TSTP Solution File: ITP028^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP028^1 : TPTP v8.1.0. Released v7.5.0.
% 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 : Sun Jul 17 00:28:49 EDT 2022
% Result : Theorem 0.46s 0.65s
% Output : Proof 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 44
% Syntax : Number of formulae : 49 ( 9 unt; 14 typ; 1 def)
% Number of atoms : 90 ( 1 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 162 ( 34 ~; 16 |; 0 &; 74 @)
% ( 14 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 22 con; 0-2 aty)
% Number of variables : 5 ( 1 ^ 4 !; 0 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_set_set_a,type,
set_set_a: $tType ).
thf(ty_set_Pr204296108_a_a_e,type,
set_Pr204296108_a_a_e: $tType ).
thf(ty_set_a,type,
set_a: $tType ).
thf(ty_produc715398134_a_a_e,type,
produc715398134_a_a_e: $tType ).
thf(ty_produc1040928388_a_a_e,type,
produc1040928388_a_a_e: produc715398134_a_a_e > set_a ).
thf(ty_a3,type,
a3: set_a ).
thf(ty_member_set_a,type,
member_set_a: set_a > set_set_a > $o ).
thf(ty_a1,type,
a1: set_a ).
thf(ty_a2,type,
a2: set_a ).
thf(ty_eigen__1,type,
eigen__1: set_a ).
thf(ty_thesis,type,
thesis: $o ).
thf(ty_image_64240033_set_a,type,
image_64240033_set_a: ( produc715398134_a_a_e > set_a ) > set_Pr204296108_a_a_e > set_set_a ).
thf(ty_c,type,
c: set_Pr204296108_a_a_e ).
thf(ty_ord_less_eq_set_a,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(h0,assumption,
! [X1: set_a > $o,X2: set_a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: set_a] :
~ ( ~ ( ~ ( ( member_set_a @ X1 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
=> ~ ( ord_less_eq_set_a @ a1 @ X1 ) )
=> ~ ( ord_less_eq_set_a @ a2 @ X1 ) )
=> ~ ( ord_less_eq_set_a @ a3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: set_a] :
( ( member_set_a @ X1 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
=> ( ( ord_less_eq_set_a @ a1 @ X1 )
=> ( ( ord_less_eq_set_a @ a2 @ X1 )
=> ( ( ord_less_eq_set_a @ a3 @ X1 )
=> thesis ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ord_less_eq_set_a @ a3 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( ~ ( ( member_set_a @ eigen__1 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
=> ~ ( ord_less_eq_set_a @ a1 @ eigen__1 ) )
=> ~ ( ord_less_eq_set_a @ a2 @ eigen__1 ) )
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( ( member_set_a @ eigen__1 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
=> ~ ( ord_less_eq_set_a @ a1 @ eigen__1 ) )
=> ~ ( ord_less_eq_set_a @ a2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP2
=> thesis ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: set_a] :
( ~ ( ~ ( ( member_set_a @ X1 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
=> ~ ( ord_less_eq_set_a @ a1 @ X1 ) )
=> ~ ( ord_less_eq_set_a @ a2 @ X1 ) )
=> ~ ( ord_less_eq_set_a @ a3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( member_set_a @ eigen__1 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
=> ( ( ord_less_eq_set_a @ a1 @ eigen__1 )
=> ( ( ord_less_eq_set_a @ a2 @ eigen__1 )
=> sP5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( member_set_a @ eigen__1 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
=> ~ ( ord_less_eq_set_a @ a1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ord_less_eq_set_a @ a2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ord_less_eq_set_a @ a1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> thesis ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP10
=> ( sP9
=> sP5 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( member_set_a @ eigen__1 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP9
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(conj_1,conjecture,
sP11 ).
thf(h1,negated_conjecture,
~ sP11,
inference(assume_negation,[status(cth)],[conj_1]) ).
thf(1,plain,
( ~ sP5
| ~ sP2
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP14
| ~ sP9
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP12
| ~ sP10
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP7
| ~ sP13
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP1
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( sP8
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP8
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP4
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP4
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP3
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP3
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP6
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(fact_1__092_060open_062_092_060exists_062a_092_060in_062fst_A_096_AC_O_Aa1_A_092_060subseteq_062_Aa_A_092_060and_062_Aa2_A_092_060subseteq_062_Aa_A_092_060and_062_Aa3_A_092_060subseteq_062_Aa_092_060close_062,axiom,
~ sP6 ).
thf(conj_0,axiom,
sP1 ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,fact_1__092_060open_062_092_060exists_062a_092_060in_062fst_A_096_AC_O_Aa1_A_092_060subseteq_062_Aa_A_092_060and_062_Aa2_A_092_060subseteq_062_Aa_A_092_060and_062_Aa3_A_092_060subseteq_062_Aa_092_060close_062,conj_0,h1]) ).
thf(14,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[13,h0]) ).
thf(0,theorem,
sP11,
inference(contra,[status(thm),contra(discharge,[h1])],[13,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP028^1 : TPTP v8.1.0. Released v7.5.0.
% 0.12/0.12 % 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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jun 3 03:37:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.46/0.65 % SZS status Theorem
% 0.46/0.65 % Mode: mode84:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=2.:SINE_DEPTH=0
% 0.46/0.65 % Inferences: 3951
% 0.46/0.65 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------