%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM601+3 : 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 : n001.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 04:57:59 PM UTC 2026
% Result : Theorem 4.68s 3.68s
% Output : CNFRefutation 4.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 57 ( 18 unt; 0 def)
% Number of atoms : 413 ( 41 equ)
% Maximal formula atoms : 181 ( 7 avg)
% Number of connectives : 567 ( 211 ~; 224 |; 105 &)
% ( 5 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 45 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 11 con; 0-2 aty)
% Number of variables : 73 ( 0 sgn 54 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mPttSet,axiom,
! [X1,X2] :
( ( aFunction0(X1)
& aElement0(X2) )
=> aSubsetOf0(sdtlbdtrb0(X1,X2),szDzozmdt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPttSet) ).
fof(m__4730,hypothesis,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ! [X2] :
( ( aSet0(X2)
& ( ( ( ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,sdtlpdtrp0(xN,szszuzczcdt0(X1))) )
| aSubsetOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X1))) )
& sbrdtbr0(X2) = xk )
| aElementOf0(X2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),xk)) ) )
=> sdtlpdtrp0(xd,X1) = sdtlpdtrp0(sdtlpdtrp0(xC,X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4730) ).
fof(m__,conjecture,
( ! [X1] :
( aElementOf0(X1,xO)
=> aElementOf0(X1,xS) )
| aSubsetOf0(xO,xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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__4891,hypothesis,
( aSet0(xO)
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X1] :
( aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
<=> ( aElementOf0(X1,szDzozmdt0(xd))
& sdtlpdtrp0(xd,X1) = szDzizrdt0(xd) ) )
& ! [X1] :
( aElementOf0(X1,xO)
<=> ? [X2] :
( aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X2) = X1 ) )
& xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4891) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__4854,hypothesis,
( aElementOf0(szDzizrdt0(xd),xT)
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X1] :
( aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
<=> ( aElementOf0(X1,szDzozmdt0(xd))
& sdtlpdtrp0(xd,X1) = szDzizrdt0(xd) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4854) ).
fof(m__3754,hypothesis,
! [X1,X2] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X2,szNzAzT0) )
=> ( sdtlseqdt0(X2,X1)
=> ( ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X1))
=> aElementOf0(X3,sdtlpdtrp0(xN,X2)) )
& aSubsetOf0(sdtlpdtrp0(xN,X1),sdtlpdtrp0(xN,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3754) ).
fof(m__3623,hypothesis,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( ( ( ( aSet0(sdtlpdtrp0(xN,X1))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> aElementOf0(X2,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,X1)) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X2) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
<=> ( aElement0(X2)
& aElementOf0(X2,sdtlpdtrp0(xN,X1))
& X2 != szmzizndt0(sdtlpdtrp0(xN,X1)) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X1)))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X1)))
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(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(mZeroLess,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> sdtlseqdt0(sz00,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroLess) ).
fof(mNATSet,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
fof(m__3291,hypothesis,
( aSet0(xT)
& isFinite0(xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3291) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
fof(m__3435,hypothesis,
( aSet0(xS)
& ! [X1] :
( aElementOf0(X1,xS)
=> aElementOf0(X1,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).
fof(m__4660,hypothesis,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,X1),sdtlpdtrp0(xN,X1))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(sdtlpdtrp0(xe,X1),X2) )
& sdtlpdtrp0(xe,X1) = szmzizndt0(sdtlpdtrp0(xN,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4660) ).
fof(c_0_15,plain,
! [X380,X381] :
( ~ aFunction0(X380)
| ~ aElement0(X381)
| aSubsetOf0(sdtlbdtrb0(X380,X381),szDzozmdt0(X380)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPttSet])]) ).
fof(c_0_16,hypothesis,
! [X465,X466] :
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ( aElementOf0(esk36_2(X465,X466),X466)
| sbrdtbr0(X466) != xk
| ~ aSet0(X466)
| sdtlpdtrp0(xd,X465) = sdtlpdtrp0(sdtlpdtrp0(xC,X465),X466)
| ~ aElementOf0(X465,szNzAzT0) )
& ( ~ aElementOf0(esk36_2(X465,X466),sdtlpdtrp0(xN,szszuzczcdt0(X465)))
| sbrdtbr0(X466) != xk
| ~ aSet0(X466)
| sdtlpdtrp0(xd,X465) = sdtlpdtrp0(sdtlpdtrp0(xC,X465),X466)
| ~ aElementOf0(X465,szNzAzT0) )
& ( ~ aSubsetOf0(X466,sdtlpdtrp0(xN,szszuzczcdt0(X465)))
| sbrdtbr0(X466) != xk
| ~ aSet0(X466)
| sdtlpdtrp0(xd,X465) = sdtlpdtrp0(sdtlpdtrp0(xC,X465),X466)
| ~ aElementOf0(X465,szNzAzT0) )
& ( ~ aElementOf0(X466,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X465)),xk))
| ~ aSet0(X466)
| sdtlpdtrp0(xd,X465) = sdtlpdtrp0(sdtlpdtrp0(xC,X465),X466)
| ~ aElementOf0(X465,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4730])])])])]) ).
fof(c_0_17,negated_conjecture,
~ ( ! [X1] :
( aElementOf0(X1,xO)
=> aElementOf0(X1,xS) )
| aSubsetOf0(xO,xS) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_18,plain,
! [X253,X254,X255,X256] :
( ( aSet0(X254)
| ~ aSubsetOf0(X254,X253)
| ~ aSet0(X253) )
& ( ~ aElementOf0(X255,X254)
| aElementOf0(X255,X253)
| ~ aSubsetOf0(X254,X253)
| ~ aSet0(X253) )
& ( aElementOf0(esk2_2(X253,X256),X256)
| ~ aSet0(X256)
| aSubsetOf0(X256,X253)
| ~ aSet0(X253) )
& ( ~ aElementOf0(esk2_2(X253,X256),X253)
| ~ aSet0(X256)
| aSubsetOf0(X256,X253)
| ~ aSet0(X253) ) ),
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_19,plain,
( aSubsetOf0(sdtlbdtrb0(X1,X2),szDzozmdt0(X1))
| ~ aFunction0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,hypothesis,
szDzozmdt0(xd) = szNzAzT0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,hypothesis,
aFunction0(xd),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_22,hypothesis,
! [X474,X475,X477,X478] :
( aSet0(xO)
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( aElementOf0(X474,szDzozmdt0(xd))
| ~ aElementOf0(X474,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& ( sdtlpdtrp0(xd,X474) = szDzizrdt0(xd)
| ~ aElementOf0(X474,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& ( ~ aElementOf0(X474,szDzozmdt0(xd))
| sdtlpdtrp0(xd,X474) != szDzizrdt0(xd)
| aElementOf0(X474,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& ( aElementOf0(esk38_1(X475),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aElementOf0(X475,xO) )
& ( sdtlpdtrp0(xe,esk38_1(X475)) = X475
| ~ aElementOf0(X475,xO) )
& ( ~ aElementOf0(X478,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| sdtlpdtrp0(xe,X478) != X477
| aElementOf0(X477,xO) )
& xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
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)],[m__4891])])])])])]) ).
fof(c_0_23,negated_conjecture,
( aElementOf0(esk40_0,xO)
& ~ aElementOf0(esk40_0,xS)
& ~ aSubsetOf0(xO,xS) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
fof(c_0_24,plain,
! [X245,X246] :
( ~ aSet0(X245)
| ~ aElementOf0(X246,X245)
| aElement0(X246) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
fof(c_0_25,hypothesis,
! [X473] :
( aElementOf0(szDzizrdt0(xd),xT)
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( aElementOf0(X473,szDzozmdt0(xd))
| ~ aElementOf0(X473,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& ( sdtlpdtrp0(xd,X473) = szDzizrdt0(xd)
| ~ aElementOf0(X473,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& ( ~ aElementOf0(X473,szDzozmdt0(xd))
| sdtlpdtrp0(xd,X473) != szDzizrdt0(xd)
| aElementOf0(X473,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4854])])])]) ).
fof(c_0_26,hypothesis,
! [X442,X443,X444] :
( ( ~ aElementOf0(X444,sdtlpdtrp0(xN,X442))
| aElementOf0(X444,sdtlpdtrp0(xN,X443))
| ~ sdtlseqdt0(X443,X442)
| ~ aElementOf0(X442,szNzAzT0)
| ~ aElementOf0(X443,szNzAzT0) )
& ( aSubsetOf0(sdtlpdtrp0(xN,X442),sdtlpdtrp0(xN,X443))
| ~ sdtlseqdt0(X443,X442)
| ~ aElementOf0(X442,szNzAzT0)
| ~ aElementOf0(X443,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3754])])])]) ).
fof(c_0_27,hypothesis,
! [X434,X436,X437,X438,X439] :
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X434)),sdtlpdtrp0(xN,X434))
| aElementOf0(esk31_1(X434),sdtlpdtrp0(xN,X434))
| ~ aSet0(sdtlpdtrp0(xN,X434))
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( ~ aElementOf0(X436,sdtlpdtrp0(xN,X434))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X434)),X436)
| aElementOf0(esk31_1(X434),sdtlpdtrp0(xN,X434))
| ~ aSet0(sdtlpdtrp0(xN,X434))
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( aSet0(sdtmndt0(sdtlpdtrp0(xN,X434),szmzizndt0(sdtlpdtrp0(xN,X434))))
| aElementOf0(esk31_1(X434),sdtlpdtrp0(xN,X434))
| ~ aSet0(sdtlpdtrp0(xN,X434))
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( aElement0(X437)
| ~ aElementOf0(X437,sdtmndt0(sdtlpdtrp0(xN,X434),szmzizndt0(sdtlpdtrp0(xN,X434))))
| aElementOf0(esk31_1(X434),sdtlpdtrp0(xN,X434))
| ~ aSet0(sdtlpdtrp0(xN,X434))
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( aElementOf0(X437,sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X437,sdtmndt0(sdtlpdtrp0(xN,X434),szmzizndt0(sdtlpdtrp0(xN,X434))))
| aElementOf0(esk31_1(X434),sdtlpdtrp0(xN,X434))
| ~ aSet0(sdtlpdtrp0(xN,X434))
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( X437 != szmzizndt0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X437,sdtmndt0(sdtlpdtrp0(xN,X434),szmzizndt0(sdtlpdtrp0(xN,X434))))
| aElementOf0(esk31_1(X434),sdtlpdtrp0(xN,X434))
| ~ aSet0(sdtlpdtrp0(xN,X434))
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( ~ aElement0(X438)
| ~ aElementOf0(X438,sdtlpdtrp0(xN,X434))
| X438 = szmzizndt0(sdtlpdtrp0(xN,X434))
| aElementOf0(X438,sdtmndt0(sdtlpdtrp0(xN,X434),szmzizndt0(sdtlpdtrp0(xN,X434))))
| aElementOf0(esk31_1(X434),sdtlpdtrp0(xN,X434))
| ~ aSet0(sdtlpdtrp0(xN,X434))
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X434)))
| aElementOf0(esk31_1(X434),sdtlpdtrp0(xN,X434))
| ~ aSet0(sdtlpdtrp0(xN,X434))
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( ~ aElementOf0(X439,sdtlpdtrp0(xN,szszuzczcdt0(X434)))
| aElementOf0(X439,sdtmndt0(sdtlpdtrp0(xN,X434),szmzizndt0(sdtlpdtrp0(xN,X434))))
| aElementOf0(esk31_1(X434),sdtlpdtrp0(xN,X434))
| ~ aSet0(sdtlpdtrp0(xN,X434))
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X434)),sdtmndt0(sdtlpdtrp0(xN,X434),szmzizndt0(sdtlpdtrp0(xN,X434))))
| aElementOf0(esk31_1(X434),sdtlpdtrp0(xN,X434))
| ~ aSet0(sdtlpdtrp0(xN,X434))
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X434)))
| aElementOf0(esk31_1(X434),sdtlpdtrp0(xN,X434))
| ~ aSet0(sdtlpdtrp0(xN,X434))
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X434)),sdtlpdtrp0(xN,X434))
| ~ aElementOf0(esk31_1(X434),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X434))
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( ~ aElementOf0(X436,sdtlpdtrp0(xN,X434))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X434)),X436)
| ~ aElementOf0(esk31_1(X434),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X434))
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( aSet0(sdtmndt0(sdtlpdtrp0(xN,X434),szmzizndt0(sdtlpdtrp0(xN,X434))))
| ~ aElementOf0(esk31_1(X434),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X434))
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( aElement0(X437)
| ~ aElementOf0(X437,sdtmndt0(sdtlpdtrp0(xN,X434),szmzizndt0(sdtlpdtrp0(xN,X434))))
| ~ aElementOf0(esk31_1(X434),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X434))
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( aElementOf0(X437,sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X437,sdtmndt0(sdtlpdtrp0(xN,X434),szmzizndt0(sdtlpdtrp0(xN,X434))))
| ~ aElementOf0(esk31_1(X434),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X434))
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( X437 != szmzizndt0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X437,sdtmndt0(sdtlpdtrp0(xN,X434),szmzizndt0(sdtlpdtrp0(xN,X434))))
| ~ aElementOf0(esk31_1(X434),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X434))
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( ~ aElement0(X438)
| ~ aElementOf0(X438,sdtlpdtrp0(xN,X434))
| X438 = szmzizndt0(sdtlpdtrp0(xN,X434))
| aElementOf0(X438,sdtmndt0(sdtlpdtrp0(xN,X434),szmzizndt0(sdtlpdtrp0(xN,X434))))
| ~ aElementOf0(esk31_1(X434),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X434))
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X434)))
| ~ aElementOf0(esk31_1(X434),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X434))
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( ~ aElementOf0(X439,sdtlpdtrp0(xN,szszuzczcdt0(X434)))
| aElementOf0(X439,sdtmndt0(sdtlpdtrp0(xN,X434),szmzizndt0(sdtlpdtrp0(xN,X434))))
| ~ aElementOf0(esk31_1(X434),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X434))
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X434)),sdtmndt0(sdtlpdtrp0(xN,X434),szmzizndt0(sdtlpdtrp0(xN,X434))))
| ~ aElementOf0(esk31_1(X434),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X434))
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X434)))
| ~ aElementOf0(esk31_1(X434),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X434))
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X434)),sdtlpdtrp0(xN,X434))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X434),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( ~ aElementOf0(X436,sdtlpdtrp0(xN,X434))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X434)),X436)
| ~ aSubsetOf0(sdtlpdtrp0(xN,X434),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( aSet0(sdtmndt0(sdtlpdtrp0(xN,X434),szmzizndt0(sdtlpdtrp0(xN,X434))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X434),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( aElement0(X437)
| ~ aElementOf0(X437,sdtmndt0(sdtlpdtrp0(xN,X434),szmzizndt0(sdtlpdtrp0(xN,X434))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X434),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( aElementOf0(X437,sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X437,sdtmndt0(sdtlpdtrp0(xN,X434),szmzizndt0(sdtlpdtrp0(xN,X434))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X434),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( X437 != szmzizndt0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X437,sdtmndt0(sdtlpdtrp0(xN,X434),szmzizndt0(sdtlpdtrp0(xN,X434))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X434),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( ~ aElement0(X438)
| ~ aElementOf0(X438,sdtlpdtrp0(xN,X434))
| X438 = szmzizndt0(sdtlpdtrp0(xN,X434))
| aElementOf0(X438,sdtmndt0(sdtlpdtrp0(xN,X434),szmzizndt0(sdtlpdtrp0(xN,X434))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X434),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X434)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X434),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( ~ aElementOf0(X439,sdtlpdtrp0(xN,szszuzczcdt0(X434)))
| aElementOf0(X439,sdtmndt0(sdtlpdtrp0(xN,X434),szmzizndt0(sdtlpdtrp0(xN,X434))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X434),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X434)),sdtmndt0(sdtlpdtrp0(xN,X434),szmzizndt0(sdtlpdtrp0(xN,X434))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X434),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,szNzAzT0) )
& ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X434)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X434),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X434))
| ~ aElementOf0(X434,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)],[m__3623])])])])])]) ).
fof(c_0_28,plain,
! [X298] :
( ~ aElementOf0(X298,szNzAzT0)
| sdtlseqdt0(sz00,X298) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroLess])]) ).
cnf(c_0_29,plain,
( aElementOf0(X1,X3)
| ~ aElementOf0(X1,X2)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_30,hypothesis,
( aSubsetOf0(sdtlbdtrb0(xd,X1),szNzAzT0)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_31,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
cnf(c_0_32,hypothesis,
( aElementOf0(esk38_1(X1),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aElementOf0(X1,xO) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_33,negated_conjecture,
aElementOf0(esk40_0,xO),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_34,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_35,hypothesis,
aElementOf0(szDzizrdt0(xd),xT),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_36,hypothesis,
aSet0(xT),
inference(split_conjunct,[status(thm)],[m__3291]) ).
cnf(c_0_37,hypothesis,
( aSubsetOf0(sdtlpdtrp0(xN,X1),sdtlpdtrp0(xN,X2))
| ~ sdtlseqdt0(X2,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_38,plain,
aElementOf0(sz00,szNzAzT0),
inference(split_conjunct,[status(thm)],[mZeroNum]) ).
cnf(c_0_39,hypothesis,
sdtlpdtrp0(xN,sz00) = xS,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_40,plain,
( sdtlseqdt0(sz00,X1)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_41,hypothesis,
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,sdtlbdtrb0(xd,X2))
| ~ aElement0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_42,negated_conjecture,
aElementOf0(esk38_1(esk40_0),sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_43,hypothesis,
aElement0(szDzizrdt0(xd)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_44,hypothesis,
( aSubsetOf0(sdtlpdtrp0(xN,X1),xS)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_40]) ).
cnf(c_0_45,hypothesis,
aElementOf0(esk38_1(esk40_0),szNzAzT0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]) ).
fof(c_0_46,hypothesis,
! [X406] :
( aSet0(xS)
& ( ~ aElementOf0(X406,xS)
| aElementOf0(X406,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3435])])]) ).
fof(c_0_47,hypothesis,
! [X463,X464] :
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ( aElementOf0(sdtlpdtrp0(xe,X463),sdtlpdtrp0(xN,X463))
| ~ aElementOf0(X463,szNzAzT0) )
& ( ~ aElementOf0(X464,sdtlpdtrp0(xN,X463))
| sdtlseqdt0(sdtlpdtrp0(xe,X463),X464)
| ~ aElementOf0(X463,szNzAzT0) )
& ( sdtlpdtrp0(xe,X463) = szmzizndt0(sdtlpdtrp0(xN,X463))
| ~ aElementOf0(X463,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4660])])])]) ).
cnf(c_0_48,hypothesis,
( sdtlpdtrp0(xe,esk38_1(X1)) = X1
| ~ aElementOf0(X1,xO) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_49,hypothesis,
aSubsetOf0(sdtlpdtrp0(xN,esk38_1(esk40_0)),xS),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_51,hypothesis,
( aElementOf0(sdtlpdtrp0(xe,X1),sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_52,negated_conjecture,
sdtlpdtrp0(xe,esk38_1(esk40_0)) = esk40_0,
inference(spm,[status(thm)],[c_0_48,c_0_33]) ).
cnf(c_0_53,hypothesis,
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,esk38_1(esk40_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_49]),c_0_50])]) ).
cnf(c_0_54,hypothesis,
aElementOf0(esk40_0,sdtlpdtrp0(xN,esk38_1(esk40_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_45]),c_0_52]) ).
cnf(c_0_55,negated_conjecture,
~ aElementOf0(esk40_0,xS),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_56,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : NUM601+3 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % 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
% 0.19/0.34 % Computer : n001.cluster.edu
% 0.19/0.34 % Model : x86_64 x86_64
% 0.19/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.34 % Memory : 8042.1875MB
% 0.19/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.34 % CPULimit : 300
% 0.19/0.34 % WCLimit : 300
% 0.19/0.34 % DateTime : Tue May 5 00:51:03 EDT 2026
% 0.19/0.34 % CPUTime :
% 0.19/0.36 % start to proof: theBenchmark
% 4.68/3.68 % Version : CSE_E---1.7
% 4.68/3.68 % Problem : theBenchmark.p
% 4.68/3.68 % SZS status Theorem for theBenchmark.p
% 4.68/3.68 % SZS output start CNFRefutation
% See solution above
% 4.68/3.69 % Total time : 2.830s
%------------------------------------------------------------------------------