TSTP Solution File: SEV189^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV189^5 : 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 : n004.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 18:05:16 EDT 2022
% Result : Theorem 0.18s 0.35s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 52
% Syntax : Number of formulae : 64 ( 16 unt; 6 typ; 2 def)
% Number of atoms : 158 ( 2 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 242 ( 58 ~; 20 |; 0 &; 86 @)
% ( 19 <=>; 59 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 21 con; 0-2 aty)
% Number of variables : 46 ( 15 ^ 31 !; 0 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_b,type,
b: $tType ).
thf(ty_eigen__2,type,
eigen__2: b > $o ).
thf(ty_cP,type,
cP: ( b > $o ) > $o ).
thf(ty_eigen__1,type,
eigen__1: b > $o ).
thf(ty_eigen__0,type,
eigen__0: ( b > $o ) > $o ).
thf(ty_cQ,type,
cQ: ( b > $o ) > $o ).
thf(h0,assumption,
! [X1: ( b > $o ) > $o,X2: b > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: b > $o] :
~ ( ( eigen__0 @ X1 )
=> ( cP @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: b > $o] :
~ ( ( eigen__0 @ X1 )
=> ( cQ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: b > $o] :
( ( eigen__0 @ X1 )
=> ~ ( ( cP @ X1 )
=> ~ ( cQ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__0 @ eigen__1 )
=> ( cP @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( cP @ eigen__1 )
=> ~ ( cQ @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: b > $o] :
( ( eigen__0 @ X1 )
=> ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( cP @ eigen__2 )
=> ~ ( cQ @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP4
=> ( cP
@ ^ [X1: b] :
! [X2: b > $o] :
( ( eigen__0 @ X2 )
=> ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( cQ @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( cQ
@ ^ [X1: b] :
! [X2: b > $o] :
( ( eigen__0 @ X2 )
=> ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( cP @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( eigen__0 @ eigen__1 )
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( eigen__0 @ eigen__2 )
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: ( b > $o ) > $o] :
( ! [X2: b > $o] :
( ( X1 @ X2 )
=> ( cQ @ X2 ) )
=> ( cQ
@ ^ [X2: b] :
! [X3: b > $o] :
( ( X1 @ X3 )
=> ( X3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( eigen__0 @ eigen__2 )
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( cP
@ ^ [X1: b] :
! [X2: b > $o] :
( ( eigen__0 @ X2 )
=> ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ! [X1: b > $o] :
( ( eigen__0 @ X1 )
=> ( cQ @ X1 ) )
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: b > $o] :
( ( eigen__0 @ X1 )
=> ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: ( b > $o ) > $o] :
( ! [X2: b > $o] :
( ( X1 @ X2 )
=> ( cP @ X2 ) )
=> ( cP
@ ^ [X2: b] :
! [X3: b > $o] :
( ( X1 @ X3 )
=> ( X3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(cTHM567_pme,conjecture,
( ~ ( sP18
=> ~ sP12 )
=> ! [X1: ( b > $o ) > $o] :
( ! [X2: b > $o] :
( ( X1 @ X2 )
=> ~ ( ( cP @ X2 )
=> ~ ( cQ @ X2 ) ) )
=> ~ ( ( cP
@ ^ [X2: b] :
! [X3: b > $o] :
( ( X1 @ X3 )
=> ( X3 @ X2 ) ) )
=> ~ ( cQ
@ ^ [X2: b] :
! [X3: b > $o] :
( ( X1 @ X3 )
=> ( X3 @ X2 ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( ~ ( sP18
=> ~ sP12 )
=> ! [X1: ( b > $o ) > $o] :
( ! [X2: b > $o] :
( ( X1 @ X2 )
=> ~ ( ( cP @ X2 )
=> ~ ( cQ @ X2 ) ) )
=> ~ ( ( cP
@ ^ [X2: b] :
! [X3: b > $o] :
( ( X1 @ X3 )
=> ( X3 @ X2 ) ) )
=> ~ ( cQ
@ ^ [X2: b] :
! [X3: b > $o] :
( ( X1 @ X3 )
=> ( X3 @ X2 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM567_pme]) ).
thf(h2,assumption,
~ ( sP18
=> ~ sP12 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: ( b > $o ) > $o] :
( ! [X2: b > $o] :
( ( X1 @ X2 )
=> ~ ( ( cP @ X2 )
=> ~ ( cQ @ X2 ) ) )
=> ~ ( ( cP
@ ^ [X2: b] :
! [X3: b > $o] :
( ( X1 @ X3 )
=> ( X3 @ X2 ) ) )
=> ~ ( cQ
@ ^ [X2: b] :
! [X3: b > $o] :
( ( X1 @ X3 )
=> ( X3 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP18,
introduced(assumption,[]) ).
thf(h5,assumption,
sP12,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP1
=> ~ ( sP14
=> ~ sP8 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP1,
introduced(assumption,[]) ).
thf(h8,assumption,
( sP14
=> ~ sP8 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(1,plain,
( sP3
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP1
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP10
| ~ sP15
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP2
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP2
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP4
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(7,plain,
( ~ sP18
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP6
| ~ sP4
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h7,h8,h6,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,h4,h7,h9]) ).
thf(10,plain,
( sP5
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP1
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP13
| ~ sP19
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP11
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP11
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP17
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(16,plain,
( ~ sP12
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP16
| ~ sP17
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h7,h8,h6,h4,h5,h2,h3,h1,h0])],[10,11,12,13,14,15,16,17,h5,h7,h10]) ).
thf(19,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h7,h8,h6,h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h10])],[h8,9,18,h9,h10]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,19,h7,h8]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__0)],[h3,20,h6]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,21,h4,h5]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,22,h2,h3]) ).
thf(24,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[23,h0]) ).
thf(0,theorem,
( ~ ( sP18
=> ~ sP12 )
=> ! [X1: ( b > $o ) > $o] :
( ! [X2: b > $o] :
( ( X1 @ X2 )
=> ~ ( ( cP @ X2 )
=> ~ ( cQ @ X2 ) ) )
=> ~ ( ( cP
@ ^ [X2: b] :
! [X3: b > $o] :
( ( X1 @ X3 )
=> ( X3 @ X2 ) ) )
=> ~ ( cQ
@ ^ [X2: b] :
! [X3: b > $o] :
( ( X1 @ X3 )
=> ( X3 @ X2 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[23,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEV189^5 : 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
% 0.12/0.32 % Computer : n004.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Tue Jun 28 15:55:23 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.18/0.35 % SZS status Theorem
% 0.18/0.35 % Mode: mode213
% 0.18/0.35 % Inferences: 33
% 0.18/0.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------