%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM581+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 : n023.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 4.41s 3.52s
% Output : CNFRefutation 4.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 41 ( 14 unt; 0 def)
% Number of atoms : 390 ( 28 equ)
% Maximal formula atoms : 181 ( 9 avg)
% Number of connectives : 542 ( 193 ~; 210 |; 110 &)
% ( 6 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 45 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(m__,conjecture,
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) ) )
=> ( ( aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X1)
& ( aElementOf0(X1,xQ)
| X1 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
=> ( ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
=> aElementOf0(X1,xS) )
| aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
fof(m__4007,hypothesis,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X1)
& ( aElementOf0(X1,xQ)
| X1 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4007) ).
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__3989,hypothesis,
aElementOf0(xi,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3989) ).
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__3989_02,hypothesis,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& X1 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
& aSet0(xQ)
& ! [X1] :
( aElementOf0(X1,xQ)
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3989_02) ).
fof(c_0_10,hypothesis,
! [X388,X389,X390] :
( ( ~ aElementOf0(X390,sdtlpdtrp0(xN,X388))
| aElementOf0(X390,sdtlpdtrp0(xN,X389))
| ~ sdtlseqdt0(X389,X388)
| ~ aElementOf0(X388,szNzAzT0)
| ~ aElementOf0(X389,szNzAzT0) )
& ( aSubsetOf0(sdtlpdtrp0(xN,X388),sdtlpdtrp0(xN,X389))
| ~ sdtlseqdt0(X389,X388)
| ~ aElementOf0(X388,szNzAzT0)
| ~ aElementOf0(X389,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_11,hypothesis,
! [X380,X382,X383,X384,X385] :
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X380)),sdtlpdtrp0(xN,X380))
| aElementOf0(esk31_1(X380),sdtlpdtrp0(xN,X380))
| ~ aSet0(sdtlpdtrp0(xN,X380))
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( ~ aElementOf0(X382,sdtlpdtrp0(xN,X380))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X380)),X382)
| aElementOf0(esk31_1(X380),sdtlpdtrp0(xN,X380))
| ~ aSet0(sdtlpdtrp0(xN,X380))
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( aSet0(sdtmndt0(sdtlpdtrp0(xN,X380),szmzizndt0(sdtlpdtrp0(xN,X380))))
| aElementOf0(esk31_1(X380),sdtlpdtrp0(xN,X380))
| ~ aSet0(sdtlpdtrp0(xN,X380))
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( aElement0(X383)
| ~ aElementOf0(X383,sdtmndt0(sdtlpdtrp0(xN,X380),szmzizndt0(sdtlpdtrp0(xN,X380))))
| aElementOf0(esk31_1(X380),sdtlpdtrp0(xN,X380))
| ~ aSet0(sdtlpdtrp0(xN,X380))
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( aElementOf0(X383,sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X383,sdtmndt0(sdtlpdtrp0(xN,X380),szmzizndt0(sdtlpdtrp0(xN,X380))))
| aElementOf0(esk31_1(X380),sdtlpdtrp0(xN,X380))
| ~ aSet0(sdtlpdtrp0(xN,X380))
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( X383 != szmzizndt0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X383,sdtmndt0(sdtlpdtrp0(xN,X380),szmzizndt0(sdtlpdtrp0(xN,X380))))
| aElementOf0(esk31_1(X380),sdtlpdtrp0(xN,X380))
| ~ aSet0(sdtlpdtrp0(xN,X380))
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( ~ aElement0(X384)
| ~ aElementOf0(X384,sdtlpdtrp0(xN,X380))
| X384 = szmzizndt0(sdtlpdtrp0(xN,X380))
| aElementOf0(X384,sdtmndt0(sdtlpdtrp0(xN,X380),szmzizndt0(sdtlpdtrp0(xN,X380))))
| aElementOf0(esk31_1(X380),sdtlpdtrp0(xN,X380))
| ~ aSet0(sdtlpdtrp0(xN,X380))
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X380)))
| aElementOf0(esk31_1(X380),sdtlpdtrp0(xN,X380))
| ~ aSet0(sdtlpdtrp0(xN,X380))
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( ~ aElementOf0(X385,sdtlpdtrp0(xN,szszuzczcdt0(X380)))
| aElementOf0(X385,sdtmndt0(sdtlpdtrp0(xN,X380),szmzizndt0(sdtlpdtrp0(xN,X380))))
| aElementOf0(esk31_1(X380),sdtlpdtrp0(xN,X380))
| ~ aSet0(sdtlpdtrp0(xN,X380))
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X380)),sdtmndt0(sdtlpdtrp0(xN,X380),szmzizndt0(sdtlpdtrp0(xN,X380))))
| aElementOf0(esk31_1(X380),sdtlpdtrp0(xN,X380))
| ~ aSet0(sdtlpdtrp0(xN,X380))
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X380)))
| aElementOf0(esk31_1(X380),sdtlpdtrp0(xN,X380))
| ~ aSet0(sdtlpdtrp0(xN,X380))
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X380)),sdtlpdtrp0(xN,X380))
| ~ aElementOf0(esk31_1(X380),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X380))
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( ~ aElementOf0(X382,sdtlpdtrp0(xN,X380))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X380)),X382)
| ~ aElementOf0(esk31_1(X380),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X380))
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( aSet0(sdtmndt0(sdtlpdtrp0(xN,X380),szmzizndt0(sdtlpdtrp0(xN,X380))))
| ~ aElementOf0(esk31_1(X380),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X380))
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( aElement0(X383)
| ~ aElementOf0(X383,sdtmndt0(sdtlpdtrp0(xN,X380),szmzizndt0(sdtlpdtrp0(xN,X380))))
| ~ aElementOf0(esk31_1(X380),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X380))
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( aElementOf0(X383,sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X383,sdtmndt0(sdtlpdtrp0(xN,X380),szmzizndt0(sdtlpdtrp0(xN,X380))))
| ~ aElementOf0(esk31_1(X380),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X380))
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( X383 != szmzizndt0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X383,sdtmndt0(sdtlpdtrp0(xN,X380),szmzizndt0(sdtlpdtrp0(xN,X380))))
| ~ aElementOf0(esk31_1(X380),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X380))
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( ~ aElement0(X384)
| ~ aElementOf0(X384,sdtlpdtrp0(xN,X380))
| X384 = szmzizndt0(sdtlpdtrp0(xN,X380))
| aElementOf0(X384,sdtmndt0(sdtlpdtrp0(xN,X380),szmzizndt0(sdtlpdtrp0(xN,X380))))
| ~ aElementOf0(esk31_1(X380),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X380))
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X380)))
| ~ aElementOf0(esk31_1(X380),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X380))
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( ~ aElementOf0(X385,sdtlpdtrp0(xN,szszuzczcdt0(X380)))
| aElementOf0(X385,sdtmndt0(sdtlpdtrp0(xN,X380),szmzizndt0(sdtlpdtrp0(xN,X380))))
| ~ aElementOf0(esk31_1(X380),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X380))
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X380)),sdtmndt0(sdtlpdtrp0(xN,X380),szmzizndt0(sdtlpdtrp0(xN,X380))))
| ~ aElementOf0(esk31_1(X380),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X380))
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X380)))
| ~ aElementOf0(esk31_1(X380),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X380))
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X380)),sdtlpdtrp0(xN,X380))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X380),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( ~ aElementOf0(X382,sdtlpdtrp0(xN,X380))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X380)),X382)
| ~ aSubsetOf0(sdtlpdtrp0(xN,X380),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( aSet0(sdtmndt0(sdtlpdtrp0(xN,X380),szmzizndt0(sdtlpdtrp0(xN,X380))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X380),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( aElement0(X383)
| ~ aElementOf0(X383,sdtmndt0(sdtlpdtrp0(xN,X380),szmzizndt0(sdtlpdtrp0(xN,X380))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X380),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( aElementOf0(X383,sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X383,sdtmndt0(sdtlpdtrp0(xN,X380),szmzizndt0(sdtlpdtrp0(xN,X380))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X380),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( X383 != szmzizndt0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X383,sdtmndt0(sdtlpdtrp0(xN,X380),szmzizndt0(sdtlpdtrp0(xN,X380))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X380),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( ~ aElement0(X384)
| ~ aElementOf0(X384,sdtlpdtrp0(xN,X380))
| X384 = szmzizndt0(sdtlpdtrp0(xN,X380))
| aElementOf0(X384,sdtmndt0(sdtlpdtrp0(xN,X380),szmzizndt0(sdtlpdtrp0(xN,X380))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X380),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X380)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X380),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( ~ aElementOf0(X385,sdtlpdtrp0(xN,szszuzczcdt0(X380)))
| aElementOf0(X385,sdtmndt0(sdtlpdtrp0(xN,X380),szmzizndt0(sdtlpdtrp0(xN,X380))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X380),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X380)),sdtmndt0(sdtlpdtrp0(xN,X380),szmzizndt0(sdtlpdtrp0(xN,X380))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X380),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,szNzAzT0) )
& ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X380)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X380),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X380))
| ~ aElementOf0(X380,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_12,plain,
! [X244] :
( ~ aElementOf0(X244,szNzAzT0)
| sdtlseqdt0(sz00,X244) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroLess])]) ).
fof(c_0_13,negated_conjecture,
~ ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) ) )
=> ( ( aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X1)
& ( aElementOf0(X1,xQ)
| X1 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
=> ( ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
=> aElementOf0(X1,xS) )
| aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_14,hypothesis,
( aSubsetOf0(sdtlpdtrp0(xN,X1),sdtlpdtrp0(xN,X2))
| ~ sdtlseqdt0(X2,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
aElementOf0(sz00,szNzAzT0),
inference(split_conjunct,[status(thm)],[mZeroNum]) ).
cnf(c_0_16,hypothesis,
sdtlpdtrp0(xN,sz00) = xS,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( sdtlseqdt0(sz00,X1)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_18,hypothesis,
! [X398,X399] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ( ~ aElementOf0(X398,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X398) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( aElement0(X399)
| ~ aElementOf0(X399,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( aElementOf0(X399,xQ)
| X399 = szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X399,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( ~ aElementOf0(X399,xQ)
| ~ aElement0(X399)
| aElementOf0(X399,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( X399 != szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElement0(X399)
| aElementOf0(X399,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4007])])])]) ).
fof(c_0_19,negated_conjecture,
! [X400,X401] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ( ~ aElementOf0(X400,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X400) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( aElement0(X401)
| ~ aElementOf0(X401,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( aElementOf0(X401,xQ)
| X401 = szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X401,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( ~ aElementOf0(X401,xQ)
| ~ aElement0(X401)
| aElementOf0(X401,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( X401 != szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElement0(X401)
| aElementOf0(X401,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aElementOf0(esk33_0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ~ aElementOf0(esk33_0,xS)
& ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])])]) ).
fof(c_0_20,plain,
! [X199,X200,X201,X202] :
( ( aSet0(X200)
| ~ aSubsetOf0(X200,X199)
| ~ aSet0(X199) )
& ( ~ aElementOf0(X201,X200)
| aElementOf0(X201,X199)
| ~ aSubsetOf0(X200,X199)
| ~ aSet0(X199) )
& ( aElementOf0(esk2_2(X199,X202),X202)
| ~ aSet0(X202)
| aSubsetOf0(X202,X199)
| ~ aSet0(X199) )
& ( ~ aElementOf0(esk2_2(X199,X202),X199)
| ~ aSet0(X202)
| aSubsetOf0(X202,X199)
| ~ aSet0(X199) ) ),
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_21,hypothesis,
( aSubsetOf0(sdtlpdtrp0(xN,X1),xS)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17]) ).
cnf(c_0_22,hypothesis,
aElementOf0(xi,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3989]) ).
fof(c_0_23,hypothesis,
! [X352] :
( aSet0(xS)
& ( ~ aElementOf0(X352,xS)
| aElementOf0(X352,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_24,hypothesis,
! [X395,X396,X397] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ( ~ aElementOf0(X395,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X395) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( aElement0(X396)
| ~ aElementOf0(X396,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( aElementOf0(X396,sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X396,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( X396 != szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X396,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( ~ aElement0(X396)
| ~ aElementOf0(X396,sdtlpdtrp0(xN,xi))
| X396 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X396,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(xQ)
& ( ~ aElementOf0(X397,xQ)
| aElementOf0(X397,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3989_02])])])]) ).
cnf(c_0_25,hypothesis,
( aElementOf0(X1,xQ)
| X1 = szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,negated_conjecture,
aElementOf0(esk33_0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
( aElementOf0(X1,X3)
| ~ aElementOf0(X1,X2)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,hypothesis,
aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,hypothesis,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
( szmzizndt0(sdtlpdtrp0(xN,xi)) = esk33_0
| aElementOf0(esk33_0,xQ) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,hypothesis,
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xi)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_33,hypothesis,
( aElementOf0(esk33_0,sdtlpdtrp0(xN,xi))
| aElementOf0(esk33_0,xQ) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,negated_conjecture,
~ aElementOf0(esk33_0,xS),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_35,hypothesis,
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X1,xQ) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_36,hypothesis,
aElementOf0(esk33_0,xQ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_37,hypothesis,
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_38,hypothesis,
aElementOf0(esk33_0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,hypothesis,
aElementOf0(esk33_0,sdtlpdtrp0(xN,xi)),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_40,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_39]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM581+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.13/0.32 % Computer : n023.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 00:48:38 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 4.41/3.52 % Version : CSE_E---1.7
% 4.41/3.52 % Problem : theBenchmark.p
% 4.41/3.52 % SZS status Theorem for theBenchmark.p
% 4.41/3.52 % SZS output start CNFRefutation
% See solution above
% 4.41/3.53 % Total time : 2.769s
%------------------------------------------------------------------------------