TSTP Solution File: SYO513^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO513^1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n016.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 19:33:08 EDT 2022
% Result : Theorem 9.72s 9.99s
% Output : Proof 9.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 46
% Syntax : Number of formulae : 54 ( 13 unt; 3 typ; 3 def)
% Number of atoms : 136 ( 19 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 124 ( 42 ~; 31 |; 0 &; 26 @)
% ( 19 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 24 con; 0-2 aty)
% Number of variables : 23 ( 11 ^ 12 !; 0 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $o > $o ).
thf(ty_eigen__4,type,
eigen__4: $o ).
thf(ty_eigen__3,type,
eigen__3: $o ).
thf(h0,assumption,
! [X1: $o > $o,X2: $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $o] :
~ ~ ( eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(h1,assumption,
! [X1: ( $o > $o ) > $o,X2: $o > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: $o > $o] :
~ ( ~ ! [X2: $o] :
~ ( X1 @ X2 )
=> ( X1
@ ( ( ^ [X2: $o] : X2 )
= X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $o] :
( X1
!= ( eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $o > $o] :
( ~ ! [X2: $o] :
~ ( X1 @ X2 )
=> ( X1
@ ( ( ^ [X2: $o] : X2 )
= X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> eigen__3 ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__4
= ( eigen__2 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> eigen__4 ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $o] :
~ ( eigen__2 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP4
= ( ( ^ [X1: $o] : X1 )
= eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP2 = sP4 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $o] :
( X1
= ( eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__2 @ ~ $false ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP2
= ( ( ^ [X1: $o] : X1 )
= eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ sP5
=> ( eigen__2
@ ( ( ^ [X1: $o] : X1 )
= eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__2
@ ( ( ^ [X1: $o] : X1 )
= eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( ~ $false )
= ( ( ^ [X1: $o] : X1 )
= eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__2 @ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( ^ [X1: $o] : X1 )
= eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: ( $o > $o ) > $o] :
~ ! [X2: $o > $o] :
( ~ ! [X3: $o] :
~ ( X2 @ X3 )
=> ( X2 @ ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( ~ $false )
= sP9 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__2 @ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> $false ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(choiceo,conjecture,
~ sP16 ).
thf(h2,negated_conjecture,
sP16,
inference(assume_negation,[status(cth)],[choiceo]) ).
thf(1,plain,
( sP13
| sP19
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP9
| sP12
| ~ sP13 ),
inference(mating_rule,[status(thm)],]) ).
thf(3,plain,
~ sP19,
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP17
| sP19
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP8
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP15
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP6
| sP4
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP14
| sP12
| ~ sP6 ),
inference(mating_rule,[status(thm)],]) ).
thf(9,plain,
( sP7
| ~ sP2
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP18
| sP14
| ~ sP7 ),
inference(mating_rule,[status(thm)],]) ).
thf(11,plain,
( sP3
| ~ sP4
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP3
| sP4
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP8
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(14,plain,
( sP15
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP10
| sP2
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP18
| sP12
| ~ sP10 ),
inference(mating_rule,[status(thm)],]) ).
thf(17,plain,
( sP5
| sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(18,plain,
( sP11
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP11
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP1
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(21,plain,
( ~ sP16
| ~ sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,h2]) ).
thf(23,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[22,h1]) ).
thf(24,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[23,h0]) ).
thf(0,theorem,
~ sP16,
inference(contra,[status(thm),contra(discharge,[h2])],[22,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO513^1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n016.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
% 0.18/0.33 % CPULimit : 300
% 0.18/0.33 % WCLimit : 600
% 0.18/0.33 % DateTime : Fri Jul 8 23:21:54 EDT 2022
% 0.18/0.33 % CPUTime :
% 9.72/9.99 % SZS status Theorem
% 9.72/9.99 % Mode: mode495
% 9.72/9.99 % Inferences: 59
% 9.72/9.99 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------