TSTP Solution File: SYN036^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYN036^5 : 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 : n011.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 11:40:36 EDT 2022
% Result : Theorem 1.95s 2.20s
% Output : Proof 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 110
% Syntax : Number of formulae : 122 ( 15 unt; 11 typ; 8 def)
% Number of atoms : 318 ( 40 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 314 ( 101 ~; 84 |; 0 &; 73 @)
% ( 40 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 52 usr; 52 con; 0-2 aty)
% ( 3 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 36 ( 8 ^ 28 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_cP,type,
cP: $i > $o ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__15,type,
eigen__15: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_cQ,type,
cQ: $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
~ ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__15,definition,
( eigen__15
= ( eps__0
@ ^ [X1: $i] :
( ( cQ @ eigen__0 )
!= ( cQ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__15])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ~ ! [X2: $i] :
( ( cP @ X1 )
= ( cP @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ~ ! [X2: $i] :
( ( cQ @ X1 )
= ( cQ @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: $i] :
( ( cP @ eigen__0 )
!= ( cP @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $i] :
~ ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
~ ( cP @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( cP @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ( cP @ eigen__2 )
= sP2 )
=> ~ ( cP @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
~ ! [X2: $i] :
( ( cQ @ X1 )
= ( cQ @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( cQ @ eigen__0 )
= ( cQ @ eigen__15 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( cP @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( cQ @ eigen__4 )
= ( cQ @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( cQ @ eigen__0 )
= ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $o] :
( ( X1
= ( cP @ eigen__6 ) )
=> X1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( !! @ cQ ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( cP @ eigen__6 )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( cP @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( sP12
= ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( sP12
= ( cP @ eigen__6 ) )
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $o] :
( ( X1 = sP2 )
=> ~ X1 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $o > $o] :
( ( X1 @ ( cP @ eigen__6 ) )
=> ! [X2: $o] :
( ( X2
= ( cP @ eigen__6 ) )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( cQ @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( cQ @ eigen__4 )
= ( cQ @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ( cP @ eigen__0 )
= ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP12 = sP2 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $o,X2: $o > $o] :
( ( X2 @ X1 )
=> ! [X3: $o] :
( ( X3 = X1 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( ~ sP4 )
= ( ( ~ sP1 )
= sP10 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( cP @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( cQ @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( ~ sP1 )
= sP10 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( cQ @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( ~ ! [X1: $i] :
~ ( cQ @ X1 ) )
= ( !! @ cP ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( !! @ cP ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP12
= ( cP @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i] :
~ ( cQ @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ( ( ~ ! [X1: $i] :
~ ! [X2: $i] :
( ( cP @ X1 )
= ( cP @ X2 ) ) )
= sP27 )
= sP22 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ sP2
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i] :
( sP26
= ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( sP23 = sP6 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ( ~ ! [X1: $i] :
~ ! [X2: $i] :
( ( cP @ X1 )
= ( cP @ X2 ) ) )
= sP27 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( cP @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: $i] :
~ ! [X2: $i] :
( ( cP @ X1 )
= ( cP @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( cQ @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( cQ @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: $o > $o] :
( ( X1 @ sP2 )
=> ! [X2: $o] :
( ( X2 = sP2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(cX2129,conjecture,
sP31 ).
thf(h1,negated_conjecture,
~ sP31,
inference(assume_negation,[status(cth)],[cX2129]) ).
thf(1,plain,
( ~ sP30
| ~ sP39 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP10
| sP39 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( sP5
| ~ sP38
| ~ sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP5
| sP38
| sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP8
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__15]) ).
thf(6,plain,
( ~ sP28
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP1
| ~ sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( sP34
| ~ sP23
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP34
| sP23
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP19
| ~ sP34 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(11,plain,
( ~ sP18
| ~ sP26
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP33
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP13
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP3
| ~ sP20
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP15
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP32
| sP2
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP40
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP21
| sP40 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP7
| sP26
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP33
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP13
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP14
| ~ sP29
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP9
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP11
| ~ sP36
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP16
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP21
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( sP1
| sP36 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(28,plain,
( sP10
| ~ sP24 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(29,plain,
( sP25
| sP1
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( sP25
| ~ sP1
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( sP22
| sP4
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP22
| ~ sP4
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
sP21,
inference(eq_ind_sym,[status(thm)],]) ).
thf(34,plain,
( sP4
| sP33 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(35,plain,
( ~ sP10
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP1
| ~ sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP25
| sP1
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP25
| ~ sP1
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP4
| ~ sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP22
| sP4
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP22
| ~ sP4
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( sP28
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(43,plain,
( sP27
| sP30
| ~ sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( sP27
| ~ sP30
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( ~ sP35
| sP37
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(46,plain,
( ~ sP35
| ~ sP37
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( sP37
| sP13 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(48,plain,
( sP30
| sP17 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(49,plain,
( ~ sP28
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP30
| ~ sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(51,plain,
( ~ sP27
| sP30
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(52,plain,
( ~ sP27
| ~ sP30
| ~ sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(53,plain,
( ~ sP37
| ~ sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(54,plain,
( sP35
| sP37
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(55,plain,
( sP35
| ~ sP37
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(56,plain,
( sP31
| ~ sP35
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(57,plain,
( sP31
| sP35
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(58,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,h1]) ).
thf(59,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[58,h0]) ).
thf(0,theorem,
sP31,
inference(contra,[status(thm),contra(discharge,[h1])],[58,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN036^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n011.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jul 12 03:33:58 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.95/2.20 % SZS status Theorem
% 1.95/2.20 % Mode: mode506
% 1.95/2.20 % Inferences: 20535
% 1.95/2.20 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------