%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM574+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 : n002.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 3.32s 1.24s
% Output : CNFRefutation 3.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 12 unt; 0 def)
% Number of atoms : 309 ( 33 equ)
% Maximal formula atoms : 181 ( 9 avg)
% Number of connectives : 447 ( 172 ~; 180 |; 73 &)
% ( 2 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 45 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 25 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__3786_02,hypothesis,
( ( ? [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__3786_02) ).
fof(m__,conjecture,
( 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(mNatExtra,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( ? [X2] :
( X1 = szszuzczcdt0(X2)
& aElementOf0(X2,szNzAzT0) )
| X1 = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtra) ).
fof(mNoScLessZr,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ~ sdtlseqdt0(szszuzczcdt0(X1),sz00) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNoScLessZr) ).
fof(m__3786,hypothesis,
( aElementOf0(xi,szNzAzT0)
& aElementOf0(xj,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3786) ).
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(c_0_6,hypothesis,
! [X100,X101] :
( ( szszuzczcdt0(X100) != xi
| ~ aElementOf0(X100,szNzAzT0)
| ~ sdtlseqdt0(xj,xi)
| ~ sdtlseqdt0(xj,xi)
| aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) )
& ( szszuzczcdt0(X100) != xi
| ~ aElementOf0(X100,szNzAzT0)
| ~ sdtlseqdt0(xj,xi)
| ~ sdtlseqdt0(xj,xi)
| aElementOf0(X101,sdtlpdtrp0(xN,xj))
| ~ aElementOf0(X101,sdtlpdtrp0(xN,xi)) ) ),
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__3786_02])])])])]) ).
fof(c_0_7,negated_conjecture,
~ ( 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_8,hypothesis,
( szszuzczcdt0(X1) != xi
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(xj,xi)
| ~ sdtlseqdt0(xj,xi)
| aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,negated_conjecture,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
& ~ aElementOf0(esk1_0,sdtlpdtrp0(xN,xj))
& aElementOf0(esk1_0,sdtlpdtrp0(xN,xi))
& sdtlseqdt0(xj,xi) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
cnf(c_0_10,hypothesis,
( ~ sdtlseqdt0(xj,xi)
| ~ aElementOf0(X1,szNzAzT0)
| szszuzczcdt0(X1) != xi
| aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ),
inference(cn,[status(thm)],[c_0_8]) ).
cnf(c_0_11,negated_conjecture,
sdtlseqdt0(xj,xi),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,negated_conjecture,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X107] :
( ( ~ aElementOf0(X107,szNzAzT0)
| X107 = sz00
| X107 = szszuzczcdt0(esk23_1(X107)) )
& ( ~ aElementOf0(X107,szNzAzT0)
| X107 = sz00
| aElementOf0(esk23_1(X107),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_14,plain,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ~ sdtlseqdt0(szszuzczcdt0(X1),sz00) ),
inference(fof_simplification,[status(thm)],[mNoScLessZr]) ).
cnf(c_0_15,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| szszuzczcdt0(X1) != xi ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11])]),c_0_12]) ).
cnf(c_0_16,plain,
( ~ aElementOf0(X1,szNzAzT0)
| X1 = sz00
| X1 = szszuzczcdt0(esk23_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,hypothesis,
aElementOf0(xi,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3786]) ).
fof(c_0_18,plain,
! [X113] :
( ~ sdtlseqdt0(szszuzczcdt0(X113),sz00)
| ~ aElementOf0(X113,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
cnf(c_0_19,hypothesis,
( ~ aElementOf0(esk23_1(xi),szNzAzT0)
| xi = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16])]),c_0_17])]) ).
cnf(c_0_20,plain,
( ~ aElementOf0(X1,szNzAzT0)
| X1 = sz00
| aElementOf0(esk23_1(X1),szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_21,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]) ).
cnf(c_0_22,plain,
( ~ sdtlseqdt0(szszuzczcdt0(X1),sz00)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,hypothesis,
xi = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_17])]) ).
fof(c_0_24,hypothesis,
! [X89,X91,X92,X93,X94] :
( ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X89),szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X89))) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X89),szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X89)),sdtmndt0(sdtlpdtrp0(xN,X89),szmzizndt0(sdtlpdtrp0(xN,X89)))) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X89),szNzAzT0)
| aElementOf0(X94,sdtmndt0(sdtlpdtrp0(xN,X89),szmzizndt0(sdtlpdtrp0(xN,X89))))
| ~ aElementOf0(X94,sdtlpdtrp0(xN,szszuzczcdt0(X89))) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X89),szNzAzT0)
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X89))) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X89),szNzAzT0)
| aElementOf0(X93,sdtmndt0(sdtlpdtrp0(xN,X89),szmzizndt0(sdtlpdtrp0(xN,X89))))
| X93 = szmzizndt0(sdtlpdtrp0(xN,X89))
| ~ aElementOf0(X93,sdtlpdtrp0(xN,X89))
| ~ aElement0(X93) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X89),szNzAzT0)
| ~ aElementOf0(X92,sdtmndt0(sdtlpdtrp0(xN,X89),szmzizndt0(sdtlpdtrp0(xN,X89))))
| X92 != szmzizndt0(sdtlpdtrp0(xN,X89)) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X89),szNzAzT0)
| ~ aElementOf0(X92,sdtmndt0(sdtlpdtrp0(xN,X89),szmzizndt0(sdtlpdtrp0(xN,X89))))
| aElementOf0(X92,sdtlpdtrp0(xN,X89)) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X89),szNzAzT0)
| ~ aElementOf0(X92,sdtmndt0(sdtlpdtrp0(xN,X89),szmzizndt0(sdtlpdtrp0(xN,X89))))
| aElement0(X92) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X89),szNzAzT0)
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X89),szmzizndt0(sdtlpdtrp0(xN,X89)))) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X89),szNzAzT0)
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X89)),X91)
| ~ aElementOf0(X91,sdtlpdtrp0(xN,X89)) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X89),szNzAzT0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X89)),sdtlpdtrp0(xN,X89)) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSet0(sdtlpdtrp0(xN,X89))
| ~ aElementOf0(esk22_1(X89),szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X89))) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSet0(sdtlpdtrp0(xN,X89))
| ~ aElementOf0(esk22_1(X89),szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X89)),sdtmndt0(sdtlpdtrp0(xN,X89),szmzizndt0(sdtlpdtrp0(xN,X89)))) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSet0(sdtlpdtrp0(xN,X89))
| ~ aElementOf0(esk22_1(X89),szNzAzT0)
| aElementOf0(X94,sdtmndt0(sdtlpdtrp0(xN,X89),szmzizndt0(sdtlpdtrp0(xN,X89))))
| ~ aElementOf0(X94,sdtlpdtrp0(xN,szszuzczcdt0(X89))) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSet0(sdtlpdtrp0(xN,X89))
| ~ aElementOf0(esk22_1(X89),szNzAzT0)
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X89))) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSet0(sdtlpdtrp0(xN,X89))
| ~ aElementOf0(esk22_1(X89),szNzAzT0)
| aElementOf0(X93,sdtmndt0(sdtlpdtrp0(xN,X89),szmzizndt0(sdtlpdtrp0(xN,X89))))
| X93 = szmzizndt0(sdtlpdtrp0(xN,X89))
| ~ aElementOf0(X93,sdtlpdtrp0(xN,X89))
| ~ aElement0(X93) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSet0(sdtlpdtrp0(xN,X89))
| ~ aElementOf0(esk22_1(X89),szNzAzT0)
| ~ aElementOf0(X92,sdtmndt0(sdtlpdtrp0(xN,X89),szmzizndt0(sdtlpdtrp0(xN,X89))))
| X92 != szmzizndt0(sdtlpdtrp0(xN,X89)) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSet0(sdtlpdtrp0(xN,X89))
| ~ aElementOf0(esk22_1(X89),szNzAzT0)
| ~ aElementOf0(X92,sdtmndt0(sdtlpdtrp0(xN,X89),szmzizndt0(sdtlpdtrp0(xN,X89))))
| aElementOf0(X92,sdtlpdtrp0(xN,X89)) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSet0(sdtlpdtrp0(xN,X89))
| ~ aElementOf0(esk22_1(X89),szNzAzT0)
| ~ aElementOf0(X92,sdtmndt0(sdtlpdtrp0(xN,X89),szmzizndt0(sdtlpdtrp0(xN,X89))))
| aElement0(X92) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSet0(sdtlpdtrp0(xN,X89))
| ~ aElementOf0(esk22_1(X89),szNzAzT0)
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X89),szmzizndt0(sdtlpdtrp0(xN,X89)))) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSet0(sdtlpdtrp0(xN,X89))
| ~ aElementOf0(esk22_1(X89),szNzAzT0)
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X89)),X91)
| ~ aElementOf0(X91,sdtlpdtrp0(xN,X89)) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSet0(sdtlpdtrp0(xN,X89))
| ~ aElementOf0(esk22_1(X89),szNzAzT0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X89)),sdtlpdtrp0(xN,X89)) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSet0(sdtlpdtrp0(xN,X89))
| aElementOf0(esk22_1(X89),sdtlpdtrp0(xN,X89))
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X89))) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSet0(sdtlpdtrp0(xN,X89))
| aElementOf0(esk22_1(X89),sdtlpdtrp0(xN,X89))
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X89)),sdtmndt0(sdtlpdtrp0(xN,X89),szmzizndt0(sdtlpdtrp0(xN,X89)))) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSet0(sdtlpdtrp0(xN,X89))
| aElementOf0(esk22_1(X89),sdtlpdtrp0(xN,X89))
| aElementOf0(X94,sdtmndt0(sdtlpdtrp0(xN,X89),szmzizndt0(sdtlpdtrp0(xN,X89))))
| ~ aElementOf0(X94,sdtlpdtrp0(xN,szszuzczcdt0(X89))) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSet0(sdtlpdtrp0(xN,X89))
| aElementOf0(esk22_1(X89),sdtlpdtrp0(xN,X89))
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X89))) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSet0(sdtlpdtrp0(xN,X89))
| aElementOf0(esk22_1(X89),sdtlpdtrp0(xN,X89))
| aElementOf0(X93,sdtmndt0(sdtlpdtrp0(xN,X89),szmzizndt0(sdtlpdtrp0(xN,X89))))
| X93 = szmzizndt0(sdtlpdtrp0(xN,X89))
| ~ aElementOf0(X93,sdtlpdtrp0(xN,X89))
| ~ aElement0(X93) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSet0(sdtlpdtrp0(xN,X89))
| aElementOf0(esk22_1(X89),sdtlpdtrp0(xN,X89))
| ~ aElementOf0(X92,sdtmndt0(sdtlpdtrp0(xN,X89),szmzizndt0(sdtlpdtrp0(xN,X89))))
| X92 != szmzizndt0(sdtlpdtrp0(xN,X89)) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSet0(sdtlpdtrp0(xN,X89))
| aElementOf0(esk22_1(X89),sdtlpdtrp0(xN,X89))
| ~ aElementOf0(X92,sdtmndt0(sdtlpdtrp0(xN,X89),szmzizndt0(sdtlpdtrp0(xN,X89))))
| aElementOf0(X92,sdtlpdtrp0(xN,X89)) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSet0(sdtlpdtrp0(xN,X89))
| aElementOf0(esk22_1(X89),sdtlpdtrp0(xN,X89))
| ~ aElementOf0(X92,sdtmndt0(sdtlpdtrp0(xN,X89),szmzizndt0(sdtlpdtrp0(xN,X89))))
| aElement0(X92) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSet0(sdtlpdtrp0(xN,X89))
| aElementOf0(esk22_1(X89),sdtlpdtrp0(xN,X89))
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X89),szmzizndt0(sdtlpdtrp0(xN,X89)))) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSet0(sdtlpdtrp0(xN,X89))
| aElementOf0(esk22_1(X89),sdtlpdtrp0(xN,X89))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X89)),X91)
| ~ aElementOf0(X91,sdtlpdtrp0(xN,X89)) )
& ( ~ aElementOf0(X89,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X89))
| ~ aSet0(sdtlpdtrp0(xN,X89))
| aElementOf0(esk22_1(X89),sdtlpdtrp0(xN,X89))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X89)),sdtlpdtrp0(xN,X89)) )
& 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_21])])])])])])]) ).
cnf(c_0_25,plain,
( ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(X1,sz00)
| X1 = sz00 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_16]),c_0_20]) ).
cnf(c_0_26,negated_conjecture,
sdtlseqdt0(xj,sz00),
inference(rw,[status(thm)],[c_0_11,c_0_23]) ).
cnf(c_0_27,hypothesis,
aElementOf0(xj,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3786]) ).
cnf(c_0_28,negated_conjecture,
aElementOf0(esk1_0,sdtlpdtrp0(xN,xi)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_29,hypothesis,
sdtlpdtrp0(xN,sz00) = xS,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,negated_conjecture,
~ aElementOf0(esk1_0,sdtlpdtrp0(xN,xj)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_31,negated_conjecture,
xj = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_32,negated_conjecture,
aElementOf0(esk1_0,xS),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_23]),c_0_29]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_29]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM574+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 02:44:32 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.45 Running first-order theorem proving
% 0.16/0.45 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
% 3.32/1.24 % Version: 3.5.1
% 3.32/1.24 % Preprocessing class: FSLSSMSMSSSNFFN.
% 3.32/1.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.32/1.24 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 3.32/1.24 % Starting new_bool_3 with 300s (1) cores
% 3.32/1.24 % Starting new_bool_1 with 300s (1) cores
% 3.32/1.24 % Starting sh5l with 300s (1) cores
% 3.32/1.24 % sh5l with pid 2256905 completed with status 0
% 3.32/1.24 % Result found by sh5l
% 3.32/1.24 % Preprocessing class: FSLSSMSMSSSNFFN.
% 3.32/1.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.32/1.24 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 3.32/1.24 % Starting new_bool_3 with 300s (1) cores
% 3.32/1.24 % Starting new_bool_1 with 300s (1) cores
% 3.32/1.24 % Starting sh5l with 300s (1) cores
% 3.32/1.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 3.32/1.24 % SinE strategy is gf500_gu_R04_F100_L20000
% 3.32/1.24 % Search class: FGHSF-SMLM32-MFFFFFNN
% 3.32/1.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 3.32/1.24 % Starting SubtermCWHack with 28s (1) cores
% 3.32/1.24 % SubtermCWHack with pid 2256913 completed with status 0
% 3.32/1.24 % Result found by SubtermCWHack
% 3.32/1.24 % Preprocessing class: FSLSSMSMSSSNFFN.
% 3.32/1.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.32/1.24 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 3.32/1.24 % Starting new_bool_3 with 300s (1) cores
% 3.32/1.24 % Starting new_bool_1 with 300s (1) cores
% 3.32/1.24 % Starting sh5l with 300s (1) cores
% 3.32/1.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 3.32/1.24 % SinE strategy is gf500_gu_R04_F100_L20000
% 3.32/1.24 % Search class: FGHSF-SMLM32-MFFFFFNN
% 3.32/1.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 3.32/1.24 % Starting SubtermCWHack with 28s (1) cores
% 3.32/1.24 % Preprocessing time : 0.163 s
% 3.32/1.24
% 3.32/1.24 % Proof found!
% 3.32/1.24 % SZS status Theorem
% 3.32/1.24 % SZS output start CNFRefutation
% See solution above
% 3.32/1.24 % Parsed axioms : 86
% 3.32/1.24 % Removed by relevancy pruning/SinE : 3
% 3.32/1.24 % Initial clauses : 4178
% 3.32/1.24 % Removed in clause preprocessing : 7
% 3.32/1.24 % Initial clauses in saturation : 4171
% 3.32/1.24 % Processed clauses : 445
% 3.32/1.24 % ...of these trivial : 0
% 3.32/1.24 % ...subsumed : 125
% 3.32/1.24 % ...remaining for further processing : 320
% 3.32/1.24 % Other redundant clauses eliminated : 38
% 3.32/1.24 % Clauses deleted for lack of memory : 0
% 3.32/1.24 % Backward-subsumed : 12
% 3.32/1.24 % Backward-rewritten : 15
% 3.32/1.24 % Generated clauses : 724
% 3.32/1.24 % ...of the previous two non-redundant : 577
% 3.32/1.24 % ...aggressively subsumed : 0
% 3.32/1.24 % Contextual simplify-reflections : 21
% 3.32/1.24 % Paramodulations : 686
% 3.32/1.24 % Factorizations : 0
% 3.32/1.24 % NegExts : 0
% 3.32/1.24 % Equation resolutions : 39
% 3.32/1.24 % Disequality decompositions : 0
% 3.32/1.24 % Total rewrite steps : 506
% 3.32/1.24 % ...of those cached : 460
% 3.32/1.24 % Propositional unsat checks : 0
% 3.32/1.24 % Propositional check models : 0
% 3.32/1.24 % Propositional check unsatisfiable : 0
% 3.32/1.24 % Propositional clauses : 0
% 3.32/1.24 % Propositional clauses after purity: 0
% 3.32/1.24 % Propositional unsat core size : 0
% 3.32/1.24 % Propositional preprocessing time : 0.000
% 3.32/1.24 % Propositional encoding time : 0.000
% 3.32/1.24 % Propositional solver time : 0.000
% 3.32/1.24 % Success case prop preproc time : 0.000
% 3.32/1.24 % Success case prop encoding time : 0.000
% 3.32/1.24 % Success case prop solver time : 0.000
% 3.32/1.24 % Current number of processed clauses : 261
% 3.32/1.24 % Positive orientable unit clauses : 51
% 3.32/1.24 % Positive unorientable unit clauses: 0
% 3.32/1.24 % Negative unit clauses : 14
% 3.32/1.24 % Non-unit-clauses : 196
% 3.32/1.24 % Current number of unprocessed clauses: 4295
% 3.32/1.24 % ...number of literals in the above : 51934
% 3.32/1.24 % Current number of archived formulas : 0
% 3.32/1.24 % Current number of archived clauses : 29
% 3.32/1.24 % Clause-clause subsumption calls (NU) : 5713
% 3.32/1.24 % Rec. Clause-clause subsumption calls : 3319
% 3.32/1.24 % Non-unit clause-clause subsumptions : 108
% 3.32/1.24 % Unit Clause-clause subsumption calls : 978
% 3.32/1.24 % Rewrite failures with RHS unbound : 0
% 3.32/1.24 % BW rewrite match attempts : 7
% 3.32/1.24 % BW rewrite match successes : 7
% 3.32/1.24 % Condensation attempts : 0
% 3.32/1.24 % Condensation successes : 0
% 3.32/1.24 % Termbank termtop insertions : 342887
% 3.32/1.24 % Search garbage collected termcells : 26612
% 3.32/1.24
% 3.32/1.24 % -------------------------------------------------
% 3.32/1.24 % User time : 0.628 s
% 3.32/1.24 % System time : 0.054 s
% 3.32/1.24 % Total time : 0.682 s
% 3.32/1.24 % Maximum resident set size: 14772 pages
% 3.32/1.24
% 3.32/1.24 % -------------------------------------------------
% 3.32/1.24 % User time : 0.633 s
% 3.32/1.24 % System time : 0.065 s
% 3.32/1.24 % Total time : 0.698 s
% 3.32/1.24 % Maximum resident set size: 4864 pages
% 3.32/1.24 % E exiting
%------------------------------------------------------------------------------