%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM574+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 04:57:52 PM UTC 2026
% Result : Theorem 3.96s 3.42s
% Output : CNFRefutation 3.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 12 unt; 0 def)
% Number of atoms : 305 ( 36 equ)
% Maximal formula atoms : 181 ( 8 avg)
% Number of connectives : 444 ( 176 ~; 190 |; 61 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 45 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 23 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__3786_02,hypothesis,
( ( sdtlseqdt0(xj,xi)
& ? [X1] :
( aElementOf0(X1,szNzAzT0)
& szszuzczcdt0(X1) = xi ) )
=> ( sdtlseqdt0(xj,xi)
=> ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> aElementOf0(X1,sdtlpdtrp0(xN,xj)) )
& aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3786_02) ).
fof(m__,conjecture,
( sdtlseqdt0(xj,xi)
=> ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> aElementOf0(X1,sdtlpdtrp0(xN,xj)) )
| aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mLessASymm,axiom,
! [X1,X2] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X2,szNzAzT0) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessASymm) ).
fof(mNatExtra,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( X1 = sz00
| ? [X2] :
( aElementOf0(X2,szNzAzT0)
& X1 = szszuzczcdt0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatExtra) ).
fof(m__3786,hypothesis,
( aElementOf0(xj,szNzAzT0)
& aElementOf0(xi,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3786) ).
fof(mZeroLess,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> sdtlseqdt0(sz00,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroLess) ).
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(c_0_7,hypothesis,
! [X382,X383] :
( ( ~ aElementOf0(X383,sdtlpdtrp0(xN,xi))
| aElementOf0(X383,sdtlpdtrp0(xN,xj))
| ~ sdtlseqdt0(xj,xi)
| ~ sdtlseqdt0(xj,xi)
| ~ aElementOf0(X382,szNzAzT0)
| szszuzczcdt0(X382) != xi )
& ( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
| ~ sdtlseqdt0(xj,xi)
| ~ sdtlseqdt0(xj,xi)
| ~ aElementOf0(X382,szNzAzT0)
| szszuzczcdt0(X382) != xi ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3786_02])])])]) ).
fof(c_0_8,negated_conjecture,
~ ( sdtlseqdt0(xj,xi)
=> ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> aElementOf0(X1,sdtlpdtrp0(xN,xj)) )
| aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_9,plain,
! [X241,X242] :
( ~ aElementOf0(X241,szNzAzT0)
| ~ aElementOf0(X242,szNzAzT0)
| ~ sdtlseqdt0(X241,X242)
| ~ sdtlseqdt0(X242,X241)
| X241 = X242 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessASymm])]) ).
cnf(c_0_10,hypothesis,
( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
| ~ sdtlseqdt0(xj,xi)
| ~ sdtlseqdt0(xj,xi)
| ~ aElementOf0(X1,szNzAzT0)
| szszuzczcdt0(X1) != xi ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,negated_conjecture,
( sdtlseqdt0(xj,xi)
& aElementOf0(esk32_0,sdtlpdtrp0(xN,xi))
& ~ aElementOf0(esk32_0,sdtlpdtrp0(xN,xj))
& ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_12,plain,
! [X232] :
( ( aElementOf0(esk5_1(X232),szNzAzT0)
| X232 = sz00
| ~ aElementOf0(X232,szNzAzT0) )
& ( X232 = szszuzczcdt0(esk5_1(X232))
| X232 = sz00
| ~ aElementOf0(X232,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mNatExtra])])])]) ).
cnf(c_0_13,plain,
( X1 = X2
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,hypothesis,
aElementOf0(xj,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3786]) ).
cnf(c_0_15,hypothesis,
( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
| szszuzczcdt0(X1) != xi
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(xj,xi) ),
inference(cn,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
sdtlseqdt0(xj,xi),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( X1 = szszuzczcdt0(esk5_1(X1))
| X1 = sz00
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,hypothesis,
aElementOf0(xi,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3786]) ).
cnf(c_0_20,plain,
( aElementOf0(esk5_1(X1),szNzAzT0)
| X1 = sz00
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_21,plain,
! [X235] :
( ~ aElementOf0(X235,szNzAzT0)
| sdtlseqdt0(sz00,X235) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroLess])]) ).
cnf(c_0_22,hypothesis,
( X1 = xj
| ~ sdtlseqdt0(xj,X1)
| ~ sdtlseqdt0(X1,xj)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_23,hypothesis,
( szszuzczcdt0(X1) != xi
| ~ aElementOf0(X1,szNzAzT0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]),c_0_17]) ).
cnf(c_0_24,hypothesis,
( szszuzczcdt0(esk5_1(xi)) = xi
| xi = sz00 ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,hypothesis,
( xi = sz00
| aElementOf0(esk5_1(xi),szNzAzT0) ),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_26,plain,
( sdtlseqdt0(sz00,X1)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_27,hypothesis,
! [X371,X373,X374,X375,X376] :
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X371)),sdtlpdtrp0(xN,X371))
| aElementOf0(esk31_1(X371),sdtlpdtrp0(xN,X371))
| ~ aSet0(sdtlpdtrp0(xN,X371))
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( ~ aElementOf0(X373,sdtlpdtrp0(xN,X371))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X371)),X373)
| aElementOf0(esk31_1(X371),sdtlpdtrp0(xN,X371))
| ~ aSet0(sdtlpdtrp0(xN,X371))
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( aSet0(sdtmndt0(sdtlpdtrp0(xN,X371),szmzizndt0(sdtlpdtrp0(xN,X371))))
| aElementOf0(esk31_1(X371),sdtlpdtrp0(xN,X371))
| ~ aSet0(sdtlpdtrp0(xN,X371))
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( aElement0(X374)
| ~ aElementOf0(X374,sdtmndt0(sdtlpdtrp0(xN,X371),szmzizndt0(sdtlpdtrp0(xN,X371))))
| aElementOf0(esk31_1(X371),sdtlpdtrp0(xN,X371))
| ~ aSet0(sdtlpdtrp0(xN,X371))
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( aElementOf0(X374,sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X374,sdtmndt0(sdtlpdtrp0(xN,X371),szmzizndt0(sdtlpdtrp0(xN,X371))))
| aElementOf0(esk31_1(X371),sdtlpdtrp0(xN,X371))
| ~ aSet0(sdtlpdtrp0(xN,X371))
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( X374 != szmzizndt0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X374,sdtmndt0(sdtlpdtrp0(xN,X371),szmzizndt0(sdtlpdtrp0(xN,X371))))
| aElementOf0(esk31_1(X371),sdtlpdtrp0(xN,X371))
| ~ aSet0(sdtlpdtrp0(xN,X371))
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( ~ aElement0(X375)
| ~ aElementOf0(X375,sdtlpdtrp0(xN,X371))
| X375 = szmzizndt0(sdtlpdtrp0(xN,X371))
| aElementOf0(X375,sdtmndt0(sdtlpdtrp0(xN,X371),szmzizndt0(sdtlpdtrp0(xN,X371))))
| aElementOf0(esk31_1(X371),sdtlpdtrp0(xN,X371))
| ~ aSet0(sdtlpdtrp0(xN,X371))
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X371)))
| aElementOf0(esk31_1(X371),sdtlpdtrp0(xN,X371))
| ~ aSet0(sdtlpdtrp0(xN,X371))
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( ~ aElementOf0(X376,sdtlpdtrp0(xN,szszuzczcdt0(X371)))
| aElementOf0(X376,sdtmndt0(sdtlpdtrp0(xN,X371),szmzizndt0(sdtlpdtrp0(xN,X371))))
| aElementOf0(esk31_1(X371),sdtlpdtrp0(xN,X371))
| ~ aSet0(sdtlpdtrp0(xN,X371))
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X371)),sdtmndt0(sdtlpdtrp0(xN,X371),szmzizndt0(sdtlpdtrp0(xN,X371))))
| aElementOf0(esk31_1(X371),sdtlpdtrp0(xN,X371))
| ~ aSet0(sdtlpdtrp0(xN,X371))
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X371)))
| aElementOf0(esk31_1(X371),sdtlpdtrp0(xN,X371))
| ~ aSet0(sdtlpdtrp0(xN,X371))
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X371)),sdtlpdtrp0(xN,X371))
| ~ aElementOf0(esk31_1(X371),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X371))
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( ~ aElementOf0(X373,sdtlpdtrp0(xN,X371))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X371)),X373)
| ~ aElementOf0(esk31_1(X371),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X371))
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( aSet0(sdtmndt0(sdtlpdtrp0(xN,X371),szmzizndt0(sdtlpdtrp0(xN,X371))))
| ~ aElementOf0(esk31_1(X371),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X371))
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( aElement0(X374)
| ~ aElementOf0(X374,sdtmndt0(sdtlpdtrp0(xN,X371),szmzizndt0(sdtlpdtrp0(xN,X371))))
| ~ aElementOf0(esk31_1(X371),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X371))
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( aElementOf0(X374,sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X374,sdtmndt0(sdtlpdtrp0(xN,X371),szmzizndt0(sdtlpdtrp0(xN,X371))))
| ~ aElementOf0(esk31_1(X371),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X371))
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( X374 != szmzizndt0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X374,sdtmndt0(sdtlpdtrp0(xN,X371),szmzizndt0(sdtlpdtrp0(xN,X371))))
| ~ aElementOf0(esk31_1(X371),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X371))
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( ~ aElement0(X375)
| ~ aElementOf0(X375,sdtlpdtrp0(xN,X371))
| X375 = szmzizndt0(sdtlpdtrp0(xN,X371))
| aElementOf0(X375,sdtmndt0(sdtlpdtrp0(xN,X371),szmzizndt0(sdtlpdtrp0(xN,X371))))
| ~ aElementOf0(esk31_1(X371),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X371))
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X371)))
| ~ aElementOf0(esk31_1(X371),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X371))
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( ~ aElementOf0(X376,sdtlpdtrp0(xN,szszuzczcdt0(X371)))
| aElementOf0(X376,sdtmndt0(sdtlpdtrp0(xN,X371),szmzizndt0(sdtlpdtrp0(xN,X371))))
| ~ aElementOf0(esk31_1(X371),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X371))
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X371)),sdtmndt0(sdtlpdtrp0(xN,X371),szmzizndt0(sdtlpdtrp0(xN,X371))))
| ~ aElementOf0(esk31_1(X371),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X371))
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X371)))
| ~ aElementOf0(esk31_1(X371),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X371))
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X371)),sdtlpdtrp0(xN,X371))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X371),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( ~ aElementOf0(X373,sdtlpdtrp0(xN,X371))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X371)),X373)
| ~ aSubsetOf0(sdtlpdtrp0(xN,X371),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( aSet0(sdtmndt0(sdtlpdtrp0(xN,X371),szmzizndt0(sdtlpdtrp0(xN,X371))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X371),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( aElement0(X374)
| ~ aElementOf0(X374,sdtmndt0(sdtlpdtrp0(xN,X371),szmzizndt0(sdtlpdtrp0(xN,X371))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X371),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( aElementOf0(X374,sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X374,sdtmndt0(sdtlpdtrp0(xN,X371),szmzizndt0(sdtlpdtrp0(xN,X371))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X371),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( X374 != szmzizndt0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X374,sdtmndt0(sdtlpdtrp0(xN,X371),szmzizndt0(sdtlpdtrp0(xN,X371))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X371),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( ~ aElement0(X375)
| ~ aElementOf0(X375,sdtlpdtrp0(xN,X371))
| X375 = szmzizndt0(sdtlpdtrp0(xN,X371))
| aElementOf0(X375,sdtmndt0(sdtlpdtrp0(xN,X371),szmzizndt0(sdtlpdtrp0(xN,X371))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X371),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X371)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X371),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( ~ aElementOf0(X376,sdtlpdtrp0(xN,szszuzczcdt0(X371)))
| aElementOf0(X376,sdtmndt0(sdtlpdtrp0(xN,X371),szmzizndt0(sdtlpdtrp0(xN,X371))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X371),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X371)),sdtmndt0(sdtlpdtrp0(xN,X371),szmzizndt0(sdtlpdtrp0(xN,X371))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X371),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,szNzAzT0) )
& ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X371)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X371),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X371))
| ~ aElementOf0(X371,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])])])])])]) ).
cnf(c_0_28,negated_conjecture,
( xj = xi
| ~ sdtlseqdt0(xi,xj) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_16]),c_0_19])]) ).
cnf(c_0_29,hypothesis,
xi = sz00,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_30,hypothesis,
sdtlseqdt0(sz00,xj),
inference(spm,[status(thm)],[c_0_26,c_0_14]) ).
cnf(c_0_31,negated_conjecture,
aElementOf0(esk32_0,sdtlpdtrp0(xN,xi)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_32,hypothesis,
sdtlpdtrp0(xN,sz00) = xS,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,negated_conjecture,
~ aElementOf0(esk32_0,sdtlpdtrp0(xN,xj)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_34,negated_conjecture,
xj = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29]),c_0_29]),c_0_30])]) ).
cnf(c_0_35,negated_conjecture,
aElementOf0(esk32_0,xS),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_29]),c_0_32]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34]),c_0_32]),c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM574+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
% 0.16/0.32 % Computer : n023.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue May 5 00:47:38 EDT 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.33 % start to proof: theBenchmark
% 3.96/3.42 % Version : CSE_E---1.7
% 3.96/3.42 % Problem : theBenchmark.p
% 3.96/3.42 % SZS status Theorem for theBenchmark.p
% 3.96/3.42 % SZS output start CNFRefutation
% See solution above
% 3.96/3.43 % Total time : 2.768s
%------------------------------------------------------------------------------