%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP115^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:08:24 AM UTC 2026
% Result : Theorem 0.54s 0.39s
% Output : Refutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 71 ( 20 unt; 0 typ; 8 def)
% Number of atoms : 360 ( 106 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 428 ( 95 ~; 91 |; 36 &; 192 @)
% ( 8 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 128 ( 125 usr; 18 con; 0-4 aty)
% Number of variables : 28 ( 0 sgn 18 !; 10 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_b: $tType ).
thf(type_def_6,type,
set_a: $tType ).
thf(type_def_7,type,
b: $tType ).
thf(type_def_8,type,
a: $tType ).
thf(type_def_9,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
minus_minus_set_a: set_a > set_a > set_a ).
thf(func_def_1,type,
minus_minus_set_b: set_b > set_b > set_b ).
thf(func_def_2,type,
inf_inf_set_a: set_a > set_a > set_a ).
thf(func_def_3,type,
inf_inf_set_b: set_b > set_b > set_b ).
thf(func_def_4,type,
inf_inf_b: b > b > b ).
thf(func_def_5,type,
lower_464587817at_a_b: a > ( a > b ) > $o ).
thf(func_def_6,type,
bot_bot_a_o: a > $o ).
thf(func_def_7,type,
bot_bot_b_o: b > $o ).
thf(func_def_8,type,
bot_bot_set_a: set_a ).
thf(func_def_9,type,
bot_bot_set_b: set_b ).
thf(func_def_10,type,
bot_bot_b: b ).
thf(func_def_11,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(func_def_12,type,
ord_less_eq_set_b: set_b > set_b > $o ).
thf(func_def_13,type,
ord_less_eq_b: b > b > $o ).
thf(func_def_14,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_15,type,
collect_b: ( b > $o ) > set_b ).
thf(func_def_16,type,
insert_a: a > set_a > set_a ).
thf(func_def_17,type,
insert_b: b > set_b > set_b ).
thf(func_def_18,type,
is_empty_a: set_a > $o ).
thf(func_def_19,type,
is_empty_b: set_b > $o ).
thf(func_def_20,type,
is_singleton_a: set_a > $o ).
thf(func_def_21,type,
is_singleton_b: set_b > $o ).
thf(func_def_22,type,
the_elem_a: set_a > a ).
thf(func_def_23,type,
the_elem_b: set_b > b ).
thf(func_def_24,type,
topolo1276428101open_a: set_a > $o ).
thf(func_def_25,type,
topolo1276428102open_b: set_b > $o ).
thf(func_def_26,type,
member_a: a > set_a > $o ).
thf(func_def_27,type,
member_b: b > set_b > $o ).
thf(func_def_28,type,
a2: b ).
thf(func_def_29,type,
f: a > b ).
thf(func_def_30,type,
thesis: $o ).
thf(func_def_31,type,
x0: a ).
thf(func_def_35,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_38,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_39,type,
vAND: $o > $o > $o ).
thf(func_def_40,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
sP0: b > b > b > $o ).
thf(func_def_42,type,
sP1: b > b > b > $o ).
thf(func_def_43,type,
sK2: set_a > a ).
thf(func_def_44,type,
sK3: ( b > $o ) > b ).
thf(func_def_45,type,
sK4: b > b > set_b ).
thf(func_def_46,type,
sK5: set_b > b > set_b ).
thf(func_def_47,type,
sK6: b > set_b > set_b ).
thf(func_def_48,type,
sK7: ( set_a > set_a > set_a ) > set_a ).
thf(func_def_49,type,
sK8: ( set_a > set_a > set_a ) > set_a ).
thf(func_def_50,type,
sK9: ( set_a > set_a > set_a ) > set_a ).
thf(func_def_51,type,
sK10: ( set_a > set_a > set_a ) > set_a ).
thf(func_def_52,type,
sK11: ( set_a > set_a > set_a ) > set_a ).
thf(func_def_53,type,
sK12: ( set_a > set_a > set_a ) > set_a ).
thf(func_def_54,type,
sK13: ( set_a > set_a > set_a ) > set_a ).
thf(func_def_55,type,
sK14: set_b > b ).
thf(func_def_56,type,
sK15: ( b > $o ) > b ).
thf(func_def_57,type,
sK16: set_b > set_a ).
thf(func_def_58,type,
sK17: set_b > b ).
thf(func_def_59,type,
sK18: ( a > $o ) > a ).
thf(func_def_60,type,
sK19: set_a > a ).
thf(func_def_61,type,
sK20: set_a > a ).
thf(func_def_62,type,
sK21: set_a > set_a > a ).
thf(func_def_63,type,
sK22: ( b > b ) > b ).
thf(func_def_64,type,
sK23: ( b > b ) > b ).
thf(func_def_65,type,
sK24: ( a > $o ) > a ).
thf(func_def_66,type,
sK25: set_a > a ).
thf(func_def_67,type,
sK26: set_b > b ).
thf(func_def_68,type,
sK27: a > set_a > set_a ).
thf(func_def_69,type,
sK28: b > b > set_b ).
thf(func_def_70,type,
sK29: b > b > set_b ).
thf(func_def_71,type,
sK30: set_b > b ).
thf(func_def_72,type,
sK31: set_b > b ).
thf(func_def_73,type,
sK32: b > b > set_b ).
thf(func_def_74,type,
sK33: set_b > set_b > b ).
thf(func_def_75,type,
sK34: set_a > a ).
thf(func_def_76,type,
sK35: ( set_b > set_b > set_b ) > set_b ).
thf(func_def_77,type,
sK36: ( set_b > set_b > set_b ) > set_b ).
thf(func_def_78,type,
sK37: ( set_b > set_b > set_b ) > set_b ).
thf(func_def_79,type,
sK38: ( set_b > set_b > set_b ) > set_b ).
thf(func_def_80,type,
sK39: ( set_b > set_b > set_b ) > set_b ).
thf(func_def_81,type,
sK40: ( set_b > set_b > set_b ) > set_b ).
thf(func_def_82,type,
sK41: ( set_b > set_b > set_b ) > set_b ).
thf(func_def_83,type,
sK42: ( b > b > $o ) > b ).
thf(func_def_84,type,
sK43: ( b > b > $o ) > b ).
thf(func_def_85,type,
sK44: ( b > b > $o ) > b ).
thf(func_def_86,type,
sK45: ( b > b > $o ) > b ).
thf(func_def_87,type,
sK46: set_b ).
thf(func_def_88,type,
sK47: set_b ).
thf(func_def_89,type,
sK48: b > b > set_b ).
thf(func_def_90,type,
sK49: a > set_a > set_a ).
thf(func_def_91,type,
sK50: ( b > b > b ) > b ).
thf(func_def_92,type,
sK51: ( b > b > b ) > b ).
thf(func_def_93,type,
sK52: ( b > b > b ) > b ).
thf(func_def_94,type,
sK53: ( b > b > b ) > b ).
thf(func_def_95,type,
sK54: ( b > b > b ) > b ).
thf(func_def_96,type,
sK55: ( b > b > b ) > b ).
thf(func_def_97,type,
sK56: ( b > b > b ) > b ).
thf(func_def_98,type,
sK57: b > b > set_b ).
thf(func_def_99,type,
sK58: b > b > set_b ).
thf(func_def_100,type,
sK59: ( b > b ) > b ).
thf(func_def_101,type,
sK60: ( b > b ) > b ).
thf(func_def_102,type,
sK61: b > b > set_b > set_b > set_b ).
thf(func_def_103,type,
sK62: set_a > set_a > a ).
thf(func_def_104,type,
sK63: ( b > b ) > b ).
thf(func_def_105,type,
sK64: ( b > b ) > b ).
thf(func_def_106,type,
sK65: set_b > set_a ).
thf(func_def_107,type,
sK66: ( b > b ) > b ).
thf(func_def_108,type,
sK67: ( b > b ) > b ).
thf(func_def_109,type,
sK68: set_b > set_b > b ).
thf(func_def_110,type,
sK69: set_a > set_a > a ).
thf(func_def_111,type,
sK70: set_a > set_a > a ).
thf(func_def_112,type,
sK71: b > b > set_b ).
thf(func_def_113,type,
sK72: set_a > a ).
thf(func_def_114,type,
sK73: set_b > b ).
thf(func_def_115,type,
sK74: set_a > a > a > set_a > set_a ).
thf(func_def_116,type,
sK75: set_b > set_b > b ).
thf(func_def_117,type,
sK76: set_b > set_b > b ).
thf(func_def_118,type,
vNOT: $o > $o ).
thf(f1,axiom,
( a2
!= ( f @ x0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062A_A_092_060noteq_062_Af_Ax0_092_060close_062) ).
thf(f2,axiom,
( ( ( f @ x0 )
!= a2 )
=> ? [X1: set_b,X0: set_b] :
( ( member_b @ ( f @ x0 ) @ X0 )
& ( topolo1276428102open_b @ X0 )
& ( topolo1276428102open_b @ X1 )
& ( member_b @ a2 @ X1 )
& ( ( inf_inf_set_b @ X0 @ X1 )
= bot_bot_set_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062f_Ax0_A_092_060noteq_062_AA_A_092_060Longrightarrow_062_A_092_060exists_062U_AV_O_Aopen_AU_A_092_060and_062_Aopen_AV_A_092_060and_062_Af_Ax0_A_092_060in_062_AU_A_092_060and_062_AA_A_092_060in_062_AV_A_092_060and_062_AU_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062) ).
thf(f356,axiom,
! [X0: set_b,X1: set_b] :
( ( ( member_b @ ( f @ x0 ) @ X0 )
& ( topolo1276428102open_b @ X1 )
& ( topolo1276428102open_b @ X0 )
& ( ( inf_inf_set_b @ X0 @ X1 )
= bot_bot_set_b )
& ( member_b @ a2 @ X1 ) )
=> thesis ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f357,conjecture,
thesis,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(f358,negated_conjecture,
~ thesis,
inference(negated_conjecture,[status(cth)],[f357]) ).
thf(f535,plain,
( ( ( f @ x0 )
!= a2 )
=> ? [X0: set_b,X1: set_b] :
( ( member_b @ ( f @ x0 ) @ X1 )
& ( topolo1276428102open_b @ X1 )
& ( topolo1276428102open_b @ X0 )
& ( member_b @ a2 @ X0 )
& ( bot_bot_set_b
= ( inf_inf_set_b @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f536,plain,
( ( a2
!= ( f @ x0 ) )
=> ? [X1: set_b,X0: set_b] :
( ( ( topolo1276428102open_b @ X0 )
= $true )
& ( bot_bot_set_b
= ( inf_inf_set_b @ X1 @ X0 ) )
& ( ( topolo1276428102open_b @ X1 )
= $true )
& ( ( member_b @ ( f @ x0 ) @ X1 )
= $true )
& ( ( member_b @ a2 @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f535]) ).
thf(f729,plain,
~ thesis,
inference(rectify,[],[f358]) ).
thf(f730,plain,
thesis != $true,
inference(fool_elimination,[],[f729]) ).
thf(f839,plain,
! [X0: set_b,X1: set_b] :
( ( ( member_b @ ( f @ x0 ) @ X0 )
& ( topolo1276428102open_b @ X1 )
& ( topolo1276428102open_b @ X0 )
& ( ( inf_inf_set_b @ X0 @ X1 )
= bot_bot_set_b )
& ( member_b @ a2 @ X1 ) )
=> thesis ),
inference(rectify,[],[f356]) ).
thf(f840,plain,
! [X1: set_b,X0: set_b] :
( ( ( ( topolo1276428102open_b @ X1 )
= $true )
& ( ( member_b @ a2 @ X1 )
= $true )
& ( ( topolo1276428102open_b @ X0 )
= $true )
& ( ( inf_inf_set_b @ X0 @ X1 )
= bot_bot_set_b )
& ( ( member_b @ ( f @ x0 ) @ X0 )
= $true ) )
=> ( thesis = $true ) ),
inference(fool_elimination,[],[f839]) ).
thf(f935,plain,
thesis != $true,
inference(flattening,[],[f730]) ).
thf(f1101,plain,
( ? [X1: set_b,X0: set_b] :
( ( ( topolo1276428102open_b @ X0 )
= $true )
& ( bot_bot_set_b
= ( inf_inf_set_b @ X1 @ X0 ) )
& ( ( topolo1276428102open_b @ X1 )
= $true )
& ( ( member_b @ ( f @ x0 ) @ X1 )
= $true )
& ( ( member_b @ a2 @ X0 )
= $true ) )
| ( a2
= ( f @ x0 ) ) ),
inference(ennf_transformation,[],[f536]) ).
thf(f1109,plain,
! [X1: set_b,X0: set_b] :
( ( thesis = $true )
| ( ( topolo1276428102open_b @ X1 )
!= $true )
| ( ( member_b @ a2 @ X1 )
!= $true )
| ( ( topolo1276428102open_b @ X0 )
!= $true )
| ( ( inf_inf_set_b @ X0 @ X1 )
!= bot_bot_set_b )
| ( ( member_b @ ( f @ x0 ) @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f840]) ).
thf(f1110,plain,
! [X0: set_b,X1: set_b] :
( ( thesis = $true )
| ( ( member_b @ ( f @ x0 ) @ X0 )
!= $true )
| ( ( topolo1276428102open_b @ X0 )
!= $true )
| ( ( inf_inf_set_b @ X0 @ X1 )
!= bot_bot_set_b )
| ( ( member_b @ a2 @ X1 )
!= $true )
| ( ( topolo1276428102open_b @ X1 )
!= $true ) ),
inference(flattening,[],[f1109]) ).
thf(f1348,plain,
( ? [X0: set_b,X1: set_b] :
( ( ( topolo1276428102open_b @ X1 )
= $true )
& ( ( inf_inf_set_b @ X0 @ X1 )
= bot_bot_set_b )
& ( ( topolo1276428102open_b @ X0 )
= $true )
& ( ( member_b @ ( f @ x0 ) @ X0 )
= $true )
& ( ( member_b @ a2 @ X1 )
= $true ) )
| ( a2
= ( f @ x0 ) ) ),
inference(rectify,[],[f1101]) ).
thf(f1349,plain,
( ( ( $true
= ( topolo1276428102open_b @ sK47 ) )
& ( bot_bot_set_b
= ( inf_inf_set_b @ sK46 @ sK47 ) )
& ( $true
= ( topolo1276428102open_b @ sK46 ) )
& ( ( member_b @ ( f @ x0 ) @ sK46 )
= $true )
& ( ( member_b @ a2 @ sK47 )
= $true ) )
| ( a2
= ( f @ x0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46,sK47]),skolemize(X0,sK46),skolemize(X1,sK47)],[f1348]) ).
thf(f1519,plain,
thesis != $true,
inference(cnf_transformation,[],[f935]) ).
thf(f1585,plain,
( a2
!= ( f @ x0 ) ),
inference(cnf_transformation,[],[f1]) ).
thf(f1744,plain,
! [X0: set_b,X1: set_b] :
( ( ( member_b @ a2 @ X1 )
!= $true )
| ( ( topolo1276428102open_b @ X0 )
!= $true )
| ( ( inf_inf_set_b @ X0 @ X1 )
!= bot_bot_set_b )
| ( ( topolo1276428102open_b @ X1 )
!= $true )
| ( thesis = $true )
| ( ( member_b @ ( f @ x0 ) @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f1110]) ).
thf(f1775,plain,
( ( a2
= ( f @ x0 ) )
| ( ( member_b @ a2 @ sK47 )
= $true ) ),
inference(cnf_transformation,[],[f1349]) ).
thf(f1776,plain,
( ( ( member_b @ ( f @ x0 ) @ sK46 )
= $true )
| ( a2
= ( f @ x0 ) ) ),
inference(cnf_transformation,[],[f1349]) ).
thf(f1777,plain,
( ( a2
= ( f @ x0 ) )
| ( $true
= ( topolo1276428102open_b @ sK46 ) ) ),
inference(cnf_transformation,[],[f1349]) ).
thf(f1778,plain,
( ( a2
= ( f @ x0 ) )
| ( bot_bot_set_b
= ( inf_inf_set_b @ sK46 @ sK47 ) ) ),
inference(cnf_transformation,[],[f1349]) ).
thf(f1779,plain,
( ( a2
= ( f @ x0 ) )
| ( $true
= ( topolo1276428102open_b @ sK47 ) ) ),
inference(cnf_transformation,[],[f1349]) ).
thf(f2167,definition,
( spl77_4
<=> ( ( member_b @ ( f @ x0 ) @ sK46 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl77_4])],[avatar_definition]) ).
thf(f2169,plain,
( ( ( member_b @ ( f @ x0 ) @ sK46 )
= $true )
| ~ spl77_4 ),
inference(avatar_component_clause,[],[f2167]) ).
thf(f2171,definition,
( spl77_5
<=> ( a2
= ( f @ x0 ) ) ),
introduced(definition,[new_symbols(definition,[spl77_5])],[avatar_definition]) ).
thf(f2174,plain,
( spl77_4
| spl77_5 ),
inference(avatar_split_clause,[],[f1776,f2171,f2167]) ).
thf(f2199,definition,
( spl77_11
<=> ( thesis = $true ) ),
introduced(definition,[new_symbols(definition,[spl77_11])],[avatar_definition]) ).
thf(f2202,plain,
~ spl77_11,
inference(avatar_split_clause,[],[f1519,f2199]) ).
thf(f2234,definition,
( spl77_18
<=> ( $true
= ( topolo1276428102open_b @ sK46 ) ) ),
introduced(definition,[new_symbols(definition,[spl77_18])],[avatar_definition]) ).
thf(f2236,plain,
( ( $true
= ( topolo1276428102open_b @ sK46 ) )
| ~ spl77_18 ),
inference(avatar_component_clause,[],[f2234]) ).
thf(f2237,plain,
( spl77_18
| spl77_5 ),
inference(avatar_split_clause,[],[f1777,f2171,f2234]) ).
thf(f2244,definition,
( spl77_20
<=> ( $true
= ( topolo1276428102open_b @ sK47 ) ) ),
introduced(definition,[new_symbols(definition,[spl77_20])],[avatar_definition]) ).
thf(f2246,plain,
( ( $true
= ( topolo1276428102open_b @ sK47 ) )
| ~ spl77_20 ),
inference(avatar_component_clause,[],[f2244]) ).
thf(f2247,plain,
( spl77_5
| spl77_20 ),
inference(avatar_split_clause,[],[f1779,f2244,f2171]) ).
thf(f2259,definition,
( spl77_23
<=> ( ( member_b @ a2 @ sK47 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl77_23])],[avatar_definition]) ).
thf(f2261,plain,
( ( ( member_b @ a2 @ sK47 )
= $true )
| ~ spl77_23 ),
inference(avatar_component_clause,[],[f2259]) ).
thf(f2262,plain,
( spl77_5
| spl77_23 ),
inference(avatar_split_clause,[],[f1775,f2259,f2171]) ).
thf(f2283,plain,
~ spl77_5,
inference(avatar_split_clause,[],[f1585,f2171]) ).
thf(f2309,definition,
( spl77_33
<=> ! [X0: set_b,X1: set_b] :
( ( ( member_b @ a2 @ X1 )
!= $true )
| ( ( member_b @ ( f @ x0 ) @ X0 )
!= $true )
| ( ( topolo1276428102open_b @ X1 )
!= $true )
| ( ( topolo1276428102open_b @ X0 )
!= $true )
| ( ( inf_inf_set_b @ X0 @ X1 )
!= bot_bot_set_b ) ) ),
introduced(definition,[new_symbols(definition,[spl77_33])],[avatar_definition]) ).
thf(f2310,plain,
( ! [X0: set_b,X1: set_b] :
( ( ( topolo1276428102open_b @ X1 )
!= $true )
| ( ( member_b @ a2 @ X1 )
!= $true )
| ( ( member_b @ ( f @ x0 ) @ X0 )
!= $true )
| ( ( inf_inf_set_b @ X0 @ X1 )
!= bot_bot_set_b )
| ( ( topolo1276428102open_b @ X0 )
!= $true ) )
| ~ spl77_33 ),
inference(avatar_component_clause,[],[f2309]) ).
thf(f2311,plain,
( spl77_11
| spl77_33 ),
inference(avatar_split_clause,[],[f1744,f2309,f2199]) ).
thf(f2313,definition,
( spl77_34
<=> ( bot_bot_set_b
= ( inf_inf_set_b @ sK46 @ sK47 ) ) ),
introduced(definition,[new_symbols(definition,[spl77_34])],[avatar_definition]) ).
thf(f2315,plain,
( ( bot_bot_set_b
= ( inf_inf_set_b @ sK46 @ sK47 ) )
| ~ spl77_34 ),
inference(avatar_component_clause,[],[f2313]) ).
thf(f2316,plain,
( spl77_34
| spl77_5 ),
inference(avatar_split_clause,[],[f1778,f2171,f2313]) ).
thf(f2356,plain,
( ! [X0: set_b,X1: set_b] :
( ( ( inf_inf_set_b @ X0 @ X1 )
!= ( inf_inf_set_b @ sK46 @ sK47 ) )
| ( ( topolo1276428102open_b @ X1 )
!= $true )
| ( ( member_b @ ( f @ x0 ) @ X0 )
!= $true )
| ( ( member_b @ a2 @ X1 )
!= $true )
| ( ( topolo1276428102open_b @ X0 )
!= $true ) )
| ~ spl77_33
| ~ spl77_34 ),
inference(forward_demodulation,[],[f2310,f2315]) ).
thf(f2363,plain,
( ( ( member_b @ ( f @ x0 ) @ sK46 )
!= $true )
| ( $true
!= ( topolo1276428102open_b @ sK47 ) )
| ( $true
!= ( topolo1276428102open_b @ sK46 ) )
| ( ( member_b @ a2 @ sK47 )
!= $true )
| ~ spl77_33
| ~ spl77_34 ),
inference(equality_resolution,[],[f2356]) ).
thf(f2367,plain,
( ( ( member_b @ a2 @ sK47 )
!= $true )
| ( $true
!= ( topolo1276428102open_b @ sK46 ) )
| ( $true
!= ( topolo1276428102open_b @ sK47 ) )
| ~ spl77_4
| ~ spl77_33
| ~ spl77_34 ),
inference(forward_subsumption_resolution,[],[f2363,f2169]) ).
thf(f2370,plain,
( ( $true
!= ( topolo1276428102open_b @ sK47 ) )
| ( $true
!= ( topolo1276428102open_b @ sK46 ) )
| ~ spl77_4
| ~ spl77_23
| ~ spl77_33
| ~ spl77_34 ),
inference(forward_subsumption_resolution,[],[f2367,f2261]) ).
thf(f2373,plain,
( ( $true
!= ( topolo1276428102open_b @ sK46 ) )
| ~ spl77_4
| ~ spl77_20
| ~ spl77_23
| ~ spl77_33
| ~ spl77_34 ),
inference(forward_subsumption_resolution,[],[f2370,f2246]) ).
thf(f2390,plain,
( $false
| ~ spl77_4
| ~ spl77_18
| ~ spl77_20
| ~ spl77_23
| ~ spl77_33
| ~ spl77_34 ),
inference(forward_subsumption_resolution,[],[f2373,f2236]) ).
thf(f2391,plain,
( ~ spl77_4
| ~ spl77_18
| ~ spl77_20
| ~ spl77_23
| ~ spl77_33
| ~ spl77_34 ),
inference(avatar_contradiction_clause,[],[f2390]) ).
cnf(s4,plain,
( spl77_4
| spl77_5 ),
inference(sat_conversion,[],[f2174]) ).
cnf(s10,plain,
~ spl77_11,
inference(sat_conversion,[],[f2202]) ).
cnf(s19,plain,
( spl77_5
| spl77_18 ),
inference(sat_conversion,[],[f2237]) ).
cnf(s21,plain,
( spl77_5
| spl77_20 ),
inference(sat_conversion,[],[f2247]) ).
cnf(s27,plain,
( spl77_5
| spl77_23 ),
inference(sat_conversion,[],[f2262]) ).
cnf(s33,plain,
~ spl77_5,
inference(sat_conversion,[],[f2283]) ).
cnf(s48,plain,
( spl77_11
| spl77_33 ),
inference(sat_conversion,[],[f2311]) ).
cnf(s50,plain,
( spl77_5
| spl77_34 ),
inference(sat_conversion,[],[f2316]) ).
cnf(s59,plain,
( ~ spl77_4
| ~ spl77_18
| ~ spl77_20
| ~ spl77_23
| ~ spl77_33
| ~ spl77_34 ),
inference(sat_conversion,[],[f2391]) ).
cnf(s60,plain,
spl77_34,
inference(rat,[],[s50,s33]) ).
cnf(s63,plain,
spl77_23,
inference(rat,[],[s27,s33]) ).
cnf(s64,plain,
spl77_20,
inference(rat,[],[s21,s33]) ).
cnf(s65,plain,
spl77_18,
inference(rat,[],[s19,s33]) ).
cnf(s67,plain,
spl77_33,
inference(rat,[],[s48,s10]) ).
cnf(s68,plain,
~ spl77_4,
inference(rat,[],[s59,s60,s65,s63,s64,s67]) ).
cnf(s69,plain,
$false,
inference(rat,[],[s4,s33,s68]) ).
thf(f2392,plain,
$false,
inference(avatar_sat_refutation,[],[s69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP115^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n013.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 19:55:07 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.23/0.27 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.54/0.39 % (2583605)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.54/0.39 % (2583616)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.54/0.39 % (2583616)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.54/0.39 % (2583616)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1880926055:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.54/0.39 % (2583610)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1996003927:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.54/0.39 % (2583611)lrs+10_16_si=on:nwc=1.5:random_seed=1474893715:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.54/0.39 % (2583612)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2860278284:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.54/0.39 % (2583614)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2809878187:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.54/0.39 % (2583613)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=798363433:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.54/0.39 % (2583615)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2713306598:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.54/0.39 % (2583612)Instruction limit reached!
% 0.54/0.39 % (2583612)------------------------------
% 0.54/0.39 % (2583612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.39 % (2583612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.39 % (2583612)CaDiCaL version: 2.1.3
% 0.54/0.39 % (2583612)Termination reason: Instruction limit
% 0.54/0.39 % (2583612)Termination phase: shuffling
% 0.54/0.39 % (2583612)Time elapsed: 0.002 s
% 0.54/0.39 % (2583612)Peak memory usage: 10 MB
% 0.54/0.39 % (2583612)Instructions burned: 3 (million)
% 0.54/0.39 % (2583611)Instruction limit reached!
% 0.54/0.39 % (2583611)------------------------------
% 0.54/0.39 % (2583611)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.39 % (2583611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.39 % (2583611)CaDiCaL version: 2.1.3
% 0.54/0.39 % (2583611)Termination reason: Instruction limit
% 0.54/0.39 % (2583611)Termination phase: Property scanning
% 0.54/0.39 % (2583611)Time elapsed: 0.009 s
% 0.54/0.39 % (2583611)Peak memory usage: 10 MB
% 0.54/0.39 % (2583611)Instructions burned: 19 (million)
% 0.54/0.39 % (2583614)Instruction limit reached!
% 0.54/0.39 % (2583614)------------------------------
% 0.54/0.39 % (2583614)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.39 % (2583614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.39 % (2583614)CaDiCaL version: 2.1.3
% 0.54/0.39 % (2583614)Termination reason: Instruction limit
% 0.54/0.39 % (2583614)Termination phase: Property scanning
% 0.54/0.39 % (2583614)Time elapsed: 0.011 s
% 0.54/0.39 % (2583614)Peak memory usage: 10 MB
% 0.54/0.39 % (2583614)Instructions burned: 26 (million)
% 0.54/0.39 % (2583624)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1379719658:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.54/0.39 % (2583624)Instruction limit reached!
% 0.54/0.39 % (2583624)------------------------------
% 0.54/0.39 % (2583624)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.39 % (2583624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.39 % (2583624)CaDiCaL version: 2.1.3
% 0.54/0.39 % (2583624)Termination reason: Instruction limit
% 0.54/0.39 % (2583624)Termination phase: shuffling
% 0.54/0.39 % (2583624)Time elapsed: 0.002 s
% 0.54/0.39 % (2583624)Peak memory usage: 10 MB
% 0.54/0.39 % (2583624)Instructions burned: 3 (million)
% 0.54/0.39 % (2583626)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.54/0.39 % (2583625)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1813475705:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.54/0.39 % (2583626)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=618082947:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.54/0.39 % (2583616)Instruction limit reached!
% 0.54/0.39 % (2583616)------------------------------
% 0.54/0.39 % (2583616)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.39 % (2583616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.39 % (2583616)CaDiCaL version: 2.1.3
% 0.54/0.39 % (2583616)Termination reason: Instruction limit
% 0.54/0.39 % (2583616)Termination phase: Saturation
% 0.54/0.39 % (2583616)Time elapsed: 0.040 s
% 0.54/0.39 % (2583616)Peak memory usage: 14 MB
% 0.54/0.39 % (2583616)Instructions burned: 160 (million)
% 0.54/0.39 % (2583625)Instruction limit reached!
% 0.54/0.39 % (2583625)------------------------------
% 0.54/0.39 % (2583625)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.39 % (2583625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.39 % (2583625)CaDiCaL version: 2.1.3
% 0.54/0.39 % (2583625)Termination reason: Instruction limit
% 0.54/0.39 % (2583625)Termination phase: shuffling
% 0.54/0.39 % (2583625)Time elapsed: 0.003 s
% 0.54/0.39 % (2583625)Peak memory usage: 10 MB
% 0.54/0.39 % (2583625)Instructions burned: 5 (million)
% 0.54/0.39 % (2583615)Instruction limit reached!
% 0.54/0.39 % (2583615)------------------------------
% 0.54/0.39 % (2583615)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.39 % (2583615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.39 % (2583615)CaDiCaL version: 2.1.3
% 0.54/0.39 % (2583615)Termination reason: Instruction limit
% 0.54/0.39 % (2583615)Termination phase: Equality resolution with deletion
% 0.54/0.39 % (2583615)Time elapsed: 0.033 s
% 0.54/0.39 % (2583615)Peak memory usage: 12 MB
% 0.54/0.39 % (2583615)Instructions burned: 75 (million)
% 0.54/0.39 % (2583626)Instruction limit reached!
% 0.54/0.39 % (2583626)------------------------------
% 0.54/0.39 % (2583626)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.39 % (2583626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.39 % (2583626)CaDiCaL version: 2.1.3
% 0.54/0.39 % (2583626)Termination reason: Instruction limit
% 0.54/0.39 % (2583626)Termination phase: shuffling
% 0.54/0.39 % (2583626)Time elapsed: 0.003 s
% 0.54/0.39 % (2583626)Peak memory usage: 10 MB
% 0.54/0.39 % (2583626)Instructions burned: 7 (million)
% 0.54/0.39 % (2583610)Instruction limit reached!
% 0.54/0.39 % (2583610)------------------------------
% 0.54/0.39 % (2583610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.39 % (2583610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.39 % (2583610)CaDiCaL version: 2.1.3
% 0.54/0.39 % (2583610)Termination reason: Instruction limit
% 0.54/0.39 % (2583610)Termination phase: Property scanning
% 0.54/0.39 % (2583610)Time elapsed: 0.038 s
% 0.54/0.39 % (2583610)Peak memory usage: 12 MB
% 0.54/0.39 % (2583610)Instructions burned: 88 (million)
% 0.54/0.39 % (2583631)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.54/0.39 % (2583631)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.54/0.39 % (2583628)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1592928659:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.54/0.39 % (2583631)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2168899919:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.54/0.39 % (2583628)Instruction limit reached!
% 0.54/0.39 % (2583628)------------------------------
% 0.54/0.39 % (2583628)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.39 % (2583628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.39 % (2583628)CaDiCaL version: 2.1.3
% 0.54/0.39 % (2583628)Termination reason: Instruction limit
% 0.54/0.39 % (2583628)Termination phase: shuffling
% 0.54/0.39 % (2583628)Time elapsed: 0.006 s
% 0.54/0.39 % (2583628)Peak memory usage: 10 MB
% 0.54/0.39 % (2583628)Instructions burned: 14 (million)
% 0.54/0.39 % (2583634)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.54/0.39 % (2583631)Instruction limit reached!
% 0.54/0.39 % (2583631)------------------------------
% 0.54/0.39 % (2583631)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.39 % (2583631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.39 % (2583631)CaDiCaL version: 2.1.3
% 0.54/0.39 % (2583631)Termination reason: Instruction limit
% 0.54/0.39 % (2583631)Termination phase: shuffling
% 0.54/0.39 % (2583631)Time elapsed: 0.007 s
% 0.54/0.39 % (2583631)Peak memory usage: 10 MB
% 0.54/0.39 % (2583631)Instructions burned: 32 (million)
% 0.54/0.39 % (2583632)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=3846267339:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.54/0.39 % (2583633)lrs+10_1_si=on:cs=on:random_seed=1073818851:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.54/0.39 % (2583634)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=2118370930:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.54/0.39 % (2583634)Instruction limit reached!
% 0.54/0.39 % (2583634)------------------------------
% 0.54/0.39 % (2583634)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.39 % (2583634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.39 % (2583634)CaDiCaL version: 2.1.3
% 0.54/0.39 % (2583634)Termination reason: Instruction limit
% 0.54/0.39 % (2583634)Termination phase: shuffling
% 0.54/0.39 % (2583634)Time elapsed: 0.002 s
% 0.54/0.39 % (2583634)Peak memory usage: 10 MB
% 0.54/0.39 % (2583634)Instructions burned: 3 (million)
% 0.54/0.39 % (2583635)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1747811677:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.54/0.39 % (2583633)Instruction limit reached!
% 0.54/0.39 % (2583633)------------------------------
% 0.54/0.39 % (2583633)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.39 % (2583633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.39 % (2583633)CaDiCaL version: 2.1.3
% 0.54/0.39 % (2583633)Termination reason: Instruction limit
% 0.54/0.39 % (2583633)Termination phase: shuffling
% 0.54/0.39 % (2583633)Time elapsed: 0.004 s
% 0.54/0.39 % (2583633)Peak memory usage: 10 MB
% 0.54/0.39 % (2583633)Instructions burned: 9 (million)
% 0.54/0.39 % (2583613) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2583605-2583613"...
% 0.54/0.39 % (2583613)...printing done.
% 0.54/0.39 % (2583639)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3866701518:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.54/0.39 % (2583613)Refutation found. Thanks to Tanya!
% 0.54/0.39 % SZS status Theorem for theBenchmark
% 0.54/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.54/0.39 % (2583613)------------------------------
% 0.54/0.39 % (2583613)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.39 % (2583613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.39 % (2583613)CaDiCaL version: 2.1.3
% 0.54/0.39 % (2583613)Termination reason: Refutation
% 0.54/0.39 % (2583613)Time elapsed: 0.061 s
% 0.54/0.39 % (2583613)Peak memory usage: 14 MB
% 0.54/0.39 % (2583613)Instructions burned: 130 (million)
% 0.54/0.39 % (2583605)Success in time 0.113 s
% 0.54/0.39 % Vampire exiting
%------------------------------------------------------------------------------