%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM535+2 : 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 01:55:24 PM UTC 2026
% Result : Theorem 0.28s 0.56s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 49 ( 10 unt; 0 def)
% Number of atoms : 994 ( 171 equ)
% Maximal formula atoms : 676 ( 20 avg)
% Number of connectives : 1452 ( 507 ~; 676 |; 228 &)
% ( 18 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 175 ( 9 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 87 ( 0 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( ( ! [X1] :
( aElementOf0(X1,sdtmndt0(xS,xx))
<=> ( X1 != xx
& aElementOf0(X1,xS)
& aElement0(X1) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [X1] :
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( X1 = xx
| aElementOf0(X1,sdtmndt0(xS,xx)) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ! [X1] :
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
=> aElementOf0(X1,xS) ) ) ) )
& ( ( ! [X1] :
( aElementOf0(X1,sdtmndt0(xS,xx))
<=> ( X1 != xx
& aElementOf0(X1,xS)
& aElement0(X1) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [X1] :
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( X1 = xx
| aElementOf0(X1,sdtmndt0(xS,xx)) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ! [X1] :
( aElementOf0(X1,xS)
=> aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mDefCons,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aSet0(X1) )
=> ! [X3] :
( X3 = sdtpldt0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( ( X4 = X2
| aElementOf0(X4,X1) )
& aElement0(X4) ) )
& aSet0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefCons) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aSet0(X1) )
=> ! [X3] :
( X3 = sdtmndt0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( X4 != X2
& aElementOf0(X4,X1)
& aElement0(X4) ) )
& aSet0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(m__617_02,hypothesis,
aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__617_02) ).
fof(m__617,hypothesis,
aSet0(xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__617) ).
fof(c_0_6,negated_conjecture,
~ ( ( ( ! [X1] :
( aElementOf0(X1,sdtmndt0(xS,xx))
<=> ( X1 != xx
& aElementOf0(X1,xS)
& aElement0(X1) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [X1] :
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( X1 = xx
| aElementOf0(X1,sdtmndt0(xS,xx)) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ! [X1] :
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
=> aElementOf0(X1,xS) ) ) ) )
& ( ( ! [X1] :
( aElementOf0(X1,sdtmndt0(xS,xx))
<=> ( X1 != xx
& aElementOf0(X1,xS)
& aElement0(X1) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [X1] :
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( X1 = xx
| aElementOf0(X1,sdtmndt0(xS,xx)) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ! [X1] :
( aElementOf0(X1,xS)
=> aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_7,negated_conjecture,
~ ( ( ( ! [X1] :
( aElementOf0(X1,sdtmndt0(xS,xx))
<=> ( X1 != xx
& aElementOf0(X1,xS)
& aElement0(X1) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [X1] :
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( X1 = xx
| aElementOf0(X1,sdtmndt0(xS,xx)) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ! [X1] :
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
=> aElementOf0(X1,xS) ) ) ) )
& ( ( ! [X1] :
( aElementOf0(X1,sdtmndt0(xS,xx))
<=> ( X1 != xx
& aElementOf0(X1,xS)
& aElement0(X1) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [X1] :
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( X1 = xx
| aElementOf0(X1,sdtmndt0(xS,xx)) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ! [X1] :
( aElementOf0(X1,xS)
=> aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_8,plain,
! [X24,X25,X26,X27,X28,X29] :
( ( ~ aElement0(X25)
| ~ aSet0(X24)
| X29 = sdtpldt0(X24,X25)
| ~ aSet0(X29)
| aElementOf0(esk4_3(X24,X25,X29),X29)
| esk4_3(X24,X25,X29) = X25
| aElementOf0(esk4_3(X24,X25,X29),X24) )
& ( ~ aElement0(X25)
| ~ aSet0(X24)
| X29 = sdtpldt0(X24,X25)
| ~ aSet0(X29)
| aElementOf0(esk4_3(X24,X25,X29),X29)
| aElement0(esk4_3(X24,X25,X29)) )
& ( ~ aElement0(X25)
| ~ aSet0(X24)
| X29 = sdtpldt0(X24,X25)
| ~ aSet0(X29)
| ~ aElementOf0(esk4_3(X24,X25,X29),X29)
| ~ aElement0(esk4_3(X24,X25,X29))
| esk4_3(X24,X25,X29) != X25 )
& ( ~ aElement0(X25)
| ~ aSet0(X24)
| X29 = sdtpldt0(X24,X25)
| ~ aSet0(X29)
| ~ aElementOf0(esk4_3(X24,X25,X29),X29)
| ~ aElement0(esk4_3(X24,X25,X29))
| ~ aElementOf0(esk4_3(X24,X25,X29),X24) )
& ( ~ aElement0(X25)
| ~ aSet0(X24)
| X26 != sdtpldt0(X24,X25)
| aElementOf0(X28,X26)
| ~ aElement0(X28)
| X28 != X25 )
& ( ~ aElement0(X25)
| ~ aSet0(X24)
| X26 != sdtpldt0(X24,X25)
| aElementOf0(X28,X26)
| ~ aElement0(X28)
| ~ aElementOf0(X28,X24) )
& ( ~ aElement0(X25)
| ~ aSet0(X24)
| X26 != sdtpldt0(X24,X25)
| ~ aElementOf0(X27,X26)
| X27 = X25
| aElementOf0(X27,X24) )
& ( ~ aElement0(X25)
| ~ aSet0(X24)
| X26 != sdtpldt0(X24,X25)
| ~ aElementOf0(X27,X26)
| aElement0(X27) )
& ( ~ aElement0(X25)
| ~ aSet0(X24)
| X26 != sdtpldt0(X24,X25)
| aSet0(X26) ) ),
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)],[mDefCons])])])])])])]) ).
fof(c_0_9,plain,
! [X38,X39] :
( aElement0(X39)
| ~ aElementOf0(X39,X38)
| ~ aSet0(X38) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
fof(c_0_10,negated_conjecture,
! [X5,X6,X8,X9] :
( ( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) )
& ( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(esk2_0,xS) )
& ( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElementOf0(esk2_0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X9)
| X9 != xx )
& ( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X9)
| ~ aElementOf0(X9,sdtmndt0(xS,xx)) )
& ( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| X9 = xx
| aElementOf0(X9,sdtmndt0(xS,xx)) )
& ( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(X9) )
& ( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElementOf0(X8,sdtmndt0(xS,xx))
| X8 = xx
| ~ aElementOf0(X8,xS)
| ~ aElement0(X8) )
& ( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| X8 != xx )
& ( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| aElementOf0(X8,xS) )
& ( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| aElement0(X8) )
& ( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| aSet0(sdtmndt0(xS,xx)) )
& ( ~ aElementOf0(esk1_0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) )
& ( ~ aElementOf0(esk1_0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(esk2_0,xS) )
& ( ~ aElementOf0(esk1_0,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElementOf0(esk2_0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ~ aElementOf0(esk1_0,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X9)
| X9 != xx )
& ( ~ aElementOf0(esk1_0,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X9)
| ~ aElementOf0(X9,sdtmndt0(xS,xx)) )
& ( ~ aElementOf0(esk1_0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| X9 = xx
| aElementOf0(X9,sdtmndt0(xS,xx)) )
& ( ~ aElementOf0(esk1_0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(X9) )
& ( ~ aElementOf0(esk1_0,sdtpldt0(sdtmndt0(xS,xx),xx))
| aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ~ aElementOf0(esk1_0,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElementOf0(X8,sdtmndt0(xS,xx))
| X8 = xx
| ~ aElementOf0(X8,xS)
| ~ aElement0(X8) )
& ( ~ aElementOf0(esk1_0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| X8 != xx )
& ( ~ aElementOf0(esk1_0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| aElementOf0(X8,xS) )
& ( ~ aElementOf0(esk1_0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| aElement0(X8) )
& ( ~ aElementOf0(esk1_0,sdtpldt0(sdtmndt0(xS,xx),xx))
| aSet0(sdtmndt0(xS,xx)) )
& ( aElementOf0(esk1_0,xS)
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) )
& ( aElementOf0(esk1_0,xS)
| ~ aElementOf0(esk2_0,xS) )
& ( aElementOf0(esk1_0,xS)
| aElementOf0(esk2_0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( aElementOf0(esk1_0,xS)
| aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X9)
| X9 != xx )
& ( aElementOf0(esk1_0,xS)
| aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X9)
| ~ aElementOf0(X9,sdtmndt0(xS,xx)) )
& ( aElementOf0(esk1_0,xS)
| ~ aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| X9 = xx
| aElementOf0(X9,sdtmndt0(xS,xx)) )
& ( aElementOf0(esk1_0,xS)
| ~ aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(X9) )
& ( aElementOf0(esk1_0,xS)
| aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( aElementOf0(esk1_0,xS)
| aElementOf0(X8,sdtmndt0(xS,xx))
| X8 = xx
| ~ aElementOf0(X8,xS)
| ~ aElement0(X8) )
& ( aElementOf0(esk1_0,xS)
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| X8 != xx )
& ( aElementOf0(esk1_0,xS)
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| aElementOf0(X8,xS) )
& ( aElementOf0(esk1_0,xS)
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| aElement0(X8) )
& ( aElementOf0(esk1_0,xS)
| aSet0(sdtmndt0(xS,xx)) )
& ( aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X6)
| X6 != xx
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) )
& ( aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X6)
| X6 != xx
| ~ aElementOf0(esk2_0,xS) )
& ( aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X6)
| X6 != xx
| aElementOf0(esk2_0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X6)
| X6 != xx
| aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X9)
| X9 != xx )
& ( aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X6)
| X6 != xx
| aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X9)
| ~ aElementOf0(X9,sdtmndt0(xS,xx)) )
& ( aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X6)
| X6 != xx
| ~ aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| X9 = xx
| aElementOf0(X9,sdtmndt0(xS,xx)) )
& ( aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X6)
| X6 != xx
| ~ aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(X9) )
& ( aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X6)
| X6 != xx
| aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X6)
| X6 != xx
| aElementOf0(X8,sdtmndt0(xS,xx))
| X8 = xx
| ~ aElementOf0(X8,xS)
| ~ aElement0(X8) )
& ( aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X6)
| X6 != xx
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| X8 != xx )
& ( aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X6)
| X6 != xx
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| aElementOf0(X8,xS) )
& ( aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X6)
| X6 != xx
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| aElement0(X8) )
& ( aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X6)
| X6 != xx
| aSet0(sdtmndt0(xS,xx)) )
& ( aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X6)
| ~ aElementOf0(X6,sdtmndt0(xS,xx))
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) )
& ( aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X6)
| ~ aElementOf0(X6,sdtmndt0(xS,xx))
| ~ aElementOf0(esk2_0,xS) )
& ( aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X6)
| ~ aElementOf0(X6,sdtmndt0(xS,xx))
| aElementOf0(esk2_0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X6)
| ~ aElementOf0(X6,sdtmndt0(xS,xx))
| aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X9)
| X9 != xx )
& ( aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X6)
| ~ aElementOf0(X6,sdtmndt0(xS,xx))
| aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X9)
| ~ aElementOf0(X9,sdtmndt0(xS,xx)) )
& ( aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X6)
| ~ aElementOf0(X6,sdtmndt0(xS,xx))
| ~ aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| X9 = xx
| aElementOf0(X9,sdtmndt0(xS,xx)) )
& ( aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X6)
| ~ aElementOf0(X6,sdtmndt0(xS,xx))
| ~ aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(X9) )
& ( aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X6)
| ~ aElementOf0(X6,sdtmndt0(xS,xx))
| aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X6)
| ~ aElementOf0(X6,sdtmndt0(xS,xx))
| aElementOf0(X8,sdtmndt0(xS,xx))
| X8 = xx
| ~ aElementOf0(X8,xS)
| ~ aElement0(X8) )
& ( aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X6)
| ~ aElementOf0(X6,sdtmndt0(xS,xx))
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| X8 != xx )
& ( aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X6)
| ~ aElementOf0(X6,sdtmndt0(xS,xx))
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| aElementOf0(X8,xS) )
& ( aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X6)
| ~ aElementOf0(X6,sdtmndt0(xS,xx))
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| aElement0(X8) )
& ( aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X6)
| ~ aElementOf0(X6,sdtmndt0(xS,xx))
| aSet0(sdtmndt0(xS,xx)) )
& ( ~ aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| X6 = xx
| aElementOf0(X6,sdtmndt0(xS,xx))
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) )
& ( ~ aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| X6 = xx
| aElementOf0(X6,sdtmndt0(xS,xx))
| ~ aElementOf0(esk2_0,xS) )
& ( ~ aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| X6 = xx
| aElementOf0(X6,sdtmndt0(xS,xx))
| aElementOf0(esk2_0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ~ aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| X6 = xx
| aElementOf0(X6,sdtmndt0(xS,xx))
| aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X9)
| X9 != xx )
& ( ~ aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| X6 = xx
| aElementOf0(X6,sdtmndt0(xS,xx))
| aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X9)
| ~ aElementOf0(X9,sdtmndt0(xS,xx)) )
& ( ~ aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| X6 = xx
| aElementOf0(X6,sdtmndt0(xS,xx))
| ~ aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| X9 = xx
| aElementOf0(X9,sdtmndt0(xS,xx)) )
& ( ~ aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| X6 = xx
| aElementOf0(X6,sdtmndt0(xS,xx))
| ~ aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(X9) )
& ( ~ aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| X6 = xx
| aElementOf0(X6,sdtmndt0(xS,xx))
| aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ~ aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| X6 = xx
| aElementOf0(X6,sdtmndt0(xS,xx))
| aElementOf0(X8,sdtmndt0(xS,xx))
| X8 = xx
| ~ aElementOf0(X8,xS)
| ~ aElement0(X8) )
& ( ~ aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| X6 = xx
| aElementOf0(X6,sdtmndt0(xS,xx))
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| X8 != xx )
& ( ~ aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| X6 = xx
| aElementOf0(X6,sdtmndt0(xS,xx))
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| aElementOf0(X8,xS) )
& ( ~ aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| X6 = xx
| aElementOf0(X6,sdtmndt0(xS,xx))
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| aElement0(X8) )
& ( ~ aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| X6 = xx
| aElementOf0(X6,sdtmndt0(xS,xx))
| aSet0(sdtmndt0(xS,xx)) )
& ( ~ aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(X6)
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) )
& ( ~ aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(X6)
| ~ aElementOf0(esk2_0,xS) )
& ( ~ aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(X6)
| aElementOf0(esk2_0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ~ aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(X6)
| aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X9)
| X9 != xx )
& ( ~ aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(X6)
| aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X9)
| ~ aElementOf0(X9,sdtmndt0(xS,xx)) )
& ( ~ aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(X6)
| ~ aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| X9 = xx
| aElementOf0(X9,sdtmndt0(xS,xx)) )
& ( ~ aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(X6)
| ~ aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(X9) )
& ( ~ aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(X6)
| aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ~ aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(X6)
| aElementOf0(X8,sdtmndt0(xS,xx))
| X8 = xx
| ~ aElementOf0(X8,xS)
| ~ aElement0(X8) )
& ( ~ aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(X6)
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| X8 != xx )
& ( ~ aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(X6)
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| aElementOf0(X8,xS) )
& ( ~ aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(X6)
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| aElement0(X8) )
& ( ~ aElementOf0(X6,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(X6)
| aSet0(sdtmndt0(xS,xx)) )
& ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) )
& ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(esk2_0,xS) )
& ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| aElementOf0(esk2_0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X9)
| X9 != xx )
& ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X9)
| ~ aElementOf0(X9,sdtmndt0(xS,xx)) )
& ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| X9 = xx
| aElementOf0(X9,sdtmndt0(xS,xx)) )
& ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(X9) )
& ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| aElementOf0(X8,sdtmndt0(xS,xx))
| X8 = xx
| ~ aElementOf0(X8,xS)
| ~ aElement0(X8) )
& ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| X8 != xx )
& ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| aElementOf0(X8,xS) )
& ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| aElement0(X8) )
& ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| aSet0(sdtmndt0(xS,xx)) )
& ( aElementOf0(X5,sdtmndt0(xS,xx))
| X5 = xx
| ~ aElementOf0(X5,xS)
| ~ aElement0(X5)
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) )
& ( aElementOf0(X5,sdtmndt0(xS,xx))
| X5 = xx
| ~ aElementOf0(X5,xS)
| ~ aElement0(X5)
| ~ aElementOf0(esk2_0,xS) )
& ( aElementOf0(X5,sdtmndt0(xS,xx))
| X5 = xx
| ~ aElementOf0(X5,xS)
| ~ aElement0(X5)
| aElementOf0(esk2_0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( aElementOf0(X5,sdtmndt0(xS,xx))
| X5 = xx
| ~ aElementOf0(X5,xS)
| ~ aElement0(X5)
| aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X9)
| X9 != xx )
& ( aElementOf0(X5,sdtmndt0(xS,xx))
| X5 = xx
| ~ aElementOf0(X5,xS)
| ~ aElement0(X5)
| aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X9)
| ~ aElementOf0(X9,sdtmndt0(xS,xx)) )
& ( aElementOf0(X5,sdtmndt0(xS,xx))
| X5 = xx
| ~ aElementOf0(X5,xS)
| ~ aElement0(X5)
| ~ aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| X9 = xx
| aElementOf0(X9,sdtmndt0(xS,xx)) )
& ( aElementOf0(X5,sdtmndt0(xS,xx))
| X5 = xx
| ~ aElementOf0(X5,xS)
| ~ aElement0(X5)
| ~ aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(X9) )
& ( aElementOf0(X5,sdtmndt0(xS,xx))
| X5 = xx
| ~ aElementOf0(X5,xS)
| ~ aElement0(X5)
| aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( aElementOf0(X5,sdtmndt0(xS,xx))
| X5 = xx
| ~ aElementOf0(X5,xS)
| ~ aElement0(X5)
| aElementOf0(X8,sdtmndt0(xS,xx))
| X8 = xx
| ~ aElementOf0(X8,xS)
| ~ aElement0(X8) )
& ( aElementOf0(X5,sdtmndt0(xS,xx))
| X5 = xx
| ~ aElementOf0(X5,xS)
| ~ aElement0(X5)
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| X8 != xx )
& ( aElementOf0(X5,sdtmndt0(xS,xx))
| X5 = xx
| ~ aElementOf0(X5,xS)
| ~ aElement0(X5)
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| aElementOf0(X8,xS) )
& ( aElementOf0(X5,sdtmndt0(xS,xx))
| X5 = xx
| ~ aElementOf0(X5,xS)
| ~ aElement0(X5)
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| aElement0(X8) )
& ( aElementOf0(X5,sdtmndt0(xS,xx))
| X5 = xx
| ~ aElementOf0(X5,xS)
| ~ aElement0(X5)
| aSet0(sdtmndt0(xS,xx)) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| X5 != xx
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| X5 != xx
| ~ aElementOf0(esk2_0,xS) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| X5 != xx
| aElementOf0(esk2_0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| X5 != xx
| aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X9)
| X9 != xx )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| X5 != xx
| aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X9)
| ~ aElementOf0(X9,sdtmndt0(xS,xx)) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| X5 != xx
| ~ aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| X9 = xx
| aElementOf0(X9,sdtmndt0(xS,xx)) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| X5 != xx
| ~ aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(X9) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| X5 != xx
| aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| X5 != xx
| aElementOf0(X8,sdtmndt0(xS,xx))
| X8 = xx
| ~ aElementOf0(X8,xS)
| ~ aElement0(X8) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| X5 != xx
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| X8 != xx )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| X5 != xx
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| aElementOf0(X8,xS) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| X5 != xx
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| aElement0(X8) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| X5 != xx
| aSet0(sdtmndt0(xS,xx)) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| aElementOf0(X5,xS)
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| aElementOf0(X5,xS)
| ~ aElementOf0(esk2_0,xS) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| aElementOf0(X5,xS)
| aElementOf0(esk2_0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| aElementOf0(X5,xS)
| aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X9)
| X9 != xx )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| aElementOf0(X5,xS)
| aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X9)
| ~ aElementOf0(X9,sdtmndt0(xS,xx)) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| aElementOf0(X5,xS)
| ~ aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| X9 = xx
| aElementOf0(X9,sdtmndt0(xS,xx)) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| aElementOf0(X5,xS)
| ~ aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(X9) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| aElementOf0(X5,xS)
| aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| aElementOf0(X5,xS)
| aElementOf0(X8,sdtmndt0(xS,xx))
| X8 = xx
| ~ aElementOf0(X8,xS)
| ~ aElement0(X8) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| aElementOf0(X5,xS)
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| X8 != xx )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| aElementOf0(X5,xS)
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| aElementOf0(X8,xS) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| aElementOf0(X5,xS)
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| aElement0(X8) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| aElementOf0(X5,xS)
| aSet0(sdtmndt0(xS,xx)) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| aElement0(X5)
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| aElement0(X5)
| ~ aElementOf0(esk2_0,xS) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| aElement0(X5)
| aElementOf0(esk2_0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| aElement0(X5)
| aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X9)
| X9 != xx )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| aElement0(X5)
| aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X9)
| ~ aElementOf0(X9,sdtmndt0(xS,xx)) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| aElement0(X5)
| ~ aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| X9 = xx
| aElementOf0(X9,sdtmndt0(xS,xx)) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| aElement0(X5)
| ~ aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(X9) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| aElement0(X5)
| aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| aElement0(X5)
| aElementOf0(X8,sdtmndt0(xS,xx))
| X8 = xx
| ~ aElementOf0(X8,xS)
| ~ aElement0(X8) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| aElement0(X5)
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| X8 != xx )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| aElement0(X5)
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| aElementOf0(X8,xS) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| aElement0(X5)
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| aElement0(X8) )
& ( ~ aElementOf0(X5,sdtmndt0(xS,xx))
| aElement0(X5)
| aSet0(sdtmndt0(xS,xx)) )
& ( aSet0(sdtmndt0(xS,xx))
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) )
& ( aSet0(sdtmndt0(xS,xx))
| ~ aElementOf0(esk2_0,xS) )
& ( aSet0(sdtmndt0(xS,xx))
| aElementOf0(esk2_0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( aSet0(sdtmndt0(xS,xx))
| aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X9)
| X9 != xx )
& ( aSet0(sdtmndt0(xS,xx))
| aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X9)
| ~ aElementOf0(X9,sdtmndt0(xS,xx)) )
& ( aSet0(sdtmndt0(xS,xx))
| ~ aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| X9 = xx
| aElementOf0(X9,sdtmndt0(xS,xx)) )
& ( aSet0(sdtmndt0(xS,xx))
| ~ aElementOf0(X9,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(X9) )
& ( aSet0(sdtmndt0(xS,xx))
| aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( aSet0(sdtmndt0(xS,xx))
| aElementOf0(X8,sdtmndt0(xS,xx))
| X8 = xx
| ~ aElementOf0(X8,xS)
| ~ aElement0(X8) )
& ( aSet0(sdtmndt0(xS,xx))
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| X8 != xx )
& ( aSet0(sdtmndt0(xS,xx))
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| aElementOf0(X8,xS) )
& ( aSet0(sdtmndt0(xS,xx))
| ~ aElementOf0(X8,sdtmndt0(xS,xx))
| aElement0(X8) )
& ( aSet0(sdtmndt0(xS,xx))
| aSet0(sdtmndt0(xS,xx)) ) ),
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_7])])])])])]) ).
fof(c_0_11,plain,
! [X1,X2] :
( ( aElement0(X2)
& aSet0(X1) )
=> ! [X3] :
( X3 = sdtmndt0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( X4 != X2
& aElementOf0(X4,X1)
& aElement0(X4) ) )
& aSet0(X3) ) ) ),
inference(fof_simplification,[status(thm)],[mDefDiff]) ).
cnf(c_0_12,plain,
( ~ aElement0(X3)
| ~ aSet0(X2)
| X4 != sdtpldt0(X2,X3)
| ~ aElementOf0(X1,X4)
| X1 = X3
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,hypothesis,
aElementOf0(xx,xS),
inference(split_conjunct,[status(thm)],[m__617_02]) ).
cnf(c_0_15,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[m__617]) ).
cnf(c_0_16,negated_conjecture,
( aSet0(sdtmndt0(xS,xx))
| aSet0(sdtmndt0(xS,xx)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_17,plain,
! [X31,X32,X33,X34,X35,X36] :
( ( ~ aElement0(X32)
| ~ aSet0(X31)
| X36 = sdtmndt0(X31,X32)
| ~ aSet0(X36)
| aElementOf0(esk5_3(X31,X32,X36),X36)
| esk5_3(X31,X32,X36) != X32 )
& ( ~ aElement0(X32)
| ~ aSet0(X31)
| X36 = sdtmndt0(X31,X32)
| ~ aSet0(X36)
| aElementOf0(esk5_3(X31,X32,X36),X36)
| aElementOf0(esk5_3(X31,X32,X36),X31) )
& ( ~ aElement0(X32)
| ~ aSet0(X31)
| X36 = sdtmndt0(X31,X32)
| ~ aSet0(X36)
| aElementOf0(esk5_3(X31,X32,X36),X36)
| aElement0(esk5_3(X31,X32,X36)) )
& ( ~ aElement0(X32)
| ~ aSet0(X31)
| X36 = sdtmndt0(X31,X32)
| ~ aSet0(X36)
| esk5_3(X31,X32,X36) = X32
| ~ aElementOf0(esk5_3(X31,X32,X36),X31)
| ~ aElement0(esk5_3(X31,X32,X36))
| ~ aElementOf0(esk5_3(X31,X32,X36),X36) )
& ( ~ aElement0(X32)
| ~ aSet0(X31)
| X33 != sdtmndt0(X31,X32)
| aElementOf0(X35,X33)
| X35 = X32
| ~ aElementOf0(X35,X31)
| ~ aElement0(X35) )
& ( ~ aElement0(X32)
| ~ aSet0(X31)
| X33 != sdtmndt0(X31,X32)
| ~ aElementOf0(X34,X33)
| X34 != X32 )
& ( ~ aElement0(X32)
| ~ aSet0(X31)
| X33 != sdtmndt0(X31,X32)
| ~ aElementOf0(X34,X33)
| aElementOf0(X34,X31) )
& ( ~ aElement0(X32)
| ~ aSet0(X31)
| X33 != sdtmndt0(X31,X32)
| ~ aElementOf0(X34,X33)
| aElement0(X34) )
& ( ~ aElement0(X32)
| ~ aSet0(X31)
| X33 != sdtmndt0(X31,X32)
| aSet0(X33) ) ),
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_11])])])])])])]) ).
cnf(c_0_18,plain,
( ~ aSet0(X3)
| ~ aElement0(X2)
| ~ aElementOf0(X1,sdtpldt0(X3,X2))
| aElementOf0(X1,X3)
| X1 = X2 ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
( ~ aElementOf0(esk1_0,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElementOf0(esk2_0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_20,hypothesis,
aElement0(xx),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
cnf(c_0_21,negated_conjecture,
aSet0(sdtmndt0(xS,xx)),
inference(cn,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( ~ aElement0(X4)
| ~ aSet0(X2)
| X3 != sdtpldt0(X2,X4)
| ~ aElement0(X1)
| ~ aElementOf0(X1,X2)
| aElementOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_23,plain,
( ~ aElement0(X4)
| ~ aSet0(X2)
| X3 != sdtmndt0(X2,X4)
| ~ aElementOf0(X1,X3)
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,negated_conjecture,
( ~ aElementOf0(esk1_0,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElementOf0(esk2_0,sdtmndt0(xS,xx))
| esk2_0 = xx ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]) ).
cnf(c_0_25,plain,
( ~ aSet0(X2)
| ~ aElement0(X3)
| ~ aElementOf0(X1,X2)
| aElementOf0(X1,sdtpldt0(X2,X3)) ),
inference(er,[status(thm)],[inference(csr,[status(thm)],[c_0_22,c_0_13])]) ).
cnf(c_0_26,negated_conjecture,
( ~ aElementOf0(esk1_0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(esk2_0,xS) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_27,negated_conjecture,
( aElementOf0(esk1_0,xS)
| aElementOf0(esk2_0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_28,plain,
( ~ aElement0(X3)
| ~ aSet0(X2)
| X4 != sdtmndt0(X2,X3)
| ~ aElementOf0(X1,X2)
| ~ aElement0(X1)
| aElementOf0(X1,X4)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_29,plain,
( ~ aSet0(X2)
| ~ aElement0(X3)
| ~ aElementOf0(X1,sdtmndt0(X2,X3))
| aElementOf0(X1,X2) ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_30,negated_conjecture,
( ~ aElementOf0(esk1_0,sdtmndt0(xS,xx))
| aElementOf0(esk2_0,sdtmndt0(xS,xx))
| esk2_0 = xx ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_20]),c_0_21])]) ).
cnf(c_0_31,negated_conjecture,
( ~ aElementOf0(esk2_0,xS)
| ~ aElementOf0(esk1_0,sdtmndt0(xS,xx)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_25]),c_0_20]),c_0_21])]) ).
cnf(c_0_32,negated_conjecture,
( aElementOf0(esk1_0,xS)
| aElementOf0(esk2_0,sdtmndt0(xS,xx))
| esk2_0 = xx ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_27]),c_0_20]),c_0_21])]) ).
cnf(c_0_33,negated_conjecture,
( ~ aElementOf0(esk2_0,xS)
| aElementOf0(esk1_0,xS) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_34,plain,
( ~ aSet0(X3)
| ~ aElement0(X2)
| ~ aElementOf0(X1,X3)
| aElementOf0(X1,sdtmndt0(X3,X2))
| X1 = X2 ),
inference(er,[status(thm)],[inference(csr,[status(thm)],[c_0_28,c_0_13])]) ).
cnf(c_0_35,negated_conjecture,
( ~ aElementOf0(esk1_0,sdtmndt0(xS,xx))
| esk2_0 = xx ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_20]),c_0_15])]),c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( aElementOf0(esk1_0,xS)
| esk2_0 = xx ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_32]),c_0_20]),c_0_15])]),c_0_33]) ).
cnf(c_0_37,negated_conjecture,
( ~ aElementOf0(esk2_0,xS)
| esk1_0 = xx ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_34]),c_0_20]),c_0_15])]),c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( esk2_0 = xx
| esk1_0 = xx ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_34]),c_0_20]),c_0_15])]),c_0_36]) ).
cnf(c_0_39,negated_conjecture,
esk1_0 = xx,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_14])]) ).
cnf(c_0_40,plain,
( ~ aElement0(X2)
| ~ aSet0(X4)
| X3 != sdtpldt0(X4,X2)
| ~ aElement0(X1)
| X1 != X2
| aElementOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_41,negated_conjecture,
( ~ aElement0(X1)
| X1 != xx
| ~ aElementOf0(esk2_0,xS)
| aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_42,negated_conjecture,
( ~ aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElementOf0(esk2_0,sdtmndt0(xS,xx))
| esk2_0 = xx ),
inference(rw,[status(thm)],[c_0_24,c_0_39]) ).
cnf(c_0_43,plain,
( ~ aSet0(X2)
| ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(X2,X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_40])]) ).
cnf(c_0_44,negated_conjecture,
( ~ aElementOf0(esk2_0,xS)
| aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_41]),c_0_20])]) ).
cnf(c_0_45,negated_conjecture,
( aElementOf0(esk2_0,sdtmndt0(xS,xx))
| esk2_0 = xx ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_20]),c_0_21])]) ).
cnf(c_0_46,negated_conjecture,
~ aElementOf0(esk2_0,xS),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_39]),c_0_44]) ).
cnf(c_0_47,negated_conjecture,
esk2_0 = xx,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_45]),c_0_20]),c_0_15])]),c_0_46]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM535+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.42 % Computer : n013.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Mon Sep 21 02:37:50 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.50 Running first-order theorem proving
% 0.17/0.50 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.28/0.56 % Version: 3.5.1
% 0.28/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.28/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.28/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.28/0.56 % Starting new_bool_1 with 300s (1) cores
% 0.28/0.56 % Starting sh5l with 300s (1) cores
% 0.28/0.56 % sh5l with pid 3965009 completed with status 0
% 0.28/0.56 % Result found by sh5l
% 0.28/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.28/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.28/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.28/0.56 % Starting new_bool_1 with 300s (1) cores
% 0.28/0.56 % Starting sh5l with 300s (1) cores
% 0.28/0.56 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.28/0.56 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.28/0.56 % Search class: FGHSF-FSLM32-SFFFFFNN
% 0.28/0.56 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.56 % Starting SubtermCWHack with 28s (1) cores
% 0.28/0.56 % SubtermCWHack with pid 3965010 completed with status 0
% 0.28/0.56 % Result found by SubtermCWHack
% 0.28/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.28/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.28/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.28/0.56 % Starting new_bool_1 with 300s (1) cores
% 0.28/0.56 % Starting sh5l with 300s (1) cores
% 0.28/0.56 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.28/0.56 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.28/0.56 % Search class: FGHSF-FSLM32-SFFFFFNN
% 0.28/0.56 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.56 % Starting SubtermCWHack with 28s (1) cores
% 0.28/0.56 % Preprocessing time : 0.005 s
% 0.28/0.56
% 0.28/0.56 % Proof found!
% 0.28/0.56 % SZS status Theorem
% 0.28/0.56 % SZS output start CNFRefutation
% See solution above
% 0.28/0.56 % Parsed axioms : 19
% 0.28/0.56 % Removed by relevancy pruning/SinE : 0
% 0.28/0.56 % Initial clauses : 208
% 0.28/0.56 % Removed in clause preprocessing : 4
% 0.28/0.56 % Initial clauses in saturation : 204
% 0.28/0.56 % Processed clauses : 216
% 0.28/0.56 % ...of these trivial : 34
% 0.28/0.56 % ...subsumed : 38
% 0.28/0.56 % ...remaining for further processing : 144
% 0.28/0.56 % Other redundant clauses eliminated : 28
% 0.28/0.56 % Clauses deleted for lack of memory : 0
% 0.28/0.56 % Backward-subsumed : 28
% 0.28/0.56 % Backward-rewritten : 45
% 0.28/0.56 % Generated clauses : 237
% 0.28/0.56 % ...of the previous two non-redundant : 185
% 0.28/0.56 % ...aggressively subsumed : 0
% 0.28/0.56 % Contextual simplify-reflections : 16
% 0.28/0.56 % Paramodulations : 212
% 0.28/0.56 % Factorizations : 0
% 0.28/0.56 % NegExts : 0
% 0.28/0.56 % Equation resolutions : 28
% 0.28/0.56 % Disequality decompositions : 0
% 0.28/0.56 % Total rewrite steps : 275
% 0.28/0.56 % ...of those cached : 265
% 0.28/0.56 % Propositional unsat checks : 0
% 0.28/0.56 % Propositional check models : 0
% 0.28/0.56 % Propositional check unsatisfiable : 0
% 0.28/0.56 % Propositional clauses : 0
% 0.28/0.56 % Propositional clauses after purity: 0
% 0.28/0.56 % Propositional unsat core size : 0
% 0.28/0.56 % Propositional preprocessing time : 0.000
% 0.28/0.56 % Propositional encoding time : 0.000
% 0.28/0.56 % Propositional solver time : 0.000
% 0.28/0.56 % Success case prop preproc time : 0.000
% 0.28/0.56 % Success case prop encoding time : 0.000
% 0.28/0.56 % Success case prop solver time : 0.000
% 0.28/0.56 % Current number of processed clauses : 46
% 0.28/0.56 % Positive orientable unit clauses : 9
% 0.28/0.56 % Positive unorientable unit clauses: 0
% 0.28/0.56 % Negative unit clauses : 3
% 0.28/0.56 % Non-unit-clauses : 34
% 0.28/0.56 % Current number of unprocessed clauses: 152
% 0.28/0.56 % ...number of literals in the above : 738
% 0.28/0.56 % Current number of archived formulas : 0
% 0.28/0.56 % Current number of archived clauses : 73
% 0.28/0.56 % Clause-clause subsumption calls (NU) : 1646
% 0.28/0.56 % Rec. Clause-clause subsumption calls : 733
% 0.28/0.56 % Non-unit clause-clause subsumptions : 58
% 0.28/0.56 % Unit Clause-clause subsumption calls : 53
% 0.28/0.56 % Rewrite failures with RHS unbound : 0
% 0.28/0.56 % BW rewrite match attempts : 3
% 0.28/0.56 % BW rewrite match successes : 3
% 0.28/0.56 % Condensation attempts : 0
% 0.28/0.56 % Condensation successes : 0
% 0.28/0.56 % Termbank termtop insertions : 14247
% 0.28/0.56 % Search garbage collected termcells : 1446
% 0.28/0.56
% 0.28/0.56 % -------------------------------------------------
% 0.28/0.56 % User time : 0.026 s
% 0.28/0.56 % System time : 0.008 s
% 0.28/0.56 % Total time : 0.034 s
% 0.28/0.56 % Maximum resident set size: 3908 pages
% 0.28/0.56
% 0.28/0.56 % -------------------------------------------------
% 0.28/0.56 % User time : 0.030 s
% 0.28/0.56 % System time : 0.014 s
% 0.28/0.56 % Total time : 0.043 s
% 0.28/0.56 % Maximum resident set size: 4608 pages
% 0.28/0.56 % E exiting
%------------------------------------------------------------------------------