TSTP Solution File: SEV257^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV257^5 : 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 18:05:36 EDT 2022
% Result : Theorem 35.20s 35.44s
% Output : Proof 35.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 38
% Syntax : Number of formulae : 46 ( 12 unt; 5 typ; 3 def)
% Number of atoms : 107 ( 7 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 141 ( 45 ~; 17 |; 0 &; 38 @)
% ( 15 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 19 con; 0-2 aty)
% Number of variables : 31 ( 12 ^ 19 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__7,type,
eigen__7: a > $o ).
thf(ty_eigen__4,type,
eigen__4: a ).
thf(ty_eigen__3,type,
eigen__3: a > $o ).
thf(ty_cOPEN,type,
cOPEN: ( a > $o ) > $o ).
thf(h0,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: a > $o] :
~ ( $false
=> ( cOPEN @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(h1,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__1
@ ^ [X1: a] :
( ( ~ ! [X2: a > $o] :
( $false
=> ~ ( X2 @ X1 ) ) )
!= $false ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: a > $o] :
~ ( $false
=> ~ ( X1 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ( cOPEN
@ ^ [X1: a] : ~ $false )
=> ~ ! [X1: ( a > $o ) > $o] :
( ! [X2: a > $o] :
( ( X1 @ X2 )
=> ( cOPEN @ X2 ) )
=> ( cOPEN
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ( X1 @ X3 )
=> ~ ( X3 @ X2 ) ) ) ) )
=> ~ ! [X1: a > $o,X2: a > $o] :
( ~ ( ( cOPEN @ X1 )
=> ~ ( cOPEN @ X2 ) )
=> ( cOPEN
@ ^ [X3: a] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: ( a > $o ) > $o] :
( ! [X2: a > $o] :
( ( X1 @ X2 )
=> ( cOPEN @ X2 ) )
=> ( cOPEN
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ( X1 @ X3 )
=> ~ ( X3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a > $o] :
( $false
=> ( cOPEN @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a > $o] :
( $false
=> ~ ( X1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( $false
=> ~ ( eigen__7 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( cOPEN
@ ^ [X1: a] :
~ ! [X2: a > $o] :
( $false
=> ~ ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( $false
=> ( cOPEN @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( ~ sP4 )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a] :
( ( ~ ! [X2: a > $o] :
( $false
=> ~ ( X2 @ X1 ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( ^ [X1: a] :
~ ! [X2: a > $o] :
( $false
=> ~ ( X2 @ X1 ) ) )
= ( ^ [X1: a] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( cOPEN
@ ^ [X1: a] : $false ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ sP1
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP3
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( cOPEN
@ ^ [X1: a] : ~ $false )
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> $false ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(cTHM625_pme,conjecture,
sP12 ).
thf(h2,negated_conjecture,
~ sP12,
inference(assume_negation,[status(cth)],[cTHM625_pme]) ).
thf(1,plain,
( sP5
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP4
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(3,plain,
( sP8
| ~ sP4
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP9
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__4]) ).
thf(5,plain,
( sP7
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP10
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP3
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(8,plain,
( ~ sP6
| sP11
| ~ sP10 ),
inference(mating_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP13
| ~ sP3
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP2
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
~ sP15,
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP14
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP1
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP12
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP12
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,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,h2]) ).
thf(17,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[16,h1]) ).
thf(18,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[17,h0]) ).
thf(0,theorem,
sP12,
inference(contra,[status(thm),contra(discharge,[h2])],[16,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SEV257^5 : TPTP v8.1.0. Released v4.0.0.
% 0.02/0.09 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.28 % DateTime : Tue Jun 28 14:51:12 EDT 2022
% 0.09/0.28 % CPUTime :
% 35.20/35.44 % SZS status Theorem
% 35.20/35.44 % Mode: mode466
% 35.20/35.44 % Inferences: 56647
% 35.20/35.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------