TSTP Solution File: ALG001^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG001^5 : 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 : n027.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 14 17:57:07 EDT 2022
% Result : Theorem 1.99s 2.20s
% Output : Proof 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 61
% Syntax : Number of formulae : 77 ( 24 unt; 10 typ; 7 def)
% Number of atoms : 151 ( 56 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 556 ( 54 ~; 23 |; 0 &; 422 @)
% ( 22 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 86 ( 86 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 35 usr; 31 con; 0-2 aty)
% Number of variables : 126 ( 7 ^ 119 !; 0 ?; 126 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_b,type,
b: $tType ).
thf(ty_g,type,
g: $tType ).
thf(ty_eigen__6,type,
eigen__6: g ).
thf(ty_eigen__2,type,
eigen__2: g > g > g ).
thf(ty_eigen__1,type,
eigen__1: b > a ).
thf(ty_eigen__0,type,
eigen__0: g > b ).
thf(ty_eigen__4,type,
eigen__4: a > a > a ).
thf(ty_eigen__5,type,
eigen__5: g ).
thf(ty_eigen__3,type,
eigen__3: b > b > b ).
thf(h0,assumption,
! [X1: ( b > b > b ) > $o,X2: b > b > b] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: b > b > b] :
~ ! [X2: a > a > a] :
( ~ ( ! [X3: g,X4: g] :
( ( eigen__0 @ ( eigen__2 @ X3 @ X4 ) )
= ( X1 @ ( eigen__0 @ X3 ) @ ( eigen__0 @ X4 ) ) )
=> ~ ! [X3: b,X4: b] :
( ( eigen__1 @ ( X1 @ X3 @ X4 ) )
= ( X2 @ ( eigen__1 @ X3 ) @ ( eigen__1 @ X4 ) ) ) )
=> ! [X3: g,X4: g] :
( ( eigen__1 @ ( eigen__0 @ ( eigen__2 @ X3 @ X4 ) ) )
= ( X2 @ ( eigen__1 @ ( eigen__0 @ X3 ) ) @ ( eigen__1 @ ( eigen__0 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(h1,assumption,
! [X1: ( b > a ) > $o,X2: b > a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__1
@ ^ [X1: b > a] :
~ ! [X2: g > g > g,X3: b > b > b,X4: a > a > a] :
( ~ ( ! [X5: g,X6: g] :
( ( eigen__0 @ ( X2 @ X5 @ X6 ) )
= ( X3 @ ( eigen__0 @ X5 ) @ ( eigen__0 @ X6 ) ) )
=> ~ ! [X5: b,X6: b] :
( ( X1 @ ( X3 @ X5 @ X6 ) )
= ( X4 @ ( X1 @ X5 ) @ ( X1 @ X6 ) ) ) )
=> ! [X5: g,X6: g] :
( ( X1 @ ( eigen__0 @ ( X2 @ X5 @ X6 ) ) )
= ( X4 @ ( X1 @ ( eigen__0 @ X5 ) ) @ ( X1 @ ( eigen__0 @ X6 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h2,assumption,
! [X1: g > $o,X2: g] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__2
@ ^ [X1: g] :
( ( eigen__1 @ ( eigen__0 @ ( eigen__2 @ eigen__5 @ X1 ) ) )
!= ( eigen__4 @ ( eigen__1 @ ( eigen__0 @ eigen__5 ) ) @ ( eigen__1 @ ( eigen__0 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(h3,assumption,
! [X1: ( g > b ) > $o,X2: g > b] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__3 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__3
@ ^ [X1: g > b] :
~ ! [X2: b > a,X3: g > g > g,X4: b > b > b,X5: a > a > a] :
( ~ ( ! [X6: g,X7: g] :
( ( X1 @ ( X3 @ X6 @ X7 ) )
= ( X4 @ ( X1 @ X6 ) @ ( X1 @ X7 ) ) )
=> ~ ! [X6: b,X7: b] :
( ( X2 @ ( X4 @ X6 @ X7 ) )
= ( X5 @ ( X2 @ X6 ) @ ( X2 @ X7 ) ) ) )
=> ! [X6: g,X7: g] :
( ( X2 @ ( X1 @ ( X3 @ X6 @ X7 ) ) )
= ( X5 @ ( X2 @ ( X1 @ X6 ) ) @ ( X2 @ ( X1 @ X7 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(h4,assumption,
! [X1: ( g > g > g ) > $o,X2: g > g > g] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__4 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__4
@ ^ [X1: g > g > g] :
~ ! [X2: b > b > b,X3: a > a > a] :
( ~ ( ! [X4: g,X5: g] :
( ( eigen__0 @ ( X1 @ X4 @ X5 ) )
= ( X2 @ ( eigen__0 @ X4 ) @ ( eigen__0 @ X5 ) ) )
=> ~ ! [X4: b,X5: b] :
( ( eigen__1 @ ( X2 @ X4 @ X5 ) )
= ( X3 @ ( eigen__1 @ X4 ) @ ( eigen__1 @ X5 ) ) ) )
=> ! [X4: g,X5: g] :
( ( eigen__1 @ ( eigen__0 @ ( X1 @ X4 @ X5 ) ) )
= ( X3 @ ( eigen__1 @ ( eigen__0 @ X4 ) ) @ ( eigen__1 @ ( eigen__0 @ X5 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(h5,assumption,
! [X1: ( a > a > a ) > $o,X2: a > a > a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__5 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__5
@ ^ [X1: a > a > a] :
~ ( ~ ( ! [X2: g,X3: g] :
( ( eigen__0 @ ( eigen__2 @ X2 @ X3 ) )
= ( eigen__3 @ ( eigen__0 @ X2 ) @ ( eigen__0 @ X3 ) ) )
=> ~ ! [X2: b,X3: b] :
( ( eigen__1 @ ( eigen__3 @ X2 @ X3 ) )
= ( X1 @ ( eigen__1 @ X2 ) @ ( eigen__1 @ X3 ) ) ) )
=> ! [X2: g,X3: g] :
( ( eigen__1 @ ( eigen__0 @ ( eigen__2 @ X2 @ X3 ) ) )
= ( X1 @ ( eigen__1 @ ( eigen__0 @ X2 ) ) @ ( eigen__1 @ ( eigen__0 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__2
@ ^ [X1: g] :
~ ! [X2: g] :
( ( eigen__1 @ ( eigen__0 @ ( eigen__2 @ X1 @ X2 ) ) )
= ( eigen__4 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) @ ( eigen__1 @ ( eigen__0 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: b > a,X2: g > g > g,X3: b > b > b,X4: a > a > a] :
( ~ ( ! [X5: g,X6: g] :
( ( eigen__0 @ ( X2 @ X5 @ X6 ) )
= ( X3 @ ( eigen__0 @ X5 ) @ ( eigen__0 @ X6 ) ) )
=> ~ ! [X5: b,X6: b] :
( ( X1 @ ( X3 @ X5 @ X6 ) )
= ( X4 @ ( X1 @ X5 ) @ ( X1 @ X6 ) ) ) )
=> ! [X5: g,X6: g] :
( ( X1 @ ( eigen__0 @ ( X2 @ X5 @ X6 ) ) )
= ( X4 @ ( X1 @ ( eigen__0 @ X5 ) ) @ ( X1 @ ( eigen__0 @ X6 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__1 @ ( eigen__3 @ ( eigen__0 @ eigen__5 ) @ ( eigen__0 @ eigen__6 ) ) )
= ( eigen__4 @ ( eigen__1 @ ( eigen__0 @ eigen__5 ) ) @ ( eigen__1 @ ( eigen__0 @ eigen__6 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ! [X1: g,X2: g] :
( ( eigen__0 @ ( eigen__2 @ X1 @ X2 ) )
= ( eigen__3 @ ( eigen__0 @ X1 ) @ ( eigen__0 @ X2 ) ) )
=> ~ ! [X1: b,X2: b] :
( ( eigen__1 @ ( eigen__3 @ X1 @ X2 ) )
= ( eigen__4 @ ( eigen__1 @ X1 ) @ ( eigen__1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__2 @ eigen__5 @ eigen__6 ) ) )
= ( eigen__4 @ ( eigen__1 @ ( eigen__0 @ eigen__5 ) ) @ ( eigen__1 @ ( eigen__0 @ eigen__6 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a > a > a] :
( ~ ( ! [X2: g,X3: g] :
( ( eigen__0 @ ( eigen__2 @ X2 @ X3 ) )
= ( eigen__3 @ ( eigen__0 @ X2 ) @ ( eigen__0 @ X3 ) ) )
=> ~ ! [X2: b,X3: b] :
( ( eigen__1 @ ( eigen__3 @ X2 @ X3 ) )
= ( X1 @ ( eigen__1 @ X2 ) @ ( eigen__1 @ X3 ) ) ) )
=> ! [X2: g,X3: g] :
( ( eigen__1 @ ( eigen__0 @ ( eigen__2 @ X2 @ X3 ) ) )
= ( X1 @ ( eigen__1 @ ( eigen__0 @ X2 ) ) @ ( eigen__1 @ ( eigen__0 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a] :
( ( X1
= ( eigen__4 @ ( eigen__1 @ ( eigen__0 @ eigen__5 ) ) @ ( eigen__1 @ ( eigen__0 @ eigen__6 ) ) ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__2 @ eigen__5 @ eigen__6 ) ) )
!= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ sP3
=> ! [X1: g,X2: g] :
( ( eigen__1 @ ( eigen__0 @ ( eigen__2 @ X1 @ X2 ) ) )
= ( eigen__4 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) @ ( eigen__1 @ ( eigen__0 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( eigen__0 @ ( eigen__2 @ eigen__5 @ eigen__6 ) )
= ( eigen__3 @ ( eigen__0 @ eigen__5 ) @ ( eigen__0 @ eigen__6 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: g,X2: g] :
( ( eigen__0 @ ( eigen__2 @ X1 @ X2 ) )
= ( eigen__3 @ ( eigen__0 @ X1 ) @ ( eigen__0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__2 @ eigen__5 @ eigen__6 ) ) )
= ( eigen__1 @ ( eigen__3 @ ( eigen__0 @ eigen__5 ) @ ( eigen__0 @ eigen__6 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: g] :
( ( eigen__1 @ ( eigen__0 @ ( eigen__2 @ eigen__5 @ X1 ) ) )
= ( eigen__4 @ ( eigen__1 @ ( eigen__0 @ eigen__5 ) ) @ ( eigen__1 @ ( eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: b] :
( ( eigen__1 @ ( eigen__3 @ ( eigen__0 @ eigen__5 ) @ X1 ) )
= ( eigen__4 @ ( eigen__1 @ ( eigen__0 @ eigen__5 ) ) @ ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: g] :
( ( eigen__0 @ ( eigen__2 @ eigen__5 @ X1 ) )
= ( eigen__3 @ ( eigen__0 @ eigen__5 ) @ ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP2
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a > $o] :
( ( X1 @ ( eigen__4 @ ( eigen__1 @ ( eigen__0 @ eigen__5 ) ) @ ( eigen__1 @ ( eigen__0 @ eigen__6 ) ) ) )
=> ! [X2: a] :
( ( X2
= ( eigen__4 @ ( eigen__1 @ ( eigen__0 @ eigen__5 ) ) @ ( eigen__1 @ ( eigen__0 @ eigen__6 ) ) ) )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: g > g > g,X2: b > b > b,X3: a > a > a] :
( ~ ( ! [X4: g,X5: g] :
( ( eigen__0 @ ( X1 @ X4 @ X5 ) )
= ( X2 @ ( eigen__0 @ X4 ) @ ( eigen__0 @ X5 ) ) )
=> ~ ! [X4: b,X5: b] :
( ( eigen__1 @ ( X2 @ X4 @ X5 ) )
= ( X3 @ ( eigen__1 @ X4 ) @ ( eigen__1 @ X5 ) ) ) )
=> ! [X4: g,X5: g] :
( ( eigen__1 @ ( eigen__0 @ ( X1 @ X4 @ X5 ) ) )
= ( X3 @ ( eigen__1 @ ( eigen__0 @ X4 ) ) @ ( eigen__1 @ ( eigen__0 @ X5 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ sP4
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: g > b,X2: b > a,X3: g > g > g,X4: b > b > b,X5: a > a > a] :
( ~ ( ! [X6: g,X7: g] :
( ( X1 @ ( X3 @ X6 @ X7 ) )
= ( X4 @ ( X1 @ X6 ) @ ( X1 @ X7 ) ) )
=> ~ ! [X6: b,X7: b] :
( ( X2 @ ( X4 @ X6 @ X7 ) )
= ( X5 @ ( X2 @ X6 ) @ ( X2 @ X7 ) ) ) )
=> ! [X6: g,X7: g] :
( ( X2 @ ( X1 @ ( X3 @ X6 @ X7 ) ) )
= ( X5 @ ( X2 @ ( X1 @ X6 ) ) @ ( X2 @ ( X1 @ X7 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: g,X2: g] :
( ( eigen__1 @ ( eigen__0 @ ( eigen__2 @ X1 @ X2 ) ) )
= ( eigen__4 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) @ ( eigen__1 @ ( eigen__0 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: b > b > b,X2: a > a > a] :
( ~ ( ! [X3: g,X4: g] :
( ( eigen__0 @ ( eigen__2 @ X3 @ X4 ) )
= ( X1 @ ( eigen__0 @ X3 ) @ ( eigen__0 @ X4 ) ) )
=> ~ ! [X3: b,X4: b] :
( ( eigen__1 @ ( X1 @ X3 @ X4 ) )
= ( X2 @ ( eigen__1 @ X3 ) @ ( eigen__1 @ X4 ) ) ) )
=> ! [X3: g,X4: g] :
( ( eigen__1 @ ( eigen__0 @ ( eigen__2 @ X3 @ X4 ) ) )
= ( X2 @ ( eigen__1 @ ( eigen__0 @ X3 ) ) @ ( eigen__1 @ ( eigen__0 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: a,X2: a > $o] :
( ( X2 @ X1 )
=> ! [X3: a] :
( ( X3 = X1 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: b,X2: b] :
( ( eigen__1 @ ( eigen__3 @ X1 @ X2 ) )
= ( eigen__4 @ ( eigen__1 @ X1 ) @ ( eigen__1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(cTHM133_pme,conjecture,
sP18 ).
thf(h6,negated_conjecture,
~ sP18,
inference(assume_negation,[status(cth)],[cTHM133_pme]) ).
thf(1,plain,
( ~ sP9
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP13
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( sP10
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP22
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP12
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP14
| ~ sP2
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP6
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP17
| sP4
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP15
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP21
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
sP21,
inference(eq_ind_sym,[status(thm)],]) ).
thf(12,plain,
( sP3
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP3
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP11
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__6]) ).
thf(15,plain,
( sP19
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__5]) ).
thf(16,plain,
( sP7
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP7
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP5
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h5])],[h5,eigendef_eigen__4]) ).
thf(19,plain,
( sP20
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(20,plain,
( sP16
| ~ sP20 ),
inference(eigen_choice_rule,[status(thm),assumptions([h4])],[h4,eigendef_eigen__2]) ).
thf(21,plain,
( sP1
| ~ sP16 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1]) ).
thf(22,plain,
( sP18
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h3])],[h3,eigendef_eigen__0]) ).
thf(23,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h5,h4,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,h6]) ).
thf(24,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h6,h4,h3,h2,h1,h0]),eigenvar_choice(discharge,[h5])],[23,h5]) ).
thf(25,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h6,h3,h2,h1,h0]),eigenvar_choice(discharge,[h4])],[24,h4]) ).
thf(26,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h6,h2,h1,h0]),eigenvar_choice(discharge,[h3])],[25,h3]) ).
thf(27,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h6,h1,h0]),eigenvar_choice(discharge,[h2])],[26,h2]) ).
thf(28,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h6,h0]),eigenvar_choice(discharge,[h1])],[27,h1]) ).
thf(29,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h6]),eigenvar_choice(discharge,[h0])],[28,h0]) ).
thf(0,theorem,
sP18,
inference(contra,[status(thm),contra(discharge,[h6])],[23,h6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : ALG001^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.33 % Computer : n027.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Wed Jun 8 20:07:12 EDT 2022
% 0.11/0.33 % CPUTime :
% 1.99/2.20 % SZS status Theorem
% 1.99/2.20 % Mode: mode506
% 1.99/2.20 % Inferences: 19454
% 1.99/2.20 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------