%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM541+2 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n007.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 04:57:45 PM UTC 2026
% Result : Theorem 1.37s 1.73s
% Output : CNFRefutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 18
% Syntax : Number of formulae : 119 ( 16 unt; 0 def)
% Number of atoms : 446 ( 116 equ)
% Maximal formula atoms : 50 ( 3 avg)
% Number of connectives : 535 ( 208 ~; 246 |; 56 &)
% ( 5 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 121 ( 1 sgn 51 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',mDefMin) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( aSet0(X1)
& ~ ? [X2] : aElementOf0(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
fof(mSubRefl,axiom,
! [X1] :
( aSet0(X1)
=> aSubsetOf0(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
fof(mCountNFin_01,axiom,
! [X1] :
( ( aSet0(X1)
& isCountable0(X1) )
=> X1 != slcrc0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin_01) ).
fof(mLessTotal,axiom,
! [X1,X2] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X2,szNzAzT0) )
=> ( sdtlseqdt0(X1,X2)
| sdtlseqdt0(szszuzczcdt0(X2),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessTotal) ).
fof(mNATSet,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(m__1936,hypothesis,
( aElementOf0(xm,szNzAzT0)
& aElementOf0(xn,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1936) ).
fof(mSuccNum,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(X1),szNzAzT0)
& szszuzczcdt0(X1) != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).
fof(mLessASymm,axiom,
! [X1,X2] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X2,szNzAzT0) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessASymm) ).
fof(mZeroLess,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> sdtlseqdt0(sz00,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroLess) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
fof(m__,conjecture,
( ( ( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
& aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) )
=> ( sdtlseqdt0(szszuzczcdt0(xm),xn)
| aElementOf0(xm,slbdtrb0(xn))
| xm = xn ) )
& ( ( ( sdtlseqdt0(szszuzczcdt0(xm),xn)
& aElementOf0(xm,slbdtrb0(xn)) )
| xm = xn )
=> ( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mLessTrans,axiom,
! [X1,X2,X3] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X2,szNzAzT0)
& aElementOf0(X3,szNzAzT0) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessTrans) ).
fof(mLessSucc,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> sdtlseqdt0(X1,szszuzczcdt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessSucc) ).
fof(mSuccLess,axiom,
! [X1,X2] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X2,szNzAzT0) )
=> ( sdtlseqdt0(X1,X2)
<=> sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccLess) ).
fof(mDefSeg,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ! [X2] :
( X2 = slbdtrb0(X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSeg) ).
fof(mLessRefl,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> sdtlseqdt0(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessRefl) ).
fof(mNatExtra,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( X1 = sz00
| ? [X2] :
( aElementOf0(X2,szNzAzT0)
& X1 = szszuzczcdt0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtra) ).
fof(c_0_18,plain,
! [X173,X174,X175,X176] :
( ( aElementOf0(X174,X173)
| X174 != szmzizndt0(X173)
| ~ aSubsetOf0(X173,szNzAzT0)
| X173 = slcrc0 )
& ( ~ aElementOf0(X175,X173)
| sdtlseqdt0(X174,X175)
| X174 != szmzizndt0(X173)
| ~ aSubsetOf0(X173,szNzAzT0)
| X173 = slcrc0 )
& ( aElementOf0(esk7_2(X173,X176),X173)
| ~ aElementOf0(X176,X173)
| X176 = szmzizndt0(X173)
| ~ aSubsetOf0(X173,szNzAzT0)
| X173 = slcrc0 )
& ( ~ sdtlseqdt0(X176,esk7_2(X173,X176))
| ~ aElementOf0(X176,X173)
| X176 = szmzizndt0(X173)
| ~ aSubsetOf0(X173,szNzAzT0)
| X173 = 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])])])])])]) ).
fof(c_0_19,plain,
! [X96,X97,X98] :
( ( aSet0(X96)
| X96 != slcrc0 )
& ( ~ aElementOf0(X97,X96)
| X96 != slcrc0 )
& ( ~ aSet0(X98)
| aElementOf0(esk1_1(X98),X98)
| X98 = 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])])])])])]) ).
cnf(c_0_20,plain,
( sdtlseqdt0(X3,X1)
| X2 = slcrc0
| ~ aElementOf0(X1,X2)
| X3 != szmzizndt0(X2)
| ~ aSubsetOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,plain,
( ~ aElementOf0(X1,X2)
| X2 != slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_22,plain,
! [X109] :
( ~ aSet0(X109)
| aSubsetOf0(X109,X109) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubRefl])]) ).
fof(c_0_23,plain,
! [X101] :
( ~ aSet0(X101)
| ~ isCountable0(X101)
| X101 != slcrc0 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCountNFin_01])]) ).
fof(c_0_24,plain,
! [X158,X159] :
( ~ aElementOf0(X158,szNzAzT0)
| ~ aElementOf0(X159,szNzAzT0)
| sdtlseqdt0(X158,X159)
| sdtlseqdt0(szszuzczcdt0(X159),X158) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessTotal])]) ).
cnf(c_0_25,plain,
( sdtlseqdt0(X1,X2)
| X1 != szmzizndt0(X3)
| ~ aSubsetOf0(X3,szNzAzT0)
| ~ aElementOf0(X2,X3) ),
inference(csr,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( aSubsetOf0(X1,X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
cnf(c_0_28,plain,
( ~ aSet0(X1)
| ~ isCountable0(X1)
| X1 != slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
( aSet0(X1)
| X1 != slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_30,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(szszuzczcdt0(X2),X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,hypothesis,
aElementOf0(xn,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__1936]) ).
fof(c_0_32,plain,
! [X141] :
( ( aElementOf0(szszuzczcdt0(X141),szNzAzT0)
| ~ aElementOf0(X141,szNzAzT0) )
& ( szszuzczcdt0(X141) != sz00
| ~ aElementOf0(X141,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSuccNum])])]) ).
fof(c_0_33,plain,
! [X153,X154] :
( ~ aElementOf0(X153,szNzAzT0)
| ~ aElementOf0(X154,szNzAzT0)
| ~ sdtlseqdt0(X153,X154)
| ~ sdtlseqdt0(X154,X153)
| X153 = X154 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessASymm])]) ).
fof(c_0_34,plain,
! [X147] :
( ~ aElementOf0(X147,szNzAzT0)
| sdtlseqdt0(sz00,X147) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroLess])]) ).
cnf(c_0_35,plain,
( sdtlseqdt0(X1,X2)
| X1 != szmzizndt0(szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_36,plain,
aElementOf0(sz00,szNzAzT0),
inference(split_conjunct,[status(thm)],[mZeroNum]) ).
cnf(c_0_37,plain,
( X1 != slcrc0
| ~ isCountable0(X1) ),
inference(csr,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_38,plain,
isCountable0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
cnf(c_0_39,hypothesis,
( sdtlseqdt0(szszuzczcdt0(xn),X1)
| sdtlseqdt0(X1,xn)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_40,plain,
( aElementOf0(szszuzczcdt0(X1),szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_41,negated_conjecture,
~ ( ( ( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
& aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) )
=> ( sdtlseqdt0(szszuzczcdt0(xm),xn)
| aElementOf0(xm,slbdtrb0(xn))
| xm = xn ) )
& ( ( ( sdtlseqdt0(szszuzczcdt0(xm),xn)
& aElementOf0(xm,slbdtrb0(xn)) )
| xm = xn )
=> ( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_42,plain,
( X1 = X2
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_43,plain,
( sdtlseqdt0(sz00,X1)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_44,plain,
( sdtlseqdt0(X1,sz00)
| X1 != szmzizndt0(szNzAzT0) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_45,plain,
( aElementOf0(X1,X2)
| X2 = slcrc0
| X1 != szmzizndt0(X2)
| ~ aSubsetOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_46,plain,
slcrc0 != szNzAzT0,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
fof(c_0_47,plain,
! [X155,X156,X157] :
( ~ aElementOf0(X155,szNzAzT0)
| ~ aElementOf0(X156,szNzAzT0)
| ~ aElementOf0(X157,szNzAzT0)
| ~ sdtlseqdt0(X155,X156)
| ~ sdtlseqdt0(X156,X157)
| sdtlseqdt0(X155,X157) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessTrans])]) ).
cnf(c_0_48,hypothesis,
( sdtlseqdt0(szszuzczcdt0(xn),szszuzczcdt0(X1))
| sdtlseqdt0(szszuzczcdt0(X1),xn)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_49,hypothesis,
aElementOf0(xm,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__1936]) ).
fof(c_0_50,negated_conjecture,
( ( sdtlseqdt0(szszuzczcdt0(xm),xn)
| xm = xn
| sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) )
& ( aElementOf0(xm,slbdtrb0(xn))
| xm = xn
| sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) )
& ( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) )
& ( ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
| sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) )
& ( sdtlseqdt0(szszuzczcdt0(xm),xn)
| xm = xn
| aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) )
& ( aElementOf0(xm,slbdtrb0(xn))
| xm = xn
| aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) )
& ( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) )
& ( ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
| aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) )
& ( sdtlseqdt0(szszuzczcdt0(xm),xn)
| xm = xn
| ~ sdtlseqdt0(szszuzczcdt0(xm),xn) )
& ( aElementOf0(xm,slbdtrb0(xn))
| xm = xn
| ~ sdtlseqdt0(szszuzczcdt0(xm),xn) )
& ( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| ~ sdtlseqdt0(szszuzczcdt0(xm),xn) )
& ( ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
| ~ sdtlseqdt0(szszuzczcdt0(xm),xn) )
& ( sdtlseqdt0(szszuzczcdt0(xm),xn)
| xm = xn
| ~ aElementOf0(xm,slbdtrb0(xn)) )
& ( aElementOf0(xm,slbdtrb0(xn))
| xm = xn
| ~ aElementOf0(xm,slbdtrb0(xn)) )
& ( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| ~ aElementOf0(xm,slbdtrb0(xn)) )
& ( ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
| ~ aElementOf0(xm,slbdtrb0(xn)) )
& ( sdtlseqdt0(szszuzczcdt0(xm),xn)
| xm = xn
| xm != xn )
& ( aElementOf0(xm,slbdtrb0(xn))
| xm = xn
| xm != xn )
& ( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| xm != xn )
& ( ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
| xm != xn ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])]) ).
cnf(c_0_51,plain,
( X1 = sz00
| ~ sdtlseqdt0(X1,sz00)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_36]),c_0_43]) ).
cnf(c_0_52,plain,
sdtlseqdt0(szmzizndt0(szNzAzT0),sz00),
inference(er,[status(thm)],[c_0_44]) ).
cnf(c_0_53,plain,
( aElementOf0(X1,szNzAzT0)
| X1 != szmzizndt0(szNzAzT0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_26]),c_0_27])]),c_0_46]) ).
cnf(c_0_54,plain,
( sdtlseqdt0(X1,X3)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X3,szNzAzT0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
fof(c_0_55,plain,
! [X151] :
( ~ aElementOf0(X151,szNzAzT0)
| sdtlseqdt0(X151,szszuzczcdt0(X151)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessSucc])]) ).
cnf(c_0_56,plain,
( X1 = szszuzczcdt0(X2)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X1)
| ~ sdtlseqdt0(X1,szszuzczcdt0(X2))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_42,c_0_40]) ).
cnf(c_0_57,hypothesis,
( sdtlseqdt0(szszuzczcdt0(xn),szszuzczcdt0(xm))
| sdtlseqdt0(szszuzczcdt0(xm),xn) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_58,negated_conjecture,
( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| ~ sdtlseqdt0(szszuzczcdt0(xm),xn) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
fof(c_0_59,plain,
! [X149,X150] :
( ( ~ sdtlseqdt0(X149,X150)
| sdtlseqdt0(szszuzczcdt0(X149),szszuzczcdt0(X150))
| ~ aElementOf0(X149,szNzAzT0)
| ~ aElementOf0(X150,szNzAzT0) )
& ( ~ sdtlseqdt0(szszuzczcdt0(X149),szszuzczcdt0(X150))
| sdtlseqdt0(X149,X150)
| ~ aElementOf0(X149,szNzAzT0)
| ~ aElementOf0(X150,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSuccLess])])]) ).
cnf(c_0_60,plain,
( szmzizndt0(szNzAzT0) = sz00
| ~ aElementOf0(szmzizndt0(szNzAzT0),szNzAzT0) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_61,plain,
aElementOf0(szmzizndt0(szNzAzT0),szNzAzT0),
inference(er,[status(thm)],[c_0_53]) ).
fof(c_0_62,plain,
! [X185,X186,X187,X188,X189] :
( ( aSet0(X186)
| X186 != slbdtrb0(X185)
| ~ aElementOf0(X185,szNzAzT0) )
& ( aElementOf0(X187,szNzAzT0)
| ~ aElementOf0(X187,X186)
| X186 != slbdtrb0(X185)
| ~ aElementOf0(X185,szNzAzT0) )
& ( sdtlseqdt0(szszuzczcdt0(X187),X185)
| ~ aElementOf0(X187,X186)
| X186 != slbdtrb0(X185)
| ~ aElementOf0(X185,szNzAzT0) )
& ( ~ aElementOf0(X188,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X188),X185)
| aElementOf0(X188,X186)
| X186 != slbdtrb0(X185)
| ~ aElementOf0(X185,szNzAzT0) )
& ( ~ aElementOf0(esk9_2(X185,X189),X189)
| ~ aElementOf0(esk9_2(X185,X189),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(esk9_2(X185,X189)),X185)
| ~ aSet0(X189)
| X189 = slbdtrb0(X185)
| ~ aElementOf0(X185,szNzAzT0) )
& ( aElementOf0(esk9_2(X185,X189),szNzAzT0)
| aElementOf0(esk9_2(X185,X189),X189)
| ~ aSet0(X189)
| X189 = slbdtrb0(X185)
| ~ aElementOf0(X185,szNzAzT0) )
& ( sdtlseqdt0(szszuzczcdt0(esk9_2(X185,X189)),X185)
| aElementOf0(esk9_2(X185,X189),X189)
| ~ aSet0(X189)
| X189 = slbdtrb0(X185)
| ~ aElementOf0(X185,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)],[mDefSeg])])])])])]) ).
cnf(c_0_63,plain,
( sdtlseqdt0(X1,szszuzczcdt0(X2))
| ~ sdtlseqdt0(X3,szszuzczcdt0(X2))
| ~ sdtlseqdt0(X1,X3)
| ~ aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_54,c_0_40]) ).
cnf(c_0_64,plain,
( sdtlseqdt0(X1,szszuzczcdt0(X1))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
fof(c_0_65,plain,
! [X152] :
( ~ aElementOf0(X152,szNzAzT0)
| sdtlseqdt0(X152,X152) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessRefl])]) ).
cnf(c_0_66,hypothesis,
( szszuzczcdt0(xn) = szszuzczcdt0(xm)
| ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_31])]),c_0_58]) ).
cnf(c_0_67,plain,
( sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_68,plain,
szmzizndt0(szNzAzT0) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61])]) ).
cnf(c_0_69,negated_conjecture,
( aElementOf0(xm,slbdtrb0(xn))
| xm = xn
| sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_70,plain,
( sdtlseqdt0(szszuzczcdt0(X1),X2)
| ~ aElementOf0(X1,X3)
| X3 != slbdtrb0(X2)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_71,plain,
( sdtlseqdt0(X1,szszuzczcdt0(X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_72,plain,
( sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(X2))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_73,negated_conjecture,
( sdtlseqdt0(szszuzczcdt0(xm),xn)
| xm = xn
| sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_74,plain,
( aElementOf0(X1,X3)
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X1),X2)
| X3 != slbdtrb0(X2)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_75,plain,
( sdtlseqdt0(X1,X1)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_76,hypothesis,
( szszuzczcdt0(xn) = szszuzczcdt0(xm)
| ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_31]),c_0_49])]) ).
cnf(c_0_77,plain,
( sdtlseqdt0(X1,X2)
| X1 != sz00
| ~ aElementOf0(X2,szNzAzT0) ),
inference(rw,[status(thm)],[c_0_35,c_0_68]) ).
cnf(c_0_78,negated_conjecture,
( szszuzczcdt0(xn) = szszuzczcdt0(xm)
| xn = xm
| aElementOf0(xm,slbdtrb0(xn))
| ~ sdtlseqdt0(szszuzczcdt0(xn),szszuzczcdt0(xm))
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_69]),c_0_49])]) ).
cnf(c_0_79,hypothesis,
( sdtlseqdt0(szszuzczcdt0(X1),xn)
| X2 != slbdtrb0(xn)
| ~ aElementOf0(X1,X2) ),
inference(spm,[status(thm)],[c_0_70,c_0_31]) ).
cnf(c_0_80,negated_conjecture,
( ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_71]),c_0_31])]) ).
cnf(c_0_81,negated_conjecture,
( xn = xm
| sdtlseqdt0(szszuzczcdt0(xm),xn)
| sdtlseqdt0(xm,xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_31]),c_0_49])]) ).
cnf(c_0_82,plain,
( aElementOf0(X1,X2)
| X2 != slbdtrb0(szszuzczcdt0(X1))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_40]) ).
cnf(c_0_83,hypothesis,
( szszuzczcdt0(xn) = szszuzczcdt0(xm)
| sz00 != xm
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_31])]) ).
cnf(c_0_84,negated_conjecture,
( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| xm != xn ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_85,hypothesis,
( sdtlseqdt0(X1,xn)
| X1 != szmzizndt0(szNzAzT0) ),
inference(spm,[status(thm)],[c_0_35,c_0_31]) ).
cnf(c_0_86,negated_conjecture,
( szszuzczcdt0(xn) = szszuzczcdt0(xm)
| xn = xm
| aElementOf0(xm,slbdtrb0(xn))
| ~ sdtlseqdt0(szszuzczcdt0(xn),szszuzczcdt0(xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_40]),c_0_31])]) ).
cnf(c_0_87,hypothesis,
( sdtlseqdt0(szszuzczcdt0(X1),xn)
| ~ aElementOf0(X1,slbdtrb0(xn)) ),
inference(er,[status(thm)],[c_0_79]) ).
cnf(c_0_88,negated_conjecture,
( xn = xm
| sdtlseqdt0(xm,xn)
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_89,plain,
( sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(X2))
| X3 != slbdtrb0(szszuzczcdt0(X2))
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,X3) ),
inference(spm,[status(thm)],[c_0_70,c_0_40]) ).
cnf(c_0_90,plain,
( aElementOf0(X1,slbdtrb0(szszuzczcdt0(X1)))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(er,[status(thm)],[c_0_82]) ).
cnf(c_0_91,hypothesis,
( szszuzczcdt0(xn) = szszuzczcdt0(xm)
| sz00 != xm ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_40]),c_0_49])]) ).
cnf(c_0_92,negated_conjecture,
( xn != xm
| ~ sdtlseqdt0(xm,xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_67]),c_0_31]),c_0_49])]) ).
cnf(c_0_93,hypothesis,
( sdtlseqdt0(X1,xn)
| X1 != sz00 ),
inference(rw,[status(thm)],[c_0_85,c_0_68]) ).
cnf(c_0_94,negated_conjecture,
( ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
| ~ sdtlseqdt0(xm,xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_67]),c_0_31]),c_0_49])]) ).
cnf(c_0_95,hypothesis,
( szszuzczcdt0(xn) = szszuzczcdt0(xm)
| xn = xm
| sdtlseqdt0(szszuzczcdt0(xm),xn) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_57]),c_0_87]) ).
cnf(c_0_96,negated_conjecture,
( xn = xm
| sdtlseqdt0(xm,xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_40]),c_0_49])]) ).
fof(c_0_97,plain,
! [X144] :
( ( aElementOf0(esk5_1(X144),szNzAzT0)
| X144 = sz00
| ~ aElementOf0(X144,szNzAzT0) )
& ( X144 = szszuzczcdt0(esk5_1(X144))
| X144 = sz00
| ~ aElementOf0(X144,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mNatExtra])])])]) ).
cnf(c_0_98,plain,
( sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(X2))
| ~ aElementOf0(X1,slbdtrb0(szszuzczcdt0(X2)))
| ~ aElementOf0(X2,szNzAzT0) ),
inference(er,[status(thm)],[c_0_89]) ).
cnf(c_0_99,hypothesis,
( aElementOf0(xn,slbdtrb0(szszuzczcdt0(xm)))
| sz00 != xm ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_31])]) ).
cnf(c_0_100,hypothesis,
( X1 = xm
| ~ sdtlseqdt0(xm,X1)
| ~ sdtlseqdt0(X1,xm)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_42,c_0_49]) ).
cnf(c_0_101,negated_conjecture,
( xn != xm
| sz00 != xm ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_102,negated_conjecture,
( szszuzczcdt0(xn) = szszuzczcdt0(xm)
| xn = xm ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_96]) ).
cnf(c_0_103,plain,
( X1 = szszuzczcdt0(esk5_1(X1))
| X1 = sz00
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_104,hypothesis,
( sdtlseqdt0(szszuzczcdt0(xn),szszuzczcdt0(xm))
| sz00 != xm ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_49])]) ).
cnf(c_0_105,hypothesis,
( sz00 != xm
| ~ sdtlseqdt0(xn,xm) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_93]),c_0_31])]),c_0_101]) ).
cnf(c_0_106,plain,
( aElementOf0(esk5_1(X1),szNzAzT0)
| X1 = sz00
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_107,negated_conjecture,
( xn = xm
| aElementOf0(xn,slbdtrb0(szszuzczcdt0(xm))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_102]),c_0_31])]) ).
cnf(c_0_108,hypothesis,
( szszuzczcdt0(esk5_1(xm)) = xm
| sz00 = xm ),
inference(spm,[status(thm)],[c_0_103,c_0_49]) ).
cnf(c_0_109,hypothesis,
sz00 != xm,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_104]),c_0_49]),c_0_31])]),c_0_105]) ).
cnf(c_0_110,hypothesis,
( sz00 = xm
| aElementOf0(esk5_1(xm),szNzAzT0) ),
inference(spm,[status(thm)],[c_0_106,c_0_49]) ).
cnf(c_0_111,negated_conjecture,
( xn = xm
| sdtlseqdt0(szszuzczcdt0(xn),szszuzczcdt0(xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_107]),c_0_49])]) ).
cnf(c_0_112,hypothesis,
( xn = xm
| ~ sdtlseqdt0(xn,xm) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_96]),c_0_31])]) ).
cnf(c_0_113,plain,
( sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(X1))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_98,c_0_90]) ).
cnf(c_0_114,hypothesis,
szszuzczcdt0(esk5_1(xm)) = xm,
inference(sr,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_115,hypothesis,
aElementOf0(esk5_1(xm),szNzAzT0),
inference(sr,[status(thm)],[c_0_110,c_0_109]) ).
cnf(c_0_116,negated_conjecture,
xn = xm,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_111]),c_0_49]),c_0_31])]),c_0_112]) ).
cnf(c_0_117,hypothesis,
sdtlseqdt0(xm,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_115])]) ).
cnf(c_0_118,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_116]),c_0_116]),c_0_117])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : NUM541+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.09 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.10/0.28 % Computer : n007.cluster.edu
% 0.10/0.28 % Model : x86_64 x86_64
% 0.10/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28 % Memory : 8042.1875MB
% 0.10/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.28 % CPULimit : 300
% 0.10/0.28 % WCLimit : 300
% 0.10/0.28 % DateTime : Tue May 5 00:42:53 EDT 2026
% 0.10/0.28 % CPUTime :
% 0.10/0.29 % start to proof: theBenchmark
% 1.37/1.73 % Version : CSE_E---1.7
% 1.37/1.73 % Problem : theBenchmark.p
% 1.37/1.73 % SZS status Theorem for theBenchmark.p
% 1.37/1.73 % SZS output start CNFRefutation
% See solution above
% 1.37/1.73 % Total time : 1.368s
%------------------------------------------------------------------------------