TSTP Solution File: SYN367^7 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYN367^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n031.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 : Fri Sep 1 03:20:40 EDT 2023
% Result : Theorem 0.60s 0.79s
% Output : Proof 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 185
% Syntax : Number of formulae : 209 ( 73 unt; 16 typ; 34 def)
% Number of atoms : 630 ( 38 equ; 5 cnn)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 1210 ( 177 ~; 70 |; 8 &; 647 @)
% ( 58 <=>; 250 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 70 ( 70 >; 0 *; 0 +; 0 <<)
% Number of symbols : 111 ( 107 usr; 105 con; 0-2 aty)
% Number of variables : 269 ( 69 ^; 194 !; 6 ?; 269 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mu,type,
mu: $tType ).
thf(ty_eigen__3,type,
eigen__3: mu ).
thf(ty_big_q,type,
big_q: mu > $i > $o ).
thf(ty_eigen__6,type,
eigen__6: mu ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_p,type,
p: $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_rel_s4,type,
rel_s4: $i > $i > $o ).
thf(ty_big_r,type,
big_r: mu > $i > $o ).
thf(ty_eigen__15,type,
eigen__15: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_exists_in_world,type,
exists_in_world: mu > $i > $o ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__12,type,
eigen__12: mu ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__15,definition,
( eigen__15
= ( eps__0
@ ^ [X1: $i] :
~ ( ( rel_s4 @ eigen__4 @ X1 )
=> ( p @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__15])]) ).
thf(h1,assumption,
! [X1: mu > $o,X2: mu] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__12,definition,
( eigen__12
= ( eps__1
@ ^ [X1: mu] :
~ ~ ( exists_in_world @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__12])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] : ( rel_s4 @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( exists_in_world @ eigen__6 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__2 @ X1 )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( p @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__2 )
=> ( ( ! [X2: $i] :
( ( rel_s4 @ eigen__2 @ X2 )
=> ( p @ X2 ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ eigen__2 @ X2 )
=> ( big_q @ X1 @ X2 ) ) )
=> ~ ( sP3
=> ~ ! [X2: $i] :
( ( rel_s4 @ eigen__2 @ X2 )
=> ( big_r @ X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( rel_s4 @ eigen__2 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( rel_s4 @ eigen__1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( exists_in_world @ eigen__12 @ eigen__1 )
=> ( ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( p @ X1 ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( big_q @ eigen__12 @ X1 ) ) )
=> ~ ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( p @ X2 ) ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( big_r @ eigen__12 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( rel_s4 @ eigen__1 @ eigen__2 )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( big_r @ eigen__6 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( p @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: mu] :
~ ( exists_in_world @ X1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i,X2: $i] :
( ~ ( ( rel_s4 @ eigen__1 @ X1 )
=> ~ ( rel_s4 @ X1 @ X2 ) )
=> ( rel_s4 @ eigen__1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP5
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__4 @ X1 )
=> ( p @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__5 @ X1 )
=> ( big_r @ eigen__6 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__5 @ X1 )
=> ( p @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( ! [X1: $i] :
( ( rel_s4 @ eigen__2 @ X1 )
=> ( p @ X1 ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__2 @ X1 )
=> ( big_q @ eigen__3 @ X1 ) ) )
=> ~ ( sP3
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__2 @ X1 )
=> ( big_r @ eigen__3 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP5
=> ( big_q @ eigen__3 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( rel_s4 @ eigen__5 @ eigen__7 )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ~ ( sP5
=> ~ ( rel_s4 @ eigen__4 @ eigen__15 ) )
=> ( rel_s4 @ eigen__2 @ eigen__15 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( rel_s4 @ eigen__5 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ~ ( ( rel_s4 @ eigen__1 @ eigen__2 )
=> ~ ( rel_s4 @ eigen__2 @ X1 ) )
=> ( rel_s4 @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i] :
( ~ ( sP5
=> ~ ( rel_s4 @ eigen__4 @ X1 ) )
=> ( rel_s4 @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP10
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( big_r @ eigen__12 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( rel_s4 @ eigen__2 @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP6
=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__1 )
=> ( ( ! [X2: $i] :
( ( rel_s4 @ eigen__1 @ X2 )
=> ( p @ X2 ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ eigen__1 @ X2 )
=> ( big_q @ X1 @ X2 ) ) )
=> ~ ( sP10
=> ~ ! [X2: $i] :
( ( rel_s4 @ eigen__1 @ X2 )
=> ( big_r @ X1 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( rel_s4 @ eigen__1 @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( rel_s4 @ eigen__4 @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( ( ! [X3: $i] :
( ( rel_s4 @ X1 @ X3 )
=> ( p @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( rel_s4 @ X1 @ X3 )
=> ~ ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( p @ X4 ) ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X1 @ X3 )
=> ( big_r @ X2 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__2 @ X1 )
=> ( big_q @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( big_q @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( exists_in_world @ eigen__3 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__5 @ X1 )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( p @ X2 ) ) )
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ( rel_s4 @ eigen__1 @ eigen__5 )
=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__5 )
=> ( ( sP15
=> ~ ! [X2: $i] :
( ( rel_s4 @ eigen__5 @ X2 )
=> ( big_q @ X1 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( rel_s4 @ eigen__5 @ X2 )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( p @ X3 ) ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ eigen__5 @ X2 )
=> ( big_r @ X1 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( exists_in_world @ eigen__12 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( rel_s4 @ X1 @ X2 )
=> ~ ( rel_s4 @ X2 @ X3 ) )
=> ( rel_s4 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: $i] :
~ ! [X2: mu] :
~ ( exists_in_world @ X2 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( sP27
=> ( p @ eigen__15 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ~ ( ( rel_s4 @ eigen__1 @ eigen__2 )
=> ~ sP24 )
=> sP26 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ( rel_s4 @ eigen__1 @ eigen__2 )
=> ~ sP24 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( rel_s4 @ eigen__1 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( p @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__5 )
=> ( ( sP15
=> ~ ! [X2: $i] :
( ( rel_s4 @ eigen__5 @ X2 )
=> ( big_q @ X1 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( rel_s4 @ eigen__5 @ X2 )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( p @ X3 ) ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ eigen__5 @ X2 )
=> ( big_r @ X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( rel_s4 @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__2 @ X1 )
=> ( p @ X1 ) )
=> ~ sP29 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( sP40
=> ~ sP15 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( sP26
=> ( p @ eigen__15 ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( sP31
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( sP3
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__2 @ X1 )
=> ( big_r @ eigen__3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( sP2
=> ( ( sP15
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__5 @ X1 )
=> ( big_q @ eigen__6 @ X1 ) ) )
=> ~ sP32 ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__1 )
=> ( ( sP41
=> ~ ! [X2: $i] :
( ( rel_s4 @ eigen__1 @ X2 )
=> ( big_q @ X1 @ X2 ) ) )
=> ~ ( sP10
=> ~ ! [X2: $i] :
( ( rel_s4 @ eigen__1 @ X2 )
=> ( big_r @ X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( ( sP15
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__5 @ X1 )
=> ( big_q @ eigen__6 @ X1 ) ) )
=> ~ sP32 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( ( sP41
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( big_q @ eigen__12 @ X1 ) ) )
=> ~ sP23 ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( sP41
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( big_q @ eigen__12 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ! [X1: $i,X2: $i] :
( ~ ( ( rel_s4 @ eigen__2 @ X1 )
=> ~ ( rel_s4 @ X1 @ X2 ) )
=> ( rel_s4 @ eigen__2 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( sP5
=> ~ sP27 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( sP15
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__5 @ X1 )
=> ( big_q @ eigen__6 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( p @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__4 @ X1 )
=> ( p @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(def_meq_prop,definition,
( meq_prop
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) ) ).
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_mbox,definition,
( mbox
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
! [X4: $i] :
( ( (~) @ ( X1 @ X3 @ X4 ) )
| ( X2 @ X4 ) ) ) ) ).
thf(def_mforall_prop,definition,
( mforall_prop
= ( ^ [X1: ( $i > $o ) > $i > $o,X2: $i] :
! [X3: $i > $o] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mtrue,definition,
( mtrue
= ( ^ [X1: $i] : $true ) ) ).
thf(def_mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mnot @ ( mor @ ( mnot @ X1 ) @ ( mnot @ X2 ) ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X1 ) @ X2 ) ) ) ).
thf(def_mimplied,definition,
( mimplied
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X2 ) @ X1 ) ) ) ).
thf(def_mequiv,definition,
( mequiv
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ ( mimplies @ X1 @ X2 ) @ ( mimplies @ X2 @ X1 ) ) ) ) ).
thf(def_mxor,definition,
( mxor
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mnot @ ( mequiv @ X1 @ X2 ) ) ) ) ).
thf(def_mdia,definition,
( mdia
= ( ^ [X1: $i > $i > $o,X2: $i > $o] : ( mnot @ ( mbox @ X1 @ ( mnot @ X2 ) ) ) ) ) ).
thf(def_mforall_ind,definition,
( mforall_ind
= ( ^ [X1: mu > $i > $o,X2: $i] :
! [X3: mu] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( exists_in_world @ X3 @ X2 )
@ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_mexists_ind,definition,
( mexists_ind
= ( ^ [X1: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X2: mu] : ( mnot @ ( X1 @ X2 ) ) ) ) ) ) ).
thf(def_mexists_prop,definition,
( mexists_prop
= ( ^ [X1: ( $i > $o ) > $i > $o] :
( mnot
@ ( mforall_prop
@ ^ [X2: $i > $o] : ( mnot @ ( X1 @ X2 ) ) ) ) ) ) ).
thf(def_mreflexive,definition,
( mreflexive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ).
thf(def_msymmetric,definition,
( msymmetric
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X2 @ X3 )
@ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_mserial,definition,
( mserial
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
? [X3: $i] : ( X1 @ X2 @ X3 ) ) ) ).
thf(def_mtransitive,definition,
( mtransitive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X3 @ X4 ) )
@ ( X1 @ X2 @ X4 ) ) ) ) ).
thf(def_meuclidean,definition,
( meuclidean
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X2 @ X4 ) )
@ ( X1 @ X3 @ X4 ) ) ) ) ).
thf(def_mpartially_functional,definition,
( mpartially_functional
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X2 @ X4 ) )
@ ( X3 = X4 ) ) ) ) ).
thf(def_mfunctional,definition,
( mfunctional
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
? [X3: $i] :
( ( X1 @ X2 @ X3 )
& ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X1 @ X2 @ X4 )
@ ( X3 = X4 ) ) ) ) ) ).
thf(def_mweakly_dense,definition,
( mweakly_dense
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X1 @ X2 @ X3 )
@ ? [X5: $i] :
( ( X1 @ X2 @ X5 )
& ( X1 @ X5 @ X3 ) ) ) ) ) ).
thf(def_mweakly_connected,definition,
( mweakly_connected
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X2 @ X4 ) )
@ ( ( X1 @ X3 @ X4 )
| ( X3 = X4 )
| ( X1 @ X4 @ X3 ) ) ) ) ) ).
thf(def_mweakly_directed,definition,
( mweakly_directed
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X2 @ X4 ) )
@ ? [X5: $i] :
( ( X1 @ X3 @ X5 )
& ( X1 @ X4 @ X5 ) ) ) ) ) ).
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_mbox_s4,definition,
( mbox_s4
= ( ^ [X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( (~) @ ( rel_s4 @ X2 @ X3 ) )
| ( X1 @ X3 ) ) ) ) ).
thf(def_mdia_s4,definition,
( mdia_s4
= ( ^ [X1: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ X1 ) ) ) ) ) ).
thf(x2118,conjecture,
! [X1: $i,X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ( ( ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ( p @ X5 ) )
=> ~ ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ( big_q @ X4 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( p @ X6 ) ) )
=> ~ ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ( big_r @ X4 @ X5 ) ) ) ) ) )
=> ( ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ( big_q @ X4 @ X5 ) ) ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ( big_r @ X4 @ X5 ) ) ) ) ) ) ) ).
thf(h2,negated_conjecture,
~ ! [X1: $i,X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ( ( ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ( p @ X5 ) )
=> ~ ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ( big_q @ X4 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( p @ X6 ) ) )
=> ~ ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ( big_r @ X4 @ X5 ) ) ) ) ) )
=> ( ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ( big_q @ X4 @ X5 ) ) ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ( big_r @ X4 @ X5 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[x2118]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( rel_s4 @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ! [X3: mu] :
( ( exists_in_world @ X3 @ X2 )
=> ( ( ! [X4: $i] :
( ( rel_s4 @ X2 @ X4 )
=> ( p @ X4 ) )
=> ~ ! [X4: $i] :
( ( rel_s4 @ X2 @ X4 )
=> ( big_q @ X3 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( rel_s4 @ X2 @ X4 )
=> ~ ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( p @ X5 ) ) )
=> ~ ! [X4: $i] :
( ( rel_s4 @ X2 @ X4 )
=> ( big_r @ X3 @ X4 ) ) ) ) ) )
=> ( ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ! [X3: mu] :
( ( exists_in_world @ X3 @ X2 )
=> ! [X4: $i] :
( ( rel_s4 @ X2 @ X4 )
=> ( big_q @ X3 @ X4 ) ) ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ! [X3: mu] :
( ( exists_in_world @ X3 @ X2 )
=> ! [X4: $i] :
( ( rel_s4 @ X2 @ X4 )
=> ( big_r @ X3 @ X4 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ( rel_s4 @ eigen__0 @ eigen__1 )
=> ( sP28
=> ( ~ ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: $i] :
( ( rel_s4 @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) )
=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: $i] :
( ( rel_s4 @ X1 @ X3 )
=> ( big_r @ X2 @ X3 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
rel_s4 @ eigen__0 @ eigen__1,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP28
=> ( ~ ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: $i] :
( ( rel_s4 @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) )
=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: $i] :
( ( rel_s4 @ X1 @ X3 )
=> ( big_r @ X2 @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP28,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: $i] :
( ( rel_s4 @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) )
=> ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: $i] :
( ( rel_s4 @ X1 @ X3 )
=> ( big_r @ X2 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: $i] :
( ( rel_s4 @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: $i] :
( ( rel_s4 @ X1 @ X3 )
=> ( big_r @ X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( sP43
=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__2 )
=> ! [X2: $i] :
( ( rel_s4 @ eigen__2 @ X2 )
=> ( big_q @ X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP43,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__2 )
=> ! [X2: $i] :
( ( rel_s4 @ eigen__2 @ X2 )
=> ( big_q @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( sP31
=> sP29 ),
introduced(assumption,[]) ).
thf(h15,assumption,
sP31,
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP29,
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(h18,assumption,
sP5,
introduced(assumption,[]) ).
thf(h19,assumption,
~ sP30,
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( sP40
=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__5 )
=> ! [X2: $i] :
( ( rel_s4 @ eigen__5 @ X2 )
=> ( big_r @ X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h21,assumption,
sP40,
introduced(assumption,[]) ).
thf(h22,assumption,
~ ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__5 )
=> ! [X2: $i] :
( ( rel_s4 @ eigen__5 @ X2 )
=> ( big_r @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h23,assumption,
~ ( sP2
=> sP14 ),
introduced(assumption,[]) ).
thf(h24,assumption,
sP2,
introduced(assumption,[]) ).
thf(h25,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(h26,assumption,
~ sP18,
introduced(assumption,[]) ).
thf(h27,assumption,
sP20,
introduced(assumption,[]) ).
thf(h28,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP39
| ~ sP43
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP38
| sP39
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP55
| ~ sP5
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP19
| sP55
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP46
| ~ sP26
| sP57 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP41
| sP46 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP21
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP22
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( sP23
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP53
| sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP52
| ~ sP53
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP7
| ~ sP34
| sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP50
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP13
| ~ sP5
| ~ sP58 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP3
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( sP48
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP17
| ~ sP5
| sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP29
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( sP44
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP16
| ~ sP44
| ~ sP48 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP47
| ~ sP31
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP4
| sP47 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP8
| ~ sP43
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP54
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP35
| sP54 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP28
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP12
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( sP37
| ~ sP57 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( sP37
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( sP58
| ~ sP37 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__15]) ).
thf(31,plain,
( ~ sP45
| ~ sP40
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP10
| sP45 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP25
| ~ sP6
| sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( sP11
| sP34 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__12]) ).
thf(35,plain,
( ~ sP1
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP36
| ~ sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP35
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP28
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP18
| ~ sP20
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP14
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(41,plain,
( sP32
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( sP56
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP51
| ~ sP56
| ~ sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( ~ sP49
| ~ sP2
| sP51 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( ~ sP42
| sP49 ),
inference(all_rule,[status(thm)],]) ).
thf(46,plain,
( ~ sP33
| ~ sP40
| sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( ~ sP28
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(a2,axiom,
sP35 ).
thf(a1,axiom,
sP1 ).
thf(nonempty_ax,axiom,
sP36 ).
thf(48,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h27,h28,h26,h24,h25,h23,h21,h22,h20,h18,h19,h17,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,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,h7,h12,h15,h18,h19,h21,h24,h27,h28,a2,a1,nonempty_ax]) ).
thf(49,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h26,h24,h25,h23,h21,h22,h20,h18,h19,h17,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h27,h28])],[h26,48,h27,h28]) ).
thf(50,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h24,h25,h23,h21,h22,h20,h18,h19,h17,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h26]),tab_negall(eigenvar,eigen__7)],[h25,49,h26]) ).
thf(51,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h23,h21,h22,h20,h18,h19,h17,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h24,h25])],[h23,50,h24,h25]) ).
thf(52,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h21,h22,h20,h18,h19,h17,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__6)],[h22,51,h23]) ).
thf(53,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h18,h19,h17,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h21,h22])],[h20,52,h21,h22]) ).
thf(54,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h18,h19,h17,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__5)],[h10,53,h20]) ).
thf(55,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h18,h19])],[h17,54,h18,h19]) ).
thf(56,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__4)],[h16,55,h17]) ).
thf(57,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,56,h15,h16]) ).
thf(58,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__3)],[h13,57,h14]) ).
thf(59,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,58,h12,h13]) ).
thf(60,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__2)],[h9,59,h11]) ).
thf(61,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,60,h9,h10]) ).
thf(62,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,61,h7,h8]) ).
thf(63,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,62,h5,h6]) ).
thf(64,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,63,h4]) ).
thf(65,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,64,h3]) ).
thf(66,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[65,h1]) ).
thf(67,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[66,h0]) ).
thf(0,theorem,
! [X1: $i,X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ( ( ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ( p @ X5 ) )
=> ~ ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ( big_q @ X4 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( p @ X6 ) ) )
=> ~ ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ( big_r @ X4 @ X5 ) ) ) ) ) )
=> ( ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ( big_q @ X4 @ X5 ) ) ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ( big_r @ X4 @ X5 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[65,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SYN367^7 : TPTP v8.1.2. Released v5.5.0.
% 0.13/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n031.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 19:05:53 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.60/0.79 % SZS status Theorem
% 0.60/0.79 % Mode: cade22grackle2xfee4
% 0.60/0.79 % Steps: 5441
% 0.60/0.79 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------