TSTP Solution File: SEU948^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU948^5 : 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 : n023.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 14:10:59 EDT 2022
% Result : Theorem 150.02s 149.78s
% Output : Proof 150.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 45
% Syntax : Number of formulae : 55 ( 20 unt; 6 typ; 5 def)
% Number of atoms : 101 ( 5 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 443 ( 91 ~; 21 |; 0 &; 213 @)
% ( 18 <=>; 100 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 103 ( 103 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 21 con; 0-2 aty)
% Number of variables : 138 ( 74 ^ 64 !; 0 ?; 138 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__2,type,
eigen__2: a > a ).
thf(ty_eigen__1,type,
eigen__1: a > a ).
thf(ty_eigen__0,type,
eigen__0: a > a ).
thf(ty_eigen__3,type,
eigen__3: ( a > a ) > $o ).
thf(ty_eigen__13,type,
eigen__13: a > a ).
thf(h0,assumption,
! [X1: ( ( a > a ) > $o ) > $o,X2: ( a > a ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: ( a > a ) > $o] :
~ ( ~ ( ( X1
@ ^ [X2: a] : X2 )
=> ~ ! [X2: a > a] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: a] : ( eigen__0 @ ( X2 @ X3 ) ) ) ) )
=> ( X1
@ ^ [X2: a] : ( eigen__1 @ ( eigen__2 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(h1,assumption,
! [X1: ( a > a ) > $o,X2: a > a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__1
@ ^ [X1: a > a] :
~ ! [X2: a > a] :
( ~ ( ! [X3: ( a > a ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : X4 )
=> ~ ! [X4: a > a] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: a] : ( eigen__0 @ ( X4 @ X5 ) ) ) ) )
=> ( X3 @ X1 ) )
=> ~ ! [X3: ( a > a ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : X4 )
=> ~ ! [X4: a > a] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: a] : ( eigen__0 @ ( X4 @ X5 ) ) ) ) )
=> ( X3 @ X2 ) ) )
=> ! [X3: ( a > a ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : X4 )
=> ~ ! [X4: a > a] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: a] : ( eigen__0 @ ( X4 @ X5 ) ) ) ) )
=> ( X3
@ ^ [X4: a] : ( X1 @ ( X2 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: a > a] :
~ ! [X2: a > a,X3: a > a] :
( ~ ( ! [X4: ( a > a ) > $o] :
( ~ ( ( X4
@ ^ [X5: a] : X5 )
=> ~ ! [X5: a > a] :
( ( X4 @ X5 )
=> ( X4
@ ^ [X6: a] : ( X1 @ ( X5 @ X6 ) ) ) ) )
=> ( X4 @ X2 ) )
=> ~ ! [X4: ( a > a ) > $o] :
( ~ ( ( X4
@ ^ [X5: a] : X5 )
=> ~ ! [X5: a > a] :
( ( X4 @ X5 )
=> ( X4
@ ^ [X6: a] : ( X1 @ ( X5 @ X6 ) ) ) ) )
=> ( X4 @ X3 ) ) )
=> ! [X4: ( a > a ) > $o] :
( ~ ( ( X4
@ ^ [X5: a] : X5 )
=> ~ ! [X5: a > a] :
( ( X4 @ X5 )
=> ( X4
@ ^ [X6: a] : ( X1 @ ( X5 @ X6 ) ) ) ) )
=> ( X4
@ ^ [X5: a] : ( X2 @ ( X3 @ X5 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: a > a] :
~ ( ~ ( ! [X2: ( a > a ) > $o] :
( ~ ( ( X2
@ ^ [X3: a] : X3 )
=> ~ ! [X3: a > a] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: a] : ( eigen__0 @ ( X3 @ X4 ) ) ) ) )
=> ( X2 @ eigen__1 ) )
=> ~ ! [X2: ( a > a ) > $o] :
( ~ ( ( X2
@ ^ [X3: a] : X3 )
=> ~ ! [X3: a > a] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: a] : ( eigen__0 @ ( X3 @ X4 ) ) ) ) )
=> ( X2 @ X1 ) ) )
=> ! [X2: ( a > a ) > $o] :
( ~ ( ( X2
@ ^ [X3: a] : X3 )
=> ~ ! [X3: a > a] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: a] : ( eigen__0 @ ( X3 @ X4 ) ) ) ) )
=> ( X2
@ ^ [X3: a] : ( eigen__1 @ ( X1 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__13,definition,
( eigen__13
= ( eps__1
@ ^ [X1: a > a] :
~ ( ( eigen__3
@ ^ [X2: a] : ( X1 @ ( eigen__2 @ X2 ) ) )
=> ( eigen__3
@ ^ [X2: a] : ( eigen__0 @ ( X1 @ ( eigen__2 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__13])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a > a,X2: a > a] :
( ~ ( ! [X3: ( a > a ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : X4 )
=> ~ ! [X4: a > a] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: a] : ( eigen__0 @ ( X4 @ X5 ) ) ) ) )
=> ( X3 @ X1 ) )
=> ~ ! [X3: ( a > a ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : X4 )
=> ~ ! [X4: a > a] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: a] : ( eigen__0 @ ( X4 @ X5 ) ) ) ) )
=> ( X3 @ X2 ) ) )
=> ! [X3: ( a > a ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : X4 )
=> ~ ! [X4: a > a] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: a] : ( eigen__0 @ ( X4 @ X5 ) ) ) ) )
=> ( X3
@ ^ [X4: a] : ( X1 @ ( X2 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ( eigen__3
@ ^ [X1: a] : X1 )
=> ~ ! [X1: a > a] :
( ( eigen__3 @ X1 )
=> ( eigen__3
@ ^ [X2: a] : ( eigen__0 @ ( X1 @ X2 ) ) ) ) )
=> ( eigen__3
@ ^ [X1: a] : ( eigen__1 @ ( eigen__2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__3
@ ^ [X1: a] : X1 )
=> ~ ! [X1: a > a] :
( ( eigen__3 @ X1 )
=> ( eigen__3
@ ^ [X2: a] : ( eigen__0 @ ( X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__3 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ! [X1: ( a > a ) > $o] :
( ~ ( ( X1
@ ^ [X2: a] : X2 )
=> ~ ! [X2: a > a] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: a] : ( eigen__0 @ ( X2 @ X3 ) ) ) ) )
=> ( X1 @ eigen__1 ) )
=> ~ ! [X1: ( a > a ) > $o] :
( ~ ( ( X1
@ ^ [X2: a] : X2 )
=> ~ ! [X2: a > a] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: a] : ( eigen__0 @ ( X2 @ X3 ) ) ) ) )
=> ( X1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eigen__3
@ ^ [X1: a] : ( eigen__13 @ ( eigen__2 @ X1 ) ) )
=> ( eigen__3
@ ^ [X1: a] : ( eigen__0 @ ( eigen__13 @ ( eigen__2 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a > a] :
( ( eigen__3
@ ^ [X2: a] : ( X1 @ ( eigen__2 @ X2 ) ) )
=> ( eigen__3
@ ^ [X2: a] : ( eigen__0 @ ( X1 @ ( eigen__2 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP4
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: ( a > a ) > $o] :
( ~ ( ( X1
@ ^ [X2: a] : X2 )
=> ~ ! [X2: a > a] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: a] : ( eigen__0 @ ( X2 @ X3 ) ) ) ) )
=> ( X1
@ ^ [X2: a] : ( eigen__1 @ ( eigen__2 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: ( a > a ) > $o] :
( ~ ( ( X1
@ ^ [X2: a] : X2 )
=> ~ ! [X2: a > a] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: a] : ( eigen__0 @ ( X2 @ X3 ) ) ) ) )
=> ( X1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__3
@ ^ [X1: a] : ( eigen__1 @ ( eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a > a] :
( ~ ( ! [X2: ( a > a ) > $o] :
( ~ ( ( X2
@ ^ [X3: a] : X3 )
=> ~ ! [X3: a > a] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: a] : ( eigen__0 @ ( X3 @ X4 ) ) ) ) )
=> ( X2 @ eigen__1 ) )
=> ~ ! [X2: ( a > a ) > $o] :
( ~ ( ( X2
@ ^ [X3: a] : X3 )
=> ~ ! [X3: a > a] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: a] : ( eigen__0 @ ( X3 @ X4 ) ) ) ) )
=> ( X2 @ X1 ) ) )
=> ! [X2: ( a > a ) > $o] :
( ~ ( ( X2
@ ^ [X3: a] : X3 )
=> ~ ! [X3: a > a] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: a] : ( eigen__0 @ ( X3 @ X4 ) ) ) ) )
=> ( X2
@ ^ [X3: a] : ( eigen__1 @ ( X1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ sP3
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a > a,X2: a > a,X3: a > a] :
( ~ ( ! [X4: ( a > a ) > $o] :
( ~ ( ( X4
@ ^ [X5: a] : X5 )
=> ~ ! [X5: a > a] :
( ( X4 @ X5 )
=> ( X4
@ ^ [X6: a] : ( X1 @ ( X5 @ X6 ) ) ) ) )
=> ( X4 @ X2 ) )
=> ~ ! [X4: ( a > a ) > $o] :
( ~ ( ( X4
@ ^ [X5: a] : X5 )
=> ~ ! [X5: a > a] :
( ( X4 @ X5 )
=> ( X4
@ ^ [X6: a] : ( X1 @ ( X5 @ X6 ) ) ) ) )
=> ( X4 @ X3 ) ) )
=> ! [X4: ( a > a ) > $o] :
( ~ ( ( X4
@ ^ [X5: a] : X5 )
=> ~ ! [X5: a > a] :
( ( X4 @ X5 )
=> ( X4
@ ^ [X6: a] : ( X1 @ ( X5 @ X6 ) ) ) ) )
=> ( X4
@ ^ [X5: a] : ( X2 @ ( X3 @ X5 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: ( a > a ) > $o] :
( ~ ( ( X1
@ ^ [X2: a] : X2 )
=> ~ ! [X2: a > a] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: a] : ( eigen__0 @ ( X2 @ X3 ) ) ) ) )
=> ( X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ sP8
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ sP5
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: a > a] :
( ( eigen__3 @ X1 )
=> ( eigen__3
@ ^ [X2: a] : ( eigen__0 @ ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(cTHM135_pme,conjecture,
sP14 ).
thf(h2,negated_conjecture,
~ sP14,
inference(assume_negation,[status(cth)],[cTHM135_pme]) ).
thf(1,plain,
( ~ sP18
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( sP7
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__13]) ).
thf(3,plain,
( ~ sP16
| sP8
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP8
| ~ sP4
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP13
| sP3
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP10
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( sP3
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP15
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( sP2
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP2
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP5
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP5
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP9
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(14,plain,
( sP17
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP17
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP12
| ~ sP17 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(17,plain,
( sP1
| ~ sP12 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1]) ).
thf(18,plain,
( sP14
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(19,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,h2]) ).
thf(20,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[19,h1]) ).
thf(21,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[20,h0]) ).
thf(0,theorem,
sP14,
inference(contra,[status(thm),contra(discharge,[h2])],[19,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU948^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 20 08:47:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 150.02/149.78 % SZS status Theorem
% 150.02/149.78 % Mode: mode446
% 150.02/149.78 % Inferences: 12249
% 150.02/149.78 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------