TSTP Solution File: ITP178^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP178^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n019.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 03:18:55 EDT 2023
% Result : Timeout 299.90s 300.17s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.15/0.20 % Problem : ITP178^1 : TPTP v8.1.2. Released v7.5.0.
% 0.20/0.21 % Command : do_cvc5 %s %d
% 0.20/0.42 % Computer : n019.cluster.edu
% 0.20/0.42 % Model : x86_64 x86_64
% 0.20/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.42 % Memory : 8042.1875MB
% 0.20/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.42 % CPULimit : 300
% 0.20/0.42 % WCLimit : 300
% 0.20/0.42 % DateTime : Sun Aug 27 16:14:28 EDT 2023
% 0.20/0.42 % CPUTime :
% 0.27/0.63 %----Proving TH0
% 0.27/0.63 %------------------------------------------------------------------------------
% 0.27/0.63 % File : ITP178^1 : TPTP v8.1.2. Released v7.5.0.
% 0.27/0.63 % Domain : Interactive Theorem Proving
% 0.27/0.63 % Problem : Sledgehammer StandardRules problem prob_429__5391446_1
% 0.27/0.63 % Version : Especial.
% 0.27/0.63 % English :
% 0.27/0.63
% 0.27/0.63 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.27/0.63 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.27/0.63 % Source : [Des21]
% 0.27/0.63 % Names : StandardRules/prob_429__5391446_1 [Des21]
% 0.27/0.63
% 0.27/0.63 % Status : Theorem
% 0.27/0.63 % Rating : 0.31 v8.1.0, 0.36 v7.5.0
% 0.27/0.63 % Syntax : Number of formulae : 541 ( 143 unt; 185 typ; 0 def)
% 0.27/0.63 % Number of atoms : 993 ( 367 equ; 0 cnn)
% 0.27/0.63 % Maximal formula atoms : 12 ( 2 avg)
% 0.27/0.63 % Number of connectives : 3581 ( 95 ~; 1 |; 131 &;2941 @)
% 0.27/0.63 % ( 0 <=>; 413 =>; 0 <=; 0 <~>)
% 0.27/0.63 % Maximal formula depth : 19 ( 7 avg)
% 0.27/0.63 % Number of types : 42 ( 41 usr)
% 0.27/0.63 % Number of type conns : 272 ( 272 >; 0 *; 0 +; 0 <<)
% 0.27/0.63 % Number of symbols : 145 ( 144 usr; 12 con; 0-6 aty)
% 0.27/0.63 % Number of variables : 1063 ( 62 ^; 951 !; 50 ?;1063 :)
% 0.27/0.63 % SPC : TH0_THM_EQU_NAR
% 0.27/0.63
% 0.27/0.63 % Comments : This file was generated by Sledgehammer 2021-02-23 15:38:28.807
% 0.27/0.63 %------------------------------------------------------------------------------
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% 0.27/0.63 member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
% 0.27/0.63
% 0.27/0.63 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_Mt__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_Mt__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_J_J,type,
% 0.27/0.63 member1449757456term_b: produc1116408039term_b > set_Pr1839611079term_b > $o ).
% 0.27/0.63
% 0.27/0.63 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J,type,
% 0.27/0.63 member584645392_a_nat: produc398057191_a_nat > set_Pr924198087_a_nat > $o ).
% 0.27/0.63
% 0.27/0.63 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_J_J,type,
% 0.27/0.63 member889223696_b_nat: produc446386919_b_nat > set_Pr1173424071_b_nat > $o ).
% 0.27/0.63
% 0.27/0.63 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.27/0.63 member2027625872at_nat: produc842455143at_nat > set_Pr1490359111at_nat > $o ).
% 0.27/0.63
% 0.27/0.63 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J_J,type,
% 0.27/0.63 member829905680_a_nat: produc116665063_a_nat > set_Pr2123625671_a_nat > $o ).
% 0.27/0.63
% 0.27/0.63 thf(sy_v_C,type,
% 0.27/0.63 c: set_a ).
% 0.27/0.63
% 0.27/0.63 thf(sy_v_u,type,
% 0.27/0.63 u: allegorical_term_b ).
% 0.27/0.63
% 0.27/0.63 thf(sy_v_v,type,
% 0.27/0.63 v: allegorical_term_b ).
% 0.27/0.63
% 0.27/0.63 thf(sy_v_x,type,
% 0.27/0.63 x: produc1871334759_a_nat ).
% 0.27/0.63
% 0.27/0.63 % Relevant facts (355)
% 0.27/0.63 thf(fact_0_assms,axiom,
% 0.27/0.63 member832397200_a_nat @ x @ ( standa1897115818ules_a @ c ) ).
% 0.27/0.63
% 0.27/0.63 % assms
% 0.27/0.63 thf(fact_1_graph__rule__translation,axiom,
% 0.27/0.63 ! [X: allego1565409692at_nat,Y: allego1565409692at_nat] :
% 0.27/0.63 ( ( graph_2111906684at_nat @ ( produc1995789403at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ X ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ X @ Y ) ) ) ) @ ( produc1564126365at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ X ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ X @ Y ) ) ) ) @ ( id_on_nat @ ( labele560327297at_nat @ ( produc1995789403at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ X ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ X @ Y ) ) ) ) ) ) )
% 0.27/0.63 & ( ( produc1564126365at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ X ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ X @ Y ) ) ) )
% 0.27/0.63 = ( restri321299017at_nat @ ( produc1564126365at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ X ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ X @ Y ) ) ) ) ) )
% 0.27/0.63 & ( finite_finite_nat @ ( labele560327297at_nat @ ( produc1564126365at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ X ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ X @ Y ) ) ) ) ) )
% 0.27/0.63 & ( finite48957584at_nat @ ( labele2032268018at_nat @ ( produc1564126365at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ X ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ X @ Y ) ) ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % graph_rule_translation
% 0.27/0.63 thf(fact_2_graph__rule__translation,axiom,
% 0.27/0.63 ! [X: allego510293162tant_a,Y: allego510293162tant_a] :
% 0.27/0.63 ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ X ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ X @ Y ) ) ) ) @ ( produc880161797_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ X ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ X @ Y ) ) ) ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ X ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ X @ Y ) ) ) ) ) ) )
% 0.27/0.63 & ( ( produc880161797_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ X ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ X @ Y ) ) ) )
% 0.27/0.63 = ( restri572569417_a_nat @ ( produc880161797_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ X ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ X @ Y ) ) ) ) ) )
% 0.27/0.63 & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ X ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ X @ Y ) ) ) ) ) )
% 0.27/0.63 & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ X ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ X @ Y ) ) ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % graph_rule_translation
% 0.27/0.63 thf(fact_3_graph__rule__translation,axiom,
% 0.27/0.63 ! [X: allegorical_term_b,Y: allegorical_term_b] :
% 0.27/0.63 ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) ) ) ) )
% 0.27/0.63 & ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) )
% 0.27/0.63 = ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) ) ) )
% 0.27/0.63 & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) ) ) )
% 0.27/0.63 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) ) ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % graph_rule_translation
% 0.27/0.63 thf(fact_4_subgraph__refl,axiom,
% 0.27/0.63 ! [G: labele935650037_a_nat] :
% 0.27/0.63 ( ( graph_2130075512at_nat @ G @ G @ ( id_on_nat @ ( labele1810595089_a_nat @ G ) ) )
% 0.27/0.63 = ( G
% 0.27/0.63 = ( restri572569417_a_nat @ G ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % subgraph_refl
% 0.27/0.63 thf(fact_5_subgraph__refl,axiom,
% 0.27/0.63 ! [G: labeled_graph_b_nat] :
% 0.27/0.63 ( ( graph_529870330at_nat @ G @ G @ ( id_on_nat @ ( labele460410879_b_nat @ G ) ) )
% 0.27/0.63 = ( G
% 0.27/0.63 = ( restrict_b_nat @ G ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % subgraph_refl
% 0.27/0.63 thf(fact_6_subgraph__restrict,axiom,
% 0.27/0.63 ! [G: labele935650037_a_nat] :
% 0.27/0.63 ( ( graph_2130075512at_nat @ G @ ( restri572569417_a_nat @ G ) @ ( id_on_nat @ ( labele1810595089_a_nat @ G ) ) )
% 0.27/0.63 = ( G
% 0.27/0.63 = ( restri572569417_a_nat @ G ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % subgraph_restrict
% 0.27/0.63 thf(fact_7_subgraph__restrict,axiom,
% 0.27/0.63 ! [G: labeled_graph_b_nat] :
% 0.27/0.63 ( ( graph_529870330at_nat @ G @ ( restrict_b_nat @ G ) @ ( id_on_nat @ ( labele460410879_b_nat @ G ) ) )
% 0.27/0.63 = ( G
% 0.27/0.63 = ( restrict_b_nat @ G ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % subgraph_restrict
% 0.27/0.63 thf(fact_8_graph__homomorphism__Id,axiom,
% 0.27/0.63 ! [A: labele935650037_a_nat] : ( graph_2130075512at_nat @ ( restri572569417_a_nat @ A ) @ ( restri572569417_a_nat @ A ) @ ( id_on_nat @ ( labele1810595089_a_nat @ A ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % graph_homomorphism_Id
% 0.27/0.63 thf(fact_9_graph__homomorphism__Id,axiom,
% 0.27/0.63 ! [A: labeled_graph_b_nat] : ( graph_529870330at_nat @ ( restrict_b_nat @ A ) @ ( restrict_b_nat @ A ) @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % graph_homomorphism_Id
% 0.27/0.63 thf(fact_10_verts__in__translation__finite_I2_J,axiom,
% 0.27/0.63 ! [X: allego1565409692at_nat] : ( finite48957584at_nat @ ( labele2032268018at_nat @ ( transl490985778at_nat @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % verts_in_translation_finite(2)
% 0.27/0.63 thf(fact_11_verts__in__translation__finite_I2_J,axiom,
% 0.27/0.63 ! [X: allego510293162tant_a] : ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( transl1275713022tant_a @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % verts_in_translation_finite(2)
% 0.27/0.63 thf(fact_12_verts__in__translation__finite_I2_J,axiom,
% 0.27/0.63 ! [X: allegorical_term_b] : ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( translation_b @ X ) ) ) ).
% 0.27/0.63
% 0.27/0.63 % verts_in_translation_finite(2)
% 0.27/0.63 thf(fact_13_are__rules_I1_J,axiom,
% 0.27/0.63 ( ( graph_2111906684at_nat @ ( produc1995789403at_nat @ standa214789732at_nat ) @ ( produc1564126365at_nat @ standa214789732at_nat ) @ ( id_on_nat @ ( labele560327297at_nat @ ( produc1995789403at_nat @ standa214789732at_nat ) ) ) )
% 0.27/0.63 & ( ( produc1564126365at_nat @ standa214789732at_nat )
% 0.27/0.63 = ( restri321299017at_nat @ ( produc1564126365at_nat @ standa214789732at_nat ) ) )
% 0.27/0.64 & ( finite_finite_nat @ ( labele560327297at_nat @ ( produc1564126365at_nat @ standa214789732at_nat ) ) )
% 0.27/0.64 & ( finite48957584at_nat @ ( labele2032268018at_nat @ ( produc1564126365at_nat @ standa214789732at_nat ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % are_rules(1)
% 0.27/0.64 thf(fact_14_are__rules_I1_J,axiom,
% 0.27/0.64 ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ standa1410829644tant_a ) @ ( produc880161797_a_nat @ standa1410829644tant_a ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ standa1410829644tant_a ) ) ) )
% 0.27/0.64 & ( ( produc880161797_a_nat @ standa1410829644tant_a )
% 0.27/0.64 = ( restri572569417_a_nat @ ( produc880161797_a_nat @ standa1410829644tant_a ) ) )
% 0.27/0.64 & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ standa1410829644tant_a ) ) )
% 0.27/0.64 & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ standa1410829644tant_a ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % are_rules(1)
% 0.27/0.64 thf(fact_15_are__rules_I1_J,axiom,
% 0.27/0.64 ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ standa879863266rule_b ) @ ( produc194497945_b_nat @ standa879863266rule_b ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ standa879863266rule_b ) ) ) )
% 0.27/0.64 & ( ( produc194497945_b_nat @ standa879863266rule_b )
% 0.27/0.64 = ( restrict_b_nat @ ( produc194497945_b_nat @ standa879863266rule_b ) ) )
% 0.27/0.64 & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ standa879863266rule_b ) ) )
% 0.27/0.64 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ standa879863266rule_b ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % are_rules(1)
% 0.27/0.64 thf(fact_16_are__rules_I2_J,axiom,
% 0.27/0.64 ! [T: product_prod_nat_nat] :
% 0.27/0.64 ( ( graph_2111906684at_nat @ ( produc1995789403at_nat @ ( standa153097263at_nat @ T ) ) @ ( produc1564126365at_nat @ ( standa153097263at_nat @ T ) ) @ ( id_on_nat @ ( labele560327297at_nat @ ( produc1995789403at_nat @ ( standa153097263at_nat @ T ) ) ) ) )
% 0.27/0.64 & ( ( produc1564126365at_nat @ ( standa153097263at_nat @ T ) )
% 0.27/0.64 = ( restri321299017at_nat @ ( produc1564126365at_nat @ ( standa153097263at_nat @ T ) ) ) )
% 0.27/0.64 & ( finite_finite_nat @ ( labele560327297at_nat @ ( produc1564126365at_nat @ ( standa153097263at_nat @ T ) ) ) )
% 0.27/0.64 & ( finite48957584at_nat @ ( labele2032268018at_nat @ ( produc1564126365at_nat @ ( standa153097263at_nat @ T ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % are_rules(2)
% 0.27/0.64 thf(fact_17_are__rules_I2_J,axiom,
% 0.27/0.64 ! [T: standard_Constant_a] :
% 0.27/0.64 ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ ( standa305748545tant_a @ T ) ) @ ( produc880161797_a_nat @ ( standa305748545tant_a @ T ) ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ ( standa305748545tant_a @ T ) ) ) ) )
% 0.27/0.64 & ( ( produc880161797_a_nat @ ( standa305748545tant_a @ T ) )
% 0.27/0.64 = ( restri572569417_a_nat @ ( produc880161797_a_nat @ ( standa305748545tant_a @ T ) ) ) )
% 0.27/0.64 & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ ( standa305748545tant_a @ T ) ) ) )
% 0.27/0.64 & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ ( standa305748545tant_a @ T ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % are_rules(2)
% 0.27/0.64 thf(fact_18_are__rules_I2_J,axiom,
% 0.27/0.64 ! [T: b] :
% 0.27/0.64 ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( standa1360217389rule_b @ T ) ) @ ( produc194497945_b_nat @ ( standa1360217389rule_b @ T ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( standa1360217389rule_b @ T ) ) ) ) )
% 0.27/0.64 & ( ( produc194497945_b_nat @ ( standa1360217389rule_b @ T ) )
% 0.27/0.64 = ( restrict_b_nat @ ( produc194497945_b_nat @ ( standa1360217389rule_b @ T ) ) ) )
% 0.27/0.64 & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( standa1360217389rule_b @ T ) ) ) )
% 0.27/0.64 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( standa1360217389rule_b @ T ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % are_rules(2)
% 0.27/0.64 thf(fact_19_verts__in__translation__finite_I1_J,axiom,
% 0.27/0.64 ! [X: allego510293162tant_a] : ( finite_finite_nat @ ( labele1810595089_a_nat @ ( transl1275713022tant_a @ X ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % verts_in_translation_finite(1)
% 0.27/0.64 thf(fact_20_verts__in__translation__finite_I1_J,axiom,
% 0.27/0.64 ! [X: allegorical_term_b] : ( finite_finite_nat @ ( labele460410879_b_nat @ ( translation_b @ X ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % verts_in_translation_finite(1)
% 0.27/0.64 thf(fact_21_are__rules_I3_J,axiom,
% 0.27/0.64 ! [I: product_prod_nat_nat] :
% 0.27/0.64 ( ( graph_2111906684at_nat @ ( produc1995789403at_nat @ ( standa2131591247at_nat @ I ) ) @ ( produc1564126365at_nat @ ( standa2131591247at_nat @ I ) ) @ ( id_on_nat @ ( labele560327297at_nat @ ( produc1995789403at_nat @ ( standa2131591247at_nat @ I ) ) ) ) )
% 0.27/0.64 & ( ( produc1564126365at_nat @ ( standa2131591247at_nat @ I ) )
% 0.27/0.64 = ( restri321299017at_nat @ ( produc1564126365at_nat @ ( standa2131591247at_nat @ I ) ) ) )
% 0.27/0.64 & ( finite_finite_nat @ ( labele560327297at_nat @ ( produc1564126365at_nat @ ( standa2131591247at_nat @ I ) ) ) )
% 0.27/0.64 & ( finite48957584at_nat @ ( labele2032268018at_nat @ ( produc1564126365at_nat @ ( standa2131591247at_nat @ I ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % are_rules(3)
% 0.27/0.64 thf(fact_22_are__rules_I3_J,axiom,
% 0.27/0.64 ! [I: standard_Constant_a] :
% 0.27/0.64 ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ ( standa63370785tant_a @ I ) ) @ ( produc880161797_a_nat @ ( standa63370785tant_a @ I ) ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ ( standa63370785tant_a @ I ) ) ) ) )
% 0.27/0.64 & ( ( produc880161797_a_nat @ ( standa63370785tant_a @ I ) )
% 0.27/0.64 = ( restri572569417_a_nat @ ( produc880161797_a_nat @ ( standa63370785tant_a @ I ) ) ) )
% 0.27/0.64 & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ ( standa63370785tant_a @ I ) ) ) )
% 0.27/0.64 & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ ( standa63370785tant_a @ I ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % are_rules(3)
% 0.27/0.64 thf(fact_23_are__rules_I3_J,axiom,
% 0.27/0.64 ! [I: b] :
% 0.27/0.64 ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( standa1329480013rule_b @ I ) ) @ ( produc194497945_b_nat @ ( standa1329480013rule_b @ I ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( standa1329480013rule_b @ I ) ) ) ) )
% 0.27/0.64 & ( ( produc194497945_b_nat @ ( standa1329480013rule_b @ I ) )
% 0.27/0.64 = ( restrict_b_nat @ ( produc194497945_b_nat @ ( standa1329480013rule_b @ I ) ) ) )
% 0.27/0.64 & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( standa1329480013rule_b @ I ) ) ) )
% 0.27/0.64 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( standa1329480013rule_b @ I ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % are_rules(3)
% 0.27/0.64 thf(fact_24_prod_Ocollapse,axiom,
% 0.27/0.64 ! [Prod: product_prod_nat_nat] :
% 0.27/0.64 ( ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) )
% 0.27/0.64 = Prod ) ).
% 0.27/0.64
% 0.27/0.64 % prod.collapse
% 0.27/0.64 thf(fact_25_prod_Ocollapse,axiom,
% 0.27/0.64 ! [Prod: produc398057191_a_nat] :
% 0.27/0.64 ( ( produc1677124439_a_nat @ ( produc1049080131_a_nat @ Prod ) @ ( produc1022852229_a_nat @ Prod ) )
% 0.27/0.64 = Prod ) ).
% 0.27/0.64
% 0.27/0.64 % prod.collapse
% 0.27/0.64 thf(fact_26_prod_Ocollapse,axiom,
% 0.27/0.64 ! [Prod: produc1871334759_a_nat] :
% 0.27/0.64 ( ( produc1676969687_a_nat @ ( produc719117507_a_nat @ Prod ) @ ( produc880161797_a_nat @ Prod ) )
% 0.27/0.64 = Prod ) ).
% 0.27/0.64
% 0.27/0.64 % prod.collapse
% 0.27/0.64 thf(fact_27_prod_Ocollapse,axiom,
% 0.27/0.64 ! [Prod: produc1478835367term_b] :
% 0.27/0.64 ( ( produc1990145943term_b @ ( produc854192515term_b @ Prod ) @ ( produc1223098053term_b @ Prod ) )
% 0.27/0.64 = Prod ) ).
% 0.27/0.64
% 0.27/0.64 % prod.collapse
% 0.27/0.64 thf(fact_28_prod_Ocollapse,axiom,
% 0.27/0.64 ! [Prod: produc1235635379_b_nat] :
% 0.27/0.64 ( ( produc951298923_b_nat @ ( produc1542243159_b_nat @ Prod ) @ ( produc194497945_b_nat @ Prod ) )
% 0.27/0.64 = Prod ) ).
% 0.27/0.64
% 0.27/0.64 % prod.collapse
% 0.27/0.64 thf(fact_29_translation__graph,axiom,
% 0.27/0.64 ( transl1275713022tant_a
% 0.27/0.64 = ( ^ [X2: allego510293162tant_a] : ( restri572569417_a_nat @ ( transl1275713022tant_a @ X2 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % translation_graph
% 0.27/0.64 thf(fact_30_translation__graph,axiom,
% 0.27/0.64 ( translation_b
% 0.27/0.64 = ( ^ [X2: allegorical_term_b] : ( restrict_b_nat @ ( translation_b @ X2 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % translation_graph
% 0.27/0.64 thf(fact_31_vertices__restrict,axiom,
% 0.27/0.64 ! [G: labele935650037_a_nat] :
% 0.27/0.64 ( ( labele1810595089_a_nat @ ( restri572569417_a_nat @ G ) )
% 0.27/0.64 = ( labele1810595089_a_nat @ G ) ) ).
% 0.27/0.64
% 0.27/0.64 % vertices_restrict
% 0.27/0.64 thf(fact_32_vertices__restrict,axiom,
% 0.27/0.64 ! [G: labeled_graph_b_nat] :
% 0.27/0.64 ( ( labele460410879_b_nat @ ( restrict_b_nat @ G ) )
% 0.27/0.64 = ( labele460410879_b_nat @ G ) ) ).
% 0.27/0.64
% 0.27/0.64 % vertices_restrict
% 0.27/0.64 thf(fact_33_old_Oprod_Oinject,axiom,
% 0.27/0.64 ! [A: nat,B: nat,A2: nat,B2: nat] :
% 0.27/0.64 ( ( ( product_Pair_nat_nat @ A @ B )
% 0.27/0.64 = ( product_Pair_nat_nat @ A2 @ B2 ) )
% 0.27/0.64 = ( ( A = A2 )
% 0.27/0.64 & ( B = B2 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % old.prod.inject
% 0.27/0.64 thf(fact_34_old_Oprod_Oinject,axiom,
% 0.27/0.64 ! [A: produc1871334759_a_nat,B: produc1871334759_a_nat,A2: produc1871334759_a_nat,B2: produc1871334759_a_nat] :
% 0.27/0.64 ( ( ( produc1677124439_a_nat @ A @ B )
% 0.27/0.64 = ( produc1677124439_a_nat @ A2 @ B2 ) )
% 0.27/0.64 = ( ( A = A2 )
% 0.27/0.64 & ( B = B2 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % old.prod.inject
% 0.27/0.64 thf(fact_35_old_Oprod_Oinject,axiom,
% 0.27/0.64 ! [A: labele935650037_a_nat,B: labele935650037_a_nat,A2: labele935650037_a_nat,B2: labele935650037_a_nat] :
% 0.27/0.64 ( ( ( produc1676969687_a_nat @ A @ B )
% 0.27/0.64 = ( produc1676969687_a_nat @ A2 @ B2 ) )
% 0.27/0.64 = ( ( A = A2 )
% 0.27/0.64 & ( B = B2 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % old.prod.inject
% 0.27/0.64 thf(fact_36_old_Oprod_Oinject,axiom,
% 0.27/0.64 ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,A2: labeled_graph_b_nat,B2: labeled_graph_b_nat] :
% 0.27/0.64 ( ( ( produc951298923_b_nat @ A @ B )
% 0.27/0.64 = ( produc951298923_b_nat @ A2 @ B2 ) )
% 0.27/0.64 = ( ( A = A2 )
% 0.27/0.64 & ( B = B2 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % old.prod.inject
% 0.27/0.64 thf(fact_37_old_Oprod_Oinject,axiom,
% 0.27/0.64 ! [A: allegorical_term_b,B: allegorical_term_b,A2: allegorical_term_b,B2: allegorical_term_b] :
% 0.27/0.64 ( ( ( produc1990145943term_b @ A @ B )
% 0.27/0.64 = ( produc1990145943term_b @ A2 @ B2 ) )
% 0.27/0.64 = ( ( A = A2 )
% 0.27/0.64 & ( B = B2 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % old.prod.inject
% 0.27/0.64 thf(fact_38_prod_Oinject,axiom,
% 0.27/0.64 ! [X1: nat,X22: nat,Y1: nat,Y2: nat] :
% 0.27/0.64 ( ( ( product_Pair_nat_nat @ X1 @ X22 )
% 0.27/0.64 = ( product_Pair_nat_nat @ Y1 @ Y2 ) )
% 0.27/0.64 = ( ( X1 = Y1 )
% 0.27/0.64 & ( X22 = Y2 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % prod.inject
% 0.27/0.64 thf(fact_39_prod_Oinject,axiom,
% 0.27/0.64 ! [X1: produc1871334759_a_nat,X22: produc1871334759_a_nat,Y1: produc1871334759_a_nat,Y2: produc1871334759_a_nat] :
% 0.27/0.64 ( ( ( produc1677124439_a_nat @ X1 @ X22 )
% 0.27/0.64 = ( produc1677124439_a_nat @ Y1 @ Y2 ) )
% 0.27/0.64 = ( ( X1 = Y1 )
% 0.27/0.64 & ( X22 = Y2 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % prod.inject
% 0.27/0.64 thf(fact_40_prod_Oinject,axiom,
% 0.27/0.64 ! [X1: labele935650037_a_nat,X22: labele935650037_a_nat,Y1: labele935650037_a_nat,Y2: labele935650037_a_nat] :
% 0.27/0.64 ( ( ( produc1676969687_a_nat @ X1 @ X22 )
% 0.27/0.64 = ( produc1676969687_a_nat @ Y1 @ Y2 ) )
% 0.27/0.64 = ( ( X1 = Y1 )
% 0.27/0.64 & ( X22 = Y2 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % prod.inject
% 0.27/0.64 thf(fact_41_prod_Oinject,axiom,
% 0.27/0.64 ! [X1: labeled_graph_b_nat,X22: labeled_graph_b_nat,Y1: labeled_graph_b_nat,Y2: labeled_graph_b_nat] :
% 0.27/0.64 ( ( ( produc951298923_b_nat @ X1 @ X22 )
% 0.27/0.64 = ( produc951298923_b_nat @ Y1 @ Y2 ) )
% 0.27/0.64 = ( ( X1 = Y1 )
% 0.27/0.64 & ( X22 = Y2 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % prod.inject
% 0.27/0.64 thf(fact_42_prod_Oinject,axiom,
% 0.27/0.64 ! [X1: allegorical_term_b,X22: allegorical_term_b,Y1: allegorical_term_b,Y2: allegorical_term_b] :
% 0.27/0.64 ( ( ( produc1990145943term_b @ X1 @ X22 )
% 0.27/0.64 = ( produc1990145943term_b @ Y1 @ Y2 ) )
% 0.27/0.64 = ( ( X1 = Y1 )
% 0.27/0.64 & ( X22 = Y2 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % prod.inject
% 0.27/0.64 thf(fact_43_restrict__idemp,axiom,
% 0.27/0.64 ! [X3: labele935650037_a_nat] :
% 0.27/0.64 ( ( restri572569417_a_nat @ ( restri572569417_a_nat @ X3 ) )
% 0.27/0.64 = ( restri572569417_a_nat @ X3 ) ) ).
% 0.27/0.64
% 0.27/0.64 % restrict_idemp
% 0.27/0.64 thf(fact_44_restrict__idemp,axiom,
% 0.27/0.64 ! [X3: labeled_graph_b_nat] :
% 0.27/0.64 ( ( restrict_b_nat @ ( restrict_b_nat @ X3 ) )
% 0.27/0.64 = ( restrict_b_nat @ X3 ) ) ).
% 0.27/0.64
% 0.27/0.64 % restrict_idemp
% 0.27/0.64 thf(fact_45_old_Oprod_Oinducts,axiom,
% 0.27/0.64 ! [P: product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 0.27/0.64 ( ! [A3: nat,B3: nat] : ( P @ ( product_Pair_nat_nat @ A3 @ B3 ) )
% 0.27/0.64 => ( P @ Prod ) ) ).
% 0.27/0.64
% 0.27/0.64 % old.prod.inducts
% 0.27/0.64 thf(fact_46_old_Oprod_Oinducts,axiom,
% 0.27/0.64 ! [P: produc398057191_a_nat > $o,Prod: produc398057191_a_nat] :
% 0.27/0.64 ( ! [A3: produc1871334759_a_nat,B3: produc1871334759_a_nat] : ( P @ ( produc1677124439_a_nat @ A3 @ B3 ) )
% 0.27/0.64 => ( P @ Prod ) ) ).
% 0.27/0.64
% 0.27/0.64 % old.prod.inducts
% 0.27/0.64 thf(fact_47_old_Oprod_Oinducts,axiom,
% 0.27/0.64 ! [P: produc1871334759_a_nat > $o,Prod: produc1871334759_a_nat] :
% 0.27/0.64 ( ! [A3: labele935650037_a_nat,B3: labele935650037_a_nat] : ( P @ ( produc1676969687_a_nat @ A3 @ B3 ) )
% 0.27/0.64 => ( P @ Prod ) ) ).
% 0.27/0.64
% 0.27/0.64 % old.prod.inducts
% 0.27/0.64 thf(fact_48_old_Oprod_Oinducts,axiom,
% 0.27/0.64 ! [P: produc1235635379_b_nat > $o,Prod: produc1235635379_b_nat] :
% 0.27/0.64 ( ! [A3: labeled_graph_b_nat,B3: labeled_graph_b_nat] : ( P @ ( produc951298923_b_nat @ A3 @ B3 ) )
% 0.27/0.64 => ( P @ Prod ) ) ).
% 0.27/0.64
% 0.27/0.64 % old.prod.inducts
% 0.27/0.64 thf(fact_49_old_Oprod_Oinducts,axiom,
% 0.27/0.64 ! [P: produc1478835367term_b > $o,Prod: produc1478835367term_b] :
% 0.27/0.64 ( ! [A3: allegorical_term_b,B3: allegorical_term_b] : ( P @ ( produc1990145943term_b @ A3 @ B3 ) )
% 0.27/0.64 => ( P @ Prod ) ) ).
% 0.27/0.64
% 0.27/0.64 % old.prod.inducts
% 0.27/0.64 thf(fact_50_old_Oprod_Oexhaust,axiom,
% 0.27/0.64 ! [Y3: product_prod_nat_nat] :
% 0.27/0.64 ~ ! [A3: nat,B3: nat] :
% 0.27/0.64 ( Y3
% 0.27/0.64 != ( product_Pair_nat_nat @ A3 @ B3 ) ) ).
% 0.27/0.64
% 0.27/0.64 % old.prod.exhaust
% 0.27/0.64 thf(fact_51_old_Oprod_Oexhaust,axiom,
% 0.27/0.64 ! [Y3: produc398057191_a_nat] :
% 0.27/0.64 ~ ! [A3: produc1871334759_a_nat,B3: produc1871334759_a_nat] :
% 0.27/0.64 ( Y3
% 0.27/0.64 != ( produc1677124439_a_nat @ A3 @ B3 ) ) ).
% 0.27/0.64
% 0.27/0.64 % old.prod.exhaust
% 0.27/0.64 thf(fact_52_old_Oprod_Oexhaust,axiom,
% 0.27/0.64 ! [Y3: produc1871334759_a_nat] :
% 0.27/0.64 ~ ! [A3: labele935650037_a_nat,B3: labele935650037_a_nat] :
% 0.27/0.64 ( Y3
% 0.27/0.64 != ( produc1676969687_a_nat @ A3 @ B3 ) ) ).
% 0.27/0.64
% 0.27/0.64 % old.prod.exhaust
% 0.27/0.64 thf(fact_53_old_Oprod_Oexhaust,axiom,
% 0.27/0.64 ! [Y3: produc1235635379_b_nat] :
% 0.27/0.64 ~ ! [A3: labeled_graph_b_nat,B3: labeled_graph_b_nat] :
% 0.27/0.64 ( Y3
% 0.27/0.64 != ( produc951298923_b_nat @ A3 @ B3 ) ) ).
% 0.27/0.64
% 0.27/0.64 % old.prod.exhaust
% 0.27/0.64 thf(fact_54_old_Oprod_Oexhaust,axiom,
% 0.27/0.64 ! [Y3: produc1478835367term_b] :
% 0.27/0.64 ~ ! [A3: allegorical_term_b,B3: allegorical_term_b] :
% 0.27/0.64 ( Y3
% 0.27/0.64 != ( produc1990145943term_b @ A3 @ B3 ) ) ).
% 0.27/0.64
% 0.27/0.64 % old.prod.exhaust
% 0.27/0.64 thf(fact_55_prod__induct3,axiom,
% 0.27/0.64 ! [P: produc398057191_a_nat > $o,X3: produc398057191_a_nat] :
% 0.27/0.64 ( ! [A3: produc1871334759_a_nat,B3: labele935650037_a_nat,C: labele935650037_a_nat] : ( P @ ( produc1677124439_a_nat @ A3 @ ( produc1676969687_a_nat @ B3 @ C ) ) )
% 0.27/0.64 => ( P @ X3 ) ) ).
% 0.27/0.64
% 0.27/0.64 % prod_induct3
% 0.27/0.64 thf(fact_56_prod__cases3,axiom,
% 0.27/0.64 ! [Y3: produc398057191_a_nat] :
% 0.27/0.64 ~ ! [A3: produc1871334759_a_nat,B3: labele935650037_a_nat,C: labele935650037_a_nat] :
% 0.27/0.64 ( Y3
% 0.27/0.64 != ( produc1677124439_a_nat @ A3 @ ( produc1676969687_a_nat @ B3 @ C ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % prod_cases3
% 0.27/0.64 thf(fact_57_Pair__inject,axiom,
% 0.27/0.64 ! [A: nat,B: nat,A2: nat,B2: nat] :
% 0.27/0.64 ( ( ( product_Pair_nat_nat @ A @ B )
% 0.27/0.64 = ( product_Pair_nat_nat @ A2 @ B2 ) )
% 0.27/0.64 => ~ ( ( A = A2 )
% 0.27/0.64 => ( B != B2 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Pair_inject
% 0.27/0.64 thf(fact_58_Pair__inject,axiom,
% 0.27/0.64 ! [A: produc1871334759_a_nat,B: produc1871334759_a_nat,A2: produc1871334759_a_nat,B2: produc1871334759_a_nat] :
% 0.27/0.64 ( ( ( produc1677124439_a_nat @ A @ B )
% 0.27/0.64 = ( produc1677124439_a_nat @ A2 @ B2 ) )
% 0.27/0.64 => ~ ( ( A = A2 )
% 0.27/0.64 => ( B != B2 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Pair_inject
% 0.27/0.64 thf(fact_59_Pair__inject,axiom,
% 0.27/0.64 ! [A: labele935650037_a_nat,B: labele935650037_a_nat,A2: labele935650037_a_nat,B2: labele935650037_a_nat] :
% 0.27/0.64 ( ( ( produc1676969687_a_nat @ A @ B )
% 0.27/0.64 = ( produc1676969687_a_nat @ A2 @ B2 ) )
% 0.27/0.64 => ~ ( ( A = A2 )
% 0.27/0.64 => ( B != B2 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Pair_inject
% 0.27/0.64 thf(fact_60_Pair__inject,axiom,
% 0.27/0.64 ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,A2: labeled_graph_b_nat,B2: labeled_graph_b_nat] :
% 0.27/0.64 ( ( ( produc951298923_b_nat @ A @ B )
% 0.27/0.64 = ( produc951298923_b_nat @ A2 @ B2 ) )
% 0.27/0.64 => ~ ( ( A = A2 )
% 0.27/0.64 => ( B != B2 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Pair_inject
% 0.27/0.64 thf(fact_61_Pair__inject,axiom,
% 0.27/0.64 ! [A: allegorical_term_b,B: allegorical_term_b,A2: allegorical_term_b,B2: allegorical_term_b] :
% 0.27/0.64 ( ( ( produc1990145943term_b @ A @ B )
% 0.27/0.64 = ( produc1990145943term_b @ A2 @ B2 ) )
% 0.27/0.64 => ~ ( ( A = A2 )
% 0.27/0.64 => ( B != B2 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Pair_inject
% 0.27/0.64 thf(fact_62_prod__cases,axiom,
% 0.27/0.64 ! [P: product_prod_nat_nat > $o,P2: product_prod_nat_nat] :
% 0.27/0.64 ( ! [A3: nat,B3: nat] : ( P @ ( product_Pair_nat_nat @ A3 @ B3 ) )
% 0.27/0.64 => ( P @ P2 ) ) ).
% 0.27/0.64
% 0.27/0.64 % prod_cases
% 0.27/0.64 thf(fact_63_prod__cases,axiom,
% 0.27/0.64 ! [P: produc398057191_a_nat > $o,P2: produc398057191_a_nat] :
% 0.27/0.64 ( ! [A3: produc1871334759_a_nat,B3: produc1871334759_a_nat] : ( P @ ( produc1677124439_a_nat @ A3 @ B3 ) )
% 0.27/0.64 => ( P @ P2 ) ) ).
% 0.27/0.64
% 0.27/0.64 % prod_cases
% 0.27/0.64 thf(fact_64_prod__cases,axiom,
% 0.27/0.64 ! [P: produc1871334759_a_nat > $o,P2: produc1871334759_a_nat] :
% 0.27/0.64 ( ! [A3: labele935650037_a_nat,B3: labele935650037_a_nat] : ( P @ ( produc1676969687_a_nat @ A3 @ B3 ) )
% 0.27/0.64 => ( P @ P2 ) ) ).
% 0.27/0.64
% 0.27/0.64 % prod_cases
% 0.27/0.64 thf(fact_65_prod__cases,axiom,
% 0.27/0.64 ! [P: produc1235635379_b_nat > $o,P2: produc1235635379_b_nat] :
% 0.27/0.64 ( ! [A3: labeled_graph_b_nat,B3: labeled_graph_b_nat] : ( P @ ( produc951298923_b_nat @ A3 @ B3 ) )
% 0.27/0.64 => ( P @ P2 ) ) ).
% 0.27/0.64
% 0.27/0.64 % prod_cases
% 0.27/0.64 thf(fact_66_prod__cases,axiom,
% 0.27/0.64 ! [P: produc1478835367term_b > $o,P2: produc1478835367term_b] :
% 0.27/0.64 ( ! [A3: allegorical_term_b,B3: allegorical_term_b] : ( P @ ( produc1990145943term_b @ A3 @ B3 ) )
% 0.27/0.64 => ( P @ P2 ) ) ).
% 0.27/0.64
% 0.27/0.64 % prod_cases
% 0.27/0.64 thf(fact_67_surj__pair,axiom,
% 0.27/0.64 ! [P2: product_prod_nat_nat] :
% 0.27/0.64 ? [X4: nat,Y4: nat] :
% 0.27/0.64 ( P2
% 0.27/0.64 = ( product_Pair_nat_nat @ X4 @ Y4 ) ) ).
% 0.27/0.64
% 0.27/0.64 % surj_pair
% 0.27/0.64 thf(fact_68_surj__pair,axiom,
% 0.27/0.64 ! [P2: produc398057191_a_nat] :
% 0.27/0.64 ? [X4: produc1871334759_a_nat,Y4: produc1871334759_a_nat] :
% 0.27/0.64 ( P2
% 0.27/0.64 = ( produc1677124439_a_nat @ X4 @ Y4 ) ) ).
% 0.27/0.64
% 0.27/0.64 % surj_pair
% 0.27/0.64 thf(fact_69_surj__pair,axiom,
% 0.27/0.64 ! [P2: produc1871334759_a_nat] :
% 0.27/0.64 ? [X4: labele935650037_a_nat,Y4: labele935650037_a_nat] :
% 0.27/0.64 ( P2
% 0.27/0.64 = ( produc1676969687_a_nat @ X4 @ Y4 ) ) ).
% 0.27/0.64
% 0.27/0.64 % surj_pair
% 0.27/0.64 thf(fact_70_surj__pair,axiom,
% 0.27/0.64 ! [P2: produc1235635379_b_nat] :
% 0.27/0.64 ? [X4: labeled_graph_b_nat,Y4: labeled_graph_b_nat] :
% 0.27/0.64 ( P2
% 0.27/0.64 = ( produc951298923_b_nat @ X4 @ Y4 ) ) ).
% 0.27/0.64
% 0.27/0.64 % surj_pair
% 0.27/0.64 thf(fact_71_surj__pair,axiom,
% 0.27/0.64 ! [P2: produc1478835367term_b] :
% 0.27/0.64 ? [X4: allegorical_term_b,Y4: allegorical_term_b] :
% 0.27/0.64 ( P2
% 0.27/0.64 = ( produc1990145943term_b @ X4 @ Y4 ) ) ).
% 0.27/0.64
% 0.27/0.64 % surj_pair
% 0.27/0.64 thf(fact_72_fst__conv,axiom,
% 0.27/0.64 ! [X1: nat,X22: nat] :
% 0.27/0.64 ( ( product_fst_nat_nat @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 0.27/0.64 = X1 ) ).
% 0.27/0.64
% 0.27/0.64 % fst_conv
% 0.27/0.64 thf(fact_73_fst__conv,axiom,
% 0.27/0.64 ! [X1: produc1871334759_a_nat,X22: produc1871334759_a_nat] :
% 0.27/0.64 ( ( produc1049080131_a_nat @ ( produc1677124439_a_nat @ X1 @ X22 ) )
% 0.27/0.64 = X1 ) ).
% 0.27/0.64
% 0.27/0.64 % fst_conv
% 0.27/0.64 thf(fact_74_fst__conv,axiom,
% 0.27/0.64 ! [X1: labele935650037_a_nat,X22: labele935650037_a_nat] :
% 0.27/0.64 ( ( produc719117507_a_nat @ ( produc1676969687_a_nat @ X1 @ X22 ) )
% 0.27/0.64 = X1 ) ).
% 0.27/0.64
% 0.27/0.64 % fst_conv
% 0.27/0.64 thf(fact_75_fst__conv,axiom,
% 0.27/0.64 ! [X1: labeled_graph_b_nat,X22: labeled_graph_b_nat] :
% 0.27/0.64 ( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ X1 @ X22 ) )
% 0.27/0.64 = X1 ) ).
% 0.27/0.64
% 0.27/0.64 % fst_conv
% 0.27/0.64 thf(fact_76_fst__conv,axiom,
% 0.27/0.64 ! [X1: allegorical_term_b,X22: allegorical_term_b] :
% 0.27/0.64 ( ( produc854192515term_b @ ( produc1990145943term_b @ X1 @ X22 ) )
% 0.27/0.64 = X1 ) ).
% 0.27/0.64
% 0.27/0.64 % fst_conv
% 0.27/0.64 thf(fact_77_fst__eqD,axiom,
% 0.27/0.64 ! [X3: nat,Y3: nat,A: nat] :
% 0.27/0.64 ( ( ( product_fst_nat_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 0.27/0.64 = A )
% 0.27/0.64 => ( X3 = A ) ) ).
% 0.27/0.64
% 0.27/0.64 % fst_eqD
% 0.27/0.64 thf(fact_78_fst__eqD,axiom,
% 0.27/0.64 ! [X3: produc1871334759_a_nat,Y3: produc1871334759_a_nat,A: produc1871334759_a_nat] :
% 0.27/0.64 ( ( ( produc1049080131_a_nat @ ( produc1677124439_a_nat @ X3 @ Y3 ) )
% 0.27/0.64 = A )
% 0.27/0.64 => ( X3 = A ) ) ).
% 0.27/0.64
% 0.27/0.64 % fst_eqD
% 0.27/0.64 thf(fact_79_fst__eqD,axiom,
% 0.27/0.64 ! [X3: labele935650037_a_nat,Y3: labele935650037_a_nat,A: labele935650037_a_nat] :
% 0.27/0.64 ( ( ( produc719117507_a_nat @ ( produc1676969687_a_nat @ X3 @ Y3 ) )
% 0.27/0.64 = A )
% 0.27/0.64 => ( X3 = A ) ) ).
% 0.27/0.64
% 0.27/0.64 % fst_eqD
% 0.27/0.64 thf(fact_80_fst__eqD,axiom,
% 0.27/0.64 ! [X3: labeled_graph_b_nat,Y3: labeled_graph_b_nat,A: labeled_graph_b_nat] :
% 0.27/0.64 ( ( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ X3 @ Y3 ) )
% 0.27/0.64 = A )
% 0.27/0.64 => ( X3 = A ) ) ).
% 0.27/0.64
% 0.27/0.64 % fst_eqD
% 0.27/0.64 thf(fact_81_fst__eqD,axiom,
% 0.27/0.64 ! [X3: allegorical_term_b,Y3: allegorical_term_b,A: allegorical_term_b] :
% 0.27/0.64 ( ( ( produc854192515term_b @ ( produc1990145943term_b @ X3 @ Y3 ) )
% 0.27/0.64 = A )
% 0.27/0.64 => ( X3 = A ) ) ).
% 0.27/0.64
% 0.27/0.64 % fst_eqD
% 0.27/0.64 thf(fact_82_snd__conv,axiom,
% 0.27/0.64 ! [X1: nat,X22: nat] :
% 0.27/0.64 ( ( product_snd_nat_nat @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 0.27/0.64 = X22 ) ).
% 0.27/0.64
% 0.27/0.64 % snd_conv
% 0.27/0.64 thf(fact_83_snd__conv,axiom,
% 0.27/0.64 ! [X1: produc1871334759_a_nat,X22: produc1871334759_a_nat] :
% 0.27/0.64 ( ( produc1022852229_a_nat @ ( produc1677124439_a_nat @ X1 @ X22 ) )
% 0.27/0.64 = X22 ) ).
% 0.27/0.64
% 0.27/0.64 % snd_conv
% 0.27/0.64 thf(fact_84_snd__conv,axiom,
% 0.27/0.64 ! [X1: labele935650037_a_nat,X22: labele935650037_a_nat] :
% 0.27/0.64 ( ( produc880161797_a_nat @ ( produc1676969687_a_nat @ X1 @ X22 ) )
% 0.27/0.64 = X22 ) ).
% 0.27/0.64
% 0.27/0.64 % snd_conv
% 0.27/0.64 thf(fact_85_snd__conv,axiom,
% 0.27/0.64 ! [X1: allegorical_term_b,X22: allegorical_term_b] :
% 0.27/0.64 ( ( produc1223098053term_b @ ( produc1990145943term_b @ X1 @ X22 ) )
% 0.27/0.64 = X22 ) ).
% 0.27/0.64
% 0.27/0.64 % snd_conv
% 0.27/0.64 thf(fact_86_snd__conv,axiom,
% 0.27/0.64 ! [X1: labeled_graph_b_nat,X22: labeled_graph_b_nat] :
% 0.27/0.64 ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X1 @ X22 ) )
% 0.27/0.64 = X22 ) ).
% 0.27/0.64
% 0.27/0.64 % snd_conv
% 0.27/0.64 thf(fact_87_snd__eqD,axiom,
% 0.27/0.64 ! [X3: nat,Y3: nat,A: nat] :
% 0.27/0.64 ( ( ( product_snd_nat_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 0.27/0.64 = A )
% 0.27/0.64 => ( Y3 = A ) ) ).
% 0.27/0.64
% 0.27/0.64 % snd_eqD
% 0.27/0.64 thf(fact_88_snd__eqD,axiom,
% 0.27/0.64 ! [X3: produc1871334759_a_nat,Y3: produc1871334759_a_nat,A: produc1871334759_a_nat] :
% 0.27/0.64 ( ( ( produc1022852229_a_nat @ ( produc1677124439_a_nat @ X3 @ Y3 ) )
% 0.27/0.64 = A )
% 0.27/0.64 => ( Y3 = A ) ) ).
% 0.27/0.64
% 0.27/0.64 % snd_eqD
% 0.27/0.64 thf(fact_89_snd__eqD,axiom,
% 0.27/0.64 ! [X3: labele935650037_a_nat,Y3: labele935650037_a_nat,A: labele935650037_a_nat] :
% 0.27/0.64 ( ( ( produc880161797_a_nat @ ( produc1676969687_a_nat @ X3 @ Y3 ) )
% 0.27/0.64 = A )
% 0.27/0.64 => ( Y3 = A ) ) ).
% 0.27/0.64
% 0.27/0.64 % snd_eqD
% 0.27/0.64 thf(fact_90_snd__eqD,axiom,
% 0.27/0.64 ! [X3: allegorical_term_b,Y3: allegorical_term_b,A: allegorical_term_b] :
% 0.27/0.64 ( ( ( produc1223098053term_b @ ( produc1990145943term_b @ X3 @ Y3 ) )
% 0.27/0.64 = A )
% 0.27/0.64 => ( Y3 = A ) ) ).
% 0.27/0.64
% 0.27/0.64 % snd_eqD
% 0.27/0.64 thf(fact_91_snd__eqD,axiom,
% 0.27/0.64 ! [X3: labeled_graph_b_nat,Y3: labeled_graph_b_nat,A: labeled_graph_b_nat] :
% 0.27/0.64 ( ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X3 @ Y3 ) )
% 0.27/0.64 = A )
% 0.27/0.64 => ( Y3 = A ) ) ).
% 0.27/0.64
% 0.27/0.64 % snd_eqD
% 0.27/0.64 thf(fact_92_prod__eq__iff,axiom,
% 0.27/0.64 ( ( ^ [Y5: produc1871334759_a_nat,Z: produc1871334759_a_nat] : ( Y5 = Z ) )
% 0.27/0.64 = ( ^ [S: produc1871334759_a_nat,T2: produc1871334759_a_nat] :
% 0.27/0.64 ( ( ( produc719117507_a_nat @ S )
% 0.27/0.64 = ( produc719117507_a_nat @ T2 ) )
% 0.27/0.64 & ( ( produc880161797_a_nat @ S )
% 0.27/0.64 = ( produc880161797_a_nat @ T2 ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % prod_eq_iff
% 0.27/0.64 thf(fact_93_prod__eq__iff,axiom,
% 0.27/0.64 ( ( ^ [Y5: produc1478835367term_b,Z: produc1478835367term_b] : ( Y5 = Z ) )
% 0.27/0.64 = ( ^ [S: produc1478835367term_b,T2: produc1478835367term_b] :
% 0.27/0.64 ( ( ( produc854192515term_b @ S )
% 0.27/0.64 = ( produc854192515term_b @ T2 ) )
% 0.27/0.64 & ( ( produc1223098053term_b @ S )
% 0.27/0.64 = ( produc1223098053term_b @ T2 ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % prod_eq_iff
% 0.27/0.64 thf(fact_94_prod__eq__iff,axiom,
% 0.27/0.64 ( ( ^ [Y5: produc1235635379_b_nat,Z: produc1235635379_b_nat] : ( Y5 = Z ) )
% 0.27/0.64 = ( ^ [S: produc1235635379_b_nat,T2: produc1235635379_b_nat] :
% 0.27/0.64 ( ( ( produc1542243159_b_nat @ S )
% 0.27/0.64 = ( produc1542243159_b_nat @ T2 ) )
% 0.27/0.64 & ( ( produc194497945_b_nat @ S )
% 0.27/0.64 = ( produc194497945_b_nat @ T2 ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % prod_eq_iff
% 0.27/0.64 thf(fact_95_prod_Oexpand,axiom,
% 0.27/0.64 ! [Prod: produc1871334759_a_nat,Prod2: produc1871334759_a_nat] :
% 0.27/0.64 ( ( ( ( produc719117507_a_nat @ Prod )
% 0.27/0.64 = ( produc719117507_a_nat @ Prod2 ) )
% 0.27/0.64 & ( ( produc880161797_a_nat @ Prod )
% 0.27/0.64 = ( produc880161797_a_nat @ Prod2 ) ) )
% 0.27/0.64 => ( Prod = Prod2 ) ) ).
% 0.27/0.64
% 0.27/0.64 % prod.expand
% 0.27/0.64 thf(fact_96_prod_Oexpand,axiom,
% 0.27/0.64 ! [Prod: produc1478835367term_b,Prod2: produc1478835367term_b] :
% 0.27/0.64 ( ( ( ( produc854192515term_b @ Prod )
% 0.27/0.64 = ( produc854192515term_b @ Prod2 ) )
% 0.27/0.64 & ( ( produc1223098053term_b @ Prod )
% 0.27/0.64 = ( produc1223098053term_b @ Prod2 ) ) )
% 0.27/0.64 => ( Prod = Prod2 ) ) ).
% 0.27/0.64
% 0.27/0.64 % prod.expand
% 0.27/0.64 thf(fact_97_prod_Oexpand,axiom,
% 0.27/0.64 ! [Prod: produc1235635379_b_nat,Prod2: produc1235635379_b_nat] :
% 0.27/0.64 ( ( ( ( produc1542243159_b_nat @ Prod )
% 0.27/0.64 = ( produc1542243159_b_nat @ Prod2 ) )
% 0.27/0.64 & ( ( produc194497945_b_nat @ Prod )
% 0.27/0.64 = ( produc194497945_b_nat @ Prod2 ) ) )
% 0.27/0.64 => ( Prod = Prod2 ) ) ).
% 0.27/0.64
% 0.27/0.64 % prod.expand
% 0.27/0.64 thf(fact_98_prod__eqI,axiom,
% 0.27/0.64 ! [P2: produc1871334759_a_nat,Q: produc1871334759_a_nat] :
% 0.27/0.64 ( ( ( produc719117507_a_nat @ P2 )
% 0.27/0.64 = ( produc719117507_a_nat @ Q ) )
% 0.27/0.64 => ( ( ( produc880161797_a_nat @ P2 )
% 0.27/0.64 = ( produc880161797_a_nat @ Q ) )
% 0.27/0.64 => ( P2 = Q ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % prod_eqI
% 0.27/0.64 thf(fact_99_prod__eqI,axiom,
% 0.27/0.64 ! [P2: produc1478835367term_b,Q: produc1478835367term_b] :
% 0.27/0.64 ( ( ( produc854192515term_b @ P2 )
% 0.27/0.64 = ( produc854192515term_b @ Q ) )
% 0.27/0.64 => ( ( ( produc1223098053term_b @ P2 )
% 0.27/0.64 = ( produc1223098053term_b @ Q ) )
% 0.27/0.64 => ( P2 = Q ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % prod_eqI
% 0.27/0.64 thf(fact_100_prod__eqI,axiom,
% 0.27/0.64 ! [P2: produc1235635379_b_nat,Q: produc1235635379_b_nat] :
% 0.27/0.64 ( ( ( produc1542243159_b_nat @ P2 )
% 0.27/0.64 = ( produc1542243159_b_nat @ Q ) )
% 0.27/0.64 => ( ( ( produc194497945_b_nat @ P2 )
% 0.27/0.64 = ( produc194497945_b_nat @ Q ) )
% 0.27/0.64 => ( P2 = Q ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % prod_eqI
% 0.27/0.64 thf(fact_101_labeled__graph_Oexpand,axiom,
% 0.27/0.64 ! [Labeled_graph: labele935650037_a_nat,Labeled_graph2: labele935650037_a_nat] :
% 0.27/0.64 ( ( ( ( labele195203296_a_nat @ Labeled_graph )
% 0.27/0.64 = ( labele195203296_a_nat @ Labeled_graph2 ) )
% 0.27/0.64 & ( ( labele1810595089_a_nat @ Labeled_graph )
% 0.27/0.64 = ( labele1810595089_a_nat @ Labeled_graph2 ) ) )
% 0.27/0.64 => ( Labeled_graph = Labeled_graph2 ) ) ).
% 0.27/0.64
% 0.27/0.64 % labeled_graph.expand
% 0.27/0.64 thf(fact_102_labeled__graph_Oexpand,axiom,
% 0.27/0.64 ! [Labeled_graph: labeled_graph_b_nat,Labeled_graph2: labeled_graph_b_nat] :
% 0.27/0.64 ( ( ( ( labeled_edges_b_nat @ Labeled_graph )
% 0.27/0.64 = ( labeled_edges_b_nat @ Labeled_graph2 ) )
% 0.27/0.64 & ( ( labele460410879_b_nat @ Labeled_graph )
% 0.27/0.64 = ( labele460410879_b_nat @ Labeled_graph2 ) ) )
% 0.27/0.64 => ( Labeled_graph = Labeled_graph2 ) ) ).
% 0.27/0.64
% 0.27/0.64 % labeled_graph.expand
% 0.27/0.64 thf(fact_103_surjective__pairing,axiom,
% 0.27/0.64 ! [T: product_prod_nat_nat] :
% 0.27/0.64 ( T
% 0.27/0.64 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ T ) @ ( product_snd_nat_nat @ T ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % surjective_pairing
% 0.27/0.64 thf(fact_104_surjective__pairing,axiom,
% 0.27/0.64 ! [T: produc398057191_a_nat] :
% 0.27/0.64 ( T
% 0.27/0.64 = ( produc1677124439_a_nat @ ( produc1049080131_a_nat @ T ) @ ( produc1022852229_a_nat @ T ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % surjective_pairing
% 0.27/0.64 thf(fact_105_surjective__pairing,axiom,
% 0.27/0.64 ! [T: produc1871334759_a_nat] :
% 0.27/0.64 ( T
% 0.27/0.64 = ( produc1676969687_a_nat @ ( produc719117507_a_nat @ T ) @ ( produc880161797_a_nat @ T ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % surjective_pairing
% 0.27/0.64 thf(fact_106_surjective__pairing,axiom,
% 0.27/0.64 ! [T: produc1478835367term_b] :
% 0.27/0.64 ( T
% 0.27/0.64 = ( produc1990145943term_b @ ( produc854192515term_b @ T ) @ ( produc1223098053term_b @ T ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % surjective_pairing
% 0.27/0.64 thf(fact_107_surjective__pairing,axiom,
% 0.27/0.64 ! [T: produc1235635379_b_nat] :
% 0.27/0.64 ( T
% 0.27/0.64 = ( produc951298923_b_nat @ ( produc1542243159_b_nat @ T ) @ ( produc194497945_b_nat @ T ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % surjective_pairing
% 0.27/0.64 thf(fact_108_prod_Oexhaust__sel,axiom,
% 0.27/0.64 ! [Prod: product_prod_nat_nat] :
% 0.27/0.64 ( Prod
% 0.27/0.64 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % prod.exhaust_sel
% 0.27/0.64 thf(fact_109_prod_Oexhaust__sel,axiom,
% 0.27/0.64 ! [Prod: produc398057191_a_nat] :
% 0.27/0.64 ( Prod
% 0.27/0.64 = ( produc1677124439_a_nat @ ( produc1049080131_a_nat @ Prod ) @ ( produc1022852229_a_nat @ Prod ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % prod.exhaust_sel
% 0.27/0.64 thf(fact_110_prod_Oexhaust__sel,axiom,
% 0.27/0.64 ! [Prod: produc1871334759_a_nat] :
% 0.27/0.64 ( Prod
% 0.27/0.64 = ( produc1676969687_a_nat @ ( produc719117507_a_nat @ Prod ) @ ( produc880161797_a_nat @ Prod ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % prod.exhaust_sel
% 0.27/0.64 thf(fact_111_prod_Oexhaust__sel,axiom,
% 0.27/0.64 ! [Prod: produc1478835367term_b] :
% 0.27/0.64 ( Prod
% 0.27/0.64 = ( produc1990145943term_b @ ( produc854192515term_b @ Prod ) @ ( produc1223098053term_b @ Prod ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % prod.exhaust_sel
% 0.27/0.64 thf(fact_112_prod_Oexhaust__sel,axiom,
% 0.27/0.64 ! [Prod: produc1235635379_b_nat] :
% 0.27/0.64 ( Prod
% 0.27/0.64 = ( produc951298923_b_nat @ ( produc1542243159_b_nat @ Prod ) @ ( produc194497945_b_nat @ Prod ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % prod.exhaust_sel
% 0.27/0.64 thf(fact_113_subgraph__preserves__hom,axiom,
% 0.27/0.64 ! [A4: labele935650037_a_nat,B4: labele935650037_a_nat,X: labele935650037_a_nat,H: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( graph_2130075512at_nat @ A4 @ B4 @ ( id_on_nat @ ( labele1810595089_a_nat @ A4 ) ) )
% 0.27/0.64 => ( ( graph_2130075512at_nat @ X @ A4 @ H )
% 0.27/0.64 => ( graph_2130075512at_nat @ X @ B4 @ H ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % subgraph_preserves_hom
% 0.27/0.64 thf(fact_114_subgraph__preserves__hom,axiom,
% 0.27/0.64 ! [A4: labeled_graph_b_nat,B4: labeled_graph_b_nat,X: labeled_graph_b_nat,H: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( graph_529870330at_nat @ A4 @ B4 @ ( id_on_nat @ ( labele460410879_b_nat @ A4 ) ) )
% 0.27/0.64 => ( ( graph_529870330at_nat @ X @ A4 @ H )
% 0.27/0.64 => ( graph_529870330at_nat @ X @ B4 @ H ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % subgraph_preserves_hom
% 0.27/0.64 thf(fact_115_subgraph__trans,axiom,
% 0.27/0.64 ! [G_1: labele935650037_a_nat,G_2: labele935650037_a_nat,G_3: labele935650037_a_nat] :
% 0.27/0.64 ( ( graph_2130075512at_nat @ G_1 @ G_2 @ ( id_on_nat @ ( labele1810595089_a_nat @ G_1 ) ) )
% 0.27/0.64 => ( ( graph_2130075512at_nat @ G_2 @ G_3 @ ( id_on_nat @ ( labele1810595089_a_nat @ G_2 ) ) )
% 0.27/0.64 => ( graph_2130075512at_nat @ G_1 @ G_3 @ ( id_on_nat @ ( labele1810595089_a_nat @ G_1 ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % subgraph_trans
% 0.27/0.64 thf(fact_116_subgraph__trans,axiom,
% 0.27/0.64 ! [G_1: labeled_graph_b_nat,G_2: labeled_graph_b_nat,G_3: labeled_graph_b_nat] :
% 0.27/0.64 ( ( graph_529870330at_nat @ G_1 @ G_2 @ ( id_on_nat @ ( labele460410879_b_nat @ G_1 ) ) )
% 0.27/0.64 => ( ( graph_529870330at_nat @ G_2 @ G_3 @ ( id_on_nat @ ( labele460410879_b_nat @ G_2 ) ) )
% 0.27/0.64 => ( graph_529870330at_nat @ G_1 @ G_3 @ ( id_on_nat @ ( labele460410879_b_nat @ G_1 ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % subgraph_trans
% 0.27/0.64 thf(fact_117_Id__onI,axiom,
% 0.27/0.64 ! [A: produc1478835367term_b,A4: set_Pr1163220871term_b] :
% 0.27/0.64 ( ( member516522448term_b @ A @ A4 )
% 0.27/0.64 => ( member1449757456term_b @ ( produc859843415term_b @ A @ A ) @ ( id_on_1664915780term_b @ A4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Id_onI
% 0.27/0.64 thf(fact_118_Id__onI,axiom,
% 0.27/0.64 ! [A: produc1235635379_b_nat,A4: set_Pr551076371_b_nat] :
% 0.27/0.64 ( ( member963855452_b_nat @ A @ A4 )
% 0.27/0.64 => ( member889223696_b_nat @ ( produc1754969175_b_nat @ A @ A ) @ ( id_on_138931664_b_nat @ A4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Id_onI
% 0.27/0.64 thf(fact_119_Id__onI,axiom,
% 0.27/0.64 ! [A: produc398057191_a_nat,A4: set_Pr924198087_a_nat] :
% 0.27/0.64 ( ( member584645392_a_nat @ A @ A4 )
% 0.27/0.64 => ( member829905680_a_nat @ ( produc170611543_a_nat @ A @ A ) @ ( id_on_1395957380_a_nat @ A4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Id_onI
% 0.27/0.64 thf(fact_120_Id__onI,axiom,
% 0.27/0.64 ! [A: product_prod_nat_nat,A4: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( member701585322at_nat @ A @ A4 )
% 0.27/0.64 => ( member2027625872at_nat @ ( produc1168807639at_nat @ A @ A ) @ ( id_on_2144791838at_nat @ A4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Id_onI
% 0.27/0.64 thf(fact_121_Id__onI,axiom,
% 0.27/0.64 ! [A: labele935650037_a_nat,A4: set_la1083530965_a_nat] :
% 0.27/0.64 ( ( member964390942_a_nat @ A @ A4 )
% 0.27/0.64 => ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ A ) @ ( id_on_689842066_a_nat @ A4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Id_onI
% 0.27/0.64 thf(fact_122_Id__onI,axiom,
% 0.27/0.64 ! [A: produc1871334759_a_nat,A4: set_Pr1987088711_a_nat] :
% 0.27/0.64 ( ( member832397200_a_nat @ A @ A4 )
% 0.27/0.64 => ( member584645392_a_nat @ ( produc1677124439_a_nat @ A @ A ) @ ( id_on_1651096324_a_nat @ A4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Id_onI
% 0.27/0.64 thf(fact_123_Id__onI,axiom,
% 0.27/0.64 ! [A: nat,A4: set_nat] :
% 0.27/0.64 ( ( member_nat @ A @ A4 )
% 0.27/0.64 => ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ A ) @ ( id_on_nat @ A4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Id_onI
% 0.27/0.64 thf(fact_124_Id__onI,axiom,
% 0.27/0.64 ! [A: labeled_graph_b_nat,A4: set_la1976028319_b_nat] :
% 0.27/0.64 ( ( member1483953152_b_nat @ A @ A4 )
% 0.27/0.64 => ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ A ) @ ( id_on_583275916_b_nat @ A4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Id_onI
% 0.27/0.64 thf(fact_125_Id__onI,axiom,
% 0.27/0.64 ! [A: allegorical_term_b,A4: set_al1193902458term_b] :
% 0.27/0.64 ( ( member93680451term_b @ A @ A4 )
% 0.27/0.64 => ( member516522448term_b @ ( produc1990145943term_b @ A @ A ) @ ( id_on_1536886967term_b @ A4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Id_onI
% 0.27/0.64 thf(fact_126_set__of__graph__rules__def,axiom,
% 0.27/0.64 ( set_of195930477at_nat
% 0.27/0.64 = ( ^ [Rs: set_Pr665622551at_nat] :
% 0.27/0.64 ! [X5: produc1391440311at_nat] :
% 0.27/0.64 ( ( member1129678944at_nat @ X5 @ Rs )
% 0.27/0.64 => ( ( graph_2111906684at_nat @ ( produc1995789403at_nat @ X5 ) @ ( produc1564126365at_nat @ X5 ) @ ( id_on_nat @ ( labele560327297at_nat @ ( produc1995789403at_nat @ X5 ) ) ) )
% 0.27/0.64 & ( ( produc1564126365at_nat @ X5 )
% 0.27/0.64 = ( restri321299017at_nat @ ( produc1564126365at_nat @ X5 ) ) )
% 0.27/0.64 & ( finite_finite_nat @ ( labele560327297at_nat @ ( produc1564126365at_nat @ X5 ) ) )
% 0.27/0.64 & ( finite48957584at_nat @ ( labele2032268018at_nat @ ( produc1564126365at_nat @ X5 ) ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % set_of_graph_rules_def
% 0.27/0.64 thf(fact_127_set__of__graph__rules__def,axiom,
% 0.27/0.64 ( set_of1384085797_a_nat
% 0.27/0.64 = ( ^ [Rs: set_Pr1987088711_a_nat] :
% 0.27/0.64 ! [X5: produc1871334759_a_nat] :
% 0.27/0.64 ( ( member832397200_a_nat @ X5 @ Rs )
% 0.27/0.64 => ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ X5 ) @ ( produc880161797_a_nat @ X5 ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ X5 ) ) ) )
% 0.27/0.64 & ( ( produc880161797_a_nat @ X5 )
% 0.27/0.64 = ( restri572569417_a_nat @ ( produc880161797_a_nat @ X5 ) ) )
% 0.27/0.64 & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ X5 ) ) )
% 0.27/0.64 & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ X5 ) ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % set_of_graph_rules_def
% 0.27/0.64 thf(fact_128_set__of__graph__rules__def,axiom,
% 0.27/0.64 ( set_of41538795_b_nat
% 0.27/0.64 = ( ^ [Rs: set_Pr551076371_b_nat] :
% 0.27/0.64 ! [X5: produc1235635379_b_nat] :
% 0.27/0.64 ( ( member963855452_b_nat @ X5 @ Rs )
% 0.27/0.64 => ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ X5 ) @ ( produc194497945_b_nat @ X5 ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ X5 ) ) ) )
% 0.27/0.64 & ( ( produc194497945_b_nat @ X5 )
% 0.27/0.64 = ( restrict_b_nat @ ( produc194497945_b_nat @ X5 ) ) )
% 0.27/0.64 & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ X5 ) ) )
% 0.27/0.64 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ X5 ) ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % set_of_graph_rules_def
% 0.27/0.64 thf(fact_129_mem__Collect__eq,axiom,
% 0.27/0.64 ! [A: produc1478835367term_b,P: produc1478835367term_b > $o] :
% 0.27/0.64 ( ( member516522448term_b @ A @ ( collec135640594term_b @ P ) )
% 0.27/0.64 = ( P @ A ) ) ).
% 0.27/0.64
% 0.27/0.64 % mem_Collect_eq
% 0.27/0.64 thf(fact_130_mem__Collect__eq,axiom,
% 0.27/0.64 ! [A: produc1235635379_b_nat,P: produc1235635379_b_nat > $o] :
% 0.27/0.64 ( ( member963855452_b_nat @ A @ ( collec1615000990_b_nat @ P ) )
% 0.27/0.64 = ( P @ A ) ) ).
% 0.27/0.64
% 0.27/0.64 % mem_Collect_eq
% 0.27/0.64 thf(fact_131_mem__Collect__eq,axiom,
% 0.27/0.64 ! [A: produc398057191_a_nat,P: produc398057191_a_nat > $o] :
% 0.27/0.64 ( ( member584645392_a_nat @ A @ ( collec1701899602_a_nat @ P ) )
% 0.27/0.64 = ( P @ A ) ) ).
% 0.27/0.64
% 0.27/0.64 % mem_Collect_eq
% 0.27/0.64 thf(fact_132_mem__Collect__eq,axiom,
% 0.27/0.64 ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 0.27/0.64 ( ( member701585322at_nat @ A @ ( collec7649004at_nat @ P ) )
% 0.27/0.64 = ( P @ A ) ) ).
% 0.27/0.64
% 0.27/0.64 % mem_Collect_eq
% 0.27/0.64 thf(fact_133_mem__Collect__eq,axiom,
% 0.27/0.64 ! [A: nat,P: nat > $o] :
% 0.27/0.64 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 0.27/0.64 = ( P @ A ) ) ).
% 0.27/0.64
% 0.27/0.64 % mem_Collect_eq
% 0.27/0.64 thf(fact_134_mem__Collect__eq,axiom,
% 0.27/0.64 ! [A: produc1871334759_a_nat,P: produc1871334759_a_nat > $o] :
% 0.27/0.64 ( ( member832397200_a_nat @ A @ ( collec357096914_a_nat @ P ) )
% 0.27/0.64 = ( P @ A ) ) ).
% 0.27/0.64
% 0.27/0.64 % mem_Collect_eq
% 0.27/0.64 thf(fact_135_Collect__mem__eq,axiom,
% 0.27/0.64 ! [A4: set_Pr1163220871term_b] :
% 0.27/0.64 ( ( collec135640594term_b
% 0.27/0.64 @ ^ [X5: produc1478835367term_b] : ( member516522448term_b @ X5 @ A4 ) )
% 0.27/0.64 = A4 ) ).
% 0.27/0.64
% 0.27/0.64 % Collect_mem_eq
% 0.27/0.64 thf(fact_136_Collect__mem__eq,axiom,
% 0.27/0.64 ! [A4: set_Pr551076371_b_nat] :
% 0.27/0.64 ( ( collec1615000990_b_nat
% 0.27/0.64 @ ^ [X5: produc1235635379_b_nat] : ( member963855452_b_nat @ X5 @ A4 ) )
% 0.27/0.64 = A4 ) ).
% 0.27/0.64
% 0.27/0.64 % Collect_mem_eq
% 0.27/0.64 thf(fact_137_Collect__mem__eq,axiom,
% 0.27/0.64 ! [A4: set_Pr924198087_a_nat] :
% 0.27/0.64 ( ( collec1701899602_a_nat
% 0.27/0.64 @ ^ [X5: produc398057191_a_nat] : ( member584645392_a_nat @ X5 @ A4 ) )
% 0.27/0.64 = A4 ) ).
% 0.27/0.64
% 0.27/0.64 % Collect_mem_eq
% 0.27/0.64 thf(fact_138_Collect__mem__eq,axiom,
% 0.27/0.64 ! [A4: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( collec7649004at_nat
% 0.27/0.64 @ ^ [X5: product_prod_nat_nat] : ( member701585322at_nat @ X5 @ A4 ) )
% 0.27/0.64 = A4 ) ).
% 0.27/0.64
% 0.27/0.64 % Collect_mem_eq
% 0.27/0.64 thf(fact_139_Collect__mem__eq,axiom,
% 0.27/0.64 ! [A4: set_nat] :
% 0.27/0.64 ( ( collect_nat
% 0.27/0.64 @ ^ [X5: nat] : ( member_nat @ X5 @ A4 ) )
% 0.27/0.64 = A4 ) ).
% 0.27/0.64
% 0.27/0.64 % Collect_mem_eq
% 0.27/0.64 thf(fact_140_Collect__mem__eq,axiom,
% 0.27/0.64 ! [A4: set_Pr1987088711_a_nat] :
% 0.27/0.64 ( ( collec357096914_a_nat
% 0.27/0.64 @ ^ [X5: produc1871334759_a_nat] : ( member832397200_a_nat @ X5 @ A4 ) )
% 0.27/0.64 = A4 ) ).
% 0.27/0.64
% 0.27/0.64 % Collect_mem_eq
% 0.27/0.64 thf(fact_141_Collect__cong,axiom,
% 0.27/0.64 ! [P: produc1871334759_a_nat > $o,Q2: produc1871334759_a_nat > $o] :
% 0.27/0.64 ( ! [X4: produc1871334759_a_nat] :
% 0.27/0.64 ( ( P @ X4 )
% 0.27/0.64 = ( Q2 @ X4 ) )
% 0.27/0.64 => ( ( collec357096914_a_nat @ P )
% 0.27/0.64 = ( collec357096914_a_nat @ Q2 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Collect_cong
% 0.27/0.64 thf(fact_142_verts__in__translation,axiom,
% 0.27/0.64 ! [X: allego510293162tant_a] : ( inv_translation @ ( labele1810595089_a_nat @ ( transl1275713022tant_a @ X ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % verts_in_translation
% 0.27/0.64 thf(fact_143_verts__in__translation,axiom,
% 0.27/0.64 ! [X: allegorical_term_b] : ( inv_translation @ ( labele460410879_b_nat @ ( translation_b @ X ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % verts_in_translation
% 0.27/0.64 thf(fact_144_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.27/0.64 ! [P: allegorical_term_b > allegorical_term_b > $o,X3: allegorical_term_b,Y3: allegorical_term_b,A: produc1478835367term_b] :
% 0.27/0.64 ( ( P @ X3 @ Y3 )
% 0.27/0.64 => ( ( A
% 0.27/0.64 = ( produc1990145943term_b @ X3 @ Y3 ) )
% 0.27/0.64 => ( P @ ( produc854192515term_b @ A ) @ ( produc1223098053term_b @ A ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % BNF_Greatest_Fixpoint.subst_Pair
% 0.27/0.64 thf(fact_145_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.27/0.64 ! [P: labeled_graph_b_nat > labeled_graph_b_nat > $o,X3: labeled_graph_b_nat,Y3: labeled_graph_b_nat,A: produc1235635379_b_nat] :
% 0.27/0.64 ( ( P @ X3 @ Y3 )
% 0.27/0.64 => ( ( A
% 0.27/0.64 = ( produc951298923_b_nat @ X3 @ Y3 ) )
% 0.27/0.64 => ( P @ ( produc1542243159_b_nat @ A ) @ ( produc194497945_b_nat @ A ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % BNF_Greatest_Fixpoint.subst_Pair
% 0.27/0.64 thf(fact_146_conjI__realizer,axiom,
% 0.27/0.64 ! [P: allegorical_term_b > $o,P2: allegorical_term_b,Q2: allegorical_term_b > $o,Q: allegorical_term_b] :
% 0.27/0.64 ( ( P @ P2 )
% 0.27/0.64 => ( ( Q2 @ Q )
% 0.27/0.64 => ( ( P @ ( produc854192515term_b @ ( produc1990145943term_b @ P2 @ Q ) ) )
% 0.27/0.64 & ( Q2 @ ( produc1223098053term_b @ ( produc1990145943term_b @ P2 @ Q ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % conjI_realizer
% 0.27/0.64 thf(fact_147_conjI__realizer,axiom,
% 0.27/0.64 ! [P: labeled_graph_b_nat > $o,P2: labeled_graph_b_nat,Q2: labeled_graph_b_nat > $o,Q: labeled_graph_b_nat] :
% 0.27/0.64 ( ( P @ P2 )
% 0.27/0.64 => ( ( Q2 @ Q )
% 0.27/0.64 => ( ( P @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ P2 @ Q ) ) )
% 0.27/0.64 & ( Q2 @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ P2 @ Q ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % conjI_realizer
% 0.27/0.64 thf(fact_148_exI__realizer,axiom,
% 0.27/0.64 ! [P: allegorical_term_b > allegorical_term_b > $o,Y3: allegorical_term_b,X3: allegorical_term_b] :
% 0.27/0.64 ( ( P @ Y3 @ X3 )
% 0.27/0.64 => ( P @ ( produc1223098053term_b @ ( produc1990145943term_b @ X3 @ Y3 ) ) @ ( produc854192515term_b @ ( produc1990145943term_b @ X3 @ Y3 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % exI_realizer
% 0.27/0.64 thf(fact_149_exI__realizer,axiom,
% 0.27/0.64 ! [P: labeled_graph_b_nat > labeled_graph_b_nat > $o,Y3: labeled_graph_b_nat,X3: labeled_graph_b_nat] :
% 0.27/0.64 ( ( P @ Y3 @ X3 )
% 0.27/0.64 => ( P @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ X3 @ Y3 ) ) @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ X3 @ Y3 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % exI_realizer
% 0.27/0.64 thf(fact_150_allegorical__term_Oinject_I1_J,axiom,
% 0.27/0.64 ! [X11: allegorical_term_b,X12: allegorical_term_b,Y11: allegorical_term_b,Y12: allegorical_term_b] :
% 0.27/0.64 ( ( ( allegorical_A_Int_b @ X11 @ X12 )
% 0.27/0.64 = ( allegorical_A_Int_b @ Y11 @ Y12 ) )
% 0.27/0.64 = ( ( X11 = Y11 )
% 0.27/0.64 & ( X12 = Y12 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % allegorical_term.inject(1)
% 0.27/0.64 thf(fact_151_fin__maintainedI,axiom,
% 0.27/0.64 ! [R: produc1235635379_b_nat,G: labeled_graph_b_nat] :
% 0.27/0.64 ( ! [F: labeled_graph_b_nat,F2: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( ( F
% 0.27/0.64 = ( restrict_b_nat @ F ) )
% 0.27/0.64 & ( finite_finite_nat @ ( labele460410879_b_nat @ F ) )
% 0.27/0.64 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ F ) ) )
% 0.27/0.64 => ( ( graph_529870330at_nat @ F @ ( produc1542243159_b_nat @ R ) @ ( id_on_nat @ ( labele460410879_b_nat @ F ) ) )
% 0.27/0.64 => ( ( extensible_b_nat_nat @ ( produc951298923_b_nat @ F @ ( produc1542243159_b_nat @ R ) ) @ G @ F2 )
% 0.27/0.64 => ( ( graph_529870330at_nat @ F @ G @ F2 )
% 0.27/0.64 => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ F @ ( produc194497945_b_nat @ R ) ) @ G @ F2 ) ) ) ) )
% 0.27/0.64 => ( fin_ma971967913at_nat @ R @ G ) ) ).
% 0.27/0.64
% 0.27/0.64 % fin_maintainedI
% 0.27/0.64 thf(fact_152_set__of__graph__rulesD_I1_J,axiom,
% 0.27/0.64 ! [Rs2: set_Pr1987088711_a_nat,R: produc1871334759_a_nat] :
% 0.27/0.64 ( ( set_of1384085797_a_nat @ Rs2 )
% 0.27/0.64 => ( ( member832397200_a_nat @ R @ Rs2 )
% 0.27/0.64 => ( ( ( produc719117507_a_nat @ R )
% 0.27/0.64 = ( restri572569417_a_nat @ ( produc719117507_a_nat @ R ) ) )
% 0.27/0.64 & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ R ) ) )
% 0.27/0.64 & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc719117507_a_nat @ R ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % set_of_graph_rulesD(1)
% 0.27/0.64 thf(fact_153_set__of__graph__rulesD_I1_J,axiom,
% 0.27/0.64 ! [Rs2: set_Pr551076371_b_nat,R: produc1235635379_b_nat] :
% 0.27/0.64 ( ( set_of41538795_b_nat @ Rs2 )
% 0.27/0.64 => ( ( member963855452_b_nat @ R @ Rs2 )
% 0.27/0.64 => ( ( ( produc1542243159_b_nat @ R )
% 0.27/0.64 = ( restrict_b_nat @ ( produc1542243159_b_nat @ R ) ) )
% 0.27/0.64 & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ R ) ) )
% 0.27/0.64 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc1542243159_b_nat @ R ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % set_of_graph_rulesD(1)
% 0.27/0.64 thf(fact_154_set__of__graph__rulesD_I2_J,axiom,
% 0.27/0.64 ! [Rs2: set_Pr1987088711_a_nat,R: produc1871334759_a_nat] :
% 0.27/0.64 ( ( set_of1384085797_a_nat @ Rs2 )
% 0.27/0.64 => ( ( member832397200_a_nat @ R @ Rs2 )
% 0.27/0.64 => ( ( ( produc880161797_a_nat @ R )
% 0.27/0.64 = ( restri572569417_a_nat @ ( produc880161797_a_nat @ R ) ) )
% 0.27/0.64 & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ R ) ) )
% 0.27/0.64 & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ R ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % set_of_graph_rulesD(2)
% 0.27/0.64 thf(fact_155_set__of__graph__rulesD_I2_J,axiom,
% 0.27/0.64 ! [Rs2: set_Pr551076371_b_nat,R: produc1235635379_b_nat] :
% 0.27/0.64 ( ( set_of41538795_b_nat @ Rs2 )
% 0.27/0.64 => ( ( member963855452_b_nat @ R @ Rs2 )
% 0.27/0.64 => ( ( ( produc194497945_b_nat @ R )
% 0.27/0.64 = ( restrict_b_nat @ ( produc194497945_b_nat @ R ) ) )
% 0.27/0.64 & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ R ) ) )
% 0.27/0.64 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ R ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % set_of_graph_rulesD(2)
% 0.27/0.64 thf(fact_156_extensible__refl,axiom,
% 0.27/0.64 ! [R: labeled_graph_b_nat,G: labeled_graph_b_nat,F3: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( graph_529870330at_nat @ R @ G @ F3 )
% 0.27/0.64 => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ R @ R ) @ G @ F3 ) ) ).
% 0.27/0.64
% 0.27/0.64 % extensible_refl
% 0.27/0.64 thf(fact_157_set__of__graph__rulesD_I3_J,axiom,
% 0.27/0.64 ! [Rs2: set_Pr1987088711_a_nat,R: produc1871334759_a_nat] :
% 0.27/0.64 ( ( set_of1384085797_a_nat @ Rs2 )
% 0.27/0.64 => ( ( member832397200_a_nat @ R @ Rs2 )
% 0.27/0.64 => ( graph_2130075512at_nat @ ( produc719117507_a_nat @ R ) @ ( produc880161797_a_nat @ R ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ R ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % set_of_graph_rulesD(3)
% 0.27/0.64 thf(fact_158_set__of__graph__rulesD_I3_J,axiom,
% 0.27/0.64 ! [Rs2: set_Pr551076371_b_nat,R: produc1235635379_b_nat] :
% 0.27/0.64 ( ( set_of41538795_b_nat @ Rs2 )
% 0.27/0.64 => ( ( member963855452_b_nat @ R @ Rs2 )
% 0.27/0.64 => ( graph_529870330at_nat @ ( produc1542243159_b_nat @ R ) @ ( produc194497945_b_nat @ R ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ R ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % set_of_graph_rulesD(3)
% 0.27/0.64 thf(fact_159_exE__realizer_H,axiom,
% 0.27/0.64 ! [P: allegorical_term_b > allegorical_term_b > $o,P2: produc1478835367term_b] :
% 0.27/0.64 ( ( P @ ( produc1223098053term_b @ P2 ) @ ( produc854192515term_b @ P2 ) )
% 0.27/0.64 => ~ ! [X4: allegorical_term_b,Y4: allegorical_term_b] :
% 0.27/0.64 ~ ( P @ Y4 @ X4 ) ) ).
% 0.27/0.64
% 0.27/0.64 % exE_realizer'
% 0.27/0.64 thf(fact_160_exE__realizer_H,axiom,
% 0.27/0.64 ! [P: labeled_graph_b_nat > labeled_graph_b_nat > $o,P2: produc1235635379_b_nat] :
% 0.27/0.64 ( ( P @ ( produc194497945_b_nat @ P2 ) @ ( produc1542243159_b_nat @ P2 ) )
% 0.27/0.64 => ~ ! [X4: labeled_graph_b_nat,Y4: labeled_graph_b_nat] :
% 0.27/0.64 ~ ( P @ Y4 @ X4 ) ) ).
% 0.27/0.64
% 0.27/0.64 % exE_realizer'
% 0.27/0.64 thf(fact_161_Id__onE,axiom,
% 0.27/0.64 ! [C2: produc398057191_a_nat,A4: set_Pr1987088711_a_nat] :
% 0.27/0.64 ( ( member584645392_a_nat @ C2 @ ( id_on_1651096324_a_nat @ A4 ) )
% 0.27/0.64 => ~ ! [X4: produc1871334759_a_nat] :
% 0.27/0.64 ( ( member832397200_a_nat @ X4 @ A4 )
% 0.27/0.64 => ( C2
% 0.27/0.64 != ( produc1677124439_a_nat @ X4 @ X4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Id_onE
% 0.27/0.64 thf(fact_162_Id__onE,axiom,
% 0.27/0.64 ! [C2: produc1871334759_a_nat,A4: set_la1083530965_a_nat] :
% 0.27/0.64 ( ( member832397200_a_nat @ C2 @ ( id_on_689842066_a_nat @ A4 ) )
% 0.27/0.64 => ~ ! [X4: labele935650037_a_nat] :
% 0.27/0.64 ( ( member964390942_a_nat @ X4 @ A4 )
% 0.27/0.64 => ( C2
% 0.27/0.64 != ( produc1676969687_a_nat @ X4 @ X4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Id_onE
% 0.27/0.64 thf(fact_163_Id__onE,axiom,
% 0.27/0.64 ! [C2: product_prod_nat_nat,A4: set_nat] :
% 0.27/0.64 ( ( member701585322at_nat @ C2 @ ( id_on_nat @ A4 ) )
% 0.27/0.64 => ~ ! [X4: nat] :
% 0.27/0.64 ( ( member_nat @ X4 @ A4 )
% 0.27/0.64 => ( C2
% 0.27/0.64 != ( product_Pair_nat_nat @ X4 @ X4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Id_onE
% 0.27/0.64 thf(fact_164_Id__onE,axiom,
% 0.27/0.64 ! [C2: produc1235635379_b_nat,A4: set_la1976028319_b_nat] :
% 0.27/0.64 ( ( member963855452_b_nat @ C2 @ ( id_on_583275916_b_nat @ A4 ) )
% 0.27/0.64 => ~ ! [X4: labeled_graph_b_nat] :
% 0.27/0.64 ( ( member1483953152_b_nat @ X4 @ A4 )
% 0.27/0.64 => ( C2
% 0.27/0.64 != ( produc951298923_b_nat @ X4 @ X4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Id_onE
% 0.27/0.64 thf(fact_165_Id__onE,axiom,
% 0.27/0.64 ! [C2: produc1478835367term_b,A4: set_al1193902458term_b] :
% 0.27/0.64 ( ( member516522448term_b @ C2 @ ( id_on_1536886967term_b @ A4 ) )
% 0.27/0.64 => ~ ! [X4: allegorical_term_b] :
% 0.27/0.64 ( ( member93680451term_b @ X4 @ A4 )
% 0.27/0.64 => ( C2
% 0.27/0.64 != ( produc1990145943term_b @ X4 @ X4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Id_onE
% 0.27/0.64 thf(fact_166_Id__on__eqI,axiom,
% 0.27/0.64 ! [A: labele935650037_a_nat,B: labele935650037_a_nat,A4: set_la1083530965_a_nat] :
% 0.27/0.64 ( ( A = B )
% 0.27/0.64 => ( ( member964390942_a_nat @ A @ A4 )
% 0.27/0.64 => ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ ( id_on_689842066_a_nat @ A4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Id_on_eqI
% 0.27/0.64 thf(fact_167_Id__on__eqI,axiom,
% 0.27/0.64 ! [A: produc1871334759_a_nat,B: produc1871334759_a_nat,A4: set_Pr1987088711_a_nat] :
% 0.27/0.64 ( ( A = B )
% 0.27/0.64 => ( ( member832397200_a_nat @ A @ A4 )
% 0.27/0.64 => ( member584645392_a_nat @ ( produc1677124439_a_nat @ A @ B ) @ ( id_on_1651096324_a_nat @ A4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Id_on_eqI
% 0.27/0.64 thf(fact_168_Id__on__eqI,axiom,
% 0.27/0.64 ! [A: nat,B: nat,A4: set_nat] :
% 0.27/0.64 ( ( A = B )
% 0.27/0.64 => ( ( member_nat @ A @ A4 )
% 0.27/0.64 => ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( id_on_nat @ A4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Id_on_eqI
% 0.27/0.64 thf(fact_169_Id__on__eqI,axiom,
% 0.27/0.64 ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,A4: set_la1976028319_b_nat] :
% 0.27/0.64 ( ( A = B )
% 0.27/0.64 => ( ( member1483953152_b_nat @ A @ A4 )
% 0.27/0.64 => ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ ( id_on_583275916_b_nat @ A4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Id_on_eqI
% 0.27/0.64 thf(fact_170_Id__on__eqI,axiom,
% 0.27/0.64 ! [A: allegorical_term_b,B: allegorical_term_b,A4: set_al1193902458term_b] :
% 0.27/0.64 ( ( A = B )
% 0.27/0.64 => ( ( member93680451term_b @ A @ A4 )
% 0.27/0.64 => ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ ( id_on_1536886967term_b @ A4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Id_on_eqI
% 0.27/0.64 thf(fact_171_Id__on__iff,axiom,
% 0.27/0.64 ! [X3: produc1871334759_a_nat,Y3: produc1871334759_a_nat,A4: set_Pr1987088711_a_nat] :
% 0.27/0.64 ( ( member584645392_a_nat @ ( produc1677124439_a_nat @ X3 @ Y3 ) @ ( id_on_1651096324_a_nat @ A4 ) )
% 0.27/0.64 = ( ( X3 = Y3 )
% 0.27/0.64 & ( member832397200_a_nat @ X3 @ A4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Id_on_iff
% 0.27/0.64 thf(fact_172_Id__on__iff,axiom,
% 0.27/0.64 ! [X3: labele935650037_a_nat,Y3: labele935650037_a_nat,A4: set_la1083530965_a_nat] :
% 0.27/0.64 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ X3 @ Y3 ) @ ( id_on_689842066_a_nat @ A4 ) )
% 0.27/0.64 = ( ( X3 = Y3 )
% 0.27/0.64 & ( member964390942_a_nat @ X3 @ A4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Id_on_iff
% 0.27/0.64 thf(fact_173_Id__on__iff,axiom,
% 0.27/0.64 ! [X3: nat,Y3: nat,A4: set_nat] :
% 0.27/0.64 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ ( id_on_nat @ A4 ) )
% 0.27/0.64 = ( ( X3 = Y3 )
% 0.27/0.64 & ( member_nat @ X3 @ A4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Id_on_iff
% 0.27/0.64 thf(fact_174_Id__on__iff,axiom,
% 0.27/0.64 ! [X3: labeled_graph_b_nat,Y3: labeled_graph_b_nat,A4: set_la1976028319_b_nat] :
% 0.27/0.64 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ X3 @ Y3 ) @ ( id_on_583275916_b_nat @ A4 ) )
% 0.27/0.64 = ( ( X3 = Y3 )
% 0.27/0.64 & ( member1483953152_b_nat @ X3 @ A4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Id_on_iff
% 0.27/0.64 thf(fact_175_Id__on__iff,axiom,
% 0.27/0.64 ! [X3: allegorical_term_b,Y3: allegorical_term_b,A4: set_al1193902458term_b] :
% 0.27/0.64 ( ( member516522448term_b @ ( produc1990145943term_b @ X3 @ Y3 ) @ ( id_on_1536886967term_b @ A4 ) )
% 0.27/0.64 = ( ( X3 = Y3 )
% 0.27/0.64 & ( member93680451term_b @ X3 @ A4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Id_on_iff
% 0.27/0.64 thf(fact_176_fin__maintained__def,axiom,
% 0.27/0.64 ( fin_ma971967913at_nat
% 0.27/0.64 = ( ^ [R2: produc1235635379_b_nat,G2: labeled_graph_b_nat] :
% 0.27/0.64 ! [F4: labeled_graph_b_nat,F5: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( ( F4
% 0.27/0.64 = ( restrict_b_nat @ F4 ) )
% 0.27/0.64 & ( finite_finite_nat @ ( labele460410879_b_nat @ F4 ) )
% 0.27/0.64 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ F4 ) ) )
% 0.27/0.64 => ( ( graph_529870330at_nat @ F4 @ ( produc1542243159_b_nat @ R2 ) @ ( id_on_nat @ ( labele460410879_b_nat @ F4 ) ) )
% 0.27/0.64 => ( ( extensible_b_nat_nat @ ( produc951298923_b_nat @ F4 @ ( produc1542243159_b_nat @ R2 ) ) @ G2 @ F5 )
% 0.27/0.64 => ( ( graph_529870330at_nat @ F4 @ G2 @ F5 )
% 0.27/0.64 => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ F4 @ ( produc194497945_b_nat @ R2 ) ) @ G2 @ F5 ) ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % fin_maintained_def
% 0.27/0.64 thf(fact_177_fair__chainD_I2_J,axiom,
% 0.27/0.64 ! [Rs2: set_Pr551076371_b_nat,S2: nat > labeled_graph_b_nat,R: produc1235635379_b_nat,I: nat,F3: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( fair_chain_b_nat_nat @ Rs2 @ S2 )
% 0.27/0.64 => ( ( member963855452_b_nat @ R @ Rs2 )
% 0.27/0.64 => ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ R ) @ ( S2 @ I ) @ F3 )
% 0.27/0.64 => ? [J: nat] : ( extensible_b_nat_nat @ R @ ( S2 @ J ) @ F3 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % fair_chainD(2)
% 0.27/0.64 thf(fact_178_identity__rules__graph__rule,axiom,
% 0.27/0.64 ! [X3: produc1871334759_a_nat,L: set_St761939237tant_a] :
% 0.27/0.64 ( ( member832397200_a_nat @ X3 @ ( standa1568205540ules_a @ L ) )
% 0.27/0.64 => ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ X3 ) @ ( produc880161797_a_nat @ X3 ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ X3 ) ) ) )
% 0.27/0.64 & ( ( produc880161797_a_nat @ X3 )
% 0.27/0.64 = ( restri572569417_a_nat @ ( produc880161797_a_nat @ X3 ) ) )
% 0.27/0.64 & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ X3 ) ) )
% 0.27/0.64 & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ X3 ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % identity_rules_graph_rule
% 0.27/0.64 thf(fact_179_maintainedI,axiom,
% 0.27/0.64 ! [A4: labeled_graph_b_nat,G: labeled_graph_b_nat,B4: labeled_graph_b_nat] :
% 0.27/0.64 ( ! [F2: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( graph_529870330at_nat @ A4 @ G @ F2 )
% 0.27/0.64 => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ A4 @ B4 ) @ G @ F2 ) )
% 0.27/0.64 => ( maintained_b_nat_nat @ ( produc951298923_b_nat @ A4 @ B4 ) @ G ) ) ).
% 0.27/0.64
% 0.27/0.64 % maintainedI
% 0.27/0.64 thf(fact_180_sndI,axiom,
% 0.27/0.64 ! [X3: produc1478835367term_b,Y3: allegorical_term_b,Z2: allegorical_term_b] :
% 0.27/0.64 ( ( X3
% 0.27/0.64 = ( produc1990145943term_b @ Y3 @ Z2 ) )
% 0.27/0.64 => ( ( produc1223098053term_b @ X3 )
% 0.27/0.64 = Z2 ) ) ).
% 0.27/0.64
% 0.27/0.64 % sndI
% 0.27/0.64 thf(fact_181_sndI,axiom,
% 0.27/0.64 ! [X3: produc1235635379_b_nat,Y3: labeled_graph_b_nat,Z2: labeled_graph_b_nat] :
% 0.27/0.64 ( ( X3
% 0.27/0.64 = ( produc951298923_b_nat @ Y3 @ Z2 ) )
% 0.27/0.64 => ( ( produc194497945_b_nat @ X3 )
% 0.27/0.64 = Z2 ) ) ).
% 0.27/0.64
% 0.27/0.64 % sndI
% 0.27/0.64 thf(fact_182_consequence__graphI,axiom,
% 0.27/0.64 ! [Rs2: set_Pr551076371_b_nat,G: labeled_graph_b_nat] :
% 0.27/0.64 ( ! [R3: produc1235635379_b_nat] :
% 0.27/0.64 ( ( member963855452_b_nat @ R3 @ Rs2 )
% 0.27/0.64 => ( maintained_b_nat_nat @ R3 @ G ) )
% 0.27/0.64 => ( ! [R3: produc1235635379_b_nat] :
% 0.27/0.64 ( ( member963855452_b_nat @ R3 @ Rs2 )
% 0.27/0.64 => ( graph_529870330at_nat @ ( produc1542243159_b_nat @ R3 ) @ ( produc194497945_b_nat @ R3 ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ R3 ) ) ) ) )
% 0.27/0.64 => ( ( G
% 0.27/0.64 = ( restrict_b_nat @ G ) )
% 0.27/0.64 => ( conseq1730780375at_nat @ Rs2 @ G ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % consequence_graphI
% 0.27/0.64 thf(fact_183_consequence__graph__def,axiom,
% 0.27/0.64 ( conseq1730780375at_nat
% 0.27/0.64 = ( ^ [Rs: set_Pr551076371_b_nat,G2: labeled_graph_b_nat] :
% 0.27/0.64 ( ( G2
% 0.27/0.64 = ( restrict_b_nat @ G2 ) )
% 0.27/0.64 & ! [X5: produc1235635379_b_nat] :
% 0.27/0.64 ( ( member963855452_b_nat @ X5 @ Rs )
% 0.27/0.64 => ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ X5 ) @ ( produc194497945_b_nat @ X5 ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ X5 ) ) ) )
% 0.27/0.64 & ( maintained_b_nat_nat @ X5 @ G2 ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % consequence_graph_def
% 0.27/0.64 thf(fact_184_maintained__def,axiom,
% 0.27/0.64 ( maintained_b_nat_nat
% 0.27/0.64 = ( ^ [R2: produc1235635379_b_nat,G2: labeled_graph_b_nat] :
% 0.27/0.64 ! [F5: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ R2 ) @ G2 @ F5 )
% 0.27/0.64 => ( extensible_b_nat_nat @ R2 @ G2 @ F5 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % maintained_def
% 0.27/0.64 thf(fact_185_maintainedD,axiom,
% 0.27/0.64 ! [A4: labeled_graph_b_nat,B4: labeled_graph_b_nat,G: labeled_graph_b_nat,F3: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( maintained_b_nat_nat @ ( produc951298923_b_nat @ A4 @ B4 ) @ G )
% 0.27/0.64 => ( ( graph_529870330at_nat @ A4 @ G @ F3 )
% 0.27/0.64 => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ A4 @ B4 ) @ G @ F3 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % maintainedD
% 0.27/0.64 thf(fact_186_fstI,axiom,
% 0.27/0.64 ! [X3: produc1235635379_b_nat,Y3: labeled_graph_b_nat,Z2: labeled_graph_b_nat] :
% 0.27/0.64 ( ( X3
% 0.27/0.64 = ( produc951298923_b_nat @ Y3 @ Z2 ) )
% 0.27/0.64 => ( ( produc1542243159_b_nat @ X3 )
% 0.27/0.64 = Y3 ) ) ).
% 0.27/0.64
% 0.27/0.64 % fstI
% 0.27/0.64 thf(fact_187_fstI,axiom,
% 0.27/0.64 ! [X3: produc1478835367term_b,Y3: allegorical_term_b,Z2: allegorical_term_b] :
% 0.27/0.64 ( ( X3
% 0.27/0.64 = ( produc1990145943term_b @ Y3 @ Z2 ) )
% 0.27/0.64 => ( ( produc854192515term_b @ X3 )
% 0.27/0.64 = Y3 ) ) ).
% 0.27/0.64
% 0.27/0.64 % fstI
% 0.27/0.64 thf(fact_188_fair__chainI,axiom,
% 0.27/0.64 ! [S2: nat > labeled_graph_b_nat,Rs2: set_Pr551076371_b_nat] :
% 0.27/0.64 ( ( chain_b_nat @ S2 )
% 0.27/0.64 => ( ! [R3: produc1235635379_b_nat,F2: set_Pr1986765409at_nat,I2: nat] :
% 0.27/0.64 ( ( member963855452_b_nat @ R3 @ Rs2 )
% 0.27/0.64 => ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ R3 ) @ ( S2 @ I2 ) @ F2 )
% 0.27/0.64 => ? [J2: nat] : ( extensible_b_nat_nat @ R3 @ ( S2 @ J2 ) @ F2 ) ) )
% 0.27/0.64 => ( fair_chain_b_nat_nat @ Rs2 @ S2 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % fair_chainI
% 0.27/0.64 thf(fact_189_maintained__holds__iff,axiom,
% 0.27/0.64 ! [G: labeled_graph_b_nat,E_L: allegorical_term_b,E_R: allegorical_term_b] :
% 0.27/0.64 ( ( G
% 0.27/0.64 = ( restrict_b_nat @ G ) )
% 0.27/0.64 => ( ( maintained_b_nat_nat @ ( produc951298923_b_nat @ ( translation_b @ E_L ) @ ( translation_b @ ( allegorical_A_Int_b @ E_L @ E_R ) ) ) @ G )
% 0.27/0.64 = ( ( semantics_b_nat @ G @ ( produc854192515term_b @ ( produc1990145943term_b @ E_L @ ( allegorical_A_Int_b @ E_L @ E_R ) ) ) )
% 0.27/0.64 = ( semantics_b_nat @ G @ ( produc1223098053term_b @ ( produc1990145943term_b @ E_L @ ( allegorical_A_Int_b @ E_L @ E_R ) ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % maintained_holds_iff
% 0.27/0.64 thf(fact_190_fair__chain__def,axiom,
% 0.27/0.64 ( fair_chain_b_nat_nat
% 0.27/0.64 = ( ^ [Rs: set_Pr551076371_b_nat,S3: nat > labeled_graph_b_nat] :
% 0.27/0.64 ( ( chain_b_nat @ S3 )
% 0.27/0.64 & ! [R2: produc1235635379_b_nat,F5: set_Pr1986765409at_nat,I3: nat] :
% 0.27/0.64 ( ( ( member963855452_b_nat @ R2 @ Rs )
% 0.27/0.64 & ( graph_529870330at_nat @ ( produc1542243159_b_nat @ R2 ) @ ( S3 @ I3 ) @ F5 ) )
% 0.27/0.64 => ? [J3: nat] : ( extensible_b_nat_nat @ R2 @ ( S3 @ J3 ) @ F5 ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % fair_chain_def
% 0.27/0.64 thf(fact_191_chain__sup__graph,axiom,
% 0.27/0.64 ! [S2: nat > labeled_graph_b_nat] :
% 0.27/0.64 ( ( chain_b_nat @ S2 )
% 0.27/0.64 => ( ( chain_sup_b_nat @ S2 )
% 0.27/0.64 = ( restrict_b_nat @ ( chain_sup_b_nat @ S2 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % chain_sup_graph
% 0.27/0.64 thf(fact_192_chain__sup__subgraph,axiom,
% 0.27/0.64 ! [S2: nat > labeled_graph_b_nat,J4: nat] :
% 0.27/0.64 ( ( chain_b_nat @ S2 )
% 0.27/0.64 => ( graph_529870330at_nat @ ( S2 @ J4 ) @ ( chain_sup_b_nat @ S2 ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( S2 @ J4 ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % chain_sup_subgraph
% 0.27/0.64 thf(fact_193_chain__then__restrict,axiom,
% 0.27/0.64 ! [S2: nat > labeled_graph_b_nat,I: nat] :
% 0.27/0.64 ( ( chain_b_nat @ S2 )
% 0.27/0.64 => ( ( S2 @ I )
% 0.27/0.64 = ( restrict_b_nat @ ( S2 @ I ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % chain_then_restrict
% 0.27/0.64 thf(fact_194_graph__homomorphism__semantics,axiom,
% 0.27/0.64 ! [A4: labeled_graph_b_nat,B4: labeled_graph_b_nat,F3: set_Pr1986765409at_nat,A: nat,B: nat,E: allegorical_term_b,A2: nat,B2: nat] :
% 0.27/0.64 ( ( graph_529870330at_nat @ A4 @ B4 @ F3 )
% 0.27/0.64 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( semantics_b_nat @ A4 @ E ) )
% 0.27/0.64 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ A2 ) @ F3 )
% 0.27/0.64 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ B @ B2 ) @ F3 )
% 0.27/0.64 => ( member701585322at_nat @ ( product_Pair_nat_nat @ A2 @ B2 ) @ ( semantics_b_nat @ B4 @ E ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % graph_homomorphism_semantics
% 0.27/0.64 thf(fact_195_semantics__in__vertices_I2_J,axiom,
% 0.27/0.64 ! [A4: labeled_graph_b_nat,A: nat,B: nat,E: allegorical_term_b] :
% 0.27/0.64 ( ( A4
% 0.27/0.64 = ( restrict_b_nat @ A4 ) )
% 0.27/0.64 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( semantics_b_nat @ A4 @ E ) )
% 0.27/0.64 => ( member_nat @ B @ ( labele460410879_b_nat @ A4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % semantics_in_vertices(2)
% 0.27/0.64 thf(fact_196_semantics__in__vertices_I1_J,axiom,
% 0.27/0.64 ! [A4: labeled_graph_b_nat,A: nat,B: nat,E: allegorical_term_b] :
% 0.27/0.64 ( ( A4
% 0.27/0.64 = ( restrict_b_nat @ A4 ) )
% 0.27/0.64 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( semantics_b_nat @ A4 @ E ) )
% 0.27/0.64 => ( member_nat @ A @ ( labele460410879_b_nat @ A4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % semantics_in_vertices(1)
% 0.27/0.64 thf(fact_197_subgraph__semantics,axiom,
% 0.27/0.64 ! [A4: labeled_graph_b_nat,B4: labeled_graph_b_nat,A: nat,B: nat,E: allegorical_term_b] :
% 0.27/0.64 ( ( graph_529870330at_nat @ A4 @ B4 @ ( id_on_nat @ ( labele460410879_b_nat @ A4 ) ) )
% 0.27/0.64 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( semantics_b_nat @ A4 @ E ) )
% 0.27/0.64 => ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( semantics_b_nat @ B4 @ E ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % subgraph_semantics
% 0.27/0.64 thf(fact_198_maintained__holds__subset__iff,axiom,
% 0.27/0.64 ! [G: labeled_graph_b_nat,E_L: allegorical_term_b,E_R: allegorical_term_b] :
% 0.27/0.64 ( ( G
% 0.27/0.64 = ( restrict_b_nat @ G ) )
% 0.27/0.64 => ( ( maintained_b_nat_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ E_L @ ( allegorical_A_Int_b @ E_L @ E_R ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ E_L @ ( allegorical_A_Int_b @ E_L @ E_R ) ) ) ) ) @ G )
% 0.27/0.64 = ( ord_le841296385at_nat @ ( semantics_b_nat @ G @ E_L ) @ ( semantics_b_nat @ G @ E_R ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % maintained_holds_subset_iff
% 0.27/0.64 thf(fact_199_find__graph__occurence,axiom,
% 0.27/0.64 ! [S2: nat > labeled_graph_b_nat,E2: set_Pr9961929at_nat,V: set_nat,F3: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( chain_b_nat @ S2 )
% 0.27/0.64 => ( ( finite1987068434at_nat @ E2 )
% 0.27/0.64 => ( ( finite_finite_nat @ V )
% 0.27/0.64 => ( ( graph_529870330at_nat @ ( labeled_LG_b_nat @ E2 @ V ) @ ( chain_sup_b_nat @ S2 ) @ F3 )
% 0.27/0.64 => ? [I2: nat] : ( graph_529870330at_nat @ ( labeled_LG_b_nat @ E2 @ V ) @ ( S2 @ I2 ) @ F3 ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % find_graph_occurence
% 0.27/0.64 thf(fact_200_eq__snd__iff,axiom,
% 0.27/0.64 ! [B: allegorical_term_b,P2: produc1478835367term_b] :
% 0.27/0.64 ( ( B
% 0.27/0.64 = ( produc1223098053term_b @ P2 ) )
% 0.27/0.64 = ( ? [A5: allegorical_term_b] :
% 0.27/0.64 ( P2
% 0.27/0.64 = ( produc1990145943term_b @ A5 @ B ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % eq_snd_iff
% 0.27/0.64 thf(fact_201_eq__snd__iff,axiom,
% 0.27/0.64 ! [B: labeled_graph_b_nat,P2: produc1235635379_b_nat] :
% 0.27/0.64 ( ( B
% 0.27/0.64 = ( produc194497945_b_nat @ P2 ) )
% 0.27/0.64 = ( ? [A5: labeled_graph_b_nat] :
% 0.27/0.64 ( P2
% 0.27/0.64 = ( produc951298923_b_nat @ A5 @ B ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % eq_snd_iff
% 0.27/0.64 thf(fact_202_eq__fst__iff,axiom,
% 0.27/0.64 ! [A: labeled_graph_b_nat,P2: produc1235635379_b_nat] :
% 0.27/0.64 ( ( A
% 0.27/0.64 = ( produc1542243159_b_nat @ P2 ) )
% 0.27/0.64 = ( ? [B5: labeled_graph_b_nat] :
% 0.27/0.64 ( P2
% 0.27/0.64 = ( produc951298923_b_nat @ A @ B5 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % eq_fst_iff
% 0.27/0.64 thf(fact_203_eq__fst__iff,axiom,
% 0.27/0.64 ! [A: allegorical_term_b,P2: produc1478835367term_b] :
% 0.27/0.64 ( ( A
% 0.27/0.64 = ( produc854192515term_b @ P2 ) )
% 0.27/0.64 = ( ? [B5: allegorical_term_b] :
% 0.27/0.64 ( P2
% 0.27/0.64 = ( produc1990145943term_b @ A @ B5 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % eq_fst_iff
% 0.27/0.64 thf(fact_204_labeled__graph_Ocollapse,axiom,
% 0.27/0.64 ! [Labeled_graph: labeled_graph_b_nat] :
% 0.27/0.64 ( ( labeled_LG_b_nat @ ( labeled_edges_b_nat @ Labeled_graph ) @ ( labele460410879_b_nat @ Labeled_graph ) )
% 0.27/0.64 = Labeled_graph ) ).
% 0.27/0.64
% 0.27/0.64 % labeled_graph.collapse
% 0.27/0.64 thf(fact_205_extensible__refl__concr,axiom,
% 0.27/0.64 ! [E_1: set_Pr9961929at_nat,V2: set_nat,G: labeled_graph_b_nat,F3: set_Pr1986765409at_nat,E_2: set_Pr9961929at_nat] :
% 0.27/0.64 ( ( graph_529870330at_nat @ ( labeled_LG_b_nat @ E_1 @ V2 ) @ G @ F3 )
% 0.27/0.64 => ( ( extensible_b_nat_nat @ ( produc951298923_b_nat @ ( labeled_LG_b_nat @ E_1 @ V2 ) @ ( labeled_LG_b_nat @ E_2 @ V2 ) ) @ G @ F3 )
% 0.27/0.64 = ( graph_529870330at_nat @ ( labeled_LG_b_nat @ E_2 @ V2 ) @ G @ F3 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % extensible_refl_concr
% 0.27/0.64 thf(fact_206_subrelI,axiom,
% 0.27/0.64 ! [R4: set_Pr1987088711_a_nat,S4: set_Pr1987088711_a_nat] :
% 0.27/0.64 ( ! [X4: labele935650037_a_nat,Y4: labele935650037_a_nat] :
% 0.27/0.64 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ X4 @ Y4 ) @ R4 )
% 0.27/0.64 => ( member832397200_a_nat @ ( produc1676969687_a_nat @ X4 @ Y4 ) @ S4 ) )
% 0.27/0.64 => ( ord_le1718765799_a_nat @ R4 @ S4 ) ) ).
% 0.27/0.64
% 0.27/0.64 % subrelI
% 0.27/0.64 thf(fact_207_subrelI,axiom,
% 0.27/0.64 ! [R4: set_Pr551076371_b_nat,S4: set_Pr551076371_b_nat] :
% 0.27/0.64 ( ! [X4: labeled_graph_b_nat,Y4: labeled_graph_b_nat] :
% 0.27/0.64 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ X4 @ Y4 ) @ R4 )
% 0.27/0.64 => ( member963855452_b_nat @ ( produc951298923_b_nat @ X4 @ Y4 ) @ S4 ) )
% 0.27/0.64 => ( ord_le13035955_b_nat @ R4 @ S4 ) ) ).
% 0.27/0.64
% 0.27/0.64 % subrelI
% 0.27/0.64 thf(fact_208_subrelI,axiom,
% 0.27/0.64 ! [R4: set_Pr1163220871term_b,S4: set_Pr1163220871term_b] :
% 0.27/0.64 ( ! [X4: allegorical_term_b,Y4: allegorical_term_b] :
% 0.27/0.64 ( ( member516522448term_b @ ( produc1990145943term_b @ X4 @ Y4 ) @ R4 )
% 0.27/0.64 => ( member516522448term_b @ ( produc1990145943term_b @ X4 @ Y4 ) @ S4 ) )
% 0.27/0.64 => ( ord_le138473255term_b @ R4 @ S4 ) ) ).
% 0.27/0.64
% 0.27/0.64 % subrelI
% 0.27/0.64 thf(fact_209_finite__has__maximal2,axiom,
% 0.27/0.64 ! [A4: set_nat,A: nat] :
% 0.27/0.64 ( ( finite_finite_nat @ A4 )
% 0.27/0.64 => ( ( member_nat @ A @ A4 )
% 0.27/0.64 => ? [X4: nat] :
% 0.27/0.64 ( ( member_nat @ X4 @ A4 )
% 0.27/0.64 & ( ord_less_eq_nat @ A @ X4 )
% 0.27/0.64 & ! [Xa: nat] :
% 0.27/0.64 ( ( member_nat @ Xa @ A4 )
% 0.27/0.64 => ( ( ord_less_eq_nat @ X4 @ Xa )
% 0.27/0.64 => ( X4 = Xa ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % finite_has_maximal2
% 0.27/0.64 thf(fact_210_finite__has__minimal2,axiom,
% 0.27/0.64 ! [A4: set_nat,A: nat] :
% 0.27/0.64 ( ( finite_finite_nat @ A4 )
% 0.27/0.64 => ( ( member_nat @ A @ A4 )
% 0.27/0.64 => ? [X4: nat] :
% 0.27/0.64 ( ( member_nat @ X4 @ A4 )
% 0.27/0.64 & ( ord_less_eq_nat @ X4 @ A )
% 0.27/0.64 & ! [Xa: nat] :
% 0.27/0.64 ( ( member_nat @ Xa @ A4 )
% 0.27/0.64 => ( ( ord_less_eq_nat @ Xa @ X4 )
% 0.27/0.64 => ( X4 = Xa ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % finite_has_minimal2
% 0.27/0.64 thf(fact_211_finite__subset,axiom,
% 0.27/0.64 ! [A4: set_nat,B4: set_nat] :
% 0.27/0.64 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.27/0.64 => ( ( finite_finite_nat @ B4 )
% 0.27/0.64 => ( finite_finite_nat @ A4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % finite_subset
% 0.27/0.64 thf(fact_212_finite__subset,axiom,
% 0.27/0.64 ! [A4: set_Pr9961929at_nat,B4: set_Pr9961929at_nat] :
% 0.27/0.64 ( ( ord_le910748009at_nat @ A4 @ B4 )
% 0.27/0.64 => ( ( finite1987068434at_nat @ B4 )
% 0.27/0.64 => ( finite1987068434at_nat @ A4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % finite_subset
% 0.27/0.64 thf(fact_213_infinite__super,axiom,
% 0.27/0.64 ! [S2: set_nat,T3: set_nat] :
% 0.27/0.64 ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 0.27/0.64 => ( ~ ( finite_finite_nat @ S2 )
% 0.27/0.64 => ~ ( finite_finite_nat @ T3 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % infinite_super
% 0.27/0.64 thf(fact_214_infinite__super,axiom,
% 0.27/0.64 ! [S2: set_Pr9961929at_nat,T3: set_Pr9961929at_nat] :
% 0.27/0.64 ( ( ord_le910748009at_nat @ S2 @ T3 )
% 0.27/0.64 => ( ~ ( finite1987068434at_nat @ S2 )
% 0.27/0.64 => ~ ( finite1987068434at_nat @ T3 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % infinite_super
% 0.27/0.64 thf(fact_215_rev__finite__subset,axiom,
% 0.27/0.64 ! [B4: set_nat,A4: set_nat] :
% 0.27/0.64 ( ( finite_finite_nat @ B4 )
% 0.27/0.64 => ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.27/0.64 => ( finite_finite_nat @ A4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % rev_finite_subset
% 0.27/0.64 thf(fact_216_rev__finite__subset,axiom,
% 0.27/0.64 ! [B4: set_Pr9961929at_nat,A4: set_Pr9961929at_nat] :
% 0.27/0.64 ( ( finite1987068434at_nat @ B4 )
% 0.27/0.64 => ( ( ord_le910748009at_nat @ A4 @ B4 )
% 0.27/0.64 => ( finite1987068434at_nat @ A4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % rev_finite_subset
% 0.27/0.64 thf(fact_217_labeled__graph_Osel_I2_J,axiom,
% 0.27/0.64 ! [X1: set_Pr9961929at_nat,X22: set_nat] :
% 0.27/0.64 ( ( labele460410879_b_nat @ ( labeled_LG_b_nat @ X1 @ X22 ) )
% 0.27/0.64 = X22 ) ).
% 0.27/0.64
% 0.27/0.64 % labeled_graph.sel(2)
% 0.27/0.64 thf(fact_218_labeled__graph_Osel_I1_J,axiom,
% 0.27/0.64 ! [X1: set_Pr9961929at_nat,X22: set_nat] :
% 0.27/0.64 ( ( labeled_edges_b_nat @ ( labeled_LG_b_nat @ X1 @ X22 ) )
% 0.27/0.64 = X1 ) ).
% 0.27/0.64
% 0.27/0.64 % labeled_graph.sel(1)
% 0.27/0.64 thf(fact_219_restrict__subsD,axiom,
% 0.27/0.64 ! [G: labeled_graph_b_nat] :
% 0.27/0.64 ( ( ord_le910748009at_nat @ ( labeled_edges_b_nat @ G ) @ ( labeled_edges_b_nat @ ( restrict_b_nat @ G ) ) )
% 0.27/0.64 => ( G
% 0.27/0.64 = ( restrict_b_nat @ G ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % restrict_subsD
% 0.27/0.64 thf(fact_220_subgraph__def2,axiom,
% 0.27/0.64 ! [G_1: labeled_graph_b_nat,G_2: labeled_graph_b_nat] :
% 0.27/0.64 ( ( G_1
% 0.27/0.64 = ( restrict_b_nat @ G_1 ) )
% 0.27/0.64 => ( ( G_2
% 0.27/0.64 = ( restrict_b_nat @ G_2 ) )
% 0.27/0.64 => ( ( graph_529870330at_nat @ G_1 @ G_2 @ ( id_on_nat @ ( labele460410879_b_nat @ G_1 ) ) )
% 0.27/0.64 = ( ( ord_less_eq_set_nat @ ( labele460410879_b_nat @ G_1 ) @ ( labele460410879_b_nat @ G_2 ) )
% 0.27/0.64 & ( ord_le910748009at_nat @ ( labeled_edges_b_nat @ G_1 ) @ ( labeled_edges_b_nat @ G_2 ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % subgraph_def2
% 0.27/0.64 thf(fact_221_labeled__graph_Oexhaust__sel,axiom,
% 0.27/0.64 ! [Labeled_graph: labeled_graph_b_nat] :
% 0.27/0.64 ( Labeled_graph
% 0.27/0.64 = ( labeled_LG_b_nat @ ( labeled_edges_b_nat @ Labeled_graph ) @ ( labele460410879_b_nat @ Labeled_graph ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % labeled_graph.exhaust_sel
% 0.27/0.64 thf(fact_222_subgraph__subset_I1_J,axiom,
% 0.27/0.64 ! [G_1: labeled_graph_b_nat,G_2: labeled_graph_b_nat] :
% 0.27/0.64 ( ( graph_529870330at_nat @ G_1 @ G_2 @ ( id_on_nat @ ( labele460410879_b_nat @ G_1 ) ) )
% 0.27/0.64 => ( ord_less_eq_set_nat @ ( labele460410879_b_nat @ G_1 ) @ ( labele460410879_b_nat @ G_2 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % subgraph_subset(1)
% 0.27/0.64 thf(fact_223_maintainedD2,axiom,
% 0.27/0.64 ! [A4: labeled_graph_b_nat,B4: labeled_graph_b_nat,G: labeled_graph_b_nat,F3: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( maintained_b_nat_nat @ ( produc951298923_b_nat @ A4 @ B4 ) @ G )
% 0.27/0.64 => ( ( graph_529870330at_nat @ A4 @ G @ F3 )
% 0.27/0.64 => ~ ! [G3: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( graph_529870330at_nat @ B4 @ G @ G3 )
% 0.27/0.64 => ~ ( ord_le841296385at_nat @ F3 @ G3 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % maintainedD2
% 0.27/0.64 thf(fact_224_subgraph__subset_I2_J,axiom,
% 0.27/0.64 ! [G_1: labeled_graph_b_nat,G_2: labeled_graph_b_nat] :
% 0.27/0.64 ( ( graph_529870330at_nat @ G_1 @ G_2 @ ( id_on_nat @ ( labele460410879_b_nat @ G_1 ) ) )
% 0.27/0.64 => ( ord_le910748009at_nat @ ( labeled_edges_b_nat @ ( restrict_b_nat @ G_1 ) ) @ ( labeled_edges_b_nat @ G_2 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % subgraph_subset(2)
% 0.27/0.64 thf(fact_225_subsetI,axiom,
% 0.27/0.64 ! [A4: set_Pr1987088711_a_nat,B4: set_Pr1987088711_a_nat] :
% 0.27/0.64 ( ! [X4: produc1871334759_a_nat] :
% 0.27/0.64 ( ( member832397200_a_nat @ X4 @ A4 )
% 0.27/0.64 => ( member832397200_a_nat @ X4 @ B4 ) )
% 0.27/0.64 => ( ord_le1718765799_a_nat @ A4 @ B4 ) ) ).
% 0.27/0.64
% 0.27/0.64 % subsetI
% 0.27/0.64 thf(fact_226_order__refl,axiom,
% 0.27/0.64 ! [X3: nat] : ( ord_less_eq_nat @ X3 @ X3 ) ).
% 0.27/0.64
% 0.27/0.64 % order_refl
% 0.27/0.64 thf(fact_227_dual__order_Oantisym,axiom,
% 0.27/0.64 ! [B: nat,A: nat] :
% 0.27/0.64 ( ( ord_less_eq_nat @ B @ A )
% 0.27/0.64 => ( ( ord_less_eq_nat @ A @ B )
% 0.27/0.64 => ( A = B ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % dual_order.antisym
% 0.27/0.64 thf(fact_228_dual__order_Oeq__iff,axiom,
% 0.27/0.64 ( ( ^ [Y5: nat,Z: nat] : ( Y5 = Z ) )
% 0.27/0.64 = ( ^ [A5: nat,B5: nat] :
% 0.27/0.64 ( ( ord_less_eq_nat @ B5 @ A5 )
% 0.27/0.64 & ( ord_less_eq_nat @ A5 @ B5 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % dual_order.eq_iff
% 0.27/0.64 thf(fact_229_dual__order_Otrans,axiom,
% 0.27/0.64 ! [B: nat,A: nat,C2: nat] :
% 0.27/0.64 ( ( ord_less_eq_nat @ B @ A )
% 0.27/0.64 => ( ( ord_less_eq_nat @ C2 @ B )
% 0.27/0.64 => ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % dual_order.trans
% 0.27/0.64 thf(fact_230_linorder__wlog,axiom,
% 0.27/0.64 ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.27/0.64 ( ! [A3: nat,B3: nat] :
% 0.27/0.64 ( ( ord_less_eq_nat @ A3 @ B3 )
% 0.27/0.64 => ( P @ A3 @ B3 ) )
% 0.27/0.64 => ( ! [A3: nat,B3: nat] :
% 0.27/0.64 ( ( P @ B3 @ A3 )
% 0.27/0.64 => ( P @ A3 @ B3 ) )
% 0.27/0.64 => ( P @ A @ B ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % linorder_wlog
% 0.27/0.64 thf(fact_231_dual__order_Orefl,axiom,
% 0.27/0.64 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.27/0.64
% 0.27/0.64 % dual_order.refl
% 0.27/0.64 thf(fact_232_order__trans,axiom,
% 0.27/0.64 ! [X3: nat,Y3: nat,Z2: nat] :
% 0.27/0.64 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.27/0.64 => ( ( ord_less_eq_nat @ Y3 @ Z2 )
% 0.27/0.64 => ( ord_less_eq_nat @ X3 @ Z2 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % order_trans
% 0.27/0.64 thf(fact_233_order__class_Oorder_Oantisym,axiom,
% 0.27/0.64 ! [A: nat,B: nat] :
% 0.27/0.64 ( ( ord_less_eq_nat @ A @ B )
% 0.27/0.64 => ( ( ord_less_eq_nat @ B @ A )
% 0.27/0.64 => ( A = B ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % order_class.order.antisym
% 0.27/0.64 thf(fact_234_ord__le__eq__trans,axiom,
% 0.27/0.64 ! [A: nat,B: nat,C2: nat] :
% 0.27/0.64 ( ( ord_less_eq_nat @ A @ B )
% 0.27/0.64 => ( ( B = C2 )
% 0.27/0.64 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % ord_le_eq_trans
% 0.27/0.64 thf(fact_235_ord__eq__le__trans,axiom,
% 0.27/0.64 ! [A: nat,B: nat,C2: nat] :
% 0.27/0.64 ( ( A = B )
% 0.27/0.64 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.27/0.64 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % ord_eq_le_trans
% 0.27/0.64 thf(fact_236_order__class_Oorder_Oeq__iff,axiom,
% 0.27/0.64 ( ( ^ [Y5: nat,Z: nat] : ( Y5 = Z ) )
% 0.27/0.64 = ( ^ [A5: nat,B5: nat] :
% 0.27/0.64 ( ( ord_less_eq_nat @ A5 @ B5 )
% 0.27/0.64 & ( ord_less_eq_nat @ B5 @ A5 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % order_class.order.eq_iff
% 0.27/0.64 thf(fact_237_antisym__conv,axiom,
% 0.27/0.64 ! [Y3: nat,X3: nat] :
% 0.27/0.64 ( ( ord_less_eq_nat @ Y3 @ X3 )
% 0.27/0.64 => ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.27/0.64 = ( X3 = Y3 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % antisym_conv
% 0.27/0.64 thf(fact_238_le__cases3,axiom,
% 0.27/0.64 ! [X3: nat,Y3: nat,Z2: nat] :
% 0.27/0.64 ( ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.27/0.64 => ~ ( ord_less_eq_nat @ Y3 @ Z2 ) )
% 0.27/0.64 => ( ( ( ord_less_eq_nat @ Y3 @ X3 )
% 0.27/0.64 => ~ ( ord_less_eq_nat @ X3 @ Z2 ) )
% 0.27/0.64 => ( ( ( ord_less_eq_nat @ X3 @ Z2 )
% 0.27/0.64 => ~ ( ord_less_eq_nat @ Z2 @ Y3 ) )
% 0.27/0.64 => ( ( ( ord_less_eq_nat @ Z2 @ Y3 )
% 0.27/0.64 => ~ ( ord_less_eq_nat @ Y3 @ X3 ) )
% 0.27/0.64 => ( ( ( ord_less_eq_nat @ Y3 @ Z2 )
% 0.27/0.64 => ~ ( ord_less_eq_nat @ Z2 @ X3 ) )
% 0.27/0.64 => ~ ( ( ord_less_eq_nat @ Z2 @ X3 )
% 0.27/0.64 => ~ ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % le_cases3
% 0.27/0.64 thf(fact_239_order_Otrans,axiom,
% 0.27/0.64 ! [A: nat,B: nat,C2: nat] :
% 0.27/0.64 ( ( ord_less_eq_nat @ A @ B )
% 0.27/0.64 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.27/0.64 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % order.trans
% 0.27/0.64 thf(fact_240_le__cases,axiom,
% 0.27/0.64 ! [X3: nat,Y3: nat] :
% 0.27/0.64 ( ~ ( ord_less_eq_nat @ X3 @ Y3 )
% 0.27/0.64 => ( ord_less_eq_nat @ Y3 @ X3 ) ) ).
% 0.27/0.64
% 0.27/0.64 % le_cases
% 0.27/0.64 thf(fact_241_eq__refl,axiom,
% 0.27/0.64 ! [X3: nat,Y3: nat] :
% 0.27/0.64 ( ( X3 = Y3 )
% 0.27/0.64 => ( ord_less_eq_nat @ X3 @ Y3 ) ) ).
% 0.27/0.64
% 0.27/0.64 % eq_refl
% 0.27/0.64 thf(fact_242_linear,axiom,
% 0.27/0.64 ! [X3: nat,Y3: nat] :
% 0.27/0.64 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.27/0.64 | ( ord_less_eq_nat @ Y3 @ X3 ) ) ).
% 0.27/0.64
% 0.27/0.64 % linear
% 0.27/0.64 thf(fact_243_antisym,axiom,
% 0.27/0.64 ! [X3: nat,Y3: nat] :
% 0.27/0.64 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.27/0.64 => ( ( ord_less_eq_nat @ Y3 @ X3 )
% 0.27/0.64 => ( X3 = Y3 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % antisym
% 0.27/0.64 thf(fact_244_eq__iff,axiom,
% 0.27/0.64 ( ( ^ [Y5: nat,Z: nat] : ( Y5 = Z ) )
% 0.27/0.64 = ( ^ [X5: nat,Y6: nat] :
% 0.27/0.64 ( ( ord_less_eq_nat @ X5 @ Y6 )
% 0.27/0.64 & ( ord_less_eq_nat @ Y6 @ X5 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % eq_iff
% 0.27/0.64 thf(fact_245_ord__le__eq__subst,axiom,
% 0.27/0.64 ! [A: nat,B: nat,F3: nat > nat,C2: nat] :
% 0.27/0.64 ( ( ord_less_eq_nat @ A @ B )
% 0.27/0.64 => ( ( ( F3 @ B )
% 0.27/0.64 = C2 )
% 0.27/0.64 => ( ! [X4: nat,Y4: nat] :
% 0.27/0.64 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.27/0.64 => ( ord_less_eq_nat @ ( F3 @ X4 ) @ ( F3 @ Y4 ) ) )
% 0.27/0.64 => ( ord_less_eq_nat @ ( F3 @ A ) @ C2 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % ord_le_eq_subst
% 0.27/0.64 thf(fact_246_ord__eq__le__subst,axiom,
% 0.27/0.64 ! [A: nat,F3: nat > nat,B: nat,C2: nat] :
% 0.27/0.64 ( ( A
% 0.27/0.64 = ( F3 @ B ) )
% 0.27/0.64 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.27/0.64 => ( ! [X4: nat,Y4: nat] :
% 0.27/0.64 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.27/0.64 => ( ord_less_eq_nat @ ( F3 @ X4 ) @ ( F3 @ Y4 ) ) )
% 0.27/0.64 => ( ord_less_eq_nat @ A @ ( F3 @ C2 ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % ord_eq_le_subst
% 0.27/0.64 thf(fact_247_order__subst2,axiom,
% 0.27/0.64 ! [A: nat,B: nat,F3: nat > nat,C2: nat] :
% 0.27/0.64 ( ( ord_less_eq_nat @ A @ B )
% 0.27/0.64 => ( ( ord_less_eq_nat @ ( F3 @ B ) @ C2 )
% 0.27/0.64 => ( ! [X4: nat,Y4: nat] :
% 0.27/0.64 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.27/0.64 => ( ord_less_eq_nat @ ( F3 @ X4 ) @ ( F3 @ Y4 ) ) )
% 0.27/0.64 => ( ord_less_eq_nat @ ( F3 @ A ) @ C2 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % order_subst2
% 0.27/0.64 thf(fact_248_order__subst1,axiom,
% 0.27/0.64 ! [A: nat,F3: nat > nat,B: nat,C2: nat] :
% 0.27/0.64 ( ( ord_less_eq_nat @ A @ ( F3 @ B ) )
% 0.27/0.64 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.27/0.64 => ( ! [X4: nat,Y4: nat] :
% 0.27/0.64 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.27/0.64 => ( ord_less_eq_nat @ ( F3 @ X4 ) @ ( F3 @ Y4 ) ) )
% 0.27/0.64 => ( ord_less_eq_nat @ A @ ( F3 @ C2 ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % order_subst1
% 0.27/0.64 thf(fact_249_subset__iff,axiom,
% 0.27/0.64 ( ord_le1718765799_a_nat
% 0.27/0.64 = ( ^ [A6: set_Pr1987088711_a_nat,B6: set_Pr1987088711_a_nat] :
% 0.27/0.64 ! [T2: produc1871334759_a_nat] :
% 0.27/0.64 ( ( member832397200_a_nat @ T2 @ A6 )
% 0.27/0.64 => ( member832397200_a_nat @ T2 @ B6 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % subset_iff
% 0.27/0.64 thf(fact_250_subset__eq,axiom,
% 0.27/0.64 ( ord_le1718765799_a_nat
% 0.27/0.64 = ( ^ [A6: set_Pr1987088711_a_nat,B6: set_Pr1987088711_a_nat] :
% 0.27/0.64 ! [X5: produc1871334759_a_nat] :
% 0.27/0.64 ( ( member832397200_a_nat @ X5 @ A6 )
% 0.27/0.64 => ( member832397200_a_nat @ X5 @ B6 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % subset_eq
% 0.27/0.64 thf(fact_251_subsetD,axiom,
% 0.27/0.64 ! [A4: set_Pr1987088711_a_nat,B4: set_Pr1987088711_a_nat,C2: produc1871334759_a_nat] :
% 0.27/0.64 ( ( ord_le1718765799_a_nat @ A4 @ B4 )
% 0.27/0.64 => ( ( member832397200_a_nat @ C2 @ A4 )
% 0.27/0.64 => ( member832397200_a_nat @ C2 @ B4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % subsetD
% 0.27/0.64 thf(fact_252_in__mono,axiom,
% 0.27/0.64 ! [A4: set_Pr1987088711_a_nat,B4: set_Pr1987088711_a_nat,X3: produc1871334759_a_nat] :
% 0.27/0.64 ( ( ord_le1718765799_a_nat @ A4 @ B4 )
% 0.27/0.64 => ( ( member832397200_a_nat @ X3 @ A4 )
% 0.27/0.64 => ( member832397200_a_nat @ X3 @ B4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % in_mono
% 0.27/0.64 thf(fact_253_chain,axiom,
% 0.27/0.64 ! [S2: nat > labeled_graph_b_nat,I: nat,J4: nat] :
% 0.27/0.64 ( ( chain_b_nat @ S2 )
% 0.27/0.64 => ( ( ord_less_eq_nat @ I @ J4 )
% 0.27/0.64 => ( graph_529870330at_nat @ ( S2 @ I ) @ ( S2 @ J4 ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( S2 @ I ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % chain
% 0.27/0.64 thf(fact_254_chain__def2,axiom,
% 0.27/0.64 ( chain_b_nat
% 0.27/0.64 = ( ^ [S3: nat > labeled_graph_b_nat] :
% 0.27/0.64 ! [I3: nat,J3: nat] :
% 0.27/0.64 ( ( ord_less_eq_nat @ I3 @ J3 )
% 0.27/0.64 => ( graph_529870330at_nat @ ( S3 @ I3 ) @ ( S3 @ J3 ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( S3 @ I3 ) ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % chain_def2
% 0.27/0.64 thf(fact_255_graph__unionI,axiom,
% 0.27/0.64 ! [G_1: labeled_graph_b_nat,G_2: labeled_graph_b_nat] :
% 0.27/0.64 ( ( ord_le910748009at_nat @ ( labeled_edges_b_nat @ G_1 ) @ ( labeled_edges_b_nat @ G_2 ) )
% 0.27/0.64 => ( ( ord_less_eq_set_nat @ ( labele460410879_b_nat @ G_1 ) @ ( labele460410879_b_nat @ G_2 ) )
% 0.27/0.64 => ( ( graph_union_b_nat @ G_1 @ G_2 )
% 0.27/0.64 = G_2 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % graph_unionI
% 0.27/0.64 thf(fact_256_extensibleD,axiom,
% 0.27/0.64 ! [R: produc1235635379_b_nat,G: labeled_graph_b_nat,F3: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( extensible_b_nat_nat @ R @ G @ F3 )
% 0.27/0.64 => ~ ! [G3: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( graph_529870330at_nat @ ( produc194497945_b_nat @ R ) @ G @ G3 )
% 0.27/0.64 => ~ ( agree_on_b_nat_nat @ ( produc1542243159_b_nat @ R ) @ F3 @ G3 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % extensibleD
% 0.27/0.64 thf(fact_257_extensible__def,axiom,
% 0.27/0.64 ( extensible_b_nat_nat
% 0.27/0.64 = ( ^ [R2: produc1235635379_b_nat,G2: labeled_graph_b_nat,F5: set_Pr1986765409at_nat] :
% 0.27/0.64 ? [G4: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( graph_529870330at_nat @ ( produc194497945_b_nat @ R2 ) @ G2 @ G4 )
% 0.27/0.64 & ( agree_on_b_nat_nat @ ( produc1542243159_b_nat @ R2 ) @ F5 @ G4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % extensible_def
% 0.27/0.64 thf(fact_258_extensibleI,axiom,
% 0.27/0.64 ! [R22: labeled_graph_b_nat,G: labeled_graph_b_nat,G5: set_Pr1986765409at_nat,R1: labeled_graph_b_nat,F3: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( graph_529870330at_nat @ R22 @ G @ G5 )
% 0.27/0.64 => ( ( agree_on_b_nat_nat @ R1 @ F3 @ G5 )
% 0.27/0.64 => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ R1 @ R22 ) @ G @ F3 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % extensibleI
% 0.27/0.64 thf(fact_259_graph__union__preserves__restrict,axiom,
% 0.27/0.64 ! [G_1: labeled_graph_b_nat,G_2: labeled_graph_b_nat] :
% 0.27/0.64 ( ( G_1
% 0.27/0.64 = ( restrict_b_nat @ G_1 ) )
% 0.27/0.64 => ( ( G_2
% 0.27/0.64 = ( restrict_b_nat @ G_2 ) )
% 0.27/0.64 => ( ( graph_union_b_nat @ G_1 @ G_2 )
% 0.27/0.64 = ( restrict_b_nat @ ( graph_union_b_nat @ G_1 @ G_2 ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % graph_union_preserves_restrict
% 0.27/0.64 thf(fact_260_subgraph__def,axiom,
% 0.27/0.64 ! [G_1: labeled_graph_b_nat,G_2: labeled_graph_b_nat] :
% 0.27/0.64 ( ( graph_529870330at_nat @ G_1 @ G_2 @ ( id_on_nat @ ( labele460410879_b_nat @ G_1 ) ) )
% 0.27/0.64 = ( ( G_1
% 0.27/0.64 = ( restrict_b_nat @ G_1 ) )
% 0.27/0.64 & ( G_2
% 0.27/0.64 = ( restrict_b_nat @ G_2 ) )
% 0.27/0.64 & ( ( graph_union_b_nat @ G_1 @ G_2 )
% 0.27/0.64 = G_2 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % subgraph_def
% 0.27/0.64 thf(fact_261_graph__union__iff,axiom,
% 0.27/0.64 ! [G_1: labeled_graph_b_nat,G_2: labeled_graph_b_nat] :
% 0.27/0.64 ( ( ( graph_union_b_nat @ G_1 @ G_2 )
% 0.27/0.64 = G_2 )
% 0.27/0.64 = ( ( ord_le910748009at_nat @ ( labeled_edges_b_nat @ G_1 ) @ ( labeled_edges_b_nat @ G_2 ) )
% 0.27/0.64 & ( ord_less_eq_set_nat @ ( labele460410879_b_nat @ G_1 ) @ ( labele460410879_b_nat @ G_2 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % graph_union_iff
% 0.27/0.64 thf(fact_262_finite__nat__set__iff__bounded__le,axiom,
% 0.27/0.64 ( finite_finite_nat
% 0.27/0.64 = ( ^ [N: set_nat] :
% 0.27/0.64 ? [M: nat] :
% 0.27/0.64 ! [X5: nat] :
% 0.27/0.64 ( ( member_nat @ X5 @ N )
% 0.27/0.64 => ( ord_less_eq_nat @ X5 @ M ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % finite_nat_set_iff_bounded_le
% 0.27/0.64 thf(fact_263_nonempty__rule,axiom,
% 0.27/0.64 ! [G: labeled_graph_b_nat] :
% 0.27/0.64 ( ( G
% 0.27/0.64 = ( restrict_b_nat @ G ) )
% 0.27/0.64 => ( ( maintained_b_nat_nat @ standa879863266rule_b @ G )
% 0.27/0.64 = ( ( labele460410879_b_nat @ G )
% 0.27/0.64 != bot_bot_set_nat ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % nonempty_rule
% 0.27/0.64 thf(fact_264_weak__universalI,axiom,
% 0.27/0.64 ! [R: produc1235635379_b_nat,G_1: labeled_graph_b_nat,F_1: set_Pr1986765409at_nat,G_2: labeled_graph_b_nat,T: itself_nat,F_2: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ! [H_1: set_Pr1986765409at_nat,H_2: set_Pr1986765409at_nat,G6: labeled_graph_b_nat] :
% 0.27/0.64 ( ( graph_529870330at_nat @ ( produc194497945_b_nat @ R ) @ G6 @ H_1 )
% 0.27/0.64 => ( ( graph_529870330at_nat @ G_1 @ G6 @ H_2 )
% 0.27/0.64 => ( ( ord_le841296385at_nat @ ( relcomp_nat_nat_nat @ F_1 @ H_2 ) @ H_1 )
% 0.27/0.64 => ? [H2: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( graph_529870330at_nat @ G_2 @ G6 @ H2 )
% 0.27/0.64 & ( ord_le841296385at_nat @ H_2 @ H2 ) ) ) ) )
% 0.27/0.64 => ( weak_u2026406106at_nat @ T @ R @ G_1 @ G_2 @ F_1 @ F_2 ) ) ).
% 0.27/0.64
% 0.27/0.64 % weak_universalI
% 0.27/0.64 thf(fact_265_Id__on__empty,axiom,
% 0.27/0.64 ( ( id_on_nat @ bot_bot_set_nat )
% 0.27/0.64 = bot_bo2130386637at_nat ) ).
% 0.27/0.64
% 0.27/0.64 % Id_on_empty
% 0.27/0.64 thf(fact_266_graph__homomorphism__composes,axiom,
% 0.27/0.64 ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,X3: set_Pr1986765409at_nat,C2: labeled_graph_b_nat,Y3: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( graph_529870330at_nat @ A @ B @ X3 )
% 0.27/0.64 => ( ( graph_529870330at_nat @ B @ C2 @ Y3 )
% 0.27/0.64 => ( graph_529870330at_nat @ A @ C2 @ ( relcomp_nat_nat_nat @ X3 @ Y3 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % graph_homomorphism_composes
% 0.27/0.64 thf(fact_267_graph__empty__e,axiom,
% 0.27/0.64 ! [V2: set_nat] :
% 0.27/0.64 ( ( labeled_LG_b_nat @ bot_bo1626616373at_nat @ V2 )
% 0.27/0.64 = ( restrict_b_nat @ ( labeled_LG_b_nat @ bot_bo1626616373at_nat @ V2 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % graph_empty_e
% 0.27/0.64 thf(fact_268_graph__homomorphism__empty,axiom,
% 0.27/0.64 ! [G: labeled_graph_b_nat,F3: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( graph_529870330at_nat @ ( labeled_LG_b_nat @ bot_bo1626616373at_nat @ bot_bot_set_nat ) @ G @ F3 )
% 0.27/0.64 = ( ( F3 = bot_bo2130386637at_nat )
% 0.27/0.64 & ( G
% 0.27/0.64 = ( restrict_b_nat @ G ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % graph_homomorphism_empty
% 0.27/0.64 thf(fact_269_bot_Oextremum,axiom,
% 0.27/0.64 ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 0.27/0.64
% 0.27/0.64 % bot.extremum
% 0.27/0.64 thf(fact_270_bot_Oextremum__unique,axiom,
% 0.27/0.64 ! [A: nat] :
% 0.27/0.64 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 0.27/0.64 = ( A = bot_bot_nat ) ) ).
% 0.27/0.64
% 0.27/0.64 % bot.extremum_unique
% 0.27/0.64 thf(fact_271_bot_Oextremum__uniqueI,axiom,
% 0.27/0.64 ! [A: nat] :
% 0.27/0.64 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 0.27/0.64 => ( A = bot_bot_nat ) ) ).
% 0.27/0.64
% 0.27/0.64 % bot.extremum_uniqueI
% 0.27/0.64 thf(fact_272_relcomp_OrelcompI,axiom,
% 0.27/0.64 ! [A: labele935650037_a_nat,B: labele935650037_a_nat,R4: set_Pr1987088711_a_nat,C2: labele935650037_a_nat,S4: set_Pr1987088711_a_nat] :
% 0.27/0.64 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ R4 )
% 0.27/0.64 => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ B @ C2 ) @ S4 )
% 0.27/0.64 => ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ C2 ) @ ( relcom1338300020_a_nat @ R4 @ S4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % relcomp.relcompI
% 0.27/0.64 thf(fact_273_relcomp_OrelcompI,axiom,
% 0.27/0.64 ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,R4: set_Pr551076371_b_nat,C2: labeled_graph_b_nat,S4: set_Pr551076371_b_nat] :
% 0.27/0.64 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ R4 )
% 0.27/0.64 => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ B @ C2 ) @ S4 )
% 0.27/0.64 => ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ C2 ) @ ( relcom1426860350_b_nat @ R4 @ S4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % relcomp.relcompI
% 0.27/0.64 thf(fact_274_relcomp_OrelcompI,axiom,
% 0.27/0.64 ! [A: allegorical_term_b,B: allegorical_term_b,R4: set_Pr1163220871term_b,C2: allegorical_term_b,S4: set_Pr1163220871term_b] :
% 0.27/0.64 ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ R4 )
% 0.27/0.64 => ( ( member516522448term_b @ ( produc1990145943term_b @ B @ C2 ) @ S4 )
% 0.27/0.64 => ( member516522448term_b @ ( produc1990145943term_b @ A @ C2 ) @ ( relcom1955155673term_b @ R4 @ S4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % relcomp.relcompI
% 0.27/0.64 thf(fact_275_relcomp_Oinducts,axiom,
% 0.27/0.64 ! [X1: labele935650037_a_nat,X22: labele935650037_a_nat,R4: set_Pr1987088711_a_nat,S4: set_Pr1987088711_a_nat,P: labele935650037_a_nat > labele935650037_a_nat > $o] :
% 0.27/0.64 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ X1 @ X22 ) @ ( relcom1338300020_a_nat @ R4 @ S4 ) )
% 0.27/0.64 => ( ! [A3: labele935650037_a_nat,B3: labele935650037_a_nat,C: labele935650037_a_nat] :
% 0.27/0.64 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A3 @ B3 ) @ R4 )
% 0.27/0.64 => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ B3 @ C ) @ S4 )
% 0.27/0.64 => ( P @ A3 @ C ) ) )
% 0.27/0.64 => ( P @ X1 @ X22 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % relcomp.inducts
% 0.27/0.64 thf(fact_276_relcomp_Oinducts,axiom,
% 0.27/0.64 ! [X1: labeled_graph_b_nat,X22: labeled_graph_b_nat,R4: set_Pr551076371_b_nat,S4: set_Pr551076371_b_nat,P: labeled_graph_b_nat > labeled_graph_b_nat > $o] :
% 0.27/0.64 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ X1 @ X22 ) @ ( relcom1426860350_b_nat @ R4 @ S4 ) )
% 0.27/0.64 => ( ! [A3: labeled_graph_b_nat,B3: labeled_graph_b_nat,C: labeled_graph_b_nat] :
% 0.27/0.64 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A3 @ B3 ) @ R4 )
% 0.27/0.64 => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ B3 @ C ) @ S4 )
% 0.27/0.64 => ( P @ A3 @ C ) ) )
% 0.27/0.64 => ( P @ X1 @ X22 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % relcomp.inducts
% 0.27/0.64 thf(fact_277_relcomp_Oinducts,axiom,
% 0.27/0.64 ! [X1: allegorical_term_b,X22: allegorical_term_b,R4: set_Pr1163220871term_b,S4: set_Pr1163220871term_b,P: allegorical_term_b > allegorical_term_b > $o] :
% 0.27/0.64 ( ( member516522448term_b @ ( produc1990145943term_b @ X1 @ X22 ) @ ( relcom1955155673term_b @ R4 @ S4 ) )
% 0.27/0.64 => ( ! [A3: allegorical_term_b,B3: allegorical_term_b,C: allegorical_term_b] :
% 0.27/0.64 ( ( member516522448term_b @ ( produc1990145943term_b @ A3 @ B3 ) @ R4 )
% 0.27/0.64 => ( ( member516522448term_b @ ( produc1990145943term_b @ B3 @ C ) @ S4 )
% 0.27/0.64 => ( P @ A3 @ C ) ) )
% 0.27/0.64 => ( P @ X1 @ X22 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % relcomp.inducts
% 0.27/0.64 thf(fact_278_relcomp_Osimps,axiom,
% 0.27/0.64 ! [A1: labele935650037_a_nat,A22: labele935650037_a_nat,R4: set_Pr1987088711_a_nat,S4: set_Pr1987088711_a_nat] :
% 0.27/0.64 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A1 @ A22 ) @ ( relcom1338300020_a_nat @ R4 @ S4 ) )
% 0.27/0.64 = ( ? [A5: labele935650037_a_nat,B5: labele935650037_a_nat,C3: labele935650037_a_nat] :
% 0.27/0.64 ( ( A1 = A5 )
% 0.27/0.64 & ( A22 = C3 )
% 0.27/0.64 & ( member832397200_a_nat @ ( produc1676969687_a_nat @ A5 @ B5 ) @ R4 )
% 0.27/0.64 & ( member832397200_a_nat @ ( produc1676969687_a_nat @ B5 @ C3 ) @ S4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % relcomp.simps
% 0.27/0.64 thf(fact_279_relcomp_Osimps,axiom,
% 0.27/0.64 ! [A1: labeled_graph_b_nat,A22: labeled_graph_b_nat,R4: set_Pr551076371_b_nat,S4: set_Pr551076371_b_nat] :
% 0.27/0.64 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A1 @ A22 ) @ ( relcom1426860350_b_nat @ R4 @ S4 ) )
% 0.27/0.64 = ( ? [A5: labeled_graph_b_nat,B5: labeled_graph_b_nat,C3: labeled_graph_b_nat] :
% 0.27/0.64 ( ( A1 = A5 )
% 0.27/0.64 & ( A22 = C3 )
% 0.27/0.64 & ( member963855452_b_nat @ ( produc951298923_b_nat @ A5 @ B5 ) @ R4 )
% 0.27/0.64 & ( member963855452_b_nat @ ( produc951298923_b_nat @ B5 @ C3 ) @ S4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % relcomp.simps
% 0.27/0.64 thf(fact_280_relcomp_Osimps,axiom,
% 0.27/0.64 ! [A1: allegorical_term_b,A22: allegorical_term_b,R4: set_Pr1163220871term_b,S4: set_Pr1163220871term_b] :
% 0.27/0.64 ( ( member516522448term_b @ ( produc1990145943term_b @ A1 @ A22 ) @ ( relcom1955155673term_b @ R4 @ S4 ) )
% 0.27/0.64 = ( ? [A5: allegorical_term_b,B5: allegorical_term_b,C3: allegorical_term_b] :
% 0.27/0.64 ( ( A1 = A5 )
% 0.27/0.64 & ( A22 = C3 )
% 0.27/0.64 & ( member516522448term_b @ ( produc1990145943term_b @ A5 @ B5 ) @ R4 )
% 0.27/0.64 & ( member516522448term_b @ ( produc1990145943term_b @ B5 @ C3 ) @ S4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % relcomp.simps
% 0.27/0.64 thf(fact_281_relcomp_Ocases,axiom,
% 0.27/0.64 ! [A1: labele935650037_a_nat,A22: labele935650037_a_nat,R4: set_Pr1987088711_a_nat,S4: set_Pr1987088711_a_nat] :
% 0.27/0.64 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A1 @ A22 ) @ ( relcom1338300020_a_nat @ R4 @ S4 ) )
% 0.27/0.64 => ~ ! [B3: labele935650037_a_nat] :
% 0.27/0.64 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A1 @ B3 ) @ R4 )
% 0.27/0.64 => ~ ( member832397200_a_nat @ ( produc1676969687_a_nat @ B3 @ A22 ) @ S4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % relcomp.cases
% 0.27/0.64 thf(fact_282_relcomp_Ocases,axiom,
% 0.27/0.64 ! [A1: labeled_graph_b_nat,A22: labeled_graph_b_nat,R4: set_Pr551076371_b_nat,S4: set_Pr551076371_b_nat] :
% 0.27/0.64 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A1 @ A22 ) @ ( relcom1426860350_b_nat @ R4 @ S4 ) )
% 0.27/0.64 => ~ ! [B3: labeled_graph_b_nat] :
% 0.27/0.64 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A1 @ B3 ) @ R4 )
% 0.27/0.64 => ~ ( member963855452_b_nat @ ( produc951298923_b_nat @ B3 @ A22 ) @ S4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % relcomp.cases
% 0.27/0.64 thf(fact_283_relcomp_Ocases,axiom,
% 0.27/0.64 ! [A1: allegorical_term_b,A22: allegorical_term_b,R4: set_Pr1163220871term_b,S4: set_Pr1163220871term_b] :
% 0.27/0.64 ( ( member516522448term_b @ ( produc1990145943term_b @ A1 @ A22 ) @ ( relcom1955155673term_b @ R4 @ S4 ) )
% 0.27/0.64 => ~ ! [B3: allegorical_term_b] :
% 0.27/0.64 ( ( member516522448term_b @ ( produc1990145943term_b @ A1 @ B3 ) @ R4 )
% 0.27/0.64 => ~ ( member516522448term_b @ ( produc1990145943term_b @ B3 @ A22 ) @ S4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % relcomp.cases
% 0.27/0.64 thf(fact_284_relcompEpair,axiom,
% 0.27/0.64 ! [A: labele935650037_a_nat,C2: labele935650037_a_nat,R4: set_Pr1987088711_a_nat,S4: set_Pr1987088711_a_nat] :
% 0.27/0.64 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ C2 ) @ ( relcom1338300020_a_nat @ R4 @ S4 ) )
% 0.27/0.64 => ~ ! [B3: labele935650037_a_nat] :
% 0.27/0.64 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B3 ) @ R4 )
% 0.27/0.64 => ~ ( member832397200_a_nat @ ( produc1676969687_a_nat @ B3 @ C2 ) @ S4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % relcompEpair
% 0.27/0.64 thf(fact_285_relcompEpair,axiom,
% 0.27/0.64 ! [A: labeled_graph_b_nat,C2: labeled_graph_b_nat,R4: set_Pr551076371_b_nat,S4: set_Pr551076371_b_nat] :
% 0.27/0.64 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ C2 ) @ ( relcom1426860350_b_nat @ R4 @ S4 ) )
% 0.27/0.64 => ~ ! [B3: labeled_graph_b_nat] :
% 0.27/0.64 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B3 ) @ R4 )
% 0.27/0.64 => ~ ( member963855452_b_nat @ ( produc951298923_b_nat @ B3 @ C2 ) @ S4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % relcompEpair
% 0.27/0.64 thf(fact_286_relcompEpair,axiom,
% 0.27/0.64 ! [A: allegorical_term_b,C2: allegorical_term_b,R4: set_Pr1163220871term_b,S4: set_Pr1163220871term_b] :
% 0.27/0.64 ( ( member516522448term_b @ ( produc1990145943term_b @ A @ C2 ) @ ( relcom1955155673term_b @ R4 @ S4 ) )
% 0.27/0.64 => ~ ! [B3: allegorical_term_b] :
% 0.27/0.64 ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B3 ) @ R4 )
% 0.27/0.64 => ~ ( member516522448term_b @ ( produc1990145943term_b @ B3 @ C2 ) @ S4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % relcompEpair
% 0.27/0.64 thf(fact_287_relcompE,axiom,
% 0.27/0.64 ! [Xz: produc1871334759_a_nat,R4: set_Pr1987088711_a_nat,S4: set_Pr1987088711_a_nat] :
% 0.27/0.64 ( ( member832397200_a_nat @ Xz @ ( relcom1338300020_a_nat @ R4 @ S4 ) )
% 0.27/0.64 => ~ ! [X4: labele935650037_a_nat,Y4: labele935650037_a_nat,Z3: labele935650037_a_nat] :
% 0.27/0.64 ( ( Xz
% 0.27/0.64 = ( produc1676969687_a_nat @ X4 @ Z3 ) )
% 0.27/0.64 => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ X4 @ Y4 ) @ R4 )
% 0.27/0.64 => ~ ( member832397200_a_nat @ ( produc1676969687_a_nat @ Y4 @ Z3 ) @ S4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % relcompE
% 0.27/0.64 thf(fact_288_relcompE,axiom,
% 0.27/0.64 ! [Xz: produc1235635379_b_nat,R4: set_Pr551076371_b_nat,S4: set_Pr551076371_b_nat] :
% 0.27/0.64 ( ( member963855452_b_nat @ Xz @ ( relcom1426860350_b_nat @ R4 @ S4 ) )
% 0.27/0.64 => ~ ! [X4: labeled_graph_b_nat,Y4: labeled_graph_b_nat,Z3: labeled_graph_b_nat] :
% 0.27/0.64 ( ( Xz
% 0.27/0.64 = ( produc951298923_b_nat @ X4 @ Z3 ) )
% 0.27/0.64 => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ X4 @ Y4 ) @ R4 )
% 0.27/0.64 => ~ ( member963855452_b_nat @ ( produc951298923_b_nat @ Y4 @ Z3 ) @ S4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % relcompE
% 0.27/0.64 thf(fact_289_relcompE,axiom,
% 0.27/0.64 ! [Xz: produc1478835367term_b,R4: set_Pr1163220871term_b,S4: set_Pr1163220871term_b] :
% 0.27/0.64 ( ( member516522448term_b @ Xz @ ( relcom1955155673term_b @ R4 @ S4 ) )
% 0.27/0.64 => ~ ! [X4: allegorical_term_b,Y4: allegorical_term_b,Z3: allegorical_term_b] :
% 0.27/0.64 ( ( Xz
% 0.27/0.64 = ( produc1990145943term_b @ X4 @ Z3 ) )
% 0.27/0.64 => ( ( member516522448term_b @ ( produc1990145943term_b @ X4 @ Y4 ) @ R4 )
% 0.27/0.64 => ~ ( member516522448term_b @ ( produc1990145943term_b @ Y4 @ Z3 ) @ S4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % relcompE
% 0.27/0.64 thf(fact_290_finite_OemptyI,axiom,
% 0.27/0.64 finite_finite_nat @ bot_bot_set_nat ).
% 0.27/0.64
% 0.27/0.64 % finite.emptyI
% 0.27/0.64 thf(fact_291_finite_OemptyI,axiom,
% 0.27/0.64 finite1987068434at_nat @ bot_bo1626616373at_nat ).
% 0.27/0.64
% 0.27/0.64 % finite.emptyI
% 0.27/0.64 thf(fact_292_infinite__imp__nonempty,axiom,
% 0.27/0.64 ! [S2: set_nat] :
% 0.27/0.64 ( ~ ( finite_finite_nat @ S2 )
% 0.27/0.64 => ( S2 != bot_bot_set_nat ) ) ).
% 0.27/0.64
% 0.27/0.64 % infinite_imp_nonempty
% 0.27/0.64 thf(fact_293_infinite__imp__nonempty,axiom,
% 0.27/0.64 ! [S2: set_Pr9961929at_nat] :
% 0.27/0.64 ( ~ ( finite1987068434at_nat @ S2 )
% 0.27/0.64 => ( S2 != bot_bo1626616373at_nat ) ) ).
% 0.27/0.64
% 0.27/0.64 % infinite_imp_nonempty
% 0.27/0.64 thf(fact_294_finite__has__minimal,axiom,
% 0.27/0.64 ! [A4: set_nat] :
% 0.27/0.64 ( ( finite_finite_nat @ A4 )
% 0.27/0.64 => ( ( A4 != bot_bot_set_nat )
% 0.27/0.64 => ? [X4: nat] :
% 0.27/0.64 ( ( member_nat @ X4 @ A4 )
% 0.27/0.64 & ! [Xa: nat] :
% 0.27/0.64 ( ( member_nat @ Xa @ A4 )
% 0.27/0.64 => ( ( ord_less_eq_nat @ Xa @ X4 )
% 0.27/0.64 => ( X4 = Xa ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % finite_has_minimal
% 0.27/0.64 thf(fact_295_finite__has__maximal,axiom,
% 0.27/0.64 ! [A4: set_nat] :
% 0.27/0.64 ( ( finite_finite_nat @ A4 )
% 0.27/0.64 => ( ( A4 != bot_bot_set_nat )
% 0.27/0.64 => ? [X4: nat] :
% 0.27/0.64 ( ( member_nat @ X4 @ A4 )
% 0.27/0.64 & ! [Xa: nat] :
% 0.27/0.64 ( ( member_nat @ Xa @ A4 )
% 0.27/0.64 => ( ( ord_less_eq_nat @ X4 @ Xa )
% 0.27/0.64 => ( X4 = Xa ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % finite_has_maximal
% 0.27/0.64 thf(fact_296_graph__homomorphism__nonempty,axiom,
% 0.27/0.64 ! [A4: labeled_graph_b_nat,B4: labeled_graph_b_nat,F3: set_Pr1986765409at_nat,E: allegorical_term_b] :
% 0.27/0.64 ( ( graph_529870330at_nat @ A4 @ B4 @ F3 )
% 0.27/0.64 => ( ( ( semantics_b_nat @ A4 @ E )
% 0.27/0.64 != bot_bo2130386637at_nat )
% 0.27/0.64 => ( ( semantics_b_nat @ B4 @ E )
% 0.27/0.64 != bot_bo2130386637at_nat ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % graph_homomorphism_nonempty
% 0.27/0.64 thf(fact_297_bounded__Max__nat,axiom,
% 0.27/0.64 ! [P: nat > $o,X3: nat,M2: nat] :
% 0.27/0.64 ( ( P @ X3 )
% 0.27/0.64 => ( ! [X4: nat] :
% 0.27/0.64 ( ( P @ X4 )
% 0.27/0.64 => ( ord_less_eq_nat @ X4 @ M2 ) )
% 0.27/0.64 => ~ ! [M3: nat] :
% 0.27/0.64 ( ( P @ M3 )
% 0.27/0.64 => ~ ! [X6: nat] :
% 0.27/0.64 ( ( P @ X6 )
% 0.27/0.64 => ( ord_less_eq_nat @ X6 @ M3 ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % bounded_Max_nat
% 0.27/0.64 thf(fact_298_Id__on__vertices__identity_I2_J,axiom,
% 0.27/0.64 ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,F3: set_Pr1986765409at_nat,Aa: nat,Ba: nat] :
% 0.27/0.64 ( ( graph_529870330at_nat @ A @ B @ F3 )
% 0.27/0.64 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Aa @ Ba ) @ F3 )
% 0.27/0.64 => ( member701585322at_nat @ ( product_Pair_nat_nat @ Aa @ Ba ) @ ( relcomp_nat_nat_nat @ F3 @ ( id_on_nat @ ( labele460410879_b_nat @ B ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Id_on_vertices_identity(2)
% 0.27/0.64 thf(fact_299_Id__on__vertices__identity_I1_J,axiom,
% 0.27/0.64 ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,F3: set_Pr1986765409at_nat,Aa: nat,Ba: nat] :
% 0.27/0.64 ( ( graph_529870330at_nat @ A @ B @ F3 )
% 0.27/0.64 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Aa @ Ba ) @ F3 )
% 0.27/0.64 => ( member701585322at_nat @ ( product_Pair_nat_nat @ Aa @ Ba ) @ ( relcomp_nat_nat_nat @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) @ F3 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Id_on_vertices_identity(1)
% 0.27/0.64 thf(fact_300_translation__homomorphism_I2_J,axiom,
% 0.27/0.64 ! [E: allegorical_term_b,G: labeled_graph_b_nat,F3: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( graph_529870330at_nat @ ( translation_b @ E ) @ G @ F3 )
% 0.27/0.64 => ( ( semantics_b_nat @ G @ E )
% 0.27/0.64 != bot_bo2130386637at_nat ) ) ).
% 0.27/0.64
% 0.27/0.64 % translation_homomorphism(2)
% 0.27/0.64 thf(fact_301_weak__universalD,axiom,
% 0.27/0.64 ! [T: itself_nat,R: produc1235635379_b_nat,G_1: labeled_graph_b_nat,G_2: labeled_graph_b_nat,F_1: set_Pr1986765409at_nat,F_2: set_Pr1986765409at_nat,G: labeled_graph_b_nat,H_12: set_Pr1986765409at_nat,H_22: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( weak_u2026406106at_nat @ T @ R @ G_1 @ G_2 @ F_1 @ F_2 )
% 0.27/0.64 => ( ( graph_529870330at_nat @ ( produc194497945_b_nat @ R ) @ G @ H_12 )
% 0.27/0.64 => ( ( graph_529870330at_nat @ G_1 @ G @ H_22 )
% 0.27/0.64 => ( ( ord_le841296385at_nat @ ( relcomp_nat_nat_nat @ F_1 @ H_22 ) @ H_12 )
% 0.27/0.64 => ? [H3: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( graph_529870330at_nat @ G_2 @ G @ H3 )
% 0.27/0.64 & ( ord_le841296385at_nat @ H_22 @ H3 ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % weak_universalD
% 0.27/0.64 thf(fact_302_weak__universal__def,axiom,
% 0.27/0.64 ( weak_u2026406106at_nat
% 0.27/0.64 = ( ^ [Uu: itself_nat,R2: produc1235635379_b_nat,G_12: labeled_graph_b_nat,G_22: labeled_graph_b_nat,F_12: set_Pr1986765409at_nat,F_22: set_Pr1986765409at_nat] :
% 0.27/0.64 ! [H_13: set_Pr1986765409at_nat,H_23: set_Pr1986765409at_nat,G2: labeled_graph_b_nat] :
% 0.27/0.64 ( ( ( graph_529870330at_nat @ ( produc194497945_b_nat @ R2 ) @ G2 @ H_13 )
% 0.27/0.64 & ( graph_529870330at_nat @ G_12 @ G2 @ H_23 )
% 0.27/0.64 & ( ord_le841296385at_nat @ ( relcomp_nat_nat_nat @ F_12 @ H_23 ) @ H_13 ) )
% 0.27/0.64 => ? [H4: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( graph_529870330at_nat @ G_22 @ G2 @ H4 )
% 0.27/0.64 & ( ord_le841296385at_nat @ H_23 @ H4 ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % weak_universal_def
% 0.27/0.64 thf(fact_303_graph__homo__union__id_I2_J,axiom,
% 0.27/0.64 ! [A4: labeled_graph_b_nat,B4: labeled_graph_b_nat,G: labeled_graph_b_nat,F3: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( graph_529870330at_nat @ ( graph_union_b_nat @ A4 @ B4 ) @ G @ F3 )
% 0.27/0.64 => ( ( B4
% 0.27/0.64 = ( restrict_b_nat @ B4 ) )
% 0.27/0.64 => ( graph_529870330at_nat @ B4 @ G @ ( relcomp_nat_nat_nat @ ( id_on_nat @ ( labele460410879_b_nat @ B4 ) ) @ F3 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % graph_homo_union_id(2)
% 0.27/0.64 thf(fact_304_graph__homo__union__id_I1_J,axiom,
% 0.27/0.64 ! [A4: labeled_graph_b_nat,B4: labeled_graph_b_nat,G: labeled_graph_b_nat,F3: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( graph_529870330at_nat @ ( graph_union_b_nat @ A4 @ B4 ) @ G @ F3 )
% 0.27/0.64 => ( ( A4
% 0.27/0.64 = ( restrict_b_nat @ A4 ) )
% 0.27/0.64 => ( graph_529870330at_nat @ A4 @ G @ ( relcomp_nat_nat_nat @ ( id_on_nat @ ( labele460410879_b_nat @ A4 ) ) @ F3 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % graph_homo_union_id(1)
% 0.27/0.64 thf(fact_305_finite__relcomp,axiom,
% 0.27/0.64 ! [R: set_Product_prod_b_b,S2: set_Pr9961929at_nat] :
% 0.27/0.64 ( ( finite1015599120od_b_b @ R )
% 0.27/0.64 => ( ( finite1987068434at_nat @ S2 )
% 0.27/0.64 => ( finite1987068434at_nat @ ( relcom14055552at_nat @ R @ S2 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % finite_relcomp
% 0.27/0.64 thf(fact_306_finite__relcomp,axiom,
% 0.27/0.64 ! [R: set_Pr9961929at_nat,S2: set_Pr1490359111at_nat] :
% 0.27/0.64 ( ( finite1987068434at_nat @ R )
% 0.27/0.64 => ( ( finite48957584at_nat @ S2 )
% 0.27/0.64 => ( finite1987068434at_nat @ ( relcom195261566at_nat @ R @ S2 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % finite_relcomp
% 0.27/0.64 thf(fact_307_subset__emptyI,axiom,
% 0.27/0.64 ! [A4: set_Pr1987088711_a_nat] :
% 0.27/0.64 ( ! [X4: produc1871334759_a_nat] :
% 0.27/0.64 ~ ( member832397200_a_nat @ X4 @ A4 )
% 0.27/0.64 => ( ord_le1718765799_a_nat @ A4 @ bot_bo1836341171_a_nat ) ) ).
% 0.27/0.64
% 0.27/0.64 % subset_emptyI
% 0.27/0.64 thf(fact_308_bot__empty__eq,axiom,
% 0.27/0.64 ( bot_bo1024461546_nat_o
% 0.27/0.64 = ( ^ [X5: produc1871334759_a_nat] : ( member832397200_a_nat @ X5 @ bot_bo1836341171_a_nat ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % bot_empty_eq
% 0.27/0.64 thf(fact_309_ssubst__Pair__rhs,axiom,
% 0.27/0.64 ! [R4: labele935650037_a_nat,S4: labele935650037_a_nat,R: set_Pr1987088711_a_nat,S5: labele935650037_a_nat] :
% 0.27/0.64 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ R4 @ S4 ) @ R )
% 0.27/0.64 => ( ( S5 = S4 )
% 0.27/0.64 => ( member832397200_a_nat @ ( produc1676969687_a_nat @ R4 @ S5 ) @ R ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % ssubst_Pair_rhs
% 0.27/0.64 thf(fact_310_ssubst__Pair__rhs,axiom,
% 0.27/0.64 ! [R4: labeled_graph_b_nat,S4: labeled_graph_b_nat,R: set_Pr551076371_b_nat,S5: labeled_graph_b_nat] :
% 0.27/0.64 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ R4 @ S4 ) @ R )
% 0.27/0.64 => ( ( S5 = S4 )
% 0.27/0.64 => ( member963855452_b_nat @ ( produc951298923_b_nat @ R4 @ S5 ) @ R ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % ssubst_Pair_rhs
% 0.27/0.64 thf(fact_311_ssubst__Pair__rhs,axiom,
% 0.27/0.64 ! [R4: allegorical_term_b,S4: allegorical_term_b,R: set_Pr1163220871term_b,S5: allegorical_term_b] :
% 0.27/0.64 ( ( member516522448term_b @ ( produc1990145943term_b @ R4 @ S4 ) @ R )
% 0.27/0.64 => ( ( S5 = S4 )
% 0.27/0.64 => ( member516522448term_b @ ( produc1990145943term_b @ R4 @ S5 ) @ R ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % ssubst_Pair_rhs
% 0.27/0.64 thf(fact_312_agree__iff__subset,axiom,
% 0.27/0.64 ! [G: labeled_graph_b_nat,X: labeled_graph_b_nat,F3: set_Pr1986765409at_nat,G5: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( graph_529870330at_nat @ G @ X @ F3 )
% 0.27/0.64 => ( ( univalent_nat_nat @ G5 )
% 0.27/0.64 => ( ( agree_on_b_nat_nat @ G @ F3 @ G5 )
% 0.27/0.64 = ( ord_le841296385at_nat @ F3 @ G5 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % agree_iff_subset
% 0.27/0.64 thf(fact_313_id__univalent,axiom,
% 0.27/0.64 ! [X3: set_nat] : ( univalent_nat_nat @ ( id_on_nat @ X3 ) ) ).
% 0.27/0.64
% 0.27/0.64 % id_univalent
% 0.27/0.64 thf(fact_314_univalentD,axiom,
% 0.27/0.64 ! [R: set_Pr1987088711_a_nat,X3: labele935650037_a_nat,Y3: labele935650037_a_nat,Z2: labele935650037_a_nat] :
% 0.27/0.64 ( ( unival1637751524_a_nat @ R )
% 0.27/0.64 => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ X3 @ Y3 ) @ R )
% 0.27/0.64 => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ X3 @ Z2 ) @ R )
% 0.27/0.64 => ( Z2 = Y3 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % univalentD
% 0.27/0.64 thf(fact_315_univalentD,axiom,
% 0.27/0.64 ! [R: set_Pr551076371_b_nat,X3: labeled_graph_b_nat,Y3: labeled_graph_b_nat,Z2: labeled_graph_b_nat] :
% 0.27/0.64 ( ( unival857119480_b_nat @ R )
% 0.27/0.64 => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ X3 @ Y3 ) @ R )
% 0.27/0.64 => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ X3 @ Z2 ) @ R )
% 0.27/0.64 => ( Z2 = Y3 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % univalentD
% 0.27/0.64 thf(fact_316_univalentD,axiom,
% 0.27/0.64 ! [R: set_Pr1163220871term_b,X3: allegorical_term_b,Y3: allegorical_term_b,Z2: allegorical_term_b] :
% 0.27/0.64 ( ( unival1191217828term_b @ R )
% 0.27/0.64 => ( ( member516522448term_b @ ( produc1990145943term_b @ X3 @ Y3 ) @ R )
% 0.27/0.64 => ( ( member516522448term_b @ ( produc1990145943term_b @ X3 @ Z2 ) @ R )
% 0.27/0.64 => ( Z2 = Y3 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % univalentD
% 0.27/0.64 thf(fact_317_univalent__def,axiom,
% 0.27/0.64 ( unival1637751524_a_nat
% 0.27/0.64 = ( ^ [R2: set_Pr1987088711_a_nat] :
% 0.27/0.64 ! [X5: labele935650037_a_nat,Y6: labele935650037_a_nat,Z4: labele935650037_a_nat] :
% 0.27/0.64 ( ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ X5 @ Y6 ) @ R2 )
% 0.27/0.64 & ( member832397200_a_nat @ ( produc1676969687_a_nat @ X5 @ Z4 ) @ R2 ) )
% 0.27/0.64 => ( Z4 = Y6 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % univalent_def
% 0.27/0.64 thf(fact_318_univalent__def,axiom,
% 0.27/0.64 ( unival857119480_b_nat
% 0.27/0.64 = ( ^ [R2: set_Pr551076371_b_nat] :
% 0.27/0.64 ! [X5: labeled_graph_b_nat,Y6: labeled_graph_b_nat,Z4: labeled_graph_b_nat] :
% 0.27/0.64 ( ( ( member963855452_b_nat @ ( produc951298923_b_nat @ X5 @ Y6 ) @ R2 )
% 0.27/0.64 & ( member963855452_b_nat @ ( produc951298923_b_nat @ X5 @ Z4 ) @ R2 ) )
% 0.27/0.64 => ( Z4 = Y6 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % univalent_def
% 0.27/0.64 thf(fact_319_univalent__def,axiom,
% 0.27/0.64 ( unival1191217828term_b
% 0.27/0.64 = ( ^ [R2: set_Pr1163220871term_b] :
% 0.27/0.64 ! [X5: allegorical_term_b,Y6: allegorical_term_b,Z4: allegorical_term_b] :
% 0.27/0.64 ( ( ( member516522448term_b @ ( produc1990145943term_b @ X5 @ Y6 ) @ R2 )
% 0.27/0.64 & ( member516522448term_b @ ( produc1990145943term_b @ X5 @ Z4 ) @ R2 ) )
% 0.27/0.64 => ( Z4 = Y6 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % univalent_def
% 0.27/0.64 thf(fact_320_find__graph__occurence__vertices,axiom,
% 0.27/0.64 ! [S2: nat > labeled_graph_b_nat,V: set_nat,F3: set_Pr1986765409at_nat] :
% 0.27/0.64 ( ( chain_b_nat @ S2 )
% 0.27/0.64 => ( ( finite_finite_nat @ V )
% 0.27/0.64 => ( ( univalent_nat_nat @ F3 )
% 0.27/0.64 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F3 @ V ) @ ( labele460410879_b_nat @ ( chain_sup_b_nat @ S2 ) ) )
% 0.27/0.64 => ? [I2: nat] : ( ord_less_eq_set_nat @ ( image_nat_nat @ F3 @ V ) @ ( labele460410879_b_nat @ ( S2 @ I2 ) ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % find_graph_occurence_vertices
% 0.27/0.64 thf(fact_321_find__graph__occurence__vertices,axiom,
% 0.27/0.64 ! [S2: nat > labeled_graph_b_nat,V: set_Pr9961929at_nat,F3: set_Pr2041158302at_nat] :
% 0.27/0.64 ( ( chain_b_nat @ S2 )
% 0.27/0.64 => ( ( finite1987068434at_nat @ V )
% 0.27/0.64 => ( ( unival633212949at_nat @ F3 )
% 0.27/0.64 => ( ( ord_less_eq_set_nat @ ( image_1356842150at_nat @ F3 @ V ) @ ( labele460410879_b_nat @ ( chain_sup_b_nat @ S2 ) ) )
% 0.27/0.64 => ? [I2: nat] : ( ord_less_eq_set_nat @ ( image_1356842150at_nat @ F3 @ V ) @ ( labele460410879_b_nat @ ( S2 @ I2 ) ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % find_graph_occurence_vertices
% 0.27/0.64 thf(fact_322_ImageI,axiom,
% 0.27/0.64 ! [A: produc1871334759_a_nat,B: produc1871334759_a_nat,R4: set_Pr924198087_a_nat,A4: set_Pr1987088711_a_nat] :
% 0.27/0.64 ( ( member584645392_a_nat @ ( produc1677124439_a_nat @ A @ B ) @ R4 )
% 0.27/0.64 => ( ( member832397200_a_nat @ A @ A4 )
% 0.27/0.64 => ( member832397200_a_nat @ B @ ( image_1168831379_a_nat @ R4 @ A4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % ImageI
% 0.27/0.64 thf(fact_323_ImageI,axiom,
% 0.27/0.64 ! [A: labele935650037_a_nat,B: labele935650037_a_nat,R4: set_Pr1987088711_a_nat,A4: set_la1083530965_a_nat] :
% 0.27/0.64 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ R4 )
% 0.27/0.64 => ( ( member964390942_a_nat @ A @ A4 )
% 0.27/0.64 => ( member964390942_a_nat @ B @ ( image_1971191571_a_nat @ R4 @ A4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % ImageI
% 0.27/0.64 thf(fact_324_ImageI,axiom,
% 0.27/0.64 ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,R4: set_Pr551076371_b_nat,A4: set_la1976028319_b_nat] :
% 0.27/0.64 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ R4 )
% 0.27/0.64 => ( ( member1483953152_b_nat @ A @ A4 )
% 0.27/0.64 => ( member1483953152_b_nat @ B @ ( image_1183964583_b_nat @ R4 @ A4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % ImageI
% 0.27/0.64 thf(fact_325_ImageI,axiom,
% 0.27/0.64 ! [A: allegorical_term_b,B: allegorical_term_b,R4: set_Pr1163220871term_b,A4: set_al1193902458term_b] :
% 0.27/0.64 ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ R4 )
% 0.27/0.64 => ( ( member93680451term_b @ A @ A4 )
% 0.27/0.64 => ( member93680451term_b @ B @ ( image_329221075term_b @ R4 @ A4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % ImageI
% 0.27/0.64 thf(fact_326_Domain__Id__on,axiom,
% 0.27/0.64 ! [A4: set_nat] :
% 0.27/0.64 ( ( domain_nat_nat @ ( id_on_nat @ A4 ) )
% 0.27/0.64 = A4 ) ).
% 0.27/0.64
% 0.27/0.64 % Domain_Id_on
% 0.27/0.64 thf(fact_327_univalent__finite_I2_J,axiom,
% 0.27/0.64 ! [R: set_Pr9961929at_nat] :
% 0.27/0.64 ( ( unival989235430at_nat @ R )
% 0.27/0.64 => ( ( finite_finite_b @ ( domain1101989710at_nat @ R ) )
% 0.27/0.64 = ( finite1987068434at_nat @ R ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % univalent_finite(2)
% 0.27/0.64 thf(fact_328_finite__Domain,axiom,
% 0.27/0.64 ! [R4: set_Pr9961929at_nat] :
% 0.27/0.64 ( ( finite1987068434at_nat @ R4 )
% 0.27/0.64 => ( finite_finite_b @ ( domain1101989710at_nat @ R4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % finite_Domain
% 0.27/0.64 thf(fact_329_finite__Image,axiom,
% 0.27/0.64 ! [R: set_Pr9961929at_nat,A4: set_b] :
% 0.27/0.64 ( ( finite1987068434at_nat @ R )
% 0.27/0.64 => ( finite772653738at_nat @ ( image_2112855445at_nat @ R @ A4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % finite_Image
% 0.27/0.64 thf(fact_330_Domain_Oinducts,axiom,
% 0.27/0.64 ! [X3: labele935650037_a_nat,R4: set_Pr1987088711_a_nat,P: labele935650037_a_nat > $o] :
% 0.27/0.64 ( ( member964390942_a_nat @ X3 @ ( domain1068567884_a_nat @ R4 ) )
% 0.27/0.64 => ( ! [A3: labele935650037_a_nat,B3: labele935650037_a_nat] :
% 0.27/0.64 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A3 @ B3 ) @ R4 )
% 0.27/0.64 => ( P @ A3 ) )
% 0.27/0.64 => ( P @ X3 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Domain.inducts
% 0.27/0.64 thf(fact_331_Domain_Oinducts,axiom,
% 0.27/0.64 ! [X3: labeled_graph_b_nat,R4: set_Pr551076371_b_nat,P: labeled_graph_b_nat > $o] :
% 0.27/0.64 ( ( member1483953152_b_nat @ X3 @ ( domain767519072_b_nat @ R4 ) )
% 0.27/0.64 => ( ! [A3: labeled_graph_b_nat,B3: labeled_graph_b_nat] :
% 0.27/0.64 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A3 @ B3 ) @ R4 )
% 0.27/0.64 => ( P @ A3 ) )
% 0.27/0.64 => ( P @ X3 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Domain.inducts
% 0.27/0.64 thf(fact_332_Domain_Oinducts,axiom,
% 0.27/0.64 ! [X3: allegorical_term_b,R4: set_Pr1163220871term_b,P: allegorical_term_b > $o] :
% 0.27/0.64 ( ( member93680451term_b @ X3 @ ( domain859272460term_b @ R4 ) )
% 0.27/0.64 => ( ! [A3: allegorical_term_b,B3: allegorical_term_b] :
% 0.27/0.64 ( ( member516522448term_b @ ( produc1990145943term_b @ A3 @ B3 ) @ R4 )
% 0.27/0.64 => ( P @ A3 ) )
% 0.27/0.64 => ( P @ X3 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Domain.inducts
% 0.27/0.64 thf(fact_333_Domain_ODomainI,axiom,
% 0.27/0.64 ! [A: labele935650037_a_nat,B: labele935650037_a_nat,R4: set_Pr1987088711_a_nat] :
% 0.27/0.64 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ R4 )
% 0.27/0.64 => ( member964390942_a_nat @ A @ ( domain1068567884_a_nat @ R4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Domain.DomainI
% 0.27/0.64 thf(fact_334_Domain_ODomainI,axiom,
% 0.27/0.64 ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,R4: set_Pr551076371_b_nat] :
% 0.27/0.64 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ R4 )
% 0.27/0.64 => ( member1483953152_b_nat @ A @ ( domain767519072_b_nat @ R4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Domain.DomainI
% 0.27/0.64 thf(fact_335_Domain_ODomainI,axiom,
% 0.27/0.64 ! [A: allegorical_term_b,B: allegorical_term_b,R4: set_Pr1163220871term_b] :
% 0.27/0.64 ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ R4 )
% 0.27/0.64 => ( member93680451term_b @ A @ ( domain859272460term_b @ R4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Domain.DomainI
% 0.27/0.64 thf(fact_336_Domain_Osimps,axiom,
% 0.27/0.64 ! [A: labele935650037_a_nat,R4: set_Pr1987088711_a_nat] :
% 0.27/0.64 ( ( member964390942_a_nat @ A @ ( domain1068567884_a_nat @ R4 ) )
% 0.27/0.64 = ( ? [A5: labele935650037_a_nat,B5: labele935650037_a_nat] :
% 0.27/0.64 ( ( A = A5 )
% 0.27/0.64 & ( member832397200_a_nat @ ( produc1676969687_a_nat @ A5 @ B5 ) @ R4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Domain.simps
% 0.27/0.64 thf(fact_337_Domain_Osimps,axiom,
% 0.27/0.64 ! [A: labeled_graph_b_nat,R4: set_Pr551076371_b_nat] :
% 0.27/0.64 ( ( member1483953152_b_nat @ A @ ( domain767519072_b_nat @ R4 ) )
% 0.27/0.64 = ( ? [A5: labeled_graph_b_nat,B5: labeled_graph_b_nat] :
% 0.27/0.64 ( ( A = A5 )
% 0.27/0.64 & ( member963855452_b_nat @ ( produc951298923_b_nat @ A5 @ B5 ) @ R4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Domain.simps
% 0.27/0.64 thf(fact_338_Domain_Osimps,axiom,
% 0.27/0.64 ! [A: allegorical_term_b,R4: set_Pr1163220871term_b] :
% 0.27/0.64 ( ( member93680451term_b @ A @ ( domain859272460term_b @ R4 ) )
% 0.27/0.64 = ( ? [A5: allegorical_term_b,B5: allegorical_term_b] :
% 0.27/0.64 ( ( A = A5 )
% 0.27/0.64 & ( member516522448term_b @ ( produc1990145943term_b @ A5 @ B5 ) @ R4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Domain.simps
% 0.27/0.64 thf(fact_339_Domain_Ocases,axiom,
% 0.27/0.64 ! [A: labele935650037_a_nat,R4: set_Pr1987088711_a_nat] :
% 0.27/0.64 ( ( member964390942_a_nat @ A @ ( domain1068567884_a_nat @ R4 ) )
% 0.27/0.64 => ~ ! [B3: labele935650037_a_nat] :
% 0.27/0.64 ~ ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B3 ) @ R4 ) ) ).
% 0.27/0.64
% 0.27/0.64 % Domain.cases
% 0.27/0.64 thf(fact_340_Domain_Ocases,axiom,
% 0.27/0.64 ! [A: labeled_graph_b_nat,R4: set_Pr551076371_b_nat] :
% 0.27/0.64 ( ( member1483953152_b_nat @ A @ ( domain767519072_b_nat @ R4 ) )
% 0.27/0.64 => ~ ! [B3: labeled_graph_b_nat] :
% 0.27/0.64 ~ ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B3 ) @ R4 ) ) ).
% 0.27/0.64
% 0.27/0.64 % Domain.cases
% 0.27/0.64 thf(fact_341_Domain_Ocases,axiom,
% 0.27/0.64 ! [A: allegorical_term_b,R4: set_Pr1163220871term_b] :
% 0.27/0.64 ( ( member93680451term_b @ A @ ( domain859272460term_b @ R4 ) )
% 0.27/0.64 => ~ ! [B3: allegorical_term_b] :
% 0.27/0.64 ~ ( member516522448term_b @ ( produc1990145943term_b @ A @ B3 ) @ R4 ) ) ).
% 0.27/0.64
% 0.27/0.64 % Domain.cases
% 0.27/0.64 thf(fact_342_Domain__iff,axiom,
% 0.27/0.64 ! [A: labele935650037_a_nat,R4: set_Pr1987088711_a_nat] :
% 0.27/0.64 ( ( member964390942_a_nat @ A @ ( domain1068567884_a_nat @ R4 ) )
% 0.27/0.64 = ( ? [Y6: labele935650037_a_nat] : ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ Y6 ) @ R4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Domain_iff
% 0.27/0.64 thf(fact_343_Domain__iff,axiom,
% 0.27/0.64 ! [A: labeled_graph_b_nat,R4: set_Pr551076371_b_nat] :
% 0.27/0.64 ( ( member1483953152_b_nat @ A @ ( domain767519072_b_nat @ R4 ) )
% 0.27/0.64 = ( ? [Y6: labeled_graph_b_nat] : ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ Y6 ) @ R4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Domain_iff
% 0.27/0.64 thf(fact_344_Domain__iff,axiom,
% 0.27/0.64 ! [A: allegorical_term_b,R4: set_Pr1163220871term_b] :
% 0.27/0.64 ( ( member93680451term_b @ A @ ( domain859272460term_b @ R4 ) )
% 0.27/0.64 = ( ? [Y6: allegorical_term_b] : ( member516522448term_b @ ( produc1990145943term_b @ A @ Y6 ) @ R4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Domain_iff
% 0.27/0.64 thf(fact_345_DomainE,axiom,
% 0.27/0.64 ! [A: labele935650037_a_nat,R4: set_Pr1987088711_a_nat] :
% 0.27/0.64 ( ( member964390942_a_nat @ A @ ( domain1068567884_a_nat @ R4 ) )
% 0.27/0.64 => ~ ! [B3: labele935650037_a_nat] :
% 0.27/0.64 ~ ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B3 ) @ R4 ) ) ).
% 0.27/0.64
% 0.27/0.64 % DomainE
% 0.27/0.64 thf(fact_346_DomainE,axiom,
% 0.27/0.64 ! [A: labeled_graph_b_nat,R4: set_Pr551076371_b_nat] :
% 0.27/0.64 ( ( member1483953152_b_nat @ A @ ( domain767519072_b_nat @ R4 ) )
% 0.27/0.64 => ~ ! [B3: labeled_graph_b_nat] :
% 0.27/0.64 ~ ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B3 ) @ R4 ) ) ).
% 0.27/0.64
% 0.27/0.64 % DomainE
% 0.27/0.64 thf(fact_347_DomainE,axiom,
% 0.27/0.64 ! [A: allegorical_term_b,R4: set_Pr1163220871term_b] :
% 0.27/0.64 ( ( member93680451term_b @ A @ ( domain859272460term_b @ R4 ) )
% 0.27/0.64 => ~ ! [B3: allegorical_term_b] :
% 0.27/0.64 ~ ( member516522448term_b @ ( produc1990145943term_b @ A @ B3 ) @ R4 ) ) ).
% 0.27/0.64
% 0.27/0.64 % DomainE
% 0.27/0.64 thf(fact_348_rev__ImageI,axiom,
% 0.27/0.64 ! [A: labele935650037_a_nat,A4: set_la1083530965_a_nat,B: labele935650037_a_nat,R4: set_Pr1987088711_a_nat] :
% 0.27/0.64 ( ( member964390942_a_nat @ A @ A4 )
% 0.27/0.64 => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ R4 )
% 0.27/0.64 => ( member964390942_a_nat @ B @ ( image_1971191571_a_nat @ R4 @ A4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % rev_ImageI
% 0.27/0.64 thf(fact_349_rev__ImageI,axiom,
% 0.27/0.64 ! [A: produc1871334759_a_nat,A4: set_Pr1987088711_a_nat,B: produc1871334759_a_nat,R4: set_Pr924198087_a_nat] :
% 0.27/0.64 ( ( member832397200_a_nat @ A @ A4 )
% 0.27/0.64 => ( ( member584645392_a_nat @ ( produc1677124439_a_nat @ A @ B ) @ R4 )
% 0.27/0.64 => ( member832397200_a_nat @ B @ ( image_1168831379_a_nat @ R4 @ A4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % rev_ImageI
% 0.27/0.64 thf(fact_350_rev__ImageI,axiom,
% 0.27/0.64 ! [A: labeled_graph_b_nat,A4: set_la1976028319_b_nat,B: labeled_graph_b_nat,R4: set_Pr551076371_b_nat] :
% 0.27/0.64 ( ( member1483953152_b_nat @ A @ A4 )
% 0.27/0.64 => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ R4 )
% 0.27/0.64 => ( member1483953152_b_nat @ B @ ( image_1183964583_b_nat @ R4 @ A4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % rev_ImageI
% 0.27/0.64 thf(fact_351_rev__ImageI,axiom,
% 0.27/0.64 ! [A: allegorical_term_b,A4: set_al1193902458term_b,B: allegorical_term_b,R4: set_Pr1163220871term_b] :
% 0.27/0.64 ( ( member93680451term_b @ A @ A4 )
% 0.27/0.64 => ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ R4 )
% 0.27/0.64 => ( member93680451term_b @ B @ ( image_329221075term_b @ R4 @ A4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % rev_ImageI
% 0.27/0.64 thf(fact_352_Image__iff,axiom,
% 0.27/0.64 ! [B: labele935650037_a_nat,R4: set_Pr1987088711_a_nat,A4: set_la1083530965_a_nat] :
% 0.27/0.64 ( ( member964390942_a_nat @ B @ ( image_1971191571_a_nat @ R4 @ A4 ) )
% 0.27/0.64 = ( ? [X5: labele935650037_a_nat] :
% 0.27/0.64 ( ( member964390942_a_nat @ X5 @ A4 )
% 0.27/0.64 & ( member832397200_a_nat @ ( produc1676969687_a_nat @ X5 @ B ) @ R4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Image_iff
% 0.27/0.64 thf(fact_353_Image__iff,axiom,
% 0.27/0.64 ! [B: labeled_graph_b_nat,R4: set_Pr551076371_b_nat,A4: set_la1976028319_b_nat] :
% 0.27/0.64 ( ( member1483953152_b_nat @ B @ ( image_1183964583_b_nat @ R4 @ A4 ) )
% 0.27/0.64 = ( ? [X5: labeled_graph_b_nat] :
% 0.27/0.64 ( ( member1483953152_b_nat @ X5 @ A4 )
% 0.27/0.64 & ( member963855452_b_nat @ ( produc951298923_b_nat @ X5 @ B ) @ R4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Image_iff
% 0.27/0.64 thf(fact_354_Image__iff,axiom,
% 0.27/0.64 ! [B: allegorical_term_b,R4: set_Pr1163220871term_b,A4: set_al1193902458term_b] :
% 0.27/0.64 ( ( member93680451term_b @ B @ ( image_329221075term_b @ R4 @ A4 ) )
% 0.27/0.64 = ( ? [X5: allegorical_term_b] :
% 0.27/0.64 ( ( member93680451term_b @ X5 @ A4 )
% 0.27/0.64 & ( member516522448term_b @ ( produc1990145943term_b @ X5 @ B ) @ R4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 % Image_iff
% 0.27/0.64
% 0.27/0.64 % Conjectures (1)
% 0.27/0.64 thf(conj_0,conjecture,
% 0.27/0.64 ( ( 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 ) ) ) ) ) ) ) ) )
% 0.27/0.73 & ( ( 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 ) ) ) ) ) )
% 0.27/0.73 = ( 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 ) ) ) ) ) ) ) )
% 0.27/0.73 & ( 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 ) ) ) ) ) ) ) )
% 0.27/0.73 & ( 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 ) ) ) ) ) ) ) ) ) ).
% 0.27/0.73
% 0.27/0.73 %------------------------------------------------------------------------------
% 0.27/0.73 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.AktYxA07U3/cvc5---1.0.5_26263.p...
% 0.27/0.73 (declare-sort $$unsorted 0)
% 0.27/0.73 (declare-sort tptp.set_Pr2123625671_a_nat 0)
% 0.27/0.73 (declare-sort tptp.produc116665063_a_nat 0)
% 0.27/0.73 (declare-sort tptp.set_Pr924198087_a_nat 0)
% 0.27/0.73 (declare-sort tptp.produc398057191_a_nat 0)
% 0.27/0.73 (declare-sort tptp.set_Pr1173424071_b_nat 0)
% 0.27/0.73 (declare-sort tptp.set_Pr1839611079term_b 0)
% 0.27/0.73 (declare-sort tptp.produc446386919_b_nat 0)
% 0.27/0.73 (declare-sort tptp.produc1116408039term_b 0)
% 0.27/0.73 (declare-sort tptp.set_Pr1987088711_a_nat 0)
% 0.27/0.73 (declare-sort tptp.set_Pr665622551at_nat 0)
% 0.27/0.73 (declare-sort tptp.produc1871334759_a_nat 0)
% 0.27/0.73 (declare-sort tptp.produc1391440311at_nat 0)
% 0.27/0.73 (declare-sort tptp.set_Pr551076371_b_nat 0)
% 0.27/0.73 (declare-sort tptp.set_Pr1647387645at_nat 0)
% 0.27/0.73 (declare-sort tptp.set_Pr1490359111at_nat 0)
% 0.27/0.73 (declare-sort tptp.set_Pr1163220871term_b 0)
% 0.27/0.73 (declare-sort tptp.set_Pr2041158302at_nat 0)
% 0.27/0.73 (declare-sort tptp.produc1235635379_b_nat 0)
% 0.27/0.73 (declare-sort tptp.produc842455143at_nat 0)
% 0.27/0.73 (declare-sort tptp.produc1478835367term_b 0)
% 0.27/0.73 (declare-sort tptp.set_la1083530965_a_nat 0)
% 0.27/0.73 (declare-sort tptp.labele935650037_a_nat 0)
% 0.27/0.73 (declare-sort tptp.labele1835409643at_nat 0)
% 0.27/0.73 (declare-sort tptp.set_Pr9961929at_nat 0)
% 0.27/0.73 (declare-sort tptp.allego510293162tant_a 0)
% 0.27/0.73 (declare-sort tptp.allego1565409692at_nat 0)
% 0.27/0.73 (declare-sort tptp.set_la1976028319_b_nat 0)
% 0.27/0.73 (declare-sort tptp.set_St761939237tant_a 0)
% 0.27/0.73 (declare-sort tptp.set_Pr1986765409at_nat 0)
% 0.27/0.73 (declare-sort tptp.set_al1193902458term_b 0)
% 0.27/0.73 (declare-sort tptp.labeled_graph_b_nat 0)
% 0.27/0.73 (declare-sort tptp.set_Product_prod_b_b 0)
% 0.27/0.73 (declare-sort tptp.standard_Constant_a 0)
% 0.27/0.73 (declare-sort tptp.product_prod_nat_nat 0)
% 0.27/0.73 (declare-sort tptp.allegorical_term_b 0)
% 0.27/0.73 (declare-sort tptp.set_nat 0)
% 0.27/0.73 (declare-sort tptp.itself_nat 0)
% 0.27/0.73 (declare-sort tptp.set_b 0)
% 0.27/0.73 (declare-sort tptp.set_a 0)
% 0.27/0.73 (declare-sort tptp.nat 0)
% 0.27/0.73 (declare-sort tptp.b 0)
% 0.27/0.73 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 0.27/0.73 (declare-fun tptp.finite1242387294at_nat (tptp.set_Pr1647387645at_nat) Bool)
% 0.27/0.73 (declare-fun tptp.finite772653738at_nat (tptp.set_Pr1986765409at_nat) Bool)
% 0.27/0.73 (declare-fun tptp.finite48957584at_nat (tptp.set_Pr1490359111at_nat) Bool)
% 0.27/0.74 (declare-fun tptp.finite1987068434at_nat (tptp.set_Pr9961929at_nat) Bool)
% 0.27/0.74 (declare-fun tptp.finite1015599120od_b_b (tptp.set_Product_prod_b_b) Bool)
% 0.27/0.74 (declare-fun tptp.finite_finite_b (tptp.set_b) Bool)
% 0.27/0.74 (declare-fun tptp.allego745587551tant_a (tptp.allego510293162tant_a tptp.allego510293162tant_a) tptp.allego510293162tant_a)
% 0.27/0.74 (declare-fun tptp.allego266765201at_nat (tptp.allego1565409692at_nat tptp.allego1565409692at_nat) tptp.allego1565409692at_nat)
% 0.27/0.74 (declare-fun tptp.allegorical_A_Int_b (tptp.allegorical_term_b tptp.allegorical_term_b) tptp.allegorical_term_b)
% 0.27/0.74 (declare-fun tptp.semantics_b_nat (tptp.labeled_graph_b_nat tptp.allegorical_term_b) tptp.set_Pr1986765409at_nat)
% 0.27/0.74 (declare-fun tptp.graph_2130075512at_nat (tptp.labele935650037_a_nat tptp.labele935650037_a_nat tptp.set_Pr1986765409at_nat) Bool)
% 0.27/0.74 (declare-fun tptp.graph_2111906684at_nat (tptp.labele1835409643at_nat tptp.labele1835409643at_nat tptp.set_Pr1986765409at_nat) Bool)
% 0.27/0.74 (declare-fun tptp.graph_529870330at_nat (tptp.labeled_graph_b_nat tptp.labeled_graph_b_nat tptp.set_Pr1986765409at_nat) Bool)
% 0.27/0.74 (declare-fun tptp.graph_union_b_nat (tptp.labeled_graph_b_nat tptp.labeled_graph_b_nat) tptp.labeled_graph_b_nat)
% 0.27/0.74 (declare-fun tptp.labeled_LG_b_nat (tptp.set_Pr9961929at_nat tptp.set_nat) tptp.labeled_graph_b_nat)
% 0.27/0.74 (declare-fun tptp.labele195203296_a_nat (tptp.labele935650037_a_nat) tptp.set_Pr1647387645at_nat)
% 0.27/0.74 (declare-fun tptp.labele2032268018at_nat (tptp.labele1835409643at_nat) tptp.set_Pr1490359111at_nat)
% 0.27/0.74 (declare-fun tptp.labeled_edges_b_nat (tptp.labeled_graph_b_nat) tptp.set_Pr9961929at_nat)
% 0.27/0.74 (declare-fun tptp.labele1810595089_a_nat (tptp.labele935650037_a_nat) tptp.set_nat)
% 0.27/0.74 (declare-fun tptp.labele560327297at_nat (tptp.labele1835409643at_nat) tptp.set_nat)
% 0.27/0.74 (declare-fun tptp.labele460410879_b_nat (tptp.labeled_graph_b_nat) tptp.set_nat)
% 0.27/0.74 (declare-fun tptp.restri572569417_a_nat (tptp.labele935650037_a_nat) tptp.labele935650037_a_nat)
% 0.27/0.74 (declare-fun tptp.restri321299017at_nat (tptp.labele1835409643at_nat) tptp.labele1835409643at_nat)
% 0.27/0.74 (declare-fun tptp.restrict_b_nat (tptp.labeled_graph_b_nat) tptp.labeled_graph_b_nat)
% 0.27/0.74 (declare-fun tptp.unival1191217828term_b (tptp.set_Pr1163220871term_b) Bool)
% 0.27/0.74 (declare-fun tptp.unival1637751524_a_nat (tptp.set_Pr1987088711_a_nat) Bool)
% 0.27/0.74 (declare-fun tptp.unival857119480_b_nat (tptp.set_Pr551076371_b_nat) Bool)
% 0.27/0.74 (declare-fun tptp.univalent_nat_nat (tptp.set_Pr1986765409at_nat) Bool)
% 0.27/0.74 (declare-fun tptp.unival633212949at_nat (tptp.set_Pr2041158302at_nat) Bool)
% 0.27/0.74 (declare-fun tptp.unival989235430at_nat (tptp.set_Pr9961929at_nat) Bool)
% 0.27/0.74 (declare-fun tptp.bot_bo1024461546_nat_o (tptp.produc1871334759_a_nat) Bool)
% 0.27/0.74 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 0.27/0.74 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 0.27/0.74 (declare-fun tptp.bot_bo1836341171_a_nat () tptp.set_Pr1987088711_a_nat)
% 0.27/0.74 (declare-fun tptp.bot_bo2130386637at_nat () tptp.set_Pr1986765409at_nat)
% 0.27/0.74 (declare-fun tptp.bot_bo1626616373at_nat () tptp.set_Pr9961929at_nat)
% 0.27/0.74 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 0.27/0.74 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 0.27/0.74 (declare-fun tptp.ord_le138473255term_b (tptp.set_Pr1163220871term_b tptp.set_Pr1163220871term_b) Bool)
% 0.27/0.74 (declare-fun tptp.ord_le1718765799_a_nat (tptp.set_Pr1987088711_a_nat tptp.set_Pr1987088711_a_nat) Bool)
% 0.27/0.74 (declare-fun tptp.ord_le13035955_b_nat (tptp.set_Pr551076371_b_nat tptp.set_Pr551076371_b_nat) Bool)
% 0.27/0.74 (declare-fun tptp.ord_le841296385at_nat (tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat) Bool)
% 0.27/0.74 (declare-fun tptp.ord_le910748009at_nat (tptp.set_Pr9961929at_nat tptp.set_Pr9961929at_nat) Bool)
% 0.27/0.74 (declare-fun tptp.produc1990145943term_b (tptp.allegorical_term_b tptp.allegorical_term_b) tptp.produc1478835367term_b)
% 0.27/0.74 (declare-fun tptp.produc1676969687_a_nat (tptp.labele935650037_a_nat tptp.labele935650037_a_nat) tptp.produc1871334759_a_nat)
% 0.27/0.74 (declare-fun tptp.produc590202991at_nat (tptp.labele1835409643at_nat tptp.labele1835409643at_nat) tptp.produc1391440311at_nat)
% 0.27/0.74 (declare-fun tptp.produc951298923_b_nat (tptp.labeled_graph_b_nat tptp.labeled_graph_b_nat) tptp.produc1235635379_b_nat)
% 0.27/0.74 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 0.27/0.74 (declare-fun tptp.produc859843415term_b (tptp.produc1478835367term_b tptp.produc1478835367term_b) tptp.produc1116408039term_b)
% 0.27/0.74 (declare-fun tptp.produc1677124439_a_nat (tptp.produc1871334759_a_nat tptp.produc1871334759_a_nat) tptp.produc398057191_a_nat)
% 0.27/0.74 (declare-fun tptp.produc1754969175_b_nat (tptp.produc1235635379_b_nat tptp.produc1235635379_b_nat) tptp.produc446386919_b_nat)
% 0.27/0.74 (declare-fun tptp.produc1168807639at_nat (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.produc842455143at_nat)
% 0.27/0.74 (declare-fun tptp.produc170611543_a_nat (tptp.produc398057191_a_nat tptp.produc398057191_a_nat) tptp.produc116665063_a_nat)
% 0.27/0.74 (declare-fun tptp.produc854192515term_b (tptp.produc1478835367term_b) tptp.allegorical_term_b)
% 0.27/0.74 (declare-fun tptp.produc719117507_a_nat (tptp.produc1871334759_a_nat) tptp.labele935650037_a_nat)
% 0.27/0.74 (declare-fun tptp.produc1995789403at_nat (tptp.produc1391440311at_nat) tptp.labele1835409643at_nat)
% 0.27/0.74 (declare-fun tptp.produc1542243159_b_nat (tptp.produc1235635379_b_nat) tptp.labeled_graph_b_nat)
% 0.27/0.74 (declare-fun tptp.product_fst_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 0.27/0.74 (declare-fun tptp.produc1049080131_a_nat (tptp.produc398057191_a_nat) tptp.produc1871334759_a_nat)
% 0.27/0.74 (declare-fun tptp.produc1223098053term_b (tptp.produc1478835367term_b) tptp.allegorical_term_b)
% 0.27/0.74 (declare-fun tptp.produc880161797_a_nat (tptp.produc1871334759_a_nat) tptp.labele935650037_a_nat)
% 0.27/0.74 (declare-fun tptp.produc1564126365at_nat (tptp.produc1391440311at_nat) tptp.labele1835409643at_nat)
% 0.27/0.74 (declare-fun tptp.produc194497945_b_nat (tptp.produc1235635379_b_nat) tptp.labeled_graph_b_nat)
% 0.27/0.74 (declare-fun tptp.product_snd_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 0.27/0.74 (declare-fun tptp.produc1022852229_a_nat (tptp.produc398057191_a_nat) tptp.produc1871334759_a_nat)
% 0.27/0.74 (declare-fun tptp.domain859272460term_b (tptp.set_Pr1163220871term_b) tptp.set_al1193902458term_b)
% 0.27/0.74 (declare-fun tptp.domain1068567884_a_nat (tptp.set_Pr1987088711_a_nat) tptp.set_la1083530965_a_nat)
% 0.27/0.74 (declare-fun tptp.domain767519072_b_nat (tptp.set_Pr551076371_b_nat) tptp.set_la1976028319_b_nat)
% 0.27/0.74 (declare-fun tptp.domain_nat_nat (tptp.set_Pr1986765409at_nat) tptp.set_nat)
% 0.27/0.74 (declare-fun tptp.domain1101989710at_nat (tptp.set_Pr9961929at_nat) tptp.set_b)
% 0.27/0.74 (declare-fun tptp.id_on_1536886967term_b (tptp.set_al1193902458term_b) tptp.set_Pr1163220871term_b)
% 0.27/0.74 (declare-fun tptp.id_on_689842066_a_nat (tptp.set_la1083530965_a_nat) tptp.set_Pr1987088711_a_nat)
% 0.27/0.74 (declare-fun tptp.id_on_583275916_b_nat (tptp.set_la1976028319_b_nat) tptp.set_Pr551076371_b_nat)
% 0.27/0.74 (declare-fun tptp.id_on_nat (tptp.set_nat) tptp.set_Pr1986765409at_nat)
% 0.27/0.74 (declare-fun tptp.id_on_1664915780term_b (tptp.set_Pr1163220871term_b) tptp.set_Pr1839611079term_b)
% 0.27/0.74 (declare-fun tptp.id_on_1651096324_a_nat (tptp.set_Pr1987088711_a_nat) tptp.set_Pr924198087_a_nat)
% 0.27/0.74 (declare-fun tptp.id_on_138931664_b_nat (tptp.set_Pr551076371_b_nat) tptp.set_Pr1173424071_b_nat)
% 0.27/0.74 (declare-fun tptp.id_on_2144791838at_nat (tptp.set_Pr1986765409at_nat) tptp.set_Pr1490359111at_nat)
% 0.27/0.74 (declare-fun tptp.id_on_1395957380_a_nat (tptp.set_Pr924198087_a_nat) tptp.set_Pr2123625671_a_nat)
% 0.27/0.74 (declare-fun tptp.image_329221075term_b (tptp.set_Pr1163220871term_b tptp.set_al1193902458term_b) tptp.set_al1193902458term_b)
% 0.27/0.74 (declare-fun tptp.image_1971191571_a_nat (tptp.set_Pr1987088711_a_nat tptp.set_la1083530965_a_nat) tptp.set_la1083530965_a_nat)
% 0.27/0.74 (declare-fun tptp.image_1183964583_b_nat (tptp.set_Pr551076371_b_nat tptp.set_la1976028319_b_nat) tptp.set_la1976028319_b_nat)
% 0.27/0.74 (declare-fun tptp.image_nat_nat (tptp.set_Pr1986765409at_nat tptp.set_nat) tptp.set_nat)
% 0.27/0.74 (declare-fun tptp.image_1168831379_a_nat (tptp.set_Pr924198087_a_nat tptp.set_Pr1987088711_a_nat) tptp.set_Pr1987088711_a_nat)
% 0.27/0.74 (declare-fun tptp.image_1356842150at_nat (tptp.set_Pr2041158302at_nat tptp.set_Pr9961929at_nat) tptp.set_nat)
% 0.27/0.74 (declare-fun tptp.image_2112855445at_nat (tptp.set_Pr9961929at_nat tptp.set_b) tptp.set_Pr1986765409at_nat)
% 0.27/0.74 (declare-fun tptp.relcom1955155673term_b (tptp.set_Pr1163220871term_b tptp.set_Pr1163220871term_b) tptp.set_Pr1163220871term_b)
% 0.27/0.74 (declare-fun tptp.relcom1338300020_a_nat (tptp.set_Pr1987088711_a_nat tptp.set_Pr1987088711_a_nat) tptp.set_Pr1987088711_a_nat)
% 0.27/0.74 (declare-fun tptp.relcom1426860350_b_nat (tptp.set_Pr551076371_b_nat tptp.set_Pr551076371_b_nat) tptp.set_Pr551076371_b_nat)
% 0.27/0.74 (declare-fun tptp.relcomp_nat_nat_nat (tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat) tptp.set_Pr1986765409at_nat)
% 0.27/0.74 (declare-fun tptp.relcom195261566at_nat (tptp.set_Pr9961929at_nat tptp.set_Pr1490359111at_nat) tptp.set_Pr9961929at_nat)
% 0.27/0.74 (declare-fun tptp.relcom14055552at_nat (tptp.set_Product_prod_b_b tptp.set_Pr9961929at_nat) tptp.set_Pr9961929at_nat)
% 0.27/0.74 (declare-fun tptp.inv_translation (tptp.set_nat) Bool)
% 0.27/0.74 (declare-fun tptp.transl1275713022tant_a (tptp.allego510293162tant_a) tptp.labele935650037_a_nat)
% 0.27/0.74 (declare-fun tptp.transl490985778at_nat (tptp.allego1565409692at_nat) tptp.labele1835409643at_nat)
% 0.27/0.74 (declare-fun tptp.translation_b (tptp.allegorical_term_b) tptp.labeled_graph_b_nat)
% 0.27/0.74 (declare-fun tptp.agree_on_b_nat_nat (tptp.labeled_graph_b_nat tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat) Bool)
% 0.27/0.74 (declare-fun tptp.chain_b_nat ((-> tptp.nat tptp.labeled_graph_b_nat)) Bool)
% 0.27/0.74 (declare-fun tptp.chain_sup_b_nat ((-> tptp.nat tptp.labeled_graph_b_nat)) tptp.labeled_graph_b_nat)
% 0.27/0.74 (declare-fun tptp.conseq1730780375at_nat (tptp.set_Pr551076371_b_nat tptp.labeled_graph_b_nat) Bool)
% 0.27/0.74 (declare-fun tptp.extensible_b_nat_nat (tptp.produc1235635379_b_nat tptp.labeled_graph_b_nat tptp.set_Pr1986765409at_nat) Bool)
% 0.27/0.74 (declare-fun tptp.fair_chain_b_nat_nat (tptp.set_Pr551076371_b_nat (-> tptp.nat tptp.labeled_graph_b_nat)) Bool)
% 0.27/0.74 (declare-fun tptp.fin_ma971967913at_nat (tptp.produc1235635379_b_nat tptp.labeled_graph_b_nat) Bool)
% 0.27/0.74 (declare-fun tptp.maintained_b_nat_nat (tptp.produc1235635379_b_nat tptp.labeled_graph_b_nat) Bool)
% 0.27/0.74 (declare-fun tptp.set_of1384085797_a_nat (tptp.set_Pr1987088711_a_nat) Bool)
% 0.27/0.74 (declare-fun tptp.set_of195930477at_nat (tptp.set_Pr665622551at_nat) Bool)
% 0.27/0.74 (declare-fun tptp.set_of41538795_b_nat (tptp.set_Pr551076371_b_nat) Bool)
% 0.27/0.74 (declare-fun tptp.weak_u2026406106at_nat (tptp.itself_nat tptp.produc1235635379_b_nat tptp.labeled_graph_b_nat tptp.labeled_graph_b_nat tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat) Bool)
% 0.27/0.74 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 0.27/0.74 (declare-fun tptp.collec135640594term_b ((-> tptp.produc1478835367term_b Bool)) tptp.set_Pr1163220871term_b)
% 0.27/0.74 (declare-fun tptp.collec357096914_a_nat ((-> tptp.produc1871334759_a_nat Bool)) tptp.set_Pr1987088711_a_nat)
% 0.27/0.74 (declare-fun tptp.collec1615000990_b_nat ((-> tptp.produc1235635379_b_nat Bool)) tptp.set_Pr551076371_b_nat)
% 0.27/0.74 (declare-fun tptp.collec7649004at_nat ((-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1986765409at_nat)
% 0.27/0.74 (declare-fun tptp.collec1701899602_a_nat ((-> tptp.produc398057191_a_nat Bool)) tptp.set_Pr924198087_a_nat)
% 0.27/0.74 (declare-fun tptp.standa1897115818ules_a (tptp.set_a) tptp.set_Pr1987088711_a_nat)
% 0.27/0.74 (declare-fun tptp.standa1568205540ules_a (tptp.set_St761939237tant_a) tptp.set_Pr1987088711_a_nat)
% 0.27/0.74 (declare-fun tptp.standa1410829644tant_a () tptp.produc1871334759_a_nat)
% 0.27/0.74 (declare-fun tptp.standa214789732at_nat () tptp.produc1391440311at_nat)
% 0.27/0.74 (declare-fun tptp.standa879863266rule_b () tptp.produc1235635379_b_nat)
% 0.27/0.74 (declare-fun tptp.standa63370785tant_a (tptp.standard_Constant_a) tptp.produc1871334759_a_nat)
% 0.27/0.74 (declare-fun tptp.standa2131591247at_nat (tptp.product_prod_nat_nat) tptp.produc1391440311at_nat)
% 0.27/0.74 (declare-fun tptp.standa1329480013rule_b (tptp.b) tptp.produc1235635379_b_nat)
% 0.27/0.74 (declare-fun tptp.standa305748545tant_a (tptp.standard_Constant_a) tptp.produc1871334759_a_nat)
% 0.27/0.74 (declare-fun tptp.standa153097263at_nat (tptp.product_prod_nat_nat) tptp.produc1391440311at_nat)
% 0.27/0.74 (declare-fun tptp.standa1360217389rule_b (tptp.b) tptp.produc1235635379_b_nat)
% 0.27/0.74 (declare-fun tptp.member93680451term_b (tptp.allegorical_term_b tptp.set_al1193902458term_b) Bool)
% 0.27/0.74 (declare-fun tptp.member964390942_a_nat (tptp.labele935650037_a_nat tptp.set_la1083530965_a_nat) Bool)
% 0.27/0.74 (declare-fun tptp.member1483953152_b_nat (tptp.labeled_graph_b_nat tptp.set_la1976028319_b_nat) Bool)
% 0.27/0.74 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 0.27/0.74 (declare-fun tptp.member516522448term_b (tptp.produc1478835367term_b tptp.set_Pr1163220871term_b) Bool)
% 0.27/0.74 (declare-fun tptp.member832397200_a_nat (tptp.produc1871334759_a_nat tptp.set_Pr1987088711_a_nat) Bool)
% 0.27/0.74 (declare-fun tptp.member1129678944at_nat (tptp.produc1391440311at_nat tptp.set_Pr665622551at_nat) Bool)
% 0.27/0.74 (declare-fun tptp.member963855452_b_nat (tptp.produc1235635379_b_nat tptp.set_Pr551076371_b_nat) Bool)
% 0.27/0.74 (declare-fun tptp.member701585322at_nat (tptp.product_prod_nat_nat tptp.set_Pr1986765409at_nat) Bool)
% 0.27/0.74 (declare-fun tptp.member1449757456term_b (tptp.produc1116408039term_b tptp.set_Pr1839611079term_b) Bool)
% 0.27/0.74 (declare-fun tptp.member584645392_a_nat (tptp.produc398057191_a_nat tptp.set_Pr924198087_a_nat) Bool)
% 0.27/0.74 (declare-fun tptp.member889223696_b_nat (tptp.produc446386919_b_nat tptp.set_Pr1173424071_b_nat) Bool)
% 0.27/0.74 (declare-fun tptp.member2027625872at_nat (tptp.produc842455143at_nat tptp.set_Pr1490359111at_nat) Bool)
% 0.27/0.74 (declare-fun tptp.member829905680_a_nat (tptp.produc116665063_a_nat tptp.set_Pr2123625671_a_nat) Bool)
% 0.27/0.74 (declare-fun tptp.c () tptp.set_a)
% 0.27/0.74 (declare-fun tptp.u () tptp.allegorical_term_b)
% 0.27/0.74 (declare-fun tptp.v () tptp.allegorical_term_b)
% 0.27/0.74 (declare-fun tptp.x () tptp.produc1871334759_a_nat)
% 0.27/0.74 (assert (@ (@ tptp.member832397200_a_nat tptp.x) (@ tptp.standa1897115818ules_a tptp.c)))
% 0.27/0.74 (assert (forall ((X tptp.allego1565409692at_nat) (Y tptp.allego1565409692at_nat)) (let ((_let_1 (@ (@ tptp.produc590202991at_nat (@ tptp.transl490985778at_nat X)) (@ tptp.transl490985778at_nat (@ (@ tptp.allego266765201at_nat X) Y))))) (let ((_let_2 (@ tptp.produc1564126365at_nat _let_1))) (let ((_let_3 (@ tptp.produc1995789403at_nat _let_1))) (and (@ (@ (@ tptp.graph_2111906684at_nat _let_3) _let_2) (@ tptp.id_on_nat (@ tptp.labele560327297at_nat _let_3))) (= _let_2 (@ tptp.restri321299017at_nat _let_2)) (@ tptp.finite_finite_nat (@ tptp.labele560327297at_nat _let_2)) (@ tptp.finite48957584at_nat (@ tptp.labele2032268018at_nat _let_2))))))))
% 0.27/0.74 (assert (forall ((X tptp.allego510293162tant_a) (Y tptp.allego510293162tant_a)) (let ((_let_1 (@ (@ tptp.produc1676969687_a_nat (@ tptp.transl1275713022tant_a X)) (@ tptp.transl1275713022tant_a (@ (@ tptp.allego745587551tant_a X) Y))))) (let ((_let_2 (@ tptp.produc880161797_a_nat _let_1))) (let ((_let_3 (@ tptp.produc719117507_a_nat _let_1))) (and (@ (@ (@ tptp.graph_2130075512at_nat _let_3) _let_2) (@ tptp.id_on_nat (@ tptp.labele1810595089_a_nat _let_3))) (= _let_2 (@ tptp.restri572569417_a_nat _let_2)) (@ tptp.finite_finite_nat (@ tptp.labele1810595089_a_nat _let_2)) (@ tptp.finite1242387294at_nat (@ tptp.labele195203296_a_nat _let_2))))))))
% 0.27/0.74 (assert (forall ((X tptp.allegorical_term_b) (Y tptp.allegorical_term_b)) (let ((_let_1 (@ (@ tptp.produc951298923_b_nat (@ tptp.translation_b X)) (@ tptp.translation_b (@ (@ tptp.allegorical_A_Int_b X) Y))))) (let ((_let_2 (@ tptp.produc194497945_b_nat _let_1))) (let ((_let_3 (@ tptp.produc1542243159_b_nat _let_1))) (and (@ (@ (@ tptp.graph_529870330at_nat _let_3) _let_2) (@ tptp.id_on_nat (@ tptp.labele460410879_b_nat _let_3))) (= _let_2 (@ tptp.restrict_b_nat _let_2)) (@ tptp.finite_finite_nat (@ tptp.labele460410879_b_nat _let_2)) (@ tptp.finite1987068434at_nat (@ tptp.labeled_edges_b_nat _let_2))))))))
% 0.27/0.74 (assert (forall ((G tptp.labele935650037_a_nat)) (= (@ (@ (@ tptp.graph_2130075512at_nat G) G) (@ tptp.id_on_nat (@ tptp.labele1810595089_a_nat G))) (= G (@ tptp.restri572569417_a_nat G)))))
% 0.27/0.74 (assert (forall ((G tptp.labeled_graph_b_nat)) (= (@ (@ (@ tptp.graph_529870330at_nat G) G) (@ tptp.id_on_nat (@ tptp.labele460410879_b_nat G))) (= G (@ tptp.restrict_b_nat G)))))
% 0.27/0.74 (assert (forall ((G tptp.labele935650037_a_nat)) (let ((_let_1 (@ tptp.restri572569417_a_nat G))) (= (@ (@ (@ tptp.graph_2130075512at_nat G) _let_1) (@ tptp.id_on_nat (@ tptp.labele1810595089_a_nat G))) (= G _let_1)))))
% 0.27/0.74 (assert (forall ((G tptp.labeled_graph_b_nat)) (let ((_let_1 (@ tptp.restrict_b_nat G))) (= (@ (@ (@ tptp.graph_529870330at_nat G) _let_1) (@ tptp.id_on_nat (@ tptp.labele460410879_b_nat G))) (= G _let_1)))))
% 0.27/0.74 (assert (forall ((A tptp.labele935650037_a_nat)) (let ((_let_1 (@ tptp.restri572569417_a_nat A))) (@ (@ (@ tptp.graph_2130075512at_nat _let_1) _let_1) (@ tptp.id_on_nat (@ tptp.labele1810595089_a_nat A))))))
% 0.27/0.74 (assert (forall ((A tptp.labeled_graph_b_nat)) (let ((_let_1 (@ tptp.restrict_b_nat A))) (@ (@ (@ tptp.graph_529870330at_nat _let_1) _let_1) (@ tptp.id_on_nat (@ tptp.labele460410879_b_nat A))))))
% 0.27/0.74 (assert (forall ((X tptp.allego1565409692at_nat)) (@ tptp.finite48957584at_nat (@ tptp.labele2032268018at_nat (@ tptp.transl490985778at_nat X)))))
% 0.27/0.74 (assert (forall ((X tptp.allego510293162tant_a)) (@ tptp.finite1242387294at_nat (@ tptp.labele195203296_a_nat (@ tptp.transl1275713022tant_a X)))))
% 0.27/0.74 (assert (forall ((X tptp.allegorical_term_b)) (@ tptp.finite1987068434at_nat (@ tptp.labeled_edges_b_nat (@ tptp.translation_b X)))))
% 0.27/0.74 (assert (let ((_let_1 (@ tptp.produc1564126365at_nat tptp.standa214789732at_nat))) (let ((_let_2 (@ tptp.produc1995789403at_nat tptp.standa214789732at_nat))) (and (@ (@ (@ tptp.graph_2111906684at_nat _let_2) _let_1) (@ tptp.id_on_nat (@ tptp.labele560327297at_nat _let_2))) (= _let_1 (@ tptp.restri321299017at_nat _let_1)) (@ tptp.finite_finite_nat (@ tptp.labele560327297at_nat _let_1)) (@ tptp.finite48957584at_nat (@ tptp.labele2032268018at_nat _let_1))))))
% 0.27/0.74 (assert (let ((_let_1 (@ tptp.produc880161797_a_nat tptp.standa1410829644tant_a))) (let ((_let_2 (@ tptp.produc719117507_a_nat tptp.standa1410829644tant_a))) (and (@ (@ (@ tptp.graph_2130075512at_nat _let_2) _let_1) (@ tptp.id_on_nat (@ tptp.labele1810595089_a_nat _let_2))) (= _let_1 (@ tptp.restri572569417_a_nat _let_1)) (@ tptp.finite_finite_nat (@ tptp.labele1810595089_a_nat _let_1)) (@ tptp.finite1242387294at_nat (@ tptp.labele195203296_a_nat _let_1))))))
% 0.27/0.74 (assert (let ((_let_1 (@ tptp.produc194497945_b_nat tptp.standa879863266rule_b))) (let ((_let_2 (@ tptp.produc1542243159_b_nat tptp.standa879863266rule_b))) (and (@ (@ (@ tptp.graph_529870330at_nat _let_2) _let_1) (@ tptp.id_on_nat (@ tptp.labele460410879_b_nat _let_2))) (= _let_1 (@ tptp.restrict_b_nat _let_1)) (@ tptp.finite_finite_nat (@ tptp.labele460410879_b_nat _let_1)) (@ tptp.finite1987068434at_nat (@ tptp.labeled_edges_b_nat _let_1))))))
% 0.27/0.74 (assert (forall ((T tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.standa153097263at_nat T))) (let ((_let_2 (@ tptp.produc1564126365at_nat _let_1))) (let ((_let_3 (@ tptp.produc1995789403at_nat _let_1))) (and (@ (@ (@ tptp.graph_2111906684at_nat _let_3) _let_2) (@ tptp.id_on_nat (@ tptp.labele560327297at_nat _let_3))) (= _let_2 (@ tptp.restri321299017at_nat _let_2)) (@ tptp.finite_finite_nat (@ tptp.labele560327297at_nat _let_2)) (@ tptp.finite48957584at_nat (@ tptp.labele2032268018at_nat _let_2))))))))
% 0.27/0.74 (assert (forall ((T tptp.standard_Constant_a)) (let ((_let_1 (@ tptp.standa305748545tant_a T))) (let ((_let_2 (@ tptp.produc880161797_a_nat _let_1))) (let ((_let_3 (@ tptp.produc719117507_a_nat _let_1))) (and (@ (@ (@ tptp.graph_2130075512at_nat _let_3) _let_2) (@ tptp.id_on_nat (@ tptp.labele1810595089_a_nat _let_3))) (= _let_2 (@ tptp.restri572569417_a_nat _let_2)) (@ tptp.finite_finite_nat (@ tptp.labele1810595089_a_nat _let_2)) (@ tptp.finite1242387294at_nat (@ tptp.labele195203296_a_nat _let_2))))))))
% 0.27/0.74 (assert (forall ((T tptp.b)) (let ((_let_1 (@ tptp.standa1360217389rule_b T))) (let ((_let_2 (@ tptp.produc194497945_b_nat _let_1))) (let ((_let_3 (@ tptp.produc1542243159_b_nat _let_1))) (and (@ (@ (@ tptp.graph_529870330at_nat _let_3) _let_2) (@ tptp.id_on_nat (@ tptp.labele460410879_b_nat _let_3))) (= _let_2 (@ tptp.restrict_b_nat _let_2)) (@ tptp.finite_finite_nat (@ tptp.labele460410879_b_nat _let_2)) (@ tptp.finite1987068434at_nat (@ tptp.labeled_edges_b_nat _let_2))))))))
% 0.27/0.74 (assert (forall ((X tptp.allego510293162tant_a)) (@ tptp.finite_finite_nat (@ tptp.labele1810595089_a_nat (@ tptp.transl1275713022tant_a X)))))
% 0.27/0.74 (assert (forall ((X tptp.allegorical_term_b)) (@ tptp.finite_finite_nat (@ tptp.labele460410879_b_nat (@ tptp.translation_b X)))))
% 0.27/0.74 (assert (forall ((I tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.standa2131591247at_nat I))) (let ((_let_2 (@ tptp.produc1564126365at_nat _let_1))) (let ((_let_3 (@ tptp.produc1995789403at_nat _let_1))) (and (@ (@ (@ tptp.graph_2111906684at_nat _let_3) _let_2) (@ tptp.id_on_nat (@ tptp.labele560327297at_nat _let_3))) (= _let_2 (@ tptp.restri321299017at_nat _let_2)) (@ tptp.finite_finite_nat (@ tptp.labele560327297at_nat _let_2)) (@ tptp.finite48957584at_nat (@ tptp.labele2032268018at_nat _let_2))))))))
% 0.27/0.74 (assert (forall ((I tptp.standard_Constant_a)) (let ((_let_1 (@ tptp.standa63370785tant_a I))) (let ((_let_2 (@ tptp.produc880161797_a_nat _let_1))) (let ((_let_3 (@ tptp.produc719117507_a_nat _let_1))) (and (@ (@ (@ tptp.graph_2130075512at_nat _let_3) _let_2) (@ tptp.id_on_nat (@ tptp.labele1810595089_a_nat _let_3))) (= _let_2 (@ tptp.restri572569417_a_nat _let_2)) (@ tptp.finite_finite_nat (@ tptp.labele1810595089_a_nat _let_2)) (@ tptp.finite1242387294at_nat (@ tptp.labele195203296_a_nat _let_2))))))))
% 0.27/0.74 (assert (forall ((I tptp.b)) (let ((_let_1 (@ tptp.standa1329480013rule_b I))) (let ((_let_2 (@ tptp.produc194497945_b_nat _let_1))) (let ((_let_3 (@ tptp.produc1542243159_b_nat _let_1))) (and (@ (@ (@ tptp.graph_529870330at_nat _let_3) _let_2) (@ tptp.id_on_nat (@ tptp.labele460410879_b_nat _let_3))) (= _let_2 (@ tptp.restrict_b_nat _let_2)) (@ tptp.finite_finite_nat (@ tptp.labele460410879_b_nat _let_2)) (@ tptp.finite1987068434at_nat (@ tptp.labeled_edges_b_nat _let_2))))))))
% 0.27/0.74 (assert (forall ((Prod tptp.product_prod_nat_nat)) (= (@ (@ tptp.product_Pair_nat_nat (@ tptp.product_fst_nat_nat Prod)) (@ tptp.product_snd_nat_nat Prod)) Prod)))
% 0.27/0.74 (assert (forall ((Prod tptp.produc398057191_a_nat)) (= (@ (@ tptp.produc1677124439_a_nat (@ tptp.produc1049080131_a_nat Prod)) (@ tptp.produc1022852229_a_nat Prod)) Prod)))
% 0.27/0.74 (assert (forall ((Prod tptp.produc1871334759_a_nat)) (= (@ (@ tptp.produc1676969687_a_nat (@ tptp.produc719117507_a_nat Prod)) (@ tptp.produc880161797_a_nat Prod)) Prod)))
% 0.27/0.74 (assert (forall ((Prod tptp.produc1478835367term_b)) (= (@ (@ tptp.produc1990145943term_b (@ tptp.produc854192515term_b Prod)) (@ tptp.produc1223098053term_b Prod)) Prod)))
% 0.27/0.74 (assert (forall ((Prod tptp.produc1235635379_b_nat)) (= (@ (@ tptp.produc951298923_b_nat (@ tptp.produc1542243159_b_nat Prod)) (@ tptp.produc194497945_b_nat Prod)) Prod)))
% 0.27/0.74 (assert (= tptp.transl1275713022tant_a (lambda ((X2 tptp.allego510293162tant_a)) (@ tptp.restri572569417_a_nat (@ tptp.transl1275713022tant_a X2)))))
% 0.27/0.74 (assert (= tptp.translation_b (lambda ((X2 tptp.allegorical_term_b)) (@ tptp.restrict_b_nat (@ tptp.translation_b X2)))))
% 0.27/0.74 (assert (forall ((G tptp.labele935650037_a_nat)) (= (@ tptp.labele1810595089_a_nat (@ tptp.restri572569417_a_nat G)) (@ tptp.labele1810595089_a_nat G))))
% 0.27/0.74 (assert (forall ((G tptp.labeled_graph_b_nat)) (= (@ tptp.labele460410879_b_nat (@ tptp.restrict_b_nat G)) (@ tptp.labele460410879_b_nat G))))
% 0.27/0.74 (assert (forall ((A tptp.nat) (B tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat A) B) (@ (@ tptp.product_Pair_nat_nat A2) B2)) (and (= A A2) (= B B2)))))
% 0.27/0.74 (assert (forall ((A tptp.produc1871334759_a_nat) (B tptp.produc1871334759_a_nat) (A2 tptp.produc1871334759_a_nat) (B2 tptp.produc1871334759_a_nat)) (= (= (@ (@ tptp.produc1677124439_a_nat A) B) (@ (@ tptp.produc1677124439_a_nat A2) B2)) (and (= A A2) (= B B2)))))
% 0.27/0.74 (assert (forall ((A tptp.labele935650037_a_nat) (B tptp.labele935650037_a_nat) (A2 tptp.labele935650037_a_nat) (B2 tptp.labele935650037_a_nat)) (= (= (@ (@ tptp.produc1676969687_a_nat A) B) (@ (@ tptp.produc1676969687_a_nat A2) B2)) (and (= A A2) (= B B2)))))
% 0.27/0.74 (assert (forall ((A tptp.labeled_graph_b_nat) (B tptp.labeled_graph_b_nat) (A2 tptp.labeled_graph_b_nat) (B2 tptp.labeled_graph_b_nat)) (= (= (@ (@ tptp.produc951298923_b_nat A) B) (@ (@ tptp.produc951298923_b_nat A2) B2)) (and (= A A2) (= B B2)))))
% 0.27/0.74 (assert (forall ((A tptp.allegorical_term_b) (B tptp.allegorical_term_b) (A2 tptp.allegorical_term_b) (B2 tptp.allegorical_term_b)) (= (= (@ (@ tptp.produc1990145943term_b A) B) (@ (@ tptp.produc1990145943term_b A2) B2)) (and (= A A2) (= B B2)))))
% 0.27/0.74 (assert (forall ((X1 tptp.nat) (X22 tptp.nat) (Y1 tptp.nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat X1) X22) (@ (@ tptp.product_Pair_nat_nat Y1) Y2)) (and (= X1 Y1) (= X22 Y2)))))
% 0.27/0.74 (assert (forall ((X1 tptp.produc1871334759_a_nat) (X22 tptp.produc1871334759_a_nat) (Y1 tptp.produc1871334759_a_nat) (Y2 tptp.produc1871334759_a_nat)) (= (= (@ (@ tptp.produc1677124439_a_nat X1) X22) (@ (@ tptp.produc1677124439_a_nat Y1) Y2)) (and (= X1 Y1) (= X22 Y2)))))
% 0.27/0.74 (assert (forall ((X1 tptp.labele935650037_a_nat) (X22 tptp.labele935650037_a_nat) (Y1 tptp.labele935650037_a_nat) (Y2 tptp.labele935650037_a_nat)) (= (= (@ (@ tptp.produc1676969687_a_nat X1) X22) (@ (@ tptp.produc1676969687_a_nat Y1) Y2)) (and (= X1 Y1) (= X22 Y2)))))
% 0.27/0.74 (assert (forall ((X1 tptp.labeled_graph_b_nat) (X22 tptp.labeled_graph_b_nat) (Y1 tptp.labeled_graph_b_nat) (Y2 tptp.labeled_graph_b_nat)) (= (= (@ (@ tptp.produc951298923_b_nat X1) X22) (@ (@ tptp.produc951298923_b_nat Y1) Y2)) (and (= X1 Y1) (= X22 Y2)))))
% 0.27/0.74 (assert (forall ((X1 tptp.allegorical_term_b) (X22 tptp.allegorical_term_b) (Y1 tptp.allegorical_term_b) (Y2 tptp.allegorical_term_b)) (= (= (@ (@ tptp.produc1990145943term_b X1) X22) (@ (@ tptp.produc1990145943term_b Y1) Y2)) (and (= X1 Y1) (= X22 Y2)))))
% 0.27/0.74 (assert (forall ((X3 tptp.labele935650037_a_nat)) (let ((_let_1 (@ tptp.restri572569417_a_nat X3))) (= (@ tptp.restri572569417_a_nat _let_1) _let_1))))
% 0.27/0.74 (assert (forall ((X3 tptp.labeled_graph_b_nat)) (let ((_let_1 (@ tptp.restrict_b_nat X3))) (= (@ tptp.restrict_b_nat _let_1) _let_1))))
% 0.27/0.74 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Prod tptp.product_prod_nat_nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (@ P (@ (@ tptp.product_Pair_nat_nat A3) B3))) (@ P Prod))))
% 0.27/0.74 (assert (forall ((P (-> tptp.produc398057191_a_nat Bool)) (Prod tptp.produc398057191_a_nat)) (=> (forall ((A3 tptp.produc1871334759_a_nat) (B3 tptp.produc1871334759_a_nat)) (@ P (@ (@ tptp.produc1677124439_a_nat A3) B3))) (@ P Prod))))
% 0.27/0.74 (assert (forall ((P (-> tptp.produc1871334759_a_nat Bool)) (Prod tptp.produc1871334759_a_nat)) (=> (forall ((A3 tptp.labele935650037_a_nat) (B3 tptp.labele935650037_a_nat)) (@ P (@ (@ tptp.produc1676969687_a_nat A3) B3))) (@ P Prod))))
% 0.27/0.74 (assert (forall ((P (-> tptp.produc1235635379_b_nat Bool)) (Prod tptp.produc1235635379_b_nat)) (=> (forall ((A3 tptp.labeled_graph_b_nat) (B3 tptp.labeled_graph_b_nat)) (@ P (@ (@ tptp.produc951298923_b_nat A3) B3))) (@ P Prod))))
% 0.27/0.74 (assert (forall ((P (-> tptp.produc1478835367term_b Bool)) (Prod tptp.produc1478835367term_b)) (=> (forall ((A3 tptp.allegorical_term_b) (B3 tptp.allegorical_term_b)) (@ P (@ (@ tptp.produc1990145943term_b A3) B3))) (@ P Prod))))
% 0.27/0.74 (assert (forall ((Y3 tptp.product_prod_nat_nat)) (not (forall ((A3 tptp.nat) (B3 tptp.nat)) (not (= Y3 (@ (@ tptp.product_Pair_nat_nat A3) B3)))))))
% 0.27/0.74 (assert (forall ((Y3 tptp.produc398057191_a_nat)) (not (forall ((A3 tptp.produc1871334759_a_nat) (B3 tptp.produc1871334759_a_nat)) (not (= Y3 (@ (@ tptp.produc1677124439_a_nat A3) B3)))))))
% 0.27/0.74 (assert (forall ((Y3 tptp.produc1871334759_a_nat)) (not (forall ((A3 tptp.labele935650037_a_nat) (B3 tptp.labele935650037_a_nat)) (not (= Y3 (@ (@ tptp.produc1676969687_a_nat A3) B3)))))))
% 0.27/0.74 (assert (forall ((Y3 tptp.produc1235635379_b_nat)) (not (forall ((A3 tptp.labeled_graph_b_nat) (B3 tptp.labeled_graph_b_nat)) (not (= Y3 (@ (@ tptp.produc951298923_b_nat A3) B3)))))))
% 0.27/0.74 (assert (forall ((Y3 tptp.produc1478835367term_b)) (not (forall ((A3 tptp.allegorical_term_b) (B3 tptp.allegorical_term_b)) (not (= Y3 (@ (@ tptp.produc1990145943term_b A3) B3)))))))
% 0.27/0.74 (assert (forall ((P (-> tptp.produc398057191_a_nat Bool)) (X3 tptp.produc398057191_a_nat)) (=> (forall ((A3 tptp.produc1871334759_a_nat) (B3 tptp.labele935650037_a_nat) (C tptp.labele935650037_a_nat)) (@ P (@ (@ tptp.produc1677124439_a_nat A3) (@ (@ tptp.produc1676969687_a_nat B3) C)))) (@ P X3))))
% 0.27/0.74 (assert (forall ((Y3 tptp.produc398057191_a_nat)) (not (forall ((A3 tptp.produc1871334759_a_nat) (B3 tptp.labele935650037_a_nat) (C tptp.labele935650037_a_nat)) (not (= Y3 (@ (@ tptp.produc1677124439_a_nat A3) (@ (@ tptp.produc1676969687_a_nat B3) C))))))))
% 0.27/0.74 (assert (forall ((A tptp.nat) (B tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A) B) (@ (@ tptp.product_Pair_nat_nat A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 0.27/0.74 (assert (forall ((A tptp.produc1871334759_a_nat) (B tptp.produc1871334759_a_nat) (A2 tptp.produc1871334759_a_nat) (B2 tptp.produc1871334759_a_nat)) (=> (= (@ (@ tptp.produc1677124439_a_nat A) B) (@ (@ tptp.produc1677124439_a_nat A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 0.27/0.74 (assert (forall ((A tptp.labele935650037_a_nat) (B tptp.labele935650037_a_nat) (A2 tptp.labele935650037_a_nat) (B2 tptp.labele935650037_a_nat)) (=> (= (@ (@ tptp.produc1676969687_a_nat A) B) (@ (@ tptp.produc1676969687_a_nat A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 0.27/0.74 (assert (forall ((A tptp.labeled_graph_b_nat) (B tptp.labeled_graph_b_nat) (A2 tptp.labeled_graph_b_nat) (B2 tptp.labeled_graph_b_nat)) (=> (= (@ (@ tptp.produc951298923_b_nat A) B) (@ (@ tptp.produc951298923_b_nat A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 0.27/0.74 (assert (forall ((A tptp.allegorical_term_b) (B tptp.allegorical_term_b) (A2 tptp.allegorical_term_b) (B2 tptp.allegorical_term_b)) (=> (= (@ (@ tptp.produc1990145943term_b A) B) (@ (@ tptp.produc1990145943term_b A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 0.27/0.74 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (P2 tptp.product_prod_nat_nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (@ P (@ (@ tptp.product_Pair_nat_nat A3) B3))) (@ P P2))))
% 0.27/0.74 (assert (forall ((P (-> tptp.produc398057191_a_nat Bool)) (P2 tptp.produc398057191_a_nat)) (=> (forall ((A3 tptp.produc1871334759_a_nat) (B3 tptp.produc1871334759_a_nat)) (@ P (@ (@ tptp.produc1677124439_a_nat A3) B3))) (@ P P2))))
% 0.27/0.74 (assert (forall ((P (-> tptp.produc1871334759_a_nat Bool)) (P2 tptp.produc1871334759_a_nat)) (=> (forall ((A3 tptp.labele935650037_a_nat) (B3 tptp.labele935650037_a_nat)) (@ P (@ (@ tptp.produc1676969687_a_nat A3) B3))) (@ P P2))))
% 0.27/0.74 (assert (forall ((P (-> tptp.produc1235635379_b_nat Bool)) (P2 tptp.produc1235635379_b_nat)) (=> (forall ((A3 tptp.labeled_graph_b_nat) (B3 tptp.labeled_graph_b_nat)) (@ P (@ (@ tptp.produc951298923_b_nat A3) B3))) (@ P P2))))
% 0.27/0.74 (assert (forall ((P (-> tptp.produc1478835367term_b Bool)) (P2 tptp.produc1478835367term_b)) (=> (forall ((A3 tptp.allegorical_term_b) (B3 tptp.allegorical_term_b)) (@ P (@ (@ tptp.produc1990145943term_b A3) B3))) (@ P P2))))
% 0.27/0.74 (assert (forall ((P2 tptp.product_prod_nat_nat)) (exists ((X4 tptp.nat) (Y4 tptp.nat)) (= P2 (@ (@ tptp.product_Pair_nat_nat X4) Y4)))))
% 0.27/0.74 (assert (forall ((P2 tptp.produc398057191_a_nat)) (exists ((X4 tptp.produc1871334759_a_nat) (Y4 tptp.produc1871334759_a_nat)) (= P2 (@ (@ tptp.produc1677124439_a_nat X4) Y4)))))
% 0.27/0.74 (assert (forall ((P2 tptp.produc1871334759_a_nat)) (exists ((X4 tptp.labele935650037_a_nat) (Y4 tptp.labele935650037_a_nat)) (= P2 (@ (@ tptp.produc1676969687_a_nat X4) Y4)))))
% 0.27/0.74 (assert (forall ((P2 tptp.produc1235635379_b_nat)) (exists ((X4 tptp.labeled_graph_b_nat) (Y4 tptp.labeled_graph_b_nat)) (= P2 (@ (@ tptp.produc951298923_b_nat X4) Y4)))))
% 0.27/0.74 (assert (forall ((P2 tptp.produc1478835367term_b)) (exists ((X4 tptp.allegorical_term_b) (Y4 tptp.allegorical_term_b)) (= P2 (@ (@ tptp.produc1990145943term_b X4) Y4)))))
% 0.27/0.74 (assert (forall ((X1 tptp.nat) (X22 tptp.nat)) (= (@ tptp.product_fst_nat_nat (@ (@ tptp.product_Pair_nat_nat X1) X22)) X1)))
% 0.27/0.74 (assert (forall ((X1 tptp.produc1871334759_a_nat) (X22 tptp.produc1871334759_a_nat)) (= (@ tptp.produc1049080131_a_nat (@ (@ tptp.produc1677124439_a_nat X1) X22)) X1)))
% 0.27/0.74 (assert (forall ((X1 tptp.labele935650037_a_nat) (X22 tptp.labele935650037_a_nat)) (= (@ tptp.produc719117507_a_nat (@ (@ tptp.produc1676969687_a_nat X1) X22)) X1)))
% 0.27/0.74 (assert (forall ((X1 tptp.labeled_graph_b_nat) (X22 tptp.labeled_graph_b_nat)) (= (@ tptp.produc1542243159_b_nat (@ (@ tptp.produc951298923_b_nat X1) X22)) X1)))
% 0.27/0.74 (assert (forall ((X1 tptp.allegorical_term_b) (X22 tptp.allegorical_term_b)) (= (@ tptp.produc854192515term_b (@ (@ tptp.produc1990145943term_b X1) X22)) X1)))
% 0.27/0.74 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat) (A tptp.nat)) (=> (= (@ tptp.product_fst_nat_nat (@ (@ tptp.product_Pair_nat_nat X3) Y3)) A) (= X3 A))))
% 0.27/0.74 (assert (forall ((X3 tptp.produc1871334759_a_nat) (Y3 tptp.produc1871334759_a_nat) (A tptp.produc1871334759_a_nat)) (=> (= (@ tptp.produc1049080131_a_nat (@ (@ tptp.produc1677124439_a_nat X3) Y3)) A) (= X3 A))))
% 0.27/0.74 (assert (forall ((X3 tptp.labele935650037_a_nat) (Y3 tptp.labele935650037_a_nat) (A tptp.labele935650037_a_nat)) (=> (= (@ tptp.produc719117507_a_nat (@ (@ tptp.produc1676969687_a_nat X3) Y3)) A) (= X3 A))))
% 0.27/0.74 (assert (forall ((X3 tptp.labeled_graph_b_nat) (Y3 tptp.labeled_graph_b_nat) (A tptp.labeled_graph_b_nat)) (=> (= (@ tptp.produc1542243159_b_nat (@ (@ tptp.produc951298923_b_nat X3) Y3)) A) (= X3 A))))
% 0.27/0.74 (assert (forall ((X3 tptp.allegorical_term_b) (Y3 tptp.allegorical_term_b) (A tptp.allegorical_term_b)) (=> (= (@ tptp.produc854192515term_b (@ (@ tptp.produc1990145943term_b X3) Y3)) A) (= X3 A))))
% 0.27/0.74 (assert (forall ((X1 tptp.nat) (X22 tptp.nat)) (= (@ tptp.product_snd_nat_nat (@ (@ tptp.product_Pair_nat_nat X1) X22)) X22)))
% 0.27/0.74 (assert (forall ((X1 tptp.produc1871334759_a_nat) (X22 tptp.produc1871334759_a_nat)) (= (@ tptp.produc1022852229_a_nat (@ (@ tptp.produc1677124439_a_nat X1) X22)) X22)))
% 0.27/0.74 (assert (forall ((X1 tptp.labele935650037_a_nat) (X22 tptp.labele935650037_a_nat)) (= (@ tptp.produc880161797_a_nat (@ (@ tptp.produc1676969687_a_nat X1) X22)) X22)))
% 0.27/0.74 (assert (forall ((X1 tptp.allegorical_term_b) (X22 tptp.allegorical_term_b)) (= (@ tptp.produc1223098053term_b (@ (@ tptp.produc1990145943term_b X1) X22)) X22)))
% 0.27/0.74 (assert (forall ((X1 tptp.labeled_graph_b_nat) (X22 tptp.labeled_graph_b_nat)) (= (@ tptp.produc194497945_b_nat (@ (@ tptp.produc951298923_b_nat X1) X22)) X22)))
% 0.27/0.74 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat) (A tptp.nat)) (=> (= (@ tptp.product_snd_nat_nat (@ (@ tptp.product_Pair_nat_nat X3) Y3)) A) (= Y3 A))))
% 0.27/0.74 (assert (forall ((X3 tptp.produc1871334759_a_nat) (Y3 tptp.produc1871334759_a_nat) (A tptp.produc1871334759_a_nat)) (=> (= (@ tptp.produc1022852229_a_nat (@ (@ tptp.produc1677124439_a_nat X3) Y3)) A) (= Y3 A))))
% 0.27/0.74 (assert (forall ((X3 tptp.labele935650037_a_nat) (Y3 tptp.labele935650037_a_nat) (A tptp.labele935650037_a_nat)) (=> (= (@ tptp.produc880161797_a_nat (@ (@ tptp.produc1676969687_a_nat X3) Y3)) A) (= Y3 A))))
% 0.27/0.74 (assert (forall ((X3 tptp.allegorical_term_b) (Y3 tptp.allegorical_term_b) (A tptp.allegorical_term_b)) (=> (= (@ tptp.produc1223098053term_b (@ (@ tptp.produc1990145943term_b X3) Y3)) A) (= Y3 A))))
% 0.27/0.74 (assert (forall ((X3 tptp.labeled_graph_b_nat) (Y3 tptp.labeled_graph_b_nat) (A tptp.labeled_graph_b_nat)) (=> (= (@ tptp.produc194497945_b_nat (@ (@ tptp.produc951298923_b_nat X3) Y3)) A) (= Y3 A))))
% 0.27/0.74 (assert (= (lambda ((Y5 tptp.produc1871334759_a_nat) (Z tptp.produc1871334759_a_nat)) (= Y5 Z)) (lambda ((S tptp.produc1871334759_a_nat) (T2 tptp.produc1871334759_a_nat)) (and (= (@ tptp.produc719117507_a_nat S) (@ tptp.produc719117507_a_nat T2)) (= (@ tptp.produc880161797_a_nat S) (@ tptp.produc880161797_a_nat T2))))))
% 0.27/0.74 (assert (= (lambda ((Y5 tptp.produc1478835367term_b) (Z tptp.produc1478835367term_b)) (= Y5 Z)) (lambda ((S tptp.produc1478835367term_b) (T2 tptp.produc1478835367term_b)) (and (= (@ tptp.produc854192515term_b S) (@ tptp.produc854192515term_b T2)) (= (@ tptp.produc1223098053term_b S) (@ tptp.produc1223098053term_b T2))))))
% 0.27/0.74 (assert (= (lambda ((Y5 tptp.produc1235635379_b_nat) (Z tptp.produc1235635379_b_nat)) (= Y5 Z)) (lambda ((S tptp.produc1235635379_b_nat) (T2 tptp.produc1235635379_b_nat)) (and (= (@ tptp.produc1542243159_b_nat S) (@ tptp.produc1542243159_b_nat T2)) (= (@ tptp.produc194497945_b_nat S) (@ tptp.produc194497945_b_nat T2))))))
% 0.27/0.74 (assert (forall ((Prod tptp.produc1871334759_a_nat) (Prod2 tptp.produc1871334759_a_nat)) (=> (and (= (@ tptp.produc719117507_a_nat Prod) (@ tptp.produc719117507_a_nat Prod2)) (= (@ tptp.produc880161797_a_nat Prod) (@ tptp.produc880161797_a_nat Prod2))) (= Prod Prod2))))
% 0.27/0.74 (assert (forall ((Prod tptp.produc1478835367term_b) (Prod2 tptp.produc1478835367term_b)) (=> (and (= (@ tptp.produc854192515term_b Prod) (@ tptp.produc854192515term_b Prod2)) (= (@ tptp.produc1223098053term_b Prod) (@ tptp.produc1223098053term_b Prod2))) (= Prod Prod2))))
% 0.27/0.74 (assert (forall ((Prod tptp.produc1235635379_b_nat) (Prod2 tptp.produc1235635379_b_nat)) (=> (and (= (@ tptp.produc1542243159_b_nat Prod) (@ tptp.produc1542243159_b_nat Prod2)) (= (@ tptp.produc194497945_b_nat Prod) (@ tptp.produc194497945_b_nat Prod2))) (= Prod Prod2))))
% 0.27/0.74 (assert (forall ((P2 tptp.produc1871334759_a_nat) (Q tptp.produc1871334759_a_nat)) (=> (= (@ tptp.produc719117507_a_nat P2) (@ tptp.produc719117507_a_nat Q)) (=> (= (@ tptp.produc880161797_a_nat P2) (@ tptp.produc880161797_a_nat Q)) (= P2 Q)))))
% 0.27/0.74 (assert (forall ((P2 tptp.produc1478835367term_b) (Q tptp.produc1478835367term_b)) (=> (= (@ tptp.produc854192515term_b P2) (@ tptp.produc854192515term_b Q)) (=> (= (@ tptp.produc1223098053term_b P2) (@ tptp.produc1223098053term_b Q)) (= P2 Q)))))
% 0.27/0.74 (assert (forall ((P2 tptp.produc1235635379_b_nat) (Q tptp.produc1235635379_b_nat)) (=> (= (@ tptp.produc1542243159_b_nat P2) (@ tptp.produc1542243159_b_nat Q)) (=> (= (@ tptp.produc194497945_b_nat P2) (@ tptp.produc194497945_b_nat Q)) (= P2 Q)))))
% 0.27/0.74 (assert (forall ((Labeled_graph tptp.labele935650037_a_nat) (Labeled_graph2 tptp.labele935650037_a_nat)) (=> (and (= (@ tptp.labele195203296_a_nat Labeled_graph) (@ tptp.labele195203296_a_nat Labeled_graph2)) (= (@ tptp.labele1810595089_a_nat Labeled_graph) (@ tptp.labele1810595089_a_nat Labeled_graph2))) (= Labeled_graph Labeled_graph2))))
% 0.27/0.74 (assert (forall ((Labeled_graph tptp.labeled_graph_b_nat) (Labeled_graph2 tptp.labeled_graph_b_nat)) (=> (and (= (@ tptp.labeled_edges_b_nat Labeled_graph) (@ tptp.labeled_edges_b_nat Labeled_graph2)) (= (@ tptp.labele460410879_b_nat Labeled_graph) (@ tptp.labele460410879_b_nat Labeled_graph2))) (= Labeled_graph Labeled_graph2))))
% 0.27/0.74 (assert (forall ((T tptp.product_prod_nat_nat)) (= T (@ (@ tptp.product_Pair_nat_nat (@ tptp.product_fst_nat_nat T)) (@ tptp.product_snd_nat_nat T)))))
% 0.27/0.74 (assert (forall ((T tptp.produc398057191_a_nat)) (= T (@ (@ tptp.produc1677124439_a_nat (@ tptp.produc1049080131_a_nat T)) (@ tptp.produc1022852229_a_nat T)))))
% 0.27/0.74 (assert (forall ((T tptp.produc1871334759_a_nat)) (= T (@ (@ tptp.produc1676969687_a_nat (@ tptp.produc719117507_a_nat T)) (@ tptp.produc880161797_a_nat T)))))
% 0.27/0.74 (assert (forall ((T tptp.produc1478835367term_b)) (= T (@ (@ tptp.produc1990145943term_b (@ tptp.produc854192515term_b T)) (@ tptp.produc1223098053term_b T)))))
% 0.27/0.74 (assert (forall ((T tptp.produc1235635379_b_nat)) (= T (@ (@ tptp.produc951298923_b_nat (@ tptp.produc1542243159_b_nat T)) (@ tptp.produc194497945_b_nat T)))))
% 0.27/0.74 (assert (forall ((Prod tptp.product_prod_nat_nat)) (= Prod (@ (@ tptp.product_Pair_nat_nat (@ tptp.product_fst_nat_nat Prod)) (@ tptp.product_snd_nat_nat Prod)))))
% 0.27/0.74 (assert (forall ((Prod tptp.produc398057191_a_nat)) (= Prod (@ (@ tptp.produc1677124439_a_nat (@ tptp.produc1049080131_a_nat Prod)) (@ tptp.produc1022852229_a_nat Prod)))))
% 0.27/0.74 (assert (forall ((Prod tptp.produc1871334759_a_nat)) (= Prod (@ (@ tptp.produc1676969687_a_nat (@ tptp.produc719117507_a_nat Prod)) (@ tptp.produc880161797_a_nat Prod)))))
% 0.27/0.74 (assert (forall ((Prod tptp.produc1478835367term_b)) (= Prod (@ (@ tptp.produc1990145943term_b (@ tptp.produc854192515term_b Prod)) (@ tptp.produc1223098053term_b Prod)))))
% 0.27/0.74 (assert (forall ((Prod tptp.produc1235635379_b_nat)) (= Prod (@ (@ tptp.produc951298923_b_nat (@ tptp.produc1542243159_b_nat Prod)) (@ tptp.produc194497945_b_nat Prod)))))
% 0.27/0.74 (assert (forall ((A4 tptp.labele935650037_a_nat) (B4 tptp.labele935650037_a_nat) (X tptp.labele935650037_a_nat) (H tptp.set_Pr1986765409at_nat)) (let ((_let_1 (@ tptp.graph_2130075512at_nat X))) (=> (@ (@ (@ tptp.graph_2130075512at_nat A4) B4) (@ tptp.id_on_nat (@ tptp.labele1810595089_a_nat A4))) (=> (@ (@ _let_1 A4) H) (@ (@ _let_1 B4) H))))))
% 0.27/0.74 (assert (forall ((A4 tptp.labeled_graph_b_nat) (B4 tptp.labeled_graph_b_nat) (X tptp.labeled_graph_b_nat) (H tptp.set_Pr1986765409at_nat)) (let ((_let_1 (@ tptp.graph_529870330at_nat X))) (=> (@ (@ (@ tptp.graph_529870330at_nat A4) B4) (@ tptp.id_on_nat (@ tptp.labele460410879_b_nat A4))) (=> (@ (@ _let_1 A4) H) (@ (@ _let_1 B4) H))))))
% 0.27/0.74 (assert (forall ((G_1 tptp.labele935650037_a_nat) (G_2 tptp.labele935650037_a_nat) (G_3 tptp.labele935650037_a_nat)) (let ((_let_1 (@ tptp.id_on_nat (@ tptp.labele1810595089_a_nat G_1)))) (let ((_let_2 (@ tptp.graph_2130075512at_nat G_1))) (=> (@ (@ _let_2 G_2) _let_1) (=> (@ (@ (@ tptp.graph_2130075512at_nat G_2) G_3) (@ tptp.id_on_nat (@ tptp.labele1810595089_a_nat G_2))) (@ (@ _let_2 G_3) _let_1)))))))
% 0.27/0.74 (assert (forall ((G_1 tptp.labeled_graph_b_nat) (G_2 tptp.labeled_graph_b_nat) (G_3 tptp.labeled_graph_b_nat)) (let ((_let_1 (@ tptp.id_on_nat (@ tptp.labele460410879_b_nat G_1)))) (let ((_let_2 (@ tptp.graph_529870330at_nat G_1))) (=> (@ (@ _let_2 G_2) _let_1) (=> (@ (@ (@ tptp.graph_529870330at_nat G_2) G_3) (@ tptp.id_on_nat (@ tptp.labele460410879_b_nat G_2))) (@ (@ _let_2 G_3) _let_1)))))))
% 0.27/0.74 (assert (forall ((A tptp.produc1478835367term_b) (A4 tptp.set_Pr1163220871term_b)) (=> (@ (@ tptp.member516522448term_b A) A4) (@ (@ tptp.member1449757456term_b (@ (@ tptp.produc859843415term_b A) A)) (@ tptp.id_on_1664915780term_b A4)))))
% 0.27/0.74 (assert (forall ((A tptp.produc1235635379_b_nat) (A4 tptp.set_Pr551076371_b_nat)) (=> (@ (@ tptp.member963855452_b_nat A) A4) (@ (@ tptp.member889223696_b_nat (@ (@ tptp.produc1754969175_b_nat A) A)) (@ tptp.id_on_138931664_b_nat A4)))))
% 0.27/0.74 (assert (forall ((A tptp.produc398057191_a_nat) (A4 tptp.set_Pr924198087_a_nat)) (=> (@ (@ tptp.member584645392_a_nat A) A4) (@ (@ tptp.member829905680_a_nat (@ (@ tptp.produc170611543_a_nat A) A)) (@ tptp.id_on_1395957380_a_nat A4)))))
% 0.27/0.74 (assert (forall ((A tptp.product_prod_nat_nat) (A4 tptp.set_Pr1986765409at_nat)) (=> (@ (@ tptp.member701585322at_nat A) A4) (@ (@ tptp.member2027625872at_nat (@ (@ tptp.produc1168807639at_nat A) A)) (@ tptp.id_on_2144791838at_nat A4)))))
% 0.27/0.74 (assert (forall ((A tptp.labele935650037_a_nat) (A4 tptp.set_la1083530965_a_nat)) (=> (@ (@ tptp.member964390942_a_nat A) A4) (@ (@ tptp.member832397200_a_nat (@ (@ tptp.produc1676969687_a_nat A) A)) (@ tptp.id_on_689842066_a_nat A4)))))
% 0.27/0.74 (assert (forall ((A tptp.produc1871334759_a_nat) (A4 tptp.set_Pr1987088711_a_nat)) (=> (@ (@ tptp.member832397200_a_nat A) A4) (@ (@ tptp.member584645392_a_nat (@ (@ tptp.produc1677124439_a_nat A) A)) (@ tptp.id_on_1651096324_a_nat A4)))))
% 0.27/0.74 (assert (forall ((A tptp.nat) (A4 tptp.set_nat)) (=> (@ (@ tptp.member_nat A) A4) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) A)) (@ tptp.id_on_nat A4)))))
% 0.27/0.74 (assert (forall ((A tptp.labeled_graph_b_nat) (A4 tptp.set_la1976028319_b_nat)) (=> (@ (@ tptp.member1483953152_b_nat A) A4) (@ (@ tptp.member963855452_b_nat (@ (@ tptp.produc951298923_b_nat A) A)) (@ tptp.id_on_583275916_b_nat A4)))))
% 0.27/0.74 (assert (forall ((A tptp.allegorical_term_b) (A4 tptp.set_al1193902458term_b)) (=> (@ (@ tptp.member93680451term_b A) A4) (@ (@ tptp.member516522448term_b (@ (@ tptp.produc1990145943term_b A) A)) (@ tptp.id_on_1536886967term_b A4)))))
% 0.27/0.74 (assert (= tptp.set_of195930477at_nat (lambda ((Rs tptp.set_Pr665622551at_nat)) (forall ((X5 tptp.produc1391440311at_nat)) (let ((_let_1 (@ tptp.produc1564126365at_nat X5))) (let ((_let_2 (@ tptp.produc1995789403at_nat X5))) (=> (@ (@ tptp.member1129678944at_nat X5) Rs) (and (@ (@ (@ tptp.graph_2111906684at_nat _let_2) _let_1) (@ tptp.id_on_nat (@ tptp.labele560327297at_nat _let_2))) (= _let_1 (@ tptp.restri321299017at_nat _let_1)) (@ tptp.finite_finite_nat (@ tptp.labele560327297at_nat _let_1)) (@ tptp.finite48957584at_nat (@ tptp.labele2032268018at_nat _let_1))))))))))
% 0.27/0.74 (assert (= tptp.set_of1384085797_a_nat (lambda ((Rs tptp.set_Pr1987088711_a_nat)) (forall ((X5 tptp.produc1871334759_a_nat)) (let ((_let_1 (@ tptp.produc880161797_a_nat X5))) (let ((_let_2 (@ tptp.produc719117507_a_nat X5))) (=> (@ (@ tptp.member832397200_a_nat X5) Rs) (and (@ (@ (@ tptp.graph_2130075512at_nat _let_2) _let_1) (@ tptp.id_on_nat (@ tptp.labele1810595089_a_nat _let_2))) (= _let_1 (@ tptp.restri572569417_a_nat _let_1)) (@ tptp.finite_finite_nat (@ tptp.labele1810595089_a_nat _let_1)) (@ tptp.finite1242387294at_nat (@ tptp.labele195203296_a_nat _let_1))))))))))
% 0.27/0.74 (assert (= tptp.set_of41538795_b_nat (lambda ((Rs tptp.set_Pr551076371_b_nat)) (forall ((X5 tptp.produc1235635379_b_nat)) (let ((_let_1 (@ tptp.produc194497945_b_nat X5))) (let ((_let_2 (@ tptp.produc1542243159_b_nat X5))) (=> (@ (@ tptp.member963855452_b_nat X5) Rs) (and (@ (@ (@ tptp.graph_529870330at_nat _let_2) _let_1) (@ tptp.id_on_nat (@ tptp.labele460410879_b_nat _let_2))) (= _let_1 (@ tptp.restrict_b_nat _let_1)) (@ tptp.finite_finite_nat (@ tptp.labele460410879_b_nat _let_1)) (@ tptp.finite1987068434at_nat (@ tptp.labeled_edges_b_nat _let_1))))))))))
% 0.27/0.74 (assert (forall ((A tptp.produc1478835367term_b) (P (-> tptp.produc1478835367term_b Bool))) (= (@ (@ tptp.member516522448term_b A) (@ tptp.collec135640594term_b P)) (@ P A))))
% 0.27/0.74 (assert (forall ((A tptp.produc1235635379_b_nat) (P (-> tptp.produc1235635379_b_nat Bool))) (= (@ (@ tptp.member963855452_b_nat A) (@ tptp.collec1615000990_b_nat P)) (@ P A))))
% 0.27/0.74 (assert (forall ((A tptp.produc398057191_a_nat) (P (-> tptp.produc398057191_a_nat Bool))) (= (@ (@ tptp.member584645392_a_nat A) (@ tptp.collec1701899602_a_nat P)) (@ P A))))
% 0.27/0.74 (assert (forall ((A tptp.product_prod_nat_nat) (P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.member701585322at_nat A) (@ tptp.collec7649004at_nat P)) (@ P A))))
% 0.27/0.74 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))))
% 0.27/0.74 (assert (forall ((A tptp.produc1871334759_a_nat) (P (-> tptp.produc1871334759_a_nat Bool))) (= (@ (@ tptp.member832397200_a_nat A) (@ tptp.collec357096914_a_nat P)) (@ P A))))
% 0.27/0.74 (assert (forall ((A4 tptp.set_Pr1163220871term_b)) (= (@ tptp.collec135640594term_b (lambda ((X5 tptp.produc1478835367term_b)) (@ (@ tptp.member516522448term_b X5) A4))) A4)))
% 0.27/0.74 (assert (forall ((A4 tptp.set_Pr551076371_b_nat)) (= (@ tptp.collec1615000990_b_nat (lambda ((X5 tptp.produc1235635379_b_nat)) (@ (@ tptp.member963855452_b_nat X5) A4))) A4)))
% 0.27/0.74 (assert (forall ((A4 tptp.set_Pr924198087_a_nat)) (= (@ tptp.collec1701899602_a_nat (lambda ((X5 tptp.produc398057191_a_nat)) (@ (@ tptp.member584645392_a_nat X5) A4))) A4)))
% 0.27/0.74 (assert (forall ((A4 tptp.set_Pr1986765409at_nat)) (= (@ tptp.collec7649004at_nat (lambda ((X5 tptp.product_prod_nat_nat)) (@ (@ tptp.member701585322at_nat X5) A4))) A4)))
% 0.27/0.74 (assert (forall ((A4 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X5 tptp.nat)) (@ (@ tptp.member_nat X5) A4))) A4)))
% 0.27/0.74 (assert (forall ((A4 tptp.set_Pr1987088711_a_nat)) (= (@ tptp.collec357096914_a_nat (lambda ((X5 tptp.produc1871334759_a_nat)) (@ (@ tptp.member832397200_a_nat X5) A4))) A4)))
% 0.27/0.74 (assert (forall ((P (-> tptp.produc1871334759_a_nat Bool)) (Q2 (-> tptp.produc1871334759_a_nat Bool))) (=> (forall ((X4 tptp.produc1871334759_a_nat)) (= (@ P X4) (@ Q2 X4))) (= (@ tptp.collec357096914_a_nat P) (@ tptp.collec357096914_a_nat Q2)))))
% 0.27/0.74 (assert (forall ((X tptp.allego510293162tant_a)) (@ tptp.inv_translation (@ tptp.labele1810595089_a_nat (@ tptp.transl1275713022tant_a X)))))
% 0.27/0.74 (assert (forall ((X tptp.allegorical_term_b)) (@ tptp.inv_translation (@ tptp.labele460410879_b_nat (@ tptp.translation_b X)))))
% 0.27/0.74 (assert (forall ((P (-> tptp.allegorical_term_b tptp.allegorical_term_b Bool)) (X3 tptp.allegorical_term_b) (Y3 tptp.allegorical_term_b) (A tptp.produc1478835367term_b)) (=> (@ (@ P X3) Y3) (=> (= A (@ (@ tptp.produc1990145943term_b X3) Y3)) (@ (@ P (@ tptp.produc854192515term_b A)) (@ tptp.produc1223098053term_b A))))))
% 0.27/0.74 (assert (forall ((P (-> tptp.labeled_graph_b_nat tptp.labeled_graph_b_nat Bool)) (X3 tptp.labeled_graph_b_nat) (Y3 tptp.labeled_graph_b_nat) (A tptp.produc1235635379_b_nat)) (=> (@ (@ P X3) Y3) (=> (= A (@ (@ tptp.produc951298923_b_nat X3) Y3)) (@ (@ P (@ tptp.produc1542243159_b_nat A)) (@ tptp.produc194497945_b_nat A))))))
% 0.27/0.74 (assert (forall ((P (-> tptp.allegorical_term_b Bool)) (P2 tptp.allegorical_term_b) (Q2 (-> tptp.allegorical_term_b Bool)) (Q tptp.allegorical_term_b)) (let ((_let_1 (@ (@ tptp.produc1990145943term_b P2) Q))) (=> (@ P P2) (=> (@ Q2 Q) (and (@ P (@ tptp.produc854192515term_b _let_1)) (@ Q2 (@ tptp.produc1223098053term_b _let_1))))))))
% 0.27/0.74 (assert (forall ((P (-> tptp.labeled_graph_b_nat Bool)) (P2 tptp.labeled_graph_b_nat) (Q2 (-> tptp.labeled_graph_b_nat Bool)) (Q tptp.labeled_graph_b_nat)) (let ((_let_1 (@ (@ tptp.produc951298923_b_nat P2) Q))) (=> (@ P P2) (=> (@ Q2 Q) (and (@ P (@ tptp.produc1542243159_b_nat _let_1)) (@ Q2 (@ tptp.produc194497945_b_nat _let_1))))))))
% 0.27/0.74 (assert (forall ((P (-> tptp.allegorical_term_b tptp.allegorical_term_b Bool)) (Y3 tptp.allegorical_term_b) (X3 tptp.allegorical_term_b)) (let ((_let_1 (@ (@ tptp.produc1990145943term_b X3) Y3))) (=> (@ (@ P Y3) X3) (@ (@ P (@ tptp.produc1223098053term_b _let_1)) (@ tptp.produc854192515term_b _let_1))))))
% 0.27/0.74 (assert (forall ((P (-> tptp.labeled_graph_b_nat tptp.labeled_graph_b_nat Bool)) (Y3 tptp.labeled_graph_b_nat) (X3 tptp.labeled_graph_b_nat)) (let ((_let_1 (@ (@ tptp.produc951298923_b_nat X3) Y3))) (=> (@ (@ P Y3) X3) (@ (@ P (@ tptp.produc194497945_b_nat _let_1)) (@ tptp.produc1542243159_b_nat _let_1))))))
% 0.27/0.74 (assert (forall ((X11 tptp.allegorical_term_b) (X12 tptp.allegorical_term_b) (Y11 tptp.allegorical_term_b) (Y12 tptp.allegorical_term_b)) (= (= (@ (@ tptp.allegorical_A_Int_b X11) X12) (@ (@ tptp.allegorical_A_Int_b Y11) Y12)) (and (= X11 Y11) (= X12 Y12)))))
% 0.27/0.74 (assert (forall ((R tptp.produc1235635379_b_nat) (G tptp.labeled_graph_b_nat)) (=> (forall ((F tptp.labeled_graph_b_nat) (F2 tptp.set_Pr1986765409at_nat)) (let ((_let_1 (@ tptp.produc951298923_b_nat F))) (let ((_let_2 (@ tptp.graph_529870330at_nat F))) (let ((_let_3 (@ tptp.produc1542243159_b_nat R))) (let ((_let_4 (@ tptp.labele460410879_b_nat F))) (=> (and (= F (@ tptp.restrict_b_nat F)) (@ tptp.finite_finite_nat _let_4) (@ tptp.finite1987068434at_nat (@ tptp.labeled_edges_b_nat F))) (=> (@ (@ _let_2 _let_3) (@ tptp.id_on_nat _let_4)) (=> (@ (@ (@ tptp.extensible_b_nat_nat (@ _let_1 _let_3)) G) F2) (=> (@ (@ _let_2 G) F2) (@ (@ (@ tptp.extensible_b_nat_nat (@ _let_1 (@ tptp.produc194497945_b_nat R))) G) F2)))))))))) (@ (@ tptp.fin_ma971967913at_nat R) G))))
% 0.27/0.74 (assert (forall ((Rs2 tptp.set_Pr1987088711_a_nat) (R tptp.produc1871334759_a_nat)) (let ((_let_1 (@ tptp.produc719117507_a_nat R))) (=> (@ tptp.set_of1384085797_a_nat Rs2) (=> (@ (@ tptp.member832397200_a_nat R) Rs2) (and (= _let_1 (@ tptp.restri572569417_a_nat _let_1)) (@ tptp.finite_finite_nat (@ tptp.labele1810595089_a_nat _let_1)) (@ tptp.finite1242387294at_nat (@ tptp.labele195203296_a_nat _let_1))))))))
% 0.27/0.74 (assert (forall ((Rs2 tptp.set_Pr551076371_b_nat) (R tptp.produc1235635379_b_nat)) (let ((_let_1 (@ tptp.produc1542243159_b_nat R))) (=> (@ tptp.set_of41538795_b_nat Rs2) (=> (@ (@ tptp.member963855452_b_nat R) Rs2) (and (= _let_1 (@ tptp.restrict_b_nat _let_1)) (@ tptp.finite_finite_nat (@ tptp.labele460410879_b_nat _let_1)) (@ tptp.finite1987068434at_nat (@ tptp.labeled_edges_b_nat _let_1))))))))
% 0.27/0.74 (assert (forall ((Rs2 tptp.set_Pr1987088711_a_nat) (R tptp.produc1871334759_a_nat)) (let ((_let_1 (@ tptp.produc880161797_a_nat R))) (=> (@ tptp.set_of1384085797_a_nat Rs2) (=> (@ (@ tptp.member832397200_a_nat R) Rs2) (and (= _let_1 (@ tptp.restri572569417_a_nat _let_1)) (@ tptp.finite_finite_nat (@ tptp.labele1810595089_a_nat _let_1)) (@ tptp.finite1242387294at_nat (@ tptp.labele195203296_a_nat _let_1))))))))
% 0.27/0.74 (assert (forall ((Rs2 tptp.set_Pr551076371_b_nat) (R tptp.produc1235635379_b_nat)) (let ((_let_1 (@ tptp.produc194497945_b_nat R))) (=> (@ tptp.set_of41538795_b_nat Rs2) (=> (@ (@ tptp.member963855452_b_nat R) Rs2) (and (= _let_1 (@ tptp.restrict_b_nat _let_1)) (@ tptp.finite_finite_nat (@ tptp.labele460410879_b_nat _let_1)) (@ tptp.finite1987068434at_nat (@ tptp.labeled_edges_b_nat _let_1))))))))
% 0.27/0.74 (assert (forall ((R tptp.labeled_graph_b_nat) (G tptp.labeled_graph_b_nat) (F3 tptp.set_Pr1986765409at_nat)) (=> (@ (@ (@ tptp.graph_529870330at_nat R) G) F3) (@ (@ (@ tptp.extensible_b_nat_nat (@ (@ tptp.produc951298923_b_nat R) R)) G) F3))))
% 0.27/0.74 (assert (forall ((Rs2 tptp.set_Pr1987088711_a_nat) (R tptp.produc1871334759_a_nat)) (let ((_let_1 (@ tptp.produc719117507_a_nat R))) (=> (@ tptp.set_of1384085797_a_nat Rs2) (=> (@ (@ tptp.member832397200_a_nat R) Rs2) (@ (@ (@ tptp.graph_2130075512at_nat _let_1) (@ tptp.produc880161797_a_nat R)) (@ tptp.id_on_nat (@ tptp.labele1810595089_a_nat _let_1))))))))
% 0.27/0.74 (assert (forall ((Rs2 tptp.set_Pr551076371_b_nat) (R tptp.produc1235635379_b_nat)) (let ((_let_1 (@ tptp.produc1542243159_b_nat R))) (=> (@ tptp.set_of41538795_b_nat Rs2) (=> (@ (@ tptp.member963855452_b_nat R) Rs2) (@ (@ (@ tptp.graph_529870330at_nat _let_1) (@ tptp.produc194497945_b_nat R)) (@ tptp.id_on_nat (@ tptp.labele460410879_b_nat _let_1))))))))
% 0.27/0.74 (assert (forall ((P (-> tptp.allegorical_term_b tptp.allegorical_term_b Bool)) (P2 tptp.produc1478835367term_b)) (=> (@ (@ P (@ tptp.produc1223098053term_b P2)) (@ tptp.produc854192515term_b P2)) (not (forall ((X4 tptp.allegorical_term_b) (Y4 tptp.allegorical_term_b)) (not (@ (@ P Y4) X4)))))))
% 0.27/0.74 (assert (forall ((P (-> tptp.labeled_graph_b_nat tptp.labeled_graph_b_nat Bool)) (P2 tptp.produc1235635379_b_nat)) (=> (@ (@ P (@ tptp.produc194497945_b_nat P2)) (@ tptp.produc1542243159_b_nat P2)) (not (forall ((X4 tptp.labeled_graph_b_nat) (Y4 tptp.labeled_graph_b_nat)) (not (@ (@ P Y4) X4)))))))
% 0.27/0.74 (assert (forall ((C2 tptp.produc398057191_a_nat) (A4 tptp.set_Pr1987088711_a_nat)) (=> (@ (@ tptp.member584645392_a_nat C2) (@ tptp.id_on_1651096324_a_nat A4)) (not (forall ((X4 tptp.produc1871334759_a_nat)) (=> (@ (@ tptp.member832397200_a_nat X4) A4) (not (= C2 (@ (@ tptp.produc1677124439_a_nat X4) X4)))))))))
% 0.27/0.74 (assert (forall ((C2 tptp.produc1871334759_a_nat) (A4 tptp.set_la1083530965_a_nat)) (=> (@ (@ tptp.member832397200_a_nat C2) (@ tptp.id_on_689842066_a_nat A4)) (not (forall ((X4 tptp.labele935650037_a_nat)) (=> (@ (@ tptp.member964390942_a_nat X4) A4) (not (= C2 (@ (@ tptp.produc1676969687_a_nat X4) X4)))))))))
% 0.27/0.74 (assert (forall ((C2 tptp.product_prod_nat_nat) (A4 tptp.set_nat)) (=> (@ (@ tptp.member701585322at_nat C2) (@ tptp.id_on_nat A4)) (not (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (not (= C2 (@ (@ tptp.product_Pair_nat_nat X4) X4)))))))))
% 0.27/0.74 (assert (forall ((C2 tptp.produc1235635379_b_nat) (A4 tptp.set_la1976028319_b_nat)) (=> (@ (@ tptp.member963855452_b_nat C2) (@ tptp.id_on_583275916_b_nat A4)) (not (forall ((X4 tptp.labeled_graph_b_nat)) (=> (@ (@ tptp.member1483953152_b_nat X4) A4) (not (= C2 (@ (@ tptp.produc951298923_b_nat X4) X4)))))))))
% 0.27/0.74 (assert (forall ((C2 tptp.produc1478835367term_b) (A4 tptp.set_al1193902458term_b)) (=> (@ (@ tptp.member516522448term_b C2) (@ tptp.id_on_1536886967term_b A4)) (not (forall ((X4 tptp.allegorical_term_b)) (=> (@ (@ tptp.member93680451term_b X4) A4) (not (= C2 (@ (@ tptp.produc1990145943term_b X4) X4)))))))))
% 0.27/0.74 (assert (forall ((A tptp.labele935650037_a_nat) (B tptp.labele935650037_a_nat) (A4 tptp.set_la1083530965_a_nat)) (=> (= A B) (=> (@ (@ tptp.member964390942_a_nat A) A4) (@ (@ tptp.member832397200_a_nat (@ (@ tptp.produc1676969687_a_nat A) B)) (@ tptp.id_on_689842066_a_nat A4))))))
% 0.27/0.74 (assert (forall ((A tptp.produc1871334759_a_nat) (B tptp.produc1871334759_a_nat) (A4 tptp.set_Pr1987088711_a_nat)) (=> (= A B) (=> (@ (@ tptp.member832397200_a_nat A) A4) (@ (@ tptp.member584645392_a_nat (@ (@ tptp.produc1677124439_a_nat A) B)) (@ tptp.id_on_1651096324_a_nat A4))))))
% 0.27/0.74 (assert (forall ((A tptp.nat) (B tptp.nat) (A4 tptp.set_nat)) (=> (= A B) (=> (@ (@ tptp.member_nat A) A4) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) (@ tptp.id_on_nat A4))))))
% 0.27/0.74 (assert (forall ((A tptp.labeled_graph_b_nat) (B tptp.labeled_graph_b_nat) (A4 tptp.set_la1976028319_b_nat)) (=> (= A B) (=> (@ (@ tptp.member1483953152_b_nat A) A4) (@ (@ tptp.member963855452_b_nat (@ (@ tptp.produc951298923_b_nat A) B)) (@ tptp.id_on_583275916_b_nat A4))))))
% 0.27/0.74 (assert (forall ((A tptp.allegorical_term_b) (B tptp.allegorical_term_b) (A4 tptp.set_al1193902458term_b)) (=> (= A B) (=> (@ (@ tptp.member93680451term_b A) A4) (@ (@ tptp.member516522448term_b (@ (@ tptp.produc1990145943term_b A) B)) (@ tptp.id_on_1536886967term_b A4))))))
% 0.27/0.74 (assert (forall ((X3 tptp.produc1871334759_a_nat) (Y3 tptp.produc1871334759_a_nat) (A4 tptp.set_Pr1987088711_a_nat)) (= (@ (@ tptp.member584645392_a_nat (@ (@ tptp.produc1677124439_a_nat X3) Y3)) (@ tptp.id_on_1651096324_a_nat A4)) (and (= X3 Y3) (@ (@ tptp.member832397200_a_nat X3) A4)))))
% 0.27/0.74 (assert (forall ((X3 tptp.labele935650037_a_nat) (Y3 tptp.labele935650037_a_nat) (A4 tptp.set_la1083530965_a_nat)) (= (@ (@ tptp.member832397200_a_nat (@ (@ tptp.produc1676969687_a_nat X3) Y3)) (@ tptp.id_on_689842066_a_nat A4)) (and (= X3 Y3) (@ (@ tptp.member964390942_a_nat X3) A4)))))
% 0.27/0.74 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat) (A4 tptp.set_nat)) (= (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y3)) (@ tptp.id_on_nat A4)) (and (= X3 Y3) (@ (@ tptp.member_nat X3) A4)))))
% 0.27/0.74 (assert (forall ((X3 tptp.labeled_graph_b_nat) (Y3 tptp.labeled_graph_b_nat) (A4 tptp.set_la1976028319_b_nat)) (= (@ (@ tptp.member963855452_b_nat (@ (@ tptp.produc951298923_b_nat X3) Y3)) (@ tptp.id_on_583275916_b_nat A4)) (and (= X3 Y3) (@ (@ tptp.member1483953152_b_nat X3) A4)))))
% 0.27/0.74 (assert (forall ((X3 tptp.allegorical_term_b) (Y3 tptp.allegorical_term_b) (A4 tptp.set_al1193902458term_b)) (= (@ (@ tptp.member516522448term_b (@ (@ tptp.produc1990145943term_b X3) Y3)) (@ tptp.id_on_1536886967term_b A4)) (and (= X3 Y3) (@ (@ tptp.member93680451term_b X3) A4)))))
% 0.27/0.74 (assert (= tptp.fin_ma971967913at_nat (lambda ((R2 tptp.produc1235635379_b_nat) (G2 tptp.labeled_graph_b_nat)) (forall ((F4 tptp.labeled_graph_b_nat) (F5 tptp.set_Pr1986765409at_nat)) (let ((_let_1 (@ tptp.produc951298923_b_nat F4))) (let ((_let_2 (@ tptp.graph_529870330at_nat F4))) (let ((_let_3 (@ tptp.produc1542243159_b_nat R2))) (let ((_let_4 (@ tptp.labele460410879_b_nat F4))) (=> (and (= F4 (@ tptp.restrict_b_nat F4)) (@ tptp.finite_finite_nat _let_4) (@ tptp.finite1987068434at_nat (@ tptp.labeled_edges_b_nat F4))) (=> (@ (@ _let_2 _let_3) (@ tptp.id_on_nat _let_4)) (=> (@ (@ (@ tptp.extensible_b_nat_nat (@ _let_1 _let_3)) G2) F5) (=> (@ (@ _let_2 G2) F5) (@ (@ (@ tptp.extensible_b_nat_nat (@ _let_1 (@ tptp.produc194497945_b_nat R2))) G2) F5)))))))))))))
% 0.27/0.74 (assert (forall ((Rs2 tptp.set_Pr551076371_b_nat) (S2 (-> tptp.nat tptp.labeled_graph_b_nat)) (R tptp.produc1235635379_b_nat) (I tptp.nat) (F3 tptp.set_Pr1986765409at_nat)) (=> (@ (@ tptp.fair_chain_b_nat_nat Rs2) S2) (=> (@ (@ tptp.member963855452_b_nat R) Rs2) (=> (@ (@ (@ tptp.graph_529870330at_nat (@ tptp.produc1542243159_b_nat R)) (@ S2 I)) F3) (exists ((J tptp.nat)) (@ (@ (@ tptp.extensible_b_nat_nat R) (@ S2 J)) F3)))))))
% 0.27/0.74 (assert (forall ((X3 tptp.produc1871334759_a_nat) (L tptp.set_St761939237tant_a)) (let ((_let_1 (@ tptp.produc880161797_a_nat X3))) (let ((_let_2 (@ tptp.produc719117507_a_nat X3))) (=> (@ (@ tptp.member832397200_a_nat X3) (@ tptp.standa1568205540ules_a L)) (and (@ (@ (@ tptp.graph_2130075512at_nat _let_2) _let_1) (@ tptp.id_on_nat (@ tptp.labele1810595089_a_nat _let_2))) (= _let_1 (@ tptp.restri572569417_a_nat _let_1)) (@ tptp.finite_finite_nat (@ tptp.labele1810595089_a_nat _let_1)) (@ tptp.finite1242387294at_nat (@ tptp.labele195203296_a_nat _let_1))))))))
% 0.27/0.74 (assert (forall ((A4 tptp.labeled_graph_b_nat) (G tptp.labeled_graph_b_nat) (B4 tptp.labeled_graph_b_nat)) (=> (forall ((F2 tptp.set_Pr1986765409at_nat)) (=> (@ (@ (@ tptp.graph_529870330at_nat A4) G) F2) (@ (@ (@ tptp.extensible_b_nat_nat (@ (@ tptp.produc951298923_b_nat A4) B4)) G) F2))) (@ (@ tptp.maintained_b_nat_nat (@ (@ tptp.produc951298923_b_nat A4) B4)) G))))
% 0.27/0.74 (assert (forall ((X3 tptp.produc1478835367term_b) (Y3 tptp.allegorical_term_b) (Z2 tptp.allegorical_term_b)) (=> (= X3 (@ (@ tptp.produc1990145943term_b Y3) Z2)) (= (@ tptp.produc1223098053term_b X3) Z2))))
% 0.27/0.74 (assert (forall ((X3 tptp.produc1235635379_b_nat) (Y3 tptp.labeled_graph_b_nat) (Z2 tptp.labeled_graph_b_nat)) (=> (= X3 (@ (@ tptp.produc951298923_b_nat Y3) Z2)) (= (@ tptp.produc194497945_b_nat X3) Z2))))
% 0.27/0.74 (assert (forall ((Rs2 tptp.set_Pr551076371_b_nat) (G tptp.labeled_graph_b_nat)) (=> (forall ((R3 tptp.produc1235635379_b_nat)) (=> (@ (@ tptp.member963855452_b_nat R3) Rs2) (@ (@ tptp.maintained_b_nat_nat R3) G))) (=> (forall ((R3 tptp.produc1235635379_b_nat)) (let ((_let_1 (@ tptp.produc1542243159_b_nat R3))) (=> (@ (@ tptp.member963855452_b_nat R3) Rs2) (@ (@ (@ tptp.graph_529870330at_nat _let_1) (@ tptp.produc194497945_b_nat R3)) (@ tptp.id_on_nat (@ tptp.labele460410879_b_nat _let_1)))))) (=> (= G (@ tptp.restrict_b_nat G)) (@ (@ tptp.conseq1730780375at_nat Rs2) G))))))
% 0.27/0.74 (assert (= tptp.conseq1730780375at_nat (lambda ((Rs tptp.set_Pr551076371_b_nat) (G2 tptp.labeled_graph_b_nat)) (and (= G2 (@ tptp.restrict_b_nat G2)) (forall ((X5 tptp.produc1235635379_b_nat)) (let ((_let_1 (@ tptp.produc1542243159_b_nat X5))) (=> (@ (@ tptp.member963855452_b_nat X5) Rs) (and (@ (@ (@ tptp.graph_529870330at_nat _let_1) (@ tptp.produc194497945_b_nat X5)) (@ tptp.id_on_nat (@ tptp.labele460410879_b_nat _let_1))) (@ (@ tptp.maintained_b_nat_nat X5) G2)))))))))
% 0.27/0.74 (assert (= tptp.maintained_b_nat_nat (lambda ((R2 tptp.produc1235635379_b_nat) (G2 tptp.labeled_graph_b_nat)) (forall ((F5 tptp.set_Pr1986765409at_nat)) (=> (@ (@ (@ tptp.graph_529870330at_nat (@ tptp.produc1542243159_b_nat R2)) G2) F5) (@ (@ (@ tptp.extensible_b_nat_nat R2) G2) F5))))))
% 0.27/0.74 (assert (forall ((A4 tptp.labeled_graph_b_nat) (B4 tptp.labeled_graph_b_nat) (G tptp.labeled_graph_b_nat) (F3 tptp.set_Pr1986765409at_nat)) (let ((_let_1 (@ (@ tptp.produc951298923_b_nat A4) B4))) (=> (@ (@ tptp.maintained_b_nat_nat _let_1) G) (=> (@ (@ (@ tptp.graph_529870330at_nat A4) G) F3) (@ (@ (@ tptp.extensible_b_nat_nat _let_1) G) F3))))))
% 0.27/0.74 (assert (forall ((X3 tptp.produc1235635379_b_nat) (Y3 tptp.labeled_graph_b_nat) (Z2 tptp.labeled_graph_b_nat)) (=> (= X3 (@ (@ tptp.produc951298923_b_nat Y3) Z2)) (= (@ tptp.produc1542243159_b_nat X3) Y3))))
% 0.27/0.74 (assert (forall ((X3 tptp.produc1478835367term_b) (Y3 tptp.allegorical_term_b) (Z2 tptp.allegorical_term_b)) (=> (= X3 (@ (@ tptp.produc1990145943term_b Y3) Z2)) (= (@ tptp.produc854192515term_b X3) Y3))))
% 0.27/0.74 (assert (forall ((S2 (-> tptp.nat tptp.labeled_graph_b_nat)) (Rs2 tptp.set_Pr551076371_b_nat)) (=> (@ tptp.chain_b_nat S2) (=> (forall ((R3 tptp.produc1235635379_b_nat) (F2 tptp.set_Pr1986765409at_nat) (I2 tptp.nat)) (=> (@ (@ tptp.member963855452_b_nat R3) Rs2) (=> (@ (@ (@ tptp.graph_529870330at_nat (@ tptp.produc1542243159_b_nat R3)) (@ S2 I2)) F2) (exists ((J2 tptp.nat)) (@ (@ (@ tptp.extensible_b_nat_nat R3) (@ S2 J2)) F2))))) (@ (@ tptp.fair_chain_b_nat_nat Rs2) S2)))))
% 0.27/0.74 (assert (forall ((G tptp.labeled_graph_b_nat) (E_L tptp.allegorical_term_b) (E_R tptp.allegorical_term_b)) (let ((_let_1 (@ (@ tptp.allegorical_A_Int_b E_L) E_R))) (let ((_let_2 (@ (@ tptp.produc1990145943term_b E_L) _let_1))) (let ((_let_3 (@ tptp.semantics_b_nat G))) (=> (= G (@ tptp.restrict_b_nat G)) (= (@ (@ tptp.maintained_b_nat_nat (@ (@ tptp.produc951298923_b_nat (@ tptp.translation_b E_L)) (@ tptp.translation_b _let_1))) G) (= (@ _let_3 (@ tptp.produc854192515term_b _let_2)) (@ _let_3 (@ tptp.produc1223098053term_b _let_2))))))))))
% 0.27/0.74 (assert (= tptp.fair_chain_b_nat_nat (lambda ((Rs tptp.set_Pr551076371_b_nat) (S3 (-> tptp.nat tptp.labeled_graph_b_nat))) (and (@ tptp.chain_b_nat S3) (forall ((R2 tptp.produc1235635379_b_nat) (F5 tptp.set_Pr1986765409at_nat) (I3 tptp.nat)) (=> (and (@ (@ tptp.member963855452_b_nat R2) Rs) (@ (@ (@ tptp.graph_529870330at_nat (@ tptp.produc1542243159_b_nat R2)) (@ S3 I3)) F5)) (exists ((J3 tptp.nat)) (@ (@ (@ tptp.extensible_b_nat_nat R2) (@ S3 J3)) F5))))))))
% 0.27/0.74 (assert (forall ((S2 (-> tptp.nat tptp.labeled_graph_b_nat))) (let ((_let_1 (@ tptp.chain_sup_b_nat S2))) (=> (@ tptp.chain_b_nat S2) (= _let_1 (@ tptp.restrict_b_nat _let_1))))))
% 0.27/0.74 (assert (forall ((S2 (-> tptp.nat tptp.labeled_graph_b_nat)) (J4 tptp.nat)) (let ((_let_1 (@ S2 J4))) (=> (@ tptp.chain_b_nat S2) (@ (@ (@ tptp.graph_529870330at_nat _let_1) (@ tptp.chain_sup_b_nat S2)) (@ tptp.id_on_nat (@ tptp.labele460410879_b_nat _let_1)))))))
% 0.27/0.74 (assert (forall ((S2 (-> tptp.nat tptp.labeled_graph_b_nat)) (I tptp.nat)) (let ((_let_1 (@ S2 I))) (=> (@ tptp.chain_b_nat S2) (= _let_1 (@ tptp.restrict_b_nat _let_1))))))
% 0.27/0.74 (assert (forall ((A4 tptp.labeled_graph_b_nat) (B4 tptp.labeled_graph_b_nat) (F3 tptp.set_Pr1986765409at_nat) (A tptp.nat) (B tptp.nat) (E tptp.allegorical_term_b) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat A))) (=> (@ (@ (@ tptp.graph_529870330at_nat A4) B4) F3) (=> (@ (@ tptp.member701585322at_nat (@ _let_1 B)) (@ (@ tptp.semantics_b_nat A4) E)) (=> (@ (@ tptp.member701585322at_nat (@ _let_1 A2)) F3) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat B) B2)) F3) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A2) B2)) (@ (@ tptp.semantics_b_nat B4) E)))))))))
% 0.27/0.74 (assert (forall ((A4 tptp.labeled_graph_b_nat) (A tptp.nat) (B tptp.nat) (E tptp.allegorical_term_b)) (=> (= A4 (@ tptp.restrict_b_nat A4)) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) (@ (@ tptp.semantics_b_nat A4) E)) (@ (@ tptp.member_nat B) (@ tptp.labele460410879_b_nat A4))))))
% 0.27/0.74 (assert (forall ((A4 tptp.labeled_graph_b_nat) (A tptp.nat) (B tptp.nat) (E tptp.allegorical_term_b)) (=> (= A4 (@ tptp.restrict_b_nat A4)) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) (@ (@ tptp.semantics_b_nat A4) E)) (@ (@ tptp.member_nat A) (@ tptp.labele460410879_b_nat A4))))))
% 0.27/0.74 (assert (forall ((A4 tptp.labeled_graph_b_nat) (B4 tptp.labeled_graph_b_nat) (A tptp.nat) (B tptp.nat) (E tptp.allegorical_term_b)) (let ((_let_1 (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) B)))) (=> (@ (@ (@ tptp.graph_529870330at_nat A4) B4) (@ tptp.id_on_nat (@ tptp.labele460410879_b_nat A4))) (=> (@ _let_1 (@ (@ tptp.semantics_b_nat A4) E)) (@ _let_1 (@ (@ tptp.semantics_b_nat B4) E)))))))
% 0.27/0.74 (assert (forall ((G tptp.labeled_graph_b_nat) (E_L tptp.allegorical_term_b) (E_R tptp.allegorical_term_b)) (let ((_let_1 (@ tptp.semantics_b_nat G))) (let ((_let_2 (@ (@ tptp.produc1990145943term_b E_L) (@ (@ tptp.allegorical_A_Int_b E_L) E_R)))) (=> (= G (@ tptp.restrict_b_nat G)) (= (@ (@ tptp.maintained_b_nat_nat (@ (@ tptp.produc951298923_b_nat (@ tptp.translation_b (@ tptp.produc854192515term_b _let_2))) (@ tptp.translation_b (@ tptp.produc1223098053term_b _let_2)))) G) (@ (@ tptp.ord_le841296385at_nat (@ _let_1 E_L)) (@ _let_1 E_R))))))))
% 0.27/0.74 (assert (forall ((S2 (-> tptp.nat tptp.labeled_graph_b_nat)) (E2 tptp.set_Pr9961929at_nat) (V tptp.set_nat) (F3 tptp.set_Pr1986765409at_nat)) (=> (@ tptp.chain_b_nat S2) (=> (@ tptp.finite1987068434at_nat E2) (=> (@ tptp.finite_finite_nat V) (=> (@ (@ (@ tptp.graph_529870330at_nat (@ (@ tptp.labeled_LG_b_nat E2) V)) (@ tptp.chain_sup_b_nat S2)) F3) (exists ((I2 tptp.nat)) (@ (@ (@ tptp.graph_529870330at_nat (@ (@ tptp.labeled_LG_b_nat E2) V)) (@ S2 I2)) F3))))))))
% 0.27/0.74 (assert (forall ((B tptp.allegorical_term_b) (P2 tptp.produc1478835367term_b)) (= (= B (@ tptp.produc1223098053term_b P2)) (exists ((A5 tptp.allegorical_term_b)) (= P2 (@ (@ tptp.produc1990145943term_b A5) B))))))
% 0.27/0.74 (assert (forall ((B tptp.labeled_graph_b_nat) (P2 tptp.produc1235635379_b_nat)) (= (= B (@ tptp.produc194497945_b_nat P2)) (exists ((A5 tptp.labeled_graph_b_nat)) (= P2 (@ (@ tptp.produc951298923_b_nat A5) B))))))
% 0.27/0.74 (assert (forall ((A tptp.labeled_graph_b_nat) (P2 tptp.produc1235635379_b_nat)) (= (= A (@ tptp.produc1542243159_b_nat P2)) (exists ((B5 tptp.labeled_graph_b_nat)) (= P2 (@ (@ tptp.produc951298923_b_nat A) B5))))))
% 0.27/0.74 (assert (forall ((A tptp.allegorical_term_b) (P2 tptp.produc1478835367term_b)) (= (= A (@ tptp.produc854192515term_b P2)) (exists ((B5 tptp.allegorical_term_b)) (= P2 (@ (@ tptp.produc1990145943term_b A) B5))))))
% 0.27/0.74 (assert (forall ((Labeled_graph tptp.labeled_graph_b_nat)) (= (@ (@ tptp.labeled_LG_b_nat (@ tptp.labeled_edges_b_nat Labeled_graph)) (@ tptp.labele460410879_b_nat Labeled_graph)) Labeled_graph)))
% 0.27/0.74 (assert (forall ((E_1 tptp.set_Pr9961929at_nat) (V2 tptp.set_nat) (G tptp.labeled_graph_b_nat) (F3 tptp.set_Pr1986765409at_nat) (E_2 tptp.set_Pr9961929at_nat)) (let ((_let_1 (@ (@ tptp.labeled_LG_b_nat E_2) V2))) (let ((_let_2 (@ (@ tptp.labeled_LG_b_nat E_1) V2))) (=> (@ (@ (@ tptp.graph_529870330at_nat _let_2) G) F3) (= (@ (@ (@ tptp.extensible_b_nat_nat (@ (@ tptp.produc951298923_b_nat _let_2) _let_1)) G) F3) (@ (@ (@ tptp.graph_529870330at_nat _let_1) G) F3)))))))
% 0.27/0.74 (assert (forall ((R4 tptp.set_Pr1987088711_a_nat) (S4 tptp.set_Pr1987088711_a_nat)) (=> (forall ((X4 tptp.labele935650037_a_nat) (Y4 tptp.labele935650037_a_nat)) (let ((_let_1 (@ tptp.member832397200_a_nat (@ (@ tptp.produc1676969687_a_nat X4) Y4)))) (=> (@ _let_1 R4) (@ _let_1 S4)))) (@ (@ tptp.ord_le1718765799_a_nat R4) S4))))
% 0.27/0.74 (assert (forall ((R4 tptp.set_Pr551076371_b_nat) (S4 tptp.set_Pr551076371_b_nat)) (=> (forall ((X4 tptp.labeled_graph_b_nat) (Y4 tptp.labeled_graph_b_nat)) (let ((_let_1 (@ tptp.member963855452_b_nat (@ (@ tptp.produc951298923_b_nat X4) Y4)))) (=> (@ _let_1 R4) (@ _let_1 S4)))) (@ (@ tptp.ord_le13035955_b_nat R4) S4))))
% 0.27/0.74 (assert (forall ((R4 tptp.set_Pr1163220871term_b) (S4 tptp.set_Pr1163220871term_b)) (=> (forall ((X4 tptp.allegorical_term_b) (Y4 tptp.allegorical_term_b)) (let ((_let_1 (@ tptp.member516522448term_b (@ (@ tptp.produc1990145943term_b X4) Y4)))) (=> (@ _let_1 R4) (@ _let_1 S4)))) (@ (@ tptp.ord_le138473255term_b R4) S4))))
% 0.27/0.74 (assert (forall ((A4 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.member_nat A) A4) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.ord_less_eq_nat A) X4) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_nat X4) Xa) (= X4 Xa))))))))))
% 0.27/0.74 (assert (forall ((A4 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.member_nat A) A4) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.ord_less_eq_nat X4) A) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_nat Xa) X4) (= X4 Xa))))))))))
% 0.27/0.74 (assert (forall ((A4 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B4) (=> (@ tptp.finite_finite_nat B4) (@ tptp.finite_finite_nat A4)))))
% 0.27/0.74 (assert (forall ((A4 tptp.set_Pr9961929at_nat) (B4 tptp.set_Pr9961929at_nat)) (=> (@ (@ tptp.ord_le910748009at_nat A4) B4) (=> (@ tptp.finite1987068434at_nat B4) (@ tptp.finite1987068434at_nat A4)))))
% 0.27/0.74 (assert (forall ((S2 tptp.set_nat) (T3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat S2) T3) (=> (not (@ tptp.finite_finite_nat S2)) (not (@ tptp.finite_finite_nat T3))))))
% 0.27/0.74 (assert (forall ((S2 tptp.set_Pr9961929at_nat) (T3 tptp.set_Pr9961929at_nat)) (=> (@ (@ tptp.ord_le910748009at_nat S2) T3) (=> (not (@ tptp.finite1987068434at_nat S2)) (not (@ tptp.finite1987068434at_nat T3))))))
% 0.27/0.74 (assert (forall ((B4 tptp.set_nat) (A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B4) (@ tptp.finite_finite_nat A4)))))
% 0.27/0.74 (assert (forall ((B4 tptp.set_Pr9961929at_nat) (A4 tptp.set_Pr9961929at_nat)) (=> (@ tptp.finite1987068434at_nat B4) (=> (@ (@ tptp.ord_le910748009at_nat A4) B4) (@ tptp.finite1987068434at_nat A4)))))
% 0.27/0.74 (assert (forall ((X1 tptp.set_Pr9961929at_nat) (X22 tptp.set_nat)) (= (@ tptp.labele460410879_b_nat (@ (@ tptp.labeled_LG_b_nat X1) X22)) X22)))
% 0.27/0.74 (assert (forall ((X1 tptp.set_Pr9961929at_nat) (X22 tptp.set_nat)) (= (@ tptp.labeled_edges_b_nat (@ (@ tptp.labeled_LG_b_nat X1) X22)) X1)))
% 0.27/0.74 (assert (forall ((G tptp.labeled_graph_b_nat)) (let ((_let_1 (@ tptp.restrict_b_nat G))) (=> (@ (@ tptp.ord_le910748009at_nat (@ tptp.labeled_edges_b_nat G)) (@ tptp.labeled_edges_b_nat _let_1)) (= G _let_1)))))
% 0.27/0.74 (assert (forall ((G_1 tptp.labeled_graph_b_nat) (G_2 tptp.labeled_graph_b_nat)) (let ((_let_1 (@ tptp.labele460410879_b_nat G_1))) (=> (= G_1 (@ tptp.restrict_b_nat G_1)) (=> (= G_2 (@ tptp.restrict_b_nat G_2)) (= (@ (@ (@ tptp.graph_529870330at_nat G_1) G_2) (@ tptp.id_on_nat _let_1)) (and (@ (@ tptp.ord_less_eq_set_nat _let_1) (@ tptp.labele460410879_b_nat G_2)) (@ (@ tptp.ord_le910748009at_nat (@ tptp.labeled_edges_b_nat G_1)) (@ tptp.labeled_edges_b_nat G_2)))))))))
% 0.27/0.74 (assert (forall ((Labeled_graph tptp.labeled_graph_b_nat)) (= Labeled_graph (@ (@ tptp.labeled_LG_b_nat (@ tptp.labeled_edges_b_nat Labeled_graph)) (@ tptp.labele460410879_b_nat Labeled_graph)))))
% 0.27/0.74 (assert (forall ((G_1 tptp.labeled_graph_b_nat) (G_2 tptp.labeled_graph_b_nat)) (let ((_let_1 (@ tptp.labele460410879_b_nat G_1))) (=> (@ (@ (@ tptp.graph_529870330at_nat G_1) G_2) (@ tptp.id_on_nat _let_1)) (@ (@ tptp.ord_less_eq_set_nat _let_1) (@ tptp.labele460410879_b_nat G_2))))))
% 0.27/0.74 (assert (forall ((A4 tptp.labeled_graph_b_nat) (B4 tptp.labeled_graph_b_nat) (G tptp.labeled_graph_b_nat) (F3 tptp.set_Pr1986765409at_nat)) (=> (@ (@ tptp.maintained_b_nat_nat (@ (@ tptp.produc951298923_b_nat A4) B4)) G) (=> (@ (@ (@ tptp.graph_529870330at_nat A4) G) F3) (not (forall ((G3 tptp.set_Pr1986765409at_nat)) (=> (@ (@ (@ tptp.graph_529870330at_nat B4) G) G3) (not (@ (@ tptp.ord_le841296385at_nat F3) G3)))))))))
% 0.27/0.74 (assert (forall ((G_1 tptp.labeled_graph_b_nat) (G_2 tptp.labeled_graph_b_nat)) (=> (@ (@ (@ tptp.graph_529870330at_nat G_1) G_2) (@ tptp.id_on_nat (@ tptp.labele460410879_b_nat G_1))) (@ (@ tptp.ord_le910748009at_nat (@ tptp.labeled_edges_b_nat (@ tptp.restrict_b_nat G_1))) (@ tptp.labeled_edges_b_nat G_2)))))
% 0.27/0.74 (assert (forall ((A4 tptp.set_Pr1987088711_a_nat) (B4 tptp.set_Pr1987088711_a_nat)) (=> (forall ((X4 tptp.produc1871334759_a_nat)) (let ((_let_1 (@ tptp.member832397200_a_nat X4))) (=> (@ _let_1 A4) (@ _let_1 B4)))) (@ (@ tptp.ord_le1718765799_a_nat A4) B4))))
% 0.27/0.74 (assert (forall ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X3) X3)))
% 0.27/0.74 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))))
% 0.27/0.74 (assert (= (lambda ((Y5 tptp.nat) (Z tptp.nat)) (= Y5 Z)) (lambda ((A5 tptp.nat) (B5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B5) A5) (@ (@ tptp.ord_less_eq_nat A5) B5)))))
% 0.27/0.74 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.27/0.74 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A) B)))))
% 0.27/0.74 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 0.27/0.74 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X3))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_nat Y3) Z2) (@ _let_1 Z2))))))
% 0.27/0.74 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A B)))))
% 0.27/0.74 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 0.27/0.74 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (@ (@ tptp.ord_less_eq_nat A) C2)))))
% 0.27/0.74 (assert (= (lambda ((Y5 tptp.nat) (Z tptp.nat)) (= Y5 Z)) (lambda ((A5 tptp.nat) (B5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A5) B5) (@ (@ tptp.ord_less_eq_nat B5) A5)))))
% 0.27/0.74 (assert (forall ((Y3 tptp.nat) (X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y3) X3) (= (@ (@ tptp.ord_less_eq_nat X3) Y3) (= X3 Y3)))))
% 0.27/0.74 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X3))) (let ((_let_2 (@ _let_1 Y3))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z2))) (let ((_let_4 (@ _let_3 X3))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y3))) (let ((_let_6 (@ _let_5 Z2))) (let ((_let_7 (@ _let_5 X3))) (let ((_let_8 (@ _let_3 Y3))) (let ((_let_9 (@ _let_1 Z2))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 0.27/0.74 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (@ _let_1 C2))))))
% 0.27/0.74 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X3) Y3)) (@ (@ tptp.ord_less_eq_nat Y3) X3))))
% 0.27/0.74 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= X3 Y3) (@ (@ tptp.ord_less_eq_nat X3) Y3))))
% 0.27/0.74 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_nat Y3) X3))))
% 0.27/0.74 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (=> (@ (@ tptp.ord_less_eq_nat Y3) X3) (= X3 Y3)))))
% 0.27/0.74 (assert (= (lambda ((Y5 tptp.nat) (Z tptp.nat)) (= Y5 Z)) (lambda ((X5 tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X5) Y6) (@ (@ tptp.ord_less_eq_nat Y6) X5)))))
% 0.27/0.74 (assert (forall ((A tptp.nat) (B tptp.nat) (F3 (-> tptp.nat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F3 B) C2) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y4) (@ (@ tptp.ord_less_eq_nat (@ F3 X4)) (@ F3 Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F3 A)) C2))))))
% 0.27/0.74 (assert (forall ((A tptp.nat) (F3 (-> tptp.nat tptp.nat)) (B tptp.nat) (C2 tptp.nat)) (=> (= A (@ F3 B)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y4) (@ (@ tptp.ord_less_eq_nat (@ F3 X4)) (@ F3 Y4)))) (@ (@ tptp.ord_less_eq_nat A) (@ F3 C2)))))))
% 0.27/0.74 (assert (forall ((A tptp.nat) (B tptp.nat) (F3 (-> tptp.nat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F3 B)) C2) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y4) (@ (@ tptp.ord_less_eq_nat (@ F3 X4)) (@ F3 Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F3 A)) C2))))))
% 0.27/0.74 (assert (forall ((A tptp.nat) (F3 (-> tptp.nat tptp.nat)) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F3 B)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y4) (@ (@ tptp.ord_less_eq_nat (@ F3 X4)) (@ F3 Y4)))) (@ _let_1 (@ F3 C2))))))))
% 0.27/0.74 (assert (= tptp.ord_le1718765799_a_nat (lambda ((A6 tptp.set_Pr1987088711_a_nat) (B6 tptp.set_Pr1987088711_a_nat)) (forall ((T2 tptp.produc1871334759_a_nat)) (let ((_let_1 (@ tptp.member832397200_a_nat T2))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 0.27/0.74 (assert (= tptp.ord_le1718765799_a_nat (lambda ((A6 tptp.set_Pr1987088711_a_nat) (B6 tptp.set_Pr1987088711_a_nat)) (forall ((X5 tptp.produc1871334759_a_nat)) (let ((_let_1 (@ tptp.member832397200_a_nat X5))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 0.27/0.74 (assert (forall ((A4 tptp.set_Pr1987088711_a_nat) (B4 tptp.set_Pr1987088711_a_nat) (C2 tptp.produc1871334759_a_nat)) (let ((_let_1 (@ tptp.member832397200_a_nat C2))) (=> (@ (@ tptp.ord_le1718765799_a_nat A4) B4) (=> (@ _let_1 A4) (@ _let_1 B4))))))
% 0.27/0.74 (assert (forall ((A4 tptp.set_Pr1987088711_a_nat) (B4 tptp.set_Pr1987088711_a_nat) (X3 tptp.produc1871334759_a_nat)) (let ((_let_1 (@ tptp.member832397200_a_nat X3))) (=> (@ (@ tptp.ord_le1718765799_a_nat A4) B4) (=> (@ _let_1 A4) (@ _let_1 B4))))))
% 0.27/0.74 (assert (forall ((S2 (-> tptp.nat tptp.labeled_graph_b_nat)) (I tptp.nat) (J4 tptp.nat)) (let ((_let_1 (@ S2 I))) (=> (@ tptp.chain_b_nat S2) (=> (@ (@ tptp.ord_less_eq_nat I) J4) (@ (@ (@ tptp.graph_529870330at_nat _let_1) (@ S2 J4)) (@ tptp.id_on_nat (@ tptp.labele460410879_b_nat _let_1))))))))
% 0.27/0.74 (assert (= tptp.chain_b_nat (lambda ((S3 (-> tptp.nat tptp.labeled_graph_b_nat))) (forall ((I3 tptp.nat) (J3 tptp.nat)) (let ((_let_1 (@ S3 I3))) (=> (@ (@ tptp.ord_less_eq_nat I3) J3) (@ (@ (@ tptp.graph_529870330at_nat _let_1) (@ S3 J3)) (@ tptp.id_on_nat (@ tptp.labele460410879_b_nat _let_1)))))))))
% 0.27/0.74 (assert (forall ((G_1 tptp.labeled_graph_b_nat) (G_2 tptp.labeled_graph_b_nat)) (=> (@ (@ tptp.ord_le910748009at_nat (@ tptp.labeled_edges_b_nat G_1)) (@ tptp.labeled_edges_b_nat G_2)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.labele460410879_b_nat G_1)) (@ tptp.labele460410879_b_nat G_2)) (= (@ (@ tptp.graph_union_b_nat G_1) G_2) G_2)))))
% 0.27/0.74 (assert (forall ((R tptp.produc1235635379_b_nat) (G tptp.labeled_graph_b_nat) (F3 tptp.set_Pr1986765409at_nat)) (=> (@ (@ (@ tptp.extensible_b_nat_nat R) G) F3) (not (forall ((G3 tptp.set_Pr1986765409at_nat)) (=> (@ (@ (@ tptp.graph_529870330at_nat (@ tptp.produc194497945_b_nat R)) G) G3) (not (@ (@ (@ tptp.agree_on_b_nat_nat (@ tptp.produc1542243159_b_nat R)) F3) G3))))))))
% 0.27/0.74 (assert (= tptp.extensible_b_nat_nat (lambda ((R2 tptp.produc1235635379_b_nat) (G2 tptp.labeled_graph_b_nat) (F5 tptp.set_Pr1986765409at_nat)) (exists ((G4 tptp.set_Pr1986765409at_nat)) (and (@ (@ (@ tptp.graph_529870330at_nat (@ tptp.produc194497945_b_nat R2)) G2) G4) (@ (@ (@ tptp.agree_on_b_nat_nat (@ tptp.produc1542243159_b_nat R2)) F5) G4))))))
% 0.27/0.74 (assert (forall ((R22 tptp.labeled_graph_b_nat) (G tptp.labeled_graph_b_nat) (G5 tptp.set_Pr1986765409at_nat) (R1 tptp.labeled_graph_b_nat) (F3 tptp.set_Pr1986765409at_nat)) (=> (@ (@ (@ tptp.graph_529870330at_nat R22) G) G5) (=> (@ (@ (@ tptp.agree_on_b_nat_nat R1) F3) G5) (@ (@ (@ tptp.extensible_b_nat_nat (@ (@ tptp.produc951298923_b_nat R1) R22)) G) F3)))))
% 0.27/0.74 (assert (forall ((G_1 tptp.labeled_graph_b_nat) (G_2 tptp.labeled_graph_b_nat)) (let ((_let_1 (@ (@ tptp.graph_union_b_nat G_1) G_2))) (=> (= G_1 (@ tptp.restrict_b_nat G_1)) (=> (= G_2 (@ tptp.restrict_b_nat G_2)) (= _let_1 (@ tptp.restrict_b_nat _let_1)))))))
% 0.27/0.74 (assert (forall ((G_1 tptp.labeled_graph_b_nat) (G_2 tptp.labeled_graph_b_nat)) (= (@ (@ (@ tptp.graph_529870330at_nat G_1) G_2) (@ tptp.id_on_nat (@ tptp.labele460410879_b_nat G_1))) (and (= G_1 (@ tptp.restrict_b_nat G_1)) (= G_2 (@ tptp.restrict_b_nat G_2)) (= (@ (@ tptp.graph_union_b_nat G_1) G_2) G_2)))))
% 0.27/0.74 (assert (forall ((G_1 tptp.labeled_graph_b_nat) (G_2 tptp.labeled_graph_b_nat)) (= (= (@ (@ tptp.graph_union_b_nat G_1) G_2) G_2) (and (@ (@ tptp.ord_le910748009at_nat (@ tptp.labeled_edges_b_nat G_1)) (@ tptp.labeled_edges_b_nat G_2)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.labele460410879_b_nat G_1)) (@ tptp.labele460410879_b_nat G_2))))))
% 0.27/0.74 (assert (= tptp.finite_finite_nat (lambda ((N tptp.set_nat)) (exists ((M tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) N) (@ (@ tptp.ord_less_eq_nat X5) M)))))))
% 0.27/0.74 (assert (forall ((G tptp.labeled_graph_b_nat)) (=> (= G (@ tptp.restrict_b_nat G)) (= (@ (@ tptp.maintained_b_nat_nat tptp.standa879863266rule_b) G) (not (= (@ tptp.labele460410879_b_nat G) tptp.bot_bot_set_nat))))))
% 0.27/0.74 (assert (forall ((R tptp.produc1235635379_b_nat) (G_1 tptp.labeled_graph_b_nat) (F_1 tptp.set_Pr1986765409at_nat) (G_2 tptp.labeled_graph_b_nat) (T tptp.itself_nat) (F_2 tptp.set_Pr1986765409at_nat)) (=> (forall ((H_1 tptp.set_Pr1986765409at_nat) (H_2 tptp.set_Pr1986765409at_nat) (G6 tptp.labeled_graph_b_nat)) (=> (@ (@ (@ tptp.graph_529870330at_nat (@ tptp.produc194497945_b_nat R)) G6) H_1) (=> (@ (@ (@ tptp.graph_529870330at_nat G_1) G6) H_2) (=> (@ (@ tptp.ord_le841296385at_nat (@ (@ tptp.relcomp_nat_nat_nat F_1) H_2)) H_1) (exists ((H2 tptp.set_Pr1986765409at_nat)) (and (@ (@ (@ tptp.graph_529870330at_nat G_2) G6) H2) (@ (@ tptp.ord_le841296385at_nat H_2) H2))))))) (@ (@ (@ (@ (@ (@ tptp.weak_u2026406106at_nat T) R) G_1) G_2) F_1) F_2))))
% 0.27/0.74 (assert (= (@ tptp.id_on_nat tptp.bot_bot_set_nat) tptp.bot_bo2130386637at_nat))
% 0.27/0.74 (assert (forall ((A tptp.labeled_graph_b_nat) (B tptp.labeled_graph_b_nat) (X3 tptp.set_Pr1986765409at_nat) (C2 tptp.labeled_graph_b_nat) (Y3 tptp.set_Pr1986765409at_nat)) (let ((_let_1 (@ tptp.graph_529870330at_nat A))) (=> (@ (@ _let_1 B) X3) (=> (@ (@ (@ tptp.graph_529870330at_nat B) C2) Y3) (@ (@ _let_1 C2) (@ (@ tptp.relcomp_nat_nat_nat X3) Y3)))))))
% 0.27/0.74 (assert (forall ((V2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.labeled_LG_b_nat tptp.bot_bo1626616373at_nat) V2))) (= _let_1 (@ tptp.restrict_b_nat _let_1)))))
% 0.27/0.74 (assert (forall ((G tptp.labeled_graph_b_nat) (F3 tptp.set_Pr1986765409at_nat)) (= (@ (@ (@ tptp.graph_529870330at_nat (@ (@ tptp.labeled_LG_b_nat tptp.bot_bo1626616373at_nat) tptp.bot_bot_set_nat)) G) F3) (and (= F3 tptp.bot_bo2130386637at_nat) (= G (@ tptp.restrict_b_nat G))))))
% 0.27/0.74 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A)))
% 0.27/0.74 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 0.27/0.74 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 0.27/0.74 (assert (forall ((A tptp.labele935650037_a_nat) (B tptp.labele935650037_a_nat) (R4 tptp.set_Pr1987088711_a_nat) (C2 tptp.labele935650037_a_nat) (S4 tptp.set_Pr1987088711_a_nat)) (let ((_let_1 (@ tptp.produc1676969687_a_nat A))) (=> (@ (@ tptp.member832397200_a_nat (@ _let_1 B)) R4) (=> (@ (@ tptp.member832397200_a_nat (@ (@ tptp.produc1676969687_a_nat B) C2)) S4) (@ (@ tptp.member832397200_a_nat (@ _let_1 C2)) (@ (@ tptp.relcom1338300020_a_nat R4) S4)))))))
% 0.27/0.74 (assert (forall ((A tptp.labeled_graph_b_nat) (B tptp.labeled_graph_b_nat) (R4 tptp.set_Pr551076371_b_nat) (C2 tptp.labeled_graph_b_nat) (S4 tptp.set_Pr551076371_b_nat)) (let ((_let_1 (@ tptp.produc951298923_b_nat A))) (=> (@ (@ tptp.member963855452_b_nat (@ _let_1 B)) R4) (=> (@ (@ tptp.member963855452_b_nat (@ (@ tptp.produc951298923_b_nat B) C2)) S4) (@ (@ tptp.member963855452_b_nat (@ _let_1 C2)) (@ (@ tptp.relcom1426860350_b_nat R4) S4)))))))
% 0.27/0.74 (assert (forall ((A tptp.allegorical_term_b) (B tptp.allegorical_term_b) (R4 tptp.set_Pr1163220871term_b) (C2 tptp.allegorical_term_b) (S4 tptp.set_Pr1163220871term_b)) (let ((_let_1 (@ tptp.produc1990145943term_b A))) (=> (@ (@ tptp.member516522448term_b (@ _let_1 B)) R4) (=> (@ (@ tptp.member516522448term_b (@ (@ tptp.produc1990145943term_b B) C2)) S4) (@ (@ tptp.member516522448term_b (@ _let_1 C2)) (@ (@ tptp.relcom1955155673term_b R4) S4)))))))
% 0.27/0.74 (assert (forall ((X1 tptp.labele935650037_a_nat) (X22 tptp.labele935650037_a_nat) (R4 tptp.set_Pr1987088711_a_nat) (S4 tptp.set_Pr1987088711_a_nat) (P (-> tptp.labele935650037_a_nat tptp.labele935650037_a_nat Bool))) (=> (@ (@ tptp.member832397200_a_nat (@ (@ tptp.produc1676969687_a_nat X1) X22)) (@ (@ tptp.relcom1338300020_a_nat R4) S4)) (=> (forall ((A3 tptp.labele935650037_a_nat) (B3 tptp.labele935650037_a_nat) (C tptp.labele935650037_a_nat)) (=> (@ (@ tptp.member832397200_a_nat (@ (@ tptp.produc1676969687_a_nat A3) B3)) R4) (=> (@ (@ tptp.member832397200_a_nat (@ (@ tptp.produc1676969687_a_nat B3) C)) S4) (@ (@ P A3) C)))) (@ (@ P X1) X22)))))
% 0.27/0.74 (assert (forall ((X1 tptp.labeled_graph_b_nat) (X22 tptp.labeled_graph_b_nat) (R4 tptp.set_Pr551076371_b_nat) (S4 tptp.set_Pr551076371_b_nat) (P (-> tptp.labeled_graph_b_nat tptp.labeled_graph_b_nat Bool))) (=> (@ (@ tptp.member963855452_b_nat (@ (@ tptp.produc951298923_b_nat X1) X22)) (@ (@ tptp.relcom1426860350_b_nat R4) S4)) (=> (forall ((A3 tptp.labeled_graph_b_nat) (B3 tptp.labeled_graph_b_nat) (C tptp.labeled_graph_b_nat)) (=> (@ (@ tptp.member963855452_b_nat (@ (@ tptp.produc951298923_b_nat A3) B3)) R4) (=> (@ (@ tptp.member963855452_b_nat (@ (@ tptp.produc951298923_b_nat B3) C)) S4) (@ (@ P A3) C)))) (@ (@ P X1) X22)))))
% 0.27/0.74 (assert (forall ((X1 tptp.allegorical_term_b) (X22 tptp.allegorical_term_b) (R4 tptp.set_Pr1163220871term_b) (S4 tptp.set_Pr1163220871term_b) (P (-> tptp.allegorical_term_b tptp.allegorical_term_b Bool))) (=> (@ (@ tptp.member516522448term_b (@ (@ tptp.produc1990145943term_b X1) X22)) (@ (@ tptp.relcom1955155673term_b R4) S4)) (=> (forall ((A3 tptp.allegorical_term_b) (B3 tptp.allegorical_term_b) (C tptp.allegorical_term_b)) (=> (@ (@ tptp.member516522448term_b (@ (@ tptp.produc1990145943term_b A3) B3)) R4) (=> (@ (@ tptp.member516522448term_b (@ (@ tptp.produc1990145943term_b B3) C)) S4) (@ (@ P A3) C)))) (@ (@ P X1) X22)))))
% 0.27/0.74 (assert (forall ((A1 tptp.labele935650037_a_nat) (A22 tptp.labele935650037_a_nat) (R4 tptp.set_Pr1987088711_a_nat) (S4 tptp.set_Pr1987088711_a_nat)) (= (@ (@ tptp.member832397200_a_nat (@ (@ tptp.produc1676969687_a_nat A1) A22)) (@ (@ tptp.relcom1338300020_a_nat R4) S4)) (exists ((A5 tptp.labele935650037_a_nat) (B5 tptp.labele935650037_a_nat) (C3 tptp.labele935650037_a_nat)) (and (= A1 A5) (= A22 C3) (@ (@ tptp.member832397200_a_nat (@ (@ tptp.produc1676969687_a_nat A5) B5)) R4) (@ (@ tptp.member832397200_a_nat (@ (@ tptp.produc1676969687_a_nat B5) C3)) S4))))))
% 0.27/0.74 (assert (forall ((A1 tptp.labeled_graph_b_nat) (A22 tptp.labeled_graph_b_nat) (R4 tptp.set_Pr551076371_b_nat) (S4 tptp.set_Pr551076371_b_nat)) (= (@ (@ tptp.member963855452_b_nat (@ (@ tptp.produc951298923_b_nat A1) A22)) (@ (@ tptp.relcom1426860350_b_nat R4) S4)) (exists ((A5 tptp.labeled_graph_b_nat) (B5 tptp.labeled_graph_b_nat) (C3 tptp.labeled_graph_b_nat)) (and (= A1 A5) (= A22 C3) (@ (@ tptp.member963855452_b_nat (@ (@ tptp.produc951298923_b_nat A5) B5)) R4) (@ (@ tptp.member963855452_b_nat (@ (@ tptp.produc951298923_b_nat B5) C3)) S4))))))
% 0.27/0.74 (assert (forall ((A1 tptp.allegorical_term_b) (A22 tptp.allegorical_term_b) (R4 tptp.set_Pr1163220871term_b) (S4 tptp.set_Pr1163220871term_b)) (= (@ (@ tptp.member516522448term_b (@ (@ tptp.produc1990145943term_b A1) A22)) (@ (@ tptp.relcom1955155673term_b R4) S4)) (exists ((A5 tptp.allegorical_term_b) (B5 tptp.allegorical_term_b) (C3 tptp.allegorical_term_b)) (and (= A1 A5) (= A22 C3) (@ (@ tptp.member516522448term_b (@ (@ tptp.produc1990145943term_b A5) B5)) R4) (@ (@ tptp.member516522448term_b (@ (@ tptp.produc1990145943term_b B5) C3)) S4))))))
% 0.27/0.74 (assert (forall ((A1 tptp.labele935650037_a_nat) (A22 tptp.labele935650037_a_nat) (R4 tptp.set_Pr1987088711_a_nat) (S4 tptp.set_Pr1987088711_a_nat)) (=> (@ (@ tptp.member832397200_a_nat (@ (@ tptp.produc1676969687_a_nat A1) A22)) (@ (@ tptp.relcom1338300020_a_nat R4) S4)) (not (forall ((B3 tptp.labele935650037_a_nat)) (=> (@ (@ tptp.member832397200_a_nat (@ (@ tptp.produc1676969687_a_nat A1) B3)) R4) (not (@ (@ tptp.member832397200_a_nat (@ (@ tptp.produc1676969687_a_nat B3) A22)) S4))))))))
% 0.27/0.74 (assert (forall ((A1 tptp.labeled_graph_b_nat) (A22 tptp.labeled_graph_b_nat) (R4 tptp.set_Pr551076371_b_nat) (S4 tptp.set_Pr551076371_b_nat)) (=> (@ (@ tptp.member963855452_b_nat (@ (@ tptp.produc951298923_b_nat A1) A22)) (@ (@ tptp.relcom1426860350_b_nat R4) S4)) (not (forall ((B3 tptp.labeled_graph_b_nat)) (=> (@ (@ tptp.member963855452_b_nat (@ (@ tptp.produc951298923_b_nat A1) B3)) R4) (not (@ (@ tptp.member963855452_b_nat (@ (@ tptp.produc951298923_b_nat B3) A22)) S4))))))))
% 0.27/0.74 (assert (forall ((A1 tptp.allegorical_term_b) (A22 tptp.allegorical_term_b) (R4 tptp.set_Pr1163220871term_b) (S4 tptp.set_Pr1163220871term_b)) (=> (@ (@ tptp.member516522448term_b (@ (@ tptp.produc1990145943term_b A1) A22)) (@ (@ tptp.relcom1955155673term_b R4) S4)) (not (forall ((B3 tptp.allegorical_term_b)) (=> (@ (@ tptp.member516522448term_b (@ (@ tptp.produc1990145943term_b A1) B3)) R4) (not (@ (@ tptp.member516522448term_b (@ (@ tptp.produc1990145943term_b B3) A22)) S4))))))))
% 0.27/0.74 (assert (forall ((A tptp.labele935650037_a_nat) (C2 tptp.labele935650037_a_nat) (R4 tptp.set_Pr1987088711_a_nat) (S4 tptp.set_Pr1987088711_a_nat)) (=> (@ (@ tptp.member832397200_a_nat (@ (@ tptp.produc1676969687_a_nat A) C2)) (@ (@ tptp.relcom1338300020_a_nat R4) S4)) (not (forall ((B3 tptp.labele935650037_a_nat)) (=> (@ (@ tptp.member832397200_a_nat (@ (@ tptp.produc1676969687_a_nat A) B3)) R4) (not (@ (@ tptp.member832397200_a_nat (@ (@ tptp.produc1676969687_a_nat B3) C2)) S4))))))))
% 0.27/0.74 (assert (forall ((A tptp.labeled_graph_b_nat) (C2 tptp.labeled_graph_b_nat) (R4 tptp.set_Pr551076371_b_nat) (S4 tptp.set_Pr551076371_b_nat)) (=> (@ (@ tptp.member963855452_b_nat (@ (@ tptp.produc951298923_b_nat A) C2)) (@ (@ tptp.relcom1426860350_b_nat R4) S4)) (not (forall ((B3 tptp.labeled_graph_b_nat)) (=> (@ (@ tptp.member963855452_b_nat (@ (@ tptp.produc951298923_b_nat A) B3)) R4) (not (@ (@ tptp.member963855452_b_nat (@ (@ tptp.produc951298923_b_nat B3) C2)) S4))))))))
% 0.27/0.74 (assert (forall ((A tptp.allegorical_term_b) (C2 tptp.allegorical_term_b) (R4 tptp.set_Pr1163220871term_b) (S4 tptp.set_Pr1163220871term_b)) (=> (@ (@ tptp.member516522448term_b (@ (@ tptp.produc1990145943term_b A) C2)) (@ (@ tptp.relcom1955155673term_b R4) S4)) (not (forall ((B3 tptp.allegorical_term_b)) (=> (@ (@ tptp.member516522448term_b (@ (@ tptp.produc1990145943term_b A) B3)) R4) (not (@ (@ tptp.member516522448term_b (@ (@ tptp.produc1990145943term_b B3) C2)) S4))))))))
% 0.27/0.74 (assert (forall ((Xz tptp.produc1871334759_a_nat) (R4 tptp.set_Pr1987088711_a_nat) (S4 tptp.set_Pr1987088711_a_nat)) (=> (@ (@ tptp.member832397200_a_nat Xz) (@ (@ tptp.relcom1338300020_a_nat R4) S4)) (not (forall ((X4 tptp.labele935650037_a_nat) (Y4 tptp.labele935650037_a_nat) (Z3 tptp.labele935650037_a_nat)) (let ((_let_1 (@ tptp.produc1676969687_a_nat X4))) (=> (= Xz (@ _let_1 Z3)) (=> (@ (@ tptp.member832397200_a_nat (@ _let_1 Y4)) R4) (not (@ (@ tptp.member832397200_a_nat (@ (@ tptp.produc1676969687_a_nat Y4) Z3)) S4))))))))))
% 0.27/0.74 (assert (forall ((Xz tptp.produc1235635379_b_nat) (R4 tptp.set_Pr551076371_b_nat) (S4 tptp.set_Pr551076371_b_nat)) (=> (@ (@ tptp.member963855452_b_nat Xz) (@ (@ tptp.relcom1426860350_b_nat R4) S4)) (not (forall ((X4 tptp.labeled_graph_b_nat) (Y4 tptp.labeled_graph_b_nat) (Z3 tptp.labeled_graph_b_nat)) (let ((_let_1 (@ tptp.produc951298923_b_nat X4))) (=> (= Xz (@ _let_1 Z3)) (=> (@ (@ tptp.member963855452_b_nat (@ _let_1 Y4)) R4) (not (@ (@ tptp.member963855452_b_nat (@ (@ tptp.produc951298923_b_nat Y4) Z3)) S4))))))))))
% 0.27/0.74 (assert (forall ((Xz tptp.produc1478835367term_b) (R4 tptp.set_Pr1163220871term_b) (S4 tptp.set_Pr1163220871term_b)) (=> (@ (@ tptp.member516522448term_b Xz) (@ (@ tptp.relcom1955155673term_b R4) S4)) (not (forall ((X4 tptp.allegorical_term_b) (Y4 tptp.allegorical_term_b) (Z3 tptp.allegorical_term_b)) (let ((_let_1 (@ tptp.produc1990145943term_b X4))) (=> (= Xz (@ _let_1 Z3)) (=> (@ (@ tptp.member516522448term_b (@ _let_1 Y4)) R4) (not (@ (@ tptp.member516522448term_b (@ (@ tptp.produc1990145943term_b Y4) Z3)) S4))))))))))
% 0.27/0.74 (assert (@ tptp.finite_finite_nat tptp.bot_bot_set_nat))
% 0.27/0.74 (assert (@ tptp.finite1987068434at_nat tptp.bot_bo1626616373at_nat))
% 0.27/0.74 (assert (forall ((S2 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S2)) (not (= S2 tptp.bot_bot_set_nat)))))
% 0.27/0.74 (assert (forall ((S2 tptp.set_Pr9961929at_nat)) (=> (not (@ tptp.finite1987068434at_nat S2)) (not (= S2 tptp.bot_bo1626616373at_nat)))))
% 0.27/0.74 (assert (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (=> (not (= A4 tptp.bot_bot_set_nat)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_nat Xa) X4) (= X4 Xa))))))))))
% 0.27/0.74 (assert (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (=> (not (= A4 tptp.bot_bot_set_nat)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_nat X4) Xa) (= X4 Xa))))))))))
% 0.27/0.74 (assert (forall ((A4 tptp.labeled_graph_b_nat) (B4 tptp.labeled_graph_b_nat) (F3 tptp.set_Pr1986765409at_nat) (E tptp.allegorical_term_b)) (=> (@ (@ (@ tptp.graph_529870330at_nat A4) B4) F3) (=> (not (= (@ (@ tptp.semantics_b_nat A4) E) tptp.bot_bo2130386637at_nat)) (not (= (@ (@ tptp.semantics_b_nat B4) E) tptp.bot_bo2130386637at_nat))))))
% 0.27/0.74 (assert (forall ((P (-> tptp.nat Bool)) (X3 tptp.nat) (M2 tptp.nat)) (=> (@ P X3) (=> (forall ((X4 tptp.nat)) (=> (@ P X4) (@ (@ tptp.ord_less_eq_nat X4) M2))) (not (forall ((M3 tptp.nat)) (=> (@ P M3) (not (forall ((X6 tptp.nat)) (=> (@ P X6) (@ (@ tptp.ord_less_eq_nat X6) M3)))))))))))
% 0.27/0.74 (assert (forall ((A tptp.labeled_graph_b_nat) (B tptp.labeled_graph_b_nat) (F3 tptp.set_Pr1986765409at_nat) (Aa tptp.nat) (Ba tptp.nat)) (let ((_let_1 (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat Aa) Ba)))) (=> (@ (@ (@ tptp.graph_529870330at_nat A) B) F3) (=> (@ _let_1 F3) (@ _let_1 (@ (@ tptp.relcomp_nat_nat_nat F3) (@ tptp.id_on_nat (@ tptp.labele460410879_b_nat B)))))))))
% 0.27/0.74 (assert (forall ((A tptp.labeled_graph_b_nat) (B tptp.labeled_graph_b_nat) (F3 tptp.set_Pr1986765409at_nat) (Aa tptp.nat) (Ba tptp.nat)) (let ((_let_1 (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat Aa) Ba)))) (=> (@ (@ (@ tptp.graph_529870330at_nat A) B) F3) (=> (@ _let_1 F3) (@ _let_1 (@ (@ tptp.relcomp_nat_nat_nat (@ tptp.id_on_nat (@ tptp.labele460410879_b_nat A))) F3)))))))
% 0.27/0.74 (assert (forall ((E tptp.allegorical_term_b) (G tptp.labeled_graph_b_nat) (F3 tptp.set_Pr1986765409at_nat)) (=> (@ (@ (@ tptp.graph_529870330at_nat (@ tptp.translation_b E)) G) F3) (not (= (@ (@ tptp.semantics_b_nat G) E) tptp.bot_bo2130386637at_nat)))))
% 0.27/0.74 (assert (forall ((T tptp.itself_nat) (R tptp.produc1235635379_b_nat) (G_1 tptp.labeled_graph_b_nat) (G_2 tptp.labeled_graph_b_nat) (F_1 tptp.set_Pr1986765409at_nat) (F_2 tptp.set_Pr1986765409at_nat) (G tptp.labeled_graph_b_nat) (H_12 tptp.set_Pr1986765409at_nat) (H_22 tptp.set_Pr1986765409at_nat)) (=> (@ (@ (@ (@ (@ (@ tptp.weak_u2026406106at_nat T) R) G_1) G_2) F_1) F_2) (=> (@ (@ (@ tptp.graph_529870330at_nat (@ tptp.produc194497945_b_nat R)) G) H_12) (=> (@ (@ (@ tptp.graph_529870330at_nat G_1) G) H_22) (=> (@ (@ tptp.ord_le841296385at_nat (@ (@ tptp.relcomp_nat_nat_nat F_1) H_22)) H_12) (exists ((H3 tptp.set_Pr1986765409at_nat)) (and (@ (@ (@ tptp.graph_529870330at_nat G_2) G) H3) (@ (@ tptp.ord_le841296385at_nat H_22) H3)))))))))
% 0.27/0.74 (assert (= tptp.weak_u2026406106at_nat (lambda ((Uu tptp.itself_nat) (R2 tptp.produc1235635379_b_nat) (G_12 tptp.labeled_graph_b_nat) (G_22 tptp.labeled_graph_b_nat) (F_12 tptp.set_Pr1986765409at_nat) (F_22 tptp.set_Pr1986765409at_nat)) (forall ((H_13 tptp.set_Pr1986765409at_nat) (H_23 tptp.set_Pr1986765409at_nat) (G2 tptp.labeled_graph_b_nat)) (=> (and (@ (@ (@ tptp.graph_529870330at_nat (@ tptp.produc194497945_b_nat R2)) G2) H_13) (@ (@ (@ tptp.graph_529870330at_nat G_12) G2) H_23) (@ (@ tptp.ord_le841296385at_nat (@ (@ tptp.relcomp_nat_nat_nat F_12) H_23)) H_13)) (exists ((H4 tptp.set_Pr1986765409at_nat)) (and (@ (@ (@ tptp.graph_529870330at_nat G_22) G2) H4) (@ (@ tptp.ord_le841296385at_nat H_23) H4))))))))
% 0.27/0.74 (assert (forall ((A4 tptp.labeled_graph_b_nat) (B4 tptp.labeled_graph_b_nat) (G tptp.labeled_graph_b_nat) (F3 tptp.set_Pr1986765409at_nat)) (=> (@ (@ (@ tptp.graph_529870330at_nat (@ (@ tptp.graph_union_b_nat A4) B4)) G) F3) (=> (= B4 (@ tptp.restrict_b_nat B4)) (@ (@ (@ tptp.graph_529870330at_nat B4) G) (@ (@ tptp.relcomp_nat_nat_nat (@ tptp.id_on_nat (@ tptp.labele460410879_b_nat B4))) F3))))))
% 0.27/0.74 (assert (forall ((A4 tptp.labeled_graph_b_nat) (B4 tptp.labeled_graph_b_nat) (G tptp.labeled_graph_b_nat) (F3 tptp.set_Pr1986765409at_nat)) (=> (@ (@ (@ tptp.graph_529870330at_nat (@ (@ tptp.graph_union_b_nat A4) B4)) G) F3) (=> (= A4 (@ tptp.restrict_b_nat A4)) (@ (@ (@ tptp.graph_529870330at_nat A4) G) (@ (@ tptp.relcomp_nat_nat_nat (@ tptp.id_on_nat (@ tptp.labele460410879_b_nat A4))) F3))))))
% 0.27/0.74 (assert (forall ((R tptp.set_Product_prod_b_b) (S2 tptp.set_Pr9961929at_nat)) (=> (@ tptp.finite1015599120od_b_b R) (=> (@ tptp.finite1987068434at_nat S2) (@ tptp.finite1987068434at_nat (@ (@ tptp.relcom14055552at_nat R) S2))))))
% 0.27/0.74 (assert (forall ((R tptp.set_Pr9961929at_nat) (S2 tptp.set_Pr1490359111at_nat)) (=> (@ tptp.finite1987068434at_nat R) (=> (@ tptp.finite48957584at_nat S2) (@ tptp.finite1987068434at_nat (@ (@ tptp.relcom195261566at_nat R) S2))))))
% 0.27/0.74 (assert (forall ((A4 tptp.set_Pr1987088711_a_nat)) (=> (forall ((X4 tptp.produc1871334759_a_nat)) (not (@ (@ tptp.member832397200_a_nat X4) A4))) (@ (@ tptp.ord_le1718765799_a_nat A4) tptp.bot_bo1836341171_a_nat))))
% 0.27/0.74 (assert (= tptp.bot_bo1024461546_nat_o (lambda ((X5 tptp.produc1871334759_a_nat)) (@ (@ tptp.member832397200_a_nat X5) tptp.bot_bo1836341171_a_nat))))
% 0.27/0.74 (assert (forall ((R4 tptp.labele935650037_a_nat) (S4 tptp.labele935650037_a_nat) (R tptp.set_Pr1987088711_a_nat) (S5 tptp.labele935650037_a_nat)) (let ((_let_1 (@ tptp.produc1676969687_a_nat R4))) (=> (@ (@ tptp.member832397200_a_nat (@ _let_1 S4)) R) (=> (= S5 S4) (@ (@ tptp.member832397200_a_nat (@ _let_1 S5)) R))))))
% 0.27/0.74 (assert (forall ((R4 tptp.labeled_graph_b_nat) (S4 tptp.labeled_graph_b_nat) (R tptp.set_Pr551076371_b_nat) (S5 tptp.labeled_graph_b_nat)) (let ((_let_1 (@ tptp.produc951298923_b_nat R4))) (=> (@ (@ tptp.member963855452_b_nat (@ _let_1 S4)) R) (=> (= S5 S4) (@ (@ tptp.member963855452_b_nat (@ _let_1 S5)) R))))))
% 0.27/0.74 (assert (forall ((R4 tptp.allegorical_term_b) (S4 tptp.allegorical_term_b) (R tptp.set_Pr1163220871term_b) (S5 tptp.allegorical_term_b)) (let ((_let_1 (@ tptp.produc1990145943term_b R4))) (=> (@ (@ tptp.member516522448term_b (@ _let_1 S4)) R) (=> (= S5 S4) (@ (@ tptp.member516522448term_b (@ _let_1 S5)) R))))))
% 0.27/0.74 (assert (forall ((G tptp.labeled_graph_b_nat) (X tptp.labeled_graph_b_nat) (F3 tptp.set_Pr1986765409at_nat) (G5 tptp.set_Pr1986765409at_nat)) (=> (@ (@ (@ tptp.graph_529870330at_nat G) X) F3) (=> (@ tptp.univalent_nat_nat G5) (= (@ (@ (@ tptp.agree_on_b_nat_nat G) F3) G5) (@ (@ tptp.ord_le841296385at_nat F3) G5))))))
% 0.27/0.74 (assert (forall ((X3 tptp.set_nat)) (@ tptp.univalent_nat_nat (@ tptp.id_on_nat X3))))
% 0.27/0.74 (assert (forall ((R tptp.set_Pr1987088711_a_nat) (X3 tptp.labele935650037_a_nat) (Y3 tptp.labele935650037_a_nat) (Z2 tptp.labele935650037_a_nat)) (let ((_let_1 (@ tptp.produc1676969687_a_nat X3))) (=> (@ tptp.unival1637751524_a_nat R) (=> (@ (@ tptp.member832397200_a_nat (@ _let_1 Y3)) R) (=> (@ (@ tptp.member832397200_a_nat (@ _let_1 Z2)) R) (= Z2 Y3)))))))
% 0.27/0.74 (assert (forall ((R tptp.set_Pr551076371_b_nat) (X3 tptp.labeled_graph_b_nat) (Y3 tptp.labeled_graph_b_nat) (Z2 tptp.labeled_graph_b_nat)) (let ((_let_1 (@ tptp.produc951298923_b_nat X3))) (=> (@ tptp.unival857119480_b_nat R) (=> (@ (@ tptp.member963855452_b_nat (@ _let_1 Y3)) R) (=> (@ (@ tptp.member963855452_b_nat (@ _let_1 Z2)) R) (= Z2 Y3)))))))
% 0.27/0.74 (assert (forall ((R tptp.set_Pr1163220871term_b) (X3 tptp.allegorical_term_b) (Y3 tptp.allegorical_term_b) (Z2 tptp.allegorical_term_b)) (let ((_let_1 (@ tptp.produc1990145943term_b X3))) (=> (@ tptp.unival1191217828term_b R) (=> (@ (@ tptp.member516522448term_b (@ _let_1 Y3)) R) (=> (@ (@ tptp.member516522448term_b (@ _let_1 Z2)) R) (= Z2 Y3)))))))
% 0.27/0.74 (assert (= tptp.unival1637751524_a_nat (lambda ((R2 tptp.set_Pr1987088711_a_nat)) (forall ((X5 tptp.labele935650037_a_nat) (Y6 tptp.labele935650037_a_nat) (Z4 tptp.labele935650037_a_nat)) (let ((_let_1 (@ tptp.produc1676969687_a_nat X5))) (=> (and (@ (@ tptp.member832397200_a_nat (@ _let_1 Y6)) R2) (@ (@ tptp.member832397200_a_nat (@ _let_1 Z4)) R2)) (= Z4 Y6)))))))
% 0.27/0.74 (assert (= tptp.unival857119480_b_nat (lambda ((R2 tptp.set_Pr551076371_b_nat)) (forall ((X5 tptp.labeled_graph_b_nat) (Y6 tptp.labeled_graph_b_nat) (Z4 tptp.labeled_graph_b_nat)) (let ((_let_1 (@ tptp.produc951298923_b_nat X5))) (=> (and (@ (@ tptp.member963855452_b_nat (@ _let_1 Y6)) R2) (@ (@ tptp.member963855452_b_nat (@ _let_1 Z4)) R2)) (= Z4 Y6)))))))
% 0.27/0.74 (assert (= tptp.unival1191217828term_b (lambda ((R2 tptp.set_Pr1163220871term_b)) (forall ((X5 tptp.allegorical_term_b) (Y6 tptp.allegorical_term_b) (Z4 tptp.allegorical_term_b)) (let ((_let_1 (@ tptp.produc1990145943term_b X5))) (=> (and (@ (@ tptp.member516522448term_b (@ _let_1 Y6)) R2) (@ (@ tptp.member516522448term_b (@ _let_1 Z4)) R2)) (= Z4 Y6)))))))
% 0.27/0.74 (assert (forall ((S2 (-> tptp.nat tptp.labeled_graph_b_nat)) (V tptp.set_nat) (F3 tptp.set_Pr1986765409at_nat)) (=> (@ tptp.chain_b_nat S2) (=> (@ tptp.finite_finite_nat V) (=> (@ tptp.univalent_nat_nat F3) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat F3) V)) (@ tptp.labele460410879_b_nat (@ tptp.chain_sup_b_nat S2))) (exists ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat F3) V)) (@ tptp.labele460410879_b_nat (@ S2 I2))))))))))
% 0.27/0.74 (assert (forall ((S2 (-> tptp.nat tptp.labeled_graph_b_nat)) (V tptp.set_Pr9961929at_nat) (F3 tptp.set_Pr2041158302at_nat)) (=> (@ tptp.chain_b_nat S2) (=> (@ tptp.finite1987068434at_nat V) (=> (@ tptp.unival633212949at_nat F3) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_1356842150at_nat F3) V)) (@ tptp.labele460410879_b_nat (@ tptp.chain_sup_b_nat S2))) (exists ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_1356842150at_nat F3) V)) (@ tptp.labele460410879_b_nat (@ S2 I2))))))))))
% 0.27/0.74 (assert (forall ((A tptp.produc1871334759_a_nat) (B tptp.produc1871334759_a_nat) (R4 tptp.set_Pr924198087_a_nat) (A4 tptp.set_Pr1987088711_a_nat)) (=> (@ (@ tptp.member584645392_a_nat (@ (@ tptp.produc1677124439_a_nat A) B)) R4) (=> (@ (@ tptp.member832397200_a_nat A) A4) (@ (@ tptp.member832397200_a_nat B) (@ (@ tptp.image_1168831379_a_nat R4) A4))))))
% 0.27/0.74 (assert (forall ((A tptp.labele935650037_a_nat) (B tptp.labele935650037_a_nat) (R4 tptp.set_Pr1987088711_a_nat) (A4 tptp.set_la1083530965_a_nat)) (=> (@ (@ tptp.member832397200_a_nat (@ (@ tptp.produc1676969687_a_nat A) B)) R4) (=> (@ (@ tptp.member964390942_a_nat A) A4) (@ (@ tptp.member964390942_a_nat B) (@ (@ tptp.image_1971191571_a_nat R4) A4))))))
% 0.27/0.74 (assert (forall ((A tptp.labeled_graph_b_nat) (B tptp.labeled_graph_b_nat) (R4 tptp.set_Pr551076371_b_nat) (A4 tptp.set_la1976028319_b_nat)) (=> (@ (@ tptp.member963855452_b_nat (@ (@ tptp.produc951298923_b_nat A) B)) R4) (=> (@ (@ tptp.member1483953152_b_nat A) A4) (@ (@ tptp.member1483953152_b_nat B) (@ (@ tptp.image_1183964583_b_nat R4) A4))))))
% 0.27/0.74 (assert (forall ((A tptp.allegorical_term_b) (B tptp.allegorical_term_b) (R4 tptp.set_Pr1163220871term_b) (A4 tptp.set_al1193902458term_b)) (=> (@ (@ tptp.member516522448term_b (@ (@ tptp.produc1990145943term_b A) B)) R4) (=> (@ (@ tptp.member93680451term_b A) A4) (@ (@ tptp.member93680451term_b B) (@ (@ tptp.image_329221075term_b R4) A4))))))
% 0.27/0.74 (assert (forall ((A4 tptp.set_nat)) (= (@ tptp.domain_nat_nat (@ tptp.id_on_nat A4)) A4)))
% 0.27/0.74 (assert (forall ((R tptp.set_Pr9961929at_nat)) (=> (@ tptp.unival989235430at_nat R) (= (@ tptp.finite_finite_b (@ tptp.domain1101989710at_nat R)) (@ tptp.finite1987068434at_nat R)))))
% 0.27/0.74 (assert (forall ((R4 tptp.set_Pr9961929at_nat)) (=> (@ tptp.finite1987068434at_nat R4) (@ tptp.finite_finite_b (@ tptp.domain1101989710at_nat R4)))))
% 0.27/0.74 (assert (forall ((R tptp.set_Pr9961929at_nat) (A4 tptp.set_b)) (=> (@ tptp.finite1987068434at_nat R) (@ tptp.finite772653738at_nat (@ (@ tptp.image_2112855445at_nat R) A4)))))
% 0.27/0.74 (assert (forall ((X3 tptp.labele935650037_a_nat) (R4 tptp.set_Pr1987088711_a_nat) (P (-> tptp.labele935650037_a_nat Bool))) (=> (@ (@ tptp.member964390942_a_nat X3) (@ tptp.domain1068567884_a_nat R4)) (=> (forall ((A3 tptp.labele935650037_a_nat) (B3 tptp.labele935650037_a_nat)) (=> (@ (@ tptp.member832397200_a_nat (@ (@ tptp.produc1676969687_a_nat A3) B3)) R4) (@ P A3))) (@ P X3)))))
% 0.27/0.74 (assert (forall ((X3 tptp.labeled_graph_b_nat) (R4 tptp.set_Pr551076371_b_nat) (P (-> tptp.labeled_graph_b_nat Bool))) (=> (@ (@ tptp.member1483953152_b_nat X3) (@ tptp.domain767519072_b_nat R4)) (=> (forall ((A3 tptp.labeled_graph_b_nat) (B3 tptp.labeled_graph_b_nat)) (=> (@ (@ tptp.member963855452_b_nat (@ (@ tptp.produc951298923_b_nat A3) B3)) R4) (@ P A3))) (@ P X3)))))
% 0.27/0.74 (assert (forall ((X3 tptp.allegorical_term_b) (R4 tptp.set_Pr1163220871term_b) (P (-> tptp.allegorical_term_b Bool))) (=> (@ (@ tptp.member93680451term_b X3) (@ tptp.domain859272460term_b R4)) (=> (forall ((A3 tptp.allegorical_term_b) (B3 tptp.allegorical_term_b)) (=> (@ (@ tptp.member516522448term_b (@ (@ tptp.produc1990145943term_b A3) B3)) R4) (@ P A3))) (@ P X3)))))
% 0.27/0.74 (assert (forall ((A tptp.labele935650037_a_nat) (B tptp.labele935650037_a_nat) (R4 tptp.set_Pr1987088711_a_nat)) (=> (@ (@ tptp.member832397200_a_nat (@ (@ tptp.produc1676969687_a_nat A) B)) R4) (@ (@ tptp.member964390942_a_nat A) (@ tptp.domain1068567884_a_nat R4)))))
% 0.27/0.74 (assert (forall ((A tptp.labeled_graph_b_nat) (B tptp.labeled_graph_b_nat) (R4 tptp.set_Pr551076371_b_nat)) (=> (@ (@ tptp.member963855452_b_nat (@ (@ tptp.produc951298923_b_nat A) B)) R4) (@ (@ tptp.member1483953152_b_nat A) (@ tptp.domain767519072_b_nat R4)))))
% 0.27/0.74 (assert (forall ((A tptp.allegorical_term_b) (B tptp.allegorical_term_b) (R4 tptp.set_Pr1163220871term_b)) (=> (@ (@ tptp.member516522448term_b (@ (@ tptp.produc1990145943term_b A) B)) R4) (@ (@ tptp.member93680451term_b A) (@ tptp.domain859272460term_b R4)))))
% 0.27/0.74 (assert (forall ((A tptp.labele935650037_a_nat) (R4 tptp.set_Pr1987088711_a_nat)) (= (@ (@ tptp.member964390942_a_nat A) (@ tptp.domain1068567884_a_nat R4)) (exists ((A5 tptp.labele935650037_a_nat) (B5 tptp.labele935650037_a_nat)) (and (= A A5) (@ (@ tptp.member832397200_a_nat (@ (@ tptp.produc1676969687_a_nat A5) B5)) R4))))))
% 0.27/0.74 (assert (forall ((A tptp.labeled_graph_b_nat) (R4 tptp.set_Pr551076371_b_nat)) (= (@ (@ tptp.member1483953152_b_nat A) (@ tptp.domain767519072_b_nat R4)) (exists ((A5 tptp.labeled_graph_b_nat) (B5 tptp.labeled_graph_b_nat)) (and (= A A5) (@ (@ tptp.member963855452_b_nat (@ (@ tptp.produc951298923_b_nat A5) B5)) R4))))))
% 0.27/0.74 (assert (forall ((A tptp.allegorical_term_b) (R4 tptp.set_Pr1163220871term_b)) (= (@ (@ tptp.member93680451term_b A) (@ tptp.domain859272460term_b R4)) (exists ((A5 tptp.allegorical_term_b) (B5 tptp.allegorical_term_b)) (and (= A A5) (@ (@ tptp.member516522448term_b (@ (@ tptp.produc1990145943term_b A5) B5)) R4))))))
% 0.27/0.74 (assert (forall ((A tptp.labele935650037_a_nat) (R4 tptp.set_Pr1987088711_a_nat)) (=> (@ (@ tptp.member964390942_a_nat A) (@ tptp.domain1068567884_a_nat R4)) (not (forall ((B3 tptp.labele935650037_a_nat)) (not (@ (@ tptp.member832397200_a_nat (@ (@ tptp.produc1676969687_a_nat A) B3)) R4)))))))
% 0.27/0.74 (assert (forall ((A tptp.labeled_graph_b_nat) (R4 tptp.set_Pr551076371_b_nat)) (=> (@ (@ tptp.member1483953152_b_nat A) (@ tptp.domain767519072_b_nat R4)) (not (forall ((B3 tptp.labeled_graph_b_nat)) (not (@ (@ tptp.member963855452_b_nat (@ (@ tptp.produc951298923_b_nat A) B3)) R4)))))))
% 0.27/0.74 (assert (forall ((A tptp.allegorical_term_b) (R4 tptp.set_Pr1163220871term_b)) (=> (@ (@ tptp.member93680451term_b A) (@ tptp.domain859272460term_b R4)) (not (forall ((B3 tptp.allegorical_term_b)) (not (@ (@ tptp.member516522448term_b (@ (@ tptp.produc1990145943term_b A) B3)) R4)))))))
% 0.27/0.74 (assert (forall ((A tptp.labele935650037_a_nat) (R4 tptp.set_Pr1987088711_a_nat)) (= (@ (@ tptp.member964390942_a_nat A) (@ tptp.domain1068567884_a_nat R4)) (exists ((Y6 tptp.labele935650037_a_nat)) (@ (@ tptp.member832397200_a_nat (@ (@ tptp.produc1676969687_a_nat A) Y6)) R4)))))
% 0.27/0.74 (assert (forall ((A tptp.labeled_graph_b_nat) (R4 tptp.set_Pr551076371_b_nat)) (= (@ (@ tptp.member1483953152_b_nat A) (@ tptp.domain767519072_b_nat R4)) (exists ((Y6 tptp.labeled_graph_b_nat)) (@ (@ tptp.member963855452_b_nat (@ (@ tptp.produc951298923_b_nat A) Y6)) R4)))))
% 0.27/0.74 (assert (forall ((A tptp.allegorical_term_b) (R4 tptp.set_Pr1163220871term_b)) (= (@ (@ tptp.member93680451term_b A) (@ tptp.domain859272460term_b R4)) (exists ((Y6 tptp.allegorical_term_b)) (@ (@ tptp.member516522448term_b (@ (@ tptp.produc1990145943term_b A) Y6)) R4)))))
% 0.27/0.74 (assert (forall ((A tptp.labele935650037_a_nat) (R4 tptp.set_Pr1987088711_a_nat)) (=> (@ (@ tptp.member964390942_a_nat A) (@ tptp.domain1068567884_a_nat R4)) (not (forall ((B3 tptp.labele935650037_a_nat)) (not (@ (@ tptp.member832397200_a_nat (@ (@ tptp.produc1676969687_a_nat A) B3)) R4)))))))
% 0.27/0.74 (assert (forall ((A tptp.labeled_graph_b_nat) (R4 tptp.set_Pr551076371_b_nat)) (=> (@ (@ tptp.member1483953152_b_nat A) (@ tptp.domain767519072_b_nat R4)) (not (forall ((B3 tptp.labeled_graph_b_nat)) (not (@ (@ tptp.member963855452_b_nat (@ (@ tptp.produc951298923_b_nat A) B3)) R4)))))))
% 0.27/0.74 (assert (forall ((A tptp.allegorical_term_b) (R4 tptp.set_Pr1163220871term_b)) (=> (@ (@ tptp.member93680451term_b A) (@ tptp.domain859272460term_b R4)) (not (forall ((B3 tptp.allegorical_term_b)) (not (@ (@ tptp.member516522448term_b (@ (@ tptp.produc1990145943term_b A) B3)) R4)))))))
% 0.27/0.74 (assert (forall ((A tptp.labele935650037_a_nat) (A4 tptp.set_la1083530965_a_nat) (B tptp.labele935650037_a_nat) (R4 tptp.set_Pr1987088711_a_nat)) (=> (@ (@ tptp.member964390942_a_nat A) A4) (=> (@ (@ tptp.member832397200_a_nat (@ (@ tptp.produc1676969687_a_nat A) B)) R4) (@ (@ tptp.member964390942_a_nat B) (@ (@ tptp.image_1971191571_a_nat R4) A4))))))
% 0.27/0.74 (assert (forall ((A tptp.produc1871334759_a_nat) (A4 tptp.set_Pr1987088711_a_nat) (B tptp.produc1871334759_a_nat) (R4 tptp.set_Pr924198087_a_nat)) (=> (@ (@ tptp.member832397200_a_nat A) A4) (=> (@ (@ tptp.member584645392_a_nat (@ (@ tptp.produc1677124439_a_nat A) B)) R4) (@ (@ tptp.member832397200_a_nat B) (@ (@ tptp.image_1168831379_a_nat R4) A4))))))
% 0.27/0.74 (assert (forall ((A tptp.labeled_graph_b_nat) (A4 tptp.set_la1976028319_b_nat) (B tptp.labeled_graph_b_nat) (R4 tptp.set_Pr551076371_b_nat)) (=> (@ (@ tptp.member1483953152_b_nat A) A4) (=> (@ (@ tptp.member963855452_b_nat (@ (@ tptp.produc951298923_b_nat A) B)) R4) (@ (@ tptp.member1483953152_b_nat B) (@ (@ tptp.image_1183964583_b_nat R4) A4))))))
% 0.27/0.74 (assert (forall ((A tptp.allegorical_term_b) (A4 tptp.set_al1193902458term_b) (B tptp.allegorical_term_b) (R4 tptp.set_Pr1163220871term_b)) (=> (@ (@ tptp.member93680451term_b A) A4) (=> (@ (@ tptp.member516522448term_b (@ (@ tptp.produc1990145943term_b A) B)) R4) (@ (@ tptp.member93680451term_b B) (@ (@ tptp.image_329221075term_b R4) A4))))))
% 0.27/0.74 (assert (forall ((B tptp.labele935650037_a_nat) (R4 tptp.set_Pr1987088711_a_nat) (A4 tptp.set_la1083530965_a_nat)) (= (@ (@ tptp.member964390942_a_nat B) (@ (@ tptp.image_1971191571_a_nat R4) A4)) (exists ((X5 tptp.labele935650037_a_nat)) (and (@ (@ tptp.member964390942_a_nat X5) A4) (@ (@ tptp.member832397200_a_nat (@ (@ tptp.produc1676969687_a_nat X5) B)) R4))))))
% 0.27/0.74 (assert (forall ((B tptp.labeled_graph_b_nat) (R4 tptp.set_Pr551076371_b_nat) (A4 tptp.set_la1976028319_b_nat)) (= (@ (@ tptp.member1483953152_b_nat B) (@ (@ tptp.image_1183964583_b_nat R4) A4)) (exists ((X5 tptp.labeled_graph_b_nat)) (and (@ (@ tptp.member1483953152_b_nat X5) A4) (@ (@ tptp.member963855/export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 28864 Alarm clock ( read result; case "$result" in
% 299.90/300.17 unsat)
% 299.90/300.17 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.90/300.17 ;;
% 299.90/300.17 sat)
% 299.90/300.17 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.90/300.17 ;;
% 299.90/300.17 esac; exit 1 )
% 299.90/300.18 Alarm clock
% 299.90/300.18 % cvc5---1.0.5 exiting
% 299.90/300.18 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------