%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP367_1 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 : Tue Sep 29 11:33:43 AM UTC 2026
% Result : Theorem 1.65s 1.87s
% Output : Refutation 6.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 52 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 50 ( 25 ~; 18 |; 5 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 20 ( 19 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 14 usr; 1 prp; 0-4 aty)
% Number of functors : 121 ( 121 usr; 37 con; 0-4 aty)
% Number of variables : 20 ( 20 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'A_ltln_set_a_ltln_set_set_fun$': $tType ).
tff(type_def_6,type,
'A_ltln_set_a_ltln_set_set_a_ltln_set_set_fun_fun$': $tType ).
tff(type_def_7,type,
'A_ltln_set_a_ltln_set_bool_fun_fun$': $tType ).
tff(type_def_8,type,
'A_ltln_set_bool_fun$': $tType ).
tff(type_def_9,type,
'A_ltln_set_set_a_ltln_set_set_a_ltln_set_set_fun_fun$': $tType ).
tff(type_def_10,type,
'A_ltln_set_set_a_ltln_set_fun$': $tType ).
tff(type_def_11,type,
'A_ltln_bool_fun$': $tType ).
tff(type_def_12,type,
'A_ltln_set_set_set$': $tType ).
tff(type_def_13,type,
'A_ltln_set$': $tType ).
tff(type_def_14,type,
'A_ltln_set_set_bool_fun$': $tType ).
tff(type_def_15,type,
'A_ltln$': $tType ).
tff(type_def_16,type,
'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$': $tType ).
tff(type_def_17,type,
'A_ltln_a_ltln_set_a_ltln_set_fun_fun$': $tType ).
tff(type_def_18,type,
'A_ltln_set_a_ltln_set_fun$': $tType ).
tff(type_def_19,type,
'A_ltln_a_ltln_set_set_fun$': $tType ).
tff(type_def_20,type,
'A_ltln_set_set_a_ltln_set_set_fun$': $tType ).
tff(type_def_21,type,
'A_ltln_a_ltln_set_fun$': $tType ).
tff(type_def_22,type,
'A_ltln_a_ltln_bool_fun_fun$': $tType ).
tff(type_def_23,type,
'A_ltln_set_set$': $tType ).
tff(func_def_0,type,
'member$': 'A_ltln$' > 'A_ltln_set_bool_fun$' ).
tff(func_def_1,type,
'subformulas_nu$': 'A_ltln_a_ltln_set_fun$' ).
tff(func_def_2,type,
'sup_fin$a': 'A_ltln_set_set_a_ltln_set_fun$' ).
tff(func_def_3,type,
'bot$': 'A_ltln_set_set$' ).
tff(func_def_4,type,
'inf_fin$a': 'A_ltln_set_set_a_ltln_set_fun$' ).
tff(func_def_5,type,
'fun_app$l': ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln$' ) > 'A_ltln_bool_fun$' ).
tff(func_def_6,type,
'bind$c': ( 'A_ltln_set$' * 'A_ltln_a_ltln_set_fun$' ) > 'A_ltln_set$' ).
tff(func_def_7,type,
'bot$c': 'A_ltln_bool_fun$' ).
tff(func_def_8,type,
'insert$': ( 'A_ltln_set_set$' * 'A_ltln_set_set_set$' ) > 'A_ltln_set_set_set$' ).
tff(func_def_9,type,
'insert$b': 'A_ltln_a_ltln_set_a_ltln_set_fun_fun$' ).
tff(func_def_10,type,
'disjnt$a': 'A_ltln_set_a_ltln_set_bool_fun_fun$' ).
tff(func_def_11,type,
'x$': 'A_ltln_set$' ).
tff(func_def_12,type,
'minus$a': 'A_ltln_set_set_a_ltln_set_set_a_ltln_set_set_fun_fun$' ).
tff(func_def_13,type,
'is_singleton$a': 'A_ltln_set_set_bool_fun$' ).
tff(func_def_14,type,
'fun_app$g': ( 'A_ltln_set_a_ltln_set_bool_fun_fun$' * 'A_ltln_set$' ) > 'A_ltln_set_bool_fun$' ).
tff(func_def_15,type,
'minus$b': 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' ).
tff(func_def_16,type,
'minus$': ( 'A_ltln_set_set_set$' * 'A_ltln_set_set_set$' ) > 'A_ltln_set_set_set$' ).
tff(func_def_17,type,
'less_eq$a': 'A_ltln_set_set$' > 'A_ltln_set_set_bool_fun$' ).
tff(func_def_18,type,
'bind$': ( 'A_ltln_set$' * 'A_ltln_a_ltln_set_set_fun$' ) > 'A_ltln_set_set$' ).
tff(func_def_19,type,
'filter$a': 'A_ltln_bool_fun$' > 'A_ltln_set_a_ltln_set_fun$' ).
tff(func_def_20,type,
'y$': 'A_ltln_set$' ).
tff(func_def_21,type,
'fun_app$h': ( 'A_ltln_a_ltln_set_fun$' * 'A_ltln$' ) > 'A_ltln_set$' ).
tff(func_def_22,type,
'subformulas_mu$': 'A_ltln_a_ltln_set_fun$' ).
tff(func_def_23,type,
'fun_app$i': ( 'A_ltln_set_set_a_ltln_set_fun$' * 'A_ltln_set_set$' ) > 'A_ltln_set$' ).
tff(func_def_24,type,
'is_empty$a': 'A_ltln_set_set_bool_fun$' ).
tff(func_def_25,type,
'fun_app$e': ( 'A_ltln_set_set_a_ltln_set_set_fun$' * 'A_ltln_set_set$' ) > 'A_ltln_set_set$' ).
tff(func_def_26,type,
'is_singleton$': 'A_ltln_set_bool_fun$' ).
tff(func_def_27,type,
'collect$a': 'A_ltln_bool_fun$' > 'A_ltln_set$' ).
tff(func_def_28,type,
'insert$a': 'A_ltln_set_a_ltln_set_set_a_ltln_set_set_fun_fun$' ).
tff(func_def_29,type,
'max$': 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' ).
tff(func_def_30,type,
'sup$b': ( 'A_ltln_set_set_set$' * 'A_ltln_set_set_set$' ) > 'A_ltln_set_set_set$' ).
tff(func_def_31,type,
'sup_fin$': 'A_ltln_set_set_set$' > 'A_ltln_set_set$' ).
tff(func_def_32,type,
'uu$': 'A_ltln_set_set$' > 'A_ltln_set_bool_fun$' ).
tff(func_def_33,type,
'inf$a': 'A_ltln_set_set_a_ltln_set_set_a_ltln_set_set_fun_fun$' ).
tff(func_def_34,type,
'inf_fin$': 'A_ltln_set_set_set$' > 'A_ltln_set_set$' ).
tff(func_def_35,type,
'bind$a': ( 'A_ltln_set_set$' * 'A_ltln_set_a_ltln_set_fun$' ) > 'A_ltln_set$' ).
tff(func_def_36,type,
'bind$b': ( 'A_ltln_set_set$' * 'A_ltln_set_a_ltln_set_set_fun$' ) > 'A_ltln_set_set$' ).
tff(func_def_37,type,
'inf$': 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' ).
tff(func_def_38,type,
'fun_app$k': ( 'A_ltln_set_a_ltln_set_set_fun$' * 'A_ltln_set$' ) > 'A_ltln_set_set$' ).
tff(func_def_39,type,
'fun_app$m': ( 'A_ltln_set_a_ltln_set_set_a_ltln_set_set_fun_fun$' * 'A_ltln_set$' ) > 'A_ltln_set_set_a_ltln_set_set_fun$' ).
tff(func_def_40,type,
'bot$a': 'A_ltln_set$' ).
tff(func_def_41,type,
'fun_app$j': ( 'A_ltln_a_ltln_set_set_fun$' * 'A_ltln$' ) > 'A_ltln_set_set$' ).
tff(func_def_42,type,
'disjnt$': 'A_ltln_set_set$' > 'A_ltln_set_set_bool_fun$' ).
tff(func_def_43,type,
'fold$a': ( 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' * 'A_ltln_set$' ) > 'A_ltln_set_set_a_ltln_set_fun$' ).
tff(func_def_44,type,
'is_empty$': 'A_ltln_set_bool_fun$' ).
tff(func_def_45,type,
'sup$a': 'A_ltln_set_set_a_ltln_set_set_a_ltln_set_set_fun_fun$' ).
tff(func_def_46,type,
'fun_app$n': ( 'A_ltln_a_ltln_set_a_ltln_set_fun_fun$' * 'A_ltln$' ) > 'A_ltln_set_a_ltln_set_fun$' ).
tff(func_def_47,type,
'fold$': 'A_ltln_a_ltln_set_a_ltln_set_fun_fun$' > 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' ).
tff(func_def_48,type,
'the_elem$': 'A_ltln_set$' > 'A_ltln$' ).
tff(func_def_49,type,
'bot$d': 'A_ltln_set_bool_fun$' ).
tff(func_def_50,type,
'fun_app$f': ( 'A_ltln_set_set_a_ltln_set_set_a_ltln_set_set_fun_fun$' * 'A_ltln_set_set$' ) > 'A_ltln_set_set_a_ltln_set_set_fun$' ).
tff(func_def_51,type,
'collect$': 'A_ltln_set_bool_fun$' > 'A_ltln_set_set$' ).
tff(func_def_52,type,
'sup$': 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' ).
tff(func_def_53,type,
'less_eq$': 'A_ltln_set_a_ltln_set_bool_fun_fun$' ).
tff(func_def_54,type,
'the_elem$a': 'A_ltln_set_set_a_ltln_set_fun$' ).
tff(func_def_55,type,
'finite$a': 'A_ltln_set_set_bool_fun$' ).
tff(func_def_56,type,
'finite$': 'A_ltln_set_bool_fun$' ).
tff(func_def_57,type,
'member$a': 'A_ltln_set$' > 'A_ltln_set_set_bool_fun$' ).
tff(func_def_58,type,
'uua$': 'A_ltln_set$' > 'A_ltln_bool_fun$' ).
tff(func_def_59,type,
'bot$b': 'A_ltln_set_set_set$' ).
tff(func_def_60,type,
'fun_app$d': ( 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' * 'A_ltln_set$' ) > 'A_ltln_set_a_ltln_set_fun$' ).
tff(func_def_61,type,
'remove$': 'A_ltln_a_ltln_set_a_ltln_set_fun_fun$' ).
tff(func_def_62,type,
'filter$': 'A_ltln_set_bool_fun$' > 'A_ltln_set_set_a_ltln_set_set_fun$' ).
tff(func_def_63,type,
'phi$': 'A_ltln$' ).
tff(func_def_64,type,
'fun_app$c': ( 'A_ltln_set_a_ltln_set_fun$' * 'A_ltln_set$' ) > 'A_ltln_set$' ).
tff(func_def_65,type,
sK4: ( 'A_ltln_set$' * 'A_ltln_set$' * 'A_ltln_set$' ) > 'A_ltln_set$' ).
tff(func_def_66,type,
sK5: ( 'A_ltln_set$' * 'A_ltln_set$' * 'A_ltln_set$' ) > 'A_ltln_set$' ).
tff(func_def_67,type,
sK6: 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' > 'A_ltln_set$' ).
tff(func_def_68,type,
sK7: 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' > 'A_ltln_set$' ).
tff(func_def_69,type,
sK8: 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' > 'A_ltln_set$' ).
tff(func_def_70,type,
sK9: 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' > 'A_ltln_set$' ).
tff(func_def_71,type,
sK10: 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' > 'A_ltln_set$' ).
tff(func_def_72,type,
sK11: 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' > 'A_ltln_set$' ).
tff(func_def_73,type,
sK12: 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' > 'A_ltln_set$' ).
tff(func_def_74,type,
sK13: ( 'A_ltln_set$' * 'A_ltln_set_bool_fun$' ) > 'A_ltln$' ).
tff(func_def_75,type,
sK14: ( 'A_ltln_set$' * 'A_ltln_set_bool_fun$' ) > 'A_ltln_set$' ).
tff(func_def_76,type,
sK15: ( 'A_ltln_set$' * 'A_ltln_set_bool_fun$' ) > 'A_ltln$' ).
tff(func_def_77,type,
sK16: ( 'A_ltln_set$' * 'A_ltln_set_bool_fun$' ) > 'A_ltln_set$' ).
tff(func_def_78,type,
sK17: 'A_ltln_set_bool_fun$' > 'A_ltln_set$' ).
tff(func_def_79,type,
sK18: 'A_ltln_set_bool_fun$' > 'A_ltln$' ).
tff(func_def_80,type,
sK19: 'A_ltln_set_bool_fun$' > 'A_ltln_set$' ).
tff(func_def_81,type,
sK20: 'A_ltln_set_bool_fun$' > 'A_ltln$' ).
tff(func_def_82,type,
sK21: 'A_ltln_set_bool_fun$' > 'A_ltln$' ).
tff(func_def_83,type,
sK22: 'A_ltln_set_bool_fun$' > 'A_ltln_set$' ).
tff(func_def_84,type,
sK23: 'A_ltln_set_bool_fun$' > 'A_ltln$' ).
tff(func_def_85,type,
sK24: 'A_ltln_set_bool_fun$' > 'A_ltln_set$' ).
tff(func_def_86,type,
sK25: 'A_ltln_set$' > 'A_ltln_set$' ).
tff(func_def_87,type,
sK26: 'A_ltln_set$' > 'A_ltln$' ).
tff(func_def_88,type,
sK27: 'A_ltln_set$' > 'A_ltln_set$' ).
tff(func_def_89,type,
sK28: 'A_ltln_set$' > 'A_ltln$' ).
tff(func_def_90,type,
sK29: 'A_ltln_set_a_ltln_set_fun$' > 'A_ltln_set$' ).
tff(func_def_91,type,
sK30: 'A_ltln_set_a_ltln_set_fun$' > 'A_ltln_set$' ).
tff(func_def_92,type,
sK31: 'A_ltln_set_a_ltln_set_fun$' > 'A_ltln_set$' ).
tff(func_def_93,type,
sK32: 'A_ltln_set_a_ltln_set_fun$' > 'A_ltln_set$' ).
tff(func_def_94,type,
sK33: 'A_ltln_set_a_ltln_set_fun$' > 'A_ltln_set$' ).
tff(func_def_95,type,
sK34: 'A_ltln_set_a_ltln_set_fun$' > 'A_ltln_set$' ).
tff(func_def_96,type,
sK35: 'A_ltln_set_a_ltln_set_fun$' > 'A_ltln_set$' ).
tff(func_def_97,type,
sK36: 'A_ltln_set_a_ltln_set_fun$' > 'A_ltln_set$' ).
tff(func_def_98,type,
sK37: 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' > 'A_ltln_set$' ).
tff(func_def_99,type,
sK38: 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' > 'A_ltln_set$' ).
tff(func_def_100,type,
sK39: 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' > 'A_ltln_set$' ).
tff(func_def_101,type,
sK40: 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' > 'A_ltln_set$' ).
tff(func_def_102,type,
sK41: 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' > 'A_ltln_set$' ).
tff(func_def_103,type,
sK42: 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' > 'A_ltln_set$' ).
tff(func_def_104,type,
sK43: 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' > 'A_ltln_set$' ).
tff(func_def_105,type,
sK44: 'A_ltln_set$' ).
tff(func_def_106,type,
sK45: 'A_ltln_set$' ).
tff(func_def_107,type,
sK46: 'A_ltln_set$' ).
tff(func_def_108,type,
sK47: 'A_ltln_set$' ).
tff(func_def_109,type,
sK48: 'A_ltln_set$' ).
tff(func_def_110,type,
sK49: 'A_ltln_set$' ).
tff(func_def_111,type,
sK50: 'A_ltln_set$' > 'A_ltln$' ).
tff(func_def_112,type,
sK51: ( 'A_ltln_set$' * 'A_ltln_set$' ) > 'A_ltln$' ).
tff(func_def_113,type,
sK52: 'A_ltln_set$' > 'A_ltln$' ).
tff(func_def_114,type,
sK53: ( 'A_ltln_set$' * 'A_ltln_set$' ) > 'A_ltln$' ).
tff(func_def_115,type,
sK54: 'A_ltln_set$' > 'A_ltln$' ).
tff(func_def_116,type,
sK55: ( 'A_ltln_set$' * 'A_ltln_set$' ) > 'A_ltln$' ).
tff(func_def_117,type,
sK56: 'A_ltln_set$' > 'A_ltln$' ).
tff(func_def_118,type,
sK57: ( 'A_ltln$' * 'A_ltln_set$' ) > 'A_ltln_set$' ).
tff(func_def_119,type,
sK58: ( 'A_ltln_set$' * 'A_ltln_set$' * 'A_ltln$' * 'A_ltln$' ) > 'A_ltln_set$' ).
tff(func_def_120,type,
sK59: ( 'A_ltln$' * 'A_ltln_set$' ) > 'A_ltln_set$' ).
tff(pred_def_1,type,
'comp_fun_idem$': 'A_ltln_set_set_a_ltln_set_set_a_ltln_set_set_fun_fun$' > $o ).
tff(pred_def_2,type,
'fun_app$b': ( 'A_ltln_set_set_bool_fun$' * 'A_ltln_set_set$' ) > $o ).
tff(pred_def_3,type,
'fun_app$a': ( 'A_ltln_set_bool_fun$' * 'A_ltln_set$' ) > $o ).
tff(pred_def_4,type,
'finite$b': 'A_ltln_set_set_set$' > $o ).
tff(pred_def_5,type,
'comp_fun_idem$a': 'A_ltln_set_a_ltln_set_a_ltln_set_fun_fun$' > $o ).
tff(pred_def_6,type,
'member$b': ( 'A_ltln_set_set$' * 'A_ltln_set_set_set$' ) > $o ).
tff(pred_def_7,type,
'comp_fun_idem$b': 'A_ltln_set_a_ltln_set_set_a_ltln_set_set_fun_fun$' > $o ).
tff(pred_def_8,type,
'fun_app$': ( 'A_ltln_bool_fun$' * 'A_ltln$' ) > $o ).
tff(pred_def_9,type,
'less_eq$b': ( 'A_ltln_set_set_set$' * 'A_ltln_set_set_set$' ) > $o ).
tff(pred_def_10,type,
'comp_fun_idem$c': 'A_ltln_a_ltln_set_a_ltln_set_fun_fun$' > $o ).
tff(pred_def_11,type,
sP0: ( 'A_ltln_set$' * 'A_ltln_set$' * 'A_ltln$' ) > $o ).
tff(pred_def_12,type,
sP1: ( 'A_ltln_set$' * 'A_ltln_set$' * 'A_ltln$' ) > $o ).
tff(pred_def_13,type,
sP2: ( 'A_ltln_set$' * 'A_ltln_set$' * 'A_ltln$' * 'A_ltln$' ) > $o ).
tff(pred_def_14,type,
sP3: ( 'A_ltln$' * 'A_ltln$' * 'A_ltln_set$' * 'A_ltln_set$' ) > $o ).
tff(f3,conjecture,
'fun_app$a'('finite$','fun_app$c'('fun_app$d'('sup$','x$'),'y$')),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture2) ).
tff(f4,negated_conjecture,
~ 'fun_app$a'('finite$','fun_app$c'('fun_app$d'('sup$','x$'),'y$')),
inference(negated_conjecture,[status(cth)],[f3]) ).
tff(f66,axiom,
! [X0: 'A_ltln_set$',X1: 'A_ltln_set$'] :
( ~ 'fun_app$a'('finite$','fun_app$c'('fun_app$d'('sup$',X0),X1))
<=> ( ~ 'fun_app$a'('finite$',X0)
| ~ 'fun_app$a'('finite$',X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom64) ).
tff(f71,axiom,
'fun_app$a'('fun_app$g'('less_eq$','y$'),'fun_app$h'('subformulas_nu$','phi$')),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom69) ).
tff(f72,axiom,
'fun_app$a'('fun_app$g'('less_eq$','x$'),'fun_app$h'('subformulas_mu$','phi$')),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom70) ).
tff(f264,axiom,
! [X0: 'A_ltln_set$',X1: 'A_ltln_set$'] :
( ( 'fun_app$a'('finite$',X0)
& 'fun_app$a'('fun_app$g'('less_eq$',X1),X0) )
=> 'fun_app$a'('finite$',X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom262) ).
tff(f289,axiom,
! [X0: 'A_ltln$'] : 'fun_app$a'('finite$','fun_app$h'('subformulas_mu$',X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom287) ).
tff(f290,axiom,
! [X0: 'A_ltln$'] : 'fun_app$a'('finite$','fun_app$h'('subformulas_nu$',X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom288) ).
tff(f642,plain,
~ 'fun_app$a'('finite$','fun_app$c'('fun_app$d'('sup$','x$'),'y$')),
inference(flattening,[],[f4]) ).
tff(f719,plain,
! [X0: 'A_ltln_set$',X1: 'A_ltln_set$'] :
( 'fun_app$a'('finite$',X1)
| ~ 'fun_app$a'('finite$',X0)
| ~ 'fun_app$a'('fun_app$g'('less_eq$',X1),X0) ),
inference(ennf_transformation,[],[f264]) ).
tff(f720,plain,
! [X0: 'A_ltln_set$',X1: 'A_ltln_set$'] :
( 'fun_app$a'('finite$',X1)
| ~ 'fun_app$a'('finite$',X0)
| ~ 'fun_app$a'('fun_app$g'('less_eq$',X1),X0) ),
inference(flattening,[],[f719]) ).
tff(f860,plain,
! [X0: 'A_ltln_set$',X1: 'A_ltln_set$'] :
( ( ~ 'fun_app$a'('finite$','fun_app$c'('fun_app$d'('sup$',X0),X1))
| ( 'fun_app$a'('finite$',X0)
& 'fun_app$a'('finite$',X1) ) )
& ( ~ 'fun_app$a'('finite$',X0)
| ~ 'fun_app$a'('finite$',X1)
| 'fun_app$a'('finite$','fun_app$c'('fun_app$d'('sup$',X0),X1)) ) ),
inference(nnf_transformation,[],[f66]) ).
tff(f861,plain,
! [X0: 'A_ltln_set$',X1: 'A_ltln_set$'] :
( ( ~ 'fun_app$a'('finite$','fun_app$c'('fun_app$d'('sup$',X0),X1))
| ( 'fun_app$a'('finite$',X0)
& 'fun_app$a'('finite$',X1) ) )
& ( ~ 'fun_app$a'('finite$',X0)
| ~ 'fun_app$a'('finite$',X1)
| 'fun_app$a'('finite$','fun_app$c'('fun_app$d'('sup$',X0),X1)) ) ),
inference(flattening,[],[f860]) ).
tff(f958,plain,
~ 'fun_app$a'('finite$','fun_app$c'('fun_app$d'('sup$','x$'),'y$')),
inference(cnf_transformation,[],[f642]) ).
tff(f959,plain,
'fun_app$a'('fun_app$g'('less_eq$','x$'),'fun_app$h'('subformulas_mu$','phi$')),
inference(cnf_transformation,[],[f72]) ).
tff(f960,plain,
'fun_app$a'('fun_app$g'('less_eq$','y$'),'fun_app$h'('subformulas_nu$','phi$')),
inference(cnf_transformation,[],[f71]) ).
tff(f1080,plain,
! [X0: 'A_ltln_set$',X1: 'A_ltln_set$'] :
( ~ 'fun_app$a'('fun_app$g'('less_eq$',X1),X0)
| ~ 'fun_app$a'('finite$',X0)
| 'fun_app$a'('finite$',X1) ),
inference(cnf_transformation,[],[f720]) ).
tff(f1083,plain,
! [X0: 'A_ltln_set$',X1: 'A_ltln_set$'] :
( 'fun_app$a'('finite$','fun_app$c'('fun_app$d'('sup$',X0),X1))
| ~ 'fun_app$a'('finite$',X1)
| ~ 'fun_app$a'('finite$',X0) ),
inference(cnf_transformation,[],[f861]) ).
tff(f1092,plain,
! [X0: 'A_ltln$'] : 'fun_app$a'('finite$','fun_app$h'('subformulas_mu$',X0)),
inference(cnf_transformation,[],[f289]) ).
tff(f1133,plain,
! [X0: 'A_ltln$'] : 'fun_app$a'('finite$','fun_app$h'('subformulas_nu$',X0)),
inference(cnf_transformation,[],[f290]) ).
tff(f1529,plain,
( ~ 'fun_app$a'('finite$','fun_app$h'('subformulas_mu$','phi$'))
| 'fun_app$a'('finite$','x$') ),
inference(resolution,[],[f1080,f959]) ).
tff(f1530,plain,
( ~ 'fun_app$a'('finite$','fun_app$h'('subformulas_nu$','phi$'))
| 'fun_app$a'('finite$','y$') ),
inference(resolution,[],[f1080,f960]) ).
tff(f1536,plain,
'fun_app$a'('finite$','y$'),
inference(forward_subsumption_resolution,[],[f1530,f1133]) ).
tff(f1537,plain,
'fun_app$a'('finite$','x$'),
inference(forward_subsumption_resolution,[],[f1529,f1092]) ).
tff(f1828,plain,
( ~ 'fun_app$a'('finite$','y$')
| ~ 'fun_app$a'('finite$','x$') ),
inference(resolution,[],[f1083,f958]) ).
tff(f1841,plain,
~ 'fun_app$a'('finite$','x$'),
inference(forward_subsumption_resolution,[],[f1828,f1536]) ).
tff(f1842,plain,
$false,
inference(forward_subsumption_resolution,[],[f1841,f1537]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ITP367_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n008.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.44 % DateTime : Sun Sep 27 12:57:09 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.48 Running first-order theorem proving
% 0.22/0.48 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.65/1.87 % (1198616)Detected formulas, will run a generic FOF schedule.
% 1.65/1.87 % (1198624)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=667079068:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.65/1.87 % (1198622)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2120406428:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.65/1.87 % (1198624)Refutation not found, incomplete strategy
% 1.65/1.87 % (1198624)------------------------------
% 1.65/1.87 % (1198624)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.65/1.87 % (1198624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/1.87 % (1198624)CaDiCaL version: 2.1.3
% 1.65/1.87 % (1198624)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.87 % (1198624)Time elapsed: 0.009 s
% 1.65/1.87 % (1198624)Peak memory usage: 89 MB
% 1.65/1.87 % (1198624)Instructions burned: 15 (million)
% 1.65/1.87 % (1198621)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3630031882:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.65/1.87 % (1198623)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2471474647:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.65/1.87 % (1198627)dis-21_1_sil=8000:lcm=predicate:random_seed=592942516:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 1.65/1.87 % (1198625)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4121592563:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.65/1.87 % (1198626)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3853559820:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.65/1.87 % (1198625)First to succeed.
% 1.65/1.87 % (1198625)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1198616"
% 1.65/1.87 % (1198626)Also succeeded, but the first one will report.
% 1.65/1.87 % (1198627)Instruction limit reached!
% 1.65/1.87 % (1198627)------------------------------
% 1.65/1.87 % (1198627)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.65/1.87 % (1198627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/1.87 % (1198627)CaDiCaL version: 2.1.3
% 1.65/1.87 % (1198627)Termination reason: Instruction limit
% 1.65/1.87 % (1198627)Termination phase: Saturation
% 1.65/1.87 % (1198627)Time elapsed: 0.111 s
% 1.65/1.87 % (1198627)Peak memory usage: 90 MB
% 1.65/1.87 % (1198627)Instructions burned: 130 (million)
% 1.65/1.87 % (1198624)------------------------------
% 1.65/1.87 % (1198624)------------------------------
% 1.65/1.87 % (1198635)lrs+10_1_sil=8000:sp=occurrence:random_seed=2124718475:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 1.65/1.87 % (1198636)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3712200361:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 1.65/1.87 % (1198635)Also succeeded, but the first one will report.
% 1.65/1.87 % (1198636)Instruction limit reached!
% 1.65/1.87 % (1198636)------------------------------
% 1.65/1.87 % (1198636)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.65/1.87 % (1198636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/1.87 % (1198636)CaDiCaL version: 2.1.3
% 1.65/1.87 % (1198636)Termination reason: Instruction limit
% 1.65/1.87 % (1198636)Termination phase: Saturation
% 1.65/1.87 % (1198636)Time elapsed: 0.100 s
% 1.65/1.87 % (1198636)Peak memory usage: 90 MB
% 1.65/1.87 % (1198636)Instructions burned: 158 (million)
% 1.65/1.87 % (1198625)Refutation found. Thanks to Tanya!
% 1.65/1.87 % SZS status Theorem for theBenchmark
% 1.65/1.87 % SZS output start Proof for theBenchmark
% See solution above
% 6.22/2.16 % (1198625)------------------------------
% 6.22/2.16 % (1198625)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.22/2.16 % (1198625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.22/2.16 % (1198625)CaDiCaL version: 2.1.3
% 6.22/2.16 % (1198625)Termination reason: Refutation
% 6.22/2.16 % (1198625)Time elapsed: 0.040 s
% 6.22/2.16 % (1198625)Peak memory usage: 89 MB
% 6.22/2.16 % (1198625)Instructions burned: 41 (million)
% 6.22/2.16 % (1198625)------------------------------
% 6.22/2.16 % (1198625)------------------------------
% 6.22/2.16 % (1198616)Success in time 0.817 s
% 6.22/2.16 % Vampire exiting
%------------------------------------------------------------------------------