TSTP Solution File: SEU945^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU945^5 : 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 : n029.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 14:10:58 EDT 2022
% Result : Theorem 1.96s 2.16s
% Output : Proof 1.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 26
% Syntax : Number of formulae : 32 ( 9 unt; 2 typ; 2 def)
% Number of atoms : 91 ( 41 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 81 ( 30 ~; 12 |; 0 &; 7 @)
% ( 11 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 15 con; 0-2 aty)
% Number of variables : 22 ( 12 ^ 10 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ( ( ^ [X3: $i] :
( ( X3 != X1 )
=> ( X3 = X1 ) ) )
= ( ^ [X3: $i] :
( ( X3 != X2 )
=> ( X3 = X2 ) ) ) )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $i] :
~ ( ( ( ^ [X2: $i] :
( ( X2 != eigen__4 )
=> ( X2 = eigen__4 ) ) )
= ( ^ [X2: $i] :
( ( X2 != X1 )
=> ( X2 = X1 ) ) ) )
=> ( eigen__4 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( ( ^ [X2: $i] :
( ( X2 != eigen__4 )
=> ( X2 = eigen__4 ) ) )
= ( ^ [X2: $i] :
( ( X2 != X1 )
=> ( X2 = X1 ) ) ) )
=> ( eigen__4 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( ( X1 != eigen__4 )
=> ( X1 = eigen__4 ) )
= ( ( X1 != eigen__5 )
=> ( X1 = eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i] :
( ( ( ^ [X3: $i] :
( ( X3 != X1 )
=> ( X3 = X1 ) ) )
= ( ^ [X3: $i] :
( ( X3 != X2 )
=> ( X3 = X2 ) ) ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__4 = eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ sP4
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i > $i > $o] :
~ ! [X2: $i,X3: $i] :
( ( ( X1 @ X2 )
= ( X1 @ X3 ) )
=> ( X2 = X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__4 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ sP7
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( ^ [X1: $i] :
( ( X1 != eigen__4 )
=> ( X1 = eigen__4 ) ) )
= ( ^ [X1: $i] :
( ( X1 != eigen__5 )
=> ( X1 = eigen__5 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP9
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP8 = sP5 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(cTHM3_pme,conjecture,
~ sP6 ).
thf(h1,negated_conjecture,
sP6,
inference(assume_negation,[status(cth)],[cTHM3_pme]) ).
thf(1,plain,
sP7,
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP8
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| sP4
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP11
| ~ sP8
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP2
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP9
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP10
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP10
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP1
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(10,plain,
( sP3
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(11,plain,
( ~ sP6
| ~ sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,h1]) ).
thf(13,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[12,h0]) ).
thf(0,theorem,
~ sP6,
inference(contra,[status(thm),contra(discharge,[h1])],[12,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU945^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n029.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 20 00:17:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.96/2.16 % SZS status Theorem
% 1.96/2.16 % Mode: mode506
% 1.96/2.16 % Inferences: 201
% 1.96/2.16 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------