%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP369_1 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 : Thu Sep 24 12:55:28 PM UTC 2026
% Result : Theorem 6.17s 2.56s
% Output : CNFRefutation 6.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 16
% Syntax : Number of formulae : 78 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 143 ( 25 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 129 ( 64 ~; 51 |; 6 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 94 ( 0 sgn 94 !; 0 ?; 94 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
'A_ltln$': $tType ).
tff(decl_sort2,type,
'A_ltln_set$': $tType ).
tff(decl_sort3,type,
'A_ltln_set_a_ltln_set_fun$': $tType ).
tff(decl_sort4,type,
'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$': $tType ).
tff(decl_26,type,
'insert$': 'A_ltln$' > 'A_ltln_set_a_ltln_set_fun$' ).
tff(decl_33,type,
'chi_1$': 'A_ltln$' ).
tff(decl_37,type,
'subformulas_nu$': 'A_ltln$' > 'A_ltln_set$' ).
tff(decl_38,type,
'fun_app$a': ( 'A_ltln_set$' * 'A_ltln_set_a_ltln_set_fun$' ) > 'A_ltln_set$' ).
tff(decl_46,type,
'less_eq$': ( 'A_ltln_set$' * 'A_ltln_set$' ) > $o ).
tff(decl_61,type,
'member$': ( 'A_ltln_set$' * 'A_ltln$' ) > $o ).
tff(decl_66,type,
'fun_app$b': ( 'A_ltln_set$' * 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' ) > 'A_ltln_set_a_ltln_set_fun$' ).
tff(decl_68,type,
'psi$': 'A_ltln$' ).
tff(decl_72,type,
'chi_2$': 'A_ltln$' ).
tff(decl_76,type,
'subformulas_mu$': 'A_ltln$' > 'A_ltln_set$' ).
tff(decl_83,type,
'subfrmlsn$': 'A_ltln$' > 'A_ltln_set$' ).
tff(decl_95,type,
'sup$': 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' ).
tff(decl_106,type,
'strongRelease_ltln$': ( 'A_ltln$' * 'A_ltln$' ) > 'A_ltln$' ).
tff(conjecture1,conjecture,
( 'less_eq$'('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$'('chi_2$')))))
& '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$'))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture1) ).
tff(axiom206,axiom,
! [X1: 'A_ltln_set$',X399: 'A_ltln_set$',X400: 'A_ltln$'] :
( 'less_eq$'(X1,X399)
=> 'less_eq$'(X1,'fun_app$a'('insert$'(X400),X399)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom206) ).
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$',X109),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom68) ).
tff(axiom15,axiom,
! [X1: 'A_ltln_set$',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/sandbox/benchmark/theBenchmark.p',axiom15) ).
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$',X1),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom56) ).
tff(axiom121,axiom,
! [X1: 'A_ltln_set$',X208: 'A_ltln_set$',X7: 'A_ltln_set$'] :
( 'less_eq$'(X1,X208)
=> 'less_eq$'(X1,'fun_app$a'('fun_app$b'('sup$',X7),X208)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom121) ).
tff(hypothesis6,hypothesis,
~ 'member$'('psi$','subformulas_nu$'('chi_1$')),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis6) ).
tff(hypothesis7,hypothesis,
~ 'member$'('psi$','subformulas_nu$'('chi_2$')),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis7) ).
tff(axiom129,axiom,
! [X1: 'A_ltln_set$',X225: 'A_ltln_set$'] :
( 'less_eq$'(X1,X225)
<=> ( 'fun_app$a'('fun_app$b'('sup$',X1),X225) = X225 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom129) ).
tff(axiom102,axiom,
! [X173: 'A_ltln$',X174: 'A_ltln_set$'] :
( 'member$'(X173,X174)
=> ( 'fun_app$a'('insert$'(X173),X174) = X174 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom102) ).
tff(hypothesis4,hypothesis,
( 'member$'('psi$','subformulas_mu$'('chi_2$'))
| 'member$'('psi$','subformulas_mu$'('chi_1$'))
| 'member$'('psi$','subformulas_nu$'('chi_2$'))
| 'member$'('psi$','subformulas_nu$'('chi_1$')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis4) ).
tff(axiom17,axiom,
! [X9: 'A_ltln$',X10: 'A_ltln_set$',X7: 'A_ltln_set$'] :
( 'less_eq$'('fun_app$a'('insert$'(X9),X10),X7)
<=> ( 'less_eq$'(X10,X7)
& 'member$'(X9,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom17) ).
tff(axiom295,axiom,
! [X487: 'A_ltln$'] : 'less_eq$'('subformulas_mu$'(X487),'subfrmlsn$'(X487)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom295) ).
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/sandbox/benchmark/theBenchmark.p',axiom125) ).
tff(axiom292,axiom,
! [X484: 'A_ltln$',X2: 'A_ltln$'] :
( 'member$'(X484,'subfrmlsn$'(X2))
=> 'less_eq$'('subformulas_nu$'(X484),'subformulas_nu$'(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom292) ).
tff(axiom294,axiom,
! [X486: 'A_ltln$',X2: 'A_ltln$'] :
( 'member$'(X486,'subfrmlsn$'(X2))
=> 'less_eq$'('subformulas_mu$'(X486),'subformulas_mu$'(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom294) ).
tff(c_0_16,negated_conjecture,
~ ( '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$')))))
& 'less_eq$'('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$'('chi_2$'))))) ),
inference(assume_negation,[status(cth)],[conjecture1]) ).
tff(c_0_17,negated_conjecture,
( ~ '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$')))))
| ~ 'less_eq$'('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$'('chi_2$'))))) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])]) ).
tff(c_0_18,plain,
! [X1869: 'A_ltln_set$',X1870: 'A_ltln_set$',X1871: 'A_ltln$'] :
( 'less_eq$'(X1869,'fun_app$a'('insert$'(X1871),X1870))
| ~ 'less_eq$'(X1869,X1870) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom206])])]) ).
tcf(c_0_19,negated_conjecture,
( ~ 'less_eq$'('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$'('chi_2$')))))
| ~ '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$'))))) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
tcf(c_0_20,plain,
! [X1: 'A_ltln_set$',X2: 'A_ltln$',X6: 'A_ltln_set$'] :
( ~ 'less_eq$'(X1,X6)
| 'less_eq$'(X1,'fun_app$a'('insert$'(X2),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
tff(c_0_21,plain,
! [X1468: 'A_ltln_set$',X1469: 'A_ltln_set$',X1470: 'A_ltln_set$'] : ( 'fun_app$a'('fun_app$b'('sup$','fun_app$a'('fun_app$b'('sup$',X1468),X1469)),X1470) = 'fun_app$a'('fun_app$b'('sup$',X1468),'fun_app$a'('fun_app$b'('sup$',X1469),X1470)) ),
inference(variable_rename,[status(thm)],[axiom68]) ).
tcf(c_0_22,negated_conjecture,
( ~ 'less_eq$'('subformulas_mu$'('psi$'),'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_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$'('chi_2$'))))) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
tcf(c_0_23,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$',X6),X7)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
tff(c_0_24,plain,
! [X1338: 'A_ltln_set$',X1339: 'A_ltln$',X1340: 'A_ltln_set$'] : ( 'fun_app$a'('fun_app$b'('sup$',X1338),'fun_app$a'('insert$'(X1339),X1340)) = 'fun_app$a'('insert$'(X1339),'fun_app$a'('fun_app$b'('sup$',X1338),X1340)) ),
inference(variable_rename,[status(thm)],[axiom15]) ).
tff(c_0_25,plain,
! [X1438: 'A_ltln_set$',X1439: 'A_ltln_set$',X1440: 'A_ltln_set$'] : ( 'fun_app$a'('fun_app$b'('sup$',X1438),'fun_app$a'('fun_app$b'('sup$',X1439),X1440)) = 'fun_app$a'('fun_app$b'('sup$',X1439),'fun_app$a'('fun_app$b'('sup$',X1438),X1440)) ),
inference(variable_rename,[status(thm)],[axiom56]) ).
tcf(c_0_26,negated_conjecture,
( ~ 'less_eq$'('subformulas_mu$'('psi$'),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_1$')),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_2$')),'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('chi_1$')),'subformulas_mu$'('chi_2$')))))
| ~ 'less_eq$'('subformulas_nu$'('psi$'),'fun_app$a'('insert$'('strongRelease_ltln$'('chi_1$','chi_2$')),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_1$')),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_2$')),'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('chi_1$')),'subformulas_mu$'('chi_2$')))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_23]) ).
tcf(c_0_27,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$',X1),X6)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
tcf(c_0_28,plain,
! [X1: 'A_ltln_set$',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_25]) ).
tff(c_0_29,plain,
! [X1636: 'A_ltln_set$',X1637: 'A_ltln_set$',X1638: 'A_ltln_set$'] :
( 'less_eq$'(X1636,'fun_app$a'('fun_app$b'('sup$',X1638),X1637))
| ~ 'less_eq$'(X1636,X1637) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom121])])]) ).
tcf(c_0_30,negated_conjecture,
( ~ 'less_eq$'('subformulas_mu$'('psi$'),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_1$')),'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('chi_1$')),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_2$')),'subformulas_mu$'('chi_2$')))))
| ~ 'less_eq$'('subformulas_nu$'('psi$'),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_1$')),'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('chi_1$')),'fun_app$a'('insert$'('strongRelease_ltln$'('chi_1$','chi_2$')),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_2$')),'subformulas_mu$'('chi_2$')))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_27]),c_0_28]) ).
tcf(c_0_31,plain,
! [X1: 'A_ltln_set$',X7: 'A_ltln_set$',X6: 'A_ltln_set$'] :
( ~ 'less_eq$'(X1,X6)
| 'less_eq$'(X1,'fun_app$a'('fun_app$b'('sup$',X7),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
tcf(c_0_32,negated_conjecture,
( ~ 'less_eq$'('subformulas_mu$'('psi$'),'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('chi_1$')),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_2$')),'subformulas_mu$'('chi_2$'))))
| ~ 'less_eq$'('subformulas_nu$'('psi$'),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_1$')),'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('chi_1$')),'fun_app$a'('insert$'('strongRelease_ltln$'('chi_1$','chi_2$')),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_2$')),'subformulas_mu$'('chi_2$')))))) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
tff(c_0_33,hypothesis,
~ 'member$'('psi$','subformulas_nu$'('chi_1$')),
inference(fof_simplification,[status(thm)],[hypothesis6]) ).
tff(c_0_34,hypothesis,
~ 'member$'('psi$','subformulas_nu$'('chi_2$')),
inference(fof_simplification,[status(thm)],[hypothesis7]) ).
tcf(c_0_35,negated_conjecture,
( ~ 'less_eq$'('subformulas_mu$'('psi$'),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_2$')),'subformulas_mu$'('chi_2$')))
| ~ 'less_eq$'('subformulas_nu$'('psi$'),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_1$')),'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('chi_1$')),'fun_app$a'('insert$'('strongRelease_ltln$'('chi_1$','chi_2$')),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_2$')),'subformulas_mu$'('chi_2$')))))) ),
inference(spm,[status(thm)],[c_0_32,c_0_31]) ).
tff(c_0_36,plain,
! [X1657: 'A_ltln_set$',X1658: 'A_ltln_set$'] :
( ( 'less_eq$'(X1657,X1658)
| ( 'fun_app$a'('fun_app$b'('sup$',X1657),X1658) != X1658 ) )
& ( ( 'fun_app$a'('fun_app$b'('sup$',X1657),X1658) = X1658 )
| ~ 'less_eq$'(X1657,X1658) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom129])])]) ).
tff(c_0_37,hypothesis,
~ 'member$'('psi$','subformulas_nu$'('chi_1$')),
inference(fof_nnf,[status(thm)],[c_0_33]) ).
tff(c_0_38,hypothesis,
~ 'member$'('psi$','subformulas_nu$'('chi_2$')),
inference(fof_nnf,[status(thm)],[c_0_34]) ).
tcf(c_0_39,negated_conjecture,
( ~ 'less_eq$'('subformulas_mu$'('psi$'),'subformulas_mu$'('chi_2$'))
| ~ 'less_eq$'('subformulas_nu$'('psi$'),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_1$')),'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('chi_1$')),'fun_app$a'('insert$'('strongRelease_ltln$'('chi_1$','chi_2$')),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_2$')),'subformulas_mu$'('chi_2$')))))) ),
inference(spm,[status(thm)],[c_0_35,c_0_31]) ).
tcf(c_0_40,plain,
! [X1: 'A_ltln_set$',X6: 'A_ltln_set$'] :
( ( 'fun_app$a'('fun_app$b'('sup$',X1),X6) != X6 )
| 'less_eq$'(X1,X6) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
tff(c_0_41,plain,
! [X1567: 'A_ltln$',X1568: 'A_ltln_set$'] :
( ( 'fun_app$a'('insert$'(X1567),X1568) = X1568 )
| ~ 'member$'(X1567,X1568) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom102])])]) ).
tcf(c_0_42,hypothesis,
( 'member$'('psi$','subformulas_mu$'('chi_2$'))
| 'member$'('psi$','subformulas_mu$'('chi_1$'))
| 'member$'('psi$','subformulas_nu$'('chi_2$'))
| 'member$'('psi$','subformulas_nu$'('chi_1$')) ),
inference(split_conjunct,[status(thm)],[hypothesis4]) ).
tcf(c_0_43,hypothesis,
~ 'member$'('psi$','subformulas_nu$'('chi_1$')),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
tcf(c_0_44,hypothesis,
~ 'member$'('psi$','subformulas_nu$'('chi_2$')),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
tcf(c_0_45,negated_conjecture,
( ~ 'less_eq$'('subformulas_nu$'('psi$'),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_1$')),'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('chi_1$')),'fun_app$a'('insert$'('strongRelease_ltln$'('chi_1$','chi_2$')),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_2$')),'subformulas_mu$'('chi_2$'))))))
| ( 'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('psi$')),'subformulas_mu$'('chi_2$')) != 'subformulas_mu$'('chi_2$') ) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
tff(c_0_46,plain,
! [X1344: 'A_ltln$',X1345: 'A_ltln_set$',X1346: 'A_ltln_set$'] :
( ( 'less_eq$'('fun_app$a'('insert$'(X1344),X1345),X1346)
| ~ 'less_eq$'(X1345,X1346)
| ~ 'member$'(X1344,X1346) )
& ( ~ 'less_eq$'('fun_app$a'('insert$'(X1344),X1345),X1346)
| 'less_eq$'(X1345,X1346) )
& ( ~ 'less_eq$'('fun_app$a'('insert$'(X1344),X1345),X1346)
| 'member$'(X1344,X1346) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom17])])])]) ).
tcf(c_0_47,plain,
! [X2: 'A_ltln$',X1: 'A_ltln_set$'] :
( ~ 'member$'(X2,X1)
| ( 'fun_app$a'('insert$'(X2),X1) = X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
tcf(c_0_48,hypothesis,
( 'member$'('psi$','subformulas_mu$'('chi_1$'))
| 'member$'('psi$','subformulas_mu$'('chi_2$')) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
tcf(c_0_49,negated_conjecture,
( ~ 'less_eq$'('subformulas_nu$'('psi$'),'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('chi_1$')),'fun_app$a'('insert$'('strongRelease_ltln$'('chi_1$','chi_2$')),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_2$')),'subformulas_mu$'('chi_2$')))))
| ( 'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('psi$')),'subformulas_mu$'('chi_2$')) != 'subformulas_mu$'('chi_2$') ) ),
inference(spm,[status(thm)],[c_0_45,c_0_31]) ).
tcf(c_0_50,plain,
! [X6: 'A_ltln_set$',X2: 'A_ltln$',X1: 'A_ltln_set$'] :
( ~ 'less_eq$'('fun_app$a'('insert$'(X2),X6),X1)
| 'member$'(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
tcf(c_0_51,hypothesis,
( 'member$'('psi$','subformulas_mu$'('chi_1$'))
| ( 'fun_app$a'('insert$'('psi$'),'subformulas_mu$'('chi_2$')) = 'subformulas_mu$'('chi_2$') ) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
tff(c_0_52,plain,
! [X2038: 'A_ltln$'] : 'less_eq$'('subformulas_mu$'(X2038),'subfrmlsn$'(X2038)),
inference(variable_rename,[status(thm)],[axiom295]) ).
tcf(c_0_53,negated_conjecture,
( ~ 'less_eq$'('subformulas_nu$'('psi$'),'fun_app$a'('insert$'('strongRelease_ltln$'('chi_1$','chi_2$')),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_2$')),'subformulas_mu$'('chi_2$'))))
| ( 'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('psi$')),'subformulas_mu$'('chi_2$')) != 'subformulas_mu$'('chi_2$') ) ),
inference(spm,[status(thm)],[c_0_49,c_0_31]) ).
tff(c_0_54,plain,
! [X1648: 'A_ltln_set$',X1649: 'A_ltln_set$',X1650: 'A_ltln_set$'] :
( 'less_eq$'(X1648,'fun_app$a'('fun_app$b'('sup$',X1649),X1650))
| ~ 'less_eq$'(X1648,X1649) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom125])])]) ).
tff(c_0_55,plain,
! [X2033: 'A_ltln$',X2034: 'A_ltln$'] :
( 'less_eq$'('subformulas_nu$'(X2033),'subformulas_nu$'(X2034))
| ~ 'member$'(X2033,'subfrmlsn$'(X2034)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom292])])]) ).
tcf(c_0_56,hypothesis,
! [X1: 'A_ltln_set$'] :
( ~ 'less_eq$'('subformulas_mu$'('chi_2$'),X1)
| 'member$'('psi$',X1)
| 'member$'('psi$','subformulas_mu$'('chi_1$')) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
tcf(c_0_57,plain,
! [X2: 'A_ltln$'] : 'less_eq$'('subformulas_mu$'(X2),'subfrmlsn$'(X2)),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
tff(c_0_58,plain,
! [X2036: 'A_ltln$',X2037: 'A_ltln$'] :
( 'less_eq$'('subformulas_mu$'(X2036),'subformulas_mu$'(X2037))
| ~ 'member$'(X2036,'subfrmlsn$'(X2037)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom294])])]) ).
tcf(c_0_59,negated_conjecture,
( ~ 'less_eq$'('subformulas_nu$'('psi$'),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_2$')),'subformulas_mu$'('chi_2$')))
| ( 'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('psi$')),'subformulas_mu$'('chi_2$')) != 'subformulas_mu$'('chi_2$') ) ),
inference(spm,[status(thm)],[c_0_53,c_0_20]) ).
tcf(c_0_60,plain,
! [X1: 'A_ltln_set$',X7: 'A_ltln_set$',X6: 'A_ltln_set$'] :
( ~ 'less_eq$'(X1,X6)
| 'less_eq$'(X1,'fun_app$a'('fun_app$b'('sup$',X6),X7)) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
tcf(c_0_61,plain,
! [X2: 'A_ltln$',X3: 'A_ltln$'] :
( ~ 'member$'(X2,'subfrmlsn$'(X3))
| 'less_eq$'('subformulas_nu$'(X2),'subformulas_nu$'(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
tcf(c_0_62,hypothesis,
( 'member$'('psi$','subformulas_mu$'('chi_1$'))
| 'member$'('psi$','subfrmlsn$'('chi_2$')) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
tcf(c_0_63,plain,
! [X2: 'A_ltln$',X3: 'A_ltln$'] :
( ~ 'member$'(X2,'subfrmlsn$'(X3))
| 'less_eq$'('subformulas_mu$'(X2),'subformulas_mu$'(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
tcf(c_0_64,negated_conjecture,
( ~ 'less_eq$'('subformulas_nu$'('psi$'),'subformulas_nu$'('chi_2$'))
| ( 'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('psi$')),'subformulas_mu$'('chi_2$')) != 'subformulas_mu$'('chi_2$') ) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
tcf(c_0_65,hypothesis,
( 'less_eq$'('subformulas_nu$'('psi$'),'subformulas_nu$'('chi_2$'))
| 'member$'('psi$','subformulas_mu$'('chi_1$')) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
tcf(c_0_66,plain,
! [X1: 'A_ltln_set$',X6: 'A_ltln_set$'] :
( ~ 'less_eq$'(X1,X6)
| ( 'fun_app$a'('fun_app$b'('sup$',X1),X6) = X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
tcf(c_0_67,hypothesis,
( 'less_eq$'('subformulas_mu$'('psi$'),'subformulas_mu$'('chi_2$'))
| 'member$'('psi$','subformulas_mu$'('chi_1$')) ),
inference(spm,[status(thm)],[c_0_63,c_0_62]) ).
tcf(c_0_68,negated_conjecture,
( ( 'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('psi$')),'subformulas_mu$'('chi_2$')) != 'subformulas_mu$'('chi_2$') )
| 'member$'('psi$','subformulas_mu$'('chi_1$')) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
tcf(c_0_69,hypothesis,
'member$'('psi$','subformulas_mu$'('chi_1$')),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]) ).
tcf(c_0_70,hypothesis,
'fun_app$a'('insert$'('psi$'),'subformulas_mu$'('chi_1$')) = 'subformulas_mu$'('chi_1$'),
inference(spm,[status(thm)],[c_0_47,c_0_69]) ).
tcf(c_0_71,hypothesis,
! [X1: 'A_ltln_set$'] :
( ~ 'less_eq$'('subformulas_mu$'('chi_1$'),X1)
| 'member$'('psi$',X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_70]) ).
tcf(c_0_72,negated_conjecture,
( ~ 'less_eq$'('subformulas_mu$'('psi$'),'subformulas_mu$'('chi_1$'))
| ~ 'less_eq$'('subformulas_nu$'('psi$'),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_1$')),'fun_app$a'('fun_app$b'('sup$','subformulas_mu$'('chi_1$')),'fun_app$a'('insert$'('strongRelease_ltln$'('chi_1$','chi_2$')),'fun_app$a'('fun_app$b'('sup$','subformulas_nu$'('chi_2$')),'subformulas_mu$'('chi_2$')))))) ),
inference(spm,[status(thm)],[c_0_32,c_0_60]) ).
tcf(c_0_73,hypothesis,
'member$'('psi$','subfrmlsn$'('chi_1$')),
inference(spm,[status(thm)],[c_0_71,c_0_57]) ).
tcf(c_0_74,negated_conjecture,
( ~ 'less_eq$'('subformulas_nu$'('psi$'),'subformulas_nu$'('chi_1$'))
| ~ 'less_eq$'('subformulas_mu$'('psi$'),'subformulas_mu$'('chi_1$')) ),
inference(spm,[status(thm)],[c_0_72,c_0_60]) ).
tcf(c_0_75,hypothesis,
'less_eq$'('subformulas_nu$'('psi$'),'subformulas_nu$'('chi_1$')),
inference(spm,[status(thm)],[c_0_61,c_0_73]) ).
tcf(c_0_76,negated_conjecture,
~ 'less_eq$'('subformulas_mu$'('psi$'),'subformulas_mu$'('chi_1$')),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75])]) ).
cnf(c_0_77,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_73]),c_0_76]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP369_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n006.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 22:35:27 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.17/2.56 % Version: 3.5.1
% 6.17/2.56 % Preprocessing class: FSLSSMSMSSSNFFN.
% 6.17/2.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.17/2.56 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 6.17/2.56 % Starting new_bool_3 with 300s (1) cores
% 6.17/2.56 % Starting new_bool_1 with 300s (1) cores
% 6.17/2.56 % Starting sh5l with 300s (1) cores
% 6.17/2.56 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1403849 completed with status 0
% 6.17/2.56 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 6.17/2.56 % Preprocessing class: FSLSSMSMSSSNFFN.
% 6.17/2.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.17/2.56 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 6.17/2.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.17/2.56 % No SInE strategy applied
% 6.17/2.56 % Search class: FGHSM-SMLM31-DFFFFFNN
% 6.17/2.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 6.17/2.56 % Starting SubtermCWHack with 136s (1) cores
% 6.17/2.56 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 6.17/2.56 % Starting SAT001_MinMin_p005000_rr_RG with 148s (1) cores
% 6.17/2.56 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 136s (1) cores
% 6.17/2.56 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 6.17/2.56 % G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with pid 1403857 completed with status 0
% 6.17/2.56 % Result found by G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y
% 6.17/2.56 % Preprocessing class: FSLSSMSMSSSNFFN.
% 6.17/2.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.17/2.56 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 6.17/2.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.17/2.56 % No SInE strategy applied
% 6.17/2.56 % Search class: FGHSM-SMLM31-DFFFFFNN
% 6.17/2.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 6.17/2.56 % Starting SubtermCWHack with 136s (1) cores
% 6.17/2.56 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 6.17/2.56 % Starting SAT001_MinMin_p005000_rr_RG with 148s (1) cores
% 6.17/2.56 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 136s (1) cores
% 6.17/2.56 % Preprocessing time : 0.044 s
% 6.17/2.56 % Presaturation interreduction done
% 6.17/2.56
% 6.17/2.56 % Proof found!
% 6.17/2.56 % SZS status Theorem
% 6.17/2.56 % SZS output start CNFRefutation
% See solution above
% 6.17/2.56 % Parsed axioms : 750
% 6.17/2.56 % Removed by relevancy pruning/SinE : 0
% 6.17/2.56 % Initial clauses : 29898
% 6.17/2.56 % Removed in clause preprocessing : 26805
% 6.17/2.56 % Initial clauses in saturation : 3093
% 6.17/2.56 % Processed clauses : 7531
% 6.17/2.56 % ...of these trivial : 60
% 6.17/2.56 % ...subsumed : 2353
% 6.17/2.56 % ...remaining for further processing : 5117
% 6.17/2.56 % Other redundant clauses eliminated : 1476
% 6.17/2.56 % Clauses deleted for lack of memory : 0
% 6.17/2.56 % Backward-subsumed : 146
% 6.17/2.56 % Backward-rewritten : 123
% 6.17/2.56 % Generated clauses : 12850
% 6.17/2.56 % ...of the previous two non-redundant : 10823
% 6.17/2.56 % ...aggressively subsumed : 0
% 6.17/2.56 % Contextual simplify-reflections : 50
% 6.17/2.56 % Paramodulations : 11345
% 6.17/2.56 % Factorizations : 26
% 6.17/2.56 % NegExts : 0
% 6.17/2.56 % Equation resolutions : 1497
% 6.17/2.56 % Disequality decompositions : 0
% 6.17/2.56 % Total rewrite steps : 6241
% 6.17/2.56 % ...of those cached : 5356
% 6.17/2.56 % Propositional unsat checks : 1
% 6.17/2.56 % Propositional check models : 1
% 6.17/2.56 % Propositional check unsatisfiable : 0
% 6.17/2.56 % Propositional clauses : 0
% 6.17/2.56 % Propositional clauses after purity: 0
% 6.17/2.56 % Propositional unsat core size : 0
% 6.17/2.56 % Propositional preprocessing time : 0.000
% 6.17/2.56 % Propositional encoding time : 0.025
% 6.17/2.56 % Propositional solver time : 0.009
% 6.17/2.56 % Success case prop preproc time : 0.000
% 6.17/2.56 % Success case prop encoding time : 0.000
% 6.17/2.56 % Success case prop solver time : 0.000
% 6.17/2.56 % Current number of processed clauses : 1675
% 6.17/2.56 % Positive orientable unit clauses : 205
% 6.17/2.56 % Positive unorientable unit clauses: 8
% 6.17/2.56 % Negative unit clauses : 399
% 6.17/2.56 % Non-unit-clauses : 1063
% 6.17/2.56 % Current number of unprocessed clauses: 8737
% 6.17/2.56 % ...number of literals in the above : 27175
% 6.17/2.56 % Current number of archived formulas : 0
% 6.17/2.56 % Current number of archived clauses : 2707
% 6.17/2.56 % Clause-clause subsumption calls (NU) : 1939718
% 6.17/2.56 % Rec. Clause-clause subsumption calls : 269882
% 6.17/2.56 % Non-unit clause-clause subsumptions : 1678
% 6.17/2.56 % Unit Clause-clause subsumption calls : 113351
% 6.17/2.56 % Rewrite failures with RHS unbound : 0
% 6.17/2.56 % BW rewrite match attempts : 472
% 6.17/2.56 % BW rewrite match successes : 370
% 6.17/2.56 % Condensation attempts : 0
% 6.17/2.56 % Condensation successes : 0
% 6.17/2.56 % Termbank termtop insertions : 1447266
% 6.17/2.56 % Search garbage collected termcells : 200833
% 6.17/2.56
% 6.17/2.56 % -------------------------------------------------
% 6.17/2.56 % User time : 1.884 s
% 6.17/2.56 % System time : 0.118 s
% 6.17/2.56 % Total time : 2.002 s
% 6.17/2.56 % Maximum resident set size: 65032 pages
% 6.17/2.56
% 6.17/2.56 % -------------------------------------------------
% 6.17/2.56 % User time : 7.502 s
% 6.17/2.56 % System time : 0.509 s
% 6.17/2.56 % Total time : 8.010 s
% 6.17/2.56 % Maximum resident set size: 6400 pages
% 6.17/2.56 % E exiting
%------------------------------------------------------------------------------