%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU820^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:31:44 AM UTC 2026
% Result : Theorem 0.22s 0.35s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 16
% Syntax : Number of formulae : 165 ( 47 unt; 0 typ; 7 def)
% Number of atoms : 2157 ( 397 equ; 0 cnn)
% Maximal formula atoms : 6 ( 13 avg)
% Number of connectives : 2648 ( 175 ~; 288 |; 120 &;1599 @)
% ( 13 <=>; 285 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 83 ( 78 usr; 26 con; 0-4 aty)
% ( 147 !!; 21 ??; 0 @@+; 0 @@-)
% Number of variables : 332 ( 0 sgn 93 !; 12 ?; 332 :)
% 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,
vacuousDall: $o ).
thf(func_def_6,type,
subset: $i > $i > $o ).
thf(func_def_7,type,
subsetemptysetimpeq: $o ).
thf(func_def_8,type,
powersetE1: $o ).
thf(func_def_9,type,
transitiveset: $i > $o ).
thf(func_def_10,type,
stricttotalorderedByIn: $i > $o ).
thf(func_def_11,type,
wellorderedByIn: $i > $o ).
thf(func_def_12,type,
ordinal: $i > $o ).
thf(func_def_13,type,
vAND: $o > $o > $o ).
thf(func_def_14,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_18,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_19,type,
vIMP: $o > $o > $o ).
thf(func_def_20,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
vNOT: $o > $o ).
thf(func_def_22,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
vOR: $o > $o > $o ).
thf(func_def_25,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_26,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
sK4: $i > $o ).
thf(func_def_48,type,
sK21: $i > $i ).
thf(func_def_52,type,
sK25: $i > $i ).
thf(func_def_53,type,
sK26: $i > $i ).
thf(func_def_59,type,
sK32: $i > $i ).
thf(func_def_60,type,
sK33: $i > $i ).
thf(func_def_61,type,
sK34: $i > $i ).
thf(func_def_62,type,
sK35: $i > $i ).
thf(func_def_64,type,
sK37: $i > $i ).
thf(func_def_66,type,
sK39: $i > $i ).
thf(func_def_67,type,
sK40: $i > $i ).
thf(func_def_68,type,
sK41: $i > $i ).
thf(func_def_69,type,
sK42: $i > $i ).
thf(func_def_81,type,
sK54: $i > $i ).
thf(func_def_83,type,
sK56: $i > $i ).
thf(func_def_84,type,
sK57: $i > $i ).
thf(func_def_87,type,
sK60: $i > $i ).
thf(func_def_89,type,
sK62: $i > $i ).
thf(func_def_91,type,
sK64: $i > $i ).
thf(func_def_94,type,
sK67: $i > $i ).
thf(func_def_96,type,
sK69: $i > $i ).
thf(func_def_97,type,
sK70: $i > $i ).
thf(func_def_105,type,
sK78: $i > $i ).
thf(func_def_107,type,
sK80: $i > $i ).
thf(func_def_111,type,
sK84: $i > $i ).
thf(func_def_113,type,
sK86: $i > $i ).
thf(func_def_114,type,
sK87: $i > $i ).
thf(func_def_123,type,
sK96: $i > $i ).
thf(func_def_125,type,
sK98: $i > $i ).
thf(func_def_133,type,
sK106: $i > $i ).
thf(func_def_134,type,
sK107: $i > $i ).
thf(func_def_137,type,
sK110: $i > $i ).
thf(func_def_138,type,
sK111: $i > $i ).
thf(func_def_139,type,
sK112: $i > $i ).
thf(func_def_141,type,
sK114: $i > $i ).
thf(f1,axiom,
( nonempty
= ( ^ [X0: $i] : ( X0 != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(f2,axiom,
( vacuousDall
= ( ! [X1: $i,X0: $i > $o] :
( ( in @ X1 @ emptyset )
=> ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(f3,axiom,
! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
=> ( X0 = emptyset ) )
= subsetemptysetimpeq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(f4,axiom,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ X1 @ X0 ) )
= powersetE1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(f5,axiom,
( ( ^ [X0: $i] :
! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) )
= transitiveset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitiveset) ).
thf(f6,axiom,
( stricttotalorderedByIn
= ( ^ [X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X2 = X3 )
| ( in @ X3 @ X2 )
| ( in @ 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 ) ) ) ) )
& ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ~ ( in @ X2 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricttotalorderedByIn) ).
thf(f7,axiom,
( wellorderedByIn
= ( ^ [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( nonempty @ X1 )
=> ? [X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 = X3 )
| ( in @ X2 @ X3 ) ) )
& ( in @ X2 @ X1 ) ) ) )
& ( stricttotalorderedByIn @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderedByIn) ).
thf(f8,axiom,
( ordinal
= ( ^ [X0: $i] :
( ( wellorderedByIn @ X0 )
& ( transitiveset @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal) ).
thf(f9,conjecture,
( vacuousDall
=> ( subsetemptysetimpeq
=> ( powersetE1
=> ( ordinal @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetOrdinal) ).
thf(f10,negated_conjecture,
~ ( vacuousDall
=> ( subsetemptysetimpeq
=> ( powersetE1
=> ( ordinal @ emptyset ) ) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
thf(f11,plain,
( ordinal
= ( ^ [X0: $i] :
( ( wellorderedByIn @ X0 )
& ( transitiveset @ X0 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f12,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( wellorderedByIn @ Y0 ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
~ ( vacuousDall
=> ( subsetemptysetimpeq
=> ( powersetE1
=> ( ordinal @ emptyset ) ) ) ),
inference(rectify,[],[f10]) ).
thf(f14,plain,
~ ( ( vacuousDall = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetE1 = $true )
=> ( ( ordinal @ emptyset )
= $true ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( stricttotalorderedByIn
= ( ^ [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( X1 = X2 )
| ( in @ X2 @ X1 )
| ( in @ X1 @ X2 ) ) ) )
& ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ( ( ( in @ X4 @ X5 )
& ( in @ X3 @ X4 ) )
=> ( in @ X3 @ X5 ) ) ) ) )
& ! [X6: $i] :
( ( in @ X6 @ X0 )
=> ~ ( in @ X6 @ X6 ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f16,plain,
( stricttotalorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) )
& ( !! @ $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 )
=> ( ( in @ Y1 @ Y2 )
| ( in @ Y2 @ Y1 )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
=> ( X0 = emptyset ) )
= subsetemptysetimpeq ),
inference(rectify,[],[f3]) ).
thf(f18,plain,
( ! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
= $true )
=> ( emptyset = X0 ) )
<=> ( subsetemptysetimpeq = $true ) ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ X1 @ X0 ) )
= powersetE1 ),
inference(rectify,[],[f4]) ).
thf(f20,plain,
( ( powersetE1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ( ( subset @ X1 @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f21,plain,
( ( ^ [X0: $i] :
! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) )
= transitiveset ),
inference(rectify,[],[f5]) ).
thf(f22,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f23,plain,
( wellorderedByIn
= ( ^ [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( nonempty @ X1 )
=> ? [X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 = X3 )
| ( in @ X2 @ X3 ) ) )
& ( in @ X2 @ X1 ) ) ) )
& ( stricttotalorderedByIn @ X0 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f24,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 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f25,plain,
( vacuousDall
= ( ! [X0: $i,X1: $i > $o] :
( ( in @ X0 @ emptyset )
=> ( X1 @ X0 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f26,plain,
( ! [X1: $i > $o,X0: $i] :
( ( ( in @ X0 @ emptyset )
= $true )
=> ( $true
= ( X1 @ X0 ) ) )
<=> ( vacuousDall = $true ) ),
inference(fool_elimination,[],[f25]) ).
thf(f27,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f28,plain,
( ( vacuousDall = $true )
<=> ! [X0: $i,X1: $i > $o] :
( ( ( in @ X0 @ emptyset )
!= $true )
| ( $true
= ( X1 @ X0 ) ) ) ),
inference(ennf_transformation,[],[f26]) ).
thf(f29,plain,
( ( ( ordinal @ emptyset )
!= $true )
& ( powersetE1 = $true )
& ( subsetemptysetimpeq = $true )
& ( vacuousDall = $true ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f30,plain,
( ( powersetE1 = $true )
& ( ( ordinal @ emptyset )
!= $true )
& ( vacuousDall = $true )
& ( subsetemptysetimpeq = $true ) ),
inference(flattening,[],[f29]) ).
thf(f31,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ X1 @ X0 )
= $true ) )
<=> ( powersetE1 = $true ) ),
inference(ennf_transformation,[],[f20]) ).
thf(f32,plain,
( ! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
!= $true )
| ( emptyset = X0 ) )
<=> ( subsetemptysetimpeq = $true ) ),
inference(ennf_transformation,[],[f18]) ).
thf(f33,plain,
( ( ! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
!= $true )
| ( emptyset = X0 ) )
| ( subsetemptysetimpeq != $true ) )
& ( ( subsetemptysetimpeq = $true )
| ? [X0: $i] :
( ( ( subset @ X0 @ emptyset )
= $true )
& ( emptyset != X0 ) ) ) ),
inference(nnf_transformation,[],[f32]) ).
thf(f34,plain,
( ( ! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
!= $true )
| ( emptyset = X0 ) )
| ( subsetemptysetimpeq != $true ) )
& ( ( subsetemptysetimpeq = $true )
| ? [X1: $i] :
( ( $true
= ( subset @ X1 @ emptyset ) )
& ( emptyset != X1 ) ) ) ),
inference(rectify,[],[f33]) ).
thf(f35,plain,
( ( ! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
!= $true )
| ( emptyset = X0 ) )
| ( subsetemptysetimpeq != $true ) )
& ( ( subsetemptysetimpeq = $true )
| ( ( ( subset @ sK0 @ emptyset )
= $true )
& ( emptyset != sK0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0)],[f34]) ).
thf(f36,plain,
( ( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( powersetE1 != $true ) )
& ( ( powersetE1 = $true )
| ? [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ( ( subset @ X1 @ X0 )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f31]) ).
thf(f37,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true ) )
| ( powersetE1 != $true ) )
& ( ( powersetE1 = $true )
| ? [X2: $i,X3: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X3 ) ) )
& ( ( subset @ X2 @ X3 )
!= $true ) ) ) ),
inference(rectify,[],[f36]) ).
thf(f38,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true ) )
| ( powersetE1 != $true ) )
& ( ( powersetE1 = $true )
| ( ( $true
= ( in @ sK1 @ ( powerset @ sK2 ) ) )
& ( ( subset @ sK1 @ sK2 )
!= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X2,sK1),skolemize(X3,sK2)],[f37]) ).
thf(f39,plain,
( ( ( vacuousDall = $true )
| ? [X0: $i,X1: $i > $o] :
( ( ( in @ X0 @ emptyset )
= $true )
& ( $true
!= ( X1 @ X0 ) ) ) )
& ( ! [X0: $i,X1: $i > $o] :
( ( ( in @ X0 @ emptyset )
!= $true )
| ( $true
= ( X1 @ X0 ) ) )
| ( vacuousDall != $true ) ) ),
inference(nnf_transformation,[],[f28]) ).
thf(f40,plain,
( ( ( vacuousDall = $true )
| ? [X0: $i,X1: $i > $o] :
( ( ( in @ X0 @ emptyset )
= $true )
& ( $true
!= ( X1 @ X0 ) ) ) )
& ( ! [X2: $i,X3: $i > $o] :
( ( ( in @ X2 @ emptyset )
!= $true )
| ( ( X3 @ X2 )
= $true ) )
| ( vacuousDall != $true ) ) ),
inference(rectify,[],[f39]) ).
thf(f41,plain,
( ( ( vacuousDall = $true )
| ( ( ( in @ sK3 @ emptyset )
= $true )
& ( ( sK4 @ sK3 )
!= $true ) ) )
& ( ! [X2: $i,X3: $i > $o] :
( ( ( in @ X2 @ emptyset )
!= $true )
| ( ( X3 @ X2 )
= $true ) )
| ( vacuousDall != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f40]) ).
thf(f42,plain,
subsetemptysetimpeq = $true,
inference(cnf_transformation,[],[f30]) ).
thf(f43,plain,
vacuousDall = $true,
inference(cnf_transformation,[],[f30]) ).
thf(f44,plain,
( ( ordinal @ emptyset )
!= $true ),
inference(cnf_transformation,[],[f30]) ).
thf(f45,plain,
powersetE1 = $true,
inference(cnf_transformation,[],[f30]) ).
thf(f46,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( wellorderedByIn @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f47,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f50,plain,
! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
!= $true )
| ( emptyset = X0 )
| ( subsetemptysetimpeq != $true ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f53,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true )
| ( powersetE1 != $true ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f54,plain,
! [X2: $i,X3: $i > $o] :
( ( ( in @ X2 @ emptyset )
!= $true )
| ( ( X3 @ X2 )
= $true )
| ( vacuousDall != $true ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f57,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f58,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 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f59,plain,
( stricttotalorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) )
& ( !! @ $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 )
=> ( ( in @ Y1 @ Y2 )
| ( in @ Y2 @ Y1 )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f62,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ~ ( in @ Y2 @ Y2 ) ) )
& ( !! @ $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 )
=> ( ( in @ Y2 @ Y3 )
| ( in @ Y3 @ Y2 )
| ( Y2 = Y3 ) ) ) ) ) ) )
@ 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 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f58,f59,f57]) ).
thf(f63,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 )
=> ~ ( in @ Y3 @ Y3 ) ) )
& ( !! @ $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 )
=> ( ( in @ Y3 @ Y4 )
| ( in @ Y4 @ Y3 )
| ( Y3 = Y4 ) ) ) ) ) ) )
@ 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 )
=> ( ( in @ Y3 @ Y4 )
| ( Y3 = Y4 ) ) ) ) ) ) ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f46,f47,f62]) ).
thf(f64,plain,
( ( ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) )
@ Y0 )
& ( ^ [Y1: $i] :
( ( ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ~ ( in @ Y3 @ Y3 ) ) )
& ( !! @ $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 )
=> ( ( in @ Y3 @ Y4 )
| ( in @ Y4 @ Y3 )
| ( Y3 = Y4 ) ) ) ) ) ) )
@ 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 )
=> ( ( in @ Y3 @ Y4 )
| ( Y3 = Y4 ) ) ) ) ) ) ) ) ) )
@ Y0 ) )
@ emptyset )
!= $true ),
inference(definition_unfolding,[],[f44,f63]) ).
thf(f65,plain,
! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
!= $true )
| ( $true != $true )
| ( emptyset = X0 ) ),
inference(definition_unfolding,[],[f50,f42]) ).
thf(f68,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( subset @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) ),
inference(definition_unfolding,[],[f53,f45]) ).
thf(f73,plain,
! [X2: $i,X3: $i > $o] :
( ( ( in @ X2 @ emptyset )
!= $true )
| ( ( X3 @ X2 )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[],[f54,f43]) ).
thf(f74,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 )
| ( Y0 = Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f75,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 )
| ( Y0 = Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f74]) ).
thf(f76,plain,
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) )
@ sK5 )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 )
| ( Y0 = Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f75]) ).
thf(f77,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 )
| ( Y0 = Y1 ) ) ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) )
@ sK5 )
= $false ) ),
inference(and_proxy_clausification,[],[f76]) ).
thf(f78,plain,
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) )
@ sK5 )
= $false )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 )
| ( Y0 = Y1 ) ) ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) )
@ sK6 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f77]) ).
thf(f79,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 )
| ( Y0 = Y1 ) ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) )
@ sK6 )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) )
@ sK5 )
= $false ) ),
inference(and_proxy_clausification,[],[f78]) ).
thf(f80,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 )
| ( Y0 = Y1 ) ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) )
@ sK6 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) )
@ sK5 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f79]) ).
thf(f81,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 )
| ( Y0 = Y1 ) ) ) ) )
@ sK7 ) )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) )
@ sK6 )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) )
@ sK5 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f80]) ).
thf(f82,plain,
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) )
@ sK5 )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) )
@ sK6 )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) )
@ sK8 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 )
| ( Y0 = Y1 ) ) ) ) )
@ sK7 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f81]) ).
thf(f83,plain,
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) )
@ sK9 )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) )
@ sK6 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 )
| ( Y0 = Y1 ) ) ) ) )
@ sK7 ) )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) )
@ sK5 )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) )
@ sK8 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f82]) ).
thf(f84,plain,
( ( $false
= ( ( in @ sK8 @ emptyset )
=> ~ ( in @ sK8 @ sK8 ) ) )
| ( $false
= ( ( in @ sK5 @ emptyset )
=> ( subset @ sK5 @ emptyset ) ) )
| ( ( ( in @ sK7 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( ( in @ sK7 @ Y0 )
| ( in @ Y0 @ sK7 )
| ( sK7 = Y0 ) ) ) ) )
= $false )
| ( $false
= ( ( in @ sK9 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( ( in @ sK9 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ sK9 @ Y1 ) ) ) ) ) ) ) )
| ( $false
= ( ( in @ sK6 @ ( powerset @ emptyset ) )
=> ( ( emptyset != sK6 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK6 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK6 )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f83]) ).
thf(f86,plain,
( ( $false
= ( ( in @ sK6 @ ( powerset @ emptyset ) )
=> ( ( emptyset != sK6 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK6 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK6 )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) ) ) ) )
| ( ( ( in @ sK7 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( ( in @ sK7 @ Y0 )
| ( in @ Y0 @ sK7 )
| ( sK7 = Y0 ) ) ) ) )
= $false )
| ( $false
= ( ( in @ sK5 @ emptyset )
=> ( subset @ sK5 @ emptyset ) ) )
| ( $true
= ( in @ sK8 @ emptyset ) )
| ( $false
= ( ( in @ sK9 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( ( in @ sK9 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ sK9 @ Y1 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f84]) ).
thf(f87,plain,
( ( $false
= ( ( in @ sK5 @ emptyset )
=> ( subset @ sK5 @ emptyset ) ) )
| ( $false
= ( ( in @ sK9 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( ( in @ sK9 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ sK9 @ Y1 ) ) ) ) ) ) ) )
| ( $true
= ( in @ sK8 @ emptyset ) )
| ( ( ( emptyset != sK6 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK6 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK6 )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) ) )
= $false )
| ( ( ( in @ sK7 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( ( in @ sK7 @ Y0 )
| ( in @ Y0 @ sK7 )
| ( sK7 = Y0 ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f86]) ).
thf(f88,plain,
( ( $true
= ( in @ sK6 @ ( powerset @ emptyset ) ) )
| ( $false
= ( ( in @ sK9 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( ( in @ sK9 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ sK9 @ Y1 ) ) ) ) ) ) ) )
| ( $true
= ( in @ sK8 @ emptyset ) )
| ( ( ( in @ sK7 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( ( in @ sK7 @ Y0 )
| ( in @ Y0 @ sK7 )
| ( sK7 = Y0 ) ) ) ) )
= $false )
| ( $false
= ( ( in @ sK5 @ emptyset )
=> ( subset @ sK5 @ emptyset ) ) ) ),
inference(imp_proxy_clausification,[],[f86]) ).
thf(f89,plain,
( ( $true
= ( in @ sK6 @ ( powerset @ emptyset ) ) )
| ( ( ( in @ sK7 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( ( in @ sK7 @ Y0 )
| ( in @ Y0 @ sK7 )
| ( sK7 = Y0 ) ) ) ) )
= $false )
| ( $true
= ( in @ sK8 @ emptyset ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( ( in @ sK9 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ sK9 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ( in @ sK5 @ emptyset )
=> ( subset @ sK5 @ emptyset ) ) ) ),
inference(imp_proxy_clausification,[],[f88]) ).
thf(f115,plain,
( ( $true
= ( in @ sK8 @ emptyset ) )
| ( $true
= ( in @ sK6 @ ( powerset @ emptyset ) ) )
| ( $true
= ( in @ sK7 @ emptyset ) )
| ( $false
= ( ( in @ sK5 @ emptyset )
=> ( subset @ sK5 @ emptyset ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( ( in @ sK9 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ sK9 @ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f89]) ).
thf(f117,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( ( in @ sK9 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ sK9 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( in @ sK6 @ ( powerset @ emptyset ) ) )
| ( $true
= ( in @ sK5 @ emptyset ) )
| ( $true
= ( in @ sK7 @ emptyset ) )
| ( $true
= ( in @ sK8 @ emptyset ) ) ),
inference(imp_proxy_clausification,[],[f115]) ).
thf(f118,plain,
( ( $true
= ( in @ sK8 @ emptyset ) )
| ( $true
= ( in @ sK5 @ emptyset ) )
| ( $true
= ( in @ sK6 @ ( powerset @ emptyset ) ) )
| ( $true
= ( in @ sK7 @ emptyset ) )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( ( in @ sK9 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ sK9 @ Y1 ) ) ) ) )
@ sK11 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f117]) ).
thf(f119,plain,
( ( $true
= ( in @ sK5 @ emptyset ) )
| ( ( ( in @ sK11 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( ( ( in @ sK9 @ sK11 )
& ( in @ sK11 @ Y0 ) )
=> ( in @ sK9 @ Y0 ) ) ) ) )
= $false )
| ( $true
= ( in @ sK7 @ emptyset ) )
| ( $true
= ( in @ sK8 @ emptyset ) )
| ( $true
= ( in @ sK6 @ ( powerset @ emptyset ) ) ) ),
inference(beta-eta_normalization,[],[f118]) ).
thf(f120,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( ( ( in @ sK9 @ sK11 )
& ( in @ sK11 @ Y0 ) )
=> ( in @ sK9 @ Y0 ) ) ) ) )
| ( $true
= ( in @ sK6 @ ( powerset @ emptyset ) ) )
| ( $true
= ( in @ sK7 @ emptyset ) )
| ( $true
= ( in @ sK8 @ emptyset ) )
| ( $true
= ( in @ sK5 @ emptyset ) ) ),
inference(imp_proxy_clausification,[],[f119]) ).
thf(f122,plain,
( ( $true
= ( in @ sK8 @ emptyset ) )
| ( $true
= ( in @ sK7 @ emptyset ) )
| ( $true
= ( in @ sK5 @ emptyset ) )
| ( $true
= ( in @ sK6 @ ( powerset @ emptyset ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( ( ( in @ sK9 @ sK11 )
& ( in @ sK11 @ Y0 ) )
=> ( in @ sK9 @ Y0 ) ) )
@ sK12 ) ) ),
inference(sigma_proxy_clausification,[],[f120]) ).
thf(f123,plain,
( ( $true
= ( in @ sK7 @ emptyset ) )
| ( $true
= ( in @ sK6 @ ( powerset @ emptyset ) ) )
| ( $false
= ( ( in @ sK12 @ emptyset )
=> ( ( ( in @ sK9 @ sK11 )
& ( in @ sK11 @ sK12 ) )
=> ( in @ sK9 @ sK12 ) ) ) )
| ( $true
= ( in @ sK5 @ emptyset ) )
| ( $true
= ( in @ sK8 @ emptyset ) ) ),
inference(beta-eta_normalization,[],[f122]) ).
thf(f125,plain,
( ( ( in @ sK12 @ emptyset )
= $true )
| ( $true
= ( in @ sK8 @ emptyset ) )
| ( $true
= ( in @ sK6 @ ( powerset @ emptyset ) ) )
| ( $true
= ( in @ sK5 @ emptyset ) )
| ( $true
= ( in @ sK7 @ emptyset ) ) ),
inference(imp_proxy_clausification,[],[f123]) ).
thf(f241,plain,
( ( ( ( in @ sK7 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( ( in @ sK7 @ Y0 )
| ( in @ Y0 @ sK7 )
| ( sK7 = Y0 ) ) ) ) )
= $false )
| ( $true
= ( in @ sK5 @ emptyset ) )
| ( $true
= ( in @ sK8 @ emptyset ) )
| ( ( ( emptyset != sK6 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK6 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK6 )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) ) )
= $false )
| ( $false
= ( ( in @ sK9 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( ( in @ sK9 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ sK9 @ Y1 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f87]) ).
thf(f243,plain,
( ( $false
= ( ( in @ sK9 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( ( in @ sK9 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ sK9 @ Y1 ) ) ) ) ) ) ) )
| ( $true
= ( in @ sK7 @ emptyset ) )
| ( $true
= ( in @ sK5 @ emptyset ) )
| ( ( ( emptyset != sK6 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK6 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK6 )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) ) )
= $false )
| ( $true
= ( in @ sK8 @ emptyset ) ) ),
inference(imp_proxy_clausification,[],[f241]) ).
thf(f245,plain,
( ( ( ( emptyset != sK6 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK6 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK6 )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) ) )
= $false )
| ( ( in @ sK9 @ emptyset )
= $true )
| ( $true
= ( in @ sK7 @ emptyset ) )
| ( $true
= ( in @ sK8 @ emptyset ) )
| ( $true
= ( in @ sK5 @ emptyset ) ) ),
inference(imp_proxy_clausification,[],[f243]) ).
thf(f247,plain,
( ( ( in @ sK9 @ emptyset )
= $true )
| ( $true
= ( in @ sK7 @ emptyset ) )
| ( $true
= ( in @ sK8 @ emptyset ) )
| ( ( emptyset != sK6 )
= $true )
| ( $true
= ( in @ sK5 @ emptyset ) ) ),
inference(imp_proxy_clausification,[],[f245]) ).
thf(f248,plain,
( ( ( emptyset = sK6 )
= $false )
| ( $true
= ( in @ sK8 @ emptyset ) )
| ( ( in @ sK9 @ emptyset )
= $true )
| ( $true
= ( in @ sK5 @ emptyset ) )
| ( $true
= ( in @ sK7 @ emptyset ) ) ),
inference(not_proxy_clausification,[],[f247]) ).
thf(f249,plain,
( ( ( in @ sK9 @ emptyset )
= $true )
| ( emptyset != sK6 )
| ( $true
= ( in @ sK8 @ emptyset ) )
| ( $true
= ( in @ sK5 @ emptyset ) )
| ( $true
= ( in @ sK7 @ emptyset ) ) ),
inference(equality_proxy_clausification,[],[f248]) ).
thf(f1748,plain,
! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
!= $true )
| ( emptyset = X0 ) ),
inference(trivial_inequality_removal,[],[f65]) ).
thf(f1749,plain,
! [X2: $i,X3: $i > $o] :
( ( ( in @ X2 @ emptyset )
!= $true )
| ( ( X3 @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[],[f73]) ).
thf(f1750,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[],[f68]) ).
thf(f1752,definition,
( spl115_1
<=> ( $true
= ( in @ sK8 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[spl115_1])],[avatar_definition]) ).
thf(f1754,plain,
( ( $true
= ( in @ sK8 @ emptyset ) )
| ~ spl115_1 ),
inference(avatar_component_clause,[],[f1752]) ).
thf(f1756,definition,
( spl115_2
<=> ( $true
= ( in @ sK6 @ ( powerset @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[spl115_2])],[avatar_definition]) ).
thf(f1758,plain,
( ( $true
= ( in @ sK6 @ ( powerset @ emptyset ) ) )
| ~ spl115_2 ),
inference(avatar_component_clause,[],[f1756]) ).
thf(f1760,definition,
( spl115_3
<=> ( $true
= ( in @ sK5 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[spl115_3])],[avatar_definition]) ).
thf(f1762,plain,
( ( $true
= ( in @ sK5 @ emptyset ) )
| ~ spl115_3 ),
inference(avatar_component_clause,[],[f1760]) ).
thf(f1764,definition,
( spl115_4
<=> ( $true
= ( in @ sK7 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[spl115_4])],[avatar_definition]) ).
thf(f1766,plain,
( ( $true
= ( in @ sK7 @ emptyset ) )
| ~ spl115_4 ),
inference(avatar_component_clause,[],[f1764]) ).
thf(f1768,definition,
( spl115_5
<=> ( ( in @ sK9 @ emptyset )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl115_5])],[avatar_definition]) ).
thf(f1770,plain,
( ( ( in @ sK9 @ emptyset )
= $true )
| ~ spl115_5 ),
inference(avatar_component_clause,[],[f1768]) ).
thf(f1807,definition,
( spl115_12
<=> ( ( in @ sK12 @ emptyset )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl115_12])],[avatar_definition]) ).
thf(f1809,plain,
( ( ( in @ sK12 @ emptyset )
= $true )
| ~ spl115_12 ),
inference(avatar_component_clause,[],[f1807]) ).
thf(f1810,plain,
( spl115_12
| spl115_4
| spl115_1
| spl115_2
| spl115_3 ),
inference(avatar_split_clause,[],[f125,f1760,f1756,f1752,f1764,f1807]) ).
thf(f1964,definition,
( spl115_39
<=> ( emptyset = sK6 ) ),
introduced(definition,[new_symbols(definition,[spl115_39])],[avatar_definition]) ).
thf(f1966,plain,
( ( emptyset != sK6 )
| spl115_39 ),
inference(avatar_component_clause,[],[f1964]) ).
thf(f1967,plain,
( spl115_4
| spl115_5
| ~ spl115_39
| spl115_3
| spl115_1 ),
inference(avatar_split_clause,[],[f249,f1752,f1760,f1964,f1768,f1764]) ).
thf(f3538,plain,
( ! [X0: $i > $o] :
( ( $true != $true )
| ( ( X0 @ sK5 )
= $true ) )
| ~ spl115_3 ),
inference(constrained_superposition,[],[f1749,f1762]) ).
thf(f3539,plain,
( ! [X0: $i > $o] :
( ( X0 @ sK5 )
= $true )
| ~ spl115_3 ),
inference(trivial_inequality_removal,[],[f3538]) ).
thf(f3542,plain,
( ! [X1: $i > $o] :
( ( ^ [Y0: $i] :
~ ( X1 @ Y0 )
@ sK5 )
= $true )
| ~ spl115_3 ),
inference(primitive_instantiation,[],[f3539]) ).
thf(f3543,plain,
( ! [X1: $i > $o] :
( ( ~ ( X1 @ sK5 ) )
= $true )
| ~ spl115_3 ),
inference(beta-eta_normalization,[],[f3542]) ).
thf(f3544,plain,
( ! [X1: $i > $o] :
( $false
= ( X1 @ sK5 ) )
| ~ spl115_3 ),
inference(not_proxy_clausification,[],[f3543]) ).
thf(f3549,plain,
( ( $false = $true )
| ~ spl115_3 ),
inference(forward_demodulation,[],[f3544,f3539]) ).
thf(f3550,plain,
( $false
| ~ spl115_3 ),
inference(trivial_inequality_removal,[],[f3549]) ).
thf(f3551,plain,
~ spl115_3,
inference(avatar_contradiction_clause,[],[f3550]) ).
thf(f3552,plain,
( ! [X0: $i > $o] :
( ( $true
= ( X0 @ sK7 ) )
| ( $true != $true ) )
| ~ spl115_4 ),
inference(constrained_superposition,[],[f1749,f1766]) ).
thf(f3553,plain,
( ! [X0: $i > $o] :
( $true
= ( X0 @ sK7 ) )
| ~ spl115_4 ),
inference(trivial_inequality_removal,[],[f3552]) ).
thf(f3556,plain,
( ! [X1: $i > $o] :
( ( ^ [Y0: $i] :
~ ( X1 @ Y0 )
@ sK7 )
= $true )
| ~ spl115_4 ),
inference(primitive_instantiation,[],[f3553]) ).
thf(f3557,plain,
( ! [X1: $i > $o] :
( ( ~ ( X1 @ sK7 ) )
= $true )
| ~ spl115_4 ),
inference(beta-eta_normalization,[],[f3556]) ).
thf(f3558,plain,
( ! [X1: $i > $o] :
( $false
= ( X1 @ sK7 ) )
| ~ spl115_4 ),
inference(not_proxy_clausification,[],[f3557]) ).
thf(f3563,plain,
( ( $false = $true )
| ~ spl115_4 ),
inference(forward_demodulation,[],[f3558,f3553]) ).
thf(f3564,plain,
( $false
| ~ spl115_4 ),
inference(trivial_inequality_removal,[],[f3563]) ).
thf(f3565,plain,
~ spl115_4,
inference(avatar_contradiction_clause,[],[f3564]) ).
thf(f3566,plain,
( ! [X0: $i > $o] :
( ( $true != $true )
| ( ( X0 @ sK9 )
= $true ) )
| ~ spl115_5 ),
inference(constrained_superposition,[],[f1749,f1770]) ).
thf(f3567,plain,
( ! [X0: $i > $o] :
( ( X0 @ sK9 )
= $true )
| ~ spl115_5 ),
inference(trivial_inequality_removal,[],[f3566]) ).
thf(f3570,plain,
( ! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i] :
~ ( X1 @ Y0 )
@ sK9 ) )
| ~ spl115_5 ),
inference(primitive_instantiation,[],[f3567]) ).
thf(f3575,plain,
( ! [X1: $i > $o] :
( $true
= ( ~ ( X1 @ sK9 ) ) )
| ~ spl115_5 ),
inference(beta-eta_normalization,[],[f3570]) ).
thf(f3576,plain,
( ! [X1: $i > $o] :
( ( X1 @ sK9 )
= $false )
| ~ spl115_5 ),
inference(not_proxy_clausification,[],[f3575]) ).
thf(f3577,plain,
( ( $false = $true )
| ~ spl115_5 ),
inference(forward_demodulation,[],[f3576,f3567]) ).
thf(f3578,plain,
( $false
| ~ spl115_5 ),
inference(trivial_inequality_removal,[],[f3577]) ).
thf(f3579,plain,
~ spl115_5,
inference(avatar_contradiction_clause,[],[f3578]) ).
thf(f3580,plain,
( ! [X0: $i > $o] :
( ( $true != $true )
| ( ( X0 @ sK8 )
= $true ) )
| ~ spl115_1 ),
inference(constrained_superposition,[],[f1749,f1754]) ).
thf(f3581,plain,
( ! [X0: $i > $o] :
( ( X0 @ sK8 )
= $true )
| ~ spl115_1 ),
inference(trivial_inequality_removal,[],[f3580]) ).
thf(f3584,plain,
( ! [X1: $i > $o] :
( ( ^ [Y0: $i] :
~ ( X1 @ Y0 )
@ sK8 )
= $true )
| ~ spl115_1 ),
inference(primitive_instantiation,[],[f3581]) ).
thf(f3588,plain,
( ! [X1: $i > $o] :
( ( ~ ( X1 @ sK8 ) )
= $true )
| ~ spl115_1 ),
inference(beta-eta_normalization,[],[f3584]) ).
thf(f3589,plain,
( ! [X1: $i > $o] :
( $false
= ( X1 @ sK8 ) )
| ~ spl115_1 ),
inference(not_proxy_clausification,[],[f3588]) ).
thf(f3591,plain,
( ( $false = $true )
| ~ spl115_1 ),
inference(forward_demodulation,[],[f3589,f3581]) ).
thf(f3592,plain,
( $false
| ~ spl115_1 ),
inference(trivial_inequality_removal,[],[f3591]) ).
thf(f3593,plain,
~ spl115_1,
inference(avatar_contradiction_clause,[],[f3592]) ).
thf(f3608,plain,
( ! [X0: $i > $o] :
( ( ( X0 @ sK12 )
= $true )
| ( $true != $true ) )
| ~ spl115_12 ),
inference(constrained_superposition,[],[f1749,f1809]) ).
thf(f3609,plain,
( ! [X0: $i > $o] :
( ( X0 @ sK12 )
= $true )
| ~ spl115_12 ),
inference(trivial_inequality_removal,[],[f3608]) ).
thf(f3612,plain,
( ! [X1: $i > $o] :
( ( ^ [Y0: $i] :
~ ( X1 @ Y0 )
@ sK12 )
= $true )
| ~ spl115_12 ),
inference(primitive_instantiation,[],[f3609]) ).
thf(f3613,plain,
( ! [X1: $i > $o] :
( ( ~ ( X1 @ sK12 ) )
= $true )
| ~ spl115_12 ),
inference(beta-eta_normalization,[],[f3612]) ).
thf(f3614,plain,
( ! [X1: $i > $o] :
( ( X1 @ sK12 )
= $false )
| ~ spl115_12 ),
inference(not_proxy_clausification,[],[f3613]) ).
thf(f3619,plain,
( ( $false = $true )
| ~ spl115_12 ),
inference(forward_demodulation,[],[f3614,f3609]) ).
thf(f3620,plain,
( $false
| ~ spl115_12 ),
inference(trivial_inequality_removal,[],[f3619]) ).
thf(f3621,plain,
~ spl115_12,
inference(avatar_contradiction_clause,[],[f3620]) ).
thf(f3678,plain,
( ( $true != $true )
| ( ( subset @ sK6 @ emptyset )
= $true )
| ~ spl115_2 ),
inference(constrained_superposition,[],[f1750,f1758]) ).
thf(f3679,plain,
( ( ( subset @ sK6 @ emptyset )
= $true )
| ~ spl115_2 ),
inference(trivial_inequality_removal,[],[f3678]) ).
thf(f3680,plain,
( ( emptyset = sK6 )
| ( $true != $true )
| ~ spl115_2 ),
inference(constrained_superposition,[],[f1748,f3679]) ).
thf(f3681,plain,
( ( emptyset = sK6 )
| ~ spl115_2 ),
inference(trivial_inequality_removal,[],[f3680]) ).
thf(f3682,plain,
( $false
| ~ spl115_2
| spl115_39 ),
inference(forward_subsumption_resolution,[],[f3681,f1966]) ).
thf(f3683,plain,
( ~ spl115_2
| spl115_39 ),
inference(avatar_contradiction_clause,[],[f3682]) ).
cnf(s12,plain,
( spl115_1
| spl115_2
| spl115_3
| spl115_4
| spl115_12 ),
inference(sat_conversion,[],[f1810]) ).
cnf(s61,plain,
( spl115_1
| spl115_3
| spl115_4
| spl115_5
| ~ spl115_39 ),
inference(sat_conversion,[],[f1967]) ).
cnf(s602,plain,
~ spl115_3,
inference(sat_conversion,[],[f3551]) ).
cnf(s604,plain,
~ spl115_4,
inference(sat_conversion,[],[f3565]) ).
cnf(s606,plain,
~ spl115_5,
inference(sat_conversion,[],[f3579]) ).
cnf(s608,plain,
~ spl115_1,
inference(sat_conversion,[],[f3593]) ).
cnf(s612,plain,
~ spl115_12,
inference(sat_conversion,[],[f3621]) ).
cnf(s621,plain,
( ~ spl115_2
| spl115_39 ),
inference(sat_conversion,[],[f3683]) ).
cnf(s1061,plain,
~ spl115_39,
inference(rat,[],[s61,s606,s604,s602,s608]) ).
cnf(s1062,plain,
~ spl115_2,
inference(rat,[],[s621,s1061]) ).
cnf(s1112,plain,
$false,
inference(rat,[],[s12,s612,s604,s602,s1062,s608]) ).
thf(f3684,plain,
$false,
inference(avatar_sat_refutation,[],[s1112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU820^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n004.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:34:37 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.22/0.35 % (1371246)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.35 % (1371271)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.35 % (1371271)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
% 0.22/0.35 % (1371265)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1426654673:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.35 % (1371267)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=700413828:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.35 % (1371271)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=3715070979:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.35 % (1371269)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2716637525:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.35 % (1371270)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1160861744:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.35 % (1371268)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=3269518365: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)
% 0.22/0.35 % (1371267)Instruction limit reached!
% 0.22/0.35 % (1371267)------------------------------
% 0.22/0.35 % (1371267)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (1371267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (1371267)CaDiCaL version: 2.1.3
% 0.22/0.35 % (1371267)Termination reason: Instruction limit
% 0.22/0.35 % (1371267)Termination phase: Saturation
% 0.22/0.35 % (1371267)Time elapsed: 0.002 s
% 0.22/0.35 % (1371267)Peak memory usage: 11 MB
% 0.22/0.35 % (1371267)Instructions burned: 4 (million)
% 0.22/0.35 % (1371266)lrs+10_16_si=on:nwc=1.5:random_seed=3151968016:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.35 % (1371269)Instruction limit reached!
% 0.22/0.35 % (1371269)------------------------------
% 0.22/0.35 % (1371269)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (1371269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (1371269)CaDiCaL version: 2.1.3
% 0.22/0.35 % (1371269)Termination reason: Instruction limit
% 0.22/0.35 % (1371269)Termination phase: Saturation
% 0.22/0.35 % (1371269)Time elapsed: 0.012 s
% 0.22/0.35 % (1371269)Peak memory usage: 12 MB
% 0.22/0.35 % (1371269)Instructions burned: 24 (million)
% 0.22/0.35 % (1371266)Instruction limit reached!
% 0.22/0.35 % (1371266)------------------------------
% 0.22/0.35 % (1371266)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (1371266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (1371266)CaDiCaL version: 2.1.3
% 0.22/0.35 % (1371266)Termination reason: Instruction limit
% 0.22/0.35 % (1371266)Termination phase: Saturation
% 0.22/0.35 % (1371266)Time elapsed: 0.015 s
% 0.22/0.35 % (1371266)Peak memory usage: 11 MB
% 0.22/0.35 % (1371266)Instructions burned: 18 (million)
% 0.22/0.35 % (1371285)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=626039649:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.35 % (1371286)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=242162617:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.35 % (1371285)Instruction limit reached!
% 0.22/0.35 % (1371285)------------------------------
% 0.22/0.35 % (1371285)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (1371285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (1371285)CaDiCaL version: 2.1.3
% 0.22/0.35 % (1371285)Termination reason: Instruction limit
% 0.22/0.35 % (1371285)Termination phase: Saturation
% 0.22/0.35 % (1371285)Time elapsed: 0.004 s
% 0.22/0.35 % (1371285)Peak memory usage: 11 MB
% 0.22/0.35 % (1371285)Instructions burned: 7 (million)
% 0.22/0.35 % (1371286)Instruction limit reached!
% 0.22/0.35 % (1371286)------------------------------
% 0.22/0.35 % (1371286)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (1371286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (1371286)CaDiCaL version: 2.1.3
% 0.22/0.35 % (1371286)Termination reason: Instruction limit
% 0.22/0.35 % (1371286)Termination phase: Saturation
% 0.22/0.35 % (1371286)Time elapsed: 0.002 s
% 0.22/0.35 % (1371286)Peak memory usage: 11 MB
% 0.22/0.35 % (1371286)Instructions burned: 11 (million)
% 0.22/0.35 % (1371270)Instruction limit reached!
% 0.22/0.35 % (1371270)------------------------------
% 0.22/0.35 % (1371270)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (1371270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (1371270)CaDiCaL version: 2.1.3
% 0.22/0.35 % (1371270)Termination reason: Instruction limit
% 0.22/0.35 % (1371270)Termination phase: Saturation
% 0.22/0.35 % (1371270)Time elapsed: 0.033 s
% 0.22/0.35 % (1371270)Peak memory usage: 13 MB
% 0.22/0.35 % (1371270)Instructions burned: 77 (million)
% 0.22/0.35 % (1371294)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
% 0.22/0.35 % (1371294)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.35 % (1371288)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.35 % (1371294)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=596880761:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.22/0.35 % (1371288)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=484134859:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.22/0.35 % (1371271)Refutation not found, incomplete strategy
% 0.22/0.35 % (1371271)------------------------------
% 0.22/0.35 % (1371271)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (1371271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (1371271)CaDiCaL version: 2.1.3
% 0.22/0.35 % (1371271)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.35 % (1371271)Time elapsed: 0.039 s
% 0.22/0.35 % (1371271)Peak memory usage: 14 MB
% 0.22/0.35 % (1371271)Instructions burned: 87 (million)
% 0.22/0.35 % (1371265) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1371246-1371265"...
% 0.22/0.35 % (1371271)------------------------------
% 0.22/0.35 % (1371271)------------------------------
% 0.22/0.35 % (1371293)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=525234366:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.22/0.35 % (1371288)Instruction limit reached!
% 0.22/0.35 % (1371288)------------------------------
% 0.22/0.35 % (1371288)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (1371288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (1371288)CaDiCaL version: 2.1.3
% 0.22/0.35 % (1371288)Termination reason: Instruction limit
% 0.22/0.35 % (1371288)Termination phase: Saturation
% 0.22/0.35 % (1371288)Time elapsed: 0.004 s
% 0.22/0.35 % (1371288)Peak memory usage: 12 MB
% 0.22/0.35 % (1371288)Instructions burned: 7 (million)
% 0.22/0.35 % (1371294)Instruction limit reached!
% 0.22/0.35 % (1371294)------------------------------
% 0.22/0.35 % (1371294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (1371294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (1371294)CaDiCaL version: 2.1.3
% 0.22/0.35 % (1371294)Termination reason: Instruction limit
% 0.22/0.35 % (1371294)Termination phase: Saturation
% 0.22/0.35 % (1371294)Time elapsed: 0.008 s
% 0.22/0.35 % (1371294)Peak memory usage: 12 MB
% 0.22/0.35 % (1371294)Instructions burned: 34 (million)
% 0.22/0.35 % (1371293)Instruction limit reached!
% 0.22/0.35 % (1371293)------------------------------
% 0.22/0.35 % (1371293)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (1371293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (1371293)CaDiCaL version: 2.1.3
% 0.22/0.35 % (1371293)Termination reason: Instruction limit
% 0.22/0.35 % (1371293)Termination phase: Saturation
% 0.22/0.35 % (1371293)Time elapsed: 0.006 s
% 0.22/0.35 % (1371293)Peak memory usage: 12 MB
% 0.22/0.35 % (1371293)Instructions burned: 13 (million)
% 0.22/0.35 % (1371297)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=429250256:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.22/0.35 % (1371306)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3843554014:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.22/0.35 % (1371306)Refutation not found, incomplete strategy
% 0.22/0.35 % (1371306)------------------------------
% 0.22/0.35 % (1371306)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (1371306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (1371306)CaDiCaL version: 2.1.3
% 0.22/0.35 % (1371306)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.35 % (1371306)Time elapsed: 0.001 s
% 0.22/0.35 % (1371306)Peak memory usage: 12 MB
% 0.22/0.35 % (1371306)Instructions burned: 4 (million)
% 0.22/0.35 % (1371306)------------------------------
% 0.22/0.35 % (1371306)------------------------------
% 0.22/0.35 % (1371265)...printing done.
% 0.22/0.35 % (1371302)lrs+10_1_si=on:cs=on:random_seed=4006019149:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.22/0.35 % (1371265)Refutation found. Thanks to Tanya!
% 0.22/0.35 % SZS status Theorem for theBenchmark
% 0.22/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.35 % (1371265)------------------------------
% 0.22/0.35 % (1371265)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (1371265)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (1371265)CaDiCaL version: 2.1.3
% 0.22/0.35 % (1371265)Termination reason: Refutation
% 0.22/0.35 % (1371265)Time elapsed: 0.054 s
% 0.22/0.35 % (1371265)Peak memory usage: 15 MB
% 0.22/0.35 % (1371265)Instructions burned: 101 (million)
% 0.22/0.35 % (1371246)Success in time 0.103 s
% 0.22/0.35 % Vampire exiting
%------------------------------------------------------------------------------