TSTP Solution File: SYO310^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO310^5 : 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 : n027.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 19:31:23 EDT 2022
% Result : Theorem 9.79s 10.01s
% Output : Proof 9.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 53
% Syntax : Number of formulae : 63 ( 21 unt; 1 typ; 1 def)
% Number of atoms : 176 ( 22 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 164 ( 78 ~; 27 |; 0 &; 22 @)
% ( 20 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 23 con; 0-2 aty)
% Number of variables : 31 ( 21 ^ 10 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__5,type,
eigen__5: $o > $o ).
thf(h0,assumption,
! [X1: $o > $o,X2: $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $o] : ( $false != $false ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ( $false
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ~ $false
=> ~ $false )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ~ $false )
= ( ~ $false
=> ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( ~ ( ( ( ^ [X1: $o] : ~ $false )
= ( ^ [X1: $o] : ~ $false ) )
=> ( ( ^ [X1: $o] : $false )
!= ( ^ [X1: $o] : $false ) ) )
=> ( ( ^ [X1: $o] : ~ $false )
= ( ^ [X1: $o] : $false ) ) )
=> ( ( ^ [X1: $o] : $false )
= ( ^ [X1: $o] : ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( $false = $false ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> $false ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( ^ [X1: $o] : ~ sP6 )
= ( ^ [X1: $o] : sP6 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__5
@ ( ~ sP6
=> ~ sP6 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__5 @ ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( ^ [X1: $o] : sP6 )
= ( ^ [X1: $o] : sP6 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( ~ sP6 )
= sP6 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ ( ( ( ^ [X1: $o] : ~ sP6 )
= ( ^ [X1: $o] : ~ sP6 ) )
=> ~ sP10 )
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( ( ^ [X1: $o] : ~ sP6 )
= ( ^ [X1: $o] : ~ sP6 ) )
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ sP6
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( ^ [X1: $o] : ~ sP6 )
= ( ^ [X1: $o] : ~ sP6 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $o > $o > $o] :
( ~ ( ~ ( ( X1 @ ~ sP6 @ ~ sP6 )
=> ~ ( X1 @ sP6 @ sP6 ) )
=> ( X1 @ sP6 @ ~ sP6 ) )
=> ( X1 @ ~ sP6 @ sP6 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $o] : sP5 ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $o] : sP1 ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( ^ [X1: $o] : sP6 )
= ( ^ [X1: $o] : ~ sP6 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $o] : sP11 ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(cOMEGA_EXAMPLE,conjecture,
~ ( ~ sP16
=> ~ ! [X1: $o > $o] :
( ( X1 @ ~ sP6 )
= ( X1 @ sP14 ) ) ) ).
thf(h1,negated_conjecture,
( ~ sP16
=> ~ ! [X1: $o > $o] :
( ( X1 @ ~ sP6 )
= ( X1 @ sP14 ) ) ),
inference(assume_negation,[status(cth)],[cOMEGA_EXAMPLE]) ).
thf(h2,assumption,
sP16,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $o > $o] :
( ( X1 @ ~ sP6 )
= ( X1 @ sP14 ) ),
introduced(assumption,[]) ).
thf(1,plain,
sP15,
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
sP5,
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP17
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(4,plain,
( sP10
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP13
| ~ sP15
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP20
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP7
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP12
| sP13
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP18
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP19
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP1
| sP6
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
~ sP6,
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP11
| sP6
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP4
| sP12
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP16
| sP4 ),
inference(all_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(h4,assumption,
sP9 != sP8,
introduced(assumption,[]) ).
thf(h5,assumption,
sP9,
introduced(assumption,[]) ).
thf(h6,assumption,
sP8,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(17,plain,
~ sP6,
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP14
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP3
| sP6
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP9
| sP8
| ~ sP3 ),
inference(mating_rule,[status(thm)],]) ).
thf(21,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h6,h4,h3,h1,h0])],[17,18,19,20,h5,h6]) ).
thf(22,plain,
( sP14
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
~ sP6,
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( sP2
| ~ sP14
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP8
| sP9
| ~ sP2 ),
inference(mating_rule,[status(thm)],]) ).
thf(26,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h4,h3,h1,h0])],[22,23,24,25,h7,h8]) ).
thf(27,plain,
$false,
inference(tab_be,[status(thm),assumptions([h4,h3,h1,h0]),tab_be(discharge,[h5,h6]),tab_be(discharge,[h7,h8])],[h4,21,26,h5,h6,h7,h8]) ).
thf(28,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__5)],[h3,27,h4]) ).
thf(29,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h2]),tab_imp(discharge,[h3])],[h1,16,28,h2,h3]) ).
thf(30,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[29,h0]) ).
thf(0,theorem,
~ ( ~ sP16
=> ~ ! [X1: $o > $o] :
( ( X1 @ ~ sP6 )
= ( X1 @ sP14 ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[29,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYO310^5 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 9 08:47:16 EDT 2022
% 0.13/0.34 % CPUTime :
% 9.79/10.01 % SZS status Theorem
% 9.79/10.01 % Mode: mode495
% 9.79/10.01 % Inferences: 122
% 9.79/10.01 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------