%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM570+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 : n004.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 01:49:36 PM UTC 2026
% Result : Theorem 95.51s 14.56s
% Output : CNFRefutation 95.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 13 unt; 0 def)
% Number of atoms : 377 ( 37 equ)
% Maximal formula atoms : 181 ( 8 avg)
% Number of connectives : 547 ( 216 ~; 222 |; 86 &)
% ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 45 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 27 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( xi != sz00
=> ( isCountable0(sdtlpdtrp0(xN,xi))
& ( aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
| ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> aElementOf0(X1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,xi)) ) )
& ? [X1] :
( szszuzczcdt0(X1) = xi
& aElementOf0(X1,szNzAzT0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mNatExtra,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( ? [X2] :
( X1 = szszuzczcdt0(X2)
& aElementOf0(X2,szNzAzT0) )
| X1 = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtra) ).
fof(mIH,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> iLess0(X1,szszuzczcdt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
fof(m__3702,hypothesis,
aElementOf0(xi,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3702) ).
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)
=> ( iLess0(X1,xi)
=> ( 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(c_0_6,negated_conjecture,
~ ( xi != sz00
=> ( isCountable0(sdtlpdtrp0(xN,xi))
& ( aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
| ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> aElementOf0(X1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,xi)) ) )
& ? [X1] :
( szszuzczcdt0(X1) = xi
& aElementOf0(X1,szNzAzT0) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_7,negated_conjecture,
~ ( xi != sz00
=> ( isCountable0(sdtlpdtrp0(xN,xi))
& ( aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
| ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> aElementOf0(X1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,xi)) ) )
& ? [X1] :
( szszuzczcdt0(X1) = xi
& aElementOf0(X1,szNzAzT0) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_8,plain,
! [X62] :
( ( ~ aElementOf0(X62,szNzAzT0)
| X62 = sz00
| X62 = szszuzczcdt0(esk5_1(X62)) )
& ( ~ aElementOf0(X62,szNzAzT0)
| X62 = sz00
| aElementOf0(esk5_1(X62),szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mNatExtra])])])])]) ).
fof(c_0_9,negated_conjecture,
! [X214] :
( ( ~ isCountable0(sdtlpdtrp0(xN,xi))
| szszuzczcdt0(X214) != xi
| ~ aElementOf0(X214,szNzAzT0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) )
& ( ~ isCountable0(sdtlpdtrp0(xN,xi))
| szszuzczcdt0(X214) != xi
| ~ aElementOf0(X214,szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(esk32_0,szNzAzT0) )
& ( ~ isCountable0(sdtlpdtrp0(xN,xi))
| szszuzczcdt0(X214) != xi
| ~ aElementOf0(X214,szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xi))
| aElementOf0(esk32_0,sdtlpdtrp0(xN,xi)) )
& xi != sz00 ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])])]) ).
fof(c_0_10,plain,
! [X82] :
( iLess0(X82,szszuzczcdt0(X82))
| ~ aElementOf0(X82,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIH])])]) ).
cnf(c_0_11,plain,
( ~ aElementOf0(X1,szNzAzT0)
| X1 = sz00
| aElementOf0(esk5_1(X1),szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,hypothesis,
aElementOf0(xi,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3702]) ).
cnf(c_0_13,negated_conjecture,
xi != sz00,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( ~ aElementOf0(X1,szNzAzT0)
| X1 = sz00
| X1 = szszuzczcdt0(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_15,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_16,hypothesis,
! [X212,X213] :
( ( ~ aElementOf0(X212,szNzAzT0)
| ~ iLess0(X212,xi)
| isCountable0(sdtlpdtrp0(xN,X212)) )
& ( ~ aElementOf0(X212,szNzAzT0)
| ~ iLess0(X212,xi)
| aSubsetOf0(sdtlpdtrp0(xN,X212),szNzAzT0) )
& ( ~ aElementOf0(X212,szNzAzT0)
| ~ iLess0(X212,xi)
| aElementOf0(X213,szNzAzT0)
| ~ aElementOf0(X213,sdtlpdtrp0(xN,X212)) )
& ( ~ aElementOf0(X212,szNzAzT0)
| ~ iLess0(X212,xi)
| aSet0(sdtlpdtrp0(xN,X212)) ) ),
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_17,plain,
( ~ aElementOf0(X1,szNzAzT0)
| iLess0(X1,szszuzczcdt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,hypothesis,
aElementOf0(esk5_1(xi),szNzAzT0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_19,hypothesis,
szszuzczcdt0(esk5_1(xi)) = xi,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_12]),c_0_13]) ).
fof(c_0_20,hypothesis,
! [X206,X208,X209,X210,X211] :
( ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X206))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X206)),sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206)))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| aElementOf0(X211,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| ~ aElementOf0(X211,sdtlpdtrp0(xN,szszuzczcdt0(X206))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X206))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| aElementOf0(X210,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| X210 = szmzizndt0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(X210,sdtlpdtrp0(xN,X206))
| ~ aElement0(X210) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| ~ aElementOf0(X209,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| X209 != szmzizndt0(sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| ~ aElementOf0(X209,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| aElementOf0(X209,sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| ~ aElementOf0(X209,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| aElement0(X209) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206)))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X206)),X208)
| ~ aElementOf0(X208,sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X206)),sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X206))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X206)),sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206)))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| aElementOf0(X211,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| ~ aElementOf0(X211,sdtlpdtrp0(xN,szszuzczcdt0(X206))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X206))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| aElementOf0(X210,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| X210 = szmzizndt0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(X210,sdtlpdtrp0(xN,X206))
| ~ aElement0(X210) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| ~ aElementOf0(X209,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| X209 != szmzizndt0(sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| ~ aElementOf0(X209,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| aElementOf0(X209,sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| ~ aElementOf0(X209,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| aElement0(X209) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206)))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X206)),X208)
| ~ aElementOf0(X208,sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X206)),sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X206))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X206)),sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206)))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| aElementOf0(X211,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| ~ aElementOf0(X211,sdtlpdtrp0(xN,szszuzczcdt0(X206))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X206))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| aElementOf0(X210,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| X210 = szmzizndt0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(X210,sdtlpdtrp0(xN,X206))
| ~ aElement0(X210) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| ~ aElementOf0(X209,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| X209 != szmzizndt0(sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| ~ aElementOf0(X209,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| aElementOf0(X209,sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| ~ aElementOf0(X209,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| aElement0(X209) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206)))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X206)),X208)
| ~ aElementOf0(X208,sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X206)),sdtlpdtrp0(xN,X206)) )
& 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_15])])])])])])]) ).
cnf(c_0_21,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| ~ iLess0(X1,xi)
| isCountable0(sdtlpdtrp0(xN,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,hypothesis,
iLess0(esk5_1(xi),xi),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_23,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X1))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,hypothesis,
isCountable0(sdtlpdtrp0(xN,esk5_1(xi))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_18])]) ).
cnf(c_0_25,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| ~ iLess0(X1,xi)
| aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X1))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,negated_conjecture,
( ~ isCountable0(sdtlpdtrp0(xN,xi))
| szszuzczcdt0(X1) != xi
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(esk32_0,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_28,hypothesis,
( ~ aSubsetOf0(sdtlpdtrp0(xN,esk5_1(xi)),szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,xi)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_19]),c_0_18])]) ).
cnf(c_0_29,hypothesis,
aSubsetOf0(sdtlpdtrp0(xN,esk5_1(xi)),szNzAzT0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_22]),c_0_18])]) ).
cnf(c_0_30,hypothesis,
( ~ aSubsetOf0(sdtlpdtrp0(xN,esk5_1(xi)),szNzAzT0)
| aSet0(sdtlpdtrp0(xN,xi)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_24]),c_0_19]),c_0_18])]) ).
cnf(c_0_31,negated_conjecture,
( ~ aSet0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(esk32_0,szNzAzT0)
| ~ aElementOf0(esk5_1(xi),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,xi)) ),
inference(spm,[status(thm)],[c_0_27,c_0_19]) ).
cnf(c_0_32,negated_conjecture,
( ~ isCountable0(sdtlpdtrp0(xN,xi))
| szszuzczcdt0(X1) != xi
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xi))
| aElementOf0(esk32_0,sdtlpdtrp0(xN,xi)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_33,hypothesis,
isCountable0(sdtlpdtrp0(xN,xi)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).
cnf(c_0_34,hypothesis,
aSet0(sdtlpdtrp0(xN,xi)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_29])]) ).
cnf(c_0_35,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_20]) ).
cnf(c_0_36,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_20]) ).
cnf(c_0_37,hypothesis,
( ~ aElementOf0(X2,szNzAzT0)
| ~ iLess0(X2,xi)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X2))
| aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_38,negated_conjecture,
( ~ aSet0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(esk32_0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,xi)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_18])]) ).
cnf(c_0_39,negated_conjecture,
( ~ aElementOf0(X1,szNzAzT0)
| szszuzczcdt0(X1) != xi
| aElementOf0(esk32_0,sdtlpdtrp0(xN,xi)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]),c_0_34])]) ).
cnf(c_0_40,hypothesis,
( ~ aElementOf0(X1,sdtlpdtrp0(xN,xi))
| aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,esk5_1(xi)),szmzizndt0(sdtlpdtrp0(xN,esk5_1(xi))))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_24]),c_0_29]),c_0_19]),c_0_18])]) ).
cnf(c_0_41,hypothesis,
( ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,esk5_1(xi)),szmzizndt0(sdtlpdtrp0(xN,esk5_1(xi)))))
| aElementOf0(X1,sdtlpdtrp0(xN,esk5_1(xi))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_24]),c_0_29]),c_0_18])]) ).
cnf(c_0_42,hypothesis,
( ~ aElementOf0(X1,sdtlpdtrp0(xN,esk5_1(xi)))
| aElementOf0(X1,szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_22]),c_0_18])]) ).
cnf(c_0_43,negated_conjecture,
~ aElementOf0(esk32_0,szNzAzT0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_33])]),c_0_34])]) ).
cnf(c_0_44,hypothesis,
aElementOf0(esk32_0,sdtlpdtrp0(xN,xi)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_19]),c_0_18])]) ).
cnf(c_0_45,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_40,c_0_41,c_0_42,c_0_43,c_0_44]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM570+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.45 % Computer : n004.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Mon Sep 21 02:41:07 UTC 2026
% 0.17/0.46 % CPUTime :
% 0.17/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.52 Running first-order theorem proving
% 0.23/0.52 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
% 95.51/14.56 % Version: 3.5.1
% 95.51/14.56 % Preprocessing class: FSLSSMSMSSSNFFN.
% 95.51/14.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 95.51/14.56 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 95.51/14.56 % Starting new_bool_3 with 300s (1) cores
% 95.51/14.56 % Starting new_bool_1 with 300s (1) cores
% 95.51/14.56 % Starting sh5l with 300s (1) cores
% 95.51/14.56 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2077162 completed with status 0
% 95.51/14.56 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 95.51/14.56 % Preprocessing class: FSLSSMSMSSSNFFN.
% 95.51/14.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 95.51/14.56 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 95.51/14.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 95.51/14.56 % No SInE strategy applied
% 95.51/14.56 % Search class: FGHSF-SMLM32-MFFFFFNN
% 95.51/14.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 95.51/14.56 % Starting SubtermCWHack with 136s (1) cores
% 95.51/14.56 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 95.51/14.56 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 95.51/14.56 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 95.51/14.56 % Starting new_bool_3 with 136s (1) cores
% 95.51/14.56 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with pid 2077172 completed with status 0
% 95.51/14.56 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d
% 95.51/14.56 % Preprocessing class: FSLSSMSMSSSNFFN.
% 95.51/14.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 95.51/14.56 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 95.51/14.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 95.51/14.56 % No SInE strategy applied
% 95.51/14.56 % Search class: FGHSF-SMLM32-MFFFFFNN
% 95.51/14.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 95.51/14.56 % Starting SubtermCWHack with 136s (1) cores
% 95.51/14.56 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 95.51/14.56 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 95.51/14.56 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 95.51/14.56 % Preprocessing time : 0.253 s
% 95.51/14.56 % Presaturation interreduction done
% 95.51/14.56 % SatCheck found unsatisfiable ground set
% 95.51/14.56
% 95.51/14.56 % Proof found!
% 95.51/14.56 % SZS status Theorem
% 95.51/14.56 % SZS output start CNFRefutation
% See solution above
% 95.51/14.56 % Parsed axioms : 84
% 95.51/14.56 % Removed by relevancy pruning/SinE : 0
% 95.51/14.56 % Initial clauses : 4184
% 95.51/14.56 % Removed in clause preprocessing : 7
% 95.51/14.56 % Initial clauses in saturation : 4177
% 95.51/14.56 % Processed clauses : 12149
% 95.51/14.56 % ...of these trivial : 296
% 95.51/14.56 % ...subsumed : 1853
% 95.51/14.56 % ...remaining for further processing : 10000
% 95.51/14.56 % Other redundant clauses eliminated : 1940
% 95.51/14.56 % Clauses deleted for lack of memory : 0
% 95.51/14.56 % Backward-subsumed : 30
% 95.51/14.56 % Backward-rewritten : 130
% 95.51/14.56 % Generated clauses : 38022
% 95.51/14.56 % ...of the previous two non-redundant : 34381
% 95.51/14.56 % ...aggressively subsumed : 0
% 95.51/14.56 % Contextual simplify-reflections : 157
% 95.51/14.56 % Paramodulations : 36268
% 95.51/14.56 % Factorizations : 6
% 95.51/14.56 % NegExts : 0
% 95.51/14.56 % Equation resolutions : 1942
% 95.51/14.56 % Disequality decompositions : 0
% 95.51/14.56 % Total rewrite steps : 24778
% 95.51/14.56 % ...of those cached : 23798
% 95.51/14.56 % Propositional unsat checks : 3
% 95.51/14.56 % Propositional check models : 2
% 95.51/14.56 % Propositional check unsatisfiable : 1
% 95.51/14.56 % Propositional clauses : 33929
% 95.51/14.56 % Propositional clauses after purity: 1514
% 95.51/14.56 % Propositional unsat core size : 5
% 95.51/14.56 % Propositional preprocessing time : 0.000
% 95.51/14.56 % Propositional encoding time : 0.161
% 95.51/14.56 % Propositional solver time : 0.018
% 95.51/14.56 % Success case prop preproc time : 0.000
% 95.51/14.56 % Success case prop encoding time : 0.099
% 95.51/14.56 % Success case prop solver time : 0.016
% 95.51/14.56 % Current number of processed clauses : 4486
% 95.51/14.56 % Positive orientable unit clauses : 1612
% 95.51/14.56 % Positive unorientable unit clauses: 0
% 95.51/14.56 % Negative unit clauses : 74
% 95.51/14.56 % Non-unit-clauses : 2800
% 95.51/14.56 % Current number of unprocessed clauses: 29443
% 95.51/14.56 % ...number of literals in the above : 122571
% 95.51/14.56 % Current number of archived formulas : 0
% 95.51/14.56 % Current number of archived clauses : 3769
% 95.51/14.56 % Clause-clause subsumption calls (NU) : 8570396
% 95.51/14.56 % Rec. Clause-clause subsumption calls : 390010
% 95.51/14.56 % Non-unit clause-clause subsumptions : 1819
% 95.51/14.56 % Unit Clause-clause subsumption calls : 470349
% 95.51/14.56 % Rewrite failures with RHS unbound : 0
% 95.51/14.56 % BW rewrite match attempts : 88384
% 95.51/14.56 % BW rewrite match successes : 57
% 95.51/14.56 % Condensation attempts : 0
% 95.51/14.56 % Condensation successes : 0
% 95.51/14.56 % Termbank termtop insertions : 1889408
% 95.51/14.56 % Search garbage collected termcells : 26842
% 95.51/14.56
% 95.51/14.56 % -------------------------------------------------
% 95.51/14.56 % User time : 13.769 s
% 95.51/14.56 % System time : 0.136 s
% 95.51/14.56 % Total time : 13.905 s
% 95.51/14.56 % Maximum resident set size: 14768 pages
% 95.51/14.56
% 95.51/14.56 % -------------------------------------------------
% 95.51/14.56 % User time : 66.309 s
% 95.51/14.56 % System time : 0.619 s
% 95.51/14.56 % Total time : 66.928 s
% 95.51/14.56 % Maximum resident set size: 4608 pages
% 95.51/14.56 % E exiting
%------------------------------------------------------------------------------