%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL620^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n019.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 01:02:08 PM UTC 2026
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i > $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(sP1,plain,
( sP1
<=> ( eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(def_mfalse,definition,
( mfalse
= ( ^ [X1: $i] : $false ) ) ).
thf(def_mtrue,definition,
( mtrue
= ( ^ [X1: $i] : ~ $false ) ) ).
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] : ( mor @ ( mnot @ X1 ) ) ) ) ).
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] :
( ( 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 = !! ).
thf(def_msatisfiable,definition,
( msatisfiable
= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [X1: $i > $o] :
~ ( !! @ X1 ) ) ) ).
thf(def_minvalid,definition,
( minvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(thm,conjecture,
! [X1: $i > $i > $o,X2: $i > $o,X3: $i > $o,X4: $i] :
( ~ ~ ~ ~ ( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) )
=> ( ~ ~ ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $i > $o,X2: $i > $o,X3: $i > $o,X4: $i] :
( ( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) )
=> ( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(h1,assumption,
~ ! [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) )
=> ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i > $o,X2: $i] :
( ( ( eigen__1 @ X2 )
=> ~ ( X1 @ X2 ) )
=> ( ( eigen__1 @ X2 )
=> ~ ( X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( ( eigen__1 @ X1 )
=> ~ ( eigen__2 @ X1 ) )
=> ( ( eigen__1 @ X1 )
=> ~ ( eigen__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ( sP1
=> ~ sP2 )
=> ( sP1
=> ~ sP2 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
( sP1
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP1
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h9,assumption,
sP1,
introduced(assumption,[]) ).
thf(h10,assumption,
sP2,
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h9,h10,h7,h5,h6,h4,h3,h2,h1,h0])],[h9,h7]) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h6,1,h9,h10]) ).
thf(3,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h9,h10,h8,h5,h6,h4,h3,h2,h1,h0])],[h10,h8]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h6,3,h9,h10]) ).
thf(5,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h5,2,4,h7,h8]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,5,h5,h6]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__3)],[h3,6,h4]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,7,h3]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,8,h2]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,9,h1]) ).
thf(0,theorem,
! [X1: $i > $i > $o,X2: $i > $o,X3: $i > $o,X4: $i] :
( ~ ~ ~ ~ ( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) )
=> ( ~ ~ ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL620^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.04 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 6 00:13:23 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % Mode: mode213
% 0.12/0.37 % Inferences: 0
% 0.12/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------