TSTP Solution File: SEU902^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU902^5 : 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 : n020.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 17:37:49 EDT 2023
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 38
% Syntax : Number of formulae : 46 ( 10 unt; 3 typ; 1 def)
% Number of atoms : 134 ( 32 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 183 ( 58 ~; 17 |; 0 &; 68 @)
% ( 15 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 17 con; 0-2 aty)
% Number of variables : 28 ( 5 ^; 23 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: ( $i > $o ) > $i ).
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_d,type,
d: $i > $o ).
thf(h0,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i > $o] :
~ ( ~ ( X1 @ ( eigen__0 @ X1 ) )
=> ( ( eigen__0 @ d )
!= ( eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(sP1,plain,
( sP1
<=> ( d
= ( ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ~ ( X2 @ ( eigen__0 @ X2 ) )
=> ( X1
!= ( eigen__0 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ( eigen__0 @ d )
= ( eigen__0 @ eigen__1 ) )
=> ( d = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( d @ ( eigen__0 @ d ) )
= ( ~ ! [X1: $i > $o] :
( ~ ( X1 @ ( eigen__0 @ X1 ) )
=> ( ( eigen__0 @ d )
!= ( eigen__0 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__1 @ ( eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( d @ X1 )
= ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i > $o] :
( ( ( eigen__0 @ d )
= ( eigen__0 @ X1 ) )
=> ( d = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( d = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ sP4
=> ( ( eigen__0 @ d )
!= ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( eigen__0 @ d )
= ( eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( d @ ( eigen__0 @ d ) )
= ( eigen__1 @ ( eigen__0 @ d ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i > $o,X2: $i > $o] :
( ( ( eigen__0 @ X1 )
= ( eigen__0 @ X2 ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( d @ ( eigen__0 @ d ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i > $o] :
( ~ ( X1 @ ( eigen__0 @ X1 ) )
=> ( ( eigen__0 @ d )
!= ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__1 @ ( eigen__0 @ d ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( d @ X1 )
= ( ~ ! [X2: $i > $o] :
( ~ ( X2 @ ( eigen__0 @ X2 ) )
=> ( X1
!= ( eigen__0 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(cTHM143_pme,conjecture,
! [X1: ( $i > $o ) > $i] :
( ~ ( ! [X2: $i > $o,X3: $i > $o] :
( ( ( X1 @ X2 )
= ( X1 @ X3 ) )
=> ( X2 = X3 ) )
=> ( d
!= ( ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ~ ( X3 @ ( X1 @ X3 ) )
=> ( X2
!= ( X1 @ X3 ) ) ) ) ) )
=> ~ ( d @ ( X1 @ d ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: ( $i > $o ) > $i] :
( ~ ( ! [X2: $i > $o,X3: $i > $o] :
( ( ( X1 @ X2 )
= ( X1 @ X3 ) )
=> ( X2 = X3 ) )
=> ( d
!= ( ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ~ ( X3 @ ( X1 @ X3 ) )
=> ( X2
!= ( X1 @ X3 ) ) ) ) ) )
=> ~ ( d @ ( X1 @ d ) ) ),
inference(assume_negation,[status(cth)],[cTHM143_pme]) ).
thf(h2,assumption,
~ ( ~ ( sP11
=> ~ sP1 )
=> ~ sP12 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP11
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP12,
introduced(assumption,[]) ).
thf(h5,assumption,
sP11,
introduced(assumption,[]) ).
thf(h6,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP14
| sP4
| ~ sP9 ),
inference(mating_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP10
| ~ sP12
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP7
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP2
| ~ sP9
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP6
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( sP8
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP8
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP13
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(10,plain,
( ~ sP3
| ~ sP12
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP15
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP11
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP1
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h6,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,h5,h6,h4]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h3,14,h5,h6]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,15,h3,h4]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,16,h2]) ).
thf(18,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[17,h0]) ).
thf(0,theorem,
! [X1: ( $i > $o ) > $i] :
( ~ ( ! [X2: $i > $o,X3: $i > $o] :
( ( ( X1 @ X2 )
= ( X1 @ X3 ) )
=> ( X2 = X3 ) )
=> ( d
!= ( ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ~ ( X3 @ ( X1 @ X3 ) )
=> ( X2
!= ( X1 @ X3 ) ) ) ) ) )
=> ~ ( d @ ( X1 @ d ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[17,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU902^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 23 14:48:15 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % Mode: cade22grackle2xfee4
% 0.20/0.41 % Steps: 276
% 0.20/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------