TSTP Solution File: SEV292^5 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV292^5 : TPTP v8.1.2. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n010.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 19:33:14 EDT 2023
% Result : Theorem 20.30s 20.52s
% Output : Proof 20.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 46
% Syntax : Number of formulae : 53 ( 12 unt; 3 typ; 6 def)
% Number of atoms : 147 ( 42 equ; 2 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 476 ( 189 ~; 21 |; 3 &; 138 @)
% ( 18 <=>; 107 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 107 ( 107 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 25 con; 0-2 aty)
% Number of variables : 129 ( 54 ^; 73 !; 2 ?; 129 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__4,type,
eigen__4: ( ( $i > $o ) > $o ) > $o ).
thf(ty_eigen__3,type,
eigen__3: ( ( $i > $o ) > $o ) > $o ).
thf(ty_cP,type,
cP: ( ( $i > $o ) > $o ) > $o ).
thf(h0,assumption,
! [X1: ( ( ( $i > $o ) > $o ) > $o ) > $o,X2: ( ( $i > $o ) > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: ( ( $i > $o ) > $o ) > $o] :
~ ( ~ ( ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ( X1
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: ( ( $i > $o ) > $o ) > $o] :
~ ( ~ ( ( X1
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ( X1
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ! [X4: $i] :
( ~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) )
=> ~ ! [X5: $i] :
( ( X5 != X4 )
=> ( ( X5 != X3 )
=> ~ ( X2 @ X5 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ( cP
@ ^ [X1: $i > $o] :
~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X3 != X2 )
=> ~ ( X1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__3
@ ^ [X1: $i > $o] :
~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X3 != X2 )
=> ~ ( X1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__3
@ ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ( X1
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ~ ! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ( X1
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ! [X4: $i] :
( ~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) )
=> ~ ! [X5: $i] :
( ( X5 != X4 )
=> ( ( X5 != X3 )
=> ~ ( X2 @ X5 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__4
@ ^ [X1: $i > $o] :
~ ! [X2: $i] :
( ( X1 @ X2 )
=> ! [X3: $i] :
( ~ ( ( X3 != X2 )
=> ~ ( X1 @ X3 ) )
=> ~ ! [X4: $i] :
( ( X4 != X3 )
=> ( ( X4 != X2 )
=> ~ ( X1 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ sP4
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: ( $i > $o ) > $o] :
( ( eigen__3 @ X1 )
=> ( eigen__3
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( X1
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( eigen__3
@ ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) )
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: ( $i > $o ) > $o] :
( ( eigen__4 @ X1 )
=> ( eigen__4
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( X1
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( eigen__4
@ ^ [X1: $i > $o] :
~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X3 != X2 )
=> ~ ( X1 @ X3 ) ) ) )
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ( X1
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ! [X4: $i] :
( ~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) )
=> ~ ! [X5: $i] :
( ( X5 != X4 )
=> ( ( X5 != X3 )
=> ~ ( X2 @ X5 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ sP8
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: ( $i > $o ) > $o] :
( ~ ( ! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: $i > $o] :
! [X4: $i] :
~ ( X3 @ X4 ) )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X3
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2 @ X1 )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X3
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) ) )
=> ( X2
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ! [X5: $i] :
( ~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) )
=> ~ ! [X6: $i] :
( ( X6 != X5 )
=> ( ( X6 != X4 )
=> ~ ( X3 @ X6 ) ) ) ) ) ) ) )
=> ~ ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__4
@ ^ [X1: $i > $o] :
~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X3 != X2 )
=> ~ ( X1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP14
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ( X1
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__3
@ ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ sP10
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(def_cZERO,definition,
( cZERO
= ( ^ [X1: $i > $o] :
( (~)
@ ? [X2: $i] : ( X1 @ X2 ) ) ) ) ).
thf(def_cSUCC,definition,
( cSUCC
= ( ^ [X1: ( $i > $o ) > $o,X2: $i > $o] :
? [X3: $i] :
( ( X2 @ X3 )
& ( X1
@ ^ [X4: $i] :
( ( (~) @ ( X4 = X3 ) )
& ( X2 @ X4 ) ) ) ) ) ) ).
thf(def_cONE,definition,
( cONE
= ( cSUCC @ cZERO ) ) ).
thf(def_c_less__eq_,definition,
( c_less__eq_
= ( ^ [X1: ( $i > $o ) > $o,X2: ( $i > $o ) > $o] :
! [X3: ( ( $i > $o ) > $o ) > $o] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( ( X3 @ X1 )
& ! [X4: ( $i > $o ) > $o] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X3 @ X4 )
@ ( X3 @ ( cSUCC @ X4 ) ) ) )
@ ( X3 @ X2 ) ) ) ) ).
thf(cBLEDSOE7A,conjecture,
( sP1
=> ~ sP13 ) ).
thf(h1,negated_conjecture,
~ ( sP1
=> ~ sP13 ),
inference(assume_negation,[status(cth)],[cBLEDSOE7A]) ).
thf(h2,assumption,
sP1,
introduced(assumption,[]) ).
thf(h3,assumption,
sP13,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP15
| ~ sP14
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP3
| ~ sP17
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP9
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP7
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( sP10
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP10
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP8
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP8
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP18
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP18
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP12
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP12
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP11
| ~ sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(14,plain,
( sP16
| ~ sP12 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(15,plain,
( ~ sP4
| ~ sP16
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP6
| sP4
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP13
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,h2,h3]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,18,h2,h3]) ).
thf(20,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[19,h0]) ).
thf(0,theorem,
( sP1
=> ~ sP13 ),
inference(contra,[status(thm),contra(discharge,[h1])],[19,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEV292^5 : TPTP v8.1.2. Bugfixed v6.2.0.
% 0.00/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.15/0.36 % Computer : n010.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 24 02:35:06 EDT 2023
% 0.15/0.36 % CPUTime :
% 20.30/20.52 % SZS status Theorem
% 20.30/20.52 % Mode: cade22grackle2x798d
% 20.30/20.52 % Steps: 138
% 20.30/20.52 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------