%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP366_1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 11:39:27 AM UTC 2026
% Result : Theorem 0.76s 0.56s
% Output : Refutation 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 6 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 1 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number arithmetic : 12 ( 0 atm; 0 fun; 12 num; 0 var)
% Number of types : 27 ( 25 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 139 ( 137 usr; 18 con; 0-4 aty)
% Number of variables : 14 ( 14 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'Int_bool_fun$': $tType ).
tff(type_def_6,type,
'Nat_nat_bool_fun_fun$': $tType ).
tff(type_def_7,type,
'A_ltln_a_ltln_fun$': $tType ).
tff(type_def_8,type,
'Int_int_fun$': $tType ).
tff(type_def_9,type,
'Nat_a_set_fun_bool_fun$': $tType ).
tff(type_def_10,type,
'Num_bool_fun$': $tType ).
tff(type_def_11,type,
'Nat_nat_fun$': $tType ).
tff(type_def_12,type,
'Nat$': $tType ).
tff(type_def_13,type,
'Num$': $tType ).
tff(type_def_14,type,
'Bool_nat_fun$': $tType ).
tff(type_def_15,type,
tlbool: $tType ).
tff(type_def_16,type,
'Nat_num_fun$': $tType ).
tff(type_def_17,type,
'A_set_a_ltln_fun$': $tType ).
tff(type_def_18,type,
'A_ltln_bool_fun$': $tType ).
tff(type_def_19,type,
'A_set$': $tType ).
tff(type_def_20,type,
'A_ltln_set$': $tType ).
tff(type_def_21,type,
'A_set_list$': $tType ).
tff(type_def_22,type,
'A_ltln$': $tType ).
tff(type_def_23,type,
'Bool_bool_fun$': $tType ).
tff(type_def_24,type,
'Nat_a_set_fun$': $tType ).
tff(type_def_25,type,
'Nat_a_set_fun_set$': $tType ).
tff(type_def_26,type,
'Nat_bool_fun$': $tType ).
tff(type_def_27,type,
'A_ltln_a_set_a_ltln_fun_fun$': $tType ).
tff(type_def_28,type,
'Nat_int_fun$': $tType ).
tff(type_def_29,type,
'A_ltln_a_ltln_bool_fun_fun$': $tType ).
tff(func_def_0,type,
'w$': 'Nat_a_set_fun$' ).
tff(func_def_1,type,
'uud$': 'Nat_nat_fun$' ).
tff(func_def_2,type,
'case_nat$a': ( tlbool * 'Nat_bool_fun$' ) > 'Nat_bool_fun$' ).
tff(func_def_3,type,
'af_letter$': 'A_ltln_a_set_a_ltln_fun_fun$' ).
tff(func_def_4,type,
'plus$': ( 'Num$' * 'Num$' ) > 'Num$' ).
tff(func_def_5,type,
'f$': ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'A_ltln_set$' ).
tff(func_def_6,type,
'g_F$': ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'A_ltln_set$' ).
tff(func_def_7,type,
'mu_stable$': 'A_ltln$' > 'Nat_a_set_fun_bool_fun$' ).
tff(func_def_8,type,
'fun_app$h': ( 'A_ltln_a_set_a_ltln_fun_fun$' * 'A_ltln$' ) > 'A_set_a_ltln_fun$' ).
tff(func_def_9,type,
'sgn$': $int > $int ).
tff(func_def_10,type,
'id$': 'A_ltln_a_ltln_fun$' ).
tff(func_def_11,type,
'dbl_dec$': $int > $int ).
tff(func_def_12,type,
'bit0$': 'Num$' > 'Num$' ).
tff(func_def_13,type,
'x$': 'A_ltln_set$' ).
tff(func_def_14,type,
'uua$': 'Nat_a_set_fun_set$' > 'Nat_a_set_fun_bool_fun$' ).
tff(func_def_15,type,
'fun_app$a': ( 'Int_int_fun$' * $int ) > $int ).
tff(func_def_16,type,
'next_ltln$': 'A_ltln_a_ltln_fun$' ).
tff(func_def_17,type,
'unf$': 'A_ltln_a_ltln_fun$' ).
tff(func_def_18,type,
def_5: ( tlbool * 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_19,type,
'pred$': 'Nat_nat_fun$' ).
tff(func_def_20,type,
'suffix$': ( 'Nat$' * 'Nat_a_set_fun$' ) > 'Nat_a_set_fun$' ).
tff(func_def_21,type,
'build$': ( 'A_set$' * 'Nat_a_set_fun$' ) > 'Nat_a_set_fun$' ).
tff(func_def_22,type,
'uug$': ( 'Bool_nat_fun$' * 'Nat_bool_fun$' ) > 'Nat_nat_fun$' ).
tff(func_def_23,type,
'num_of_nat$': 'Nat_num_fun$' ).
tff(func_def_24,type,
'collect$': 'Nat_a_set_fun_bool_fun$' > 'Nat_a_set_fun_set$' ).
tff(func_def_25,type,
'of_nat$': 'Nat_int_fun$' ).
tff(func_def_26,type,
'conc$': ( 'A_set_list$' * 'Nat_a_set_fun$' ) > 'Nat_a_set_fun$' ).
tff(func_def_27,type,
'fun_app$k': ( 'Nat_int_fun$' * 'Nat$' ) > $int ).
tff(func_def_28,type,
'g$': ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'A_ltln_set$' ).
tff(func_def_29,type,
def_10: ( 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_30,type,
'gF_advice$': ( 'A_ltln$' * 'A_ltln_set$' ) > 'A_ltln$' ).
tff(func_def_31,type,
'foldl$': ( 'A_ltln_a_set_a_ltln_fun_fun$' * 'A_ltln$' * 'A_set_list$' ) > 'A_ltln$' ).
tff(func_def_32,type,
'dbl_inc$': $int > $int ).
tff(func_def_33,type,
def_1: ( 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_34,type,
'subsequence$': ( 'Nat_a_set_fun$' * 'Nat$' * 'Nat$' ) > 'A_set_list$' ).
tff(func_def_35,type,
tltrue: tlbool ).
tff(func_def_36,type,
def_8: ( 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_37,type,
'uui$': 'Nat_bool_fun$' ).
tff(func_def_38,type,
'uuf$': ( 'Nat_bool_fun$' * 'Nat_nat_fun$' ) > 'Nat_bool_fun$' ).
tff(func_def_39,type,
'fun_app$e': ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_40,type,
'inc$': 'Num$' > 'Num$' ).
tff(func_def_41,type,
'uub$': $int > 'Int_bool_fun$' ).
tff(func_def_42,type,
'numeral$': 'Num$' > $int ).
tff(func_def_43,type,
def_9: ( tlbool * 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_44,type,
'fun_app$p': ( 'Nat_num_fun$' * 'Nat$' ) > 'Num$' ).
tff(func_def_45,type,
'sub$': ( 'Num$' * 'Num$' ) > $int ).
tff(func_def_46,type,
'bit1$': 'Num$' > 'Num$' ).
tff(func_def_47,type,
'nu_stable$': 'A_ltln$' > 'Nat_a_set_fun_bool_fun$' ).
tff(func_def_48,type,
'dbl$': $int > $int ).
tff(func_def_49,type,
'f_G$': ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'A_ltln_set$' ).
tff(func_def_50,type,
'one$': 'Num$' ).
tff(func_def_51,type,
'fun_app$f': ( 'Bool_nat_fun$' * tlbool ) > 'Nat$' ).
tff(func_def_52,type,
'case_nat$': ( 'Nat$' * 'Nat_nat_fun$' ) > 'Nat_nat_fun$' ).
tff(func_def_53,type,
'fun_app$i': ( 'A_ltln_a_ltln_fun$' * 'A_ltln$' ) > 'A_ltln$' ).
tff(func_def_54,type,
'fun_app$n': ( 'Nat_nat_bool_fun_fun$' * 'Nat$' ) > 'Nat_bool_fun$' ).
tff(func_def_55,type,
'fG_advice$': ( 'A_ltln$' * 'A_ltln_set$' ) > 'A_ltln$' ).
tff(func_def_56,type,
def_4: ( tlbool * 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_57,type,
'uu$': 'A_ltln$' > 'Nat_a_set_fun_bool_fun$' ).
tff(func_def_58,type,
'language_ltln$': 'A_ltln$' > 'Nat_a_set_fun_set$' ).
tff(func_def_59,type,
'fun_app$g': ( 'A_set_a_ltln_fun$' * 'A_set$' ) > 'A_ltln$' ).
tff(func_def_60,type,
tlfalse: tlbool ).
tff(func_def_61,type,
'fun_app$j': ( 'Nat_a_set_fun$' * 'Nat$' ) > 'A_set$' ).
tff(func_def_62,type,
'nat$': $int > 'Nat$' ).
tff(func_def_63,type,
'uuj$': 'Nat_bool_fun$' ).
tff(func_def_64,type,
'less$': 'Num$' > 'Num_bool_fun$' ).
tff(func_def_65,type,
def_2: ( 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_66,type,
def_6: ( 'Bool_bool_fun$' * tlbool ) > tlbool ).
tff(func_def_67,type,
'uue$': ( 'Nat_nat_fun$' * 'Nat_nat_fun$' ) > 'Nat_nat_fun$' ).
tff(func_def_68,type,
'uuc$': $int > 'Int_int_fun$' ).
tff(func_def_69,type,
'fun_app$m': ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln$' ) > 'A_ltln_bool_fun$' ).
tff(func_def_70,type,
'uuh$': ( 'Bool_bool_fun$' * 'Nat_bool_fun$' ) > 'Nat_bool_fun$' ).
tff(func_def_71,type,
def_3: ( 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_72,type,
def_7: ( tlbool * 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_73,type,
'phi$': 'A_ltln$' ).
tff(func_def_81,type,
sK0: 'A_ltln_a_ltln_bool_fun_fun$' > 'A_ltln$' ).
tff(func_def_82,type,
sK1: 'A_ltln_a_ltln_bool_fun_fun$' > 'A_ltln$' ).
tff(func_def_83,type,
sK2: 'A_ltln_a_ltln_bool_fun_fun$' > 'A_set$' ).
tff(func_def_84,type,
sK3: ( 'Nat_a_set_fun_bool_fun$' * 'Nat_a_set_fun_bool_fun$' ) > 'Nat_a_set_fun$' ).
tff(func_def_85,type,
sK4: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_86,type,
sK5: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_87,type,
sK6: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_88,type,
sK7: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_89,type,
sK8: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_90,type,
sK9: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_91,type,
sK10: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_92,type,
sK11: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_93,type,
sK12: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_94,type,
sK13: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_95,type,
sK14: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_96,type,
sK15: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_97,type,
sK16: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_98,type,
sK17: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_99,type,
sK18: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_100,type,
sK19: 'Nat_num_fun$' > 'Nat$' ).
tff(func_def_101,type,
sK20: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_102,type,
sK21: 'Nat_num_fun$' > 'Nat$' ).
tff(func_def_103,type,
sK22: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_104,type,
sK23: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_105,type,
sK24: 'Nat$' > 'Nat$' ).
tff(func_def_106,type,
sK25: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_107,type,
sK26: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_108,type,
sK27: 'Nat$' > 'Nat$' ).
tff(func_def_109,type,
sK28: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_110,type,
sK29: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_111,type,
sK30: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_112,type,
sK31: 'Nat$' > 'Nat$' ).
tff(func_def_113,type,
sK32: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_114,type,
sK33: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_115,type,
sK34: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_116,type,
sK35: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_117,type,
sK36: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_118,type,
sK37: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_119,type,
sK38: 'Nat$' > 'Nat$' ).
tff(func_def_120,type,
sK39: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_121,type,
sK40: ( 'Nat_a_set_fun$' * 'A_ltln$' * 'A_ltln_set$' ) > 'Nat$' ).
tff(func_def_122,type,
sK41: ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_fun$' ) > 'A_ltln$' ).
tff(func_def_123,type,
sK42: ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_fun$' ) > 'A_ltln$' ).
tff(func_def_124,type,
sK43: ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_fun$' ) > 'A_ltln_set$' ).
tff(func_def_125,type,
sK44: 'A_ltln_a_ltln_fun$' > 'Nat_a_set_fun$' ).
tff(func_def_126,type,
sK45: 'A_ltln_a_ltln_fun$' > 'A_ltln$' ).
tff(func_def_127,type,
sK46: 'A_ltln_a_ltln_fun$' > 'A_ltln_set$' ).
tff(func_def_128,type,
sK47: 'A_ltln_a_ltln_fun$' > 'Nat_a_set_fun$' ).
tff(func_def_129,type,
sK48: 'A_ltln_a_ltln_fun$' > 'A_ltln$' ).
tff(func_def_130,type,
sK49: 'A_ltln_a_ltln_fun$' > 'A_ltln_set$' ).
tff(func_def_131,type,
sK50: ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_fun$' ) > 'A_ltln$' ).
tff(func_def_132,type,
sK51: ( 'Nat_a_set_fun$' * 'A_ltln$' * 'A_ltln_set$' * 'A_ltln$' ) > 'Nat$' ).
tff(func_def_133,type,
sK52: ( 'Nat_a_set_fun$' * 'A_ltln$' * 'A_ltln_set$' ) > 'Nat$' ).
tff(func_def_134,type,
sK53: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_135,type,
sK54: 'A_ltln_a_ltln_fun$' > 'A_ltln$' ).
tff(func_def_136,type,
sK55: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_137,type,
sK56: 'Num_bool_fun$' > 'Num$' ).
tff(func_def_138,type,
sK57: 'Num$' > 'Num$' ).
tff(func_def_139,type,
sK58: 'Num$' > 'Num$' ).
tff(func_def_140,type,
sK59: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_141,type,
sK60: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_142,type,
sK61: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_143,type,
sK62: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(pred_def_1,type,
'fun_app$b': ( 'Nat_a_set_fun_bool_fun$' * 'Nat_a_set_fun$' ) > $o ).
tff(pred_def_2,type,
'idx_sequence$': 'Nat_nat_fun$' > $o ).
tff(pred_def_3,type,
'fun_app$l': ( 'A_ltln_bool_fun$' * 'A_ltln$' ) > $o ).
tff(pred_def_4,type,
'fun_app$c': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_5,type,
'member$': ( 'Nat_a_set_fun$' * 'Nat_a_set_fun_set$' ) > $o ).
tff(pred_def_6,type,
'fun_app$d': ( 'Bool_bool_fun$' * tlbool ) > $o ).
tff(pred_def_7,type,
'fun_app$': ( 'Int_bool_fun$' * $int ) > $o ).
tff(pred_def_8,type,
'gF_advice_congruent$': ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_fun$' ) > $o ).
tff(pred_def_9,type,
'fun_app$o': ( 'Num_bool_fun$' * 'Num$' ) > $o ).
tff(pred_def_10,type,
'gF_advice_congruent_axioms$': ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_fun$' ) > $o ).
tff(pred_def_11,type,
'semantics_ltln$': ( 'Nat_a_set_fun$' * 'A_ltln$' ) > $o ).
tff(pred_def_12,type,
'af_congruent_axioms$': 'A_ltln_a_ltln_bool_fun_fun$' > $o ).
tff(f12,conjecture,
'semantics_ltln$'('suffix$'('nat$'(1),'w$'),'gF_advice$'('fun_app$g'('fun_app$h'('af_letter$','fun_app$i'('next_ltln$','phi$')),'fun_app$j'('w$','nat$'(0))),'x$')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture11) ).
tff(f13,negated_conjecture,
~ 'semantics_ltln$'('suffix$'('nat$'(1),'w$'),'gF_advice$'('fun_app$g'('fun_app$h'('af_letter$','fun_app$i'('next_ltln$','phi$')),'fun_app$j'('w$','nat$'(0))),'x$')),
inference(negated_conjecture,[status(cth)],[f12]) ).
tff(f14,axiom,
'semantics_ltln$'('w$','gF_advice$'('fun_app$i'('unf$','fun_app$i'('next_ltln$','phi$')),'x$')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom12) ).
tff(f17,axiom,
! [X0: 'Nat_a_set_fun$',X1: 'A_ltln$'] :
( 'semantics_ltln$'(X0,'fun_app$i'('next_ltln$',X1))
<=> 'semantics_ltln$'('suffix$'('nat$'(1),X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom15) ).
tff(f20,axiom,
! [X0: 'A_ltln$',X1: 'A_ltln_set$'] : ( 'gF_advice$'('fun_app$i'('next_ltln$',X0),X1) = 'fun_app$i'('next_ltln$','gF_advice$'(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom18) ).
tff(f21,axiom,
! [X0: 'A_ltln$',X1: 'A_set$'] : ( 'fun_app$g'('fun_app$h'('af_letter$','fun_app$i'('next_ltln$',X0)),X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom19) ).
tff(f23,axiom,
! [X0: 'A_ltln$'] : ( 'fun_app$i'('unf$','fun_app$i'('next_ltln$',X0)) = 'fun_app$i'('next_ltln$',X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom21) ).
tff(f623,plain,
~ 'semantics_ltln$'('suffix$'('nat$'(1),'w$'),'gF_advice$'('fun_app$g'('fun_app$h'('af_letter$','fun_app$i'('next_ltln$','phi$')),'fun_app$j'('w$','nat$'(0))),'x$')),
inference(flattening,[],[f13]) ).
tff(f865,plain,
~ 'semantics_ltln$'('suffix$'('nat$'(1),'w$'),'gF_advice$'('fun_app$g'('fun_app$h'('af_letter$','fun_app$i'('next_ltln$','phi$')),'fun_app$j'('w$','nat$'(0))),'x$')),
inference(cnf_transformation,[],[f623]) ).
tff(f866,plain,
'semantics_ltln$'('w$','gF_advice$'('fun_app$i'('unf$','fun_app$i'('next_ltln$','phi$')),'x$')),
inference(cnf_transformation,[],[f14]) ).
tff(f870,plain,
! [X0: 'Nat_a_set_fun$',X1: 'A_ltln$'] :
( ~ 'semantics_ltln$'(X0,'fun_app$i'('next_ltln$',X1))
| 'semantics_ltln$'('suffix$'('nat$'(1),X0),X1) ),
inference(cnf_transformation,[],[f17]) ).
tff(f874,plain,
! [X0: 'A_ltln$',X1: 'A_ltln_set$'] : ( 'gF_advice$'('fun_app$i'('next_ltln$',X0),X1) = 'fun_app$i'('next_ltln$','gF_advice$'(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
tff(f875,plain,
! [X0: 'A_ltln$',X1: 'A_set$'] : ( 'fun_app$g'('fun_app$h'('af_letter$','fun_app$i'('next_ltln$',X0)),X1) = X0 ),
inference(cnf_transformation,[],[f21]) ).
tff(f877,plain,
! [X0: 'A_ltln$'] : ( 'fun_app$i'('next_ltln$',X0) = 'fun_app$i'('unf$','fun_app$i'('next_ltln$',X0)) ),
inference(cnf_transformation,[],[f23]) ).
tff(f2841,plain,
~ 'semantics_ltln$'('suffix$'('nat$'(1),'w$'),'gF_advice$'('phi$','x$')),
inference(superposition,[],[f865,f875]) ).
tff(f2842,plain,
'semantics_ltln$'('w$','gF_advice$'('fun_app$i'('next_ltln$','phi$'),'x$')),
inference(superposition,[],[f866,f877]) ).
tff(f3903,plain,
'semantics_ltln$'('w$','fun_app$i'('next_ltln$','gF_advice$'('phi$','x$'))),
inference(superposition,[],[f2842,f874]) ).
tff(f3909,plain,
'semantics_ltln$'('suffix$'('nat$'(1),'w$'),'gF_advice$'('phi$','x$')),
inference(resolution,[],[f3903,f870]) ).
tff(f3910,plain,
$false,
inference(forward_subsumption_resolution,[],[f3909,f2841]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP366_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n007.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
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 12:53:55 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.76/0.56 % (1393229)Will run a generic schedule for satisfiability detection.
% 0.76/0.56 % (1393234)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1319826797_2999 on theBenchmark for (2999ds/0Mi)
% 0.76/0.56 % (1393235)% WARNING: option uhcvi not known.
% 0.76/0.56 % (1393236)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1175225692:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.76/0.56 % (1393237)dis+10_1_sil=32000:sp=arity:random_seed=4139990042:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.76/0.56 % (1393235)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1107908970:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.76/0.56 % (1393238)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=591873819:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.76/0.56 % (1393240)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=144296647:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.76/0.56 % (1393239)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3706628938:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.76/0.56 % (1393234)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.76/0.56 % (1393234)Terminated due to inappropriate strategy.
% 0.76/0.56 % (1393234)------------------------------
% 0.76/0.56 % (1393234)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.56 % (1393234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.56 % (1393234)CaDiCaL version: 2.1.3
% 0.76/0.56 % (1393234)Termination reason: Inappropriate
% 0.76/0.56 % (1393234)Time elapsed: 0.018 s
% 0.76/0.56 % (1393234)Peak memory usage: 12 MB
% 0.76/0.56 % (1393234)Instructions burned: 70 (million)
% 0.76/0.56 % (1393234)------------------------------
% 0.76/0.56 % (1393234)------------------------------
% 0.76/0.56 % (1393248)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2175786171:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.76/0.56 % (1393248)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.76/0.56 % (1393248)Terminated due to inappropriate strategy.
% 0.76/0.56 % (1393248)------------------------------
% 0.76/0.56 % (1393248)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.56 % (1393248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.56 % (1393248)CaDiCaL version: 2.1.3
% 0.76/0.56 % (1393248)Termination reason: Inappropriate
% 0.76/0.56 % (1393248)Time elapsed: 0.015 s
% 0.76/0.56 % (1393248)Peak memory usage: 11 MB
% 0.76/0.56 % (1393248)Instructions burned: 62 (million)
% 0.76/0.56 % (1393248)------------------------------
% 0.76/0.56 % (1393248)------------------------------
% 0.76/0.56 % (1393237)Instruction limit reached!
% 0.76/0.56 % (1393237)------------------------------
% 0.76/0.56 % (1393237)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.56 % (1393237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.56 % (1393237)CaDiCaL version: 2.1.3
% 0.76/0.56 % (1393237)Termination reason: Instruction limit
% 0.76/0.56 % (1393237)Termination phase: Saturation
% 0.76/0.56 % (1393237)Time elapsed: 0.052 s
% 0.76/0.56 % (1393237)Peak memory usage: 13 MB
% 0.76/0.56 % (1393237)Instructions burned: 104 (million)
% 0.76/0.56 % (1393238)Instruction limit reached!
% 0.76/0.56 % (1393238)------------------------------
% 0.76/0.56 % (1393238)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.56 % (1393238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.56 % (1393238)CaDiCaL version: 2.1.3
% 0.76/0.56 % (1393238)Termination reason: Instruction limit
% 0.76/0.56 % (1393238)Termination phase: Saturation
% 0.76/0.56 % (1393238)Time elapsed: 0.059 s
% 0.76/0.56 % (1393238)Peak memory usage: 13 MB
% 0.76/0.56 % (1393238)Instructions burned: 117 (million)
% 0.76/0.56 % (1393250)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3213353605:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.76/0.56 % (1393239)Instruction limit reached!
% 0.76/0.56 % (1393239)------------------------------
% 0.76/0.56 % (1393239)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.56 % (1393239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.56 % (1393239)CaDiCaL version: 2.1.3
% 0.76/0.56 % (1393239)Termination reason: Instruction limit
% 0.76/0.56 % (1393239)Termination phase: Saturation
% 0.76/0.56 % (1393239)Time elapsed: 0.066 s
% 0.76/0.56 % (1393239)Peak memory usage: 13 MB
% 0.76/0.56 % (1393239)Instructions burned: 131 (million)
% 0.76/0.56 % (1393251)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=4077041089:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.76/0.56 % (1393253)ott-21_1_sil=16000:fs=off:random_seed=3078419645:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.76/0.56 % (1393254)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=173940373:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.76/0.56 % (1393240)Instruction limit reached!
% 0.76/0.56 % (1393240)------------------------------
% 0.76/0.56 % (1393240)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.56 % (1393240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.56 % (1393240)CaDiCaL version: 2.1.3
% 0.76/0.56 % (1393240)Termination reason: Instruction limit
% 0.76/0.56 % (1393240)Termination phase: Saturation
% 0.76/0.56 % (1393240)Time elapsed: 0.090 s
% 0.76/0.56 % (1393240)Peak memory usage: 14 MB
% 0.76/0.56 % (1393240)Instructions burned: 160 (million)
% 0.76/0.56 % (1393235) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1393229-1393235"...
% 0.76/0.56 % (1393235)...printing done.
% 0.76/0.56 % (1393235)Refutation found. Thanks to Tanya!
% 0.76/0.56 % SZS status Theorem for theBenchmark
% 0.76/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 0.76/0.56 % (1393235)------------------------------
% 0.76/0.56 % (1393235)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.56 % (1393235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.56 % (1393235)CaDiCaL version: 2.1.3
% 0.76/0.56 % (1393235)Termination reason: Refutation
% 0.76/0.56 % (1393235)Time elapsed: 0.093 s
% 0.76/0.56 % (1393235)Peak memory usage: 14 MB
% 0.76/0.56 % (1393235)Instructions burned: 160 (million)
% 0.76/0.56 % (1393229)Success in time 0.152 s
% 0.76/0.56 % Vampire exiting
%------------------------------------------------------------------------------