TSTP Solution File: SYN041^4 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYN041^4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n023.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 : Thu Jul 21 11:40:40 EDT 2022
% Result : Theorem 0.19s 0.35s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 76
% Syntax : Number of formulae : 89 ( 37 unt; 8 typ; 21 def)
% Number of atoms : 247 ( 21 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 405 ( 64 ~; 20 |; 0 &; 215 @)
% ( 19 <=>; 85 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 47 usr; 46 con; 0-2 aty)
% ( 2 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 88 ( 29 ^ 59 !; 0 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_p,type,
p: $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_q,type,
q: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_irel,type,
irel: $i > $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( q @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__3 @ X1 )
=> ( q @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ( irel @ eigen__1 @ eigen__3 )
=> ~ ( irel @ eigen__3 @ eigen__4 ) )
=> ( irel @ eigen__1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( q @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( irel @ eigen__1 @ eigen__3 )
=> ~ ( irel @ eigen__3 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( q @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ~ ( ( irel @ eigen__1 @ eigen__3 )
=> ~ ( irel @ eigen__3 @ X1 ) )
=> ( irel @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( irel @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( irel @ X1 @ X2 )
=> ~ ( irel @ X2 @ X3 ) )
=> ( irel @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( irel @ eigen__1 @ eigen__4 )
=> ( q @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( irel @ eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( irel @ eigen__0 @ eigen__1 )
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP6
=> ( q @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( q @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( q @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i,X2: $i] :
( ~ ( ( irel @ eigen__1 @ X1 )
=> ~ ( irel @ X1 @ X2 ) )
=> ( irel @ eigen__1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP9
=> ( ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( p @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( q @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( irel @ eigen__1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( p @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( q @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( irel @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( q @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
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_mimplies,definition,
( mimplies
= ( ^ [X1: $i > $o] : ( mor @ ( mnot @ X1 ) ) ) ) ).
thf(def_mbox_s4,definition,
( mbox_s4
= ( ^ [X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ).
thf(def_iatom,definition,
( iatom
= ( ^ [X1: $i > $o] : X1 ) ) ).
thf(def_inot,definition,
( inot
= ( ^ [X1: $i > $o] : ( mnot @ ( mbox_s4 @ X1 ) ) ) ) ).
thf(def_itrue,definition,
( itrue
= ( ^ [X1: $i] : ~ $false ) ) ).
thf(def_ifalse,definition,
( ifalse
= ( inot @ itrue ) ) ).
thf(def_iand,definition,
iand = mand ).
thf(def_ior,definition,
( ior
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ) ).
thf(def_iimplies,definition,
( iimplies
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mimplies @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ) ).
thf(def_iimplied,definition,
( iimplied
= ( ^ [X1: $i > $o,X2: $i > $o] : ( iimplies @ X2 @ X1 ) ) ) ).
thf(def_iequiv,definition,
( iequiv
= ( ^ [X1: $i > $o,X2: $i > $o] : ( iand @ ( iimplies @ X1 @ X2 ) @ ( iimplies @ X2 @ X1 ) ) ) ) ).
thf(def_ixor,definition,
( ixor
= ( ^ [X1: $i > $o,X2: $i > $o] : ( inot @ ( iequiv @ X1 @ X2 ) ) ) ) ).
thf(def_ivalid,definition,
ivalid = !! ).
thf(def_isatisfiable,definition,
( isatisfiable
= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_icountersatisfiable,definition,
( icountersatisfiable
= ( ^ [X1: $i > $o] :
~ ( !! @ X1 ) ) ) ).
thf(def_iinvalid,definition,
( iinvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(pel3,conjecture,
! [X1: $i] :
( ~ ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( p @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( q @ X4 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( q @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p @ X3 ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( p @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( q @ X4 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( q @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p @ X3 ) ) ) ) ),
inference(assume_negation,[status(cth)],[pel3]) ).
thf(h2,assumption,
~ ( sP4
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( q @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP4,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( q @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP18
=> ( sP12
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( p @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP18,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP12
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( p @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP12,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( p @ X1 ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( ( irel @ eigen__1 @ eigen__2 )
=> ( p @ eigen__2 ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
irel @ eigen__1 @ eigen__2,
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( p @ eigen__2 ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP7
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP14
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP1
| sP3
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP3
| ~ sP9
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP8
| ~ sP16
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP11
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP11
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP19
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(11,plain,
( sP17
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP15
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP15
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP2
| ~ sP15 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(15,plain,
( ~ sP4
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP10
| ~ sP18
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(trans_axiom,axiom,
sP7 ).
thf(17,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h10,h8,h9,h6,h7,h5,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,trans_axiom,h3,h6,h8]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h6,h7,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,17,h11,h12]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h9,h6,h7,h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__2)],[h9,18,h10]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,19,h8,h9]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,20,h6,h7]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__1)],[h4,21,h5]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,22,h3,h4]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,23,h2]) ).
thf(25,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[24,h0]) ).
thf(0,theorem,
! [X1: $i] :
( ~ ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( p @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( q @ X4 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( q @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p @ X3 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[24,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN041^4 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.32 % Computer : n023.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 600
% 0.13/0.32 % DateTime : Mon Jul 11 21:15:54 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.35 % SZS status Theorem
% 0.19/0.35 % Mode: mode213
% 0.19/0.35 % Inferences: 34
% 0.19/0.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------