TSTP Solution File: SEU894^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU894^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n032.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 14:10:43 EDT 2022
% Result : Theorem 26.29s 25.95s
% Output : Proof 26.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 19
% Syntax : Number of formulae : 25 ( 6 unt; 2 typ; 1 def)
% Number of atoms : 60 ( 32 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 175 ( 52 ~; 7 |; 0 &; 63 @)
% ( 7 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 10 con; 0-2 aty)
% Number of variables : 48 ( 7 ^ 41 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ( ( ( eigen__0 @ X1 )
= X1 )
=> ~ ! [X2: $i] :
( ( ( eigen__0 @ X2 )
= X2 )
=> ( X1 = X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ! [X1: ( $i > $i ) > $o] :
( ~ ( ( X1 @ eigen__0 )
=> ~ ! [X2: $i > $i] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i] : ( eigen__0 @ ( X2 @ X3 ) ) ) ) )
=> ( X1 @ eigen__0 ) )
=> ! [X1: $i] :
( ( ( eigen__0 @ X1 )
= X1 )
=> ~ ! [X2: $i] :
( ( ( eigen__0 @ X2 )
= X2 )
=> ( X1 = X2 ) ) ) )
=> ~ ! [X1: $i] :
( ( eigen__0 @ X1 )
!= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ( eigen__0 @ eigen__1 )
= eigen__1 )
=> ~ ! [X1: $i] :
( ( ( eigen__0 @ X1 )
= X1 )
=> ( eigen__1 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( ( eigen__0 @ X1 )
= X1 )
=> ~ ! [X2: $i] :
( ( ( eigen__0 @ X2 )
= X2 )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ! [X1: ( $i > $i ) > $o] :
( ~ ( ( X1 @ eigen__0 )
=> ~ ! [X2: $i > $i] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i] : ( eigen__0 @ ( X2 @ X3 ) ) ) ) )
=> ( X1 @ eigen__0 ) )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i > $i] :
~ ( ~ ( ! [X2: ( $i > $i ) > $o] :
( ~ ( ( X2 @ eigen__0 )
=> ~ ! [X3: $i > $i] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i] : ( eigen__0 @ ( X3 @ X4 ) ) ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: $i] :
( ( ( X1 @ X2 )
= X2 )
=> ~ ! [X3: $i] :
( ( ( X1 @ X3 )
= X3 )
=> ( X2 = X3 ) ) ) )
=> ~ ! [X2: $i] :
( ( eigen__0 @ X2 )
!= X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eigen__0 @ eigen__1 )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
!= X1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(cTHM15_0_pme,conjecture,
! [X1: $i > $i] :
~ ! [X2: $i > $i] :
~ ( ~ ( ! [X3: ( $i > $i ) > $o] :
( ~ ( ( X3 @ X1 )
=> ~ ! [X4: $i > $i] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i] : ( X1 @ ( X4 @ X5 ) ) ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: $i] :
( ( ( X2 @ X3 )
= X3 )
=> ~ ! [X4: $i] :
( ( ( X2 @ X4 )
= X4 )
=> ( X3 = X4 ) ) ) )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
!= X3 ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i > $i] :
~ ! [X2: $i > $i] :
~ ( ~ ( ! [X3: ( $i > $i ) > $o] :
( ~ ( ( X3 @ X1 )
=> ~ ! [X4: $i > $i] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i] : ( X1 @ ( X4 @ X5 ) ) ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: $i] :
( ( ( X2 @ X3 )
= X3 )
=> ~ ! [X4: $i] :
( ( ( X2 @ X4 )
= X4 )
=> ( X3 = X4 ) ) ) )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
!= X3 ) ),
inference(assume_negation,[status(cth)],[cTHM15_0_pme]) ).
thf(h2,assumption,
sP5,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP7
| ~ sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( sP2
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP3
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(4,plain,
( sP4
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP1
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP5
| ~ sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,h2]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,8,h2]) ).
thf(10,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[9,h0]) ).
thf(0,theorem,
! [X1: $i > $i] :
~ ! [X2: $i > $i] :
~ ( ~ ( ! [X3: ( $i > $i ) > $o] :
( ~ ( ( X3 @ X1 )
=> ~ ! [X4: $i > $i] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i] : ( X1 @ ( X4 @ X5 ) ) ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: $i] :
( ( ( X2 @ X3 )
= X3 )
=> ~ ! [X4: $i] :
( ( ( X2 @ X4 )
= X4 )
=> ( X3 = X4 ) ) ) )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
!= X3 ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[9,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SEU894^5 : TPTP v8.1.0. Released v4.0.0.
% 0.09/0.10 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Mon Jun 20 06:45:18 EDT 2022
% 0.10/0.29 % CPUTime :
% 26.29/25.95 % SZS status Theorem
% 26.29/25.95 % Mode: mode461
% 26.29/25.95 % Inferences: 9
% 26.29/25.95 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------