TSTP Solution File: ITP178^1 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP178^1 : 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 : n010.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 04:02:45 EDT 2023
% Result : Theorem 120.66s 121.18s
% Output : Proof 120.66s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_allegorical_term_b,type,
allegorical_term_b: $tType ).
thf(ty_produc1990145943term_b,type,
produc1990145943term_b: allegorical_term_b > allegorical_term_b > produc1478835367term_b ).
thf(ty_restrict_b_nat,type,
restrict_b_nat: labeled_graph_b_nat > labeled_graph_b_nat ).
thf(ty_finite1987068434at_nat,type,
finite1987068434at_nat: set_Pr9961929at_nat > $o ).
thf(ty_finite_finite_nat,type,
finite_finite_nat: set_nat > $o ).
thf(ty_produc1542243159_b_nat,type,
produc1542243159_b_nat: produc1235635379_b_nat > labeled_graph_b_nat ).
thf(ty_v,type,
v: allegorical_term_b ).
thf(ty_u,type,
u: allegorical_term_b ).
thf(ty_translation_b,type,
translation_b: allegorical_term_b > labeled_graph_b_nat ).
thf(ty_id_on_nat,type,
id_on_nat: set_nat > set_Pr1986765409at_nat ).
thf(ty_labeled_edges_b_nat,type,
labeled_edges_b_nat: labeled_graph_b_nat > set_Pr9961929at_nat ).
thf(ty_graph_529870330at_nat,type,
graph_529870330at_nat: labeled_graph_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > $o ).
thf(ty_allegorical_A_Int_b,type,
allegorical_A_Int_b: allegorical_term_b > allegorical_term_b > allegorical_term_b ).
thf(ty_labele460410879_b_nat,type,
labele460410879_b_nat: labeled_graph_b_nat > set_nat ).
thf(ty_produc194497945_b_nat,type,
produc194497945_b_nat: produc1235635379_b_nat > labeled_graph_b_nat ).
thf(ty_produc854192515term_b,type,
produc854192515term_b: produc1478835367term_b > allegorical_term_b ).
thf(ty_produc951298923_b_nat,type,
produc951298923_b_nat: labeled_graph_b_nat > labeled_graph_b_nat > produc1235635379_b_nat ).
thf(ty_produc1223098053term_b,type,
produc1223098053term_b: produc1478835367term_b > allegorical_term_b ).
thf(sP1,plain,
( sP1
<=> ! [X1: allegorical_term_b,X2: allegorical_term_b] :
~ ( ~ ( ~ ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X2 ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X2 ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X2 ) ) ) ) ) ) )
=> ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X2 ) ) ) )
!= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X2 ) ) ) ) ) ) )
=> ~ ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X2 ) ) ) ) ) ) )
=> ~ ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X2 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ~ ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) )
=> ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) )
!= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) )
=> ~ ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) )
=> ~ ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) )
= ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) )
=> ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) )
!= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: allegorical_term_b] :
( ( produc854192515term_b @ ( produc1990145943term_b @ u @ X1 ) )
= u ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) )
= ( allegorical_A_Int_b @ u @ v ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( u
= ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ sP4
=> ~ ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) )
= ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
=> ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
!= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
=> ~ ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) )
= ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) )
= ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
= ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( allegorical_A_Int_b @ u @ v )
= ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) )
= ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) )
= ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: allegorical_term_b,X2: allegorical_term_b] :
( ( produc1223098053term_b @ ( produc1990145943term_b @ X1 @ X2 ) )
= X2 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( translation_b @ ( allegorical_A_Int_b @ u @ v ) )
= ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
=> ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
!= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ sP11
=> ~ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) )
= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( translation_b @ u )
= ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) )
= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: allegorical_term_b] :
~ ( ~ ( ~ ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ X1 ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ X1 ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ X1 ) ) ) ) ) ) )
=> ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ X1 ) ) ) )
!= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ X1 ) ) ) ) ) ) )
=> ~ ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ X1 ) ) ) ) ) ) )
=> ~ ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ X1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: allegorical_term_b] :
( ( produc1223098053term_b @ ( produc1990145943term_b @ u @ X1 ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) )
= u ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: allegorical_term_b,X2: allegorical_term_b] :
( ( produc854192515term_b @ ( produc1990145943term_b @ X1 @ X2 ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(conj_0,conjecture,
~ sP24 ).
thf(h0,negated_conjecture,
sP24,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP31
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP5
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP21
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP34
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( sP25
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP28
| sP33
| ~ sP14
| ~ sP25 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(7,plain,
( sP10
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP18
| sP27
| ~ sP10 ),
inference(mating_rule,[status(thm)],]) ).
thf(9,plain,
( sP20
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP7
| sP19
| ~ sP20 ),
inference(mating_rule,[status(thm)],]) ).
thf(11,plain,
( sP17
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP15
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP14
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP6
| sP16 ),
inference(symeq,[status(thm)],]) ).
thf(15,plain,
( sP22
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP13
| ~ sP22
| ~ sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP3
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP12
| sP29
| ~ sP15
| ~ sP14
| ~ sP3 ),
inference(mating_rule,[status(thm)],]) ).
thf(19,plain,
( sP4
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP4
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP9
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP9
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP2
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( sP2
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP32
| sP8 ),
inference(symeq,[status(thm)],]) ).
thf(26,plain,
( sP26
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP30
| ~ sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP1
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP23
| ~ sP29
| ~ sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP11
| sP23
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP24
| sP11
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(fact_85_snd__conv,axiom,
sP21 ).
thf(fact_76_fst__conv,axiom,
sP34 ).
thf(fact_3_graph__rule__translation,axiom,
sP1 ).
thf(32,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,fact_85_snd__conv,fact_76_fst__conv,fact_3_graph__rule__translation,h0]) ).
thf(0,theorem,
~ sP24,
inference(contra,[status(thm),contra(discharge,[h0])],[32,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ITP178^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 16:02:49 EDT 2023
% 0.13/0.35 % CPUTime :
% 120.66/121.18 % SZS status Theorem
% 120.66/121.18 % Mode: cade22sinegrackle2xec37
% 120.66/121.18 % Steps: 4172
% 120.66/121.18 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------