%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM577+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 : n011.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 01:49:38 PM UTC 2026
% Result : Theorem 109.20s 17.40s
% Output : CNFRefutation 109.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 55 ( 17 unt; 0 def)
% Number of atoms : 572 ( 47 equ)
% Maximal formula atoms : 181 ( 10 avg)
% Number of connectives : 786 ( 269 ~; 314 |; 157 &)
% ( 6 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 58 ( 6 avg)
% Maximal term depth : 4 ( 2 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 : 74 ( 0 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( sdtlseqdt0(szszuzczcdt0(xn),xm)
=> ( ~ ( szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(sdtlpdtrp0(xN,xn))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xm)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xn))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xm))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xm)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xm)) )
& ( ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn)) )
=> ( ( ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( X1 != szmzizndt0(sdtlpdtrp0(xN,xn))
& aElementOf0(X1,sdtlpdtrp0(xN,xn))
& aElement0(X1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
=> ( aSubsetOf0(sdtlpdtrp0(xN,xm),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xm))
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mSuccNum,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( szszuzczcdt0(X1) != sz00
& aElementOf0(szszuzczcdt0(X1),szNzAzT0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).
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__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__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(m__3904,hypothesis,
( aElementOf0(xm,szNzAzT0)
& aElementOf0(xn,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3904) ).
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(c_0_7,negated_conjecture,
~ ( sdtlseqdt0(szszuzczcdt0(xn),xm)
=> ( ~ ( szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(sdtlpdtrp0(xN,xn))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xm)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xn))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xm))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xm)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xm)) )
& ( ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn)) )
=> ( ( ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( X1 != szmzizndt0(sdtlpdtrp0(xN,xn))
& aElementOf0(X1,sdtlpdtrp0(xN,xn))
& aElement0(X1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
=> ( aSubsetOf0(sdtlpdtrp0(xN,xm),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xm))
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_8,plain,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( szszuzczcdt0(X1) != sz00
& aElementOf0(szszuzczcdt0(X1),szNzAzT0) ) ),
inference(fof_simplification,[status(thm)],[mSuccNum]) ).
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,negated_conjecture,
~ ( sdtlseqdt0(szszuzczcdt0(xn),xm)
=> ( ~ ( szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(sdtlpdtrp0(xN,xn))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xm)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xn))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xm))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xm)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xm)) )
& ( ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn)) )
=> ( ( ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( X1 != szmzizndt0(sdtlpdtrp0(xN,xn))
& aElementOf0(X1,sdtlpdtrp0(xN,xn))
& aElement0(X1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
=> ( aSubsetOf0(sdtlpdtrp0(xN,xm),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xm))
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X59] :
( ( ~ aElementOf0(X59,szNzAzT0)
| szszuzczcdt0(X59) != sz00 )
& ( ~ aElementOf0(X59,szNzAzT0)
| aElementOf0(szszuzczcdt0(X59),szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
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,hypothesis,
! [X212,X213] :
( ( ~ aElementOf0(X212,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,X212)) )
& ( ~ aElementOf0(X212,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X212),szNzAzT0) )
& ( ~ aElementOf0(X212,szNzAzT0)
| aElementOf0(X213,szNzAzT0)
| ~ aElementOf0(X213,sdtlpdtrp0(xN,X212)) )
& ( ~ aElementOf0(X212,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,X212)) ) ),
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])])])])]) ).
fof(c_0_14,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_15,negated_conjecture,
! [X217,X218,X220,X221] :
( ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(sdtlpdtrp0(xN,xn)) )
& ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xm)),X221)
| ~ aElementOf0(X221,sdtlpdtrp0(xN,xn)) )
& ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xn)) )
& ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xm)),X220)
| ~ aElementOf0(X220,sdtlpdtrp0(xN,xm)) )
& ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xm)) )
& ( ~ aElementOf0(esk32_0,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(sdtlpdtrp0(xN,xn)) )
& ( ~ aElementOf0(esk32_0,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xm)),X221)
| ~ aElementOf0(X221,sdtlpdtrp0(xN,xn)) )
& ( ~ aElementOf0(esk32_0,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xn)) )
& ( ~ aElementOf0(esk32_0,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xm)),X220)
| ~ aElementOf0(X220,sdtlpdtrp0(xN,xm)) )
& ( ~ aElementOf0(esk32_0,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xm)) )
& ( aElementOf0(esk32_0,sdtlpdtrp0(xN,xm))
| szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(sdtlpdtrp0(xN,xn)) )
& ( aElementOf0(esk32_0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xm)),X221)
| ~ aElementOf0(X221,sdtlpdtrp0(xN,xn)) )
& ( aElementOf0(esk32_0,sdtlpdtrp0(xN,xm))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xn)) )
& ( aElementOf0(esk32_0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xm)),X220)
| ~ aElementOf0(X220,sdtlpdtrp0(xN,xm)) )
& ( aElementOf0(esk32_0,sdtlpdtrp0(xN,xm))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xm)) )
& ( aElementOf0(X218,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| X218 = szmzizndt0(sdtlpdtrp0(xN,xn))
| ~ aElementOf0(X218,sdtlpdtrp0(xN,xn))
| ~ aElement0(X218)
| szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(sdtlpdtrp0(xN,xn)) )
& ( aElementOf0(X218,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| X218 = szmzizndt0(sdtlpdtrp0(xN,xn))
| ~ aElementOf0(X218,sdtlpdtrp0(xN,xn))
| ~ aElement0(X218)
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xm)),X221)
| ~ aElementOf0(X221,sdtlpdtrp0(xN,xn)) )
& ( aElementOf0(X218,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| X218 = szmzizndt0(sdtlpdtrp0(xN,xn))
| ~ aElementOf0(X218,sdtlpdtrp0(xN,xn))
| ~ aElement0(X218)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xn)) )
& ( aElementOf0(X218,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| X218 = szmzizndt0(sdtlpdtrp0(xN,xn))
| ~ aElementOf0(X218,sdtlpdtrp0(xN,xn))
| ~ aElement0(X218)
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xm)),X220)
| ~ aElementOf0(X220,sdtlpdtrp0(xN,xm)) )
& ( aElementOf0(X218,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| X218 = szmzizndt0(sdtlpdtrp0(xN,xn))
| ~ aElementOf0(X218,sdtlpdtrp0(xN,xn))
| ~ aElement0(X218)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xm)) )
& ( ~ aElementOf0(X218,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| X218 != szmzizndt0(sdtlpdtrp0(xN,xn))
| szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(sdtlpdtrp0(xN,xn)) )
& ( ~ aElementOf0(X218,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| X218 != szmzizndt0(sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xm)),X221)
| ~ aElementOf0(X221,sdtlpdtrp0(xN,xn)) )
& ( ~ aElementOf0(X218,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| X218 != szmzizndt0(sdtlpdtrp0(xN,xn))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xn)) )
& ( ~ aElementOf0(X218,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| X218 != szmzizndt0(sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xm)),X220)
| ~ aElementOf0(X220,sdtlpdtrp0(xN,xm)) )
& ( ~ aElementOf0(X218,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| X218 != szmzizndt0(sdtlpdtrp0(xN,xn))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xm)) )
& ( ~ aElementOf0(X218,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(X218,sdtlpdtrp0(xN,xn))
| szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(sdtlpdtrp0(xN,xn)) )
& ( ~ aElementOf0(X218,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(X218,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xm)),X221)
| ~ aElementOf0(X221,sdtlpdtrp0(xN,xn)) )
& ( ~ aElementOf0(X218,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(X218,sdtlpdtrp0(xN,xn))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xn)) )
& ( ~ aElementOf0(X218,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(X218,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xm)),X220)
| ~ aElementOf0(X220,sdtlpdtrp0(xN,xm)) )
& ( ~ aElementOf0(X218,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(X218,sdtlpdtrp0(xN,xn))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xm)) )
& ( ~ aElementOf0(X218,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElement0(X218)
| szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(sdtlpdtrp0(xN,xn)) )
& ( ~ aElementOf0(X218,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElement0(X218)
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xm)),X221)
| ~ aElementOf0(X221,sdtlpdtrp0(xN,xn)) )
& ( ~ aElementOf0(X218,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElement0(X218)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xn)) )
& ( ~ aElementOf0(X218,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElement0(X218)
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xm)),X220)
| ~ aElementOf0(X220,sdtlpdtrp0(xN,xm)) )
& ( ~ aElementOf0(X218,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElement0(X218)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xm)) )
& ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(sdtlpdtrp0(xN,xn)) )
& ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xm)),X221)
| ~ aElementOf0(X221,sdtlpdtrp0(xN,xn)) )
& ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xn)) )
& ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xm)),X220)
| ~ aElementOf0(X220,sdtlpdtrp0(xN,xm)) )
& ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xm)) )
& ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X217)
| ~ aElementOf0(X217,sdtlpdtrp0(xN,xn))
| szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(sdtlpdtrp0(xN,xn)) )
& ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X217)
| ~ aElementOf0(X217,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xm)),X221)
| ~ aElementOf0(X221,sdtlpdtrp0(xN,xn)) )
& ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X217)
| ~ aElementOf0(X217,sdtlpdtrp0(xN,xn))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xn)) )
& ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X217)
| ~ aElementOf0(X217,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xm)),X220)
| ~ aElementOf0(X220,sdtlpdtrp0(xN,xm)) )
& ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X217)
| ~ aElementOf0(X217,sdtlpdtrp0(xN,xn))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xm)) )
& ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(sdtlpdtrp0(xN,xn)) )
& ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xm)),X221)
| ~ aElementOf0(X221,sdtlpdtrp0(xN,xn)) )
& ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xn)) )
& ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xm)),X220)
| ~ aElementOf0(X220,sdtlpdtrp0(xN,xm)) )
& ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xm)) )
& sdtlseqdt0(szszuzczcdt0(xn),xm) ),
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)],[c_0_10])])])])])]) ).
cnf(c_0_16,plain,
( ~ aElementOf0(X1,szNzAzT0)
| aElementOf0(szszuzczcdt0(X1),szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,hypothesis,
aElementOf0(xn,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3904]) ).
cnf(c_0_18,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_12]) ).
cnf(c_0_19,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X1))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_22,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_23,hypothesis,
( ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(X2,X1)
| aSubsetOf0(sdtlpdtrp0(xN,X1),sdtlpdtrp0(xN,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,negated_conjecture,
sdtlseqdt0(szszuzczcdt0(xn),xm),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_25,hypothesis,
aElementOf0(szszuzczcdt0(xn),szNzAzT0),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_26,hypothesis,
aElementOf0(xm,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3904]) ).
cnf(c_0_27,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_28,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_18,c_0_19]),c_0_20]) ).
cnf(c_0_29,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_21,c_0_19]),c_0_20]) ).
cnf(c_0_30,plain,
( ~ aSet0(X3)
| ~ aSubsetOf0(X2,X3)
| ~ aElementOf0(X1,X2)
| aElementOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,negated_conjecture,
aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]) ).
cnf(c_0_32,hypothesis,
aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(spm,[status(thm)],[c_0_27,c_0_25]) ).
cnf(c_0_33,negated_conjecture,
( aElementOf0(esk32_0,sdtlpdtrp0(xN,xm))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xm)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_34,negated_conjecture,
( aElementOf0(esk32_0,sdtlpdtrp0(xN,xm))
| szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(sdtlpdtrp0(xN,xn)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_35,hypothesis,
( ~ aElementOf0(X2,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X2))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X2),szNzAzT0)
| ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X2),szmzizndt0(sdtlpdtrp0(xN,X2))))
| X1 != szmzizndt0(sdtlpdtrp0(xN,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_36,hypothesis,
aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))),
inference(spm,[status(thm)],[c_0_28,c_0_17]) ).
cnf(c_0_37,hypothesis,
aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))),
inference(spm,[status(thm)],[c_0_29,c_0_17]) ).
cnf(c_0_38,negated_conjecture,
( ~ aElementOf0(X1,sdtlpdtrp0(xN,xm))
| aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_39,negated_conjecture,
( aElementOf0(esk32_0,sdtlpdtrp0(xN,xm))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xm)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) ),
inference(er,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_35,c_0_19]),c_0_20])]) ).
cnf(c_0_41,hypothesis,
( ~ aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_36]),c_0_37])]) ).
cnf(c_0_42,negated_conjecture,
( aElementOf0(esk32_0,sdtlpdtrp0(xN,xm))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,hypothesis,
~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))),
inference(spm,[status(thm)],[c_0_40,c_0_17]) ).
cnf(c_0_44,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X1))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_45,negated_conjecture,
aElementOf0(esk32_0,sdtlpdtrp0(xN,xm)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_46,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_44,c_0_19]),c_0_20]) ).
cnf(c_0_47,negated_conjecture,
aElementOf0(esk32_0,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(spm,[status(thm)],[c_0_38,c_0_45]) ).
cnf(c_0_48,hypothesis,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,xm)),
inference(spm,[status(thm)],[c_0_46,c_0_26]) ).
cnf(c_0_49,negated_conjecture,
( ~ aElementOf0(esk32_0,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(sdtlpdtrp0(xN,xn)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_50,hypothesis,
aElementOf0(esk32_0,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))),
inference(spm,[status(thm)],[c_0_41,c_0_47]) ).
cnf(c_0_51,hypothesis,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xm)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(spm,[status(thm)],[c_0_38,c_0_48]) ).
cnf(c_0_52,negated_conjecture,
szmzizndt0(sdtlpdtrp0(xN,xm)) = szmzizndt0(sdtlpdtrp0(xN,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]) ).
cnf(c_0_53,hypothesis,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(rw,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_54,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_53]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM577+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.46 % Computer : n011.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Mon Sep 21 02:41:40 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.53 Running first-order theorem proving
% 0.24/0.53 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
% 109.20/17.40 % Version: 3.5.1
% 109.20/17.40 % Preprocessing class: FSLSSMSMSSSNFFN.
% 109.20/17.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 109.20/17.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 109.20/17.40 % Starting new_bool_3 with 300s (1) cores
% 109.20/17.40 % Starting new_bool_1 with 300s (1) cores
% 109.20/17.40 % Starting sh5l with 300s (1) cores
% 109.20/17.40 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 793483 completed with status 0
% 109.20/17.40 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 109.20/17.40 % Preprocessing class: FSLSSMSMSSSNFFN.
% 109.20/17.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 109.20/17.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 109.20/17.40 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 109.20/17.40 % No SInE strategy applied
% 109.20/17.40 % Search class: FGHSF-SMLM32-MFFFFFNN
% 109.20/17.40 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 109.20/17.40 % Starting SubtermCWHack with 136s (1) cores
% 109.20/17.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 109.20/17.40 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 109.20/17.40 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 109.20/17.40 % Starting new_bool_3 with 136s (1) cores
% 109.20/17.40 % new_bool_3 with pid 793493 completed with status 0
% 109.20/17.40 % Result found by new_bool_3
% 109.20/17.40 % Preprocessing class: FSLSSMSMSSSNFFN.
% 109.20/17.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 109.20/17.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 109.20/17.40 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 109.20/17.40 % No SInE strategy applied
% 109.20/17.40 % Search class: FGHSF-SMLM32-MFFFFFNN
% 109.20/17.40 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 109.20/17.40 % Starting SubtermCWHack with 136s (1) cores
% 109.20/17.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 109.20/17.40 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 109.20/17.40 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 109.20/17.40 % Starting new_bool_3 with 136s (1) cores
% 109.20/17.40 % Preprocessing time : 0.253 s
% 109.20/17.40 % Presaturation interreduction done
% 109.20/17.40
% 109.20/17.40 % Proof found!
% 109.20/17.40 % SZS status Theorem
% 109.20/17.40 % SZS output start CNFRefutation
% See solution above
% 109.20/17.40 % Parsed axioms : 87
% 109.20/17.40 % Removed by relevancy pruning/SinE : 0
% 109.20/17.40 % Initial clauses : 4237
% 109.20/17.40 % Removed in clause preprocessing : 7
% 109.20/17.40 % Initial clauses in saturation : 4230
% 109.20/17.40 % Processed clauses : 15063
% 109.20/17.40 % ...of these trivial : 522
% 109.20/17.40 % ...subsumed : 1922
% 109.20/17.40 % ...remaining for further processing : 12619
% 109.20/17.40 % Other redundant clauses eliminated : 1945
% 109.20/17.40 % Clauses deleted for lack of memory : 0
% 109.20/17.40 % Backward-subsumed : 137
% 109.20/17.40 % Backward-rewritten : 240
% 109.20/17.40 % Generated clauses : 49811
% 109.20/17.40 % ...of the previous two non-redundant : 44706
% 109.20/17.40 % ...aggressively subsumed : 0
% 109.20/17.40 % Contextual simplify-reflections : 177
% 109.20/17.40 % Paramodulations : 48052
% 109.20/17.40 % Factorizations : 6
% 109.20/17.40 % NegExts : 0
% 109.20/17.40 % Equation resolutions : 1947
% 109.20/17.40 % Disequality decompositions : 0
% 109.20/17.40 % Total rewrite steps : 38077
% 109.20/17.40 % ...of those cached : 35914
% 109.20/17.40 % Propositional unsat checks : 3
% 109.20/17.40 % Propositional check models : 2
% 109.20/17.40 % Propositional check unsatisfiable : 0
% 109.20/17.40 % Propositional clauses : 0
% 109.20/17.40 % Propositional clauses after purity: 0
% 109.20/17.40 % Propositional unsat core size : 0
% 109.20/17.40 % Propositional preprocessing time : 0.000
% 109.20/17.40 % Propositional encoding time : 0.153
% 109.20/17.40 % Propositional solver time : 0.143
% 109.20/17.40 % Success case prop preproc time : 0.000
% 109.20/17.40 % Success case prop encoding time : 0.000
% 109.20/17.40 % Success case prop solver time : 0.000
% 109.20/17.40 % Current number of processed clauses : 6852
% 109.20/17.40 % Positive orientable unit clauses : 3459
% 109.20/17.40 % Positive unorientable unit clauses: 0
% 109.20/17.40 % Negative unit clauses : 182
% 109.20/17.40 % Non-unit-clauses : 3211
% 109.20/17.40 % Current number of unprocessed clauses: 36474
% 109.20/17.40 % ...number of literals in the above : 142792
% 109.20/17.40 % Current number of archived formulas : 0
% 109.20/17.40 % Current number of archived clauses : 4017
% 109.20/17.40 % Clause-clause subsumption calls (NU) : 9236792
% 109.20/17.40 % Rec. Clause-clause subsumption calls : 367649
% 109.20/17.40 % Non-unit clause-clause subsumptions : 1925
% 109.20/17.40 % Unit Clause-clause subsumption calls : 236151
% 109.20/17.40 % Rewrite failures with RHS unbound : 0
% 109.20/17.40 % BW rewrite match attempts : 150824
% 109.20/17.40 % BW rewrite match successes : 138
% 109.20/17.40 % Condensation attempts : 0
% 109.20/17.40 % Condensation successes : 0
% 109.20/17.40 % Termbank termtop insertions : 2138682
% 109.20/17.40 % Search garbage collected termcells : 27161
% 109.20/17.40
% 109.20/17.40 % -------------------------------------------------
% 109.20/17.40 % User time : 16.459 s
% 109.20/17.40 % System time : 0.181 s
% 109.20/17.40 % Total time : 16.639 s
% 109.20/17.40 % Maximum resident set size: 15036 pages
% 109.20/17.40
% 109.20/17.40 % -------------------------------------------------
% 109.20/17.40 % User time : 77.897 s
% 109.20/17.40 % System time : 1.008 s
% 109.20/17.40 % Total time : 78.905 s
% 109.20/17.40 % Maximum resident set size: 4608 pages
% 109.20/17.40 % E exiting
%------------------------------------------------------------------------------