TSTP Solution File: ITP369_1 by E-SAT---3.1.00
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%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : ITP369_1 : TPTP v8.2.0. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n015.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 : Mon May 20 22:21:06 EDT 2024
% Result : Theorem 19.07s 3.22s
% Output : CNFRefutation 19.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 49
% Syntax : Number of formulae : 147 ( 69 unt; 20 typ; 0 def)
% Number of atoms : 216 ( 46 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 159 ( 70 ~; 66 |; 12 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 19 ( 12 >; 7 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-2 aty)
% Number of variables : 185 ( 0 sgn 185 !; 0 ?; 185 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
'A_ltln$': $tType ).
tff(decl_sort2,type,
'A_ltln_set$': $tType ).
tff(decl_sort3,type,
'A_ltln_set_a_ltln_set_fun$': $tType ).
tff(decl_sort4,type,
'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$': $tType ).
tff(decl_23,type,
'restricted_subformulas_inner$': 'A_ltln$' > 'A_ltln_set$' ).
tff(decl_25,type,
'insert$': 'A_ltln$' > 'A_ltln_set_a_ltln_set_fun$' ).
tff(decl_32,type,
'chi_1$': 'A_ltln$' ).
tff(decl_36,type,
'subformulas_nu$': 'A_ltln$' > 'A_ltln_set$' ).
tff(decl_37,type,
'fun_app$a': ( 'A_ltln_set_a_ltln_set_fun$' * 'A_ltln_set$' ) > 'A_ltln_set$' ).
tff(decl_43,type,
'until_ltln$': ( 'A_ltln$' * 'A_ltln$' ) > 'A_ltln$' ).
tff(decl_45,type,
'less_eq$': ( 'A_ltln_set$' * 'A_ltln_set$' ) > $o ).
tff(decl_60,type,
'member$': ( 'A_ltln$' * 'A_ltln_set$' ) > $o ).
tff(decl_65,type,
'fun_app$b': ( 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' * 'A_ltln_set$' ) > 'A_ltln_set_a_ltln_set_fun$' ).
tff(decl_67,type,
'psi$': 'A_ltln$' ).
tff(decl_71,type,
'chi_2$': 'A_ltln$' ).
tff(decl_75,type,
'subformulas_mu$': 'A_ltln$' > 'A_ltln_set$' ).
tff(decl_82,type,
'subfrmlsn$': 'A_ltln$' > 'A_ltln_set$' ).
tff(decl_94,type,
'sup$': 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' ).
tff(decl_105,type,
'strongRelease_ltln$': ( 'A_ltln$' * 'A_ltln$' ) > 'A_ltln$' ).
tff(decl_248,type,
esk131_2: ( 'A_ltln_set$' * 'A_ltln_set$' ) > 'A_ltln$' ).
tff(hypothesis6,hypothesis,
~ 'member$'('psi$','subformulas_nu$'('chi_1$')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis6) ).
tff(hypothesis7,hypothesis,
~ 'member$'('psi$','subformulas_nu$'('chi_2$')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis7) ).
tff(axiom102,axiom,
! [X173: 'A_ltln$',X174: 'A_ltln_set$'] :
( 'member$'(X173,X174)
=> ( 'fun_app$a'('insert$'(X173),X174) = X174 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom102) ).
tff(hypothesis4,hypothesis,
( 'member$'('psi$','subformulas_nu$'('chi_1$'))
| 'member$'('psi$','subformulas_nu$'('chi_2$'))
| 'member$'('psi$','subformulas_mu$'('chi_1$'))
| 'member$'('psi$','subformulas_mu$'('chi_2$')) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis4) ).
tff(conjecture1,conjecture,
( 'less_eq$'('subformulas_nu$'('psi$'),'fun_app$a'('insert$'('strongRelease_ltln$'('chi_1$','chi_2$')),'fun_app$a'('fun_app$b'('sup$','fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_1$')),'subformulas_nu$'('chi_2$'))),'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('chi_1$')),'subformulas_mu$'('chi_2$')))))
& 'less_eq$'('subformulas_mu$'('psi$'),'fun_app$a'('insert$'('strongRelease_ltln$'('chi_1$','chi_2$')),'fun_app$a'('fun_app$b'('sup$','fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_1$')),'subformulas_nu$'('chi_2$'))),'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('chi_1$')),'subformulas_mu$'('chi_2$'))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture1) ).
tff(axiom17,axiom,
! [X9: 'A_ltln$',X10: 'A_ltln_set$',X7: 'A_ltln_set$'] :
( 'less_eq$'('fun_app$a'('insert$'(X9),X10),X7)
<=> ( 'member$'(X9,X7)
& 'less_eq$'(X10,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom17) ).
tff(axiom15,axiom,
! [X1: 'A_ltln_set$',X2: 'A_ltln$',X7: 'A_ltln_set$'] : ( 'fun_app$a'('fun_app$b'('sup$',X1),'fun_app$a'('insert$'(X2),X7)) = 'fun_app$a'('insert$'(X2),'fun_app$a'('fun_app$b'('sup$',X1),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom15) ).
tff(axiom296,axiom,
! [X488: 'A_ltln$',X2: 'A_ltln$'] : ( 'subformulas_nu$'('until_ltln$'(X488,X2)) = 'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'(X488)),'subformulas_nu$'(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom296) ).
tff(axiom88,axiom,
! [X1: 'A_ltln_set$'] : 'less_eq$'(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom88) ).
tff(axiom56,axiom,
! [X1: 'A_ltln_set$',X85: 'A_ltln_set$',X7: 'A_ltln_set$'] : ( 'fun_app$a'('fun_app$b'('sup$',X1),'fun_app$a'('fun_app$b'('sup$',X85),X7)) = 'fun_app$a'('fun_app$b'('sup$',X85),'fun_app$a'('fun_app$b'('sup$',X1),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom56) ).
tff(axiom321,axiom,
! [X1: 'A_ltln_set$',X528: 'A_ltln_set$',X7: 'A_ltln_set$'] :
( ( 'less_eq$'(X1,X528)
& 'less_eq$'(X7,X1) )
=> 'less_eq$'(X7,X528) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom321) ).
tff(axiom13,axiom,
! [X4: 'A_ltln$'] : 'less_eq$'('restricted_subformulas_inner$'(X4),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'(X4)),'subformulas_mu$'(X4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom13) ).
tff(axiom226,axiom,
! [X422: 'A_ltln$'] : 'less_eq$'('fun_app$a'('fun_app$b'('sup$','subformulas_mu$'(X422)),'subformulas_nu$'(X422)),'subfrmlsn$'(X422)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom226) ).
tff(axiom62,axiom,
! [X1: 'A_ltln_set$',X97: 'A_ltln_set$'] : ( 'fun_app$a'('fun_app$b'('sup$',X1),X97) = 'fun_app$a'('fun_app$b'('sup$',X97),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom62) ).
tff(axiom125,axiom,
! [X1: 'A_ltln_set$',X218: 'A_ltln_set$',X7: 'A_ltln_set$'] :
( 'less_eq$'(X1,X218)
=> 'less_eq$'(X1,'fun_app$a'('fun_app$b'('sup$',X218),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom125) ).
tff(axiom89,axiom,
! [X1: 'A_ltln_set$',X149: 'A_ltln_set$'] :
( 'less_eq$'(X1,X149)
<=> ! [X150: 'A_ltln$'] :
( 'member$'(X150,X1)
=> 'member$'(X150,X149) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom89) ).
tff(axiom295,axiom,
! [X487: 'A_ltln$'] : 'less_eq$'('subformulas_mu$'(X487),'subfrmlsn$'(X487)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom295) ).
tff(axiom121,axiom,
! [X1: 'A_ltln_set$',X208: 'A_ltln_set$',X7: 'A_ltln_set$'] :
( 'less_eq$'(X1,X208)
=> 'less_eq$'(X1,'fun_app$a'('fun_app$b'('sup$',X7),X208)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom121) ).
tff(axiom9,axiom,
'member$'('psi$','restricted_subformulas_inner$'('strongRelease_ltln$'('chi_1$','chi_2$'))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom9) ).
tff(axiom26,axiom,
! [X31: 'A_ltln$',X2: 'A_ltln$'] : ( 'subformulas_nu$'('strongRelease_ltln$'(X31,X2)) = 'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'(X31)),'subformulas_nu$'(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom26) ).
tff(axiom292,axiom,
! [X484: 'A_ltln$',X2: 'A_ltln$'] :
( 'member$'(X484,'subfrmlsn$'(X2))
=> 'less_eq$'('subformulas_nu$'(X484),'subformulas_nu$'(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom292) ).
tff(axiom294,axiom,
! [X486: 'A_ltln$',X2: 'A_ltln$'] :
( 'member$'(X486,'subfrmlsn$'(X2))
=> 'less_eq$'('subformulas_mu$'(X486),'subformulas_mu$'(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom294) ).
tff(axiom106,axiom,
! [X182: 'A_ltln$',X183: 'A_ltln_set$'] : 'member$'(X182,'fun_app$a'('insert$'(X182),X183)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom106) ).
tff(axiom16,axiom,
! [X1: 'A_ltln_set$',X8: 'A_ltln_set$',X7: 'A_ltln_set$'] :
( 'less_eq$'('fun_app$a'('fun_app$b'('sup$',X1),X8),X7)
<=> ( 'less_eq$'(X1,X7)
& 'less_eq$'(X8,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom16) ).
tff(axiom145,axiom,
! [X1: 'A_ltln_set$',X253: 'A_ltln_set$'] :
( 'less_eq$'(X1,X253)
<=> ( X253 = 'fun_app$a'('fun_app$b'('sup$',X253),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom145) ).
tff(axiom68,axiom,
! [X1: 'A_ltln_set$',X109: 'A_ltln_set$',X7: 'A_ltln_set$'] : ( 'fun_app$a'('fun_app$b'('sup$','fun_app$a'('fun_app$b'('sup$',X1),X109)),X7) = 'fun_app$a'('fun_app$b'('sup$',X1),'fun_app$a'('fun_app$b'('sup$',X109),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom68) ).
tff(axiom14,axiom,
! [X5: 'A_ltln$',X6: 'A_ltln_set$',X7: 'A_ltln_set$'] : ( 'fun_app$a'('fun_app$b'('sup$','fun_app$a'('insert$'(X5),X6)),X7) = 'fun_app$a'('insert$'(X5),'fun_app$a'('fun_app$b'('sup$',X6),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom14) ).
tff(axiom45,axiom,
! [X1: 'A_ltln_set$'] : ( 'fun_app$a'('fun_app$b'('sup$',X1),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom45) ).
tff(axiom137,axiom,
! [X1: 'A_ltln_set$',X239: 'A_ltln_set$'] : 'less_eq$'(X1,'fun_app$a'('fun_app$b'('sup$',X239),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom137) ).
tff(c_0_29,hypothesis,
~ 'member$'('psi$','subformulas_nu$'('chi_1$')),
inference(fof_simplification,[status(thm)],[hypothesis6]) ).
tff(c_0_30,hypothesis,
~ 'member$'('psi$','subformulas_nu$'('chi_2$')),
inference(fof_simplification,[status(thm)],[hypothesis7]) ).
tff(c_0_31,hypothesis,
~ 'member$'('psi$','subformulas_nu$'('chi_1$')),
inference(fof_nnf,[status(thm)],[c_0_29]) ).
tff(c_0_32,hypothesis,
~ 'member$'('psi$','subformulas_nu$'('chi_2$')),
inference(fof_nnf,[status(thm)],[c_0_30]) ).
tff(c_0_33,plain,
! [X1665: 'A_ltln$',X1666: 'A_ltln_set$'] :
( ~ 'member$'(X1665,X1666)
| ( 'fun_app$a'('insert$'(X1665),X1666) = X1666 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom102])])]) ).
tcf(c_0_34,hypothesis,
( 'member$'('psi$','subformulas_nu$'('chi_1$'))
| 'member$'('psi$','subformulas_nu$'('chi_2$'))
| 'member$'('psi$','subformulas_mu$'('chi_1$'))
| 'member$'('psi$','subformulas_mu$'('chi_2$')) ),
inference(split_conjunct,[status(thm)],[hypothesis4]) ).
tcf(c_0_35,hypothesis,
~ 'member$'('psi$','subformulas_nu$'('chi_1$')),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
tcf(c_0_36,hypothesis,
~ 'member$'('psi$','subformulas_nu$'('chi_2$')),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
tff(c_0_37,negated_conjecture,
~ ( 'less_eq$'('subformulas_nu$'('psi$'),'fun_app$a'('insert$'('strongRelease_ltln$'('chi_1$','chi_2$')),'fun_app$a'('fun_app$b'('sup$','fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_1$')),'subformulas_nu$'('chi_2$'))),'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('chi_1$')),'subformulas_mu$'('chi_2$')))))
& 'less_eq$'('subformulas_mu$'('psi$'),'fun_app$a'('insert$'('strongRelease_ltln$'('chi_1$','chi_2$')),'fun_app$a'('fun_app$b'('sup$','fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_1$')),'subformulas_nu$'('chi_2$'))),'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('chi_1$')),'subformulas_mu$'('chi_2$'))))) ),
inference(assume_negation,[status(cth)],[conjecture1]) ).
tff(c_0_38,plain,
! [X1642: 'A_ltln$',X1643: 'A_ltln_set$',X1644: 'A_ltln_set$'] :
( ( 'member$'(X1642,X1644)
| ~ 'less_eq$'('fun_app$a'('insert$'(X1642),X1643),X1644) )
& ( 'less_eq$'(X1643,X1644)
| ~ 'less_eq$'('fun_app$a'('insert$'(X1642),X1643),X1644) )
& ( ~ 'member$'(X1642,X1644)
| ~ 'less_eq$'(X1643,X1644)
| 'less_eq$'('fun_app$a'('insert$'(X1642),X1643),X1644) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom17])])])]) ).
tcf(c_0_39,plain,
! [X2: 'A_ltln$',X1: 'A_ltln_set$'] :
( ( 'fun_app$a'('insert$'(X2),X1) = X1 )
| ~ 'member$'(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
tcf(c_0_40,hypothesis,
( 'member$'('psi$','subformulas_mu$'('chi_2$'))
| 'member$'('psi$','subformulas_mu$'('chi_1$')) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
tff(c_0_41,negated_conjecture,
( ~ 'less_eq$'('subformulas_nu$'('psi$'),'fun_app$a'('insert$'('strongRelease_ltln$'('chi_1$','chi_2$')),'fun_app$a'('fun_app$b'('sup$','fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_1$')),'subformulas_nu$'('chi_2$'))),'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('chi_1$')),'subformulas_mu$'('chi_2$')))))
| ~ 'less_eq$'('subformulas_mu$'('psi$'),'fun_app$a'('insert$'('strongRelease_ltln$'('chi_1$','chi_2$')),'fun_app$a'('fun_app$b'('sup$','fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_1$')),'subformulas_nu$'('chi_2$'))),'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('chi_1$')),'subformulas_mu$'('chi_2$'))))) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])]) ).
tff(c_0_42,plain,
! [X1639: 'A_ltln_set$',X1640: 'A_ltln$',X1641: 'A_ltln_set$'] : ( 'fun_app$a'('fun_app$b'('sup$',X1639),'fun_app$a'('insert$'(X1640),X1641)) = 'fun_app$a'('insert$'(X1640),'fun_app$a'('fun_app$b'('sup$',X1639),X1641)) ),
inference(variable_rename,[status(thm)],[axiom15]) ).
tff(c_0_43,plain,
! [X1620: 'A_ltln$',X1621: 'A_ltln$'] : ( 'subformulas_nu$'('until_ltln$'(X1620,X1621)) = 'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'(X1620)),'subformulas_nu$'(X1621)) ),
inference(variable_rename,[status(thm)],[axiom296]) ).
tcf(c_0_44,plain,
! [X6: 'A_ltln_set$',X2: 'A_ltln$',X1: 'A_ltln_set$'] :
( 'less_eq$'('fun_app$a'('insert$'(X2),X6),X1)
| ~ 'member$'(X2,X1)
| ~ 'less_eq$'(X6,X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
tcf(c_0_45,hypothesis,
( ( 'fun_app$a'('insert$'('psi$'),'subformulas_mu$'('chi_2$')) = 'subformulas_mu$'('chi_2$') )
| 'member$'('psi$','subformulas_mu$'('chi_1$')) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
tff(c_0_46,plain,
! [X1346: 'A_ltln_set$'] : 'less_eq$'(X1346,X1346),
inference(variable_rename,[status(thm)],[axiom88]) ).
tcf(c_0_47,negated_conjecture,
( ~ 'less_eq$'('subformulas_nu$'('psi$'),'fun_app$a'('insert$'('strongRelease_ltln$'('chi_1$','chi_2$')),'fun_app$a'('fun_app$b'('sup$','fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_1$')),'subformulas_nu$'('chi_2$'))),'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('chi_1$')),'subformulas_mu$'('chi_2$')))))
| ~ 'less_eq$'('subformulas_mu$'('psi$'),'fun_app$a'('insert$'('strongRelease_ltln$'('chi_1$','chi_2$')),'fun_app$a'('fun_app$b'('sup$','fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_1$')),'subformulas_nu$'('chi_2$'))),'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('chi_1$')),'subformulas_mu$'('chi_2$'))))) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
tcf(c_0_48,plain,
! [X1: 'A_ltln_set$',X2: 'A_ltln$',X6: 'A_ltln_set$'] : 'fun_app$a'('fun_app$b'('sup$',X1),'fun_app$a'('insert$'(X2),X6)) = 'fun_app$a'('insert$'(X2),'fun_app$a'('fun_app$b'('sup$',X1),X6)),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
tcf(c_0_49,plain,
! [X2: 'A_ltln$',X3: 'A_ltln$'] : 'subformulas_nu$'('until_ltln$'(X2,X3)) = 'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'(X2)),'subformulas_nu$'(X3)),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
tff(c_0_50,plain,
! [X1523: 'A_ltln_set$',X1524: 'A_ltln_set$',X1525: 'A_ltln_set$'] : ( 'fun_app$a'('fun_app$b'('sup$',X1523),'fun_app$a'('fun_app$b'('sup$',X1524),X1525)) = 'fun_app$a'('fun_app$b'('sup$',X1524),'fun_app$a'('fun_app$b'('sup$',X1523),X1525)) ),
inference(variable_rename,[status(thm)],[axiom56]) ).
tff(c_0_51,plain,
! [X1479: 'A_ltln_set$',X1480: 'A_ltln_set$',X1481: 'A_ltln_set$'] :
( ~ 'less_eq$'(X1479,X1480)
| ~ 'less_eq$'(X1481,X1479)
| 'less_eq$'(X1481,X1480) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom321])])]) ).
tff(c_0_52,plain,
! [X1570: 'A_ltln$'] : 'less_eq$'('restricted_subformulas_inner$'(X1570),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'(X1570)),'subformulas_mu$'(X1570))),
inference(variable_rename,[status(thm)],[axiom13]) ).
tff(c_0_53,plain,
! [X1575: 'A_ltln$'] : 'less_eq$'('fun_app$a'('fun_app$b'('sup$','subformulas_mu$'(X1575)),'subformulas_nu$'(X1575)),'subfrmlsn$'(X1575)),
inference(variable_rename,[status(thm)],[axiom226]) ).
tff(c_0_54,plain,
! [X1529: 'A_ltln_set$',X1530: 'A_ltln_set$'] : ( 'fun_app$a'('fun_app$b'('sup$',X1529),X1530) = 'fun_app$a'('fun_app$b'('sup$',X1530),X1529) ),
inference(variable_rename,[status(thm)],[axiom62]) ).
tcf(c_0_55,hypothesis,
! [X1: 'A_ltln_set$'] :
( ( 'fun_app$a'('insert$'('psi$'),'subformulas_mu$'('chi_2$')) = 'subformulas_mu$'('chi_2$') )
| 'less_eq$'('fun_app$a'('insert$'('psi$'),X1),'subformulas_mu$'('chi_1$'))
| ~ 'less_eq$'(X1,'subformulas_mu$'('chi_1$')) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
tcf(c_0_56,plain,
! [X1: 'A_ltln_set$'] : 'less_eq$'(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
tcf(c_0_57,negated_conjecture,
( ~ 'less_eq$'('subformulas_nu$'('psi$'),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('until_ltln$'('chi_1$','chi_2$'))),'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('chi_1$')),'fun_app$a'('insert$'('strongRelease_ltln$'('chi_1$','chi_2$')),'subformulas_mu$'('chi_2$')))))
| ~ 'less_eq$'('subformulas_mu$'('psi$'),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('until_ltln$'('chi_1$','chi_2$'))),'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('chi_1$')),'fun_app$a'('insert$'('strongRelease_ltln$'('chi_1$','chi_2$')),'subformulas_mu$'('chi_2$'))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_48]),c_0_48]),c_0_49]),c_0_48]) ).
tcf(c_0_58,plain,
! [X1: 'A_ltln_set$',X6: 'A_ltln_set$',X7: 'A_ltln_set$'] : 'fun_app$a'('fun_app$b'('sup$',X1),'fun_app$a'('fun_app$b'('sup$',X6),X7)) = 'fun_app$a'('fun_app$b'('sup$',X6),'fun_app$a'('fun_app$b'('sup$',X1),X7)),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
tff(c_0_59,plain,
! [X1356: 'A_ltln_set$',X1357: 'A_ltln_set$',X1358: 'A_ltln_set$'] :
( ~ 'less_eq$'(X1356,X1357)
| 'less_eq$'(X1356,'fun_app$a'('fun_app$b'('sup$',X1357),X1358)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom125])])]) ).
tff(c_0_60,plain,
! [X1949: 'A_ltln_set$',X1950: 'A_ltln_set$',X1951: 'A_ltln$',X1952: 'A_ltln_set$',X1953: 'A_ltln_set$'] :
( ( ~ 'less_eq$'(X1949,X1950)
| ~ 'member$'(X1951,X1949)
| 'member$'(X1951,X1950) )
& ( 'member$'(esk131_2(X1952,X1953),X1952)
| 'less_eq$'(X1952,X1953) )
& ( ~ 'member$'(esk131_2(X1952,X1953),X1953)
| 'less_eq$'(X1952,X1953) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom89])])])])])])]) ).
tcf(c_0_61,plain,
! [X7: 'A_ltln_set$',X6: 'A_ltln_set$',X1: 'A_ltln_set$'] :
( 'less_eq$'(X7,X6)
| ~ 'less_eq$'(X1,X6)
| ~ 'less_eq$'(X7,X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
tcf(c_0_62,plain,
! [X2: 'A_ltln$'] : 'less_eq$'('restricted_subformulas_inner$'(X2),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'(X2)),'subformulas_mu$'(X2))),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
tcf(c_0_63,plain,
! [X2: 'A_ltln$'] : 'less_eq$'('fun_app$a'('fun_app$b'('sup$','subformulas_mu$'(X2)),'subformulas_nu$'(X2)),'subfrmlsn$'(X2)),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
tcf(c_0_64,plain,
! [X6: 'A_ltln_set$',X1: 'A_ltln_set$'] : 'fun_app$a'('fun_app$b'('sup$',X1),X6) = 'fun_app$a'('fun_app$b'('sup$',X6),X1),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
tcf(c_0_65,hypothesis,
( ( 'fun_app$a'('insert$'('psi$'),'subformulas_mu$'('chi_2$')) = 'subformulas_mu$'('chi_2$') )
| 'less_eq$'('fun_app$a'('insert$'('psi$'),'subformulas_mu$'('chi_1$')),'subformulas_mu$'('chi_1$')) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
tff(c_0_66,plain,
! [X1580: 'A_ltln$'] : 'less_eq$'('subformulas_mu$'(X1580),'subfrmlsn$'(X1580)),
inference(variable_rename,[status(thm)],[axiom295]) ).
tcf(c_0_67,negated_conjecture,
( ~ 'less_eq$'('subformulas_nu$'('psi$'),'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('chi_1$')),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('until_ltln$'('chi_1$','chi_2$'))),'fun_app$a'('insert$'('strongRelease_ltln$'('chi_1$','chi_2$')),'subformulas_mu$'('chi_2$')))))
| ~ 'less_eq$'('subformulas_mu$'('psi$'),'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('chi_1$')),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('until_ltln$'('chi_1$','chi_2$'))),'fun_app$a'('insert$'('strongRelease_ltln$'('chi_1$','chi_2$')),'subformulas_mu$'('chi_2$'))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58]),c_0_58]) ).
tcf(c_0_68,plain,
! [X1: 'A_ltln_set$',X7: 'A_ltln_set$',X6: 'A_ltln_set$'] :
( 'less_eq$'(X1,'fun_app$a'('fun_app$b'('sup$',X6),X7))
| ~ 'less_eq$'(X1,X6) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
tff(c_0_69,plain,
! [X1353: 'A_ltln_set$',X1354: 'A_ltln_set$',X1355: 'A_ltln_set$'] :
( ~ 'less_eq$'(X1353,X1354)
| 'less_eq$'(X1353,'fun_app$a'('fun_app$b'('sup$',X1355),X1354)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom121])])]) ).
tcf(c_0_70,plain,
! [X6: 'A_ltln_set$',X2: 'A_ltln$',X1: 'A_ltln_set$'] :
( 'member$'(X2,X6)
| ~ 'less_eq$'(X1,X6)
| ~ 'member$'(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
tcf(c_0_71,plain,
'member$'('psi$','restricted_subformulas_inner$'('strongRelease_ltln$'('chi_1$','chi_2$'))),
inference(split_conjunct,[status(thm)],[axiom9]) ).
tcf(c_0_72,plain,
! [X2: 'A_ltln$',X1: 'A_ltln_set$'] :
( 'less_eq$'('restricted_subformulas_inner$'(X2),X1)
| ~ 'less_eq$'('fun_app$a'('fun_app$b'('sup$','subformulas_nu$'(X2)),'subformulas_mu$'(X2)),X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
tcf(c_0_73,plain,
! [X2: 'A_ltln$'] : 'less_eq$'('fun_app$a'('fun_app$b'('sup$','subformulas_nu$'(X2)),'subformulas_mu$'(X2)),'subfrmlsn$'(X2)),
inference(rw,[status(thm)],[c_0_63,c_0_64]) ).
tff(c_0_74,plain,
! [X1615: 'A_ltln$',X1616: 'A_ltln$'] : ( 'subformulas_nu$'('strongRelease_ltln$'(X1615,X1616)) = 'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'(X1615)),'subformulas_nu$'(X1616)) ),
inference(variable_rename,[status(thm)],[axiom26]) ).
tcf(c_0_75,hypothesis,
! [X1: 'A_ltln_set$'] :
( ( 'fun_app$a'('insert$'('psi$'),'subformulas_mu$'('chi_2$')) = 'subformulas_mu$'('chi_2$') )
| 'less_eq$'('fun_app$a'('insert$'('psi$'),'subformulas_mu$'('chi_1$')),X1)
| ~ 'less_eq$'('subformulas_mu$'('chi_1$'),X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_65]) ).
tcf(c_0_76,plain,
! [X2: 'A_ltln$'] : 'less_eq$'('subformulas_mu$'(X2),'subfrmlsn$'(X2)),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
tcf(c_0_77,negated_conjecture,
( ~ 'less_eq$'('subformulas_nu$'('psi$'),'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('chi_1$')),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('until_ltln$'('chi_1$','chi_2$'))),'fun_app$a'('insert$'('strongRelease_ltln$'('chi_1$','chi_2$')),'subformulas_mu$'('chi_2$')))))
| ~ 'less_eq$'('subformulas_mu$'('psi$'),'subformulas_mu$'('chi_1$')) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
tcf(c_0_78,plain,
! [X1: 'A_ltln_set$',X7: 'A_ltln_set$',X6: 'A_ltln_set$'] :
( 'less_eq$'(X1,'fun_app$a'('fun_app$b'('sup$',X7),X6))
| ~ 'less_eq$'(X1,X6) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
tff(c_0_79,plain,
! [X1617: 'A_ltln$',X1618: 'A_ltln$'] :
( ~ 'member$'(X1617,'subfrmlsn$'(X1618))
| 'less_eq$'('subformulas_nu$'(X1617),'subformulas_nu$'(X1618)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom292])])]) ).
tcf(c_0_80,plain,
! [X1: 'A_ltln_set$'] :
( 'member$'('psi$',X1)
| ~ 'less_eq$'('restricted_subformulas_inner$'('strongRelease_ltln$'('chi_1$','chi_2$')),X1) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
tcf(c_0_81,plain,
! [X2: 'A_ltln$'] : 'less_eq$'('restricted_subformulas_inner$'(X2),'subfrmlsn$'(X2)),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
tcf(c_0_82,plain,
! [X2: 'A_ltln$',X3: 'A_ltln$'] : 'subformulas_nu$'('strongRelease_ltln$'(X2,X3)) = 'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'(X2)),'subformulas_nu$'(X3)),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
tff(c_0_83,plain,
! [X1578: 'A_ltln$',X1579: 'A_ltln$'] :
( ~ 'member$'(X1578,'subfrmlsn$'(X1579))
| 'less_eq$'('subformulas_mu$'(X1578),'subformulas_mu$'(X1579)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom294])])]) ).
tcf(c_0_84,plain,
! [X6: 'A_ltln_set$',X2: 'A_ltln$',X1: 'A_ltln_set$'] :
( 'member$'(X2,X1)
| ~ 'less_eq$'('fun_app$a'('insert$'(X2),X6),X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
tcf(c_0_85,hypothesis,
( ( 'fun_app$a'('insert$'('psi$'),'subformulas_mu$'('chi_2$')) = 'subformulas_mu$'('chi_2$') )
| 'less_eq$'('fun_app$a'('insert$'('psi$'),'subformulas_mu$'('chi_1$')),'subfrmlsn$'('chi_1$')) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
tcf(c_0_86,negated_conjecture,
( ~ 'less_eq$'('subformulas_nu$'('psi$'),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('until_ltln$'('chi_1$','chi_2$'))),'fun_app$a'('insert$'('strongRelease_ltln$'('chi_1$','chi_2$')),'subformulas_mu$'('chi_2$'))))
| ~ 'less_eq$'('subformulas_mu$'('psi$'),'subformulas_mu$'('chi_1$')) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
tcf(c_0_87,plain,
! [X2: 'A_ltln$',X3: 'A_ltln$'] :
( 'less_eq$'('subformulas_nu$'(X2),'subformulas_nu$'(X3))
| ~ 'member$'(X2,'subfrmlsn$'(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
tcf(c_0_88,plain,
'member$'('psi$','subfrmlsn$'('strongRelease_ltln$'('chi_1$','chi_2$'))),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
tcf(c_0_89,plain,
! [X2: 'A_ltln$',X3: 'A_ltln$'] : 'subformulas_nu$'('strongRelease_ltln$'(X2,X3)) = 'subformulas_nu$'('until_ltln$'(X2,X3)),
inference(rw,[status(thm)],[c_0_82,c_0_49]) ).
tcf(c_0_90,plain,
! [X2: 'A_ltln$',X3: 'A_ltln$'] :
( 'less_eq$'('subformulas_mu$'(X2),'subformulas_mu$'(X3))
| ~ 'member$'(X2,'subfrmlsn$'(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
tcf(c_0_91,hypothesis,
( ( 'fun_app$a'('insert$'('psi$'),'subformulas_mu$'('chi_2$')) = 'subformulas_mu$'('chi_2$') )
| 'member$'('psi$','subfrmlsn$'('chi_1$')) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
tcf(c_0_92,negated_conjecture,
( ~ 'less_eq$'('subformulas_nu$'('psi$'),'subformulas_nu$'('until_ltln$'('chi_1$','chi_2$')))
| ~ 'less_eq$'('subformulas_mu$'('psi$'),'subformulas_mu$'('chi_1$')) ),
inference(spm,[status(thm)],[c_0_86,c_0_68]) ).
tcf(c_0_93,plain,
'less_eq$'('subformulas_nu$'('psi$'),'subformulas_nu$'('until_ltln$'('chi_1$','chi_2$'))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]) ).
tcf(c_0_94,hypothesis,
( ( 'fun_app$a'('insert$'('psi$'),'subformulas_mu$'('chi_2$')) = 'subformulas_mu$'('chi_2$') )
| 'less_eq$'('subformulas_mu$'('psi$'),'subformulas_mu$'('chi_1$')) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
tcf(c_0_95,negated_conjecture,
~ 'less_eq$'('subformulas_mu$'('psi$'),'subformulas_mu$'('chi_1$')),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_93])]) ).
tcf(c_0_96,hypothesis,
'fun_app$a'('insert$'('psi$'),'subformulas_mu$'('chi_2$')) = 'subformulas_mu$'('chi_2$'),
inference(sr,[status(thm)],[c_0_94,c_0_95]) ).
tcf(c_0_97,hypothesis,
! [X1: 'A_ltln_set$'] :
( 'member$'('psi$',X1)
| ~ 'less_eq$'('subformulas_mu$'('chi_2$'),X1) ),
inference(spm,[status(thm)],[c_0_84,c_0_96]) ).
tff(c_0_98,plain,
! [X1676: 'A_ltln$',X1677: 'A_ltln_set$'] : 'member$'(X1676,'fun_app$a'('insert$'(X1676),X1677)),
inference(variable_rename,[status(thm)],[axiom106]) ).
tcf(c_0_99,hypothesis,
! [X1: 'A_ltln_set$'] :
( ( 'fun_app$a'('insert$'('psi$'),X1) = X1 )
| ~ 'less_eq$'('subformulas_mu$'('chi_2$'),X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_97]) ).
tcf(c_0_100,plain,
! [X2: 'A_ltln$',X1: 'A_ltln_set$'] : 'member$'(X2,'fun_app$a'('insert$'(X2),X1)),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
tcf(c_0_101,hypothesis,
'fun_app$a'('insert$'('psi$'),'subfrmlsn$'('chi_2$')) = 'subfrmlsn$'('chi_2$'),
inference(spm,[status(thm)],[c_0_99,c_0_76]) ).
tff(c_0_102,plain,
! [X1330: 'A_ltln_set$',X1331: 'A_ltln_set$',X1332: 'A_ltln_set$'] :
( ( 'less_eq$'(X1330,X1332)
| ~ 'less_eq$'('fun_app$a'('fun_app$b'('sup$',X1330),X1331),X1332) )
& ( 'less_eq$'(X1331,X1332)
| ~ 'less_eq$'('fun_app$a'('fun_app$b'('sup$',X1330),X1331),X1332) )
& ( ~ 'less_eq$'(X1330,X1332)
| ~ 'less_eq$'(X1331,X1332)
| 'less_eq$'('fun_app$a'('fun_app$b'('sup$',X1330),X1331),X1332) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom16])])])]) ).
tff(c_0_103,plain,
! [X1367: 'A_ltln_set$',X1368: 'A_ltln_set$'] :
( ( ~ 'less_eq$'(X1367,X1368)
| ( X1368 = 'fun_app$a'('fun_app$b'('sup$',X1368),X1367) ) )
& ( ( X1368 != 'fun_app$a'('fun_app$b'('sup$',X1368),X1367) )
| 'less_eq$'(X1367,X1368) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom145])])]) ).
tcf(c_0_104,hypothesis,
'member$'('psi$','subfrmlsn$'('chi_2$')),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
tcf(c_0_105,plain,
! [X1: 'A_ltln_set$',X7: 'A_ltln_set$',X6: 'A_ltln_set$'] :
( 'less_eq$'(X1,X6)
| ~ 'less_eq$'('fun_app$a'('fun_app$b'('sup$',X1),X7),X6) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
tcf(c_0_106,plain,
! [X1: 'A_ltln_set$',X6: 'A_ltln_set$'] :
( 'less_eq$'(X6,X1)
| ( X1 != 'fun_app$a'('fun_app$b'('sup$',X1),X6) ) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
tcf(c_0_107,plain,
! [X1: 'A_ltln_set$',X6: 'A_ltln_set$'] :
( ( X6 = 'fun_app$a'('fun_app$b'('sup$',X6),X1) )
| ~ 'less_eq$'(X1,X6) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
tcf(c_0_108,hypothesis,
'less_eq$'('subformulas_mu$'('psi$'),'subformulas_mu$'('chi_2$')),
inference(spm,[status(thm)],[c_0_90,c_0_104]) ).
tcf(c_0_109,plain,
! [X1: 'A_ltln_set$',X7: 'A_ltln_set$',X6: 'A_ltln_set$'] :
( 'less_eq$'(X1,X6)
| ( 'fun_app$a'('fun_app$b'('sup$',X6),'fun_app$a'('fun_app$b'('sup$',X1),X7)) != X6 ) ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
tcf(c_0_110,hypothesis,
'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('psi$')),'subformulas_mu$'('chi_2$')) = 'subformulas_mu$'('chi_2$'),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_64]) ).
tff(c_0_111,plain,
! [X1533: 'A_ltln_set$',X1534: 'A_ltln_set$',X1535: 'A_ltln_set$'] : ( 'fun_app$a'('fun_app$b'('sup$','fun_app$a'('fun_app$b'('sup$',X1533),X1534)),X1535) = 'fun_app$a'('fun_app$b'('sup$',X1533),'fun_app$a'('fun_app$b'('sup$',X1534),X1535)) ),
inference(variable_rename,[status(thm)],[axiom68]) ).
tff(c_0_112,plain,
! [X1636: 'A_ltln$',X1637: 'A_ltln_set$',X1638: 'A_ltln_set$'] : ( 'fun_app$a'('fun_app$b'('sup$','fun_app$a'('insert$'(X1636),X1637)),X1638) = 'fun_app$a'('insert$'(X1636),'fun_app$a'('fun_app$b'('sup$',X1637),X1638)) ),
inference(variable_rename,[status(thm)],[axiom14]) ).
tff(c_0_113,plain,
! [X1521: 'A_ltln_set$'] : ( 'fun_app$a'('fun_app$b'('sup$',X1521),X1521) = X1521 ),
inference(variable_rename,[status(thm)],[axiom45]) ).
tff(c_0_114,plain,
! [X1363: 'A_ltln_set$',X1364: 'A_ltln_set$'] : 'less_eq$'(X1363,'fun_app$a'('fun_app$b'('sup$',X1364),X1363)),
inference(variable_rename,[status(thm)],[axiom137]) ).
tcf(c_0_115,hypothesis,
! [X1: 'A_ltln_set$'] :
( 'less_eq$'('subformulas_mu$'('psi$'),X1)
| ( 'fun_app$a'('fun_app$b'('sup$',X1),'subformulas_mu$'('chi_2$')) != X1 ) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
tcf(c_0_116,plain,
! [X1: 'A_ltln_set$',X6: 'A_ltln_set$',X7: 'A_ltln_set$'] : 'fun_app$a'('fun_app$b'('sup$','fun_app$a'('fun_app$b'('sup$',X1),X6)),X7) = 'fun_app$a'('fun_app$b'('sup$',X1),'fun_app$a'('fun_app$b'('sup$',X6),X7)),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
tcf(c_0_117,plain,
! [X1: 'A_ltln_set$',X2: 'A_ltln$',X6: 'A_ltln_set$'] : 'fun_app$a'('fun_app$b'('sup$','fun_app$a'('insert$'(X2),X1)),X6) = 'fun_app$a'('insert$'(X2),'fun_app$a'('fun_app$b'('sup$',X1),X6)),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
tcf(c_0_118,plain,
! [X1: 'A_ltln_set$'] : 'fun_app$a'('fun_app$b'('sup$',X1),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_113]) ).
tcf(c_0_119,hypothesis,
'less_eq$'('subformulas_nu$'('psi$'),'subformulas_nu$'('chi_2$')),
inference(spm,[status(thm)],[c_0_87,c_0_104]) ).
tcf(c_0_120,plain,
! [X6: 'A_ltln_set$',X1: 'A_ltln_set$'] : 'less_eq$'(X1,'fun_app$a'('fun_app$b'('sup$',X6),X1)),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
tcf(c_0_121,negated_conjecture,
~ 'less_eq$'('subformulas_nu$'('psi$'),'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('chi_1$')),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('until_ltln$'('chi_1$','chi_2$'))),'fun_app$a'('insert$'('strongRelease_ltln$'('chi_1$','chi_2$')),'subformulas_mu$'('chi_2$'))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_115]),c_0_116]),c_0_116]),c_0_117]),c_0_118])]) ).
tcf(c_0_122,hypothesis,
! [X1: 'A_ltln_set$'] :
( 'less_eq$'('subformulas_nu$'('psi$'),X1)
| ~ 'less_eq$'('subformulas_nu$'('chi_2$'),X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_119]) ).
tcf(c_0_123,plain,
! [X3: 'A_ltln$',X2: 'A_ltln$'] : 'less_eq$'('subformulas_nu$'(X2),'subformulas_nu$'('until_ltln$'(X3,X2))),
inference(spm,[status(thm)],[c_0_120,c_0_49]) ).
tcf(c_0_124,negated_conjecture,
~ 'less_eq$'('subformulas_nu$'('psi$'),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('until_ltln$'('chi_1$','chi_2$'))),'fun_app$a'('insert$'('strongRelease_ltln$'('chi_1$','chi_2$')),'subformulas_mu$'('chi_2$')))),
inference(spm,[status(thm)],[c_0_121,c_0_78]) ).
tcf(c_0_125,hypothesis,
! [X2: 'A_ltln$'] : 'less_eq$'('subformulas_nu$'('psi$'),'subformulas_nu$'('until_ltln$'(X2,'chi_2$'))),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_126,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_68]),c_0_125])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ITP369_1 : TPTP v8.2.0. Released v8.0.0.
% 0.12/0.14 % Command : run_E %s %d THM
% 0.14/0.37 % Computer : n015.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Sat May 18 16:44:38 EDT 2024
% 0.14/0.37 % CPUTime :
% 0.24/0.49 Running first-order model finding
% 0.24/0.49 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.07/3.22 # Version: 3.1.0
% 19.07/3.22 # Preprocessing class: FSLSSMSMSSSNFFN.
% 19.07/3.22 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 19.07/3.22 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 19.07/3.22 # Starting new_bool_3 with 300s (1) cores
% 19.07/3.22 # Starting new_bool_1 with 300s (1) cores
% 19.07/3.22 # Starting sh5l with 300s (1) cores
% 19.07/3.22 # new_bool_3 with pid 20981 completed with status 0
% 19.07/3.22 # Result found by new_bool_3
% 19.07/3.22 # Preprocessing class: FSLSSMSMSSSNFFN.
% 19.07/3.22 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 19.07/3.22 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 19.07/3.22 # Starting new_bool_3 with 300s (1) cores
% 19.07/3.22 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 19.07/3.22 # Search class: FGHSM-FSLM31-DFFFFFNN
% 19.07/3.22 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 19.07/3.22 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 19.07/3.22 # G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 20985 completed with status 0
% 19.07/3.22 # Result found by G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 19.07/3.22 # Preprocessing class: FSLSSMSMSSSNFFN.
% 19.07/3.22 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 19.07/3.22 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 19.07/3.22 # Starting new_bool_3 with 300s (1) cores
% 19.07/3.22 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 19.07/3.22 # Search class: FGHSM-FSLM31-DFFFFFNN
% 19.07/3.22 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 19.07/3.22 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 19.07/3.22 # Preprocessing time : 0.014 s
% 19.07/3.22 # Presaturation interreduction done
% 19.07/3.22
% 19.07/3.22 # Proof found!
% 19.07/3.22 # SZS status Theorem
% 19.07/3.22 # SZS output start CNFRefutation
% See solution above
% 19.07/3.22 # Parsed axioms : 750
% 19.07/3.22 # Removed by relevancy pruning/SinE : 360
% 19.07/3.22 # Initial clauses : 17836
% 19.07/3.22 # Removed in clause preprocessing : 16900
% 19.07/3.22 # Initial clauses in saturation : 936
% 19.07/3.22 # Processed clauses : 12687
% 19.07/3.22 # ...of these trivial : 380
% 19.07/3.22 # ...subsumed : 8157
% 19.07/3.22 # ...remaining for further processing : 4150
% 19.07/3.22 # Other redundant clauses eliminated : 1409
% 19.07/3.22 # Clauses deleted for lack of memory : 0
% 19.07/3.22 # Backward-subsumed : 762
% 19.07/3.22 # Backward-rewritten : 248
% 19.07/3.22 # Generated clauses : 103545
% 19.07/3.22 # ...of the previous two non-redundant : 92972
% 19.07/3.22 # ...aggressively subsumed : 0
% 19.07/3.22 # Contextual simplify-reflections : 37
% 19.07/3.22 # Paramodulations : 102124
% 19.07/3.22 # Factorizations : 0
% 19.07/3.22 # NegExts : 0
% 19.07/3.22 # Equation resolutions : 1431
% 19.07/3.22 # Disequality decompositions : 0
% 19.07/3.22 # Total rewrite steps : 33144
% 19.07/3.22 # ...of those cached : 30018
% 19.07/3.22 # Propositional unsat checks : 0
% 19.07/3.22 # Propositional check models : 0
% 19.07/3.22 # Propositional check unsatisfiable : 0
% 19.07/3.22 # Propositional clauses : 0
% 19.07/3.22 # Propositional clauses after purity: 0
% 19.07/3.22 # Propositional unsat core size : 0
% 19.07/3.22 # Propositional preprocessing time : 0.000
% 19.07/3.22 # Propositional encoding time : 0.000
% 19.07/3.22 # Propositional solver time : 0.000
% 19.07/3.22 # Success case prop preproc time : 0.000
% 19.07/3.22 # Success case prop encoding time : 0.000
% 19.07/3.22 # Success case prop solver time : 0.000
% 19.07/3.22 # Current number of processed clauses : 2233
% 19.07/3.22 # Positive orientable unit clauses : 647
% 19.07/3.22 # Positive unorientable unit clauses: 4
% 19.07/3.22 # Negative unit clauses : 476
% 19.07/3.22 # Non-unit-clauses : 1106
% 19.07/3.22 # Current number of unprocessed clauses: 81305
% 19.07/3.22 # ...number of literals in the above : 306577
% 19.07/3.22 # Current number of archived formulas : 0
% 19.07/3.22 # Current number of archived clauses : 1679
% 19.07/3.22 # Clause-clause subsumption calls (NU) : 744238
% 19.07/3.22 # Rec. Clause-clause subsumption calls : 255416
% 19.07/3.22 # Non-unit clause-clause subsumptions : 4680
% 19.07/3.22 # Unit Clause-clause subsumption calls : 68499
% 19.07/3.22 # Rewrite failures with RHS unbound : 0
% 19.07/3.22 # BW rewrite match attempts : 1279
% 19.07/3.22 # BW rewrite match successes : 268
% 19.07/3.22 # Condensation attempts : 0
% 19.07/3.22 # Condensation successes : 0
% 19.07/3.22 # Termbank termtop insertions : 3309333
% 19.07/3.22 # Search garbage collected termcells : 124933
% 19.07/3.22
% 19.07/3.22 # -------------------------------------------------
% 19.07/3.22 # User time : 2.539 s
% 19.07/3.22 # System time : 0.101 s
% 19.07/3.22 # Total time : 2.640 s
% 19.07/3.22 # Maximum resident set size: 40860 pages
% 19.07/3.22
% 19.07/3.22 # -------------------------------------------------
% 19.07/3.22 # User time : 2.575 s
% 19.07/3.22 # System time : 0.110 s
% 19.07/3.22 # Total time : 2.685 s
% 19.07/3.22 # Maximum resident set size: 3500 pages
% 19.07/3.22 % E---3.1 exiting
%------------------------------------------------------------------------------