TSTP Solution File: LCL597^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL597^1 : TPTP v8.1.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n026.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 : 600s
% DateTime : Sun Jul 17 14:09:00 EDT 2022
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 33
% Syntax : Number of formulae : 41 ( 25 unt; 1 typ; 18 def)
% Number of atoms : 99 ( 18 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 153 ( 32 ~; 7 |; 0 &; 68 @)
% ( 7 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 28 usr; 29 con; 0-2 aty)
% ( 2 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 74 ( 29 ^ 45 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ( ! [X2: $i] :
( $false
=> ( eigen__0 @ X2 ) )
=> ! [X2: $i] :
( $false
=> ! [X3: $i] :
( $false
=> ( eigen__0 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h1,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: $i > $o] :
~ ! [X2: $i] :
( ! [X3: $i] :
( $false
=> ( X1 @ X3 ) )
=> ! [X3: $i] :
( $false
=> ! [X4: $i] :
( $false
=> ( X1 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ( $false
=> ! [X2: $i] :
( $false
=> ( eigen__0 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i > $o,X2: $i] :
( ! [X3: $i] :
( $false
=> ( X1 @ X3 ) )
=> ! [X3: $i] :
( $false
=> ! [X4: $i] :
( $false
=> ( X1 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( $false
=> ! [X1: $i] :
( $false
=> ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( $false
=> ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] : sP2 ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( sP3
=> sP4 ) ),
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
<=> ( sP3
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
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] :
( ~ ~ ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X2 @ X5 ) ) ) ) ).
thf(h2,negated_conjecture,
sP6,
inference(assume_negation,[status(cth)],[thm]) ).
thf(1,plain,
( sP2
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP4
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(3,plain,
( sP7
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP7
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP5
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(6,plain,
( sP1
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(7,plain,
( ~ sP6
| ~ sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,h2]) ).
thf(9,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[8,h1]) ).
thf(10,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[9,h0]) ).
thf(0,theorem,
~ ! [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 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[8,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : LCL597^1 : TPTP v8.1.0. Released v3.6.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n026.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 : 600
% 0.13/0.34 % DateTime : Sat Jul 2 18:38:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % Mode: mode213
% 0.19/0.38 % Inferences: 125
% 0.19/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------