%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU690^2 : 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 : n005.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 09:36:26 AM UTC 2026
% Result : Theorem 1.68s 1.33s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 14
% Syntax : Number of formulae : 126 ( 37 unt; 0 typ; 8 def)
% Number of atoms : 1838 ( 386 equ; 0 cnn)
% Maximal formula atoms : 22 ( 14 avg)
% Number of connectives : 2659 ( 158 ~; 273 |; 32 &;1930 @)
% ( 8 <=>; 182 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 21 usr; 17 con; 0-4 aty)
% ( 76 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 330 ( 111 ^; 205 !; 14 ?; 330 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_4,type,
kpair: $i > $i > $i ).
thf(func_def_5,type,
cartprod: $i > $i > $i ).
thf(func_def_6,type,
breln: $i > $i > $i > $o ).
thf(func_def_25,type,
sK5: $i > $i > $i > $i > $i ).
thf(func_def_26,type,
sK6: $i > $i > $i > $i > $i ).
thf(f261,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f149,f156,f183,f190,f210,f216,f227,f237,f260]) ).
thf(f260,plain,
( spl4_6
| ~ spl4_7
| spl4_11
| spl4_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f259]) ).
thf(f259,plain,
( $false
| spl4_6
| ~ spl4_7
| spl4_11
| spl4_12 ),
inference(subsumption_resolution,[status(thm)],[f258,f208]) ).
thf(f208,plain,
( ( $false
!= ( subset @ sK3 @ ( cartprod @ sK1 @ sK0 ) ) )
| spl4_12 ),
inference(avatar_component_clause,[status(thm)],[f207]) ).
thf(f207,definition,
( spl4_12
<=> ( $false
= ( subset @ sK3 @ ( cartprod @ sK1 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_12])],[avatar_definition]) ).
thf(f258,plain,
( ( $false
= ( subset @ sK3 @ ( cartprod @ sK1 @ sK0 ) ) )
| spl4_6
| ~ spl4_7
| spl4_11 ),
inference(subsumption_resolution,[status(thm)],[f257,f204]) ).
thf(f204,plain,
( ( ( subset @ sK2 @ ( cartprod @ sK1 @ sK0 ) )
!= $false )
| spl4_11 ),
inference(avatar_component_clause,[status(thm)],[f203]) ).
thf(f203,definition,
( spl4_11
<=> ( ( subset @ sK2 @ ( cartprod @ sK1 @ sK0 ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl4_11])],[avatar_definition]) ).
thf(f257,plain,
( ( ( subset @ sK2 @ ( cartprod @ sK1 @ sK0 ) )
= $false )
| ( $false
= ( subset @ sK3 @ ( cartprod @ sK1 @ sK0 ) ) )
| spl4_6
| ~ spl4_7 ),
inference(subsumption_resolution,[status(thm)],[f256,f147]) ).
thf(f147,plain,
( ( $true
!= ( subset @ sK3 @ sK2 ) )
| spl4_6 ),
inference(avatar_component_clause,[status(thm)],[f146]) ).
thf(f146,definition,
( spl4_6
<=> ( $true
= ( subset @ sK3 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_6])],[avatar_definition]) ).
thf(f256,plain,
( ( $true
= ( subset @ sK3 @ sK2 ) )
| ( ( subset @ sK2 @ ( cartprod @ sK1 @ sK0 ) )
= $false )
| ( $false
= ( subset @ sK3 @ ( cartprod @ sK1 @ sK0 ) ) )
| ~ spl4_7 ),
inference(trivial_inequality_removal,[status(thm)],[f255]) ).
thf(f255,plain,
( ( ( subset @ sK2 @ ( cartprod @ sK1 @ sK0 ) )
= $false )
| ( $true
= ( subset @ sK3 @ sK2 ) )
| ( $true != $true )
| ( $false
= ( subset @ sK3 @ ( cartprod @ sK1 @ sK0 ) ) )
| ~ spl4_7 ),
inference(duplicate_literal_removal,[status(thm)],[f254]) ).
thf(f254,plain,
( ( $false
= ( subset @ sK3 @ ( cartprod @ sK1 @ sK0 ) ) )
| ( $true != $true )
| ( ( subset @ sK2 @ ( cartprod @ sK1 @ sK0 ) )
= $false )
| ( ( subset @ sK2 @ ( cartprod @ sK1 @ sK0 ) )
= $false )
| ( $true
= ( subset @ sK3 @ sK2 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ sK1 @ sK0 ) ) )
| ~ spl4_7 ),
inference(superposition,[status(thm)],[f155,f49]) ).
thf(f49,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ X1 ) )
| ( ( subset @ X3 @ X4 )
= $true )
| ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) )
| ( $false
= ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) )
| ( $false
= ( ( in @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) @ X3 )
=> ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) @ X4 ) ) ) ) ) )
| ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) )
| ( ( subset @ X3 @ X4 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) )
| ( ( subset @ X3 @ X4 )
= $true )
| ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X3 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X4 ) ) ) ) )
@ ( sK5 @ X3 @ X1 @ X4 @ X2 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X3 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X4 ) ) ) ) ) ) )
| ( ( subset @ X3 @ X4 )
= $true )
| ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) )
| ( $false
= ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X3 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X4 ) ) ) ) ) )
=> ( subset @ X3 @ X4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X3 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X4 ) ) ) ) ) )
=> ( subset @ X3 @ X4 ) ) ) )
| ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) )
| ( ( ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ X1 @ X2 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X3 )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) )
=> ( subset @ X3 @ Y0 ) ) )
@ X4 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ X1 @ X2 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X3 )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) )
=> ( subset @ X3 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ X1 @ X2 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X3 )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) )
=> ( subset @ X3 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ X1 @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ ( cartprod @ X1 @ X2 ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X2 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ X1 @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ ( cartprod @ X1 @ X2 ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X2 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ ( cartprod @ X1 @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ ( cartprod @ X1 @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y1 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( subset @ Y1 @ Y2 ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ ( cartprod @ X1 @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ ( cartprod @ X1 @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y1 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( subset @ Y1 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( subset @ Y3 @ ( cartprod @ Y0 @ Y1 ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ ( kpair @ Y4 @ Y5 ) @ Y2 )
=> ( in @ ( kpair @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( subset @ Y2 @ Y3 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( subset @ Y3 @ ( cartprod @ Y0 @ Y1 ) )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ ( kpair @ Y4 @ Y5 ) @ Y2 )
=> ( in @ ( kpair @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( subset @ Y2 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y0
@ Y1
@ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( ^ [Y4: $i,Y5: $i,Y6: $i] : ( subset @ Y6 @ ( cartprod @ Y4 @ Y5 ) )
@ Y0
@ Y1
@ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ ( kpair @ Y4 @ Y5 ) @ Y2 )
=> ( in @ ( kpair @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( subset @ Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f27,f29]) ).
thf(f29,plain,
( subbreln
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y0
@ Y1
@ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( ^ [Y4: $i,Y5: $i,Y6: $i] : ( subset @ Y6 @ ( cartprod @ Y4 @ Y5 ) )
@ Y0
@ Y1
@ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ ( kpair @ Y4 @ Y5 ) @ Y2 )
=> ( in @ ( kpair @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( subset @ Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f20,f28,f28]) ).
thf(f28,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) )
= breln ),
file('/export/starexec/sandbox/tmp/tmp.aS5P4VwYv7/DTF2THF_13171.p',breln) ).
thf(f20,plain,
( subbreln
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( breln @ Y0 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( breln @ Y0 @ Y1 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ ( kpair @ Y4 @ Y5 ) @ Y2 )
=> ( in @ ( kpair @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( subset @ Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( subbreln
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( breln @ Y0 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( breln @ Y0 @ Y1 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ ( kpair @ Y4 @ Y5 ) @ Y2 )
=> ( in @ ( kpair @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( subset @ Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( subbreln
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( breln @ X2 @ X1 @ X0 )
=> ! [X3: $i] :
( ( breln @ X2 @ X1 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X0 )
=> ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) )
=> ( subset @ X0 @ X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( subbreln
= ( ! [X3: $i,X1: $i,X0: $i] :
( ( breln @ X0 @ X1 @ X3 )
=> ! [X4: $i] :
( ( breln @ X0 @ X1 @ X4 )
=> ( ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X3 )
=> ( in @ ( kpair @ X5 @ X6 ) @ X4 ) ) ) )
=> ( subset @ X3 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aS5P4VwYv7/DTF2THF_13171.p',subbreln) ).
thf(f27,plain,
subbreln = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( subbreln = $true )
& ( setextsub = $true )
& ( $true
= ( breln @ sK1 @ sK0 @ sK2 ) )
& ( sK3 != sK2 )
& ( $true
= ( breln @ sK1 @ sK0 @ sK3 ) )
& ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK1 ) )
| ! [X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ sK3 )
= $true )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK2 ) )
| ( $true
!= ( in @ X5 @ sK0 ) ) ) )
& ! [X6: $i] :
( ( $true
!= ( in @ X6 @ sK1 ) )
| ! [X7: $i] :
( ( ( in @ X7 @ sK0 )
!= $true )
| ( ( in @ ( kpair @ X6 @ X7 ) @ sK3 )
!= $true )
| ( $true
= ( in @ ( kpair @ X6 @ X7 ) @ sK2 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f15,f17,f16]) ).
thf(f16,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( breln @ X1 @ X0 @ X2 ) )
& ? [X3: $i] :
( ( X2 != X3 )
& ( $true
= ( breln @ X1 @ X0 @ X3 ) )
& ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X1 ) )
| ! [X5: $i] :
( ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X2 ) )
| ( ( in @ X5 @ X0 )
!= $true ) ) )
& ! [X6: $i] :
( ( ( in @ X6 @ X1 )
!= $true )
| ! [X7: $i] :
( ( ( in @ X7 @ X0 )
!= $true )
| ( $true
!= ( in @ ( kpair @ X6 @ X7 ) @ X3 ) )
| ( ( in @ ( kpair @ X6 @ X7 ) @ X2 )
= $true ) ) ) ) )
=> ( ( $true
= ( breln @ sK1 @ sK0 @ sK2 ) )
& ? [X3: $i] :
( ( sK2 != X3 )
& ( $true
= ( breln @ sK1 @ sK0 @ X3 ) )
& ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK1 ) )
| ! [X5: $i] :
( ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK2 ) )
| ( $true
!= ( in @ X5 @ sK0 ) ) ) )
& ! [X6: $i] :
( ( $true
!= ( in @ X6 @ sK1 ) )
| ! [X7: $i] :
( ( ( in @ X7 @ sK0 )
!= $true )
| ( $true
!= ( in @ ( kpair @ X6 @ X7 ) @ X3 ) )
| ( $true
= ( in @ ( kpair @ X6 @ X7 ) @ sK2 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ? [X3: $i] :
( ( sK2 != X3 )
& ( $true
= ( breln @ sK1 @ sK0 @ X3 ) )
& ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK1 ) )
| ! [X5: $i] :
( ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK2 ) )
| ( $true
!= ( in @ X5 @ sK0 ) ) ) )
& ! [X6: $i] :
( ( $true
!= ( in @ X6 @ sK1 ) )
| ! [X7: $i] :
( ( ( in @ X7 @ sK0 )
!= $true )
| ( $true
!= ( in @ ( kpair @ X6 @ X7 ) @ X3 ) )
| ( $true
= ( in @ ( kpair @ X6 @ X7 ) @ sK2 ) ) ) ) )
=> ( ( sK3 != sK2 )
& ( $true
= ( breln @ sK1 @ sK0 @ sK3 ) )
& ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK1 ) )
| ! [X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ sK3 )
= $true )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK2 ) )
| ( $true
!= ( in @ X5 @ sK0 ) ) ) )
& ! [X6: $i] :
( ( $true
!= ( in @ X6 @ sK1 ) )
| ! [X7: $i] :
( ( ( in @ X7 @ sK0 )
!= $true )
| ( ( in @ ( kpair @ X6 @ X7 ) @ sK3 )
!= $true )
| ( $true
= ( in @ ( kpair @ X6 @ X7 ) @ sK2 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ( subbreln = $true )
& ( setextsub = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( breln @ X1 @ X0 @ X2 ) )
& ? [X3: $i] :
( ( X2 != X3 )
& ( $true
= ( breln @ X1 @ X0 @ X3 ) )
& ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X1 ) )
| ! [X5: $i] :
( ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X2 ) )
| ( ( in @ X5 @ X0 )
!= $true ) ) )
& ! [X6: $i] :
( ( ( in @ X6 @ X1 )
!= $true )
| ! [X7: $i] :
( ( ( in @ X7 @ X0 )
!= $true )
| ( $true
!= ( in @ ( kpair @ X6 @ X7 ) @ X3 ) )
| ( ( in @ ( kpair @ X6 @ X7 ) @ X2 )
= $true ) ) ) ) ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( X2 != X3 )
& ! [X6: $i] :
( ! [X7: $i] :
( ( ( in @ ( kpair @ X6 @ X7 ) @ X2 )
= $true )
| ( $true
!= ( in @ ( kpair @ X6 @ X7 ) @ X3 ) )
| ( ( in @ X7 @ X0 )
!= $true ) )
| ( ( in @ X6 @ X1 )
!= $true ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X2 ) )
| ( ( in @ X5 @ X0 )
!= $true ) )
| ( $true
!= ( in @ X4 @ X1 ) ) )
& ( $true
= ( breln @ X1 @ X0 @ X3 ) ) )
& ( $true
= ( breln @ X1 @ X0 @ X2 ) ) )
& ( subbreln = $true )
& ( setextsub = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( setextsub = $true )
=> ( ( subbreln = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( breln @ X1 @ X0 @ X2 ) )
=> ! [X3: $i] :
( ( $true
= ( breln @ X1 @ X0 @ X3 ) )
=> ( ! [X4: $i] :
( ( $true
= ( in @ X4 @ X1 ) )
=> ! [X5: $i] :
( ( ( in @ X5 @ X0 )
= $true )
=> ( ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X2 ) )
=> ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) ) )
=> ( ! [X6: $i] :
( ( ( in @ X6 @ X1 )
= $true )
=> ! [X7: $i] :
( ( ( in @ X7 @ X0 )
= $true )
=> ( ( $true
= ( in @ ( kpair @ X6 @ X7 ) @ X3 ) )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X2 )
= $true ) ) ) )
=> ( X2 = X3 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( setextsub
=> ( subbreln
=> ! [X0: $i,X1: $i,X2: $i] :
( ( breln @ X1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( breln @ X1 @ X0 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) )
=> ( ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X0 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X3 )
=> ( in @ ( kpair @ X6 @ X7 ) @ X2 ) ) ) )
=> ( X2 = X3 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( setextsub
=> ( subbreln
=> ! [X1: $i,X0: $i,X3: $i] :
( ( breln @ X0 @ X1 @ X3 )
=> ! [X4: $i] :
( ( breln @ X0 @ X1 @ X4 )
=> ( ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X3 )
=> ( in @ ( kpair @ X5 @ X6 ) @ X4 ) ) ) )
=> ( ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X4 )
=> ( in @ ( kpair @ X5 @ X6 ) @ X3 ) ) ) )
=> ( X3 = X4 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( setextsub
=> ( subbreln
=> ! [X1: $i,X0: $i,X3: $i] :
( ( breln @ X0 @ X1 @ X3 )
=> ! [X4: $i] :
( ( breln @ X0 @ X1 @ X4 )
=> ( ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X3 )
=> ( in @ ( kpair @ X5 @ X6 ) @ X4 ) ) ) )
=> ( ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X4 )
=> ( in @ ( kpair @ X5 @ X6 ) @ X3 ) ) ) )
=> ( X3 = X4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aS5P4VwYv7/DTF2THF_13171.p',eqbreln) ).
thf(f155,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ ( sK5 @ sK3 @ X0 @ sK2 @ sK0 ) @ sK1 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ sK0 ) ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK0 ) ) ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[status(thm)],[f154]) ).
thf(f154,definition,
( spl4_7
<=> ! [X0: $i] :
( ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ sK0 ) ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK0 ) ) )
| ( $true
!= ( in @ ( sK5 @ sK3 @ X0 @ sK2 @ sK0 ) @ sK1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_7])],[avatar_definition]) ).
thf(f237,plain,
( ~ spl4_6
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f236]) ).
thf(f236,plain,
( $false
| ~ spl4_6
| ~ spl4_9 ),
inference(trivial_inequality_removal,[status(thm)],[f228]) ).
thf(f228,plain,
( ( $false = $true )
| ~ spl4_6
| ~ spl4_9 ),
inference(superposition,[status(thm)],[f182,f167]) ).
thf(f167,plain,
( ( $false
= ( subset @ sK2 @ sK3 ) )
| ~ spl4_6 ),
inference(subsumption_resolution,[status(thm)],[f166,f24]) ).
thf(f24,plain,
sK3 != sK2,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f166,plain,
( ( sK3 = sK2 )
| ( $false
= ( subset @ sK2 @ sK3 ) )
| ~ spl4_6 ),
inference(trivial_inequality_removal,[status(thm)],[f158]) ).
thf(f158,plain,
( ( $false
= ( subset @ sK2 @ sK3 ) )
| ( sK3 = sK2 )
| ( $false = $true )
| ~ spl4_6 ),
inference(superposition,[status(thm)],[f148,f62]) ).
thf(f62,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( subset @ X2 @ X1 ) )
| ( X1 = X2 )
| ( $false
= ( subset @ X1 @ X2 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( X2 = X1 ) )
| ( $false
= ( subset @ X1 @ X2 ) )
| ( $false
= ( subset @ X2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: $i,X1: $i] :
( ( ( ( subset @ X1 @ X2 )
=> ( X2 = X1 ) )
= $true )
| ( $false
= ( subset @ X2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( subset @ X2 @ X1 )
=> ( ( subset @ X1 @ X2 )
=> ( X2 = X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ Y0 @ X1 )
=> ( ( subset @ X1 @ Y0 )
=> ( Y0 = X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ X1 )
=> ( ( subset @ X1 @ Y0 )
=> ( Y0 = X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f56]) ).
thf(f56,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f26,f19]) ).
thf(f19,plain,
( setextsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( setextsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( setextsub
= ( ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( setextsub
= ( ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aS5P4VwYv7/DTF2THF_13171.p',setextsub) ).
thf(f26,plain,
setextsub = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f148,plain,
( ( $true
= ( subset @ sK3 @ sK2 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[status(thm)],[f146]) ).
thf(f182,plain,
( ( $true
= ( subset @ sK2 @ sK3 ) )
| ~ spl4_9 ),
inference(avatar_component_clause,[status(thm)],[f180]) ).
thf(f180,definition,
( spl4_9
<=> ( $true
= ( subset @ sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_9])],[avatar_definition]) ).
thf(f227,plain,
~ spl4_12,
inference(avatar_contradiction_clause,[status(thm)],[f226]) ).
thf(f226,plain,
( $false
| ~ spl4_12 ),
inference(trivial_inequality_removal,[status(thm)],[f223]) ).
thf(f223,plain,
( ( $false = $true )
| ~ spl4_12 ),
inference(superposition,[status(thm)],[f64,f209]) ).
thf(f209,plain,
( ( $false
= ( subset @ sK3 @ ( cartprod @ sK1 @ sK0 ) ) )
| ~ spl4_12 ),
inference(avatar_component_clause,[status(thm)],[f207]) ).
thf(f64,plain,
( $true
= ( subset @ sK3 @ ( cartprod @ sK1 @ sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
( $true
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) )
@ sK1
@ sK0
@ sK3 ) ),
inference(definition_unfolding,[status(thm)],[f23,f28]) ).
thf(f23,plain,
( $true
= ( breln @ sK1 @ sK0 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f216,plain,
~ spl4_11,
inference(avatar_contradiction_clause,[status(thm)],[f215]) ).
thf(f215,plain,
( $false
| ~ spl4_11 ),
inference(trivial_inequality_removal,[status(thm)],[f212]) ).
thf(f212,plain,
( ( $false = $true )
| ~ spl4_11 ),
inference(superposition,[status(thm)],[f63,f205]) ).
thf(f205,plain,
( ( ( subset @ sK2 @ ( cartprod @ sK1 @ sK0 ) )
= $false )
| ~ spl4_11 ),
inference(avatar_component_clause,[status(thm)],[f203]) ).
thf(f63,plain,
( ( subset @ sK2 @ ( cartprod @ sK1 @ sK0 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
( $true
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) )
@ sK1
@ sK0
@ sK2 ) ),
inference(definition_unfolding,[status(thm)],[f25,f28]) ).
thf(f25,plain,
( $true
= ( breln @ sK1 @ sK0 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f210,plain,
( spl4_11
| spl4_12
| spl4_9
| ~ spl4_10 ),
inference(avatar_split_clause,[status(thm)],[f201,f188,f180,f207,f203]) ).
thf(f188,definition,
( spl4_10
<=> ! [X0: $i] :
( ( $false
= ( subset @ sK2 @ ( cartprod @ sK1 @ X0 ) ) )
| ( $true
!= ( in @ ( sK6 @ sK1 @ X0 @ sK2 @ sK3 ) @ sK0 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ sK1 @ X0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_10])],[avatar_definition]) ).
thf(f201,plain,
( ( $true
= ( subset @ sK2 @ sK3 ) )
| ( ( subset @ sK2 @ ( cartprod @ sK1 @ sK0 ) )
= $false )
| ( $false
= ( subset @ sK3 @ ( cartprod @ sK1 @ sK0 ) ) )
| ~ spl4_10 ),
inference(trivial_inequality_removal,[status(thm)],[f200]) ).
thf(f200,plain,
( ( ( subset @ sK2 @ ( cartprod @ sK1 @ sK0 ) )
= $false )
| ( $true != $true )
| ( $true
= ( subset @ sK2 @ sK3 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ sK1 @ sK0 ) ) )
| ~ spl4_10 ),
inference(duplicate_literal_removal,[status(thm)],[f199]) ).
thf(f199,plain,
( ( ( subset @ sK2 @ ( cartprod @ sK1 @ sK0 ) )
= $false )
| ( $true != $true )
| ( ( subset @ sK2 @ ( cartprod @ sK1 @ sK0 ) )
= $false )
| ( $true
= ( subset @ sK2 @ sK3 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ sK1 @ sK0 ) ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ sK1 @ sK0 ) ) )
| ~ spl4_10 ),
inference(superposition,[status(thm)],[f189,f53]) ).
thf(f53,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( sK6 @ X1 @ X2 @ X3 @ X4 ) @ X2 ) )
| ( $false
= ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) )
| ( ( subset @ X3 @ X4 )
= $true )
| ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( subset @ X3 @ X4 )
= $true )
| ( $false
= ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) )
| ( $false
= ( ( in @ ( sK6 @ X1 @ X2 @ X3 @ X4 ) @ X2 )
=> ( ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ ( sK6 @ X1 @ X2 @ X3 @ X4 ) ) @ X3 )
=> ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ ( sK6 @ X1 @ X2 @ X3 @ X4 ) ) @ X4 ) ) ) )
| ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( subset @ X3 @ X4 )
= $true )
| ( $false
= ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) )
| ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) @ X3 )
=> ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) @ X4 ) ) )
@ ( sK6 @ X1 @ X2 @ X3 @ X4 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) @ X3 )
=> ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ Y0 ) @ X4 ) ) ) ) )
| ( ( subset @ X3 @ X4 )
= $true )
| ( $false
= ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) )
| ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f189,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ ( sK6 @ sK1 @ X0 @ sK2 @ sK3 ) @ sK0 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK1 @ X0 ) ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ sK1 @ X0 ) ) ) )
| ~ spl4_10 ),
inference(avatar_component_clause,[status(thm)],[f188]) ).
thf(f190,plain,
( spl4_10
| spl4_9
| ~ spl4_8 ),
inference(avatar_split_clause,[status(thm)],[f186,f177,f180,f188]) ).
thf(f177,definition,
( spl4_8
<=> ! [X0: $i,X1: $i] :
( ( ( subset @ sK2 @ ( cartprod @ X0 @ X1 ) )
= $false )
| ( ( in @ ( sK6 @ X0 @ X1 @ sK2 @ sK3 ) @ sK0 )
!= $true )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X1 ) ) )
| ( $true
!= ( in @ ( sK5 @ sK2 @ X0 @ sK3 @ X1 ) @ sK1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_8])],[avatar_definition]) ).
thf(f186,plain,
( ! [X0: $i] :
( ( $false
= ( subset @ sK2 @ ( cartprod @ sK1 @ X0 ) ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ sK1 @ X0 ) ) )
| ( $true
= ( subset @ sK2 @ sK3 ) )
| ( $true
!= ( in @ ( sK6 @ sK1 @ X0 @ sK2 @ sK3 ) @ sK0 ) ) )
| ~ spl4_8 ),
inference(trivial_inequality_removal,[status(thm)],[f185]) ).
thf(f185,plain,
( ! [X0: $i] :
( ( $true
= ( subset @ sK2 @ sK3 ) )
| ( $true != $true )
| ( $true
!= ( in @ ( sK6 @ sK1 @ X0 @ sK2 @ sK3 ) @ sK0 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ sK1 @ X0 ) ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK1 @ X0 ) ) ) )
| ~ spl4_8 ),
inference(duplicate_literal_removal,[status(thm)],[f184]) ).
thf(f184,plain,
( ! [X0: $i] :
( ( $false
= ( subset @ sK2 @ ( cartprod @ sK1 @ X0 ) ) )
| ( $true
= ( subset @ sK2 @ sK3 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ sK1 @ X0 ) ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ sK1 @ X0 ) ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ sK1 @ X0 ) ) )
| ( $true != $true )
| ( $true
!= ( in @ ( sK6 @ sK1 @ X0 @ sK2 @ sK3 ) @ sK0 ) ) )
| ~ spl4_8 ),
inference(superposition,[status(thm)],[f178,f49]) ).
thf(f178,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK5 @ sK2 @ X0 @ sK3 @ X1 ) @ sK1 ) )
| ( ( subset @ sK2 @ ( cartprod @ X0 @ X1 ) )
= $false )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X1 ) ) )
| ( ( in @ ( sK6 @ X0 @ X1 @ sK2 @ sK3 ) @ sK0 )
!= $true ) )
| ~ spl4_8 ),
inference(avatar_component_clause,[status(thm)],[f177]) ).
thf(f183,plain,
( spl4_8
| spl4_9 ),
inference(avatar_split_clause,[status(thm)],[f173,f180,f177]) ).
thf(f173,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ sK2 @ ( cartprod @ X0 @ X1 ) )
= $false )
| ( $true
= ( subset @ sK2 @ sK3 ) )
| ( $true
!= ( in @ ( sK5 @ sK2 @ X0 @ sK3 @ X1 ) @ sK1 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X1 ) ) )
| ( ( in @ ( sK6 @ X0 @ X1 @ sK2 @ sK3 ) @ sK0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f172]) ).
thf(f172,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( subset @ sK2 @ ( cartprod @ X0 @ X1 ) )
= $false )
| ( ( in @ ( sK6 @ X0 @ X1 @ sK2 @ sK3 ) @ sK0 )
!= $true )
| ( $true
= ( subset @ sK2 @ sK3 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X1 ) ) )
| ( $true
!= ( in @ ( sK5 @ sK2 @ X0 @ sK3 @ X1 ) @ sK1 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f170]) ).
thf(f170,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X1 ) ) )
| ( $true != $true )
| ( $true
= ( subset @ sK2 @ sK3 ) )
| ( $true
!= ( in @ ( sK5 @ sK2 @ X0 @ sK3 @ X1 ) @ sK1 ) )
| ( ( in @ ( sK6 @ X0 @ X1 @ sK2 @ sK3 ) @ sK0 )
!= $true )
| ( ( subset @ sK2 @ ( cartprod @ X0 @ X1 ) )
= $false )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X1 ) ) )
| ( ( subset @ sK2 @ ( cartprod @ X0 @ X1 ) )
= $false )
| ( $true
= ( subset @ sK2 @ sK3 ) ) ),
inference(superposition,[status(thm)],[f111,f55]) ).
thf(f55,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ ( sK6 @ X1 @ X2 @ X3 @ X4 ) ) @ X3 ) )
| ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) )
| ( $false
= ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) )
| ( ( subset @ X3 @ X4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( subset @ X3 @ X4 )
= $true )
| ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) )
| ( $false
= ( ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ ( sK6 @ X1 @ X2 @ X3 @ X4 ) ) @ X3 )
=> ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ ( sK6 @ X1 @ X2 @ X3 @ X4 ) ) @ X4 ) ) )
| ( $false
= ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f51]) ).
thf(f111,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( kpair @ ( sK5 @ X0 @ X1 @ sK3 @ X2 ) @ ( sK6 @ X1 @ X2 @ X0 @ sK3 ) ) @ sK2 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X1 @ X2 ) ) )
| ( $true
= ( subset @ X0 @ sK3 ) )
| ( $false
= ( subset @ X0 @ ( cartprod @ X1 @ X2 ) ) )
| ( $true
!= ( in @ ( sK5 @ X0 @ X1 @ sK3 @ X2 ) @ sK1 ) )
| ( $true
!= ( in @ ( sK6 @ X1 @ X2 @ X0 @ sK3 ) @ sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f105]) ).
thf(f105,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( subset @ X0 @ ( cartprod @ X1 @ X2 ) ) )
| ( $true
!= ( in @ ( sK6 @ X1 @ X2 @ X0 @ sK3 ) @ sK0 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X1 @ X2 ) ) )
| ( $false = $true )
| ( $true
!= ( in @ ( sK5 @ X0 @ X1 @ sK3 @ X2 ) @ sK1 ) )
| ( $true
!= ( in @ ( kpair @ ( sK5 @ X0 @ X1 @ sK3 @ X2 ) @ ( sK6 @ X1 @ X2 @ X0 @ sK3 ) ) @ sK2 ) )
| ( $true
= ( subset @ X0 @ sK3 ) ) ),
inference(superposition,[status(thm)],[f54,f22]) ).
thf(f22,plain,
! [X4: $i,X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ sK3 )
= $true )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK2 ) )
| ( $true
!= ( in @ X5 @ sK0 ) )
| ( $true
!= ( in @ X4 @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f54,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) @ ( sK6 @ X1 @ X2 @ X3 @ X4 ) ) @ X4 ) )
| ( $false
= ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) )
| ( ( subset @ X3 @ X4 )
= $true )
| ( $false
= ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f156,plain,
( spl4_7
| spl4_6
| ~ spl4_5 ),
inference(avatar_split_clause,[status(thm)],[f152,f143,f146,f154]) ).
thf(f143,definition,
( spl4_5
<=> ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK5 @ sK3 @ X0 @ sK2 @ X1 ) @ sK1 ) )
| ( ( subset @ sK2 @ ( cartprod @ X0 @ X1 ) )
= $false )
| ( $true
!= ( in @ ( sK6 @ X0 @ X1 @ sK3 @ sK2 ) @ sK0 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition]) ).
thf(f152,plain,
( ! [X0: $i] :
( ( $true
= ( subset @ sK3 @ sK2 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ sK0 ) ) )
| ( $true
!= ( in @ ( sK5 @ sK3 @ X0 @ sK2 @ sK0 ) @ sK1 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK0 ) ) ) )
| ~ spl4_5 ),
inference(trivial_inequality_removal,[status(thm)],[f151]) ).
thf(f151,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( in @ ( sK5 @ sK3 @ X0 @ sK2 @ sK0 ) @ sK1 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK0 ) ) )
| ( $true
= ( subset @ sK3 @ sK2 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ sK0 ) ) ) )
| ~ spl4_5 ),
inference(duplicate_literal_removal,[status(thm)],[f150]) ).
thf(f150,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK0 ) ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ sK0 ) ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X0 @ sK0 ) ) )
| ( $true
= ( subset @ sK3 @ sK2 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ sK0 ) ) )
| ( $true
!= ( in @ ( sK5 @ sK3 @ X0 @ sK2 @ sK0 ) @ sK1 ) ) )
| ~ spl4_5 ),
inference(superposition,[status(thm)],[f144,f53]) ).
thf(f144,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK6 @ X0 @ X1 @ sK3 @ sK2 ) @ sK0 ) )
| ( ( subset @ sK2 @ ( cartprod @ X0 @ X1 ) )
= $false )
| ( $true
!= ( in @ ( sK5 @ sK3 @ X0 @ sK2 @ X1 ) @ sK1 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X1 ) ) ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[status(thm)],[f143]) ).
thf(f149,plain,
( spl4_5
| spl4_6 ),
inference(avatar_split_clause,[status(thm)],[f141,f146,f143]) ).
thf(f141,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK5 @ sK3 @ X0 @ sK2 @ X1 ) @ sK1 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X1 ) ) )
| ( $true
= ( subset @ sK3 @ sK2 ) )
| ( $true
!= ( in @ ( sK6 @ X0 @ X1 @ sK3 @ sK2 ) @ sK0 ) )
| ( ( subset @ sK2 @ ( cartprod @ X0 @ X1 ) )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f140]) ).
thf(f140,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK5 @ sK3 @ X0 @ sK2 @ X1 ) @ sK1 ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X1 ) ) )
| ( $true
!= ( in @ ( sK6 @ X0 @ X1 @ sK3 @ sK2 ) @ sK0 ) )
| ( $true != $true )
| ( ( subset @ sK2 @ ( cartprod @ X0 @ X1 ) )
= $false )
| ( $true
= ( subset @ sK3 @ sK2 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f136]) ).
thf(f136,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ sK3 @ sK2 ) )
| ( $true != $true )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X1 ) ) )
| ( $false
= ( subset @ sK3 @ ( cartprod @ X0 @ X1 ) ) )
| ( ( subset @ sK2 @ ( cartprod @ X0 @ X1 ) )
= $false )
| ( $true
!= ( in @ ( sK5 @ sK3 @ X0 @ sK2 @ X1 ) @ sK1 ) )
| ( $true
!= ( in @ ( sK6 @ X0 @ X1 @ sK3 @ sK2 ) @ sK0 ) )
| ( $true
= ( subset @ sK3 @ sK2 ) )
| ( ( subset @ sK2 @ ( cartprod @ X0 @ X1 ) )
= $false ) ),
inference(superposition,[status(thm)],[f109,f55]) ).
thf(f109,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( kpair @ ( sK5 @ X0 @ X1 @ sK2 @ X2 ) @ ( sK6 @ X1 @ X2 @ X0 @ sK2 ) ) @ sK3 )
!= $true )
| ( $true
!= ( in @ ( sK5 @ X0 @ X1 @ sK2 @ X2 ) @ sK1 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X1 @ X2 ) ) )
| ( $true
= ( subset @ X0 @ sK2 ) )
| ( $false
= ( subset @ X0 @ ( cartprod @ X1 @ X2 ) ) )
| ( ( in @ ( sK6 @ X1 @ X2 @ X0 @ sK2 ) @ sK0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f106]) ).
thf(f106,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( subset @ X0 @ sK2 ) )
| ( $false
= ( subset @ sK2 @ ( cartprod @ X1 @ X2 ) ) )
| ( ( in @ ( sK6 @ X1 @ X2 @ X0 @ sK2 ) @ sK0 )
!= $true )
| ( $true
!= ( in @ ( sK5 @ X0 @ X1 @ sK2 @ X2 ) @ sK1 ) )
| ( ( in @ ( kpair @ ( sK5 @ X0 @ X1 @ sK2 @ X2 ) @ ( sK6 @ X1 @ X2 @ X0 @ sK2 ) ) @ sK3 )
!= $true )
| ( $false
= ( subset @ X0 @ ( cartprod @ X1 @ X2 ) ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f21,f54]) ).
thf(f21,plain,
! [X6: $i,X7: $i] :
( ( $true
= ( in @ ( kpair @ X6 @ X7 ) @ sK2 ) )
| ( $true
!= ( in @ X6 @ sK1 ) )
| ( ( in @ ( kpair @ X6 @ X7 ) @ sK3 )
!= $true )
| ( ( in @ X7 @ sK0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU690^2 : 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
% 0.15/0.34 % Computer : n005.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:30:59 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.47 ---- Original DTF file ---
% 0.27/0.47 thf(spec,logic,$$dhol).
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 % File : SEU690^2 : TPTP v9.2.1. Released v3.7.0.
% 0.27/0.47 % Domain : Set Theory
% 0.27/0.47 % Problem : Functions - Extensionality and Beta Reduction
% 0.27/0.47 % Version : Especial > Reduced > Especial.
% 0.27/0.47 % English : (! A:i.! B:i.! R:i.breln A B R -> (! S:i.breln A B S ->
% 0.27/0.47 % (! x:i.in x A -> (! y:i.in y B -> in (kpair x y) R ->
% 0.27/0.47 % in (kpair x y) S)) -> (! x:i.in x A -> (! y:i.in y B ->
% 0.27/0.47 % in (kpair x y) S -> in (kpair x y) R)) -> R = S))
% 0.27/0.47
% 0.27/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.27/0.47 % Source : [Bro08]
% 0.27/0.47 % Names : ZFC192l [Bro08]
% 0.27/0.47
% 0.27/0.47 % Status : Theorem
% 0.27/0.47 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 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 v3.7.0
% 0.27/0.47 % Syntax : Number of formulae : 11 ( 3 unt; 7 typ; 3 def)
% 0.27/0.47 % Number of atoms : 30 ( 5 equ; 0 cnn)
% 0.27/0.47 % Maximal formula atoms : 13 ( 7 avg)
% 0.27/0.47 % Number of connectives : 78 ( 0 ~; 0 |; 0 &; 58 @)
% 0.27/0.47 % ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% 0.27/0.47 % Maximal formula depth : 20 ( 6 avg)
% 0.27/0.47 % Number of types : 2 ( 0 usr)
% 0.27/0.47 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.27/0.47 % Number of symbols : 8 ( 7 usr; 2 con; 0-3 aty)
% 0.27/0.47 % Number of variables : 19 ( 3 ^; 16 !; 0 ?; 19 :)
% 0.27/0.47 % SPC : TH0_THM_EQU_NAR
% 0.27/0.47
% 0.27/0.47 % Comments : http://mathgate.info/detsetitem.php?id=244
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 thf(in_type,type,
% 0.27/0.47 in: $i > $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(subset_type,type,
% 0.27/0.47 subset: $i > $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(setextsub_type,type,
% 0.27/0.47 setextsub: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setextsub,definition,
% 0.27/0.47 ( setextsub
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( subset @ A @ B )
% 0.27/0.47 => ( ( subset @ B @ A )
% 0.27/0.47 => ( A = B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(kpair_type,type,
% 0.27/0.47 kpair: $i > $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(cartprod_type,type,
% 0.27/0.47 cartprod: $i > $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(breln_type,type,
% 0.27/0.47 breln: $i > $i > $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(breln,definition,
% 0.27/0.47 ( breln
% 0.27/0.47 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(subbreln_type,type,
% 0.27/0.47 subbreln: $o ).
% 0.27/0.47
% 0.27/0.47 thf(subbreln,definition,
% 0.27/0.47 ( subbreln
% 0.27/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.27/0.47 ( ( breln @ A @ B @ R )
% 0.27/0.47 => ! [S: $i] :
% 0.27/0.47 ( ( breln @ A @ B @ S )
% 0.27/0.47 => ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.27/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.27/0.47 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(eqbreln,conjecture,
% 0.27/0.47 ( setextsub
% 0.27/0.47 => ( subbreln
% 0.27/0.47 => ! [A: $i,B: $i,R: $i] :
% 0.27/0.47 ( ( breln @ A @ B @ R )
% 0.27/0.47 => ! [S: $i] :
% 0.27/0.47 ( ( breln @ A @ B @ S )
% 0.27/0.47 => ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.27/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.27/0.47 => ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.27/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.27/0.47 => ( R = S ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 1.50/1.29 ---- Embedded in THF ---
% 1.50/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.29 %%% Generated on Tue Feb 24 12:31:00 EST 2026
% 1.50/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.29 %%% Logic specification used:
% 1.50/1.29 %%% thf(spec, logic, $$dhol).
% 1.50/1.29
% 1.50/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.aS5P4VwYv7/DTF2DTF13171.p
% See solution above
% 1.50/1.29 ------------------------
% 1.68/1.30 ---- Cleaned THF ---
% 1.68/1.30 thf(in_type,type,
% 1.68/1.30 in: $i > $i > $o ).
% 1.68/1.30
% 1.68/1.30 thf(subset_type,type,
% 1.68/1.30 subset: $i > $i > $o ).
% 1.68/1.30
% 1.68/1.30 thf(setextsub_type,type,
% 1.68/1.30 setextsub: $o ).
% 1.68/1.30
% 1.68/1.30 thf(setextsub,definition,
% 1.68/1.30 ( setextsub
% 1.68/1.30 = ( ! [A: $i,B: $i] :
% 1.68/1.30 ( ( subset @ A @ B )
% 1.68/1.30 => ( ( subset @ B @ A )
% 1.68/1.30 => ( A = B ) ) ) ) ) ).
% 1.68/1.30
% 1.68/1.30 thf(kpair_type,type,
% 1.68/1.30 kpair: $i > $i > $i ).
% 1.68/1.30
% 1.68/1.30 thf(cartprod_type,type,
% 1.68/1.30 cartprod: $i > $i > $i ).
% 1.68/1.30
% 1.68/1.30 thf(breln_type,type,
% 1.68/1.30 breln: $i > $i > $i > $o ).
% 1.68/1.30
% 1.68/1.30 thf(breln,definition,
% 1.68/1.30 ( breln
% 1.68/1.30 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 1.68/1.30
% 1.68/1.30 thf(subbreln_type,type,
% 1.68/1.30 subbreln: $o ).
% 1.68/1.30
% 1.68/1.30 thf(subbreln,definition,
% 1.68/1.30 ( subbreln
% 1.68/1.30 = ( ! [A: $i,B: $i,R: $i] :
% 1.68/1.30 ( ( breln @ A @ B @ R )
% 1.68/1.30 => ! [S: $i] :
% 1.68/1.30 ( ( breln @ A @ B @ S )
% 1.68/1.30 => ( ! [Xx: $i] :
% 1.68/1.30 ( ( in @ Xx @ A )
% 1.68/1.30 => ! [Xy: $i] :
% 1.68/1.30 ( ( in @ Xy @ B )
% 1.68/1.30 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 1.68/1.30 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 1.68/1.30 => ( subset @ R @ S ) ) ) ) ) ) ).
% 1.68/1.30
% 1.68/1.30 thf(eqbreln,conjecture,
% 1.68/1.30 ( setextsub
% 1.68/1.30 => ( subbreln
% 1.68/1.30 => ! [A: $i,B: $i,R: $i] :
% 1.68/1.30 ( ( breln @ A @ B @ R )
% 1.68/1.30 => ! [S: $i] :
% 1.68/1.30 ( ( breln @ A @ B @ S )
% 1.68/1.30 => ( ! [Xx: $i] :
% 1.68/1.30 ( ( in @ Xx @ A )
% 1.68/1.30 => ! [Xy: $i] :
% 1.68/1.30 ( ( in @ Xy @ B )
% 1.68/1.30 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 1.68/1.30 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 1.68/1.30 => ( ! [Xx: $i] :
% 1.68/1.30 ( ( in @ Xx @ A )
% 1.68/1.30 => ! [Xy: $i] :
% 1.68/1.30 ( ( in @ Xy @ B )
% 1.68/1.30 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 1.68/1.30 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 1.68/1.30 => ( R = S ) ) ) ) ) ) ) ).
% 1.68/1.30 ------------------------
% 1.68/1.31 % (13363)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13171 for (3000ds/183Mi)
% 1.68/1.32 % (13366)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13171 for (3000ds/2Mi)
% 1.68/1.32 % (13366)Instruction limit reached!
% 1.68/1.32 % (13366)------------------------------
% 1.68/1.32 % (13366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.32 % (13366)Termination reason: Unknown
% 1.68/1.32 % (13366)Termination phase: Property scanning
% 1.68/1.32
% 1.68/1.32 % (13366)Memory used [KB]: 1023
% 1.68/1.32 % (13366)Time elapsed: 0.002 s
% 1.68/1.32 % (13366)Instructions burned: 3 (million)
% 1.68/1.32 % (13366)------------------------------
% 1.68/1.32 % (13366)------------------------------
% 1.68/1.32 % (13369)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13171 for (3000ds/18Mi)
% 1.68/1.32 % (13367)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_13171 for (3000ds/2Mi)
% 1.68/1.32 % (13364)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_13171 for (3000ds/4Mi)
% 1.68/1.32 % (13367)Instruction limit reached!
% 1.68/1.32 % (13367)------------------------------
% 1.68/1.32 % (13367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.32 % (13367)Termination reason: Unknown
% 1.68/1.32 % (13367)Termination phase: Property scanning
% 1.68/1.32
% 1.68/1.32 % (13367)Memory used [KB]: 1023
% 1.68/1.32 % (13367)Time elapsed: 0.003 s
% 1.68/1.32 % (13367)Instructions burned: 3 (million)
% 1.68/1.32 % (13367)------------------------------
% 1.68/1.32 % (13367)------------------------------
% 1.68/1.32 % (13364)Instruction limit reached!
% 1.68/1.32 % (13364)------------------------------
% 1.68/1.32 % (13364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.32 % (13364)Termination reason: Unknown
% 1.68/1.32 % (13364)Termination phase: Saturation
% 1.68/1.32
% 1.68/1.32 % (13364)Memory used [KB]: 5500
% 1.68/1.32 % (13364)Time elapsed: 0.004 s
% 1.68/1.32 % (13364)Instructions burned: 5 (million)
% 1.68/1.32 % (13364)------------------------------
% 1.68/1.32 % (13364)------------------------------
% 1.68/1.33 % (13370)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13171 for (2999ds/3Mi)
% 1.68/1.33 % (13363)First to succeed.
% 1.68/1.33 % (13370)Instruction limit reached!
% 1.68/1.33 % (13370)------------------------------
% 1.68/1.33 % (13370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.33 % (13370)Termination reason: Unknown
% 1.68/1.33 % (13370)Termination phase: Property scanning
% 1.68/1.33
% 1.68/1.33 % (13370)Memory used [KB]: 1023
% 1.68/1.33 % (13370)Time elapsed: 0.002 s
% 1.68/1.33 % (13370)Instructions burned: 4 (million)
% 1.68/1.33 % (13370)------------------------------
% 1.68/1.33 % (13370)------------------------------
% 1.68/1.33 % (13363)Refutation found. Thanks to Tanya!
% 1.68/1.33 % SZS status Theorem for DTF2THF_13171
% 1.68/1.33 % SZS output start Proof for DTF2THF_13171
% 1.68/1.33 thf(func_def_0, type, in: $i > $i > $o).
% 1.68/1.33 thf(func_def_1, type, subset: $i > $i > $o).
% 1.68/1.33 thf(func_def_4, type, kpair: $i > $i > $i).
% 1.68/1.33 thf(func_def_5, type, cartprod: $i > $i > $i).
% 1.68/1.33 thf(func_def_6, type, breln: $i > $i > $i > $o).
% 1.68/1.33 thf(func_def_25, type, sK5: $i > $i > $i > $i > $i).
% 1.68/1.33 thf(func_def_26, type, sK6: $i > $i > $i > $i > $i).
% 1.68/1.33 thf(f261,plain,(
% 1.68/1.33 $false),
% 1.68/1.33 inference(avatar_sat_refutation,[status(thm)],[f149,f156,f183,f190,f210,f216,f227,f237,f260])).
% 1.68/1.33 thf(f260,plain,(
% 1.68/1.33 spl4_6 | ~spl4_7 | spl4_11 | spl4_12),
% 1.68/1.33 inference(avatar_contradiction_clause,[status(thm)],[f259])).
% 1.68/1.33 thf(f259,plain,(
% 1.68/1.33 $false | (spl4_6 | ~spl4_7 | spl4_11 | spl4_12)),
% 1.68/1.33 inference(subsumption_resolution,[status(thm)],[f258,f208])).
% 1.68/1.33 thf(f208,plain,(
% 1.68/1.33 ($false != (subset @ sK3 @ (cartprod @ sK1 @ sK0))) | spl4_12),
% 1.68/1.33 inference(avatar_component_clause,[status(thm)],[f207])).
% 1.68/1.33 thf(f207,definition,(
% 1.68/1.33 spl4_12 <=> ($false = (subset @ sK3 @ (cartprod @ sK1 @ sK0)))),
% 1.68/1.33 introduced(definition,[new_symbols(naming,[spl4_12])],[avatar_definition])).
% 1.68/1.33 thf(f258,plain,(
% 1.68/1.33 ($false = (subset @ sK3 @ (cartprod @ sK1 @ sK0))) | (spl4_6 | ~spl4_7 | spl4_11)),
% 1.68/1.33 inference(subsumption_resolution,[status(thm)],[f257,f204])).
% 1.68/1.33 thf(f204,plain,(
% 1.68/1.33 ((subset @ sK2 @ (cartprod @ sK1 @ sK0)) != $false) | spl4_11),
% 1.68/1.33 inference(avatar_component_clause,[status(thm)],[f203])).
% 1.68/1.33 thf(f203,definition,(
% 1.68/1.33 spl4_11 <=> ((subset @ sK2 @ (cartprod @ sK1 @ sK0)) = $false)),
% 1.68/1.33 introduced(definition,[new_symbols(naming,[spl4_11])],[avatar_definition])).
% 1.68/1.33 thf(f257,plain,(
% 1.68/1.33 ((subset @ sK2 @ (cartprod @ sK1 @ sK0)) = $false) | ($false = (subset @ sK3 @ (cartprod @ sK1 @ sK0))) | (spl4_6 | ~spl4_7)),
% 1.68/1.33 inference(subsumption_resolution,[status(thm)],[f256,f147])).
% 1.68/1.33 thf(f147,plain,(
% 1.68/1.33 ($true != (subset @ sK3 @ sK2)) | spl4_6),
% 1.68/1.33 inference(avatar_component_clause,[status(thm)],[f146])).
% 1.68/1.33 thf(f146,definition,(
% 1.68/1.33 spl4_6 <=> ($true = (subset @ sK3 @ sK2))),
% 1.68/1.33 introduced(definition,[new_symbols(naming,[spl4_6])],[avatar_definition])).
% 1.68/1.33 thf(f256,plain,(
% 1.68/1.33 ($true = (subset @ sK3 @ sK2)) | ((subset @ sK2 @ (cartprod @ sK1 @ sK0)) = $false) | ($false = (subset @ sK3 @ (cartprod @ sK1 @ sK0))) | ~spl4_7),
% 1.68/1.33 inference(trivial_inequality_removal,[status(thm)],[f255])).
% 1.68/1.33 thf(f255,plain,(
% 1.68/1.33 ((subset @ sK2 @ (cartprod @ sK1 @ sK0)) = $false) | ($true = (subset @ sK3 @ sK2)) | ($true != $true) | ($false = (subset @ sK3 @ (cartprod @ sK1 @ sK0))) | ~spl4_7),
% 1.68/1.33 inference(duplicate_literal_removal,[status(thm)],[f254])).
% 1.68/1.33 thf(f254,plain,(
% 1.68/1.33 ($false = (subset @ sK3 @ (cartprod @ sK1 @ sK0))) | ($true != $true) | ((subset @ sK2 @ (cartprod @ sK1 @ sK0)) = $false) | ((subset @ sK2 @ (cartprod @ sK1 @ sK0)) = $false) | ($true = (subset @ sK3 @ sK2)) | ($false = (subset @ sK3 @ (cartprod @ sK1 @ sK0))) | ~spl4_7),
% 1.68/1.33 inference(superposition,[status(thm)],[f155,f49])).
% 1.68/1.33 thf(f49,plain,(
% 1.68/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (in @ (sK5 @ X3 @ X1 @ X4 @ X2) @ X1)) | ((subset @ X3 @ X4) = $true) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ($false = (subset @ X4 @ (cartprod @ X1 @ X2)))) )),
% 1.68/1.33 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.68/1.33 thf(f47,plain,(
% 1.68/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (subset @ X4 @ (cartprod @ X1 @ X2))) | ($false = ((in @ (sK5 @ X3 @ X1 @ X4 @ X2) @ X1) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X3) => (in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X4))))))) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ((subset @ X3 @ X4) = $true)) )),
% 1.68/1.33 inference(beta_eta_normalization,[status(thm)],[f46])).
% 1.68/1.33 thf(f46,plain,(
% 1.68/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (subset @ X4 @ (cartprod @ X1 @ X2))) | ((subset @ X3 @ X4) = $true) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ($false = ((^[Y0 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X3) => (in @ (kpair @ Y0 @ Y1) @ X4))))))) @ (sK5 @ X3 @ X1 @ X4 @ X2)))) )),
% 1.68/1.33 inference(sigma_clausification,[status(thm)],[f45])).
% 1.68/1.33 thf(f45,plain,(
% 1.68/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (subset @ X4 @ (cartprod @ X1 @ X2))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X3) => (in @ (kpair @ Y0 @ Y1) @ X4))))))))) | ((subset @ X3 @ X4) = $true) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2)))) )),
% 1.68/1.33 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.68/1.33 thf(f44,plain,(
% 1.68/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ($false = (subset @ X4 @ (cartprod @ X1 @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X3) => (in @ (kpair @ Y0 @ Y1) @ X4)))))))) => (subset @ X3 @ X4)))) )),
% 1.68/1.33 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.68/1.33 thf(f43,plain,(
% 1.68/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((subset @ X4 @ (cartprod @ X1 @ X2)) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X3) => (in @ (kpair @ Y0 @ Y1) @ X4)))))))) => (subset @ X3 @ X4)))) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2)))) )),
% 1.68/1.33 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.68/1.33 thf(f42,plain,(
% 1.68/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | (((^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ X1 @ X2)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ X3) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => (subset @ X3 @ Y0)))) @ X4) = $true)) )),
% 1.68/1.33 inference(pi_clausification,[status(thm)],[f41])).
% 1.68/1.33 thf(f41,plain,(
% 1.68/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ X1 @ X2)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ X3) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => (subset @ X3 @ Y0))))))) )),
% 1.68/1.33 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.68/1.33 thf(f40,plain,(
% 1.68/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((subset @ X3 @ (cartprod @ X1 @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ X1 @ X2)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ X3) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => (subset @ X3 @ Y0)))))))) )),
% 1.68/1.33 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.68/1.33 thf(f39,plain,(
% 1.68/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ X1 @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ X1 @ X2)) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X2) => ((in @ (kpair @ Y2 @ Y3) @ Y0) => (in @ (kpair @ Y2 @ Y3) @ Y1)))))))) => (subset @ Y0 @ Y1))))))) @ X3))) )),
% 1.68/1.33 inference(pi_clausification,[status(thm)],[f38])).
% 1.68/1.33 thf(f38,plain,(
% 1.68/1.33 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ X1 @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ X1 @ X2)) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X2) => ((in @ (kpair @ Y2 @ Y3) @ Y0) => (in @ (kpair @ Y2 @ Y3) @ Y1)))))))) => (subset @ Y0 @ Y1)))))))))) )),
% 1.68/1.33 inference(beta_eta_normalization,[status(thm)],[f37])).
% 1.68/1.33 thf(f37,plain,(
% 1.68/1.33 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ X1 @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ (cartprod @ X1 @ Y0)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y1 @ Y2))))))))) @ X2))) )),
% 1.68/1.33 inference(pi_clausification,[status(thm)],[f36])).
% 1.68/1.33 thf(f36,plain,(
% 1.68/1.33 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ X1 @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ (cartprod @ X1 @ Y0)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y1 @ Y2)))))))))) = $true)) )),
% 1.68/1.33 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.68/1.33 thf(f35,plain,(
% 1.68/1.33 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ (cartprod @ Y0 @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((subset @ Y3 @ (cartprod @ Y0 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => (subset @ Y2 @ Y3))))))))))) @ X1))) )),
% 1.68/1.33 inference(pi_clausification,[status(thm)],[f34])).
% 1.68/1.33 thf(f34,plain,(
% 1.68/1.33 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ (cartprod @ Y0 @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((subset @ Y3 @ (cartprod @ Y0 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => (subset @ Y2 @ Y3)))))))))))) = $true)),
% 1.68/1.33 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.68/1.33 thf(f30,plain,(
% 1.68/1.33 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: (((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (subset @ Y6 @ (cartprod @ Y4 @ Y5))))))) @ Y0 @ Y1 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => (subset @ Y2 @ Y3)))))))))))))),
% 1.68/1.33 inference(definition_unfolding,[status(thm)],[f27,f29])).
% 1.68/1.33 thf(f29,plain,(
% 1.68/1.33 (subbreln = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: (((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (subset @ Y6 @ (cartprod @ Y4 @ Y5))))))) @ Y0 @ Y1 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => (subset @ Y2 @ Y3)))))))))))))),
% 1.68/1.33 inference(definition_unfolding,[status(thm)],[f20,f28,f28])).
% 1.68/1.33 thf(f28,plain,(
% 1.68/1.33 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.68/1.33 inference(cnf_transformation,[status(thm)],[f7])).
% 1.68/1.33 thf(f7,plain,(
% 1.68/1.33 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.68/1.33 inference(fool_elimination,[status(thm)],[f2])).
% 1.68/1.33 thf(f2,axiom,(
% 1.68/1.33 ((^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))) = breln)),
% 1.68/1.33 file('/export/starexec/sandbox/tmp/tmp.aS5P4VwYv7/DTF2THF_13171.p',breln)).
% 1.68/1.33 thf(f20,plain,(
% 1.68/1.33 (subbreln = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((breln @ Y0 @ Y1 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => (subset @ Y2 @ Y3)))))))))))))),
% 1.68/1.33 inference(cnf_transformation,[status(thm)],[f9])).
% 1.68/1.33 thf(f9,plain,(
% 1.68/1.33 (subbreln = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((breln @ Y0 @ Y1 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => (subset @ Y2 @ Y3)))))))))))))),
% 1.68/1.33 inference(fool_elimination,[status(thm)],[f8])).
% 1.68/1.33 thf(f8,plain,(
% 1.68/1.33 (subbreln = ! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X2 @ X1 @ X0) => ! [X3 : $i] : ((breln @ X2 @ X1 @ X3) => (! [X4 : $i] : ((in @ X4 @ X2) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X0) => (in @ (kpair @ X4 @ X5) @ X3)))) => (subset @ X0 @ X3)))))),
% 1.68/1.33 inference(rectify,[status(thm)],[f3])).
% 1.68/1.33 thf(f3,axiom,(
% 1.68/1.33 (subbreln = ! [X3 : $i,X1 : $i,X0 : $i] : ((breln @ X0 @ X1 @ X3) => ! [X4 : $i] : ((breln @ X0 @ X1 @ X4) => (! [X5 : $i] : ((in @ X5 @ X0) => ! [X6 : $i] : ((in @ X6 @ X1) => ((in @ (kpair @ X5 @ X6) @ X3) => (in @ (kpair @ X5 @ X6) @ X4)))) => (subset @ X3 @ X4)))))),
% 1.68/1.33 file('/export/starexec/sandbox/tmp/tmp.aS5P4VwYv7/DTF2THF_13171.p',subbreln)).
% 1.68/1.33 thf(f27,plain,(
% 1.68/1.33 (subbreln = $true)),
% 1.68/1.33 inference(cnf_transformation,[status(thm)],[f18])).
% 1.68/1.33 thf(f18,plain,(
% 1.68/1.33 (subbreln = $true) & (setextsub = $true) & (($true = (breln @ sK1 @ sK0 @ sK2)) & ((sK3 != sK2) & ($true = (breln @ sK1 @ sK0 @ sK3)) & ! [X4 : $i] : (($true != (in @ X4 @ sK1)) | ! [X5 : $i] : (((in @ (kpair @ X4 @ X5) @ sK3) = $true) | ($true != (in @ (kpair @ X4 @ X5) @ sK2)) | ($true != (in @ X5 @ sK0)))) & ! [X6 : $i] : (($true != (in @ X6 @ sK1)) | ! [X7 : $i] : (((in @ X7 @ sK0) != $true) | ((in @ (kpair @ X6 @ X7) @ sK3) != $true) | ($true = (in @ (kpair @ X6 @ X7) @ sK2))))))),
% 1.68/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f15,f17,f16])).
% 1.68/1.33 thf(f16,plain,(
% 1.68/1.33 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (breln @ X1 @ X0 @ X2)) & ? [X3 : $i] : ((X2 != X3) & ($true = (breln @ X1 @ X0 @ X3)) & ! [X4 : $i] : (($true != (in @ X4 @ X1)) | ! [X5 : $i] : (($true = (in @ (kpair @ X4 @ X5) @ X3)) | ($true != (in @ (kpair @ X4 @ X5) @ X2)) | ((in @ X5 @ X0) != $true))) & ! [X6 : $i] : (((in @ X6 @ X1) != $true) | ! [X7 : $i] : (((in @ X7 @ X0) != $true) | ($true != (in @ (kpair @ X6 @ X7) @ X3)) | ((in @ (kpair @ X6 @ X7) @ X2) = $true))))) => (($true = (breln @ sK1 @ sK0 @ sK2)) & ? [X3 : $i] : ((sK2 != X3) & ($true = (breln @ sK1 @ sK0 @ X3)) & ! [X4 : $i] : (($true != (in @ X4 @ sK1)) | ! [X5 : $i] : (($true = (in @ (kpair @ X4 @ X5) @ X3)) | ($true != (in @ (kpair @ X4 @ X5) @ sK2)) | ($true != (in @ X5 @ sK0)))) & ! [X6 : $i] : (($true != (in @ X6 @ sK1)) | ! [X7 : $i] : (((in @ X7 @ sK0) != $true) | ($true != (in @ (kpair @ X6 @ X7) @ X3)) | ($true = (in @ (kpair @ X6 @ X7) @ sK2))))))),
% 1.68/1.33 introduced(definition,[],[choice_axiom])).
% 1.68/1.33 thf(f17,plain,(
% 1.68/1.33 ? [X3 : $i] : ((sK2 != X3) & ($true = (breln @ sK1 @ sK0 @ X3)) & ! [X4 : $i] : (($true != (in @ X4 @ sK1)) | ! [X5 : $i] : (($true = (in @ (kpair @ X4 @ X5) @ X3)) | ($true != (in @ (kpair @ X4 @ X5) @ sK2)) | ($true != (in @ X5 @ sK0)))) & ! [X6 : $i] : (($true != (in @ X6 @ sK1)) | ! [X7 : $i] : (((in @ X7 @ sK0) != $true) | ($true != (in @ (kpair @ X6 @ X7) @ X3)) | ($true = (in @ (kpair @ X6 @ X7) @ sK2))))) => ((sK3 != sK2) & ($true = (breln @ sK1 @ sK0 @ sK3)) & ! [X4 : $i] : (($true != (in @ X4 @ sK1)) | ! [X5 : $i] : (((in @ (kpair @ X4 @ X5) @ sK3) = $true) | ($true != (in @ (kpair @ X4 @ X5) @ sK2)) | ($true != (in @ X5 @ sK0)))) & ! [X6 : $i] : (($true != (in @ X6 @ sK1)) | ! [X7 : $i] : (((in @ X7 @ sK0) != $true) | ((in @ (kpair @ X6 @ X7) @ sK3) != $true) | ($true = (in @ (kpair @ X6 @ X7) @ sK2)))))),
% 1.68/1.33 introduced(definition,[],[choice_axiom])).
% 1.68/1.33 thf(f15,plain,(
% 1.68/1.33 (subbreln = $true) & (setextsub = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (breln @ X1 @ X0 @ X2)) & ? [X3 : $i] : ((X2 != X3) & ($true = (breln @ X1 @ X0 @ X3)) & ! [X4 : $i] : (($true != (in @ X4 @ X1)) | ! [X5 : $i] : (($true = (in @ (kpair @ X4 @ X5) @ X3)) | ($true != (in @ (kpair @ X4 @ X5) @ X2)) | ((in @ X5 @ X0) != $true))) & ! [X6 : $i] : (((in @ X6 @ X1) != $true) | ! [X7 : $i] : (((in @ X7 @ X0) != $true) | ($true != (in @ (kpair @ X6 @ X7) @ X3)) | ((in @ (kpair @ X6 @ X7) @ X2) = $true)))))),
% 1.68/1.33 inference(flattening,[status(thm)],[f14])).
% 1.68/1.33 thf(f14,plain,(
% 1.68/1.33 (? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : ((((X2 != X3) & ! [X6 : $i] : (! [X7 : $i] : ((((in @ (kpair @ X6 @ X7) @ X2) = $true) | ($true != (in @ (kpair @ X6 @ X7) @ X3))) | ((in @ X7 @ X0) != $true)) | ((in @ X6 @ X1) != $true))) & ! [X4 : $i] : (! [X5 : $i] : ((($true = (in @ (kpair @ X4 @ X5) @ X3)) | ($true != (in @ (kpair @ X4 @ X5) @ X2))) | ((in @ X5 @ X0) != $true)) | ($true != (in @ X4 @ X1)))) & ($true = (breln @ X1 @ X0 @ X3))) & ($true = (breln @ X1 @ X0 @ X2))) & (subbreln = $true)) & (setextsub = $true)),
% 1.68/1.33 inference(ennf_transformation,[status(thm)],[f11])).
% 1.68/1.33 thf(f11,plain,(
% 1.68/1.33 ~((setextsub = $true) => ((subbreln = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (breln @ X1 @ X0 @ X2)) => ! [X3 : $i] : (($true = (breln @ X1 @ X0 @ X3)) => (! [X4 : $i] : (($true = (in @ X4 @ X1)) => ! [X5 : $i] : (((in @ X5 @ X0) = $true) => (($true = (in @ (kpair @ X4 @ X5) @ X2)) => ($true = (in @ (kpair @ X4 @ X5) @ X3))))) => (! [X6 : $i] : (((in @ X6 @ X1) = $true) => ! [X7 : $i] : (((in @ X7 @ X0) = $true) => (($true = (in @ (kpair @ X6 @ X7) @ X3)) => ((in @ (kpair @ X6 @ X7) @ X2) = $true)))) => (X2 = X3)))))))),
% 1.68/1.33 inference(fool_elimination,[status(thm)],[f10])).
% 1.68/1.33 thf(f10,plain,(
% 1.68/1.33 ~(setextsub => (subbreln => ! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X1 @ X0 @ X2) => ! [X3 : $i] : ((breln @ X1 @ X0 @ X3) => (! [X4 : $i] : ((in @ X4 @ X1) => ! [X5 : $i] : ((in @ X5 @ X0) => ((in @ (kpair @ X4 @ X5) @ X2) => (in @ (kpair @ X4 @ X5) @ X3)))) => (! [X6 : $i] : ((in @ X6 @ X1) => ! [X7 : $i] : ((in @ X7 @ X0) => ((in @ (kpair @ X6 @ X7) @ X3) => (in @ (kpair @ X6 @ X7) @ X2)))) => (X2 = X3)))))))),
% 1.68/1.33 inference(rectify,[status(thm)],[f5])).
% 1.68/1.33 thf(f5,negated_conjecture,(
% 1.68/1.33 ~(setextsub => (subbreln => ! [X1 : $i,X0 : $i,X3 : $i] : ((breln @ X0 @ X1 @ X3) => ! [X4 : $i] : ((breln @ X0 @ X1 @ X4) => (! [X5 : $i] : ((in @ X5 @ X0) => ! [X6 : $i] : ((in @ X6 @ X1) => ((in @ (kpair @ X5 @ X6) @ X3) => (in @ (kpair @ X5 @ X6) @ X4)))) => (! [X5 : $i] : ((in @ X5 @ X0) => ! [X6 : $i] : ((in @ X6 @ X1) => ((in @ (kpair @ X5 @ X6) @ X4) => (in @ (kpair @ X5 @ X6) @ X3)))) => (X3 = X4)))))))),
% 1.68/1.33 inference(negated_conjecture,[status(cth)],[f4])).
% 1.68/1.33 thf(f4,conjecture,(
% 1.68/1.33 setextsub => (subbreln => ! [X1 : $i,X0 : $i,X3 : $i] : ((breln @ X0 @ X1 @ X3) => ! [X4 : $i] : ((breln @ X0 @ X1 @ X4) => (! [X5 : $i] : ((in @ X5 @ X0) => ! [X6 : $i] : ((in @ X6 @ X1) => ((in @ (kpair @ X5 @ X6) @ X3) => (in @ (kpair @ X5 @ X6) @ X4)))) => (! [X5 : $i] : ((in @ X5 @ X0) => ! [X6 : $i] : ((in @ X6 @ X1) => ((in @ (kpair @ X5 @ X6) @ X4) => (in @ (kpair @ X5 @ X6) @ X3)))) => (X3 = X4))))))),
% 1.68/1.33 file('/export/starexec/sandbox/tmp/tmp.aS5P4VwYv7/DTF2THF_13171.p',eqbreln)).
% 1.68/1.33 thf(f155,plain,(
% 1.68/1.33 ( ! [X0 : $i] : (($true != (in @ (sK5 @ sK3 @ X0 @ sK2 @ sK0) @ sK1)) | ($false = (subset @ sK3 @ (cartprod @ X0 @ sK0))) | ($false = (subset @ sK2 @ (cartprod @ X0 @ sK0)))) ) | ~spl4_7),
% 1.68/1.33 inference(avatar_component_clause,[status(thm)],[f154])).
% 1.68/1.33 thf(f154,definition,(
% 1.68/1.33 spl4_7 <=> ! [X0 : $i] : (($false = (subset @ sK3 @ (cartprod @ X0 @ sK0))) | ($false = (subset @ sK2 @ (cartprod @ X0 @ sK0))) | ($true != (in @ (sK5 @ sK3 @ X0 @ sK2 @ sK0) @ sK1)))),
% 1.68/1.33 introduced(definition,[new_symbols(naming,[spl4_7])],[avatar_definition])).
% 1.68/1.33 thf(f237,plain,(
% 1.68/1.33 ~spl4_6 | ~spl4_9),
% 1.68/1.33 inference(avatar_contradiction_clause,[status(thm)],[f236])).
% 1.68/1.33 thf(f236,plain,(
% 1.68/1.33 $false | (~spl4_6 | ~spl4_9)),
% 1.68/1.33 inference(trivial_inequality_removal,[status(thm)],[f228])).
% 1.68/1.33 thf(f228,plain,(
% 1.68/1.33 ($false = $true) | (~spl4_6 | ~spl4_9)),
% 1.68/1.33 inference(superposition,[status(thm)],[f182,f167])).
% 1.68/1.33 thf(f167,plain,(
% 1.68/1.33 ($false = (subset @ sK2 @ sK3)) | ~spl4_6),
% 1.68/1.33 inference(subsumption_resolution,[status(thm)],[f166,f24])).
% 1.68/1.33 thf(f24,plain,(
% 1.68/1.33 (sK3 != sK2)),
% 1.68/1.33 inference(cnf_transformation,[status(thm)],[f18])).
% 1.68/1.33 thf(f166,plain,(
% 1.68/1.33 (sK3 = sK2) | ($false = (subset @ sK2 @ sK3)) | ~spl4_6),
% 1.68/1.33 inference(trivial_inequality_removal,[status(thm)],[f158])).
% 1.68/1.33 thf(f158,plain,(
% 1.68/1.33 ($false = (subset @ sK2 @ sK3)) | (sK3 = sK2) | ($false = $true) | ~spl4_6),
% 1.68/1.33 inference(superposition,[status(thm)],[f148,f62])).
% 1.68/1.33 thf(f62,plain,(
% 1.68/1.33 ( ! [X2 : $i,X1 : $i] : (($false = (subset @ X2 @ X1)) | (X1 = X2) | ($false = (subset @ X1 @ X2))) )),
% 1.68/1.33 inference(equality_proxy_clausification,[status(thm)],[f61])).
% 1.68/1.33 thf(f61,plain,(
% 1.68/1.33 ( ! [X2 : $i,X1 : $i] : (($true = (X2 = X1)) | ($false = (subset @ X1 @ X2)) | ($false = (subset @ X2 @ X1))) )),
% 1.68/1.33 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.68/1.33 thf(f60,plain,(
% 1.68/1.33 ( ! [X2 : $i,X1 : $i] : ((((subset @ X1 @ X2) => (X2 = X1)) = $true) | ($false = (subset @ X2 @ X1))) )),
% 1.68/1.33 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.68/1.33 thf(f59,plain,(
% 1.68/1.33 ( ! [X2 : $i,X1 : $i] : (($true = ((subset @ X2 @ X1) => ((subset @ X1 @ X2) => (X2 = X1))))) )),
% 1.68/1.33 inference(beta_eta_normalization,[status(thm)],[f58])).
% 1.68/1.33 thf(f58,plain,(
% 1.68/1.33 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((subset @ Y0 @ X1) => ((subset @ X1 @ Y0) => (Y0 = X1)))) @ X2))) )),
% 1.68/1.33 inference(pi_clausification,[status(thm)],[f57])).
% 1.68/1.33 thf(f57,plain,(
% 1.68/1.33 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ X1) => ((subset @ X1 @ Y0) => (Y0 = X1))))))) )),
% 1.68/1.33 inference(beta_eta_normalization,[status(thm)],[f56])).
% 1.68/1.33 thf(f56,plain,(
% 1.68/1.33 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0)))))) @ X1))) )),
% 1.68/1.33 inference(pi_clausification,[status(thm)],[f31])).
% 1.68/1.33 thf(f31,plain,(
% 1.68/1.33 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))))),
% 1.68/1.33 inference(definition_unfolding,[status(thm)],[f26,f19])).
% 1.68/1.33 thf(f19,plain,(
% 1.68/1.33 (setextsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))))),
% 1.68/1.33 inference(cnf_transformation,[status(thm)],[f13])).
% 1.68/1.33 thf(f13,plain,(
% 1.68/1.33 (setextsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))))),
% 1.68/1.33 inference(fool_elimination,[status(thm)],[f12])).
% 1.68/1.33 thf(f12,plain,(
% 1.68/1.33 (setextsub = ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X0) => (X0 = X1))))),
% 1.68/1.33 inference(rectify,[status(thm)],[f1])).
% 1.68/1.33 thf(f1,axiom,(
% 1.68/1.33 (setextsub = ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X0) => (X0 = X1))))),
% 1.68/1.33 file('/export/starexec/sandbox/tmp/tmp.aS5P4VwYv7/DTF2THF_13171.p',setextsub)).
% 1.68/1.33 thf(f26,plain,(
% 1.68/1.33 (setextsub = $true)),
% 1.68/1.33 inference(cnf_transformation,[status(thm)],[f18])).
% 1.68/1.33 thf(f148,plain,(
% 1.68/1.33 ($true = (subset @ sK3 @ sK2)) | ~spl4_6),
% 1.68/1.33 inference(avatar_component_clause,[status(thm)],[f146])).
% 1.68/1.33 thf(f182,plain,(
% 1.68/1.33 ($true = (subset @ sK2 @ sK3)) | ~spl4_9),
% 1.68/1.33 inference(avatar_component_clause,[status(thm)],[f180])).
% 1.68/1.33 thf(f180,definition,(
% 1.68/1.33 spl4_9 <=> ($true = (subset @ sK2 @ sK3))),
% 1.68/1.33 introduced(definition,[new_symbols(naming,[spl4_9])],[avatar_definition])).
% 1.68/1.33 thf(f227,plain,(
% 1.68/1.33 ~spl4_12),
% 1.68/1.33 inference(avatar_contradiction_clause,[status(thm)],[f226])).
% 1.68/1.33 thf(f226,plain,(
% 1.68/1.33 $false | ~spl4_12),
% 1.68/1.33 inference(trivial_inequality_removal,[status(thm)],[f223])).
% 1.68/1.33 thf(f223,plain,(
% 1.68/1.33 ($false = $true) | ~spl4_12),
% 1.68/1.33 inference(superposition,[status(thm)],[f64,f209])).
% 1.68/1.33 thf(f209,plain,(
% 1.68/1.33 ($false = (subset @ sK3 @ (cartprod @ sK1 @ sK0))) | ~spl4_12),
% 1.68/1.33 inference(avatar_component_clause,[status(thm)],[f207])).
% 1.68/1.33 thf(f64,plain,(
% 1.68/1.33 ($true = (subset @ sK3 @ (cartprod @ sK1 @ sK0)))),
% 1.68/1.33 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.68/1.33 thf(f33,plain,(
% 1.68/1.33 ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ sK1 @ sK0 @ sK3))),
% 1.68/1.33 inference(definition_unfolding,[status(thm)],[f23,f28])).
% 1.68/1.33 thf(f23,plain,(
% 1.68/1.33 ($true = (breln @ sK1 @ sK0 @ sK3))),
% 1.68/1.33 inference(cnf_transformation,[status(thm)],[f18])).
% 1.68/1.33 thf(f216,plain,(
% 1.68/1.33 ~spl4_11),
% 1.68/1.33 inference(avatar_contradiction_clause,[status(thm)],[f215])).
% 1.68/1.33 thf(f215,plain,(
% 1.68/1.33 $false | ~spl4_11),
% 1.68/1.33 inference(trivial_inequality_removal,[status(thm)],[f212])).
% 1.68/1.33 thf(f212,plain,(
% 1.68/1.33 ($false = $true) | ~spl4_11),
% 1.68/1.33 inference(superposition,[status(thm)],[f63,f205])).
% 1.68/1.33 thf(f205,plain,(
% 1.68/1.33 ((subset @ sK2 @ (cartprod @ sK1 @ sK0)) = $false) | ~spl4_11),
% 1.68/1.33 inference(avatar_component_clause,[status(thm)],[f203])).
% 1.68/1.33 thf(f63,plain,(
% 1.68/1.33 ((subset @ sK2 @ (cartprod @ sK1 @ sK0)) = $true)),
% 1.68/1.33 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.68/1.33 thf(f32,plain,(
% 1.68/1.33 ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ sK1 @ sK0 @ sK2))),
% 1.68/1.33 inference(definition_unfolding,[status(thm)],[f25,f28])).
% 1.68/1.33 thf(f25,plain,(
% 1.68/1.33 ($true = (breln @ sK1 @ sK0 @ sK2))),
% 1.68/1.33 inference(cnf_transformation,[status(thm)],[f18])).
% 1.68/1.33 thf(f210,plain,(
% 1.68/1.33 spl4_11 | spl4_12 | spl4_9 | ~spl4_10),
% 1.68/1.33 inference(avatar_split_clause,[status(thm)],[f201,f188,f180,f207,f203])).
% 1.68/1.33 thf(f188,definition,(
% 1.68/1.33 spl4_10 <=> ! [X0 : $i] : (($false = (subset @ sK2 @ (cartprod @ sK1 @ X0))) | ($true != (in @ (sK6 @ sK1 @ X0 @ sK2 @ sK3) @ sK0)) | ($false = (subset @ sK3 @ (cartprod @ sK1 @ X0))))),
% 1.68/1.33 introduced(definition,[new_symbols(naming,[spl4_10])],[avatar_definition])).
% 1.68/1.33 thf(f201,plain,(
% 1.68/1.33 ($true = (subset @ sK2 @ sK3)) | ((subset @ sK2 @ (cartprod @ sK1 @ sK0)) = $false) | ($false = (subset @ sK3 @ (cartprod @ sK1 @ sK0))) | ~spl4_10),
% 1.68/1.33 inference(trivial_inequality_removal,[status(thm)],[f200])).
% 1.68/1.33 thf(f200,plain,(
% 1.68/1.33 ((subset @ sK2 @ (cartprod @ sK1 @ sK0)) = $false) | ($true != $true) | ($true = (subset @ sK2 @ sK3)) | ($false = (subset @ sK3 @ (cartprod @ sK1 @ sK0))) | ~spl4_10),
% 1.68/1.33 inference(duplicate_literal_removal,[status(thm)],[f199])).
% 1.68/1.33 thf(f199,plain,(
% 1.68/1.33 ((subset @ sK2 @ (cartprod @ sK1 @ sK0)) = $false) | ($true != $true) | ((subset @ sK2 @ (cartprod @ sK1 @ sK0)) = $false) | ($true = (subset @ sK2 @ sK3)) | ($false = (subset @ sK3 @ (cartprod @ sK1 @ sK0))) | ($false = (subset @ sK3 @ (cartprod @ sK1 @ sK0))) | ~spl4_10),
% 1.68/1.33 inference(superposition,[status(thm)],[f189,f53])).
% 1.68/1.33 thf(f53,plain,(
% 1.68/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (in @ (sK6 @ X1 @ X2 @ X3 @ X4) @ X2)) | ($false = (subset @ X4 @ (cartprod @ X1 @ X2))) | ((subset @ X3 @ X4) = $true) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2)))) )),
% 1.68/1.33 inference(binary_proxy_clausification,[status(thm)],[f51])).
% 1.68/1.33 thf(f51,plain,(
% 1.68/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((subset @ X3 @ X4) = $true) | ($false = (subset @ X4 @ (cartprod @ X1 @ X2))) | ($false = ((in @ (sK6 @ X1 @ X2 @ X3 @ X4) @ X2) => ((in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ (sK6 @ X1 @ X2 @ X3 @ X4)) @ X3) => (in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ (sK6 @ X1 @ X2 @ X3 @ X4)) @ X4)))) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2)))) )),
% 1.68/1.33 inference(beta_eta_normalization,[status(thm)],[f50])).
% 1.68/1.33 thf(f50,plain,(
% 1.68/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((subset @ X3 @ X4) = $true) | ($false = (subset @ X4 @ (cartprod @ X1 @ X2))) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ($false = ((^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X3) => (in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X4)))) @ (sK6 @ X1 @ X2 @ X3 @ X4)))) )),
% 1.68/1.33 inference(sigma_clausification,[status(thm)],[f48])).
% 1.68/1.33 thf(f48,plain,(
% 1.68/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X3) => (in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X4)))))) | ((subset @ X3 @ X4) = $true) | ($false = (subset @ X4 @ (cartprod @ X1 @ X2))) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2)))) )),
% 1.68/1.33 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.68/1.33 thf(f189,plain,(
% 1.68/1.33 ( ! [X0 : $i] : (($true != (in @ (sK6 @ sK1 @ X0 @ sK2 @ sK3) @ sK0)) | ($false = (subset @ sK2 @ (cartprod @ sK1 @ X0))) | ($false = (subset @ sK3 @ (cartprod @ sK1 @ X0)))) ) | ~spl4_10),
% 1.68/1.33 inference(avatar_component_clause,[status(thm)],[f188])).
% 1.68/1.33 thf(f190,plain,(
% 1.68/1.33 spl4_10 | spl4_9 | ~spl4_8),
% 1.68/1.33 inference(avatar_split_clause,[status(thm)],[f186,f177,f180,f188])).
% 1.68/1.33 thf(f177,definition,(
% 1.68/1.33 spl4_8 <=> ! [X0 : $i,X1 : $i] : (((subset @ sK2 @ (cartprod @ X0 @ X1)) = $false) | ((in @ (sK6 @ X0 @ X1 @ sK2 @ sK3) @ sK0) != $true) | ($false = (subset @ sK3 @ (cartprod @ X0 @ X1))) | ($true != (in @ (sK5 @ sK2 @ X0 @ sK3 @ X1) @ sK1)))),
% 1.68/1.33 introduced(definition,[new_symbols(naming,[spl4_8])],[avatar_definition])).
% 1.68/1.33 thf(f186,plain,(
% 1.68/1.33 ( ! [X0 : $i] : (($false = (subset @ sK2 @ (cartprod @ sK1 @ X0))) | ($false = (subset @ sK3 @ (cartprod @ sK1 @ X0))) | ($true = (subset @ sK2 @ sK3)) | ($true != (in @ (sK6 @ sK1 @ X0 @ sK2 @ sK3) @ sK0))) ) | ~spl4_8),
% 1.68/1.33 inference(trivial_inequality_removal,[status(thm)],[f185])).
% 1.68/1.33 thf(f185,plain,(
% 1.68/1.33 ( ! [X0 : $i] : (($true = (subset @ sK2 @ sK3)) | ($true != $true) | ($true != (in @ (sK6 @ sK1 @ X0 @ sK2 @ sK3) @ sK0)) | ($false = (subset @ sK3 @ (cartprod @ sK1 @ X0))) | ($false = (subset @ sK2 @ (cartprod @ sK1 @ X0)))) ) | ~spl4_8),
% 1.68/1.33 inference(duplicate_literal_removal,[status(thm)],[f184])).
% 1.68/1.33 thf(f184,plain,(
% 1.68/1.33 ( ! [X0 : $i] : (($false = (subset @ sK2 @ (cartprod @ sK1 @ X0))) | ($true = (subset @ sK2 @ sK3)) | ($false = (subset @ sK2 @ (cartprod @ sK1 @ X0))) | ($false = (subset @ sK3 @ (cartprod @ sK1 @ X0))) | ($false = (subset @ sK3 @ (cartprod @ sK1 @ X0))) | ($true != $true) | ($true != (in @ (sK6 @ sK1 @ X0 @ sK2 @ sK3) @ sK0))) ) | ~spl4_8),
% 1.68/1.33 inference(superposition,[status(thm)],[f178,f49])).
% 1.68/1.33 thf(f178,plain,(
% 1.68/1.33 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (sK5 @ sK2 @ X0 @ sK3 @ X1) @ sK1)) | ((subset @ sK2 @ (cartprod @ X0 @ X1)) = $false) | ($false = (subset @ sK3 @ (cartprod @ X0 @ X1))) | ((in @ (sK6 @ X0 @ X1 @ sK2 @ sK3) @ sK0) != $true)) ) | ~spl4_8),
% 1.68/1.33 inference(avatar_component_clause,[status(thm)],[f177])).
% 1.68/1.33 thf(f183,plain,(
% 1.68/1.33 spl4_8 | spl4_9),
% 1.68/1.33 inference(avatar_split_clause,[status(thm)],[f173,f180,f177])).
% 1.68/1.33 thf(f173,plain,(
% 1.68/1.33 ( ! [X0 : $i,X1 : $i] : (((subset @ sK2 @ (cartprod @ X0 @ X1)) = $false) | ($true = (subset @ sK2 @ sK3)) | ($true != (in @ (sK5 @ sK2 @ X0 @ sK3 @ X1) @ sK1)) | ($false = (subset @ sK3 @ (cartprod @ X0 @ X1))) | ((in @ (sK6 @ X0 @ X1 @ sK2 @ sK3) @ sK0) != $true)) )),
% 1.68/1.33 inference(trivial_inequality_removal,[status(thm)],[f172])).
% 1.68/1.33 thf(f172,plain,(
% 1.68/1.33 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((subset @ sK2 @ (cartprod @ X0 @ X1)) = $false) | ((in @ (sK6 @ X0 @ X1 @ sK2 @ sK3) @ sK0) != $true) | ($true = (subset @ sK2 @ sK3)) | ($false = (subset @ sK3 @ (cartprod @ X0 @ X1))) | ($true != (in @ (sK5 @ sK2 @ X0 @ sK3 @ X1) @ sK1))) )),
% 1.68/1.33 inference(duplicate_literal_removal,[status(thm)],[f170])).
% 1.68/1.33 thf(f170,plain,(
% 1.68/1.33 ( ! [X0 : $i,X1 : $i] : (($false = (subset @ sK3 @ (cartprod @ X0 @ X1))) | ($true != $true) | ($true = (subset @ sK2 @ sK3)) | ($true != (in @ (sK5 @ sK2 @ X0 @ sK3 @ X1) @ sK1)) | ((in @ (sK6 @ X0 @ X1 @ sK2 @ sK3) @ sK0) != $true) | ((subset @ sK2 @ (cartprod @ X0 @ X1)) = $false) | ($false = (subset @ sK3 @ (cartprod @ X0 @ X1))) | ((subset @ sK2 @ (cartprod @ X0 @ X1)) = $false) | ($true = (subset @ sK2 @ sK3))) )),
% 1.68/1.33 inference(superposition,[status(thm)],[f111,f55])).
% 1.68/1.33 thf(f55,plain,(
% 1.68/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ (sK6 @ X1 @ X2 @ X3 @ X4)) @ X3)) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ($false = (subset @ X4 @ (cartprod @ X1 @ X2))) | ((subset @ X3 @ X4) = $true)) )),
% 1.68/1.33 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.68/1.33 thf(f52,plain,(
% 1.68/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((subset @ X3 @ X4) = $true) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ($false = ((in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ (sK6 @ X1 @ X2 @ X3 @ X4)) @ X3) => (in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ (sK6 @ X1 @ X2 @ X3 @ X4)) @ X4))) | ($false = (subset @ X4 @ (cartprod @ X1 @ X2)))) )),
% 1.68/1.33 inference(binary_proxy_clausification,[status(thm)],[f51])).
% 1.68/1.33 thf(f111,plain,(
% 1.68/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (kpair @ (sK5 @ X0 @ X1 @ sK3 @ X2) @ (sK6 @ X1 @ X2 @ X0 @ sK3)) @ sK2)) | ($false = (subset @ sK3 @ (cartprod @ X1 @ X2))) | ($true = (subset @ X0 @ sK3)) | ($false = (subset @ X0 @ (cartprod @ X1 @ X2))) | ($true != (in @ (sK5 @ X0 @ X1 @ sK3 @ X2) @ sK1)) | ($true != (in @ (sK6 @ X1 @ X2 @ X0 @ sK3) @ sK0))) )),
% 1.68/1.33 inference(trivial_inequality_removal,[status(thm)],[f105])).
% 1.68/1.33 thf(f105,plain,(
% 1.68/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (subset @ X0 @ (cartprod @ X1 @ X2))) | ($true != (in @ (sK6 @ X1 @ X2 @ X0 @ sK3) @ sK0)) | ($false = (subset @ sK3 @ (cartprod @ X1 @ X2))) | ($false = $true) | ($true != (in @ (sK5 @ X0 @ X1 @ sK3 @ X2) @ sK1)) | ($true != (in @ (kpair @ (sK5 @ X0 @ X1 @ sK3 @ X2) @ (sK6 @ X1 @ X2 @ X0 @ sK3)) @ sK2)) | ($true = (subset @ X0 @ sK3))) )),
% 1.68/1.33 inference(superposition,[status(thm)],[f54,f22])).
% 1.68/1.33 thf(f22,plain,(
% 1.68/1.33 ( ! [X4 : $i,X5 : $i] : (((in @ (kpair @ X4 @ X5) @ sK3) = $true) | ($true != (in @ (kpair @ X4 @ X5) @ sK2)) | ($true != (in @ X5 @ sK0)) | ($true != (in @ X4 @ sK1))) )),
% 1.68/1.33 inference(cnf_transformation,[status(thm)],[f18])).
% 1.68/1.33 thf(f54,plain,(
% 1.68/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ (sK6 @ X1 @ X2 @ X3 @ X4)) @ X4)) | ($false = (subset @ X4 @ (cartprod @ X1 @ X2))) | ((subset @ X3 @ X4) = $true) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2)))) )),
% 1.68/1.33 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.68/1.33 thf(f156,plain,(
% 1.68/1.33 spl4_7 | spl4_6 | ~spl4_5),
% 1.68/1.33 inference(avatar_split_clause,[status(thm)],[f152,f143,f146,f154])).
% 1.68/1.33 thf(f143,definition,(
% 1.68/1.33 spl4_5 <=> ! [X0 : $i,X1 : $i] : (($true != (in @ (sK5 @ sK3 @ X0 @ sK2 @ X1) @ sK1)) | ((subset @ sK2 @ (cartprod @ X0 @ X1)) = $false) | ($true != (in @ (sK6 @ X0 @ X1 @ sK3 @ sK2) @ sK0)) | ($false = (subset @ sK3 @ (cartprod @ X0 @ X1))))),
% 1.68/1.33 introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition])).
% 1.68/1.33 thf(f152,plain,(
% 1.68/1.33 ( ! [X0 : $i] : (($true = (subset @ sK3 @ sK2)) | ($false = (subset @ sK3 @ (cartprod @ X0 @ sK0))) | ($true != (in @ (sK5 @ sK3 @ X0 @ sK2 @ sK0) @ sK1)) | ($false = (subset @ sK2 @ (cartprod @ X0 @ sK0)))) ) | ~spl4_5),
% 1.68/1.33 inference(trivial_inequality_removal,[status(thm)],[f151])).
% 1.68/1.33 thf(f151,plain,(
% 1.68/1.33 ( ! [X0 : $i] : (($true != $true) | ($true != (in @ (sK5 @ sK3 @ X0 @ sK2 @ sK0) @ sK1)) | ($false = (subset @ sK2 @ (cartprod @ X0 @ sK0))) | ($true = (subset @ sK3 @ sK2)) | ($false = (subset @ sK3 @ (cartprod @ X0 @ sK0)))) ) | ~spl4_5),
% 1.68/1.33 inference(duplicate_literal_removal,[status(thm)],[f150])).
% 1.68/1.33 thf(f150,plain,(
% 1.68/1.33 ( ! [X0 : $i] : (($true != $true) | ($false = (subset @ sK2 @ (cartprod @ X0 @ sK0))) | ($false = (subset @ sK3 @ (cartprod @ X0 @ sK0))) | ($false = (subset @ sK2 @ (cartprod @ X0 @ sK0))) | ($true = (subset @ sK3 @ sK2)) | ($false = (subset @ sK3 @ (cartprod @ X0 @ sK0))) | ($true != (in @ (sK5 @ sK3 @ X0 @ sK2 @ sK0) @ sK1))) ) | ~spl4_5),
% 1.68/1.33 inference(superposition,[status(thm)],[f144,f53])).
% 1.68/1.33 thf(f144,plain,(
% 1.68/1.33 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (sK6 @ X0 @ X1 @ sK3 @ sK2) @ sK0)) | ((subset @ sK2 @ (cartprod @ X0 @ X1)) = $false) | ($true != (in @ (sK5 @ sK3 @ X0 @ sK2 @ X1) @ sK1)) | ($false = (subset @ sK3 @ (cartprod @ X0 @ X1)))) ) | ~spl4_5),
% 1.68/1.33 inference(avatar_component_clause,[status(thm)],[f143])).
% 1.68/1.33 thf(f149,plain,(
% 1.68/1.33 spl4_5 | spl4_6),
% 1.68/1.33 inference(avatar_split_clause,[status(thm)],[f141,f146,f143])).
% 1.68/1.33 thf(f141,plain,(
% 1.68/1.33 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (sK5 @ sK3 @ X0 @ sK2 @ X1) @ sK1)) | ($false = (subset @ sK3 @ (cartprod @ X0 @ X1))) | ($true = (subset @ sK3 @ sK2)) | ($true != (in @ (sK6 @ X0 @ X1 @ sK3 @ sK2) @ sK0)) | ((subset @ sK2 @ (cartprod @ X0 @ X1)) = $false)) )),
% 1.68/1.33 inference(trivial_inequality_removal,[status(thm)],[f140])).
% 1.68/1.33 thf(f140,plain,(
% 1.68/1.33 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (sK5 @ sK3 @ X0 @ sK2 @ X1) @ sK1)) | ($false = (subset @ sK3 @ (cartprod @ X0 @ X1))) | ($true != (in @ (sK6 @ X0 @ X1 @ sK3 @ sK2) @ sK0)) | ($true != $true) | ((subset @ sK2 @ (cartprod @ X0 @ X1)) = $false) | ($true = (subset @ sK3 @ sK2))) )),
% 1.68/1.33 inference(duplicate_literal_removal,[status(thm)],[f136])).
% 1.68/1.33 thf(f136,plain,(
% 1.68/1.33 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ sK3 @ sK2)) | ($true != $true) | ($false = (subset @ sK3 @ (cartprod @ X0 @ X1))) | ($false = (subset @ sK3 @ (cartprod @ X0 @ X1))) | ((subset @ sK2 @ (cartprod @ X0 @ X1)) = $false) | ($true != (in @ (sK5 @ sK3 @ X0 @ sK2 @ X1) @ sK1)) | ($true != (in @ (sK6 @ X0 @ X1 @ sK3 @ sK2) @ sK0)) | ($true = (subset @ sK3 @ sK2)) | ((subset @ sK2 @ (cartprod @ X0 @ X1)) = $false)) )),
% 1.68/1.33 inference(superposition,[status(thm)],[f109,f55])).
% 1.68/1.33 thf(f109,plain,(
% 1.68/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (kpair @ (sK5 @ X0 @ X1 @ sK2 @ X2) @ (sK6 @ X1 @ X2 @ X0 @ sK2)) @ sK3) != $true) | ($true != (in @ (sK5 @ X0 @ X1 @ sK2 @ X2) @ sK1)) | ($false = (subset @ sK2 @ (cartprod @ X1 @ X2))) | ($true = (subset @ X0 @ sK2)) | ($false = (subset @ X0 @ (cartprod @ X1 @ X2))) | ((in @ (sK6 @ X1 @ X2 @ X0 @ sK2) @ sK0) != $true)) )),
% 1.68/1.33 inference(trivial_inequality_removal,[status(thm)],[f106])).
% 1.68/1.33 thf(f106,plain,(
% 1.68/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (subset @ X0 @ sK2)) | ($false = (subset @ sK2 @ (cartprod @ X1 @ X2))) | ((in @ (sK6 @ X1 @ X2 @ X0 @ sK2) @ sK0) != $true) | ($true != (in @ (sK5 @ X0 @ X1 @ sK2 @ X2) @ sK1)) | ((in @ (kpair @ (sK5 @ X0 @ X1 @ sK2 @ X2) @ (sK6 @ X1 @ X2 @ X0 @ sK2)) @ sK3) != $true) | ($false = (subset @ X0 @ (cartprod @ X1 @ X2))) | ($false = $true)) )),
% 1.68/1.33 inference(superposition,[status(thm)],[f21,f54])).
% 1.68/1.33 thf(f21,plain,(
% 1.68/1.33 ( ! [X6 : $i,X7 : $i] : (($true = (in @ (kpair @ X6 @ X7) @ sK2)) | ($true != (in @ X6 @ sK1)) | ((in @ (kpair @ X6 @ X7) @ sK3) != $true) | ((in @ X7 @ sK0) != $true)) )),
% 1.68/1.33 inference(cnf_transformation,[status(thm)],[f18])).
% 1.68/1.33 % SZS output end Proof for DTF2THF_13171
% 1.68/1.33 % (13363)------------------------------
% 1.68/1.33 % (13363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.33 % (13363)Termination reason: Refutation
% 1.68/1.33
% 1.68/1.33 % (13363)Memory used [KB]: 5884
% 1.68/1.33 % (13363)Time elapsed: 0.017 s
% 1.68/1.33 % (13363)Instructions burned: 39 (million)
% 1.68/1.33 % (13363)------------------------------
% 1.68/1.33 % (13363)------------------------------
% 1.68/1.33 % (13362)Success in time 0.023 s
%------------------------------------------------------------------------------