TSTP Solution File: SYO067^4.001 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO067^4.001 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n012.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 : Fri Sep 1 04:45:01 EDT 2023
% Result : Theorem 0.19s 0.61s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 113
% Syntax : Number of formulae : 123 ( 35 unt; 9 typ; 24 def)
% Number of atoms : 364 ( 24 equ; 3 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 571 ( 76 ~; 48 |; 1 &; 294 @)
% ( 41 <=>; 111 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 74 ( 70 usr; 70 con; 0-2 aty)
% Number of variables : 114 ( 38 ^; 74 !; 2 ?; 114 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_p1,type,
p1: $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_f,type,
f: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $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 )
=> ( p1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__0 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__5 @ X1 )
=> ( p1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__3 @ X1 )
=> ( f @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__4 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( irel @ X1 @ X2 )
=> ~ ( irel @ X2 @ X3 ) )
=> ( irel @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ( irel @ eigen__3 @ eigen__5 )
=> ~ ( irel @ eigen__5 @ eigen__6 ) )
=> ( irel @ eigen__3 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( irel @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( f @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( irel @ eigen__3 @ eigen__5 )
=> ~ ( irel @ eigen__5 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ( irel @ eigen__3 @ eigen__4 )
=> ~ ( irel @ eigen__4 @ eigen__5 ) )
=> ( irel @ eigen__3 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( irel @ eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( f @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ ! [X1: $i] :
( ( irel @ eigen__5 @ X1 )
=> ( p1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__5 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( irel @ eigen__3 @ eigen__4 )
=> ( f @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( irel @ eigen__1 @ eigen__3 )
=> ( ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( p1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( f @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP7
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ~ ( ( irel @ eigen__3 @ eigen__4 )
=> ~ ( irel @ eigen__4 @ X1 ) )
=> ( irel @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( irel @ eigen__4 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( irel @ eigen__5 @ X1 )
=> ( p1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( irel @ eigen__3 @ eigen__6 )
=> ( p1 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( irel @ eigen__3 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( f @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP3
=> ( f @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( f @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( f @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( irel @ eigen__5 @ eigen__6 )
=> ( p1 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ~ ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( p1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( p1 @ X1 ) )
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( p1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( f @ X4 ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( irel @ eigen__5 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i] : ( irel @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( p1 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i] :
( ~ ( sP17
=> ~ ( irel @ eigen__5 @ X1 ) )
=> ( irel @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( sP14
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( f @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( irel @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ( irel @ eigen__0 @ eigen__1 )
=> sP25 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( irel @ eigen__3 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: $i,X2: $i] :
( ~ ( ( irel @ eigen__3 @ X1 )
=> ~ ( irel @ X1 @ X2 ) )
=> ( irel @ eigen__3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( f @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( sP34
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( p1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
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,X2: $i > $o] : ( mor @ ( mnot @ X1 ) @ X2 ) ) ) ).
thf(def_mbox_s4,definition,
( mbox_s4
= ( ^ [X1: $i > $o,X2: $i] :
! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( 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] : $true ) ) ).
thf(def_ifalse,definition,
( ifalse
= ( inot @ itrue ) ) ).
thf(def_iand,definition,
( iand
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ X1 @ X2 ) ) ) ).
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
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_isatisfiable,definition,
( isatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_icountersatisfiable,definition,
( icountersatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_iinvalid,definition,
( iinvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(con,conjecture,
! [X1: $i] : ( f @ X1 ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i] : ( f @ X1 ),
inference(assume_negation,[status(cth)],[con]) ).
thf(h2,assumption,
~ sP38,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP5
| ~ sP17
| ~ sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP5
| sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP31
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP39
| ~ sP34
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP6
| sP39
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP37
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP13
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP16
| ~ sP36
| sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP40
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP37
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP1
| sP37 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( sP24
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP24
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP15
| ~ sP24 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(15,plain,
( sP9
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP12
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP12
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP18
| ~ sP12 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(19,plain,
( ~ sP32
| ~ sP14
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP23
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP4
| ~ sP18
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP29
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP27
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( sP10
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP10
| sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP22
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(27,plain,
( sP26
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP26
| sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( sP11
| ~ sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( sP41
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(31,plain,
( sP25
| ~ sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP35
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( sP21
| ~ sP35 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(34,plain,
( ~ sP20
| ~ sP3
| sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP33
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP8
| ~ sP21
| sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP29
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP27
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(axiom1,axiom,
sP27 ).
thf(trans_axiom,axiom,
sP1 ).
thf(refl_axiom,axiom,
sP29 ).
thf(39,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,h2,axiom1,trans_axiom,refl_axiom]) ).
thf(40,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,39,h2]) ).
thf(41,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[40,h0]) ).
thf(0,theorem,
! [X1: $i] : ( f @ X1 ),
inference(contra,[status(thm),contra(discharge,[h1])],[40,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO067^4.001 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 04:49:55 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.61 % SZS status Theorem
% 0.19/0.61 % Mode: cade22grackle2xfee4
% 0.19/0.61 % Steps: 2031
% 0.19/0.61 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------