TSTP Solution File: SEV252^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV252^5 : 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 : Thu Aug 31 19:33:08 EDT 2023
% Result : Theorem 181.57s 181.80s
% Output : Proof 181.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 95
% Syntax : Number of formulae : 112 ( 29 unt; 7 typ; 4 def)
% Number of atoms : 283 ( 10 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 723 ( 151 ~; 45 |; 0 &; 330 @)
% ( 38 <=>; 159 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 78 ( 78 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 47 usr; 45 con; 0-2 aty)
% Number of variables : 175 ( 27 ^; 148 !; 0 ?; 175 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__12,type,
eigen__12: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__0,type,
eigen__0: ( $i > $o ) > $i > $o ).
thf(ty_eigen__13,type,
eigen__13: $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i > $o ).
thf(ty_eigen__24,type,
eigen__24: $i ).
thf(h0,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i > $o] :
~ ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(h1,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__12,definition,
( eigen__12
= ( eps__1
@ ^ [X1: $i] :
~ ( ( eigen__3 @ X1 )
=> ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__12])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: $i] :
~ ( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__24,definition,
( eigen__24
= ( eps__1
@ ^ [X1: $i] :
~ ( ( eigen__13 @ X1 )
=> ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__24])]) ).
thf(sP1,plain,
( sP1
<=> ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ! [X1: $i] :
( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) )
=> ! [X1: $i] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
=> ( eigen__0
@ ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__3 @ eigen__2 )
=> ( eigen__0 @ eigen__3 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( eigen__3 @ X1 )
=> ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eigen__0 @ eigen__3 @ eigen__2 )
=> ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__3 @ eigen__12 )
=> ~ ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__12 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ! [X1: $i] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
=> ( eigen__0
@ ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) )
@ X1 ) )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( eigen__3 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( eigen__0 @ eigen__3 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( eigen__13 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( eigen__0 @ eigen__13 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( eigen__13 @ X1 )
=> ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP11
=> ! [X1: $i] :
( ( eigen__0 @ eigen__13 @ X1 )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
=> ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( eigen__0
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( eigen__0 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
=> ( eigen__0 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( eigen__13 @ eigen__24 )
=> ~ ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__24 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP5
=> ! [X1: $i] :
( ( eigen__0 @ eigen__3 @ X1 )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__13 @ eigen__24 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__0 @ eigen__3 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( eigen__13 @ eigen__1 )
=> ( eigen__0 @ eigen__13 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ( eigen__3 @ X1 )
=> ( eigen__0 @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ sP4
=> ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__13 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eigen__3 @ eigen__12 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( eigen__0 @ eigen__13 @ eigen__1 )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__0 @ eigen__13 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: $i] :
( ( eigen__0 @ X1 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__13 @ X1 )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__3 @ X1 )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ! [X1: $i] :
( ( eigen__13 @ X1 )
=> ( eigen__0 @ eigen__13 @ X1 ) )
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i] :
( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__12 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( sP19
=> ~ ( eigen__3 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( eigen__3 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i] :
( ( eigen__13 @ X1 )
=> ( eigen__0 @ eigen__13 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__24 ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( sP19
=> ~ sP23 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: $i] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
=> ( eigen__0
@ ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(cTHM2A_EXPANDED_pme,conjecture,
! [X1: ( $i > $o ) > $i > $o] :
( ~ ( ! [X2: $i > $o,X3: $i > $o] :
( ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X1 @ X3 @ X4 ) ) )
=> ~ ! [X2: $i > $o,X3: $i > $o] :
( ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X1 @ X3 @ X4 ) ) ) )
=> ! [X2: $i] :
( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
= ( ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X1 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) ) ) ) ).
thf(h2,negated_conjecture,
~ ! [X1: ( $i > $o ) > $i > $o] :
( ~ ( ! [X2: $i > $o,X3: $i > $o] :
( ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X1 @ X3 @ X4 ) ) )
=> ~ ! [X2: $i > $o,X3: $i > $o] :
( ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X1 @ X3 @ X4 ) ) ) )
=> ! [X2: $i] :
( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
= ( ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X1 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM2A_EXPANDED_pme]) ).
thf(h3,assumption,
~ ( ~ ( sP26
=> ~ sP26 )
=> ! [X1: $i] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
= ( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP26
=> ~ sP26 ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
= ( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP26,
introduced(assumption,[]) ).
thf(h7,assumption,
( sP1 != ~ sP27 ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP1,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP27,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h11,assumption,
sP27,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP6
| ~ sP17
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP37
| ~ sP19
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP32
| sP37 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( sP7
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP7
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP29
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( sP5
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__12]) ).
thf(8,plain,
( ~ sP15
| ~ sP5
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP9
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP26
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP3
| ~ sP34
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP19
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP2
| ~ sP31
| sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP13
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP8
| ~ sP38
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP33
| sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP33
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP4
| ~ sP33 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(19,plain,
( sP20
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP20
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP31
| ~ sP20 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(22,plain,
( ~ sP26
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP27
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h7,h6,h6,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,h6,h8,h9]) ).
thf(h12,assumption,
~ ( sP35
=> ~ sP22 ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP35,
introduced(assumption,[]) ).
thf(h14,assumption,
sP22,
introduced(assumption,[]) ).
thf(25,plain,
( ~ sP24
| ~ sP25
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP30
| ~ sP35
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP36
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( sP14
| sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( sP14
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP28
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(31,plain,
( sP11
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__24]) ).
thf(32,plain,
( ~ sP12
| ~ sP11
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP10
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP26
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP18
| ~ sP22
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP35
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h14,h12,h10,h11,h7,h6,h6,h4,h5,h3,h2,h1,h0])],[25,26,27,28,29,30,31,32,33,34,35,36,h6,h10,h13,h14]) ).
thf(38,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h10,h11,h7,h6,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,37,h13,h14]) ).
thf(39,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h11,h7,h6,h6,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__13)],[h11,38,h12]) ).
thf(40,plain,
$false,
inference(tab_be,[status(thm),assumptions([h7,h6,h6,h4,h5,h3,h2,h1,h0]),tab_be(discharge,[h8,h9]),tab_be(discharge,[h10,h11])],[h7,24,39,h8,h9,h10,h11]) ).
thf(41,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h6,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__1)],[h5,40,h7]) ).
thf(42,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h6])],[h4,41,h6,h6]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,42,h4,h5]) ).
thf(44,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,43,h3]) ).
thf(45,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[44,h1]) ).
thf(46,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[45,h0]) ).
thf(0,theorem,
! [X1: ( $i > $o ) > $i > $o] :
( ~ ( ! [X2: $i > $o,X3: $i > $o] :
( ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X1 @ X3 @ X4 ) ) )
=> ~ ! [X2: $i > $o,X3: $i > $o] :
( ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X1 @ X3 @ X4 ) ) ) )
=> ! [X2: $i] :
( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
= ( ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X1 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[44,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SEV252^5 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 24 03:47:07 EDT 2023
% 0.21/0.36 % CPUTime :
% 181.57/181.80 % SZS status Theorem
% 181.57/181.80 % Mode: cade22grackle2x2d0b
% 181.57/181.80 % Steps: 249
% 181.57/181.80 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------