TSTP Solution File: SEV382^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV382^5 : 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 : n018.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 18:06:08 EDT 2022
% Result : Theorem 35.30s 35.52s
% Output : Proof 35.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 34
% Syntax : Number of formulae : 43 ( 13 unt; 4 typ; 3 def)
% Number of atoms : 96 ( 3 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 226 ( 60 ~; 15 |; 0 &; 83 @)
% ( 13 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 19 con; 0-2 aty)
% ( 5 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 50 ( 3 ^ 47 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__12,type,
eigen__12: a ).
thf(ty_eigen__1,type,
eigen__1: a > $o ).
thf(ty_eigen__0,type,
eigen__0: a > a > $o ).
thf(h0,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ! [X2: a > $o] :
( ~ ! [X3: a] :
~ ( X2 @ X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ~ ! [X4: a] :
( ( eigen__0 @ X4 @ X3 )
=> ~ ( X2 @ X4 ) ) ) )
=> ~ ! [X2: a] :
( ! [X3: a] :
( ( eigen__0 @ X3 @ X2 )
=> ( X1 @ X3 ) )
=> ( X1 @ X2 ) ) )
=> ( !! @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
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 > $o] :
( ~ ( ! [X3: a > $o] :
( ~ ! [X4: a] :
~ ( X3 @ X4 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ~ ! [X5: a] :
( ( X1 @ X5 @ X4 )
=> ~ ( X3 @ X5 ) ) ) )
=> ~ ! [X3: a] :
( ! [X4: a] :
( ( X1 @ X4 @ X3 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) )
=> ( !! @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(h2,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__12,definition,
( eigen__12
= ( eps__2
@ ^ [X1: a] :
~ ( ~ ( eigen__1 @ X1 )
=> ~ ! [X2: a] :
( ( eigen__0 @ X2 @ X1 )
=> ( eigen__1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__12])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a > $o] :
( ~ ! [X3: a] :
~ ( X2 @ X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ~ ! [X4: a] :
( ( eigen__0 @ X4 @ X3 )
=> ~ ( X2 @ X4 ) ) ) )
=> ~ ! [X2: a] :
( ! [X3: a] :
( ( eigen__0 @ X3 @ X2 )
=> ( X1 @ X3 ) )
=> ( X1 @ X2 ) ) )
=> ( !! @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a > $o] :
( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( eigen__0 @ X3 @ X2 )
=> ~ ( X1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( eigen__1 @ eigen__12 )
=> ~ ! [X1: a] :
( ( eigen__0 @ X1 @ eigen__12 )
=> ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a] :
( ( eigen__0 @ X1 @ eigen__12 )
=> ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( !! @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP4
=> ( eigen__1 @ eigen__12 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__1 @ eigen__12 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ( sP2
=> ~ ! [X1: a] :
( ! [X2: a] :
( ( eigen__0 @ X2 @ X1 )
=> ( eigen__1 @ X2 ) )
=> ( eigen__1 @ X1 ) ) )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a > a > $o,X2: a > $o] :
( ~ ( ! [X3: a > $o] :
( ~ ! [X4: a] :
~ ( X3 @ X4 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ~ ! [X5: a] :
( ( X1 @ X5 @ X4 )
=> ~ ( X3 @ X5 ) ) ) )
=> ~ ! [X3: a] :
( ! [X4: a] :
( ( X1 @ X4 @ X3 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) )
=> ( !! @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a] :
( ! [X2: a] :
( ( eigen__0 @ X2 @ X1 )
=> ( eigen__1 @ X2 ) )
=> ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a] :
( ~ ( eigen__1 @ X1 )
=> ~ ! [X2: a] :
( ( eigen__0 @ X2 @ X1 )
=> ( eigen__1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP2
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ sP5
=> ~ sP11 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(cTRANS_IND,conjecture,
sP9 ).
thf(h3,negated_conjecture,
~ sP9,
inference(assume_negation,[status(cth)],[cTRANS_IND]) ).
thf(1,plain,
( ~ sP6
| ~ sP4
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP10
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( sP3
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP3
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP11
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__12]) ).
thf(6,plain,
( ~ sP13
| sP5
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP2
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( sP12
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP12
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP8
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP8
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP1
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(13,plain,
( sP9
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(14,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,h3]) ).
thf(15,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h1,h0]),eigenvar_choice(discharge,[h2])],[14,h2]) ).
thf(16,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h0]),eigenvar_choice(discharge,[h1])],[15,h1]) ).
thf(17,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3]),eigenvar_choice(discharge,[h0])],[16,h0]) ).
thf(0,theorem,
sP9,
inference(contra,[status(thm),contra(discharge,[h3])],[14,h3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV382^5 : 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 : n018.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 : Tue Jun 28 09:47:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 35.30/35.52 % SZS status Theorem
% 35.30/35.52 % Mode: mode466
% 35.30/35.52 % Inferences: 55635
% 35.30/35.52 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------