%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM539+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 : n029.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 04:57:44 PM UTC 2026
% Result : Theorem 1.32s 1.73s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 38 ( 14 unt; 0 def)
% Number of atoms : 129 ( 35 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 155 ( 64 ~; 63 |; 19 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 47 ( 1 sgn 22 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(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(m__1779,hypothesis,
( aSubsetOf0(xS,szNzAzT0)
& aSubsetOf0(xT,szNzAzT0)
& xS != slcrc0
& xT != slcrc0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1779) ).
fof(mNATSet,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
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(m__1802,hypothesis,
( aElementOf0(szmzizndt0(xS),xT)
& aElementOf0(szmzizndt0(xT),xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1802) ).
fof(m__,conjecture,
szmzizndt0(xS) = szmzizndt0(xT),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(c_0_8,plain,
! [X96,X97,X98,X99] :
( ( aSet0(X97)
| ~ aSubsetOf0(X97,X96)
| ~ aSet0(X96) )
& ( ~ aElementOf0(X98,X97)
| aElementOf0(X98,X96)
| ~ aSubsetOf0(X97,X96)
| ~ aSet0(X96) )
& ( aElementOf0(esk2_2(X96,X99),X99)
| ~ aSet0(X99)
| aSubsetOf0(X99,X96)
| ~ aSet0(X96) )
& ( ~ aElementOf0(esk2_2(X96,X99),X96)
| ~ aSet0(X99)
| aSubsetOf0(X99,X96)
| ~ aSet0(X96) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefSub])])])])])]) ).
fof(c_0_9,plain,
! [X167,X168,X169,X170] :
( ( aElementOf0(X168,X167)
| X168 != szmzizndt0(X167)
| ~ aSubsetOf0(X167,szNzAzT0)
| X167 = slcrc0 )
& ( ~ aElementOf0(X169,X167)
| sdtlseqdt0(X168,X169)
| X168 != szmzizndt0(X167)
| ~ aSubsetOf0(X167,szNzAzT0)
| X167 = slcrc0 )
& ( aElementOf0(esk7_2(X167,X170),X167)
| ~ aElementOf0(X170,X167)
| X170 = szmzizndt0(X167)
| ~ aSubsetOf0(X167,szNzAzT0)
| X167 = slcrc0 )
& ( ~ sdtlseqdt0(X170,esk7_2(X167,X170))
| ~ aElementOf0(X170,X167)
| X170 = szmzizndt0(X167)
| ~ aSubsetOf0(X167,szNzAzT0)
| X167 = 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_10,plain,
! [X90,X91,X92] :
( ( aSet0(X90)
| X90 != slcrc0 )
& ( ~ aElementOf0(X91,X90)
| X90 != slcrc0 )
& ( ~ aSet0(X92)
| aElementOf0(esk1_1(X92),X92)
| X92 = 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_11,plain,
( aElementOf0(X1,X3)
| ~ aElementOf0(X1,X2)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,hypothesis,
aSubsetOf0(xT,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__1779]) ).
cnf(c_0_13,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
cnf(c_0_14,plain,
( sdtlseqdt0(X3,X1)
| X2 = slcrc0
| ~ aElementOf0(X1,X2)
| X3 != szmzizndt0(X2)
| ~ aSubsetOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( ~ aElementOf0(X1,X2)
| X2 != slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( aElementOf0(X1,X2)
| X2 = slcrc0
| X1 != szmzizndt0(X2)
| ~ aSubsetOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,hypothesis,
xT != slcrc0,
inference(split_conjunct,[status(thm)],[m__1779]) ).
fof(c_0_18,plain,
! [X147,X148] :
( ~ aElementOf0(X147,szNzAzT0)
| ~ aElementOf0(X148,szNzAzT0)
| ~ sdtlseqdt0(X147,X148)
| ~ sdtlseqdt0(X148,X147)
| X147 = X148 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessASymm])]) ).
cnf(c_0_19,hypothesis,
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,xT) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
cnf(c_0_20,hypothesis,
aElementOf0(szmzizndt0(xS),xT),
inference(split_conjunct,[status(thm)],[m__1802]) ).
cnf(c_0_21,plain,
( sdtlseqdt0(X1,X2)
| X1 != szmzizndt0(X3)
| ~ aSubsetOf0(X3,szNzAzT0)
| ~ aElementOf0(X2,X3) ),
inference(csr,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,hypothesis,
aSubsetOf0(xS,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__1779]) ).
cnf(c_0_23,hypothesis,
( aElementOf0(X1,xT)
| X1 != szmzizndt0(xT) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_12]),c_0_17]) ).
cnf(c_0_24,plain,
( X1 = X2
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,hypothesis,
aElementOf0(szmzizndt0(xS),szNzAzT0),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,hypothesis,
( sdtlseqdt0(X1,X2)
| X1 != szmzizndt0(xS)
| ~ aElementOf0(X2,xS) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,hypothesis,
aElementOf0(szmzizndt0(xT),xS),
inference(split_conjunct,[status(thm)],[m__1802]) ).
cnf(c_0_28,hypothesis,
aElementOf0(szmzizndt0(xT),xT),
inference(er,[status(thm)],[c_0_23]) ).
fof(c_0_29,negated_conjecture,
szmzizndt0(xS) != szmzizndt0(xT),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_30,hypothesis,
( X1 = szmzizndt0(xS)
| ~ sdtlseqdt0(szmzizndt0(xS),X1)
| ~ sdtlseqdt0(X1,szmzizndt0(xS))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,hypothesis,
( sdtlseqdt0(X1,szmzizndt0(xT))
| X1 != szmzizndt0(xS) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,hypothesis,
aElementOf0(szmzizndt0(xT),szNzAzT0),
inference(spm,[status(thm)],[c_0_19,c_0_28]) ).
cnf(c_0_33,negated_conjecture,
szmzizndt0(xS) != szmzizndt0(xT),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_34,hypothesis,
( sdtlseqdt0(X1,X2)
| X1 != szmzizndt0(xT)
| ~ aElementOf0(X2,xT) ),
inference(spm,[status(thm)],[c_0_21,c_0_12]) ).
cnf(c_0_35,hypothesis,
~ sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]),c_0_33]) ).
cnf(c_0_36,hypothesis,
( sdtlseqdt0(X1,szmzizndt0(xS))
| X1 != szmzizndt0(xT) ),
inference(spm,[status(thm)],[c_0_34,c_0_20]) ).
cnf(c_0_37,hypothesis,
$false,
inference(spm,[status(thm)],[c_0_35,c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM539+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n029.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 00:44:14 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.32/1.73 % Version : CSE_E---1.7
% 1.32/1.73 % Problem : theBenchmark.p
% 1.32/1.73 % SZS status Theorem for theBenchmark.p
% 1.32/1.73 % SZS output start CNFRefutation
% See solution above
% 1.32/1.73 % Total time : 1.373s
%------------------------------------------------------------------------------