TSTP Solution File: SET557^6 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SET557^6 : TPTP v8.1.0. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n028.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 : 600s
% DateTime : Tue Jul 19 04:53:54 EDT 2022
% Result : Theorem 64.13s 64.30s
% Output : Proof 64.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 37
% Syntax : Number of formulae : 45 ( 11 unt; 4 typ; 2 def)
% Number of atoms : 118 ( 14 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 200 ( 51 ~; 19 |; 0 &; 79 @)
% ( 14 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 18 con; 0-2 aty)
% Number of variables : 36 ( 7 ^ 29 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eigen__0 @ X1 )
=> ( ( eigen__1 @ X1 )
!= ( ^ [X2: $i] :
~ ( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ X1 ) )
=> ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ( ! [X1: $i] :
( ~ ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ X1 ) )
=> ( eigen__0 @ X1 ) )
=> ~ ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ( ( eigen__1 @ X1 )
!= ( ^ [X2: $i] :
~ ( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( eigen__1 @ eigen__4 @ X1 )
= ( ~ ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ~ ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ X1 ) )
=> ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X2 ) )
=> ~ ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( ( eigen__1 @ X2 )
!= X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__0 @ eigen__5 )
=> ( eigen__1 @ eigen__5 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eigen__1 @ eigen__4 @ eigen__4 )
= ( ~ ( ( eigen__0 @ eigen__4 )
=> ( eigen__1 @ eigen__4 @ eigen__4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__1 @ eigen__4 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ( ( eigen__1 @ X1 )
!= ( ^ [X2: $i] :
~ ( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( eigen__0 @ eigen__4 )
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( eigen__0 @ eigen__4 )
=> ( ( eigen__1 @ eigen__4 )
!= ( ^ [X1: $i] :
~ ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__0 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__0 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( eigen__1 @ eigen__4 )
= ( ^ [X1: $i] :
~ ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ sP5
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(cTHM43_pme,conjecture,
! [X1: $i > $o,X2: $i > $i > $o] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X1 @ X4 ) )
=> ~ ! [X4: $i] :
( ( X1 @ X4 )
=> ( ( X2 @ X4 )
!= X3 ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i > $o,X2: $i > $i > $o] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X1 @ X4 ) )
=> ~ ! [X4: $i] :
( ( X1 @ X4 )
=> ( ( X2 @ X4 )
!= X3 ) ) ),
inference(assume_negation,[status(cth)],[cTHM43_pme]) ).
thf(h2,assumption,
~ ! [X1: $i > $i > $o] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X3 ) )
=> ~ ! [X3: $i] :
( ( eigen__0 @ X3 )
=> ( ( X1 @ X3 )
!= X2 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP4,
introduced(assumption,[]) ).
thf(1,plain,
( sP9
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP9
| ~ sP12
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP6
| ~ sP7
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP6
| sP7
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP2
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP13
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP10
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP10
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP5
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP14
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP14
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP3
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(13,plain,
( sP8
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(14,plain,
( ~ sP1
| ~ sP3
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP4
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,h3]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,16,h3]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,17,h2]) ).
thf(19,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[18,h0]) ).
thf(0,theorem,
! [X1: $i > $o,X2: $i > $i > $o] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X1 @ X4 ) )
=> ~ ! [X4: $i] :
( ( X1 @ X4 )
=> ( ( X2 @ X4 )
!= X3 ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[18,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET557^6 : TPTP v8.1.0. Released v5.1.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n028.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 : 600
% 0.12/0.33 % DateTime : Sun Jul 10 14:41:27 EDT 2022
% 0.12/0.33 % CPUTime :
% 64.13/64.30 % SZS status Theorem
% 64.13/64.30 % Mode: mode453
% 64.13/64.30 % Inferences: 165
% 64.13/64.30 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------