TSTP Solution File: SEV062^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV062^5 : 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 : n020.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 18:04:41 EDT 2022
% Result : Theorem 0.17s 0.35s
% Output : Proof 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 58
% Syntax : Number of formulae : 72 ( 18 unt; 7 typ; 3 def)
% Number of atoms : 156 ( 3 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 535 ( 117 ~; 23 |; 0 &; 264 @)
% ( 21 <=>; 110 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 29 usr; 28 con; 0-2 aty)
% Number of variables : 123 ( 3 ^ 120 !; 0 ?; 123 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__3,type,
eigen__3: $i > $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( ( eigen__3 @ eigen__4 @ eigen__5 )
=> ~ ( eigen__0 @ eigen__5 @ X1 ) )
=> ( eigen__3 @ eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i,X3: $i] :
( ~ ( ( eigen__3 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__3 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ~ ( ( eigen__3 @ eigen__4 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__3 @ eigen__4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__3 @ X1 @ X2 )
=> ~ ( eigen__3 @ X2 @ X3 ) )
=> ( eigen__3 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__3 @ X1 @ X2 ) )
=> ~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__3 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__3 @ X1 @ X3 ) ) )
=> ( eigen__3 @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__3 @ eigen__4 @ eigen__5 )
=> ~ ( eigen__3 @ eigen__5 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__5 @ X1 )
=> ( eigen__3 @ eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__0 @ eigen__5 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ( eigen__3 @ eigen__4 @ eigen__5 )
=> ~ sP5 )
=> ( eigen__3 @ eigen__4 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__3 @ X1 @ X2 ) )
=> ~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__3 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__3 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__3 @ eigen__4 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__3 @ eigen__4 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP5
=> ( eigen__3 @ eigen__5 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__3 @ eigen__5 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__3 @ eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ~ ( sP11
=> ~ ( eigen__3 @ eigen__5 @ X1 ) )
=> ( eigen__3 @ eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__3 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ sP3
=> ( eigen__3 @ eigen__4 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__3 @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__3 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__3 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
( ~ ( sP11
=> ~ ( eigen__0 @ eigen__5 @ X1 ) )
=> ( eigen__3 @ eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__3 @ eigen__4 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP11
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( eigen__0 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__3 @ eigen__4 @ X1 )
=> ~ ( eigen__3 @ X1 @ X2 ) )
=> ( eigen__3 @ eigen__4 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(cT146A_pme,conjecture,
! [X1: $i > $i > $o,X2: $i,X3: $i] :
( ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X1 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i > $i > $o,X2: $i,X3: $i] :
( ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X1 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ),
inference(assume_negation,[status(cth)],[cT146A_pme]) ).
thf(h2,assumption,
~ ! [X1: $i,X2: $i] :
( ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( eigen__0 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__1 @ X1 ) )
=> ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP20
=> ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__1 @ eigen__2 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP20,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__1 @ eigen__2 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( sP13
=> ~ sP1 )
=> sP15 ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP13
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP15,
introduced(assumption,[]) ).
thf(h10,assumption,
sP13,
introduced(assumption,[]) ).
thf(h11,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP13
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP4
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP9
| ~ sP5
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP1
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP21
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP12
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP14
| sP3
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP3
| ~ sP11
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP19
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP19
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP6
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP6
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP17
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(14,plain,
( sP8
| ~ sP17 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(15,plain,
( sP16
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(16,plain,
( ~ sP20
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP2
| sP7
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP7
| ~ sP13
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h11,h8,h9,h7,h5,h6,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,h5,h10,h11,h9]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h8,19,h10,h11]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,20,h8,h9]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__3)],[h6,21,h7]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,22,h5,h6]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__2)],[h3,23,h4]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,24,h3]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,25,h2]) ).
thf(27,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[26,h0]) ).
thf(0,theorem,
! [X1: $i > $i > $o,X2: $i,X3: $i] :
( ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X1 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[26,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEV062^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.33 % Computer : n020.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
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 600
% 0.17/0.33 % DateTime : Tue Jun 28 17:17:16 EDT 2022
% 0.17/0.33 % CPUTime :
% 0.17/0.35 % SZS status Theorem
% 0.17/0.35 % Mode: mode213
% 0.17/0.35 % Inferences: 18
% 0.17/0.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------