TSTP Solution File: SWV444^1 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SWV444^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% 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 : Thu Aug 31 22:49:15 EDT 2023
% Result : Theorem 0.68s 0.85s
% Output : Proof 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 122
% Syntax : Number of formulae : 142 ( 64 unt; 14 typ; 35 def)
% Number of atoms : 426 ( 35 equ; 3 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 711 ( 49 ~; 31 |; 2 &; 427 @)
% ( 28 <=>; 174 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 57 ( 57 >; 0 *; 0 +; 0 <<)
% Number of symbols : 80 ( 76 usr; 75 con; 0-2 aty)
% Number of variables : 198 ( 52 ^; 142 !; 4 ?; 198 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_individuals,type,
individuals: $tType ).
thf(ty_loca,type,
loca: individuals ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__0,type,
eigen__0: individuals ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_relr,type,
relr: $i > $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__17,type,
eigen__17: $i ).
thf(ty_princ_inj,type,
princ_inj: individuals > $i > $o ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_reli,type,
reli: $i > $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__17,definition,
( eigen__17
= ( eps__0
@ ^ [X1: $i] :
~ ( ( reli @ eigen__6 @ X1 )
=> ( princ_inj @ loca @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__17])]) ).
thf(sP1,plain,
( sP1
<=> ( eigen__1 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( relr @ eigen__4 @ X1 )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ( princ_inj @ loca @ X3 ) )
=> ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ( eigen__1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( reli @ eigen__5 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( princ_inj @ loca @ eigen__17 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( reli @ eigen__6 @ X1 )
=> ( ( princ_inj @ eigen__0 @ X1 )
=> ( princ_inj @ loca @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( princ_inj @ eigen__0 @ eigen__17 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( reli @ eigen__6 @ eigen__17 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i,X2: $i] :
( ( reli @ X1 @ X2 )
=> ! [X3: individuals,X4: $i] :
( ( reli @ X2 @ X4 )
=> ( ( princ_inj @ X3 @ X4 )
=> ( princ_inj @ loca @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( reli @ eigen__5 @ X1 )
=> ! [X2: individuals,X3: $i] :
( ( reli @ X1 @ X3 )
=> ( ( princ_inj @ X2 @ X3 )
=> ( princ_inj @ loca @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP3
=> ( ! [X1: $i] :
( ( reli @ eigen__6 @ X1 )
=> ( princ_inj @ loca @ X1 ) )
=> ! [X1: $i] :
( ( reli @ eigen__6 @ X1 )
=> ( eigen__1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP7
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( reli @ eigen__3 @ X1 )
=> ! [X2: $i] :
( ( relr @ X1 @ X2 )
=> ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ( princ_inj @ loca @ X4 ) )
=> ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ( eigen__1 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( reli @ eigen__6 @ X1 )
=> ( princ_inj @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( relr @ eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP6
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ! [X1: $i] :
( ( reli @ eigen__6 @ X1 )
=> ( princ_inj @ loca @ X1 ) )
=> ! [X1: $i] :
( ( reli @ eigen__6 @ X1 )
=> ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
( ( reli @ eigen__5 @ X1 )
=> ( ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( princ_inj @ loca @ X2 ) )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( eigen__1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP7
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( reli @ eigen__3 @ eigen__4 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: individuals,X2: $i] :
( ( reli @ eigen__6 @ X2 )
=> ( ( princ_inj @ X1 @ X2 )
=> ( princ_inj @ loca @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP14
=> sP17 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( reli @ eigen__6 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( reli @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP7
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP22
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i] :
( ( reli @ eigen__6 @ X1 )
=> ( princ_inj @ loca @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP3
=> sP20 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
( ( reli @ eigen__6 @ X1 )
=> ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
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_cs4_atom,definition,
( cs4_atom
= ( ^ [X1: $i > $o] : ( mbox @ reli @ X1 ) ) ) ).
thf(def_cs4_and,definition,
( cs4_and
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ X1 @ X2 ) ) ) ).
thf(def_cs4_or,definition,
( cs4_or
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ X1 @ X2 ) ) ) ).
thf(def_cs4_impl,definition,
( cs4_impl
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mbox @ reli @ ( mimpl @ X1 @ X2 ) ) ) ) ).
thf(def_cs4_true,definition,
cs4_true = mtrue ).
thf(def_cs4_false,definition,
cs4_false = mfalse ).
thf(def_cs4_all,definition,
( cs4_all
= ( ^ [X1: individuals > $i > $o] : ( mbox @ reli @ ( mall @ X1 ) ) ) ) ).
thf(def_cs4_box,definition,
( cs4_box
= ( ^ [X1: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ X1 ) ) ) ) ).
thf(def_cs4_valid,definition,
( cs4_valid
= ( ^ [X1: $i > $o] : ( mvalid @ X1 ) ) ) ).
thf(def_bl_atom,definition,
( bl_atom
= ( ^ [X1: $i > $o] : ( cs4_atom @ X1 ) ) ) ).
thf(def_bl_princ,definition,
( bl_princ
= ( ^ [X1: $i > $o] : ( cs4_atom @ X1 ) ) ) ).
thf(def_bl_and,definition,
( bl_and
= ( ^ [X1: $i > $o,X2: $i > $o] : ( cs4_and @ X1 @ X2 ) ) ) ).
thf(def_bl_or,definition,
( bl_or
= ( ^ [X1: $i > $o,X2: $i > $o] : ( cs4_or @ X1 @ X2 ) ) ) ).
thf(def_bl_impl,definition,
( bl_impl
= ( ^ [X1: $i > $o,X2: $i > $o] : ( cs4_impl @ X1 @ X2 ) ) ) ).
thf(def_bl_all,definition,
( bl_all
= ( ^ [X1: individuals > $i > $o] : ( cs4_all @ X1 ) ) ) ).
thf(def_bl_true,definition,
bl_true = cs4_true ).
thf(def_bl_false,definition,
bl_false = cs4_false ).
thf(def_bl_says,definition,
( bl_says
= ( ^ [X1: individuals,X2: $i > $o] : ( cs4_box @ ( cs4_impl @ ( bl_princ @ ( princ_inj @ X1 ) ) @ X2 ) ) ) ) ).
thf(def_bl_valid,definition,
bl_valid = mvalid ).
thf(bl_strength,conjecture,
! [X1: individuals,X2: $i > $o,X3: $i,X4: $i] :
( ( reli @ X3 @ X4 )
=> ( ! [X5: $i] :
( ( reli @ X4 @ X5 )
=> ! [X6: $i] :
( ( relr @ X5 @ X6 )
=> ! [X7: $i] :
( ( reli @ X6 @ X7 )
=> ( ! [X8: $i] :
( ( reli @ X7 @ X8 )
=> ( princ_inj @ loca @ X8 ) )
=> ! [X8: $i] :
( ( reli @ X7 @ X8 )
=> ( X2 @ X8 ) ) ) ) ) )
=> ! [X5: $i] :
( ( reli @ X4 @ X5 )
=> ! [X6: $i] :
( ( relr @ X5 @ X6 )
=> ! [X7: $i] :
( ( reli @ X6 @ X7 )
=> ( ! [X8: $i] :
( ( reli @ X7 @ X8 )
=> ( princ_inj @ X1 @ X8 ) )
=> ! [X8: $i] :
( ( reli @ X7 @ X8 )
=> ( X2 @ X8 ) ) ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: individuals,X2: $i > $o,X3: $i,X4: $i] :
( ( reli @ X3 @ X4 )
=> ( ! [X5: $i] :
( ( reli @ X4 @ X5 )
=> ! [X6: $i] :
( ( relr @ X5 @ X6 )
=> ! [X7: $i] :
( ( reli @ X6 @ X7 )
=> ( ! [X8: $i] :
( ( reli @ X7 @ X8 )
=> ( princ_inj @ loca @ X8 ) )
=> ! [X8: $i] :
( ( reli @ X7 @ X8 )
=> ( X2 @ X8 ) ) ) ) ) )
=> ! [X5: $i] :
( ( reli @ X4 @ X5 )
=> ! [X6: $i] :
( ( relr @ X5 @ X6 )
=> ! [X7: $i] :
( ( reli @ X6 @ X7 )
=> ( ! [X8: $i] :
( ( reli @ X7 @ X8 )
=> ( princ_inj @ X1 @ X8 ) )
=> ! [X8: $i] :
( ( reli @ X7 @ X8 )
=> ( X2 @ X8 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[bl_strength]) ).
thf(h2,assumption,
~ ! [X1: $i > $o,X2: $i,X3: $i] :
( ( reli @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ! [X5: $i] :
( ( relr @ X4 @ X5 )
=> ! [X6: $i] :
( ( reli @ X5 @ X6 )
=> ( ! [X7: $i] :
( ( reli @ X6 @ X7 )
=> ( princ_inj @ loca @ X7 ) )
=> ! [X7: $i] :
( ( reli @ X6 @ X7 )
=> ( X1 @ X7 ) ) ) ) ) )
=> ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ! [X5: $i] :
( ( relr @ X4 @ X5 )
=> ! [X6: $i] :
( ( reli @ X5 @ X6 )
=> ( ! [X7: $i] :
( ( reli @ X6 @ X7 )
=> ( princ_inj @ eigen__0 @ X7 ) )
=> ! [X7: $i] :
( ( reli @ X6 @ X7 )
=> ( X1 @ X7 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i,X2: $i] :
( ( reli @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ! [X4: $i] :
( ( relr @ X3 @ X4 )
=> ! [X5: $i] :
( ( reli @ X4 @ X5 )
=> ( ! [X6: $i] :
( ( reli @ X5 @ X6 )
=> ( princ_inj @ loca @ X6 ) )
=> ! [X6: $i] :
( ( reli @ X5 @ X6 )
=> ( eigen__1 @ X6 ) ) ) ) ) )
=> ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ! [X4: $i] :
( ( relr @ X3 @ X4 )
=> ! [X5: $i] :
( ( reli @ X4 @ X5 )
=> ( ! [X6: $i] :
( ( reli @ X5 @ X6 )
=> ( princ_inj @ eigen__0 @ X6 ) )
=> ! [X6: $i] :
( ( reli @ X5 @ X6 )
=> ( eigen__1 @ X6 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i] :
( ( reli @ eigen__2 @ X1 )
=> ( ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ! [X3: $i] :
( ( relr @ X2 @ X3 )
=> ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ( ! [X5: $i] :
( ( reli @ X4 @ X5 )
=> ( princ_inj @ loca @ X5 ) )
=> ! [X5: $i] :
( ( reli @ X4 @ X5 )
=> ( eigen__1 @ X5 ) ) ) ) ) )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ! [X3: $i] :
( ( relr @ X2 @ X3 )
=> ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ( ! [X5: $i] :
( ( reli @ X4 @ X5 )
=> ( princ_inj @ eigen__0 @ X5 ) )
=> ! [X5: $i] :
( ( reli @ X4 @ X5 )
=> ( eigen__1 @ X5 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ( reli @ eigen__2 @ eigen__3 )
=> ( sP12
=> ! [X1: $i] :
( ( reli @ eigen__3 @ X1 )
=> ! [X2: $i] :
( ( relr @ X1 @ X2 )
=> ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ( princ_inj @ eigen__0 @ X4 ) )
=> ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ( eigen__1 @ X4 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
reli @ eigen__2 @ eigen__3,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP12
=> ! [X1: $i] :
( ( reli @ eigen__3 @ X1 )
=> ! [X2: $i] :
( ( relr @ X1 @ X2 )
=> ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ( princ_inj @ eigen__0 @ X4 ) )
=> ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ( eigen__1 @ X4 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP12,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $i] :
( ( reli @ eigen__3 @ X1 )
=> ! [X2: $i] :
( ( relr @ X1 @ X2 )
=> ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ( princ_inj @ eigen__0 @ X4 ) )
=> ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ( eigen__1 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP23
=> ! [X1: $i] :
( ( relr @ eigen__4 @ X1 )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ( princ_inj @ eigen__0 @ X3 ) )
=> ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ( eigen__1 @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP23,
introduced(assumption,[]) ).
thf(h12,assumption,
~ ! [X1: $i] :
( ( relr @ eigen__4 @ X1 )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ( princ_inj @ eigen__0 @ X3 ) )
=> ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ( eigen__1 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( sP14
=> ! [X1: $i] :
( ( reli @ eigen__5 @ X1 )
=> ( ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( princ_inj @ eigen__0 @ X2 ) )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( eigen__1 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
sP14,
introduced(assumption,[]) ).
thf(h15,assumption,
~ ! [X1: $i] :
( ( reli @ eigen__5 @ X1 )
=> ( ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( princ_inj @ eigen__0 @ X2 ) )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( eigen__1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ ( sP3
=> ( sP13
=> sP28 ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
sP3,
introduced(assumption,[]) ).
thf(h18,assumption,
~ ( sP13
=> sP28 ),
introduced(assumption,[]) ).
thf(h19,assumption,
sP13,
introduced(assumption,[]) ).
thf(h20,assumption,
~ sP28,
introduced(assumption,[]) ).
thf(h21,assumption,
~ sP25,
introduced(assumption,[]) ).
thf(h22,assumption,
sP22,
introduced(assumption,[]) ).
thf(h23,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP15
| ~ sP6
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP18
| ~ sP7
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP24
| ~ sP7
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP13
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP5
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP21
| ~ sP14
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP2
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP19
| ~ sP23
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP12
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP10
| ~ sP3
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP27
| ~ sP3
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP17
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP9
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP8
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP20
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( sP11
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP11
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP26
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__17]) ).
thf(19,plain,
( ~ sP16
| ~ sP26
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP25
| ~ sP22
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP28
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(loca_strength,axiom,
sP8 ).
thf(22,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h22,h23,h21,h19,h20,h17,h18,h16,h14,h15,h13,h11,h12,h10,h8,h9,h6,h7,h5,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,h8,h11,h14,h17,h19,h22,h23,loca_strength]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h19,h20,h17,h18,h16,h14,h15,h13,h11,h12,h10,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h22,h23])],[h21,22,h22,h23]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h19,h20,h17,h18,h16,h14,h15,h13,h11,h12,h10,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h21]),tab_negall(eigenvar,eigen__7)],[h20,23,h21]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h18,h16,h14,h15,h13,h11,h12,h10,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,24,h19,h20]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h14,h15,h13,h11,h12,h10,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h16,25,h17,h18]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h15,h13,h11,h12,h10,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__6)],[h15,26,h16]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h11,h12,h10,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,27,h14,h15]) ).
thf(29,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h12,h10,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__5)],[h12,28,h13]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,29,h11,h12]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__4)],[h9,30,h10]) ).
thf(32,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,31,h8,h9]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,32,h6,h7]) ).
thf(34,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__3)],[h4,33,h5]) ).
thf(35,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__2)],[h3,34,h4]) ).
thf(36,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,35,h3]) ).
thf(37,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,36,h2]) ).
thf(38,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[37,h0]) ).
thf(0,theorem,
! [X1: individuals,X2: $i > $o,X3: $i,X4: $i] :
( ( reli @ X3 @ X4 )
=> ( ! [X5: $i] :
( ( reli @ X4 @ X5 )
=> ! [X6: $i] :
( ( relr @ X5 @ X6 )
=> ! [X7: $i] :
( ( reli @ X6 @ X7 )
=> ( ! [X8: $i] :
( ( reli @ X7 @ X8 )
=> ( princ_inj @ loca @ X8 ) )
=> ! [X8: $i] :
( ( reli @ X7 @ X8 )
=> ( X2 @ X8 ) ) ) ) ) )
=> ! [X5: $i] :
( ( reli @ X4 @ X5 )
=> ! [X6: $i] :
( ( relr @ X5 @ X6 )
=> ! [X7: $i] :
( ( reli @ X6 @ X7 )
=> ( ! [X8: $i] :
( ( reli @ X7 @ X8 )
=> ( princ_inj @ X1 @ X8 ) )
=> ! [X8: $i] :
( ( reli @ X7 @ X8 )
=> ( X2 @ X8 ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[37,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV444^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n014.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 : 300
% 0.13/0.34 % DateTime : Tue Aug 29 06:21:45 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.68/0.85 % SZS status Theorem
% 0.68/0.85 % Mode: cade22grackle2xfee4
% 0.68/0.85 % Steps: 6479
% 0.68/0.85 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------