%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM629+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 01:49:50 PM UTC 2026
% Result : Theorem 3.75s 1.10s
% Output : CNFRefutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 53 ( 16 unt; 0 def)
% Number of atoms : 404 ( 38 equ)
% Maximal formula atoms : 181 ( 7 avg)
% Number of connectives : 547 ( 196 ~; 203 |; 118 &)
% ( 5 <=>; 25 =>; 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 : 26 ( 26 usr; 15 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__5585,hypothesis,
( xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))
& ! [X1] :
( aElementOf0(X1,xD)
<=> ( X1 != szmzizndt0(sdtlpdtrp0(xN,xn))
& aElementOf0(X1,sdtlpdtrp0(xN,xn))
& aElement0(X1) ) )
& aSet0(xD)
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5585) ).
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(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__5147,hypothesis,
( xp = szmzizndt0(xQ)
& ! [X1] :
( aElementOf0(X1,xQ)
=> sdtlseqdt0(xp,X1) )
& aElementOf0(xp,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5147) ).
fof(m__5078,hypothesis,
( aElementOf0(xQ,slbdtsldtrb0(xO,xK))
& sbrdtbr0(xQ) = xK
& aSubsetOf0(xQ,xO)
& ! [X1] :
( aElementOf0(X1,xQ)
=> aElementOf0(X1,xO) )
& aSet0(xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5078) ).
fof(m__4660,hypothesis,
( ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( sdtlpdtrp0(xe,X1) = szmzizndt0(sdtlpdtrp0(xN,X1))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(sdtlpdtrp0(xe,X1),X2) )
& aElementOf0(sdtlpdtrp0(xe,X1),sdtlpdtrp0(xN,X1)) ) )
& szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4660) ).
fof(m__3671,hypothesis,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( isCountable0(sdtlpdtrp0(xN,X1))
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> aElementOf0(X2,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3671) ).
fof(m__5309,hypothesis,
( sdtlpdtrp0(xe,xn) = xp
& aElementOf0(xn,szNzAzT0)
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xd,xn) = szDzizrdt0(xd)
& aElementOf0(xn,szDzozmdt0(xd)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5309) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(m__,conjecture,
( aElementOf0(xP,slbdtsldtrb0(xD,xk))
| aSubsetOf0(xP,xD)
| ! [X1] :
( aElementOf0(X1,xP)
=> aElementOf0(X1,xD) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__5334,hypothesis,
( aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& ! [X1] :
( aElementOf0(X1,xP)
=> aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5334) ).
fof(c_0_11,hypothesis,
( xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))
& ! [X1] :
( aElementOf0(X1,xD)
<=> ( X1 != szmzizndt0(sdtlpdtrp0(xN,xn))
& aElementOf0(X1,sdtlpdtrp0(xN,xn))
& aElement0(X1) ) )
& aSet0(xD)
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X1) ) ),
inference(fof_simplification,[status(thm)],[m__5585]) ).
fof(c_0_12,hypothesis,
! [X98,X99] :
( xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))
& ( aElementOf0(X99,xD)
| X99 = szmzizndt0(sdtlpdtrp0(xN,xn))
| ~ aElementOf0(X99,sdtlpdtrp0(xN,xn))
| ~ aElement0(X99) )
& ( ~ aElementOf0(X99,xD)
| X99 != szmzizndt0(sdtlpdtrp0(xN,xn)) )
& ( ~ aElementOf0(X99,xD)
| aElementOf0(X99,sdtlpdtrp0(xN,xn)) )
& ( ~ aElementOf0(X99,xD)
| aElement0(X99) )
& aSet0(xD)
& ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X98)
| ~ aElementOf0(X98,sdtlpdtrp0(xN,xn)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])]) ).
fof(c_0_13,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_14,plain,
! [X204,X205] :
( aElement0(X205)
| ~ aElementOf0(X205,X204)
| ~ aSet0(X204) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
fof(c_0_15,hypothesis,
! [X91] :
( xp = szmzizndt0(xQ)
& ( sdtlseqdt0(xp,X91)
| ~ aElementOf0(X91,xQ) )
& aElementOf0(xp,xQ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__5147])])])]) ).
fof(c_0_16,hypothesis,
! [X85] :
( aElementOf0(xQ,slbdtsldtrb0(xO,xK))
& sbrdtbr0(xQ) = xK
& aSubsetOf0(xQ,xO)
& ( aElementOf0(X85,xO)
| ~ aElementOf0(X85,xQ) )
& aSet0(xQ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__5078])])])]) ).
fof(c_0_17,hypothesis,
! [X65,X66] :
( ( ~ aElementOf0(X65,szNzAzT0)
| sdtlpdtrp0(xe,X65) = szmzizndt0(sdtlpdtrp0(xN,X65)) )
& ( ~ aElementOf0(X65,szNzAzT0)
| sdtlseqdt0(sdtlpdtrp0(xe,X65),X66)
| ~ aElementOf0(X66,sdtlpdtrp0(xN,X65)) )
& ( ~ aElementOf0(X65,szNzAzT0)
| aElementOf0(sdtlpdtrp0(xe,X65),sdtlpdtrp0(xN,X65)) )
& szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe) ),
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__4660])])])])]) ).
cnf(c_0_18,hypothesis,
( ~ aElementOf0(X1,xD)
| X1 != szmzizndt0(sdtlpdtrp0(xN,xn)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_19,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_13])])])])])])]) ).
fof(c_0_20,hypothesis,
! [X42,X43] :
( ( ~ aElementOf0(X42,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,X42)) )
& ( ~ aElementOf0(X42,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X42),szNzAzT0) )
& ( ~ aElementOf0(X42,szNzAzT0)
| aElementOf0(X43,szNzAzT0)
| ~ aElementOf0(X43,sdtlpdtrp0(xN,X42)) )
& ( ~ aElementOf0(X42,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,X42)) ) ),
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_21,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,hypothesis,
aElementOf0(xp,xQ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,hypothesis,
aSet0(xQ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aElementOf0(sdtlpdtrp0(xe,X1),sdtlpdtrp0(xN,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,hypothesis,
sdtlpdtrp0(xe,xn) = xp,
inference(split_conjunct,[status(thm)],[m__5309]) ).
cnf(c_0_26,hypothesis,
aElementOf0(xn,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__5309]) ).
cnf(c_0_27,hypothesis,
~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),xD),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_28,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| sdtlpdtrp0(xe,X1) = szmzizndt0(sdtlpdtrp0(xN,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_29,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X1))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_30,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_31,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_32,hypothesis,
( ~ aElementOf0(X1,sdtlpdtrp0(xN,xn))
| ~ aElement0(X1)
| aElementOf0(X1,xD)
| X1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_33,hypothesis,
aElement0(xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_34,hypothesis,
aElementOf0(xp,sdtlpdtrp0(xN,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_35,hypothesis,
~ aElementOf0(xp,xD),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_25]),c_0_26])]) ).
cnf(c_0_36,hypothesis,
xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_37,plain,
! [X122,X123,X124,X125] :
( ( ~ aSet0(X122)
| aSubsetOf0(X125,X122)
| ~ aSet0(X125)
| ~ aElementOf0(esk26_2(X122,X125),X122) )
& ( ~ aSet0(X122)
| aSubsetOf0(X125,X122)
| ~ aSet0(X125)
| aElementOf0(esk26_2(X122,X125),X125) )
& ( ~ aSet0(X122)
| ~ aSubsetOf0(X123,X122)
| aElementOf0(X124,X122)
| ~ aElementOf0(X124,X123) )
& ( ~ aSet0(X122)
| ~ aSubsetOf0(X123,X122)
| aSet0(X123) ) ),
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)],[mDefSub])])])])])])]) ).
cnf(c_0_38,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_39,hypothesis,
szmzizndt0(sdtlpdtrp0(xN,xn)) = xp,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]),c_0_35]) ).
cnf(c_0_40,hypothesis,
sdtmndt0(sdtlpdtrp0(xN,xn),xp) = xD,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_28]),c_0_25]),c_0_26])]) ).
fof(c_0_41,negated_conjecture,
~ ( aElementOf0(xP,slbdtsldtrb0(xD,xk))
| aSubsetOf0(xP,xD)
| ! [X1] :
( aElementOf0(X1,xP)
=> aElementOf0(X1,xD) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_42,plain,
( ~ aSet0(X3)
| ~ aSubsetOf0(X2,X3)
| ~ aElementOf0(X1,X2)
| aElementOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,hypothesis,
aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xD),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_26])]) ).
cnf(c_0_44,hypothesis,
aSet0(xD),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_45,hypothesis,
! [X97] :
( aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& ( aElementOf0(X97,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(X97,xP) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__5334])])])]) ).
fof(c_0_46,negated_conjecture,
( ~ aElementOf0(xP,slbdtsldtrb0(xD,xk))
& ~ aSubsetOf0(xP,xD)
& ~ aElementOf0(esk23_0,xD)
& aElementOf0(esk23_0,xP) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])])]) ).
cnf(c_0_47,hypothesis,
( ~ aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(X1,xD) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).
cnf(c_0_48,hypothesis,
( ~ aElementOf0(X1,xP)
| aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_49,negated_conjecture,
~ aElementOf0(esk23_0,xD),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_50,hypothesis,
( ~ aElementOf0(X1,xP)
| aElementOf0(X1,xD) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_51,negated_conjecture,
aElementOf0(esk23_0,xP),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_52,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM629+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n002.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Mon Sep 21 02:48:17 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 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
% 3.75/1.10 % Version: 3.5.1
% 3.75/1.10 % Preprocessing class: FSLSSMSMSSSNFFN.
% 3.75/1.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.75/1.10 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 3.75/1.10 % Starting new_bool_3 with 300s (1) cores
% 3.75/1.10 % Starting new_bool_1 with 300s (1) cores
% 3.75/1.10 % Starting sh5l with 300s (1) cores
% 3.75/1.10 % new_bool_3 with pid 2264659 completed with status 0
% 3.75/1.10 % Result found by new_bool_3
% 3.75/1.10 % Preprocessing class: FSLSSMSMSSSNFFN.
% 3.75/1.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.75/1.10 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 3.75/1.10 % Starting new_bool_3 with 300s (1) cores
% 3.75/1.10 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 3.75/1.10 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 3.75/1.10 % Search class: FGHSF-SMLM32-MFFFFFNN
% 3.75/1.10 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 3.75/1.10 % Starting SubtermCWHack with 31s (1) cores
% 3.75/1.10 % SubtermCWHack with pid 2264698 completed with status 0
% 3.75/1.10 % Result found by SubtermCWHack
% 3.75/1.10 % Preprocessing class: FSLSSMSMSSSNFFN.
% 3.75/1.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.75/1.10 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 3.75/1.10 % Starting new_bool_3 with 300s (1) cores
% 3.75/1.10 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 3.75/1.10 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 3.75/1.10 % Search class: FGHSF-SMLM32-MFFFFFNN
% 3.75/1.10 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 3.75/1.10 % Starting SubtermCWHack with 31s (1) cores
% 3.75/1.10 % Preprocessing time : 0.095 s
% 3.75/1.10
% 3.75/1.10 % Proof found!
% 3.75/1.10 % SZS status Theorem
% 3.75/1.10 % SZS output start CNFRefutation
% See solution above
% 3.75/1.10 % Parsed axioms : 115
% 3.75/1.10 % Removed by relevancy pruning/SinE : 9
% 3.75/1.10 % Initial clauses : 4903
% 3.75/1.10 % Removed in clause preprocessing : 7
% 3.75/1.10 % Initial clauses in saturation : 4896
% 3.75/1.10 % Processed clauses : 2947
% 3.75/1.10 % ...of these trivial : 68
% 3.75/1.10 % ...subsumed : 1146
% 3.75/1.10 % ...remaining for further processing : 1733
% 3.75/1.10 % Other redundant clauses eliminated : 56
% 3.75/1.10 % Clauses deleted for lack of memory : 0
% 3.75/1.10 % Backward-subsumed : 161
% 3.75/1.10 % Backward-rewritten : 186
% 3.75/1.10 % Generated clauses : 10951
% 3.75/1.10 % ...of the previous two non-redundant : 9586
% 3.75/1.11 % ...aggressively subsumed : 0
% 3.75/1.11 % Contextual simplify-reflections : 45
% 3.75/1.11 % Paramodulations : 10896
% 3.75/1.11 % Factorizations : 0
% 3.75/1.11 % NegExts : 0
% 3.75/1.11 % Equation resolutions : 58
% 3.75/1.11 % Disequality decompositions : 0
% 3.75/1.11 % Total rewrite steps : 8134
% 3.75/1.11 % ...of those cached : 7915
% 3.75/1.11 % Propositional unsat checks : 0
% 3.75/1.11 % Propositional check models : 0
% 3.75/1.11 % Propositional check unsatisfiable : 0
% 3.75/1.11 % Propositional clauses : 0
% 3.75/1.11 % Propositional clauses after purity: 0
% 3.75/1.11 % Propositional unsat core size : 0
% 3.75/1.11 % Propositional preprocessing time : 0.000
% 3.75/1.11 % Propositional encoding time : 0.000
% 3.75/1.11 % Propositional solver time : 0.000
% 3.75/1.11 % Success case prop preproc time : 0.000
% 3.75/1.11 % Success case prop encoding time : 0.000
% 3.75/1.11 % Success case prop solver time : 0.000
% 3.75/1.11 % Current number of processed clauses : 1342
% 3.75/1.11 % Positive orientable unit clauses : 231
% 3.75/1.11 % Positive unorientable unit clauses: 0
% 3.75/1.11 % Negative unit clauses : 48
% 3.75/1.11 % Non-unit-clauses : 1063
% 3.75/1.11 % Current number of unprocessed clauses: 10666
% 3.75/1.11 % ...number of literals in the above : 84813
% 3.75/1.11 % Current number of archived formulas : 0
% 3.75/1.11 % Current number of archived clauses : 349
% 3.75/1.11 % Clause-clause subsumption calls (NU) : 222724
% 3.75/1.11 % Rec. Clause-clause subsumption calls : 95790
% 3.75/1.11 % Non-unit clause-clause subsumptions : 1008
% 3.75/1.11 % Unit Clause-clause subsumption calls : 13184
% 3.75/1.11 % Rewrite failures with RHS unbound : 0
% 3.75/1.11 % BW rewrite match attempts : 165
% 3.75/1.11 % BW rewrite match successes : 32
% 3.75/1.11 % Condensation attempts : 0
% 3.75/1.11 % Condensation successes : 0
% 3.75/1.11 % Termbank termtop insertions : 575641
% 3.75/1.11 % Search garbage collected termcells : 31617
% 3.75/1.11
% 3.75/1.11 % -------------------------------------------------
% 3.75/1.11 % User time : 0.579 s
% 3.75/1.11 % System time : 0.039 s
% 3.75/1.11 % Total time : 0.618 s
% 3.75/1.11 % Maximum resident set size: 16116 pages
% 3.75/1.11
% 3.75/1.11 % -------------------------------------------------
% 3.75/1.11 % User time : 0.585 s
% 3.75/1.11 % System time : 0.046 s
% 3.75/1.11 % Total time : 0.631 s
% 3.75/1.11 % Maximum resident set size: 5120 pages
% 3.75/1.11 % E exiting
%------------------------------------------------------------------------------