%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO886^9 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n006.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 Oct 9 03:24:23 PM UTC 2025
% Result : Theorem 1.55s 1.78s
% Output : Proof 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 113
% Syntax : Number of formulae : 133 ( 55 unt; 0 typ; 26 def)
% Number of atoms : 400 ( 26 equ; 3 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 714 ( 55 ~; 38 |; 2 &; 430 @)
% ( 36 <=>; 153 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% Number of symbols : 77 ( 73 usr; 73 con; 0-2 aty)
% Number of variables : 211 ( 42 ^; 165 !; 4 ?; 211 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_individuals,type,
individuals: $tType ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_relr,type,
relr: $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__6,type,
eigen__6: individuals ).
thf(ty_eigen__28,type,
eigen__28: $i ).
thf(ty_eigen__0,type,
eigen__0: individuals > $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_reli,type,
reli: $i > $i > $o ).
thf(ty_eigen__22,type,
eigen__22: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__22,definition,
( eigen__22
= ( eps__0
@ ^ [X1: $i] :
~ ( ( reli @ eigen__3 @ X1 )
=> ! [X2: $i] :
( ( relr @ X1 @ X2 )
=> ( eigen__0 @ eigen__6 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__22])]) ).
thf(eigendef_eigen__28,definition,
( eigen__28
= ( eps__0
@ ^ [X1: $i] :
~ ( ( relr @ eigen__22 @ X1 )
=> ( eigen__0 @ eigen__6 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__28])]) ).
thf(sP1,plain,
( sP1
<=> ( ! [X1: $i] :
( ( reli @ eigen__3 @ X1 )
=> ! [X2: $i] :
( ( relr @ X1 @ X2 )
=> ( eigen__0 @ eigen__6 @ X2 ) ) )
=> ! [X1: $i] :
( ( relr @ eigen__3 @ X1 )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( eigen__0 @ eigen__6 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( reli @ eigen__5 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ! [X3: $i] :
( ( relr @ X2 @ X3 )
=> ( eigen__0 @ eigen__6 @ X3 ) ) )
=> ! [X2: $i] :
( ( relr @ X1 @ X2 )
=> ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ( eigen__0 @ eigen__6 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP2
=> ( eigen__0 @ eigen__6 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( reli @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i > $o,X2: $i] :
( ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ! [X4: $i] :
( ( relr @ X3 @ X4 )
=> ( X1 @ X4 ) ) )
=> ! [X3: $i] :
( ( relr @ X2 @ X3 )
=> ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ( X1 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( reli @ eigen__4 @ eigen__5 )
=> ! [X1: $i] :
( ( reli @ eigen__5 @ X1 )
=> ( eigen__0 @ eigen__6 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( relr @ eigen__3 @ eigen__4 )
=> ! [X1: $i] :
( ( reli @ eigen__4 @ X1 )
=> ( eigen__0 @ eigen__6 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( eigen__0 @ eigen__6 @ X2 ) )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ( eigen__0 @ eigen__6 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__0 @ eigen__6 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ! [X1: $i] :
( ( reli @ eigen__4 @ X1 )
=> ( eigen__0 @ eigen__6 @ X1 ) )
=> ! [X1: $i] :
( ( reli @ eigen__4 @ X1 )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( eigen__0 @ eigen__6 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( reli @ eigen__4 @ X1 )
=> ( eigen__0 @ eigen__6 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( reli @ eigen__5 @ X1 )
=> ( eigen__0 @ eigen__6 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( reli @ eigen__3 @ eigen__22 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( relr @ eigen__22 @ eigen__28 )
=> ! [X1: $i] :
( ( reli @ eigen__28 @ X1 )
=> ( eigen__0 @ eigen__6 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( relr @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
( ( reli @ eigen__2 @ X1 )
=> ! [X2: individuals,X3: $i] :
( ( reli @ X1 @ X3 )
=> ! [X4: $i] :
( ( relr @ X3 @ X4 )
=> ! [X5: $i] :
( ( reli @ X4 @ X5 )
=> ( eigen__0 @ X2 @ X5 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i > $o,X2: $i] :
( ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ( X1 @ X3 ) )
=> ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ( X1 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ( relr @ eigen__22 @ X1 )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( eigen__0 @ eigen__6 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i > $o,X2: $i] :
( ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ( X1 @ X3 ) )
=> ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ( relr @ eigen__22 @ X1 )
=> ( eigen__0 @ eigen__6 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( relr @ eigen__22 @ eigen__28 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP22
=> ( eigen__0 @ eigen__6 @ eigen__28 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i] :
( ( reli @ eigen__28 @ X1 )
=> ( eigen__0 @ eigen__6 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( reli @ eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i] :
( ( relr @ eigen__3 @ X1 )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( eigen__0 @ eigen__6 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( eigen__0 @ eigen__6 @ eigen__28 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
( ( reli @ eigen__4 @ X1 )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( eigen__0 @ eigen__6 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP14
=> sP21 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( eigen__0 @ eigen__6 @ X2 ) )
=> ( eigen__0 @ eigen__6 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i] :
( ( reli @ eigen__3 @ X1 )
=> ! [X2: $i] :
( ( relr @ X1 @ X2 )
=> ( eigen__0 @ eigen__6 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( sP24
=> sP27 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( sP5
=> ! [X1: individuals,X2: $i] :
( ( reli @ eigen__3 @ X2 )
=> ! [X3: $i] :
( ( relr @ X2 @ X3 )
=> ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ( eigen__0 @ X1 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: $i] :
( ( reli @ eigen__3 @ X1 )
=> ! [X2: $i] :
( ( relr @ X1 @ X2 )
=> ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ( eigen__0 @ eigen__6 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( sP14
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: individuals,X2: $i] :
( ( reli @ eigen__3 @ X2 )
=> ! [X3: $i] :
( ( relr @ X2 @ X3 )
=> ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ( eigen__0 @ X1 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
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(cs4_barcan,conjecture,
! [X1: individuals > $i > $o,X2: $i,X3: $i] :
( ( reli @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ! [X5: individuals,X6: $i] :
( ( reli @ X4 @ X6 )
=> ! [X7: $i] :
( ( relr @ X6 @ X7 )
=> ! [X8: $i] :
( ( reli @ X7 @ X8 )
=> ( X1 @ X5 @ X8 ) ) ) ) )
=> ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ! [X5: $i] :
( ( relr @ X4 @ X5 )
=> ! [X6: $i] :
( ( reli @ X5 @ X6 )
=> ! [X7: individuals,X8: $i] :
( ( reli @ X6 @ X8 )
=> ( X1 @ X7 @ X8 ) ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: individuals > $i > $o,X2: $i,X3: $i] :
( ( reli @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ! [X5: individuals,X6: $i] :
( ( reli @ X4 @ X6 )
=> ! [X7: $i] :
( ( relr @ X6 @ X7 )
=> ! [X8: $i] :
( ( reli @ X7 @ X8 )
=> ( X1 @ X5 @ X8 ) ) ) ) )
=> ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ! [X5: $i] :
( ( relr @ X4 @ X5 )
=> ! [X6: $i] :
( ( reli @ X5 @ X6 )
=> ! [X7: individuals,X8: $i] :
( ( reli @ X6 @ X8 )
=> ( X1 @ X7 @ X8 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cs4_barcan]) ).
thf(h2,assumption,
~ ! [X1: $i,X2: $i] :
( ( reli @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ! [X4: individuals,X5: $i] :
( ( reli @ X3 @ X5 )
=> ! [X6: $i] :
( ( relr @ X5 @ X6 )
=> ! [X7: $i] :
( ( reli @ X6 @ X7 )
=> ( eigen__0 @ X4 @ X7 ) ) ) ) )
=> ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ! [X4: $i] :
( ( relr @ X3 @ X4 )
=> ! [X5: $i] :
( ( reli @ X4 @ X5 )
=> ! [X6: individuals,X7: $i] :
( ( reli @ X5 @ X7 )
=> ( eigen__0 @ X6 @ X7 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( reli @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ! [X3: individuals,X4: $i] :
( ( reli @ X2 @ X4 )
=> ! [X5: $i] :
( ( relr @ X4 @ X5 )
=> ! [X6: $i] :
( ( reli @ X5 @ X6 )
=> ( eigen__0 @ X3 @ X6 ) ) ) ) )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ! [X3: $i] :
( ( relr @ X2 @ X3 )
=> ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ! [X5: individuals,X6: $i] :
( ( reli @ X4 @ X6 )
=> ( eigen__0 @ X5 @ X6 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ( reli @ eigen__1 @ eigen__2 )
=> ( sP17
=> ! [X1: $i] :
( ( reli @ eigen__2 @ X1 )
=> ! [X2: $i] :
( ( relr @ X1 @ X2 )
=> ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ! [X4: individuals,X5: $i] :
( ( reli @ X3 @ X5 )
=> ( eigen__0 @ X4 @ X5 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
reli @ eigen__1 @ eigen__2,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP17
=> ! [X1: $i] :
( ( reli @ eigen__2 @ X1 )
=> ! [X2: $i] :
( ( relr @ X1 @ X2 )
=> ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ! [X4: individuals,X5: $i] :
( ( reli @ X3 @ X5 )
=> ( eigen__0 @ X4 @ X5 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP17,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $i] :
( ( reli @ eigen__2 @ X1 )
=> ! [X2: $i] :
( ( relr @ X1 @ X2 )
=> ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ! [X4: individuals,X5: $i] :
( ( reli @ X3 @ X5 )
=> ( eigen__0 @ X4 @ X5 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP5
=> ! [X1: $i] :
( ( relr @ eigen__3 @ X1 )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ! [X3: individuals,X4: $i] :
( ( reli @ X2 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP5,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ! [X1: $i] :
( ( relr @ eigen__3 @ X1 )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ! [X3: individuals,X4: $i] :
( ( reli @ X2 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( sP16
=> ! [X1: $i] :
( ( reli @ eigen__4 @ X1 )
=> ! [X2: individuals,X3: $i] :
( ( reli @ X1 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP16,
introduced(assumption,[]) ).
thf(h14,assumption,
~ ! [X1: $i] :
( ( reli @ eigen__4 @ X1 )
=> ! [X2: individuals,X3: $i] :
( ( reli @ X1 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP25
=> ! [X1: individuals,X2: $i] :
( ( reli @ eigen__5 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP25,
introduced(assumption,[]) ).
thf(h17,assumption,
~ ! [X1: individuals,X2: $i] :
( ( reli @ eigen__5 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(h19,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h20,assumption,
sP2,
introduced(assumption,[]) ).
thf(h21,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP35
| ~ sP14
| sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP15
| ~ sP22
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP19
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP34
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP32
| ~ sP24
| sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP30
| sP32 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( sP23
| ~ sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( sP23
| sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( sP21
| ~ sP23 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__28]) ).
thf(10,plain,
( sP29
| ~ sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( sP29
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( sP31
| ~ sP29 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__22]) ).
thf(13,plain,
( ~ sP7
| ~ sP25
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP28
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP11
| ~ sP12
| sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP1
| ~ sP31
| sP26 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP9
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP3
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP20
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP18
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP6
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP36
| sP34 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP33
| ~ sP5
| sP36 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP8
| ~ sP16
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP26
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP17
| sP33 ),
inference(all_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP4
| ~ sP2
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP13
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(ax_i_r_commute,axiom,
sP6 ).
thf(trans_axiom_i,axiom,
sP18 ).
thf(refl_axiom_i,axiom,
sP20 ).
thf(29,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h20,h21,h19,h18,h16,h17,h15,h13,h14,h12,h10,h11,h9,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,h7,h10,h13,h16,h20,h21,ax_i_r_commute,trans_axiom_i,refl_axiom_i]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h18,h16,h17,h15,h13,h14,h12,h10,h11,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h20,h21])],[h19,29,h20,h21]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h18,h16,h17,h15,h13,h14,h12,h10,h11,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h19]),tab_negall(eigenvar,eigen__7)],[h18,30,h19]) ).
thf(32,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h17,h15,h13,h14,h12,h10,h11,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__6)],[h17,31,h18]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h13,h14,h12,h10,h11,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,32,h16,h17]) ).
thf(34,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h14,h12,h10,h11,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__5)],[h14,33,h15]) ).
thf(35,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h10,h11,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,34,h13,h14]) ).
thf(36,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h11,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__4)],[h11,35,h12]) ).
thf(37,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,36,h10,h11]) ).
thf(38,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__3)],[h8,37,h9]) ).
thf(39,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,38,h7,h8]) ).
thf(40,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,39,h5,h6]) ).
thf(41,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__2)],[h3,40,h4]) ).
thf(42,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,41,h3]) ).
thf(43,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,42,h2]) ).
thf(44,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[43,h0]) ).
thf(0,theorem,
! [X1: individuals > $i > $o,X2: $i,X3: $i] :
( ( reli @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ! [X5: individuals,X6: $i] :
( ( reli @ X4 @ X6 )
=> ! [X7: $i] :
( ( relr @ X6 @ X7 )
=> ! [X8: $i] :
( ( reli @ X7 @ X8 )
=> ( X1 @ X5 @ X8 ) ) ) ) )
=> ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ! [X5: $i] :
( ( relr @ X4 @ X5 )
=> ! [X6: $i] :
( ( reli @ X5 @ X6 )
=> ! [X7: individuals,X8: $i] :
( ( reli @ X6 @ X8 )
=> ( X1 @ X7 @ X8 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[43,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYO886^9 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Oct 9 01:16:53 EDT 2025
% 0.13/0.35 % CPUTime :
% 1.55/1.78 % SZS status Theorem
% 1.55/1.78 % Mode: cade22grackle2xfee4
% 1.55/1.78 % Steps: 14451
% 1.55/1.78 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------