TSTP Solution File: SEU705^2 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU705^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n008.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 : Tue Jul 19 13:57:54 EDT 2022
% Result : Theorem 44.99s 45.14s
% Output : Proof 44.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 81
% Syntax : Number of formulae : 90 ( 18 unt; 10 typ; 10 def)
% Number of atoms : 351 ( 96 equ; 0 cnn)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 737 ( 208 ~; 36 |; 0 &; 282 @)
% ( 31 <=>; 180 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 49 usr; 45 con; 0-2 aty)
% Number of variables : 122 ( 47 ^ 75 !; 0 ?; 122 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_subset,type,
subset: $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $o ).
thf(ty_setunion,type,
setunion: $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_setadjoin,type,
setadjoin: $i > $i > $i ).
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] :
~ ( ( in @ X1 @ eigen__1 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ eigen__1
@ ^ [X3: $i] :
( ( eigen__2
=> ( X3 != X1 ) )
=> ~ ( ~ eigen__2
=> ( X3 != X2 ) ) ) ) )
@ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) ) )
@ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h1,assumption,
! [X1: $o > $o,X2: $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: $o] :
~ ! [X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ eigen__1
@ ^ [X4: $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) ) )
@ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ X1 @ eigen__1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ eigen__1
@ ^ [X2: $i] :
( ( eigen__2
=> ( X2 != eigen__3 ) )
=> ~ ( ~ eigen__2
=> ( X2 != X1 ) ) ) ) )
@ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( subset @ X1 @ X2 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( in
@ ( setunion
@ ( dsetconstr @ eigen__1
@ ^ [X1: $i] :
( ( eigen__2
=> ( X1 != eigen__3 ) )
=> ~ ( ~ eigen__2
=> ( X1 != eigen__4 ) ) ) ) )
@ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( subset
@ ( dsetconstr @ eigen__1
@ ^ [X1: $i] :
( ( eigen__2
=> ( X1 != eigen__3 ) )
=> ~ ( ~ eigen__2
=> ( X1 != eigen__4 ) ) ) )
@ eigen__1 )
=> ( ( in
@ ( setunion
@ ( dsetconstr @ eigen__1
@ ^ [X1: $i] :
( ( eigen__2
=> ( X1 != eigen__3 ) )
=> ~ ( ~ eigen__2
=> ( X1 != eigen__4 ) ) ) ) )
@ ( dsetconstr @ eigen__1
@ ^ [X1: $i] :
( ( eigen__2
=> ( X1 != eigen__3 ) )
=> ~ ( ~ eigen__2
=> ( X1 != eigen__4 ) ) ) ) )
=> sP2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ! [X1: $i] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( X1
!= ( setadjoin @ X2 @ emptyset ) ) )
=> ( in @ ( setunion @ X1 ) @ X1 ) )
=> ( ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) ) )
=> ( ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) ) )
@ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i] :
( ( subset
@ ( dsetconstr @ eigen__1
@ ^ [X3: $i] :
( ( eigen__2
=> ( X3 != eigen__3 ) )
=> ~ ( ~ eigen__2
=> ( X3 != eigen__4 ) ) ) )
@ X1 )
=> ( ( in @ X2
@ ( dsetconstr @ eigen__1
@ ^ [X3: $i] :
( ( eigen__2
=> ( X3 != eigen__3 ) )
=> ~ ( ~ eigen__2
=> ( X3 != eigen__4 ) ) ) ) )
=> ( in @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( subset
@ ( dsetconstr @ eigen__1
@ ^ [X2: $i] :
( ( eigen__2
=> ( X2 != eigen__3 ) )
=> ~ ( ~ eigen__2
=> ( X2 != eigen__4 ) ) ) )
@ eigen__1 )
=> ( ( in @ X1
@ ( dsetconstr @ eigen__1
@ ^ [X2: $i] :
( ( eigen__2
=> ( X2 != eigen__3 ) )
=> ~ ( ~ eigen__2
=> ( X2 != eigen__4 ) ) ) ) )
=> ( in @ X1 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( in @ X1
@ ( dsetconstr @ eigen__1
@ ^ [X2: $i] :
( ( eigen__2
=> ( X2 != eigen__3 ) )
=> ~ ( ~ eigen__2
=> ( X2 != eigen__4 ) ) ) ) )
=> ( ( dsetconstr @ eigen__1
@ ^ [X2: $i] :
( ( eigen__2
=> ( X2 != eigen__3 ) )
=> ~ ( ~ eigen__2
=> ( X2 != eigen__4 ) ) ) )
!= ( setadjoin @ X1 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( in @ eigen__4 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ~ ! [X2: $i] :
( ( in @ X2
@ ( dsetconstr @ eigen__1
@ ^ [X3: $i] :
( ( eigen__2
=> ( X3 != eigen__3 ) )
=> ~ ( ~ eigen__2
=> ( X3 != X1 ) ) ) ) )
=> ( ( dsetconstr @ eigen__1
@ ^ [X3: $i] :
( ( eigen__2
=> ( X3 != eigen__3 ) )
=> ~ ( ~ eigen__2
=> ( X3 != X1 ) ) ) )
!= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( in
@ ( setunion
@ ( dsetconstr @ eigen__1
@ ^ [X1: $i] :
( ( eigen__2
=> ( X1 != eigen__3 ) )
=> ~ ( ~ eigen__2
=> ( X1 != eigen__4 ) ) ) ) )
@ ( dsetconstr @ eigen__1
@ ^ [X1: $i] :
( ( eigen__2
=> ( X1 != eigen__3 ) )
=> ~ ( ~ eigen__2
=> ( X1 != eigen__4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP10
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( in @ eigen__3 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i > $o] : ( subset @ ( dsetconstr @ eigen__1 @ X1 ) @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) ) )
=> ( ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) ) )
@ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP8
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) ) )
=> ( ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP12
=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ eigen__1
@ ^ [X2: $i] :
( ( eigen__2
=> ( X2 != eigen__3 ) )
=> ~ ( ~ eigen__2
=> ( X2 != X1 ) ) ) ) )
@ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP8
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ~ ! [X3: $i] :
( ( in @ X3
@ ( dsetconstr @ eigen__1
@ ^ [X4: $i] :
( ( eigen__2
=> ( X4 != X1 ) )
=> ~ ( ~ eigen__2
=> ( X4 != X2 ) ) ) ) )
=> ( ( dsetconstr @ eigen__1
@ ^ [X4: $i] :
( ( eigen__2
=> ( X4 != X1 ) )
=> ~ ( ~ eigen__2
=> ( X4 != X2 ) ) ) )
!= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( subset
@ ( dsetconstr @ eigen__1
@ ^ [X1: $i] :
( ( eigen__2
=> ( X1 != eigen__3 ) )
=> ~ ( ~ eigen__2
=> ( X1 != eigen__4 ) ) ) )
@ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP1
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( X1
!= ( setadjoin @ X2 @ emptyset ) ) )
=> ( in @ ( setunion @ X1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP12
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $o,X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__1 )
=> ~ ! [X4: $i] :
( ( in @ X4
@ ( dsetconstr @ eigen__1
@ ^ [X5: $i] :
( ( X1
=> ( X5 != X2 ) )
=> ~ ( ~ X1
=> ( X5 != X3 ) ) ) ) )
=> ( ( dsetconstr @ eigen__1
@ ^ [X5: $i] :
( ( X1
=> ( X5 != X2 ) )
=> ~ ( ~ X1
=> ( X5 != X3 ) ) ) )
!= ( setadjoin @ X4 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ sP7
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ eigen__1
@ ^ [X3: $i] :
( ( eigen__2
=> ( X3 != X1 ) )
=> ~ ( ~ eigen__2
=> ( X3 != X2 ) ) ) ) )
@ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $o,X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ eigen__1
@ ^ [X4: $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) ) )
@ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ eigen__1
@ ^ [X2: $i] :
( ( eigen__2
=> ( X2 != eigen__3 ) )
=> ~ ( ~ eigen__2
=> ( X2 != X1 ) ) ) ) )
@ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(def_subsetE,definition,
subsetE = sP1 ).
thf(def_sepSubset,definition,
sepSubset = sP30 ).
thf(def_singleton,definition,
( singleton
= ( ^ [X1: $i] :
~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( X1
!= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ).
thf(def_theprop,definition,
( theprop
= ( ! [X1: $i] :
( ( singleton @ X1 )
=> ( in @ ( setunion @ X1 ) @ X1 ) ) ) ) ).
thf(def_ifSingleton,definition,
( ifSingleton
= ( ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( singleton
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) ) ) ) ) ) ) ).
thf(def_if,definition,
( if
= ( ^ [X1: $i,X2: $o,X3: $i,X4: $i] :
( setunion
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) ) ) ) ) ).
thf(ifp,conjecture,
sP22 ).
thf(h2,negated_conjecture,
~ sP22,
inference(assume_negation,[status(cth)],[ifp]) ).
thf(1,plain,
( ~ sP6
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP3
| ~ sP21
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP11
| ~ sP10
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP5
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP26
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP20
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP25
| ~ sP12
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP9
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP15
| ~ sP8
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP27
| sP7
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP13
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP1
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP23
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( sP18
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP18
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP30
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP16
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( sP31
| ~ sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(19,plain,
( sP17
| ~ sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP17
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP28
| ~ sP17 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(22,plain,
( sP29
| ~ sP28 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(23,plain,
( sP24
| ~ sP29 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(24,plain,
( sP14
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP14
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP4
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP4
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP19
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( sP19
| sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( sP22
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( sP22
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,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,h2]) ).
thf(33,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[32,h1]) ).
thf(34,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[33,h0]) ).
thf(0,theorem,
sP22,
inference(contra,[status(thm),contra(discharge,[h2])],[32,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU705^2 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n008.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 : 600
% 0.12/0.33 % DateTime : Sun Jun 19 16:24:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 44.99/45.14 % SZS status Theorem
% 44.99/45.14 % Mode: mode459
% 44.99/45.14 % Inferences: 1315
% 44.99/45.14 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------