TSTP Solution File: SEV019^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV019^5 : 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 : n007.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 18:04:28 EDT 2022
% Result : Theorem 0.99s 1.34s
% Output : Proof 0.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 109
% Syntax : Number of formulae : 130 ( 28 unt; 11 typ; 3 def)
% Number of atoms : 309 ( 26 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 512 ( 151 ~; 48 |; 0 &; 197 @)
% ( 41 <=>; 75 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 52 usr; 49 con; 0-2 aty)
% Number of variables : 86 ( 3 ^ 83 !; 0 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__25,type,
eigen__25: a ).
thf(ty_eigen__24,type,
eigen__24: a ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_eigen__26,type,
eigen__26: a ).
thf(ty_eigen__11,type,
eigen__11: a ).
thf(ty_eigen__10,type,
eigen__10: a ).
thf(ty_eigen__8,type,
eigen__8: a > $o ).
thf(ty_eigen__41,type,
eigen__41: a > $o ).
thf(ty_eigen__20,type,
eigen__20: a > $o ).
thf(ty_cQ,type,
cQ: a > a > $o ).
thf(h0,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) ) )
=> ~ ( X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__41,definition,
( eigen__41
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) ) )
=> ~ ( X1 @ eigen__24 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__41])]) ).
thf(eigendef_eigen__20,definition,
( eigen__20
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) ) )
=> ~ ( X1 @ eigen__10 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__20])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a] :
~ ! [X2: a > $o] :
( ~ ( ~ ! [X3: a] :
~ ( X2 @ X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X2 @ X4 )
= ( cQ @ X3 @ X4 ) ) ) )
=> ~ ( X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( cQ @ eigen__10 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] :
( ( eigen__20 @ X1 )
= ( cQ @ eigen__11 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__41 @ eigen__25 )
= ( cQ @ eigen__24 @ eigen__25 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a] :
( ( eigen__20 @ X1 )
=> ! [X2: a] :
( ( eigen__20 @ X2 )
= ( cQ @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a] :
( ( eigen__8 @ X1 )
=> ! [X2: a] :
( ( eigen__8 @ X2 )
= ( cQ @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__20 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a] :
( ( eigen__41 @ X1 )
=> ! [X2: a] :
( ( eigen__41 @ X2 )
= ( cQ @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ ( ~ ! [X1: a] :
~ ( eigen__41 @ X1 )
=> ~ sP8 )
=> ~ ( eigen__41 @ eigen__24 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP7 = sP2 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a] :
( ( eigen__8 @ X1 )
= ( cQ @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a] :
( ( eigen__20 @ X1 )
= ( cQ @ eigen__10 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( cQ @ eigen__24 @ eigen__26 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__41 @ eigen__25 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__41 @ eigen__26 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( eigen__20 @ eigen__10 )
= ( cQ @ eigen__11 @ eigen__10 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP7
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: a > $o] :
( ~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) ) )
=> ~ ( X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( eigen__41 @ eigen__24 )
=> ! [X1: a] :
( ( eigen__41 @ X1 )
= ( cQ @ eigen__24 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP14
=> ! [X1: a] :
( ( eigen__41 @ X1 )
= ( cQ @ eigen__25 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP15 = sP13 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: a > $o] :
( ~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) ) )
=> ~ ( X1 @ eigen__10 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ~ ! [X1: a] :
~ ( eigen__41 @ X1 )
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( eigen__20 @ eigen__10 )
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( eigen__8 @ eigen__0 )
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( eigen__8 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ ! [X1: a] :
~ ( eigen__8 @ X1 )
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( cQ @ eigen__24 @ eigen__25 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( eigen__41 @ eigen__24 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: a] :
( ( eigen__41 @ X1 )
= ( cQ @ eigen__25 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ~ ( ~ ! [X1: a] :
~ ( eigen__20 @ X1 )
=> ~ sP5 )
=> ~ ( eigen__20 @ eigen__10 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ ! [X1: a] :
~ ( eigen__20 @ X1 )
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( cQ @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: a] :
( ( eigen__41 @ X1 )
= ( cQ @ eigen__24 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ~ sP27
=> ~ sP26 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: a > $o] :
( ~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( cQ @ X2 @ X3 ) ) ) )
=> ~ ( X1 @ eigen__24 ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( eigen__20 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( sP15
= ( cQ @ eigen__25 @ eigen__26 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( cQ @ eigen__11 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( cQ @ eigen__25 @ eigen__26 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( sP26 = sP33 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(cTHM559_pme,conjecture,
( sP1
=> ~ ( ~ ( ! [X1: a] : ( cQ @ X1 @ X1 )
=> ~ ! [X1: a,X2: a] :
( ( cQ @ X1 @ X2 )
=> ( cQ @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( cQ @ X1 @ X2 )
=> ~ ( cQ @ X2 @ X3 ) )
=> ( cQ @ X1 @ X3 ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( sP1
=> ~ ( ~ ( ! [X1: a] : ( cQ @ X1 @ X1 )
=> ~ ! [X1: a,X2: a] :
( ( cQ @ X1 @ X2 )
=> ( cQ @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( cQ @ X1 @ X2 )
=> ~ ( cQ @ X2 @ X3 ) )
=> ( cQ @ X1 @ X3 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM559_pme]) ).
thf(h2,assumption,
sP1,
introduced(assumption,[]) ).
thf(h3,assumption,
( ~ ( ! [X1: a] : ( cQ @ X1 @ X1 )
=> ~ ! [X1: a,X2: a] :
( ( cQ @ X1 @ X2 )
=> ( cQ @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( cQ @ X1 @ X2 )
=> ~ ( cQ @ X2 @ X3 ) )
=> ( cQ @ X1 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
( ! [X1: a] : ( cQ @ X1 @ X1 )
=> ~ ! [X1: a,X2: a] :
( ( cQ @ X1 @ X2 )
=> ( cQ @ X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( cQ @ X1 @ X2 )
=> ~ ( cQ @ X2 @ X3 ) )
=> ( cQ @ X1 @ X3 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: a] : ( cQ @ X1 @ X1 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: a,X2: a] :
( ( cQ @ X1 @ X2 )
=> ( cQ @ X2 @ X1 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP33,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP41
| ~ sP26
| sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP11
| sP41 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP6
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP25
| ~ sP26
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP27
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP35
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP35
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP18
| ~ sP35 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(9,plain,
( ~ sP1
| ~ sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,h2,h8]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__0)],[h6,10,h8]) ).
thf(h9,assumption,
~ ! [X1: a] :
( ( cQ @ eigen__10 @ X1 )
=> ( cQ @ X1 @ eigen__10 ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP2
=> sP39 ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP2,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP39,
introduced(assumption,[]) ).
thf(12,plain,
( ~ sP16
| ~ sP37
| sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP10
| sP7
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP3
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP17
| ~ sP7
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP12
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP5
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP5
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP24
| ~ sP37
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP32
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP31
| sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP31
| ~ sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP22
| ~ sP31 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__20]) ).
thf(24,plain,
( ~ sP1
| ~ sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h10,h9,h7,h4,h2,h3,h1,h0])],[12,13,14,15,16,17,18,19,20,21,22,23,24,h2,h11,h12]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h9,h7,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,25,h11,h12]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h7,h4,h2,h3,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__11)],[h9,26,h10]) ).
thf(28,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h4,h2,h3,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__10)],[h7,27,h9]) ).
thf(29,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_imp(discharge,[h6]),tab_imp(discharge,[h7])],[h4,11,28,h6,h7]) ).
thf(h13,assumption,
~ ! [X1: a,X2: a] :
( ~ ( ( cQ @ eigen__24 @ X1 )
=> ~ ( cQ @ X1 @ X2 ) )
=> ( cQ @ eigen__24 @ X2 ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ! [X1: a] :
( ~ ( sP28
=> ~ ( cQ @ eigen__25 @ X1 ) )
=> ( cQ @ eigen__24 @ X1 ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( ~ ( sP28
=> ~ sP40 )
=> sP13 ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ ( sP28
=> ~ sP40 ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(h18,assumption,
sP28,
introduced(assumption,[]) ).
thf(h19,assumption,
sP40,
introduced(assumption,[]) ).
thf(30,plain,
( ~ sP21
| ~ sP15
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP38
| sP15
| ~ sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP34
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP30
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP4
| sP14
| ~ sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP20
| ~ sP14
| sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP34
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP8
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP8
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP19
| ~ sP29
| sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( sP23
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( sP9
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( sP9
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( sP36
| ~ sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__41]) ).
thf(44,plain,
( ~ sP1
| ~ sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(45,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h18,h19,h16,h17,h15,h14,h13,h5,h2,h3,h1,h0])],[30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,h2,h18,h19,h17]) ).
thf(46,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h17,h15,h14,h13,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h18,h19])],[h16,45,h18,h19]) ).
thf(47,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h14,h13,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,46,h16,h17]) ).
thf(48,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h13,h5,h2,h3,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__26)],[h14,47,h15]) ).
thf(49,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h5,h2,h3,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__25)],[h13,48,h14]) ).
thf(50,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h2,h3,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__24)],[h5,49,h13]) ).
thf(51,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h2,h3,h1,h0]),tab_imp(discharge,[h4]),tab_imp(discharge,[h5])],[h3,29,50,h4,h5]) ).
thf(52,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,51,h2,h3]) ).
thf(53,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[52,h0]) ).
thf(0,theorem,
( sP1
=> ~ ( ~ ( ! [X1: a] : ( cQ @ X1 @ X1 )
=> ~ ! [X1: a,X2: a] :
( ( cQ @ X1 @ X2 )
=> ( cQ @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( cQ @ X1 @ X2 )
=> ~ ( cQ @ X2 @ X3 ) )
=> ( cQ @ X1 @ X3 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[52,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV019^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n007.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 : Tue Jun 28 14:49:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.99/1.34 % SZS status Theorem
% 0.99/1.34 % Mode: mode213
% 0.99/1.34 % Inferences: 1809
% 0.99/1.34 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------