TSTP Solution File: SYO325^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO325^5 : 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 : n006.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 : Fri Sep 1 04:46:16 EDT 2023
% Result : Theorem 60.62s 60.81s
% Output : Proof 60.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 54
% Syntax : Number of formulae : 62 ( 11 unt; 5 typ; 3 def)
% Number of atoms : 159 ( 3 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 345 ( 70 ~; 28 |; 0 &; 152 @)
% ( 23 <=>; 72 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 29 usr; 28 con; 0-2 aty)
% Number of variables : 77 ( 14 ^; 63 !; 0 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_cK,type,
cK: ( a > $o ) > a > $o ).
thf(ty_eigen__4,type,
eigen__4: a > $o ).
thf(ty_eigen__63,type,
eigen__63: a ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__63,definition,
( eigen__63
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__4 @ X1 )
=> ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__63])]) ).
thf(h1,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__1
@ ^ [X1: a > $o] :
~ ( ! [X2: a] :
( ( X1 @ X2 )
=> ( cK @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: a] :
( ( cK @ X1 @ X3 )
=> ( cK @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ! [X1: a] :
( ( eigen__4 @ X1 )
=> ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) )
=> ! [X1: a] :
( ( cK @ eigen__4 @ X1 )
=> ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( eigen__4 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: a] :
( ( cK @ eigen__4 @ X2 )
=> ( cK @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
=> ( X1 @ X2 ) )
=> ! [X2: a] :
( ( cK
@ ^ [X3: a] :
~ ! [X4: a > $o] :
( ! [X5: a] :
( ( X4 @ X5 )
=> ( cK @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
=> ( cK @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( cK @ eigen__4 @ eigen__3 )
=> ( cK
@ ^ [X1: a] :
~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__4 @ eigen__63 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a] :
( ( eigen__4 @ X1 )
=> ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a] :
( ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP6
=> ~ ! [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cK @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__63 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a] :
( ( eigen__4 @ X1 )
=> ( cK @ eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP10
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP10
=> ~ ( eigen__4 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cK @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( eigen__4 @ eigen__3 )
=> ( cK @ eigen__4 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP8
=> ! [X1: a] :
( ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
=> ( cK
@ ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a] :
( ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
=> ( cK
@ ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( cK @ eigen__4 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP1
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__4 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: a] :
( ( cK @ eigen__4 @ X1 )
=> ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( cK
@ ^ [X1: a] :
~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cK @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__63 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ~ sP13
=> sP21 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(cTHM116_1SS,conjecture,
sP18 ).
thf(h2,negated_conjecture,
~ sP18,
inference(assume_negation,[status(cth)],[cTHM116_1SS]) ).
thf(1,plain,
( ~ sP5
| ~ sP17
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP20
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP11
| ~ sP10
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP22
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( sP9
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP9
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP7
| ~ sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__63]) ).
thf(8,plain,
( ~ sP2
| ~ sP7
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP1
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP14
| ~ sP19
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP10
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( sP12
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP12
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP13
| ~ sP12 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__4]) ).
thf(16,plain,
( sP23
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP23
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP8
| ~ sP23 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(19,plain,
( ~ sP15
| ~ sP8
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP4
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP1
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( sP18
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP18
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([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,h2]) ).
thf(25,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[24,h1]) ).
thf(26,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[25,h0]) ).
thf(0,theorem,
sP18,
inference(contra,[status(thm),contra(discharge,[h2])],[24,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYO325^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 04:32:07 EDT 2023
% 0.14/0.35 % CPUTime :
% 60.62/60.81 % SZS status Theorem
% 60.62/60.81 % Mode: cade22grackle2x34cb
% 60.62/60.81 % Steps: 5086
% 60.62/60.81 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------