TSTP Solution File: SYO063^4 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO063^4 : 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 : n003.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 04:44:59 EDT 2023
% Result : Theorem 4.62s 4.77s
% Output : Proof 4.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 111
% Syntax : Number of formulae : 121 ( 35 unt; 10 typ; 21 def)
% Number of atoms : 390 ( 21 equ; 3 cnn)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 676 ( 121 ~; 45 |; 1 &; 319 @)
% ( 38 <=>; 152 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 72 ( 68 usr; 65 con; 0-2 aty)
% Number of variables : 135 ( 35 ^; 98 !; 2 ?; 135 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__17,type,
eigen__17: $i ).
thf(ty_eigen__3,type,
eigen__3: $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_p,type,
p: $i > $o ).
thf(ty_s,type,
s: $i > $o ).
thf(ty_r,type,
r: $i > $o ).
thf(ty_irel,type,
irel: $i > $i > $o ).
thf(ty_t,type,
t: $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 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( t @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( r @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__17,definition,
( eigen__17
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__3 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( q @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( t @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( r @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__17])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( t @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( r @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( irel @ X1 @ X2 )
=> ~ ( irel @ X2 @ X3 ) )
=> ( irel @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [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 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( t @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( r @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( irel @ eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( s @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP4
=> ~ ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( q @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( t @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( r @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( irel @ eigen__3 @ eigen__17 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p @ X2 ) ) )
=> ( sP5
=> ~ sP5 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ ( ( irel @ eigen__1 @ eigen__3 )
=> ~ sP7 )
=> ( irel @ eigen__1 @ eigen__17 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( irel @ eigen__17 @ X1 )
=> ( p @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( q @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( t @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( r @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP10
=> ! [X1: $i] :
( ( irel @ eigen__17 @ X1 )
=> ( q @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( t @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( r @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( irel @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ~ ( ( irel @ eigen__1 @ eigen__3 )
=> ~ ( irel @ eigen__3 @ X1 ) )
=> ( irel @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( irel @ eigen__1 @ eigen__17 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP1
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( p @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ! [X1: $i] :
( ( irel @ eigen__17 @ X1 )
=> ( t @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__17 @ X1 )
=> ( r @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP5
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( irel @ eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( p @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP20
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i] : ( s @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i] : ( irel @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( irel @ eigen__1 @ eigen__1 )
=> ~ sP21 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP14
=> ~ sP20 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( sP20
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP7
=> ~ ( sP12
=> ~ sP18 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( irel @ eigen__1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i,X2: $i] :
( ~ ( ( irel @ eigen__0 @ X1 )
=> ~ ( irel @ X1 @ X2 ) )
=> ( irel @ eigen__0 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( sP12
=> ~ sP18 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i,X2: $i] :
( ~ ( ( irel @ eigen__1 @ X1 )
=> ~ ( irel @ X1 @ X2 ) )
=> ( irel @ eigen__1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: $i] :
( ~ ( sP14
=> ~ ( irel @ eigen__1 @ X1 ) )
=> ( irel @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ~ sP27
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( sP7
=> sP18 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( t @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( r @ X4 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( sP16
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
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] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( p @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( q @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( t @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( r @ X4 ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( p @ X4 ) ) )
=> ( ( s @ X2 )
=> ~ ( s @ X2 ) ) ) ) ) ).
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 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( t @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( r @ X4 ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( p @ X4 ) ) )
=> ( ( s @ X2 )
=> ~ ( s @ X2 ) ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(h2,assumption,
~ ( sP3
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p @ X3 ) ) )
=> ( ( s @ X1 )
=> ~ ( s @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP3,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p @ X3 ) ) )
=> ( ( s @ X1 )
=> ~ ( s @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP14
=> ~ sP8 ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP14,
introduced(assumption,[]) ).
thf(h7,assumption,
sP8,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP36
| ~ sP7
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP28
| ~ sP20
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP9
| sP28
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP38
| ~ sP16
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP25
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP13
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP15
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( sP12
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP32
| ~ sP12
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP29
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP29
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP11
| ~ sP29 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__17]) ).
thf(13,plain,
( ~ sP6
| ~ sP4
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP27
| ~ sP14
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP35
| sP27
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP3
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP33
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP34
| sP35 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP31
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP2
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( sP22
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP22
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP1
| ~ sP22 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(24,plain,
( ~ sP17
| ~ sP1
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP26
| ~ sP30
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP24
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP23
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP2
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP37
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP25
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP19
| ~ sP5
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP8
| sP25
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(axiom2,axiom,
sP37 ).
thf(axiom1,axiom,
sP23 ).
thf(trans_axiom,axiom,
sP2 ).
thf(refl_axiom,axiom,
sP24 ).
thf(33,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h7,h5,h3,h4,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,h3,h6,h7,axiom2,axiom1,trans_axiom,refl_axiom]) ).
thf(34,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,33,h6,h7]) ).
thf(35,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__1)],[h4,34,h5]) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,35,h3,h4]) ).
thf(37,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,36,h2]) ).
thf(38,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[37,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 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( t @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( r @ X4 ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( p @ X4 ) ) )
=> ( ( s @ X2 )
=> ~ ( s @ X2 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[37,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO063^4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n003.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Aug 26 00:27:39 EDT 2023
% 0.13/0.33 % CPUTime :
% 4.62/4.77 % SZS status Theorem
% 4.62/4.77 % Mode: cade22grackle2xfee4
% 4.62/4.77 % Steps: 27916
% 4.62/4.77 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------