TSTP Solution File: ITP176^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP176^1 : 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 : n018.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 00:29:23 EDT 2022
% Result : Theorem 23.40s 23.45s
% Output : Proof 23.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 51
% Syntax : Number of formulae : 56 ( 11 unt; 16 typ; 1 def)
% Number of atoms : 101 ( 21 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 281 ( 21 ~; 21 |; 0 &; 216 @)
% ( 16 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 28 usr; 24 con; 0-2 aty)
% Number of variables : 20 ( 11 ^ 9 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_set_b,type,
set_b: $tType ).
thf(ty_labele1159362096nt_a_b,type,
labele1159362096nt_a_b: $tType ).
thf(ty_b,type,
b: $tType ).
thf(ty_standard_Constant_a,type,
standard_Constant_a: $tType ).
thf(ty_set_Product_prod_b_b,type,
set_Product_prod_b_b: $tType ).
thf(ty_bot_bot_set_b,type,
bot_bot_set_b: set_b ).
thf(ty_eigen__2,type,
eigen__2: b ).
thf(ty_member_b,type,
member_b: b > set_b > $o ).
thf(ty_getRel904497637nt_a_b,type,
getRel904497637nt_a_b: standard_Constant_a > labele1159362096nt_a_b > set_Product_prod_b_b ).
thf(ty_image_b_b,type,
image_b_b: set_Product_prod_b_b > set_b > set_b ).
thf(ty_y,type,
y: b ).
thf(ty_insert_b,type,
insert_b: b > set_b > set_b ).
thf(ty_hilbert_Eps_b,type,
hilbert_Eps_b: ( b > $o ) > b ).
thf(ty_standard_S_Idt_a,type,
standard_S_Idt_a: standard_Constant_a ).
thf(ty_g,type,
g: labele1159362096nt_a_b ).
thf(ty_x,type,
x: b ).
thf(h0,assumption,
! [X1: b > $o,X2: b] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: b] :
( ( member_b @ X1 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ y @ bot_bot_set_b ) ) )
!= ( member_b @ X1 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_b ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ( ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_b ) )
= ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ y @ bot_bot_set_b ) ) )
=> ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ y @ bot_bot_set_b ) )
= ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_b ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__2 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( hilbert_Eps_b
@ ^ [X1: b] : ( member_b @ X1 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ y @ bot_bot_set_b ) ) ) )
= ( hilbert_Eps_b
@ ^ [X1: b] : ( member_b @ X1 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_b ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( member_b @ eigen__2 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ y @ bot_bot_set_b ) ) )
= ( member_b @ eigen__2 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_b ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP3
=> ( ( hilbert_Eps_b
@ ^ [X1: b] : ( member_b @ X1 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_b ) ) ) )
= ( hilbert_Eps_b
@ ^ [X1: b] : ( member_b @ X1 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ y @ bot_bot_set_b ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: b] :
( ( member_b @ X1 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ y @ bot_bot_set_b ) ) )
= ( member_b @ X1 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_b ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( member_b @ eigen__2 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_b ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: b] :
( ( ( hilbert_Eps_b
@ ^ [X2: b] : ( member_b @ X2 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ y @ bot_bot_set_b ) ) ) )
= X1 )
=> ( X1
= ( hilbert_Eps_b
@ ^ [X2: b] : ( member_b @ X2 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ y @ bot_bot_set_b ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: set_b,X2: set_b] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_b ) )
= ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ y @ bot_bot_set_b ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( ^ [X1: b] : ( member_b @ X1 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ y @ bot_bot_set_b ) ) ) )
= ( ^ [X1: b] : ( member_b @ X1 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_b ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: b,X2: b] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( member_b @ eigen__2 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ y @ bot_bot_set_b ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: set_b] :
( ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_b ) )
= X1 )
=> ( X1
= ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_b ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( hilbert_Eps_b
@ ^ [X1: b] : ( member_b @ X1 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_b ) ) ) )
= ( hilbert_Eps_b
@ ^ [X1: b] : ( member_b @ X1 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ y @ bot_bot_set_b ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ y @ bot_bot_set_b ) )
= ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_b ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(conj_0,conjecture,
sP15 ).
thf(h1,negated_conjecture,
~ sP15,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP13
| sP7
| ~ sP2
| ~ sP16 ),
inference(mating_rule,[status(thm)],]) ).
thf(2,plain,
sP2,
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP7
| sP13
| ~ sP2
| ~ sP10 ),
inference(mating_rule,[status(thm)],]) ).
thf(4,plain,
( sP4
| ~ sP13
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP4
| sP13
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP6
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(7,plain,
( sP11
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP1
| ~ sP10
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP14
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP9
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
sP9,
inference(eq_sym,[status(thm)],]) ).
thf(12,plain,
( sP3
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP5
| ~ sP3
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP8
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
sP12,
inference(eq_sym,[status(thm)],]) ).
thf(fact_0__092_060open_062getRel_AS__Idt_AG_A_096_096_A_123x_125_A_061_AgetRel_AS__Idt_AG_A_096_096_A_123y_125_092_060close_062,axiom,
sP10 ).
thf(17,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,h1,fact_0__092_060open_062getRel_AS__Idt_AG_A_096_096_A_123x_125_A_061_AgetRel_AS__Idt_AG_A_096_096_A_123y_125_092_060close_062]) ).
thf(18,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[17,h0]) ).
thf(0,theorem,
sP15,
inference(contra,[status(thm),contra(discharge,[h1])],[17,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ITP176^1 : TPTP v8.1.0. Released v7.5.0.
% 0.10/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % 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 : Thu Jun 2 23:04:31 EDT 2022
% 0.12/0.34 % CPUTime :
% 23.40/23.45 % SZS status Theorem
% 23.40/23.45 % Mode: mode9a:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=1.:SINE_DEPTH=0
% 23.40/23.45 % Inferences: 316
% 23.40/23.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------