TSTP Solution File: SYO376^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO376^5 : 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 19:31:44 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 86
% Syntax : Number of formulae : 96 ( 14 unt; 6 typ; 3 def)
% Number of atoms : 283 ( 26 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 255 ( 74 ~; 59 |; 0 &; 54 @)
% ( 35 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 42 usr; 40 con; 0-2 aty)
% Number of variables : 17 ( 8 ^ 9 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cG,type,
cG: $o > $o ).
thf(ty_eigen__2,type,
eigen__2: $o ).
thf(ty_cP,type,
cP: ( $o > $o ) > $o ).
thf(ty_eigen__1,type,
eigen__1: $o ).
thf(ty_eigen__0,type,
eigen__0: $o ).
thf(ty_cF,type,
cF: $o > $o ).
thf(h0,assumption,
! [X1: $o > $o,X2: $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $o] :
( ( cG @ X1 )
!= ( ( cF @ X1 )
=> ( cG @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $o] :
( ( cG @ X1 )
!= ( ~ ( cF @ X1 )
=> ( cG @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $o] :
( ( cF @ X1 )
!= ( ~ ( cF @ X1 )
=> ( cG @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ( cP
@ ^ [X1: $o] :
( ~ ( cF @ X1 )
=> ( cG @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $o] :
( ( cG @ X1 )
= ( ( cF @ X1 )
=> ( cG @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( cF
= ( ^ [X1: $o] :
( ~ ( cF @ X1 )
=> ( cG @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> eigen__2 ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( cG @ eigen__1 )
= ( ( cF @ eigen__1 )
=> ( cG @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> eigen__1 ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( cF @ sP7 )
=> ( cG @ sP7 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( cG @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP7 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( cG
= ( ^ [X1: $o] :
( ~ ( cF @ X1 )
=> ( cG @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( cF @ sP4 )
= ( ~ ( cF @ sP4 )
=> ( cG @ sP4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( cF @ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( cF @ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__0 = sP4 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> eigen__0 ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ ( cF @ sP16 )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( cG
= ( ^ [X1: $o] :
( ( cF @ X1 )
=> ( cG @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP4 = sP7 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $o,X2: $o] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( cF @ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $o] :
( ( sP4 = X1 )
=> ( X1 = sP4 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP4 = sP16 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( cP @ cG ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( cP
@ ^ [X1: $o] :
( ( cF @ X1 )
=> ( cG @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( cG @ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ sP14
=> ( cG @ sP4 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( cG @ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $o] :
( ( sP7 = X1 )
=> ( X1 = sP7 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( sP23
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $o] :
( ( cG @ X1 )
= ( ~ ( cF @ X1 )
=> ( cG @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( sP9 = sP17 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( cP @ cF ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: $o] :
( ( cF @ X1 )
= ( ~ ( cF @ X1 )
=> ( cG @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( sP10
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(cTHM627,conjecture,
( ~ ( sP33
=> ~ sP24 )
=> ( ~ sP1
=> sP25 ) ) ).
thf(h1,negated_conjecture,
~ ( ~ ( sP33
=> ~ sP24 )
=> ( ~ sP1
=> sP25 ) ),
inference(assume_negation,[status(cth)],[cTHM627]) ).
thf(h2,assumption,
~ ( sP33
=> ~ sP24 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ sP1
=> sP25 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP33,
introduced(assumption,[]) ).
thf(h5,assumption,
sP24,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP25,
introduced(assumption,[]) ).
thf(1,plain,
( sP23
| ~ sP4
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP23
| sP4
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP30
| ~ sP23
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP22
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( sP19
| ~ sP4
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP19
| sP4
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP20
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( sP10
| ~ sP7
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP10
| sP7
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP35
| ~ sP10
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP29
| sP35 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP20
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( sP27
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP21
| sP14
| ~ sP15 ),
inference(mating_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP28
| sP26
| ~ sP19 ),
inference(mating_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP27
| sP14
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP8
| ~ sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP21
| sP13
| ~ sP6 ),
inference(mating_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP8
| ~ sP13
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP17
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP17
| sP21
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP12
| ~ sP14
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP12
| sP14
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( sP34
| ~ sP12 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(25,plain,
( sP5
| ~ sP26
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP5
| sP26
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP2
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(28,plain,
( sP32
| ~ sP9
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( sP32
| sP9
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
sP20,
inference(eq_sym,[status(thm)],]) ).
thf(31,plain,
( sP31
| ~ sP32 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(32,plain,
( sP3
| ~ sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( sP18
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( sP11
| ~ sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP33
| sP1
| ~ sP3 ),
inference(mating_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP24
| sP25
| ~ sP18 ),
inference(mating_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP24
| sP1
| ~ sP11 ),
inference(mating_rule,[status(thm)],]) ).
thf(38,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,h4,h5,h6,h7]) ).
thf(39,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h3,38,h6,h7]) ).
thf(40,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,39,h4,h5]) ).
thf(41,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,40,h2,h3]) ).
thf(42,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[41,h0]) ).
thf(0,theorem,
( ~ ( sP33
=> ~ sP24 )
=> ( ~ sP1
=> sP25 ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[41,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO376^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n009.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 01:46:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % Mode: mode213
% 0.13/0.39 % Inferences: 82
% 0.13/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------