TSTP Solution File: SWV433^2 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SWV433^2 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n016.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 : Thu Aug 31 22:49:12 EDT 2023
% Result : Theorem 159.03s 159.25s
% Output : Proof 159.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 165
% Syntax : Number of formulae : 176 ( 42 unt; 11 typ; 29 def)
% Number of atoms : 531 ( 29 equ; 3 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 806 ( 117 ~; 76 |; 2 &; 375 @)
% ( 62 <=>; 174 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% Number of symbols : 104 ( 100 usr; 98 con; 0-2 aty)
% Number of variables : 158 ( 47 ^; 107 !; 4 ?; 158 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_deletefile1,type,
deletefile1: $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_bob,type,
bob: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__12,type,
eigen__12: $i ).
thf(ty_alice,type,
alice: $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_admin,type,
admin: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_rel,type,
rel: $i > $i > $o ).
thf(ty_eigen__41,type,
eigen__41: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
~ ( ( rel @ eigen__1 @ X1 )
=> ( ~ ( admin @ X1 )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__12,definition,
( eigen__12
= ( eps__0
@ ^ [X1: $i] :
~ ( ( rel @ eigen__4 @ X1 )
=> ( ~ ( bob @ X1 )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__12])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ( ( rel @ eigen__3 @ X1 )
=> ( ~ ( admin @ X1 )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__41,definition,
( eigen__41
= ( eps__0
@ ^ [X1: $i] :
~ ( ( rel @ eigen__12 @ X1 )
=> ( ~ ( bob @ X1 )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__41])]) ).
thf(sP1,plain,
( sP1
<=> ( rel @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ! [X1: $i] :
( ( rel @ eigen__4 @ X1 )
=> ( ~ ( bob @ X1 )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( rel @ eigen__4 @ X1 )
=> ( deletefile1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( rel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( ~ ( admin @ X2 )
=> ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( deletefile1 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( rel @ eigen__12 @ X1 )
=> ( deletefile1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( admin @ eigen__3 )
=> ! [X1: $i] :
( ( rel @ eigen__3 @ X1 )
=> ( deletefile1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i,X2: $i] :
( ( rel @ X1 @ X2 )
=> ( ~ ( admin @ X2 )
=> ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( rel @ X3 @ X4 )
=> ( ~ ( bob @ X4 )
=> ! [X5: $i] :
( ( rel @ X4 @ X5 )
=> ( deletefile1 @ X5 ) ) ) )
=> ! [X4: $i] :
( ( rel @ X3 @ X4 )
=> ( deletefile1 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( rel @ eigen__1 @ eigen__3 )
=> ( ~ ( admin @ eigen__3 )
=> ! [X1: $i] :
( ( rel @ eigen__3 @ X1 )
=> ( ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( ~ ( bob @ X2 )
=> ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( deletefile1 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ( admin @ eigen__4 )
=> ! [X1: $i] :
( ( rel @ eigen__4 @ X1 )
=> ( ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( ~ ( bob @ X2 )
=> ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( deletefile1 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( rel @ eigen__3 @ X1 )
=> ( ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( ~ ( bob @ X2 )
=> ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( deletefile1 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ! [X1: $i] :
( ( rel @ eigen__1 @ X1 )
=> ( deletefile1 @ X1 ) )
=> ( deletefile1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( rel @ eigen__12 @ eigen__41 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( rel @ eigen__1 @ X1 )
=> ( ~ ( admin @ X1 )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( rel @ eigen__3 @ eigen__4 )
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( alice @ eigen__41 )
=> ( bob @ eigen__41 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( rel @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ ( bob @ eigen__12 )
=> ! [X1: $i] :
( ( rel @ eigen__12 @ X1 )
=> ( ( alice @ X1 )
=> ( bob @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( rel @ eigen__1 @ eigen__3 )
=> ( ! [X1: $i] :
( ( rel @ eigen__3 @ X1 )
=> ( ~ ( admin @ X1 )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( rel @ eigen__3 @ X1 )
=> ( deletefile1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i,X2: $i] :
( ( rel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( ~ ( admin @ X3 )
=> ! [X4: $i] :
( ( rel @ X3 @ X4 )
=> ( deletefile1 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( deletefile1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP15
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ( rel @ eigen__4 @ X1 )
=> ( ~ ( bob @ X1 )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP11
=> ( ~ ( alice @ eigen__41 )
=> ! [X1: $i] :
( ( rel @ eigen__41 @ X1 )
=> ( deletefile1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ ( admin @ eigen__4 )
=> ! [X1: $i] :
( ( rel @ eigen__4 @ X1 )
=> ( deletefile1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ~ ( bob @ eigen__41 )
=> ! [X1: $i] :
( ( rel @ eigen__41 @ X1 )
=> ( deletefile1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( bob @ eigen__12 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i] :
( ( rel @ eigen__12 @ X1 )
=> ( ~ ( bob @ X1 )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i] :
( ( rel @ eigen__41 @ X1 )
=> ( deletefile1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( rel @ eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
( ( rel @ eigen__3 @ X1 )
=> ( deletefile1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i] :
( ( rel @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( ~ ( admin @ X2 )
=> ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( deletefile1 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( sP25
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP1
=> ( sP12
=> ! [X1: $i] :
( ( rel @ eigen__1 @ X1 )
=> ( deletefile1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ ( admin @ eigen__3 )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ( rel @ eigen__4 @ eigen__12 )
=> ( ~ sP24
=> sP4 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( alice @ eigen__41 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i] :
( ( rel @ eigen__4 @ X1 )
=> ( ~ ( bob @ X1 )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( ( alice @ X2 )
=> ( bob @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: $i] :
( ( rel @ eigen__12 @ X1 )
=> ( ~ ( alice @ X1 )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( sP11
=> sP23 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( sP12
=> ! [X1: $i] :
( ( rel @ eigen__1 @ X1 )
=> ( deletefile1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( sP27
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: $i,X2: $i] :
( ( rel @ X1 @ X2 )
=> ( ~ ( alice @ X2 )
=> ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( deletefile1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( sP11
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: $i] :
( ( rel @ eigen__1 @ X1 )
=> ( deletefile1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( deletefile1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( ~ sP24
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: $i] :
( ( rel @ eigen__12 @ X1 )
=> ( ( alice @ X1 )
=> ( bob @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( rel @ eigen__4 @ eigen__12 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ! [X1: $i > $o,X2: $i] :
( ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( X1 @ X3 ) )
=> ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( ~ sP34
=> sP26 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ! [X1: $i] :
( ( rel @ eigen__3 @ X1 )
=> ( ~ ( admin @ X1 )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( ~ ( bob @ X3 )
=> ! [X4: $i] :
( ( rel @ X3 @ X4 )
=> ( deletefile1 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( deletefile1 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ! [X1: $i] :
( ( rel @ eigen__4 @ X1 )
=> ( ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( ~ ( bob @ X2 )
=> ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( deletefile1 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( bob @ eigen__41 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( admin @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( sP46
=> sP30 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ! [X1: $i] :
( ( rel @ eigen__1 @ X1 )
=> ( ~ ( admin @ X1 )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( ~ ( bob @ X3 )
=> ! [X4: $i] :
( ( rel @ X3 @ X4 )
=> ( deletefile1 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( deletefile1 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) )
=> ( deletefile1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ! [X1: $i,X2: $i] :
( ( rel @ X1 @ X2 )
=> ( ~ ( bob @ X2 )
=> ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( ( alice @ X3 )
=> ( bob @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( ! [X1: $i] :
( ( rel @ eigen__3 @ X1 )
=> ( ~ ( admin @ X1 )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ) ) )
=> sP28 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( sP15
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( sP46
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( admin @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ! [X1: $i] :
( ( rel @ eigen__3 @ X1 )
=> ( ~ ( admin @ X1 )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ! [X1: $i] :
( ( rel @ eigen__4 @ X1 )
=> ( deletefile1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(def_mfalse,definition,
( mfalse
= ( ^ [X1: $i] : $false ) ) ).
thf(def_mtrue,definition,
( mtrue
= ( ^ [X1: $i] : $true ) ) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: $i > $o,X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
| ( X2 @ X3 ) ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ).
thf(def_mimpl,definition,
( mimpl
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X1 ) @ X2 ) ) ) ).
thf(def_miff,definition,
( miff
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ ( mimpl @ X1 @ X2 ) @ ( mimpl @ X2 @ X1 ) ) ) ) ).
thf(def_mbox,definition,
( mbox
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X1 @ X3 @ X4 )
@ ( X2 @ X4 ) ) ) ) ).
thf(def_mdia,definition,
( mdia
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
? [X4: $i] :
( ( X1 @ X3 @ X4 )
& ( X2 @ X4 ) ) ) ) ).
thf(def_mall,definition,
( mall
= ( ^ [X1: individuals > $i > $o,X2: $i] :
! [X3: individuals] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mexists,definition,
( mexists
= ( ^ [X1: individuals > $i > $o,X2: $i] :
? [X3: individuals] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mvalid,definition,
( mvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_msatisfiable,definition,
( msatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_minvalid,definition,
( minvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_icl_atom,definition,
( icl_atom
= ( ^ [X1: $i > $o] : ( mbox @ rel @ X1 ) ) ) ).
thf(def_icl_princ,definition,
( icl_princ
= ( ^ [X1: $i > $o] : X1 ) ) ).
thf(def_icl_and,definition,
( icl_and
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ X1 @ X2 ) ) ) ).
thf(def_icl_or,definition,
( icl_or
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ X1 @ X2 ) ) ) ).
thf(def_icl_impl,definition,
( icl_impl
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mbox @ rel @ ( mimpl @ X1 @ X2 ) ) ) ) ).
thf(def_icl_true,definition,
icl_true = mtrue ).
thf(def_icl_false,definition,
icl_false = mfalse ).
thf(def_icl_says,definition,
( icl_says
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mbox @ rel @ ( mor @ X1 @ X2 ) ) ) ) ).
thf(def_iclval,definition,
( iclval
= ( ^ [X1: $i > $o] : ( mvalid @ X1 ) ) ) ).
thf(def_icl_impl_princ,definition,
( icl_impl_princ
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mbox @ rel @ ( mimpl @ X1 @ X2 ) ) ) ) ).
thf(conj,conjecture,
! [X1: $i,X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i,X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(h2,assumption,
~ ! [X1: $i] :
( ( rel @ eigen__0 @ X1 )
=> ( deletefile1 @ X1 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP1
=> sP43 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP1,
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP43,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP14
| ~ sP34
| sP51 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP48
| sP34
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP21
| ~ sP11
| sP48 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP41
| ~ sP11
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP23
| ~ sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP23
| ~ sP51 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP36
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP45
| sP41 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( sP44
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP44
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP37
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP37
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP25
| ~ sP37 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__41]) ).
thf(14,plain,
( ~ sP30
| ~ sP25
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP16
| sP24
| sP45 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP53
| ~ sP46
| sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP59
| ~ sP46
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP40
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP35
| sP59 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP50
| sP53 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( sP33
| ~ sP44 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP33
| sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP20
| ~ sP33 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__12]) ).
thf(24,plain,
( ~ sP2
| ~ sP20
| sP62 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP19
| ~ sP15
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP5
| ~ sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP5
| ~ sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP10
| ~ sP42
| sP43 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP9
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP32
| sP52
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP8
| sP60
| sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP7
| ~ sP27
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP13
| ~ sP15
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP55
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP56
| sP35 ),
inference(all_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP49
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP54
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP47
| sP55 ),
inference(all_rule,[status(thm)],]) ).
thf(39,plain,
( sP22
| ~ sP62 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( sP22
| ~ sP60 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP6
| sP54 ),
inference(all_rule,[status(thm)],]) ).
thf(42,plain,
( ~ sP6
| sP49 ),
inference(all_rule,[status(thm)],]) ).
thf(43,plain,
( sP58
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( sP58
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( ~ sP17
| ~ sP27
| sP57 ),
inference(prop_rule,[status(thm)],]) ).
thf(46,plain,
( sP61
| ~ sP58 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(47,plain,
( ~ sP57
| ~ sP61
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP29
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(49,plain,
( sP39
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(50,plain,
( sP39
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(51,plain,
( sP12
| ~ sP39 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(52,plain,
( ~ sP38
| ~ sP12
| sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(53,plain,
( ~ sP31
| ~ sP1
| sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(54,plain,
( ~ sP3
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(55,plain,
( ~ sP18
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(56,plain,
( ~ sP18
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(refl_axiom,axiom,
sP47 ).
thf(ax1,axiom,
sP18 ).
thf(ax2,axiom,
sP6 ).
thf(ax3,axiom,
sP56 ).
thf(ax4,axiom,
sP40 ).
thf(57,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,refl_axiom,ax1,ax2,ax3,ax4,h4,h5]) ).
thf(58,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,57,h4,h5]) ).
thf(59,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,58,h3]) ).
thf(60,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,59,h2]) ).
thf(61,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[60,h0]) ).
thf(0,theorem,
! [X1: $i,X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[60,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWV433^2 : TPTP v8.1.2. Released v3.6.0.
% 0.10/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.11/0.33 % Computer : n016.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Tue Aug 29 06:26:30 EDT 2023
% 0.11/0.33 % CPUTime :
% 159.03/159.25 % SZS status Theorem
% 159.03/159.25 % Mode: cade22grackle2x01b3
% 159.03/159.25 % Steps: 71495
% 159.03/159.25 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------