TSTP Solution File: LCL621^1 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : LCL621^1 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n031.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 08:03:49 EDT 2023
% Result : Theorem 20.15s 20.38s
% Output : Proof 20.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 73
% Syntax : Number of formulae : 86 ( 33 unt; 6 typ; 16 def)
% Number of atoms : 200 ( 16 equ; 3 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 432 ( 88 ~; 24 |; 2 &; 206 @)
% ( 21 <=>; 91 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 44 usr; 44 con; 0-2 aty)
% Number of variables : 117 ( 31 ^; 82 !; 4 ?; 117 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__2,type,
eigen__2: $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eigen__0 @ eigen__4 @ X1 )
=> ~ ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__4 @ X1 )
=> ~ ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__0 @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( sP2
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__1 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__0 @ eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X2 @ X5 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP5
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP5
=> ( sP4
=> ~ ( eigen__2 @ eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP2
=> ! [X1: $i] :
( ( eigen__0 @ eigen__4 @ X1 )
=> ( eigen__0 @ eigen__3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( eigen__0 @ eigen__3 @ eigen__5 )
=> ( eigen__2 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__3 @ X1 )
=> ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__0 @ eigen__3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP4
=> ~ ( eigen__2 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__2 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP5
=> ( eigen__0 @ eigen__3 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__3 @ X1 )
=> ( eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__4 @ X1 )
=> ( ( eigen__1 @ X1 )
=> ~ ( eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i > $o,X2: $i] :
( ! [X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X3 ) )
=> ! [X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ! [X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X1 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__4 @ X1 )
=> ( eigen__0 @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__3 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eigen__0 @ eigen__3 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__0 @ eigen__3 @ X2 ) )
=> ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( eigen__0 @ eigen__3 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
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(thm,conjecture,
! [X1: $i > $i > $o,X2: $i > $o,X3: $i > $o,X4: $i] :
( ~ ( ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ~ ! [X6: $i] :
( ( X1 @ X5 @ X6 )
=> ~ ( X2 @ X6 ) ) )
=> ~ ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X3 @ X5 ) ) )
=> ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ~ ! [X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( ( X2 @ X6 )
=> ~ ( X3 @ X6 ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i > $i > $o,X2: $i > $o,X3: $i > $o,X4: $i] :
( ~ ( ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ~ ! [X6: $i] :
( ( X1 @ X5 @ X6 )
=> ~ ( X2 @ X6 ) ) )
=> ~ ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X3 @ X5 ) ) )
=> ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ~ ! [X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( ( X2 @ X6 )
=> ~ ( X3 @ X6 ) ) ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(h2,assumption,
~ ! [X1: $i > $o,X2: $i > $o,X3: $i] :
( ~ ( ! [X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ~ ! [X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ~ ( X1 @ X5 ) ) )
=> ~ ! [X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X4 ) ) )
=> ! [X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ~ ! [X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( ( X1 @ X5 )
=> ~ ( X2 @ X5 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i > $o,X2: $i] :
( ~ ( ! [X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ~ ( eigen__1 @ X4 ) ) )
=> ~ ! [X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ! [X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( ( eigen__1 @ X4 )
=> ~ ( X1 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i] :
( ~ ( ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ~ ( eigen__1 @ X3 ) ) )
=> ~ ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__2 @ X2 ) ) )
=> ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( ( eigen__1 @ X3 )
=> ~ ( eigen__2 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ ( sP19
=> ~ sP15 )
=> ! [X1: $i] :
( ( eigen__0 @ eigen__3 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( ( eigen__1 @ X2 )
=> ~ ( eigen__2 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP19
=> ~ sP15 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i] :
( ( eigen__0 @ eigen__3 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( ( eigen__1 @ X2 )
=> ~ ( eigen__2 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP19,
introduced(assumption,[]) ).
thf(h9,assumption,
sP15,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP2
=> ~ sP16 ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP2,
introduced(assumption,[]) ).
thf(h12,assumption,
sP16,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP12
| ~ sP4
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP8
| ~ sP5
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP10
| ~ sP20
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP14
| ~ sP5
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP16
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP15
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP18
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP9
| ~ sP2
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP11
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( sP7
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP7
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP21
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( sP1
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(14,plain,
( ~ sP17
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP3
| ~ sP2
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP6
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP19
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(k4,axiom,
sP6 ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([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,k4,h8,h9,h11,h12]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,18,h11,h12]) ).
thf(20,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)],[h7,19,h10]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,20,h8,h9]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,21,h6,h7]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__3)],[h4,22,h5]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__2)],[h3,23,h4]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,24,h3]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,25,h2]) ).
thf(27,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[26,h0]) ).
thf(0,theorem,
! [X1: $i > $i > $o,X2: $i > $o,X3: $i > $o,X4: $i] :
( ~ ( ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ~ ! [X6: $i] :
( ( X1 @ X5 @ X6 )
=> ~ ( X2 @ X6 ) ) )
=> ~ ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X3 @ X5 ) ) )
=> ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ~ ! [X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( ( X2 @ X6 )
=> ~ ( X3 @ X6 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[26,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : LCL621^1 : TPTP v8.1.2. Released v3.6.0.
% 0.00/0.09 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.08/0.28 % Computer : n031.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Thu Aug 24 18:34:21 EDT 2023
% 0.08/0.28 % CPUTime :
% 20.15/20.38 % SZS status Theorem
% 20.15/20.38 % Mode: cade22grackle2x798d
% 20.15/20.38 % Steps: 369
% 20.15/20.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------