%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM588+1 : 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 : 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 01:49:40 PM UTC 2026
% Result : Theorem 0.16s 10.69s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 74 ( 14 unt; 0 def)
% Number of atoms : 357 ( 71 equ)
% Maximal formula atoms : 52 ( 4 avg)
% Number of connectives : 469 ( 186 ~; 194 |; 57 &)
% ( 10 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 8 con; 0-3 aty)
% Number of variables : 120 ( 0 sgn 66 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ! [X2] :
( ( isCountable0(X2)
& aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) )
=> ! [X3] :
( ( aElementOf0(X3,slbdtsldtrb0(X2,xk))
& aSet0(X3) )
=> aElementOf0(X3,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))),xk)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
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(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/sandbox2/benchmark/theBenchmark.p',mDefMin) ).
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(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__3671,hypothesis,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( isCountable0(sdtlpdtrp0(xN,X1))
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3671) ).
fof(mCountNFin_01,axiom,
! [X1] :
( ( isCountable0(X1)
& aSet0(X1) )
=> X1 != slcrc0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin_01) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( ~ ? [X2] : aElementOf0(X2,X1)
& aSet0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
fof(mNATSet,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(mDefSel,axiom,
! [X1,X2] :
( ( aElementOf0(X2,szNzAzT0)
& aSet0(X1) )
=> ! [X3] :
( X3 = slbdtsldtrb0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( sbrdtbr0(X4) = X2
& aSubsetOf0(X4,X1) ) )
& aSet0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
fof(m__3533,hypothesis,
( szszuzczcdt0(xk) = xK
& aElementOf0(xk,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3533) ).
fof(mSubTrans,axiom,
! [X1,X2,X3] :
( ( aSet0(X3)
& aSet0(X2)
& aSet0(X1) )
=> ( ( aSubsetOf0(X2,X3)
& aSubsetOf0(X1,X2) )
=> aSubsetOf0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubTrans) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ! [X2] :
( ( isCountable0(X2)
& aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) )
=> ! [X3] :
( ( aElementOf0(X3,slbdtsldtrb0(X2,xk))
& aSet0(X3) )
=> aElementOf0(X3,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))),xk)) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_13,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]) ).
fof(c_0_14,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_15,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])])])])])])]) ).
fof(c_0_16,negated_conjecture,
( ~ aElementOf0(esk24_0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,esk22_0),szmzizndt0(sdtlpdtrp0(xN,esk22_0))),xk))
& aElementOf0(esk24_0,slbdtsldtrb0(esk23_0,xk))
& aSet0(esk24_0)
& isCountable0(esk23_0)
& aSubsetOf0(esk23_0,sdtmndt0(sdtlpdtrp0(xN,esk22_0),szmzizndt0(sdtlpdtrp0(xN,esk22_0))))
& aElementOf0(esk22_0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
fof(c_0_17,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_13])])])])])])]) ).
fof(c_0_18,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_14])])])])])])]) ).
cnf(c_0_19,plain,
( ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
aSubsetOf0(esk23_0,sdtmndt0(sdtlpdtrp0(xN,esk22_0),szmzizndt0(sdtlpdtrp0(xN,esk22_0)))),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( ~ aElement0(X3)
| ~ aSet0(X2)
| X1 != sdtmndt0(X2,X3)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,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_23,plain,
( ~ aSubsetOf0(X2,szNzAzT0)
| X1 != szmzizndt0(X2)
| X2 = slcrc0
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,negated_conjecture,
( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,esk22_0),szmzizndt0(sdtlpdtrp0(xN,esk22_0))))
| aSet0(esk23_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
( ~ aSet0(X1)
| ~ aElement0(X2)
| aSet0(sdtmndt0(X1,X2)) ),
inference(er,[status(thm)],[c_0_21]) ).
cnf(c_0_26,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( ~ aSubsetOf0(X1,szNzAzT0)
| aElementOf0(szmzizndt0(X1),X1)
| X1 = slcrc0 ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
( ~ aSet0(sdtlpdtrp0(xN,esk22_0))
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,esk22_0)))
| aSet0(esk23_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
( ~ aSet0(X1)
| ~ aSubsetOf0(X1,szNzAzT0)
| aElement0(szmzizndt0(X1))
| X1 = slcrc0 ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_30,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_31,plain,
! [X1] :
( ( isCountable0(X1)
& aSet0(X1) )
=> X1 != slcrc0 ),
inference(fof_simplification,[status(thm)],[mCountNFin_01]) ).
fof(c_0_32,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_33,negated_conjecture,
( ~ aSet0(sdtlpdtrp0(xN,esk22_0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,esk22_0),szNzAzT0)
| aSet0(esk23_0)
| sdtlpdtrp0(xN,esk22_0) = slcrc0 ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,negated_conjecture,
aElementOf0(esk22_0,szNzAzT0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_36,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
fof(c_0_37,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_31])])]) ).
cnf(c_0_38,plain,
( X1 != slcrc0
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_39,plain,
! [X120,X121,X122,X123,X124,X125] :
( ( ~ aElementOf0(X121,szNzAzT0)
| ~ aSet0(X120)
| X125 = slbdtsldtrb0(X120,X121)
| ~ aSet0(X125)
| aElementOf0(esk11_3(X120,X121,X125),X125)
| sbrdtbr0(esk11_3(X120,X121,X125)) = X121 )
& ( ~ aElementOf0(X121,szNzAzT0)
| ~ aSet0(X120)
| X125 = slbdtsldtrb0(X120,X121)
| ~ aSet0(X125)
| aElementOf0(esk11_3(X120,X121,X125),X125)
| aSubsetOf0(esk11_3(X120,X121,X125),X120) )
& ( ~ aElementOf0(X121,szNzAzT0)
| ~ aSet0(X120)
| X125 = slbdtsldtrb0(X120,X121)
| ~ aSet0(X125)
| sbrdtbr0(esk11_3(X120,X121,X125)) != X121
| ~ aSubsetOf0(esk11_3(X120,X121,X125),X120)
| ~ aElementOf0(esk11_3(X120,X121,X125),X125) )
& ( ~ aElementOf0(X121,szNzAzT0)
| ~ aSet0(X120)
| X122 != slbdtsldtrb0(X120,X121)
| aElementOf0(X124,X122)
| sbrdtbr0(X124) != X121
| ~ aSubsetOf0(X124,X120) )
& ( ~ aElementOf0(X121,szNzAzT0)
| ~ aSet0(X120)
| X122 != slbdtsldtrb0(X120,X121)
| ~ aElementOf0(X123,X122)
| sbrdtbr0(X123) = X121 )
& ( ~ aElementOf0(X121,szNzAzT0)
| ~ aSet0(X120)
| X122 != slbdtsldtrb0(X120,X121)
| ~ aElementOf0(X123,X122)
| aSubsetOf0(X123,X120) )
& ( ~ aElementOf0(X121,szNzAzT0)
| ~ aSet0(X120)
| X122 != slbdtsldtrb0(X120,X121)
| aSet0(X122) ) ),
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)],[mDefSel])])])])])])]) ).
cnf(c_0_40,hypothesis,
( ~ aSet0(sdtlpdtrp0(xN,esk22_0))
| aSet0(esk23_0)
| sdtlpdtrp0(xN,esk22_0) = slcrc0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).
cnf(c_0_41,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_34]),c_0_36])]) ).
cnf(c_0_42,plain,
( X1 != slcrc0
| ~ isCountable0(X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,plain,
aSet0(slcrc0),
inference(er,[status(thm)],[c_0_38]) ).
cnf(c_0_44,plain,
( ~ aElementOf0(X2,szNzAzT0)
| ~ aSet0(X4)
| X3 != slbdtsldtrb0(X4,X2)
| ~ aElementOf0(X1,X3)
| sbrdtbr0(X1) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_45,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_46,hypothesis,
( aSet0(esk23_0)
| sdtlpdtrp0(xN,esk22_0) = slcrc0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_35])]) ).
cnf(c_0_47,plain,
~ isCountable0(slcrc0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_42]),c_0_43])]) ).
cnf(c_0_48,plain,
( ~ aElementOf0(X3,szNzAzT0)
| ~ aSet0(X2)
| X4 != slbdtsldtrb0(X2,X3)
| sbrdtbr0(X1) != X3
| ~ aSubsetOf0(X1,X2)
| aElementOf0(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_49,plain,
( ~ aSet0(X3)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,slbdtsldtrb0(X3,X2))
| sbrdtbr0(X1) = X2 ),
inference(er,[status(thm)],[c_0_44]) ).
cnf(c_0_50,negated_conjecture,
aElementOf0(esk24_0,slbdtsldtrb0(esk23_0,xk)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_51,hypothesis,
aElementOf0(xk,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3533]) ).
cnf(c_0_52,hypothesis,
aSet0(esk23_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_35])]),c_0_47]) ).
fof(c_0_53,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])])]) ).
cnf(c_0_54,plain,
( ~ aSet0(X2)
| ~ aElementOf0(sbrdtbr0(X1),szNzAzT0)
| ~ aSubsetOf0(X1,X2)
| aElementOf0(X1,slbdtsldtrb0(X2,sbrdtbr0(X1))) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_48])]) ).
cnf(c_0_55,negated_conjecture,
sbrdtbr0(esk24_0) = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_52])]) ).
cnf(c_0_56,plain,
( ~ aSubsetOf0(X2,X3)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X3)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aSubsetOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_57,plain,
( ~ aElementOf0(X4,szNzAzT0)
| ~ aSet0(X2)
| X3 != slbdtsldtrb0(X2,X4)
| ~ aElementOf0(X1,X3)
| aSubsetOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_58,negated_conjecture,
~ aElementOf0(esk24_0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,esk22_0),szmzizndt0(sdtlpdtrp0(xN,esk22_0))),xk)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_59,negated_conjecture,
( ~ aSet0(X1)
| ~ aSubsetOf0(esk24_0,X1)
| aElementOf0(esk24_0,slbdtsldtrb0(X1,xk)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_51])]) ).
cnf(c_0_60,plain,
( ~ aSet0(X2)
| ~ aSubsetOf0(X1,X3)
| ~ aSubsetOf0(X3,X2)
| aSubsetOf0(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_56,c_0_19]),c_0_19]) ).
cnf(c_0_61,plain,
( ~ aSet0(X2)
| ~ aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X1,slbdtsldtrb0(X2,X3))
| aSubsetOf0(X1,X2) ),
inference(er,[status(thm)],[c_0_57]) ).
cnf(c_0_62,plain,
( ~ aSet0(X3)
| ~ aSubsetOf0(X2,X3)
| ~ aElementOf0(X1,X2)
| aElementOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_63,negated_conjecture,
( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,esk22_0),szmzizndt0(sdtlpdtrp0(xN,esk22_0))))
| ~ aSubsetOf0(esk24_0,sdtmndt0(sdtlpdtrp0(xN,esk22_0),szmzizndt0(sdtlpdtrp0(xN,esk22_0)))) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_64,negated_conjecture,
( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,esk22_0),szmzizndt0(sdtlpdtrp0(xN,esk22_0))))
| ~ aSubsetOf0(X1,esk23_0)
| aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,esk22_0),szmzizndt0(sdtlpdtrp0(xN,esk22_0)))) ),
inference(spm,[status(thm)],[c_0_60,c_0_20]) ).
cnf(c_0_65,negated_conjecture,
aSubsetOf0(esk24_0,esk23_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_50]),c_0_51]),c_0_52])]) ).
cnf(c_0_66,hypothesis,
( ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X2))
| aElementOf0(X1,szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_34]),c_0_36])]) ).
cnf(c_0_67,negated_conjecture,
~ aSet0(sdtmndt0(sdtlpdtrp0(xN,esk22_0),szmzizndt0(sdtlpdtrp0(xN,esk22_0)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65])]) ).
cnf(c_0_68,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),szNzAzT0)
| sdtlpdtrp0(xN,X1) = slcrc0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_27]),c_0_34]) ).
cnf(c_0_69,negated_conjecture,
( ~ aSet0(sdtlpdtrp0(xN,esk22_0))
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,esk22_0))) ),
inference(spm,[status(thm)],[c_0_67,c_0_25]) ).
cnf(c_0_70,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aElement0(szmzizndt0(sdtlpdtrp0(xN,X1)))
| sdtlpdtrp0(xN,X1) = slcrc0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_68]),c_0_36])]) ).
cnf(c_0_71,hypothesis,
( ~ aSet0(sdtlpdtrp0(xN,esk22_0))
| sdtlpdtrp0(xN,esk22_0) = slcrc0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_35])]) ).
cnf(c_0_72,hypothesis,
sdtlpdtrp0(xN,esk22_0) = slcrc0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_41]),c_0_35])]) ).
cnf(c_0_73,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_72]),c_0_35])]),c_0_47]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM588+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/10.53 % Computer : n007.cluster.edu
% 0.11/10.53 % Model : x86_64 x86_64
% 0.11/10.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.53 % Memory : 8046.5625MB
% 0.11/10.53 % OS : Linux 6.8.0-71-generic
% 0.11/10.53 % CPULimit : 300
% 0.11/10.53 % WCLimit : 300
% 0.11/10.53 % DateTime : Mon Sep 21 02:40:16 UTC 2026
% 0.11/10.54 % CPUTime :
% 0.11/10.54 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/10.58 Running first-order theorem proving
% 0.11/10.58 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
% 0.16/10.69 % Version: 3.5.1
% 0.16/10.69 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.16/10.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/10.69 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.16/10.69 % Starting new_bool_3 with 300s (1) cores
% 0.16/10.69 % Starting new_bool_1 with 300s (1) cores
% 0.16/10.69 % Starting sh5l with 300s (1) cores
% 0.16/10.69 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 4187680 completed with status 0
% 0.16/10.69 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.16/10.69 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.16/10.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/10.69 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.16/10.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/10.69 % No SInE strategy applied
% 0.16/10.69 % Search class: FGHSF-FSLM32-MFFFFFNN
% 0.16/10.69 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/10.69 % Starting SubtermCWHack with 151s (1) cores
% 0.16/10.69 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 901s (1) cores
% 0.16/10.69 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 0.16/10.69 % Starting G-E--_302_C18_F1_URBAN_S0Y with 151s (1) cores
% 0.16/10.69 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0U with 146s (1) cores
% 0.16/10.69 % G-E--_300_C18_F1_SE_CS_SP_S0Y with pid 4187698 completed with status 0
% 0.16/10.69 % Result found by G-E--_300_C18_F1_SE_CS_SP_S0Y
% 0.16/10.69 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.16/10.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/10.69 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.16/10.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/10.69 % No SInE strategy applied
% 0.16/10.69 % Search class: FGHSF-FSLM32-MFFFFFNN
% 0.16/10.69 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/10.69 % Starting SubtermCWHack with 151s (1) cores
% 0.16/10.69 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 901s (1) cores
% 0.16/10.69 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 0.16/10.69 % Preprocessing time : 0.004 s
% 0.16/10.69
% 0.16/10.69 % Proof found!
% 0.16/10.69 % SZS status Theorem
% 0.16/10.69 % SZS output start CNFRefutation
% See solution above
% 0.16/10.69 % Parsed axioms : 88
% 0.16/10.69 % Removed by relevancy pruning/SinE : 0
% 0.16/10.69 % Initial clauses : 182
% 0.16/10.69 % Removed in clause preprocessing : 7
% 0.16/10.69 % Initial clauses in saturation : 175
% 0.16/10.69 % Processed clauses : 901
% 0.16/10.69 % ...of these trivial : 4
% 0.16/10.69 % ...subsumed : 336
% 0.16/10.69 % ...remaining for further processing : 561
% 0.16/10.69 % Other redundant clauses eliminated : 41
% 0.16/10.69 % Clauses deleted for lack of memory : 0
% 0.16/10.69 % Backward-subsumed : 57
% 0.16/10.69 % Backward-rewritten : 30
% 0.16/10.69 % Generated clauses : 1679
% 0.16/10.69 % ...of the previous two non-redundant : 1463
% 0.16/10.69 % ...aggressively subsumed : 0
% 0.16/10.69 % Contextual simplify-reflections : 70
% 0.16/10.69 % Paramodulations : 1638
% 0.16/10.69 % Factorizations : 0
% 0.16/10.69 % NegExts : 0
% 0.16/10.69 % Equation resolutions : 43
% 0.16/10.69 % Disequality decompositions : 0
% 0.16/10.69 % Total rewrite steps : 1151
% 0.16/10.69 % ...of those cached : 1091
% 0.16/10.69 % Propositional unsat checks : 0
% 0.16/10.69 % Propositional check models : 0
% 0.16/10.69 % Propositional check unsatisfiable : 0
% 0.16/10.69 % Propositional clauses : 0
% 0.16/10.69 % Propositional clauses after purity: 0
% 0.16/10.69 % Propositional unsat core size : 0
% 0.16/10.69 % Propositional preprocessing time : 0.000
% 0.16/10.69 % Propositional encoding time : 0.000
% 0.16/10.69 % Propositional solver time : 0.000
% 0.16/10.69 % Success case prop preproc time : 0.000
% 0.16/10.69 % Success case prop encoding time : 0.000
% 0.16/10.69 % Success case prop solver time : 0.000
% 0.16/10.69 % Current number of processed clauses : 440
% 0.16/10.69 % Positive orientable unit clauses : 66
% 0.16/10.69 % Positive unorientable unit clauses: 0
% 0.16/10.69 % Negative unit clauses : 31
% 0.16/10.69 % Non-unit-clauses : 343
% 0.16/10.69 % Current number of unprocessed clauses: 635
% 0.16/10.69 % ...number of literals in the above : 3112
% 0.16/10.69 % Current number of archived formulas : 0
% 0.16/10.69 % Current number of archived clauses : 88
% 0.16/10.69 % Clause-clause subsumption calls (NU) : 12913
% 0.16/10.69 % Rec. Clause-clause subsumption calls : 6846
% 0.16/10.69 % Non-unit clause-clause subsumptions : 283
% 0.16/10.69 % Unit Clause-clause subsumption calls : 1686
% 0.16/10.69 % Rewrite failures with RHS unbound : 0
% 0.16/10.69 % BW rewrite match attempts : 12
% 0.16/10.69 % BW rewrite match successes : 12
% 0.16/10.69 % Condensation attempts : 0
% 0.16/10.69 % Condensation successes : 0
% 0.16/10.69 % Termbank termtop insertions : 40346
% 0.16/10.69 % Search garbage collected termcells : 3616
% 0.16/10.69
% 0.16/10.69 % -------------------------------------------------
% 0.16/10.69 % User time : 0.087 s
% 0.16/10.69 % System time : 0.007 s
% 0.16/10.69 % Total time : 0.094 s
% 0.16/10.69 % Maximum resident set size: 4260 pages
% 0.16/10.69
% 0.16/10.69 % -------------------------------------------------
% 0.16/10.69 % User time : 0.385 s
% 0.16/10.69 % System time : 0.036 s
% 0.16/10.69 % Total time : 0.421 s
% 0.16/10.69 % Maximum resident set size: 4608 pages
% 0.16/10.69 % E exiting
%------------------------------------------------------------------------------