TSTP Solution File: SET046^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SET046^5 : 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 04:50:19 EDT 2022
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 32
% Syntax : Number of formulae : 38 ( 6 unt; 3 typ; 1 def)
% Number of atoms : 102 ( 1 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 200 ( 48 ~; 17 |; 0 &; 86 @)
% ( 13 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 17 con; 0-2 aty)
% Number of variables : 22 ( 1 ^ 21 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_cF,type,
cF: $i > $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
~ ( ( cF @ eigen__0 @ X1 )
=> ~ ( cF @ X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(sP1,plain,
( sP1
<=> ( cF @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( cF @ eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( sP2
=> ~ ( cF @ eigen__3 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ! [X1: $i] :
( ( cF @ eigen__0 @ X1 )
=> ~ ( cF @ X1 @ eigen__0 ) )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( cF @ eigen__3 @ X1 )
=> ~ ( cF @ X1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP1
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( sP1
=> ! [X1: $i] :
( ( cF @ eigen__0 @ X1 )
=> ~ ( cF @ X1 @ eigen__0 ) ) )
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( cF @ eigen__3 @ eigen__0 )
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( ( cF @ eigen__3 @ eigen__0 )
=> sP5 )
=> ~ ( sP5
=> ( cF @ eigen__3 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( cF @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
~ ( ( ( cF @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( cF @ X1 @ X2 )
=> ~ ( cF @ X2 @ X1 ) ) )
=> ~ ( ! [X2: $i] :
( ( cF @ X1 @ X2 )
=> ~ ( cF @ X2 @ X1 ) )
=> ( cF @ X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP10
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( cF @ eigen__0 @ X1 )
=> ~ ( cF @ X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(cPELL42,conjecture,
! [X1: $i] :
~ ! [X2: $i] :
~ ( ( ( cF @ X2 @ X1 )
=> ! [X3: $i] :
( ( cF @ X2 @ X3 )
=> ~ ( cF @ X3 @ X2 ) ) )
=> ~ ( ! [X3: $i] :
( ( cF @ X2 @ X3 )
=> ~ ( cF @ X3 @ X2 ) )
=> ( cF @ X2 @ X1 ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i] :
~ ! [X2: $i] :
~ ( ( ( cF @ X2 @ X1 )
=> ! [X3: $i] :
( ( cF @ X2 @ X3 )
=> ~ ( cF @ X3 @ X2 ) ) )
=> ~ ( ! [X3: $i] :
( ( cF @ X2 @ X3 )
=> ~ ( cF @ X3 @ X2 ) )
=> ( cF @ X2 @ X1 ) ) ),
inference(assume_negation,[status(cth)],[cPELL42]) ).
thf(h2,assumption,
sP11,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP5
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP8
| ~ sP10
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP12
| ~ sP10
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP9
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP11
| ~ sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( sP3
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP3
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP6
| ~ sP1
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP13
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(10,plain,
( ~ sP13
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP4
| ~ sP13
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP7
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP11
| ~ sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,h2]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,14,h2]) ).
thf(16,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[15,h0]) ).
thf(0,theorem,
! [X1: $i] :
~ ! [X2: $i] :
~ ( ( ( cF @ X2 @ X1 )
=> ! [X3: $i] :
( ( cF @ X2 @ X3 )
=> ~ ( cF @ X3 @ X2 ) ) )
=> ~ ( ! [X3: $i] :
( ( cF @ X2 @ X3 )
=> ~ ( cF @ X3 @ X2 ) )
=> ( cF @ X2 @ X1 ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[15,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET046^5 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jul 11 01:58:16 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % Mode: mode213
% 0.19/0.37 % Inferences: 275
% 0.19/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------