TSTP Solution File: SEU546^2 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU546^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n031.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 17:18:31 EDT 2023
% Result : Theorem 20.20s 20.46s
% Output : Proof 20.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 34
% Syntax : Number of formulae : 42 ( 13 unt; 3 typ; 3 def)
% Number of atoms : 94 ( 29 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 117 ( 36 ~; 13 |; 2 &; 34 @)
% ( 12 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 18 con; 0-2 aty)
% Number of variables : 39 ( 9 ^; 28 !; 2 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eigen__0 @ X1 )
=> ( eigen__1 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
= ( X1 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> $false ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP3
= ( eigen__2 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP3
=> ( eigen__1 = eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__1 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP4 = ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ( eigen__1 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__2 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP4
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(def_exu,definition,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X3 )
@ ( X2 = X3 ) ) ) ) ) ).
thf(def_exuI1,definition,
( exuI1
= ( ! [X1: $i > $o] :
( ^ [X2: $o,X3: $o] :
( X2
=> X3 )
@ ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X3 )
@ ( X2 = X3 ) ) )
@ ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
thf(exuI2,conjecture,
! [X1: $i > $o] :
( ~ ! [X2: $i] :
~ ! [X3: $i] :
( ( X1 @ X3 )
= ( X3 = X2 ) )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i > $o] :
( ~ ! [X2: $i] :
~ ! [X3: $i] :
( ( X1 @ X3 )
= ( X3 = X2 ) )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ),
inference(assume_negation,[status(cth)],[exuI2]) ).
thf(h2,assumption,
~ ( ~ ! [X1: $i] :
~ ! [X2: $i] :
( ( eigen__0 @ X2 )
= ( X2 = X1 ) )
=> ~ sP9 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
~ ! [X2: $i] :
( ( eigen__0 @ X2 )
= ( X2 = X1 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP9,
introduced(assumption,[]) ).
thf(h5,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP5
| ~ sP3
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP1
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP11
| sP7 ),
inference(symeq,[status(thm)],]) ).
thf(4,plain,
( sP6
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP6
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP10
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(7,plain,
~ sP2,
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP12
| ~ sP4
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP8
| sP4
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP9
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP1
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,h5,h4]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__1)],[h3,12,h5]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,13,h3,h4]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,14,h2]) ).
thf(16,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[15,h0]) ).
thf(0,theorem,
! [X1: $i > $o] :
( ~ ! [X2: $i] :
~ ! [X3: $i] :
( ( X1 @ X3 )
= ( X3 = X2 ) )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[15,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU546^2 : TPTP v8.1.2. Released v3.7.0.
% 0.13/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n031.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 : Wed Aug 23 14:15:35 EDT 2023
% 0.14/0.35 % CPUTime :
% 20.20/20.46 % SZS status Theorem
% 20.20/20.46 % Mode: cade22grackle2x798d
% 20.20/20.46 % Steps: 33
% 20.20/20.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------