TSTP Solution File: SYO245^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO245^5 : 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 : n029.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 : Thu Jul 21 19:31:04 EDT 2022
% Result : Theorem 47.13s 47.36s
% Output : Proof 47.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 45
% Syntax : Number of formulae : 52 ( 12 unt; 2 typ; 2 def)
% Number of atoms : 139 ( 43 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 275 ( 94 ~; 23 |; 0 &; 99 @)
% ( 20 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 46 ( 46 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 23 con; 0-2 aty)
% Number of variables : 57 ( 17 ^ 40 !; 0 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: ( $i > $o ) > $i ).
thf(h0,assumption,
! [X1: ( ( $i > $o ) > $i ) > $o,X2: ( $i > $o ) > $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: ( $i > $o ) > $i] :
~ ~ ! [X2: $i > $o,X3: $i > $o] :
( ( ( X1 @ X2 )
= ( X1 @ X3 ) )
=> ( X2 = X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(h1,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: $i > $o] :
~ ( ~ ( X1 @ ( eigen__0 @ X1 ) )
=> ( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ~ ( X3 @ ( eigen__0 @ X3 ) )
=> ( X2
!= ( eigen__0 @ X3 ) ) ) )
!= ( eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i > $o] :
( ~ ( X1 @ ( eigen__0 @ X1 ) )
=> ( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ~ ( X3 @ ( eigen__0 @ X3 ) )
=> ( X2
!= ( eigen__0 @ X3 ) ) ) )
!= ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( ~ ! [X2: $i > $o] :
( ~ ( X2 @ ( eigen__0 @ X2 ) )
=> ( X1
!= ( eigen__0 @ X2 ) ) ) )
= ( eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ~ ( X2 @ ( eigen__0 @ X2 ) )
=> ( X1
!= ( eigen__0 @ X2 ) ) ) )
= eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__2
@ ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ~ ( X2 @ ( eigen__0 @ X2 ) )
=> ( X1
!= ( eigen__0 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ~ ( X2 @ ( eigen__0 @ X2 ) )
=> ( X1
!= ( eigen__0 @ X2 ) ) ) )
= ( eigen__0 @ eigen__2 ) )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $o > $o] :
( ( X1 @ ~ sP1 )
=> ! [X2: $o] :
( ( ( ~ sP1 )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $o,X2: $o > $o] :
( ( X2 @ X1 )
=> ! [X3: $o] :
( ( X1 = X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( ( ~ sP1 )
= sP4 )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__2 @ ( eigen__0 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i > $o] :
( ( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ~ ( X3 @ ( eigen__0 @ X3 ) )
=> ( X2
!= ( eigen__0 @ X3 ) ) ) )
= ( eigen__0 @ X1 ) )
=> ( ( ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ~ ( X3 @ ( eigen__0 @ X3 ) )
=> ( X2
!= ( eigen__0 @ X3 ) ) ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ sP1
=> ! [X1: $o] :
( ( ( ~ sP1 )
= X1 )
=> X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ sP9
=> ( ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ~ ( X2 @ ( eigen__0 @ X2 ) )
=> ( X1
!= ( eigen__0 @ X2 ) ) ) )
!= ( eigen__0 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: ( $i > $o ) > $i] :
~ ! [X2: $i > $o,X3: $i > $o] :
( ( ( X1 @ X2 )
= ( X1 @ X3 ) )
=> ( X2 = X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ! [X1: ( $i > $o ) > $i] :
( ~ ! [X2: $i > $o] :
( ~ ( X2 @ ( X1 @ X2 ) )
=> ( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ~ ( X4 @ ( X1 @ X4 ) )
=> ( X3
!= ( X1 @ X4 ) ) ) )
!= ( X1 @ X2 ) ) )
=> ~ ! [X2: $i > $o] :
( ~ ( X2 @ ( X1 @ X2 ) )
=> ( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ~ ( X4 @ ( X1 @ X4 ) )
=> ( X3
!= ( X1 @ X4 ) ) ) )
!= ( X1 @ X2 ) ) ) )
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( ~ sP1 )
= sP4 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP1
=> ( ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ~ ( X2 @ ( eigen__0 @ X2 ) )
=> ( X1
!= ( eigen__0 @ X2 ) ) ) )
!= ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ~ ( X2 @ ( eigen__0 @ X2 ) )
=> ( X1
!= ( eigen__0 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $o] :
( ( ( ~ sP1 )
= X1 )
=> X1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ~ ( X2 @ ( eigen__0 @ X2 ) )
=> ( X1
!= ( eigen__0 @ X2 ) ) ) )
= ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ~ ( X2 @ ( eigen__0 @ X2 ) )
=> ( X1
!= ( eigen__0 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i > $o,X2: $i > $o] :
( ( ( eigen__0 @ X1 )
= ( eigen__0 @ X2 ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ~ ( X2 @ ( eigen__0 @ X2 ) )
=> ( X1
!= ( eigen__0 @ X2 ) ) ) )
= ( eigen__0 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(cTHM193A,conjecture,
sP14 ).
thf(h2,negated_conjecture,
~ sP14,
inference(assume_negation,[status(cth)],[cTHM193A]) ).
thf(1,plain,
sP18,
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP4
| sP9
| ~ sP20 ),
inference(mating_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP2
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP8
| ~ sP15
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP17
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP11
| sP1
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP6
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP7
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
sP7,
inference(eq_ind,[status(thm)],]) ).
thf(10,plain,
( ~ sP3
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP10
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP5
| ~ sP20
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP12
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP12
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP1
| ~ sP12 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(16,plain,
( ~ sP16
| ~ sP1
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP19
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP1
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( sP13
| sP19 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(20,plain,
( sP14
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,h2]) ).
thf(22,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[21,h1]) ).
thf(23,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[22,h0]) ).
thf(0,theorem,
sP14,
inference(contra,[status(thm),contra(discharge,[h2])],[21,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SYO245^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jul 9 11:41:45 EDT 2022
% 0.14/0.35 % CPUTime :
% 47.13/47.36 % SZS status Theorem
% 47.13/47.36 % Mode: mode371
% 47.13/47.36 % Inferences: 18362
% 47.13/47.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------