TSTP Solution File: SEV385^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV385^5 : 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 : n016.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 18:06:09 EDT 2022
% Result : Theorem 1.97s 2.24s
% Output : Proof 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 47
% Syntax : Number of formulae : 55 ( 13 unt; 7 typ; 3 def)
% Number of atoms : 136 ( 59 equ; 6 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 138 ( 55 ~; 22 |; 0 &; 17 @)
% ( 18 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 27 con; 0-2 aty)
% Number of variables : 29 ( 9 ^ 20 !; 0 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_b,type,
b: $tType ).
thf(ty_eigen__7,type,
eigen__7: b ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_eigen__4,type,
eigen__4: b ).
thf(ty_y,type,
y: a ).
thf(ty_x,type,
x: b ).
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] :
~ ( ( y = X1 )
=> ~ ! [X2: b] :
( ( ^ [X3: b] :
~ ( ( x = X3 )
=> ( X1 != y ) ) )
!= ( (=) @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h1,assumption,
! [X1: b > $o,X2: b] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__1
@ ^ [X1: b] :
~ ( ( x = X1 )
=> ( y = y ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__1
@ ^ [X1: b] :
( ( ~ ( ( x = X1 )
=> ( eigen__1 != y ) ) )
!= ( x = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(sP1,plain,
( sP1
<=> ( ! [X1: b] :
( ( x = X1 )
=> ( y = y ) )
=> ~ ! [X1: a] :
( ( y = X1 )
=> ~ ! [X2: b] :
( ( ^ [X3: b] :
~ ( ( x = X3 )
=> ( X1 != y ) ) )
!= ( (=) @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( x = eigen__4 )
=> ( y = y ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: b] :
( ( ^ [X2: b] :
~ ( ( x = X2 )
=> ( eigen__1 != y ) ) )
!= ( (=) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( y = eigen__1 )
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( ^ [X1: b] :
~ ( ( x = X1 )
=> ( eigen__1 != y ) ) )
= ( (=) @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a,X2: a] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( y = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( x = eigen__7 )
=> ( eigen__1 != y ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( y = y ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__1 = y ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: b] :
( ( x = X1 )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: b > a] :
( ! [X2: b] :
( ( x = X2 )
=> ( y
= ( X1 @ X2 ) ) )
=> ~ ! [X2: a] :
( ( y = X2 )
=> ~ ! [X3: b] :
( ( ^ [X4: b] :
~ ( ( x = X4 )
=> ( X2
!= ( X1 @ X4 ) ) ) )
!= ( (=) @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP7
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( x = eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a] :
( ( y = X1 )
=> ( X1 = y ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: b] :
( ( ~ ( ( x = X1 )
=> ~ sP10 ) )
= ( x = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a] :
( ( y = X1 )
=> ~ ! [X2: b] :
( ( ^ [X3: b] :
~ ( ( x = X3 )
=> ( X1 != y ) ) )
!= ( (=) @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( ~ sP8 )
= sP14 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(cX6004_pme,conjecture,
~ sP12 ).
thf(h2,negated_conjecture,
sP12,
inference(assume_negation,[status(cth)],[cX6004_pme]) ).
thf(1,plain,
( sP8
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP8
| ~ sP14
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP18
| sP8
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP18
| ~ sP8
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP16
| ~ sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__7]) ).
thf(6,plain,
( sP5
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP3
| ~ sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
sP9,
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP2
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP11
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__4]) ).
thf(11,plain,
( ~ sP13
| ~ sP7
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP15
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP6
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
sP6,
inference(eq_sym,[status(thm)],]) ).
thf(15,plain,
( sP4
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP4
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP17
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(18,plain,
( ~ sP1
| ~ sP11
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP12
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,h2]) ).
thf(21,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[20,h1]) ).
thf(22,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[21,h0]) ).
thf(0,theorem,
~ sP12,
inference(contra,[status(thm),contra(discharge,[h2])],[20,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV385^5 : 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 : n016.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 27 20:04:51 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.97/2.24 % SZS status Theorem
% 1.97/2.24 % Mode: mode506
% 1.97/2.24 % Inferences: 60378
% 1.97/2.24 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------