TSTP Solution File: LCL609^1 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : LCL609^1 : 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 : n018.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 08:03:47 EDT 2023
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_individuals,type,
individuals: $tType ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: individuals > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: individuals ).
thf(sP1,plain,
( sP1
<=> ! [X1: individuals,X2: $i] : ( eigen__0 @ X1 @ X2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] : ( eigen__0 @ eigen__2 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__0 @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
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: individuals > $i > $o] :
( ! [X2: individuals,X3: $i] : ( X1 @ X2 @ X3 )
=> ! [X2: $i,X3: individuals] : ( X1 @ X3 @ X2 ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: individuals > $i > $o] :
( ! [X2: individuals,X3: $i] : ( X1 @ X2 @ X3 )
=> ! [X2: $i,X3: individuals] : ( X1 @ X3 @ X2 ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(h1,assumption,
~ ( ! [X1: individuals] : ( !! @ ( eigen__0 @ X1 ) )
=> ! [X1: $i,X2: individuals] : ( eigen__0 @ X2 @ X1 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP1,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i,X2: individuals] : ( eigen__0 @ X2 @ X1 ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: individuals] : ( eigen__0 @ X1 @ eigen__1 ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP1
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h4,h2,h3,h1,h0])],[1,2,h2,h5]) ).
thf(4,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,3,h5]) ).
thf(5,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,4,h4]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,5,h2,h3]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,6,h1]) ).
thf(0,theorem,
! [X1: individuals > $i > $o] :
( ! [X2: individuals,X3: $i] : ( X1 @ X2 @ X3 )
=> ! [X2: $i,X3: individuals] : ( X1 @ X3 @ X2 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL609^1 : TPTP v8.1.2. Released v3.6.0.
% 0.12/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 17:41:13 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % Mode: cade22grackle2xfee4
% 0.19/0.40 % Steps: 6
% 0.19/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------