%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU820^2 : 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 : 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 08:34:09 AM UTC 2026
% Result : Theorem 0.12s 0.28s
% Output : Refutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 16
% Syntax : Number of formulae : 141 ( 67 unt; 0 typ; 7 def)
% Number of atoms : 1906 ( 304 equ; 0 cnn)
% Maximal formula atoms : 5 ( 13 avg)
% Number of connectives : 2542 ( 94 ~; 224 |; 97 &;1613 @)
% ( 7 <=>; 318 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 54 usr; 21 con; 0-4 aty)
% ( 172 !!; 17 ??; 0 @@+; 0 @@-)
% Number of variables : 307 ( 2 sgn 55 !; 2 ?; 307 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(func_def_16,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_17,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_18,type,
vIMP: $o > $o > $o ).
thf(func_def_19,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vAND: $o > $o > $o ).
thf(func_def_21,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
vOR: $o > $o > $o ).
thf(func_def_24,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_96,type,
sK69: $i > $i ).
thf(func_def_98,type,
sK71: $i > $i ).
thf(func_def_101,type,
sK74: $i > $i ).
thf(func_def_103,type,
sK76: $i > $i ).
thf(func_def_108,type,
sK81: $i > $i ).
thf(func_def_110,type,
sK83: $i > $i ).
thf(func_def_113,type,
sK86: $i > $i ).
thf(func_def_115,type,
sK88: $i > $i ).
thf(func_def_120,type,
sK93: $i > $i ).
thf(func_def_122,type,
sK95: $i > $i ).
thf(func_def_125,type,
sK98: $i > $i ).
thf(func_def_127,type,
sK100: $i > $i ).
thf(func_def_132,type,
sK105: $i > $i ).
thf(func_def_134,type,
sK107: $i > $i ).
thf(func_def_137,type,
sK110: $i > $i ).
thf(func_def_139,type,
sK112: $i > $i ).
thf(f1,axiom,
( nonempty
= ( ^ [X0: $i] : ( X0 != emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty) ).
thf(f2,axiom,
( vacuousDall
= ( ! [X0: $i > $o,X1: $i] :
( ( in @ X1 @ emptyset )
=> ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vacuousDall) ).
thf(f3,axiom,
( subsetemptysetimpeq
= ( ! [X0: $i] :
( ( subset @ X0 @ emptyset )
=> ( X0 = emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(f4,axiom,
( powersetE1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE1) ).
thf(f5,axiom,
( transitiveset
= ( ^ [X0: $i] :
! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitiveset) ).
thf(f6,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(f7,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(f8,axiom,
( ordinal
= ( ^ [X0: $i] :
( ( wellorderedByIn @ X0 )
& ( transitiveset @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordinal) ).
thf(f9,conjecture,
( vacuousDall
=> ( subsetemptysetimpeq
=> ( powersetE1
=> ( ordinal @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetOrdinal) ).
thf(f10,negated_conjecture,
~ ( vacuousDall
=> ( subsetemptysetimpeq
=> ( powersetE1
=> ( ordinal @ emptyset ) ) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
thf(f11,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f12,plain,
( vacuousDall
= ( ! [X0: $i > $o,X1: $i] :
( ( in @ X1 @ emptyset )
=> ( X0 @ X1 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f13,plain,
( vacuousDall
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ emptyset )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( subsetemptysetimpeq
= ( ! [X0: $i] :
( ( subset @ X0 @ emptyset )
=> ( X0 = emptyset ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f15,plain,
( subsetemptysetimpeq
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ emptyset )
=> ( emptyset = Y0 ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
( powersetE1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f17,plain,
( powersetE1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
( transitiveset
= ( ^ [X0: $i] :
! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f19,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,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,[],[f6]) ).
thf(f21,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,[],[f20]) ).
thf(f22,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,[],[f7]) ).
thf(f23,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,[],[f22]) ).
thf(f24,plain,
( ordinal
= ( ^ [X0: $i] :
( ( wellorderedByIn @ X0 )
& ( transitiveset @ X0 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f25,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( wellorderedByIn @ Y0 ) ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f26,plain,
~ ( vacuousDall
=> ( subsetemptysetimpeq
=> ( powersetE1
=> ( ordinal @ emptyset ) ) ) ),
inference(rectify,[],[f10]) ).
thf(f27,plain,
~ ( ( vacuousDall = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetE1 = $true )
=> ( ( ordinal @ emptyset )
= $true ) ) ) ),
inference(fool_elimination,[],[f26]) ).
thf(f28,plain,
( ( ( ordinal @ emptyset )
!= $true )
& ( powersetE1 = $true )
& ( subsetemptysetimpeq = $true )
& ( vacuousDall = $true ) ),
inference(ennf_transformation,[],[f27]) ).
thf(f29,plain,
( ( ( ordinal @ emptyset )
!= $true )
& ( powersetE1 = $true )
& ( subsetemptysetimpeq = $true )
& ( vacuousDall = $true ) ),
inference(flattening,[],[f28]) ).
thf(f30,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f31,plain,
( vacuousDall
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ emptyset )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f32,plain,
( subsetemptysetimpeq
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ emptyset )
=> ( emptyset = Y0 ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f33,plain,
( powersetE1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f34,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f35,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,[],[f21]) ).
thf(f36,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,[],[f23]) ).
thf(f37,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( wellorderedByIn @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f38,plain,
vacuousDall = $true,
inference(cnf_transformation,[],[f29]) ).
thf(f39,plain,
subsetemptysetimpeq = $true,
inference(cnf_transformation,[],[f29]) ).
thf(f40,plain,
powersetE1 = $true,
inference(cnf_transformation,[],[f29]) ).
thf(f41,plain,
( ( ordinal @ emptyset )
!= $true ),
inference(cnf_transformation,[],[f29]) ).
thf(f44,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,[],[f36,f35,f30]) ).
thf(f45,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,[],[f37,f34,f44]) ).
thf(f46,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ emptyset )
=> ( Y1 @ Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f31,f38]) ).
thf(f47,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ emptyset )
=> ( emptyset = Y0 ) ) )
= $true ),
inference(definition_unfolding,[],[f32,f39]) ).
thf(f48,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ Y0 @ Y1 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f33,f40]) ).
thf(f49,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 ) )
@ emptyset ) ),
inference(definition_unfolding,[],[f41,f45]) ).
thf(f50,plain,
( $true
!= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) )
& ( !! @ $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 )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f49]) ).
thf(f51,plain,
( ( $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 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) ) ) ),
inference(and_proxy_clausification,[],[f50]) ).
thf(f52,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) ) )
| ( $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 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f51]) ).
thf(f53,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) ) ) )
@ sK0 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) ) )
| ( $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 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f52]) ).
thf(f54,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) ) ) )
@ sK0 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) )
@ sK1 ) )
| ( $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 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f53]) ).
thf(f55,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) ) ) )
@ sK0 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) )
@ sK1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) ) ) )
| ( $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 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f54]) ).
thf(f56,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) ) ) )
@ sK0 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) )
@ sK2 ) )
| ( $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 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f55]) ).
thf(f57,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) ) ) )
@ sK0 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) )
@ sK2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) ) )
| ( $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,[],[f56]) ).
thf(f58,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) ) ) )
@ sK0 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) )
@ sK3 ) )
| ( $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,[],[f57]) ).
thf(f59,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) ) ) )
@ sK0 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ~ ( in @ Y0 @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) )
@ sK3 ) )
| ( $false
= ( ^ [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 ) ) ) ) ) ) )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f58]) ).
thf(f60,plain,
( ( $false
= ( ( in @ sK0 @ ( powerset @ emptyset ) )
=> ( ( emptyset != sK0 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 ) ) ) ) ) ) ) ) )
| ( $false
= ( ( in @ sK1 @ emptyset )
=> ( subset @ sK1 @ emptyset ) ) )
| ( $false
= ( ( in @ sK2 @ emptyset )
=> ~ ( in @ sK2 @ sK2 ) ) )
| ( $false
= ( ( in @ sK3 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( ( sK3 = Y0 )
| ( in @ sK3 @ Y0 )
| ( in @ Y0 @ sK3 ) ) ) ) ) )
| ( $false
= ( ( in @ sK4 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( ( in @ sK4 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ sK4 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f59]) ).
thf(f61,plain,
( ( $false
= ( ( emptyset != sK0 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( ( Y0 = Y1 )
| ( in @ Y0 @ Y1 ) ) ) ) ) ) ) )
| ( $false
= ( ( in @ sK1 @ emptyset )
=> ( subset @ sK1 @ emptyset ) ) )
| ( $false
= ( ( in @ sK2 @ emptyset )
=> ~ ( in @ sK2 @ sK2 ) ) )
| ( $false
= ( ( in @ sK3 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( ( sK3 = Y0 )
| ( in @ sK3 @ Y0 )
| ( in @ Y0 @ sK3 ) ) ) ) ) )
| ( $false
= ( ( in @ sK4 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( ( in @ sK4 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ sK4 @ Y1 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f60]) ).
thf(f62,plain,
( ( $true
= ( in @ sK0 @ ( powerset @ emptyset ) ) )
| ( $false
= ( ( in @ sK1 @ emptyset )
=> ( subset @ sK1 @ emptyset ) ) )
| ( $false
= ( ( in @ sK2 @ emptyset )
=> ~ ( in @ sK2 @ sK2 ) ) )
| ( $false
= ( ( in @ sK3 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( ( sK3 = Y0 )
| ( in @ sK3 @ Y0 )
| ( in @ Y0 @ sK3 ) ) ) ) ) )
| ( $false
= ( ( in @ sK4 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( ( in @ sK4 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ sK4 @ Y1 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f60]) ).
thf(f64,plain,
( ( $true
= ( in @ sK0 @ ( powerset @ emptyset ) ) )
| ( $true
= ( in @ sK1 @ emptyset ) )
| ( $false
= ( ( in @ sK2 @ emptyset )
=> ~ ( in @ sK2 @ sK2 ) ) )
| ( $false
= ( ( in @ sK3 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( ( sK3 = Y0 )
| ( in @ sK3 @ Y0 )
| ( in @ Y0 @ sK3 ) ) ) ) ) )
| ( $false
= ( ( in @ sK4 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( ( in @ sK4 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ sK4 @ Y1 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f62]) ).
thf(f66,plain,
( ( $true
= ( in @ sK0 @ ( powerset @ emptyset ) ) )
| ( $true
= ( in @ sK1 @ emptyset ) )
| ( $true
= ( in @ sK2 @ emptyset ) )
| ( $false
= ( ( in @ sK3 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( ( sK3 = Y0 )
| ( in @ sK3 @ Y0 )
| ( in @ Y0 @ sK3 ) ) ) ) ) )
| ( $false
= ( ( in @ sK4 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( ( in @ sK4 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ sK4 @ Y1 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f64]) ).
thf(f67,plain,
( ( $true
= ( in @ sK0 @ ( powerset @ emptyset ) ) )
| ( $true
= ( in @ sK1 @ emptyset ) )
| ( $true
= ( in @ sK2 @ emptyset ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( ( sK3 = Y0 )
| ( in @ sK3 @ Y0 )
| ( in @ Y0 @ sK3 ) ) ) ) )
| ( $false
= ( ( in @ sK4 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( ( in @ sK4 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ sK4 @ Y1 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f66]) ).
thf(f83,plain,
( ( $true
= ( in @ sK0 @ ( powerset @ emptyset ) ) )
| ( $true
= ( in @ sK1 @ emptyset ) )
| ( $true
= ( in @ sK2 @ emptyset ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( ( sK3 = Y0 )
| ( in @ sK3 @ Y0 )
| ( in @ Y0 @ sK3 ) ) )
@ sK7 ) )
| ( $false
= ( ( in @ sK4 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( ( in @ sK4 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ sK4 @ Y1 ) ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f67]) ).
thf(f85,plain,
( ( $true
= ( in @ sK0 @ ( powerset @ emptyset ) ) )
| ( $true
= ( in @ sK1 @ emptyset ) )
| ( $true
= ( in @ sK2 @ emptyset ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( ( sK3 = Y0 )
| ( in @ sK3 @ Y0 )
| ( in @ Y0 @ sK3 ) ) )
@ sK7 ) )
| ( $true
= ( in @ sK4 @ emptyset ) ) ),
inference(imp_proxy_clausification,[],[f83]) ).
thf(f86,plain,
( ( $true
= ( in @ sK0 @ ( powerset @ emptyset ) ) )
| ( $true
= ( in @ sK1 @ emptyset ) )
| ( $true
= ( in @ sK2 @ emptyset ) )
| ( $false
= ( ( in @ sK7 @ emptyset )
=> ( ( sK3 = sK7 )
| ( in @ sK3 @ sK7 )
| ( in @ sK7 @ sK3 ) ) ) )
| ( $true
= ( in @ sK4 @ emptyset ) ) ),
inference(beta-eta_normalization,[],[f85]) ).
thf(f88,plain,
( ( $true
= ( in @ sK0 @ ( powerset @ emptyset ) ) )
| ( $true
= ( in @ sK1 @ emptyset ) )
| ( $true
= ( in @ sK2 @ emptyset ) )
| ( $true
= ( in @ sK7 @ emptyset ) )
| ( $true
= ( in @ sK4 @ emptyset ) ) ),
inference(imp_proxy_clausification,[],[f86]) ).
thf(f376,plain,
( ( $true
= ( emptyset != sK0 ) )
| ( $false
= ( ( in @ sK1 @ emptyset )
=> ( subset @ sK1 @ emptyset ) ) )
| ( $false
= ( ( in @ sK2 @ emptyset )
=> ~ ( in @ sK2 @ sK2 ) ) )
| ( $false
= ( ( in @ sK3 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( ( sK3 = Y0 )
| ( in @ sK3 @ Y0 )
| ( in @ Y0 @ sK3 ) ) ) ) ) )
| ( $false
= ( ( in @ sK4 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( ( in @ sK4 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ sK4 @ Y1 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f61]) ).
thf(f377,plain,
( ( $false
= ( emptyset = sK0 ) )
| ( $false
= ( ( in @ sK1 @ emptyset )
=> ( subset @ sK1 @ emptyset ) ) )
| ( $false
= ( ( in @ sK2 @ emptyset )
=> ~ ( in @ sK2 @ sK2 ) ) )
| ( $false
= ( ( in @ sK3 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( ( sK3 = Y0 )
| ( in @ sK3 @ Y0 )
| ( in @ Y0 @ sK3 ) ) ) ) ) )
| ( $false
= ( ( in @ sK4 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( ( in @ sK4 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ sK4 @ Y1 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f376]) ).
thf(f378,plain,
( ( emptyset != sK0 )
| ( $false
= ( ( in @ sK1 @ emptyset )
=> ( subset @ sK1 @ emptyset ) ) )
| ( $false
= ( ( in @ sK2 @ emptyset )
=> ~ ( in @ sK2 @ sK2 ) ) )
| ( $false
= ( ( in @ sK3 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( ( sK3 = Y0 )
| ( in @ sK3 @ Y0 )
| ( in @ Y0 @ sK3 ) ) ) ) ) )
| ( $false
= ( ( in @ sK4 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( ( in @ sK4 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ sK4 @ Y1 ) ) ) ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f377]) ).
thf(f380,plain,
( ( emptyset != sK0 )
| ( $true
= ( in @ sK1 @ emptyset ) )
| ( $false
= ( ( in @ sK2 @ emptyset )
=> ~ ( in @ sK2 @ sK2 ) ) )
| ( $false
= ( ( in @ sK3 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( ( sK3 = Y0 )
| ( in @ sK3 @ Y0 )
| ( in @ Y0 @ sK3 ) ) ) ) ) )
| ( $false
= ( ( in @ sK4 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( ( in @ sK4 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ sK4 @ Y1 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f378]) ).
thf(f382,plain,
( ( emptyset != sK0 )
| ( $true
= ( in @ sK1 @ emptyset ) )
| ( $true
= ( in @ sK2 @ emptyset ) )
| ( $false
= ( ( in @ sK3 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( ( sK3 = Y0 )
| ( in @ sK3 @ Y0 )
| ( in @ Y0 @ sK3 ) ) ) ) ) )
| ( $false
= ( ( in @ sK4 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( ( in @ sK4 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ sK4 @ Y1 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f380]) ).
thf(f384,plain,
( ( emptyset != sK0 )
| ( $true
= ( in @ sK1 @ emptyset ) )
| ( $true
= ( in @ sK2 @ emptyset ) )
| ( $true
= ( in @ sK3 @ emptyset ) )
| ( $false
= ( ( in @ sK4 @ emptyset )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( ( in @ sK4 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ sK4 @ Y1 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f382]) ).
thf(f386,plain,
( ( emptyset != sK0 )
| ( $true
= ( in @ sK1 @ emptyset ) )
| ( $true
= ( in @ sK2 @ emptyset ) )
| ( $true
= ( in @ sK3 @ emptyset ) )
| ( $true
= ( in @ sK4 @ emptyset ) ) ),
inference(imp_proxy_clausification,[],[f384]) ).
thf(f1620,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f48]) ).
thf(f1621,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( subset @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f1620]) ).
thf(f1622,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( subset @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f1621]) ).
thf(f1623,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( subset @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f1622]) ).
thf(f1624,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X2 ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f1623]) ).
thf(f1625,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ Y0 @ emptyset )
=> ( emptyset = Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f47]) ).
thf(f1626,plain,
! [X1: $i] :
( $true
= ( ( subset @ X1 @ emptyset )
=> ( emptyset = X1 ) ) ),
inference(beta-eta_normalization,[],[f1625]) ).
thf(f1627,plain,
! [X1: $i] :
( ( $false
= ( subset @ X1 @ emptyset ) )
| ( $true
= ( emptyset = X1 ) ) ),
inference(imp_proxy_clausification,[],[f1626]) ).
thf(f1628,plain,
! [X1: $i] :
( ( $false
= ( subset @ X1 @ emptyset ) )
| ( emptyset = X1 ) ),
inference(equality_proxy_clausification,[],[f1627]) ).
thf(f1629,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ emptyset )
=> ( Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f46]) ).
thf(f1630,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X1 @ emptyset )
=> ( Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f1629]) ).
thf(f1631,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( ( in @ X1 @ emptyset )
=> ( Y0 @ X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f1630]) ).
thf(f1632,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ( in @ X1 @ emptyset )
=> ( X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f1631]) ).
thf(f1633,plain,
! [X2: $i > $o,X1: $i] :
( ( ( in @ X1 @ emptyset )
= $false )
| ( $true
= ( X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1632]) ).
thf(f1635,definition,
( spl117_1
<=> ( $true
= ( in @ sK4 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[spl117_1])],[avatar_definition]) ).
thf(f1637,plain,
( ( $true
= ( in @ sK4 @ emptyset ) )
| ~ spl117_1 ),
inference(avatar_component_clause,[],[f1635]) ).
thf(f1639,definition,
( spl117_2
<=> ( $true
= ( in @ sK3 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[spl117_2])],[avatar_definition]) ).
thf(f1641,plain,
( ( $true
= ( in @ sK3 @ emptyset ) )
| ~ spl117_2 ),
inference(avatar_component_clause,[],[f1639]) ).
thf(f1643,definition,
( spl117_3
<=> ( $true
= ( in @ sK2 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[spl117_3])],[avatar_definition]) ).
thf(f1645,plain,
( ( $true
= ( in @ sK2 @ emptyset ) )
| ~ spl117_3 ),
inference(avatar_component_clause,[],[f1643]) ).
thf(f1647,definition,
( spl117_4
<=> ( $true
= ( in @ sK1 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[spl117_4])],[avatar_definition]) ).
thf(f1649,plain,
( ( $true
= ( in @ sK1 @ emptyset ) )
| ~ spl117_4 ),
inference(avatar_component_clause,[],[f1647]) ).
thf(f1651,definition,
( spl117_5
<=> ( $true
= ( in @ sK0 @ ( powerset @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[spl117_5])],[avatar_definition]) ).
thf(f1653,plain,
( ( $true
= ( in @ sK0 @ ( powerset @ emptyset ) ) )
| ~ spl117_5 ),
inference(avatar_component_clause,[],[f1651]) ).
thf(f1681,definition,
( spl117_11
<=> ( $true
= ( in @ sK7 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[spl117_11])],[avatar_definition]) ).
thf(f1683,plain,
( ( $true
= ( in @ sK7 @ emptyset ) )
| ~ spl117_11 ),
inference(avatar_component_clause,[],[f1681]) ).
thf(f1684,plain,
( spl117_1
| spl117_11
| spl117_3
| spl117_4
| spl117_5 ),
inference(avatar_split_clause,[],[f88,f1651,f1647,f1643,f1681,f1635]) ).
thf(f2151,definition,
( spl117_100
<=> ( emptyset = sK0 ) ),
introduced(definition,[new_symbols(definition,[spl117_100])],[avatar_definition]) ).
thf(f2154,plain,
( spl117_1
| spl117_2
| spl117_3
| spl117_4
| ~ spl117_100 ),
inference(avatar_split_clause,[],[f386,f2151,f1647,f1643,f1639,f1635]) ).
thf(f3515,plain,
! [X1: $i] :
( ( ( in @ X1 @ emptyset )
= $false )
| ( $true
= ( ^ [Y0: $i] : $false
@ X1 ) ) ),
inference(primitive_instantiation,[],[f1633]) ).
thf(f3525,plain,
( ! [X0: $i > $o] :
( ( $true = $false )
| ( $true
= ( X0 @ sK2 ) ) )
| ~ spl117_3 ),
inference(constrained_superposition,[],[f1645,f1633]) ).
thf(f3553,plain,
( ! [X0: $i > $o] :
( $true
= ( X0 @ sK2 ) )
| ~ spl117_3 ),
inference(trivial_inequality_removal,[],[f3525]) ).
thf(f3563,plain,
! [X1: $i] :
( ( ( in @ X1 @ emptyset )
= $false )
| ( $true = $false ) ),
inference(beta-eta_normalization,[],[f3515]) ).
thf(f3564,plain,
! [X1: $i] :
( ( in @ X1 @ emptyset )
= $false ),
inference(trivial_inequality_removal,[],[f3563]) ).
thf(f3567,plain,
( ( $true
= ( ^ [Y0: $i] : $false
@ sK2 ) )
| ~ spl117_3 ),
inference(primitive_instantiation,[],[f3553]) ).
thf(f3581,plain,
( ( $true = $false )
| ~ spl117_3 ),
inference(beta-eta_normalization,[],[f3567]) ).
thf(f3582,plain,
( $false
| ~ spl117_3 ),
inference(trivial_inequality_removal,[],[f3581]) ).
thf(f3583,plain,
~ spl117_3,
inference(avatar_contradiction_clause,[],[f3582]) ).
thf(f3588,plain,
( ( $true = $false )
| ~ spl117_4 ),
inference(constrained_superposition,[],[f1649,f3564]) ).
thf(f3592,plain,
( $false
| ~ spl117_4 ),
inference(trivial_inequality_removal,[],[f3588]) ).
thf(f3593,plain,
~ spl117_4,
inference(avatar_contradiction_clause,[],[f3592]) ).
thf(f3594,plain,
( ( $true = $false )
| ~ spl117_1 ),
inference(constrained_superposition,[],[f1637,f3564]) ).
thf(f3598,plain,
( $false
| ~ spl117_1 ),
inference(trivial_inequality_removal,[],[f3594]) ).
thf(f3599,plain,
~ spl117_1,
inference(avatar_contradiction_clause,[],[f3598]) ).
thf(f3601,plain,
( ( $true = $false )
| ~ spl117_2 ),
inference(constrained_superposition,[],[f1641,f3564]) ).
thf(f3605,plain,
( $false
| ~ spl117_2 ),
inference(trivial_inequality_removal,[],[f3601]) ).
thf(f3606,plain,
~ spl117_2,
inference(avatar_contradiction_clause,[],[f3605]) ).
thf(f3616,plain,
( ( $true = $false )
| ~ spl117_11 ),
inference(constrained_superposition,[],[f1683,f3564]) ).
thf(f3620,plain,
( $false
| ~ spl117_11 ),
inference(trivial_inequality_removal,[],[f3616]) ).
thf(f3621,plain,
~ spl117_11,
inference(avatar_contradiction_clause,[],[f3620]) ).
thf(f3626,plain,
! [X0: $i] :
( ( $true = $false )
| ( emptyset = X0 )
| ( $false
= ( in @ X0 @ ( powerset @ emptyset ) ) ) ),
inference(constrained_superposition,[],[f1628,f1624]) ).
thf(f3629,plain,
! [X0: $i] :
( ( $false
= ( in @ X0 @ ( powerset @ emptyset ) ) )
| ( emptyset = X0 ) ),
inference(trivial_inequality_removal,[],[f3626]) ).
thf(f3822,plain,
( ( $true = $false )
| ( emptyset = sK0 )
| ~ spl117_5 ),
inference(constrained_superposition,[],[f3629,f1653]) ).
thf(f3823,plain,
( ( emptyset = sK0 )
| ~ spl117_5 ),
inference(trivial_inequality_removal,[],[f3822]) ).
thf(f3825,plain,
( spl117_100
| ~ spl117_5 ),
inference(avatar_split_clause,[],[f3823,f1651,f2151]) ).
cnf(s7,plain,
( spl117_1
| spl117_3
| spl117_4
| spl117_5
| spl117_11 ),
inference(sat_conversion,[],[f1684]) ).
cnf(s121,plain,
( spl117_1
| spl117_2
| spl117_3
| spl117_4
| ~ spl117_100 ),
inference(sat_conversion,[],[f2154]) ).
cnf(s601,plain,
~ spl117_3,
inference(sat_conversion,[],[f3583]) ).
cnf(s603,plain,
~ spl117_4,
inference(sat_conversion,[],[f3593]) ).
cnf(s605,plain,
~ spl117_1,
inference(sat_conversion,[],[f3599]) ).
cnf(s607,plain,
~ spl117_2,
inference(sat_conversion,[],[f3606]) ).
cnf(s611,plain,
~ spl117_11,
inference(sat_conversion,[],[f3621]) ).
cnf(s616,plain,
( ~ spl117_5
| spl117_100 ),
inference(sat_conversion,[],[f3825]) ).
cnf(s1017,plain,
~ spl117_100,
inference(rat,[],[s121,s603,s601,s607,s605]) ).
cnf(s1018,plain,
~ spl117_5,
inference(rat,[],[s616,s1017]) ).
cnf(s1132,plain,
$false,
inference(rat,[],[s7,s611,s1018,s603,s601,s605]) ).
thf(f3826,plain,
$false,
inference(avatar_sat_refutation,[],[s1132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU820^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.19 % Computer : n004.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Tue Sep 29 14:34:37 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.22 Running first-order model finding
% 0.12/0.22 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
% 0.12/0.28 % (1371393)Will run a generic schedule for satisfiability detection.
% 0.12/0.28 % (1371403)% WARNING: option uhcvi not known.
% 0.12/0.28 % (1371402)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2191080380_3000 on theBenchmark for (3000ds/0Mi)
% 0.12/0.28 % (1371404)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3204290323:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.12/0.28 % (1371405)dis+10_1_sil=32000:sp=arity:random_seed=2641293921:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.12/0.28 % (1371403)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=986144657:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.12/0.28 % (1371406)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1507023922:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.12/0.28 % (1371407)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1197931050:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.12/0.28 % (1371408)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=10549944:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.12/0.28 % (1371403)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.12/0.28 % (1371406)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.12/0.28 % Exception at run slice level
% 0.12/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.28 % (1371403)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.12/0.28 % (1371422)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=916740632:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.12/0.28 % Exception at run slice level
% 0.12/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.28 % (1371408) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1371393-1371408"...
% 0.12/0.28 % (1371408)...printing done.
% 0.12/0.28 % (1371408)Refutation found. Thanks to Tanya!
% 0.12/0.28 % SZS status Theorem for theBenchmark
% 0.12/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.28/0.28 % (1371408)------------------------------
% 0.28/0.28 % (1371408)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.28 % (1371408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.28 % (1371408)CaDiCaL version: 2.1.3
% 0.28/0.28 % (1371408)Termination reason: Refutation
% 0.28/0.28 % (1371408)Time elapsed: 0.030 s
% 0.28/0.28 % (1371408)Peak memory usage: 14 MB
% 0.28/0.28 % (1371408)Instructions burned: 105 (million)
% 0.28/0.28 % (1371393)Success in time 0.052 s
% 0.28/0.28 % Vampire exiting
%------------------------------------------------------------------------------