TSTP Solution File: SEV164^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV164^5 : 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 : n020.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 18:05:10 EDT 2022
% Result : Theorem 1.97s 2.17s
% Output : Proof 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 26
% Syntax : Number of formulae : 36 ( 14 unt; 5 typ; 4 def)
% Number of atoms : 61 ( 7 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 111 ( 33 ~; 11 |; 0 &; 56 @)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 14 con; 0-2 aty)
% Number of variables : 52 ( 30 ^ 22 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__2,type,
eigen__2: ( a > a > a ) > a ).
thf(ty_eigen__0,type,
eigen__0: a > a > $o ).
thf(ty_eigen__4,type,
eigen__4: a ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
~ ( eigen__0 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(h1,assumption,
! [X1: ( a > a > $o ) > $o,X2: a > a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: a > a > $o] :
( ( ~ ! [X2: a,X3: a] :
~ ( X1 @ X2 @ X3 ) )
!= ( ~ ! [X2: ( a > a > a ) > a] :
~ ( X1
@ ( X2
@ ^ [X3: a,X4: a] : X3 )
@ ( X2
@ ^ [X3: a,X4: a] : X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(h2,assumption,
! [X1: ( ( a > a > a ) > a ) > $o,X2: ( a > a > a ) > a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__2
@ ^ [X1: ( a > a > a ) > a] :
~ ~ ( eigen__0
@ ( X1
@ ^ [X2: a,X3: a] : X2 )
@ ( X1
@ ^ [X2: a,X3: a] : X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: a] :
~ ~ ( eigen__0 @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ( ( ~ ! [X1: a,X2: a] :
~ ( eigen__0 @ X1 @ X2 ) )
= ( ~ ! [X1: ( a > a > a ) > a] :
~ ( eigen__0
@ ( X1
@ ^ [X2: a,X3: a] : X2 )
@ ( X1
@ ^ [X2: a,X3: a] : X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: ( a > a > a ) > a] :
~ ( eigen__0
@ ( X1
@ ^ [X2: a,X3: a] : X2 )
@ ( X1
@ ^ [X2: a,X3: a] : X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] :
~ ( eigen__0
@ ( eigen__2
@ ^ [X2: a,X3: a] : X2 )
@ X1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a,X2: a] :
~ ( eigen__0 @ X1 @ X2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__0 @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a > a > $o] :
( ( ~ ! [X2: a,X3: a] :
~ ( X1 @ X2 @ X3 ) )
= ( ~ ! [X2: ( a > a > a ) > a] :
~ ( X1
@ ( X2
@ ^ [X3: a,X4: a] : X3 )
@ ( X2
@ ^ [X3: a,X4: a] : X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__0
@ ( eigen__2
@ ^ [X1: a,X2: a] : X1 )
@ ( eigen__2
@ ^ [X1: a,X2: a] : X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a] :
~ ( eigen__0 @ eigen__3 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(cTHM185_pme,conjecture,
sP6 ).
thf(h3,negated_conjecture,
~ sP6,
inference(assume_negation,[status(cth)],[cTHM185_pme]) ).
thf(1,plain,
( ~ sP2
| ~ sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( sP8
| sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(3,plain,
( sP4
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(4,plain,
( ~ sP4
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP3
| ~ sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( sP2
| sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__2]) ).
thf(7,plain,
( sP1
| sP4
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP1
| ~ sP4
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP6
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,h3]) ).
thf(11,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h1,h0]),eigenvar_choice(discharge,[h2])],[10,h2]) ).
thf(12,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h0]),eigenvar_choice(discharge,[h1])],[11,h1]) ).
thf(13,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3]),eigenvar_choice(discharge,[h0])],[12,h0]) ).
thf(0,theorem,
sP6,
inference(contra,[status(thm),contra(discharge,[h3])],[10,h3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : SEV164^5 : TPTP v8.1.0. Released v4.0.0.
% 0.05/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 28 17:23:46 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.97/2.17 % SZS status Theorem
% 1.97/2.17 % Mode: mode506
% 1.97/2.17 % Inferences: 1027
% 1.97/2.17 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------