TSTP Solution File: SEV146^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV146^5 : 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 18:05:04 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 72
% Syntax : Number of formulae : 94 ( 30 unt; 10 typ; 1 def)
% Number of atoms : 193 ( 1 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 799 ( 214 ~; 22 |; 0 &; 322 @)
% ( 21 <=>; 220 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 31 usr; 29 con; 0-2 aty)
% Number of variables : 177 ( 1 ^ 176 !; 0 ?; 177 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__6,type,
eigen__6: a ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_eigen__7,type,
eigen__7: a > $o ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_eigen__0,type,
eigen__0: a > a > $o ).
thf(ty_eigen__4,type,
eigen__4: a ).
thf(ty_eigen__5,type,
eigen__5: a ).
thf(ty_eigen__3,type,
eigen__3: a > $o ).
thf(ty_eigen__8,type,
eigen__8: a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__0 @ eigen__5 @ X1 )
=> ( eigen__7 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(sP1,plain,
( sP1
<=> ( eigen__7 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__7 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__7 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__4 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__0 @ eigen__1 @ eigen__2 )
=> ( eigen__3 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__0 @ eigen__5 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ! [X1: a] :
( ( eigen__0 @ eigen__4 @ X1 )
=> ( eigen__7 @ X1 ) )
=> ~ sP2 )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( sP1
=> ~ sP5 )
=> ( eigen__7 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP5
=> ( eigen__7 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__7 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a] :
( ( eigen__0 @ eigen__5 @ X1 )
=> ( eigen__7 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__5 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP1
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a] :
( ~ ( sP1
=> ~ ( eigen__0 @ eigen__5 @ X1 ) )
=> ( eigen__7 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ! [X1: a] :
( ( eigen__0 @ eigen__4 @ X1 )
=> ( eigen__7 @ X1 ) )
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a] :
( ( eigen__0 @ eigen__1 @ X1 )
=> ( eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__3 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__7 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: a] :
( ( eigen__0 @ eigen__4 @ X1 )
=> ( eigen__7 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ~ ( sP10
=> ~ sP2 )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP10
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( eigen__0 @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(cTHM525_pme,conjecture,
! [X1: a > a > $o] :
~ ( ! [X2: a,X3: a] :
( ( X1 @ X2 @ X3 )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( X1 @ X2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( X1 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( X1 @ X2 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( X1 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X3 ) )
=> ~ ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( X1 @ X3 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( X1 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( X1 @ X2 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( X1 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: a > a > $o] :
~ ( ! [X2: a,X3: a] :
( ( X1 @ X2 @ X3 )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( X1 @ X2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( X1 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( X1 @ X2 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( X1 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X3 ) )
=> ~ ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( X1 @ X3 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( X1 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( X1 @ X2 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( X1 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM525_pme]) ).
thf(h2,assumption,
( ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__0 @ X1 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__0 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X2 ) )
=> ~ ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__0 @ X2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__0 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__0 @ X1 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__0 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: a,X2: a,X3: a] :
( ~ ( ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__0 @ X1 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__0 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X2 ) )
=> ~ ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__0 @ X2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__0 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__0 @ X1 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__0 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: a] :
( ( eigen__0 @ eigen__1 @ X1 )
=> ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ eigen__1 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__0 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP21
=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__1 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__2 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP21,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__1 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__2 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ( sP15
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__3 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__3 @ X2 ) ) )
=> sP16 ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP15
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__3 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__3 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP16,
introduced(assumption,[]) ).
thf(h12,assumption,
sP15,
introduced(assumption,[]) ).
thf(h13,assumption,
! [X1: a,X2: a] :
( ~ ( ( eigen__3 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__3 @ X2 ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP15
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP4
| ~ sP21
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h12,h13,h10,h11,h9,h7,h8,h6,h5,h3,h2,h1,h0])],[1,2,h7,h12,h11]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h9,h7,h8,h6,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h10,3,h12,h13]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h7,h8,h6,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,4,h10,h11]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h6,h5,h3,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__3)],[h8,5,h9]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,6,h7,h8]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__2)],[h5,7,h6]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__1)],[h3,8,h5]) ).
thf(h14,assumption,
~ ! [X1: a,X2: a] :
( ~ ( ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ eigen__4 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X1 ) )
=> ~ ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ eigen__4 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ! [X1: a] :
( ~ ( sP3
=> ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ eigen__5 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__0 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) )
=> ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ eigen__4 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__0 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ ( ~ ( sP3
=> ~ sP11 )
=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__4 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__6 ) ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( sP3
=> ~ sP11 ),
introduced(assumption,[]) ).
thf(h18,assumption,
~ ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__4 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__6 ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
sP3,
introduced(assumption,[]) ).
thf(h20,assumption,
sP11,
introduced(assumption,[]) ).
thf(h21,assumption,
~ ( ~ sP14
=> sP9 ),
introduced(assumption,[]) ).
thf(h22,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(h23,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h24,assumption,
sP18,
introduced(assumption,[]) ).
thf(h25,assumption,
sP2,
introduced(assumption,[]) ).
thf(10,plain,
( ~ sP13
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP7
| sP12
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP12
| ~ sP1
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP8
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP8
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP2
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( sP10
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(17,plain,
( ~ sP3
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP6
| sP14
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP14
| ~ sP18
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP11
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP19
| sP20
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP20
| ~ sP10
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h24,h25,h22,h23,h21,h19,h20,h17,h18,h16,h15,h14,h4,h2,h1,h0])],[10,11,12,13,14,15,16,17,18,19,20,21,22,h19,h20,h24,h25,h23]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h22,h23,h21,h19,h20,h17,h18,h16,h15,h14,h4,h2,h1,h0]),tab_negimp(discharge,[h24,h25])],[h22,23,h24,h25]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h19,h20,h17,h18,h16,h15,h14,h4,h2,h1,h0]),tab_negimp(discharge,[h22,h23])],[h21,24,h22,h23]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h19,h20,h17,h18,h16,h15,h14,h4,h2,h1,h0]),tab_negall(discharge,[h21]),tab_negall(eigenvar,eigen__7)],[h18,25,h21]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h18,h16,h15,h14,h4,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h17,26,h19,h20]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h15,h14,h4,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h16,27,h17,h18]) ).
thf(29,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h15,h14,h4,h2,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__6)],[h15,28,h16]) ).
thf(30,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h4,h2,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__5)],[h14,29,h15]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h2,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__4)],[h4,30,h14]) ).
thf(32,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h2,h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[h2,9,31,h3,h4]) ).
thf(33,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,32,h2]) ).
thf(34,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[33,h0]) ).
thf(0,theorem,
! [X1: a > a > $o] :
~ ( ! [X2: a,X3: a] :
( ( X1 @ X2 @ X3 )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( X1 @ X2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( X1 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( X1 @ X2 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( X1 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X3 ) )
=> ~ ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( X1 @ X3 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( X1 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( X1 @ X2 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( X1 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[33,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEV146^5 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 28 15:13:07 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % Mode: mode213
% 0.13/0.39 % Inferences: 37
% 0.13/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------