%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM621+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:49:48 PM UTC 2026
% Result : Theorem 0.46s 0.74s
% Output : CNFRefutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 22
% Syntax : Number of formulae : 101 ( 30 unt; 0 def)
% Number of atoms : 350 ( 86 equ)
% Maximal formula atoms : 52 ( 3 avg)
% Number of connectives : 410 ( 161 ~; 168 |; 53 &)
% ( 8 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 12 con; 0-3 aty)
% Number of variables : 109 ( 0 sgn 56 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefMin,axiom,
! [X1] :
( ( X1 != slcrc0
& aSubsetOf0(X1,szNzAzT0) )
=> ! [X2] :
( X2 = szmzizndt0(X1)
<=> ( ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X2,X3) )
& aElementOf0(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefMin) ).
fof(m__,conjecture,
( aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
=> aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mSubTrans,axiom,
! [X1,X2,X3] :
( ( aSet0(X3)
& aSet0(X2)
& aSet0(X1) )
=> ( ( aSubsetOf0(X2,X3)
& aSubsetOf0(X1,X2) )
=> aSubsetOf0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubTrans) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(m__3671,hypothesis,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( isCountable0(sdtlpdtrp0(xN,X1))
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
fof(m__4660,hypothesis,
( ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> sdtlpdtrp0(xe,X1) = szmzizndt0(sdtlpdtrp0(xN,X1)) )
& szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4660) ).
fof(m__5401,hypothesis,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5401) ).
fof(mNATSet,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
fof(m__5309,hypothesis,
( sdtlpdtrp0(xe,xn) = xp
& aElementOf0(xn,szNzAzT0)
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5309) ).
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/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(m__5389,hypothesis,
( xx = sdtlpdtrp0(xe,xm)
& aElementOf0(xm,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5389) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__5106,hypothesis,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5106) ).
fof(m__5093,hypothesis,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5093) ).
fof(m__5164,hypothesis,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& aSet0(xP) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5164) ).
fof(m__5147,hypothesis,
xp = szmzizndt0(xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).
fof(m__5173,hypothesis,
aElementOf0(xp,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5173) ).
fof(mCountNFin_01,axiom,
! [X1] :
( ( isCountable0(X1)
& aSet0(X1) )
=> X1 != slcrc0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin_01) ).
fof(mLessASymm,axiom,
! [X1,X2] :
( ( aElementOf0(X2,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( ( sdtlseqdt0(X2,X1)
& sdtlseqdt0(X1,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessASymm) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( ~ ? [X2] : aElementOf0(X2,X1)
& aSet0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(m__5365,hypothesis,
( aElementOf0(xx,xO)
& aElementOf0(xx,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5365) ).
fof(m__5348,hypothesis,
aElementOf0(xx,xP),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5348) ).
fof(c_0_22,plain,
! [X1] :
( ( X1 != slcrc0
& aSubsetOf0(X1,szNzAzT0) )
=> ! [X2] :
( X2 = szmzizndt0(X1)
<=> ( ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X2,X3) )
& aElementOf0(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[mDefMin]) ).
fof(c_0_23,plain,
! [X94,X95,X96,X97] :
( ( X94 = slcrc0
| ~ aSubsetOf0(X94,szNzAzT0)
| X97 = szmzizndt0(X94)
| ~ aElementOf0(X97,X94)
| ~ sdtlseqdt0(X97,esk7_2(X94,X97)) )
& ( X94 = slcrc0
| ~ aSubsetOf0(X94,szNzAzT0)
| X97 = szmzizndt0(X94)
| ~ aElementOf0(X97,X94)
| aElementOf0(esk7_2(X94,X97),X94) )
& ( X94 = slcrc0
| ~ aSubsetOf0(X94,szNzAzT0)
| X95 != szmzizndt0(X94)
| sdtlseqdt0(X95,X96)
| ~ aElementOf0(X96,X94) )
& ( X94 = slcrc0
| ~ aSubsetOf0(X94,szNzAzT0)
| X95 != szmzizndt0(X94)
| aElementOf0(X95,X94) ) ),
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_22])])])])])])]) ).
fof(c_0_24,negated_conjecture,
~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
=> aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_25,plain,
! [X29,X30,X31] :
( aSubsetOf0(X29,X31)
| ~ aSubsetOf0(X30,X31)
| ~ aSubsetOf0(X29,X30)
| ~ aSet0(X31)
| ~ aSet0(X30)
| ~ aSet0(X29) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubTrans])])]) ).
fof(c_0_26,plain,
! [X19,X20,X21,X22] :
( ( ~ aSet0(X19)
| aSubsetOf0(X22,X19)
| ~ aSet0(X22)
| ~ aElementOf0(esk2_2(X19,X22),X19) )
& ( ~ aSet0(X19)
| aSubsetOf0(X22,X19)
| ~ aSet0(X22)
| aElementOf0(esk2_2(X19,X22),X22) )
& ( ~ aSet0(X19)
| ~ aSubsetOf0(X20,X19)
| aElementOf0(X21,X19)
| ~ aElementOf0(X21,X20) )
& ( ~ aSet0(X19)
| ~ aSubsetOf0(X20,X19)
| aSet0(X20) ) ),
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_27,plain,
( ~ aSubsetOf0(X2,szNzAzT0)
| X3 != szmzizndt0(X2)
| ~ aElementOf0(X1,X2)
| X2 = slcrc0
| sdtlseqdt0(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_28,negated_conjecture,
( ~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])]) ).
fof(c_0_29,hypothesis,
! [X184] :
( ( ~ aElementOf0(X184,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,X184)) )
& ( ~ aElementOf0(X184,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X184),szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3671])])])]) ).
fof(c_0_30,hypothesis,
! [X204] :
( ( sdtlpdtrp0(xe,X204) = szmzizndt0(sdtlpdtrp0(xN,X204))
| ~ aElementOf0(X204,szNzAzT0) )
& szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4660])])])]) ).
cnf(c_0_31,plain,
( ~ aSubsetOf0(X2,X3)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X3)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aSubsetOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
( ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
( ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,szNzAzT0)
| sdtlseqdt0(szmzizndt0(X1),X2)
| X1 = slcrc0 ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_34,hypothesis,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
inference(split_conjunct,[status(thm)],[m__5401]) ).
cnf(c_0_35,plain,
( ~ aSet0(X3)
| ~ aSubsetOf0(X2,X3)
| ~ aElementOf0(X1,X2)
| aElementOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,negated_conjecture,
aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_37,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
cnf(c_0_39,plain,
( ~ aSubsetOf0(X2,szNzAzT0)
| X1 != szmzizndt0(X2)
| X2 = slcrc0
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_40,hypothesis,
sdtlpdtrp0(xe,xn) = xp,
inference(split_conjunct,[status(thm)],[m__5309]) ).
cnf(c_0_41,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| sdtlpdtrp0(xe,X1) = szmzizndt0(sdtlpdtrp0(xN,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_42,hypothesis,
aElementOf0(xn,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__5309]) ).
cnf(c_0_43,plain,
( ~ aSet0(X2)
| ~ aSubsetOf0(X1,X3)
| ~ aSubsetOf0(X3,X2)
| aSubsetOf0(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_31,c_0_32]),c_0_32]) ).
fof(c_0_44,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_45,hypothesis,
( ~ aElementOf0(X1,sdtlpdtrp0(xN,xm))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| sdtlseqdt0(xx,X1)
| sdtlpdtrp0(xN,xm) = slcrc0 ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_46,hypothesis,
aElementOf0(xm,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__5389]) ).
cnf(c_0_47,negated_conjecture,
( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xn))
| aElementOf0(X1,sdtlpdtrp0(xN,xm)) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_48,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_37]),c_0_38])]) ).
cnf(c_0_49,plain,
( ~ aSubsetOf0(X1,szNzAzT0)
| aElementOf0(szmzizndt0(X1),X1)
| X1 = slcrc0 ),
inference(er,[status(thm)],[c_0_39]) ).
cnf(c_0_50,hypothesis,
szmzizndt0(sdtlpdtrp0(xN,xn)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]) ).
cnf(c_0_51,hypothesis,
( ~ aElementOf0(X2,szNzAzT0)
| ~ aSubsetOf0(X1,sdtlpdtrp0(xN,X2))
| aSubsetOf0(X1,szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_37]),c_0_38])]) ).
fof(c_0_52,plain,
! [X39,X40,X41,X42,X43,X44] :
( ( ~ aElement0(X40)
| ~ aSet0(X39)
| X44 = sdtmndt0(X39,X40)
| ~ aSet0(X44)
| aElementOf0(esk4_3(X39,X40,X44),X44)
| esk4_3(X39,X40,X44) != X40 )
& ( ~ aElement0(X40)
| ~ aSet0(X39)
| X44 = sdtmndt0(X39,X40)
| ~ aSet0(X44)
| aElementOf0(esk4_3(X39,X40,X44),X44)
| aElementOf0(esk4_3(X39,X40,X44),X39) )
& ( ~ aElement0(X40)
| ~ aSet0(X39)
| X44 = sdtmndt0(X39,X40)
| ~ aSet0(X44)
| aElementOf0(esk4_3(X39,X40,X44),X44)
| aElement0(esk4_3(X39,X40,X44)) )
& ( ~ aElement0(X40)
| ~ aSet0(X39)
| X44 = sdtmndt0(X39,X40)
| ~ aSet0(X44)
| esk4_3(X39,X40,X44) = X40
| ~ aElementOf0(esk4_3(X39,X40,X44),X39)
| ~ aElement0(esk4_3(X39,X40,X44))
| ~ aElementOf0(esk4_3(X39,X40,X44),X44) )
& ( ~ aElement0(X40)
| ~ aSet0(X39)
| X41 != sdtmndt0(X39,X40)
| aElementOf0(X43,X41)
| X43 = X40
| ~ aElementOf0(X43,X39)
| ~ aElement0(X43) )
& ( ~ aElement0(X40)
| ~ aSet0(X39)
| X41 != sdtmndt0(X39,X40)
| ~ aElementOf0(X42,X41)
| X42 != X40 )
& ( ~ aElement0(X40)
| ~ aSet0(X39)
| X41 != sdtmndt0(X39,X40)
| ~ aElementOf0(X42,X41)
| aElementOf0(X42,X39) )
& ( ~ aElement0(X40)
| ~ aSet0(X39)
| X41 != sdtmndt0(X39,X40)
| ~ aElementOf0(X42,X41)
| aElement0(X42) )
& ( ~ aElement0(X40)
| ~ aSet0(X39)
| X41 != sdtmndt0(X39,X40)
| aSet0(X41) ) ),
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_44])])])])])])]) ).
fof(c_0_53,plain,
! [X9,X10] :
( aElement0(X10)
| ~ aElementOf0(X10,X9)
| ~ aSet0(X9) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
cnf(c_0_54,hypothesis,
aSubsetOf0(xQ,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__5106]) ).
cnf(c_0_55,hypothesis,
( ~ aElementOf0(X1,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,X1)
| sdtlpdtrp0(xN,xm) = slcrc0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_37]),c_0_46])]) ).
cnf(c_0_56,hypothesis,
( ~ aElementOf0(X1,sdtlpdtrp0(xN,xn))
| aElementOf0(X1,sdtlpdtrp0(xN,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_46])]) ).
cnf(c_0_57,hypothesis,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
| aElementOf0(xp,sdtlpdtrp0(xN,xn))
| sdtlpdtrp0(xN,xn) = slcrc0 ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_58,negated_conjecture,
aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_36]),c_0_46])]) ).
fof(c_0_59,hypothesis,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ),
inference(fof_simplification,[status(thm)],[m__5093]) ).
cnf(c_0_60,plain,
( ~ aElement0(X4)
| ~ aSet0(X2)
| X3 != sdtmndt0(X2,X4)
| ~ aElementOf0(X1,X3)
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_61,hypothesis,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(split_conjunct,[status(thm)],[m__5164]) ).
cnf(c_0_62,hypothesis,
xp = szmzizndt0(xQ),
inference(split_conjunct,[status(thm)],[m__5147]) ).
cnf(c_0_63,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_64,hypothesis,
aElementOf0(xp,xQ),
inference(split_conjunct,[status(thm)],[m__5173]) ).
cnf(c_0_65,hypothesis,
aSet0(xQ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_54]),c_0_38])]) ).
fof(c_0_66,plain,
! [X1] :
( ( isCountable0(X1)
& aSet0(X1) )
=> X1 != slcrc0 ),
inference(fof_simplification,[status(thm)],[mCountNFin_01]) ).
fof(c_0_67,plain,
! [X72,X73] :
( X72 = X73
| ~ sdtlseqdt0(X73,X72)
| ~ sdtlseqdt0(X72,X73)
| ~ aElementOf0(X73,szNzAzT0)
| ~ aElementOf0(X72,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessASymm])])]) ).
cnf(c_0_68,hypothesis,
( ~ aElementOf0(X1,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(xx,X1)
| sdtlpdtrp0(xN,xm) = slcrc0 ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_69,hypothesis,
( aElementOf0(xp,sdtlpdtrp0(xN,xn))
| sdtlpdtrp0(xN,xn) = slcrc0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]) ).
cnf(c_0_70,hypothesis,
( ~ aElementOf0(X1,xQ)
| aElementOf0(X1,szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_54]),c_0_38])]) ).
fof(c_0_71,hypothesis,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ),
inference(fof_nnf,[status(thm)],[c_0_59]) ).
cnf(c_0_72,plain,
( ~ aSet0(X2)
| ~ aElement0(X3)
| ~ aElementOf0(X1,sdtmndt0(X2,X3))
| aElementOf0(X1,X2) ),
inference(er,[status(thm)],[c_0_60]) ).
cnf(c_0_73,hypothesis,
sdtmndt0(xQ,xp) = xP,
inference(rw,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_74,hypothesis,
aElement0(xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65])]) ).
fof(c_0_75,plain,
! [X18] :
( X18 != slcrc0
| ~ isCountable0(X18)
| ~ aSet0(X18) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_66])])]) ).
fof(c_0_76,plain,
! [X12,X13,X14] :
( ( X14 = slcrc0
| aElementOf0(esk1_1(X14),X14)
| ~ aSet0(X14) )
& ( X12 != slcrc0
| ~ aElementOf0(X13,X12) )
& ( X12 != slcrc0
| aSet0(X12) ) ),
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)],[mDefEmp])])])])])])]) ).
cnf(c_0_77,plain,
( ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_78,hypothesis,
( sdtlseqdt0(xx,xp)
| sdtlpdtrp0(xN,xm) = slcrc0
| sdtlpdtrp0(xN,xn) = slcrc0 ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_79,hypothesis,
aElementOf0(xx,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__5365]) ).
cnf(c_0_80,hypothesis,
aElementOf0(xp,szNzAzT0),
inference(spm,[status(thm)],[c_0_70,c_0_64]) ).
cnf(c_0_81,hypothesis,
xQ != slcrc0,
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_82,hypothesis,
( ~ aElementOf0(X1,xP)
| aElementOf0(X1,xQ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]),c_0_65])]) ).
cnf(c_0_83,hypothesis,
aElementOf0(xx,xP),
inference(split_conjunct,[status(thm)],[m__5348]) ).
cnf(c_0_84,plain,
( X1 != slcrc0
| ~ isCountable0(X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_85,plain,
( X1 != slcrc0
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_86,plain,
( ~ aElement0(X2)
| ~ aSet0(X4)
| X3 != sdtmndt0(X4,X2)
| ~ aElementOf0(X1,X3)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_87,hypothesis,
( ~ sdtlseqdt0(xp,xx)
| xp = xx
| sdtlpdtrp0(xN,xn) = slcrc0
| sdtlpdtrp0(xN,xm) = slcrc0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]),c_0_80])]) ).
cnf(c_0_88,hypothesis,
( ~ aElementOf0(X1,xQ)
| sdtlseqdt0(xp,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_62]),c_0_54])]),c_0_81]) ).
cnf(c_0_89,hypothesis,
aElementOf0(xx,xQ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_90,plain,
( ~ aSet0(slcrc0)
| ~ isCountable0(slcrc0) ),
inference(er,[status(thm)],[c_0_84]) ).
cnf(c_0_91,plain,
aSet0(slcrc0),
inference(er,[status(thm)],[c_0_85]) ).
cnf(c_0_92,plain,
( ~ aSet0(X2)
| ~ aElement0(X1)
| ~ aElementOf0(X1,sdtmndt0(X2,X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_86])]) ).
cnf(c_0_93,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_94,hypothesis,
( xp = xx
| sdtlpdtrp0(xN,xm) = slcrc0
| sdtlpdtrp0(xN,xn) = slcrc0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89])]) ).
cnf(c_0_95,plain,
~ isCountable0(slcrc0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_91])]) ).
cnf(c_0_96,hypothesis,
( ~ aElement0(xp)
| ~ aElementOf0(xp,xP) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_73]),c_0_65])]) ).
cnf(c_0_97,hypothesis,
( xp = xx
| sdtlpdtrp0(xN,xn) = slcrc0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_46])]),c_0_95]) ).
cnf(c_0_98,hypothesis,
~ aElementOf0(xp,xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_74])]) ).
cnf(c_0_99,hypothesis,
xp = xx,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_97]),c_0_42])]),c_0_95]) ).
cnf(c_0_100,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_99]),c_0_83])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM621+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.45 % Computer : n007.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 02:43:05 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.52 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.46/0.74 % Version: 3.5.1
% 0.46/0.74 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.46/0.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.46/0.74 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.46/0.74 % Starting new_bool_3 with 300s (1) cores
% 0.46/0.74 % Starting new_bool_1 with 300s (1) cores
% 0.46/0.74 % Starting sh5l with 300s (1) cores
% 0.46/0.74 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 502 completed with status 0
% 0.46/0.74 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.46/0.74 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.46/0.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.46/0.74 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.46/0.74 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.46/0.74 % No SInE strategy applied
% 0.46/0.74 % Search class: FGHSF-FSLM31-MFFFFFNN
% 0.46/0.74 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.46/0.74 % Starting SubtermCWHack with 136s (1) cores
% 0.46/0.74 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.46/0.74 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.46/0.74 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.46/0.74 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S070I with 136s (1) cores
% 0.46/0.74 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 513 completed with status 0
% 0.46/0.74 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.46/0.74 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.46/0.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.46/0.74 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.46/0.74 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.46/0.74 % No SInE strategy applied
% 0.46/0.74 % Search class: FGHSF-FSLM31-MFFFFFNN
% 0.46/0.74 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.46/0.74 % Starting SubtermCWHack with 136s (1) cores
% 0.46/0.74 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.46/0.74 % Preprocessing time : 0.006 s
% 0.46/0.74 % Presaturation interreduction done
% 0.46/0.74
% 0.46/0.74 % Proof found!
% 0.46/0.74 % SZS status Theorem
% 0.46/0.74 % SZS output start CNFRefutation
% See solution above
% 0.46/0.74 % Parsed axioms : 118
% 0.46/0.74 % Removed by relevancy pruning/SinE : 0
% 0.46/0.74 % Initial clauses : 227
% 0.46/0.74 % Removed in clause preprocessing : 7
% 0.46/0.74 % Initial clauses in saturation : 220
% 0.46/0.74 % Processed clauses : 1031
% 0.46/0.74 % ...of these trivial : 19
% 0.46/0.74 % ...subsumed : 207
% 0.46/0.74 % ...remaining for further processing : 805
% 0.46/0.74 % Other redundant clauses eliminated : 57
% 0.46/0.74 % Clauses deleted for lack of memory : 0
% 0.46/0.74 % Backward-subsumed : 26
% 0.46/0.74 % Backward-rewritten : 32
% 0.46/0.74 % Generated clauses : 2253
% 0.46/0.74 % ...of the previous two non-redundant : 1997
% 0.46/0.74 % ...aggressively subsumed : 0
% 0.46/0.74 % Contextual simplify-reflections : 50
% 0.46/0.74 % Paramodulations : 2198
% 0.46/0.74 % Factorizations : 0
% 0.46/0.74 % NegExts : 0
% 0.46/0.74 % Equation resolutions : 60
% 0.46/0.74 % Disequality decompositions : 0
% 0.46/0.74 % Total rewrite steps : 1724
% 0.46/0.74 % ...of those cached : 1620
% 0.46/0.74 % Propositional unsat checks : 0
% 0.46/0.74 % Propositional check models : 0
% 0.46/0.74 % Propositional check unsatisfiable : 0
% 0.46/0.74 % Propositional clauses : 0
% 0.46/0.74 % Propositional clauses after purity: 0
% 0.46/0.74 % Propositional unsat core size : 0
% 0.46/0.74 % Propositional preprocessing time : 0.000
% 0.46/0.74 % Propositional encoding time : 0.000
% 0.46/0.74 % Propositional solver time : 0.000
% 0.46/0.74 % Success case prop preproc time : 0.000
% 0.46/0.74 % Success case prop encoding time : 0.000
% 0.46/0.74 % Success case prop solver time : 0.000
% 0.46/0.74 % Current number of processed clauses : 489
% 0.46/0.74 % Positive orientable unit clauses : 118
% 0.46/0.74 % Positive unorientable unit clauses: 0
% 0.46/0.74 % Negative unit clauses : 21
% 0.46/0.74 % Non-unit-clauses : 350
% 0.46/0.74 % Current number of unprocessed clauses: 1359
% 0.46/0.74 % ...number of literals in the above : 6973
% 0.46/0.74 % Current number of archived formulas : 0
% 0.46/0.74 % Current number of archived clauses : 276
% 0.46/0.74 % Clause-clause subsumption calls (NU) : 21310
% 0.46/0.74 % Rec. Clause-clause subsumption calls : 7527
% 0.46/0.74 % Non-unit clause-clause subsumptions : 203
% 0.46/0.74 % Unit Clause-clause subsumption calls : 3003
% 0.46/0.74 % Rewrite failures with RHS unbound : 0
% 0.46/0.74 % BW rewrite match attempts : 13
% 0.46/0.74 % BW rewrite match successes : 12
% 0.46/0.74 % Condensation attempts : 0
% 0.46/0.74 % Condensation successes : 0
% 0.46/0.74 % Termbank termtop insertions : 56448
% 0.46/0.74 % Search garbage collected termcells : 3751
% 0.46/0.74
% 0.46/0.74 % -------------------------------------------------
% 0.46/0.74 % User time : 0.171 s
% 0.46/0.74 % System time : 0.017 s
% 0.46/0.74 % Total time : 0.188 s
% 0.46/0.74 % Maximum resident set size: 4288 pages
% 0.46/0.74
% 0.46/0.74 % -------------------------------------------------
% 0.46/0.74 % User time : 0.763 s
% 0.46/0.74 % System time : 0.062 s
% 0.46/0.74 % Total time : 0.825 s
% 0.46/0.74 % Maximum resident set size: 4608 pages
% 0.46/0.74 % E exiting
%------------------------------------------------------------------------------