TSTP Solution File: SEU933^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU933^5 : 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 : n015.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 14:10:55 EDT 2022
% Result : Theorem 47.41s 47.70s
% Output : Proof 47.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 37
% Syntax : Number of formulae : 44 ( 15 unt; 4 typ; 2 def)
% Number of atoms : 84 ( 13 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 171 ( 41 ~; 17 |; 0 &; 57 @)
% ( 15 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 20 con; 0-2 aty)
% Number of variables : 52 ( 26 ^ 26 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $i ).
thf(ty_b,type,
b: $i ).
thf(ty_eigen__0,type,
eigen__0: ( $i > $i ) > $o ).
thf(ty_eigen__4,type,
eigen__4: $i > $i ).
thf(h0,assumption,
! [X1: ( ( $i > $i ) > $o ) > $o,X2: ( $i > $i ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: ( $i > $i ) > $o] :
~ ( ~ ( ( X1
@ ^ [X2: $i] : a )
=> ~ ! [X2: $i > $i] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i] : a ) ) )
=> ( X1
@ ^ [X2: $i] : a ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(h1,assumption,
! [X1: ( $i > $i ) > $o,X2: $i > $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__1
@ ^ [X1: $i > $i] :
~ ( ( a
= ( X1 @ b ) )
=> ( a = a ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ( a = b ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i > $i] :
( ! [X2: ( $i > $i ) > $o] :
( ~ ( ( X2
@ ^ [X3: $i] : a )
=> ~ ! [X3: $i > $i] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i] : a ) ) )
=> ( X2
@ ^ [X3: $i] : ( X1 @ a ) ) )
=> ! [X2: ( $i > $i ) > $o] :
( ~ ( ( X2
@ ^ [X3: $i] : a )
=> ~ ! [X3: $i > $i] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i] : a ) ) )
=> ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( ( a = a )
=> ~ ! [X1: $i > $i] :
( ( a
= ( X1 @ b ) )
=> ( a = a ) ) )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__0
@ ^ [X1: $i] : a )
=> ~ ! [X1: $i > $i] :
( ( eigen__0 @ X1 )
=> ( eigen__0
@ ^ [X2: $i] : a ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: ( $i > $i ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i] : a )
=> ~ ! [X2: $i > $i] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i] : a ) ) )
=> ( X1
@ ^ [X2: $i] : X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ! [X1: ( $i > $i ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i] : a )
=> ~ ! [X2: $i > $i] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i] : a ) ) )
=> ( X1
@ ^ [X2: $i] : a ) )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: ( $i > $i ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i] : a )
=> ~ ! [X2: $i > $i] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i] : a ) ) )
=> ( X1
@ ^ [X2: $i] : a ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i > $i,X2: $i > $i] :
( ! [X3: ( $i > $i ) > $o] :
( ~ ( ( X3 @ X1 )
=> ~ ! [X4: $i > $i] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i] : ( X1 @ ( X4 @ X5 ) ) ) ) )
=> ( X3
@ ^ [X4: $i] : ( X2 @ ( X1 @ X4 ) ) ) )
=> ! [X3: ( $i > $i ) > $o] :
( ~ ( ( X3 @ X1 )
=> ~ ! [X4: $i > $i] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i] : ( X1 @ ( X4 @ X5 ) ) ) ) )
=> ( X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ sP1
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( a
= ( eigen__4 @ b ) )
=> ( a = a ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( a = a ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ sP4
=> ( eigen__0
@ ^ [X1: $i] : a ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__0
@ ^ [X1: $i] : a ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP11
=> ~ ! [X1: $i > $i] :
( ( a
= ( X1 @ b ) )
=> sP11 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i > $i] :
( ( a
= ( X1 @ b ) )
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(cTHM196B_pme,conjecture,
sP9 ).
thf(h2,negated_conjecture,
~ sP9,
inference(assume_negation,[status(cth)],[cTHM196B_pme]) ).
thf(1,plain,
( sP4
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP10
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP12
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP12
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP15
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__4]) ).
thf(6,plain,
sP11,
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP14
| ~ sP11
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP3
| sP14
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP7
| ~ sP12 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(10,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP6
| ~ sP7
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP2
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP8
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( sP9
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP9
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,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,h2]) ).
thf(17,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[16,h1]) ).
thf(18,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[17,h0]) ).
thf(0,theorem,
sP9,
inference(contra,[status(thm),contra(discharge,[h2])],[16,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU933^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n015.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 : Sun Jun 19 20:22:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 47.41/47.70 % SZS status Theorem
% 47.41/47.70 % Mode: mode371
% 47.41/47.70 % Inferences: 72972
% 47.41/47.70 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------