%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU818^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 08:33:49 AM UTC 2026
% Result : Theorem 0.23s 0.35s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 441 ( 78 equ; 0 cnn)
% Maximal formula atoms : 5 ( 10 avg)
% Number of connectives : 774 ( 23 ~; 26 |; 59 &; 500 @)
% ( 0 <=>; 106 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 150 ( 145 usr; 9 con; 0-4 aty)
% ( 54 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 128 ( 93 ^; 29 !; 6 ?; 128 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
powerset: $i > $i ).
thf(func_def_3,type,
nonempty: $i > $o ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_5,type,
subsetI1: $o ).
thf(func_def_7,type,
transitiveset: $i > $o ).
thf(func_def_8,type,
stricttotalorderedByIn: $i > $o ).
thf(func_def_9,type,
wellorderedByIn: $i > $o ).
thf(func_def_10,type,
ordinal: $i > $o ).
thf(func_def_11,type,
ordinalTransSet: $o ).
thf(func_def_12,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_14,type,
vNOT: $o > $o ).
thf(func_def_15,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_16,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_17,type,
vIMP: $o > $o > $o ).
thf(func_def_18,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vAND: $o > $o > $o ).
thf(func_def_21,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vOR: $o > $o > $o ).
thf(func_def_23,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_28,type,
sK2: $i > $i ).
thf(func_def_29,type,
sK3: $i > $i ).
thf(func_def_30,type,
sK4: $i > $i ).
thf(func_def_31,type,
sK5: $i > $i ).
thf(func_def_32,type,
sK6: $i > $i ).
thf(func_def_33,type,
sK7: $i > $i ).
thf(func_def_34,type,
sK8: $i > $i ).
thf(func_def_35,type,
sK9: $i > $i ).
thf(func_def_36,type,
sK10: $i > $i ).
thf(func_def_37,type,
sK11: $i > $i ).
thf(func_def_38,type,
sK12: $i > $i ).
thf(func_def_39,type,
sK13: $i > $i ).
thf(func_def_40,type,
sK14: $i > $i ).
thf(func_def_41,type,
sK15: $i > $i ).
thf(func_def_42,type,
sK16: $i > $i ).
thf(func_def_43,type,
sK17: $i > $i ).
thf(func_def_44,type,
sK18: $i > $i ).
thf(func_def_45,type,
sK19: $i > $i ).
thf(func_def_46,type,
sK20: $i > $i ).
thf(func_def_47,type,
sK21: $i > $i ).
thf(func_def_48,type,
sK22: $i > $i ).
thf(func_def_49,type,
sK23: $i > $i ).
thf(func_def_50,type,
sK24: $i > $i ).
thf(func_def_51,type,
sK25: $i > $i ).
thf(func_def_52,type,
sK26: $i > $i ).
thf(func_def_53,type,
sK27: $i > $i ).
thf(func_def_54,type,
sK28: $i > $i ).
thf(func_def_55,type,
sK29: $i > $i ).
thf(func_def_56,type,
sK30: $i > $i ).
thf(func_def_57,type,
sK31: $i > $i ).
thf(func_def_58,type,
sK32: $i > $i ).
thf(func_def_59,type,
sK33: $i > $i ).
thf(func_def_60,type,
sK34: $i > $i ).
thf(func_def_61,type,
sK35: $i > $i ).
thf(func_def_62,type,
sK36: $i > $i ).
thf(func_def_63,type,
sK37: $i > $i ).
thf(func_def_64,type,
sK38: $i > $i ).
thf(func_def_65,type,
sK39: $i > $i ).
thf(func_def_66,type,
sK40: $i > $i ).
thf(func_def_67,type,
sK41: $i > $i ).
thf(func_def_68,type,
sK42: $i > $i ).
thf(func_def_69,type,
sK43: $i > $i ).
thf(func_def_70,type,
sK44: $i > $i ).
thf(func_def_71,type,
sK45: $i > $i ).
thf(func_def_72,type,
sK46: $i > $i ).
thf(func_def_73,type,
sK47: $i > $i ).
thf(func_def_74,type,
sK48: $i > $i ).
thf(func_def_75,type,
sK49: $i > $i ).
thf(func_def_76,type,
sK50: $i > $i ).
thf(func_def_77,type,
sK51: $i > $i ).
thf(func_def_78,type,
sK52: $i > $i ).
thf(func_def_79,type,
sK53: $i > $i ).
thf(func_def_80,type,
sK54: $i > $i ).
thf(func_def_81,type,
sK55: $i > $i ).
thf(func_def_82,type,
sK56: $i > $i ).
thf(func_def_83,type,
sK57: $i > $i ).
thf(func_def_84,type,
sK58: $i > $i ).
thf(func_def_85,type,
sK59: $i > $i ).
thf(func_def_86,type,
sK60: $i > $i ).
thf(func_def_87,type,
sK61: $i > $i ).
thf(func_def_88,type,
sK62: $i > $i ).
thf(func_def_89,type,
sK63: $i > $i ).
thf(func_def_90,type,
sK64: $i > $i ).
thf(func_def_91,type,
sK65: $i > $i ).
thf(func_def_92,type,
sK66: $i > $i ).
thf(func_def_93,type,
sK67: $i > $i ).
thf(func_def_94,type,
sK68: $i > $i ).
thf(func_def_95,type,
sK69: $i > $i ).
thf(func_def_96,type,
sK70: $i > $i ).
thf(func_def_97,type,
sK71: $i > $i ).
thf(func_def_98,type,
sK72: $i > $i > $i ).
thf(func_def_99,type,
sK73: $i > $i ).
thf(func_def_100,type,
sK74: $i > $i > $i ).
thf(func_def_101,type,
sK75: $i > $i ).
thf(func_def_102,type,
sK76: $i > $i ).
thf(func_def_103,type,
sK77: $i > $i > $i ).
thf(func_def_104,type,
sK78: $i > $i ).
thf(func_def_105,type,
sK79: $i > $i > $i ).
thf(func_def_106,type,
sK80: $i > $i ).
thf(func_def_107,type,
sK81: $i > $i ).
thf(func_def_108,type,
sK82: $i > $i ).
thf(func_def_109,type,
sK83: $i > $i ).
thf(func_def_110,type,
sK84: $i > $i > $i ).
thf(func_def_111,type,
sK85: $i > $i ).
thf(func_def_112,type,
sK86: $i > $i > $i ).
thf(func_def_113,type,
sK87: $i > $i ).
thf(func_def_114,type,
sK88: $i > $i ).
thf(func_def_115,type,
sK89: $i > $i > $i ).
thf(func_def_116,type,
sK90: $i > $i ).
thf(func_def_117,type,
sK91: $i > $i > $i ).
thf(func_def_118,type,
sK92: $i > $i ).
thf(func_def_119,type,
sK93: $i > $i ).
thf(func_def_120,type,
sK94: $i > $i ).
thf(func_def_121,type,
sK95: $i > $i ).
thf(func_def_122,type,
sK96: $i > $i > $i ).
thf(func_def_123,type,
sK97: $i > $i ).
thf(func_def_124,type,
sK98: $i > $i > $i ).
thf(func_def_125,type,
sK99: $i > $i ).
thf(func_def_126,type,
sK100: $i > $i ).
thf(func_def_127,type,
sK101: $i > $i > $i ).
thf(func_def_128,type,
sK102: $i > $i ).
thf(func_def_129,type,
sK103: $i > $i > $i ).
thf(func_def_130,type,
sK104: $i > $i ).
thf(func_def_131,type,
sK105: $i > $i ).
thf(func_def_132,type,
sK106: $i > $i ).
thf(func_def_133,type,
sK107: $i > $i ).
thf(func_def_134,type,
sK108: $i > $i > $i ).
thf(func_def_135,type,
sK109: $i > $i ).
thf(func_def_136,type,
sK110: $i > $i > $i ).
thf(func_def_137,type,
sK111: $i > $i ).
thf(func_def_138,type,
sK112: $i > $i ).
thf(func_def_139,type,
sK113: $i > $i > $i ).
thf(func_def_140,type,
sK114: $i > $i ).
thf(func_def_141,type,
sK115: $i > $i > $i ).
thf(func_def_142,type,
sK116: $i > $i ).
thf(func_def_143,type,
sK117: $i > $i ).
thf(func_def_144,type,
sK118: $i > $i ).
thf(func_def_145,type,
sK119: $i > $i ).
thf(func_def_146,type,
sK120: $i > $i > $i ).
thf(f1,axiom,
( nonempty
= ( ^ [X0: $i] : ( X0 != emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty) ).
thf(f3,axiom,
( transitiveset
= ( ^ [X0: $i] :
! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitiveset) ).
thf(f4,axiom,
( stricttotalorderedByIn
= ( ^ [X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ~ ( in @ X2 @ X2 ) )
& ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X2 )
| ( in @ X2 @ X3 )
| ( X2 = X3 ) ) ) )
& ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ( in @ X2 @ X3 )
& ( in @ X1 @ X2 ) )
=> ( in @ X1 @ X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stricttotalorderedByIn) ).
thf(f5,axiom,
( wellorderedByIn
= ( ^ [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( nonempty @ X1 )
=> ? [X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X2 @ X3 )
| ( X2 = X3 ) ) )
& ( in @ X2 @ X1 ) ) ) )
& ( stricttotalorderedByIn @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellorderedByIn) ).
thf(f6,axiom,
( ordinal
= ( ^ [X0: $i] :
( ( wellorderedByIn @ X0 )
& ( transitiveset @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordinal) ).
thf(f8,conjecture,
( subsetI1
=> ( ordinalTransSet
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordinalTransSet1) ).
thf(f9,negated_conjecture,
~ ( subsetI1
=> ( ordinalTransSet
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f10,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f13,plain,
( transitiveset
= ( ^ [X0: $i] :
! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f14,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( stricttotalorderedByIn
= ( ^ [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ~ ( in @ X1 @ X1 ) )
& ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X2 )
| ( in @ X2 @ X3 )
| ( X2 = X3 ) ) ) )
& ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X0 )
=> ( ( ( in @ X5 @ X6 )
& ( in @ X4 @ X5 ) )
=> ( in @ X4 @ X6 ) ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f16,plain,
( stricttotalorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y3 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 = Y2 )
| ( in @ Y1 @ Y2 )
| ( in @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( wellorderedByIn
= ( ^ [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( nonempty @ X1 )
=> ? [X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X2 @ X3 )
| ( X2 = X3 ) ) )
& ( in @ X2 @ X1 ) ) ) )
& ( stricttotalorderedByIn @ X0 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f18,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( stricttotalorderedByIn @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 = Y3 )
| ( in @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
( ordinal
= ( ^ [X0: $i] :
( ( wellorderedByIn @ X0 )
& ( transitiveset @ X0 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f20,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( wellorderedByIn @ Y0 ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f23,plain,
~ ( subsetI1
=> ( ordinalTransSet
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f24,plain,
~ ( ( subsetI1 = $true )
=> ( ( ordinalTransSet = $true )
=> ! [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
=> ! [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( subset @ X1 @ X0 )
= $true ) ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f25,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
& ( ( in @ X1 @ X0 )
= $true ) )
& ( ( ordinal @ X0 )
= $true ) )
& ( ordinalTransSet = $true )
& ( subsetI1 = $true ) ),
inference(ennf_transformation,[],[f24]) ).
thf(f26,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
& ( ( in @ X1 @ X0 )
= $true ) )
& ( ( ordinal @ X0 )
= $true ) )
& ( ordinalTransSet = $true )
& ( subsetI1 = $true ) ),
inference(flattening,[],[f25]) ).
thf(f27,plain,
( ( $true
!= ( subset @ sK1 @ sK0 ) )
& ( $true
= ( in @ sK1 @ sK0 ) )
& ( $true
= ( ordinal @ sK0 ) )
& ( ordinalTransSet = $true )
& ( subsetI1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f26]) ).
thf(f28,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f30,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f31,plain,
( stricttotalorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y3 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 = Y2 )
| ( in @ Y1 @ Y2 )
| ( in @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f32,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( stricttotalorderedByIn @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 = Y3 )
| ( in @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f33,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( wellorderedByIn @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f37,plain,
( $true
= ( ordinal @ sK0 ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f38,plain,
( $true
= ( in @ sK1 @ sK0 ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f39,plain,
( $true
!= ( subset @ sK1 @ sK0 ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f42,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y3 @ Y4 ) )
=> ( in @ Y2 @ Y4 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 = Y3 )
| ( in @ Y2 @ Y3 )
| ( in @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ~ ( in @ Y2 @ Y2 ) ) ) )
@ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( ^ [Y2: $i] : ( emptyset != Y2 )
@ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 = Y3 )
| ( in @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f32,f31,f28]) ).
thf(f43,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) )
@ Y0 )
& ( ^ [Y1: $i] :
( ( ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y2 )
=> ( ( ( in @ Y3 @ Y4 )
& ( in @ Y4 @ Y5 ) )
=> ( in @ Y3 @ Y5 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y3 = Y4 )
| ( in @ Y3 @ Y4 )
| ( in @ Y4 @ Y3 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ~ ( in @ Y3 @ Y3 ) ) ) )
@ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( ^ [Y3: $i] : ( emptyset != Y3 )
@ Y2 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y3 = Y4 )
| ( in @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f33,f30,f42]) ).
thf(f46,plain,
( $true
= ( ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) )
@ Y0 )
& ( ^ [Y1: $i] :
( ( ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y2 )
=> ( ( ( in @ Y3 @ Y4 )
& ( in @ Y4 @ Y5 ) )
=> ( in @ Y3 @ Y5 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y3 = Y4 )
| ( in @ Y3 @ Y4 )
| ( in @ Y4 @ Y3 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ~ ( in @ Y3 @ Y3 ) ) ) )
@ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( ^ [Y3: $i] : ( emptyset != Y3 )
@ Y2 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y3 = Y4 )
| ( in @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) )
@ Y0 ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f37,f43]) ).
thf(f47,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( subset @ Y0 @ sK0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK0 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ sK0 ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f46]) ).
thf(f49,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( subset @ Y0 @ sK0 ) ) ) ),
inference(and_proxy_clausification,[],[f47]) ).
thf(f50,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( subset @ Y0 @ sK0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f49]) ).
thf(f51,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ sK0 )
=> ( subset @ X1 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f50]) ).
thf(f52,plain,
! [X1: $i] :
( ( $true
= ( subset @ X1 @ sK0 ) )
| ( $false
= ( in @ X1 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f51]) ).
thf(f1919,plain,
( ( $true != $true )
| ( ( in @ sK1 @ sK0 )
= $false ) ),
inference(constrained_superposition,[],[f39,f52]) ).
thf(f1920,plain,
( ( in @ sK1 @ sK0 )
= $false ),
inference(trivial_inequality_removal,[],[f1919]) ).
thf(f1947,plain,
$true = $false,
inference(constrained_superposition,[],[f38,f1920]) ).
thf(f1948,plain,
$false,
inference(trivial_inequality_removal,[],[f1947]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU818^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 % Computer : n002.cluster.edu
% 0.07/0.21 % Model : x86_64 x86_64
% 0.07/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.21 % Memory : 8046.5625MB
% 0.07/0.21 % OS : Linux 6.8.0-71-generic
% 0.07/0.21 % CPULimit : 300
% 0.07/0.21 % WCLimit : 300
% 0.07/0.21 % DateTime : Tue Sep 29 14:36:52 UTC 2026
% 0.07/0.21 % CPUTime :
% 0.07/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.24 Running first-order model finding
% 0.07/0.24 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
% 0.23/0.35 % (1378009)Will run a generic schedule for satisfiability detection.
% 0.23/0.35 % (1378014)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1965689077_2999 on theBenchmark for (2999ds/0Mi)
% 0.23/0.35 % Exception at run slice level
% 0.23/0.35 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.35 % (1378022)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2146287365:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.23/0.35 % Exception at run slice level
% 0.23/0.35 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.35 % (1378015)% WARNING: option uhcvi not known.
% 0.23/0.35 % (1378015)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2428461368:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.23/0.35 % (1378024)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=4234068574:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.23/0.35 % (1378015)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.23/0.35 % (1378015)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.23/0.35 % (1378024)Instruction limit reached!
% 0.23/0.35 % (1378024)------------------------------
% 0.23/0.35 % (1378024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.35 % (1378024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.35 % (1378024)CaDiCaL version: 2.1.3
% 0.23/0.35 % (1378024)Termination reason: Instruction limit
% 0.23/0.35 % (1378024)Termination phase: Saturation
% 0.23/0.35 % (1378024)Time elapsed: 0.028 s
% 0.23/0.35 % (1378024)Peak memory usage: 12 MB
% 0.23/0.35 % (1378024)Instructions burned: 132 (million)
% 0.23/0.35 % (1378019)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=681744521:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.23/0.35 % (1378018)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3249957959:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.23/0.35 % (1378027)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=1753773021:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.23/0.35 % (1378018)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.23/0.35 % (1378027)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.23/0.35 % (1378027)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.23/0.35 % (1378017)dis+10_1_sil=32000:sp=arity:random_seed=2127144559:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.23/0.35 % (1378020)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=805595460:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.23/0.35 % (1378015) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1378009-1378015"...
% 0.23/0.35 % (1378016)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1058416599:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.23/0.35 % (1378015)...printing done.
% 0.23/0.35 % (1378015)Refutation found. Thanks to Tanya!
% 0.23/0.35 % SZS status Theorem for theBenchmark
% 0.23/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.35 % (1378015)------------------------------
% 0.23/0.35 % (1378015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.35 % (1378015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.35 % (1378015)CaDiCaL version: 2.1.3
% 0.23/0.35 % (1378015)Termination reason: Refutation
% 0.23/0.35 % (1378015)Time elapsed: 0.054 s
% 0.23/0.35 % (1378015)Peak memory usage: 12 MB
% 0.23/0.35 % (1378015)Instructions burned: 97 (million)
% 0.23/0.35 % (1378009)Success in time 0.106 s
% 0.23/0.35 % Vampire exiting
%------------------------------------------------------------------------------