%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM603+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 : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:49:44 PM UTC 2026
% Result : Theorem 1.08s 0.77s
% Output : CNFRefutation 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 6 unt; 0 def)
% Number of atoms : 269 ( 16 equ)
% Maximal formula atoms : 181 ( 13 avg)
% Number of connectives : 402 ( 153 ~; 162 |; 69 &)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 45 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 25 !; 0 ?)
% 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__,conjecture,
( aSubsetOf0(sdtlpdtrp0(xN,xi),xS)
| ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> aElementOf0(X1,xS) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__3754,hypothesis,
! [X1,X2] :
( ( aElementOf0(X2,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( sdtlseqdt0(X2,X1)
=> ( 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(mZeroLess,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> sdtlseqdt0(sz00,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroLess) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
fof(m__5034,hypothesis,
( sdtlpdtrp0(xe,xi) = xx
& aElementOf0(xi,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5034) ).
fof(c_0_6,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_7,negated_conjecture,
~ ( aSubsetOf0(sdtlpdtrp0(xN,xi),xS)
| ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> aElementOf0(X1,xS) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_8,hypothesis,
! [X44,X45,X46] :
( ( ~ aElementOf0(X45,szNzAzT0)
| ~ aElementOf0(X44,szNzAzT0)
| ~ sdtlseqdt0(X45,X44)
| aSubsetOf0(sdtlpdtrp0(xN,X44),sdtlpdtrp0(xN,X45)) )
& ( ~ aElementOf0(X45,szNzAzT0)
| ~ aElementOf0(X44,szNzAzT0)
| ~ sdtlseqdt0(X45,X44)
| aElementOf0(X46,sdtlpdtrp0(xN,X45))
| ~ aElementOf0(X46,sdtlpdtrp0(xN,X44)) ) ),
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])])])])]) ).
fof(c_0_9,plain,
! [X159] :
( sdtlseqdt0(sz00,X159)
| ~ aElementOf0(X159,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroLess])])]) ).
fof(c_0_10,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_6])])])])])])]) ).
fof(c_0_11,negated_conjecture,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS)
& ~ aElementOf0(esk22_0,xS)
& aElementOf0(esk22_0,sdtlpdtrp0(xN,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_12,hypothesis,
( ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(X2,X1)
| aSubsetOf0(sdtlpdtrp0(xN,X1),sdtlpdtrp0(xN,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( ~ aElementOf0(X1,szNzAzT0)
| sdtlseqdt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,hypothesis,
sdtlpdtrp0(xN,sz00) = xS,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
aElementOf0(sz00,szNzAzT0),
inference(split_conjunct,[status(thm)],[mZeroNum]) ).
cnf(c_0_16,negated_conjecture,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X1),xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]) ).
cnf(c_0_18,hypothesis,
aElementOf0(xi,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__5034]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM603+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 02:42:05 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 1.08/0.77 % Version: 3.5.1
% 1.08/0.77 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.08/0.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.08/0.77 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.08/0.77 % Starting new_bool_3 with 300s (1) cores
% 1.08/0.77 % Starting new_bool_1 with 300s (1) cores
% 1.08/0.77 % Starting sh5l with 300s (1) cores
% 1.08/0.77 % new_bool_1 with pid 4191699 completed with status 0
% 1.08/0.77 % Result found by new_bool_1
% 1.08/0.77 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.08/0.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.08/0.77 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.08/0.77 % Starting new_bool_3 with 300s (1) cores
% 1.08/0.77 % Starting new_bool_1 with 300s (1) cores
% 1.08/0.77 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.08/0.77 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.08/0.77 % Search class: FGHSF-SMLM32-MFFFFFNN
% 1.08/0.77 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 1.08/0.77 % Starting SubtermCWHack with 28s (1) cores
% 1.08/0.77 % SubtermCWHack with pid 4191753 completed with status 0
% 1.08/0.77 % Result found by SubtermCWHack
% 1.08/0.77 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.08/0.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.08/0.77 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.08/0.77 % Starting new_bool_3 with 300s (1) cores
% 1.08/0.77 % Starting new_bool_1 with 300s (1) cores
% 1.08/0.77 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.08/0.77 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.08/0.77 % Search class: FGHSF-SMLM32-MFFFFFNN
% 1.08/0.77 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 1.08/0.77 % Starting SubtermCWHack with 28s (1) cores
% 1.08/0.77 % Preprocessing time : 0.096 s
% 1.08/0.77
% 1.08/0.77 % Proof found!
% 1.08/0.77 % SZS status Theorem
% 1.08/0.77 % SZS output start CNFRefutation
% See solution above
% 1.08/0.77 % Parsed axioms : 100
% 1.08/0.77 % Removed by relevancy pruning/SinE : 2
% 1.08/0.77 % Initial clauses : 4873
% 1.08/0.77 % Removed in clause preprocessing : 7
% 1.08/0.77 % Initial clauses in saturation : 4866
% 1.08/0.77 % Processed clauses : 975
% 1.08/0.77 % ...of these trivial : 15
% 1.08/0.77 % ...subsumed : 297
% 1.08/0.77 % ...remaining for further processing : 663
% 1.08/0.77 % Other redundant clauses eliminated : 45
% 1.08/0.77 % Clauses deleted for lack of memory : 0
% 1.08/0.77 % Backward-subsumed : 24
% 1.08/0.77 % Backward-rewritten : 27
% 1.08/0.77 % Generated clauses : 2516
% 1.08/0.77 % ...of the previous two non-redundant : 2143
% 1.08/0.77 % ...aggressively subsumed : 0
% 1.08/0.77 % Contextual simplify-reflections : 17
% 1.08/0.77 % Paramodulations : 2472
% 1.08/0.77 % Factorizations : 0
% 1.08/0.77 % NegExts : 0
% 1.08/0.77 % Equation resolutions : 46
% 1.08/0.77 % Disequality decompositions : 0
% 1.08/0.77 % Total rewrite steps : 1576
% 1.08/0.77 % ...of those cached : 1473
% 1.08/0.77 % Propositional unsat checks : 0
% 1.08/0.77 % Propositional check models : 0
% 1.08/0.77 % Propositional check unsatisfiable : 0
% 1.08/0.77 % Propositional clauses : 0
% 1.08/0.77 % Propositional clauses after purity: 0
% 1.08/0.77 % Propositional unsat core size : 0
% 1.08/0.77 % Propositional preprocessing time : 0.000
% 1.08/0.77 % Propositional encoding time : 0.000
% 1.08/0.77 % Propositional solver time : 0.000
% 1.08/0.77 % Success case prop preproc time : 0.000
% 1.08/0.77 % Success case prop encoding time : 0.000
% 1.08/0.77 % Success case prop solver time : 0.000
% 1.08/0.77 % Current number of processed clauses : 574
% 1.08/0.77 % Positive orientable unit clauses : 116
% 1.08/0.77 % Positive unorientable unit clauses: 0
% 1.08/0.77 % Negative unit clauses : 24
% 1.08/0.77 % Non-unit-clauses : 434
% 1.08/0.77 % Current number of unprocessed clauses: 5651
% 1.08/0.77 % ...number of literals in the above : 59767
% 1.08/0.77 % Current number of archived formulas : 0
% 1.08/0.77 % Current number of archived clauses : 53
% 1.08/0.77 % Clause-clause subsumption calls (NU) : 26478
% 1.08/0.77 % Rec. Clause-clause subsumption calls : 17792
% 1.08/0.77 % Non-unit clause-clause subsumptions : 216
% 1.08/0.77 % Unit Clause-clause subsumption calls : 2659
% 1.08/0.77 % Rewrite failures with RHS unbound : 0
% 1.08/0.77 % BW rewrite match attempts : 22
% 1.08/0.77 % BW rewrite match successes : 20
% 1.08/0.77 % Condensation attempts : 0
% 1.08/0.77 % Condensation successes : 0
% 1.08/0.77 % Termbank termtop insertions : 416627
% 1.08/0.77 % Search garbage collected termcells : 31601
% 1.08/0.77
% 1.08/0.77 % -------------------------------------------------
% 1.08/0.77 % User time : 0.295 s
% 1.08/0.77 % System time : 0.033 s
% 1.08/0.77 % Total time : 0.328 s
% 1.08/0.77 % Maximum resident set size: 16100 pages
% 1.08/0.77
% 1.08/0.77 % -------------------------------------------------
% 1.08/0.77 % User time : 0.300 s
% 1.08/0.77 % System time : 0.041 s
% 1.08/0.77 % Total time : 0.340 s
% 1.08/0.77 % Maximum resident set size: 5120 pages
% 1.08/0.77 % E exiting
%------------------------------------------------------------------------------