TSTP Solution File: ITP176^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP176^1 : 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 : n012.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 04:02:44 EDT 2023
% Result : Theorem 0.20s 0.47s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 33
% Syntax : Number of formulae : 38 ( 9 unt; 12 typ; 1 def)
% Number of atoms : 61 ( 8 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 163 ( 13 ~; 14 |; 0 &; 126 @)
% ( 9 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 21 con; 0-2 aty)
% Number of variables : 8 ( 5 ^; 3 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_b,type,
b: $tType ).
thf(ty_getRel904497637nt_a_b,type,
getRel904497637nt_a_b: standard_Constant_a > labele1159362096nt_a_b > set_Product_prod_b_b ).
thf(ty_g,type,
g: labele1159362096nt_a_b ).
thf(ty_bot_bot_set_b,type,
bot_bot_set_b: set_b ).
thf(ty_standard_S_Idt_a,type,
standard_S_Idt_a: standard_Constant_a ).
thf(ty_hilbert_Eps_b,type,
hilbert_Eps_b: ( b > $o ) > b ).
thf(ty_image_b_b,type,
image_b_b: set_Product_prod_b_b > set_b > set_b ).
thf(ty_member_b,type,
member_b: b > set_b > $o ).
thf(ty_insert_b,type,
insert_b: b > set_b > set_b ).
thf(ty_eigen__0,type,
eigen__0: b ).
thf(ty_y,type,
y: 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__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: b] :
( ( member_b @ X1 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_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,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> $false ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( member_b @ eigen__0 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_b ) ) )
= ( member_b @ eigen__0 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ y @ bot_bot_set_b ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ^ [X1: b] : ( member_b @ X1 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_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,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( member_b @ eigen__0 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ y @ bot_bot_set_b ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: b] :
( ( member_b @ X1 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_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
<=> ( ( 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,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( member_b @ eigen__0 @ ( 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
<=> ( ( 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,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( 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,[sP9])]) ).
thf(conj_0,conjecture,
sP6 ).
thf(h1,negated_conjecture,
~ sP6,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP7
| sP4
| ~ sP8
| sP1 ),
inference(mating_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP4
| sP7
| ~ sP9
| sP1 ),
inference(mating_rule,[status(thm)],]) ).
thf(3,plain,
~ sP1,
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP2
| ~ sP7
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP2
| sP7
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP5
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(7,plain,
( sP3
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP6
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP8
| sP9 ),
inference(symeq,[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,
sP8 ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,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(11,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[10,h0]) ).
thf(0,theorem,
sP6,
inference(contra,[status(thm),contra(discharge,[h1])],[10,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ITP176^1 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 12:06:25 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 % Mode: cade22sinegrackle2x6978
% 0.20/0.47 % Steps: 1039
% 0.20/0.47 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------