TSTP Solution File: SEV295^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV295^5 : TPTP v8.1.0. Bugfixed v6.2.0.
% 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 18:05:46 EDT 2022
% Result : Theorem 25.80s 26.22s
% Output : Proof 25.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 45
% Syntax : Number of formulae : 51 ( 12 unt; 3 typ; 6 def)
% Number of atoms : 141 ( 24 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 426 ( 165 ~; 21 |; 0 &; 146 @)
% ( 18 <=>; 76 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 132 ( 132 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 26 usr; 24 con; 0-2 aty)
% Number of variables : 120 ( 52 ^ 68 !; 0 ?; 120 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: ( $i > $o ) > $o ).
thf(ty_eigen__1,type,
eigen__1: ( $i > $o ) > $o ).
thf(ty_r,type,
r: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
thf(h0,assumption,
! [X1: ( ( $i > $o ) > $o ) > $o,X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: ( $i > $o ) > $o] :
~ ( ~ ! [X2: ( $i > $o ) > $o] :
~ ( r @ X1 @ X2 )
=> ~ ! [X2: ( $i > $o ) > $o] :
~ ( r
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X1
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) )
@ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: ( $i > $o ) > $o] :
~ ~ ( r @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ! [X2: ( $i > $o ) > $o] :
( ! [X3: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: $i > $o] :
! [X5: $i] :
~ ( X4 @ X5 ) )
=> ~ ! [X4: ( $i > $o ) > $o] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i > $o] :
~ ! [X6: $i] :
( ( X5 @ X6 )
=> ~ ( X4
@ ^ [X7: $i] :
~ ( ( X7 != X6 )
=> ~ ( X5 @ X7 ) ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ( X1 @ X2 ) ) )
=> ~ ( r
@ ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 )
@ ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) )
=> ~ ! [X1: ( $i > $o ) > $o,X2: ( $i > $o ) > $o] :
( ( r @ X1 @ X2 )
=> ( r
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X1
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) )
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: ( $i > $o ) > $o] :
~ ( r
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( eigen__1
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) )
@ X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ! [X2: ( $i > $o ) > $o] :
( ! [X3: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: $i > $o] :
! [X5: $i] :
~ ( X4 @ X5 ) )
=> ~ ! [X4: ( $i > $o ) > $o] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i > $o] :
~ ! [X6: $i] :
( ( X5 @ X6 )
=> ~ ( X4
@ ^ [X7: $i] :
~ ( ( X7 != X6 )
=> ~ ( X5 @ X7 ) ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: ( $i > $o ) > $o,X2: ( $i > $o ) > $o] :
( ( r @ X1 @ X2 )
=> ( r
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X1
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) )
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( r
@ ^ [X1: $i > $o] :
~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ( eigen__1
@ ^ [X3: $i] :
~ ( ( X3 != X2 )
=> ~ ( X1 @ X3 ) ) ) )
@ ^ [X1: $i > $o] :
~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ( eigen__2
@ ^ [X3: $i] :
~ ( ( X3 != X2 )
=> ~ ( X1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: ( $i > $o ) > $o] :
~ ( r @ eigen__1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ! [X1: ( $i > $o ) > $o] :
~ ( r
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 )
@ X1 )
=> ~ ! [X1: ( $i > $o ) > $o] :
( ~ ! [X2: ( $i > $o ) > $o] :
~ ( r @ X1 @ X2 )
=> ~ ! [X2: ( $i > $o ) > $o] :
~ ( r
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X1
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) )
@ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: ( $i > $o ) > $o] :
( ~ ! [X2: ( $i > $o ) > $o] :
~ ( r @ X1 @ X2 )
=> ~ ! [X2: ( $i > $o ) > $o] :
~ ( r
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X1
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) )
@ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( r @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: ( $i > $o ) > $o] :
( ( r @ eigen__1 @ X1 )
=> ( r
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( eigen__1
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) )
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( X1
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: ( $i > $o ) > $o] :
( ! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: $i > $o] :
! [X4: $i] :
~ ( X3 @ X4 ) )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X3
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP9
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ sP1
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( r
@ ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 )
@ ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: ( $i > $o ) > $o] :
~ ( r
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 )
@ X1 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ sP7
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP3
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ sP6
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(def_cZERO,definition,
( cZERO
= ( ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_cSUCC,definition,
( cSUCC
= ( ^ [X1: ( $i > $o ) > $o,X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( X1
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ) ).
thf(def_cNAT,definition,
( cNAT
= ( ^ [X1: ( $i > $o ) > $o] :
! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2 @ cZERO )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2 @ ( cSUCC @ X3 ) ) ) )
=> ( X2 @ X1 ) ) ) ) ).
thf(def_cINDUCTION,definition,
( cINDUCTION
= ( ! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1 @ cZERO )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( cSUCC @ X2 ) ) ) )
=> ! [X2: ( $i > $o ) > $o] :
( ( cNAT @ X2 )
=> ( X1 @ X2 ) ) ) ) ) ).
thf(cTHM130_NAT,conjecture,
sP13 ).
thf(h1,negated_conjecture,
~ sP13,
inference(assume_negation,[status(cth)],[cTHM130_NAT]) ).
thf(1,plain,
( ~ sP2
| ~ sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP15
| ~ sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP4
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP10
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP12
| ~ sP9
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP6
| sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(7,plain,
( sP18
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP18
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP8
| ~ sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(10,plain,
( ~ sP3
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP16
| sP7
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP7
| sP15
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP17
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP17
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP1
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP1
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP13
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP13
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,h1]) ).
thf(20,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[19,h0]) ).
thf(0,theorem,
sP13,
inference(contra,[status(thm),contra(discharge,[h1])],[19,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEV295^5 : TPTP v8.1.0. Bugfixed v6.2.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.32 % Computer : n028.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Mon Jun 27 17:38:56 EDT 2022
% 0.17/0.32 % CPUTime :
% 25.80/26.22 % SZS status Theorem
% 25.80/26.22 % Mode: mode454
% 25.80/26.22 % Inferences: 23
% 25.80/26.22 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------