TSTP Solution File: ITP028^1 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP028^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -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 : 300s
% DateTime : Thu Aug 31 04:01:35 EDT 2023
% Result : Theorem 0.19s 0.48s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 200
% Syntax : Number of formulae : 247 ( 85 unt; 21 typ; 1 def)
% Number of atoms : 494 ( 1 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 655 ( 182 ~; 79 |; 0 &; 206 @)
% ( 70 <=>; 118 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 90 ( 88 usr; 85 con; 0-2 aty)
% Number of variables : 5 ( 1 ^; 4 !; 0 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_produc715398134_a_a_e,type,
produc715398134_a_a_e: $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_set_set_a,type,
set_set_a: $tType ).
thf(ty_c,type,
c: set_Pr204296108_a_a_e ).
thf(ty_member_set_a,type,
member_set_a: set_a > set_set_a > $o ).
thf(ty_a2,type,
a2: set_a ).
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_eigen__7,type,
eigen__7: set_a ).
thf(ty_ord_less_eq_set_a,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(ty_eigen__4,type,
eigen__4: set_a ).
thf(ty_eigen__2,type,
eigen__2: set_a ).
thf(ty_a3,type,
a3: set_a ).
thf(ty_eigen__6,type,
eigen__6: set_a ).
thf(ty_a1,type,
a1: set_a ).
thf(ty_eigen__3,type,
eigen__3: set_a ).
thf(ty_thesis,type,
thesis: $o ).
thf(ty_eigen__0,type,
eigen__0: set_a ).
thf(ty_eigen__1,type,
eigen__1: set_a ).
thf(ty_eigen__5,type,
eigen__5: set_a ).
thf(ty_produc1040928388_a_a_e,type,
produc1040928388_a_a_e: produc715398134_a_a_e > set_a ).
thf(h0,assumption,
! [X1: set_a > $o,X2: set_a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( 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__7])]) ).
thf(sP1,plain,
( sP1
<=> ( ord_less_eq_set_a @ a3 @ eigen__0 ) ),
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
<=> ( ( ord_less_eq_set_a @ a1 @ eigen__5 )
=> ( ( ord_less_eq_set_a @ a2 @ eigen__5 )
=> ( ( ord_less_eq_set_a @ a3 @ eigen__5 )
=> thesis ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ord_less_eq_set_a @ a1 @ eigen__3 )
=> ( ( ord_less_eq_set_a @ a2 @ eigen__3 )
=> ( ( ord_less_eq_set_a @ a3 @ eigen__3 )
=> thesis ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( member_set_a @ eigen__5 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP2
=> thesis ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ord_less_eq_set_a @ a2 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( member_set_a @ eigen__6 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
=> ( ( ord_less_eq_set_a @ a1 @ eigen__6 )
=> ( sP7
=> ( ( ord_less_eq_set_a @ a3 @ eigen__6 )
=> thesis ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ord_less_eq_set_a @ a1 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( ord_less_eq_set_a @ a2 @ eigen__0 )
=> ( sP1
=> thesis ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ord_less_eq_set_a @ a1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( member_set_a @ eigen__4 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP9
=> ( sP7
=> ( ( ord_less_eq_set_a @ a3 @ eigen__6 )
=> thesis ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( member_set_a @ eigen__0 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ord_less_eq_set_a @ a3 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP11
=> ( ( ord_less_eq_set_a @ a2 @ eigen__1 )
=> sP6 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ord_less_eq_set_a @ a3 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP12
=> ( ( ord_less_eq_set_a @ a1 @ eigen__4 )
=> ( ( ord_less_eq_set_a @ a2 @ eigen__4 )
=> ( ( ord_less_eq_set_a @ a3 @ eigen__4 )
=> thesis ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP14
=> ( ( ord_less_eq_set_a @ a1 @ eigen__0 )
=> sP10 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ord_less_eq_set_a @ a1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( member_set_a @ eigen__7 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
=> ( ( ord_less_eq_set_a @ a1 @ eigen__7 )
=> ( ( ord_less_eq_set_a @ a2 @ eigen__7 )
=> ( ( ord_less_eq_set_a @ a3 @ eigen__7 )
=> thesis ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ord_less_eq_set_a @ a2 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP1
=> thesis ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ord_less_eq_set_a @ a3 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP5
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( member_set_a @ eigen__1 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( member_set_a @ eigen__3 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ( ord_less_eq_set_a @ a2 @ eigen__7 )
=> ( ( ord_less_eq_set_a @ a3 @ eigen__7 )
=> thesis ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ord_less_eq_set_a @ a2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ord_less_eq_set_a @ a1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ( ord_less_eq_set_a @ a1 @ eigen__2 )
=> ( sP22
=> ( sP17
=> thesis ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( sP29
=> ( sP24
=> thesis ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( sP26
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ( ord_less_eq_set_a @ a3 @ eigen__5 )
=> thesis ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> thesis ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ( ord_less_eq_set_a @ a1 @ eigen__0 )
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ( ord_less_eq_set_a @ a1 @ eigen__7 )
=> sP28 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ( member_set_a @ eigen__2 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
=> sP31 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ord_less_eq_set_a @ a2 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ord_less_eq_set_a @ a3 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( sP7
=> ( sP15
=> sP35 ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( sP17
=> sP35 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( sP24
=> sP35 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( ord_less_eq_set_a @ a2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( member_set_a @ eigen__6 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ord_less_eq_set_a @ a1 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ! [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 )
=> sP35 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( ord_less_eq_set_a @ a2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( ord_less_eq_set_a @ a2 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( sP20
=> ( sP49
=> ( ( ord_less_eq_set_a @ a3 @ eigen__4 )
=> sP35 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( ord_less_eq_set_a @ a2 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( sP49
=> ( ( ord_less_eq_set_a @ a3 @ eigen__4 )
=> sP35 ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( sP44
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( ord_less_eq_set_a @ a3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( sP15
=> sP35 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( sP22
=> sP42 ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( sP54
=> sP35 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( sP51
=> sP34 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( ord_less_eq_set_a @ a1 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( sP40
=> sP35 ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ! [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,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( ( member_set_a @ eigen__7 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
=> ~ sP46 ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( sP27
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ( ~ ( ~ sP62
=> ~ sP39 )
=> ~ sP40 ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( ord_less_eq_set_a @ a1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( ord_less_eq_set_a @ a1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ( ~ sP62
=> ~ sP39 ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ( member_set_a @ eigen__2 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( ord_less_eq_set_a @ a3 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ( member_set_a @ eigen__7 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(conj_1,conjecture,
sP35 ).
thf(h1,negated_conjecture,
~ sP35,
inference(assume_negation,[status(cth)],[conj_1]) ).
thf(h2,assumption,
ord_less_eq_set_a @ a2 @ a3,
introduced(assumption,[]) ).
thf(h3,assumption,
ord_less_eq_set_a @ a3 @ a2,
introduced(assumption,[]) ).
thf(h4,assumption,
ord_less_eq_set_a @ a1 @ a3,
introduced(assumption,[]) ).
thf(h5,assumption,
ord_less_eq_set_a @ a3 @ a1,
introduced(assumption,[]) ).
thf(h6,assumption,
ord_less_eq_set_a @ a1 @ a2,
introduced(assumption,[]) ).
thf(h7,assumption,
ord_less_eq_set_a @ a2 @ a1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP60
| ~ sP40
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP28
| ~ sP39
| sP60 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP37
| ~ sP46
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP21
| ~ sP70
| sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP47
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( sP62
| sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP62
| sP70 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP67
| sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP67
| ~ sP62 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP64
| sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP64
| ~ sP67 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP61
| ~ sP64 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(conj_0,axiom,
sP47 ).
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,
~ sP61 ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h1,conj_0,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]) ).
thf(h8,assumption,
~ ( ~ ( ~ ( sP45
=> ~ sP9 )
=> ~ sP7 )
=> ~ sP15 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ( sP45
=> ~ sP9 )
=> ~ sP7 ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP15,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( sP45
=> ~ sP9 ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP7,
introduced(assumption,[]) ).
thf(h13,assumption,
sP45,
introduced(assumption,[]) ).
thf(h14,assumption,
sP9,
introduced(assumption,[]) ).
thf(14,plain,
( ~ sP55
| ~ sP15
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP41
| ~ sP7
| sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP13
| ~ sP9
| sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP8
| ~ sP45
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP47
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h14,h11,h12,h9,h10,h8,h7,h4,h2,h1,h0])],[14,15,16,17,18,h1,conj_0,h13,h14,h12,h10]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h9,h10,h8,h7,h4,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h11,19,h13,h14]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h8,h7,h4,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,20,h11,h12]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h7,h4,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,21,h9,h10]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h4,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__6)],[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_062,22,h8]) ).
thf(fact_2__092_060open_062a1_A_092_060subseteq_062_Aa2_A_092_060or_062_Aa2_A_092_060subseteq_062_Aa1_092_060close_062,axiom,
( ~ ( ord_less_eq_set_a @ a1 @ a2 )
=> ( ord_less_eq_set_a @ a2 @ a1 ) ) ).
thf(24,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h4,h2,h1,h0]),tab_imp(discharge,[h6]),tab_imp(discharge,[h7])],[fact_2__092_060open_062a1_A_092_060subseteq_062_Aa2_A_092_060or_062_Aa2_A_092_060subseteq_062_Aa1_092_060close_062,13,23,h6,h7]) ).
thf(h15,assumption,
~ ( ~ ( ~ ( sP5
=> ~ sP59 )
=> ~ sP51 )
=> ~ sP69 ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ ( ~ ( sP5
=> ~ sP59 )
=> ~ sP51 ),
introduced(assumption,[]) ).
thf(h17,assumption,
sP69,
introduced(assumption,[]) ).
thf(h18,assumption,
~ ( sP5
=> ~ sP59 ),
introduced(assumption,[]) ).
thf(h19,assumption,
sP51,
introduced(assumption,[]) ).
thf(h20,assumption,
sP5,
introduced(assumption,[]) ).
thf(h21,assumption,
sP59,
introduced(assumption,[]) ).
thf(25,plain,
( ~ sP34
| ~ sP69
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP58
| ~ sP51
| sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP3
| ~ sP59
| sP58 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP25
| ~ sP5
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP47
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h20,h21,h18,h19,h16,h17,h15,h6,h5,h2,h1,h0])],[25,26,27,28,29,h1,conj_0,h20,h21,h19,h17]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h19,h16,h17,h15,h6,h5,h2,h1,h0]),tab_negimp(discharge,[h20,h21])],[h18,30,h20,h21]) ).
thf(32,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h17,h15,h6,h5,h2,h1,h0]),tab_negimp(discharge,[h18,h19])],[h16,31,h18,h19]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h6,h5,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,32,h16,h17]) ).
thf(34,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h5,h2,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__5)],[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_062,33,h15]) ).
thf(h22,assumption,
~ ( ~ ( ~ ( sP12
=> ~ sP20 )
=> ~ sP49 )
=> ~ sP54 ),
introduced(assumption,[]) ).
thf(h23,assumption,
~ ( ~ ( sP12
=> ~ sP20 )
=> ~ sP49 ),
introduced(assumption,[]) ).
thf(h24,assumption,
sP54,
introduced(assumption,[]) ).
thf(h25,assumption,
~ ( sP12
=> ~ sP20 ),
introduced(assumption,[]) ).
thf(h26,assumption,
sP49,
introduced(assumption,[]) ).
thf(h27,assumption,
sP12,
introduced(assumption,[]) ).
thf(h28,assumption,
sP20,
introduced(assumption,[]) ).
thf(35,plain,
( ~ sP57
| ~ sP54
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP52
| ~ sP49
| sP57 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP50
| ~ sP20
| sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP18
| ~ sP12
| sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP47
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(40,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h27,h28,h25,h26,h23,h24,h22,h7,h5,h2,h1,h0])],[35,36,37,38,39,h1,conj_0,h27,h28,h26,h24]) ).
thf(41,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h25,h26,h23,h24,h22,h7,h5,h2,h1,h0]),tab_negimp(discharge,[h27,h28])],[h25,40,h27,h28]) ).
thf(42,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h23,h24,h22,h7,h5,h2,h1,h0]),tab_negimp(discharge,[h25,h26])],[h23,41,h25,h26]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h22,h7,h5,h2,h1,h0]),tab_negimp(discharge,[h23,h24])],[h22,42,h23,h24]) ).
thf(44,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h5,h2,h1,h0]),tab_negall(discharge,[h22]),tab_negall(eigenvar,eigen__4)],[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_062,43,h22]) ).
thf(45,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h2,h1,h0]),tab_imp(discharge,[h6]),tab_imp(discharge,[h7])],[fact_2__092_060open_062a1_A_092_060subseteq_062_Aa2_A_092_060or_062_Aa2_A_092_060subseteq_062_Aa1_092_060close_062,34,44,h6,h7]) ).
thf(fact_3__092_060open_062a1_A_092_060subseteq_062_Aa3_A_092_060or_062_Aa3_A_092_060subseteq_062_Aa1_092_060close_062,axiom,
( ~ ( ord_less_eq_set_a @ a1 @ a3 )
=> ( ord_less_eq_set_a @ a3 @ a1 ) ) ).
thf(46,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h2,h1,h0]),tab_imp(discharge,[h4]),tab_imp(discharge,[h5])],[fact_3__092_060open_062a1_A_092_060subseteq_062_Aa3_A_092_060or_062_Aa3_A_092_060subseteq_062_Aa1_092_060close_062,24,45,h4,h5]) ).
thf(h29,assumption,
~ ( ~ ( ~ ( sP27
=> ~ sP30 )
=> ~ sP29 )
=> ~ sP24 ),
introduced(assumption,[]) ).
thf(h30,assumption,
~ ( ~ ( sP27
=> ~ sP30 )
=> ~ sP29 ),
introduced(assumption,[]) ).
thf(h31,assumption,
sP24,
introduced(assumption,[]) ).
thf(h32,assumption,
~ ( sP27
=> ~ sP30 ),
introduced(assumption,[]) ).
thf(h33,assumption,
sP29,
introduced(assumption,[]) ).
thf(h34,assumption,
sP27,
introduced(assumption,[]) ).
thf(h35,assumption,
sP30,
introduced(assumption,[]) ).
thf(47,plain,
( ~ sP43
| ~ sP24
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP32
| ~ sP29
| sP43 ),
inference(prop_rule,[status(thm)],]) ).
thf(49,plain,
( ~ sP4
| ~ sP30
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP63
| ~ sP27
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(51,plain,
( ~ sP47
| sP63 ),
inference(all_rule,[status(thm)],]) ).
thf(52,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h34,h35,h32,h33,h30,h31,h29,h6,h4,h3,h1,h0])],[47,48,49,50,51,h1,conj_0,h34,h35,h33,h31]) ).
thf(53,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h32,h33,h30,h31,h29,h6,h4,h3,h1,h0]),tab_negimp(discharge,[h34,h35])],[h32,52,h34,h35]) ).
thf(54,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h30,h31,h29,h6,h4,h3,h1,h0]),tab_negimp(discharge,[h32,h33])],[h30,53,h32,h33]) ).
thf(55,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h29,h6,h4,h3,h1,h0]),tab_negimp(discharge,[h30,h31])],[h29,54,h30,h31]) ).
thf(56,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h4,h3,h1,h0]),tab_negall(discharge,[h29]),tab_negall(eigenvar,eigen__3)],[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_062,55,h29]) ).
thf(h36,assumption,
~ ( ~ ( ~ ( sP68
=> ~ sP66 )
=> ~ sP22 )
=> ~ sP17 ),
introduced(assumption,[]) ).
thf(h37,assumption,
~ ( ~ ( sP68
=> ~ sP66 )
=> ~ sP22 ),
introduced(assumption,[]) ).
thf(h38,assumption,
sP17,
introduced(assumption,[]) ).
thf(h39,assumption,
~ ( sP68
=> ~ sP66 ),
introduced(assumption,[]) ).
thf(h40,assumption,
sP22,
introduced(assumption,[]) ).
thf(h41,assumption,
sP68,
introduced(assumption,[]) ).
thf(h42,assumption,
sP66,
introduced(assumption,[]) ).
thf(57,plain,
( ~ sP42
| ~ sP17
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(58,plain,
( ~ sP56
| ~ sP22
| sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(59,plain,
( ~ sP31
| ~ sP66
| sP56 ),
inference(prop_rule,[status(thm)],]) ).
thf(60,plain,
( ~ sP38
| ~ sP68
| sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(61,plain,
( ~ sP47
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(62,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h41,h42,h39,h40,h37,h38,h36,h7,h4,h3,h1,h0])],[57,58,59,60,61,h1,conj_0,h41,h42,h40,h38]) ).
thf(63,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h39,h40,h37,h38,h36,h7,h4,h3,h1,h0]),tab_negimp(discharge,[h41,h42])],[h39,62,h41,h42]) ).
thf(64,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h37,h38,h36,h7,h4,h3,h1,h0]),tab_negimp(discharge,[h39,h40])],[h37,63,h39,h40]) ).
thf(65,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h36,h7,h4,h3,h1,h0]),tab_negimp(discharge,[h37,h38])],[h36,64,h37,h38]) ).
thf(66,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h4,h3,h1,h0]),tab_negall(discharge,[h36]),tab_negall(eigenvar,eigen__2)],[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_062,65,h36]) ).
thf(67,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h4,h3,h1,h0]),tab_imp(discharge,[h6]),tab_imp(discharge,[h7])],[fact_2__092_060open_062a1_A_092_060subseteq_062_Aa2_A_092_060or_062_Aa2_A_092_060subseteq_062_Aa1_092_060close_062,56,66,h6,h7]) ).
thf(h43,assumption,
~ ( ~ ( ~ ( sP26
=> ~ sP11 )
=> ~ sP44 )
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h44,assumption,
~ ( ~ ( sP26
=> ~ sP11 )
=> ~ sP44 ),
introduced(assumption,[]) ).
thf(h45,assumption,
sP2,
introduced(assumption,[]) ).
thf(h46,assumption,
~ ( sP26
=> ~ sP11 ),
introduced(assumption,[]) ).
thf(h47,assumption,
sP44,
introduced(assumption,[]) ).
thf(h48,assumption,
sP26,
introduced(assumption,[]) ).
thf(h49,assumption,
sP11,
introduced(assumption,[]) ).
thf(68,plain,
( ~ sP6
| ~ sP2
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(69,plain,
( ~ sP53
| ~ sP44
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(70,plain,
( ~ sP16
| ~ sP11
| sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(71,plain,
( ~ sP33
| ~ sP26
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(72,plain,
( ~ sP47
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(73,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h48,h49,h46,h47,h44,h45,h43,h6,h5,h3,h1,h0])],[68,69,70,71,72,h1,conj_0,h48,h49,h47,h45]) ).
thf(74,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h46,h47,h44,h45,h43,h6,h5,h3,h1,h0]),tab_negimp(discharge,[h48,h49])],[h46,73,h48,h49]) ).
thf(75,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h44,h45,h43,h6,h5,h3,h1,h0]),tab_negimp(discharge,[h46,h47])],[h44,74,h46,h47]) ).
thf(76,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h43,h6,h5,h3,h1,h0]),tab_negimp(discharge,[h44,h45])],[h43,75,h44,h45]) ).
thf(77,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h5,h3,h1,h0]),tab_negall(discharge,[h43]),tab_negall(eigenvar,eigen__1)],[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_062,76,h43]) ).
thf(h50,assumption,
~ ( ~ ( ~ ( sP14
=> ~ sP65 )
=> ~ sP48 )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h51,assumption,
~ ( ~ ( sP14
=> ~ sP65 )
=> ~ sP48 ),
introduced(assumption,[]) ).
thf(h52,assumption,
sP1,
introduced(assumption,[]) ).
thf(h53,assumption,
~ ( sP14
=> ~ sP65 ),
introduced(assumption,[]) ).
thf(h54,assumption,
sP48,
introduced(assumption,[]) ).
thf(h55,assumption,
sP14,
introduced(assumption,[]) ).
thf(h56,assumption,
sP65,
introduced(assumption,[]) ).
thf(78,plain,
( ~ sP23
| ~ sP1
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(79,plain,
( ~ sP10
| ~ sP48
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(80,plain,
( ~ sP36
| ~ sP65
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(81,plain,
( ~ sP19
| ~ sP14
| sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(82,plain,
( ~ sP47
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(83,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h55,h56,h53,h54,h51,h52,h50,h7,h5,h3,h1,h0])],[78,79,80,81,82,h1,conj_0,h55,h56,h54,h52]) ).
thf(84,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h53,h54,h51,h52,h50,h7,h5,h3,h1,h0]),tab_negimp(discharge,[h55,h56])],[h53,83,h55,h56]) ).
thf(85,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h51,h52,h50,h7,h5,h3,h1,h0]),tab_negimp(discharge,[h53,h54])],[h51,84,h53,h54]) ).
thf(86,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h50,h7,h5,h3,h1,h0]),tab_negimp(discharge,[h51,h52])],[h50,85,h51,h52]) ).
thf(87,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h5,h3,h1,h0]),tab_negall(discharge,[h50]),tab_negall(eigenvar,eigen__0)],[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_062,86,h50]) ).
thf(88,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h3,h1,h0]),tab_imp(discharge,[h6]),tab_imp(discharge,[h7])],[fact_2__092_060open_062a1_A_092_060subseteq_062_Aa2_A_092_060or_062_Aa2_A_092_060subseteq_062_Aa1_092_060close_062,77,87,h6,h7]) ).
thf(89,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h3,h1,h0]),tab_imp(discharge,[h4]),tab_imp(discharge,[h5])],[fact_3__092_060open_062a1_A_092_060subseteq_062_Aa3_A_092_060or_062_Aa3_A_092_060subseteq_062_Aa1_092_060close_062,67,88,h4,h5]) ).
thf(fact_4__092_060open_062a2_A_092_060subseteq_062_Aa3_A_092_060or_062_Aa3_A_092_060subseteq_062_Aa2_092_060close_062,axiom,
( ~ ( ord_less_eq_set_a @ a2 @ a3 )
=> ( ord_less_eq_set_a @ a3 @ a2 ) ) ).
thf(90,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h2]),tab_imp(discharge,[h3])],[fact_4__092_060open_062a2_A_092_060subseteq_062_Aa3_A_092_060or_062_Aa3_A_092_060subseteq_062_Aa2_092_060close_062,46,89,h2,h3]) ).
thf(91,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[90,h0]) ).
thf(0,theorem,
sP35,
inference(contra,[status(thm),contra(discharge,[h1])],[90,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ITP028^1 : TPTP v8.1.2. Released v7.5.0.
% 0.06/0.12 % Command : lash -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 : 300
% 0.12/0.33 % DateTime : Sun Aug 27 12:57:23 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 % Mode: cade22sinegrackle2x6978
% 0.19/0.48 % Steps: 781
% 0.19/0.48 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------