%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM541+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n021.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 1.62s 2.11s
% Output : CNFRefutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 112 ( 13 unt; 0 def)
% Number of atoms : 396 ( 87 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 489 ( 205 ~; 230 |; 32 &)
% ( 7 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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 : 144 ( 1 sgn 49 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mLessTotal,axiom,
! [X1,X2] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X2,szNzAzT0) )
=> ( sdtlseqdt0(X1,X2)
| sdtlseqdt0(szszuzczcdt0(X2),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessTotal) ).
fof(mDefMin,axiom,
! [X1] :
( ( aSubsetOf0(X1,szNzAzT0)
& X1 != slcrc0 )
=> ! [X2] :
( X2 = szmzizndt0(X1)
<=> ( aElementOf0(X2,X1)
& ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefMin) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( aSet0(X1)
& ~ ? [X2] : aElementOf0(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
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/sandbox/benchmark/theBenchmark.p',mDefSeg) ).
fof(mSuccLess,axiom,
! [X1,X2] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X2,szNzAzT0) )
=> ( sdtlseqdt0(X1,X2)
<=> sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccLess) ).
fof(mSuccNum,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(X1),szNzAzT0)
& szszuzczcdt0(X1) != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNum) ).
fof(m__1936,hypothesis,
( aElementOf0(xm,szNzAzT0)
& aElementOf0(xn,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1936) ).
fof(mSubRefl,axiom,
! [X1] :
( aSet0(X1)
=> aSubsetOf0(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubRefl) ).
fof(m__,conjecture,
( aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
<=> ( aElementOf0(xm,slbdtrb0(xn))
| xm = xn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
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(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/sandbox/benchmark/theBenchmark.p',mLessTrans) ).
fof(mLessSucc,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> sdtlseqdt0(X1,szszuzczcdt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessSucc) ).
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(mLessRefl,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> sdtlseqdt0(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessRefl) ).
fof(c_0_17,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])]) ).
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])])])])])]) ).
fof(c_0_20,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])])])])])]) ).
fof(c_0_21,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])])]) ).
fof(c_0_22,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])])]) ).
cnf(c_0_23,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(szszuzczcdt0(X2),X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,hypothesis,
aElementOf0(xm,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__1936]) ).
cnf(c_0_25,plain,
( aElementOf0(esk7_2(X1,X2),X1)
| X2 = szmzizndt0(X1)
| X1 = slcrc0
| ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( ~ aElementOf0(X1,X2)
| X2 != slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_27,plain,
! [X109] :
( ~ aSet0(X109)
| aSubsetOf0(X109,X109) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubRefl])]) ).
fof(c_0_28,negated_conjecture,
~ ( aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
<=> ( aElementOf0(xm,slbdtrb0(xn))
| xm = xn ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_29,plain,
( aElementOf0(X1,X3)
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X1),X2)
| X3 != slbdtrb0(X2)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,plain,
( sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,plain,
( aElementOf0(szszuzczcdt0(X1),szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,hypothesis,
( sdtlseqdt0(szszuzczcdt0(xm),X1)
| sdtlseqdt0(X1,xm)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_33,hypothesis,
aElementOf0(xn,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__1936]) ).
cnf(c_0_34,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_35,plain,
( X1 = szmzizndt0(X2)
| X2 = slcrc0
| ~ sdtlseqdt0(X1,esk7_2(X2,X1))
| ~ aElementOf0(X1,X2)
| ~ aSubsetOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_36,plain,
! [X147] :
( ~ aElementOf0(X147,szNzAzT0)
| sdtlseqdt0(sz00,X147) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroLess])]) ).
cnf(c_0_37,plain,
( X1 = szmzizndt0(X2)
| aElementOf0(esk7_2(X2,X1),X2)
| ~ aSubsetOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,X2) ),
inference(csr,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_38,plain,
( aSubsetOf0(X1,X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_39,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
fof(c_0_40,negated_conjecture,
( ( ~ aElementOf0(xm,slbdtrb0(xn))
| ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) )
& ( xm != xn
| ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) )
& ( aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
| aElementOf0(xm,slbdtrb0(xn))
| xm = xn ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])]) ).
cnf(c_0_41,plain,
( aElementOf0(X1,X2)
| X2 != slbdtrb0(szszuzczcdt0(X3))
| ~ sdtlseqdt0(X1,X3)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X3,szNzAzT0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_42,hypothesis,
( sdtlseqdt0(szszuzczcdt0(xm),xn)
| sdtlseqdt0(xn,xm) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_43,plain,
( sdtlseqdt0(X1,X2)
| X1 != szmzizndt0(X3)
| ~ aSubsetOf0(X3,szNzAzT0)
| ~ aElementOf0(X2,X3) ),
inference(csr,[status(thm)],[c_0_34,c_0_26]) ).
cnf(c_0_44,plain,
( X1 = szmzizndt0(X2)
| ~ sdtlseqdt0(X1,esk7_2(X2,X1))
| ~ aSubsetOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,X2) ),
inference(csr,[status(thm)],[c_0_35,c_0_26]) ).
cnf(c_0_45,plain,
( sdtlseqdt0(sz00,X1)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_46,plain,
( X1 = szmzizndt0(szNzAzT0)
| aElementOf0(esk7_2(szNzAzT0,X1),szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).
cnf(c_0_47,plain,
aElementOf0(sz00,szNzAzT0),
inference(split_conjunct,[status(thm)],[mZeroNum]) ).
fof(c_0_48,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])]) ).
cnf(c_0_49,negated_conjecture,
( ~ aElementOf0(xm,slbdtrb0(xn))
| ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_50,plain,
( aElementOf0(X1,slbdtrb0(szszuzczcdt0(X2)))
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(er,[status(thm)],[c_0_41]) ).
cnf(c_0_51,hypothesis,
( sdtlseqdt0(xn,xm)
| aElementOf0(xm,X1)
| X1 != slbdtrb0(xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_42]),c_0_33]),c_0_24])]) ).
cnf(c_0_52,plain,
( sdtlseqdt0(X1,X2)
| X1 != szmzizndt0(szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_38]),c_0_39])]) ).
cnf(c_0_53,plain,
( szmzizndt0(X1) = sz00
| ~ aSubsetOf0(X1,szNzAzT0)
| ~ aElementOf0(esk7_2(X1,sz00),szNzAzT0)
| ~ aElementOf0(sz00,X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_54,plain,
( szmzizndt0(szNzAzT0) = sz00
| aElementOf0(esk7_2(szNzAzT0,sz00),szNzAzT0) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_55,plain,
( sdtlseqdt0(szszuzczcdt0(X1),X2)
| ~ aElementOf0(X1,X3)
| X3 != slbdtrb0(X2)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_56,plain,
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,X2)
| X2 != slbdtrb0(X3)
| ~ aElementOf0(X3,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_57,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_58,plain,
( X1 = X2
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_59,negated_conjecture,
( ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xm,slbdtrb0(xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_24]),c_0_33])]) ).
cnf(c_0_60,hypothesis,
( sdtlseqdt0(xn,xm)
| aElementOf0(xm,slbdtrb0(xn)) ),
inference(er,[status(thm)],[c_0_51]) ).
cnf(c_0_61,negated_conjecture,
( xm != xn
| ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn))) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_62,hypothesis,
( sdtlseqdt0(X1,xn)
| X1 != szmzizndt0(szNzAzT0) ),
inference(spm,[status(thm)],[c_0_52,c_0_33]) ).
cnf(c_0_63,plain,
( szmzizndt0(szNzAzT0) = sz00
| ~ aSubsetOf0(szNzAzT0,szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_47])]) ).
cnf(c_0_64,hypothesis,
( sdtlseqdt0(szszuzczcdt0(X1),xn)
| X2 != slbdtrb0(xn)
| ~ aElementOf0(X1,X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_33]) ).
cnf(c_0_65,hypothesis,
( aElementOf0(X1,szNzAzT0)
| X2 != slbdtrb0(xn)
| ~ aElementOf0(X1,X2) ),
inference(spm,[status(thm)],[c_0_56,c_0_33]) ).
cnf(c_0_66,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_57]) ).
fof(c_0_67,plain,
! [X151] :
( ~ aElementOf0(X151,szNzAzT0)
| sdtlseqdt0(X151,szszuzczcdt0(X151)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessSucc])]) ).
cnf(c_0_68,plain,
( sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(X2))
| X3 != slbdtrb0(szszuzczcdt0(X2))
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,X3) ),
inference(spm,[status(thm)],[c_0_55,c_0_31]) ).
cnf(c_0_69,plain,
( aElementOf0(X1,szNzAzT0)
| X2 != slbdtrb0(szszuzczcdt0(X3))
| ~ aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X1,X2) ),
inference(spm,[status(thm)],[c_0_56,c_0_31]) ).
fof(c_0_70,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_71,hypothesis,
( X1 = xn
| ~ sdtlseqdt0(xn,X1)
| ~ sdtlseqdt0(X1,xn)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_58,c_0_33]) ).
cnf(c_0_72,negated_conjecture,
( sdtlseqdt0(xn,xm)
| ~ sdtlseqdt0(xm,xn) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_73,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_61,c_0_50]),c_0_24]),c_0_33])]) ).
cnf(c_0_74,hypothesis,
( sdtlseqdt0(X1,xn)
| X1 != sz00
| ~ aSubsetOf0(szNzAzT0,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_75,plain,
( X1 = szszuzczcdt0(X2)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X1)
| ~ sdtlseqdt0(X1,szszuzczcdt0(X2))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_58,c_0_31]) ).
cnf(c_0_76,hypothesis,
( sdtlseqdt0(szszuzczcdt0(X1),xn)
| ~ aElementOf0(X1,slbdtrb0(xn)) ),
inference(er,[status(thm)],[c_0_64]) ).
cnf(c_0_77,hypothesis,
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,slbdtrb0(xn)) ),
inference(er,[status(thm)],[c_0_65]) ).
cnf(c_0_78,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_66,c_0_31]) ).
cnf(c_0_79,plain,
( sdtlseqdt0(X1,szszuzczcdt0(X1))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_80,plain,
( sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(X2))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_81,plain,
( sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(X2))
| ~ aElementOf0(X1,slbdtrb0(szszuzczcdt0(X2)))
| ~ aElementOf0(X2,szNzAzT0) ),
inference(er,[status(thm)],[c_0_68]) ).
cnf(c_0_82,plain,
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,slbdtrb0(szszuzczcdt0(X2)))
| ~ aElementOf0(X2,szNzAzT0) ),
inference(er,[status(thm)],[c_0_69]) ).
cnf(c_0_83,hypothesis,
( sdtlseqdt0(X1,xn)
| ~ sdtlseqdt0(X2,xn)
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_66,c_0_33]) ).
cnf(c_0_84,plain,
( X1 = szszuzczcdt0(esk5_1(X1))
| X1 = sz00
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_85,hypothesis,
~ sdtlseqdt0(xm,xn),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_24])]),c_0_73]) ).
cnf(c_0_86,hypothesis,
( sdtlseqdt0(X1,xn)
| X1 != sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_38]),c_0_39])]) ).
fof(c_0_87,plain,
! [X152] :
( ~ aElementOf0(X152,szNzAzT0)
| sdtlseqdt0(X152,X152) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessRefl])]) ).
cnf(c_0_88,hypothesis,
( szszuzczcdt0(X1) = xn
| ~ sdtlseqdt0(xn,szszuzczcdt0(X1))
| ~ aElementOf0(X1,slbdtrb0(xn)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_33])]),c_0_77]) ).
cnf(c_0_89,plain,
( sdtlseqdt0(X1,szszuzczcdt0(X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_90,plain,
( sdtlseqdt0(X1,X2)
| ~ aElementOf0(X1,slbdtrb0(szszuzczcdt0(X2)))
| ~ aElementOf0(X2,szNzAzT0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]) ).
cnf(c_0_91,negated_conjecture,
( aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
| aElementOf0(xm,slbdtrb0(xn))
| xm = xn ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_92,hypothesis,
( sdtlseqdt0(xn,xm)
| sdtlseqdt0(X1,xn)
| ~ sdtlseqdt0(X1,szszuzczcdt0(xm))
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_83,c_0_42]) ).
cnf(c_0_93,hypothesis,
( szszuzczcdt0(esk5_1(xm)) = xm
| xm = sz00 ),
inference(spm,[status(thm)],[c_0_84,c_0_24]) ).
cnf(c_0_94,hypothesis,
xm != sz00,
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_95,plain,
( sdtlseqdt0(X1,X1)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_96,plain,
( aElementOf0(esk5_1(X1),szNzAzT0)
| X1 = sz00
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_97,hypothesis,
( szszuzczcdt0(X1) = xn
| ~ sdtlseqdt0(xn,X1)
| ~ aElementOf0(X1,slbdtrb0(xn)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_33])]),c_0_77]) ).
cnf(c_0_98,negated_conjecture,
( xn = xm
| aElementOf0(xm,slbdtrb0(xn)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_33])]),c_0_85]) ).
cnf(c_0_99,hypothesis,
( sdtlseqdt0(xn,xm)
| sdtlseqdt0(X1,xn)
| ~ sdtlseqdt0(X1,szszuzczcdt0(xm))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_31]),c_0_24])]) ).
cnf(c_0_100,hypothesis,
szszuzczcdt0(esk5_1(xm)) = xm,
inference(sr,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_101,plain,
( aElementOf0(X1,X2)
| X2 != slbdtrb0(szszuzczcdt0(X1))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_95]),c_0_31]) ).
cnf(c_0_102,hypothesis,
( xm = sz00
| aElementOf0(esk5_1(xm),szNzAzT0) ),
inference(spm,[status(thm)],[c_0_96,c_0_24]) ).
cnf(c_0_103,hypothesis,
( szszuzczcdt0(xm) = xn
| xn = xm
| ~ sdtlseqdt0(xn,xm) ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_104,hypothesis,
sdtlseqdt0(xn,xm),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_79]),c_0_24])]),c_0_85]) ).
cnf(c_0_105,hypothesis,
( X1 != slbdtrb0(xn)
| ~ aElementOf0(esk5_1(xm),X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_100]),c_0_85]) ).
cnf(c_0_106,plain,
( aElementOf0(X1,slbdtrb0(szszuzczcdt0(X1)))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(er,[status(thm)],[c_0_101]) ).
cnf(c_0_107,hypothesis,
aElementOf0(esk5_1(xm),szNzAzT0),
inference(sr,[status(thm)],[c_0_102,c_0_94]) ).
cnf(c_0_108,hypothesis,
( szszuzczcdt0(xm) = xn
| xn = xm ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_104])]) ).
cnf(c_0_109,hypothesis,
slbdtrb0(xn) != slbdtrb0(xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_100]),c_0_107])]) ).
cnf(c_0_110,hypothesis,
xn = xm,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_108]),c_0_24])]),c_0_85]) ).
cnf(c_0_111,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_110])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.29 % Problem : NUM541+1 : TPTP v9.2.1. Released v4.0.0.
% 0.06/0.29 % 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
% 0.11/0.50 % Computer : n021.cluster.edu
% 0.11/0.50 % Model : x86_64 x86_64
% 0.11/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.50 % Memory : 8042.1875MB
% 0.11/0.50 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.50 % CPULimit : 300
% 0.11/0.50 % WCLimit : 300
% 0.11/0.50 % DateTime : Tue May 5 00:44:25 EDT 2026
% 0.11/0.50 % CPUTime :
% 0.11/0.51 % start to proof: theBenchmark
% 1.62/2.11 % Version : CSE_E---1.7
% 1.62/2.11 % Problem : theBenchmark.p
% 1.62/2.11 % SZS status Theorem for theBenchmark.p
% 1.62/2.11 % SZS output start CNFRefutation
% See solution above
% 1.71/2.11 % Total time : 1.393s
%------------------------------------------------------------------------------