%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM580+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:57:54 PM UTC 2026
% Result : Theorem 4.26s 3.27s
% Output : CNFRefutation 4.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 17
% Syntax : Number of formulae : 89 ( 17 unt; 0 def)
% Number of atoms : 414 ( 100 equ)
% Maximal formula atoms : 52 ( 4 avg)
% Number of connectives : 551 ( 226 ~; 238 |; 55 &)
% ( 9 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 9 con; 0-3 aty)
% Number of variables : 127 ( 0 sgn 67 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefRst,axiom,
! [X1] :
( aFunction0(X1)
=> ! [X2] :
( aSubsetOf0(X2,szDzozmdt0(X1))
=> ! [X3] :
( X3 = sdtexdt0(X1,X2)
<=> ( aFunction0(X3)
& szDzozmdt0(X3) = X2
& ! [X4] :
( aElementOf0(X4,X2)
=> sdtlpdtrp0(X3,X4) = sdtlpdtrp0(X1,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefRst) ).
fof(mDefSel,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aElementOf0(X2,szNzAzT0) )
=> ! [X3] :
( X3 = slbdtsldtrb0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aSubsetOf0(X4,X1)
& sbrdtbr0(X4) = X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSel) ).
fof(mDomSet,axiom,
! [X1] :
( aFunction0(X1)
=> aSet0(szDzozmdt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDomSet) ).
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aElement0(X2) )
=> ! [X3] :
( X3 = sdtmndt0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aElement0(X4)
& aElementOf0(X4,X1)
& X4 != X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(mDefMin,axiom,
! [X1] :
( ( aSubsetOf0(X1,szNzAzT0)
& X1 != slcrc0 )
=> ! [X2] :
( X2 = szmzizndt0(X1)
<=> ( aElementOf0(X2,X1)
& ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefMin) ).
fof(m__3623,hypothesis,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( ( aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X1)) )
=> ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X1))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3623) ).
fof(m__3989_02,hypothesis,
aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3989_02) ).
fof(m__3533,hypothesis,
( aElementOf0(xk,szNzAzT0)
& szszuzczcdt0(xk) = xK ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3533) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( aSet0(X1)
& ~ ? [X2] : aElementOf0(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(m__3671,hypothesis,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
fof(mCountNFin_01,axiom,
! [X1] :
( ( aSet0(X1)
& isCountable0(X1) )
=> X1 != slcrc0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin_01) ).
fof(mCardCons,axiom,
! [X1] :
( ( aSet0(X1)
& isFinite0(X1) )
=> ! [X2] :
( aElement0(X2)
=> ( ~ aElementOf0(X2,X1)
=> sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardCons) ).
fof(m__3989,hypothesis,
aElementOf0(xi,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3989) ).
fof(m__,conjecture,
sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mCardNum,axiom,
! [X1] :
( aSet0(X1)
=> ( aElementOf0(sbrdtbr0(X1),szNzAzT0)
<=> isFinite0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardNum) ).
fof(c_0_17,plain,
! [X308,X309,X310,X311,X312] :
( ( aFunction0(X310)
| X310 != sdtexdt0(X308,X309)
| ~ aSubsetOf0(X309,szDzozmdt0(X308))
| ~ aFunction0(X308) )
& ( szDzozmdt0(X310) = X309
| X310 != sdtexdt0(X308,X309)
| ~ aSubsetOf0(X309,szDzozmdt0(X308))
| ~ aFunction0(X308) )
& ( ~ aElementOf0(X311,X309)
| sdtlpdtrp0(X310,X311) = sdtlpdtrp0(X308,X311)
| X310 != sdtexdt0(X308,X309)
| ~ aSubsetOf0(X309,szDzozmdt0(X308))
| ~ aFunction0(X308) )
& ( aElementOf0(esk17_3(X308,X309,X312),X309)
| ~ aFunction0(X312)
| szDzozmdt0(X312) != X309
| X312 = sdtexdt0(X308,X309)
| ~ aSubsetOf0(X309,szDzozmdt0(X308))
| ~ aFunction0(X308) )
& ( sdtlpdtrp0(X312,esk17_3(X308,X309,X312)) != sdtlpdtrp0(X308,esk17_3(X308,X309,X312))
| ~ aFunction0(X312)
| szDzozmdt0(X312) != X309
| X312 = sdtexdt0(X308,X309)
| ~ aSubsetOf0(X309,szDzozmdt0(X308))
| ~ aFunction0(X308) ) ),
inference(distribute,[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)],[mDefRst])])])])])]) ).
fof(c_0_18,plain,
! [X263,X264,X265,X266,X267,X268] :
( ( aSet0(X265)
| X265 != slbdtsldtrb0(X263,X264)
| ~ aSet0(X263)
| ~ aElementOf0(X264,szNzAzT0) )
& ( aSubsetOf0(X266,X263)
| ~ aElementOf0(X266,X265)
| X265 != slbdtsldtrb0(X263,X264)
| ~ aSet0(X263)
| ~ aElementOf0(X264,szNzAzT0) )
& ( sbrdtbr0(X266) = X264
| ~ aElementOf0(X266,X265)
| X265 != slbdtsldtrb0(X263,X264)
| ~ aSet0(X263)
| ~ aElementOf0(X264,szNzAzT0) )
& ( ~ aSubsetOf0(X267,X263)
| sbrdtbr0(X267) != X264
| aElementOf0(X267,X265)
| X265 != slbdtsldtrb0(X263,X264)
| ~ aSet0(X263)
| ~ aElementOf0(X264,szNzAzT0) )
& ( ~ aElementOf0(esk11_3(X263,X264,X268),X268)
| ~ aSubsetOf0(esk11_3(X263,X264,X268),X263)
| sbrdtbr0(esk11_3(X263,X264,X268)) != X264
| ~ aSet0(X268)
| X268 = slbdtsldtrb0(X263,X264)
| ~ aSet0(X263)
| ~ aElementOf0(X264,szNzAzT0) )
& ( aSubsetOf0(esk11_3(X263,X264,X268),X263)
| aElementOf0(esk11_3(X263,X264,X268),X268)
| ~ aSet0(X268)
| X268 = slbdtsldtrb0(X263,X264)
| ~ aSet0(X263)
| ~ aElementOf0(X264,szNzAzT0) )
& ( sbrdtbr0(esk11_3(X263,X264,X268)) = X264
| aElementOf0(esk11_3(X263,X264,X268),X268)
| ~ aSet0(X268)
| X268 = slbdtsldtrb0(X263,X264)
| ~ aSet0(X263)
| ~ aElementOf0(X264,szNzAzT0) ) ),
inference(distribute,[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])])])])])]) ).
fof(c_0_19,plain,
! [X283] :
( ~ aFunction0(X283)
| aSet0(szDzozmdt0(X283)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDomSet])]) ).
cnf(c_0_20,plain,
( szDzozmdt0(X1) = X2
| X1 != sdtexdt0(X3,X2)
| ~ aSubsetOf0(X2,szDzozmdt0(X3))
| ~ aFunction0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
( aFunction0(X1)
| X1 != sdtexdt0(X2,X3)
| ~ aSubsetOf0(X3,szDzozmdt0(X2))
| ~ aFunction0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
( sbrdtbr0(X1) = X2
| ~ aElementOf0(X1,X3)
| X3 != slbdtsldtrb0(X4,X2)
| ~ aSet0(X4)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_23,plain,
! [X186,X187,X188,X189,X190,X191] :
( ( aSet0(X188)
| X188 != sdtmndt0(X186,X187)
| ~ aSet0(X186)
| ~ aElement0(X187) )
& ( aElement0(X189)
| ~ aElementOf0(X189,X188)
| X188 != sdtmndt0(X186,X187)
| ~ aSet0(X186)
| ~ aElement0(X187) )
& ( aElementOf0(X189,X186)
| ~ aElementOf0(X189,X188)
| X188 != sdtmndt0(X186,X187)
| ~ aSet0(X186)
| ~ aElement0(X187) )
& ( X189 != X187
| ~ aElementOf0(X189,X188)
| X188 != sdtmndt0(X186,X187)
| ~ aSet0(X186)
| ~ aElement0(X187) )
& ( ~ aElement0(X190)
| ~ aElementOf0(X190,X186)
| X190 = X187
| aElementOf0(X190,X188)
| X188 != sdtmndt0(X186,X187)
| ~ aSet0(X186)
| ~ aElement0(X187) )
& ( ~ aElementOf0(esk4_3(X186,X187,X191),X191)
| ~ aElement0(esk4_3(X186,X187,X191))
| ~ aElementOf0(esk4_3(X186,X187,X191),X186)
| esk4_3(X186,X187,X191) = X187
| ~ aSet0(X191)
| X191 = sdtmndt0(X186,X187)
| ~ aSet0(X186)
| ~ aElement0(X187) )
& ( aElement0(esk4_3(X186,X187,X191))
| aElementOf0(esk4_3(X186,X187,X191),X191)
| ~ aSet0(X191)
| X191 = sdtmndt0(X186,X187)
| ~ aSet0(X186)
| ~ aElement0(X187) )
& ( aElementOf0(esk4_3(X186,X187,X191),X186)
| aElementOf0(esk4_3(X186,X187,X191),X191)
| ~ aSet0(X191)
| X191 = sdtmndt0(X186,X187)
| ~ aSet0(X186)
| ~ aElement0(X187) )
& ( esk4_3(X186,X187,X191) != X187
| aElementOf0(esk4_3(X186,X187,X191),X191)
| ~ aSet0(X191)
| X191 = sdtmndt0(X186,X187)
| ~ aSet0(X186)
| ~ aElement0(X187) ) ),
inference(distribute,[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)],[mDefDiff])])])])])]) ).
fof(c_0_24,plain,
! [X237,X238,X239,X240] :
( ( aElementOf0(X238,X237)
| X238 != szmzizndt0(X237)
| ~ aSubsetOf0(X237,szNzAzT0)
| X237 = slcrc0 )
& ( ~ aElementOf0(X239,X237)
| sdtlseqdt0(X238,X239)
| X238 != szmzizndt0(X237)
| ~ aSubsetOf0(X237,szNzAzT0)
| X237 = slcrc0 )
& ( aElementOf0(esk7_2(X237,X240),X237)
| ~ aElementOf0(X240,X237)
| X240 = szmzizndt0(X237)
| ~ aSubsetOf0(X237,szNzAzT0)
| X237 = slcrc0 )
& ( ~ sdtlseqdt0(X240,esk7_2(X237,X240))
| ~ aElementOf0(X240,X237)
| X240 = szmzizndt0(X237)
| ~ aSubsetOf0(X237,szNzAzT0)
| X237 = slcrc0 ) ),
inference(distribute,[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)],[mDefMin])])])])])]) ).
cnf(c_0_25,plain,
( aSet0(szDzozmdt0(X1))
| ~ aFunction0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( szDzozmdt0(sdtexdt0(X1,X2)) = X2
| ~ aFunction0(X1)
| ~ aSubsetOf0(X2,szDzozmdt0(X1)) ),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( aFunction0(sdtexdt0(X1,X2))
| ~ aFunction0(X1)
| ~ aSubsetOf0(X2,szDzozmdt0(X1)) ),
inference(er,[status(thm)],[c_0_21]) ).
fof(c_0_28,hypothesis,
! [X325] :
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X325)),sdtmndt0(sdtlpdtrp0(xN,X325),szmzizndt0(sdtlpdtrp0(xN,X325))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X325),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X325))
| ~ aElementOf0(X325,szNzAzT0) )
& ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X325)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X325),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X325))
| ~ aElementOf0(X325,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3623])])])]) ).
cnf(c_0_29,plain,
( sbrdtbr0(X1) = X2
| ~ aElementOf0(X1,slbdtsldtrb0(X3,X2))
| ~ aElementOf0(X2,szNzAzT0)
| ~ aSet0(X3) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_30,hypothesis,
aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)),
inference(split_conjunct,[status(thm)],[m__3989_02]) ).
cnf(c_0_31,hypothesis,
aElementOf0(xk,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3533]) ).
cnf(c_0_32,plain,
( aSet0(X1)
| X1 != sdtmndt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_33,plain,
! [X158,X159] :
( ~ aSet0(X158)
| ~ aElementOf0(X159,X158)
| aElement0(X159) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
cnf(c_0_34,plain,
( aElementOf0(X1,X2)
| X2 = slcrc0
| X1 != szmzizndt0(X2)
| ~ aSubsetOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_35,plain,
( aSet0(X1)
| ~ aFunction0(X2)
| ~ aSubsetOf0(X1,szDzozmdt0(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_36,hypothesis,
szDzozmdt0(xN) = szNzAzT0,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_37,hypothesis,
aFunction0(xN),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,plain,
( aSubsetOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X3 != slbdtsldtrb0(X2,X4)
| ~ aSet0(X2)
| ~ aElementOf0(X4,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_39,hypothesis,
( sbrdtbr0(xQ) = xk
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_40,plain,
( aSet0(sdtmndt0(X1,X2))
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_32]) ).
cnf(c_0_41,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_42,plain,
( X1 = slcrc0
| aElementOf0(szmzizndt0(X1),X1)
| ~ aSubsetOf0(X1,szNzAzT0) ),
inference(er,[status(thm)],[c_0_34]) ).
cnf(c_0_43,hypothesis,
( aSet0(X1)
| ~ aSubsetOf0(X1,szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).
fof(c_0_44,plain,
! [X160,X161,X162] :
( ( aSet0(X160)
| X160 != slcrc0 )
& ( ~ aElementOf0(X161,X160)
| X160 != slcrc0 )
& ( ~ aSet0(X162)
| aElementOf0(esk1_1(X162),X162)
| X162 = slcrc0 ) ),
inference(distribute,[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])])])])])]) ).
fof(c_0_45,plain,
! [X166,X167,X168,X169] :
( ( aSet0(X167)
| ~ aSubsetOf0(X167,X166)
| ~ aSet0(X166) )
& ( ~ aElementOf0(X168,X167)
| aElementOf0(X168,X166)
| ~ aSubsetOf0(X167,X166)
| ~ aSet0(X166) )
& ( aElementOf0(esk2_2(X166,X169),X169)
| ~ aSet0(X169)
| aSubsetOf0(X169,X166)
| ~ aSet0(X166) )
& ( ~ aElementOf0(esk2_2(X166,X169),X166)
| ~ aSet0(X169)
| aSubsetOf0(X169,X166)
| ~ aSet0(X166) ) ),
inference(distribute,[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_46,plain,
( aSubsetOf0(X1,X2)
| ~ aElementOf0(X1,slbdtsldtrb0(X2,X3))
| ~ aElementOf0(X3,szNzAzT0)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_38]) ).
cnf(c_0_47,hypothesis,
( sbrdtbr0(xQ) = xk
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ aSet0(sdtlpdtrp0(xN,xi)) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_48,plain,
( X1 = slcrc0
| aElement0(szmzizndt0(X1))
| ~ aSubsetOf0(X1,szNzAzT0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
fof(c_0_49,hypothesis,
! [X326] :
( ( aSubsetOf0(sdtlpdtrp0(xN,X326),szNzAzT0)
| ~ aElementOf0(X326,szNzAzT0) )
& ( isCountable0(sdtlpdtrp0(xN,X326))
| ~ aElementOf0(X326,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3671])])]) ).
fof(c_0_50,plain,
! [X165] :
( ~ aSet0(X165)
| ~ isCountable0(X165)
| X165 != slcrc0 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCountNFin_01])]) ).
cnf(c_0_51,plain,
( aSet0(X1)
| X1 != slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_52,plain,
( aSet0(X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_53,hypothesis,
( aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_30]),c_0_31])]) ).
fof(c_0_54,plain,
! [X1] :
( ( aSet0(X1)
& isFinite0(X1) )
=> ! [X2] :
( aElement0(X2)
=> ( ~ aElementOf0(X2,X1)
=> sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1)) ) ) ),
inference(fof_simplification,[status(thm)],[mCardCons]) ).
cnf(c_0_55,hypothesis,
( sdtlpdtrp0(xN,xi) = slcrc0
| sbrdtbr0(xQ) = xk
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_43]) ).
cnf(c_0_56,hypothesis,
( aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_57,hypothesis,
aElementOf0(xi,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3989]) ).
cnf(c_0_58,plain,
( ~ aSet0(X1)
| ~ isCountable0(X1)
| X1 != slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_59,plain,
aSet0(slcrc0),
inference(er,[status(thm)],[c_0_51]) ).
cnf(c_0_60,hypothesis,
( aSet0(xQ)
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
fof(c_0_61,negated_conjecture,
sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
fof(c_0_62,plain,
! [X228,X229] :
( ~ aSet0(X228)
| ~ isFinite0(X228)
| ~ aElement0(X229)
| aElementOf0(X229,X228)
| sbrdtbr0(sdtpldt0(X228,X229)) = szszuzczcdt0(sbrdtbr0(X228)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_54])])]) ).
fof(c_0_63,plain,
! [X226] :
( ( ~ aElementOf0(sbrdtbr0(X226),szNzAzT0)
| isFinite0(X226)
| ~ aSet0(X226) )
& ( ~ isFinite0(X226)
| aElementOf0(sbrdtbr0(X226),szNzAzT0)
| ~ aSet0(X226) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardNum])])]) ).
cnf(c_0_64,hypothesis,
( isCountable0(sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_65,hypothesis,
( sdtlpdtrp0(xN,xi) = slcrc0
| sbrdtbr0(xQ) = xk ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57])]) ).
cnf(c_0_66,plain,
~ isCountable0(slcrc0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_58]),c_0_59])]) ).
cnf(c_0_67,hypothesis,
( aSet0(xQ)
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ aSet0(sdtlpdtrp0(xN,xi)) ),
inference(spm,[status(thm)],[c_0_60,c_0_40]) ).
cnf(c_0_68,negated_conjecture,
sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK,
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_69,plain,
( aElementOf0(X2,X1)
| sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1))
| ~ aSet0(X1)
| ~ isFinite0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_70,plain,
( isFinite0(X1)
| ~ aElementOf0(sbrdtbr0(X1),szNzAzT0)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_71,hypothesis,
sbrdtbr0(xQ) = xk,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_57])]),c_0_66]) ).
cnf(c_0_72,hypothesis,
( sdtlpdtrp0(xN,xi) = slcrc0
| aSet0(xQ)
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_48]),c_0_43]) ).
cnf(c_0_73,plain,
( aElementOf0(X1,X3)
| ~ aElementOf0(X1,X2)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_74,negated_conjecture,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ)
| szszuzczcdt0(sbrdtbr0(xQ)) != xK
| ~ isFinite0(xQ)
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ aSet0(xQ) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_75,hypothesis,
szszuzczcdt0(xk) = xK,
inference(split_conjunct,[status(thm)],[m__3533]) ).
cnf(c_0_76,hypothesis,
( isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_31])]) ).
cnf(c_0_77,hypothesis,
( sdtlpdtrp0(xN,xi) = slcrc0
| aSet0(xQ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_56]),c_0_57])]) ).
cnf(c_0_78,plain,
( X1 != X2
| ~ aElementOf0(X1,X3)
| X3 != sdtmndt0(X4,X2)
| ~ aSet0(X4)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_79,hypothesis,
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X1,xQ)
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(spm,[status(thm)],[c_0_73,c_0_53]) ).
cnf(c_0_80,negated_conjecture,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ)
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ aSet0(xQ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_71]),c_0_75])]),c_0_76]) ).
cnf(c_0_81,hypothesis,
aSet0(xQ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_77]),c_0_57])]),c_0_66]) ).
cnf(c_0_82,plain,
( ~ aElementOf0(X1,sdtmndt0(X2,X1))
| ~ aElement0(X1)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_78])]) ).
cnf(c_0_83,hypothesis,
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X1,xQ)
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ aSet0(sdtlpdtrp0(xN,xi)) ),
inference(spm,[status(thm)],[c_0_79,c_0_40]) ).
cnf(c_0_84,negated_conjecture,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ)
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81])]) ).
cnf(c_0_85,hypothesis,
( ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ aSet0(sdtlpdtrp0(xN,xi)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84]) ).
cnf(c_0_86,hypothesis,
( sdtlpdtrp0(xN,xi) = slcrc0
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_48]),c_0_43]) ).
cnf(c_0_87,hypothesis,
sdtlpdtrp0(xN,xi) = slcrc0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_56]),c_0_57])]) ).
cnf(c_0_88,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_87]),c_0_57])]),c_0_66]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM580+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n011.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 00:47:32 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 4.26/3.27 % Version : CSE_E---1.7
% 4.26/3.27 % Problem : theBenchmark.p
% 4.26/3.27 % SZS status Theorem for theBenchmark.p
% 4.26/3.27 % SZS output start CNFRefutation
% See solution above
% 4.26/3.28 % Total time : 2.375s
%------------------------------------------------------------------------------