TSTP Solution File: SYO304^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO304^5 : 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 : n029.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 04:46:13 EDT 2023
% Result : Theorem 0.21s 0.67s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 35
% Syntax : Number of formulae : 45 ( 16 unt; 5 typ; 3 def)
% Number of atoms : 84 ( 23 equ; 1 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 115 ( 19 ~; 16 |; 0 &; 48 @)
% ( 12 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 18 con; 0-2 aty)
% Number of variables : 50 ( 29 ^; 21 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__0,type,
eigen__0: ( a > a > $o ) > $o ).
thf(ty_eigen__3,type,
eigen__3: a > $o ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(h0,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ( X1 @ eigen__1 )
=> ( X1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(h1,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__1
@ ^ [X1: a] :
( ( ^ [X2: a] :
! [X3: a > $o] :
( ( X3 @ X1 )
=> ( X3 @ X2 ) ) )
!= ( ^ [X2: a] : ( X1 = X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: a] :
( ( ! [X2: a > $o] :
( ( X2 @ eigen__1 )
=> ( X2 @ X1 ) ) )
!= ( eigen__1 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ( eigen__0
@ ^ [X1: a,X2: a] :
! [X3: a > $o] :
( ( X3 @ X1 )
=> ( X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ! [X1: a > $o] :
( ( X1 @ eigen__1 )
=> ( X1 @ eigen__2 ) ) )
= ( eigen__1 = eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__3 @ eigen__1 )
=> ( eigen__3 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ^ [X1: a] :
! [X2: a > $o] :
( ( X2 @ eigen__1 )
=> ( X2 @ X1 ) ) )
= ( ^ [X1: a] : ( eigen__1 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a] :
( ( ! [X2: a > $o] :
( ( X2 @ eigen__1 )
=> ( X2 @ X1 ) ) )
= ( eigen__1 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__1 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__3 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( ^ [X1: a,X2: a] :
! [X3: a > $o] :
( ( X3 @ X1 )
=> ( X3 @ X2 ) ) )
= ( ^ [X1: a,X2: a] : ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__0
@ ^ [X1: a,X2: a] : ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a > $o] :
( ( X1 @ eigen__1 )
=> ( X1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__3 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a] :
( ( ^ [X2: a] :
! [X3: a > $o] :
( ( X3 @ X1 )
=> ( X3 @ X2 ) ) )
= ( ^ [X2: a] : ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(cE2_eq__pme,conjecture,
! [X1: ( a > a > $o ) > $o] :
( ( X1
@ ^ [X2: a,X3: a] :
! [X4: a > $o] :
( ( X4 @ X2 )
=> ( X4 @ X3 ) ) )
=> ( X1
@ ^ [X2: a,X3: a] : ( X2 = X3 ) ) ) ).
thf(h2,negated_conjecture,
~ ! [X1: ( a > a > $o ) > $o] :
( ( X1
@ ^ [X2: a,X3: a] :
! [X4: a > $o] :
( ( X4 @ X2 )
=> ( X4 @ X3 ) ) )
=> ( X1
@ ^ [X2: a,X3: a] : ( X2 = X3 ) ) ),
inference(assume_negation,[status(cth)],[cE2_eq__pme]) ).
thf(h3,assumption,
~ ( sP1
=> ( eigen__0 @ (=) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP1,
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP10
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP7
| sP11
| ~ sP6 ),
inference(mating_rule,[status(thm)],]) ).
thf(3,plain,
( sP3
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP3
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP10
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(6,plain,
( sP2
| ~ sP10
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP2
| sP10
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP5
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(9,plain,
( sP4
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP12
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1]) ).
thf(11,plain,
( sP8
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP1
| sP9
| ~ sP8 ),
inference(mating_rule,[status(thm)],]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h4,h5]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,13,h4,h5]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,14,h3]) ).
thf(16,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[15,h1]) ).
thf(17,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[16,h0]) ).
thf(0,theorem,
! [X1: ( a > a > $o ) > $o] :
( ( X1
@ ^ [X2: a,X3: a] :
! [X4: a > $o] :
( ( X4 @ X2 )
=> ( X4 @ X3 ) ) )
=> ( X1
@ ^ [X2: a,X3: a] : ( X2 = X3 ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[15,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.21 % Problem : SYO304^5 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.21 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.16/0.41 % Computer : n029.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8042.1875MB
% 0.16/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Aug 26 04:33:24 EDT 2023
% 0.16/0.41 % CPUTime :
% 0.21/0.67 % SZS status Theorem
% 0.21/0.67 % Mode: cade22grackle2xfee4
% 0.21/0.67 % Steps: 39318
% 0.21/0.67 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------