%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU557^1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:24:30 AM UTC 2026
% Result : Theorem 0.07s 0.28s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 371 ( 32 equ; 0 cnn)
% Maximal formula atoms : 86 ( 12 avg)
% Number of connectives : 494 ( 25 ~; 24 |; 86 &; 113 @)
% ( 5 <=>; 241 =>; 0 <=; 0 <~>)
% Maximal formula depth : 87 ( 15 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 82 ( 80 usr; 76 con; 0-2 aty)
% Number of variables : 62 ( 16 ^; 40 !; 6 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_24,type,
exu: ( $i > $o ) > $o ).
thf(decl_25,type,
setextAx: $o ).
thf(decl_27,type,
emptysetAx: $o ).
thf(decl_29,type,
setadjoinAx: $o ).
thf(decl_31,type,
powersetAx: $o ).
thf(decl_33,type,
setunionAx: $o ).
thf(decl_35,type,
omega0Ax: $o ).
thf(decl_36,type,
omegaSAx: $o ).
thf(decl_37,type,
omegaIndAx: $o ).
thf(decl_38,type,
replAx: $o ).
thf(decl_39,type,
foundationAx: $o ).
thf(decl_40,type,
wellorderingAx: $o ).
thf(decl_41,type,
descr: ( $i > $o ) > $i ).
thf(decl_42,type,
descrp: $o ).
thf(decl_44,type,
dsetconstrI: $o ).
thf(decl_45,type,
dsetconstrEL: $o ).
thf(decl_46,type,
dsetconstrER: $o ).
thf(decl_47,type,
exuE1: $o ).
thf(decl_49,type,
prop2setE: $o ).
thf(decl_50,type,
emptysetE: $o ).
thf(decl_51,type,
emptysetimpfalse: $o ).
thf(decl_52,type,
notinemptyset: $o ).
thf(decl_53,type,
exuE3e: $o ).
thf(decl_54,type,
setext: $o ).
thf(decl_55,type,
emptyI: $o ).
thf(decl_56,type,
noeltsimpempty: $o ).
thf(decl_57,type,
setbeta: $o ).
thf(decl_59,type,
nonemptyE1: $o ).
thf(decl_60,type,
nonemptyI: $o ).
thf(decl_61,type,
nonemptyI1: $o ).
thf(decl_62,type,
setadjoinIL: $o ).
thf(decl_63,type,
emptyinunitempty: $o ).
thf(decl_64,type,
setadjoinIR: $o ).
thf(decl_65,type,
setadjoinE: $o ).
thf(decl_66,type,
setadjoinOr: $o ).
thf(decl_67,type,
setoftrueEq: $o ).
thf(decl_68,type,
powersetI: $o ).
thf(decl_69,type,
emptyinPowerset: $o ).
thf(decl_70,type,
emptyInPowerset: $o ).
thf(decl_71,type,
powersetE: $o ).
thf(decl_72,type,
setunionI: $o ).
thf(decl_73,type,
setunionE: $o ).
thf(decl_74,type,
subPowSU: $o ).
thf(decl_75,type,
exuE2: $o ).
thf(decl_76,type,
nonemptyImpWitness: $o ).
thf(decl_77,type,
uniqinunit: $o ).
thf(decl_78,type,
notinsingleton: $o ).
thf(decl_79,type,
eqinunit: $o ).
thf(decl_80,type,
singletonsswitch: $o ).
thf(decl_81,type,
upairsetE: $o ).
thf(decl_82,type,
upairsetIL: $o ).
thf(decl_83,type,
upairsetIR: $o ).
thf(decl_84,type,
emptyE1: $o ).
thf(decl_85,type,
vacuousDall: $o ).
thf(decl_86,type,
quantDeMorgan1: $o ).
thf(decl_87,type,
quantDeMorgan2: $o ).
thf(decl_88,type,
quantDeMorgan3: $o ).
thf(decl_89,type,
quantDeMorgan4: $o ).
thf(decl_90,type,
prop2setI: $o ).
thf(decl_92,type,
prop2set2propI: $o ).
thf(decl_93,type,
notdexE: $o ).
thf(decl_94,type,
notdallE: $o ).
thf(decl_95,type,
exuI1: $o ).
thf(decl_96,type,
exuI3: $o ).
thf(decl_97,type,
exuI2: $o ).
thf(decl_98,type,
inCongP: $o ).
thf(decl_99,type,
in__Cong: $o ).
thf(decl_100,type,
exuE3u: $o ).
thf(decl_101,type,
exu__Cong: $o ).
thf(decl_102,type,
emptyset__Cong: $o ).
thf(decl_103,type,
setadjoin__Cong: $o ).
thf(decl_104,type,
powerset__Cong: $o ).
thf(decl_105,type,
setunion__Cong: $o ).
thf(decl_106,type,
omega__Cong: $o ).
thf(decl_107,type,
exuEu: $o ).
thf(decl_108,type,
esk1_2: ( $i > $o ) > $i > $i ).
thf(decl_109,type,
epred1_0: $i > $o ).
thf(decl_110,type,
epred2_0: $i > $o ).
thf(decl_111,type,
esk2_0: $i ).
thf(decl_112,type,
esk3_0: $i ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.t5JL4nnguh/E---3.1_1319401.p',descrp) ).
thf(exu,axiom,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.t5JL4nnguh/E---3.1_1319401.p',exu) ).
thf(descr__Cong,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.t5JL4nnguh/E---3.1_1319401.p',descr__Cong) ).
thf(c_0_3,plain,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[descrp]) ).
thf(c_0_4,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_5,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[descr__Cong]) ).
thf(c_0_6,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X24: $i] :
( ( X1 @ X24 )
& ! [X25: $i] :
( ( X1 @ X25 )
=> ( X24 = X25 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_3,c_0_4]) ).
thf(c_0_7,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( ! [X26: $i > $o] :
( ? [X27: $i] :
( ( X26 @ X27 )
& ! [X28: $i] :
( ( X26 @ X28 )
=> ( X27 = X28 ) ) )
=> ( X26
@ ( descr
@ ^ [Z0: $i] : ( X26 @ Z0 ) ) ) )
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X29: $i] :
( ( X1 @ X29 )
& ! [X30: $i] :
( ( X1 @ X30 )
=> ( X29 = X30 ) ) )
=> ( ? [X31: $i] :
( ( X17 @ X31 )
& ! [X32: $i] :
( ( X17 @ X32 )
=> ( X31 = X32 ) ) )
=> ( ( descr @ X1 )
= ( descr @ X17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_5]),c_0_4]),c_0_6])]) ).
thf(c_0_8,negated_conjecture,
! [X33: $i > $o,X34: $i,X38: $i,X39: $i,X41: $i,X43: $i] :
( setextAx
& emptysetAx
& setadjoinAx
& powersetAx
& setunionAx
& omega0Ax
& omegaSAx
& omegaIndAx
& replAx
& foundationAx
& wellorderingAx
& ( ( X33 @ ( esk1_2 @ X33 @ X34 ) )
| ~ ( X33 @ X34 )
| ( X33 @ ( descr @ X33 ) ) )
& ( ( X34
!= ( esk1_2 @ X33 @ X34 ) )
| ~ ( X33 @ X34 )
| ( X33 @ ( descr @ X33 ) ) )
& dsetconstrI
& dsetconstrEL
& dsetconstrER
& exuE1
& prop2setE
& emptysetE
& emptysetimpfalse
& notinemptyset
& exuE3e
& setext
& emptyI
& noeltsimpempty
& setbeta
& nonemptyE1
& nonemptyI
& nonemptyI1
& setadjoinIL
& emptyinunitempty
& setadjoinIR
& setadjoinE
& setadjoinOr
& setoftrueEq
& powersetI
& emptyinPowerset
& emptyInPowerset
& powersetE
& setunionI
& setunionE
& subPowSU
& exuE2
& nonemptyImpWitness
& uniqinunit
& notinsingleton
& eqinunit
& singletonsswitch
& upairsetE
& upairsetIL
& upairsetIR
& emptyE1
& vacuousDall
& quantDeMorgan1
& quantDeMorgan2
& quantDeMorgan3
& quantDeMorgan4
& prop2setI
& prop2set2propI
& notdexE
& notdallE
& exuI1
& exuI3
& exuI2
& inCongP
& in__Cong
& exuE3u
& exu__Cong
& emptyset__Cong
& setadjoin__Cong
& powerset__Cong
& setunion__Cong
& omega__Cong
& exuEu
& ( ~ ( epred1_0 @ X38 )
| ( epred2_0 @ X39 )
| ( X38 != X39 ) )
& ( ~ ( epred2_0 @ X39 )
| ( epred1_0 @ X38 )
| ( X38 != X39 ) )
& ( epred1_0 @ esk2_0 )
& ( ~ ( epred1_0 @ X41 )
| ( esk2_0 = X41 ) )
& ( epred2_0 @ esk3_0 )
& ( ~ ( epred2_0 @ X43 )
| ( esk3_0 = X43 ) )
& ( ( descr @ epred1_0 )
!= ( descr @ epred2_0 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])])]) ).
thf(c_0_9,negated_conjecture,
! [X3: $i,X2: $i] :
( ( epred1_0 @ X3 )
| ~ ( epred2_0 @ X2 )
| ( X3 != X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_10,negated_conjecture,
! [X2: $i] :
( ( epred1_0 @ X2 )
| ~ ( epred2_0 @ X2 ) ),
inference(er,[status(thm)],[c_0_9]) ).
thf(c_0_11,negated_conjecture,
epred2_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,negated_conjecture,
! [X2: $i] :
( ( esk2_0 = X2 )
| ~ ( epred1_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,negated_conjecture,
epred1_0 @ esk3_0,
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_14,negated_conjecture,
! [X2: $i] :
( ( esk3_0 = X2 )
| ~ ( epred2_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_15,negated_conjecture,
esk3_0 = esk2_0,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_16,negated_conjecture,
! [X2: $i] :
( ( esk2_0 = X2 )
| ~ ( epred2_0 @ X2 ) ),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i > $o,X2: $i] :
( ( X1 @ ( esk1_2 @ X1 @ X2 ) )
| ( X1 @ ( descr @ X1 ) )
| ~ ( X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i > $o,X2: $i] :
( ( X1 @ ( descr @ X1 ) )
| ( X2
!= ( esk1_2 @ X1 @ X2 ) )
| ~ ( X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_19,negated_conjecture,
! [X2: $i] :
( ( ( esk1_2 @ epred2_0 @ X2 )
= esk2_0 )
| ( epred2_0 @ ( descr @ epred2_0 ) )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_20,negated_conjecture,
epred2_0 @ esk2_0,
inference(rw,[status(thm)],[c_0_11,c_0_15]) ).
thf(c_0_21,negated_conjecture,
epred2_0 @ ( descr @ epred2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19])]),c_0_20])]) ).
thf(c_0_22,negated_conjecture,
! [X2: $i] :
( ( ( esk1_2 @ epred1_0 @ X2 )
= esk2_0 )
| ( epred1_0 @ ( descr @ epred1_0 ) )
| ~ ( epred1_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
thf(c_0_23,negated_conjecture,
epred1_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_24,negated_conjecture,
( ( descr @ epred1_0 )
!= ( descr @ epred2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_25,negated_conjecture,
( ( descr @ epred2_0 )
= esk2_0 ),
inference(spm,[status(thm)],[c_0_16,c_0_21]) ).
thf(c_0_26,negated_conjecture,
epred1_0 @ ( descr @ epred1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_22])]),c_0_23])]) ).
thf(c_0_27,negated_conjecture,
( ( descr @ epred1_0 )
!= esk2_0 ),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_28,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_26]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU557^1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n002.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:52:37 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.25 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.t5JL4nnguh/E---3.1_1319401.p
% 0.07/0.28 % Version: 3.5.1-ho
% 0.07/0.28 % Preprocessing class: HSMSSLSSLLLCHSA.
% 0.07/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.28 % Starting new_ho_9 with 1500s (5) cores
% 0.07/0.28 % Starting post_as_ho9 with 300s (1) cores
% 0.07/0.28 % Starting sh2lt with 300s (1) cores
% 0.07/0.28 % Starting full_lambda_10 with 300s (1) cores
% 0.07/0.28 % full_lambda_10 with pid 1319427 completed with status 0
% 0.07/0.28 % Result found by full_lambda_10
% 0.07/0.28 % Preprocessing class: HSMSSLSSLLLCHSA.
% 0.07/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.28 % Starting new_ho_9 with 1500s (5) cores
% 0.07/0.28 % Starting post_as_ho9 with 300s (1) cores
% 0.07/0.28 % Starting sh2lt with 300s (1) cores
% 0.07/0.28 % Starting full_lambda_10 with 300s (1) cores
% 0.07/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,5,20000,3.0,true))
% 0.07/0.28 % SinE strategy is GSinE(CountFormulas,hypos,5,,5,20000,3.0,true)
% 0.07/0.28 % Search class: HGUSF-FFSM21-SHSMMFBN
% 0.07/0.28 % partial match(4): HGHSF-FFMM21-SHSFFFBN
% 0.07/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.28 % SubtermCWHack with pid 1319429 completed with status 0
% 0.07/0.28 % Result found by SubtermCWHack
% 0.07/0.28 % Preprocessing class: HSMSSLSSLLLCHSA.
% 0.07/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.28 % Starting new_ho_9 with 1500s (5) cores
% 0.07/0.28 % Starting post_as_ho9 with 300s (1) cores
% 0.07/0.28 % Starting sh2lt with 300s (1) cores
% 0.07/0.28 % Starting full_lambda_10 with 300s (1) cores
% 0.07/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,5,20000,3.0,true))
% 0.07/0.28 % SinE strategy is GSinE(CountFormulas,hypos,5,,5,20000,3.0,true)
% 0.07/0.28 % Search class: HGUSF-FFSM21-SHSMMFBN
% 0.07/0.28 % partial match(4): HGHSF-FFMM21-SHSFFFBN
% 0.07/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.28 % Preprocessing time : 0.002 s
% 0.07/0.28
% 0.07/0.28 % Proof found!
% 0.07/0.28 % SZS status Theorem
% 0.07/0.28 % SZS output start CNFRefutation
% See solution above
% 0.07/0.28 % Parsed axioms : 161
% 0.07/0.28 % Removed by relevancy pruning/SinE : 158
% 0.07/0.28 % Initial clauses : 81
% 0.07/0.28 % Removed in clause preprocessing : 0
% 0.07/0.28 % Initial clauses in saturation : 81
% 0.07/0.28 % Processed clauses : 96
% 0.07/0.28 % ...of these trivial : 0
% 0.07/0.28 % ...subsumed : 1
% 0.07/0.28 % ...remaining for further processing : 95
% 0.07/0.28 % Other redundant clauses eliminated : 4
% 0.07/0.28 % Clauses deleted for lack of memory : 0
% 0.07/0.28 % Backward-subsumed : 0
% 0.07/0.28 % Backward-rewritten : 9
% 0.07/0.28 % Generated clauses : 22
% 0.07/0.28 % ...of the previous two non-redundant : 17
% 0.07/0.28 % ...aggressively subsumed : 0
% 0.07/0.28 % Contextual simplify-reflections : 0
% 0.07/0.28 % Paramodulations : 18
% 0.07/0.28 % Factorizations : 0
% 0.07/0.28 % NegExts : 0
% 0.07/0.28 % Equation resolutions : 4
% 0.07/0.28 % Disequality decompositions : 0
% 0.07/0.28 % Total rewrite steps : 18
% 0.07/0.28 % ...of those cached : 12
% 0.07/0.28 % Propositional unsat checks : 0
% 0.07/0.28 % Propositional check models : 0
% 0.07/0.28 % Propositional check unsatisfiable : 0
% 0.07/0.28 % Propositional clauses : 0
% 0.07/0.28 % Propositional clauses after purity: 0
% 0.07/0.28 % Propositional unsat core size : 0
% 0.07/0.28 % Propositional preprocessing time : 0.000
% 0.07/0.28 % Propositional encoding time : 0.000
% 0.07/0.28 % Propositional solver time : 0.000
% 0.07/0.28 % Success case prop preproc time : 0.000
% 0.07/0.28 % Success case prop encoding time : 0.000
% 0.07/0.28 % Success case prop solver time : 0.000
% 0.07/0.28 % Current number of processed clauses : 84
% 0.07/0.28 % Positive orientable unit clauses : 77
% 0.07/0.28 % Positive unorientable unit clauses: 0
% 0.07/0.28 % Negative unit clauses : 1
% 0.07/0.28 % Non-unit-clauses : 6
% 0.07/0.28 % Current number of unprocessed clauses: 1
% 0.07/0.28 % ...number of literals in the above : 3
% 0.07/0.28 % Current number of archived formulas : 0
% 0.07/0.28 % Current number of archived clauses : 9
% 0.07/0.28 % Clause-clause subsumption calls (NU) : 28
% 0.07/0.28 % Rec. Clause-clause subsumption calls : 28
% 0.07/0.28 % Non-unit clause-clause subsumptions : 1
% 0.07/0.28 % Unit Clause-clause subsumption calls : 0
% 0.07/0.28 % Rewrite failures with RHS unbound : 0
% 0.07/0.28 % BW rewrite match attempts : 4
% 0.07/0.28 % BW rewrite match successes : 4
% 0.07/0.28 % Condensation attempts : 0
% 0.07/0.28 % Condensation successes : 0
% 0.07/0.28 % Termbank termtop insertions : 5512
% 0.07/0.28 % Search garbage collected termcells : 2265
% 0.07/0.28
% 0.07/0.28 % -------------------------------------------------
% 0.07/0.28 % User time : 0.008 s
% 0.07/0.28 % System time : 0.003 s
% 0.07/0.28 % Total time : 0.011 s
% 0.07/0.28 % Maximum resident set size: 4308 pages
% 0.07/0.28
% 0.07/0.28 % -------------------------------------------------
% 0.07/0.28 % User time : 0.012 s
% 0.07/0.28 % System time : 0.008 s
% 0.07/0.28 % Total time : 0.020 s
% 0.07/0.28 % Maximum resident set size: 5120 pages
% 0.07/0.28 % E exiting
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