TSTP Solution File: SYO111^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO111^5 : 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 : n009.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 : Thu Jul 21 19:30:21 EDT 2022
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 67
% Syntax : Number of formulae : 101 ( 46 unt; 12 typ; 2 def)
% Number of atoms : 204 ( 2 equ; 0 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 297 ( 137 ~; 20 |; 0 &; 48 @)
% ( 16 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 28 con; 0-2 aty)
% ( 23 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 9 ( 2 ^ 7 !; 0 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_cG,type,
cG: $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__10,type,
eigen__10: $i ).
thf(ty_eigen__8,type,
eigen__8: $i ).
thf(ty_eigen__9,type,
eigen__9: $i ).
thf(ty_cM,type,
cM: $i > $o ).
thf(ty_cN,type,
cN: $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( cN @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( cN @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ~ ( cM @ X1 )
=> ~ ! [X2: $i] :
~ ( cN @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( cM @ eigen__0 )
=> ~ ! [X1: $i] :
~ ( cN @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( cN @ eigen__2 )
=> ~ ( !! @ cG ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
~ ( cN @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( cM @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ sP5
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( cM @ eigen__4 )
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( cN @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( cM @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( cN @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( cN @ eigen__6 )
=> ~ ( !! @ cG ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( !! @ cG ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP10
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( cN @ X1 )
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( cN @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( cM @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(cTHM80,conjecture,
( ( ~ ( ~ ( ~ ( !! @ cM )
=> ~ sP12 )
=> ~ ( ~ ( !! @ cM )
=> ~ sP4 ) )
=> ~ ( ~ sP4
=> ~ sP12 ) )
=> ( ~ ( ~ ( ~ ( !! @ cM )
=> ~ sP12 )
=> ~ sP1 )
=> ~ sP14 ) ) ).
thf(h1,negated_conjecture,
~ ( ( ~ ( ~ ( ~ ( !! @ cM )
=> ~ sP12 )
=> ~ ( ~ ( !! @ cM )
=> ~ sP4 ) )
=> ~ ( ~ sP4
=> ~ sP12 ) )
=> ( ~ ( ~ ( ~ ( !! @ cM )
=> ~ sP12 )
=> ~ sP1 )
=> ~ sP14 ) ),
inference(assume_negation,[status(cth)],[cTHM80]) ).
thf(h2,assumption,
( ~ ( ~ ( ~ ( !! @ cM )
=> ~ sP12 )
=> ~ ( ~ ( !! @ cM )
=> ~ sP4 ) )
=> ~ ( ~ sP4
=> ~ sP12 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( ~ ( ~ ( !! @ cM )
=> ~ sP12 )
=> ~ sP1 )
=> ~ sP14 ),
introduced(assumption,[]) ).
thf(h4,assumption,
( ~ ( ~ ( !! @ cM )
=> ~ sP12 )
=> ~ ( ~ ( !! @ cM )
=> ~ sP4 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ sP4
=> ~ sP12 ),
introduced(assumption,[]) ).
thf(h6,assumption,
( ~ ( !! @ cM )
=> ~ sP12 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( !! @ cM )
=> ~ sP4 ),
introduced(assumption,[]) ).
thf(h8,assumption,
!! @ cM,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( ~ ( ~ ( !! @ cM )
=> ~ sP12 )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP14,
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( ~ ( !! @ cM )
=> ~ sP12 ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP1,
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( !! @ cM ),
introduced(assumption,[]) ).
thf(h15,assumption,
sP12,
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP16,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP14
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP3
| ~ sP8
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP4
| sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(4,plain,
( ~ sP1
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP2
| sP16
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h16,h14,h15,h12,h13,h10,h11,h8,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,h16,h15,h13,h11]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h15,h12,h13,h10,h11,h8,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__0)],[h14,6,h16]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h10,h11,h8,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h12,7,h14,h15]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h8,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h10,8,h12,h13]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h3,9,h10,h11]) ).
thf(h17,assumption,
~ ( cG @ eigen__3 ),
introduced(assumption,[]) ).
thf(h18,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(11,plain,
( ~ sP14
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP11
| ~ sP15
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP4
| sP15 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(14,plain,
( ~ sP1
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP7
| sP9
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h18,h14,h15,h12,h13,h10,h11,h17,h9,h6,h4,h2,h3,h1,h0])],[11,12,13,14,15,h18,h15,h13,h11]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h15,h12,h13,h10,h11,h17,h9,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__4)],[h14,16,h18]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h10,h11,h17,h9,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h12,17,h14,h15]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h17,h9,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h10,18,h12,h13]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h9,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h3,19,h10,h11]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__3)],[h9,20,h17]) ).
thf(22,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h6,h4,h2,h3,h1,h0]),tab_imp(discharge,[h8]),tab_imp(discharge,[h9])],[h6,10,21,h8,h9]) ).
thf(h19,assumption,
sP4,
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( cM @ eigen__7 ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(23,plain,
( ~ sP1
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP6
| sP5
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h21,h14,h15,h12,h13,h10,h11,h20,h14,h19,h7,h4,h2,h3,h1,h0])],[23,24,h19,h21,h13]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h15,h12,h13,h10,h11,h20,h14,h19,h7,h4,h2,h3,h1,h0]),tab_negall(discharge,[h21]),tab_negall(eigenvar,eigen__8)],[h14,25,h21]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h10,h11,h20,h14,h19,h7,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h12,26,h14,h15]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h20,h14,h19,h7,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h10,27,h12,h13]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h14,h19,h7,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h3,28,h10,h11]) ).
thf(30,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h19,h7,h4,h2,h3,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__7)],[h14,29,h20]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h19])],[h7,30,h14,h19]) ).
thf(32,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_imp(discharge,[h6]),tab_imp(discharge,[h7])],[h4,22,31,h6,h7]) ).
thf(h22,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h23,assumption,
sP10,
introduced(assumption,[]) ).
thf(h24,assumption,
~ ( cM @ eigen__10 ),
introduced(assumption,[]) ).
thf(33,plain,
( ~ sP14
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP13
| ~ sP10
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h24,h14,h15,h12,h13,h10,h11,h23,h22,h15,h5,h2,h3,h1,h0])],[33,34,h23,h15,h11]) ).
thf(36,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h15,h12,h13,h10,h11,h23,h22,h15,h5,h2,h3,h1,h0]),tab_negall(discharge,[h24]),tab_negall(eigenvar,eigen__10)],[h14,35,h24]) ).
thf(37,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h10,h11,h23,h22,h15,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h12,36,h14,h15]) ).
thf(38,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h23,h22,h15,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h10,37,h12,h13]) ).
thf(39,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h23,h22,h15,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h3,38,h10,h11]) ).
thf(40,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h22,h15,h5,h2,h3,h1,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__9)],[h22,39,h23]) ).
thf(41,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h2,h3,h1,h0]),tab_negimp(discharge,[h22,h15])],[h5,40,h22,h15]) ).
thf(42,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h2,h3,h1,h0]),tab_imp(discharge,[h4]),tab_imp(discharge,[h5])],[h2,32,41,h4,h5]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,42,h2,h3]) ).
thf(44,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[43,h0]) ).
thf(0,theorem,
( ( ~ ( ~ ( ~ ( !! @ cM )
=> ~ sP12 )
=> ~ ( ~ ( !! @ cM )
=> ~ sP4 ) )
=> ~ ( ~ sP4
=> ~ sP12 ) )
=> ( ~ ( ~ ( ~ ( !! @ cM )
=> ~ sP12 )
=> ~ sP1 )
=> ~ sP14 ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[43,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO111^5 : 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
% 0.12/0.33 % Computer : n009.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 : Fri Jul 8 18:53:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % Mode: mode213
% 0.12/0.37 % Inferences: 35
% 0.12/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------