%------------------------------------------------------------------------------
% File : E-SAT---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 : n005.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 01:55:33 PM UTC 2026
% Result : Theorem 0.96s 0.70s
% Output : CNFRefutation 0.96s
% 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,
! [X47,X48] :
( ( szszuzczcdt0(X47) != xi
| ~ aElementOf0(X47,szNzAzT0)
| ~ sdtlseqdt0(xj,xi)
| ~ sdtlseqdt0(xj,xi)
| aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) )
& ( szszuzczcdt0(X47) != xi
| ~ aElementOf0(X47,szNzAzT0)
| ~ sdtlseqdt0(xj,xi)
| ~ sdtlseqdt0(xj,xi)
| aElementOf0(X48,sdtlpdtrp0(xN,xj))
| ~ aElementOf0(X48,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(esk13_0,sdtlpdtrp0(xN,xj))
& aElementOf0(esk13_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,
! [X121] :
( ( ~ aElementOf0(X121,szNzAzT0)
| X121 = sz00
| X121 = szszuzczcdt0(esk23_1(X121)) )
& ( ~ aElementOf0(X121,szNzAzT0)
| X121 = sz00
| aElementOf0(esk23_1(X121),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,
! [X124] :
( ~ sdtlseqdt0(szszuzczcdt0(X124),sz00)
| ~ aElementOf0(X124,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,
! [X36,X38,X39,X40,X41] :
( ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X36),szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X36))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X36),szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X36)),sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36)))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X36),szNzAzT0)
| aElementOf0(X41,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| ~ aElementOf0(X41,sdtlpdtrp0(xN,szszuzczcdt0(X36))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X36),szNzAzT0)
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X36))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X36),szNzAzT0)
| aElementOf0(X40,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| X40 = szmzizndt0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(X40,sdtlpdtrp0(xN,X36))
| ~ aElement0(X40) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X36),szNzAzT0)
| ~ aElementOf0(X39,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| X39 != szmzizndt0(sdtlpdtrp0(xN,X36)) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X36),szNzAzT0)
| ~ aElementOf0(X39,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| aElementOf0(X39,sdtlpdtrp0(xN,X36)) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X36),szNzAzT0)
| ~ aElementOf0(X39,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| aElement0(X39) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X36),szNzAzT0)
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36)))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X36),szNzAzT0)
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X36)),X38)
| ~ aElementOf0(X38,sdtlpdtrp0(xN,X36)) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X36),szNzAzT0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X36)),sdtlpdtrp0(xN,X36)) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(esk12_1(X36),szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X36))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(esk12_1(X36),szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X36)),sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36)))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(esk12_1(X36),szNzAzT0)
| aElementOf0(X41,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| ~ aElementOf0(X41,sdtlpdtrp0(xN,szszuzczcdt0(X36))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(esk12_1(X36),szNzAzT0)
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X36))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(esk12_1(X36),szNzAzT0)
| aElementOf0(X40,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| X40 = szmzizndt0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(X40,sdtlpdtrp0(xN,X36))
| ~ aElement0(X40) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(esk12_1(X36),szNzAzT0)
| ~ aElementOf0(X39,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| X39 != szmzizndt0(sdtlpdtrp0(xN,X36)) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(esk12_1(X36),szNzAzT0)
| ~ aElementOf0(X39,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| aElementOf0(X39,sdtlpdtrp0(xN,X36)) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(esk12_1(X36),szNzAzT0)
| ~ aElementOf0(X39,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| aElement0(X39) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(esk12_1(X36),szNzAzT0)
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36)))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(esk12_1(X36),szNzAzT0)
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X36)),X38)
| ~ aElementOf0(X38,sdtlpdtrp0(xN,X36)) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(esk12_1(X36),szNzAzT0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X36)),sdtlpdtrp0(xN,X36)) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| aElementOf0(esk12_1(X36),sdtlpdtrp0(xN,X36))
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X36))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| aElementOf0(esk12_1(X36),sdtlpdtrp0(xN,X36))
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X36)),sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36)))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| aElementOf0(esk12_1(X36),sdtlpdtrp0(xN,X36))
| aElementOf0(X41,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| ~ aElementOf0(X41,sdtlpdtrp0(xN,szszuzczcdt0(X36))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| aElementOf0(esk12_1(X36),sdtlpdtrp0(xN,X36))
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X36))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| aElementOf0(esk12_1(X36),sdtlpdtrp0(xN,X36))
| aElementOf0(X40,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| X40 = szmzizndt0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(X40,sdtlpdtrp0(xN,X36))
| ~ aElement0(X40) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| aElementOf0(esk12_1(X36),sdtlpdtrp0(xN,X36))
| ~ aElementOf0(X39,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| X39 != szmzizndt0(sdtlpdtrp0(xN,X36)) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| aElementOf0(esk12_1(X36),sdtlpdtrp0(xN,X36))
| ~ aElementOf0(X39,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| aElementOf0(X39,sdtlpdtrp0(xN,X36)) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| aElementOf0(esk12_1(X36),sdtlpdtrp0(xN,X36))
| ~ aElementOf0(X39,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| aElement0(X39) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| aElementOf0(esk12_1(X36),sdtlpdtrp0(xN,X36))
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36)))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| aElementOf0(esk12_1(X36),sdtlpdtrp0(xN,X36))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X36)),X38)
| ~ aElementOf0(X38,sdtlpdtrp0(xN,X36)) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| aElementOf0(esk12_1(X36),sdtlpdtrp0(xN,X36))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X36)),sdtlpdtrp0(xN,X36)) )
& 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(esk13_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(esk13_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(esk13_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
% 0.00/0.02 % Problem : NUM574+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 02:41:48 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.40 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
% 0.96/0.70 % Version: 3.5.1
% 0.96/0.70 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.96/0.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.96/0.70 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.96/0.70 % Starting new_bool_3 with 300s (1) cores
% 0.96/0.70 % Starting new_bool_1 with 300s (1) cores
% 0.96/0.70 % Starting sh5l with 300s (1) cores
% 0.96/0.70 % new_bool_3 with pid 2377959 completed with status 0
% 0.96/0.70 % Result found by new_bool_3
% 0.96/0.70 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.96/0.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.96/0.70 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.96/0.70 % Starting new_bool_3 with 300s (1) cores
% 0.96/0.70 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.96/0.70 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.96/0.70 % Search class: FGHSF-SMLM32-MFFFFFNN
% 0.96/0.70 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.96/0.70 % Starting SubtermCWHack with 31s (1) cores
% 0.96/0.70 % SubtermCWHack with pid 2377988 completed with status 0
% 0.96/0.70 % Result found by SubtermCWHack
% 0.96/0.70 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.96/0.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.96/0.70 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.96/0.70 % Starting new_bool_3 with 300s (1) cores
% 0.96/0.70 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.96/0.70 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.96/0.70 % Search class: FGHSF-SMLM32-MFFFFFNN
% 0.96/0.70 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.96/0.70 % Starting SubtermCWHack with 31s (1) cores
% 0.96/0.70 % Preprocessing time : 0.082 s
% 0.96/0.70
% 0.96/0.70 % Proof found!
% 0.96/0.70 % SZS status Theorem
% 0.96/0.70 % SZS output start CNFRefutation
% See solution above
% 0.96/0.70 % Parsed axioms : 86
% 0.96/0.70 % Removed by relevancy pruning/SinE : 5
% 0.96/0.70 % Initial clauses : 4170
% 0.96/0.70 % Removed in clause preprocessing : 7
% 0.96/0.70 % Initial clauses in saturation : 4163
% 0.96/0.70 % Processed clauses : 447
% 0.96/0.70 % ...of these trivial : 1
% 0.96/0.70 % ...subsumed : 119
% 0.96/0.70 % ...remaining for further processing : 327
% 0.96/0.70 % Other redundant clauses eliminated : 36
% 0.96/0.70 % Clauses deleted for lack of memory : 0
% 0.96/0.70 % Backward-subsumed : 15
% 0.96/0.70 % Backward-rewritten : 22
% 0.96/0.70 % Generated clauses : 744
% 0.96/0.70 % ...of the previous two non-redundant : 594
% 0.96/0.70 % ...aggressively subsumed : 0
% 0.96/0.70 % Contextual simplify-reflections : 16
% 0.96/0.70 % Paramodulations : 708
% 0.96/0.70 % Factorizations : 0
% 0.96/0.70 % NegExts : 0
% 0.96/0.70 % Equation resolutions : 37
% 0.96/0.70 % Disequality decompositions : 0
% 0.96/0.70 % Total rewrite steps : 568
% 0.96/0.70 % ...of those cached : 517
% 0.96/0.70 % Propositional unsat checks : 0
% 0.96/0.70 % Propositional check models : 0
% 0.96/0.70 % Propositional check unsatisfiable : 0
% 0.96/0.70 % Propositional clauses : 0
% 0.96/0.70 % Propositional clauses after purity: 0
% 0.96/0.70 % Propositional unsat core size : 0
% 0.96/0.70 % Propositional preprocessing time : 0.000
% 0.96/0.70 % Propositional encoding time : 0.000
% 0.96/0.70 % Propositional solver time : 0.000
% 0.96/0.70 % Success case prop preproc time : 0.000
% 0.96/0.70 % Success case prop encoding time : 0.000
% 0.96/0.70 % Success case prop solver time : 0.000
% 0.96/0.70 % Current number of processed clauses : 261
% 0.96/0.70 % Positive orientable unit clauses : 57
% 0.96/0.70 % Positive unorientable unit clauses: 0
% 0.96/0.70 % Negative unit clauses : 17
% 0.96/0.70 % Non-unit-clauses : 187
% 0.96/0.70 % Current number of unprocessed clauses: 4286
% 0.96/0.70 % ...number of literals in the above : 51877
% 0.96/0.70 % Current number of archived formulas : 0
% 0.96/0.70 % Current number of archived clauses : 39
% 0.96/0.70 % Clause-clause subsumption calls (NU) : 4756
% 0.96/0.70 % Rec. Clause-clause subsumption calls : 2901
% 0.96/0.70 % Non-unit clause-clause subsumptions : 96
% 0.96/0.70 % Unit Clause-clause subsumption calls : 1004
% 0.96/0.70 % Rewrite failures with RHS unbound : 0
% 0.96/0.70 % BW rewrite match attempts : 11
% 0.96/0.70 % BW rewrite match successes : 11
% 0.96/0.70 % Condensation attempts : 0
% 0.96/0.70 % Condensation successes : 0
% 0.96/0.70 % Termbank termtop insertions : 342233
% 0.96/0.70 % Search garbage collected termcells : 26346
% 0.96/0.70
% 0.96/0.70 % -------------------------------------------------
% 0.96/0.70 % User time : 0.247 s
% 0.96/0.70 % System time : 0.024 s
% 0.96/0.70 % Total time : 0.271 s
% 0.96/0.70 % Maximum resident set size: 15028 pages
% 0.96/0.70
% 0.96/0.70 % -------------------------------------------------
% 0.96/0.70 % User time : 0.250 s
% 0.96/0.70 % System time : 0.033 s
% 0.96/0.70 % Total time : 0.283 s
% 0.96/0.70 % Maximum resident set size: 4608 pages
% 0.96/0.70 % E exiting
%------------------------------------------------------------------------------