%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.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 : Tue May 5 06:58:56 PM UTC 2026
% Result : Theorem 1.82s 1.34s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 8
% Syntax : Number of formulae : 86 ( 19 unt; 0 typ; 4 def)
% Number of atoms : 1575 ( 469 equ; 0 cnn)
% Maximal formula atoms : 39 ( 18 avg)
% Number of connectives : 3286 ( 691 ~; 470 |; 288 &;1599 @)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 6 avg)
% Number of types : 6 ( 4 usr)
% Number of type conns : 508 ( 508 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 45 usr; 10 con; 0-3 aty)
% ( 222 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 845 ( 689 ^; 140 !; 16 ?; 845 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_7,type,
d_unsorted: $tType ).
thf(type_def_8,type,
d_mu: $tType ).
thf(func_def_0,type,
unsorted: $tType ).
thf(func_def_1,type,
mu: $tType ).
thf(func_def_2,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_3,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_15,type,
mtrue: $i > $o ).
thf(func_def_16,type,
mfalse: $i > $o ).
thf(func_def_17,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_19,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_31,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_33,type,
d_unsorted: $tType ).
thf(func_def_34,type,
d_mu: $tType ).
thf(func_def_35,type,
d2unsorted: d_unsorted > $i ).
thf(func_def_36,type,
d2mu: d_mu > mu ).
thf(func_def_37,type,
d_unsorted_0: d_unsorted ).
thf(func_def_38,type,
d_mu_0: d_mu ).
thf(func_def_52,type,
sK0: $i > d_unsorted ).
thf(func_def_53,type,
sK1: mu > d_mu ).
thf(func_def_55,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_56,type,
sK4: $i > $o ).
thf(func_def_57,type,
sK5: $i > $o ).
thf(f335,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f301,f302,f306,f310,f321,f334]) ).
thf(f334,plain,
( ~ spl2_1
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f333]) ).
thf(f333,plain,
( $false
| ~ spl2_1
| ~ spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f329]) ).
thf(f329,plain,
( ( $false = $true )
| ~ spl2_1
| ~ spl2_4 ),
inference(superposition,[status(thm)],[f299,f287]) ).
thf(f287,plain,
( ( $true
= ( sK5 @ sK6 ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f285]) ).
thf(f285,definition,
( spl2_1
<=> ( $true
= ( sK5 @ sK6 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f299,plain,
( ( $false
= ( sK5 @ sK6 ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f297]) ).
thf(f297,definition,
( spl2_4
<=> ( $false
= ( sK5 @ sK6 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f321,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f320]) ).
thf(f320,plain,
( $false
| ~ spl2_2
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f317]) ).
thf(f317,plain,
( ( $false = $true )
| ~ spl2_2
| ~ spl2_3 ),
inference(superposition,[status(thm)],[f291,f295]) ).
thf(f295,plain,
( ( ( sK4 @ sK6 )
= $true )
| ~ spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f293]) ).
thf(f293,definition,
( spl2_3
<=> ( ( sK4 @ sK6 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f291,plain,
( ( $false
= ( sK4 @ sK6 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f289]) ).
thf(f289,definition,
( spl2_2
<=> ( $false
= ( sK4 @ sK6 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f310,plain,
( spl2_3
| spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f237,f285,f293]) ).
thf(f237,plain,
( ( ( sK4 @ sK6 )
= $true )
| ( $true
= ( sK5 @ sK6 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f236]) ).
thf(f236,plain,
( ( ( sK4 @ sK6 )
= $true )
| ( $true
= ( sK5 @ sK6 ) )
| ( $true
= ( sK5 @ sK6 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f235]) ).
thf(f235,plain,
( ( ( ~ ( sK5 @ sK6 ) )
= $false )
| ( ( sK4 @ sK6 )
= $true )
| ( $true
= ( sK5 @ sK6 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f232]) ).
thf(f232,plain,
( ( $false
= ( ~ ( sK4 @ sK6 ) ) )
| ( ( ~ ( sK5 @ sK6 ) )
= $false )
| ( $true
= ( sK5 @ sK6 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f231]) ).
thf(f231,plain,
( ( $true
= ( sK5 @ sK6 ) )
| ( ( ( sK4 @ sK6 )
| ~ ( sK5 @ sK6 ) )
= $false )
| ( $false
= ( ~ ( sK4 @ sK6 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f229]) ).
thf(f229,plain,
( ( $false
= ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) )
| ( ( ( sK4 @ sK6 )
| ~ ( sK5 @ sK6 ) )
= $false )
| ( $true
= ( sK5 @ sK6 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f228]) ).
thf(f228,plain,
( ( ( ~ ( ( sK4 @ sK6 )
| ~ ( sK5 @ sK6 ) ) )
= $true )
| ( $false
= ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) )
| ( $true
= ( sK5 @ sK6 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f227]) ).
thf(f227,plain,
( ( $true
= ( ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) ) )
| ( ( ~ ( ( sK4 @ sK6 )
| ~ ( sK5 @ sK6 ) ) )
= $true )
| ( $true
= ( sK5 @ sK6 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f226]) ).
thf(f226,plain,
( ( ( ~ ( sK5 @ sK6 ) )
= $false )
| ( $true
= ( ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) ) )
| ( ( ~ ( ( sK4 @ sK6 )
| ~ ( sK5 @ sK6 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f224]) ).
thf(f224,plain,
( ( ( ~ ( sK5 @ sK6 )
| ( sK4 @ sK6 ) )
= $false )
| ( $true
= ( ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) ) )
| ( ( ~ ( ( sK4 @ sK6 )
| ~ ( sK5 @ sK6 ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f223]) ).
thf(f223,plain,
( ( ( ~ ( ~ ( sK5 @ sK6 )
| ( sK4 @ sK6 ) ) )
= $true )
| ( ( ~ ( ( sK4 @ sK6 )
| ~ ( sK5 @ sK6 ) ) )
= $true )
| ( $true
= ( ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f222]) ).
thf(f222,plain,
( ( $true
= ( ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) ) )
| ( ( ~ ( ~ ( sK5 @ sK6 )
| ( sK4 @ sK6 ) ) )
= $true )
| ( $true
= ( ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) ) )
| ( ( ~ ( ( sK4 @ sK6 )
| ~ ( sK5 @ sK6 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f221]) ).
thf(f221,plain,
( ( $true
= ( ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) )
| ~ ( ( sK4 @ sK6 )
| ~ ( sK5 @ sK6 ) ) ) )
| ( $true
= ( ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) ) )
| ( ( ~ ( ~ ( sK5 @ sK6 )
| ( sK4 @ sK6 ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f220]) ).
thf(f220,plain,
( ( ( ~ ( ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) )
| ~ ( ( sK4 @ sK6 )
| ~ ( sK5 @ sK6 ) ) ) )
= $false )
| ( ( ~ ( ~ ( sK5 @ sK6 )
| ( sK4 @ sK6 ) ) )
= $true )
| ( $true
= ( ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f219]) ).
thf(f219,plain,
( ( ( ~ ( ~ ( sK5 @ sK6 )
| ( sK4 @ sK6 ) )
| ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) )
| ~ ( ( sK4 @ sK6 )
| ~ ( sK5 @ sK6 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f218]) ).
thf(f218,plain,
( ( ( ~ ( ~ ( ~ ( sK5 @ sK6 )
| ( sK4 @ sK6 ) )
| ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) )
| ~ ( ( sK4 @ sK6 )
| ~ ( sK5 @ sK6 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f216]) ).
thf(f216,plain,
( ( ~ ( ~ ( ~ ( sK5 @ sK6 )
| ( sK4 @ sK6 ) )
| ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) ) )
!= ( ~ ( ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) )
| ~ ( ( sK4 @ sK6 )
| ~ ( sK5 @ sK6 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f215]) ).
thf(f215,plain,
( ( ^ [Y0: $i] :
~ ( ~ ( ~ ( sK4 @ Y0 )
| ( sK5 @ Y0 ) )
| ~ ( ( sK4 @ Y0 )
| ~ ( sK5 @ Y0 ) ) )
@ sK6 )
!= ( ^ [Y0: $i] :
~ ( ~ ( ~ ( sK5 @ Y0 )
| ( sK4 @ Y0 ) )
| ~ ( ~ ( sK4 @ Y0 )
| ( sK5 @ Y0 ) ) )
@ sK6 ) ),
inference(negative_extensionality,[status(thm)],[f214]) ).
thf(f214,plain,
( ( ^ [Y0: $i] :
~ ( ~ ( ~ ( sK5 @ Y0 )
| ( sK4 @ Y0 ) )
| ~ ( ~ ( sK4 @ Y0 )
| ( sK5 @ Y0 ) ) ) )
!= ( ^ [Y0: $i] :
~ ( ~ ( ~ ( sK4 @ Y0 )
| ( sK5 @ Y0 ) )
| ~ ( ( sK4 @ Y0 )
| ~ ( sK5 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f213]) ).
thf(f213,plain,
( ( ^ [Y0: $i > $o,Y1: $i] :
~ ( ~ ( ~ ( Y0 @ Y1 )
| ( sK4 @ Y1 ) )
| ~ ( ~ ( sK4 @ Y1 )
| ( Y0 @ Y1 ) ) )
@ sK5 )
!= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( ~ ( ~ ( sK4 @ Y1 )
| ( Y0 @ Y1 ) )
| ~ ( ( sK4 @ Y1 )
| ~ ( Y0 @ Y1 ) ) )
@ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f212]) ).
thf(f212,plain,
( ( ^ [Y0: $i > $o,Y1: $i] :
~ ( ~ ( ~ ( Y0 @ Y1 )
| ( sK4 @ Y1 ) )
| ~ ( ~ ( sK4 @ Y1 )
| ( Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( ~ ( ~ ( sK4 @ Y1 )
| ( Y0 @ Y1 ) )
| ~ ( ( sK4 @ Y1 )
| ~ ( Y0 @ Y1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f211]) ).
thf(f211,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( ~ ( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
| ~ ( ( Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) ) )
@ sK4 )
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( ~ ( ~ ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
| ~ ( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) )
@ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f56]) ).
thf(f56,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( ~ ( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
| ~ ( ( Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) ) ) )
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( ~ ( ~ ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
| ~ ( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
~ ( ~ ( Y3 @ Y4 )
| ~ ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ~ ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ~ ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ Y1
@ Y0 ) ) )
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( ~ ( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
| ~ ( ( Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f17,f38,f25,f44,f44]) ).
thf(f44,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( mexists_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
~ ( !! @ mu
@ ^ [Y2: mu] :
~ ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( meq_ind @ ( d2mu @ d_mu_0 ) @ ( d2mu @ d_mu_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( mcountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( mweakly_directed
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y0 @ Y2 @ Y4 ) ) ) ) ) ) ) ) )
& ! [X0: d_unsorted,X1: d_unsorted] :
( ( ( d2unsorted @ X1 )
!= ( d2unsorted @ X0 ) )
| ( X0 = X1 ) )
& ! [X2: $i] :
( ( d2unsorted @ ( sK0 @ X2 ) )
= X2 )
& ( meq_prop
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) )
& ( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( mxor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( ( Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) )
| ~ ( ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) ) )
& ( mexists_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
~ ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
~ ( Y0 @ Y2 @ Y1 ) ) ) )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( ( mfalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ! [X4: d_mu,X5: d_mu] :
( ( X4 = X5 )
| ( ( d2mu @ X5 )
!= ( d2mu @ X4 ) ) )
& ( msatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( mimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( ~ ( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
| ~ ( ( Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) ) ) ) )
& ( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
& ( mserial
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) )
& ( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ! [X6: d_unsorted] : ( d_unsorted_0 = X6 )
& ( mfunctional
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 = Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( mweakly_dense
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ) )
& ! [X7: mu] :
( ( d2mu @ ( sK1 @ X7 ) )
= X7 )
& ! [X9: d_mu] : ( d_mu_0 = X9 )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( ~ ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) )
& ( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y1 @ Y3 ) ) ) ) )
& ( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) )
& ( minvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( ( mtrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( mweakly_connected
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y3 = Y1 )
| ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( mpartially_functional
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f15,f14]) ).
thf(f14,plain,
! [X2: $i] :
( ? [X3: d_unsorted] :
( ( d2unsorted @ X3 )
= X2 )
=> ( ( d2unsorted @ ( sK0 @ X2 ) )
= X2 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
! [X7: mu] :
( ? [X8: d_mu] :
( ( d2mu @ X8 )
= X7 )
=> ( ( d2mu @ ( sK1 @ X7 ) )
= X7 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ( mexists_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
~ ( !! @ mu
@ ^ [Y2: mu] :
~ ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( meq_ind @ ( d2mu @ d_mu_0 ) @ ( d2mu @ d_mu_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( mcountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( mweakly_directed
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y0 @ Y2 @ Y4 ) ) ) ) ) ) ) ) )
& ! [X0: d_unsorted,X1: d_unsorted] :
( ( ( d2unsorted @ X1 )
!= ( d2unsorted @ X0 ) )
| ( X0 = X1 ) )
& ! [X2: $i] :
? [X3: d_unsorted] :
( ( d2unsorted @ X3 )
= X2 )
& ( meq_prop
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) )
& ( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( mxor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( ( Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) )
| ~ ( ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) ) )
& ( mexists_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
~ ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
~ ( Y0 @ Y2 @ Y1 ) ) ) )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( ( mfalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ! [X4: d_mu,X5: d_mu] :
( ( X4 = X5 )
| ( ( d2mu @ X5 )
!= ( d2mu @ X4 ) ) )
& ( msatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( mimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( ~ ( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
| ~ ( ( Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) ) ) ) )
& ( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
& ( mserial
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) )
& ( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ! [X6: d_unsorted] : ( d_unsorted_0 = X6 )
& ( mfunctional
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 = Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( mweakly_dense
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ) )
& ! [X7: mu] :
? [X8: d_mu] :
( ( d2mu @ X8 )
= X7 )
& ! [X9: d_mu] : ( d_mu_0 = X9 )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( ~ ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) )
& ( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y1 @ Y3 ) ) ) ) )
& ( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) )
& ( minvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( ( mtrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( mweakly_connected
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y3 = Y1 )
| ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( mpartially_functional
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,plain,
( ( mexists_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
~ ( !! @ mu
@ ^ [Y2: mu] :
~ ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( meq_ind @ ( d2mu @ d_mu_0 ) @ ( d2mu @ d_mu_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( mcountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( mweakly_directed
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y0 @ Y2 @ Y4 ) ) ) ) ) ) ) ) )
& ! [X2: d_unsorted,X3: d_unsorted] :
( ( ( d2unsorted @ X2 )
!= ( d2unsorted @ X3 ) )
| ( X2 = X3 ) )
& ! [X4: $i] :
? [X5: d_unsorted] :
( ( d2unsorted @ X5 )
= X4 )
& ( meq_prop
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) )
& ( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( mxor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( ( Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) )
| ~ ( ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) ) )
& ( mexists_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
~ ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
~ ( Y0 @ Y2 @ Y1 ) ) ) )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( ( mfalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ! [X8: d_mu,X9: d_mu] :
( ( X8 = X9 )
| ( ( d2mu @ X8 )
!= ( d2mu @ X9 ) ) )
& ( msatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( mimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( ~ ( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
| ~ ( ( Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) ) ) ) )
& ( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
& ( mserial
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) )
& ( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ! [X0: d_unsorted] : ( d_unsorted_0 = X0 )
& ( mfunctional
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 = Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( mweakly_dense
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ) )
& ! [X6: mu] :
? [X7: d_mu] :
( ( d2mu @ X7 )
= X6 )
& ! [X1: d_mu] : ( d_mu_0 = X1 )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( ~ ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) )
& ( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y1 @ Y3 ) ) ) ) )
& ( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) )
& ( minvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( ( mtrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( mweakly_connected
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y3 = Y1 )
| ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( mpartially_functional
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( msatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( mweakly_directed
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y0 @ Y2 @ Y4 ) ) ) ) ) ) ) ) )
& ( mserial
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( ( mfalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ! [X8: d_mu,X9: d_mu] :
( ( ( d2mu @ X8 )
= ( d2mu @ X9 ) )
=> ( X8 = X9 ) )
& ( ( meq_ind @ ( d2mu @ d_mu_0 ) @ ( d2mu @ d_mu_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( mpartially_functional
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ! [X0: d_unsorted] : ( d_unsorted_0 = X0 )
& ( mxor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( ( Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) )
| ~ ( ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( ( mtrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) )
& ! [X6: mu] :
? [X7: d_mu] :
( ( d2mu @ X7 )
= X6 )
& ( mcountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ! [X4: $i] :
? [X5: d_unsorted] :
( ( d2unsorted @ X5 )
= X4 )
& ( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) )
& ( mexists_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
~ ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
~ ( Y0 @ Y2 @ Y1 ) ) ) )
& ( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ! [X2: d_unsorted,X3: d_unsorted] :
( ( ( d2unsorted @ X2 )
= ( d2unsorted @ X3 ) )
=> ( X2 = X3 ) )
& ( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( ~ ( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
| ~ ( ( Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) ) ) ) )
& ( mexists_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
~ ( !! @ mu
@ ^ [Y2: mu] :
~ ( Y0 @ Y2 @ Y1 ) ) ) )
& ( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( ~ ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) )
& ( minvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( mimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) )
& ( mweakly_dense
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ) )
& ( mweakly_connected
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y3 = Y1 )
| ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ! [X1: d_mu] : ( d_mu_0 = X1 )
& ( mfunctional
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 = Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( meq_prop
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) )
& ( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y1 @ Y3 ) ) ) ) )
& ( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( ~ ( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
| ~ ( ( Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) ) ) ) )
& ( msatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ! [X0: d_unsorted] : ( d_unsorted_0 = X0 )
& ( mweakly_directed
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y0 @ Y2 @ Y4 ) ) ) ) ) ) ) ) )
& ( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( meq_ind @ ( d2mu @ d_mu_0 ) @ ( d2mu @ d_mu_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( mfunctional
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 = Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( mxor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( ( Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) )
| ~ ( ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) ) )
& ! [X1: d_mu] : ( d_mu_0 = X1 )
& ( meq_prop
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) )
& ( mweakly_connected
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y3 = Y1 )
| ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( mimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
& ! [X2: d_unsorted,X3: d_unsorted] :
( ( ( d2unsorted @ X2 )
= ( d2unsorted @ X3 ) )
=> ( X2 = X3 ) )
& ( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) )
& ( minvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ! [X4: $i] :
? [X5: d_unsorted] :
( ( d2unsorted @ X5 )
= X4 )
& ( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y1 @ Y3 ) ) ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( ~ ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( mcountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( mexists_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
~ ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
~ ( Y0 @ Y2 @ Y1 ) ) ) )
& ( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( mfalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( mexists_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
~ ( !! @ mu
@ ^ [Y2: mu] :
~ ( Y0 @ Y2 @ Y1 ) ) ) )
& ( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) )
& ! [X6: mu] :
? [X7: d_mu] :
( ( d2mu @ X7 )
= X6 )
& ( mweakly_dense
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ) )
& ( ( mtrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( mserial
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( mpartially_functional
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ! [X8: d_mu,X9: d_mu] :
( ( ( d2mu @ X8 )
= ( d2mu @ X9 ) )
=> ( X8 = X9 ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( ~ ( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
| ~ ( ( Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) ) ) ) )
& ( msatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ! [X7: d_unsorted] : ( d_unsorted_0 = X7 )
& ( mweakly_directed
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y0 @ Y2 @ Y4 ) ) ) ) ) ) ) ) )
& ( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( meq_ind @ ( d2mu @ d_mu_0 ) @ ( d2mu @ d_mu_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( mfunctional
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 = Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) )
& ( mxor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( ( Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) )
| ~ ( ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) ) )
& ! [X26: d_mu] : ( d_mu_0 = X26 )
& ( meq_prop
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) )
& ( mweakly_connected
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y3 = Y1 )
| ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( mimplied
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
& ! [X41: d_unsorted,X42: d_unsorted] :
( ( ( d2unsorted @ X42 )
= ( d2unsorted @ X41 ) )
=> ( X41 = X42 ) )
& ( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) )
& ( minvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
& ( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ! [X55: $i] :
? [X56: d_unsorted] :
( ( d2unsorted @ X56 )
= X55 )
& ( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y1 @ Y3 ) ) ) ) )
& ( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( ~ ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) )
& ( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) )
& ( mcountersatisfiable
= ( ^ [Y0: $i > $o] :
~ ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
& ( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) )
& ( mexists_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
~ ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
~ ( Y0 @ Y2 @ Y1 ) ) ) )
& ( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( mfalse @ ( d2unsorted @ d_unsorted_0 ) )
!= $true )
& ( mexists_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
~ ( !! @ mu
@ ^ [Y2: mu] :
~ ( Y0 @ Y2 @ Y1 ) ) ) )
& ( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) )
& ! [X83: mu] :
? [X84: d_mu] :
( ( d2mu @ X84 )
= X83 )
& ( mweakly_dense
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ) )
& ( ( mtrue @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
& ( mserial
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( mpartially_functional
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ! [X96: d_mu,X97: d_mu] :
( ( ( d2mu @ X96 )
= ( d2mu @ X97 ) )
=> ( X96 = X97 ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) )
& ( mequiv
= ( ^ [X2: $i > $o,X3: $i > $o,X4: $i] :
~ ( ~ ( ~ ( X3 @ X4 )
| ( X2 @ X4 ) )
| ~ ( ( X3 @ X4 )
| ~ ( X2 @ X4 ) ) ) ) )
& ( msatisfiable
= ( ^ [X5: $i > $o] :
~ ! [X6: $i] :
~ ( X5 @ X6 ) ) )
& ! [X7: d_unsorted] : ( d_unsorted_0 = X7 )
& ( ( ^ [X8: $i > $i > $o] :
! [X9: $i,X10: $i,X11: $i] :
( ~ ! [X12: $i] :
( ~ ( X8 @ X10 @ X12 )
| ~ ( X8 @ X9 @ X12 ) )
| ~ ( X8 @ X11 @ X10 )
| ~ ( X8 @ X11 @ X9 ) ) )
= mweakly_directed )
& ( ( ^ [X13: mu > $i > $o,X14: $i] :
! [X15: mu] : ( X13 @ X15 @ X14 ) )
= mforall_ind )
& ( meq_ind @ ( d2mu @ d_mu_0 ) @ ( d2mu @ d_mu_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
& ( mfunctional
= ( ^ [X16: $i > $i > $o] :
! [X17: $i] :
~ ! [X18: $i] :
( ~ ! [X19: $i] :
( ~ ( X16 @ X17 @ X19 )
| ( X18 = X19 ) )
| ~ ( X16 @ X17 @ X18 ) ) ) )
& ( mimplies
= ( ^ [X20: $i > $o,X21: $i > $o,X22: $i] :
( ( X21 @ X22 )
| ~ ( X20 @ X22 ) ) ) )
& ( mxor
= ( ^ [X23: $i > $o,X24: $i > $o,X25: $i] :
( ~ ( ~ ( X23 @ X25 )
| ( X24 @ X25 ) )
| ~ ( ~ ( X24 @ X25 )
| ( X23 @ X25 ) ) ) ) )
& ! [X26: d_mu] : ( d_mu_0 = X26 )
& ( meq_prop
= ( ^ [X27: $i > $o,X28: $i > $o,X29: $i] :
( ( X28 @ X29 )
= ( X27 @ X29 ) ) ) )
& ( ( ^ [X30: $i > $i > $o] :
! [X31: $i,X32: $i,X33: $i] :
( ( X30 @ X33 @ X31 )
| ( X30 @ X31 @ X33 )
| ( X31 = X33 )
| ~ ( X30 @ X32 @ X31 )
| ~ ( X30 @ X32 @ X33 ) ) )
= mweakly_connected )
& ( ( ^ [X34: $i > $o,X35: $i > $o,X36: $i] :
( ( X34 @ X36 )
| ~ ( X35 @ X36 ) ) )
= mimplied )
& ( mtransitive
= ( ^ [X37: $i > $i > $o] :
! [X38: $i,X39: $i,X40: $i] :
( ~ ( X37 @ X38 @ X40 )
| ~ ( X37 @ X40 @ X39 )
| ( X37 @ X38 @ X39 ) ) ) )
& ! [X41: d_unsorted,X42: d_unsorted] :
( ( ( d2unsorted @ X42 )
= ( d2unsorted @ X41 ) )
=> ( X41 = X42 ) )
& ( meuclidean
= ( ^ [X43: $i > $i > $o] :
! [X44: $i,X45: $i,X46: $i] :
( ( X43 @ X46 @ X44 )
| ~ ( X43 @ X45 @ X46 )
| ~ ( X43 @ X45 @ X44 ) ) ) )
& ( mbox
= ( ^ [X47: $i > $i > $o,X48: $i > $o,X49: $i] :
! [X50: $i] :
( ( X48 @ X50 )
| ~ ( X47 @ X49 @ X50 ) ) ) )
& ( minvalid
= ( ^ [X51: $i > $o] :
! [X52: $i] :
~ ( X51 @ X52 ) ) )
& ( mvalid
= ( ^ [X53: $i > $o] :
! [X54: $i] : ( X53 @ X54 ) ) )
& ! [X55: $i] :
? [X56: d_unsorted] :
( ( d2unsorted @ X56 )
= X55 )
& ( ( ^ [X57: $i > $i > $o,X58: $i > $o,X59: $i] :
~ ! [X60: $i] :
( ~ ( X58 @ X60 )
| ~ ( X57 @ X59 @ X60 ) ) )
= mdia )
& ( ( ^ [X61: $i > $o,X62: $i > $o,X63: $i] :
~ ( ~ ( X61 @ X63 )
| ~ ( X62 @ X63 ) ) )
= mand )
& ( ( ^ [X64: $i > $o,X65: $i > $o,X66: $i] :
( ( X64 @ X66 )
| ( X65 @ X66 ) ) )
= mor )
& ( mcountersatisfiable
= ( ^ [X67: $i > $o] :
~ ! [X68: $i] : ( X67 @ X68 ) ) )
& ( ( ^ [X69: $i > $o,X70: $i] :
~ ( X69 @ X70 ) )
= mnot )
& ( mexists_prop
= ( ^ [X71: ( $i > $o ) > $i > $o,X72: $i] :
~ ! [X73: $i > $o] :
~ ( X71 @ X73 @ X72 ) ) )
& ( msymmetric
= ( ^ [X74: $i > $i > $o] :
! [X75: $i,X76: $i] :
( ~ ( X74 @ X75 @ X76 )
| ( X74 @ X76 @ X75 ) ) ) )
& ~ ( mfalse @ ( d2unsorted @ d_unsorted_0 ) )
& ( mexists_ind
= ( ^ [X77: mu > $i > $o,X78: $i] :
~ ! [X79: mu] :
~ ( X77 @ X79 @ X78 ) ) )
& ( mforall_prop
= ( ^ [X80: ( $i > $o ) > $i > $o,X81: $i] :
! [X82: $i > $o] : ( X80 @ X82 @ X81 ) ) )
& ! [X83: mu] :
? [X84: d_mu] :
( ( d2mu @ X84 )
= X83 )
& ( ( ^ [X85: $i > $i > $o] :
! [X86: $i,X87: $i] :
( ~ ! [X88: $i] :
( ~ ( X85 @ X88 @ X87 )
| ~ ( X85 @ X86 @ X88 ) )
| ~ ( X85 @ X86 @ X87 ) ) )
= mweakly_dense )
& ( mtrue @ ( d2unsorted @ d_unsorted_0 ) )
& ( mserial
= ( ^ [X89: $i > $i > $o] :
! [X90: $i] :
~ ! [X91: $i] :
~ ( X89 @ X90 @ X91 ) ) )
& ( ( ^ [X92: $i > $i > $o] :
! [X93: $i,X94: $i,X95: $i] :
( ~ ( X92 @ X95 @ X93 )
| ~ ( X92 @ X95 @ X94 )
| ( X93 = X94 ) ) )
= mpartially_functional )
& ! [X96: d_mu,X97: d_mu] :
( ( ( d2mu @ X96 )
= ( d2mu @ X97 ) )
=> ( X96 = X97 ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( mreflexive
= ( ^ [X15: $i > $i > $o] :
! [X17: $i] : ( X15 @ X17 @ X17 ) ) )
& ( mequiv
= ( ^ [X11: $i > $o,X12: $i > $o,X13: $i] :
~ ( ~ ( ~ ( X12 @ X13 )
| ( X11 @ X13 ) )
| ~ ( ( X12 @ X13 )
| ~ ( X11 @ X13 ) ) ) ) )
& ( msatisfiable
= ( ^ [X11: $i > $o] :
~ ! [X10: $i] :
~ ( X11 @ X10 ) ) )
& ! [X1: d_unsorted] : ( d_unsorted_0 = X1 )
& ( ( ^ [X15: $i > $i > $o] :
! [X0: $i,X18: $i,X17: $i] :
( ~ ! [X16: $i] :
( ~ ( X15 @ X18 @ X16 )
| ~ ( X15 @ X0 @ X16 ) )
| ~ ( X15 @ X17 @ X18 )
| ~ ( X15 @ X17 @ X0 ) ) )
= mweakly_directed )
& ( ( ^ [X11: mu > $i > $o,X10: $i] :
! [X8: mu] : ( X11 @ X8 @ X10 ) )
= mforall_ind )
& ( meq_ind @ ( d2mu @ d_mu_0 ) @ ( d2mu @ d_mu_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
& ( mfunctional
= ( ^ [X15: $i > $i > $o] :
! [X17: $i] :
~ ! [X18: $i] :
( ~ ! [X0: $i] :
( ~ ( X15 @ X17 @ X0 )
| ( X0 = X18 ) )
| ~ ( X15 @ X17 @ X18 ) ) ) )
& ( mimplies
= ( ^ [X11: $i > $o,X12: $i > $o,X13: $i] :
( ( X12 @ X13 )
| ~ ( X11 @ X13 ) ) ) )
& ( mxor
= ( ^ [X11: $i > $o,X12: $i > $o,X13: $i] :
( ~ ( ~ ( X11 @ X13 )
| ( X12 @ X13 ) )
| ~ ( ~ ( X12 @ X13 )
| ( X11 @ X13 ) ) ) ) )
& ! [X5: d_mu] : ( d_mu_0 = X5 )
& ( meq_prop
= ( ^ [X8: $i > $o,X9: $i > $o,X10: $i] :
( ( X8 @ X10 )
= ( X9 @ X10 ) ) ) )
& ( ( ^ [X15: $i > $i > $o] :
! [X0: $i,X17: $i,X18: $i] :
( ( X15 @ X18 @ X0 )
| ( X15 @ X0 @ X18 )
| ( X0 = X18 )
| ~ ( X15 @ X17 @ X0 )
| ~ ( X15 @ X17 @ X18 ) ) )
= mweakly_connected )
& ( ( ^ [X11: $i > $o,X12: $i > $o,X13: $i] :
( ( X11 @ X13 )
| ~ ( X12 @ X13 ) ) )
= mimplied )
& ( mtransitive
= ( ^ [X15: $i > $i > $o] :
! [X17: $i,X0: $i,X18: $i] :
( ~ ( X15 @ X17 @ X18 )
| ~ ( X15 @ X18 @ X0 )
| ( X15 @ X17 @ X0 ) ) ) )
& ! [X3: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X2 )
= ( d2unsorted @ X3 ) )
=> ( X2 = X3 ) )
& ( meuclidean
= ( ^ [X15: $i > $i > $o] :
! [X0: $i,X17: $i,X18: $i] :
( ( X15 @ X18 @ X0 )
| ~ ( X15 @ X17 @ X18 )
| ~ ( X15 @ X17 @ X0 ) ) ) )
& ( mbox
= ( ^ [X15: $i > $i > $o,X11: $i > $o,X10: $i] :
! [X16: $i] :
( ( X11 @ X16 )
| ~ ( X15 @ X10 @ X16 ) ) ) )
& ( minvalid
= ( ^ [X11: $i > $o] :
! [X10: $i] :
~ ( X11 @ X10 ) ) )
& ( mvalid
= ( ^ [X11: $i > $o] :
! [X10: $i] : ( X11 @ X10 ) ) )
& ! [X0: $i] :
? [X1: d_unsorted] :
( ( d2unsorted @ X1 )
= X0 )
& ( ( ^ [X15: $i > $i > $o,X11: $i > $o,X13: $i] :
~ ! [X16: $i] :
( ~ ( X11 @ X16 )
| ~ ( X15 @ X13 @ X16 ) ) )
= mdia )
& ( ( ^ [X11: $i > $o,X12: $i > $o,X13: $i] :
~ ( ~ ( X11 @ X13 )
| ~ ( X12 @ X13 ) ) )
= mand )
& ( ( ^ [X11: $i > $o,X12: $i > $o,X10: $i] :
( ( X11 @ X10 )
| ( X12 @ X10 ) ) )
= mor )
& ( mcountersatisfiable
= ( ^ [X11: $i > $o] :
~ ! [X10: $i] : ( X11 @ X10 ) ) )
& ( ( ^ [X11: $i > $o,X10: $i] :
~ ( X11 @ X10 ) )
= mnot )
& ( mexists_prop
= ( ^ [X11: ( $i > $o ) > $i > $o,X13: $i] :
~ ! [X14: $i > $o] :
~ ( X11 @ X14 @ X13 ) ) )
& ( msymmetric
= ( ^ [X15: $i > $i > $o] :
! [X17: $i,X18: $i] :
( ~ ( X15 @ X17 @ X18 )
| ( X15 @ X18 @ X17 ) ) ) )
& ~ ( mfalse @ ( d2unsorted @ d_unsorted_0 ) )
& ( mexists_ind
= ( ^ [X11: mu > $i > $o,X13: $i] :
~ ! [X8: mu] :
~ ( X11 @ X8 @ X13 ) ) )
& ( mforall_prop
= ( ^ [X11: ( $i > $o ) > $i > $o,X10: $i] :
! [X14: $i > $o] : ( X11 @ X14 @ X10 ) ) )
& ! [X4: mu] :
? [X5: d_mu] :
( ( d2mu @ X5 )
= X4 )
& ( ( ^ [X15: $i > $i > $o] :
! [X17: $i,X18: $i] :
( ~ ! [X19: $i] :
( ~ ( X15 @ X19 @ X18 )
| ~ ( X15 @ X17 @ X19 ) )
| ~ ( X15 @ X17 @ X18 ) ) )
= mweakly_dense )
& ( mtrue @ ( d2unsorted @ d_unsorted_0 ) )
& ( mserial
= ( ^ [X15: $i > $i > $o] :
! [X17: $i] :
~ ! [X18: $i] :
~ ( X15 @ X17 @ X18 ) ) )
& ( ( ^ [X15: $i > $i > $o] :
! [X18: $i,X0: $i,X17: $i] :
( ~ ( X15 @ X17 @ X18 )
| ~ ( X15 @ X17 @ X0 )
| ( X0 = X18 ) ) )
= mpartially_functional )
& ! [X7: d_mu,X6: d_mu] :
( ( ( d2mu @ X6 )
= ( d2mu @ X7 ) )
=> ( X6 = X7 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.5NVEwxc0Z5/DTF2THF_27794.p',lcl698_1) ).
thf(f25,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( ~ ( Y1 @ Y2 )
| ~ ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f38,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
~ ( ~ ( ~ ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
| ~ ( ( Y0 @ Y2 )
| ~ ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f17,plain,
( mequiv
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( mequiv
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( mequiv
!= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) )
!= mequiv ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
( ( ^ [X11: $i > $o,X12: $i > $o] : ( mand @ ( mimplies @ X11 @ X12 ) @ ( mimplies @ X12 @ X11 ) ) )
!= mequiv ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( ( ^ [X11: $i > $o,X12: $i > $o] : ( mand @ ( mimplies @ X11 @ X12 ) @ ( mimplies @ X12 @ X11 ) ) )
= mequiv ),
file('/export/starexec/sandbox2/tmp/tmp.5NVEwxc0Z5/DTF2THF_27794.p',mequiv) ).
thf(f306,plain,
( spl2_2
| spl2_4 ),
inference(avatar_split_clause,[status(thm)],[f247,f297,f289]) ).
thf(f247,plain,
( ( $false
= ( sK5 @ sK6 ) )
| ( $false
= ( sK4 @ sK6 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f246]) ).
thf(f246,plain,
( ( $false
= ( sK4 @ sK6 ) )
| ( $false
= ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f245]) ).
thf(f245,plain,
( ( $false
= ( sK4 @ sK6 ) )
| ( $false
= ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) )
| ( $false
= ( sK4 @ sK6 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f243]) ).
thf(f243,plain,
( ( ( ( sK4 @ sK6 )
| ~ ( sK5 @ sK6 ) )
= $false )
| ( $false
= ( sK4 @ sK6 ) )
| ( $false
= ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f242]) ).
thf(f242,plain,
( ( $false
= ( sK4 @ sK6 ) )
| ( $true
= ( ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) ) )
| ( ( ( sK4 @ sK6 )
| ~ ( sK5 @ sK6 ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f225]) ).
thf(f225,plain,
( ( ( ~ ( ( sK4 @ sK6 )
| ~ ( sK5 @ sK6 ) ) )
= $true )
| ( $false
= ( sK4 @ sK6 ) )
| ( $true
= ( ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f224]) ).
thf(f302,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f270,f289,f285]) ).
thf(f270,plain,
( ( $false
= ( sK4 @ sK6 ) )
| ( $true
= ( sK5 @ sK6 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f269]) ).
thf(f269,plain,
( ( $true
= ( sK5 @ sK6 ) )
| ( $true
= ( ~ ( sK4 @ sK6 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f268]) ).
thf(f268,plain,
( $true
= ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f267]) ).
thf(f267,plain,
( ( $true
= ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) )
| ( $true
= ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f260]) ).
thf(f260,plain,
( ( $false
= ( ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) ) )
| ( $true
= ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f259]) ).
thf(f259,plain,
( ( ( ~ ( ~ ( sK5 @ sK6 )
| ( sK4 @ sK6 ) )
| ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) )
= $false )
| ( $true
= ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f258]) ).
thf(f258,plain,
( ( $false
= ( ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) ) )
| ( ( ~ ( ~ ( sK5 @ sK6 )
| ( sK4 @ sK6 ) )
| ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f256]) ).
thf(f256,plain,
( ( $false
= ( ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) )
| ~ ( ( sK4 @ sK6 )
| ~ ( sK5 @ sK6 ) ) ) )
| ( ( ~ ( ~ ( sK5 @ sK6 )
| ( sK4 @ sK6 ) )
| ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f255]) ).
thf(f255,plain,
( ( ( ~ ( ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) )
| ~ ( ( sK4 @ sK6 )
| ~ ( sK5 @ sK6 ) ) ) )
= $true )
| ( ( ~ ( ~ ( sK5 @ sK6 )
| ( sK4 @ sK6 ) )
| ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f217]) ).
thf(f217,plain,
( ( ( ~ ( ~ ( ~ ( sK5 @ sK6 )
| ( sK4 @ sK6 ) )
| ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) )
| ~ ( ( sK4 @ sK6 )
| ~ ( sK5 @ sK6 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f216]) ).
thf(f301,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[status(thm)],[f278,f297,f293]) ).
thf(f278,plain,
( ( ( sK4 @ sK6 )
= $true )
| ( $false
= ( sK5 @ sK6 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f277]) ).
thf(f277,plain,
( ( ( ~ ( sK5 @ sK6 ) )
= $true )
| ( ( sK4 @ sK6 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f276]) ).
thf(f276,plain,
( ( ( ~ ( sK5 @ sK6 ) )
= $true )
| ( ( sK4 @ sK6 )
= $true )
| ( ( sK4 @ sK6 )
= $true )
| ( ( ~ ( sK5 @ sK6 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f275]) ).
thf(f275,plain,
( ( ( ~ ( sK5 @ sK6 )
| ( sK4 @ sK6 ) )
= $true )
| ( ( ~ ( sK5 @ sK6 ) )
= $true )
| ( ( sK4 @ sK6 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f274]) ).
thf(f274,plain,
( ( ( ( sK4 @ sK6 )
| ~ ( sK5 @ sK6 ) )
= $true )
| ( ( ~ ( sK5 @ sK6 )
| ( sK4 @ sK6 ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f273]) ).
thf(f273,plain,
( ( ( ~ ( ~ ( sK5 @ sK6 )
| ( sK4 @ sK6 ) ) )
= $false )
| ( ( ( sK4 @ sK6 )
| ~ ( sK5 @ sK6 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f271]) ).
thf(f271,plain,
( ( ( ~ ( ~ ( sK5 @ sK6 )
| ( sK4 @ sK6 ) )
| ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) )
= $false )
| ( ( ( sK4 @ sK6 )
| ~ ( sK5 @ sK6 ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f257]) ).
thf(f257,plain,
( ( ( ~ ( ( sK4 @ sK6 )
| ~ ( sK5 @ sK6 ) ) )
= $false )
| ( ( ~ ( ~ ( sK5 @ sK6 )
| ( sK4 @ sK6 ) )
| ~ ( ~ ( sK4 @ sK6 )
| ( sK5 @ sK6 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f256]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n014.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 May 5 09:27:36 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.30/0.46 % Domain : Software Verification
% 0.30/0.46 % Problem : Benchmark: LCL698^1, Active target: mequiv
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [Kon26] Kondylidou (2026), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Kon26]
% 0.30/0.46 % Names : ALG444^1__005__axclos.verify [Kon26]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : ? v9.3.0
% 0.30/0.46 % Syntax : Number of formulae : 41 ( 1 unt; 39 typ; 0 def)
% 0.30/0.46 % Number of atoms : 76 ( 41 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 39 ( 38 avg)
% 0.30/0.46 % Number of connectives : 229 ( 52 ~; 30 |; 36 &; 109 @)
% 0.30/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 40 ( 21 avg)
% 0.30/0.46 % Number of types : 6 ( 4 usr)
% 0.30/0.46 % Number of type conns : 172 ( 172 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 36 ( 35 usr; 2 con; 0-3 aty)
% 0.30/0.46 % Number of variables : 100 ( 53 ^; 45 !; 2 ?; 100 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments :
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(unsorted_type,type,
% 0.30/0.46 unsorted: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(mu_type,type,
% 0.30/0.46 mu: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(meq_ind_decl,type,
% 0.30/0.46 meq_ind: mu > mu > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(meq_prop_decl,type,
% 0.30/0.46 meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mnot_decl,type,
% 0.30/0.46 mnot: ( $i > $o ) > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mor_decl,type,
% 0.30/0.46 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mand_decl,type,
% 0.30/0.46 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mimplies_decl,type,
% 0.30/0.46 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mimplied_decl,type,
% 0.30/0.46 mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mequiv_decl,type,
% 0.30/0.46 mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mxor_decl,type,
% 0.30/0.46 mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mforall_ind_decl,type,
% 0.30/0.46 mforall_ind: ( mu > $i > $o ) > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mforall_prop_decl,type,
% 0.30/0.46 mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mexists_ind_decl,type,
% 0.30/0.46 mexists_ind: ( mu > $i > $o ) > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mexists_prop_decl,type,
% 0.30/0.46 mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mtrue_decl,type,
% 0.30/0.46 mtrue: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mfalse_decl,type,
% 0.30/0.46 mfalse: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mbox_decl,type,
% 0.30/0.46 mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mdia_decl,type,
% 0.30/0.46 mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mreflexive_decl,type,
% 0.30/0.46 mreflexive: ( $i > $i > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(msymmetric_decl,type,
% 0.30/0.46 msymmetric: ( $i > $i > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mserial_decl,type,
% 0.30/0.46 mserial: ( $i > $i > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mtransitive_decl,type,
% 0.30/0.46 mtransitive: ( $i > $i > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(meuclidean_decl,type,
% 0.30/0.46 meuclidean: ( $i > $i > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mpartially_functional_decl,type,
% 0.30/0.46 mpartially_functional: ( $i > $i > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mfunctional_decl,type,
% 0.30/0.46 mfunctional: ( $i > $i > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mweakly_dense_decl,type,
% 0.30/0.46 mweakly_dense: ( $i > $i > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mweakly_connected_decl,type,
% 0.30/0.46 mweakly_connected: ( $i > $i > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mweakly_directed_decl,type,
% 0.30/0.46 mweakly_directed: ( $i > $i > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mvalid_decl,type,
% 0.30/0.46 mvalid: ( $i > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(minvalid_decl,type,
% 0.30/0.46 minvalid: ( $i > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(msatisfiable_decl,type,
% 0.30/0.46 msatisfiable: ( $i > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mcountersatisfiable_decl,type,
% 0.30/0.46 mcountersatisfiable: ( $i > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 %----Types of the domains
% 0.30/0.46 thf(d_unsorted_type,type,
% 0.30/0.46 d_unsorted: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(d_mu_type,type,
% 0.30/0.46 d_mu: $tType ).
% 0.30/0.46
% 0.30/0.46 %----Types of the promotion functions
% 0.30/0.46 thf(d2unsorted_decl,type,
% 0.30/0.46 d2unsorted: d_unsorted > $i ).
% 0.30/0.46
% 0.30/0.46 thf(d2mu_decl,type,
% 0.30/0.46 d2mu: d_mu > mu ).
% 0.30/0.46
% 0.30/0.46 %----Types of the domain elements
% 0.30/0.46 thf(d_unsorted_0_decl,type,
% 0.30/0.46 d_unsorted_0: d_unsorted ).
% 0.30/0.46
% 0.30/0.46 thf(d_mu_0_decl,type,
% 0.30/0.46 d_mu_0: d_mu ).
% 0.30/0.46
% 0.30/0.46 thf(lcl698_1,axiom,
% 0.30/0.46 ( ! [U: $i] :
% 0.30/0.46 ? [DU: d_unsorted] :
% 0.30/0.46 ( U
% 0.30/0.46 = ( d2unsorted @ DU ) )
% 0.30/0.46 & ! [DU: d_unsorted] : ( DU = d_unsorted_0 )
% 0.30/0.46 & ! [DU1: d_unsorted,DU2: d_unsorted] :
% 0.30/0.46 ( ( ( d2unsorted @ DU1 )
% 0.30/0.46 = ( d2unsorted @ DU2 ) )
% 0.30/0.46 => ( DU1 = DU2 ) )
% 0.30/0.46 & ! [M: mu] :
% 0.30/0.46 ? [DM: d_mu] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( d2mu @ DM ) )
% 0.30/0.46 & ! [DM: d_mu] : ( DM = d_mu_0 )
% 0.30/0.46 & ! [DM1: d_mu,DM2: d_mu] :
% 0.30/0.46 ( ( ( d2mu @ DM1 )
% 0.30/0.46 = ( d2mu @ DM2 ) )
% 0.30/0.46 => ( DM1 = DM2 ) )
% 0.30/0.46 & ( meq_prop
% 0.30/0.46 = ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
% 0.30/0.46 ( ( X @ W )
% 0.30/0.46 = ( Y @ W ) ) ) )
% 0.30/0.46 & ( mnot
% 0.30/0.46 = ( ^ [Phi: $i > $o,W: $i] :
% 0.30/0.46 ~ ( Phi @ W ) ) )
% 0.30/0.46 & ( mor
% 0.30/0.46 = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
% 0.30/0.46 ( ( Phi @ W )
% 0.30/0.46 | ( Psi @ W ) ) ) )
% 0.30/0.46 & ( mand
% 0.30/0.46 = ( ^ [Phi: $i > $o,Psi: $i > $o,Flatten_var_0: $i] :
% 0.30/0.46 ~ ( ~ ( Phi @ Flatten_var_0 )
% 0.30/0.46 | ~ ( Psi @ Flatten_var_0 ) ) ) )
% 0.30/0.46 & ( mimplies
% 0.30/0.46 = ( ^ [Phi: $i > $o,Psi: $i > $o,Flatten_var_0: $i] :
% 0.30/0.46 ( ~ ( Phi @ Flatten_var_0 )
% 0.30/0.46 | ( Psi @ Flatten_var_0 ) ) ) )
% 0.30/0.46 & ( mimplied
% 0.30/0.46 = ( ^ [Phi: $i > $o,Psi: $i > $o,Flatten_var_0: $i] :
% 0.30/0.46 ( ~ ( Psi @ Flatten_var_0 )
% 0.30/0.46 | ( Phi @ Flatten_var_0 ) ) ) )
% 0.30/0.46 & ( mequiv
% 0.30/0.46 = ( ^ [Phi: $i > $o,Psi: $i > $o,Flatten_var_0: $i] :
% 0.30/0.46 ~ ( ~ ( ~ ( Phi @ Flatten_var_0 )
% 0.30/0.46 | ( Psi @ Flatten_var_0 ) )
% 0.30/0.46 | ~ ( ~ ( Psi @ Flatten_var_0 )
% 0.30/0.46 | ( Phi @ Flatten_var_0 ) ) ) ) )
% 0.30/0.46 & ( mxor
% 0.30/0.46 = ( ^ [Phi: $i > $o,Psi: $i > $o,Flatten_var_0: $i] :
% 0.30/0.46 ( ~ ( ~ ( Phi @ Flatten_var_0 )
% 0.30/0.46 | ( Psi @ Flatten_var_0 ) )
% 0.30/0.46 | ~ ( ~ ( Psi @ Flatten_var_0 )
% 0.30/0.46 | ( Phi @ Flatten_var_0 ) ) ) ) )
% 0.30/0.46 & ( mforall_ind
% 0.30/0.46 = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.30/0.46 ! [X: mu] : ( Phi @ X @ W ) ) )
% 0.30/0.46 & ( mforall_prop
% 0.30/0.46 = ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
% 0.30/0.46 ! [P: $i > $o] : ( Phi @ P @ W ) ) )
% 0.30/0.46 & ( mexists_ind
% 0.30/0.46 = ( ^ [Phi: mu > $i > $o,Flatten_var_0: $i] :
% 0.30/0.46 ~ ! [X: mu] :
% 0.30/0.46 ~ ( Phi @ X @ Flatten_var_0 ) ) )
% 0.30/0.46 & ( mexists_prop
% 0.30/0.46 = ( ^ [Phi: ( $i > $o ) > $i > $o,Flatten_var_0: $i] :
% 0.30/0.46 ~ ! [P: $i > $o] :
% 0.30/0.46 ~ ( Phi @ P @ Flatten_var_0 ) ) )
% 0.30/0.46 & ( mbox
% 0.30/0.46 = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
% 0.30/0.46 ! [V: $i] :
% 0.30/0.46 ( ~ ( R @ W @ V )
% 0.30/0.46 | ( Phi @ V ) ) ) )
% 0.30/0.46 & ( mdia
% 0.30/0.46 = ( ^ [R: $i > $i > $o,Phi: $i > $o,Flatten_var_0: $i] :
% 0.30/0.46 ~ ! [V: $i] :
% 0.30/0.46 ( ~ ( R @ Flatten_var_0 @ V )
% 0.30/0.46 | ~ ( Phi @ V ) ) ) )
% 0.30/0.46 & ( mreflexive
% 0.30/0.46 = ( ^ [R: $i > $i > $o] :
% 0.30/0.46 ! [S: $i] : ( R @ S @ S ) ) )
% 0.30/0.46 & ( msymmetric
% 0.30/0.46 = ( ^ [R: $i > $i > $o] :
% 0.30/0.46 ! [S: $i,T: $i] :
% 0.30/0.46 ( ~ ( R @ S @ T )
% 0.30/0.46 | ( R @ T @ S ) ) ) )
% 0.30/0.46 & ( mserial
% 0.30/0.46 = ( ^ [R: $i > $i > $o] :
% 0.30/0.46 ! [S: $i] :
% 0.30/0.46 ~ ! [T: $i] :
% 0.30/0.46 ~ ( R @ S @ T ) ) )
% 0.30/0.46 & ( mtransitive
% 0.30/0.46 = ( ^ [R: $i > $i > $o] :
% 0.30/0.46 ! [S: $i,T: $i,U: $i] :
% 0.30/0.46 ( ~ ( R @ S @ T )
% 0.30/0.46 | ~ ( R @ T @ U )
% 0.30/0.46 | ( R @ S @ U ) ) ) )
% 0.30/0.46 & ( meuclidean
% 0.30/0.46 = ( ^ [R: $i > $i > $o] :
% 0.30/0.46 ! [S: $i,T: $i,U: $i] :
% 0.30/0.46 ( ~ ( R @ S @ T )
% 0.30/0.46 | ~ ( R @ S @ U )
% 0.30/0.46 | ( R @ T @ U ) ) ) )
% 0.30/0.46 & ( mpartially_functional
% 0.30/0.46 = ( ^ [R: $i > $i > $o] :
% 0.30/0.46 ! [S: $i,T: $i,U: $i] :
% 0.30/0.46 ( ~ ( R @ S @ T )
% 0.30/0.46 | ~ ( R @ S @ U )
% 0.30/0.46 | ( T = U ) ) ) )
% 0.30/0.46 & ( mfunctional
% 0.30/0.46 = ( ^ [R: $i > $i > $o] :
% 0.30/0.46 ! [S: $i] :
% 0.30/0.46 ~ ! [T: $i] :
% 0.30/0.46 ( ~ ( R @ S @ T )
% 0.30/0.46 | ~ ! [U: $i] :
% 0.30/0.46 ( ~ ( R @ S @ U )
% 0.30/0.46 | ( T = U ) ) ) ) )
% 0.30/0.46 & ( mweakly_dense
% 0.30/0.46 = ( ^ [R: $i > $i > $o] :
% 0.30/0.46 ! [S: $i,T: $i] :
% 0.30/0.46 ( ~ ( R @ S @ T )
% 0.30/0.46 | ~ ! [Bound_variable_953: $i] :
% 0.30/0.46 ( ~ ( R @ S @ Bound_variable_953 )
% 0.30/0.46 | ~ ( R @ Bound_variable_953 @ T ) ) ) ) )
% 0.30/0.46 & ( mweakly_connected
% 0.30/0.46 = ( ^ [R: $i > $i > $o] :
% 0.30/0.46 ! [S: $i,T: $i,U: $i] :
% 0.30/0.46 ( ~ ( R @ S @ T )
% 0.30/0.46 | ~ ( R @ S @ U )
% 0.30/0.46 | ( R @ T @ U )
% 0.30/0.46 | ( T = U )
% 0.30/0.46 | ( R @ U @ T ) ) ) )
% 0.30/0.46 & ( mweakly_directed
% 0.30/0.46 = ( ^ [R: $i > $i > $o] :
% 0.30/0.46 ! [S: $i,T: $i,U: $i] :
% 0.30/0.46 ( ~ ( R @ S @ T )
% 0.30/0.46 | ~ ( R @ S @ U )
% 0.30/0.46 | ~ ! [V: $i] :
% 0.30/0.46 ( ~ ( R @ T @ V )
% 0.30/0.46 | ~ ( R @ U @ V ) ) ) ) )
% 0.30/0.46 & ( mvalid
% 0.30/0.46 = ( ^ [Phi: $i > $o] :
% 0.30/0.46 ! [W: $i] : ( Phi @ W ) ) )
% 0.30/0.46 & ( minvalid
% 0.30/0.46 = ( ^ [Phi: $i > $o] :
% 0.30/0.46 ! [W: $i] :
% 0.30/0.46 ~ ( Phi @ W ) ) )
% 0.30/0.46 & ( msatisfiable
% 0.30/0.46 = ( ^ [Phi: $i > $o] :
% 0.30/0.46 ~ ! [W: $i] :
% 0.30/0.46 ~ ( Phi @ W ) ) )
% 0.30/0.46 & ( mcountersatisfiable
% 0.30/0.46 = ( ^ [Phi: $i > $o] :
% 0.30/0.46 ~ ! [W: $i] : ( Phi @ W ) ) )
% 0.30/0.46 & ( meq_ind @ ( d2mu @ d_mu_0 ) @ ( d2mu @ d_mu_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
% 0.30/0.46 & ( mtrue @ ( d2unsorted @ d_unsorted_0 ) )
% 0.30/0.46 & ~ ( mfalse @ ( d2unsorted @ d_unsorted_0 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mequiv,conjecture,
% 0.30/0.46 ( mequiv
% 0.30/0.46 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.59/1.29 ---- Embedded in THF ---
% 1.59/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.59/1.29 %%% Generated on Tue May 05 09:27:37 EDT 2026
% 1.59/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.59/1.29 %%% Logic specification used:
% 1.59/1.29 %%% thf(spec, logic, $$dhol).
% 1.59/1.29
% 1.59/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.5NVEwxc0Z5/DTF2DTF27794.p
% See solution above
% 1.59/1.29 ------------------------
% 1.82/1.30 ---- Cleaned THF ---
% 1.82/1.30 thf(unsorted_type,type,
% 1.82/1.30 unsorted: $tType ).
% 1.82/1.30
% 1.82/1.30 thf(mu_type,type,
% 1.82/1.30 mu: $tType ).
% 1.82/1.30
% 1.82/1.30 thf(meq_ind_decl,type,
% 1.82/1.30 meq_ind: mu > mu > $i > $o ).
% 1.82/1.30
% 1.82/1.30 thf(meq_prop_decl,type,
% 1.82/1.30 meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.82/1.30
% 1.82/1.30 thf(mnot_decl,type,
% 1.82/1.30 mnot: ( $i > $o ) > $i > $o ).
% 1.82/1.30
% 1.82/1.30 thf(mor_decl,type,
% 1.82/1.30 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.82/1.30
% 1.82/1.30 thf(mand_decl,type,
% 1.82/1.30 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.82/1.30
% 1.82/1.30 thf(mimplies_decl,type,
% 1.82/1.30 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.82/1.30
% 1.82/1.30 thf(mimplied_decl,type,
% 1.82/1.30 mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.82/1.30
% 1.82/1.30 thf(mequiv_decl,type,
% 1.82/1.30 mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.82/1.30
% 1.82/1.30 thf(mxor_decl,type,
% 1.82/1.30 mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.82/1.30
% 1.82/1.30 thf(mforall_ind_decl,type,
% 1.82/1.30 mforall_ind: ( mu > $i > $o ) > $i > $o ).
% 1.82/1.30
% 1.82/1.30 thf(mforall_prop_decl,type,
% 1.82/1.30 mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 1.82/1.30
% 1.82/1.30 thf(mexists_ind_decl,type,
% 1.82/1.30 mexists_ind: ( mu > $i > $o ) > $i > $o ).
% 1.82/1.30
% 1.82/1.30 thf(mexists_prop_decl,type,
% 1.82/1.30 mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 1.82/1.30
% 1.82/1.30 thf(mtrue_decl,type,
% 1.82/1.30 mtrue: $i > $o ).
% 1.82/1.30
% 1.82/1.30 thf(mfalse_decl,type,
% 1.82/1.30 mfalse: $i > $o ).
% 1.82/1.30
% 1.82/1.30 thf(mbox_decl,type,
% 1.82/1.30 mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.82/1.30
% 1.82/1.30 thf(mdia_decl,type,
% 1.82/1.30 mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 1.82/1.30
% 1.82/1.30 thf(mreflexive_decl,type,
% 1.82/1.30 mreflexive: ( $i > $i > $o ) > $o ).
% 1.82/1.30
% 1.82/1.30 thf(msymmetric_decl,type,
% 1.82/1.30 msymmetric: ( $i > $i > $o ) > $o ).
% 1.82/1.30
% 1.82/1.30 thf(mserial_decl,type,
% 1.82/1.30 mserial: ( $i > $i > $o ) > $o ).
% 1.82/1.30
% 1.82/1.30 thf(mtransitive_decl,type,
% 1.82/1.30 mtransitive: ( $i > $i > $o ) > $o ).
% 1.82/1.30
% 1.82/1.30 thf(meuclidean_decl,type,
% 1.82/1.30 meuclidean: ( $i > $i > $o ) > $o ).
% 1.82/1.30
% 1.82/1.30 thf(mpartially_functional_decl,type,
% 1.82/1.30 mpartially_functional: ( $i > $i > $o ) > $o ).
% 1.82/1.30
% 1.82/1.30 thf(mfunctional_decl,type,
% 1.82/1.30 mfunctional: ( $i > $i > $o ) > $o ).
% 1.82/1.30
% 1.82/1.30 thf(mweakly_dense_decl,type,
% 1.82/1.30 mweakly_dense: ( $i > $i > $o ) > $o ).
% 1.82/1.30
% 1.82/1.30 thf(mweakly_connected_decl,type,
% 1.82/1.30 mweakly_connected: ( $i > $i > $o ) > $o ).
% 1.82/1.30
% 1.82/1.30 thf(mweakly_directed_decl,type,
% 1.82/1.30 mweakly_directed: ( $i > $i > $o ) > $o ).
% 1.82/1.30
% 1.82/1.30 thf(mvalid_decl,type,
% 1.82/1.30 mvalid: ( $i > $o ) > $o ).
% 1.82/1.30
% 1.82/1.30 thf(minvalid_decl,type,
% 1.82/1.30 minvalid: ( $i > $o ) > $o ).
% 1.82/1.30
% 1.82/1.30 thf(msatisfiable_decl,type,
% 1.82/1.30 msatisfiable: ( $i > $o ) > $o ).
% 1.82/1.30
% 1.82/1.30 thf(mcountersatisfiable_decl,type,
% 1.82/1.30 mcountersatisfiable: ( $i > $o ) > $o ).
% 1.82/1.30
% 1.82/1.30 thf(d_unsorted_type,type,
% 1.82/1.30 d_unsorted: $tType ).
% 1.82/1.30
% 1.82/1.30 thf(d_mu_type,type,
% 1.82/1.30 d_mu: $tType ).
% 1.82/1.30
% 1.82/1.30 thf(d2unsorted_decl,type,
% 1.82/1.30 d2unsorted: d_unsorted > $i ).
% 1.82/1.30
% 1.82/1.30 thf(d2mu_decl,type,
% 1.82/1.30 d2mu: d_mu > mu ).
% 1.82/1.30
% 1.82/1.30 thf(d_unsorted_0_decl,type,
% 1.82/1.30 d_unsorted_0: d_unsorted ).
% 1.82/1.30
% 1.82/1.30 thf(d_mu_0_decl,type,
% 1.82/1.30 d_mu_0: d_mu ).
% 1.82/1.30
% 1.82/1.30 thf(lcl698_1,axiom,
% 1.82/1.30 ( ! [U: $i] :
% 1.82/1.30 ? [DU: d_unsorted] :
% 1.82/1.30 ( U
% 1.82/1.30 = ( d2unsorted @ DU ) )
% 1.82/1.30 & ! [DU: d_unsorted] : ( DU = d_unsorted_0 )
% 1.82/1.30 & ! [DU1: d_unsorted,DU2: d_unsorted] :
% 1.82/1.30 ( ( ( d2unsorted @ DU1 )
% 1.82/1.30 = ( d2unsorted @ DU2 ) )
% 1.82/1.30 => ( DU1 = DU2 ) )
% 1.82/1.30 & ! [M: mu] :
% 1.82/1.30 ? [DM: d_mu] :
% 1.82/1.30 ( M
% 1.82/1.30 = ( d2mu @ DM ) )
% 1.82/1.30 & ! [DM: d_mu] : ( DM = d_mu_0 )
% 1.82/1.30 & ! [DM1: d_mu,DM2: d_mu] :
% 1.82/1.30 ( ( ( d2mu @ DM1 )
% 1.82/1.30 = ( d2mu @ DM2 ) )
% 1.82/1.30 => ( DM1 = DM2 ) )
% 1.82/1.30 & ( meq_prop
% 1.82/1.30 = ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
% 1.82/1.30 ( ( X @ W )
% 1.82/1.30 = ( Y @ W ) ) ) )
% 1.82/1.30 & ( mnot
% 1.82/1.30 = ( ^ [Phi: $i > $o,W: $i] :
% 1.82/1.30 ~ ( Phi @ W ) ) )
% 1.82/1.30 & ( mor
% 1.82/1.30 = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
% 1.82/1.30 ( ( Phi @ W )
% 1.82/1.30 | ( Psi @ W ) ) ) )
% 1.82/1.30 & ( mand
% 1.82/1.30 = ( ^ [Phi: $i > $o,Psi: $i > $o,Flatten_var_0: $i] :
% 1.82/1.30 ~ ( ~ ( Phi @ Flatten_var_0 )
% 1.82/1.30 | ~ ( Psi @ Flatten_var_0 ) ) ) )
% 1.82/1.30 & ( mimplies
% 1.82/1.30 = ( ^ [Phi: $i > $o,Psi: $i > $o,Flatten_var_0: $i] :
% 1.82/1.30 ( ~ ( Phi @ Flatten_var_0 )
% 1.82/1.30 | ( Psi @ Flatten_var_0 ) ) ) )
% 1.82/1.30 & ( mimplied
% 1.82/1.30 = ( ^ [Phi: $i > $o,Psi: $i > $o,Flatten_var_0: $i] :
% 1.82/1.30 ( ~ ( Psi @ Flatten_var_0 )
% 1.82/1.30 | ( Phi @ Flatten_var_0 ) ) ) )
% 1.82/1.30 & ( mequiv
% 1.82/1.30 = ( ^ [Phi: $i > $o,Psi: $i > $o,Flatten_var_0: $i] :
% 1.82/1.30 ~ ( ~ ( ~ ( Phi @ Flatten_var_0 )
% 1.82/1.30 | ( Psi @ Flatten_var_0 ) )
% 1.82/1.30 | ~ ( ~ ( Psi @ Flatten_var_0 )
% 1.82/1.30 | ( Phi @ Flatten_var_0 ) ) ) ) )
% 1.82/1.30 & ( mxor
% 1.82/1.30 = ( ^ [Phi: $i > $o,Psi: $i > $o,Flatten_var_0: $i] :
% 1.82/1.30 ( ~ ( ~ ( Phi @ Flatten_var_0 )
% 1.82/1.30 | ( Psi @ Flatten_var_0 ) )
% 1.82/1.30 | ~ ( ~ ( Psi @ Flatten_var_0 )
% 1.82/1.30 | ( Phi @ Flatten_var_0 ) ) ) ) )
% 1.82/1.30 & ( mforall_ind
% 1.82/1.30 = ( ^ [Phi: mu > $i > $o,W: $i] :
% 1.82/1.30 ! [X: mu] : ( Phi @ X @ W ) ) )
% 1.82/1.30 & ( mforall_prop
% 1.82/1.30 = ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
% 1.82/1.30 ! [P: $i > $o] : ( Phi @ P @ W ) ) )
% 1.82/1.30 & ( mexists_ind
% 1.82/1.30 = ( ^ [Phi: mu > $i > $o,Flatten_var_0: $i] :
% 1.82/1.30 ~ ! [X: mu] :
% 1.82/1.30 ~ ( Phi @ X @ Flatten_var_0 ) ) )
% 1.82/1.30 & ( mexists_prop
% 1.82/1.30 = ( ^ [Phi: ( $i > $o ) > $i > $o,Flatten_var_0: $i] :
% 1.82/1.30 ~ ! [P: $i > $o] :
% 1.82/1.30 ~ ( Phi @ P @ Flatten_var_0 ) ) )
% 1.82/1.30 & ( mbox
% 1.82/1.30 = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
% 1.82/1.30 ! [V: $i] :
% 1.82/1.30 ( ~ ( R @ W @ V )
% 1.82/1.30 | ( Phi @ V ) ) ) )
% 1.82/1.30 & ( mdia
% 1.82/1.30 = ( ^ [R: $i > $i > $o,Phi: $i > $o,Flatten_var_0: $i] :
% 1.82/1.31 ~ ! [V: $i] :
% 1.82/1.31 ( ~ ( R @ Flatten_var_0 @ V )
% 1.82/1.31 | ~ ( Phi @ V ) ) ) )
% 1.82/1.31 & ( mreflexive
% 1.82/1.31 = ( ^ [R: $i > $i > $o] :
% 1.82/1.31 ! [S: $i] : ( R @ S @ S ) ) )
% 1.82/1.31 & ( msymmetric
% 1.82/1.31 = ( ^ [R: $i > $i > $o] :
% 1.82/1.31 ! [S: $i,T: $i] :
% 1.82/1.31 ( ~ ( R @ S @ T )
% 1.82/1.31 | ( R @ T @ S ) ) ) )
% 1.82/1.31 & ( mserial
% 1.82/1.31 = ( ^ [R: $i > $i > $o] :
% 1.82/1.31 ! [S: $i] :
% 1.82/1.31 ~ ! [T: $i] :
% 1.82/1.31 ~ ( R @ S @ T ) ) )
% 1.82/1.31 & ( mtransitive
% 1.82/1.31 = ( ^ [R: $i > $i > $o] :
% 1.82/1.31 ! [S: $i,T: $i,U: $i] :
% 1.82/1.31 ( ~ ( R @ S @ T )
% 1.82/1.31 | ~ ( R @ T @ U )
% 1.82/1.31 | ( R @ S @ U ) ) ) )
% 1.82/1.31 & ( meuclidean
% 1.82/1.31 = ( ^ [R: $i > $i > $o] :
% 1.82/1.31 ! [S: $i,T: $i,U: $i] :
% 1.82/1.31 ( ~ ( R @ S @ T )
% 1.82/1.31 | ~ ( R @ S @ U )
% 1.82/1.31 | ( R @ T @ U ) ) ) )
% 1.82/1.31 & ( mpartially_functional
% 1.82/1.31 = ( ^ [R: $i > $i > $o] :
% 1.82/1.31 ! [S: $i,T: $i,U: $i] :
% 1.82/1.31 ( ~ ( R @ S @ T )
% 1.82/1.31 | ~ ( R @ S @ U )
% 1.82/1.31 | ( T = U ) ) ) )
% 1.82/1.31 & ( mfunctional
% 1.82/1.31 = ( ^ [R: $i > $i > $o] :
% 1.82/1.31 ! [S: $i] :
% 1.82/1.31 ~ ! [T: $i] :
% 1.82/1.31 ( ~ ( R @ S @ T )
% 1.82/1.31 | ~ ! [U: $i] :
% 1.82/1.31 ( ~ ( R @ S @ U )
% 1.82/1.31 | ( T = U ) ) ) ) )
% 1.82/1.31 & ( mweakly_dense
% 1.82/1.31 = ( ^ [R: $i > $i > $o] :
% 1.82/1.31 ! [S: $i,T: $i] :
% 1.82/1.31 ( ~ ( R @ S @ T )
% 1.82/1.31 | ~ ! [Bound_variable_953: $i] :
% 1.82/1.31 ( ~ ( R @ S @ Bound_variable_953 )
% 1.82/1.31 | ~ ( R @ Bound_variable_953 @ T ) ) ) ) )
% 1.82/1.31 & ( mweakly_connected
% 1.82/1.31 = ( ^ [R: $i > $i > $o] :
% 1.82/1.31 ! [S: $i,T: $i,U: $i] :
% 1.82/1.31 ( ~ ( R @ S @ T )
% 1.82/1.31 | ~ ( R @ S @ U )
% 1.82/1.31 | ( R @ T @ U )
% 1.82/1.31 | ( T = U )
% 1.82/1.31 | ( R @ U @ T ) ) ) )
% 1.82/1.31 & ( mweakly_directed
% 1.82/1.31 = ( ^ [R: $i > $i > $o] :
% 1.82/1.31 ! [S: $i,T: $i,U: $i] :
% 1.82/1.31 ( ~ ( R @ S @ T )
% 1.82/1.31 | ~ ( R @ S @ U )
% 1.82/1.31 | ~ ! [V: $i] :
% 1.82/1.31 ( ~ ( R @ T @ V )
% 1.82/1.31 | ~ ( R @ U @ V ) ) ) ) )
% 1.82/1.31 & ( mvalid
% 1.82/1.31 = ( ^ [Phi: $i > $o] :
% 1.82/1.31 ! [W: $i] : ( Phi @ W ) ) )
% 1.82/1.31 & ( minvalid
% 1.82/1.31 = ( ^ [Phi: $i > $o] :
% 1.82/1.31 ! [W: $i] :
% 1.82/1.31 ~ ( Phi @ W ) ) )
% 1.82/1.31 & ( msatisfiable
% 1.82/1.31 = ( ^ [Phi: $i > $o] :
% 1.82/1.31 ~ ! [W: $i] :
% 1.82/1.31 ~ ( Phi @ W ) ) )
% 1.82/1.31 & ( mcountersatisfiable
% 1.82/1.31 = ( ^ [Phi: $i > $o] :
% 1.82/1.31 ~ ! [W: $i] : ( Phi @ W ) ) )
% 1.82/1.31 & ( meq_ind @ ( d2mu @ d_mu_0 ) @ ( d2mu @ d_mu_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
% 1.82/1.31 & ( mtrue @ ( d2unsorted @ d_unsorted_0 ) )
% 1.82/1.31 & ~ ( mfalse @ ( d2unsorted @ d_unsorted_0 ) ) ) ).
% 1.82/1.31
% 1.82/1.31 thf(mequiv,conjecture,
% 1.82/1.31 ( mequiv
% 1.82/1.31 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ) ).
% 1.82/1.31 ------------------------
% 1.82/1.32 % (28013)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27794 for (2999ds/183Mi)
% 1.82/1.32 % (28014)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_27794 for (2999ds/4Mi)
% 1.82/1.32 % (28016)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27794 for (2999ds/2Mi)
% 1.82/1.32 % (28016)Instruction limit reached!
% 1.82/1.32 % (28016)------------------------------
% 1.82/1.32 % (28016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.32 % (28016)Termination reason: Unknown
% 1.82/1.32 % (28016)Termination phase: shuffling
% 1.82/1.32
% 1.82/1.32 % (28016)Memory used [KB]: 1023
% 1.82/1.32 % (28016)Time elapsed: 0.002 s
% 1.82/1.32 % (28016)Instructions burned: 3 (million)
% 1.82/1.32 % (28016)------------------------------
% 1.82/1.32 % (28016)------------------------------
% 1.82/1.32 % (28014)Instruction limit reached!
% 1.82/1.32 % (28014)------------------------------
% 1.82/1.32 % (28014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.32 % (28014)Termination reason: Unknown
% 1.82/1.32 % (28014)Termination phase: Property scanning
% 1.82/1.32
% 1.82/1.32 % (28014)Memory used [KB]: 1151
% 1.82/1.32 % (28014)Time elapsed: 0.003 s
% 1.82/1.32 % (28014)Instructions burned: 7 (million)
% 1.82/1.32 % (28014)------------------------------
% 1.82/1.32 % (28014)------------------------------
% 1.82/1.33 % (28015)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_27794 for (2999ds/27Mi)
% 1.82/1.33 % (28017)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_27794 for (2999ds/2Mi)
% 1.82/1.33 % (28018)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_27794 for (2999ds/275Mi)
% 1.82/1.33 % (28019)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27794 for (2999ds/18Mi)
% 1.82/1.33 % (28017)Instruction limit reached!
% 1.82/1.33 % (28017)------------------------------
% 1.82/1.33 % (28017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.33 % (28017)Termination reason: Unknown
% 1.82/1.33 % (28017)Termination phase: shuffling
% 1.82/1.33
% 1.82/1.33 % (28017)Memory used [KB]: 1023
% 1.82/1.33 % (28017)Time elapsed: 0.004 s
% 1.82/1.33 % (28017)Instructions burned: 3 (million)
% 1.82/1.33 % (28017)------------------------------
% 1.82/1.33 % (28017)------------------------------
% 1.82/1.33 % (28013)First to succeed.
% 1.82/1.33 % (28020)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27794 for (2999ds/3Mi)
% 1.82/1.33 % (28021)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_27794 for (2999ds/37Mi)
% 1.82/1.33 % (28020)Instruction limit reached!
% 1.82/1.33 % (28020)------------------------------
% 1.82/1.33 % (28020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.33 % (28020)Termination reason: Unknown
% 1.82/1.33 % (28020)Termination phase: shuffling
% 1.82/1.33
% 1.82/1.33 % (28020)Memory used [KB]: 1151
% 1.82/1.33 % (28020)Time elapsed: 0.003 s
% 1.82/1.33 % (28020)Instructions burned: 4 (million)
% 1.82/1.33 % (28020)------------------------------
% 1.82/1.33 % (28020)------------------------------
% 1.82/1.33 % (28018)Refutation not found, incomplete strategy
% 1.82/1.33 % (28018)------------------------------
% 1.82/1.33 % (28018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.33 % (28018)Termination reason: Refutation not found, incomplete strategy
% 1.82/1.33
% 1.82/1.33
% 1.82/1.33 % (28018)Memory used [KB]: 5628
% 1.82/1.33 % (28018)Time elapsed: 0.007 s
% 1.82/1.33 % (28018)Instructions burned: 8 (million)
% 1.82/1.33 % (28018)------------------------------
% 1.82/1.33 % (28018)------------------------------
% 1.82/1.34 % (28015)Also succeeded, but the first one will report.
% 1.82/1.34 % (28013)Refutation found. Thanks to Tanya!
% 1.82/1.34 % SZS status Theorem for DTF2THF_27794
% 1.82/1.34 % SZS output start Proof for DTF2THF_27794
% 1.82/1.34 thf(type_def_5, type, mu: $tType).
% 1.82/1.34 thf(type_def_7, type, d_unsorted: $tType).
% 1.82/1.34 thf(type_def_8, type, d_mu: $tType).
% 1.82/1.34 thf(func_def_0, type, unsorted: $tType).
% 1.82/1.34 thf(func_def_1, type, mu: $tType).
% 1.82/1.34 thf(func_def_2, type, meq_ind: mu > mu > $i > $o).
% 1.82/1.34 thf(func_def_3, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 1.82/1.34 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 1.82/1.34 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 1.82/1.34 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 1.82/1.34 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 1.82/1.34 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 1.82/1.34 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 1.82/1.34 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 1.82/1.34 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 1.82/1.34 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 1.82/1.34 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 1.82/1.34 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 1.82/1.34 thf(func_def_15, type, mtrue: $i > $o).
% 1.82/1.34 thf(func_def_16, type, mfalse: $i > $o).
% 1.82/1.34 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 1.82/1.34 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 1.82/1.34 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 1.82/1.34 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 1.82/1.34 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 1.82/1.34 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 1.82/1.34 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 1.82/1.34 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 1.82/1.34 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 1.82/1.34 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 1.82/1.34 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 1.82/1.34 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 1.82/1.34 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 1.82/1.34 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 1.82/1.34 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 1.82/1.34 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 1.82/1.34 thf(func_def_33, type, d_unsorted: $tType).
% 1.82/1.34 thf(func_def_34, type, d_mu: $tType).
% 1.82/1.34 thf(func_def_35, type, d2unsorted: d_unsorted > $i).
% 1.82/1.34 thf(func_def_36, type, d2mu: d_mu > mu).
% 1.82/1.34 thf(func_def_37, type, d_unsorted_0: d_unsorted).
% 1.82/1.34 thf(func_def_38, type, d_mu_0: d_mu).
% 1.82/1.34 thf(func_def_52, type, sK0: $i > d_unsorted).
% 1.82/1.34 thf(func_def_53, type, sK1: mu > d_mu).
% 1.82/1.34 thf(func_def_55, type, ph3: !>[X0: $tType]:(X0)).
% 1.82/1.34 thf(func_def_56, type, sK4: $i > $o).
% 1.82/1.34 thf(func_def_57, type, sK5: $i > $o).
% 1.82/1.34 thf(f335,plain,(
% 1.82/1.34 $false),
% 1.82/1.34 inference(avatar_sat_refutation,[status(thm)],[f301,f302,f306,f310,f321,f334])).
% 1.82/1.34 thf(f334,plain,(
% 1.82/1.34 ~spl2_1 | ~spl2_4),
% 1.82/1.34 inference(avatar_contradiction_clause,[status(thm)],[f333])).
% 1.82/1.34 thf(f333,plain,(
% 1.82/1.34 $false | (~spl2_1 | ~spl2_4)),
% 1.82/1.34 inference(trivial_inequality_removal,[status(thm)],[f329])).
% 1.82/1.34 thf(f329,plain,(
% 1.82/1.34 ($false = $true) | (~spl2_1 | ~spl2_4)),
% 1.82/1.34 inference(superposition,[status(thm)],[f299,f287])).
% 1.82/1.34 thf(f287,plain,(
% 1.82/1.34 ($true = (sK5 @ sK6)) | ~spl2_1),
% 1.82/1.34 inference(avatar_component_clause,[status(thm)],[f285])).
% 1.82/1.34 thf(f285,definition,(
% 1.82/1.34 spl2_1 <=> ($true = (sK5 @ sK6))),
% 1.82/1.34 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.82/1.34 thf(f299,plain,(
% 1.82/1.34 ($false = (sK5 @ sK6)) | ~spl2_4),
% 1.82/1.34 inference(avatar_component_clause,[status(thm)],[f297])).
% 1.82/1.34 thf(f297,definition,(
% 1.82/1.34 spl2_4 <=> ($false = (sK5 @ sK6))),
% 1.82/1.34 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.82/1.34 thf(f321,plain,(
% 1.82/1.34 ~spl2_2 | ~spl2_3),
% 1.82/1.34 inference(avatar_contradiction_clause,[status(thm)],[f320])).
% 1.82/1.34 thf(f320,plain,(
% 1.82/1.34 $false | (~spl2_2 | ~spl2_3)),
% 1.82/1.34 inference(trivial_inequality_removal,[status(thm)],[f317])).
% 1.82/1.34 thf(f317,plain,(
% 1.82/1.34 ($false = $true) | (~spl2_2 | ~spl2_3)),
% 1.82/1.34 inference(superposition,[status(thm)],[f291,f295])).
% 1.82/1.34 thf(f295,plain,(
% 1.82/1.34 ((sK4 @ sK6) = $true) | ~spl2_3),
% 1.82/1.34 inference(avatar_component_clause,[status(thm)],[f293])).
% 1.82/1.34 thf(f293,definition,(
% 1.82/1.34 spl2_3 <=> ((sK4 @ sK6) = $true)),
% 1.82/1.34 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.82/1.34 thf(f291,plain,(
% 1.82/1.34 ($false = (sK4 @ sK6)) | ~spl2_2),
% 1.82/1.34 inference(avatar_component_clause,[status(thm)],[f289])).
% 1.82/1.34 thf(f289,definition,(
% 1.82/1.34 spl2_2 <=> ($false = (sK4 @ sK6))),
% 1.82/1.34 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.82/1.34 thf(f310,plain,(
% 1.82/1.34 spl2_3 | spl2_1),
% 1.82/1.34 inference(avatar_split_clause,[status(thm)],[f237,f285,f293])).
% 1.82/1.34 thf(f237,plain,(
% 1.82/1.34 ((sK4 @ sK6) = $true) | ($true = (sK5 @ sK6))),
% 1.82/1.34 inference(duplicate_literal_removal,[status(thm)],[f236])).
% 1.82/1.34 thf(f236,plain,(
% 1.82/1.34 ((sK4 @ sK6) = $true) | ($true = (sK5 @ sK6)) | ($true = (sK5 @ sK6))),
% 1.82/1.34 inference(not_proxy_clausification,[status(thm)],[f235])).
% 1.82/1.34 thf(f235,plain,(
% 1.82/1.34 ((~ (sK5 @ sK6)) = $false) | ((sK4 @ sK6) = $true) | ($true = (sK5 @ sK6))),
% 1.82/1.34 inference(not_proxy_clausification,[status(thm)],[f232])).
% 1.82/1.34 thf(f232,plain,(
% 1.82/1.34 ($false = (~ (sK4 @ sK6))) | ((~ (sK5 @ sK6)) = $false) | ($true = (sK5 @ sK6))),
% 1.82/1.34 inference(binary_proxy_clausification,[status(thm)],[f231])).
% 1.82/1.34 thf(f231,plain,(
% 1.82/1.34 ($true = (sK5 @ sK6)) | (((sK4 @ sK6) | (~ (sK5 @ sK6))) = $false) | ($false = (~ (sK4 @ sK6)))),
% 1.82/1.34 inference(binary_proxy_clausification,[status(thm)],[f229])).
% 1.82/1.34 thf(f229,plain,(
% 1.82/1.34 ($false = ((~ (sK4 @ sK6)) | (sK5 @ sK6))) | (((sK4 @ sK6) | (~ (sK5 @ sK6))) = $false) | ($true = (sK5 @ sK6))),
% 1.82/1.34 inference(not_proxy_clausification,[status(thm)],[f228])).
% 1.82/1.34 thf(f228,plain,(
% 1.82/1.34 ((~ ((sK4 @ sK6) | (~ (sK5 @ sK6)))) = $true) | ($false = ((~ (sK4 @ sK6)) | (sK5 @ sK6))) | ($true = (sK5 @ sK6))),
% 1.82/1.34 inference(not_proxy_clausification,[status(thm)],[f227])).
% 1.82/1.34 thf(f227,plain,(
% 1.82/1.34 ($true = (~ ((~ (sK4 @ sK6)) | (sK5 @ sK6)))) | ((~ ((sK4 @ sK6) | (~ (sK5 @ sK6)))) = $true) | ($true = (sK5 @ sK6))),
% 1.82/1.34 inference(not_proxy_clausification,[status(thm)],[f226])).
% 1.82/1.34 thf(f226,plain,(
% 1.82/1.34 ((~ (sK5 @ sK6)) = $false) | ($true = (~ ((~ (sK4 @ sK6)) | (sK5 @ sK6)))) | ((~ ((sK4 @ sK6) | (~ (sK5 @ sK6)))) = $true)),
% 1.82/1.34 inference(binary_proxy_clausification,[status(thm)],[f224])).
% 1.82/1.34 thf(f224,plain,(
% 1.82/1.34 (((~ (sK5 @ sK6)) | (sK4 @ sK6)) = $false) | ($true = (~ ((~ (sK4 @ sK6)) | (sK5 @ sK6)))) | ((~ ((sK4 @ sK6) | (~ (sK5 @ sK6)))) = $true)),
% 1.82/1.34 inference(not_proxy_clausification,[status(thm)],[f223])).
% 1.82/1.34 thf(f223,plain,(
% 1.82/1.34 ((~ ((~ (sK5 @ sK6)) | (sK4 @ sK6))) = $true) | ((~ ((sK4 @ sK6) | (~ (sK5 @ sK6)))) = $true) | ($true = (~ ((~ (sK4 @ sK6)) | (sK5 @ sK6))))),
% 1.82/1.34 inference(duplicate_literal_removal,[status(thm)],[f222])).
% 1.82/1.34 thf(f222,plain,(
% 1.82/1.34 ($true = (~ ((~ (sK4 @ sK6)) | (sK5 @ sK6)))) | ((~ ((~ (sK5 @ sK6)) | (sK4 @ sK6))) = $true) | ($true = (~ ((~ (sK4 @ sK6)) | (sK5 @ sK6)))) | ((~ ((sK4 @ sK6) | (~ (sK5 @ sK6)))) = $true)),
% 1.82/1.34 inference(binary_proxy_clausification,[status(thm)],[f221])).
% 1.82/1.34 thf(f221,plain,(
% 1.82/1.34 ($true = ((~ ((~ (sK4 @ sK6)) | (sK5 @ sK6))) | (~ ((sK4 @ sK6) | (~ (sK5 @ sK6)))))) | ($true = (~ ((~ (sK4 @ sK6)) | (sK5 @ sK6)))) | ((~ ((~ (sK5 @ sK6)) | (sK4 @ sK6))) = $true)),
% 1.82/1.34 inference(not_proxy_clausification,[status(thm)],[f220])).
% 1.82/1.34 thf(f220,plain,(
% 1.82/1.34 ((~ ((~ ((~ (sK4 @ sK6)) | (sK5 @ sK6))) | (~ ((sK4 @ sK6) | (~ (sK5 @ sK6)))))) = $false) | ((~ ((~ (sK5 @ sK6)) | (sK4 @ sK6))) = $true) | ($true = (~ ((~ (sK4 @ sK6)) | (sK5 @ sK6))))),
% 1.82/1.34 inference(binary_proxy_clausification,[status(thm)],[f219])).
% 1.82/1.34 thf(f219,plain,(
% 1.82/1.34 (((~ ((~ (sK5 @ sK6)) | (sK4 @ sK6))) | (~ ((~ (sK4 @ sK6)) | (sK5 @ sK6)))) = $true) | ((~ ((~ ((~ (sK4 @ sK6)) | (sK5 @ sK6))) | (~ ((sK4 @ sK6) | (~ (sK5 @ sK6)))))) = $false)),
% 1.82/1.34 inference(not_proxy_clausification,[status(thm)],[f218])).
% 1.82/1.34 thf(f218,plain,(
% 1.82/1.34 ((~ ((~ ((~ (sK5 @ sK6)) | (sK4 @ sK6))) | (~ ((~ (sK4 @ sK6)) | (sK5 @ sK6))))) = $false) | ((~ ((~ ((~ (sK4 @ sK6)) | (sK5 @ sK6))) | (~ ((sK4 @ sK6) | (~ (sK5 @ sK6)))))) = $false)),
% 1.82/1.34 inference(binary_proxy_clausification,[status(thm)],[f216])).
% 1.82/1.34 thf(f216,plain,(
% 1.82/1.34 ((~ ((~ ((~ (sK5 @ sK6)) | (sK4 @ sK6))) | (~ ((~ (sK4 @ sK6)) | (sK5 @ sK6))))) != (~ ((~ ((~ (sK4 @ sK6)) | (sK5 @ sK6))) | (~ ((sK4 @ sK6) | (~ (sK5 @ sK6)))))))),
% 1.82/1.34 inference(beta_eta_normalization,[status(thm)],[f215])).
% 1.82/1.34 thf(f215,plain,(
% 1.82/1.34 (((^[Y0 : $i]: (~ ((~ ((~ (sK4 @ Y0)) | (sK5 @ Y0))) | (~ ((sK4 @ Y0) | (~ (sK5 @ Y0))))))) @ sK6) != ((^[Y0 : $i]: (~ ((~ ((~ (sK5 @ Y0)) | (sK4 @ Y0))) | (~ ((~ (sK4 @ Y0)) | (sK5 @ Y0)))))) @ sK6))),
% 1.82/1.34 inference(negative_extensionality,[status(thm)],[f214])).
% 1.82/1.34 thf(f214,plain,(
% 1.82/1.34 ((^[Y0 : $i]: (~ ((~ ((~ (sK5 @ Y0)) | (sK4 @ Y0))) | (~ ((~ (sK4 @ Y0)) | (sK5 @ Y0)))))) != (^[Y0 : $i]: (~ ((~ ((~ (sK4 @ Y0)) | (sK5 @ Y0))) | (~ ((sK4 @ Y0) | (~ (sK5 @ Y0))))))))),
% 1.82/1.34 inference(beta_eta_normalization,[status(thm)],[f213])).
% 1.82/1.34 thf(f213,plain,(
% 1.82/1.34 (((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ ((~ ((~ (Y0 @ Y1)) | (sK4 @ Y1))) | (~ ((~ (sK4 @ Y1)) | (Y0 @ Y1)))))))) @ sK5) != ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ ((~ ((~ (sK4 @ Y1)) | (Y0 @ Y1))) | (~ ((sK4 @ Y1) | (~ (Y0 @ Y1))))))))) @ sK5))),
% 1.82/1.34 inference(negative_extensionality,[status(thm)],[f212])).
% 1.82/1.34 thf(f212,plain,(
% 1.82/1.34 ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ ((~ ((~ (Y0 @ Y1)) | (sK4 @ Y1))) | (~ ((~ (sK4 @ Y1)) | (Y0 @ Y1)))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ ((~ ((~ (sK4 @ Y1)) | (Y0 @ Y1))) | (~ ((sK4 @ Y1) | (~ (Y0 @ Y1))))))))))),
% 1.82/1.34 inference(beta_eta_normalization,[status(thm)],[f211])).
% 1.82/1.34 thf(f211,plain,(
% 1.82/1.34 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ ((~ ((~ (Y0 @ Y2)) | (Y1 @ Y2))) | (~ ((Y0 @ Y2) | (~ (Y1 @ Y2))))))))))) @ sK4) != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ ((~ ((~ (Y1 @ Y2)) | (Y0 @ Y2))) | (~ ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))))) @ sK4))),
% 1.82/1.34 inference(negative_extensionality,[status(thm)],[f56])).
% 1.82/1.34 thf(f56,plain,(
% 1.82/1.34 ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ ((~ ((~ (Y0 @ Y2)) | (Y1 @ Y2))) | (~ ((Y0 @ Y2) | (~ (Y1 @ Y2))))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ ((~ ((~ (Y1 @ Y2)) | (Y0 @ Y2))) | (~ ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))))))),
% 1.82/1.34 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.82/1.34 thf(f55,plain,(
% 1.82/1.34 ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ ((~ (Y3 @ Y4)) | (~ (Y2 @ Y4))))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((~ (Y2 @ Y4)) | (Y3 @ Y4))))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((~ (Y2 @ Y4)) | (Y3 @ Y4))))))) @ Y1 @ Y0))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ ((~ ((~ (Y0 @ Y2)) | (Y1 @ Y2))) | (~ ((Y0 @ Y2) | (~ (Y1 @ Y2))))))))))))),
% 1.82/1.34 inference(definition_unfolding,[status(thm)],[f17,f38,f25,f44,f44])).
% 1.82/1.34 thf(f44,plain,(
% 1.82/1.34 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2))))))))),
% 1.82/1.34 inference(cnf_transformation,[status(thm)],[f16])).
% 1.82/1.34 thf(f16,plain,(
% 1.82/1.34 (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (~ (!! @ mu @ (^[Y2 : mu]: (~ (Y0 @ Y2 @ Y1))))))))) & ((meq_ind @ (d2mu @ d_mu_0) @ (d2mu @ d_mu_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (mcountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (mweakly_directed = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y1 @ Y2))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y0 @ Y2 @ Y4))))))))))))))) & ! [X0 : d_unsorted,X1 : d_unsorted] : (((d2unsorted @ X1) != (d2unsorted @ X0)) | (X0 = X1)) & ! [X2 : $i] : ((d2unsorted @ (sK0 @ X2)) = X2) & (meq_prop = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) = (Y0 @ Y2)))))))) & (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y2 @ Y1))))))))) & (mxor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ ((Y0 @ Y2) | (~ (Y1 @ Y2)))) | (~ ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))))) & (mexists_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (~ (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (~ (Y0 @ Y2 @ Y1))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & ((mfalse @ (d2unsorted @ d_unsorted_0)) != $true) & ! [X4 : d_mu,X5 : d_mu] : ((X4 = X5) | ((d2mu @ X5) != (d2mu @ X4))) & (msatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (mimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y1 @ Y2)) | (Y0 @ Y2)))))))) & (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ ((~ ((~ (Y0 @ Y2)) | (Y1 @ Y2))) | (~ ((Y0 @ Y2) | (~ (Y1 @ Y2)))))))))))) & (meuclidean = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y1 @ Y3)))))))))) & (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) | (~ (Y0 @ Y1 @ Y2))) | (~ (Y0 @ Y3 @ Y1))))))))))) & (mserial = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))))) & (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3)))))))))) & (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X6 : d_unsorted] : (d_unsorted_0 = X6) & (mfunctional = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y2 = Y3) | (~ (Y0 @ Y1 @ Y3)))))))))))))) & (mweakly_dense = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y3 @ Y1))))))))))))) & ! [X7 : mu] : ((d2mu @ (sK1 @ X7)) = X7) & ! [X9 : d_mu] : (d_mu_0 = X9) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ ((~ (Y1 @ Y2)) | (~ (Y0 @ Y2)))))))))) & (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (~ (Y1 @ Y3)))))))))))) & (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1))))))) & (minvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ((mtrue @ (d2unsorted @ d_unsorted_0)) = $true) & (mweakly_connected = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y3 = Y1)) | (Y0 @ Y3 @ Y1)) | (Y0 @ Y1 @ Y3)))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (mpartially_functional = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y3 = Y2) | (~ (Y0 @ Y1 @ Y2))) | (~ (Y0 @ Y1 @ Y3)))))))))))),
% 1.82/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f15,f14])).
% 1.82/1.34 thf(f14,plain,(
% 1.82/1.34 ! [X2 : $i] : (? [X3 : d_unsorted] : ((d2unsorted @ X3) = X2) => ((d2unsorted @ (sK0 @ X2)) = X2))),
% 1.82/1.34 introduced(definition,[],[choice_axiom])).
% 1.82/1.34 thf(f15,plain,(
% 1.82/1.34 ! [X7 : mu] : (? [X8 : d_mu] : ((d2mu @ X8) = X7) => ((d2mu @ (sK1 @ X7)) = X7))),
% 1.82/1.34 introduced(definition,[],[choice_axiom])).
% 1.82/1.34 thf(f13,plain,(
% 1.82/1.34 (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (~ (!! @ mu @ (^[Y2 : mu]: (~ (Y0 @ Y2 @ Y1))))))))) & ((meq_ind @ (d2mu @ d_mu_0) @ (d2mu @ d_mu_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (mcountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (mweakly_directed = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y1 @ Y2))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y0 @ Y2 @ Y4))))))))))))))) & ! [X0 : d_unsorted,X1 : d_unsorted] : (((d2unsorted @ X1) != (d2unsorted @ X0)) | (X0 = X1)) & ! [X2 : $i] : ? [X3 : d_unsorted] : ((d2unsorted @ X3) = X2) & (meq_prop = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) = (Y0 @ Y2)))))))) & (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y2 @ Y1))))))))) & (mxor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ ((Y0 @ Y2) | (~ (Y1 @ Y2)))) | (~ ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))))) & (mexists_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (~ (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (~ (Y0 @ Y2 @ Y1))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & ((mfalse @ (d2unsorted @ d_unsorted_0)) != $true) & ! [X4 : d_mu,X5 : d_mu] : ((X4 = X5) | ((d2mu @ X5) != (d2mu @ X4))) & (msatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (mimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y1 @ Y2)) | (Y0 @ Y2)))))))) & (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ ((~ ((~ (Y0 @ Y2)) | (Y1 @ Y2))) | (~ ((Y0 @ Y2) | (~ (Y1 @ Y2)))))))))))) & (meuclidean = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y1 @ Y3)))))))))) & (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) | (~ (Y0 @ Y1 @ Y2))) | (~ (Y0 @ Y3 @ Y1))))))))))) & (mserial = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))))) & (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3)))))))))) & (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X6 : d_unsorted] : (d_unsorted_0 = X6) & (mfunctional = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y2 = Y3) | (~ (Y0 @ Y1 @ Y3)))))))))))))) & (mweakly_dense = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y3 @ Y1))))))))))))) & ! [X7 : mu] : ? [X8 : d_mu] : ((d2mu @ X8) = X7) & ! [X9 : d_mu] : (d_mu_0 = X9) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ ((~ (Y1 @ Y2)) | (~ (Y0 @ Y2)))))))))) & (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (~ (Y1 @ Y3)))))))))))) & (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1))))))) & (minvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ((mtrue @ (d2unsorted @ d_unsorted_0)) = $true) & (mweakly_connected = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y3 = Y1)) | (Y0 @ Y3 @ Y1)) | (Y0 @ Y1 @ Y3)))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (mpartially_functional = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y3 = Y2) | (~ (Y0 @ Y1 @ Y2))) | (~ (Y0 @ Y1 @ Y3)))))))))))),
% 1.82/1.34 inference(rectify,[status(thm)],[f12])).
% 1.82/1.34 thf(f12,plain,(
% 1.82/1.34 (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (~ (!! @ mu @ (^[Y2 : mu]: (~ (Y0 @ Y2 @ Y1))))))))) & ((meq_ind @ (d2mu @ d_mu_0) @ (d2mu @ d_mu_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (mcountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (mweakly_directed = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y1 @ Y2))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y0 @ Y2 @ Y4))))))))))))))) & ! [X2 : d_unsorted,X3 : d_unsorted] : (((d2unsorted @ X2) != (d2unsorted @ X3)) | (X2 = X3)) & ! [X4 : $i] : ? [X5 : d_unsorted] : ((d2unsorted @ X5) = X4) & (meq_prop = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) = (Y0 @ Y2)))))))) & (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y2 @ Y1))))))))) & (mxor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ ((Y0 @ Y2) | (~ (Y1 @ Y2)))) | (~ ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))))) & (mexists_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (~ (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (~ (Y0 @ Y2 @ Y1))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & ((mfalse @ (d2unsorted @ d_unsorted_0)) != $true) & ! [X8 : d_mu,X9 : d_mu] : ((X8 = X9) | ((d2mu @ X8) != (d2mu @ X9))) & (msatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (mimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y1 @ Y2)) | (Y0 @ Y2)))))))) & (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ ((~ ((~ (Y0 @ Y2)) | (Y1 @ Y2))) | (~ ((Y0 @ Y2) | (~ (Y1 @ Y2)))))))))))) & (meuclidean = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y1 @ Y3)))))))))) & (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) | (~ (Y0 @ Y1 @ Y2))) | (~ (Y0 @ Y3 @ Y1))))))))))) & (mserial = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))))) & (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3)))))))))) & (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & (mfunctional = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y2 = Y3) | (~ (Y0 @ Y1 @ Y3)))))))))))))) & (mweakly_dense = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y3 @ Y1))))))))))))) & ! [X6 : mu] : ? [X7 : d_mu] : ((d2mu @ X7) = X6) & ! [X1 : d_mu] : (d_mu_0 = X1) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ ((~ (Y1 @ Y2)) | (~ (Y0 @ Y2)))))))))) & (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (~ (Y1 @ Y3)))))))))))) & (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1))))))) & (minvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ((mtrue @ (d2unsorted @ d_unsorted_0)) = $true) & (mweakly_connected = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y3 = Y1)) | (Y0 @ Y3 @ Y1)) | (Y0 @ Y1 @ Y3)))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (mpartially_functional = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y3 = Y2) | (~ (Y0 @ Y1 @ Y2))) | (~ (Y0 @ Y1 @ Y3)))))))))))),
% 1.82/1.34 inference(ennf_transformation,[status(thm)],[f11])).
% 1.82/1.34 thf(f11,plain,(
% 1.82/1.34 (msatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mweakly_directed = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y1 @ Y2))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y0 @ Y2 @ Y4))))))))))))))) & (mserial = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))))) & ((mfalse @ (d2unsorted @ d_unsorted_0)) != $true) & ! [X8 : d_mu,X9 : d_mu] : (((d2mu @ X8) = (d2mu @ X9)) => (X8 = X9)) & ((meq_ind @ (d2mu @ d_mu_0) @ (d2mu @ d_mu_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (mpartially_functional = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y3 = Y2) | (~ (Y0 @ Y1 @ Y2))) | (~ (Y0 @ Y1 @ Y3))))))))))) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & (mxor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ ((Y0 @ Y2) | (~ (Y1 @ Y2)))) | (~ ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & ((mtrue @ (d2unsorted @ d_unsorted_0)) = $true) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1))))))) & ! [X6 : mu] : ? [X7 : d_mu] : ((d2mu @ X7) = X6) & (mcountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & ! [X4 : $i] : ? [X5 : d_unsorted] : ((d2unsorted @ X5) = X4) & (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1))))))) & (mexists_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (~ (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (~ (Y0 @ Y2 @ Y1))))))))) & (meuclidean = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y1 @ Y3)))))))))) & ! [X2 : d_unsorted,X3 : d_unsorted] : (((d2unsorted @ X2) = (d2unsorted @ X3)) => (X2 = X3)) & (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ ((~ ((~ (Y0 @ Y2)) | (Y1 @ Y2))) | (~ ((Y0 @ Y2) | (~ (Y1 @ Y2)))))))))))) & (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (~ (!! @ mu @ (^[Y2 : mu]: (~ (Y0 @ Y2 @ Y1))))))))) & (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ ((~ (Y1 @ Y2)) | (~ (Y0 @ Y2)))))))))) & (minvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y1 @ Y2)) | (Y0 @ Y2)))))))) & (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3)))))))))) & (mweakly_dense = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y3 @ Y1))))))))))))) & (mweakly_connected = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y3 = Y1)) | (Y0 @ Y3 @ Y1)) | (Y0 @ Y1 @ Y3)))))))))) & ! [X1 : d_mu] : (d_mu_0 = X1) & (mfunctional = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y2 = Y3) | (~ (Y0 @ Y1 @ Y3)))))))))))))) & (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y2 @ Y1))))))))) & (meq_prop = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) = (Y0 @ Y2)))))))) & (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (~ (Y1 @ Y3)))))))))))) & (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) | (~ (Y0 @ Y1 @ Y2))) | (~ (Y0 @ Y3 @ Y1)))))))))))),
% 1.82/1.34 inference(flattening,[status(thm)],[f10])).
% 1.82/1.34 thf(f10,plain,(
% 1.82/1.34 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ ((~ ((~ (Y0 @ Y2)) | (Y1 @ Y2))) | (~ ((Y0 @ Y2) | (~ (Y1 @ Y2)))))))))))) & (msatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & (mweakly_directed = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y1 @ Y2))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y0 @ Y2 @ Y4))))))))))))))) & (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1))))))) & ((meq_ind @ (d2mu @ d_mu_0) @ (d2mu @ d_mu_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (mfunctional = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y2 = Y3) | (~ (Y0 @ Y1 @ Y3)))))))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (mxor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ ((Y0 @ Y2) | (~ (Y1 @ Y2)))) | (~ ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))))) & ! [X1 : d_mu] : (d_mu_0 = X1) & (meq_prop = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) = (Y0 @ Y2)))))))) & (mweakly_connected = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y3 = Y1)) | (Y0 @ Y3 @ Y1)) | (Y0 @ Y1 @ Y3)))))))))) & (mimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y1 @ Y2)) | (Y0 @ Y2)))))))) & (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) | (~ (Y0 @ Y1 @ Y2))) | (~ (Y0 @ Y3 @ Y1))))))))))) & ! [X2 : d_unsorted,X3 : d_unsorted] : (((d2unsorted @ X2) = (d2unsorted @ X3)) => (X2 = X3)) & (meuclidean = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y1 @ Y3)))))))))) & (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3)))))))))) & (minvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & ! [X4 : $i] : ? [X5 : d_unsorted] : ((d2unsorted @ X5) = X4) & (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (~ (Y1 @ Y3)))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ ((~ (Y1 @ Y2)) | (~ (Y0 @ Y2)))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (mcountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mexists_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (~ (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (~ (Y0 @ Y2 @ Y1))))))))) & (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y2 @ Y1))))))))) & ~((mfalse @ (d2unsorted @ d_unsorted_0)) = $true) & (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (~ (!! @ mu @ (^[Y2 : mu]: (~ (Y0 @ Y2 @ Y1))))))))) & (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1))))))) & ! [X6 : mu] : ? [X7 : d_mu] : ((d2mu @ X7) = X6) & (mweakly_dense = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y3 @ Y1))))))))))))) & ((mtrue @ (d2unsorted @ d_unsorted_0)) = $true) & (mserial = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))))) & (mpartially_functional = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y3 = Y2) | (~ (Y0 @ Y1 @ Y2))) | (~ (Y0 @ Y1 @ Y3))))))))))) & ! [X8 : d_mu,X9 : d_mu] : (((d2mu @ X8) = (d2mu @ X9)) => (X8 = X9))),
% 1.82/1.34 inference(rectify,[status(thm)],[f8])).
% 1.82/1.34 thf(f8,plain,(
% 1.82/1.34 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ ((~ ((~ (Y0 @ Y2)) | (Y1 @ Y2))) | (~ ((Y0 @ Y2) | (~ (Y1 @ Y2)))))))))))) & (msatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & ! [X7 : d_unsorted] : (d_unsorted_0 = X7) & (mweakly_directed = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y1 @ Y2))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y0 @ Y2 @ Y4))))))))))))))) & (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1))))))) & ((meq_ind @ (d2mu @ d_mu_0) @ (d2mu @ d_mu_0) @ (d2unsorted @ d_unsorted_0)) = $true) & (mfunctional = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y2 = Y3) | (~ (Y0 @ Y1 @ Y3)))))))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (mxor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ ((Y0 @ Y2) | (~ (Y1 @ Y2)))) | (~ ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))))) & ! [X26 : d_mu] : (d_mu_0 = X26) & (meq_prop = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) = (Y0 @ Y2)))))))) & (mweakly_connected = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y3 = Y1)) | (Y0 @ Y3 @ Y1)) | (Y0 @ Y1 @ Y3)))))))))) & (mimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y1 @ Y2)) | (Y0 @ Y2)))))))) & (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) | (~ (Y0 @ Y1 @ Y2))) | (~ (Y0 @ Y3 @ Y1))))))))))) & ! [X41 : d_unsorted,X42 : d_unsorted] : (((d2unsorted @ X42) = (d2unsorted @ X41)) => (X41 = X42)) & (meuclidean = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y1 @ Y3)))))))))) & (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3)))))))))) & (minvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & ! [X55 : $i] : ? [X56 : d_unsorted] : ((d2unsorted @ X56) = X55) & (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (~ (Y1 @ Y3)))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ ((~ (Y1 @ Y2)) | (~ (Y0 @ Y2)))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (mcountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mexists_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (~ (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (~ (Y0 @ Y2 @ Y1))))))))) & (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y2 @ Y1))))))))) & ~((mfalse @ (d2unsorted @ d_unsorted_0)) = $true) & (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (~ (!! @ mu @ (^[Y2 : mu]: (~ (Y0 @ Y2 @ Y1))))))))) & (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1))))))) & ! [X83 : mu] : ? [X84 : d_mu] : ((d2mu @ X84) = X83) & (mweakly_dense = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y3 @ Y1))))))))))))) & ((mtrue @ (d2unsorted @ d_unsorted_0)) = $true) & (mserial = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))))) & (mpartially_functional = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y3 = Y2) | (~ (Y0 @ Y1 @ Y2))) | (~ (Y0 @ Y1 @ Y3))))))))))) & ! [X96 : d_mu,X97 : d_mu] : (((d2mu @ X96) = (d2mu @ X97)) => (X96 = X97))),
% 1.82/1.34 inference(fool_elimination,[status(thm)],[f7])).
% 1.82/1.34 thf(f7,plain,(
% 1.82/1.34 (mreflexive = (^[X0 : $i > $i > $o] : (! [X1 : $i] : (X0 @ X1 @ X1)))) & (mequiv = (^[X2 : $i > $o, X3 : $i > $o, X4 : $i] : (~(~(~(X3 @ X4) | (X2 @ X4)) | ~((X3 @ X4) | ~(X2 @ X4)))))) & (msatisfiable = (^[X5 : $i > $o] : (~! [X6 : $i] : ~(X5 @ X6)))) & ! [X7 : d_unsorted] : (d_unsorted_0 = X7) & ((^[X8 : $i > $i > $o] : (! [X9 : $i,X10 : $i,X11 : $i] : (~! [X12 : $i] : (~(X8 @ X10 @ X12) | ~(X8 @ X9 @ X12)) | ~(X8 @ X11 @ X10) | ~(X8 @ X11 @ X9)))) = mweakly_directed) & ((^[X13 : mu > $i > $o, X14 : $i] : (! [X15 : mu] : (X13 @ X15 @ X14))) = mforall_ind) & (meq_ind @ (d2mu @ d_mu_0) @ (d2mu @ d_mu_0) @ (d2unsorted @ d_unsorted_0)) & (mfunctional = (^[X16 : $i > $i > $o] : (! [X17 : $i] : ~! [X18 : $i] : (~! [X19 : $i] : (~(X16 @ X17 @ X19) | (X18 = X19)) | ~(X16 @ X17 @ X18))))) & (mimplies = (^[X20 : $i > $o, X21 : $i > $o, X22 : $i] : ((X21 @ X22) | ~(X20 @ X22)))) & (mxor = (^[X23 : $i > $o, X24 : $i > $o, X25 : $i] : (~(~(X23 @ X25) | (X24 @ X25)) | ~(~(X24 @ X25) | (X23 @ X25))))) & ! [X26 : d_mu] : (d_mu_0 = X26) & (meq_prop = (^[X27 : $i > $o, X28 : $i > $o, X29 : $i] : (((X28 @ X29) = (X27 @ X29))))) & ((^[X30 : $i > $i > $o] : (! [X31 : $i,X32 : $i,X33 : $i] : ((X30 @ X33 @ X31) | (X30 @ X31 @ X33) | (X31 = X33) | ~(X30 @ X32 @ X31) | ~(X30 @ X32 @ X33)))) = mweakly_connected) & ((^[X34 : $i > $o, X35 : $i > $o, X36 : $i] : ((X34 @ X36) | ~(X35 @ X36))) = mimplied) & (mtransitive = (^[X37 : $i > $i > $o] : (! [X38 : $i,X39 : $i,X40 : $i] : (~(X37 @ X38 @ X40) | ~(X37 @ X40 @ X39) | (X37 @ X38 @ X39))))) & ! [X41 : d_unsorted,X42 : d_unsorted] : (((d2unsorted @ X42) = (d2unsorted @ X41)) => (X41 = X42)) & (meuclidean = (^[X43 : $i > $i > $o] : (! [X44 : $i,X45 : $i,X46 : $i] : ((X43 @ X46 @ X44) | ~(X43 @ X45 @ X46) | ~(X43 @ X45 @ X44))))) & (mbox = (^[X47 : $i > $i > $o, X48 : $i > $o, X49 : $i] : (! [X50 : $i] : ((X48 @ X50) | ~(X47 @ X49 @ X50))))) & (minvalid = (^[X51 : $i > $o] : (! [X52 : $i] : ~(X51 @ X52)))) & (mvalid = (^[X53 : $i > $o] : (! [X54 : $i] : (X53 @ X54)))) & ! [X55 : $i] : ? [X56 : d_unsorted] : ((d2unsorted @ X56) = X55) & ((^[X57 : $i > $i > $o, X58 : $i > $o, X59 : $i] : (~! [X60 : $i] : (~(X58 @ X60) | ~(X57 @ X59 @ X60)))) = mdia) & ((^[X61 : $i > $o, X62 : $i > $o, X63 : $i] : (~(~(X61 @ X63) | ~(X62 @ X63)))) = mand) & ((^[X64 : $i > $o, X65 : $i > $o, X66 : $i] : ((X64 @ X66) | (X65 @ X66))) = mor) & (mcountersatisfiable = (^[X67 : $i > $o] : (~! [X68 : $i] : (X67 @ X68)))) & ((^[X69 : $i > $o, X70 : $i] : (~(X69 @ X70))) = mnot) & (mexists_prop = (^[X71 : ($i > $o) > $i > $o, X72 : $i] : (~! [X73 : $i > $o] : ~(X71 @ X73 @ X72)))) & (msymmetric = (^[X74 : $i > $i > $o] : (! [X75 : $i,X76 : $i] : (~(X74 @ X75 @ X76) | (X74 @ X76 @ X75))))) & ~(mfalse @ (d2unsorted @ d_unsorted_0)) & (mexists_ind = (^[X77 : mu > $i > $o, X78 : $i] : (~! [X79 : mu] : ~(X77 @ X79 @ X78)))) & (mforall_prop = (^[X80 : ($i > $o) > $i > $o, X81 : $i] : (! [X82 : $i > $o] : (X80 @ X82 @ X81)))) & ! [X83 : mu] : ? [X84 : d_mu] : ((d2mu @ X84) = X83) & ((^[X85 : $i > $i > $o] : (! [X86 : $i,X87 : $i] : (~! [X88 : $i] : (~(X85 @ X88 @ X87) | ~(X85 @ X86 @ X88)) | ~(X85 @ X86 @ X87)))) = mweakly_dense) & (mtrue @ (d2unsorted @ d_unsorted_0)) & (mserial = (^[X89 : $i > $i > $o] : (! [X90 : $i] : ~! [X91 : $i] : ~(X89 @ X90 @ X91)))) & ((^[X92 : $i > $i > $o] : (! [X93 : $i,X94 : $i,X95 : $i] : (~(X92 @ X95 @ X93) | ~(X92 @ X95 @ X94) | (X93 = X94)))) = mpartially_functional) & ! [X96 : d_mu,X97 : d_mu] : (((d2mu @ X96) = (d2mu @ X97)) => (X96 = X97))),
% 1.82/1.34 inference(rectify,[status(thm)],[f1])).
% 1.82/1.34 thf(f1,axiom,(
% 1.82/1.34 (mreflexive = (^[X15 : $i > $i > $o] : (! [X17 : $i] : (X15 @ X17 @ X17)))) & (mequiv = (^[X11 : $i > $o, X12 : $i > $o, X13 : $i] : (~(~(~(X12 @ X13) | (X11 @ X13)) | ~((X12 @ X13) | ~(X11 @ X13)))))) & (msatisfiable = (^[X11 : $i > $o] : (~! [X10 : $i] : ~(X11 @ X10)))) & ! [X1 : d_unsorted] : (d_unsorted_0 = X1) & ((^[X15 : $i > $i > $o] : (! [X0 : $i,X18 : $i,X17 : $i] : (~! [X16 : $i] : (~(X15 @ X18 @ X16) | ~(X15 @ X0 @ X16)) | ~(X15 @ X17 @ X18) | ~(X15 @ X17 @ X0)))) = mweakly_directed) & ((^[X11 : mu > $i > $o, X10 : $i] : (! [X8 : mu] : (X11 @ X8 @ X10))) = mforall_ind) & (meq_ind @ (d2mu @ d_mu_0) @ (d2mu @ d_mu_0) @ (d2unsorted @ d_unsorted_0)) & (mfunctional = (^[X15 : $i > $i > $o] : (! [X17 : $i] : ~! [X18 : $i] : (~! [X0 : $i] : (~(X15 @ X17 @ X0) | (X0 = X18)) | ~(X15 @ X17 @ X18))))) & (mimplies = (^[X11 : $i > $o, X12 : $i > $o, X13 : $i] : ((X12 @ X13) | ~(X11 @ X13)))) & (mxor = (^[X11 : $i > $o, X12 : $i > $o, X13 : $i] : (~(~(X11 @ X13) | (X12 @ X13)) | ~(~(X12 @ X13) | (X11 @ X13))))) & ! [X5 : d_mu] : (d_mu_0 = X5) & (meq_prop = (^[X8 : $i > $o, X9 : $i > $o, X10 : $i] : (((X8 @ X10) = (X9 @ X10))))) & ((^[X15 : $i > $i > $o] : (! [X0 : $i,X17 : $i,X18 : $i] : ((X15 @ X18 @ X0) | (X15 @ X0 @ X18) | (X0 = X18) | ~(X15 @ X17 @ X0) | ~(X15 @ X17 @ X18)))) = mweakly_connected) & ((^[X11 : $i > $o, X12 : $i > $o, X13 : $i] : ((X11 @ X13) | ~(X12 @ X13))) = mimplied) & (mtransitive = (^[X15 : $i > $i > $o] : (! [X17 : $i,X0 : $i,X18 : $i] : (~(X15 @ X17 @ X18) | ~(X15 @ X18 @ X0) | (X15 @ X17 @ X0))))) & ! [X3 : d_unsorted,X2 : d_unsorted] : (((d2unsorted @ X2) = (d2unsorted @ X3)) => (X2 = X3)) & (meuclidean = (^[X15 : $i > $i > $o] : (! [X0 : $i,X17 : $i,X18 : $i] : ((X15 @ X18 @ X0) | ~(X15 @ X17 @ X18) | ~(X15 @ X17 @ X0))))) & (mbox = (^[X15 : $i > $i > $o, X11 : $i > $o, X10 : $i] : (! [X16 : $i] : ((X11 @ X16) | ~(X15 @ X10 @ X16))))) & (minvalid = (^[X11 : $i > $o] : (! [X10 : $i] : ~(X11 @ X10)))) & (mvalid = (^[X11 : $i > $o] : (! [X10 : $i] : (X11 @ X10)))) & ! [X0 : $i] : ? [X1 : d_unsorted] : ((d2unsorted @ X1) = X0) & ((^[X15 : $i > $i > $o, X11 : $i > $o, X13 : $i] : (~! [X16 : $i] : (~(X11 @ X16) | ~(X15 @ X13 @ X16)))) = mdia) & ((^[X11 : $i > $o, X12 : $i > $o, X13 : $i] : (~(~(X11 @ X13) | ~(X12 @ X13)))) = mand) & ((^[X11 : $i > $o, X12 : $i > $o, X10 : $i] : ((X11 @ X10) | (X12 @ X10))) = mor) & (mcountersatisfiable = (^[X11 : $i > $o] : (~! [X10 : $i] : (X11 @ X10)))) & ((^[X11 : $i > $o, X10 : $i] : (~(X11 @ X10))) = mnot) & (mexists_prop = (^[X11 : ($i > $o) > $i > $o, X13 : $i] : (~! [X14 : $i > $o] : ~(X11 @ X14 @ X13)))) & (msymmetric = (^[X15 : $i > $i > $o] : (! [X17 : $i,X18 : $i] : (~(X15 @ X17 @ X18) | (X15 @ X18 @ X17))))) & ~(mfalse @ (d2unsorted @ d_unsorted_0)) & (mexists_ind = (^[X11 : mu > $i > $o, X13 : $i] : (~! [X8 : mu] : ~(X11 @ X8 @ X13)))) & (mforall_prop = (^[X11 : ($i > $o) > $i > $o, X10 : $i] : (! [X14 : $i > $o] : (X11 @ X14 @ X10)))) & ! [X4 : mu] : ? [X5 : d_mu] : ((d2mu @ X5) = X4) & ((^[X15 : $i > $i > $o] : (! [X17 : $i,X18 : $i] : (~! [X19 : $i] : (~(X15 @ X19 @ X18) | ~(X15 @ X17 @ X19)) | ~(X15 @ X17 @ X18)))) = mweakly_dense) & (mtrue @ (d2unsorted @ d_unsorted_0)) & (mserial = (^[X15 : $i > $i > $o] : (! [X17 : $i] : ~! [X18 : $i] : ~(X15 @ X17 @ X18)))) & ((^[X15 : $i > $i > $o] : (! [X18 : $i,X0 : $i,X17 : $i] : (~(X15 @ X17 @ X18) | ~(X15 @ X17 @ X0) | (X0 = X18)))) = mpartially_functional) & ! [X7 : d_mu,X6 : d_mu] : (((d2mu @ X6) = (d2mu @ X7)) => (X6 = X7))),
% 1.82/1.34 file('/export/starexec/sandbox2/tmp/tmp.5NVEwxc0Z5/DTF2THF_27794.p',lcl698_1)).
% 1.82/1.34 thf(f25,plain,(
% 1.82/1.34 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ ((~ (Y1 @ Y2)) | (~ (Y0 @ Y2))))))))))),
% 1.82/1.34 inference(cnf_transformation,[status(thm)],[f16])).
% 1.82/1.34 thf(f38,plain,(
% 1.82/1.34 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ ((~ ((~ (Y0 @ Y2)) | (Y1 @ Y2))) | (~ ((Y0 @ Y2) | (~ (Y1 @ Y2))))))))))))),
% 1.82/1.34 inference(cnf_transformation,[status(thm)],[f16])).
% 1.82/1.34 thf(f17,plain,(
% 1.82/1.34 (mequiv != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 1.82/1.34 inference(cnf_transformation,[status(thm)],[f9])).
% 1.82/1.34 thf(f9,plain,(
% 1.82/1.34 (mequiv != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 1.82/1.34 inference(flattening,[status(thm)],[f6])).
% 1.82/1.34 thf(f6,plain,(
% 1.82/1.34 ~(mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 1.82/1.34 inference(fool_elimination,[status(thm)],[f5])).
% 1.82/1.34 thf(f5,plain,(
% 1.82/1.34 ~((^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))) = mequiv)),
% 1.82/1.34 inference(rectify,[status(thm)],[f3])).
% 1.82/1.34 thf(f3,negated_conjecture,(
% 1.82/1.34 ~((^[X11 : $i > $o, X12 : $i > $o] : (mand @ (mimplies @ X11 @ X12) @ (mimplies @ X12 @ X11))) = mequiv)),
% 1.82/1.34 inference(negated_conjecture,[status(cth)],[f2])).
% 1.82/1.34 thf(f2,conjecture,(
% 1.82/1.34 ((^[X11 : $i > $o, X12 : $i > $o] : (mand @ (mimplies @ X11 @ X12) @ (mimplies @ X12 @ X11))) = mequiv)),
% 1.82/1.34 file('/export/starexec/sandbox2/tmp/tmp.5NVEwxc0Z5/DTF2THF_27794.p',mequiv)).
% 1.82/1.34 thf(f306,plain,(
% 1.82/1.34 spl2_2 | spl2_4),
% 1.82/1.34 inference(avatar_split_clause,[status(thm)],[f247,f297,f289])).
% 1.82/1.34 thf(f247,plain,(
% 1.82/1.34 ($false = (sK5 @ sK6)) | ($false = (sK4 @ sK6))),
% 1.82/1.34 inference(binary_proxy_clausification,[status(thm)],[f246])).
% 1.82/1.34 thf(f246,plain,(
% 1.82/1.34 ($false = (sK4 @ sK6)) | ($false = ((~ (sK4 @ sK6)) | (sK5 @ sK6)))),
% 1.82/1.34 inference(duplicate_literal_removal,[status(thm)],[f245])).
% 1.82/1.34 thf(f245,plain,(
% 1.82/1.34 ($false = (sK4 @ sK6)) | ($false = ((~ (sK4 @ sK6)) | (sK5 @ sK6))) | ($false = (sK4 @ sK6))),
% 1.82/1.34 inference(binary_proxy_clausification,[status(thm)],[f243])).
% 1.82/1.34 thf(f243,plain,(
% 1.82/1.34 (((sK4 @ sK6) | (~ (sK5 @ sK6))) = $false) | ($false = (sK4 @ sK6)) | ($false = ((~ (sK4 @ sK6)) | (sK5 @ sK6)))),
% 1.82/1.34 inference(not_proxy_clausification,[status(thm)],[f242])).
% 1.82/1.34 thf(f242,plain,(
% 1.82/1.34 ($false = (sK4 @ sK6)) | ($true = (~ ((~ (sK4 @ sK6)) | (sK5 @ sK6)))) | (((sK4 @ sK6) | (~ (sK5 @ sK6))) = $false)),
% 1.82/1.34 inference(not_proxy_clausification,[status(thm)],[f225])).
% 1.82/1.34 thf(f225,plain,(
% 1.82/1.34 ((~ ((sK4 @ sK6) | (~ (sK5 @ sK6)))) = $true) | ($false = (sK4 @ sK6)) | ($true = (~ ((~ (sK4 @ sK6)) | (sK5 @ sK6))))),
% 1.82/1.34 inference(binary_proxy_clausification,[status(thm)],[f224])).
% 1.82/1.34 thf(f302,plain,(
% 1.82/1.34 spl2_1 | spl2_2),
% 1.82/1.34 inference(avatar_split_clause,[status(thm)],[f270,f289,f285])).
% 1.82/1.34 thf(f270,plain,(
% 1.82/1.34 ($false = (sK4 @ sK6)) | ($true = (sK5 @ sK6))),
% 1.82/1.34 inference(not_proxy_clausification,[status(thm)],[f269])).
% 1.82/1.34 thf(f269,plain,(
% 1.82/1.34 ($true = (sK5 @ sK6)) | ($true = (~ (sK4 @ sK6)))),
% 1.82/1.34 inference(binary_proxy_clausification,[status(thm)],[f268])).
% 1.82/1.34 thf(f268,plain,(
% 1.82/1.34 ($true = ((~ (sK4 @ sK6)) | (sK5 @ sK6)))),
% 1.82/1.34 inference(duplicate_literal_removal,[status(thm)],[f267])).
% 1.82/1.34 thf(f267,plain,(
% 1.82/1.34 ($true = ((~ (sK4 @ sK6)) | (sK5 @ sK6))) | ($true = ((~ (sK4 @ sK6)) | (sK5 @ sK6)))),
% 1.82/1.34 inference(not_proxy_clausification,[status(thm)],[f260])).
% 1.82/1.34 thf(f260,plain,(
% 1.82/1.34 ($false = (~ ((~ (sK4 @ sK6)) | (sK5 @ sK6)))) | ($true = ((~ (sK4 @ sK6)) | (sK5 @ sK6)))),
% 1.82/1.34 inference(binary_proxy_clausification,[status(thm)],[f259])).
% 1.82/1.34 thf(f259,plain,(
% 1.82/1.34 (((~ ((~ (sK5 @ sK6)) | (sK4 @ sK6))) | (~ ((~ (sK4 @ sK6)) | (sK5 @ sK6)))) = $false) | ($true = ((~ (sK4 @ sK6)) | (sK5 @ sK6)))),
% 1.82/1.34 inference(not_proxy_clausification,[status(thm)],[f258])).
% 1.82/1.34 thf(f258,plain,(
% 1.82/1.34 ($false = (~ ((~ (sK4 @ sK6)) | (sK5 @ sK6)))) | (((~ ((~ (sK5 @ sK6)) | (sK4 @ sK6))) | (~ ((~ (sK4 @ sK6)) | (sK5 @ sK6)))) = $false)),
% 1.82/1.34 inference(binary_proxy_clausification,[status(thm)],[f256])).
% 1.82/1.34 thf(f256,plain,(
% 1.82/1.34 ($false = ((~ ((~ (sK4 @ sK6)) | (sK5 @ sK6))) | (~ ((sK4 @ sK6) | (~ (sK5 @ sK6)))))) | (((~ ((~ (sK5 @ sK6)) | (sK4 @ sK6))) | (~ ((~ (sK4 @ sK6)) | (sK5 @ sK6)))) = $false)),
% 1.82/1.34 inference(not_proxy_clausification,[status(thm)],[f255])).
% 1.82/1.34 thf(f255,plain,(
% 1.82/1.34 ((~ ((~ ((~ (sK4 @ sK6)) | (sK5 @ sK6))) | (~ ((sK4 @ sK6) | (~ (sK5 @ sK6)))))) = $true) | (((~ ((~ (sK5 @ sK6)) | (sK4 @ sK6))) | (~ ((~ (sK4 @ sK6)) | (sK5 @ sK6)))) = $false)),
% 1.82/1.34 inference(not_proxy_clausification,[status(thm)],[f217])).
% 1.82/1.34 thf(f217,plain,(
% 1.82/1.34 ((~ ((~ ((~ (sK5 @ sK6)) | (sK4 @ sK6))) | (~ ((~ (sK4 @ sK6)) | (sK5 @ sK6))))) = $true) | ((~ ((~ ((~ (sK4 @ sK6)) | (sK5 @ sK6))) | (~ ((sK4 @ sK6) | (~ (sK5 @ sK6)))))) = $true)),
% 1.82/1.34 inference(binary_proxy_clausification,[status(thm)],[f216])).
% 1.82/1.34 thf(f301,plain,(
% 1.82/1.34 spl2_3 | spl2_4),
% 1.82/1.34 inference(avatar_split_clause,[status(thm)],[f278,f297,f293])).
% 1.82/1.34 thf(f278,plain,(
% 1.82/1.34 ((sK4 @ sK6) = $true) | ($false = (sK5 @ sK6))),
% 1.82/1.34 inference(not_proxy_clausification,[status(thm)],[f277])).
% 1.82/1.34 thf(f277,plain,(
% 1.82/1.34 ((~ (sK5 @ sK6)) = $true) | ((sK4 @ sK6) = $true)),
% 1.82/1.34 inference(duplicate_literal_removal,[status(thm)],[f276])).
% 1.82/1.34 thf(f276,plain,(
% 1.82/1.34 ((~ (sK5 @ sK6)) = $true) | ((sK4 @ sK6) = $true) | ((sK4 @ sK6) = $true) | ((~ (sK5 @ sK6)) = $true)),
% 1.82/1.34 inference(binary_proxy_clausification,[status(thm)],[f275])).
% 1.82/1.34 thf(f275,plain,(
% 1.82/1.34 (((~ (sK5 @ sK6)) | (sK4 @ sK6)) = $true) | ((~ (sK5 @ sK6)) = $true) | ((sK4 @ sK6) = $true)),
% 1.82/1.34 inference(binary_proxy_clausification,[status(thm)],[f274])).
% 1.82/1.34 thf(f274,plain,(
% 1.82/1.34 (((sK4 @ sK6) | (~ (sK5 @ sK6))) = $true) | (((~ (sK5 @ sK6)) | (sK4 @ sK6)) = $true)),
% 1.82/1.34 inference(not_proxy_clausification,[status(thm)],[f273])).
% 1.82/1.34 thf(f273,plain,(
% 1.82/1.34 ((~ ((~ (sK5 @ sK6)) | (sK4 @ sK6))) = $false) | (((sK4 @ sK6) | (~ (sK5 @ sK6))) = $true)),
% 1.82/1.34 inference(binary_proxy_clausification,[status(thm)],[f271])).
% 1.82/1.34 thf(f271,plain,(
% 1.82/1.34 (((~ ((~ (sK5 @ sK6)) | (sK4 @ sK6))) | (~ ((~ (sK4 @ sK6)) | (sK5 @ sK6)))) = $false) | (((sK4 @ sK6) | (~ (sK5 @ sK6))) = $true)),
% 1.82/1.34 inference(not_proxy_clausification,[status(thm)],[f257])).
% 1.82/1.34 thf(f257,plain,(
% 1.82/1.34 ((~ ((sK4 @ sK6) | (~ (sK5 @ sK6)))) = $false) | (((~ ((~ (sK5 @ sK6)) | (sK4 @ sK6))) | (~ ((~ (sK4 @ sK6)) | (sK5 @ sK6)))) = $false)),
% 1.82/1.34 inference(binary_proxy_clausification,[status(thm)],[f256])).
% 1.82/1.34 % SZS output end Proof for DTF2THF_27794
% 1.82/1.34 % (28013)------------------------------
% 1.82/1.34 % (28013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.34 % (28013)Termination reason: Refutation
% 1.82/1.34
% 1.82/1.34 % (28013)Memory used [KB]: 6012
% 1.82/1.34 % (28013)Time elapsed: 0.016 s
% 1.82/1.34 % (28013)Instructions burned: 31 (million)
% 1.82/1.34 % (28013)------------------------------
% 1.82/1.34 % (28013)------------------------------
% 1.82/1.34 % (28012)Success in time 0.025 s
%------------------------------------------------------------------------------