%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM601+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 : n013.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 01:49:43 PM UTC 2026
% Result : Theorem 1.23s 0.87s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 7 unt; 0 def)
% Number of atoms : 358 ( 31 equ)
% Maximal formula atoms : 181 ( 10 avg)
% Number of connectives : 513 ( 190 ~; 201 |; 97 &)
% ( 3 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 45 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 41 !; 2 ?)
% 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__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(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(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
fof(m__3435,hypothesis,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [X1] :
( aElementOf0(X1,xS)
=> aElementOf0(X1,szNzAzT0) )
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
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__4982,hypothesis,
! [X1] :
( ( aElementOf0(X1,xO)
| ? [X2] :
( sdtlpdtrp0(xe,X2) = X1
& aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
=> ? [X2] :
( sdtlpdtrp0(xe,X2) = X1
& aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xd,X2) = szDzizrdt0(xd)
& aElementOf0(X2,szNzAzT0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4982) ).
fof(m__,conjecture,
( aSubsetOf0(xO,xS)
| ! [X1] :
( aElementOf0(X1,xO)
=> aElementOf0(X1,xS) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(c_0_9,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_10,hypothesis,
! [X214,X215,X216] :
( ( ~ aElementOf0(X215,szNzAzT0)
| ~ aElementOf0(X214,szNzAzT0)
| ~ sdtlseqdt0(X215,X214)
| aSubsetOf0(sdtlpdtrp0(xN,X214),sdtlpdtrp0(xN,X215)) )
& ( ~ aElementOf0(X215,szNzAzT0)
| ~ aElementOf0(X214,szNzAzT0)
| ~ sdtlseqdt0(X215,X214)
| aElementOf0(X216,sdtlpdtrp0(xN,X215))
| ~ aElementOf0(X216,sdtlpdtrp0(xN,X214)) ) ),
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_11,plain,
! [X67] :
( sdtlseqdt0(sz00,X67)
| ~ aElementOf0(X67,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroLess])])]) ).
fof(c_0_12,hypothesis,
! [X206,X208,X209,X210,X211] :
( ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X206))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X206)),sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206)))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| aElementOf0(X211,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| ~ aElementOf0(X211,sdtlpdtrp0(xN,szszuzczcdt0(X206))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X206))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| aElementOf0(X210,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| X210 = szmzizndt0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(X210,sdtlpdtrp0(xN,X206))
| ~ aElement0(X210) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| ~ aElementOf0(X209,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| X209 != szmzizndt0(sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| ~ aElementOf0(X209,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| aElementOf0(X209,sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| ~ aElementOf0(X209,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| aElement0(X209) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206)))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X206)),X208)
| ~ aElementOf0(X208,sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X206)),sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X206))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X206)),sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206)))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| aElementOf0(X211,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| ~ aElementOf0(X211,sdtlpdtrp0(xN,szszuzczcdt0(X206))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X206))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| aElementOf0(X210,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| X210 = szmzizndt0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(X210,sdtlpdtrp0(xN,X206))
| ~ aElement0(X210) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| ~ aElementOf0(X209,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| X209 != szmzizndt0(sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| ~ aElementOf0(X209,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| aElementOf0(X209,sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| ~ aElementOf0(X209,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| aElement0(X209) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206)))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X206)),X208)
| ~ aElementOf0(X208,sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X206)),sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X206))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X206)),sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206)))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| aElementOf0(X211,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| ~ aElementOf0(X211,sdtlpdtrp0(xN,szszuzczcdt0(X206))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X206))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| aElementOf0(X210,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| X210 = szmzizndt0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(X210,sdtlpdtrp0(xN,X206))
| ~ aElement0(X210) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| ~ aElementOf0(X209,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| X209 != szmzizndt0(sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| ~ aElementOf0(X209,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| aElementOf0(X209,sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| ~ aElementOf0(X209,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| aElement0(X209) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206)))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X206)),X208)
| ~ aElementOf0(X208,sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X206)),sdtlpdtrp0(xN,X206)) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])])])])]) ).
fof(c_0_13,plain,
! [X20,X21,X22,X23] :
( ( ~ aSet0(X20)
| aSubsetOf0(X23,X20)
| ~ aSet0(X23)
| ~ aElementOf0(esk2_2(X20,X23),X20) )
& ( ~ aSet0(X20)
| aSubsetOf0(X23,X20)
| ~ aSet0(X23)
| aElementOf0(esk2_2(X20,X23),X23) )
& ( ~ aSet0(X20)
| ~ aSubsetOf0(X21,X20)
| aElementOf0(X22,X20)
| ~ aElementOf0(X22,X21) )
& ( ~ aSet0(X20)
| ~ aSubsetOf0(X21,X20)
| aSet0(X21) ) ),
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_14,hypothesis,
( ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(X2,X1)
| aSubsetOf0(sdtlpdtrp0(xN,X1),sdtlpdtrp0(xN,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( ~ aElementOf0(X1,szNzAzT0)
| sdtlseqdt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,hypothesis,
sdtlpdtrp0(xN,sz00) = xS,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
aElementOf0(sz00,szNzAzT0),
inference(split_conjunct,[status(thm)],[mZeroNum]) ).
fof(c_0_18,hypothesis,
! [X178] :
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ( aElementOf0(X178,szNzAzT0)
| ~ aElementOf0(X178,xS) )
& aSet0(xS) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3435])])])]) ).
fof(c_0_19,hypothesis,
! [X235,X236] :
( ( ~ aElementOf0(X235,szNzAzT0)
| sdtlpdtrp0(xe,X235) = szmzizndt0(sdtlpdtrp0(xN,X235)) )
& ( ~ aElementOf0(X235,szNzAzT0)
| sdtlseqdt0(sdtlpdtrp0(xe,X235),X236)
| ~ aElementOf0(X236,sdtlpdtrp0(xN,X235)) )
& ( ~ aElementOf0(X235,szNzAzT0)
| aElementOf0(sdtlpdtrp0(xe,X235),sdtlpdtrp0(xN,X235)) )
& 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])])])])]) ).
fof(c_0_20,hypothesis,
! [X251,X252] :
( ( ~ aElementOf0(X251,xO)
| sdtlpdtrp0(xe,esk39_1(X251)) = X251 )
& ( ~ aElementOf0(X251,xO)
| aElementOf0(esk39_1(X251),sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& ( ~ aElementOf0(X251,xO)
| sdtlpdtrp0(xd,esk39_1(X251)) = szDzizrdt0(xd) )
& ( ~ aElementOf0(X251,xO)
| aElementOf0(esk39_1(X251),szNzAzT0) )
& ( sdtlpdtrp0(xe,X252) != X251
| ~ aElementOf0(X252,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| sdtlpdtrp0(xe,esk39_1(X251)) = X251 )
& ( sdtlpdtrp0(xe,X252) != X251
| ~ aElementOf0(X252,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(esk39_1(X251),sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& ( sdtlpdtrp0(xe,X252) != X251
| ~ aElementOf0(X252,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| sdtlpdtrp0(xd,esk39_1(X251)) = szDzizrdt0(xd) )
& ( sdtlpdtrp0(xe,X252) != X251
| ~ aElementOf0(X252,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| aElementOf0(esk39_1(X251),szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4982])])])])])]) ).
cnf(c_0_21,plain,
( ~ aSet0(X3)
| ~ aSubsetOf0(X2,X3)
| ~ aElementOf0(X1,X2)
| aElementOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,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_14,c_0_15]),c_0_16]),c_0_17])]) ).
cnf(c_0_23,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aElementOf0(sdtlpdtrp0(xe,X1),sdtlpdtrp0(xN,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,hypothesis,
( ~ aElementOf0(X1,xO)
| sdtlpdtrp0(xe,esk39_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,hypothesis,
( ~ aElementOf0(X1,xO)
| aElementOf0(esk39_1(X1),szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_27,negated_conjecture,
~ ( aSubsetOf0(xO,xS)
| ! [X1] :
( aElementOf0(X1,xO)
=> aElementOf0(X1,xS) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_28,hypothesis,
( ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X2))
| aElementOf0(X1,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_29,hypothesis,
( ~ aElementOf0(X1,xO)
| aElementOf0(X1,sdtlpdtrp0(xN,esk39_1(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
fof(c_0_30,negated_conjecture,
( ~ aSubsetOf0(xO,xS)
& ~ aElementOf0(esk40_0,xS)
& aElementOf0(esk40_0,xO) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])]) ).
cnf(c_0_31,hypothesis,
( ~ aElementOf0(X1,xO)
| aElementOf0(X1,xS) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_26]) ).
cnf(c_0_32,negated_conjecture,
aElementOf0(esk40_0,xO),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_33,negated_conjecture,
~ aElementOf0(esk40_0,xS),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM601+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.35 % Computer : n013.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Mon Sep 21 02:43:36 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 1.23/0.87 % Version: 3.5.1
% 1.23/0.87 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.23/0.87 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.23/0.87 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.23/0.87 % Starting new_bool_3 with 300s (1) cores
% 1.23/0.87 % Starting new_bool_1 with 300s (1) cores
% 1.23/0.87 % Starting sh5l with 300s (1) cores
% 1.23/0.87 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 3974271 completed with status 0
% 1.23/0.87 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 1.23/0.87 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.23/0.87 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.23/0.87 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.23/0.87 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.23/0.87 % No SInE strategy applied
% 1.23/0.87 % Search class: FGHSF-SMLM32-MFFFFFNN
% 1.23/0.87 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.23/0.87 % Starting SubtermCWHack with 136s (1) cores
% 1.23/0.87 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.23/0.87 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 1.23/0.87 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 1.23/0.87 % Starting new_bool_3 with 136s (1) cores
% 1.23/0.87 % SubtermCWHack with pid 3974275 completed with status 0
% 1.23/0.87 % Result found by SubtermCWHack
% 1.23/0.87 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.23/0.87 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.23/0.87 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.23/0.87 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.23/0.87 % No SInE strategy applied
% 1.23/0.87 % Search class: FGHSF-SMLM32-MFFFFFNN
% 1.23/0.87 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.23/0.87 % Starting SubtermCWHack with 136s (1) cores
% 1.23/0.87 % Preprocessing time : 0.090 s
% 1.23/0.87
% 1.23/0.87 % Proof found!
% 1.23/0.87 % SZS status Theorem
% 1.23/0.87 % SZS output start CNFRefutation
% See solution above
% 1.23/0.87 % Parsed axioms : 98
% 1.23/0.87 % Removed by relevancy pruning/SinE : 0
% 1.23/0.87 % Initial clauses : 4877
% 1.23/0.87 % Removed in clause preprocessing : 7
% 1.23/0.87 % Initial clauses in saturation : 4870
% 1.23/0.87 % Processed clauses : 1161
% 1.23/0.87 % ...of these trivial : 25
% 1.23/0.87 % ...subsumed : 387
% 1.23/0.87 % ...remaining for further processing : 749
% 1.23/0.87 % Other redundant clauses eliminated : 53
% 1.23/0.87 % Clauses deleted for lack of memory : 0
% 1.23/0.87 % Backward-subsumed : 24
% 1.23/0.87 % Backward-rewritten : 22
% 1.23/0.87 % Generated clauses : 3392
% 1.23/0.87 % ...of the previous two non-redundant : 2846
% 1.23/0.87 % ...aggressively subsumed : 0
% 1.23/0.87 % Contextual simplify-reflections : 23
% 1.23/0.87 % Paramodulations : 3340
% 1.23/0.87 % Factorizations : 0
% 1.23/0.87 % NegExts : 0
% 1.23/0.87 % Equation resolutions : 55
% 1.23/0.87 % Disequality decompositions : 0
% 1.23/0.87 % Total rewrite steps : 2212
% 1.23/0.87 % ...of those cached : 2096
% 1.23/0.87 % Propositional unsat checks : 0
% 1.23/0.87 % Propositional check models : 0
% 1.23/0.87 % Propositional check unsatisfiable : 0
% 1.23/0.87 % Propositional clauses : 0
% 1.23/0.87 % Propositional clauses after purity: 0
% 1.23/0.87 % Propositional unsat core size : 0
% 1.23/0.87 % Propositional preprocessing time : 0.000
% 1.23/0.87 % Propositional encoding time : 0.000
% 1.23/0.87 % Propositional solver time : 0.000
% 1.23/0.87 % Success case prop preproc time : 0.000
% 1.23/0.87 % Success case prop encoding time : 0.000
% 1.23/0.87 % Success case prop solver time : 0.000
% 1.23/0.87 % Current number of processed clauses : 658
% 1.23/0.87 % Positive orientable unit clauses : 123
% 1.23/0.87 % Positive unorientable unit clauses: 0
% 1.23/0.87 % Negative unit clauses : 24
% 1.23/0.87 % Non-unit-clauses : 511
% 1.23/0.87 % Current number of unprocessed clauses: 6180
% 1.23/0.87 % ...number of literals in the above : 62382
% 1.23/0.87 % Current number of archived formulas : 0
% 1.23/0.87 % Current number of archived clauses : 48
% 1.23/0.87 % Clause-clause subsumption calls (NU) : 28543
% 1.23/0.87 % Rec. Clause-clause subsumption calls : 17783
% 1.23/0.87 % Non-unit clause-clause subsumptions : 301
% 1.23/0.87 % Unit Clause-clause subsumption calls : 3724
% 1.23/0.87 % Rewrite failures with RHS unbound : 0
% 1.23/0.87 % BW rewrite match attempts : 45
% 1.23/0.87 % BW rewrite match successes : 17
% 1.23/0.87 % Condensation attempts : 0
% 1.23/0.87 % Condensation successes : 0
% 1.23/0.87 % Termbank termtop insertions : 431767
% 1.23/0.87 % Search garbage collected termcells : 31817
% 1.23/0.87
% 1.23/0.87 % -------------------------------------------------
% 1.23/0.87 % User time : 0.373 s
% 1.23/0.87 % System time : 0.024 s
% 1.23/0.87 % Total time : 0.397 s
% 1.23/0.87 % Maximum resident set size: 16096 pages
% 1.23/0.87
% 1.23/0.87 % -------------------------------------------------
% 1.23/0.87 % User time : 1.278 s
% 1.23/0.87 % System time : 0.097 s
% 1.23/0.87 % Total time : 1.375 s
% 1.23/0.87 % Maximum resident set size: 4864 pages
% 1.23/0.87 % E exiting
%------------------------------------------------------------------------------