%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL584^1 : 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 : n011.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 01:02:04 PM UTC 2026
% Result : Theorem 0.11s 0.41s
% Output : Proof 0.11s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_b,type,
b: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_r,type,
r: $i > $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(sP1,plain,
( sP1
<=> ( r @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( b @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( r @ eigen__0 @ eigen__2 )
=> ~ ( ( a @ eigen__2 )
=> ~ sP2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP1
=> ~ ( ( a @ eigen__1 )
=> ~ ( b @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( r @ eigen__0 @ eigen__3 )
=> ( a @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( r @ eigen__0 @ eigen__3 )
=> ( b @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( r @ eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( a @ eigen__2 )
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( r @ eigen__0 @ X1 )
=> ~ ( ( a @ X1 )
=> ~ ( b @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( a @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( r @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( a @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( r @ eigen__0 @ X1 )
=> ( a @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( r @ eigen__0 @ X1 )
=> ( b @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP10
=> ~ ( b @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( b @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
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] :
~ ( ( ~ ~ ! [X2: $i] :
( ( r @ X1 @ X2 )
=> ~ ( ( a @ X2 )
=> ~ ( b @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( r @ X1 @ X2 )
=> ( a @ X2 ) )
=> ~ ! [X2: $i] :
( ( r @ X1 @ X2 )
=> ( b @ X2 ) ) ) )
=> ~ ( ~ ~ ~ ( ! [X2: $i] :
( ( r @ X1 @ X2 )
=> ( a @ X2 ) )
=> ~ ! [X2: $i] :
( ( r @ X1 @ X2 )
=> ( b @ X2 ) ) )
=> ! [X2: $i] :
( ( r @ X1 @ X2 )
=> ~ ( ( a @ X2 )
=> ~ ( b @ X2 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i] :
~ ( ( ! [X2: $i] :
( ( r @ X1 @ X2 )
=> ~ ( ( a @ X2 )
=> ~ ( b @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( r @ X1 @ X2 )
=> ( a @ X2 ) )
=> ~ ! [X2: $i] :
( ( r @ X1 @ X2 )
=> ( b @ X2 ) ) ) )
=> ~ ( ~ ( ! [X2: $i] :
( ( r @ X1 @ X2 )
=> ( a @ X2 ) )
=> ~ ! [X2: $i] :
( ( r @ X1 @ X2 )
=> ( b @ X2 ) ) )
=> ! [X2: $i] :
( ( r @ X1 @ X2 )
=> ~ ( ( a @ X2 )
=> ~ ( b @ X2 ) ) ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(h1,assumption,
( ( sP9
=> ~ ( sP13
=> ~ sP14 ) )
=> ~ ( ~ ( sP13
=> ~ sP14 )
=> sP9 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP9
=> ~ ( sP13
=> ~ sP14 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( sP13
=> ~ sP14 )
=> sP9 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP9,
introduced(assumption,[]) ).
thf(h5,assumption,
( sP13
=> ~ sP14 ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP1
=> sP10 ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP1,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(1,plain,
( sP15
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP9
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP4
| ~ sP1
| ~ sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h10,h8,h6,h4,h5,h2,h1,h0])],[1,2,3,h4,h9,h10]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h6,h4,h5,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,4,h9,h10]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h4,h5,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h6,5,h8]) ).
thf(h11,assumption,
~ ( sP11
=> sP2 ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP11,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(7,plain,
( sP8
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP9
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP3
| ~ sP11
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h12,h13,h11,h7,h4,h5,h2,h1,h0])],[7,8,9,h4,h12,h13]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h7,h4,h5,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,10,h12,h13]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h4,h5,h2,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__2)],[h7,11,h11]) ).
thf(13,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h4,h5,h2,h1,h0]),tab_imp(discharge,[h6]),tab_imp(discharge,[h7])],[h5,6,12,h6,h7]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,13,h4,h5]) ).
thf(h14,assumption,
~ ( sP13
=> ~ sP14 ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h16,assumption,
sP13,
introduced(assumption,[]) ).
thf(h17,assumption,
sP14,
introduced(assumption,[]) ).
thf(h18,assumption,
~ ( sP7
=> ~ ( sP12
=> ~ sP16 ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
sP7,
introduced(assumption,[]) ).
thf(h20,assumption,
( sP12
=> ~ sP16 ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h22,assumption,
~ sP16,
introduced(assumption,[]) ).
thf(15,plain,
( ~ sP13
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP5
| ~ sP7
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h21,h19,h20,h18,h16,h17,h14,h15,h3,h1,h0])],[15,16,h16,h19,h21]) ).
thf(18,plain,
( ~ sP14
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP6
| ~ sP7
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h22,h19,h20,h18,h16,h17,h14,h15,h3,h1,h0])],[18,19,h17,h19,h22]) ).
thf(21,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h19,h20,h18,h16,h17,h14,h15,h3,h1,h0]),tab_imp(discharge,[h21]),tab_imp(discharge,[h22])],[h20,17,20,h21,h22]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h16,h17,h14,h15,h3,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,21,h19,h20]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h17,h14,h15,h3,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__3)],[h15,22,h18]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h3,h1,h0]),tab_negimp(discharge,[h16,h17])],[h14,23,h16,h17]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h3,24,h14,h15]) ).
thf(26,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h2]),tab_imp(discharge,[h3])],[h1,14,25,h2,h3]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,26,h1]) ).
thf(0,theorem,
! [X1: $i] :
~ ( ( ~ ~ ! [X2: $i] :
( ( r @ X1 @ X2 )
=> ~ ( ( a @ X2 )
=> ~ ( b @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( r @ X1 @ X2 )
=> ( a @ X2 ) )
=> ~ ! [X2: $i] :
( ( r @ X1 @ X2 )
=> ( b @ X2 ) ) ) )
=> ~ ( ~ ~ ~ ( ! [X2: $i] :
( ( r @ X1 @ X2 )
=> ( a @ X2 ) )
=> ~ ! [X2: $i] :
( ( r @ X1 @ X2 )
=> ( b @ X2 ) ) )
=> ! [X2: $i] :
( ( r @ X1 @ X2 )
=> ~ ( ( a @ X2 )
=> ~ ( b @ X2 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[27,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL584^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.03 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 6 02:11:14 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.41 % SZS status Theorem
% 0.11/0.41 % Mode: mode213
% 0.11/0.41 % Inferences: 14
% 0.11/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------