%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : LCL690^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 12:27:18 PM UTC 2026
% Result : Theorem 20.24s 20.73s
% Output : Proof 20.24s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
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 > $o ).
thf(ty_relr,type,
relr: $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_reli,type,
reli: $i > $i > $o ).
thf(sP1,plain,
( sP1
<=> ( reli @ eigen__6 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( reli @ eigen__6 @ X1 )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( eigen__0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( reli @ eigen__3 @ X1 )
=> ! [X2: $i] :
( ( relr @ X1 @ X2 )
=> ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ( eigen__0 @ X4 ) )
=> ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ( eigen__1 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( reli @ eigen__4 @ X1 )
=> ! [X2: $i] :
( ( relr @ X1 @ X2 )
=> ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ( eigen__0 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( eigen__0 @ X2 ) )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ( eigen__0 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( relr @ eigen__5 @ X1 )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( eigen__0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ! [X1: $i] :
( ( reli @ eigen__7 @ X1 )
=> ( eigen__1 @ X1 ) )
=> ( eigen__1 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( relr @ eigen__5 @ X1 )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ( eigen__0 @ X3 ) )
=> ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ( eigen__1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( reli @ eigen__3 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ! [X1: $i] :
( ( reli @ eigen__7 @ X1 )
=> ( eigen__0 @ X1 ) )
=> ! [X1: $i] :
( ( reli @ eigen__7 @ X1 )
=> ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( relr @ eigen__5 @ eigen__6 )
=> ! [X1: $i] :
( ( reli @ eigen__6 @ X1 )
=> ( ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( eigen__0 @ X2 ) )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( eigen__1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( reli @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( reli @ eigen__6 @ X1 )
=> ( ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( eigen__0 @ X2 ) )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( eigen__1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( reli @ eigen__4 @ X1 )
=> ( reli @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( relr @ eigen__5 @ eigen__6 )
=> ! [X1: $i] :
( ( reli @ eigen__6 @ X1 )
=> ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP12
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ! [X1: $i] :
( ( reli @ eigen__6 @ X1 )
=> ( eigen__0 @ X1 ) )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i > $o,X2: $i] :
( ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ( X1 @ X3 ) )
=> ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [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,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP1
=> ! [X1: $i] :
( ( reli @ eigen__7 @ X1 )
=> ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( reli @ eigen__4 @ eigen__5 )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP9
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( reli @ eigen__4 @ eigen__5 )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( relr @ eigen__5 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP1
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( eigen__1 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( reli @ eigen__3 @ X2 ) )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ( reli @ eigen__3 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( eigen__1 @ X2 ) )
=> ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i] :
( ( reli @ eigen__3 @ X1 )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( reli @ eigen__3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i] :
( ( reli @ eigen__6 @ X1 )
=> ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i] :
( ( reli @ eigen__7 @ X1 )
=> ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( reli @ eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i] :
( ( reli @ eigen__7 @ X1 )
=> ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
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_k,conjecture,
! [X1: $i > $o,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 )
=> ( X1 @ X8 ) )
=> ! [X8: $i] :
( ( reli @ X7 @ X8 )
=> ( X2 @ X8 ) ) ) ) ) )
=> ! [X5: $i] :
( ( reli @ X4 @ X5 )
=> ( ! [X6: $i] :
( ( reli @ X5 @ X6 )
=> ! [X7: $i] :
( ( relr @ X6 @ X7 )
=> ! [X8: $i] :
( ( reli @ X7 @ X8 )
=> ( X1 @ X8 ) ) ) )
=> ! [X6: $i] :
( ( reli @ X5 @ X6 )
=> ! [X7: $i] :
( ( relr @ X6 @ X7 )
=> ! [X8: $i] :
( ( reli @ X7 @ X8 )
=> ( X2 @ X8 ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $o,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 )
=> ( X1 @ X8 ) )
=> ! [X8: $i] :
( ( reli @ X7 @ X8 )
=> ( X2 @ X8 ) ) ) ) ) )
=> ! [X5: $i] :
( ( reli @ X4 @ X5 )
=> ( ! [X6: $i] :
( ( reli @ X5 @ X6 )
=> ! [X7: $i] :
( ( relr @ X6 @ X7 )
=> ! [X8: $i] :
( ( reli @ X7 @ X8 )
=> ( X1 @ X8 ) ) ) )
=> ! [X6: $i] :
( ( reli @ X5 @ X6 )
=> ! [X7: $i] :
( ( relr @ X6 @ X7 )
=> ! [X8: $i] :
( ( reli @ X7 @ X8 )
=> ( X2 @ X8 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cs4_k]) ).
thf(h1,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 )
=> ( eigen__0 @ X7 ) )
=> ! [X7: $i] :
( ( reli @ X6 @ X7 )
=> ( X1 @ X7 ) ) ) ) ) )
=> ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ( ! [X5: $i] :
( ( reli @ X4 @ X5 )
=> ! [X6: $i] :
( ( relr @ X5 @ X6 )
=> ! [X7: $i] :
( ( reli @ X6 @ X7 )
=> ( eigen__0 @ X7 ) ) ) )
=> ! [X5: $i] :
( ( reli @ X4 @ X5 )
=> ! [X6: $i] :
( ( relr @ X5 @ X6 )
=> ! [X7: $i] :
( ( reli @ X6 @ X7 )
=> ( X1 @ X7 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,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 )
=> ( eigen__0 @ X6 ) )
=> ! [X6: $i] :
( ( reli @ X5 @ X6 )
=> ( eigen__1 @ X6 ) ) ) ) ) )
=> ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ! [X5: $i] :
( ( relr @ X4 @ X5 )
=> ! [X6: $i] :
( ( reli @ X5 @ X6 )
=> ( eigen__0 @ X6 ) ) ) )
=> ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ! [X5: $i] :
( ( relr @ X4 @ X5 )
=> ! [X6: $i] :
( ( reli @ X5 @ X6 )
=> ( eigen__1 @ X6 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,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 )
=> ( eigen__0 @ X5 ) )
=> ! [X5: $i] :
( ( reli @ X4 @ X5 )
=> ( eigen__1 @ X5 ) ) ) ) ) )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ! [X4: $i] :
( ( relr @ X3 @ X4 )
=> ! [X5: $i] :
( ( reli @ X4 @ X5 )
=> ( eigen__0 @ X5 ) ) ) )
=> ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ! [X4: $i] :
( ( relr @ X3 @ X4 )
=> ! [X5: $i] :
( ( reli @ X4 @ X5 )
=> ( eigen__1 @ X5 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ( reli @ eigen__2 @ eigen__3 )
=> ( sP3
=> ! [X1: $i] :
( ( reli @ eigen__3 @ X1 )
=> ( ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ! [X3: $i] :
( ( relr @ X2 @ X3 )
=> ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ( eigen__0 @ X4 ) ) ) )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ! [X3: $i] :
( ( relr @ X2 @ X3 )
=> ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ( eigen__1 @ X4 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
reli @ eigen__2 @ eigen__3,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP3
=> ! [X1: $i] :
( ( reli @ eigen__3 @ X1 )
=> ( ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ! [X3: $i] :
( ( relr @ X2 @ X3 )
=> ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ( eigen__0 @ X4 ) ) ) )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ! [X3: $i] :
( ( relr @ X2 @ X3 )
=> ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ( eigen__1 @ X4 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP3,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $i] :
( ( reli @ eigen__3 @ X1 )
=> ( ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ! [X3: $i] :
( ( relr @ X2 @ X3 )
=> ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ( eigen__0 @ X4 ) ) ) )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ! [X3: $i] :
( ( relr @ X2 @ X3 )
=> ! [X4: $i] :
( ( reli @ X3 @ X4 )
=> ( eigen__1 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP12
=> ( sP4
=> ! [X1: $i] :
( ( reli @ eigen__4 @ X1 )
=> ! [X2: $i] :
( ( relr @ X1 @ X2 )
=> ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ( eigen__1 @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP12,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( sP4
=> ! [X1: $i] :
( ( reli @ eigen__4 @ X1 )
=> ! [X2: $i] :
( ( relr @ X1 @ X2 )
=> ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ( eigen__1 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP4,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ! [X1: $i] :
( ( reli @ eigen__4 @ X1 )
=> ! [X2: $i] :
( ( relr @ X1 @ X2 )
=> ! [X3: $i] :
( ( reli @ X2 @ X3 )
=> ( eigen__1 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( sP32
=> ! [X1: $i] :
( ( relr @ eigen__5 @ X1 )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( eigen__1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
sP32,
introduced(assumption,[]) ).
thf(h16,assumption,
~ ! [X1: $i] :
( ( relr @ eigen__5 @ X1 )
=> ! [X2: $i] :
( ( reli @ X1 @ X2 )
=> ( eigen__1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( sP24
=> ! [X1: $i] :
( ( reli @ eigen__6 @ X1 )
=> ( eigen__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
sP24,
introduced(assumption,[]) ).
thf(h19,assumption,
~ ! [X1: $i] :
( ( reli @ eigen__6 @ X1 )
=> ( eigen__1 @ X1 ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( sP1
=> sP26 ),
introduced(assumption,[]) ).
thf(h21,assumption,
sP1,
introduced(assumption,[]) ).
thf(h22,assumption,
~ sP26,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP10
| ~ sP33
| sP31 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP21
| ~ sP32
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP25
| ~ sP1
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP14
| sP21 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP20
| ~ sP1
| sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP13
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP16
| ~ sP12
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP2
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP11
| ~ sP24
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP15
| ~ sP24
| sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP7
| ~ sP31
| sP26 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP29
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP17
| ~ sP30
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP8
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP6
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP28
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP27
| sP29 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP5
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP22
| ~ sP9
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP23
| ~ sP32
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP18
| sP28 ),
inference(all_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP19
| sP27 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP19
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP3
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP4
| sP23 ),
inference(all_rule,[status(thm)],[]) ).
thf(refl_axiom_i,axiom,
sP18 ).
thf(trans_axiom_i,axiom,
sP19 ).
thf(26,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h21,h22,h20,h18,h19,h17,h15,h16,h14,h12,h13,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,refl_axiom_i,trans_axiom_i,h7,h10,h12,h15,h18,h21,h22]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h18,h19,h17,h15,h16,h14,h12,h13,h10,h11,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h21,h22])],[h20,26,h21,h22]) ).
thf(28,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h18,h19,h17,h15,h16,h14,h12,h13,h10,h11,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__7)],[h19,27,h20]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h15,h16,h14,h12,h13,h10,h11,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h18,h19])],[h17,28,h18,h19]) ).
thf(30,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h15,h16,h14,h12,h13,h10,h11,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__6)],[h16,29,h17]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h10,h11,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,30,h15,h16]) ).
thf(32,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h13,h10,h11,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__5)],[h13,31,h14]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,32,h12,h13]) ).
thf(34,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,33,h10,h11]) ).
thf(35,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__4)],[h8,34,h9]) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,35,h7,h8]) ).
thf(37,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,36,h5,h6]) ).
thf(38,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__3)],[h3,37,h4]) ).
thf(39,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,38,h3]) ).
thf(40,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,39,h2]) ).
thf(41,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,40,h1]) ).
thf(0,theorem,
! [X1: $i > $o,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 )
=> ( X1 @ X8 ) )
=> ! [X8: $i] :
( ( reli @ X7 @ X8 )
=> ( X2 @ X8 ) ) ) ) ) )
=> ! [X5: $i] :
( ( reli @ X4 @ X5 )
=> ( ! [X6: $i] :
( ( reli @ X5 @ X6 )
=> ! [X7: $i] :
( ( relr @ X6 @ X7 )
=> ! [X8: $i] :
( ( reli @ X7 @ X8 )
=> ( X1 @ X8 ) ) ) )
=> ! [X6: $i] :
( ( reli @ X5 @ X6 )
=> ! [X7: $i] :
( ( relr @ X6 @ X7 )
=> ! [X8: $i] :
( ( reli @ X7 @ X8 )
=> ( X2 @ X8 ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[41,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL690^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 4 20:22:44 UTC 2026
% 0.09/0.35 % CPUTime :
% 20.24/20.73 % SZS status Theorem
% 20.24/20.73 % Mode: cade22grackle2x798d
% 20.24/20.73 % Steps: 3373
% 20.24/20.73 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------