TSTP Solution File: SEV138^5 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV138^5 : 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 : n004.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 19:32:43 EDT 2023
% Result : Theorem 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 52
% Syntax : Number of formulae : 66 ( 19 unt; 7 typ; 1 def)
% Number of atoms : 135 ( 1 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 526 ( 141 ~; 19 |; 0 &; 208 @)
% ( 17 <=>; 141 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 23 con; 0-2 aty)
% Number of variables : 113 ( 1 ^; 112 !; 0 ?; 113 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__0,type,
eigen__0: a > a > $o ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_eigen__4,type,
eigen__4: a > $o ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_eigen__6,type,
eigen__6: a ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__4 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ! [X1: a] :
( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__4 @ X1 ) )
=> ~ sP1 )
=> ( eigen__4 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ! [X1: a] :
( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__4 @ X1 ) )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [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(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( ! [X1: a] :
( ( eigen__0 @ eigen__1 @ X1 )
=> ( eigen__4 @ X1 ) )
=> ~ sP1 )
=> ( eigen__4 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eigen__4 @ eigen__2 )
=> ~ ( eigen__0 @ eigen__2 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__4 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a] :
( ~ ( ( eigen__4 @ eigen__2 )
=> ~ ( eigen__0 @ eigen__2 @ X1 ) )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__4 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__0 @ eigen__2 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a] :
( ( eigen__0 @ eigen__1 @ X1 )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__4 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP11
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP10
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a] :
( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ sP6
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__2 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(cTHM150_pme,conjecture,
! [X1: a > a > $o,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,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)],[cTHM150_pme]) ).
thf(h2,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(h3,assumption,
~ ! [X1: a,X2: a] :
( ~ ( ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ eigen__1 @ 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__1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: a] :
( ~ ( sP4
=> ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ eigen__2 @ 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__1 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__0 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ ( sP4
=> ~ sP17 )
=> ! [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__3 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP4
=> ~ sP17 ),
introduced(assumption,[]) ).
thf(h7,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__3 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP4,
introduced(assumption,[]) ).
thf(h9,assumption,
sP17,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( ~ sP13
=> sP12 ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h13,assumption,
sP11,
introduced(assumption,[]) ).
thf(h14,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP6
| ~ sP9
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP16
| sP6
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP8
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP1
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( sP14
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP14
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP15
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(8,plain,
( ~ sP3
| ~ sP15
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP13
| ~ sP11
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP2
| sP3
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP5
| sP13
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP17
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP4
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h14,h11,h12,h10,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,h8,h9,h13,h14,h12]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h10,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h11,14,h13,h14]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,15,h11,h12]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__4)],[h7,16,h10]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,17,h8,h9]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,18,h6,h7]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__3)],[h4,19,h5]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__2)],[h3,20,h4]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,21,h3]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,22,h2]) ).
thf(24,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[23,h0]) ).
thf(0,theorem,
! [X1: a > a > $o,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])],[23,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV138^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 01:58:08 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 % Mode: cade22grackle2xfee4
% 0.21/0.43 % Steps: 163
% 0.21/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------