TSTP Solution File: SEV186^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV186^5 : 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 : n024.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 18:05:15 EDT 2022
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 61
% Syntax : Number of formulae : 77 ( 22 unt; 8 typ; 1 def)
% Number of atoms : 147 ( 1 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 345 ( 66 ~; 21 |; 0 &; 135 @)
% ( 20 <=>; 103 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 81 ( 81 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 28 usr; 24 con; 0-2 aty)
% Number of variables : 92 ( 1 ^ 91 !; 0 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_b,type,
b: $tType ).
thf(ty_eigen__6,type,
eigen__6: b ).
thf(ty_eigen__2,type,
eigen__2: b > $o ).
thf(ty_eigen__1,type,
eigen__1: ( b > $o ) > $o ).
thf(ty_eigen__0,type,
eigen__0: ( b > $o ) > ( b > $o ) > $o ).
thf(ty_eigen__4,type,
eigen__4: b ).
thf(ty_eigen__5,type,
eigen__5: b > $o ).
thf(ty_eigen__3,type,
eigen__3: b > $o ).
thf(h0,assumption,
! [X1: b > $o,X2: b] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: b] :
~ ( ( eigen__2 @ X1 )
=> ( eigen__5 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: b] :
( ( eigen__2 @ X1 )
=> ( eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__1 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( sP2
=> ( eigen__5 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__2 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP4
=> ! [X1: b > $o] :
( ( eigen__1 @ X1 )
=> ( X1 @ eigen__6 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: b] :
( ( eigen__2 @ X1 )
=> ! [X2: b > $o] :
( ( eigen__1 @ X2 )
=> ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP1
=> ~ ( eigen__0 @ eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__5 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP4
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: b > $o] :
( ( eigen__1 @ X1 )
=> ! [X2: b > $o,X3: b > $o] :
( ~ ( ! [X4: b] :
( ( X2 @ X4 )
=> ( X1 @ X4 ) )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ! [X4: b] :
( ( X3 @ X4 )
=> ( X1 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: b > $o,X2: b > $o] :
( ~ ( ! [X3: b] :
( ( X1 @ X3 )
=> ( eigen__5 @ X3 ) )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ! [X3: b] :
( ( X2 @ X3 )
=> ( eigen__5 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: b > $o] :
( ( eigen__1 @ X1 )
=> ( X1 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: b] :
( ( eigen__3 @ X1 )
=> ( eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: b > $o] :
( ~ ( sP1
=> ~ ( eigen__0 @ eigen__2 @ X1 ) )
=> ! [X2: b] :
( ( X1 @ X2 )
=> ( eigen__5 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ sP7
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__5 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP2
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__0 @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP15
=> sP17 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(cTHM565_pme,conjecture,
! [X1: ( b > $o ) > ( b > $o ) > $o,X2: ( b > $o ) > $o] :
( ! [X3: b > $o] :
( ( X2 @ X3 )
=> ! [X4: b > $o,X5: b > $o] :
( ~ ( ! [X6: b] :
( ( X4 @ X6 )
=> ( X3 @ X6 ) )
=> ~ ( X1 @ X4 @ X5 ) )
=> ! [X6: b] :
( ( X5 @ X6 )
=> ( X3 @ X6 ) ) ) )
=> ! [X3: b > $o,X4: b > $o] :
( ~ ( ! [X5: b] :
( ( X3 @ X5 )
=> ! [X6: b > $o] :
( ( X2 @ X6 )
=> ( X6 @ X5 ) ) )
=> ~ ( X1 @ X3 @ X4 ) )
=> ! [X5: b] :
( ( X4 @ X5 )
=> ! [X6: b > $o] :
( ( X2 @ X6 )
=> ( X6 @ X5 ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: ( b > $o ) > ( b > $o ) > $o,X2: ( b > $o ) > $o] :
( ! [X3: b > $o] :
( ( X2 @ X3 )
=> ! [X4: b > $o,X5: b > $o] :
( ~ ( ! [X6: b] :
( ( X4 @ X6 )
=> ( X3 @ X6 ) )
=> ~ ( X1 @ X4 @ X5 ) )
=> ! [X6: b] :
( ( X5 @ X6 )
=> ( X3 @ X6 ) ) ) )
=> ! [X3: b > $o,X4: b > $o] :
( ~ ( ! [X5: b] :
( ( X3 @ X5 )
=> ! [X6: b > $o] :
( ( X2 @ X6 )
=> ( X6 @ X5 ) ) )
=> ~ ( X1 @ X3 @ X4 ) )
=> ! [X5: b] :
( ( X4 @ X5 )
=> ! [X6: b > $o] :
( ( X2 @ X6 )
=> ( X6 @ X5 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM565_pme]) ).
thf(h2,assumption,
~ ! [X1: ( b > $o ) > $o] :
( ! [X2: b > $o] :
( ( X1 @ X2 )
=> ! [X3: b > $o,X4: b > $o] :
( ~ ( ! [X5: b] :
( ( X3 @ X5 )
=> ( X2 @ X5 ) )
=> ~ ( eigen__0 @ X3 @ X4 ) )
=> ! [X5: b] :
( ( X4 @ X5 )
=> ( X2 @ X5 ) ) ) )
=> ! [X2: b > $o,X3: b > $o] :
( ~ ( ! [X4: b] :
( ( X2 @ X4 )
=> ! [X5: b > $o] :
( ( X1 @ X5 )
=> ( X5 @ X4 ) ) )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ! [X4: b] :
( ( X3 @ X4 )
=> ! [X5: b > $o] :
( ( X1 @ X5 )
=> ( X5 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP10
=> ! [X1: b > $o,X2: b > $o] :
( ~ ( ! [X3: b] :
( ( X1 @ X3 )
=> ! [X4: b > $o] :
( ( eigen__1 @ X4 )
=> ( X4 @ X3 ) ) )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ! [X3: b] :
( ( X2 @ X3 )
=> ! [X4: b > $o] :
( ( eigen__1 @ X4 )
=> ( X4 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP10,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: b > $o,X2: b > $o] :
( ~ ( ! [X3: b] :
( ( X1 @ X3 )
=> ! [X4: b > $o] :
( ( eigen__1 @ X4 )
=> ( X4 @ X3 ) ) )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ! [X3: b] :
( ( X2 @ X3 )
=> ! [X4: b > $o] :
( ( eigen__1 @ X4 )
=> ( X4 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: b > $o] :
( ~ ( sP6
=> ~ ( eigen__0 @ eigen__2 @ X1 ) )
=> ! [X2: b] :
( ( X1 @ X2 )
=> ! [X3: b > $o] :
( ( eigen__1 @ X3 )
=> ( X3 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( sP6
=> ~ sP19 )
=> ! [X1: b] :
( ( eigen__3 @ X1 )
=> ! [X2: b > $o] :
( ( eigen__1 @ X2 )
=> ( X2 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP6
=> ~ sP19 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: b] :
( ( eigen__3 @ X1 )
=> ! [X2: b > $o] :
( ( eigen__1 @ X2 )
=> ( X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP6,
introduced(assumption,[]) ).
thf(h11,assumption,
sP19,
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( sP15
=> ! [X1: b > $o] :
( ( eigen__1 @ X1 )
=> ( X1 @ eigen__4 ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP15,
introduced(assumption,[]) ).
thf(h14,assumption,
~ ! [X1: b > $o] :
( ( eigen__1 @ X1 )
=> ( X1 @ eigen__4 ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP2
=> sP17 ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP2,
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP6
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP5
| ~ sP4
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP12
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP3
| ~ sP2
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP9
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP9
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP1
| ~ sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(8,plain,
( ~ sP13
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP20
| ~ sP15
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP11
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP14
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP16
| sP7
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP7
| ~ sP1
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP10
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP18
| ~ sP2
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h16,h17,h15,h13,h14,h12,h10,h11,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,h4,h10,h11,h13,h16,h17]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h13,h14,h12,h10,h11,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,16,h16,h17]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h14,h12,h10,h11,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__5)],[h14,17,h15]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h10,h11,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,18,h13,h14]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h11,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__4)],[h9,19,h12]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h8,20,h10,h11]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,21,h8,h9]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__3)],[h6,22,h7]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__2)],[h5,23,h6]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,24,h4,h5]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,25,h3]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,26,h2]) ).
thf(28,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[27,h0]) ).
thf(0,theorem,
! [X1: ( b > $o ) > ( b > $o ) > $o,X2: ( b > $o ) > $o] :
( ! [X3: b > $o] :
( ( X2 @ X3 )
=> ! [X4: b > $o,X5: b > $o] :
( ~ ( ! [X6: b] :
( ( X4 @ X6 )
=> ( X3 @ X6 ) )
=> ~ ( X1 @ X4 @ X5 ) )
=> ! [X6: b] :
( ( X5 @ X6 )
=> ( X3 @ X6 ) ) ) )
=> ! [X3: b > $o,X4: b > $o] :
( ~ ( ! [X5: b] :
( ( X3 @ X5 )
=> ! [X6: b > $o] :
( ( X2 @ X6 )
=> ( X6 @ X5 ) ) )
=> ~ ( X1 @ X3 @ X4 ) )
=> ! [X5: b] :
( ( X4 @ X5 )
=> ! [X6: b > $o] :
( ( X2 @ X6 )
=> ( X6 @ X5 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[27,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEV186^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 28 11:13:16 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % Mode: mode213
% 0.12/0.37 % Inferences: 54
% 0.12/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------