TSTP Solution File: LCL588^1 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : LCL588^1 : 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 : n011.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 08:03:42 EDT 2023
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_b,type,
b: $i > $o ).
thf(ty_a,type,
a: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_r,type,
r: $i > $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(sP1,plain,
( sP1
<=> ( a @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( r @ eigen__0 @ eigen__1 )
=> ( b @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( r @ eigen__0 @ X1 )
=> ~ ( a @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( r @ eigen__0 @ X1 )
=> ( b @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( r @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( b @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP5
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ sP3
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
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] :
( ( ~ ! [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 ) )
=> ! [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,
~ ( sP8
=> ! [X1: $i] :
( ( r @ eigen__0 @ X1 )
=> ( ( a @ X1 )
=> ( b @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP8,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( r @ eigen__0 @ X1 )
=> ( ( a @ X1 )
=> ( b @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP5
=> ( sP1
=> sP6 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP5,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP1
=> sP6 ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP1,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP7
| ~ sP5
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| ~ sP5
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP3
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP4
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP8
| sP3
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,h2,h5,h7,h8]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,6,h7,h8]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,7,h5,h6]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,8,h4]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,9,h2,h3]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,10,h1]) ).
thf(0,theorem,
! [X1: $i] :
( ( ~ ! [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])],[11,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL588^1 : TPTP v8.1.2. Released v3.6.0.
% 0.07/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.32 % Computer : n011.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Aug 25 04:21:38 EDT 2023
% 0.12/0.32 % CPUTime :
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % Mode: cade22grackle2xfee4
% 0.12/0.39 % Steps: 12
% 0.12/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------