TSTP Solution File: LCL728^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL728^5 : 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 : n003.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 : Sun Jul 17 14:10:37 EDT 2022
% Result : Theorem 33.23s 33.43s
% Output : Proof 33.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 21
% Syntax : Number of formulae : 28 ( 11 unt; 4 typ; 2 def)
% Number of atoms : 49 ( 2 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 106 ( 30 ~; 7 |; 0 &; 50 @)
% ( 7 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 11 con; 0-2 aty)
% Number of variables : 29 ( 2 ^ 23 !; 0 ?; 29 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_b,type,
b: $tType ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_eigen__0,type,
eigen__0: a > b > $o ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ! [X2: b] :
~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__0 @ X1
@ @+[X2: b] : ( eigen__0 @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h1,assumption,
! [X1: ( a > b > $o ) > $o,X2: a > b > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: a > b > $o] :
~ ~ ! [X2: a > b] :
~ ! [X3: a] :
( ~ ! [X4: b] :
~ ( X1 @ X3 @ X4 )
=> ( X1 @ X3 @ ( X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: b] :
~ ( eigen__0 @ eigen__1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a] :
( ~ ! [X2: b] :
~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__0 @ X1
@ @+[X2: b] : ( eigen__0 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ sP1
=> ( eigen__0 @ eigen__1
@ @+[X1: b] : ( eigen__0 @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a > b > $o] :
~ ! [X2: a > b] :
~ ! [X3: a] :
( ~ ! [X4: b] :
~ ( X1 @ X3 @ X4 )
=> ( X1 @ X3 @ ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ! [X1: ( b > $o ) > $o] :
( ! [X2: b > $o] :
( ( X1 @ X2 )
=> ~ ! [X3: b] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( b > $o ) > b] :
~ ! [X3: b > $o] :
( ( X1 @ X3 )
=> ( X3 @ ( X2 @ X3 ) ) ) )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__0 @ eigen__1
@ @+[X1: b] : ( eigen__0 @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a > b] :
~ ! [X2: a] :
( ~ ! [X3: b] :
~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__0 @ X2 @ ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(cTHM532,conjecture,
sP5 ).
thf(h2,negated_conjecture,
~ sP5,
inference(assume_negation,[status(cth)],[cTHM532]) ).
thf(1,plain,
( sP6
| sP1 ),
inference(choice_rule,[status(thm)],]) ).
thf(2,plain,
( sP3
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP3
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP2
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(5,plain,
( ~ sP7
| ~ sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( sP4
| sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(7,plain,
( sP5
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,h2]) ).
thf(9,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[8,h1]) ).
thf(10,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[9,h0]) ).
thf(0,theorem,
sP5,
inference(contra,[status(thm),contra(discharge,[h2])],[8,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL728^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 4 02:21:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 33.23/33.43 % SZS status Theorem
% 33.23/33.43 % Mode: mode448
% 33.23/33.43 % Inferences: 34
% 33.23/33.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------