TSTP Solution File: SEV246^5 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV246^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n022.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 : 300s
% DateTime : Thu Aug 31 19:33:06 EDT 2023
% Result : Theorem 201.53s 181.20s
% Output : Proof 201.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 62
% Syntax : Number of formulae : 74 ( 15 unt; 5 typ; 3 def)
% Number of atoms : 184 ( 3 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 542 ( 109 ~; 29 |; 0 &; 255 @)
% ( 25 <=>; 124 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 32 usr; 31 con; 0-2 aty)
% Number of variables : 140 ( 24 ^; 116 !; 0 ?; 140 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__12,type,
eigen__12: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__0,type,
eigen__0: ( $i > $o ) > $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i > $o ).
thf(h0,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i > $o] :
~ ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(h1,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__12,definition,
( eigen__12
= ( eps__1
@ ^ [X1: $i] :
~ ( ( eigen__3 @ X1 )
=> ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__12])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: $i] :
~ ( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ! [X1: $i] :
( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) )
=> ! [X1: $i] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
=> ( eigen__0
@ ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__3 @ eigen__2 )
=> ( eigen__0 @ eigen__3 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( eigen__3 @ X1 )
=> ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eigen__0 @ eigen__3 @ eigen__2 )
=> ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__3 @ eigen__12 )
=> ~ ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__12 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ! [X1: $i] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
=> ( eigen__0
@ ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) )
@ X1 ) )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( eigen__3 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( eigen__0 @ eigen__3 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
=> ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( eigen__0
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( eigen__0 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
=> ( eigen__0 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP5
=> ! [X1: $i] :
( ( eigen__0 @ eigen__3 @ X1 )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__0 @ eigen__3 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( eigen__3 @ X1 )
=> ( eigen__0 @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ sP4
=> ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__3 @ eigen__12 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: $i] :
( ( eigen__0 @ X1 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__3 @ X1 )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__12 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP13
=> ~ ( eigen__3 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eigen__3 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP13
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
=> ( eigen__0
@ ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(cTHM2A_ONE_pme,conjecture,
! [X1: ( $i > $o ) > $i > $o] :
( ! [X2: $i > $o,X3: $i > $o] :
( ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X1 @ X3 @ X4 ) ) )
=> ! [X2: $i] :
( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
=> ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X1 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) ) ) ).
thf(h2,negated_conjecture,
~ ! [X1: ( $i > $o ) > $i > $o] :
( ! [X2: $i > $o,X3: $i > $o] :
( ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X1 @ X3 @ X4 ) ) )
=> ! [X2: $i] :
( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
=> ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X1 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM2A_ONE_pme]) ).
thf(h3,assumption,
~ ( sP17
=> ! [X1: $i] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
=> ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP17,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
=> ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP1
=> ~ sP18 ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP1,
introduced(assumption,[]) ).
thf(h8,assumption,
sP18,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP6
| ~ sP12
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP24
| ~ sP13
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP21
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( sP7
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP7
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP19
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( sP5
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__12]) ).
thf(8,plain,
( ~ sP11
| ~ sP5
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP9
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP17
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP3
| ~ sP23
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP13
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP2
| ~ sP20
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP10
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP8
| ~ sP25
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP22
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP22
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP4
| ~ sP22 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(19,plain,
( sP14
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP14
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP20
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(22,plain,
( ~ sP17
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP18
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h6,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,h4,h7,h8]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,24,h7,h8]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,25,h6]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,26,h4,h5]) ).
thf(28,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,27,h3]) ).
thf(29,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[28,h1]) ).
thf(30,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[29,h0]) ).
thf(0,theorem,
! [X1: ( $i > $o ) > $i > $o] :
( ! [X2: $i > $o,X3: $i > $o] :
( ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X1 @ X3 @ X4 ) ) )
=> ! [X2: $i] :
( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
=> ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X1 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[28,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV246^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.17/0.34 % Computer : n022.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Thu Aug 24 03:10:41 EDT 2023
% 0.17/0.34 % CPUTime :
% 201.53/181.20 % SZS status Theorem
% 201.53/181.20 % Mode: cade22grackle2x2d0b
% 201.53/181.20 % Steps: 115
% 201.53/181.20 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------