TSTP Solution File: NUM541+2 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM541+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 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 : Thu Aug 31 10:38:33 EDT 2023
% Result : Theorem 0.20s 0.67s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 46
% Syntax : Number of formulae : 122 ( 12 unt; 29 typ; 0 def)
% Number of atoms : 387 ( 90 equ)
% Maximal formula atoms : 50 ( 4 avg)
% Number of connectives : 475 ( 181 ~; 215 |; 55 &)
% ( 5 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 39 ( 24 >; 15 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 5 con; 0-3 aty)
% Number of variables : 111 ( 1 sgn; 49 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
aSet0: $i > $o ).
tff(decl_23,type,
aElement0: $i > $o ).
tff(decl_24,type,
aElementOf0: ( $i * $i ) > $o ).
tff(decl_25,type,
isFinite0: $i > $o ).
tff(decl_26,type,
slcrc0: $i ).
tff(decl_27,type,
isCountable0: $i > $o ).
tff(decl_28,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(decl_29,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(decl_30,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(decl_31,type,
szNzAzT0: $i ).
tff(decl_32,type,
sz00: $i ).
tff(decl_33,type,
szszuzczcdt0: $i > $i ).
tff(decl_34,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(decl_35,type,
iLess0: ( $i * $i ) > $o ).
tff(decl_36,type,
sbrdtbr0: $i > $i ).
tff(decl_37,type,
szmzizndt0: $i > $i ).
tff(decl_38,type,
szmzazxdt0: $i > $i ).
tff(decl_39,type,
slbdtrb0: $i > $i ).
tff(decl_40,type,
xm: $i ).
tff(decl_41,type,
xn: $i ).
tff(decl_42,type,
esk1_1: $i > $i ).
tff(decl_43,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_44,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
esk5_1: $i > $i ).
tff(decl_47,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_48,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk9_2: ( $i * $i ) > $i ).
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(mSubRefl,axiom,
! [X1] :
( aSet0(X1)
=> aSubsetOf0(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubRefl) ).
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/sandbox/benchmark/theBenchmark.p',m__) ).
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(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(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(m__1936,hypothesis,
( aElementOf0(xm,szNzAzT0)
& aElementOf0(xn,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1936) ).
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(mSuccNum,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(X1),szNzAzT0)
& szszuzczcdt0(X1) != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNum) ).
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(mLessSucc,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> sdtlseqdt0(X1,szszuzczcdt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessSucc) ).
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(mLessRefl,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> sdtlseqdt0(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessRefl) ).
fof(c_0_17,plain,
! [X84,X85,X86,X87] :
( ( aElementOf0(X85,X84)
| X85 != szmzizndt0(X84)
| ~ aSubsetOf0(X84,szNzAzT0)
| X84 = slcrc0 )
& ( ~ aElementOf0(X86,X84)
| sdtlseqdt0(X85,X86)
| X85 != szmzizndt0(X84)
| ~ aSubsetOf0(X84,szNzAzT0)
| X84 = slcrc0 )
& ( aElementOf0(esk7_2(X84,X87),X84)
| ~ aElementOf0(X87,X84)
| X87 = szmzizndt0(X84)
| ~ aSubsetOf0(X84,szNzAzT0)
| X84 = slcrc0 )
& ( ~ sdtlseqdt0(X87,esk7_2(X84,X87))
| ~ aElementOf0(X87,X84)
| X87 = szmzizndt0(X84)
| ~ aSubsetOf0(X84,szNzAzT0)
| X84 = 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_18,plain,
! [X7,X8,X9] :
( ( aSet0(X7)
| X7 != slcrc0 )
& ( ~ aElementOf0(X8,X7)
| X7 != slcrc0 )
& ( ~ aSet0(X9)
| aElementOf0(esk1_1(X9),X9)
| X9 = 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_19,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_17]) ).
cnf(c_0_20,plain,
( ~ aElementOf0(X1,X2)
| X2 != slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_21,plain,
! [X20] :
( ~ aSet0(X20)
| aSubsetOf0(X20,X20) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubRefl])]) ).
fof(c_0_22,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__]) ).
fof(c_0_23,plain,
! [X69,X70] :
( ~ aElementOf0(X69,szNzAzT0)
| ~ aElementOf0(X70,szNzAzT0)
| sdtlseqdt0(X69,X70)
| sdtlseqdt0(szszuzczcdt0(X70),X69) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessTotal])]) ).
cnf(c_0_24,plain,
( sdtlseqdt0(X3,X1)
| X2 = slcrc0
| ~ aElementOf0(X1,X2)
| X3 != szmzizndt0(X2)
| ~ aSubsetOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,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_17]) ).
fof(c_0_26,plain,
! [X58] :
( ~ aElementOf0(X58,szNzAzT0)
| sdtlseqdt0(sz00,X58) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroLess])]) ).
cnf(c_0_27,plain,
( X1 = szmzizndt0(X2)
| aElementOf0(esk7_2(X2,X1),X2)
| ~ aSubsetOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,X2) ),
inference(csr,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_28,plain,
( aSubsetOf0(X1,X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
fof(c_0_30,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_22])]) ).
fof(c_0_31,plain,
! [X60,X61] :
( ( ~ sdtlseqdt0(X60,X61)
| sdtlseqdt0(szszuzczcdt0(X60),szszuzczcdt0(X61))
| ~ aElementOf0(X60,szNzAzT0)
| ~ aElementOf0(X61,szNzAzT0) )
& ( ~ sdtlseqdt0(szszuzczcdt0(X60),szszuzczcdt0(X61))
| sdtlseqdt0(X60,X61)
| ~ aElementOf0(X60,szNzAzT0)
| ~ aElementOf0(X61,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSuccLess])])]) ).
cnf(c_0_32,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(szszuzczcdt0(X2),X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,hypothesis,
aElementOf0(xm,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__1936]) ).
cnf(c_0_34,plain,
( sdtlseqdt0(X1,X2)
| X1 != szmzizndt0(X3)
| ~ aSubsetOf0(X3,szNzAzT0)
| ~ aElementOf0(X2,X3) ),
inference(csr,[status(thm)],[c_0_24,c_0_20]) ).
cnf(c_0_35,plain,
( X1 = szmzizndt0(X2)
| ~ sdtlseqdt0(X1,esk7_2(X2,X1))
| ~ aSubsetOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,X2) ),
inference(csr,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_36,plain,
( sdtlseqdt0(sz00,X1)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_37,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_27,c_0_28]),c_0_29])]) ).
cnf(c_0_38,plain,
aElementOf0(sz00,szNzAzT0),
inference(split_conjunct,[status(thm)],[mZeroNum]) ).
fof(c_0_39,plain,
! [X64,X65] :
( ~ aElementOf0(X64,szNzAzT0)
| ~ aElementOf0(X65,szNzAzT0)
| ~ sdtlseqdt0(X64,X65)
| ~ sdtlseqdt0(X65,X64)
| X64 = X65 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessASymm])]) ).
cnf(c_0_40,negated_conjecture,
( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| ~ sdtlseqdt0(szszuzczcdt0(xm),xn) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_41,plain,
( sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_42,hypothesis,
aElementOf0(xn,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__1936]) ).
cnf(c_0_43,hypothesis,
( sdtlseqdt0(szszuzczcdt0(xm),X1)
| sdtlseqdt0(X1,xm)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_44,plain,
( sdtlseqdt0(X1,X2)
| X1 != szmzizndt0(szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_28]),c_0_29])]) ).
cnf(c_0_45,plain,
( szmzizndt0(X1) = sz00
| ~ aSubsetOf0(X1,szNzAzT0)
| ~ aElementOf0(esk7_2(X1,sz00),szNzAzT0)
| ~ aElementOf0(sz00,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_46,plain,
( szmzizndt0(szNzAzT0) = sz00
| aElementOf0(esk7_2(szNzAzT0,sz00),szNzAzT0) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_47,plain,
( X1 = X2
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_48,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_40,c_0_41]),c_0_42]),c_0_33])]) ).
cnf(c_0_49,hypothesis,
( sdtlseqdt0(szszuzczcdt0(xm),xn)
| sdtlseqdt0(xn,xm) ),
inference(spm,[status(thm)],[c_0_43,c_0_42]) ).
cnf(c_0_50,negated_conjecture,
( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| xm != xn ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_51,hypothesis,
( sdtlseqdt0(X1,xn)
| X1 != szmzizndt0(szNzAzT0) ),
inference(spm,[status(thm)],[c_0_44,c_0_42]) ).
cnf(c_0_52,plain,
( szmzizndt0(szNzAzT0) = sz00
| ~ aSubsetOf0(szNzAzT0,szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_38])]) ).
fof(c_0_53,plain,
! [X66,X67,X68] :
( ~ aElementOf0(X66,szNzAzT0)
| ~ aElementOf0(X67,szNzAzT0)
| ~ aElementOf0(X68,szNzAzT0)
| ~ sdtlseqdt0(X66,X67)
| ~ sdtlseqdt0(X67,X68)
| sdtlseqdt0(X66,X68) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessTrans])]) ).
fof(c_0_54,plain,
! [X52] :
( ( aElementOf0(szszuzczcdt0(X52),szNzAzT0)
| ~ aElementOf0(X52,szNzAzT0) )
& ( szszuzczcdt0(X52) != sz00
| ~ aElementOf0(X52,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSuccNum])])]) ).
fof(c_0_55,plain,
! [X55] :
( ( aElementOf0(esk5_1(X55),szNzAzT0)
| X55 = sz00
| ~ aElementOf0(X55,szNzAzT0) )
& ( X55 = szszuzczcdt0(esk5_1(X55))
| X55 = sz00
| ~ aElementOf0(X55,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mNatExtra])])])]) ).
cnf(c_0_56,hypothesis,
( X1 = xn
| ~ sdtlseqdt0(xn,X1)
| ~ sdtlseqdt0(X1,xn)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_47,c_0_42]) ).
cnf(c_0_57,negated_conjecture,
( sdtlseqdt0(xn,xm)
| ~ sdtlseqdt0(xm,xn) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_58,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_50,c_0_41]),c_0_42]),c_0_33])]) ).
cnf(c_0_59,hypothesis,
( sdtlseqdt0(X1,xn)
| X1 != sz00
| ~ aSubsetOf0(szNzAzT0,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_60,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_53]) ).
cnf(c_0_61,plain,
( aElementOf0(szszuzczcdt0(X1),szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
fof(c_0_62,plain,
! [X62] :
( ~ aElementOf0(X62,szNzAzT0)
| sdtlseqdt0(X62,szszuzczcdt0(X62)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessSucc])]) ).
fof(c_0_63,plain,
! [X96,X97,X98,X99,X100] :
( ( aSet0(X97)
| X97 != slbdtrb0(X96)
| ~ aElementOf0(X96,szNzAzT0) )
& ( aElementOf0(X98,szNzAzT0)
| ~ aElementOf0(X98,X97)
| X97 != slbdtrb0(X96)
| ~ aElementOf0(X96,szNzAzT0) )
& ( sdtlseqdt0(szszuzczcdt0(X98),X96)
| ~ aElementOf0(X98,X97)
| X97 != slbdtrb0(X96)
| ~ aElementOf0(X96,szNzAzT0) )
& ( ~ aElementOf0(X99,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X99),X96)
| aElementOf0(X99,X97)
| X97 != slbdtrb0(X96)
| ~ aElementOf0(X96,szNzAzT0) )
& ( ~ aElementOf0(esk9_2(X96,X100),X100)
| ~ aElementOf0(esk9_2(X96,X100),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(esk9_2(X96,X100)),X96)
| ~ aSet0(X100)
| X100 = slbdtrb0(X96)
| ~ aElementOf0(X96,szNzAzT0) )
& ( aElementOf0(esk9_2(X96,X100),szNzAzT0)
| aElementOf0(esk9_2(X96,X100),X100)
| ~ aSet0(X100)
| X100 = slbdtrb0(X96)
| ~ aElementOf0(X96,szNzAzT0) )
& ( sdtlseqdt0(szszuzczcdt0(esk9_2(X96,X100)),X96)
| aElementOf0(esk9_2(X96,X100),X100)
| ~ aSet0(X100)
| X100 = slbdtrb0(X96)
| ~ aElementOf0(X96,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_64,plain,
( X1 = szszuzczcdt0(esk5_1(X1))
| X1 = sz00
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_65,hypothesis,
~ sdtlseqdt0(xm,xn),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_33])]),c_0_58]) ).
cnf(c_0_66,hypothesis,
( sdtlseqdt0(X1,xn)
| X1 != sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_28]),c_0_29])]) ).
fof(c_0_67,plain,
! [X63] :
( ~ aElementOf0(X63,szNzAzT0)
| sdtlseqdt0(X63,X63) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessRefl])]) ).
cnf(c_0_68,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_60,c_0_61]) ).
cnf(c_0_69,plain,
( sdtlseqdt0(X1,szszuzczcdt0(X1))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_70,plain,
( sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(X2))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_71,negated_conjecture,
( sdtlseqdt0(szszuzczcdt0(xm),xn)
| xm = xn
| sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_72,plain,
( sdtlseqdt0(szszuzczcdt0(X1),X2)
| ~ aElementOf0(X1,X3)
| X3 != slbdtrb0(X2)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_73,hypothesis,
( szszuzczcdt0(esk5_1(xm)) = xm
| sz00 = xm ),
inference(spm,[status(thm)],[c_0_64,c_0_33]) ).
cnf(c_0_74,hypothesis,
sz00 != xm,
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_75,plain,
( aElementOf0(X1,X3)
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X1),X2)
| X3 != slbdtrb0(X2)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_76,plain,
( sdtlseqdt0(X1,X1)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_77,plain,
( aElementOf0(esk5_1(X1),szNzAzT0)
| X1 = sz00
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_78,plain,
( sdtlseqdt0(X1,szszuzczcdt0(X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_79,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_70,c_0_71]),c_0_42]),c_0_33])]) ).
cnf(c_0_80,hypothesis,
( sdtlseqdt0(szszuzczcdt0(X1),xn)
| X2 != slbdtrb0(xn)
| ~ aElementOf0(X1,X2) ),
inference(spm,[status(thm)],[c_0_72,c_0_42]) ).
cnf(c_0_81,hypothesis,
szszuzczcdt0(esk5_1(xm)) = xm,
inference(sr,[status(thm)],[c_0_73,c_0_74]) ).
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_75,c_0_76]),c_0_61]) ).
cnf(c_0_83,hypothesis,
( sz00 = xm
| aElementOf0(esk5_1(xm),szNzAzT0) ),
inference(spm,[status(thm)],[c_0_77,c_0_33]) ).
cnf(c_0_84,negated_conjecture,
( ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_78]),c_0_42])]) ).
cnf(c_0_85,negated_conjecture,
( xn = xm
| sdtlseqdt0(szszuzczcdt0(xm),xn) ),
inference(sr,[status(thm)],[c_0_79,c_0_65]) ).
cnf(c_0_86,hypothesis,
( X1 != slbdtrb0(xn)
| ~ aElementOf0(esk5_1(xm),X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_65]) ).
cnf(c_0_87,plain,
( aElementOf0(X1,slbdtrb0(szszuzczcdt0(X1)))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(er,[status(thm)],[c_0_82]) ).
cnf(c_0_88,hypothesis,
aElementOf0(esk5_1(xm),szNzAzT0),
inference(sr,[status(thm)],[c_0_83,c_0_74]) ).
cnf(c_0_89,negated_conjecture,
( xn = xm
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_90,hypothesis,
slbdtrb0(xn) != slbdtrb0(xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_81]),c_0_88])]) ).
cnf(c_0_91,negated_conjecture,
xn = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_61]),c_0_33])]) ).
cnf(c_0_92,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_91])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM541+2 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 17:40:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.67 % Version : CSE_E---1.5
% 0.20/0.67 % Problem : theBenchmark.p
% 0.20/0.67 % Proof found
% 0.20/0.67 % SZS status Theorem for theBenchmark.p
% 0.20/0.67 % SZS output start Proof
% See solution above
% 0.20/0.69 % Total time : 0.095000 s
% 0.20/0.69 % SZS output end Proof
% 0.20/0.69 % Total time : 0.100000 s
%------------------------------------------------------------------------------