%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU717^2 : 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 : n015.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 08:30:56 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 33
% Syntax : Number of formulae : 208 ( 59 unt; 0 typ; 30 def)
% Number of atoms : 1567 ( 330 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 1712 ( 169 ~; 304 |; 20 &;1035 @)
% ( 20 <=>; 116 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 47 usr; 35 con; 0-4 aty)
% ( 48 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 198 ( 0 sgn 135 !; 9 ?; 198 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
subset: $i > $i > $o ).
thf(func_def_3,type,
powersetI1: $o ).
thf(func_def_5,type,
subsetTI: $o ).
thf(func_def_6,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_7,type,
vIMP: $o > $o > $o ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_19,type,
sF4: $o ).
thf(func_def_20,type,
sF5: $o ).
thf(func_def_21,type,
sF6: $i > $o ).
thf(func_def_22,type,
sF7: $i > $o ).
thf(func_def_23,type,
sF8: $i > $o ).
thf(func_def_25,type,
sF10: $o ).
thf(func_def_26,type,
sF11: $o ).
thf(func_def_27,type,
sF12: $o ).
thf(func_def_28,type,
sK13: $i > $i > $i > $i ).
thf(f1,axiom,
! [X1: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
=> ( in @ X1 @ ( powerset @ X0 ) ) )
= powersetI1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(f2,axiom,
( subsetTI
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) )
=> ( subset @ X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTI) ).
thf(f3,conjecture,
( powersetI1
=> ( subsetTI
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) )
=> ( in @ X1 @ ( powerset @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetTI1) ).
thf(f4,negated_conjecture,
~ ( powersetI1
=> ( subsetTI
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) )
=> ( in @ X1 @ ( powerset @ X2 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( subsetTI
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ X0 )
=> ( in @ X3 @ X2 ) ) )
=> ( subset @ X0 @ X2 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f6,plain,
( subsetTI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( subset @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
~ ( powersetI1
=> ( subsetTI
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) )
=> ( in @ X1 @ ( powerset @ X2 ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f8,plain,
~ ( ( powersetI1 = $true )
=> ( ( subsetTI = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ X1 )
= $true )
=> ( ( in @ X3 @ X2 )
= $true ) ) )
=> ( ( in @ X1 @ ( powerset @ X2 ) )
= $true ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
=> ( in @ X0 @ ( powerset @ X1 ) ) )
= powersetI1 ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( powersetI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
!= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( subsetTI = $true )
& ( powersetI1 = $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f12,plain,
( ( powersetI1 = $true )
& ? [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
& ( ( in @ X1 @ ( powerset @ X2 ) )
!= $true ) ) )
& ( subsetTI = $true ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ( powersetI1 = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
& ( $true
!= ( in @ X0 @ ( powerset @ X2 ) ) ) ) )
& ( subsetTI = $true ) ),
inference(rectify,[],[f12]) ).
thf(f14,plain,
( ( powersetI1 = $true )
& ( $true
= ( in @ sK0 @ ( powerset @ sK1 ) ) )
& ( $true
= ( in @ sK2 @ ( powerset @ sK1 ) ) )
& ! [X3: $i] :
( ( $true
= ( in @ X3 @ sK2 ) )
| ( ( in @ X3 @ sK1 )
!= $true )
| ( ( in @ X3 @ sK0 )
!= $true ) )
& ( ( in @ sK0 @ ( powerset @ sK2 ) )
!= $true )
& ( subsetTI = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f13]) ).
thf(f15,plain,
subsetTI = $true,
inference(cnf_transformation,[],[f14]) ).
thf(f16,plain,
( ( in @ sK0 @ ( powerset @ sK2 ) )
!= $true ),
inference(cnf_transformation,[],[f14]) ).
thf(f17,plain,
! [X3: $i] :
( ( $true
= ( in @ X3 @ sK2 ) )
| ( ( in @ X3 @ sK1 )
!= $true )
| ( ( in @ X3 @ sK0 )
!= $true ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f18,plain,
( $true
= ( in @ sK2 @ ( powerset @ sK1 ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f19,plain,
( $true
= ( in @ sK0 @ ( powerset @ sK1 ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f20,plain,
powersetI1 = $true,
inference(cnf_transformation,[],[f14]) ).
thf(f21,plain,
( powersetI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f22,plain,
( subsetTI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( subset @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f25,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f21,f20]) ).
thf(f26,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( subset @ Y1 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f22,f15]) ).
thf(f27,definition,
( sF3
= ( powerset @ sK1 ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f28,definition,
( sF4
= ( in @ sK0 @ sF3 ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f29,plain,
( ( in @ sK0 @ sF3 )
= sF4 ),
inference(reorient_equations,[],[f28]) ).
thf(f30,plain,
sF4 = $true,
inference(definition_folding,[],[f19,f29,f27]) ).
thf(f31,definition,
( sF5
= ( in @ sK2 @ sF3 ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f32,plain,
sF5 = $true,
inference(definition_folding,[],[f18,f31,f27]) ).
thf(f33,definition,
! [X3: $i] :
( ( sF6 @ X3 )
= ( in @ X3 @ sK2 ) ),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
thf(f34,definition,
! [X3: $i] :
( ( sF7 @ X3 )
= ( in @ X3 @ sK1 ) ),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
thf(f35,definition,
! [X3: $i] :
( ( sF8 @ X3 )
= ( in @ X3 @ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
thf(f36,plain,
! [X3: $i] :
( ( in @ X3 @ sK0 )
= ( sF8 @ X3 ) ),
inference(reorient_equations,[],[f35]) ).
thf(f37,plain,
! [X3: $i] :
( ( $true
= ( sF6 @ X3 ) )
| ( ( sF7 @ X3 )
!= $true )
| ( $true
!= ( sF8 @ X3 ) ) ),
inference(definition_folding,[],[f17,f36,f34,f33]) ).
thf(f38,definition,
( sF9
= ( powerset @ sK2 ) ),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
thf(f39,definition,
( sF10
= ( in @ sK0 @ sF9 ) ),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
thf(f40,plain,
sF10 != $true,
inference(definition_folding,[],[f16,f39,f38]) ).
thf(f41,definition,
( sF11
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
thf(f42,plain,
sF11 = $true,
inference(definition_folding,[],[f25,f41]) ).
thf(f43,definition,
( sF12
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( subset @ Y1 @ Y2 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
thf(f44,plain,
sF12 = $true,
inference(definition_folding,[],[f26,f43]) ).
thf(f46,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( subset @ Y1 @ Y2 ) ) ) ) ) ) )
= $true )
| ( sF12 = $false ) ),
inference(iff_proxy_clausification,[],[f43]) ).
thf(f47,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( subset @ Y1 @ Y2 ) ) ) ) ) )
@ X1 )
= $true )
| ( sF12 = $false ) ),
inference(pi_proxy_clausification,[],[f46]) ).
thf(f48,plain,
! [X1: $i] :
( ( sF12 = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ X1 ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f47]) ).
thf(f49,plain,
! [X2: $i,X1: $i] :
( ( sF12 = $false )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ X1 ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f48]) ).
thf(f50,plain,
! [X2: $i,X1: $i] :
( ( ( ( in @ X2 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y1 @ X2 )
=> ( in @ Y1 @ Y0 ) ) ) )
=> ( subset @ X2 @ Y0 ) ) ) ) )
= $true )
| ( sF12 = $false ) ),
inference(beta-eta_normalization,[],[f49]) ).
thf(f51,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y1 @ X2 )
=> ( in @ Y1 @ Y0 ) ) ) )
=> ( subset @ X2 @ Y0 ) ) ) ) )
| ( sF12 = $false ) ),
inference(imp_proxy_clausification,[],[f50]) ).
thf(f52,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF12 = $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y1 @ X2 )
=> ( in @ Y1 @ Y0 ) ) ) )
=> ( subset @ X2 @ Y0 ) ) )
@ X3 )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f51]) ).
thf(f53,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF12 = $false )
| ( ( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X3 ) ) ) )
=> ( subset @ X2 @ X3 ) ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f52]) ).
thf(f54,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X3 ) ) ) )
=> ( subset @ X2 @ X3 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( sF12 = $false ) ),
inference(imp_proxy_clausification,[],[f53]) ).
thf(f55,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X3 ) ) ) )
= $false )
| ( $true
= ( subset @ X2 @ X3 ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( sF12 = $false )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f54]) ).
thf(f56,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( subset @ X2 @ X3 ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X3 ) ) )
@ ( sK13 @ X3 @ X1 @ X2 ) )
= $false )
| ( sF12 = $false )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f55]) ).
thf(f57,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( subset @ X2 @ X3 ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( ( ( in @ ( sK13 @ X3 @ X1 @ X2 ) @ X1 )
=> ( ( in @ ( sK13 @ X3 @ X1 @ X2 ) @ X2 )
=> ( in @ ( sK13 @ X3 @ X1 @ X2 ) @ X3 ) ) )
= $false )
| ( sF12 = $false ) ),
inference(beta-eta_normalization,[],[f56]) ).
thf(f58,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( subset @ X2 @ X3 ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( sF12 = $false )
| ( ( ( in @ ( sK13 @ X3 @ X1 @ X2 ) @ X2 )
=> ( in @ ( sK13 @ X3 @ X1 @ X2 ) @ X3 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f57]) ).
thf(f59,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ ( sK13 @ X3 @ X1 @ X2 ) @ X1 )
= $true )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( sF12 = $false )
| ( $true
= ( subset @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f57]) ).
thf(f60,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( $true
= ( subset @ X2 @ X3 ) )
| ( sF12 = $false )
| ( ( in @ ( sK13 @ X3 @ X1 @ X2 ) @ X3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f58]) ).
thf(f61,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK13 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( $true
= ( subset @ X2 @ X3 ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( sF12 = $false ) ),
inference(imp_proxy_clausification,[],[f58]) ).
thf(f78,plain,
( ( sF10 = $true )
| ( ( in @ sK0 @ sF9 )
= $false ) ),
inference(iff_proxy_clausification,[],[f39]) ).
thf(f81,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) ) )
| ( sF11 = $false ) ),
inference(iff_proxy_clausification,[],[f41]) ).
thf(f82,plain,
! [X1: $i] :
( ( sF11 = $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( in @ Y1 @ ( powerset @ Y0 ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f81]) ).
thf(f83,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ X1 )
=> ( in @ Y0 @ ( powerset @ X1 ) ) ) )
= $true )
| ( sF11 = $false ) ),
inference(beta-eta_normalization,[],[f82]) ).
thf(f84,plain,
! [X2: $i,X1: $i] :
( ( sF11 = $false )
| ( ( ^ [Y0: $i] :
( ( subset @ Y0 @ X1 )
=> ( in @ Y0 @ ( powerset @ X1 ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f83]) ).
thf(f85,plain,
! [X2: $i,X1: $i] :
( ( ( ( subset @ X2 @ X1 )
=> ( in @ X2 @ ( powerset @ X1 ) ) )
= $true )
| ( sF11 = $false ) ),
inference(beta-eta_normalization,[],[f84]) ).
thf(f86,plain,
! [X2: $i,X1: $i] :
( ( sF11 = $false )
| ( $false
= ( subset @ X2 @ X1 ) )
| ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f85]) ).
thf(f93,plain,
! [X3: $i] :
( ( ( in @ X3 @ sK1 )
= $false )
| ( ( sF7 @ X3 )
= $true ) ),
inference(iff_proxy_clausification,[],[f34]) ).
thf(f96,plain,
! [X3: $i] :
( ( $true
= ( in @ X3 @ sK2 ) )
| ( ( sF6 @ X3 )
= $false ) ),
inference(iff_proxy_clausification,[],[f33]) ).
thf(f98,plain,
! [X3: $i] :
( ( ( in @ X3 @ sK0 )
= $false )
| ( $true
= ( sF8 @ X3 ) ) ),
inference(iff_proxy_clausification,[],[f36]) ).
thf(f99,plain,
( ( ( in @ sK0 @ sF3 )
= $true )
| ( sF4 = $false ) ),
inference(iff_proxy_clausification,[],[f29]) ).
thf(f102,plain,
( ( ( in @ sK2 @ sF3 )
= $true )
| ( sF5 = $false ) ),
inference(iff_proxy_clausification,[],[f31]) ).
thf(f104,definition,
( spl19_1
<=> ( sF12 = $false ) ),
introduced(definition,[new_symbols(definition,[spl19_1])],[avatar_definition]) ).
thf(f106,plain,
( ( sF12 = $false )
| ~ spl19_1 ),
inference(avatar_component_clause,[],[f104]) ).
thf(f108,definition,
( spl19_2
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( $true
= ( subset @ X2 @ X3 ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ ( sK13 @ X3 @ X1 @ X2 ) @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl19_2])],[avatar_definition]) ).
thf(f109,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ ( sK13 @ X3 @ X1 @ X2 ) @ X1 )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( $true
= ( subset @ X2 @ X3 ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false ) )
| ~ spl19_2 ),
inference(avatar_component_clause,[],[f108]) ).
thf(f110,plain,
( spl19_1
| spl19_2 ),
inference(avatar_split_clause,[],[f59,f108,f104]) ).
thf(f112,definition,
( spl19_3
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $true
= ( in @ ( sK13 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( $true
= ( subset @ X2 @ X3 ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl19_3])],[avatar_definition]) ).
thf(f113,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK13 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false )
| ( $true
= ( subset @ X2 @ X3 ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false ) )
| ~ spl19_3 ),
inference(avatar_component_clause,[],[f112]) ).
thf(f114,plain,
( spl19_3
| spl19_1 ),
inference(avatar_split_clause,[],[f61,f104,f112]) ).
thf(f116,definition,
( spl19_4
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ ( sK13 @ X3 @ X1 @ X2 ) @ X3 )
= $false )
| ( $true
= ( subset @ X2 @ X3 ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl19_4])],[avatar_definition]) ).
thf(f117,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ ( sK13 @ X3 @ X1 @ X2 ) @ X3 )
= $false )
| ( $true
= ( subset @ X2 @ X3 ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X3 @ ( powerset @ X1 ) )
= $false ) )
| ~ spl19_4 ),
inference(avatar_component_clause,[],[f116]) ).
thf(f118,plain,
( spl19_1
| spl19_4 ),
inference(avatar_split_clause,[],[f60,f116,f104]) ).
thf(f124,definition,
( spl19_6
<=> ( sF12 = $true ) ),
introduced(definition,[new_symbols(definition,[spl19_6])],[avatar_definition]) ).
thf(f126,plain,
( ( sF12 = $true )
| ~ spl19_6 ),
inference(avatar_component_clause,[],[f124]) ).
thf(f143,definition,
( spl19_10
<=> ( ( in @ sK0 @ sF9 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl19_10])],[avatar_definition]) ).
thf(f144,plain,
( ( ( in @ sK0 @ sF9 )
!= $true )
| spl19_10 ),
inference(avatar_component_clause,[],[f143]) ).
thf(f145,plain,
( ( ( in @ sK0 @ sF9 )
= $true )
| ~ spl19_10 ),
inference(avatar_component_clause,[],[f143]) ).
thf(f152,definition,
( spl19_12
<=> ( ( in @ sK0 @ sF9 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl19_12])],[avatar_definition]) ).
thf(f154,plain,
( ( ( in @ sK0 @ sF9 )
= $false )
| ~ spl19_12 ),
inference(avatar_component_clause,[],[f152]) ).
thf(f156,definition,
( spl19_13
<=> ( sF10 = $true ) ),
introduced(definition,[new_symbols(definition,[spl19_13])],[avatar_definition]) ).
thf(f159,plain,
( spl19_12
| spl19_13 ),
inference(avatar_split_clause,[],[f78,f156,f152]) ).
thf(f161,definition,
( spl19_14
<=> ( sF11 = $false ) ),
introduced(definition,[new_symbols(definition,[spl19_14])],[avatar_definition]) ).
thf(f163,plain,
( ( sF11 = $false )
| ~ spl19_14 ),
inference(avatar_component_clause,[],[f161]) ).
thf(f165,definition,
( spl19_15
<=> ! [X2: $i,X1: $i] :
( ( $false
= ( subset @ X2 @ X1 ) )
| ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl19_15])],[avatar_definition]) ).
thf(f166,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( subset @ X2 @ X1 ) ) )
| ~ spl19_15 ),
inference(avatar_component_clause,[],[f165]) ).
thf(f167,plain,
( spl19_14
| spl19_15 ),
inference(avatar_split_clause,[],[f86,f165,f161]) ).
thf(f169,definition,
( spl19_16
<=> ( sF11 = $true ) ),
introduced(definition,[new_symbols(definition,[spl19_16])],[avatar_definition]) ).
thf(f171,plain,
( ( sF11 = $true )
| ~ spl19_16 ),
inference(avatar_component_clause,[],[f169]) ).
thf(f182,plain,
spl19_6,
inference(avatar_split_clause,[],[f44,f124]) ).
thf(f184,definition,
( spl19_19
<=> ( ( in @ sK0 @ sF3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl19_19])],[avatar_definition]) ).
thf(f185,plain,
( ( ( in @ sK0 @ sF3 )
!= $false )
| spl19_19 ),
inference(avatar_component_clause,[],[f184]) ).
thf(f186,plain,
( ( ( in @ sK0 @ sF3 )
= $false )
| ~ spl19_19 ),
inference(avatar_component_clause,[],[f184]) ).
thf(f188,definition,
( spl19_20
<=> ( sF4 = $true ) ),
introduced(definition,[new_symbols(definition,[spl19_20])],[avatar_definition]) ).
thf(f190,plain,
( ( sF4 = $true )
| ~ spl19_20 ),
inference(avatar_component_clause,[],[f188]) ).
thf(f193,definition,
( spl19_21
<=> ( sF4 = $false ) ),
introduced(definition,[new_symbols(definition,[spl19_21])],[avatar_definition]) ).
thf(f195,plain,
( ( sF4 = $false )
| ~ spl19_21 ),
inference(avatar_component_clause,[],[f193]) ).
thf(f197,definition,
( spl19_22
<=> ( ( in @ sK0 @ sF3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl19_22])],[avatar_definition]) ).
thf(f199,plain,
( ( ( in @ sK0 @ sF3 )
= $true )
| ~ spl19_22 ),
inference(avatar_component_clause,[],[f197]) ).
thf(f200,plain,
( spl19_21
| spl19_22 ),
inference(avatar_split_clause,[],[f99,f197,f193]) ).
thf(f202,definition,
( spl19_23
<=> ( sF5 = $false ) ),
introduced(definition,[new_symbols(definition,[spl19_23])],[avatar_definition]) ).
thf(f204,plain,
( ( sF5 = $false )
| ~ spl19_23 ),
inference(avatar_component_clause,[],[f202]) ).
thf(f206,definition,
( spl19_24
<=> ( ( in @ sK2 @ sF3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl19_24])],[avatar_definition]) ).
thf(f208,plain,
( ( ( in @ sK2 @ sF3 )
= $true )
| ~ spl19_24 ),
inference(avatar_component_clause,[],[f206]) ).
thf(f209,plain,
( spl19_23
| spl19_24 ),
inference(avatar_split_clause,[],[f102,f206,f202]) ).
thf(f211,definition,
( spl19_25
<=> ( sF5 = $true ) ),
introduced(definition,[new_symbols(definition,[spl19_25])],[avatar_definition]) ).
thf(f213,plain,
( ( sF5 = $true )
| ~ spl19_25 ),
inference(avatar_component_clause,[],[f211]) ).
thf(f219,plain,
spl19_20,
inference(avatar_split_clause,[],[f30,f188]) ).
thf(f220,plain,
spl19_25,
inference(avatar_split_clause,[],[f32,f211]) ).
thf(f221,plain,
~ spl19_13,
inference(avatar_split_clause,[],[f40,f156]) ).
thf(f222,plain,
spl19_16,
inference(avatar_split_clause,[],[f42,f169]) ).
thf(f223,plain,
( ( $true = $false )
| ~ spl19_20
| ~ spl19_21 ),
inference(forward_demodulation,[],[f195,f190]) ).
thf(f224,plain,
( $false
| ~ spl19_20
| ~ spl19_21 ),
inference(trivial_inequality_removal,[],[f223]) ).
thf(f225,plain,
( ~ spl19_20
| ~ spl19_21 ),
inference(avatar_contradiction_clause,[],[f224]) ).
thf(f244,plain,
( ( $true = $false )
| ~ spl19_23
| ~ spl19_25 ),
inference(forward_demodulation,[],[f213,f204]) ).
thf(f245,plain,
( $false
| ~ spl19_23
| ~ spl19_25 ),
inference(trivial_inequality_removal,[],[f244]) ).
thf(f246,plain,
( ~ spl19_23
| ~ spl19_25 ),
inference(avatar_contradiction_clause,[],[f245]) ).
thf(f249,plain,
( ( $true = $false )
| ~ spl19_14
| ~ spl19_16 ),
inference(forward_demodulation,[],[f171,f163]) ).
thf(f250,plain,
( $false
| ~ spl19_14
| ~ spl19_16 ),
inference(trivial_inequality_removal,[],[f249]) ).
thf(f251,plain,
( ~ spl19_14
| ~ spl19_16 ),
inference(avatar_contradiction_clause,[],[f250]) ).
thf(f254,plain,
( ( $true = $false )
| ~ spl19_10
| ~ spl19_12 ),
inference(forward_demodulation,[],[f154,f145]) ).
thf(f255,plain,
( $false
| ~ spl19_10
| ~ spl19_12 ),
inference(trivial_inequality_removal,[],[f254]) ).
thf(f256,plain,
( ~ spl19_10
| ~ spl19_12 ),
inference(avatar_contradiction_clause,[],[f255]) ).
thf(f265,plain,
( ( $true = $false )
| ~ spl19_19
| ~ spl19_22 ),
inference(forward_demodulation,[],[f199,f186]) ).
thf(f266,plain,
( $false
| ~ spl19_19
| ~ spl19_22 ),
inference(trivial_inequality_removal,[],[f265]) ).
thf(f267,plain,
( ~ spl19_19
| ~ spl19_22 ),
inference(avatar_contradiction_clause,[],[f266]) ).
thf(f289,plain,
( ! [X0: $i] :
( ( ( subset @ X0 @ sK2 )
= $false )
| ( ( in @ X0 @ sF9 )
= $true ) )
| ~ spl19_15 ),
inference(constrained_superposition,[],[f166,f38]) ).
thf(f295,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ sK1 ) )
= $false )
| ( $true
= ( sF7 @ ( sK13 @ X0 @ sK1 @ X1 ) ) )
| ( ( subset @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ ( powerset @ sK1 ) )
= $false )
| ( $true = $false ) )
| ~ spl19_2 ),
inference(constrained_superposition,[],[f109,f93]) ).
thf(f301,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ ( powerset @ sK1 ) )
= $false )
| ( $true
= ( sF7 @ ( sK13 @ X0 @ sK1 @ X1 ) ) )
| ( ( in @ X0 @ ( powerset @ sK1 ) )
= $false ) )
| ~ spl19_2 ),
inference(trivial_inequality_removal,[],[f295]) ).
thf(f307,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
| ( $true
= ( sF7 @ ( sK13 @ X0 @ sK1 @ X1 ) ) )
| ( ( in @ X0 @ ( powerset @ sK1 ) )
= $false )
| ( ( in @ X1 @ sF3 )
= $false ) )
| ~ spl19_2 ),
inference(forward_demodulation,[],[f301,f27]) ).
thf(f311,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( sF7 @ ( sK13 @ X0 @ sK1 @ X1 ) ) )
| ( ( subset @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ sF3 )
= $false )
| ( ( in @ X0 @ sF3 )
= $false ) )
| ~ spl19_2 ),
inference(forward_demodulation,[],[f307,f27]) ).
thf(f317,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ sK0 @ ( powerset @ X1 ) )
= $false )
| ( $true = $false )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $false )
| ( $true
= ( subset @ sK0 @ X0 ) )
| ( $true
= ( sF8 @ ( sK13 @ X0 @ X1 @ sK0 ) ) ) )
| ~ spl19_3 ),
inference(constrained_superposition,[],[f98,f113]) ).
thf(f324,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( sF8 @ ( sK13 @ X0 @ X1 @ sK0 ) ) )
| ( ( in @ sK0 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $false )
| ( $true
= ( subset @ sK0 @ X0 ) ) )
| ~ spl19_3 ),
inference(trivial_inequality_removal,[],[f317]) ).
thf(f402,plain,
( ( $true = $false )
| ~ spl19_1
| ~ spl19_6 ),
inference(forward_demodulation,[],[f106,f126]) ).
thf(f403,plain,
( $false
| ~ spl19_1
| ~ spl19_6 ),
inference(trivial_inequality_removal,[],[f402]) ).
thf(f404,plain,
( ~ spl19_1
| ~ spl19_6 ),
inference(avatar_contradiction_clause,[],[f403]) ).
thf(f411,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ sK2 @ ( powerset @ X0 ) )
= $false )
| ( ( sF6 @ ( sK13 @ sK2 @ X0 @ X1 ) )
= $false )
| ( $true = $false )
| ( $true
= ( subset @ X1 @ sK2 ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false ) )
| ~ spl19_4 ),
inference(constrained_superposition,[],[f117,f96]) ).
thf(f425,plain,
( ! [X0: $i,X1: $i] :
( ( ( sF6 @ ( sK13 @ sK2 @ X0 @ X1 ) )
= $false )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( $true
= ( subset @ X1 @ sK2 ) )
| ( ( in @ sK2 @ ( powerset @ X0 ) )
= $false ) )
| ~ spl19_4 ),
inference(trivial_inequality_removal,[],[f411]) ).
thf(f537,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ sK2 @ ( powerset @ X0 ) )
= $false )
| ( ( sF8 @ ( sK13 @ sK2 @ X0 @ X1 ) )
!= $true )
| ( $true
= ( subset @ X1 @ sK2 ) )
| ( ( sF7 @ ( sK13 @ sK2 @ X0 @ X1 ) )
!= $true ) )
| ~ spl19_4 ),
inference(constrained_superposition,[],[f37,f425]) ).
thf(f540,plain,
( ! [X0: $i,X1: $i] :
( ( ( sF8 @ ( sK13 @ sK2 @ X0 @ X1 ) )
!= $true )
| ( $true
= ( subset @ X1 @ sK2 ) )
| ( ( sF7 @ ( sK13 @ sK2 @ X0 @ X1 ) )
!= $true )
| ( ( in @ sK2 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false ) )
| ~ spl19_4 ),
inference(trivial_inequality_removal,[],[f537]) ).
thf(f550,plain,
( ! [X0: $i] :
( ( ( in @ sK2 @ ( powerset @ X0 ) )
= $false )
| ( $true != $true )
| ( $false
= ( in @ sK0 @ ( powerset @ X0 ) ) )
| ( ( subset @ sK0 @ sK2 )
= $true )
| ( $false
= ( in @ sK0 @ ( powerset @ X0 ) ) )
| ( ( subset @ sK0 @ sK2 )
= $true )
| ( ( sF7 @ ( sK13 @ sK2 @ X0 @ sK0 ) )
!= $true )
| ( ( in @ sK2 @ ( powerset @ X0 ) )
= $false ) )
| ~ spl19_3
| ~ spl19_4 ),
inference(constrained_superposition,[],[f540,f324]) ).
thf(f552,plain,
( ! [X0: $i] :
( ( $false
= ( in @ sK0 @ ( powerset @ X0 ) ) )
| ( $true != $true )
| ( ( sF7 @ ( sK13 @ sK2 @ X0 @ sK0 ) )
!= $true )
| ( ( in @ sK2 @ ( powerset @ X0 ) )
= $false )
| ( ( subset @ sK0 @ sK2 )
= $true ) )
| ~ spl19_3
| ~ spl19_4 ),
inference(duplicate_literal_removal,[],[f550]) ).
thf(f553,plain,
( ! [X0: $i] :
( ( ( sF7 @ ( sK13 @ sK2 @ X0 @ sK0 ) )
!= $true )
| ( $false
= ( in @ sK0 @ ( powerset @ X0 ) ) )
| ( ( in @ sK2 @ ( powerset @ X0 ) )
= $false )
| ( ( subset @ sK0 @ sK2 )
= $true ) )
| ~ spl19_3
| ~ spl19_4 ),
inference(trivial_inequality_removal,[],[f552]) ).
thf(f558,definition,
( spl19_29
<=> ! [X0: $i] :
( ( ( sF7 @ ( sK13 @ sK2 @ X0 @ sK0 ) )
!= $true )
| ( ( in @ sK2 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ sK0 @ ( powerset @ X0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl19_29])],[avatar_definition]) ).
thf(f559,plain,
( ! [X0: $i] :
( ( ( sF7 @ ( sK13 @ sK2 @ X0 @ sK0 ) )
!= $true )
| ( $false
= ( in @ sK0 @ ( powerset @ X0 ) ) )
| ( ( in @ sK2 @ ( powerset @ X0 ) )
= $false ) )
| ~ spl19_29 ),
inference(avatar_component_clause,[],[f558]) ).
thf(f561,definition,
( spl19_30
<=> ( ( subset @ sK0 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl19_30])],[avatar_definition]) ).
thf(f563,plain,
( ( ( subset @ sK0 @ sK2 )
= $true )
| ~ spl19_30 ),
inference(avatar_component_clause,[],[f561]) ).
thf(f564,plain,
( spl19_29
| spl19_30
| ~ spl19_3
| ~ spl19_4 ),
inference(avatar_split_clause,[],[f553,f116,f112,f561,f558]) ).
thf(f612,plain,
( ( $true != $true )
| ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $false )
| ( ( in @ sK0 @ sF3 )
= $false )
| ( ( subset @ sK0 @ sK2 )
= $true )
| ( ( in @ sK2 @ ( powerset @ sK1 ) )
= $false )
| ( ( in @ sK2 @ sF3 )
= $false )
| ~ spl19_2
| ~ spl19_29 ),
inference(constrained_superposition,[],[f559,f311]) ).
thf(f614,plain,
( ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $false )
| ( ( subset @ sK0 @ sK2 )
= $true )
| ( ( in @ sK0 @ sF3 )
= $false )
| ( ( in @ sK2 @ sF3 )
= $false )
| ( ( in @ sK2 @ ( powerset @ sK1 ) )
= $false )
| ~ spl19_2
| ~ spl19_29 ),
inference(trivial_inequality_removal,[],[f612]) ).
thf(f617,plain,
( ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $false )
| ( ( in @ sK2 @ ( powerset @ sK1 ) )
= $false )
| ( ( subset @ sK0 @ sK2 )
= $true )
| ( ( in @ sK2 @ sF3 )
= $false )
| ~ spl19_2
| spl19_19
| ~ spl19_29 ),
inference(forward_subsumption_resolution,[],[f614,f185]) ).
thf(f618,plain,
( ( ( in @ sK0 @ sF3 )
= $false )
| ( ( subset @ sK0 @ sK2 )
= $true )
| ( ( in @ sK2 @ sF3 )
= $false )
| ( ( in @ sK2 @ ( powerset @ sK1 ) )
= $false )
| ~ spl19_2
| spl19_19
| ~ spl19_29 ),
inference(forward_demodulation,[],[f617,f27]) ).
thf(f619,plain,
( ( ( in @ sK2 @ ( powerset @ sK1 ) )
= $false )
| ( ( in @ sK2 @ sF3 )
= $false )
| ( ( subset @ sK0 @ sK2 )
= $true )
| ~ spl19_2
| spl19_19
| ~ spl19_29 ),
inference(forward_subsumption_resolution,[],[f618,f185]) ).
thf(f620,plain,
( ( ( subset @ sK0 @ sK2 )
= $true )
| ( ( in @ sK2 @ sF3 )
= $false )
| ( ( in @ sK2 @ sF3 )
= $false )
| ~ spl19_2
| spl19_19
| ~ spl19_29 ),
inference(forward_demodulation,[],[f619,f27]) ).
thf(f621,plain,
( ( ( in @ sK2 @ sF3 )
= $false )
| ( ( subset @ sK0 @ sK2 )
= $true )
| ~ spl19_2
| spl19_19
| ~ spl19_29 ),
inference(duplicate_literal_removal,[],[f620]) ).
thf(f622,plain,
( ( ( subset @ sK0 @ sK2 )
= $true )
| ( $true = $false )
| ~ spl19_2
| spl19_19
| ~ spl19_24
| ~ spl19_29 ),
inference(forward_demodulation,[],[f621,f208]) ).
thf(f623,plain,
( ( ( subset @ sK0 @ sK2 )
= $true )
| ~ spl19_2
| spl19_19
| ~ spl19_24
| ~ spl19_29 ),
inference(trivial_inequality_removal,[],[f622]) ).
thf(f624,plain,
( spl19_30
| ~ spl19_2
| spl19_19
| ~ spl19_24
| ~ spl19_29 ),
inference(avatar_split_clause,[],[f623,f558,f206,f184,f108,f561]) ).
thf(f625,plain,
( ( ( in @ sK0 @ sF9 )
= $true )
| ( $true = $false )
| ~ spl19_15
| ~ spl19_30 ),
inference(constrained_superposition,[],[f563,f289]) ).
thf(f630,plain,
( ( ( in @ sK0 @ sF9 )
= $true )
| ~ spl19_15
| ~ spl19_30 ),
inference(trivial_inequality_removal,[],[f625]) ).
thf(f635,plain,
( $false
| spl19_10
| ~ spl19_15
| ~ spl19_30 ),
inference(forward_subsumption_resolution,[],[f630,f144]) ).
thf(f636,plain,
( spl19_10
| ~ spl19_15
| ~ spl19_30 ),
inference(avatar_contradiction_clause,[],[f635]) ).
cnf(s1,plain,
( spl19_1
| spl19_2 ),
inference(sat_conversion,[],[f110]) ).
cnf(s2,plain,
( spl19_1
| spl19_3 ),
inference(sat_conversion,[],[f114]) ).
cnf(s3,plain,
( spl19_1
| spl19_4 ),
inference(sat_conversion,[],[f118]) ).
cnf(s9,plain,
( spl19_12
| spl19_13 ),
inference(sat_conversion,[],[f159]) ).
cnf(s10,plain,
( spl19_14
| spl19_15 ),
inference(sat_conversion,[],[f167]) ).
cnf(s13,plain,
spl19_6,
inference(sat_conversion,[],[f182]) ).
cnf(s15,plain,
( spl19_21
| spl19_22 ),
inference(sat_conversion,[],[f200]) ).
cnf(s16,plain,
( spl19_23
| spl19_24 ),
inference(sat_conversion,[],[f209]) ).
cnf(s18,plain,
spl19_20,
inference(sat_conversion,[],[f219]) ).
cnf(s19,plain,
spl19_25,
inference(sat_conversion,[],[f220]) ).
cnf(s20,plain,
~ spl19_13,
inference(sat_conversion,[],[f221]) ).
cnf(s21,plain,
spl19_16,
inference(sat_conversion,[],[f222]) ).
cnf(s22,plain,
( ~ spl19_20
| ~ spl19_21 ),
inference(sat_conversion,[],[f225]) ).
cnf(s24,plain,
( ~ spl19_23
| ~ spl19_25 ),
inference(sat_conversion,[],[f246]) ).
cnf(s25,plain,
( ~ spl19_14
| ~ spl19_16 ),
inference(sat_conversion,[],[f251]) ).
cnf(s26,plain,
( ~ spl19_10
| ~ spl19_12 ),
inference(sat_conversion,[],[f256]) ).
cnf(s28,plain,
( ~ spl19_19
| ~ spl19_22 ),
inference(sat_conversion,[],[f267]) ).
cnf(s31,plain,
( ~ spl19_1
| ~ spl19_6 ),
inference(sat_conversion,[],[f404]) ).
cnf(s32,plain,
( ~ spl19_3
| ~ spl19_4
| spl19_29
| spl19_30 ),
inference(sat_conversion,[],[f564]) ).
cnf(s35,plain,
( ~ spl19_2
| spl19_19
| ~ spl19_24
| ~ spl19_29
| spl19_30 ),
inference(sat_conversion,[],[f624]) ).
cnf(s37,plain,
( spl19_10
| ~ spl19_15
| ~ spl19_30 ),
inference(sat_conversion,[],[f636]) ).
cnf(s38,plain,
~ spl19_14,
inference(rat,[],[s25,s21]) ).
cnf(s40,plain,
~ spl19_23,
inference(rat,[],[s24,s19]) ).
cnf(s41,plain,
~ spl19_21,
inference(rat,[],[s22,s18]) ).
cnf(s42,plain,
spl19_24,
inference(rat,[],[s16,s40]) ).
cnf(s43,plain,
spl19_22,
inference(rat,[],[s15,s41]) ).
cnf(s44,plain,
~ spl19_19,
inference(rat,[],[s28,s43]) ).
cnf(s45,plain,
~ spl19_1,
inference(rat,[],[s31,s13]) ).
cnf(s46,plain,
spl19_15,
inference(rat,[],[s10,s38]) ).
cnf(s47,plain,
spl19_12,
inference(rat,[],[s9,s20]) ).
cnf(s48,plain,
~ spl19_10,
inference(rat,[],[s26,s47]) ).
cnf(s49,plain,
~ spl19_30,
inference(rat,[],[s37,s46,s48]) ).
cnf(s50,plain,
spl19_4,
inference(rat,[],[s3,s45]) ).
cnf(s51,plain,
spl19_3,
inference(rat,[],[s2,s45]) ).
cnf(s52,plain,
spl19_29,
inference(rat,[],[s32,s49,s50,s51]) ).
cnf(s53,plain,
~ spl19_2,
inference(rat,[],[s35,s49,s44,s42,s52]) ).
cnf(s54,plain,
$false,
inference(rat,[],[s1,s53,s45]) ).
thf(f637,plain,
$false,
inference(avatar_sat_refutation,[],[s54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU717^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n015.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 14:18:10 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.23 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
% 0.19/0.28 % (3593131)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.28 % (3593142)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.28 % (3593142)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
% 0.19/0.28 % (3593142)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=1457102195:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.28 % (3593138)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4085953460:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.28 % (3593136)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1351156492:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.28 % (3593137)lrs+10_16_si=on:nwc=1.5:random_seed=1101427152:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.28 % (3593140)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1818864764:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.28 % (3593139)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=2536622829: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)
% 0.19/0.28 % (3593138)Refutation not found, incomplete strategy
% 0.19/0.28 % (3593138)------------------------------
% 0.19/0.28 % (3593138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (3593138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (3593138)CaDiCaL version: 2.1.3
% 0.19/0.28 % (3593138)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.28 % (3593138)Time elapsed: 0.002 s
% 0.19/0.28 % (3593138)Peak memory usage: 12 MB
% 0.19/0.28 % (3593138)Instructions burned: 2 (million)
% 0.19/0.28 % (3593138)------------------------------
% 0.19/0.28 % (3593138)------------------------------
% 0.19/0.28 % (3593142) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3593131-3593142"...
% 0.19/0.28 % (3593140) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3593131-3593140"...
% 0.19/0.28 % (3593136) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3593131-3593136"...
% 0.19/0.28 % (3593139) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3593131-3593139"...
% 0.19/0.28 % (3593142)...printing done.
% 0.19/0.28 % (3593140)...printing done.
% 0.19/0.28 % (3593142)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.28 % (3593142)------------------------------
% 0.19/0.28 % (3593142)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (3593142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (3593142)CaDiCaL version: 2.1.3
% 0.19/0.28 % (3593142)Termination reason: Refutation
% 0.19/0.28 % (3593142)Time elapsed: 0.014 s
% 0.19/0.28 % (3593142)Peak memory usage: 13 MB
% 0.19/0.28 % (3593142)Instructions burned: 45 (million)
% 0.19/0.28 % (3593131)Success in time 0.045 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------