlseqdt0(xj,xi),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_37,hypothesis,
aElementOf0(xi,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3786]) ).
cnf(c_0_38,negated_conjecture,
( ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(X1,esk1_0)
| aElementOf0(esk2_0,sdtlpdtrp0(xN,X1)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_39,hypothesis,
( sdtlseqdt0(xj,esk1_0)
| sdtlseqdt0(xi,xj) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,negated_conjecture,
~ aElementOf0(esk2_0,sdtlpdtrp0(xN,xj)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_41,negated_conjecture,
( ~ sdtlseqdt0(xi,xj)
| xj = xi ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_34]),c_0_37])]) ).
cnf(c_0_42,hypothesis,
sdtlseqdt0(xi,xj),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_34])]),c_0_40]) ).
cnf(c_0_43,negated_conjecture,
xj = xi,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_43]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM573+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n006.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 02:41:14 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 94.72/12.40 % Version: 3.5.1
% 94.72/12.40 % Preprocessing class: FSLSSMSMSSSNFFN.
% 94.72/12.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 94.72/12.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 94.72/12.40 % Starting new_bool_3 with 300s (1) cores
% 94.72/12.40 % Starting new_bool_1 with 300s (1) cores
% 94.72/12.40 % Starting sh5l with 300s (1) cores
% 94.72/12.40 % sh5l with pid 1830340 completed with status 0
% 94.72/12.40 % Result found by sh5l
% 94.72/12.40 % Preprocessing class: FSLSSMSMSSSNFFN.
% 94.72/12.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 94.72/12.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 94.72/12.40 % Starting new_bool_3 with 300s (1) cores
% 94.72/12.40 % Starting new_bool_1 with 300s (1) cores
% 94.72/12.40 % Starting sh5l with 300s (1) cores
% 94.72/12.40 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 94.72/12.40 % SinE strategy is gf500_gu_R04_F100_L20000
% 94.72/12.40 % Search class: FGHSF-SMLM32-MFFFFFNN
% 94.72/12.40 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 94.72/12.40 % Starting SubtermCWHack with 28s (1) cores
% 94.72/12.40 % SubtermCWHack with pid 1830355 completed with status 0
% 94.72/12.40 % Result found by SubtermCWHack
% 94.72/12.40 % Preprocessing class: FSLSSMSMSSSNFFN.
% 94.72/12.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 94.72/12.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 94.72/12.40 % Starting new_bool_3 with 300s (1) cores
% 94.72/12.40 % Starting new_bool_1 with 300s (1) cores
% 94.72/12.40 % Starting sh5l with 300s (1) cores
% 94.72/12.40 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 94.72/12.40 % SinE strategy is gf500_gu_R04_F100_L20000
% 94.72/12.40 % Search class: FGHSF-SMLM32-MFFFFFNN
% 94.72/12.40 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 94.72/12.40 % Starting SubtermCWHack with 28s (1) cores
% 94.72/12.40 % Preprocessing time : 0.086 s
% 94.72/12.40
% 94.72/12.40 % Proof found!
% 94.72/12.40 % SZS status Theorem
% 94.72/12.40 % SZS output start CNFRefutation
% See solution above
% 94.72/12.40 % Parsed axioms : 85
% 94.72/12.40 % Removed by relevancy pruning/SinE : 3
% 94.72/12.40 % Initial clauses : 4179
% 94.72/12.40 % Removed in clause preprocessing : 7
% 94.72/12.40 % Initial clauses in saturation : 4172
% 94.72/12.40 % Processed clauses : 25869
% 94.72/12.40 % ...of these trivial : 26
% 94.72/12.40 % ...subsumed : 16395
% 94.72/12.40 % ...remaining for further processing : 9448
% 94.72/12.40 % Other redundant clauses eliminated : 827
% 94.72/12.40 % Clauses deleted for lack of memory : 0
% 94.72/12.40 % Backward-subsumed : 1217
% 94.72/12.40 % Backward-rewritten : 3459
% 94.72/12.40 % Generated clauses : 107273
% 94.72/12.40 % ...of the previous two non-redundant : 98362
% 94.72/12.40 % ...aggressively subsumed : 0
% 94.72/12.40 % Contextual simplify-reflections : 164
% 94.72/12.40 % Paramodulations : 106519
% 94.72/12.40 % Factorizations : 0
% 94.72/12.40 % NegExts : 0
% 94.72/12.40 % Equation resolutions : 828
% 94.72/12.40 % Disequality decompositions : 0
% 94.72/12.40 % Total rewrite steps : 70665
% 94.72/12.40 % ...of those cached : 70557
% 94.72/12.40 % Propositional unsat checks : 0
% 94.72/12.40 % Propositional check models : 0
% 94.72/12.40 % Propositional check unsatisfiable : 0
% 94.72/12.40 % Propositional clauses : 0
% 94.72/12.40 % Propositional clauses after purity: 0
% 94.72/12.40 % Propositional unsat core size : 0
% 94.72/12.40 % Propositional preprocessing time : 0.000
% 94.72/12.40 % Propositional encoding time : 0.000
% 94.72/12.40 % Propositional solver time : 0.000
% 94.72/12.40 % Success case prop preproc time : 0.000
% 94.72/12.40 % Success case prop encoding time : 0.000
% 94.72/12.40 % Success case prop solver time : 0.000
% 94.72/12.40 % Current number of processed clauses : 4024
% 94.72/12.40 % Positive orientable unit clauses : 104
% 94.72/12.40 % Positive unorientable unit clauses: 0
% 94.72/12.40 % Negative unit clauses : 32
% 94.72/12.40 % Non-unit-clauses : 3888
% 94.72/12.40 % Current number of unprocessed clauses: 73015
% 94.72/12.40 % ...number of literals in the above : 473535
% 94.72/12.40 % Current number of archived formulas : 0
% 94.72/12.40 % Current number of archived clauses : 4678
% 94.72/12.40 % Clause-clause subsumption calls (NU) : 25628835
% 94.72/12.40 % Rec. Clause-clause subsumption calls : 2525751
% 94.72/12.40 % Non-unit clause-clause subsumptions : 14839
% 94.72/12.40 % Unit Clause-clause subsumption calls : 46270
% 94.72/12.40 % Rewrite failures with RHS unbound : 0
% 94.72/12.40 % BW rewrite match attempts : 69
% 94.72/12.40 % BW rewrite match successes : 31
% 94.72/12.40 % Condensation attempts : 0
% 94.72/12.40 % Condensation successes : 0
% 94.72/12.40 % Termbank termtop insertions : 2647679
% 94.72/12.40 % Search garbage collected termcells : 26598
% 94.72/12.40
% 94.72/12.40 % -------------------------------------------------
% 94.72/12.40 % User time : 11.795 s
% 94.72/12.40 % System time : 0.117 s
% 94.72/12.40 % Total time : 11.913 s
% 94.72/12.40 % Maximum resident set size: 14976 pages
% 94.72/12.40
% 94.72/12.40 % -------------------------------------------------
% 94.72/12.40 % User time : 11.802 s
% 94.72/12.40 % System time : 0.122 s
% 94.72/12.40 % Total time : 11.924 s
% 94.72/12.40 % Maximum resident set size: 4608 pages
% 94.72/12.40 % E exiting
%------------------------------------------------------------------------------