%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU737^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:36:47 AM UTC 2026
% Result : Theorem 1.71s 1.36s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 10
% Syntax : Number of formulae : 96 ( 37 unt; 0 typ; 4 def)
% Number of atoms : 1107 ( 221 equ; 0 cnn)
% Maximal formula atoms : 9 ( 11 avg)
% Number of connectives : 1682 ( 35 ~; 125 |; 28 &;1257 @)
% ( 4 <=>; 169 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 13 con; 0-3 aty)
% ( 64 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 211 ( 74 ^; 126 !; 11 ?; 211 :)
% Comments :
%------------------------------------------------------------------------------
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,
setminus: $i > $i > $i ).
thf(func_def_21,type,
sK4: $i > $i > $i > $i ).
thf(f189,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f91,f167,f173,f182,f188]) ).
thf(f188,plain,
~ spl3_3,
inference(avatar_contradiction_clause,[status(thm)],[f187]) ).
thf(f187,plain,
( $false
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f183]) ).
thf(f183,plain,
( ( $false = $true )
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f89,f26]) ).
thf(f26,plain,
( ( in @ sK0 @ ( powerset @ sK1 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( complementT_lem = $true )
& ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $true )
& ( ( in @ sK2 @ ( powerset @ sK1 ) )
= $true )
& ( ( subset @ sK2 @ ( setminus @ sK1 @ sK0 ) )
!= $true )
& ( ( subset @ sK0 @ ( setminus @ sK1 @ sK2 ) )
= $true )
& ( subsetTI = $true )
& ( contraSubsetComplement = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f16,f18,f17]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ( ( subset @ X2 @ ( setminus @ X1 @ X0 ) )
!= $true )
& ( ( subset @ X0 @ ( setminus @ X1 @ X2 ) )
= $true ) ) )
=> ( ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $true )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK1 ) ) )
& ( ( subset @ X2 @ ( setminus @ sK1 @ sK0 ) )
!= $true )
& ( ( subset @ sK0 @ ( setminus @ sK1 @ X2 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK1 ) ) )
& ( ( subset @ X2 @ ( setminus @ sK1 @ sK0 ) )
!= $true )
& ( ( subset @ sK0 @ ( setminus @ sK1 @ X2 ) )
= $true ) )
=> ( ( ( in @ sK2 @ ( powerset @ sK1 ) )
= $true )
& ( ( subset @ sK2 @ ( setminus @ sK1 @ sK0 ) )
!= $true )
& ( ( subset @ sK0 @ ( setminus @ sK1 @ sK2 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ( complementT_lem = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ( ( subset @ X2 @ ( setminus @ X1 @ X0 ) )
!= $true )
& ( ( subset @ X0 @ ( setminus @ X1 @ X2 ) )
= $true ) ) )
& ( subsetTI = $true )
& ( contraSubsetComplement = $true ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( subset @ X2 @ ( setminus @ X1 @ X0 ) )
!= $true )
& ( ( subset @ X0 @ ( setminus @ X1 @ X2 ) )
= $true )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( contraSubsetComplement = $true )
& ( subsetTI = $true )
& ( complementT_lem = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ( complementT_lem = $true )
=> ( ( subsetTI = $true )
=> ( ( contraSubsetComplement = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ( ( ( subset @ X0 @ ( setminus @ X1 @ X2 ) )
= $true )
=> ( ( subset @ X2 @ ( setminus @ X1 @ X0 ) )
= $true ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( complementT_lem
=> ( subsetTI
=> ( contraSubsetComplement
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( subset @ X0 @ ( setminus @ X1 @ X2 ) )
=> ( subset @ X2 @ ( setminus @ X1 @ X0 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( complementT_lem
=> ( subsetTI
=> ( contraSubsetComplement
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
=> ( subset @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( complementT_lem
=> ( subsetTI
=> ( contraSubsetComplement
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
=> ( subset @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lj4biKboPJ/DTF2THF_27624.p',complementTcontraSubset) ).
thf(f89,plain,
( ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $false )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f87]) ).
thf(f87,definition,
( spl3_3
<=> ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f182,plain,
( spl3_3
| ~ spl3_6 ),
inference(avatar_split_clause,[status(thm)],[f179,f162,f87]) ).
thf(f162,definition,
( spl3_6
<=> ( $false
= ( in @ ( setminus @ sK1 @ sK0 ) @ ( powerset @ sK1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition]) ).
thf(f179,plain,
( ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $false )
| ~ spl3_6 ),
inference(trivial_inequality_removal,[status(thm)],[f177]) ).
thf(f177,plain,
( ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $false )
| ( $false = $true )
| ~ spl3_6 ),
inference(superposition,[status(thm)],[f164,f37]) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( ( ( in @ ( setminus @ X1 @ X2 ) @ ( powerset @ X1 ) )
= $true )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X2 ) @ ( powerset @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ Y0 ) @ ( powerset @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ Y0 ) @ ( powerset @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( in @ ( setminus @ Y0 @ Y1 ) @ ( powerset @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( in @ ( setminus @ Y0 @ Y1 ) @ ( powerset @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f28,f27]) ).
thf(f27,plain,
complementT_lem = $true,
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f28,plain,
( complementT_lem
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( in @ ( setminus @ Y0 @ Y1 ) @ ( powerset @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( complementT_lem
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( in @ ( setminus @ Y0 @ Y1 ) @ ( powerset @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( complementT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( complementT_lem
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lj4biKboPJ/DTF2THF_27624.p',complementT_lem) ).
thf(f164,plain,
( ( $false
= ( in @ ( setminus @ sK1 @ sK0 ) @ ( powerset @ sK1 ) ) )
| ~ spl3_6 ),
inference(avatar_component_clause,[status(thm)],[f162]) ).
thf(f173,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[status(thm)],[f172]) ).
thf(f172,plain,
( $false
| ~ spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f168]) ).
thf(f168,plain,
( ( $false = $true )
| ~ spl3_1 ),
inference(superposition,[status(thm)],[f82,f25]) ).
thf(f25,plain,
( ( in @ sK2 @ ( powerset @ sK1 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f82,plain,
( ( $false
= ( in @ sK2 @ ( powerset @ sK1 ) ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f80]) ).
thf(f80,definition,
( spl3_1
<=> ( $false
= ( in @ sK2 @ ( powerset @ sK1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f167,plain,
( spl3_1
| spl3_6
| ~ spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f166,f84,f162,f80]) ).
thf(f84,definition,
( spl3_2
<=> ! [X0: $i] :
( ( $false
= ( in @ X0 @ sK1 ) )
| ( $false
= ( in @ X0 @ sK2 ) )
| ( ( in @ X0 @ ( setminus @ sK1 @ sK0 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f166,plain,
( ( $false
= ( in @ sK2 @ ( powerset @ sK1 ) ) )
| ( $false
= ( in @ ( setminus @ sK1 @ sK0 ) @ ( powerset @ sK1 ) ) )
| ~ spl3_2 ),
inference(subsumption_resolution,[status(thm)],[f157,f24]) ).
thf(f24,plain,
( ( subset @ sK2 @ ( setminus @ sK1 @ sK0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f157,plain,
( ( $false
= ( in @ ( setminus @ sK1 @ sK0 ) @ ( powerset @ sK1 ) ) )
| ( $false
= ( in @ sK2 @ ( powerset @ sK1 ) ) )
| ( ( subset @ sK2 @ ( setminus @ sK1 @ sK0 ) )
= $true )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f156]) ).
thf(f156,plain,
( ( ( subset @ sK2 @ ( setminus @ sK1 @ sK0 ) )
= $true )
| ( $false
= ( in @ ( setminus @ sK1 @ sK0 ) @ ( powerset @ sK1 ) ) )
| ( $false = $true )
| ( $false
= ( in @ sK2 @ ( powerset @ sK1 ) ) )
| ~ spl3_2 ),
inference(duplicate_literal_removal,[status(thm)],[f154]) ).
thf(f154,plain,
( ( $false
= ( in @ ( setminus @ sK1 @ sK0 ) @ ( powerset @ sK1 ) ) )
| ( $false
= ( in @ sK2 @ ( powerset @ sK1 ) ) )
| ( $false
= ( in @ ( setminus @ sK1 @ sK0 ) @ ( powerset @ sK1 ) ) )
| ( $false = $true )
| ( ( subset @ sK2 @ ( setminus @ sK1 @ sK0 ) )
= $true )
| ( $false
= ( in @ sK2 @ ( powerset @ sK1 ) ) )
| ~ spl3_2 ),
inference(superposition,[status(thm)],[f144,f50]) ).
thf(f50,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X1 )
= $true )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( ( subset @ X2 @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X1 )
=> ( ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X2 )
=> ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X3 ) ) )
= $false )
| ( ( subset @ X2 @ X3 )
= $true )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f47]) ).
thf(f47,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( subset @ X2 @ X3 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X3 ) ) )
@ ( sK4 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( subset @ X2 @ X3 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X3 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X3 ) ) ) )
=> ( subset @ X2 @ X3 ) )
= $true )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X3 ) ) ) )
=> ( subset @ X2 @ X3 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y1 @ X2 )
=> ( in @ Y1 @ Y0 ) ) ) )
=> ( subset @ X2 @ Y0 ) ) )
@ X3 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( 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 ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,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 ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i,X1: $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 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: $i] :
( ( !! @ $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 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,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 ),
inference(pi_clausification,[status(thm)],[f32]) ).
thf(f32,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,[status(thm)],[f29,f22]) ).
thf(f22,plain,
subsetTI = $true,
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f29,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,[status(thm)],[f14]) ).
thf(f14,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,[status(thm)],[f13]) ).
thf(f13,plain,
! [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 ) ) ) )
= subsetTI ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [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 ) ) ) )
= subsetTI ),
file('/export/starexec/sandbox/tmp/tmp.lj4biKboPJ/DTF2THF_27624.p',subsetTI) ).
thf(f144,plain,
( ! [X0: $i] :
( ( $false
= ( in @ ( sK4 @ ( setminus @ sK1 @ sK0 ) @ X0 @ sK2 ) @ sK1 ) )
| ( ( in @ sK2 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( setminus @ sK1 @ sK0 ) @ ( powerset @ X0 ) ) ) )
| ~ spl3_2 ),
inference(subsumption_resolution,[status(thm)],[f143,f24]) ).
thf(f143,plain,
( ! [X0: $i] :
( ( ( subset @ sK2 @ ( setminus @ sK1 @ sK0 ) )
= $true )
| ( $false
= ( in @ ( sK4 @ ( setminus @ sK1 @ sK0 ) @ X0 @ sK2 ) @ sK1 ) )
| ( $false
= ( in @ ( setminus @ sK1 @ sK0 ) @ ( powerset @ X0 ) ) )
| ( ( in @ sK2 @ ( powerset @ X0 ) )
= $false ) )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f142]) ).
thf(f142,plain,
( ! [X0: $i] :
( ( ( in @ sK2 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( setminus @ sK1 @ sK0 ) @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ ( sK4 @ ( setminus @ sK1 @ sK0 ) @ X0 @ sK2 ) @ sK1 ) )
| ( $false = $true )
| ( ( subset @ sK2 @ ( setminus @ sK1 @ sK0 ) )
= $true ) )
| ~ spl3_2 ),
inference(duplicate_literal_removal,[status(thm)],[f135]) ).
thf(f135,plain,
( ! [X0: $i] :
( ( $false
= ( in @ ( setminus @ sK1 @ sK0 ) @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ ( setminus @ sK1 @ sK0 ) @ ( powerset @ X0 ) ) )
| ( $false = $true )
| ( ( subset @ sK2 @ ( setminus @ sK1 @ sK0 ) )
= $true )
| ( ( in @ sK2 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ sK2 @ ( powerset @ X0 ) )
= $false )
| ( $false
= ( in @ ( sK4 @ ( setminus @ sK1 @ sK0 ) @ X0 @ sK2 ) @ sK1 ) )
| ( ( subset @ sK2 @ ( setminus @ sK1 @ sK0 ) )
= $true ) )
| ~ spl3_2 ),
inference(superposition,[status(thm)],[f52,f95]) ).
thf(f95,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK4 @ ( setminus @ sK1 @ sK0 ) @ X0 @ X1 ) @ sK2 ) )
| ( ( subset @ X1 @ ( setminus @ sK1 @ sK0 ) )
= $true )
| ( $false
= ( in @ ( setminus @ sK1 @ sK0 ) @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ ( sK4 @ ( setminus @ sK1 @ sK0 ) @ X0 @ X1 ) @ sK1 ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false ) )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f93]) ).
thf(f93,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK4 @ ( setminus @ sK1 @ sK0 ) @ X0 @ X1 ) @ sK1 ) )
| ( $false
= ( in @ ( sK4 @ ( setminus @ sK1 @ sK0 ) @ X0 @ X1 ) @ sK2 ) )
| ( $false = $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $false )
| ( ( subset @ X1 @ ( setminus @ sK1 @ sK0 ) )
= $true )
| ( $false
= ( in @ ( setminus @ sK1 @ sK0 ) @ ( powerset @ X0 ) ) ) )
| ~ spl3_2 ),
inference(superposition,[status(thm)],[f51,f85]) ).
thf(f85,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ ( setminus @ sK1 @ sK0 ) )
= $true )
| ( $false
= ( in @ X0 @ sK2 ) )
| ( $false
= ( in @ X0 @ sK1 ) ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f84]) ).
thf(f51,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( subset @ X2 @ X3 )
= $true )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( subset @ X2 @ X3 )
= $true )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X2 )
=> ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f52,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X2 )
= $true )
| ( ( subset @ X2 @ X3 )
= $true )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f91,plain,
( spl3_1
| spl3_3
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f77,f84,f87,f80]) ).
thf(f77,plain,
! [X0: $i] :
( ( ( in @ X0 @ ( setminus @ sK1 @ sK0 ) )
= $true )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( $false
= ( in @ sK2 @ ( powerset @ sK1 ) ) )
| ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $false )
| ( $false
= ( in @ X0 @ sK2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f74]) ).
thf(f74,plain,
! [X0: $i] :
( ( $false
= ( in @ X0 @ sK1 ) )
| ( ( in @ X0 @ ( setminus @ sK1 @ sK0 ) )
= $true )
| ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $false )
| ( $false = $true )
| ( $false
= ( in @ sK2 @ ( powerset @ sK1 ) ) )
| ( $false
= ( in @ X0 @ sK2 ) ) ),
inference(superposition,[status(thm)],[f65,f23]) ).
thf(f23,plain,
( ( subset @ sK0 @ ( setminus @ sK1 @ sK2 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f65,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( subset @ X2 @ ( setminus @ X1 @ X3 ) ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( ( in @ X4 @ ( setminus @ X1 @ X2 ) )
= $true )
| ( $false
= ( in @ X4 @ X1 ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( in @ X4 @ X3 )
=> ( in @ X4 @ ( setminus @ X1 @ X2 ) ) )
= $true )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( subset @ X2 @ ( setminus @ X1 @ X3 ) ) )
| ( $false
= ( in @ X4 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( subset @ X2 @ ( setminus @ X1 @ X3 ) ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ X3 )
=> ( in @ X4 @ ( setminus @ X1 @ X2 ) ) ) )
= $true )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f62]) ).
thf(f62,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( subset @ X2 @ ( setminus @ X1 @ X3 ) ) )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X3 )
=> ( in @ Y0 @ ( setminus @ X1 @ X2 ) ) ) )
@ X4 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X2 @ ( setminus @ X1 @ X3 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X3 )
=> ( in @ Y0 @ ( setminus @ X1 @ X2 ) ) ) ) )
= $true )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( ( ( subset @ X2 @ ( setminus @ X1 @ X3 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X3 )
=> ( in @ Y0 @ ( setminus @ X1 @ X2 ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( subset @ X2 @ ( setminus @ X1 @ X3 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X3 )
=> ( in @ Y0 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) )
= $true )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( ( subset @ X2 @ ( setminus @ X1 @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) )
@ X3 )
= $true )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(pi_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( ( subset @ X2 @ ( setminus @ X1 @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( ( subset @ X2 @ ( setminus @ X1 @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ X1 ) )
=> ( ( subset @ Y0 @ ( setminus @ X1 @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setminus @ X1 @ Y0 ) ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ X1 ) )
=> ( ( subset @ Y0 @ ( setminus @ X1 @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( setminus @ X1 @ Y0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f53]) ).
thf(f53,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( subset @ Y1 @ ( setminus @ Y0 @ Y2 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ ( setminus @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( subset @ Y1 @ ( setminus @ Y0 @ Y2 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ ( setminus @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f21,f20]) ).
thf(f20,plain,
( contraSubsetComplement
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( subset @ Y1 @ ( setminus @ Y0 @ Y2 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ ( setminus @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( contraSubsetComplement
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( subset @ Y1 @ ( setminus @ Y0 @ Y2 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ ( setminus @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( contraSubsetComplement
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( subset @ X0 @ ( setminus @ X1 @ X2 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ ( setminus @ X1 @ X0 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( contraSubsetComplement
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lj4biKboPJ/DTF2THF_27624.p',contraSubsetComplement) ).
thf(f21,plain,
contraSubsetComplement = $true,
inference(cnf_transformation,[status(thm)],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU737^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n011.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:32:17 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.47 ---- Original DTF file ---
% 0.19/0.47 thf(spec,logic,$$dhol).
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % File : SEU737^2 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.47 % Domain : Set Theory
% 0.19/0.47 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.19/0.47 % Version : Especial > Reduced > Especial.
% 0.19/0.47 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.19/0.47 % subset X (setminus A Y) -> subset Y (setminus A X)))
% 0.19/0.47
% 0.19/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.47 % Source : [Bro08]
% 0.19/0.47 % Names : ZFC239l [Bro08]
% 0.19/0.47 % : ZFC268l [Bro08]
% 0.19/0.47
% 0.19/0.47 % Status : Theorem
% 0.19/0.47 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.19/0.47 % Syntax : Number of formulae : 11 ( 3 unt; 7 typ; 3 def)
% 0.19/0.47 % Number of atoms : 27 ( 3 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 7 ( 6 avg)
% 0.19/0.47 % Number of connectives : 71 ( 0 ~; 0 |; 0 &; 54 @)
% 0.19/0.47 % ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 13 ( 4 avg)
% 0.19/0.47 % Number of types : 2 ( 0 usr)
% 0.19/0.47 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.19/0.47 % Number of symbols : 8 ( 7 usr; 3 con; 0-2 aty)
% 0.19/0.47 % Number of variables : 13 ( 0 ^; 13 !; 0 ?; 13 :)
% 0.19/0.47 % SPC : TH0_THM_EQU_NAR
% 0.19/0.47
% 0.19/0.47 % Comments : http://mathgate.info/detsetitem.php?id=299
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 thf(in_type,type,
% 0.19/0.47 in: $i > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(powerset_type,type,
% 0.19/0.47 powerset: $i > $i ).
% 0.19/0.47
% 0.19/0.47 thf(subset_type,type,
% 0.19/0.47 subset: $i > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(setminus_type,type,
% 0.19/0.47 setminus: $i > $i > $i ).
% 0.19/0.47
% 0.19/0.47 thf(complementT_lem_type,type,
% 0.19/0.47 complementT_lem: $o ).
% 0.19/0.47
% 0.19/0.47 thf(complementT_lem,definition,
% 0.19/0.47 ( complementT_lem
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(subsetTI_type,type,
% 0.19/0.47 subsetTI: $o ).
% 0.19/0.47
% 0.19/0.47 thf(subsetTI,definition,
% 0.19/0.47 ( subsetTI
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Y: $i] :
% 0.19/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.47 => ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( in @ Xx @ X )
% 0.19/0.47 => ( in @ Xx @ Y ) ) )
% 0.19/0.47 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(contraSubsetComplement_type,type,
% 0.19/0.47 contraSubsetComplement: $o ).
% 0.19/0.47
% 0.19/0.47 thf(contraSubsetComplement,definition,
% 0.19/0.47 ( contraSubsetComplement
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Y: $i] :
% 0.19/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.47 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( in @ Xx @ Y )
% 0.19/0.47 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(complementTcontraSubset,conjecture,
% 0.19/0.47 ( complementT_lem
% 0.19/0.47 => ( subsetTI
% 0.19/0.47 => ( contraSubsetComplement
% 0.19/0.47 => ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Y: $i] :
% 0.19/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.47 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.19/0.47 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 ------------------------
% 1.50/1.30 ---- Embedded in THF ---
% 1.71/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.71/1.30 %%% Generated on Tue Feb 24 12:32:18 EST 2026
% 1.71/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 1.71/1.30 %%% Logic specification used:
% 1.71/1.30 %%% thf(spec, logic, $$dhol).
% 1.71/1.30
% 1.71/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.lj4biKboPJ/DTF2DTF27624.p
% See solution above
% 1.71/1.30 ------------------------
% 1.71/1.31 ---- Cleaned THF ---
% 1.71/1.31 thf(in_type,type,
% 1.71/1.31 in: $i > $i > $o ).
% 1.71/1.31
% 1.71/1.31 thf(powerset_type,type,
% 1.71/1.31 powerset: $i > $i ).
% 1.71/1.31
% 1.71/1.31 thf(subset_type,type,
% 1.71/1.31 subset: $i > $i > $o ).
% 1.71/1.31
% 1.71/1.31 thf(setminus_type,type,
% 1.71/1.31 setminus: $i > $i > $i ).
% 1.71/1.31
% 1.71/1.31 thf(complementT_lem_type,type,
% 1.71/1.31 complementT_lem: $o ).
% 1.71/1.31
% 1.71/1.31 thf(complementT_lem,definition,
% 1.71/1.31 ( complementT_lem
% 1.71/1.31 = ( ! [A: $i,X: $i] :
% 1.71/1.31 ( ( in @ X @ ( powerset @ A ) )
% 1.71/1.31 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 1.71/1.31
% 1.71/1.31 thf(subsetTI_type,type,
% 1.71/1.31 subsetTI: $o ).
% 1.71/1.31
% 1.71/1.31 thf(subsetTI,definition,
% 1.71/1.31 ( subsetTI
% 1.71/1.31 = ( ! [A: $i,X: $i] :
% 1.71/1.31 ( ( in @ X @ ( powerset @ A ) )
% 1.71/1.31 => ! [Y: $i] :
% 1.71/1.31 ( ( in @ Y @ ( powerset @ A ) )
% 1.71/1.31 => ( ! [Xx: $i] :
% 1.71/1.31 ( ( in @ Xx @ A )
% 1.71/1.31 => ( ( in @ Xx @ X )
% 1.71/1.31 => ( in @ Xx @ Y ) ) )
% 1.71/1.31 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 1.71/1.31
% 1.71/1.31 thf(contraSubsetComplement_type,type,
% 1.71/1.31 contraSubsetComplement: $o ).
% 1.71/1.31
% 1.71/1.31 thf(contraSubsetComplement,definition,
% 1.71/1.31 ( contraSubsetComplement
% 1.71/1.31 = ( ! [A: $i,X: $i] :
% 1.71/1.31 ( ( in @ X @ ( powerset @ A ) )
% 1.71/1.31 => ! [Y: $i] :
% 1.71/1.31 ( ( in @ Y @ ( powerset @ A ) )
% 1.71/1.31 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 1.71/1.31 => ! [Xx: $i] :
% 1.71/1.31 ( ( in @ Xx @ A )
% 1.71/1.31 => ( ( in @ Xx @ Y )
% 1.71/1.31 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 1.71/1.31
% 1.71/1.31 thf(complementTcontraSubset,conjecture,
% 1.71/1.31 ( complementT_lem
% 1.71/1.31 => ( subsetTI
% 1.71/1.31 => ( contraSubsetComplement
% 1.71/1.31 => ! [A: $i,X: $i] :
% 1.71/1.31 ( ( in @ X @ ( powerset @ A ) )
% 1.71/1.31 => ! [Y: $i] :
% 1.71/1.31 ( ( in @ Y @ ( powerset @ A ) )
% 1.71/1.31 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 1.71/1.31 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 1.71/1.31 ------------------------
% 1.71/1.33 % (27958)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_27624 for (2999ds/2Mi)
% 1.71/1.33 % (27958)Instruction limit reached!
% 1.71/1.33 % (27958)------------------------------
% 1.71/1.33 % (27958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.33 % (27958)Termination reason: Unknown
% 1.71/1.33 % (27958)Termination phase: Function definition elimination
% 1.71/1.33
% 1.71/1.33 % (27958)Memory used [KB]: 1023
% 1.71/1.33 % (27958)Time elapsed: 0.002 s
% 1.71/1.33 % (27958)Instructions burned: 3 (million)
% 1.71/1.33 % (27958)------------------------------
% 1.71/1.33 % (27958)------------------------------
% 1.71/1.33 % (27957)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27624 for (2999ds/2Mi)
% 1.71/1.34 % (27957)Instruction limit reached!
% 1.71/1.34 % (27957)------------------------------
% 1.71/1.34 % (27957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.34 % (27957)Termination reason: Unknown
% 1.71/1.34 % (27957)Termination phase: Property scanning
% 1.71/1.34
% 1.71/1.34 % (27957)Memory used [KB]: 895
% 1.71/1.34 % (27957)Time elapsed: 0.003 s
% 1.71/1.34 % (27957)Instructions burned: 2 (million)
% 1.71/1.34 % (27957)------------------------------
% 1.71/1.34 % (27957)------------------------------
% 1.71/1.34 % (27954)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27624 for (2999ds/183Mi)
% 1.71/1.34 % (27955)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_27624 for (2999ds/4Mi)
% 1.71/1.34 % (27956)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_27624 for (2999ds/27Mi)
% 1.71/1.34 % (27960)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27624 for (2999ds/18Mi)
% 1.71/1.34 % (27959)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_27624 for (2999ds/275Mi)
% 1.71/1.34 % (27955)Instruction limit reached!
% 1.71/1.34 % (27955)------------------------------
% 1.71/1.34 % (27955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.34 % (27955)Termination reason: Unknown
% 1.71/1.34 % (27955)Termination phase: Property scanning
% 1.71/1.34
% 1.71/1.34 % (27955)Memory used [KB]: 1023
% 1.71/1.34 % (27955)Time elapsed: 0.004 s
% 1.71/1.34 % (27955)Instructions burned: 4 (million)
% 1.71/1.34 % (27955)------------------------------
% 1.71/1.34 % (27955)------------------------------
% 1.71/1.34 % (27961)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27624 for (2999ds/3Mi)
% 1.71/1.34 % (27961)Instruction limit reached!
% 1.71/1.34 % (27961)------------------------------
% 1.71/1.34 % (27961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.34 % (27961)Termination reason: Unknown
% 1.71/1.34 % (27961)Termination phase: Saturation
% 1.71/1.34
% 1.71/1.34 % (27961)Memory used [KB]: 5500
% 1.71/1.34 % (27961)Time elapsed: 0.003 s
% 1.71/1.34 % (27961)Instructions burned: 4 (million)
% 1.71/1.34 % (27961)------------------------------
% 1.71/1.34 % (27961)------------------------------
% 1.71/1.35 % (27960)Instruction limit reached!
% 1.71/1.35 % (27960)------------------------------
% 1.71/1.35 % (27960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.35 % (27960)Termination reason: Unknown
% 1.71/1.35 % (27960)Termination phase: Saturation
% 1.71/1.35
% 1.71/1.35 % (27960)Memory used [KB]: 5628
% 1.71/1.35 % (27960)Time elapsed: 0.013 s
% 1.71/1.35 % (27960)Instructions burned: 18 (million)
% 1.71/1.35 % (27960)------------------------------
% 1.71/1.35 % (27960)------------------------------
% 1.71/1.35 % (27956)Instruction limit reached!
% 1.71/1.35 % (27956)------------------------------
% 1.71/1.35 % (27956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.35 % (27956)Termination reason: Unknown
% 1.71/1.35 % (27956)Termination phase: Saturation
% 1.71/1.35
% 1.71/1.35 % (27956)Memory used [KB]: 5628
% 1.71/1.35 % (27956)Time elapsed: 0.019 s
% 1.71/1.35 % (27956)Instructions burned: 28 (million)
% 1.71/1.35 % (27956)------------------------------
% 1.71/1.35 % (27956)------------------------------
% 1.71/1.35 % (27962)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_27624 for (2999ds/37Mi)
% 1.71/1.35 % (27964)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27624 for (2999ds/3Mi)
% 1.71/1.35 % (27954)First to succeed.
% 1.71/1.35 % (27964)Instruction limit reached!
% 1.71/1.35 % (27964)------------------------------
% 1.71/1.35 % (27964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.35 % (27964)Termination reason: Unknown
% 1.71/1.35 % (27964)Termination phase: Saturation
% 1.71/1.35
% 1.71/1.35 % (27964)Memory used [KB]: 5500
% 1.71/1.35 % (27964)Time elapsed: 0.003 s
% 1.71/1.35 % (27964)Instructions burned: 4 (million)
% 1.71/1.35 % (27964)------------------------------
% 1.71/1.35 % (27964)------------------------------
% 1.71/1.36 % (27963)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_27624 for (2999ds/15Mi)
% 1.71/1.36 % (27954)Refutation found. Thanks to Tanya!
% 1.71/1.36 % SZS status Theorem for DTF2THF_27624
% 1.71/1.36 % SZS output start Proof for DTF2THF_27624
% 1.71/1.36 thf(func_def_0, type, in: $i > $i > $o).
% 1.71/1.36 thf(func_def_1, type, powerset: $i > $i).
% 1.71/1.36 thf(func_def_2, type, subset: $i > $i > $o).
% 1.71/1.36 thf(func_def_3, type, setminus: $i > $i > $i).
% 1.71/1.36 thf(func_def_21, type, sK4: $i > $i > $i > $i).
% 1.71/1.36 thf(f189,plain,(
% 1.71/1.36 $false),
% 1.71/1.36 inference(avatar_sat_refutation,[status(thm)],[f91,f167,f173,f182,f188])).
% 1.71/1.36 thf(f188,plain,(
% 1.71/1.36 ~spl3_3),
% 1.71/1.36 inference(avatar_contradiction_clause,[status(thm)],[f187])).
% 1.71/1.36 thf(f187,plain,(
% 1.71/1.36 $false | ~spl3_3),
% 1.71/1.36 inference(trivial_inequality_removal,[status(thm)],[f183])).
% 1.71/1.36 thf(f183,plain,(
% 1.71/1.36 ($false = $true) | ~spl3_3),
% 1.71/1.36 inference(superposition,[status(thm)],[f89,f26])).
% 1.71/1.36 thf(f26,plain,(
% 1.71/1.36 ((in @ sK0 @ (powerset @ sK1)) = $true)),
% 1.71/1.36 inference(cnf_transformation,[status(thm)],[f19])).
% 1.71/1.36 thf(f19,plain,(
% 1.71/1.36 (complementT_lem = $true) & (((in @ sK0 @ (powerset @ sK1)) = $true) & (((in @ sK2 @ (powerset @ sK1)) = $true) & ((subset @ sK2 @ (setminus @ sK1 @ sK0)) != $true) & ((subset @ sK0 @ (setminus @ sK1 @ sK2)) = $true))) & (subsetTI = $true) & (contraSubsetComplement = $true)),
% 1.71/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f16,f18,f17])).
% 1.71/1.36 thf(f17,plain,(
% 1.71/1.36 ? [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ((subset @ X2 @ (setminus @ X1 @ X0)) != $true) & ((subset @ X0 @ (setminus @ X1 @ X2)) = $true))) => (((in @ sK0 @ (powerset @ sK1)) = $true) & ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK1))) & ((subset @ X2 @ (setminus @ sK1 @ sK0)) != $true) & ((subset @ sK0 @ (setminus @ sK1 @ X2)) = $true)))),
% 1.71/1.36 introduced(definition,[],[choice_axiom])).
% 1.71/1.36 thf(f18,plain,(
% 1.71/1.36 ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK1))) & ((subset @ X2 @ (setminus @ sK1 @ sK0)) != $true) & ((subset @ sK0 @ (setminus @ sK1 @ X2)) = $true)) => (((in @ sK2 @ (powerset @ sK1)) = $true) & ((subset @ sK2 @ (setminus @ sK1 @ sK0)) != $true) & ((subset @ sK0 @ (setminus @ sK1 @ sK2)) = $true))),
% 1.71/1.36 introduced(definition,[],[choice_axiom])).
% 1.71/1.36 thf(f16,plain,(
% 1.71/1.36 (complementT_lem = $true) & ? [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ((subset @ X2 @ (setminus @ X1 @ X0)) != $true) & ((subset @ X0 @ (setminus @ X1 @ X2)) = $true))) & (subsetTI = $true) & (contraSubsetComplement = $true)),
% 1.71/1.36 inference(flattening,[status(thm)],[f15])).
% 1.71/1.36 thf(f15,plain,(
% 1.71/1.36 ((? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((subset @ X2 @ (setminus @ X1 @ X0)) != $true) & ((subset @ X0 @ (setminus @ X1 @ X2)) = $true)) & ((in @ X2 @ (powerset @ X1)) = $true)) & ((in @ X0 @ (powerset @ X1)) = $true)) & (contraSubsetComplement = $true)) & (subsetTI = $true)) & (complementT_lem = $true)),
% 1.71/1.36 inference(ennf_transformation,[status(thm)],[f12])).
% 1.71/1.36 thf(f12,plain,(
% 1.71/1.36 ~((complementT_lem = $true) => ((subsetTI = $true) => ((contraSubsetComplement = $true) => ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => (((subset @ X0 @ (setminus @ X1 @ X2)) = $true) => ((subset @ X2 @ (setminus @ X1 @ X0)) = $true)))))))),
% 1.71/1.36 inference(fool_elimination,[status(thm)],[f11])).
% 1.71/1.36 thf(f11,plain,(
% 1.71/1.36 ~(complementT_lem => (subsetTI => (contraSubsetComplement => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ((subset @ X0 @ (setminus @ X1 @ X2)) => (subset @ X2 @ (setminus @ X1 @ X0))))))))),
% 1.71/1.36 inference(rectify,[status(thm)],[f5])).
% 1.71/1.36 thf(f5,negated_conjecture,(
% 1.71/1.36 ~(complementT_lem => (subsetTI => (contraSubsetComplement => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((subset @ X1 @ (setminus @ X0 @ X2)) => (subset @ X2 @ (setminus @ X0 @ X1))))))))),
% 1.71/1.36 inference(negated_conjecture,[status(cth)],[f4])).
% 1.71/1.36 thf(f4,conjecture,(
% 1.71/1.36 complementT_lem => (subsetTI => (contraSubsetComplement => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((subset @ X1 @ (setminus @ X0 @ X2)) => (subset @ X2 @ (setminus @ X0 @ X1)))))))),
% 1.71/1.36 file('/export/starexec/sandbox/tmp/tmp.lj4biKboPJ/DTF2THF_27624.p',complementTcontraSubset)).
% 1.71/1.36 thf(f89,plain,(
% 1.71/1.36 ((in @ sK0 @ (powerset @ sK1)) = $false) | ~spl3_3),
% 1.71/1.36 inference(avatar_component_clause,[status(thm)],[f87])).
% 1.71/1.36 thf(f87,definition,(
% 1.71/1.36 spl3_3 <=> ((in @ sK0 @ (powerset @ sK1)) = $false)),
% 1.71/1.36 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.71/1.36 thf(f182,plain,(
% 1.71/1.36 spl3_3 | ~spl3_6),
% 1.71/1.36 inference(avatar_split_clause,[status(thm)],[f179,f162,f87])).
% 1.71/1.36 thf(f162,definition,(
% 1.71/1.36 spl3_6 <=> ($false = (in @ (setminus @ sK1 @ sK0) @ (powerset @ sK1)))),
% 1.71/1.36 introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition])).
% 1.71/1.36 thf(f179,plain,(
% 1.71/1.36 ((in @ sK0 @ (powerset @ sK1)) = $false) | ~spl3_6),
% 1.71/1.36 inference(trivial_inequality_removal,[status(thm)],[f177])).
% 1.71/1.36 thf(f177,plain,(
% 1.71/1.36 ((in @ sK0 @ (powerset @ sK1)) = $false) | ($false = $true) | ~spl3_6),
% 1.71/1.36 inference(superposition,[status(thm)],[f164,f37])).
% 1.71/1.36 thf(f37,plain,(
% 1.71/1.36 ( ! [X2 : $i,X1 : $i] : (((in @ (setminus @ X1 @ X2) @ (powerset @ X1)) = $true) | ($false = (in @ X2 @ (powerset @ X1)))) )),
% 1.71/1.36 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.71/1.36 thf(f36,plain,(
% 1.71/1.36 ( ! [X2 : $i,X1 : $i] : ((((in @ X2 @ (powerset @ X1)) => (in @ (setminus @ X1 @ X2) @ (powerset @ X1))) = $true)) )),
% 1.71/1.36 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.71/1.36 thf(f35,plain,(
% 1.71/1.36 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (in @ (setminus @ X1 @ Y0) @ (powerset @ X1)))) @ X2) = $true)) )),
% 1.71/1.36 inference(pi_clausification,[status(thm)],[f34])).
% 1.71/1.36 thf(f34,plain,(
% 1.71/1.36 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (in @ (setminus @ X1 @ Y0) @ (powerset @ X1))))) = $true)) )),
% 1.71/1.36 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.71/1.36 thf(f33,plain,(
% 1.71/1.36 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ Y1) @ (powerset @ Y0)))))) @ X1) = $true)) )),
% 1.71/1.36 inference(pi_clausification,[status(thm)],[f31])).
% 1.71/1.36 thf(f31,plain,(
% 1.71/1.36 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ Y1) @ (powerset @ Y0))))))) = $true)),
% 1.71/1.36 inference(definition_unfolding,[status(thm)],[f28,f27])).
% 1.71/1.36 thf(f27,plain,(
% 1.71/1.36 (complementT_lem = $true)),
% 1.71/1.36 inference(cnf_transformation,[status(thm)],[f19])).
% 1.71/1.36 thf(f28,plain,(
% 1.71/1.36 (complementT_lem = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ Y1) @ (powerset @ Y0))))))))),
% 1.71/1.36 inference(cnf_transformation,[status(thm)],[f8])).
% 1.71/1.36 thf(f8,plain,(
% 1.71/1.36 (complementT_lem = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ Y1) @ (powerset @ Y0))))))))),
% 1.71/1.36 inference(fool_elimination,[status(thm)],[f7])).
% 1.71/1.36 thf(f7,plain,(
% 1.71/1.36 (complementT_lem = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (in @ (setminus @ X1 @ X0) @ (powerset @ X1))))),
% 1.71/1.36 inference(rectify,[status(thm)],[f1])).
% 1.71/1.36 thf(f1,axiom,(
% 1.71/1.36 (complementT_lem = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))))),
% 1.71/1.36 file('/export/starexec/sandbox/tmp/tmp.lj4biKboPJ/DTF2THF_27624.p',complementT_lem)).
% 1.71/1.36 thf(f164,plain,(
% 1.71/1.36 ($false = (in @ (setminus @ sK1 @ sK0) @ (powerset @ sK1))) | ~spl3_6),
% 1.71/1.36 inference(avatar_component_clause,[status(thm)],[f162])).
% 1.71/1.36 thf(f173,plain,(
% 1.71/1.36 ~spl3_1),
% 1.71/1.36 inference(avatar_contradiction_clause,[status(thm)],[f172])).
% 1.71/1.36 thf(f172,plain,(
% 1.71/1.36 $false | ~spl3_1),
% 1.71/1.36 inference(trivial_inequality_removal,[status(thm)],[f168])).
% 1.71/1.36 thf(f168,plain,(
% 1.71/1.36 ($false = $true) | ~spl3_1),
% 1.71/1.36 inference(superposition,[status(thm)],[f82,f25])).
% 1.71/1.36 thf(f25,plain,(
% 1.71/1.36 ((in @ sK2 @ (powerset @ sK1)) = $true)),
% 1.71/1.36 inference(cnf_transformation,[status(thm)],[f19])).
% 1.71/1.36 thf(f82,plain,(
% 1.71/1.36 ($false = (in @ sK2 @ (powerset @ sK1))) | ~spl3_1),
% 1.71/1.36 inference(avatar_component_clause,[status(thm)],[f80])).
% 1.71/1.36 thf(f80,definition,(
% 1.71/1.36 spl3_1 <=> ($false = (in @ sK2 @ (powerset @ sK1)))),
% 1.71/1.36 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.71/1.36 thf(f167,plain,(
% 1.71/1.36 spl3_1 | spl3_6 | ~spl3_2),
% 1.71/1.36 inference(avatar_split_clause,[status(thm)],[f166,f84,f162,f80])).
% 1.71/1.36 thf(f84,definition,(
% 1.71/1.36 spl3_2 <=> ! [X0 : $i] : (($false = (in @ X0 @ sK1)) | ($false = (in @ X0 @ sK2)) | ((in @ X0 @ (setminus @ sK1 @ sK0)) = $true))),
% 1.71/1.36 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.71/1.36 thf(f166,plain,(
% 1.71/1.36 ($false = (in @ sK2 @ (powerset @ sK1))) | ($false = (in @ (setminus @ sK1 @ sK0) @ (powerset @ sK1))) | ~spl3_2),
% 1.71/1.36 inference(subsumption_resolution,[status(thm)],[f157,f24])).
% 1.71/1.36 thf(f24,plain,(
% 1.71/1.36 ((subset @ sK2 @ (setminus @ sK1 @ sK0)) != $true)),
% 1.71/1.36 inference(cnf_transformation,[status(thm)],[f19])).
% 1.71/1.36 thf(f157,plain,(
% 1.71/1.36 ($false = (in @ (setminus @ sK1 @ sK0) @ (powerset @ sK1))) | ($false = (in @ sK2 @ (powerset @ sK1))) | ((subset @ sK2 @ (setminus @ sK1 @ sK0)) = $true) | ~spl3_2),
% 1.71/1.36 inference(trivial_inequality_removal,[status(thm)],[f156])).
% 1.71/1.36 thf(f156,plain,(
% 1.71/1.36 ((subset @ sK2 @ (setminus @ sK1 @ sK0)) = $true) | ($false = (in @ (setminus @ sK1 @ sK0) @ (powerset @ sK1))) | ($false = $true) | ($false = (in @ sK2 @ (powerset @ sK1))) | ~spl3_2),
% 1.71/1.36 inference(duplicate_literal_removal,[status(thm)],[f154])).
% 1.71/1.36 thf(f154,plain,(
% 1.71/1.36 ($false = (in @ (setminus @ sK1 @ sK0) @ (powerset @ sK1))) | ($false = (in @ sK2 @ (powerset @ sK1))) | ($false = (in @ (setminus @ sK1 @ sK0) @ (powerset @ sK1))) | ($false = $true) | ((subset @ sK2 @ (setminus @ sK1 @ sK0)) = $true) | ($false = (in @ sK2 @ (powerset @ sK1))) | ~spl3_2),
% 1.71/1.36 inference(superposition,[status(thm)],[f144,f50])).
% 1.71/1.36 thf(f50,plain,(
% 1.71/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ (sK4 @ X3 @ X1 @ X2) @ X1) = $true) | ($false = (in @ X2 @ (powerset @ X1))) | ($false = (in @ X3 @ (powerset @ X1))) | ((subset @ X2 @ X3) = $true)) )),
% 1.71/1.36 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.71/1.36 thf(f48,plain,(
% 1.71/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X2 @ (powerset @ X1))) | (((in @ (sK4 @ X3 @ X1 @ X2) @ X1) => ((in @ (sK4 @ X3 @ X1 @ X2) @ X2) => (in @ (sK4 @ X3 @ X1 @ X2) @ X3))) = $false) | ((subset @ X2 @ X3) = $true) | ($false = (in @ X3 @ (powerset @ X1)))) )),
% 1.71/1.36 inference(beta_eta_normalization,[status(thm)],[f47])).
% 1.71/1.36 thf(f47,plain,(
% 1.71/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X2 @ (powerset @ X1))) | ((subset @ X2 @ X3) = $true) | ($false = ((^[Y0 : $i]: ((in @ Y0 @ X1) => ((in @ Y0 @ X2) => (in @ Y0 @ X3)))) @ (sK4 @ X3 @ X1 @ X2))) | ($false = (in @ X3 @ (powerset @ X1)))) )),
% 1.71/1.36 inference(sigma_clausification,[status(thm)],[f46])).
% 1.71/1.36 thf(f46,plain,(
% 1.71/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X3 @ (powerset @ X1))) | ($false = (in @ X2 @ (powerset @ X1))) | ((subset @ X2 @ X3) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((in @ Y0 @ X2) => (in @ Y0 @ X3))))))) )),
% 1.71/1.36 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.71/1.36 thf(f45,plain,(
% 1.71/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X2 @ (powerset @ X1))) | (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((in @ Y0 @ X2) => (in @ Y0 @ X3))))) => (subset @ X2 @ X3)) = $true) | ($false = (in @ X3 @ (powerset @ X1)))) )),
% 1.71/1.36 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.71/1.36 thf(f44,plain,(
% 1.71/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X2 @ (powerset @ X1))) | (((in @ X3 @ (powerset @ X1)) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((in @ Y0 @ X2) => (in @ Y0 @ X3))))) => (subset @ X2 @ X3))) = $true)) )),
% 1.71/1.36 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.71/1.36 thf(f43,plain,(
% 1.71/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X2 @ (powerset @ X1))) | (((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((in @ Y1 @ X2) => (in @ Y1 @ Y0))))) => (subset @ X2 @ Y0)))) @ X3) = $true)) )),
% 1.71/1.36 inference(pi_clausification,[status(thm)],[f42])).
% 1.71/1.36 thf(f42,plain,(
% 1.71/1.36 ( ! [X2 : $i,X1 : $i] : (($false = (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)) )),
% 1.71/1.36 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.71/1.36 thf(f41,plain,(
% 1.71/1.36 ( ! [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)) )),
% 1.71/1.36 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.71/1.36 thf(f40,plain,(
% 1.71/1.36 ( ! [X2 : $i,X1 : $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))))))) @ X2) = $true)) )),
% 1.71/1.36 inference(pi_clausification,[status(thm)],[f39])).
% 1.71/1.36 thf(f39,plain,(
% 1.71/1.36 ( ! [X1 : $i] : (((!! @ $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)))))))) = $true)) )),
% 1.71/1.36 inference(beta_eta_normalization,[status(thm)],[f38])).
% 1.71/1.36 thf(f38,plain,(
% 1.71/1.36 ( ! [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)) )),
% 1.71/1.36 inference(pi_clausification,[status(thm)],[f32])).
% 1.71/1.36 thf(f32,plain,(
% 1.71/1.36 ((!! @ $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)),
% 1.71/1.36 inference(definition_unfolding,[status(thm)],[f29,f22])).
% 1.71/1.36 thf(f22,plain,(
% 1.71/1.36 (subsetTI = $true)),
% 1.71/1.36 inference(cnf_transformation,[status(thm)],[f19])).
% 1.71/1.36 thf(f29,plain,(
% 1.71/1.36 (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)))))))))))),
% 1.71/1.36 inference(cnf_transformation,[status(thm)],[f14])).
% 1.71/1.36 thf(f14,plain,(
% 1.71/1.36 (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)))))))))))),
% 1.71/1.36 inference(fool_elimination,[status(thm)],[f13])).
% 1.71/1.36 thf(f13,plain,(
% 1.71/1.36 (! [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)))) = subsetTI)),
% 1.71/1.36 inference(rectify,[status(thm)],[f2])).
% 1.71/1.36 thf(f2,axiom,(
% 1.71/1.36 (! [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)))) = subsetTI)),
% 1.71/1.36 file('/export/starexec/sandbox/tmp/tmp.lj4biKboPJ/DTF2THF_27624.p',subsetTI)).
% 1.71/1.36 thf(f144,plain,(
% 1.71/1.36 ( ! [X0 : $i] : (($false = (in @ (sK4 @ (setminus @ sK1 @ sK0) @ X0 @ sK2) @ sK1)) | ((in @ sK2 @ (powerset @ X0)) = $false) | ($false = (in @ (setminus @ sK1 @ sK0) @ (powerset @ X0)))) ) | ~spl3_2),
% 1.71/1.36 inference(subsumption_resolution,[status(thm)],[f143,f24])).
% 1.71/1.36 thf(f143,plain,(
% 1.71/1.36 ( ! [X0 : $i] : (((subset @ sK2 @ (setminus @ sK1 @ sK0)) = $true) | ($false = (in @ (sK4 @ (setminus @ sK1 @ sK0) @ X0 @ sK2) @ sK1)) | ($false = (in @ (setminus @ sK1 @ sK0) @ (powerset @ X0))) | ((in @ sK2 @ (powerset @ X0)) = $false)) ) | ~spl3_2),
% 1.71/1.36 inference(trivial_inequality_removal,[status(thm)],[f142])).
% 1.71/1.36 thf(f142,plain,(
% 1.71/1.36 ( ! [X0 : $i] : (((in @ sK2 @ (powerset @ X0)) = $false) | ($false = (in @ (setminus @ sK1 @ sK0) @ (powerset @ X0))) | ($false = (in @ (sK4 @ (setminus @ sK1 @ sK0) @ X0 @ sK2) @ sK1)) | ($false = $true) | ((subset @ sK2 @ (setminus @ sK1 @ sK0)) = $true)) ) | ~spl3_2),
% 1.71/1.36 inference(duplicate_literal_removal,[status(thm)],[f135])).
% 1.71/1.36 thf(f135,plain,(
% 1.71/1.36 ( ! [X0 : $i] : (($false = (in @ (setminus @ sK1 @ sK0) @ (powerset @ X0))) | ($false = (in @ (setminus @ sK1 @ sK0) @ (powerset @ X0))) | ($false = $true) | ((subset @ sK2 @ (setminus @ sK1 @ sK0)) = $true) | ((in @ sK2 @ (powerset @ X0)) = $false) | ((in @ sK2 @ (powerset @ X0)) = $false) | ($false = (in @ (sK4 @ (setminus @ sK1 @ sK0) @ X0 @ sK2) @ sK1)) | ((subset @ sK2 @ (setminus @ sK1 @ sK0)) = $true)) ) | ~spl3_2),
% 1.71/1.36 inference(superposition,[status(thm)],[f52,f95])).
% 1.71/1.36 thf(f95,plain,(
% 1.71/1.36 ( ! [X0 : $i,X1 : $i] : (($false = (in @ (sK4 @ (setminus @ sK1 @ sK0) @ X0 @ X1) @ sK2)) | ((subset @ X1 @ (setminus @ sK1 @ sK0)) = $true) | ($false = (in @ (setminus @ sK1 @ sK0) @ (powerset @ X0))) | ($false = (in @ (sK4 @ (setminus @ sK1 @ sK0) @ X0 @ X1) @ sK1)) | ((in @ X1 @ (powerset @ X0)) = $false)) ) | ~spl3_2),
% 1.71/1.36 inference(trivial_inequality_removal,[status(thm)],[f93])).
% 1.71/1.36 thf(f93,plain,(
% 1.71/1.36 ( ! [X0 : $i,X1 : $i] : (($false = (in @ (sK4 @ (setminus @ sK1 @ sK0) @ X0 @ X1) @ sK1)) | ($false = (in @ (sK4 @ (setminus @ sK1 @ sK0) @ X0 @ X1) @ sK2)) | ($false = $true) | ((in @ X1 @ (powerset @ X0)) = $false) | ((subset @ X1 @ (setminus @ sK1 @ sK0)) = $true) | ($false = (in @ (setminus @ sK1 @ sK0) @ (powerset @ X0)))) ) | ~spl3_2),
% 1.71/1.36 inference(superposition,[status(thm)],[f51,f85])).
% 1.71/1.36 thf(f85,plain,(
% 1.71/1.36 ( ! [X0 : $i] : (((in @ X0 @ (setminus @ sK1 @ sK0)) = $true) | ($false = (in @ X0 @ sK2)) | ($false = (in @ X0 @ sK1))) ) | ~spl3_2),
% 1.71/1.36 inference(avatar_component_clause,[status(thm)],[f84])).
% 1.71/1.36 thf(f51,plain,(
% 1.71/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ (sK4 @ X3 @ X1 @ X2) @ X3)) | ($false = (in @ X2 @ (powerset @ X1))) | ((subset @ X2 @ X3) = $true) | ($false = (in @ X3 @ (powerset @ X1)))) )),
% 1.71/1.36 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.71/1.36 thf(f49,plain,(
% 1.71/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((subset @ X2 @ X3) = $true) | ($false = (in @ X2 @ (powerset @ X1))) | ($false = (in @ X3 @ (powerset @ X1))) | ($false = ((in @ (sK4 @ X3 @ X1 @ X2) @ X2) => (in @ (sK4 @ X3 @ X1 @ X2) @ X3)))) )),
% 1.71/1.36 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.71/1.36 thf(f52,plain,(
% 1.71/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ (sK4 @ X3 @ X1 @ X2) @ X2) = $true) | ((subset @ X2 @ X3) = $true) | ($false = (in @ X2 @ (powerset @ X1))) | ($false = (in @ X3 @ (powerset @ X1)))) )),
% 1.71/1.36 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.71/1.36 thf(f91,plain,(
% 1.71/1.36 spl3_1 | spl3_3 | spl3_2),
% 1.71/1.36 inference(avatar_split_clause,[status(thm)],[f77,f84,f87,f80])).
% 1.71/1.36 thf(f77,plain,(
% 1.71/1.36 ( ! [X0 : $i] : (((in @ X0 @ (setminus @ sK1 @ sK0)) = $true) | ($false = (in @ X0 @ sK1)) | ($false = (in @ sK2 @ (powerset @ sK1))) | ((in @ sK0 @ (powerset @ sK1)) = $false) | ($false = (in @ X0 @ sK2))) )),
% 1.71/1.36 inference(trivial_inequality_removal,[status(thm)],[f74])).
% 1.71/1.36 thf(f74,plain,(
% 1.71/1.36 ( ! [X0 : $i] : (($false = (in @ X0 @ sK1)) | ((in @ X0 @ (setminus @ sK1 @ sK0)) = $true) | ((in @ sK0 @ (powerset @ sK1)) = $false) | ($false = $true) | ($false = (in @ sK2 @ (powerset @ sK1))) | ($false = (in @ X0 @ sK2))) )),
% 1.71/1.36 inference(superposition,[status(thm)],[f65,f23])).
% 1.71/1.36 thf(f23,plain,(
% 1.71/1.36 ((subset @ sK0 @ (setminus @ sK1 @ sK2)) = $true)),
% 1.71/1.36 inference(cnf_transformation,[status(thm)],[f19])).
% 1.71/1.36 thf(f65,plain,(
% 1.71/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (subset @ X2 @ (setminus @ X1 @ X3))) | ($false = (in @ X4 @ X3)) | ($false = (in @ X3 @ (powerset @ X1))) | ((in @ X4 @ (setminus @ X1 @ X2)) = $true) | ($false = (in @ X4 @ X1)) | ($false = (in @ X2 @ (powerset @ X1)))) )),
% 1.71/1.36 inference(binary_proxy_clausification,[status(thm)],[f64])).
% 1.71/1.36 thf(f64,plain,(
% 1.71/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((in @ X4 @ X3) => (in @ X4 @ (setminus @ X1 @ X2))) = $true) | ($false = (in @ X2 @ (powerset @ X1))) | ($false = (in @ X3 @ (powerset @ X1))) | ($false = (subset @ X2 @ (setminus @ X1 @ X3))) | ($false = (in @ X4 @ X1))) )),
% 1.71/1.36 inference(binary_proxy_clausification,[status(thm)],[f63])).
% 1.71/1.36 thf(f63,plain,(
% 1.71/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (subset @ X2 @ (setminus @ X1 @ X3))) | ($false = (in @ X2 @ (powerset @ X1))) | (((in @ X4 @ X1) => ((in @ X4 @ X3) => (in @ X4 @ (setminus @ X1 @ X2)))) = $true) | ($false = (in @ X3 @ (powerset @ X1)))) )),
% 1.71/1.36 inference(beta_eta_normalization,[status(thm)],[f62])).
% 1.71/1.36 thf(f62,plain,(
% 1.71/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (in @ X2 @ (powerset @ X1))) | ($false = (in @ X3 @ (powerset @ X1))) | ($false = (subset @ X2 @ (setminus @ X1 @ X3))) | (((^[Y0 : $i]: ((in @ Y0 @ X1) => ((in @ Y0 @ X3) => (in @ Y0 @ (setminus @ X1 @ X2))))) @ X4) = $true)) )),
% 1.71/1.36 inference(pi_clausification,[status(thm)],[f61])).
% 1.71/1.36 thf(f61,plain,(
% 1.71/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (subset @ X2 @ (setminus @ X1 @ X3))) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((in @ Y0 @ X3) => (in @ Y0 @ (setminus @ X1 @ X2)))))) = $true) | ($false = (in @ X3 @ (powerset @ X1))) | ($false = (in @ X2 @ (powerset @ X1)))) )),
% 1.71/1.36 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.71/1.36 thf(f60,plain,(
% 1.71/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X2 @ (powerset @ X1))) | ($false = (in @ X3 @ (powerset @ X1))) | (((subset @ X2 @ (setminus @ X1 @ X3)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((in @ Y0 @ X3) => (in @ Y0 @ (setminus @ X1 @ X2))))))) = $true)) )),
% 1.71/1.36 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.71/1.36 thf(f59,plain,(
% 1.71/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X3 @ (powerset @ X1)) => ((subset @ X2 @ (setminus @ X1 @ X3)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((in @ Y0 @ X3) => (in @ Y0 @ (setminus @ X1 @ X2)))))))) = $true) | ($false = (in @ X2 @ (powerset @ X1)))) )),
% 1.71/1.36 inference(beta_eta_normalization,[status(thm)],[f58])).
% 1.71/1.36 thf(f58,plain,(
% 1.71/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => ((subset @ X2 @ (setminus @ X1 @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((in @ Y1 @ Y0) => (in @ Y1 @ (setminus @ X1 @ X2))))))))) @ X3) = $true) | ($false = (in @ X2 @ (powerset @ X1)))) )),
% 1.71/1.36 inference(pi_clausification,[status(thm)],[f57])).
% 1.71/1.36 thf(f57,plain,(
% 1.71/1.36 ( ! [X2 : $i,X1 : $i] : (($false = (in @ X2 @ (powerset @ X1))) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => ((subset @ X2 @ (setminus @ X1 @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((in @ Y1 @ Y0) => (in @ Y1 @ (setminus @ X1 @ X2)))))))))) = $true)) )),
% 1.71/1.36 inference(binary_proxy_clausification,[status(thm)],[f56])).
% 1.71/1.36 thf(f56,plain,(
% 1.71/1.36 ( ! [X2 : $i,X1 : $i] : ((((in @ X2 @ (powerset @ X1)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => ((subset @ X2 @ (setminus @ X1 @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((in @ Y1 @ Y0) => (in @ Y1 @ (setminus @ X1 @ X2))))))))))) = $true)) )),
% 1.71/1.36 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.71/1.36 thf(f55,plain,(
% 1.71/1.36 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X1)) => ((subset @ Y0 @ (setminus @ X1 @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((in @ Y2 @ Y1) => (in @ Y2 @ (setminus @ X1 @ Y0)))))))))))) @ X2) = $true)) )),
% 1.71/1.36 inference(pi_clausification,[status(thm)],[f54])).
% 1.71/1.36 thf(f54,plain,(
% 1.71/1.36 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X1)) => ((subset @ Y0 @ (setminus @ X1 @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((in @ Y2 @ Y1) => (in @ Y2 @ (setminus @ X1 @ Y0))))))))))))) = $true)) )),
% 1.71/1.36 inference(beta_eta_normalization,[status(thm)],[f53])).
% 1.71/1.36 thf(f53,plain,(
% 1.71/1.36 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((subset @ Y1 @ (setminus @ Y0 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y2) => (in @ Y3 @ (setminus @ Y0 @ Y1)))))))))))))) @ X1) = $true)) )),
% 1.71/1.36 inference(pi_clausification,[status(thm)],[f30])).
% 1.71/1.36 thf(f30,plain,(
% 1.71/1.36 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((subset @ Y1 @ (setminus @ Y0 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y2) => (in @ Y3 @ (setminus @ Y0 @ Y1))))))))))))))) = $true)),
% 1.71/1.36 inference(definition_unfolding,[status(thm)],[f21,f20])).
% 1.71/1.36 thf(f20,plain,(
% 1.71/1.36 (contraSubsetComplement = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((subset @ Y1 @ (setminus @ Y0 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y2) => (in @ Y3 @ (setminus @ Y0 @ Y1))))))))))))))))),
% 1.71/1.36 inference(cnf_transformation,[status(thm)],[f10])).
% 1.71/1.36 thf(f10,plain,(
% 1.71/1.36 (contraSubsetComplement = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((subset @ Y1 @ (setminus @ Y0 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ Y2) => (in @ Y3 @ (setminus @ Y0 @ Y1))))))))))))))))),
% 1.71/1.36 inference(fool_elimination,[status(thm)],[f9])).
% 1.71/1.36 thf(f9,plain,(
% 1.71/1.36 (contraSubsetComplement = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ((subset @ X0 @ (setminus @ X1 @ X2)) => ! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ X2) => (in @ X3 @ (setminus @ X1 @ X0))))))))),
% 1.71/1.36 inference(rectify,[status(thm)],[f3])).
% 1.71/1.36 thf(f3,axiom,(
% 1.71/1.36 (contraSubsetComplement = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((subset @ X1 @ (setminus @ X0 @ X2)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X2) => (in @ X3 @ (setminus @ X0 @ X1))))))))),
% 1.71/1.36 file('/export/starexec/sandbox/tmp/tmp.lj4biKboPJ/DTF2THF_27624.p',contraSubsetComplement)).
% 1.71/1.36 thf(f21,plain,(
% 1.71/1.36 (contraSubsetComplement = $true)),
% 1.71/1.36 inference(cnf_transformation,[status(thm)],[f19])).
% 1.71/1.36 % SZS output end Proof for DTF2THF_27624
% 1.71/1.36 % (27954)------------------------------
% 1.71/1.36 % (27954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.36 % (27954)Termination reason: Refutation
% 1.71/1.36
% 1.71/1.36 % (27954)Memory used [KB]: 5756
% 1.71/1.36 % (27954)Time elapsed: 0.025 s
% 1.71/1.36 % (27954)Instructions burned: 31 (million)
% 1.71/1.36 % (27954)------------------------------
% 1.71/1.36 % (27954)------------------------------
% 1.71/1.36 % (27953)Success in time 0.037 s
%------------------------------------------------------------------------------