TSTP Solution File: SWW473^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SWW473^1 : TPTP v8.1.0. Released v5.3.0.
% 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 : Thu Jul 21 01:21:54 EDT 2022
% Result : Theorem 184.06s 184.37s
% Output : Proof 184.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 78
% Syntax : Number of formulae : 83 ( 15 unt; 12 typ; 1 def)
% Number of atoms : 218 ( 12 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 286 ( 38 ~; 33 |; 0 &; 149 @)
% ( 32 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 43 usr; 36 con; 0-3 aty)
% Number of variables : 30 ( 1 ^ 29 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_x_a,type,
x_a: $tType ).
thf(ty_pname,type,
pname: $tType ).
thf(ty_member_a,type,
member_a: x_a > ( x_a > $o ) > $o ).
thf(ty_ord_less_eq_a_o,type,
ord_less_eq_a_o: ( x_a > $o ) > ( x_a > $o ) > $o ).
thf(ty_mgt_call,type,
mgt_call: pname > x_a ).
thf(ty_insert_a,type,
insert_a: x_a > ( x_a > $o ) > x_a > $o ).
thf(ty_eigen__1,type,
eigen__1: x_a ).
thf(ty_u,type,
u: pname > $o ).
thf(ty_pn,type,
pn: pname ).
thf(ty_image_pname_a,type,
image_pname_a: ( pname > x_a ) > ( pname > $o ) > x_a > $o ).
thf(ty_member_pname,type,
member_pname: pname > ( pname > $o ) > $o ).
thf(ty_g,type,
g: x_a > $o ).
thf(h0,assumption,
! [X1: x_a > $o,X2: x_a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: x_a] :
~ ( ( member_a @ X1 @ ( insert_a @ ( mgt_call @ pn ) @ g ) )
=> ( member_a @ X1 @ ( image_pname_a @ mgt_call @ u ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: x_a > $o,X2: x_a > $o] :
( ( ord_less_eq_a_o @ X1 @ X2 )
=> ( ( member_a @ eigen__1 @ X1 )
=> ( member_a @ eigen__1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: x_a > $o] :
( ( ord_less_eq_a_o @ g @ X1 )
=> ( ( member_a @ eigen__1 @ g )
=> ( member_a @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: pname > $o] :
( ( member_pname @ pn @ X1 )
=> ( member_a @ ( mgt_call @ pn ) @ ( image_pname_a @ mgt_call @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: x_a] :
( ( member_a @ X1 @ ( insert_a @ ( mgt_call @ pn ) @ g ) )
=> ( member_a @ X1 @ ( image_pname_a @ mgt_call @ u ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( member_pname @ pn @ u )
=> ( member_a @ ( mgt_call @ pn ) @ ( image_pname_a @ mgt_call @ u ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: pname > x_a,X2: pname,X3: pname > $o] :
( ( member_pname @ X2 @ X3 )
=> ( member_a @ ( X1 @ X2 ) @ ( image_pname_a @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP4
=> ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: x_a > $o] :
( ! [X2: x_a] :
( ( member_a @ X2 @ X1 )
=> ( member_a @ X2 @ ( image_pname_a @ mgt_call @ u ) ) )
=> ( ord_less_eq_a_o @ X1 @ ( image_pname_a @ mgt_call @ u ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: x_a,X2: x_a] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: pname,X2: pname > $o] :
( ( member_pname @ X1 @ X2 )
=> ( member_a @ ( mgt_call @ X1 ) @ ( image_pname_a @ mgt_call @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( member_a @ eigen__1 @ ( insert_a @ ( mgt_call @ pn ) @ g ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: x_a > $o] :
( ( member_a @ eigen__1 @ ( insert_a @ ( mgt_call @ pn ) @ X1 ) )
=> ( ( eigen__1
!= ( mgt_call @ pn ) )
=> ( member_a @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: x_a,X2: x_a > $o,X3: x_a > $o] :
( ( ord_less_eq_a_o @ X2 @ X3 )
=> ( ( member_a @ X1 @ X2 )
=> ( member_a @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__1
= ( mgt_call @ pn ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP15
=> ( ( mgt_call @ pn )
= eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: x_a,X2: x_a > $o] :
( ( member_a @ eigen__1 @ ( insert_a @ X1 @ X2 ) )
=> ( ( eigen__1 != X1 )
=> ( member_a @ eigen__1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: x_a > $o,X2: x_a > $o] :
( ! [X3: x_a] :
( ( member_a @ X3 @ X2 )
=> ( member_a @ X3 @ X1 ) )
=> ( ord_less_eq_a_o @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( image_pname_a @ mgt_call @ u )
= ( image_pname_a @ mgt_call @ u ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP11
=> ( ~ sP15
=> ( member_a @ eigen__1 @ g ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( member_a @ eigen__1 @ g ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: x_a] :
( ( eigen__1 = X1 )
=> ( X1 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( member_pname @ pn @ u ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( member_a @ eigen__1 @ ( image_pname_a @ mgt_call @ u ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( member_a @ ( mgt_call @ pn ) @ ( image_pname_a @ mgt_call @ u ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP13
=> ( sP21
=> sP24 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ~ sP15
=> sP21 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: x_a,X2: x_a,X3: x_a > $o] :
( ( member_a @ X1 @ ( insert_a @ X2 @ X3 ) )
=> ( ( X1 != X2 )
=> ( member_a @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ( mgt_call @ pn )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP11
=> sP24 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( sP21
=> sP24 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(conj_6,conjecture,
sP25 ).
thf(h1,negated_conjecture,
~ sP25,
inference(assume_negation,[status(cth)],[conj_6]) ).
thf(1,plain,
( ~ sP26
| sP24
| ~ sP30
| ~ sP19 ),
inference(mating_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP10
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP3
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP5
| ~ sP23
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP2
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP27
| ~ sP13
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP32
| ~ sP21
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP1
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP6
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP14
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
sP19,
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP16
| ~ sP15
| sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP22
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP9
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
sP9,
inference(eq_sym,[status(thm)],]) ).
thf(16,plain,
( ~ sP29
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP17
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP12
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP20
| ~ sP11
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP28
| sP15
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP31
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP31
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP4
| ~ sP31 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(24,plain,
( ~ sP18
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP8
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP7
| ~ sP4
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(fact_188_insertE,axiom,
sP29 ).
thf(fact_181_subsetD,axiom,
sP14 ).
thf(fact_261_imageI,axiom,
sP6 ).
thf(fact_290_subsetI,axiom,
sP18 ).
thf(conj_1,axiom,
sP13 ).
thf(conj_4,axiom,
sP23 ).
thf(27,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,fact_188_insertE,fact_181_subsetD,fact_261_imageI,fact_290_subsetI,conj_1,conj_4,h1]) ).
thf(28,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[27,h0]) ).
thf(0,theorem,
sP25,
inference(contra,[status(thm),contra(discharge,[h1])],[27,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW473^1 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n024.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 5 16:13:05 EDT 2022
% 0.12/0.34 % CPUTime :
% 184.06/184.37 % SZS status Theorem
% 184.06/184.37 % Mode: mode454:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=3.:SINE_DEPTH=0
% 184.06/184.37 % Inferences: 2356
% 184.06/184.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------