TSTP Solution File: SYO098^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO098^5 : 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 : n027.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 19:30:17 EDT 2022
% Result : Theorem 0.14s 0.37s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 31
% Syntax : Number of formulae : 37 ( 7 unt; 4 typ; 1 def)
% Number of atoms : 74 ( 1 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 112 ( 30 ~; 13 |; 0 &; 42 @)
% ( 12 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 16 con; 0-2 aty)
% Number of variables : 13 ( 1 ^ 12 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_cR,type,
cR: $i > $i > $o ).
thf(ty_cQ,type,
cQ: $i > $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ( cQ @ X1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
~ ( cR @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( cQ @ eigen__0 @ eigen__0 )
=> ! [X1: $i] : ( cQ @ X1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( cR @ eigen__0 @ eigen__0 )
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ~ ( cR @ eigen__1 @ X1 )
=> ~ ( ( cQ @ X1 @ eigen__1 )
=> ! [X2: $i] : ( cQ @ X2 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( cQ @ eigen__1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( cR @ eigen__1 @ eigen__1 )
=> ~ ( sP5
=> ! [X1: $i] : ( cQ @ X1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( cR @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i,X2: $i] :
( ~ ( cR @ X1 @ X2 )
=> ~ ( ( cQ @ X2 @ X1 )
=> ! [X3: $i] : ( cQ @ X3 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] : ( cQ @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ~ ( cR @ eigen__0 @ X1 )
=> ~ ( ( cQ @ X1 @ eigen__0 )
=> sP9 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP5
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( cR @ eigen__1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(cTHM65,conjecture,
( sP1
=> ~ sP8 ) ).
thf(h1,negated_conjecture,
~ ( sP1
=> ~ sP8 ),
inference(assume_negation,[status(cth)],[cTHM65]) ).
thf(h2,assumption,
sP1,
introduced(assumption,[]) ).
thf(h3,assumption,
sP8,
introduced(assumption,[]) ).
thf(1,plain,
( sP11
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP4
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP6
| sP12
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP8
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP1
| ~ sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( sP9
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(7,plain,
( sP2
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP10
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP3
| sP7
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP8
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP1
| ~ sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,h2,h3]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,12,h2,h3]) ).
thf(14,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[13,h0]) ).
thf(0,theorem,
( sP1
=> ~ sP8 ),
inference(contra,[status(thm),contra(discharge,[h1])],[13,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO098^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jul 8 22:11:16 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.37 % SZS status Theorem
% 0.14/0.37 % Mode: mode213
% 0.14/0.37 % Inferences: 28
% 0.14/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------