TSTP Solution File: SWV428^2 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SWV428^2 : 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 22:49:10 EDT 2023
% Result : Theorem 0.17s 0.48s
% Output : Proof 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 97
% Syntax : Number of formulae : 106 ( 38 unt; 8 typ; 26 def)
% Number of atoms : 297 ( 26 equ; 3 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 423 ( 55 ~; 34 |; 2 &; 213 @)
% ( 30 <=>; 89 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 68 ( 64 usr; 63 con; 0-2 aty)
% Number of variables : 111 ( 43 ^; 64 !; 4 ?; 111 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_deletefile1,type,
deletefile1: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_bob,type,
bob: $i > $o ).
thf(ty_rel,type,
rel: $i > $i > $o ).
thf(ty_admin,type,
admin: $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $i] :
~ ( ( rel @ eigen__5 @ X1 )
=> ( deletefile1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $i] :
~ ( ( rel @ eigen__1 @ X1 )
=> ( ~ ( admin @ X1 )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( rel @ eigen__1 @ X1 )
=> ( ~ ( admin @ X1 )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( ~ ( bob @ X3 )
=> ! [X4: $i] :
( ( rel @ X3 @ X4 )
=> ( deletefile1 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( deletefile1 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( rel @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i] :
( ( rel @ X1 @ X2 )
=> ( ~ ( bob @ X2 )
=> ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( deletefile1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( rel @ eigen__1 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( rel @ eigen__5 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( deletefile1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ! [X1: $i] :
( ( rel @ eigen__6 @ X1 )
=> ( deletefile1 @ X1 ) )
=> ( deletefile1 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( deletefile1 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP4
=> ( ~ ( admin @ eigen__5 )
=> ! [X1: $i] :
( ( rel @ eigen__5 @ X1 )
=> ( ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( ~ ( bob @ X2 )
=> ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( deletefile1 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( admin @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ! [X1: $i] :
( ( rel @ eigen__1 @ X1 )
=> ( deletefile1 @ X1 ) )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP2
=> ( ! [X1: $i] :
( ( rel @ eigen__1 @ X1 )
=> ( ~ ( admin @ X1 )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( rel @ eigen__1 @ X1 )
=> ( deletefile1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( rel @ eigen__1 @ X1 )
=> ( ~ ( admin @ X1 )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) )
=> ( deletefile1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP5
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ( rel @ eigen__6 @ X1 )
=> ( ~ ( bob @ X1 )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i,X2: $i] :
( ( rel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( ~ ( admin @ X3 )
=> ! [X4: $i] :
( ( rel @ X3 @ X4 )
=> ( deletefile1 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( deletefile1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i > $o,X2: $i] :
( ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( X1 @ X3 ) )
=> ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ~ sP10
=> ! [X1: $i] :
( ( rel @ eigen__5 @ X1 )
=> ( deletefile1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP5
=> ( sP16
=> ! [X1: $i] :
( ( rel @ eigen__6 @ X1 )
=> ( deletefile1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ( rel @ eigen__5 @ X1 )
=> ( deletefile1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i] :
( ( rel @ eigen__5 @ X1 )
=> ( ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( ~ ( bob @ X2 )
=> ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( deletefile1 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i] :
( ( rel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( ~ ( admin @ X2 )
=> ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( deletefile1 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ sP10
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i,X2: $i] :
( ( rel @ X1 @ X2 )
=> ( ~ ( admin @ X2 )
=> ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( rel @ X3 @ X4 )
=> ( ~ ( bob @ X4 )
=> ! [X5: $i] :
( ( rel @ X4 @ X5 )
=> ( deletefile1 @ X5 ) ) ) )
=> ! [X4: $i] :
( ( rel @ X3 @ X4 )
=> ( deletefile1 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP4
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i] :
( ( rel @ eigen__6 @ X1 )
=> ( deletefile1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( sP16
=> sP27 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i] :
( ( rel @ eigen__1 @ X1 )
=> ( deletefile1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( sP13
=> sP29 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
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(def_icl_atom,definition,
( icl_atom
= ( ^ [X1: $i > $o] : ( mbox @ rel @ X1 ) ) ) ).
thf(def_icl_princ,definition,
( icl_princ
= ( ^ [X1: $i > $o] : X1 ) ) ).
thf(def_icl_and,definition,
( icl_and
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ X1 @ X2 ) ) ) ).
thf(def_icl_or,definition,
( icl_or
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ X1 @ X2 ) ) ) ).
thf(def_icl_impl,definition,
( icl_impl
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mbox @ rel @ ( mimpl @ X1 @ X2 ) ) ) ) ).
thf(def_icl_true,definition,
icl_true = mtrue ).
thf(def_icl_false,definition,
icl_false = mfalse ).
thf(def_icl_says,definition,
( icl_says
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mbox @ rel @ ( mor @ X1 @ X2 ) ) ) ) ).
thf(def_iclval,definition,
( iclval
= ( ^ [X1: $i > $o] : ( mvalid @ X1 ) ) ) ).
thf(ex1,conjecture,
! [X1: $i,X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i,X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ),
inference(assume_negation,[status(cth)],[ex1]) ).
thf(h2,assumption,
~ ! [X1: $i] :
( ( rel @ eigen__0 @ X1 )
=> ( deletefile1 @ X1 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP2
=> sP6 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP2,
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP28
| ~ sP16
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP20
| ~ sP5
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP7
| ~ sP27
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP3
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP14
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP22
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP24
| sP10
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP9
| ~ sP4
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP1
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP12
| ~ sP2
| sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP23
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP17
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( sP15
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP15
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP21
| ~ sP15 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(16,plain,
( sP19
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP19
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP26
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP26
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP13
| ~ sP26 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(21,plain,
( ~ sP30
| ~ sP13
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP11
| ~ sP29
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP25
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP14
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP18
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(ax3,axiom,
sP3 ).
thf(ax2,axiom,
sP25 ).
thf(ax1,axiom,
sP17 ).
thf(refl_axiom,axiom,
sP18 ).
thf(26,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,h4,h5,ax3,ax2,ax1,refl_axiom]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,26,h4,h5]) ).
thf(28,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,27,h3]) ).
thf(29,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,28,h2]) ).
thf(30,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[29,h0]) ).
thf(0,theorem,
! [X1: $i,X2: $i] :
( ( rel @ X1 @ X2 )
=> ( deletefile1 @ X2 ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[29,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWV428^2 : TPTP v8.1.2. Released v3.6.0.
% 0.06/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.11/0.32 % Computer : n018.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Aug 29 10:10:47 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.17/0.48 % SZS status Theorem
% 0.17/0.48 % Mode: cade22grackle2xfee4
% 0.17/0.48 % Steps: 1592
% 0.17/0.48 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------