TSTP Solution File: LCL958^18 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL958^18 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 14:12:11 EDT 2022
% Result : Theorem 25.83s 26.14s
% Output : Proof 25.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 118
% Syntax : Number of formulae : 131 ( 29 unt; 15 typ; 18 def)
% Number of atoms : 403 ( 19 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 804 ( 109 ~; 49 |; 0 &; 430 @)
% ( 45 <=>; 167 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 74 ( 71 usr; 69 con; 0-2 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 139 ( 31 ^ 108 !; 0 ?; 139 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mworld,type,
mworld: $tType ).
thf(ty_eigen__14,type,
eigen__14: mworld ).
thf(ty_eigen__12,type,
eigen__12: mworld ).
thf(ty_eiw_di,type,
eiw_di: $i > mworld > $o ).
thf(ty_eigen__1,type,
eigen__1: mworld ).
thf(ty_eigen__15,type,
eigen__15: mworld ).
thf(ty_mrel,type,
mrel: mworld > mworld > $o ).
thf(ty_eigen__19,type,
eigen__19: mworld ).
thf(ty_eigen__11,type,
eigen__11: $i ).
thf(ty_eigen__17,type,
eigen__17: mworld ).
thf(ty_eigen__13,type,
eigen__13: $i ).
thf(ty_big_p,type,
big_p: $i > mworld > $o ).
thf(ty_big_q,type,
big_q: $i > mworld > $o ).
thf(ty_mactual,type,
mactual: mworld ).
thf(ty_eigen__18,type,
eigen__18: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( eiw_di @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(h1,assumption,
! [X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__15,definition,
( eigen__15
= ( eps__1
@ ^ [X1: mworld] :
~ ( ( mrel @ eigen__14 @ X1 )
=> ( big_p @ eigen__13 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__15])]) ).
thf(eigendef_eigen__17,definition,
( eigen__17
= ( eps__1
@ ^ [X1: mworld] :
~ ( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_p @ eigen__13 @ X4 ) )
=> ( ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_q @ eigen__13 @ X4 ) )
=> ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_p @ X2 @ X4 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__17])]) ).
thf(eigendef_eigen__14,definition,
( eigen__14
= ( eps__1
@ ^ [X1: mworld] :
~ ( ( mrel @ eigen__12 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_p @ eigen__11 @ X2 ) )
=> ( ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_q @ eigen__11 @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_p @ eigen__13 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__14])]) ).
thf(eigendef_eigen__12,definition,
( eigen__12
= ( eps__1
@ ^ [X1: mworld] :
~ ( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_p @ eigen__11 @ X4 ) )
=> ( ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_q @ eigen__11 @ X4 ) )
=> ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_p @ X2 @ X4 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__12])]) ).
thf(eigendef_eigen__18,definition,
( eigen__18
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eiw_di @ X1 @ eigen__17 )
=> ! [X2: mworld] :
( ( mrel @ eigen__17 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_p @ eigen__13 @ X3 ) )
=> ( ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_q @ eigen__13 @ X3 ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_p @ X1 @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__18])]) ).
thf(eigendef_eigen__13,definition,
( eigen__13
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eiw_di @ X1 @ eigen__12 )
=> ! [X2: mworld] :
( ( mrel @ eigen__12 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_p @ eigen__11 @ X3 ) )
=> ( ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_q @ eigen__11 @ X3 ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_p @ X1 @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__13])]) ).
thf(eigendef_eigen__19,definition,
( eigen__19
= ( eps__1
@ ^ [X1: mworld] :
~ ( ( mrel @ eigen__17 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_p @ eigen__13 @ X2 ) )
=> ( ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_q @ eigen__13 @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_p @ eigen__18 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__19])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: mworld] :
~ ! [X2: $i] :
~ ( eiw_di @ X2 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__17 )
=> ! [X2: mworld] :
( ( mrel @ eigen__17 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_p @ eigen__13 @ X3 ) )
=> ( ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_q @ eigen__13 @ X3 ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_p @ X1 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: mworld] :
( ( mrel @ eigen__17 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_p @ eigen__13 @ X2 ) )
=> ( ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_q @ eigen__13 @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_p @ eigen__18 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( mrel @ eigen__17 @ eigen__19 )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__19 @ X1 )
=> ( big_p @ eigen__13 @ X1 ) )
=> ( ~ ! [X1: mworld] :
( ( mrel @ eigen__19 @ X1 )
=> ( big_q @ eigen__13 @ X1 ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__19 @ X1 )
=> ( big_p @ eigen__18 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eiw_di @ eigen__18 @ eigen__17 )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( mrel @ eigen__12 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( mrel @ eigen__14 @ eigen__15 )
=> ( big_p @ eigen__13 @ eigen__15 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: mworld] :
( ( mrel @ eigen__14 @ X1 )
=> ( big_p @ eigen__13 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eiw_di @ eigen__13 @ eigen__12 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP9
=> ! [X1: mworld] :
( ( mrel @ eigen__12 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_p @ eigen__11 @ X2 ) )
=> ( ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_q @ eigen__11 @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_p @ eigen__13 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( !! @ ( mrel @ eigen__19 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( !! @ ( mrel @ eigen__12 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__12 )
=> ! [X2: mworld] :
( ( mrel @ eigen__12 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_p @ eigen__11 @ X3 ) )
=> ( ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_q @ eigen__11 @ X3 ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_p @ X1 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ~ ( ( eiw_di @ X1 @ eigen__1 )
=> ~ ( mrel @ eigen__1 @ mactual ) )
=> ( eiw_di @ X1 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( mrel @ eigen__1 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( big_p @ eigen__13 @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ ( ( eiw_di @ eigen__11 @ eigen__1 )
=> ~ sP15 )
=> ( eiw_di @ eigen__11 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( !! @ ( mrel @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( mrel @ eigen__19 @ eigen__15 )
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( eiw_di @ eigen__13 @ mactual )
=> ~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_p @ eigen__13 @ X4 ) )
=> ( ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_q @ eigen__13 @ X4 ) )
=> ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_p @ X2 @ X4 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( mrel @ eigen__19 @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( mrel @ mactual @ eigen__17 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ! [X1: mworld] :
( ( mrel @ eigen__14 @ X1 )
=> ( big_p @ eigen__11 @ X1 ) )
=> ( ~ ! [X1: mworld] :
( ( mrel @ eigen__14 @ X1 )
=> ( big_q @ eigen__11 @ X1 ) )
=> sP8 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP9
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( mrel @ mactual @ eigen__12 )
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_p @ eigen__13 @ X4 ) )
=> ( ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_q @ eigen__13 @ X4 ) )
=> ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_p @ X2 @ X4 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: mworld,X2: $i] :
( ~ ( ( eiw_di @ X2 @ eigen__12 )
=> ~ ( mrel @ eigen__12 @ X1 ) )
=> ( eiw_di @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: mworld,X2: $i] :
( ~ ( ( eiw_di @ X2 @ eigen__1 )
=> ~ ( mrel @ eigen__1 @ X1 ) )
=> ( eiw_di @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( eiw_di @ eigen__11 @ eigen__1 )
=> ~ sP15 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ( eiw_di @ eigen__11 @ mactual )
=> ~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_p @ eigen__11 @ X4 ) )
=> ( ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_q @ eigen__11 @ X4 ) )
=> ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_p @ X2 @ X4 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: mworld,X2: mworld,X3: $i] :
( ~ ( ( eiw_di @ X3 @ X1 )
=> ~ ( mrel @ X1 @ X2 ) )
=> ( eiw_di @ X3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: mworld] :
( ( mrel @ eigen__19 @ X1 )
=> ( big_p @ eigen__13 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: mworld] : ( !! @ ( mrel @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: mworld] :
( ( mrel @ eigen__12 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_p @ eigen__11 @ X2 ) )
=> ( ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_q @ eigen__11 @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_p @ eigen__13 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( sP32
=> ( ~ ! [X1: mworld] :
( ( mrel @ eigen__19 @ X1 )
=> ( big_q @ eigen__13 @ X1 ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__19 @ X1 )
=> ( big_p @ eigen__18 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ( mrel @ eigen__12 @ eigen__14 )
=> sP23 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: $i] :
~ ( eiw_di @ X1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: $i] :
( ~ ( ( eiw_di @ X1 @ eigen__12 )
=> ~ sP6 )
=> ( eiw_di @ X1 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ~ sP24
=> ( eiw_di @ eigen__13 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_p @ eigen__11 @ X4 ) )
=> ( ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_q @ eigen__11 @ X4 ) )
=> ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_p @ X2 @ X4 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ~ ! [X1: mworld] :
( ( mrel @ eigen__14 @ X1 )
=> ( big_q @ eigen__11 @ X1 ) )
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( eiw_di @ eigen__13 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ~ ! [X2: mworld] :
( ( mrel @ mactual @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( big_p @ X1 @ X5 ) )
=> ( ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( big_q @ X1 @ X5 ) )
=> ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( big_p @ X3 @ X5 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( eiw_di @ eigen__11 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( eiw_di @ eigen__11 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(def_mlocal,definition,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: mworld > $o,X2: mworld] :
~ ( X1 @ X2 ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_mequiv,definition,
( mequiv
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) ) ).
thf(def_mbox,definition,
( mbox
= ( ^ [X1: mworld > $o,X2: mworld] :
! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ).
thf(def_mdia,definition,
( mdia
= ( ^ [X1: mworld > $o,X2: mworld] :
~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ~ ( X1 @ X3 ) ) ) ) ).
thf(def_mforall_di,definition,
( mforall_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_mexists_di,definition,
( mexists_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
~ ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(x2137,conjecture,
~ sP43 ).
thf(h2,negated_conjecture,
sP43,
inference(assume_negation,[status(cth)],[x2137]) ).
thf(1,plain,
( ~ sP11
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP33
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP12
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP32
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP19
| ~ sP21
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP35
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP4
| ~ sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP3
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__19]) ).
thf(9,plain,
( sP5
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP2
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__18]) ).
thf(11,plain,
( sP22
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP26
| ~ sP22 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__17]) ).
thf(13,plain,
( ~ sP43
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP20
| ~ sP42
| ~ sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP38
| sP39 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP39
| sP24
| sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP24
| ~ sP9
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP27
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP31
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP33
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP18
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( sP7
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP8
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__15]) ).
thf(24,plain,
( sP41
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP23
| ~ sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP36
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP34
| ~ sP36 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__14]) ).
thf(28,plain,
( sP10
| ~ sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( sP10
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( sP13
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__13]) ).
thf(31,plain,
( sP25
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP40
| ~ sP25 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__12]) ).
thf(33,plain,
( ~ sP43
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP30
| ~ sP44
| ~ sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP14
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP17
| sP29
| sP44 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP29
| ~ sP45
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( sP37
| sP45 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).
thf(39,plain,
( ~ sP28
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP31
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP1
| ~ sP37 ),
inference(all_rule,[status(thm)],]) ).
thf(42,plain,
( ~ sP33
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(eiw_di_cumul,axiom,
sP31 ).
thf(eiw_di_nonempty,axiom,
sP1 ).
thf(mrel_universal,axiom,
sP33 ).
thf(43,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([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,h2,eiw_di_cumul,eiw_di_nonempty,mrel_universal]) ).
thf(44,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[43,h1]) ).
thf(45,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[44,h0]) ).
thf(0,theorem,
~ sP43,
inference(contra,[status(thm),contra(discharge,[h2])],[43,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LCL958^18 : TPTP v8.1.0. Released v8.1.0.
% 0.04/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 4 23:56:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 25.83/26.14 % SZS status Theorem
% 25.83/26.14 % Mode: mode461
% 25.83/26.14 % Inferences: 2016
% 25.83/26.14 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------