%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP179^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 : Wed Feb 25 08:56:12 AM UTC 2026
% Result : Theorem 21.27s 4.33s
% Output : Refutation 21.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP179^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n016.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:29:21 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : ITP179^2 : TPTP v9.2.1. Released v7.5.0.
% 0.30/0.46 % Domain : Interactive Theorem Proving
% 0.30/0.46 % Problem : Sledgehammer StandardRules problem prob_555__5392816_1
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Des21]
% 0.30/0.46 % Names : StandardRules/prob_555__5392816_1 [Des21]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v8.1.0, 0.25 v7.5.0
% 0.30/0.46 % Syntax : Number of formulae : 340 ( 141 unt; 59 typ; 0 def)
% 0.30/0.46 % Number of atoms : 691 ( 260 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 13 ( 2 avg)
% 0.30/0.46 % Number of connectives : 5618 ( 68 ~; 6 |; 54 &;5227 @)
% 0.30/0.46 % ( 0 <=>; 263 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 28 ( 8 avg)
% 0.30/0.46 % Number of types : 4 ( 3 usr)
% 0.30/0.46 % Number of type conns : 109 ( 109 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 57 ( 56 usr; 4 con; 0-6 aty)
% 0.30/0.46 % Number of variables : 1121 ( 41 ^;1000 !; 11 ?;1121 :)
% 0.30/0.46 % ( 69 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.46 % SPC : TH1_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 16:23:56.500
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % Could-be-implicit typings (8)
% 0.30/0.46 thf(ty_t_LabeledGraphSemantics_OStandard__Constant,type,
% 0.30/0.46 standard_Constant: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_LabeledGraphs_Olabeled__graph,type,
% 0.30/0.46 labeled_graph: $tType > $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Product__Type_Oprod,type,
% 0.30/0.46 product_prod: $tType > $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Sum__Type_Osum,type,
% 0.30/0.46 sum_sum: $tType > $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Set_Oset,type,
% 0.30/0.46 set: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Nat_Onat,type,
% 0.30/0.46 nat: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_tf_b,type,
% 0.30/0.46 b: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_tf_a,type,
% 0.30/0.46 a: $tType ).
% 0.30/0.46
% 0.30/0.46 % Explicit typings (51)
% 0.30/0.46 thf(sy_cl_HOL_Otype,type,
% 0.30/0.46 type:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Oone,type,
% 0.30/0.46 one:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Ozero,type,
% 0.30/0.46 zero:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Obot,type,
% 0.30/0.46 bot:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Oord,type,
% 0.30/0.46 ord:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Oorder,type,
% 0.30/0.46 order:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Olinorder,type,
% 0.30/0.46 linorder:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Opreorder,type,
% 0.30/0.46 preorder:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Rings_Ozero__neq__one,type,
% 0.30/0.46 zero_neq_one:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Oorder__bot,type,
% 0.30/0.46 order_bot:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 0.30/0.46 linord1659791738miring:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.30/0.46 canoni770627133id_add:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Equiv__Relations_Oequiv,type,
% 0.30/0.46 equiv_equiv:
% 0.30/0.46 !>[A: $tType] : ( ( set @ A ) > ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.30/0.46 one_one:
% 0.30/0.46 !>[A: $tType] : A ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.30/0.46 zero_zero:
% 0.30/0.46 !>[A: $tType] : A ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_LabeledGraphSemantics_OStandard__Constant_OS__Bot,type,
% 0.30/0.46 standard_S_Bot:
% 0.30/0.46 !>[V: $tType] : ( standard_Constant @ V ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_LabeledGraphSemantics_OStandard__Constant_OS__Idt,type,
% 0.30/0.46 standard_S_Idt:
% 0.30/0.46 !>[V: $tType] : ( standard_Constant @ V ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_LabeledGraphSemantics_OgetRel,type,
% 0.30/0.46 getRel:
% 0.30/0.46 !>[B: $tType,A: $tType] : ( B > ( labeled_graph @ B @ A ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_LabeledGraphs_Oedge__preserving,type,
% 0.30/0.46 edge_preserving:
% 0.30/0.46 !>[A: $tType,B: $tType,C: $tType] : ( ( set @ ( product_prod @ A @ B ) ) > ( set @ ( product_prod @ C @ ( product_prod @ A @ A ) ) ) > ( set @ ( product_prod @ C @ ( product_prod @ B @ B ) ) ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_LabeledGraphs_Ograph__homomorphism,type,
% 0.30/0.46 graph_homomorphism:
% 0.30/0.46 !>[A: $tType,B: $tType,C: $tType] : ( ( labeled_graph @ A @ B ) > ( labeled_graph @ A @ C ) > ( set @ ( product_prod @ B @ C ) ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_LabeledGraphs_Ograph__union,type,
% 0.30/0.46 graph_union:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( ( labeled_graph @ A @ B ) > ( labeled_graph @ A @ B ) > ( labeled_graph @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_LabeledGraphs_Olabeled__graph_OLG,type,
% 0.30/0.46 labeled_LG:
% 0.30/0.46 !>[L: $tType,V: $tType] : ( ( set @ ( product_prod @ L @ ( product_prod @ V @ V ) ) ) > ( set @ V ) > ( labeled_graph @ L @ V ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_LabeledGraphs_Olabeled__graph_Oedges,type,
% 0.30/0.46 labeled_edges:
% 0.30/0.46 !>[L: $tType,V: $tType] : ( ( labeled_graph @ L @ V ) > ( set @ ( product_prod @ L @ ( product_prod @ V @ V ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_LabeledGraphs_Olabeled__graph_Overtices,type,
% 0.30/0.46 labeled_vertices:
% 0.30/0.46 !>[L: $tType,V: $tType] : ( ( labeled_graph @ L @ V ) > ( set @ V ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_LabeledGraphs_Omap__graph,type,
% 0.30/0.46 map_graph:
% 0.30/0.46 !>[C: $tType,B: $tType,A: $tType] : ( ( set @ ( product_prod @ C @ B ) ) > ( labeled_graph @ A @ C ) > ( labeled_graph @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_LabeledGraphs_Oon__triple,type,
% 0.30/0.46 on_triple:
% 0.30/0.46 !>[B: $tType,C: $tType,A: $tType] : ( ( set @ ( product_prod @ B @ C ) ) > ( set @ ( product_prod @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( product_prod @ A @ ( product_prod @ C @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_LabeledGraphs_Orestrict,type,
% 0.30/0.46 restrict:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( ( labeled_graph @ A @ B ) > ( labeled_graph @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_MissingRelation_Ounivalent,type,
% 0.30/0.46 univalent:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ B ) ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.30/0.46 bot_bot:
% 0.30/0.46 !>[A: $tType] : A ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.30/0.46 ord_less_eq:
% 0.30/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair,type,
% 0.30/0.46 product_Pair:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.30/0.46 product_rec_prod:
% 0.30/0.46 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Relation_ODomain,type,
% 0.30/0.46 domain:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ B ) ) > ( set @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Relation_OId__on,type,
% 0.30/0.46 id_on:
% 0.30/0.46 !>[A: $tType] : ( ( set @ A ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Relation_OImage,type,
% 0.30/0.46 image:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ B ) ) > ( set @ A ) > ( set @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_RulesAndChains_Omaintained,type,
% 0.30/0.46 maintained:
% 0.30/0.46 !>[L: $tType,X: $tType,V: $tType] : ( ( product_prod @ ( labeled_graph @ L @ X ) @ ( labeled_graph @ L @ X ) ) > ( labeled_graph @ L @ V ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_OCollect,type,
% 0.30/0.46 collect:
% 0.30/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Oinsert,type,
% 0.30/0.46 insert:
% 0.30/0.46 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Ois__singleton,type,
% 0.30/0.46 is_singleton:
% 0.30/0.46 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Othe__elem,type,
% 0.30/0.46 the_elem:
% 0.30/0.46 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_StandardRules__Mirabelle__xlrcbcygrg_Ocongruence__rule,type,
% 0.30/0.46 standa1068660421e_rule:
% 0.30/0.46 !>[L: $tType] : ( L > L > ( product_prod @ ( labeled_graph @ L @ nat ) @ ( labeled_graph @ L @ nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_StandardRules__Mirabelle__xlrcbcygrg_Ononempty__rule,type,
% 0.30/0.46 standa244753842y_rule:
% 0.30/0.46 !>[L: $tType] : ( product_prod @ ( labeled_graph @ L @ nat ) @ ( labeled_graph @ L @ nat ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_StandardRules__Mirabelle__xlrcbcygrg_Oreflexivity__rule,type,
% 0.30/0.46 standa245363227y_rule:
% 0.30/0.46 !>[L: $tType] : ( L > ( product_prod @ ( labeled_graph @ L @ nat ) @ ( labeled_graph @ L @ nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_StandardRules__Mirabelle__xlrcbcygrg_Osymmetry__rule,type,
% 0.30/0.46 standa1805702094y_rule:
% 0.30/0.46 !>[L: $tType] : ( L > ( product_prod @ ( labeled_graph @ L @ nat ) @ ( labeled_graph @ L @ nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_StandardRules__Mirabelle__xlrcbcygrg_Otop__rule,type,
% 0.30/0.46 standa400804411p_rule:
% 0.30/0.46 !>[L: $tType] : ( L > ( product_prod @ ( labeled_graph @ L @ nat ) @ ( labeled_graph @ L @ nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_StandardRules__Mirabelle__xlrcbcygrg_Otransitive__rule,type,
% 0.30/0.46 standa2114124375e_rule:
% 0.30/0.46 !>[L: $tType] : ( L > ( product_prod @ ( labeled_graph @ L @ nat ) @ ( labeled_graph @ L @ nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member,type,
% 0.30/0.46 member:
% 0.30/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_G,type,
% 0.30/0.46 g: labeled_graph @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_f____,type,
% 0.30/0.46 f: set @ ( product_prod @ nat @ ( sum_sum @ a @ b ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_l,type,
% 0.30/0.46 l: standard_Constant @ a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_v____,type,
% 0.30/0.46 v: sum_sum @ a @ b ).
% 0.30/0.46
% 0.30/0.46 % Relevant facts (253)
% 0.30/0.46 thf(fact_0_g,axiom,
% 0.30/0.46 ( g
% 0.30/0.46 = ( restrict @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) @ g ) ) ).
% 0.30/0.46
% 0.30/0.46 % g
% 0.30/0.46 thf(fact_1_v,axiom,
% 0.30/0.46 member @ ( sum_sum @ a @ b ) @ v @ ( labeled_vertices @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) @ g ) ).
% 0.30/0.46
% 0.30/0.46 % v
% 0.30/0.46 thf(fact_2__092_060open_062edge__preserving_A_123_I0_058_058_063_Hc1_M_Av_J_125_A_123_IS__Idt_M_A0_058_058_063_Hc1_M_A0_058_058_063_Hc1_J_125_A_Iedges_AG_J_092_060close_062,axiom,
% 0.30/0.46 ! [C2: $tType] :
% 0.30/0.46 ( ( zero @ C2 )
% 0.30/0.46 => ( edge_preserving @ C2 @ ( sum_sum @ a @ b ) @ ( standard_Constant @ a ) @ ( insert @ ( product_prod @ C2 @ ( sum_sum @ a @ b ) ) @ ( product_Pair @ C2 @ ( sum_sum @ a @ b ) @ ( zero_zero @ C2 ) @ v ) @ ( bot_bot @ ( set @ ( product_prod @ C2 @ ( sum_sum @ a @ b ) ) ) ) ) @ ( insert @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ C2 @ C2 ) ) @ ( product_Pair @ ( standard_Constant @ a ) @ ( product_prod @ C2 @ C2 ) @ ( standard_S_Idt @ a ) @ ( product_Pair @ C2 @ C2 @ ( zero_zero @ C2 ) @ ( zero_zero @ C2 ) ) ) @ ( bot_bot @ ( set @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ C2 @ C2 ) ) ) ) ) @ ( labeled_edges @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) @ g ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>edge_preserving {(0::?'c1, v)} {(S_Idt, 0::?'c1, 0::?'c1)} (edges G)\<close>
% 0.30/0.46 thf(fact_3_r,axiom,
% 0.30/0.46 ord_less_eq @ ( set @ ( sum_sum @ a @ b ) ) @ ( image @ nat @ ( sum_sum @ a @ b ) @ f @ ( insert @ nat @ ( zero_zero @ nat ) @ ( bot_bot @ ( set @ nat ) ) ) ) @ ( labeled_vertices @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) @ g ) ).
% 0.30/0.46
% 0.30/0.46 % r
% 0.30/0.46 thf(fact_4_f,axiom,
% 0.30/0.46 ( f
% 0.30/0.46 = ( insert @ ( product_prod @ nat @ ( sum_sum @ a @ b ) ) @ ( product_Pair @ nat @ ( sum_sum @ a @ b ) @ ( zero_zero @ nat ) @ v ) @ ( bot_bot @ ( set @ ( product_prod @ nat @ ( sum_sum @ a @ b ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % f
% 0.30/0.46 thf(fact_5_d,axiom,
% 0.30/0.46 ( ( domain @ nat @ ( sum_sum @ a @ b ) @ f )
% 0.30/0.46 = ( insert @ nat @ ( zero_zero @ nat ) @ ( bot_bot @ ( set @ nat ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % d
% 0.30/0.46 thf(fact_6_graph__single,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,A2: A,B2: B,C3: B] :
% 0.30/0.46 ( ( labeled_LG @ A @ B @ ( insert @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( product_Pair @ A @ ( product_prod @ B @ B ) @ A2 @ ( product_Pair @ B @ B @ B2 @ C3 ) ) @ ( bot_bot @ ( set @ ( product_prod @ A @ ( product_prod @ B @ B ) ) ) ) ) @ ( insert @ B @ B2 @ ( insert @ B @ C3 @ ( bot_bot @ ( set @ B ) ) ) ) )
% 0.30/0.46 = ( restrict @ A @ B @ ( labeled_LG @ A @ B @ ( insert @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( product_Pair @ A @ ( product_prod @ B @ B ) @ A2 @ ( product_Pair @ B @ B @ B2 @ C3 ) ) @ ( bot_bot @ ( set @ ( product_prod @ A @ ( product_prod @ B @ B ) ) ) ) ) @ ( insert @ B @ B2 @ ( insert @ B @ C3 @ ( bot_bot @ ( set @ B ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % graph_single
% 0.30/0.46 thf(fact_7__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062v_O_A_I0_M_Av_J_A_092_060in_062_Af_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.30/0.46 ~ ! [V2: sum_sum @ a @ b] :
% 0.30/0.46 ~ ( member @ ( product_prod @ nat @ ( sum_sum @ a @ b ) ) @ ( product_Pair @ nat @ ( sum_sum @ a @ b ) @ ( zero_zero @ nat ) @ V2 ) @ f ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>\<And>thesis. (\<And>v. (0, v) \<in> f \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.30/0.46 thf(fact_8_u,axiom,
% 0.30/0.46 univalent @ nat @ ( sum_sum @ a @ b ) @ f ).
% 0.30/0.46
% 0.30/0.46 % u
% 0.30/0.46 thf(fact_9_Domain__insert,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,A2: A,B2: B,R: set @ ( product_prod @ A @ B )] :
% 0.30/0.46 ( ( domain @ A @ B @ ( insert @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ B2 ) @ R ) )
% 0.30/0.46 = ( insert @ A @ A2 @ ( domain @ A @ B @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Domain_insert
% 0.30/0.46 thf(fact_10_Image__singleton__iff,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,B2: A,R: set @ ( product_prod @ B @ A ),A2: B] :
% 0.30/0.46 ( ( member @ A @ B2 @ ( image @ B @ A @ R @ ( insert @ B @ A2 @ ( bot_bot @ ( set @ B ) ) ) ) )
% 0.30/0.46 = ( member @ ( product_prod @ B @ A ) @ ( product_Pair @ B @ A @ A2 @ B2 ) @ R ) ) ).
% 0.30/0.46
% 0.30/0.46 % Image_singleton_iff
% 0.30/0.46 thf(fact_11_graph__empty__e,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,V3: set @ B] :
% 0.30/0.46 ( ( labeled_LG @ A @ B @ ( bot_bot @ ( set @ ( product_prod @ A @ ( product_prod @ B @ B ) ) ) ) @ V3 )
% 0.30/0.46 = ( restrict @ A @ B @ ( labeled_LG @ A @ B @ ( bot_bot @ ( set @ ( product_prod @ A @ ( product_prod @ B @ B ) ) ) ) @ V3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % graph_empty_e
% 0.30/0.46 thf(fact_12_labeled__graph_Ocollapse,axiom,
% 0.30/0.46 ! [V: $tType,L: $tType,Labeled_graph: labeled_graph @ L @ V] :
% 0.30/0.46 ( ( labeled_LG @ L @ V @ ( labeled_edges @ L @ V @ Labeled_graph ) @ ( labeled_vertices @ L @ V @ Labeled_graph ) )
% 0.30/0.46 = Labeled_graph ) ).
% 0.30/0.46
% 0.30/0.46 % labeled_graph.collapse
% 0.30/0.46 thf(fact_13_Domain__empty,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( domain @ A @ B @ ( bot_bot @ ( set @ ( product_prod @ A @ B ) ) ) )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Domain_empty
% 0.30/0.46 thf(fact_14_Image__empty1,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,X2: set @ B] :
% 0.30/0.46 ( ( image @ B @ A @ ( bot_bot @ ( set @ ( product_prod @ B @ A ) ) ) @ X2 )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Image_empty1
% 0.30/0.46 thf(fact_15_restrict__idemp,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,X3: labeled_graph @ A @ B] :
% 0.30/0.46 ( ( restrict @ A @ B @ ( restrict @ A @ B @ X3 ) )
% 0.30/0.46 = ( restrict @ A @ B @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % restrict_idemp
% 0.30/0.46 thf(fact_16_labeled__graph_Oinject,axiom,
% 0.30/0.46 ! [L: $tType,V: $tType,X1: set @ ( product_prod @ L @ ( product_prod @ V @ V ) ),X22: set @ V,Y1: set @ ( product_prod @ L @ ( product_prod @ V @ V ) ),Y2: set @ V] :
% 0.30/0.46 ( ( ( labeled_LG @ L @ V @ X1 @ X22 )
% 0.30/0.46 = ( labeled_LG @ L @ V @ Y1 @ Y2 ) )
% 0.30/0.46 = ( ( X1 = Y1 )
% 0.30/0.46 & ( X22 = Y2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % labeled_graph.inject
% 0.30/0.46 thf(fact_17_v__gr,axiom,
% 0.30/0.46 ! [A3: sum_sum @ a @ b,B3: sum_sum @ a @ b] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ ( sum_sum @ a @ b ) @ ( sum_sum @ a @ b ) ) ) @ ( product_Pair @ ( standard_Constant @ a ) @ ( product_prod @ ( sum_sum @ a @ b ) @ ( sum_sum @ a @ b ) ) @ ( standard_S_Idt @ a ) @ ( product_Pair @ ( sum_sum @ a @ b ) @ ( sum_sum @ a @ b ) @ A3 @ B3 ) ) @ ( labeled_edges @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) @ g ) )
% 0.30/0.46 = ( ( member @ ( sum_sum @ a @ b ) @ A3 @ ( labeled_vertices @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) @ g ) )
% 0.30/0.46 & ( B3 = A3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % v_gr
% 0.30/0.46 thf(fact_18__092_060open_062_IS__Idt_M_Av_M_Av_J_A_092_060in_062_Aedges_AG_092_060close_062,axiom,
% 0.30/0.46 member @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ ( sum_sum @ a @ b ) @ ( sum_sum @ a @ b ) ) ) @ ( product_Pair @ ( standard_Constant @ a ) @ ( product_prod @ ( sum_sum @ a @ b ) @ ( sum_sum @ a @ b ) ) @ ( standard_S_Idt @ a ) @ ( product_Pair @ ( sum_sum @ a @ b ) @ ( sum_sum @ a @ b ) @ v @ v ) ) @ ( labeled_edges @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) @ g ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>(S_Idt, v, v) \<in> edges G\<close>
% 0.30/0.46 thf(fact_19_ImageI,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,A2: A,B2: B,R: set @ ( product_prod @ A @ B ),A4: set @ A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ B2 ) @ R )
% 0.30/0.46 => ( ( member @ A @ A2 @ A4 )
% 0.30/0.46 => ( member @ B @ B2 @ ( image @ A @ B @ R @ A4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ImageI
% 0.30/0.46 thf(fact_20_Image__empty2,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,R2: set @ ( product_prod @ B @ A )] :
% 0.30/0.46 ( ( image @ B @ A @ R2 @ ( bot_bot @ ( set @ B ) ) )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Image_empty2
% 0.30/0.46 thf(fact_21_vertices__restrict,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,G: labeled_graph @ B @ A] :
% 0.30/0.46 ( ( labeled_vertices @ B @ A @ ( restrict @ B @ A @ G ) )
% 0.30/0.46 = ( labeled_vertices @ B @ A @ G ) ) ).
% 0.30/0.46
% 0.30/0.46 % vertices_restrict
% 0.30/0.46 thf(fact_22__092_060open_062graph__homomorphism_A_ILG_A_123_125_A_1230_125_J_AG_Af_092_060close_062,axiom,
% 0.30/0.46 graph_homomorphism @ ( standard_Constant @ a ) @ nat @ ( sum_sum @ a @ b ) @ ( labeled_LG @ ( standard_Constant @ a ) @ nat @ ( bot_bot @ ( set @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) ) ) ) @ ( insert @ nat @ ( zero_zero @ nat ) @ ( bot_bot @ ( set @ nat ) ) ) ) @ g @ f ).
% 0.30/0.46
% 0.30/0.46 % \<open>graph_homomorphism (LG {} {0}) G f\<close>
% 0.30/0.46 thf(fact_23_labeled__graph_Oexhaust,axiom,
% 0.30/0.46 ! [L: $tType,V: $tType,Y: labeled_graph @ L @ V] :
% 0.30/0.46 ~ ! [X12: set @ ( product_prod @ L @ ( product_prod @ V @ V ) ),X23: set @ V] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( labeled_LG @ L @ V @ X12 @ X23 ) ) ).
% 0.30/0.46
% 0.30/0.46 % labeled_graph.exhaust
% 0.30/0.46 thf(fact_24_labeled__graph_Oinduct,axiom,
% 0.30/0.46 ! [V: $tType,L: $tType,P: ( labeled_graph @ L @ V ) > $o,Labeled_graph: labeled_graph @ L @ V] :
% 0.30/0.46 ( ! [X1a: set @ ( product_prod @ L @ ( product_prod @ V @ V ) ),X2a: set @ V] : ( P @ ( labeled_LG @ L @ V @ X1a @ X2a ) )
% 0.30/0.46 => ( P @ Labeled_graph ) ) ).
% 0.30/0.46
% 0.30/0.46 % labeled_graph.induct
% 0.30/0.46 thf(fact_25_rev__ImageI,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,A2: A,A4: set @ A,B2: B,R: set @ ( product_prod @ A @ B )] :
% 0.30/0.46 ( ( member @ A @ A2 @ A4 )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ B2 ) @ R )
% 0.30/0.46 => ( member @ B @ B2 @ ( image @ A @ B @ R @ A4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rev_ImageI
% 0.30/0.46 thf(fact_26_Image__iff,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,B2: A,R: set @ ( product_prod @ B @ A ),A4: set @ B] :
% 0.30/0.46 ( ( member @ A @ B2 @ ( image @ B @ A @ R @ A4 ) )
% 0.30/0.46 = ( ? [X4: B] :
% 0.30/0.46 ( ( member @ B @ X4 @ A4 )
% 0.30/0.46 & ( member @ ( product_prod @ B @ A ) @ ( product_Pair @ B @ A @ X4 @ B2 ) @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Image_iff
% 0.30/0.46 thf(fact_27_ImageE,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,B2: A,R: set @ ( product_prod @ B @ A ),A4: set @ B] :
% 0.30/0.46 ( ( member @ A @ B2 @ ( image @ B @ A @ R @ A4 ) )
% 0.30/0.46 => ~ ! [X5: B] :
% 0.30/0.46 ( ( member @ ( product_prod @ B @ A ) @ ( product_Pair @ B @ A @ X5 @ B2 ) @ R )
% 0.30/0.46 => ~ ( member @ B @ X5 @ A4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ImageE
% 0.30/0.46 thf(fact_28_Image__mono,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,R3: set @ ( product_prod @ A @ B ),R: set @ ( product_prod @ A @ B ),A5: set @ A,A4: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R3 @ R )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ A5 @ A4 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ B ) @ ( image @ A @ B @ R3 @ A5 ) @ ( image @ A @ B @ R @ A4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Image_mono
% 0.30/0.46 thf(fact_29_Domain_Oinducts,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,X3: A,R: set @ ( product_prod @ A @ B ),P: A > $o] :
% 0.30/0.46 ( ( member @ A @ X3 @ ( domain @ A @ B @ R ) )
% 0.30/0.46 => ( ! [A6: A,B4: B] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A6 @ B4 ) @ R )
% 0.30/0.46 => ( P @ A6 ) )
% 0.30/0.46 => ( P @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Domain.inducts
% 0.30/0.46 thf(fact_30_Domain_ODomainI,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,A2: A,B2: B,R: set @ ( product_prod @ A @ B )] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ B2 ) @ R )
% 0.30/0.46 => ( member @ A @ A2 @ ( domain @ A @ B @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Domain.DomainI
% 0.30/0.46 thf(fact_31_Domain_Osimps,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,A2: A,R: set @ ( product_prod @ A @ B )] :
% 0.30/0.46 ( ( member @ A @ A2 @ ( domain @ A @ B @ R ) )
% 0.30/0.46 = ( ? [A7: A,B5: B] :
% 0.30/0.46 ( ( A2 = A7 )
% 0.30/0.46 & ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A7 @ B5 ) @ R ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Domain.simps
% 0.30/0.46 thf(fact_32_Domain_Ocases,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,A2: A,R: set @ ( product_prod @ A @ B )] :
% 0.30/0.46 ( ( member @ A @ A2 @ ( domain @ A @ B @ R ) )
% 0.30/0.46 => ~ ! [B4: B] :
% 0.30/0.46 ~ ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ B4 ) @ R ) ) ).
% 0.30/0.46
% 0.30/0.46 % Domain.cases
% 0.30/0.46 thf(fact_33_Domain__iff,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,A2: A,R: set @ ( product_prod @ A @ B )] :
% 0.30/0.46 ( ( member @ A @ A2 @ ( domain @ A @ B @ R ) )
% 0.30/0.46 = ( ? [Y3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ Y3 ) @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Domain_iff
% 0.30/0.46 thf(fact_34_DomainE,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,A2: A,R: set @ ( product_prod @ A @ B )] :
% 0.30/0.46 ( ( member @ A @ A2 @ ( domain @ A @ B @ R ) )
% 0.30/0.46 => ~ ! [B4: B] :
% 0.30/0.46 ~ ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ B4 ) @ R ) ) ).
% 0.30/0.46
% 0.30/0.46 % DomainE
% 0.30/0.46 thf(fact_35_Domain__mono,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R @ S )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ ( domain @ A @ B @ R ) @ ( domain @ A @ B @ S ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Domain_mono
% 0.30/0.46 thf(fact_36_labeled__graph_Oexpand,axiom,
% 0.30/0.46 ! [V: $tType,L: $tType,Labeled_graph: labeled_graph @ L @ V,Labeled_graph2: labeled_graph @ L @ V] :
% 0.30/0.46 ( ( ( ( labeled_edges @ L @ V @ Labeled_graph )
% 0.30/0.46 = ( labeled_edges @ L @ V @ Labeled_graph2 ) )
% 0.30/0.46 & ( ( labeled_vertices @ L @ V @ Labeled_graph )
% 0.30/0.46 = ( labeled_vertices @ L @ V @ Labeled_graph2 ) ) )
% 0.30/0.46 => ( Labeled_graph = Labeled_graph2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % labeled_graph.expand
% 0.30/0.46 thf(fact_37_labeled__graph_Osel_I2_J,axiom,
% 0.30/0.46 ! [L: $tType,V: $tType,X1: set @ ( product_prod @ L @ ( product_prod @ V @ V ) ),X22: set @ V] :
% 0.30/0.46 ( ( labeled_vertices @ L @ V @ ( labeled_LG @ L @ V @ X1 @ X22 ) )
% 0.30/0.46 = X22 ) ).
% 0.30/0.46
% 0.30/0.46 % labeled_graph.sel(2)
% 0.30/0.46 thf(fact_38_labeled__graph_Osel_I1_J,axiom,
% 0.30/0.46 ! [V: $tType,L: $tType,X1: set @ ( product_prod @ L @ ( product_prod @ V @ V ) ),X22: set @ V] :
% 0.30/0.46 ( ( labeled_edges @ L @ V @ ( labeled_LG @ L @ V @ X1 @ X22 ) )
% 0.30/0.46 = X1 ) ).
% 0.30/0.46
% 0.30/0.46 % labeled_graph.sel(1)
% 0.30/0.46 thf(fact_39_Domain__empty__iff,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B )] :
% 0.30/0.46 ( ( ( domain @ A @ B @ R )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( R
% 0.30/0.46 = ( bot_bot @ ( set @ ( product_prod @ A @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Domain_empty_iff
% 0.30/0.46 thf(fact_40_edge__preserving__atomic,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C: $tType,H1: set @ ( product_prod @ A @ B ),E1: set @ ( product_prod @ C @ ( product_prod @ A @ A ) ),E2: set @ ( product_prod @ C @ ( product_prod @ B @ B ) ),V1: A,V12: B,V22: A,V23: B,K: C] :
% 0.30/0.46 ( ( edge_preserving @ A @ B @ C @ H1 @ E1 @ E2 )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ V1 @ V12 ) @ H1 )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ V22 @ V23 ) @ H1 )
% 0.30/0.46 => ( ( member @ ( product_prod @ C @ ( product_prod @ A @ A ) ) @ ( product_Pair @ C @ ( product_prod @ A @ A ) @ K @ ( product_Pair @ A @ A @ V1 @ V22 ) ) @ E1 )
% 0.30/0.46 => ( member @ ( product_prod @ C @ ( product_prod @ B @ B ) ) @ ( product_Pair @ C @ ( product_prod @ B @ B ) @ K @ ( product_Pair @ B @ B @ V12 @ V23 ) ) @ E2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % edge_preserving_atomic
% 0.30/0.46 thf(fact_41_labeled__graph_Oexhaust__sel,axiom,
% 0.30/0.46 ! [V: $tType,L: $tType,Labeled_graph: labeled_graph @ L @ V] :
% 0.30/0.46 ( Labeled_graph
% 0.30/0.46 = ( labeled_LG @ L @ V @ ( labeled_edges @ L @ V @ Labeled_graph ) @ ( labeled_vertices @ L @ V @ Labeled_graph ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % labeled_graph.exhaust_sel
% 0.30/0.46 thf(fact_42_singleton__insert__inj__eq_H,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,A4: set @ A,B2: A] :
% 0.30/0.46 ( ( ( insert @ A @ A2 @ A4 )
% 0.30/0.46 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 = ( ( A2 = B2 )
% 0.30/0.46 & ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % singleton_insert_inj_eq'
% 0.30/0.46 thf(fact_43_singleton__insert__inj__eq,axiom,
% 0.30/0.46 ! [A: $tType,B2: A,A2: A,A4: set @ A] :
% 0.30/0.46 ( ( ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( insert @ A @ A2 @ A4 ) )
% 0.30/0.46 = ( ( A2 = B2 )
% 0.30/0.46 & ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % singleton_insert_inj_eq
% 0.30/0.46 thf(fact_44_univalent__empty,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] : ( univalent @ A @ B @ ( bot_bot @ ( set @ ( product_prod @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % univalent_empty
% 0.30/0.46 thf(fact_45_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,P: A > $o] :
% 0.30/0.46 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.30/0.46 = ( P @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_46_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] :
% 0.30/0.46 ( ( collect @ A
% 0.30/0.46 @ ^ [X4: A] : ( member @ A @ X4 @ A4 ) )
% 0.30/0.46 = A4 ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_47_Collect__cong,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.46 ( ! [X5: A] :
% 0.30/0.46 ( ( P @ X5 )
% 0.30/0.46 = ( Q @ X5 ) )
% 0.30/0.46 => ( ( collect @ A @ P )
% 0.30/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_cong
% 0.30/0.46 thf(fact_48_ext,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,F: A > B,G2: A > B] :
% 0.30/0.46 ( ! [X5: A] :
% 0.30/0.46 ( ( F @ X5 )
% 0.30/0.46 = ( G2 @ X5 ) )
% 0.30/0.46 => ( F = G2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % ext
% 0.30/0.46 thf(fact_49_insert__subset,axiom,
% 0.30/0.46 ! [A: $tType,X3: A,A4: set @ A,B6: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X3 @ A4 ) @ B6 )
% 0.30/0.46 = ( ( member @ A @ X3 @ B6 )
% 0.30/0.46 & ( ord_less_eq @ ( set @ A ) @ A4 @ B6 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_subset
% 0.30/0.46 thf(fact_50_singletonI,axiom,
% 0.30/0.46 ! [A: $tType,A2: A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % singletonI
% 0.30/0.46 thf(fact_51_empty__subsetI,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A4 ) ).
% 0.30/0.46
% 0.30/0.46 % empty_subsetI
% 0.30/0.46 thf(fact_52_subset__empty,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( A4
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_empty
% 0.30/0.46 thf(fact_53_le__zero__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( canoni770627133id_add @ A )
% 0.30/0.46 => ! [N: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 0.30/0.46 = ( N
% 0.30/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_zero_eq
% 0.30/0.46 thf(fact_54_reflexivity__rule__def,axiom,
% 0.30/0.46 ! [L: $tType] :
% 0.30/0.46 ( ( standa245363227y_rule @ L )
% 0.30/0.46 = ( ^ [T2: L] : ( product_Pair @ ( labeled_graph @ L @ nat ) @ ( labeled_graph @ L @ nat ) @ ( labeled_LG @ L @ nat @ ( bot_bot @ ( set @ ( product_prod @ L @ ( product_prod @ nat @ nat ) ) ) ) @ ( insert @ nat @ ( zero_zero @ nat ) @ ( bot_bot @ ( set @ nat ) ) ) ) @ ( labeled_LG @ L @ nat @ ( insert @ ( product_prod @ L @ ( product_prod @ nat @ nat ) ) @ ( product_Pair @ L @ ( product_prod @ nat @ nat ) @ T2 @ ( product_Pair @ nat @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ) @ ( bot_bot @ ( set @ ( product_prod @ L @ ( product_prod @ nat @ nat ) ) ) ) ) @ ( insert @ nat @ ( zero_zero @ nat ) @ ( bot_bot @ ( set @ nat ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % reflexivity_rule_def
% 0.30/0.46 thf(fact_55_nonempty__rule__def,axiom,
% 0.30/0.46 ! [L: $tType] :
% 0.30/0.46 ( ( standa244753842y_rule @ L )
% 0.30/0.46 = ( product_Pair @ ( labeled_graph @ L @ nat ) @ ( labeled_graph @ L @ nat ) @ ( labeled_LG @ L @ nat @ ( bot_bot @ ( set @ ( product_prod @ L @ ( product_prod @ nat @ nat ) ) ) ) @ ( bot_bot @ ( set @ nat ) ) ) @ ( labeled_LG @ L @ nat @ ( bot_bot @ ( set @ ( product_prod @ L @ ( product_prod @ nat @ nat ) ) ) ) @ ( insert @ nat @ ( zero_zero @ nat ) @ ( bot_bot @ ( set @ nat ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nonempty_rule_def
% 0.30/0.46 thf(fact_56_empty__iff,axiom,
% 0.30/0.46 ! [A: $tType,C3: A] :
% 0.30/0.46 ~ ( member @ A @ C3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % empty_iff
% 0.30/0.46 thf(fact_57_all__not__in__conv,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] :
% 0.30/0.46 ( ( ! [X4: A] :
% 0.30/0.46 ~ ( member @ A @ X4 @ A4 ) )
% 0.30/0.46 = ( A4
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % all_not_in_conv
% 0.30/0.46 thf(fact_58_Collect__empty__eq,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o] :
% 0.30/0.46 ( ( ( collect @ A @ P )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( ! [X4: A] :
% 0.30/0.46 ~ ( P @ X4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_empty_eq
% 0.30/0.46 thf(fact_59_empty__Collect__eq,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o] :
% 0.30/0.46 ( ( ( bot_bot @ ( set @ A ) )
% 0.30/0.46 = ( collect @ A @ P ) )
% 0.30/0.46 = ( ! [X4: A] :
% 0.30/0.46 ~ ( P @ X4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % empty_Collect_eq
% 0.30/0.46 thf(fact_60_subsetI,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B6: set @ A] :
% 0.30/0.46 ( ! [X5: A] :
% 0.30/0.46 ( ( member @ A @ X5 @ A4 )
% 0.30/0.46 => ( member @ A @ X5 @ B6 ) )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ A4 @ B6 ) ) ).
% 0.30/0.46
% 0.30/0.46 % subsetI
% 0.30/0.46 thf(fact_61_subset__antisym,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B6: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B6 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B6 @ A4 )
% 0.30/0.46 => ( A4 = B6 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_antisym
% 0.30/0.46 thf(fact_62_insertCI,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B6: set @ A,B2: A] :
% 0.30/0.46 ( ( ~ ( member @ A @ A2 @ B6 )
% 0.30/0.46 => ( A2 = B2 ) )
% 0.30/0.46 => ( member @ A @ A2 @ ( insert @ A @ B2 @ B6 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertCI
% 0.30/0.46 thf(fact_63_insert__iff,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A,A4: set @ A] :
% 0.30/0.46 ( ( member @ A @ A2 @ ( insert @ A @ B2 @ A4 ) )
% 0.30/0.46 = ( ( A2 = B2 )
% 0.30/0.46 | ( member @ A @ A2 @ A4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_iff
% 0.30/0.46 thf(fact_64_insert__absorb2,axiom,
% 0.30/0.46 ! [A: $tType,X3: A,A4: set @ A] :
% 0.30/0.46 ( ( insert @ A @ X3 @ ( insert @ A @ X3 @ A4 ) )
% 0.30/0.46 = ( insert @ A @ X3 @ A4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_absorb2
% 0.30/0.46 thf(fact_65_graph__homomorphism__empty,axiom,
% 0.30/0.46 ! [B: $tType,C: $tType,A: $tType,G: labeled_graph @ A @ C,F: set @ ( product_prod @ B @ C )] :
% 0.30/0.46 ( ( graph_homomorphism @ A @ B @ C @ ( labeled_LG @ A @ B @ ( bot_bot @ ( set @ ( product_prod @ A @ ( product_prod @ B @ B ) ) ) ) @ ( bot_bot @ ( set @ B ) ) ) @ G @ F )
% 0.30/0.46 = ( ( F
% 0.30/0.46 = ( bot_bot @ ( set @ ( product_prod @ B @ C ) ) ) )
% 0.30/0.46 & ( G
% 0.30/0.46 = ( restrict @ A @ C @ G ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % graph_homomorphism_empty
% 0.30/0.46 thf(fact_66_edge__preserving__subset,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C: $tType,R_1: set @ ( product_prod @ A @ B ),R_2: set @ ( product_prod @ A @ B ),E_1: set @ ( product_prod @ C @ ( product_prod @ A @ A ) ),E_2: set @ ( product_prod @ C @ ( product_prod @ A @ A ) ),G: set @ ( product_prod @ C @ ( product_prod @ B @ B ) )] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R_1 @ R_2 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ ( product_prod @ C @ ( product_prod @ A @ A ) ) ) @ E_1 @ E_2 )
% 0.30/0.46 => ( ( edge_preserving @ A @ B @ C @ R_2 @ E_2 @ G )
% 0.30/0.46 => ( edge_preserving @ A @ B @ C @ R_1 @ E_1 @ G ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % edge_preserving_subset
% 0.30/0.46 thf(fact_67_subrelI,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 0.30/0.46 ( ! [X5: A,Y4: B] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X5 @ Y4 ) @ R )
% 0.30/0.46 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X5 @ Y4 ) @ S ) )
% 0.30/0.46 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R @ S ) ) ).
% 0.30/0.46
% 0.30/0.46 % subrelI
% 0.30/0.46 thf(fact_68_restrict__subsD,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,G: labeled_graph @ A @ B] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ ( product_prod @ B @ B ) ) ) @ ( labeled_edges @ A @ B @ G ) @ ( labeled_edges @ A @ B @ ( restrict @ A @ B @ G ) ) )
% 0.30/0.46 => ( G
% 0.30/0.46 = ( restrict @ A @ B @ G ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % restrict_subsD
% 0.30/0.46 thf(fact_69_zero__reorient,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( zero @ A )
% 0.30/0.46 => ! [X3: A] :
% 0.30/0.46 ( ( ( zero_zero @ A )
% 0.30/0.46 = X3 )
% 0.30/0.46 = ( X3
% 0.30/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_reorient
% 0.30/0.46 thf(fact_70_emptyE,axiom,
% 0.30/0.46 ! [A: $tType,A2: A] :
% 0.30/0.46 ~ ( member @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % emptyE
% 0.30/0.46 thf(fact_71_equals0D,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,A2: A] :
% 0.30/0.46 ( ( A4
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 => ~ ( member @ A @ A2 @ A4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % equals0D
% 0.30/0.46 thf(fact_72_equals0I,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] :
% 0.30/0.46 ( ! [Y4: A] :
% 0.30/0.46 ~ ( member @ A @ Y4 @ A4 )
% 0.30/0.46 => ( A4
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % equals0I
% 0.30/0.46 thf(fact_73_ex__in__conv,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] :
% 0.30/0.46 ( ( ? [X4: A] : ( member @ A @ X4 @ A4 ) )
% 0.30/0.46 = ( A4
% 0.30/0.46 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ex_in_conv
% 0.30/0.46 thf(fact_74_in__mono,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B6: set @ A,X3: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B6 )
% 0.30/0.46 => ( ( member @ A @ X3 @ A4 )
% 0.30/0.46 => ( member @ A @ X3 @ B6 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % in_mono
% 0.30/0.46 thf(fact_75_subsetD,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B6: set @ A,C3: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B6 )
% 0.30/0.46 => ( ( member @ A @ C3 @ A4 )
% 0.30/0.46 => ( member @ A @ C3 @ B6 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subsetD
% 0.30/0.46 thf(fact_76_equalityE,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B6: set @ A] :
% 0.30/0.46 ( ( A4 = B6 )
% 0.30/0.46 => ~ ( ( ord_less_eq @ ( set @ A ) @ A4 @ B6 )
% 0.30/0.46 => ~ ( ord_less_eq @ ( set @ A ) @ B6 @ A4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % equalityE
% 0.30/0.46 thf(fact_77_subset__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) )
% 0.30/0.46 = ( ^ [A8: set @ A,B7: set @ A] :
% 0.30/0.46 ! [X4: A] :
% 0.30/0.46 ( ( member @ A @ X4 @ A8 )
% 0.30/0.46 => ( member @ A @ X4 @ B7 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_eq
% 0.30/0.46 thf(fact_78_equalityD1,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B6: set @ A] :
% 0.30/0.46 ( ( A4 = B6 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ A4 @ B6 ) ) ).
% 0.30/0.46
% 0.30/0.46 % equalityD1
% 0.30/0.46 thf(fact_79_equalityD2,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B6: set @ A] :
% 0.30/0.46 ( ( A4 = B6 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ B6 @ A4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % equalityD2
% 0.30/0.46 thf(fact_80_subset__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) )
% 0.30/0.46 = ( ^ [A8: set @ A,B7: set @ A] :
% 0.30/0.46 ! [T2: A] :
% 0.30/0.46 ( ( member @ A @ T2 @ A8 )
% 0.30/0.46 => ( member @ A @ T2 @ B7 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_iff
% 0.30/0.46 thf(fact_81_subset__refl,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ A4 ) ).
% 0.30/0.46
% 0.30/0.46 % subset_refl
% 0.30/0.46 thf(fact_82_Collect__mono,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.46 ( ! [X5: A] :
% 0.30/0.46 ( ( P @ X5 )
% 0.30/0.46 => ( Q @ X5 ) )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mono
% 0.30/0.46 thf(fact_83_subset__trans,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B6: set @ A,C4: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B6 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B6 @ C4 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ A4 @ C4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_trans
% 0.30/0.46 thf(fact_84_set__eq__subset,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ^ [Y5: set @ A,Z: set @ A] : ( Y5 = Z ) )
% 0.30/0.46 = ( ^ [A8: set @ A,B7: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A8 @ B7 )
% 0.30/0.46 & ( ord_less_eq @ ( set @ A ) @ B7 @ A8 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % set_eq_subset
% 0.30/0.46 thf(fact_85_Collect__mono__iff,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.30/0.46 = ( ! [X4: A] :
% 0.30/0.46 ( ( P @ X4 )
% 0.30/0.46 => ( Q @ X4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mono_iff
% 0.30/0.46 thf(fact_86_insertE,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A,A4: set @ A] :
% 0.30/0.46 ( ( member @ A @ A2 @ ( insert @ A @ B2 @ A4 ) )
% 0.30/0.46 => ( ( A2 != B2 )
% 0.30/0.46 => ( member @ A @ A2 @ A4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertE
% 0.30/0.46 thf(fact_87_insertI1,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B6: set @ A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ B6 ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertI1
% 0.30/0.46 thf(fact_88_insertI2,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B6: set @ A,B2: A] :
% 0.30/0.46 ( ( member @ A @ A2 @ B6 )
% 0.30/0.46 => ( member @ A @ A2 @ ( insert @ A @ B2 @ B6 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertI2
% 0.30/0.46 thf(fact_89_Set_Oset__insert,axiom,
% 0.30/0.46 ! [A: $tType,X3: A,A4: set @ A] :
% 0.30/0.46 ( ( member @ A @ X3 @ A4 )
% 0.30/0.46 => ~ ! [B8: set @ A] :
% 0.30/0.46 ( ( A4
% 0.30/0.46 = ( insert @ A @ X3 @ B8 ) )
% 0.30/0.46 => ( member @ A @ X3 @ B8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Set.set_insert
% 0.30/0.46 thf(fact_90_insert__ident,axiom,
% 0.30/0.46 ! [A: $tType,X3: A,A4: set @ A,B6: set @ A] :
% 0.30/0.46 ( ~ ( member @ A @ X3 @ A4 )
% 0.30/0.46 => ( ~ ( member @ A @ X3 @ B6 )
% 0.30/0.46 => ( ( ( insert @ A @ X3 @ A4 )
% 0.30/0.46 = ( insert @ A @ X3 @ B6 ) )
% 0.30/0.46 = ( A4 = B6 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_ident
% 0.30/0.46 thf(fact_91_insert__absorb,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,A4: set @ A] :
% 0.30/0.46 ( ( member @ A @ A2 @ A4 )
% 0.30/0.46 => ( ( insert @ A @ A2 @ A4 )
% 0.30/0.46 = A4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_absorb
% 0.30/0.46 thf(fact_92_insert__eq__iff,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,A4: set @ A,B2: A,B6: set @ A] :
% 0.30/0.46 ( ~ ( member @ A @ A2 @ A4 )
% 0.30/0.46 => ( ~ ( member @ A @ B2 @ B6 )
% 0.30/0.46 => ( ( ( insert @ A @ A2 @ A4 )
% 0.30/0.46 = ( insert @ A @ B2 @ B6 ) )
% 0.30/0.46 = ( ( ( A2 = B2 )
% 0.30/0.46 => ( A4 = B6 ) )
% 0.30/0.46 & ( ( A2 != B2 )
% 0.30/0.46 => ? [C5: set @ A] :
% 0.30/0.46 ( ( A4
% 0.30/0.46 = ( insert @ A @ B2 @ C5 ) )
% 0.30/0.46 & ~ ( member @ A @ B2 @ C5 )
% 0.30/0.46 & ( B6
% 0.30/0.46 = ( insert @ A @ A2 @ C5 ) )
% 0.30/0.46 & ~ ( member @ A @ A2 @ C5 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_eq_iff
% 0.30/0.46 thf(fact_93_insert__commute,axiom,
% 0.30/0.46 ! [A: $tType,X3: A,Y: A,A4: set @ A] :
% 0.30/0.46 ( ( insert @ A @ X3 @ ( insert @ A @ Y @ A4 ) )
% 0.30/0.46 = ( insert @ A @ Y @ ( insert @ A @ X3 @ A4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_commute
% 0.30/0.46 thf(fact_94_mk__disjoint__insert,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,A4: set @ A] :
% 0.30/0.46 ( ( member @ A @ A2 @ A4 )
% 0.30/0.46 => ? [B8: set @ A] :
% 0.30/0.46 ( ( A4
% 0.30/0.46 = ( insert @ A @ A2 @ B8 ) )
% 0.30/0.46 & ~ ( member @ A @ A2 @ B8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mk_disjoint_insert
% 0.30/0.46 thf(fact_95_zero__le,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( canoni770627133id_add @ A )
% 0.30/0.46 => ! [X3: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_le
% 0.30/0.46 thf(fact_96_singletonD,axiom,
% 0.30/0.46 ! [A: $tType,B2: A,A2: A] :
% 0.30/0.46 ( ( member @ A @ B2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 => ( B2 = A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % singletonD
% 0.30/0.46 thf(fact_97_singleton__iff,axiom,
% 0.30/0.46 ! [A: $tType,B2: A,A2: A] :
% 0.30/0.46 ( ( member @ A @ B2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 = ( B2 = A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % singleton_iff
% 0.30/0.46 thf(fact_98_doubleton__eq__iff,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A,C3: A,D: A] :
% 0.30/0.46 ( ( ( insert @ A @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 = ( insert @ A @ C3 @ ( insert @ A @ D @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/0.46 = ( ( ( A2 = C3 )
% 0.30/0.46 & ( B2 = D ) )
% 0.30/0.46 | ( ( A2 = D )
% 0.30/0.46 & ( B2 = C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % doubleton_eq_iff
% 0.30/0.46 thf(fact_99_insert__not__empty,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,A4: set @ A] :
% 0.30/0.46 ( ( insert @ A @ A2 @ A4 )
% 0.30/0.46 != ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_not_empty
% 0.30/0.46 thf(fact_100_singleton__inject,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A] :
% 0.30/0.46 ( ( ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 => ( A2 = B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % singleton_inject
% 0.30/0.46 thf(fact_101_insert__mono,axiom,
% 0.30/0.46 ! [A: $tType,C4: set @ A,D2: set @ A,A2: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ C4 @ D2 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ A2 @ C4 ) @ ( insert @ A @ A2 @ D2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_mono
% 0.30/0.46 thf(fact_102_subset__insert,axiom,
% 0.30/0.46 ! [A: $tType,X3: A,A4: set @ A,B6: set @ A] :
% 0.30/0.46 ( ~ ( member @ A @ X3 @ A4 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ X3 @ B6 ) )
% 0.30/0.46 = ( ord_less_eq @ ( set @ A ) @ A4 @ B6 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_insert
% 0.30/0.46 thf(fact_103_subset__insertI,axiom,
% 0.30/0.46 ! [A: $tType,B6: set @ A,A2: A] : ( ord_less_eq @ ( set @ A ) @ B6 @ ( insert @ A @ A2 @ B6 ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_insertI
% 0.30/0.46 thf(fact_104_subset__insertI2,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B6: set @ A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B6 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ B2 @ B6 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_insertI2
% 0.30/0.46 thf(fact_105_univalentD,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,R2: set @ ( product_prod @ A @ B ),X3: A,Y: B,Z2: B] :
% 0.30/0.46 ( ( univalent @ A @ B @ R2 )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y ) @ R2 )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Z2 ) @ R2 )
% 0.30/0.46 => ( Z2 = Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % univalentD
% 0.30/0.46 thf(fact_106_univalent__def,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( univalent @ A @ B )
% 0.30/0.46 = ( ^ [R4: set @ ( product_prod @ A @ B )] :
% 0.30/0.46 ! [X4: A,Y3: B,Z3: B] :
% 0.30/0.46 ( ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y3 ) @ R4 )
% 0.30/0.46 & ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Z3 ) @ R4 ) )
% 0.30/0.46 => ( Z3 = Y3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % univalent_def
% 0.30/0.46 thf(fact_107_graph__homomorphismI,axiom,
% 0.30/0.46 ! [B: $tType,C: $tType,A: $tType,S: labeled_graph @ B @ A,H: set @ ( product_prod @ A @ C ),T3: labeled_graph @ B @ C] :
% 0.30/0.46 ( ( ( labeled_vertices @ B @ A @ S )
% 0.30/0.46 = ( domain @ A @ C @ H ) )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ C ) @ ( image @ A @ C @ H @ ( labeled_vertices @ B @ A @ S ) ) @ ( labeled_vertices @ B @ C @ T3 ) )
% 0.30/0.46 => ( ( univalent @ A @ C @ H )
% 0.30/0.46 => ( ( edge_preserving @ A @ C @ B @ H @ ( labeled_edges @ B @ A @ S ) @ ( labeled_edges @ B @ C @ T3 ) )
% 0.30/0.46 => ( ( S
% 0.30/0.46 = ( restrict @ B @ A @ S ) )
% 0.30/0.46 => ( ( T3
% 0.30/0.46 = ( restrict @ B @ C @ T3 ) )
% 0.30/0.46 => ( graph_homomorphism @ B @ A @ C @ S @ T3 @ H ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % graph_homomorphismI
% 0.30/0.46 thf(fact_108_graph__homomorphism__def,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( graph_homomorphism @ A @ B @ C )
% 0.30/0.46 = ( ^ [G_1: labeled_graph @ A @ B,G_2: labeled_graph @ A @ C,F2: set @ ( product_prod @ B @ C )] :
% 0.30/0.46 ( ( ( labeled_vertices @ A @ B @ G_1 )
% 0.30/0.46 = ( domain @ B @ C @ F2 ) )
% 0.30/0.46 & ( G_1
% 0.30/0.46 = ( restrict @ A @ B @ G_1 ) )
% 0.30/0.46 & ( G_2
% 0.30/0.46 = ( restrict @ A @ C @ G_2 ) )
% 0.30/0.46 & ( ord_less_eq @ ( set @ C ) @ ( image @ B @ C @ F2 @ ( labeled_vertices @ A @ B @ G_1 ) ) @ ( labeled_vertices @ A @ C @ G_2 ) )
% 0.30/0.46 & ( univalent @ B @ C @ F2 )
% 0.30/0.46 & ( edge_preserving @ B @ C @ A @ F2 @ ( labeled_edges @ A @ B @ G_1 ) @ ( labeled_edges @ A @ C @ G_2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % graph_homomorphism_def
% 0.30/0.46 thf(fact_109_subset__singletonD,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,X3: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 => ( ( A4
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 | ( A4
% 0.30/0.46 = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_singletonD
% 0.30/0.46 thf(fact_110_subset__singleton__iff,axiom,
% 0.30/0.46 ! [A: $tType,X2: set @ A,A2: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ X2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 = ( ( X2
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 | ( X2
% 0.30/0.46 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_singleton_iff
% 0.30/0.46 thf(fact_111_univalent__insert,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,A2: B,R2: set @ ( product_prod @ B @ A ),B2: A] :
% 0.30/0.46 ( ! [C6: A] :
% 0.30/0.46 ~ ( member @ ( product_prod @ B @ A ) @ ( product_Pair @ B @ A @ A2 @ C6 ) @ R2 )
% 0.30/0.46 => ( ( univalent @ B @ A @ ( insert @ ( product_prod @ B @ A ) @ ( product_Pair @ B @ A @ A2 @ B2 ) @ R2 ) )
% 0.30/0.46 = ( univalent @ B @ A @ R2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % univalent_insert
% 0.30/0.46 thf(fact_112_graph__homomorphism__concr__graph,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C: $tType,G: labeled_graph @ A @ B,E: set @ ( product_prod @ A @ ( product_prod @ C @ C ) ),V3: set @ C,X3: set @ ( product_prod @ C @ B )] :
% 0.30/0.46 ( ( G
% 0.30/0.46 = ( restrict @ A @ B @ G ) )
% 0.30/0.46 => ( ( ( labeled_LG @ A @ C @ E @ V3 )
% 0.30/0.46 = ( restrict @ A @ C @ ( labeled_LG @ A @ C @ E @ V3 ) ) )
% 0.30/0.46 => ( ( graph_homomorphism @ A @ C @ B @ ( labeled_LG @ A @ C @ E @ V3 ) @ G @ X3 )
% 0.30/0.46 = ( ( ord_less_eq @ ( set @ B ) @ ( image @ C @ B @ X3 @ V3 ) @ ( labeled_vertices @ A @ B @ G ) )
% 0.30/0.46 & ( ord_less_eq @ ( set @ ( product_prod @ A @ ( product_prod @ B @ B ) ) ) @ ( image @ ( product_prod @ A @ ( product_prod @ C @ C ) ) @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( on_triple @ C @ B @ A @ X3 ) @ E ) @ ( labeled_edges @ A @ B @ G ) )
% 0.30/0.46 & ( univalent @ C @ B @ X3 )
% 0.30/0.46 & ( ( domain @ C @ B @ X3 )
% 0.30/0.46 = V3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % graph_homomorphism_concr_graph
% 0.30/0.46 thf(fact_113_le0,axiom,
% 0.30/0.46 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 0.30/0.46
% 0.30/0.46 % le0
% 0.30/0.46 thf(fact_114_bot__nat__0_Oextremum,axiom,
% 0.30/0.46 ! [A2: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A2 ) ).
% 0.30/0.46
% 0.30/0.46 % bot_nat_0.extremum
% 0.30/0.46 thf(fact_115_the__elem__eq,axiom,
% 0.30/0.46 ! [A: $tType,X3: A] :
% 0.30/0.46 ( ( the_elem @ A @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 = X3 ) ).
% 0.30/0.46
% 0.30/0.46 % the_elem_eq
% 0.30/0.46 thf(fact_116_bot__apply,axiom,
% 0.30/0.46 ! [C: $tType,D3: $tType] :
% 0.30/0.46 ( ( bot @ C )
% 0.30/0.46 => ( ( bot_bot @ ( D3 > C ) )
% 0.30/0.46 = ( ^ [X4: D3] : ( bot_bot @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_apply
% 0.30/0.46 thf(fact_117_prod_Oinject,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,X1: A,X22: B,Y1: A,Y2: B] :
% 0.30/0.46 ( ( ( product_Pair @ A @ B @ X1 @ X22 )
% 0.30/0.46 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 0.30/0.46 = ( ( X1 = Y1 )
% 0.30/0.46 & ( X22 = Y2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod.inject
% 0.30/0.46 thf(fact_118_old_Oprod_Oinject,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,A2: A,B2: B,A9: A,B9: B] :
% 0.30/0.46 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.30/0.46 = ( product_Pair @ A @ B @ A9 @ B9 ) )
% 0.30/0.46 = ( ( A2 = A9 )
% 0.30/0.46 & ( B2 = B9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.inject
% 0.30/0.46 thf(fact_119_order__refl,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_refl
% 0.30/0.46 thf(fact_120_on__triple__univ,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType,F: set @ ( product_prod @ A @ B )] :
% 0.30/0.46 ( ( univalent @ A @ B @ F )
% 0.30/0.46 => ( univalent @ ( product_prod @ C @ ( product_prod @ A @ A ) ) @ ( product_prod @ C @ ( product_prod @ B @ B ) ) @ ( on_triple @ A @ B @ C @ F ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % on_triple_univ
% 0.30/0.46 thf(fact_121_on__triple,axiom,
% 0.30/0.46 ! [B: $tType,C: $tType,A: $tType,L1: A,V1: B,V22: B,L2: A,V32: C,V4: C,R2: set @ ( product_prod @ B @ C )] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( product_prod @ A @ ( product_prod @ C @ C ) ) ) @ ( product_Pair @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( product_prod @ A @ ( product_prod @ C @ C ) ) @ ( product_Pair @ A @ ( product_prod @ B @ B ) @ L1 @ ( product_Pair @ B @ B @ V1 @ V22 ) ) @ ( product_Pair @ A @ ( product_prod @ C @ C ) @ L2 @ ( product_Pair @ C @ C @ V32 @ V4 ) ) ) @ ( on_triple @ B @ C @ A @ R2 ) )
% 0.30/0.46 = ( ( member @ ( product_prod @ B @ C ) @ ( product_Pair @ B @ C @ V1 @ V32 ) @ R2 )
% 0.30/0.46 & ( member @ ( product_prod @ B @ C ) @ ( product_Pair @ B @ C @ V22 @ V4 ) @ R2 )
% 0.30/0.46 & ( L1 = L2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % on_triple
% 0.30/0.46 thf(fact_122_edge__preservingI,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType,R2: set @ ( product_prod @ C @ B ),E3: set @ ( product_prod @ A @ ( product_prod @ C @ C ) ),G: set @ ( product_prod @ A @ ( product_prod @ B @ B ) )] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ ( product_prod @ B @ B ) ) ) @ ( image @ ( product_prod @ A @ ( product_prod @ C @ C ) ) @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( on_triple @ C @ B @ A @ R2 ) @ E3 ) @ G )
% 0.30/0.46 => ( edge_preserving @ C @ B @ A @ R2 @ E3 @ G ) ) ).
% 0.30/0.46
% 0.30/0.46 % edge_preservingI
% 0.30/0.46 thf(fact_123_Nat_Oex__has__greatest__nat,axiom,
% 0.30/0.46 ! [P: nat > $o,K: nat,B2: nat] :
% 0.30/0.46 ( ( P @ K )
% 0.30/0.46 => ( ! [Y4: nat] :
% 0.30/0.46 ( ( P @ Y4 )
% 0.30/0.46 => ( ord_less_eq @ nat @ Y4 @ B2 ) )
% 0.30/0.46 => ? [X5: nat] :
% 0.30/0.46 ( ( P @ X5 )
% 0.30/0.46 & ! [Y6: nat] :
% 0.30/0.46 ( ( P @ Y6 )
% 0.30/0.46 => ( ord_less_eq @ nat @ Y6 @ X5 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Nat.ex_has_greatest_nat
% 0.30/0.46 thf(fact_124_nat__le__linear,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ M @ N )
% 0.30/0.46 | ( ord_less_eq @ nat @ N @ M ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_le_linear
% 0.30/0.46 thf(fact_125_le__antisym,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ M @ N )
% 0.30/0.46 => ( ( ord_less_eq @ nat @ N @ M )
% 0.30/0.46 => ( M = N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_antisym
% 0.30/0.46 thf(fact_126_eq__imp__le,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( M = N )
% 0.30/0.46 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_imp_le
% 0.30/0.46 thf(fact_127_le__trans,axiom,
% 0.30/0.46 ! [I: nat,J: nat,K: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ I @ J )
% 0.30/0.46 => ( ( ord_less_eq @ nat @ J @ K )
% 0.30/0.46 => ( ord_less_eq @ nat @ I @ K ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_trans
% 0.30/0.46 thf(fact_128_le__refl,axiom,
% 0.30/0.46 ! [N: nat] : ( ord_less_eq @ nat @ N @ N ) ).
% 0.30/0.46
% 0.30/0.46 % le_refl
% 0.30/0.46 thf(fact_129_bot__nat__def,axiom,
% 0.30/0.46 ( ( bot_bot @ nat )
% 0.30/0.46 = ( zero_zero @ nat ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_nat_def
% 0.30/0.46 thf(fact_130_bot__empty__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bot_bot @ ( A > $o ) )
% 0.30/0.46 = ( ^ [X4: A] : ( member @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_empty_eq
% 0.30/0.46 thf(fact_131_bot__set__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bot_bot @ ( set @ A ) )
% 0.30/0.46 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_set_def
% 0.30/0.46 thf(fact_132_edge__preserving,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( edge_preserving @ A @ B @ C )
% 0.30/0.46 = ( ^ [R4: set @ ( product_prod @ A @ B ),E4: set @ ( product_prod @ C @ ( product_prod @ A @ A ) )] : ( ord_less_eq @ ( set @ ( product_prod @ C @ ( product_prod @ B @ B ) ) ) @ ( image @ ( product_prod @ C @ ( product_prod @ A @ A ) ) @ ( product_prod @ C @ ( product_prod @ B @ B ) ) @ ( on_triple @ A @ B @ C @ R4 ) @ E4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % edge_preserving
% 0.30/0.46 thf(fact_133_on__tripleD_I1_J,axiom,
% 0.30/0.46 ! [B: $tType,C: $tType,A: $tType,L1: A,V1: B,V22: B,L2: A,V32: C,V4: C,R2: set @ ( product_prod @ B @ C )] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( product_prod @ A @ ( product_prod @ C @ C ) ) ) @ ( product_Pair @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( product_prod @ A @ ( product_prod @ C @ C ) ) @ ( product_Pair @ A @ ( product_prod @ B @ B ) @ L1 @ ( product_Pair @ B @ B @ V1 @ V22 ) ) @ ( product_Pair @ A @ ( product_prod @ C @ C ) @ L2 @ ( product_Pair @ C @ C @ V32 @ V4 ) ) ) @ ( on_triple @ B @ C @ A @ R2 ) )
% 0.30/0.46 => ( L2 = L1 ) ) ).
% 0.30/0.46
% 0.30/0.46 % on_tripleD(1)
% 0.30/0.46 thf(fact_134_on__tripleD_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType,B: $tType,L1: A,V1: B,V22: B,L2: A,V32: C,V4: C,R2: set @ ( product_prod @ B @ C )] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( product_prod @ A @ ( product_prod @ C @ C ) ) ) @ ( product_Pair @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( product_prod @ A @ ( product_prod @ C @ C ) ) @ ( product_Pair @ A @ ( product_prod @ B @ B ) @ L1 @ ( product_Pair @ B @ B @ V1 @ V22 ) ) @ ( product_Pair @ A @ ( product_prod @ C @ C ) @ L2 @ ( product_Pair @ C @ C @ V32 @ V4 ) ) ) @ ( on_triple @ B @ C @ A @ R2 ) )
% 0.30/0.46 => ( member @ ( product_prod @ B @ C ) @ ( product_Pair @ B @ C @ V1 @ V32 ) @ R2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % on_tripleD(2)
% 0.30/0.46 thf(fact_135_on__tripleD_I3_J,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType,B: $tType,L1: A,V1: B,V22: B,L2: A,V32: C,V4: C,R2: set @ ( product_prod @ B @ C )] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( product_prod @ A @ ( product_prod @ C @ C ) ) ) @ ( product_Pair @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( product_prod @ A @ ( product_prod @ C @ C ) ) @ ( product_Pair @ A @ ( product_prod @ B @ B ) @ L1 @ ( product_Pair @ B @ B @ V1 @ V22 ) ) @ ( product_Pair @ A @ ( product_prod @ C @ C ) @ L2 @ ( product_Pair @ C @ C @ V32 @ V4 ) ) ) @ ( on_triple @ B @ C @ A @ R2 ) )
% 0.30/0.46 => ( member @ ( product_prod @ B @ C ) @ ( product_Pair @ B @ C @ V22 @ V4 ) @ R2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % on_tripleD(3)
% 0.30/0.46 thf(fact_136_on__triple__dest,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType,R2: set @ ( product_prod @ C @ B ),E3: set @ ( product_prod @ A @ ( product_prod @ C @ C ) ),G: set @ ( product_prod @ A @ ( product_prod @ B @ B ) ),L3: A,X3: C,Y: C,Xx: B,Yy: B] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ ( product_prod @ B @ B ) ) ) @ ( image @ ( product_prod @ A @ ( product_prod @ C @ C ) ) @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( on_triple @ C @ B @ A @ R2 ) @ E3 ) @ G )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ ( product_prod @ C @ C ) ) @ ( product_Pair @ A @ ( product_prod @ C @ C ) @ L3 @ ( product_Pair @ C @ C @ X3 @ Y ) ) @ E3 )
% 0.30/0.46 => ( ( member @ ( product_prod @ C @ B ) @ ( product_Pair @ C @ B @ X3 @ Xx ) @ R2 )
% 0.30/0.46 => ( ( member @ ( product_prod @ C @ B ) @ ( product_Pair @ C @ B @ Y @ Yy ) @ R2 )
% 0.30/0.46 => ( member @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( product_Pair @ A @ ( product_prod @ B @ B ) @ L3 @ ( product_Pair @ B @ B @ Xx @ Yy ) ) @ G ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % on_triple_dest
% 0.30/0.46 thf(fact_137_dual__order_Oantisym,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [B2: A,A2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( A2 = B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.antisym
% 0.30/0.46 thf(fact_138_dual__order_Oeq__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ( ( ^ [Y5: A,Z: A] : ( Y5 = Z ) )
% 0.30/0.46 = ( ^ [A7: A,B5: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B5 @ A7 )
% 0.30/0.46 & ( ord_less_eq @ A @ A7 @ B5 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.eq_iff
% 0.30/0.46 thf(fact_139_dual__order_Otrans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [B2: A,A2: A,C3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ C3 @ B2 )
% 0.30/0.46 => ( ord_less_eq @ A @ C3 @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.trans
% 0.30/0.46 thf(fact_140_linorder__wlog,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [P: A > A > $o,A2: A,B2: A] :
% 0.30/0.46 ( ! [A6: A,B4: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A6 @ B4 )
% 0.30/0.46 => ( P @ A6 @ B4 ) )
% 0.30/0.46 => ( ! [A6: A,B4: A] :
% 0.30/0.46 ( ( P @ B4 @ A6 )
% 0.30/0.46 => ( P @ A6 @ B4 ) )
% 0.30/0.46 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linorder_wlog
% 0.30/0.46 thf(fact_141_dual__order_Orefl,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.refl
% 0.30/0.46 thf(fact_142_order__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X3: A,Y: A,Z2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X3 @ Y )
% 0.30/0.46 => ( ( ord_less_eq @ A @ Y @ Z2 )
% 0.30/0.46 => ( ord_less_eq @ A @ X3 @ Z2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_trans
% 0.30/0.46 thf(fact_143_order__class_Oorder_Oantisym,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.46 => ( A2 = B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_class.order.antisym
% 0.30/0.46 thf(fact_144_ord__le__eq__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( B2 = C3 )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_trans
% 0.30/0.46 thf(fact_145_ord__eq__le__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C3: A] :
% 0.30/0.46 ( ( A2 = B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B2 @ C3 )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_trans
% 0.30/0.46 thf(fact_146_order__class_Oorder_Oeq__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ( ( ^ [Y5: A,Z: A] : ( Y5 = Z ) )
% 0.30/0.46 = ( ^ [A7: A,B5: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A7 @ B5 )
% 0.30/0.46 & ( ord_less_eq @ A @ B5 @ A7 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_class.order.eq_iff
% 0.30/0.46 thf(fact_147_antisym__conv,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [Y: A,X3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ Y @ X3 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ X3 @ Y )
% 0.30/0.46 = ( X3 = Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym_conv
% 0.30/0.46 thf(fact_148_le__cases3,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X3: A,Y: A,Z2: A] :
% 0.30/0.46 ( ( ( ord_less_eq @ A @ X3 @ Y )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Y @ Z2 ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ Y @ X3 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ X3 @ Z2 ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ X3 @ Z2 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Z2 @ Y ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ Z2 @ Y )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Y @ X3 ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ Y @ Z2 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Z2 @ X3 ) )
% 0.30/0.46 => ~ ( ( ord_less_eq @ A @ Z2 @ X3 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ X3 @ Y ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_cases3
% 0.30/0.46 thf(fact_149_order_Otrans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B2 @ C3 )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order.trans
% 0.30/0.46 thf(fact_150_le__cases,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X3: A,Y: A] :
% 0.30/0.46 ( ~ ( ord_less_eq @ A @ X3 @ Y )
% 0.30/0.46 => ( ord_less_eq @ A @ Y @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_cases
% 0.30/0.46 thf(fact_151_eq__refl,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X3: A,Y: A] :
% 0.30/0.46 ( ( X3 = Y )
% 0.30/0.46 => ( ord_less_eq @ A @ X3 @ Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_refl
% 0.30/0.46 thf(fact_152_linear,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X3: A,Y: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X3 @ Y )
% 0.30/0.46 | ( ord_less_eq @ A @ Y @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linear
% 0.30/0.46 thf(fact_153_antisym,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [X3: A,Y: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X3 @ Y )
% 0.30/0.46 => ( ( ord_less_eq @ A @ Y @ X3 )
% 0.30/0.46 => ( X3 = Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym
% 0.30/0.46 thf(fact_154_eq__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ( ( ^ [Y5: A,Z: A] : ( Y5 = Z ) )
% 0.30/0.46 = ( ^ [X4: A,Y3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 0.30/0.46 & ( ord_less_eq @ A @ Y3 @ X4 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_iff
% 0.30/0.46 thf(fact_155_ord__le__eq__subst,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ( ord @ B )
% 0.30/0.46 & ( ord @ A ) )
% 0.30/0.46 => ! [A2: A,B2: A,F: A > B,C3: B] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ( F @ B2 )
% 0.30/0.46 = C3 )
% 0.30/0.46 => ( ! [X5: A,Y4: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X5 @ Y4 )
% 0.30/0.46 => ( ord_less_eq @ B @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.30/0.46 => ( ord_less_eq @ B @ ( F @ A2 ) @ C3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_subst
% 0.30/0.46 thf(fact_156_ord__eq__le__subst,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ( ord @ B )
% 0.30/0.46 & ( ord @ A ) )
% 0.30/0.46 => ! [A2: A,F: B > A,B2: B,C3: B] :
% 0.30/0.46 ( ( A2
% 0.30/0.46 = ( F @ B2 ) )
% 0.30/0.46 => ( ( ord_less_eq @ B @ B2 @ C3 )
% 0.30/0.46 => ( ! [X5: B,Y4: B] :
% 0.30/0.46 ( ( ord_less_eq @ B @ X5 @ Y4 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ ( F @ C3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_subst
% 0.30/0.46 thf(fact_157_order__subst2,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType] :
% 0.30/0.46 ( ( ( order @ C )
% 0.30/0.46 & ( order @ A ) )
% 0.30/0.46 => ! [A2: A,B2: A,F: A > C,C3: C] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ C @ ( F @ B2 ) @ C3 )
% 0.30/0.46 => ( ! [X5: A,Y4: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X5 @ Y4 )
% 0.30/0.46 => ( ord_less_eq @ C @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.30/0.46 => ( ord_less_eq @ C @ ( F @ A2 ) @ C3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst2
% 0.30/0.46 thf(fact_158_order__subst1,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ( order @ B )
% 0.30/0.46 & ( order @ A ) )
% 0.30/0.46 => ! [A2: A,F: B > A,B2: B,C3: B] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 0.30/0.46 => ( ( ord_less_eq @ B @ B2 @ C3 )
% 0.30/0.46 => ( ! [X5: B,Y4: B] :
% 0.30/0.46 ( ( ord_less_eq @ B @ X5 @ Y4 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ ( F @ C3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst1
% 0.30/0.46 thf(fact_159_le__fun__def,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ( ( ord_less_eq @ ( A > B ) )
% 0.30/0.46 = ( ^ [F2: A > B,G3: A > B] :
% 0.30/0.46 ! [X4: A] : ( ord_less_eq @ B @ ( F2 @ X4 ) @ ( G3 @ X4 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_fun_def
% 0.30/0.46 thf(fact_160_le__funI,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ! [F: A > B,G2: A > B] :
% 0.30/0.46 ( ! [X5: A] : ( ord_less_eq @ B @ ( F @ X5 ) @ ( G2 @ X5 ) )
% 0.30/0.46 => ( ord_less_eq @ ( A > B ) @ F @ G2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_funI
% 0.30/0.46 thf(fact_161_le__funE,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ! [F: A > B,G2: A > B,X3: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( A > B ) @ F @ G2 )
% 0.30/0.46 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( G2 @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_funE
% 0.30/0.46 thf(fact_162_le__funD,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ! [F: A > B,G2: A > B,X3: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( A > B ) @ F @ G2 )
% 0.30/0.46 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( G2 @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_funD
% 0.30/0.46 thf(fact_163_old_Oprod_Oinducts,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.30/0.46 ( ! [A6: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A6 @ B4 ) )
% 0.30/0.46 => ( P @ Prod ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.inducts
% 0.30/0.46 thf(fact_164_old_Oprod_Oexhaust,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 0.30/0.46 ~ ! [A6: A,B4: B] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( product_Pair @ A @ B @ A6 @ B4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.exhaust
% 0.30/0.46 thf(fact_165_Pair__inject,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,A2: A,B2: B,A9: A,B9: B] :
% 0.30/0.46 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.30/0.46 = ( product_Pair @ A @ B @ A9 @ B9 ) )
% 0.30/0.46 => ~ ( ( A2 = A9 )
% 0.30/0.46 => ( B2 != B9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Pair_inject
% 0.30/0.46 thf(fact_166_prod__cases,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P2: product_prod @ A @ B] :
% 0.30/0.46 ( ! [A6: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A6 @ B4 ) )
% 0.30/0.46 => ( P @ P2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases
% 0.30/0.46 thf(fact_167_surj__pair,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,P2: product_prod @ A @ B] :
% 0.30/0.46 ? [X5: A,Y4: B] :
% 0.30/0.46 ( P2
% 0.30/0.46 = ( product_Pair @ A @ B @ X5 @ Y4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % surj_pair
% 0.30/0.46 thf(fact_168_bot__fun__def,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( bot @ B )
% 0.30/0.46 => ( ( bot_bot @ ( A > B ) )
% 0.30/0.46 = ( ^ [X4: A] : ( bot_bot @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_fun_def
% 0.30/0.46 thf(fact_169_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.30/0.46 ! [A2: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ A2 @ ( zero_zero @ nat ) )
% 0.30/0.46 => ( A2
% 0.30/0.46 = ( zero_zero @ nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_nat_0.extremum_uniqueI
% 0.30/0.46 thf(fact_170_bot__nat__0_Oextremum__unique,axiom,
% 0.30/0.46 ! [A2: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ A2 @ ( zero_zero @ nat ) )
% 0.30/0.46 = ( A2
% 0.30/0.46 = ( zero_zero @ nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_nat_0.extremum_unique
% 0.30/0.46 thf(fact_171_le__0__eq,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ N @ ( zero_zero @ nat ) )
% 0.30/0.46 = ( N
% 0.30/0.46 = ( zero_zero @ nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_0_eq
% 0.30/0.46 thf(fact_172_less__eq__nat_Osimps_I1_J,axiom,
% 0.30/0.46 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 0.30/0.46
% 0.30/0.46 % less_eq_nat.simps(1)
% 0.30/0.46 thf(fact_173_bot_Oextremum__uniqueI,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order_bot @ A )
% 0.30/0.46 => ! [A2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 0.30/0.46 => ( A2
% 0.30/0.46 = ( bot_bot @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot.extremum_uniqueI
% 0.30/0.46 thf(fact_174_bot_Oextremum__unique,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order_bot @ A )
% 0.30/0.46 => ! [A2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 0.30/0.46 = ( A2
% 0.30/0.46 = ( bot_bot @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot.extremum_unique
% 0.30/0.46 thf(fact_175_bot_Oextremum,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order_bot @ A )
% 0.30/0.46 => ! [A2: A] : ( ord_less_eq @ A @ ( bot_bot @ A ) @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot.extremum
% 0.30/0.46 thf(fact_176_prod__induct7,axiom,
% 0.30/0.46 ! [G4: $tType,F3: $tType,E5: $tType,D3: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ ( product_prod @ F3 @ G4 ) ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ ( product_prod @ F3 @ G4 ) ) ) ) )] :
% 0.30/0.46 ( ! [A6: A,B4: B,C6: C,D4: D3,E6: E5,F4: F3,G5: G4] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ ( product_prod @ F3 @ G4 ) ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ ( product_prod @ F3 @ G4 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ ( product_prod @ F3 @ G4 ) ) ) @ C6 @ ( product_Pair @ D3 @ ( product_prod @ E5 @ ( product_prod @ F3 @ G4 ) ) @ D4 @ ( product_Pair @ E5 @ ( product_prod @ F3 @ G4 ) @ E6 @ ( product_Pair @ F3 @ G4 @ F4 @ G5 ) ) ) ) ) ) )
% 0.30/0.46 => ( P @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_induct7
% 0.30/0.46 thf(fact_177_prod__induct6,axiom,
% 0.30/0.46 ! [F3: $tType,E5: $tType,D3: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ F3 ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ F3 ) ) ) )] :
% 0.30/0.46 ( ! [A6: A,B4: B,C6: C,D4: D3,E6: E5,F4: F3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ F3 ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ F3 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ F3 ) ) @ C6 @ ( product_Pair @ D3 @ ( product_prod @ E5 @ F3 ) @ D4 @ ( product_Pair @ E5 @ F3 @ E6 @ F4 ) ) ) ) ) )
% 0.30/0.46 => ( P @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_induct6
% 0.30/0.46 thf(fact_178_prod__induct5,axiom,
% 0.30/0.46 ! [E5: $tType,D3: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ E5 ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ E5 ) ) )] :
% 0.30/0.46 ( ! [A6: A,B4: B,C6: C,D4: D3,E6: E5] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ E5 ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D3 @ E5 ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D3 @ E5 ) @ C6 @ ( product_Pair @ D3 @ E5 @ D4 @ E6 ) ) ) ) )
% 0.30/0.46 => ( P @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_induct5
% 0.30/0.46 thf(fact_179_prod__induct4,axiom,
% 0.30/0.46 ! [D3: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D3 ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D3 ) )] :
% 0.30/0.46 ( ! [A6: A,B4: B,C6: C,D4: D3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D3 ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ D3 ) @ B4 @ ( product_Pair @ C @ D3 @ C6 @ D4 ) ) ) )
% 0.30/0.46 => ( P @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_induct4
% 0.30/0.46 thf(fact_180_prod__induct3,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.30/0.46 ( ! [A6: A,B4: B,C6: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A6 @ ( product_Pair @ B @ C @ B4 @ C6 ) ) )
% 0.30/0.46 => ( P @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_induct3
% 0.30/0.46 thf(fact_181_prod__cases7,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C: $tType,D3: $tType,E5: $tType,F3: $tType,G4: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ ( product_prod @ F3 @ G4 ) ) ) ) )] :
% 0.30/0.46 ~ ! [A6: A,B4: B,C6: C,D4: D3,E6: E5,F4: F3,G5: G4] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ ( product_prod @ F3 @ G4 ) ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ ( product_prod @ F3 @ G4 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ ( product_prod @ F3 @ G4 ) ) ) @ C6 @ ( product_Pair @ D3 @ ( product_prod @ E5 @ ( product_prod @ F3 @ G4 ) ) @ D4 @ ( product_Pair @ E5 @ ( product_prod @ F3 @ G4 ) @ E6 @ ( product_Pair @ F3 @ G4 @ F4 @ G5 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases7
% 0.30/0.46 thf(fact_182_prod__cases6,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C: $tType,D3: $tType,E5: $tType,F3: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ F3 ) ) ) )] :
% 0.30/0.46 ~ ! [A6: A,B4: B,C6: C,D4: D3,E6: E5,F4: F3] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ F3 ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ F3 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ F3 ) ) @ C6 @ ( product_Pair @ D3 @ ( product_prod @ E5 @ F3 ) @ D4 @ ( product_Pair @ E5 @ F3 @ E6 @ F4 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases6
% 0.30/0.46 thf(fact_183_prod__cases5,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C: $tType,D3: $tType,E5: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ E5 ) ) )] :
% 0.30/0.46 ~ ! [A6: A,B4: B,C6: C,D4: D3,E6: E5] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ E5 ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D3 @ E5 ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D3 @ E5 ) @ C6 @ ( product_Pair @ D3 @ E5 @ D4 @ E6 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases5
% 0.30/0.46 thf(fact_184_prod__cases4,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C: $tType,D3: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D3 ) )] :
% 0.30/0.46 ~ ! [A6: A,B4: B,C6: C,D4: D3] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D3 ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ D3 ) @ B4 @ ( product_Pair @ C @ D3 @ C6 @ D4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases4
% 0.30/0.46 thf(fact_185_prod__cases3,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.30/0.46 ~ ! [A6: A,B4: B,C6: C] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A6 @ ( product_Pair @ B @ C @ B4 @ C6 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases3
% 0.30/0.46 thf(fact_186_old_Oprod_Orec,axiom,
% 0.30/0.46 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.30/0.46 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.30/0.46 = ( F1 @ A2 @ B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.rec
% 0.30/0.46 thf(fact_187_is__singleton__the__elem,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( is_singleton @ A )
% 0.30/0.46 = ( ^ [A8: set @ A] :
% 0.30/0.46 ( A8
% 0.30/0.46 = ( insert @ A @ ( the_elem @ A @ A8 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_singleton_the_elem
% 0.30/0.46 thf(fact_188_top__rule__def,axiom,
% 0.30/0.46 ! [L: $tType] :
% 0.30/0.46 ( ( standa400804411p_rule @ L )
% 0.30/0.46 = ( ^ [T2: L] : ( product_Pair @ ( labeled_graph @ L @ nat ) @ ( labeled_graph @ L @ nat ) @ ( labeled_LG @ L @ nat @ ( bot_bot @ ( set @ ( product_prod @ L @ ( product_prod @ nat @ nat ) ) ) ) @ ( insert @ nat @ ( zero_zero @ nat ) @ ( insert @ nat @ ( one_one @ nat ) @ ( bot_bot @ ( set @ nat ) ) ) ) ) @ ( labeled_LG @ L @ nat @ ( insert @ ( product_prod @ L @ ( product_prod @ nat @ nat ) ) @ ( product_Pair @ L @ ( product_prod @ nat @ nat ) @ T2 @ ( product_Pair @ nat @ nat @ ( zero_zero @ nat ) @ ( one_one @ nat ) ) ) @ ( bot_bot @ ( set @ ( product_prod @ L @ ( product_prod @ nat @ nat ) ) ) ) ) @ ( insert @ nat @ ( zero_zero @ nat ) @ ( insert @ nat @ ( one_one @ nat ) @ ( bot_bot @ ( set @ nat ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % top_rule_def
% 0.30/0.46 thf(fact_189_map__graph__def,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C: $tType] :
% 0.30/0.46 ( ( map_graph @ C @ B @ A )
% 0.30/0.46 = ( ^ [F2: set @ ( product_prod @ C @ B ),G6: labeled_graph @ A @ C] : ( labeled_LG @ A @ B @ ( image @ ( product_prod @ A @ ( product_prod @ C @ C ) ) @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( on_triple @ C @ B @ A @ F2 ) @ ( labeled_edges @ A @ C @ G6 ) ) @ ( image @ C @ B @ F2 @ ( labeled_vertices @ A @ C @ G6 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_graph_def
% 0.30/0.46 thf(fact_190_map__graph__preserves__restricted,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType,G: labeled_graph @ A @ B,F: set @ ( product_prod @ B @ C )] :
% 0.30/0.46 ( ( G
% 0.30/0.46 = ( restrict @ A @ B @ G ) )
% 0.30/0.46 => ( ( map_graph @ B @ C @ A @ F @ G )
% 0.30/0.46 = ( restrict @ A @ C @ ( map_graph @ B @ C @ A @ F @ G ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_graph_preserves_restricted
% 0.30/0.46 thf(fact_191_map__graph__selectors_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType,B: $tType,F: set @ ( product_prod @ C @ A ),G: labeled_graph @ B @ C] :
% 0.30/0.46 ( ( labeled_vertices @ B @ A @ ( map_graph @ C @ A @ B @ F @ G ) )
% 0.30/0.46 = ( image @ C @ A @ F @ ( labeled_vertices @ B @ C @ G ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_graph_selectors(1)
% 0.30/0.46 thf(fact_192_is__singletonI,axiom,
% 0.30/0.46 ! [A: $tType,X3: A] : ( is_singleton @ A @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_singletonI
% 0.30/0.46 thf(fact_193_map__graph__edge__preserving,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,C: $tType,F: set @ ( product_prod @ A @ B ),G: labeled_graph @ C @ A] : ( edge_preserving @ A @ B @ C @ F @ ( labeled_edges @ C @ A @ G ) @ ( labeled_edges @ C @ B @ ( map_graph @ A @ B @ C @ F @ G ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_graph_edge_preserving
% 0.30/0.46 thf(fact_194_map__graph__selectors_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType,B: $tType,F: set @ ( product_prod @ C @ A ),G: labeled_graph @ B @ C] :
% 0.30/0.46 ( ( labeled_edges @ B @ A @ ( map_graph @ C @ A @ B @ F @ G ) )
% 0.30/0.46 = ( image @ ( product_prod @ B @ ( product_prod @ C @ C ) ) @ ( product_prod @ B @ ( product_prod @ A @ A ) ) @ ( on_triple @ C @ A @ B @ F ) @ ( labeled_edges @ B @ C @ G ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_graph_selectors(2)
% 0.30/0.46 thf(fact_195_map__graph__homo,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType,F: set @ ( product_prod @ A @ B ),G: labeled_graph @ C @ A] :
% 0.30/0.46 ( ( univalent @ A @ B @ F )
% 0.30/0.46 => ( ( ( labeled_vertices @ C @ A @ G )
% 0.30/0.46 = ( domain @ A @ B @ F ) )
% 0.30/0.46 => ( ( G
% 0.30/0.46 = ( restrict @ C @ A @ G ) )
% 0.30/0.46 => ( graph_homomorphism @ C @ A @ B @ G @ ( map_graph @ A @ B @ C @ F @ G ) @ F ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_graph_homo
% 0.30/0.46 thf(fact_196_one__reorient,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( one @ A )
% 0.30/0.46 => ! [X3: A] :
% 0.30/0.46 ( ( ( one_one @ A )
% 0.30/0.46 = X3 )
% 0.30/0.46 = ( X3
% 0.30/0.46 = ( one_one @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % one_reorient
% 0.30/0.46 thf(fact_197_is__singletonI_H,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] :
% 0.30/0.46 ( ( A4
% 0.30/0.46 != ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 => ( ! [X5: A,Y4: A] :
% 0.30/0.46 ( ( member @ A @ X5 @ A4 )
% 0.30/0.46 => ( ( member @ A @ Y4 @ A4 )
% 0.30/0.46 => ( X5 = Y4 ) ) )
% 0.30/0.46 => ( is_singleton @ A @ A4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_singletonI'
% 0.30/0.46 thf(fact_198_map__graph__returns__restricted,axiom,
% 0.30/0.46 ! [C: $tType,A: $tType,B: $tType,G: labeled_graph @ B @ A,F: set @ ( product_prod @ A @ C )] :
% 0.30/0.46 ( ( ( labeled_vertices @ B @ A @ G )
% 0.30/0.46 = ( domain @ A @ C @ F ) )
% 0.30/0.46 => ( ( map_graph @ A @ C @ B @ F @ G )
% 0.30/0.46 = ( restrict @ B @ C @ ( map_graph @ A @ C @ B @ F @ G ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_graph_returns_restricted
% 0.30/0.46 thf(fact_199_is__singletonE,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] :
% 0.30/0.46 ( ( is_singleton @ A @ A4 )
% 0.30/0.46 => ~ ! [X5: A] :
% 0.30/0.46 ( A4
% 0.30/0.46 != ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_singletonE
% 0.30/0.46 thf(fact_200_is__singleton__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( is_singleton @ A )
% 0.30/0.46 = ( ^ [A8: set @ A] :
% 0.30/0.46 ? [X4: A] :
% 0.30/0.46 ( A8
% 0.30/0.46 = ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_singleton_def
% 0.30/0.46 thf(fact_201_map__graph__homo__simp,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType,G: labeled_graph @ A @ B,F: set @ ( product_prod @ B @ C )] :
% 0.30/0.46 ( ( graph_homomorphism @ A @ B @ C @ G @ ( map_graph @ B @ C @ A @ F @ G ) @ F )
% 0.30/0.46 = ( ( univalent @ B @ C @ F )
% 0.30/0.46 & ( ( labeled_vertices @ A @ B @ G )
% 0.30/0.46 = ( domain @ B @ C @ F ) )
% 0.30/0.46 & ( G
% 0.30/0.46 = ( restrict @ A @ B @ G ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_graph_homo_simp
% 0.30/0.46 thf(fact_202_not__one__le__zero,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord1659791738miring @ A )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_one_le_zero
% 0.30/0.46 thf(fact_203_zero__le__one,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord1659791738miring @ A )
% 0.30/0.46 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_le_one
% 0.30/0.46 thf(fact_204_zero__neq__one,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( zero_neq_one @ A )
% 0.30/0.46 => ( ( zero_zero @ A )
% 0.30/0.46 != ( one_one @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_neq_one
% 0.30/0.46 thf(fact_205_graph__homomorphism__def2,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType] :
% 0.30/0.46 ( ( graph_homomorphism @ A @ B @ C )
% 0.30/0.46 = ( ^ [G_1: labeled_graph @ A @ B,G_2: labeled_graph @ A @ C,F2: set @ ( product_prod @ B @ C )] :
% 0.30/0.46 ( ( ( labeled_vertices @ A @ B @ G_1 )
% 0.30/0.46 = ( domain @ B @ C @ F2 ) )
% 0.30/0.46 & ( univalent @ B @ C @ F2 )
% 0.30/0.46 & ( G_1
% 0.30/0.46 = ( restrict @ A @ B @ G_1 ) )
% 0.30/0.46 & ( G_2
% 0.30/0.46 = ( restrict @ A @ C @ G_2 ) )
% 0.30/0.46 & ( ( graph_union @ A @ C @ ( map_graph @ B @ C @ A @ F2 @ G_1 ) @ G_2 )
% 0.30/0.46 = G_2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % graph_homomorphism_def2
% 0.30/0.46 thf(fact_206_Collect__empty__eq__bot,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o] :
% 0.30/0.46 ( ( ( collect @ A @ P )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( P
% 0.30/0.46 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_empty_eq_bot
% 0.30/0.46 thf(fact_207_graph__union__idemp_I3_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,A4: labeled_graph @ A @ B,B6: labeled_graph @ A @ B] :
% 0.30/0.46 ( ( graph_union @ A @ B @ A4 @ ( graph_union @ A @ B @ B6 @ A4 ) )
% 0.30/0.46 = ( graph_union @ A @ B @ B6 @ A4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % graph_union_idemp(3)
% 0.30/0.46 thf(fact_208_graph__union__idemp_I2_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,A4: labeled_graph @ A @ B,B6: labeled_graph @ A @ B] :
% 0.30/0.46 ( ( graph_union @ A @ B @ A4 @ ( graph_union @ A @ B @ A4 @ B6 ) )
% 0.30/0.46 = ( graph_union @ A @ B @ A4 @ B6 ) ) ).
% 0.30/0.46
% 0.30/0.46 % graph_union_idemp(2)
% 0.30/0.46 thf(fact_209_graph__union__idemp_I1_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,A4: labeled_graph @ A @ B] :
% 0.30/0.46 ( ( graph_union @ A @ B @ A4 @ A4 )
% 0.30/0.46 = A4 ) ).
% 0.30/0.46
% 0.30/0.46 % graph_union_idemp(1)
% 0.30/0.46 thf(fact_210_graph__union__preserves__restrict,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,G_12: labeled_graph @ A @ B,G_22: labeled_graph @ A @ B] :
% 0.30/0.46 ( ( G_12
% 0.30/0.46 = ( restrict @ A @ B @ G_12 ) )
% 0.30/0.46 => ( ( G_22
% 0.30/0.46 = ( restrict @ A @ B @ G_22 ) )
% 0.30/0.46 => ( ( graph_union @ A @ B @ G_12 @ G_22 )
% 0.30/0.46 = ( restrict @ A @ B @ ( graph_union @ A @ B @ G_12 @ G_22 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % graph_union_preserves_restrict
% 0.30/0.46 thf(fact_211_graph__unionI,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,G_12: labeled_graph @ A @ B,G_22: labeled_graph @ A @ B] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ ( product_prod @ B @ B ) ) ) @ ( labeled_edges @ A @ B @ G_12 ) @ ( labeled_edges @ A @ B @ G_22 ) )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ B ) @ ( labeled_vertices @ A @ B @ G_12 ) @ ( labeled_vertices @ A @ B @ G_22 ) )
% 0.30/0.46 => ( ( graph_union @ A @ B @ G_12 @ G_22 )
% 0.30/0.46 = G_22 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % graph_unionI
% 0.30/0.46 thf(fact_212_graph__union__iff,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,G_12: labeled_graph @ A @ B,G_22: labeled_graph @ A @ B] :
% 0.30/0.46 ( ( ( graph_union @ A @ B @ G_12 @ G_22 )
% 0.30/0.46 = G_22 )
% 0.30/0.46 = ( ( ord_less_eq @ ( set @ ( product_prod @ A @ ( product_prod @ B @ B ) ) ) @ ( labeled_edges @ A @ B @ G_12 ) @ ( labeled_edges @ A @ B @ G_22 ) )
% 0.30/0.46 & ( ord_less_eq @ ( set @ B ) @ ( labeled_vertices @ A @ B @ G_12 ) @ ( labeled_vertices @ A @ B @ G_22 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % graph_union_iff
% 0.30/0.46 thf(fact_213_less__by__empty,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ ( product_prod @ A @ A ),B6: set @ ( product_prod @ A @ A )] :
% 0.30/0.46 ( ( A4
% 0.30/0.46 = ( bot_bot @ ( set @ ( product_prod @ A @ A ) ) ) )
% 0.30/0.46 => ( ord_less_eq @ ( set @ ( product_prod @ A @ A ) ) @ A4 @ B6 ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_by_empty
% 0.30/0.46 thf(fact_214_on__triple__ID__restrict,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,G: labeled_graph @ A @ B] :
% 0.30/0.46 ( ( image @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( on_triple @ B @ B @ A @ ( id_on @ B @ ( labeled_vertices @ A @ B @ G ) ) ) @ ( labeled_edges @ A @ B @ G ) )
% 0.30/0.46 = ( labeled_edges @ A @ B @ ( restrict @ A @ B @ G ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % on_triple_ID_restrict
% 0.30/0.46 thf(fact_215_Id__onI,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,A4: set @ A] :
% 0.30/0.46 ( ( member @ A @ A2 @ A4 )
% 0.30/0.46 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ A2 ) @ ( id_on @ A @ A4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Id_onI
% 0.30/0.46 thf(fact_216_Domain__Id__on,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] :
% 0.30/0.46 ( ( domain @ A @ A @ ( id_on @ A @ A4 ) )
% 0.30/0.46 = A4 ) ).
% 0.30/0.46
% 0.30/0.46 % Domain_Id_on
% 0.30/0.46 thf(fact_217_id__univalent,axiom,
% 0.30/0.46 ! [A: $tType,X3: set @ A] : ( univalent @ A @ A @ ( id_on @ A @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % id_univalent
% 0.30/0.46 thf(fact_218_edge__preserving__Id,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,Y: set @ A,X3: set @ ( product_prod @ B @ ( product_prod @ A @ A ) )] : ( edge_preserving @ A @ A @ B @ ( id_on @ A @ Y ) @ X3 @ X3 ) ).
% 0.30/0.46
% 0.30/0.46 % edge_preserving_Id
% 0.30/0.46 thf(fact_219_Id__on__empty,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( id_on @ A @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( bot_bot @ ( set @ ( product_prod @ A @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Id_on_empty
% 0.30/0.46 thf(fact_220_graph__homomorphism__Id,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,A2: labeled_graph @ A @ B] : ( graph_homomorphism @ A @ B @ B @ ( restrict @ A @ B @ A2 ) @ ( restrict @ A @ B @ A2 ) @ ( id_on @ B @ ( labeled_vertices @ A @ B @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % graph_homomorphism_Id
% 0.30/0.46 thf(fact_221_subgraph__restrict,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,G: labeled_graph @ A @ B] :
% 0.30/0.46 ( ( graph_homomorphism @ A @ B @ B @ G @ ( restrict @ A @ B @ G ) @ ( id_on @ B @ ( labeled_vertices @ A @ B @ G ) ) )
% 0.30/0.46 = ( G
% 0.30/0.46 = ( restrict @ A @ B @ G ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subgraph_restrict
% 0.30/0.46 thf(fact_222_subgraph__refl,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,G: labeled_graph @ A @ B] :
% 0.30/0.46 ( ( graph_homomorphism @ A @ B @ B @ G @ G @ ( id_on @ B @ ( labeled_vertices @ A @ B @ G ) ) )
% 0.30/0.46 = ( G
% 0.30/0.46 = ( restrict @ A @ B @ G ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subgraph_refl
% 0.30/0.46 thf(fact_223_map__graph__preserves__subgraph,axiom,
% 0.30/0.46 ! [C: $tType,B: $tType,A: $tType,A4: labeled_graph @ A @ B,B6: labeled_graph @ A @ B,F: set @ ( product_prod @ B @ C )] :
% 0.30/0.46 ( ( graph_homomorphism @ A @ B @ B @ A4 @ B6 @ ( id_on @ B @ ( labeled_vertices @ A @ B @ A4 ) ) )
% 0.30/0.46 => ( graph_homomorphism @ A @ C @ C @ ( map_graph @ B @ C @ A @ F @ A4 ) @ ( map_graph @ B @ C @ A @ F @ B6 ) @ ( id_on @ C @ ( labeled_vertices @ A @ C @ ( map_graph @ B @ C @ A @ F @ A4 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_graph_preserves_subgraph
% 0.30/0.46 thf(fact_224_map__graph__fn__id_I2_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,X2: labeled_graph @ A @ B] :
% 0.30/0.46 ( ( map_graph @ B @ B @ A @ ( id_on @ B @ ( labeled_vertices @ A @ B @ X2 ) ) @ X2 )
% 0.30/0.46 = ( restrict @ A @ B @ X2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_graph_fn_id(2)
% 0.30/0.46 thf(fact_225_Id__on__iff,axiom,
% 0.30/0.46 ! [A: $tType,X3: A,Y: A,A4: set @ A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y ) @ ( id_on @ A @ A4 ) )
% 0.30/0.46 = ( ( X3 = Y )
% 0.30/0.46 & ( member @ A @ X3 @ A4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Id_on_iff
% 0.30/0.46 thf(fact_226_Id__on__eqI,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A,A4: set @ A] :
% 0.30/0.46 ( ( A2 = B2 )
% 0.30/0.46 => ( ( member @ A @ A2 @ A4 )
% 0.30/0.46 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( id_on @ A @ A4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Id_on_eqI
% 0.30/0.46 thf(fact_227_Id__onE,axiom,
% 0.30/0.46 ! [A: $tType,C3: product_prod @ A @ A,A4: set @ A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ C3 @ ( id_on @ A @ A4 ) )
% 0.30/0.46 => ~ ! [X5: A] :
% 0.30/0.46 ( ( member @ A @ X5 @ A4 )
% 0.30/0.46 => ( C3
% 0.30/0.46 != ( product_Pair @ A @ A @ X5 @ X5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Id_onE
% 0.30/0.46 thf(fact_228_subgraph__preserves__hom,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,C: $tType,A4: labeled_graph @ A @ B,B6: labeled_graph @ A @ B,X2: labeled_graph @ A @ C,H: set @ ( product_prod @ C @ B )] :
% 0.30/0.46 ( ( graph_homomorphism @ A @ B @ B @ A4 @ B6 @ ( id_on @ B @ ( labeled_vertices @ A @ B @ A4 ) ) )
% 0.30/0.46 => ( ( graph_homomorphism @ A @ C @ B @ X2 @ A4 @ H )
% 0.30/0.46 => ( graph_homomorphism @ A @ C @ B @ X2 @ B6 @ H ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subgraph_preserves_hom
% 0.30/0.46 thf(fact_229_subgraph__trans,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,G_12: labeled_graph @ A @ B,G_22: labeled_graph @ A @ B,G_3: labeled_graph @ A @ B] :
% 0.30/0.46 ( ( graph_homomorphism @ A @ B @ B @ G_12 @ G_22 @ ( id_on @ B @ ( labeled_vertices @ A @ B @ G_12 ) ) )
% 0.30/0.46 => ( ( graph_homomorphism @ A @ B @ B @ G_22 @ G_3 @ ( id_on @ B @ ( labeled_vertices @ A @ B @ G_22 ) ) )
% 0.30/0.46 => ( graph_homomorphism @ A @ B @ B @ G_12 @ G_3 @ ( id_on @ B @ ( labeled_vertices @ A @ B @ G_12 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subgraph_trans
% 0.30/0.46 thf(fact_230_subgraph__subset_I1_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,G_12: labeled_graph @ A @ B,G_22: labeled_graph @ A @ B] :
% 0.30/0.46 ( ( graph_homomorphism @ A @ B @ B @ G_12 @ G_22 @ ( id_on @ B @ ( labeled_vertices @ A @ B @ G_12 ) ) )
% 0.30/0.46 => ( ord_less_eq @ ( set @ B ) @ ( labeled_vertices @ A @ B @ G_12 ) @ ( labeled_vertices @ A @ B @ G_22 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subgraph_subset(1)
% 0.30/0.46 thf(fact_231_subgraph__def,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,G_12: labeled_graph @ A @ B,G_22: labeled_graph @ A @ B] :
% 0.30/0.46 ( ( graph_homomorphism @ A @ B @ B @ G_12 @ G_22 @ ( id_on @ B @ ( labeled_vertices @ A @ B @ G_12 ) ) )
% 0.30/0.46 = ( ( G_12
% 0.30/0.46 = ( restrict @ A @ B @ G_12 ) )
% 0.30/0.46 & ( G_22
% 0.30/0.46 = ( restrict @ A @ B @ G_22 ) )
% 0.30/0.46 & ( ( graph_union @ A @ B @ G_12 @ G_22 )
% 0.30/0.46 = G_22 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subgraph_def
% 0.30/0.46 thf(fact_232_subgraph__subset_I2_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,G_12: labeled_graph @ A @ B,G_22: labeled_graph @ A @ B] :
% 0.30/0.46 ( ( graph_homomorphism @ A @ B @ B @ G_12 @ G_22 @ ( id_on @ B @ ( labeled_vertices @ A @ B @ G_12 ) ) )
% 0.30/0.46 => ( ord_less_eq @ ( set @ ( product_prod @ A @ ( product_prod @ B @ B ) ) ) @ ( labeled_edges @ A @ B @ ( restrict @ A @ B @ G_12 ) ) @ ( labeled_edges @ A @ B @ G_22 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subgraph_subset(2)
% 0.30/0.46 thf(fact_233_subgraph__def2,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,G_12: labeled_graph @ A @ B,G_22: labeled_graph @ A @ B] :
% 0.30/0.46 ( ( G_12
% 0.30/0.46 = ( restrict @ A @ B @ G_12 ) )
% 0.30/0.46 => ( ( G_22
% 0.30/0.46 = ( restrict @ A @ B @ G_22 ) )
% 0.30/0.46 => ( ( graph_homomorphism @ A @ B @ B @ G_12 @ G_22 @ ( id_on @ B @ ( labeled_vertices @ A @ B @ G_12 ) ) )
% 0.30/0.46 = ( ( ord_less_eq @ ( set @ B ) @ ( labeled_vertices @ A @ B @ G_12 ) @ ( labeled_vertices @ A @ B @ G_22 ) )
% 0.30/0.46 & ( ord_less_eq @ ( set @ ( product_prod @ A @ ( product_prod @ B @ B ) ) ) @ ( labeled_edges @ A @ B @ G_12 ) @ ( labeled_edges @ A @ B @ G_22 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subgraph_def2
% 0.30/0.46 thf(fact_234_gr_I1_J,axiom,
% 0.30/0.46 ( ( getRel @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) @ ( standard_S_Idt @ a ) @ g )
% 0.30/0.46 = ( id_on @ ( sum_sum @ a @ b ) @ ( labeled_vertices @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) @ g ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % gr(1)
% 0.30/0.46 thf(fact_235_insert__subsetI,axiom,
% 0.30/0.46 ! [A: $tType,X3: A,A4: set @ A,X2: set @ A] :
% 0.30/0.46 ( ( member @ A @ X3 @ A4 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ X2 @ A4 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X3 @ X2 ) @ A4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_subsetI
% 0.30/0.46 thf(fact_236_ssubst__Pair__rhs,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,R: A,S: B,R2: set @ ( product_prod @ A @ B ),S2: B] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R @ S ) @ R2 )
% 0.30/0.46 => ( ( S2 = S )
% 0.30/0.46 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R @ S2 ) @ R2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ssubst_Pair_rhs
% 0.30/0.46 thf(fact_237_subset__emptyI,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] :
% 0.30/0.46 ( ! [X5: A] :
% 0.30/0.46 ~ ( member @ A @ X5 @ A4 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_emptyI
% 0.30/0.46 thf(fact_238_getRel__subgraph,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,Y: A,Z2: A,L3: B,G: labeled_graph @ B @ A,G7: labeled_graph @ B @ A] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y @ Z2 ) @ ( getRel @ B @ A @ L3 @ G ) )
% 0.30/0.46 => ( ( graph_homomorphism @ B @ A @ A @ G @ G7 @ ( id_on @ A @ ( labeled_vertices @ B @ A @ G ) ) )
% 0.30/0.46 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y @ Z2 ) @ ( getRel @ B @ A @ L3 @ G7 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % getRel_subgraph
% 0.30/0.46 thf(fact_239_gr_I2_J,axiom,
% 0.30/0.46 ( ( getRel @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) @ ( standard_S_Bot @ a ) @ g )
% 0.30/0.46 = ( bot_bot @ ( set @ ( product_prod @ ( sum_sum @ a @ b ) @ ( sum_sum @ a @ b ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % gr(2)
% 0.30/0.46 thf(fact_240_Standard__Constant_Odistinct_I7_J,axiom,
% 0.30/0.46 ! [V: $tType] :
% 0.30/0.46 ( ( standard_S_Bot @ V )
% 0.30/0.46 != ( standard_S_Idt @ V ) ) ).
% 0.30/0.46
% 0.30/0.46 % Standard_Constant.distinct(7)
% 0.30/0.46 thf(fact_241_getRel__homR,axiom,
% 0.30/0.46 ! [C: $tType,A: $tType,B: $tType,Y: A,Z2: A,L3: B,G: labeled_graph @ B @ A,U: C,F: set @ ( product_prod @ A @ C ),V3: C] :
% 0.30/0.46 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y @ Z2 ) @ ( getRel @ B @ A @ L3 @ G ) )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ C ) @ ( product_Pair @ A @ C @ Y @ U ) @ F )
% 0.30/0.46 => ( ( member @ ( product_prod @ A @ C ) @ ( product_Pair @ A @ C @ Z2 @ V3 ) @ F )
% 0.30/0.46 => ( member @ ( product_prod @ C @ C ) @ ( product_Pair @ C @ C @ U @ V3 ) @ ( getRel @ B @ C @ L3 @ ( map_graph @ A @ C @ B @ F @ G ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % getRel_homR
% 0.30/0.46 thf(fact_242_getRel__dom_I2_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,G: labeled_graph @ A @ B,A2: B,B2: B,L3: A] :
% 0.30/0.46 ( ( G
% 0.30/0.46 = ( restrict @ A @ B @ G ) )
% 0.30/0.46 => ( ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ A2 @ B2 ) @ ( getRel @ A @ B @ L3 @ G ) )
% 0.30/0.46 => ( member @ B @ B2 @ ( labeled_vertices @ A @ B @ G ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % getRel_dom(2)
% 0.30/0.46 thf(fact_243_getRel__dom_I1_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,G: labeled_graph @ A @ B,A2: B,B2: B,L3: A] :
% 0.30/0.46 ( ( G
% 0.30/0.46 = ( restrict @ A @ B @ G ) )
% 0.30/0.46 => ( ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ A2 @ B2 ) @ ( getRel @ A @ B @ L3 @ G ) )
% 0.30/0.46 => ( member @ B @ A2 @ ( labeled_vertices @ A @ B @ G ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % getRel_dom(1)
% 0.30/0.46 thf(fact_244_nonempty__rule,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,G: labeled_graph @ A @ B] :
% 0.30/0.46 ( ( G
% 0.30/0.46 = ( restrict @ A @ B @ G ) )
% 0.30/0.46 => ( ( maintained @ A @ nat @ B @ ( standa244753842y_rule @ A ) @ G )
% 0.30/0.46 = ( ( labeled_vertices @ A @ B @ G )
% 0.30/0.46 != ( bot_bot @ ( set @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nonempty_rule
% 0.30/0.46 thf(fact_245_le__numeral__extra_I4_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord1659791738miring @ A )
% 0.30/0.46 => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_numeral_extra(4)
% 0.30/0.46 thf(fact_246__092_060open_062maintained_A_Isymmetry__rule_AS__Idt_J_AG_092_060close_062,axiom,
% 0.30/0.46 maintained @ ( standard_Constant @ a ) @ nat @ ( sum_sum @ a @ b ) @ ( standa1805702094y_rule @ ( standard_Constant @ a ) @ ( standard_S_Idt @ a ) ) @ g ).
% 0.30/0.46
% 0.30/0.46 % \<open>maintained (symmetry_rule S_Idt) G\<close>
% 0.30/0.46 thf(fact_247__092_060open_062maintained_A_Itransitive__rule_AS__Idt_J_AG_092_060close_062,axiom,
% 0.30/0.46 maintained @ ( standard_Constant @ a ) @ nat @ ( sum_sum @ a @ b ) @ ( standa2114124375e_rule @ ( standard_Constant @ a ) @ ( standard_S_Idt @ a ) ) @ g ).
% 0.30/0.46
% 0.30/0.46 % \<open>maintained (transitive_rule S_Idt) G\<close>
% 0.30/0.46 thf(fact_248_le__numeral__extra_I3_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord1659791738miring @ A )
% 0.30/0.46 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_numeral_extra(3)
% 0.30/0.46 thf(fact_249__092_060open_062maintained_A_Icongruence__rule_AS__Idt_Al_J_AG_092_060close_062,axiom,
% 0.30/0.46 maintained @ ( standard_Constant @ a ) @ nat @ ( sum_sum @ a @ b ) @ ( standa1068660421e_rule @ ( standard_Constant @ a ) @ ( standard_S_Idt @ a ) @ l ) @ g ).
% 0.30/0.46
% 0.30/0.46 % \<open>maintained (congruence_rule S_Idt l) G\<close>
% 0.30/0.46 thf(fact_250_maintained__refl,axiom,
% 0.30/0.46 ! [B: $tType,C: $tType,A: $tType,R2: labeled_graph @ A @ B,G: labeled_graph @ A @ C] : ( maintained @ A @ B @ C @ ( product_Pair @ ( labeled_graph @ A @ B ) @ ( labeled_graph @ A @ B ) @ R2 @ R2 ) @ G ) ).
% 0.30/0.46
% 0.30/0.46 % maintained_refl
% 0.30/0.46 thf(fact_251_maintainedD2,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType,B: $tType,A4: labeled_graph @ A @ B,B6: labeled_graph @ A @ B,G: labeled_graph @ A @ C,F: set @ ( product_prod @ B @ C )] :
% 0.30/0.46 ( ( maintained @ A @ B @ C @ ( product_Pair @ ( labeled_graph @ A @ B ) @ ( labeled_graph @ A @ B ) @ A4 @ B6 ) @ G )
% 0.30/0.46 => ( ( graph_homomorphism @ A @ B @ C @ A4 @ G @ F )
% 0.30/0.46 => ~ ! [G5: set @ ( product_prod @ B @ C )] :
% 0.30/0.46 ( ( graph_homomorphism @ A @ B @ C @ B6 @ G @ G5 )
% 0.30/0.46 => ~ ( ord_less_eq @ ( set @ ( product_prod @ B @ C ) ) @ F @ G5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % maintainedD2
% 0.30/0.46 thf(fact_252_equivalence,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,G: labeled_graph @ A @ B,I2: A] :
% 0.30/0.46 ( ( G
% 0.30/0.46 = ( restrict @ A @ B @ G ) )
% 0.30/0.46 => ( ! [X5: product_prod @ ( labeled_graph @ A @ nat ) @ ( labeled_graph @ A @ nat )] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( labeled_graph @ A @ nat ) @ ( labeled_graph @ A @ nat ) ) @ X5 @ ( insert @ ( product_prod @ ( labeled_graph @ A @ nat ) @ ( labeled_graph @ A @ nat ) ) @ ( standa245363227y_rule @ A @ I2 ) @ ( insert @ ( product_prod @ ( labeled_graph @ A @ nat ) @ ( labeled_graph @ A @ nat ) ) @ ( standa2114124375e_rule @ A @ I2 ) @ ( insert @ ( product_prod @ ( labeled_graph @ A @ nat ) @ ( labeled_graph @ A @ nat ) ) @ ( standa1805702094y_rule @ A @ I2 ) @ ( bot_bot @ ( set @ ( product_prod @ ( labeled_graph @ A @ nat ) @ ( labeled_graph @ A @ nat ) ) ) ) ) ) ) )
% 0.30/0.46 => ( maintained @ A @ nat @ B @ X5 @ G ) )
% 0.30/0.46 => ( equiv_equiv @ B @ ( labeled_vertices @ A @ B @ G ) @ ( getRel @ A @ B @ I2 @ G ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % equivalence
% 0.30/0.46
% 0.30/0.46 % Type constructors (27)
% 0.30/0.46 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 0.30/0.46 ! [A10: $tType,A11: $tType] :
% 0.30/0.46 ( ( order_bot @ A11 )
% 0.30/0.46 => ( order_bot @ ( A10 > A11 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.30/0.46 ! [A10: $tType,A11: $tType] :
% 0.30/0.46 ( ( preorder @ A11 )
% 0.30/0.46 => ( preorder @ ( A10 > A11 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.30/0.46 ! [A10: $tType,A11: $tType] :
% 0.30/0.46 ( ( order @ A11 )
% 0.30/0.46 => ( order @ ( A10 > A11 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Orderings_Oord,axiom,
% 0.30/0.46 ! [A10: $tType,A11: $tType] :
% 0.30/0.46 ( ( ord @ A11 )
% 0.30/0.46 => ( ord @ ( A10 > A11 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Orderings_Obot,axiom,
% 0.30/0.46 ! [A10: $tType,A11: $tType] :
% 0.30/0.46 ( ( bot @ A11 )
% 0.30/0.46 => ( bot @ ( A10 > A11 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.30/0.46 canoni770627133id_add @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring,axiom,
% 0.30/0.46 linord1659791738miring @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Orderings_Oorder__bot_1,axiom,
% 0.30/0.46 order_bot @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Rings_Ozero__neq__one,axiom,
% 0.30/0.46 zero_neq_one @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Orderings_Opreorder_2,axiom,
% 0.30/0.46 preorder @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.30/0.46 linorder @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Orderings_Oorder_3,axiom,
% 0.30/0.46 order @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Orderings_Oord_4,axiom,
% 0.30/0.46 ord @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Orderings_Obot_5,axiom,
% 0.30/0.46 bot @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 0.30/0.46 zero @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 0.30/0.46 one @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Orderings_Oorder__bot_6,axiom,
% 0.30/0.46 ! [A10: $tType] : ( order_bot @ ( set @ A10 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Orderings_Opreorder_7,axiom,
% 0.30/0.46 ! [A10: $tType] : ( preorder @ ( set @ A10 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Orderings_Oorder_8,axiom,
% 0.30/0.46 ! [A10: $tType] : ( order @ ( set @ A10 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Orderings_Oord_9,axiom,
% 0.30/0.46 ! [A10: $tType] : ( ord @ ( set @ A10 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Orderings_Obot_10,axiom,
% 0.30/0.46 ! [A10: $tType] : ( bot @ ( set @ A10 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Oorder__bot_11,axiom,
% 0.30/0.46 order_bot @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Opreorder_12,axiom,
% 0.30/0.46 preorder @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Olinorder_13,axiom,
% 0.30/0.46 linorder @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Oorder_14,axiom,
% 0.30/0.46 order @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Oord_15,axiom,
% 0.30/0.46 ord @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Obot_16,axiom,
% 0.30/0.46 bot @ $o ).
% 0.30/0.46
% 0.30/0.46 % Conjectures (1)
% 0.30/0.46 thf(conj_0,conjecture,
% 0.30/0.46 ( ( ( labeled_vertices @ ( standard_Constant @ a ) @ nat @ ( labeled_LG @ ( standard_Constant @ a ) @ nat @ ( insert @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) ) @ ( product_Pair @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) @ ( standard_S_Idt @ a ) @ ( product_Pair @ nat @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ) @ ( bot_bot @ ( set @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) ) ) ) ) @ ( insert @ nat @ ( zero_zero @ nat ) @ ( bot_bot @ ( set @ nat ) ) ) ) )
% 0.30/0.46 = ( domain @ nat @ ( sum_sum @ a @ b ) @ ( insert @ ( product_prod @ nat @ ( sum_sum @ a @ b ) ) @ ( product_Pair @ nat @ ( sum_sum @ a @ b ) @ ( zero_zero @ nat ) @ v ) @ ( bot_bot @ ( set @ ( product_prod @ nat @ ( sum_sum @ a @ b ) ) ) ) ) ) )
% 0.30/0.46 & ( ( labeled_LG @ ( standard_Constant @ a ) @ nat @ ( insert @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) ) @ ( product_Pair @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) @ ( standard_S_Idt @ a ) @ ( product_Pair @ nat @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ) @ ( bot_bot @ ( set @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) ) ) ) ) @ ( insert @ nat @ ( zero_zero @ nat ) @ ( bot_bot @ ( set @ nat ) ) ) )
% 0.30/0.46 = ( restrict @ ( standard_Constant @ a ) @ nat @ ( labeled_LG @ ( standard_Constant @ a ) @ nat @ ( insert @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) ) @ ( product_Pair @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) @ ( standard_S_Idt @ a ) @ ( product_Pair @ nat @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ) @ ( bot_bot @ ( set @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) ) ) ) ) @ ( insert @ nat @ ( zero_zero @ nat ) @ ( bot_bot @ ( set @ nat ) ) ) ) ) )
% 0.30/0.46 & ( g
% 0.30/0.46 = ( restrict @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) @ g ) )
% 0.30/0.46 & ( ord_less_eq @ ( set @ ( sum_sum @ a @ b ) ) @ ( image @ nat @ ( sum_sum @ a @ b ) @ ( insert @ ( product_prod @ nat @ ( sum_sum @ a @ b ) ) @ ( product_Pair @ nat @ ( sum_sum @ a @ b ) @ ( zero_zero @ nat ) @ v ) @ ( bot_bot @ ( set @ ( product_prod @ nat @ ( sum_sum @ a @ b ) ) ) ) ) @ ( labeled_vertices @ ( standard_Constant @ a ) @ nat @ ( labeled_LG @ ( standard_Constant @ a ) @ nat @ ( insert @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) ) @ ( product_Pair @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) @ ( standard_S_Idt @ a ) @ ( product_Pair @ nat @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ) @ ( bot_bot @ ( set @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) ) ) ) ) @ ( insert @ nat @ ( zero_zero @ nat ) @ ( bot_bot @ ( set @ nat ) ) ) ) ) ) @ ( labeled_vertices @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) @ g ) )
% 0.30/0.46 & ( univalent @ nat @ ( sum_sum @ a @ b ) @ ( insert @ ( product_prod @ nat @ ( sum_sum @ a @ b ) ) @ ( product_Pair @ nat @ ( sum_sum @ a @ b ) @ ( zero_zero @ nat ) @ v ) @ ( bot_bot @ ( set @ ( product_prod @ nat @ ( sum_sum @ a @ b ) ) ) ) ) )
% 0.30/0.46 & ( edge_preserving @ nat @ ( sum_sum @ a @ b ) @ ( standard_Constant @ a ) @ ( insert @ ( product_prod @ nat @ ( sum_sum @ a @ b ) ) @ ( product_Pair @ nat @ ( sum_sum @ a @ b ) @ ( zero_zero @ nat ) @ v ) @ ( bot_bot @ ( set @ ( product_prod @ nat @ ( sum_sum @ a @ b ) ) ) ) ) @ ( labeled_edges @ ( standard_Constant @ a ) @ nat @ ( labeled_LG @ ( standard_Constant @ a ) @ nat @ ( insert @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) ) @ ( product_Pair @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) @ ( standard_S_Idt @ a ) @ ( product_Pair @ nat @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ) @ ( bot_bot @ ( set @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) ) ) ) ) @ ( insert @ nat @ ( zero_zero @ nat ) @ ( bot_bot @ ( set @ nat ) ) ) ) ) @ ( labeled_edges @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) @ g ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 2.86/1.53 ---- Embedded in THF ---
% 2.86/1.53 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.86/1.53 %%% Generated on Tue Feb 24 08:29:22 EST 2026
% 2.86/1.53 %%% using '$$dhol' embedding, version 1.3.0.
% 2.86/1.53 %%% Logic specification used:
% 2.86/1.53 %%% thf(spec, logic, $$dhol).
% 2.86/1.53
% 2.86/1.53 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.L5LtdenOSc/DTF2DTF15863.p
% 2.86/1.53 thf(ty_t_LabeledGraphSemantics_OStandard__Constant, type, standard_Constant: ($tType > $tType)).
% 2.86/1.53 thf(ty_t_LabeledGraphs_Olabeled__graph, type, labeled_graph: ($tType > ($tType > $tType))).
% 2.86/1.53 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.86/1.53 thf(ty_t_Sum__Type_Osum, type, sum_sum: ($tType > ($tType > $tType))).
% 2.86/1.53 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.86/1.53 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.86/1.53 thf(ty_tf_b, type, b: $tType).
% 2.86/1.53 thf(ty_tf_a, type, a: $tType).
% 2.86/1.53 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.86/1.53 thf(sy_cl_Groups_Oone, type, one: (!> [A:$tType]: ($o))).
% 2.86/1.53 thf(sy_cl_Groups_Ozero, type, zero: (!> [A:$tType]: ($o))).
% 2.86/1.53 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: ($o))).
% 2.86/1.53 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.86/1.53 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 2.86/1.53 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.86/1.53 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 2.86/1.53 thf(sy_cl_Rings_Ozero__neq__one, type, zero_neq_one: (!> [A:$tType]: ($o))).
% 2.86/1.53 thf(sy_cl_Orderings_Oorder__bot, type, order_bot: (!> [A:$tType]: ($o))).
% 2.86/1.53 thf(sy_cl_Rings_Olinordered__nonzero__semiring, type, linord1659791738miring: (!> [A:$tType]: ($o))).
% 2.86/1.53 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: ($o))).
% 2.86/1.53 thf(sy_c_Equiv__Relations_Oequiv, type, equiv_equiv: (!> [A:$tType]: (((set @ A) > ((set @ ((product_prod @ A) @ A)) > $o))))).
% 2.86/1.53 thf(sy_c_Groups_Oone__class_Oone, type, one_one: (!> [A:$tType]: (A))).
% 2.86/1.53 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 2.86/1.53 thf(sy_c_LabeledGraphSemantics_OStandard__Constant_OS__Bot, type, standard_S_Bot: (!> [V:$tType]: ((standard_Constant @ V)))).
% 2.86/1.53 thf(sy_c_LabeledGraphSemantics_OStandard__Constant_OS__Idt, type, standard_S_Idt: (!> [V:$tType]: ((standard_Constant @ V)))).
% 2.86/1.53 thf(sy_c_LabeledGraphSemantics_OgetRel, type, getRel: (!> [B:$tType,A:$tType]: ((B > (((labeled_graph @ B) @ A) > (set @ ((product_prod @ A) @ A))))))).
% 2.86/1.53 thf(sy_c_LabeledGraphs_Oedge__preserving, type, edge_preserving: (!> [A:$tType,B:$tType,C:$tType]: (((set @ ((product_prod @ A) @ B)) > ((set @ ((product_prod @ C) @ ((product_prod @ A) @ A))) > ((set @ ((product_prod @ C) @ ((product_prod @ B) @ B))) > $o)))))).
% 2.86/1.53 thf(sy_c_LabeledGraphs_Ograph__homomorphism, type, graph_homomorphism: (!> [A:$tType,B:$tType,C:$tType]: ((((labeled_graph @ A) @ B) > (((labeled_graph @ A) @ C) > ((set @ ((product_prod @ B) @ C)) > $o)))))).
% 2.86/1.53 thf(sy_c_LabeledGraphs_Ograph__union, type, graph_union: (!> [A:$tType,B:$tType]: ((((labeled_graph @ A) @ B) > (((labeled_graph @ A) @ B) > ((labeled_graph @ A) @ B)))))).
% 2.86/1.53 thf(sy_c_LabeledGraphs_Olabeled__graph_OLG, type, labeled_LG: (!> [L:$tType,V:$tType]: (((set @ ((product_prod @ L) @ ((product_prod @ V) @ V))) > ((set @ V) > ((labeled_graph @ L) @ V)))))).
% 2.86/1.53 thf(sy_c_LabeledGraphs_Olabeled__graph_Oedges, type, labeled_edges: (!> [L:$tType,V:$tType]: ((((labeled_graph @ L) @ V) > (set @ ((product_prod @ L) @ ((product_prod @ V) @ V))))))).
% 2.86/1.53 thf(sy_c_LabeledGraphs_Olabeled__graph_Overtices, type, labeled_vertices: (!> [L:$tType,V:$tType]: ((((labeled_graph @ L) @ V) > (set @ V))))).
% 2.86/1.53 thf(sy_c_LabeledGraphs_Omap__graph, type, map_graph: (!> [C:$tType,B:$tType,A:$tType]: (((set @ ((product_prod @ C) @ B)) > (((labeled_graph @ A) @ C) > ((labeled_graph @ A) @ B)))))).
% 2.86/1.53 thf(sy_c_LabeledGraphs_Oon__triple, type, on_triple: (!> [B:$tType,C:$tType,A:$tType]: (((set @ ((product_prod @ B) @ C)) > (set @ ((product_prod @ ((product_prod @ A) @ ((product_prod @ B) @ B))) @ ((product_prod @ A) @ ((product_prod @ C) @ C)))))))).
% 2.86/1.53 thf(sy_c_LabeledGraphs_Orestrict, type, restrict: (!> [A:$tType,B:$tType]: ((((labeled_graph @ A) @ B) > ((labeled_graph @ A) @ B))))).
% 2.86/1.53 thf(sy_c_MissingRelation_Ounivalent, type, univalent: (!> [A:$tType,B:$tType]: (((set @ ((product_prod @ A) @ B)) > $o)))).
% 2.86/1.53 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 2.86/1.53 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.86/1.53 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 2.86/1.53 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 2.86/1.53 thf(sy_c_Relation_ODomain, type, domain: (!> [A:$tType,B:$tType]: (((set @ ((product_prod @ A) @ B)) > (set @ A))))).
% 2.86/1.53 thf(sy_c_Relation_OId__on, type, id_on: (!> [A:$tType]: (((set @ A) > (set @ ((product_prod @ A) @ A)))))).
% 2.86/1.53 thf(sy_c_Relation_OImage, type, image: (!> [A:$tType,B:$tType]: (((set @ ((product_prod @ A) @ B)) > ((set @ A) > (set @ B)))))).
% 2.86/1.53 thf(sy_c_RulesAndChains_Omaintained, type, maintained: (!> [L:$tType,X:$tType,V:$tType]: ((((product_prod @ ((labeled_graph @ L) @ X)) @ ((labeled_graph @ L) @ X)) > (((labeled_graph @ L) @ V) > $o))))).
% 2.86/1.53 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.86/1.53 thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 2.86/1.53 thf(sy_c_Set_Ois__singleton, type, is_singleton: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.86/1.53 thf(sy_c_Set_Othe__elem, type, the_elem: (!> [A:$tType]: (((set @ A) > A)))).
% 2.86/1.53 thf(sy_c_StandardRules__Mirabelle__xlrcbcygrg_Ocongruence__rule, type, standa1068660421e_rule: (!> [L:$tType]: ((L > (L > ((product_prod @ ((labeled_graph @ L) @ nat)) @ ((labeled_graph @ L) @ nat))))))).
% 2.86/1.53 thf(sy_c_StandardRules__Mirabelle__xlrcbcygrg_Ononempty__rule, type, standa244753842y_rule: (!> [L:$tType]: (((product_prod @ ((labeled_graph @ L) @ nat)) @ ((labeled_graph @ L) @ nat))))).
% 2.86/1.53 thf(sy_c_StandardRules__Mirabelle__xlrcbcygrg_Oreflexivity__rule, type, standa245363227y_rule: (!> [L:$tType]: ((L > ((product_prod @ ((labeled_graph @ L) @ nat)) @ ((labeled_graph @ L) @ nat)))))).
% 2.86/1.53 thf(sy_c_StandardRules__Mirabelle__xlrcbcygrg_Osymmetry__rule, type, standa1805702094y_rule: (!> [L:$tType]: ((L > ((product_prod @ ((labeled_graph @ L) @ nat)) @ ((labeled_graph @ L) @ nat)))))).
% 2.86/1.53 thf(sy_c_StandardRules__Mirabelle__xlrcbcygrg_Otop__rule, type, standa400804411p_rule: (!> [L:$tType]: ((L > ((product_prod @ ((labeled_graph @ L) @ nat)) @ ((labeled_graph @ L) @ nat)))))).
% 2.86/1.53 thf(sy_c_StandardRules__Mirabelle__xlrcbcygrg_Otransitive__rule, type, standa2114124375e_rule: (!> [L:$tType]: ((L > ((product_prod @ ((labeled_graph @ L) @ nat)) @ ((labeled_graph @ L) @ nat)))))).
% 2.86/1.53 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.86/1.53 thf(sy_v_G, type, g: ((labeled_graph @ (standard_Constant @ a)) @ ((sum_sum @ a) @ b))).
% 2.86/1.53 thf(sy_v_f____, type, f: (set @ ((product_prod @ nat) @ ((sum_sum @ a) @ b)))).
% 2.86/1.53 thf(sy_v_l, type, l: (standard_Constant @ a)).
% 2.86/1.53 thf(sy_v_v____, type, v: ((sum_sum @ a) @ b)).
% 2.86/1.53 thf(fact_0_g, axiom, (g = (((restrict @ (standard_Constant @ a)) @ ((sum_sum @ a) @ b)) @ g))).
% 2.86/1.53 thf(fact_1_v, axiom, (((member @ ((sum_sum @ a) @ b)) @ v) @ (((labeled_vertices @ (standard_Constant @ a)) @ ((sum_sum @ a) @ b)) @ g))).
% 2.86/1.53 thf(fact_2__092_060open_062edge__preserving_A_123_I0_058_058_063_Hc1_M_Av_J_125_A_123_IS__Idt_M_A0_058_058_063_Hc1_M_A0_058_058_063_Hc1_J_125_A_Iedges_AG_J_092_060close_062, axiom, (! [C2:$tType]: (((zero @ C2) => ((((((edge_preserving @ C2) @ ((sum_sum @ a) @ b)) @ (standard_Constant @ a)) @ (((insert @ ((product_prod @ C2) @ ((sum_sum @ a) @ b))) @ ((((product_Pair @ C2) @ ((sum_sum @ a) @ b)) @ (zero_zero @ C2)) @ v)) @ (bot_bot @ (set @ ((product_prod @ C2) @ ((sum_sum @ a) @ b)))))) @ (((insert @ ((product_prod @ (standard_Constant @ a)) @ ((product_prod @ C2) @ C2))) @ ((((product_Pair @ (standard_Constant @ a)) @ ((product_prod @ C2) @ C2)) @ (standard_S_Idt @ a)) @ ((((product_Pair @ C2) @ C2) @ (zero_zero @ C2)) @ (zero_zero @ C2)))) @ (bot_bot @ (set @ ((product_prod @ (standard_Constant @ a)) @ ((product_prod @ C2) @ C2)))))) @ (((labeled_edges @ (standard_Constant @ a)) @ ((sum_sum @ a) @ b)) @ g)))))).
% 2.86/1.53 thf(fact_3_r, axiom, (((ord_less_eq @ (set @ ((sum_sum @ a) @ b))) @ ((((image @ nat) @ ((sum_sum @ a) @ b)) @ f) @ (((insert @ nat) @ (zero_zero @ nat)) @ (bot_bot @ (set @ nat))))) @ (((labeled_vertices @ (standard_Constant @ a)) @ ((sum_sum @ a) @ b)) @ g))).
% 2.86/1.53 thf(fact_4_f, axiom, (f = (((insert @ ((product_prod @ nat) @ ((sum_sum @ a) @ b))) @ ((((product_Pair @ nat) @ ((sum_sum @ a) @ b)) @ (zero_zero @ nat)) @ v)) @ (bot_bot @ (set @ ((product_prod @ nat) @ ((sum_sum @ a) @ b))))))).
% 2.86/1.53 thf(fact_5_d, axiom, ((((domain @ nat) @ ((sum_sum @ a) @ b)) @ f) = (((insert @ nat) @ (zero_zero @ nat)) @ (bot_bot @ (set @ nat))))).
% 2.86/1.53 thf(fact_6_graph__single, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,C3:B]: ((((((labeled_LG @ A) @ B) @ (((insert @ ((product_prod @ A) @ ((product_prod @ B) @ B))) @ ((((product_Pair @ A) @ ((product_prod @ B) @ B)) @ A2) @ ((((product_Pair @ B) @ B) @ B2) @ C3))) @ (bot_bot @ (set @ ((product_prod @ A) @ ((product_prod @ B) @ B)))))) @ (((insert @ B) @ B2) @ (((insert @ B) @ C3) @ (bot_bot @ (set @ B))))) = (((restrict @ A) @ B) @ ((((labeled_LG @ A) @ B) @ (((insert @ ((product_prod @ A) @ ((product_prod @ B) @ B))) @ ((((product_Pair @ A) @ ((product_prod @ B) @ B)) @ A2) @ ((((product_Pair @ B) @ B) @ B2) @ C3))) @ (bot_bot @ (set @ ((product_prod @ A) @ ((product_prod @ B) @ B)))))) @ (((insert @ B) @ B2) @ (((insert @ B) @ C3) @ (bot_bot @ (set @ B)))))))))).
% 2.86/1.53 thf(fact_7__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062v_O_A_I0_M_Av_J_A_092_060in_062_Af_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [V2:((sum_sum @ a) @ b)]: ((~ ((((member @ ((product_prod @ nat) @ ((sum_sum @ a) @ b))) @ ((((product_Pair @ nat) @ ((sum_sum @ a) @ b)) @ (zero_zero @ nat)) @ V2)) @ f)))))))).
% 2.86/1.53 thf(fact_8_u, axiom, (((univalent @ nat) @ ((sum_sum @ a) @ b)) @ f)).
% 2.86/1.53 thf(fact_9_Domain__insert, axiom, (! [B:$tType,A:$tType,A2:A,B2:B,R:(set @ ((product_prod @ A) @ B))]: (((((domain @ A) @ B) @ (((insert @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) @ R)) = (((insert @ A) @ A2) @ (((domain @ A) @ B) @ R)))))).
% 2.86/1.53 thf(fact_10_Image__singleton__iff, axiom, (! [A:$tType,B:$tType,B2:A,R:(set @ ((product_prod @ B) @ A)),A2:B]: (((((member @ A) @ B2) @ ((((image @ B) @ A) @ R) @ (((insert @ B) @ A2) @ (bot_bot @ (set @ B))))) = (((member @ ((product_prod @ B) @ A)) @ ((((product_Pair @ B) @ A) @ A2) @ B2)) @ R))))).
% 2.86/1.53 thf(fact_11_graph__empty__e, axiom, (! [A:$tType,B:$tType,V3:(set @ B)]: ((((((labeled_LG @ A) @ B) @ (bot_bot @ (set @ ((product_prod @ A) @ ((product_prod @ B) @ B))))) @ V3) = (((restrict @ A) @ B) @ ((((labeled_LG @ A) @ B) @ (bot_bot @ (set @ ((product_prod @ A) @ ((product_prod @ B) @ B))))) @ V3)))))).
% 2.86/1.53 thf(fact_12_labeled__graph_Ocollapse, axiom, (! [V:$tType,L:$tType,Labeled_graph:((labeled_graph @ L) @ V)]: ((((((labeled_LG @ L) @ V) @ (((labeled_edges @ L) @ V) @ Labeled_graph)) @ (((labeled_vertices @ L) @ V) @ Labeled_graph)) = Labeled_graph)))).
% 2.86/1.53 thf(fact_13_Domain__empty, axiom, (! [B:$tType,A:$tType]: (((((domain @ A) @ B) @ (bot_bot @ (set @ ((product_prod @ A) @ B)))) = (bot_bot @ (set @ A)))))).
% 2.86/1.53 thf(fact_14_Image__empty1, axiom, (! [B:$tType,A:$tType,X2:(set @ B)]: ((((((image @ B) @ A) @ (bot_bot @ (set @ ((product_prod @ B) @ A)))) @ X2) = (bot_bot @ (set @ A)))))).
% 2.86/1.53 thf(fact_15_restrict__idemp, axiom, (! [B:$tType,A:$tType,X3:((labeled_graph @ A) @ B)]: (((((restrict @ A) @ B) @ (((restrict @ A) @ B) @ X3)) = (((restrict @ A) @ B) @ X3))))).
% 2.86/1.53 thf(fact_16_labeled__graph_Oinject, axiom, (! [L:$tType,V:$tType,X1:(set @ ((product_prod @ L) @ ((product_prod @ V) @ V))),X22:(set @ V),Y1:(set @ ((product_prod @ L) @ ((product_prod @ V) @ V))),Y2:(set @ V)]: (((((((labeled_LG @ L) @ V) @ X1) @ X22) = ((((labeled_LG @ L) @ V) @ Y1) @ Y2)) = ((X1 = Y1) & (X22 = Y2)))))).
% 2.86/1.53 thf(fact_17_v__gr, axiom, (! [A3:((sum_sum @ a) @ b),B3:((sum_sum @ a) @ b)]: (((((member @ ((product_prod @ (standard_Constant @ a)) @ ((product_prod @ ((sum_sum @ a) @ b)) @ ((sum_sum @ a) @ b)))) @ ((((product_Pair @ (standard_Constant @ a)) @ ((product_prod @ ((sum_sum @ a) @ b)) @ ((sum_sum @ a) @ b))) @ (standard_S_Idt @ a)) @ ((((product_Pair @ ((sum_sum @ a) @ b)) @ ((sum_sum @ a) @ b)) @ A3) @ B3))) @ (((labeled_edges @ (standard_Constant @ a)) @ ((sum_sum @ a) @ b)) @ g)) = ((((member @ ((sum_sum @ a) @ b)) @ A3) @ (((labeled_vertices @ (standard_Constant @ a)) @ ((sum_sum @ a) @ b)) @ g)) & (B3 = A3)))))).
% 2.86/1.53 thf(fact_18__092_060open_062_IS__Idt_M_Av_M_Av_J_A_092_060in_062_Aedges_AG_092_060close_062, axiom, (((member @ ((product_prod @ (standard_Constant @ a)) @ ((product_prod @ ((sum_sum @ a) @ b)) @ ((sum_sum @ a) @ b)))) @ ((((product_Pair @ (standard_Constant @ a)) @ ((product_prod @ ((sum_sum @ a) @ b)) @ ((sum_sum @ a) @ b))) @ (standard_S_Idt @ a)) @ ((((product_Pair @ ((sum_sum @ a) @ b)) @ ((sum_sum @ a) @ b)) @ v) @ v))) @ (((labeled_edges @ (standard_Constant @ a)) @ ((sum_sum @ a) @ b)) @ g))).
% 2.86/1.53 thf(fact_19_ImageI, axiom, (! [B:$tType,A:$tType,A2:A,B2:B,R:(set @ ((product_prod @ A) @ B)),A4:(set @ A)]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) @ R) => ((((member @ A) @ A2) @ A4) => (((member @ B) @ B2) @ ((((image @ A) @ B) @ R) @ A4))))))).
% 2.86/1.53 thf(fact_20_Image__empty2, axiom, (! [B:$tType,A:$tType,R2:(set @ ((product_prod @ B) @ A))]: ((((((image @ B) @ A) @ R2) @ (bot_bot @ (set @ B))) = (bot_bot @ (set @ A)))))).
% 2.86/1.53 thf(fact_21_vertices__restrict, axiom, (! [A:$tType,B:$tType,G:((labeled_graph @ B) @ A)]: (((((labeled_vertices @ B) @ A) @ (((restrict @ B) @ A) @ G)) = (((labeled_vertices @ B) @ A) @ G))))).
% 2.86/1.53 thf(fact_22__092_060open_062graph__homomorphism_A_ILG_A_123_125_A_1230_125_J_AG_Af_092_060close_062, axiom, ((((((graph_homomorphism @ (standard_Constant @ a)) @ nat) @ ((sum_sum @ a) @ b)) @ ((((labeled_LG @ (standard_Constant @ a)) @ nat) @ (bot_bot @ (set @ ((product_prod @ (standard_Constant @ a)) @ ((product_prod @ nat) @ nat))))) @ (((insert @ nat) @ (zero_zero @ nat)) @ (bot_bot @ (set @ nat))))) @ g) @ f)).
% 2.86/1.53 thf(fact_23_labeled__graph_Oexhaust, axiom, (! [L:$tType,V:$tType,Y:((labeled_graph @ L) @ V)]: ((~ ((! [X12:(set @ ((product_prod @ L) @ ((product_prod @ V) @ V))),X23:(set @ V)]: ((Y != ((((labeled_LG @ L) @ V) @ X12) @ X23))))))))).
% 2.86/1.53 thf(fact_24_labeled__graph_Oinduct, axiom, (! [V:$tType,L:$tType,P:(((labeled_graph @ L) @ V) > $o),Labeled_graph:((labeled_graph @ L) @ V)]: (((! [X1a:(set @ ((product_prod @ L) @ ((product_prod @ V) @ V))),X2a:(set @ V)]: ((P @ ((((labeled_LG @ L) @ V) @ X1a) @ X2a)))) => (P @ Labeled_graph))))).
% 2.86/1.53 thf(fact_25_rev__ImageI, axiom, (! [B:$tType,A:$tType,A2:A,A4:(set @ A),B2:B,R:(set @ ((product_prod @ A) @ B))]: (((((member @ A) @ A2) @ A4) => ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) @ R) => (((member @ B) @ B2) @ ((((image @ A) @ B) @ R) @ A4))))))).
% 2.86/1.53 thf(fact_26_Image__iff, axiom, (! [A:$tType,B:$tType,B2:A,R:(set @ ((product_prod @ B) @ A)),A4:(set @ B)]: (((((member @ A) @ B2) @ ((((image @ B) @ A) @ R) @ A4)) = (? [X4:B]: (((((member @ B) @ X4) @ A4) & (((member @ ((product_prod @ B) @ A)) @ ((((product_Pair @ B) @ A) @ X4) @ B2)) @ R)))))))).
% 2.86/1.53 thf(fact_27_ImageE, axiom, (! [A:$tType,B:$tType,B2:A,R:(set @ ((product_prod @ B) @ A)),A4:(set @ B)]: (((((member @ A) @ B2) @ ((((image @ B) @ A) @ R) @ A4)) => (~ ((! [X5:B]: (((((member @ ((product_prod @ B) @ A)) @ ((((product_Pair @ B) @ A) @ X5) @ B2)) @ R) => (~ ((((member @ B) @ X5) @ A4)))))))))))).
% 2.86/1.53 thf(fact_28_Image__mono, axiom, (! [B:$tType,A:$tType,R3:(set @ ((product_prod @ A) @ B)),R:(set @ ((product_prod @ A) @ B)),A5:(set @ A),A4:(set @ A)]: (((((ord_less_eq @ (set @ ((product_prod @ A) @ B))) @ R3) @ R) => ((((ord_less_eq @ (set @ A)) @ A5) @ A4) => (((ord_less_eq @ (set @ B)) @ ((((image @ A) @ B) @ R3) @ A5)) @ ((((image @ A) @ B) @ R) @ A4))))))).
% 2.86/1.53 thf(fact_29_Domain_Oinducts, axiom, (! [B:$tType,A:$tType,X3:A,R:(set @ ((product_prod @ A) @ B)),P:(A > $o)]: (((((member @ A) @ X3) @ (((domain @ A) @ B) @ R)) => ((! [A6:A,B4:B]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ A6) @ B4)) @ R) => (P @ A6)))) => (P @ X3)))))).
% 2.86/1.53 thf(fact_30_Domain_ODomainI, axiom, (! [B:$tType,A:$tType,A2:A,B2:B,R:(set @ ((product_prod @ A) @ B))]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) @ R) => (((member @ A) @ A2) @ (((domain @ A) @ B) @ R)))))).
% 2.86/1.53 thf(fact_31_Domain_Osimps, axiom, (! [B:$tType,A:$tType,A2:A,R:(set @ ((product_prod @ A) @ B))]: (((((member @ A) @ A2) @ (((domain @ A) @ B) @ R)) = (? [A7:A,B5:B]: (((A2 = A7) & (((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ A7) @ B5)) @ R)))))))).
% 2.86/1.53 thf(fact_32_Domain_Ocases, axiom, (! [B:$tType,A:$tType,A2:A,R:(set @ ((product_prod @ A) @ B))]: (((((member @ A) @ A2) @ (((domain @ A) @ B) @ R)) => (~ ((! [B4:B]: ((~ ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ A2) @ B4)) @ R))))))))))).
% 2.86/1.53 thf(fact_33_Domain__iff, axiom, (! [A:$tType,B:$tType,A2:A,R:(set @ ((product_prod @ A) @ B))]: (((((member @ A) @ A2) @ (((domain @ A) @ B) @ R)) = (? [Y3:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ A2) @ Y3)) @ R))))))).
% 2.86/1.53 thf(fact_34_DomainE, axiom, (! [B:$tType,A:$tType,A2:A,R:(set @ ((product_prod @ A) @ B))]: (((((member @ A) @ A2) @ (((domain @ A) @ B) @ R)) => (~ ((! [B4:B]: ((~ ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ A2) @ B4)) @ R))))))))))).
% 2.86/1.53 thf(fact_35_Domain__mono, axiom, (! [B:$tType,A:$tType,R:(set @ ((product_prod @ A) @ B)),S:(set @ ((product_prod @ A) @ B))]: (((((ord_less_eq @ (set @ ((product_prod @ A) @ B))) @ R) @ S) => (((ord_less_eq @ (set @ A)) @ (((domain @ A) @ B) @ R)) @ (((domain @ A) @ B) @ S)))))).
% 2.86/1.53 thf(fact_36_labeled__graph_Oexpand, axiom, (! [V:$tType,L:$tType,Labeled_graph:((labeled_graph @ L) @ V),Labeled_graph2:((labeled_graph @ L) @ V)]: (((((((labeled_edges @ L) @ V) @ Labeled_graph) = (((labeled_edges @ L) @ V) @ Labeled_graph2)) & ((((labeled_vertices @ L) @ V) @ Labeled_graph) = (((labeled_vertices @ L) @ V) @ Labeled_graph2))) => (Labeled_graph = Labeled_graph2))))).
% 2.86/1.53 thf(fact_37_labeled__graph_Osel_I2_J, axiom, (! [L:$tType,V:$tType,X1:(set @ ((product_prod @ L) @ ((product_prod @ V) @ V))),X22:(set @ V)]: (((((labeled_vertices @ L) @ V) @ ((((labeled_LG @ L) @ V) @ X1) @ X22)) = X22)))).
% 2.86/1.53 thf(fact_38_labeled__graph_Osel_I1_J, axiom, (! [V:$tType,L:$tType,X1:(set @ ((product_prod @ L) @ ((product_prod @ V) @ V))),X22:(set @ V)]: (((((labeled_edges @ L) @ V) @ ((((labeled_LG @ L) @ V) @ X1) @ X22)) = X1)))).
% 2.86/1.53 thf(fact_39_Domain__empty__iff, axiom, (! [B:$tType,A:$tType,R:(set @ ((product_prod @ A) @ B))]: ((((((domain @ A) @ B) @ R) = (bot_bot @ (set @ A))) = (R = (bot_bot @ (set @ ((product_prod @ A) @ B)))))))).
% 2.86/1.53 thf(fact_40_edge__preserving__atomic, axiom, (! [A:$tType,B:$tType,C:$tType,H1:(set @ ((product_prod @ A) @ B)),E1:(set @ ((product_prod @ C) @ ((product_prod @ A) @ A))),E2:(set @ ((product_prod @ C) @ ((product_prod @ B) @ B))),V1:A,V12:B,V22:A,V23:B,K:C]: ((((((((edge_preserving @ A) @ B) @ C) @ H1) @ E1) @ E2) => ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ V1) @ V12)) @ H1) => ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ V22) @ V23)) @ H1) => ((((member @ ((product_prod @ C) @ ((product_prod @ A) @ A))) @ ((((product_Pair @ C) @ ((product_prod @ A) @ A)) @ K) @ ((((product_Pair @ A) @ A) @ V1) @ V22))) @ E1) => (((member @ ((product_prod @ C) @ ((product_prod @ B) @ B))) @ ((((product_Pair @ C) @ ((product_prod @ B) @ B)) @ K) @ ((((product_Pair @ B) @ B) @ V12) @ V23))) @ E2)))))))).
% 2.86/1.53 thf(fact_41_labeled__graph_Oexhaust__sel, axiom, (! [V:$tType,L:$tType,Labeled_graph:((labeled_graph @ L) @ V)]: ((Labeled_graph = ((((labeled_LG @ L) @ V) @ (((labeled_edges @ L) @ V) @ Labeled_graph)) @ (((labeled_vertices @ L) @ V) @ Labeled_graph)))))).
% 2.86/1.53 thf(fact_42_singleton__insert__inj__eq_H, axiom, (! [A:$tType,A2:A,A4:(set @ A),B2:A]: ((((((insert @ A) @ A2) @ A4) = (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) = ((A2 = B2) & (((ord_less_eq @ (set @ A)) @ A4) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A))))))))).
% 2.86/1.53 thf(fact_43_singleton__insert__inj__eq, axiom, (! [A:$tType,B2:A,A2:A,A4:(set @ A)]: ((((((insert @ A) @ B2) @ (bot_bot @ (set @ A))) = (((insert @ A) @ A2) @ A4)) = ((A2 = B2) & (((ord_less_eq @ (set @ A)) @ A4) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A))))))))).
% 2.86/1.53 thf(fact_44_univalent__empty, axiom, (! [B:$tType,A:$tType]: ((((univalent @ A) @ B) @ (bot_bot @ (set @ ((product_prod @ A) @ B))))))).
% 2.86/1.53 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.86/1.53 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X4:A]: ((((member @ A) @ X4) @ A4)))) = A4)))).
% 2.86/1.53 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X5:A]: (((P @ X5) = (Q @ X5)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.86/1.53 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G2:(A > B)]: (((! [X5:A]: (((F @ X5) = (G2 @ X5)))) => (F = G2))))).
% 2.86/1.53 thf(fact_49_insert__subset, axiom, (! [A:$tType,X3:A,A4:(set @ A),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((insert @ A) @ X3) @ A4)) @ B6) = ((((member @ A) @ X3) @ B6) & (((ord_less_eq @ (set @ A)) @ A4) @ B6)))))).
% 2.86/1.53 thf(fact_50_singletonI, axiom, (! [A:$tType,A2:A]: ((((member @ A) @ A2) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))))).
% 2.86/1.53 thf(fact_51_empty__subsetI, axiom, (! [A:$tType,A4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (bot_bot @ (set @ A))) @ A4)))).
% 2.86/1.53 thf(fact_52_subset__empty, axiom, (! [A:$tType,A4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ (bot_bot @ (set @ A))) = (A4 = (bot_bot @ (set @ A))))))).
% 2.86/1.53 thf(fact_53_le__zero__eq, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((((ord_less_eq @ A) @ N) @ (zero_zero @ A)) = (N = (zero_zero @ A))))))))).
% 2.86/1.53 thf(fact_54_reflexivity__rule__def, axiom, (! [L:$tType]: (((standa245363227y_rule @ L) = (^ [T2:L]: (((((product_Pair @ ((labeled_graph @ L) @ nat)) @ ((labeled_graph @ L) @ nat)) @ ((((labeled_LG @ L) @ nat) @ (bot_bot @ (set @ ((product_prod @ L) @ ((product_prod @ nat) @ nat))))) @ (((insert @ nat) @ (zero_zero @ nat)) @ (bot_bot @ (set @ nat))))) @ ((((labeled_LG @ L) @ nat) @ (((insert @ ((product_prod @ L) @ ((product_prod @ nat) @ nat))) @ ((((product_Pair @ L) @ ((product_prod @ nat) @ nat)) @ T2) @ ((((product_Pair @ nat) @ nat) @ (zero_zero @ nat)) @ (zero_zero @ nat)))) @ (bot_bot @ (set @ ((product_prod @ L) @ ((product_prod @ nat) @ nat)))))) @ (((insert @ nat) @ (zero_zero @ nat)) @ (bot_bot @ (set @ nat))))))))))).
% 2.86/1.53 thf(fact_55_nonempty__rule__def, axiom, (! [L:$tType]: (((standa244753842y_rule @ L) = ((((product_Pair @ ((labeled_graph @ L) @ nat)) @ ((labeled_graph @ L) @ nat)) @ ((((labeled_LG @ L) @ nat) @ (bot_bot @ (set @ ((product_prod @ L) @ ((product_prod @ nat) @ nat))))) @ (bot_bot @ (set @ nat)))) @ ((((labeled_LG @ L) @ nat) @ (bot_bot @ (set @ ((product_prod @ L) @ ((product_prod @ nat) @ nat))))) @ (((insert @ nat) @ (zero_zero @ nat)) @ (bot_bot @ (set @ nat))))))))).
% 2.86/1.53 thf(fact_56_empty__iff, axiom, (! [A:$tType,C3:A]: ((~ ((((member @ A) @ C3) @ (bot_bot @ (set @ A)))))))).
% 2.86/1.53 thf(fact_57_all__not__in__conv, axiom, (! [A:$tType,A4:(set @ A)]: (((! [X4:A]: ((~ ((((member @ A) @ X4) @ A4))))) = (A4 = (bot_bot @ (set @ A))))))).
% 2.86/1.53 thf(fact_58_Collect__empty__eq, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (! [X4:A]: ((~ ((P @ X4))))))))).
% 2.86/1.53 thf(fact_59_empty__Collect__eq, axiom, (! [A:$tType,P:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P)) = (! [X4:A]: ((~ ((P @ X4))))))))).
% 2.86/1.53 thf(fact_60_subsetI, axiom, (! [A:$tType,A4:(set @ A),B6:(set @ A)]: (((! [X5:A]: (((((member @ A) @ X5) @ A4) => (((member @ A) @ X5) @ B6)))) => (((ord_less_eq @ (set @ A)) @ A4) @ B6))))).
% 2.86/1.53 thf(fact_61_subset__antisym, axiom, (! [A:$tType,A4:(set @ A),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B6) => ((((ord_less_eq @ (set @ A)) @ B6) @ A4) => (A4 = B6)))))).
% 2.86/1.53 thf(fact_62_insertCI, axiom, (! [A:$tType,A2:A,B6:(set @ A),B2:A]: ((((~ ((((member @ A) @ A2) @ B6))) => (A2 = B2)) => (((member @ A) @ A2) @ (((insert @ A) @ B2) @ B6)))))).
% 2.86/1.53 thf(fact_63_insert__iff, axiom, (! [A:$tType,A2:A,B2:A,A4:(set @ A)]: (((((member @ A) @ A2) @ (((insert @ A) @ B2) @ A4)) = ((A2 = B2) | (((member @ A) @ A2) @ A4)))))).
% 2.86/1.53 thf(fact_64_insert__absorb2, axiom, (! [A:$tType,X3:A,A4:(set @ A)]: (((((insert @ A) @ X3) @ (((insert @ A) @ X3) @ A4)) = (((insert @ A) @ X3) @ A4))))).
% 2.86/1.53 thf(fact_65_graph__homomorphism__empty, axiom, (! [B:$tType,C:$tType,A:$tType,G:((labeled_graph @ A) @ C),F:(set @ ((product_prod @ B) @ C))]: ((((((((graph_homomorphism @ A) @ B) @ C) @ ((((labeled_LG @ A) @ B) @ (bot_bot @ (set @ ((product_prod @ A) @ ((product_prod @ B) @ B))))) @ (bot_bot @ (set @ B)))) @ G) @ F) = ((F = (bot_bot @ (set @ ((product_prod @ B) @ C)))) & (G = (((restrict @ A) @ C) @ G))))))).
% 2.86/1.53 thf(fact_66_edge__preserving__subset, axiom, (! [A:$tType,B:$tType,C:$tType,R_1:(set @ ((product_prod @ A) @ B)),R_2:(set @ ((product_prod @ A) @ B)),E_1:(set @ ((product_prod @ C) @ ((product_prod @ A) @ A))),E_2:(set @ ((product_prod @ C) @ ((product_prod @ A) @ A))),G:(set @ ((product_prod @ C) @ ((product_prod @ B) @ B)))]: (((((ord_less_eq @ (set @ ((product_prod @ A) @ B))) @ R_1) @ R_2) => ((((ord_less_eq @ (set @ ((product_prod @ C) @ ((product_prod @ A) @ A)))) @ E_1) @ E_2) => (((((((edge_preserving @ A) @ B) @ C) @ R_2) @ E_2) @ G) => ((((((edge_preserving @ A) @ B) @ C) @ R_1) @ E_1) @ G))))))).
% 2.86/1.53 thf(fact_67_subrelI, axiom, (! [B:$tType,A:$tType,R:(set @ ((product_prod @ A) @ B)),S:(set @ ((product_prod @ A) @ B))]: (((! [X5:A,Y4:B]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X5) @ Y4)) @ R) => (((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X5) @ Y4)) @ S)))) => (((ord_less_eq @ (set @ ((product_prod @ A) @ B))) @ R) @ S))))).
% 2.86/1.53 thf(fact_68_restrict__subsD, axiom, (! [B:$tType,A:$tType,G:((labeled_graph @ A) @ B)]: (((((ord_less_eq @ (set @ ((product_prod @ A) @ ((product_prod @ B) @ B)))) @ (((labeled_edges @ A) @ B) @ G)) @ (((labeled_edges @ A) @ B) @ (((restrict @ A) @ B) @ G))) => (G = (((restrict @ A) @ B) @ G)))))).
% 2.86/1.53 thf(fact_69_zero__reorient, axiom, (! [A:$tType]: (((zero @ A) => (! [X3:A]: ((((zero_zero @ A) = X3) = (X3 = (zero_zero @ A))))))))).
% 2.86/1.53 thf(fact_70_emptyE, axiom, (! [A:$tType,A2:A]: ((~ ((((member @ A) @ A2) @ (bot_bot @ (set @ A)))))))).
% 2.86/1.53 thf(fact_71_equals0D, axiom, (! [A:$tType,A4:(set @ A),A2:A]: (((A4 = (bot_bot @ (set @ A))) => (~ ((((member @ A) @ A2) @ A4))))))).
% 2.86/1.53 thf(fact_72_equals0I, axiom, (! [A:$tType,A4:(set @ A)]: (((! [Y4:A]: ((~ ((((member @ A) @ Y4) @ A4))))) => (A4 = (bot_bot @ (set @ A))))))).
% 2.86/1.53 thf(fact_73_ex__in__conv, axiom, (! [A:$tType,A4:(set @ A)]: (((? [X4:A]: ((((member @ A) @ X4) @ A4))) = (A4 != (bot_bot @ (set @ A))))))).
% 2.86/1.53 thf(fact_74_in__mono, axiom, (! [A:$tType,A4:(set @ A),B6:(set @ A),X3:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B6) => ((((member @ A) @ X3) @ A4) => (((member @ A) @ X3) @ B6)))))).
% 2.86/1.53 thf(fact_75_subsetD, axiom, (! [A:$tType,A4:(set @ A),B6:(set @ A),C3:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B6) => ((((member @ A) @ C3) @ A4) => (((member @ A) @ C3) @ B6)))))).
% 2.86/1.53 thf(fact_76_equalityE, axiom, (! [A:$tType,A4:(set @ A),B6:(set @ A)]: (((A4 = B6) => (~ (((((ord_less_eq @ (set @ A)) @ A4) @ B6) => (~ ((((ord_less_eq @ (set @ A)) @ B6) @ A4)))))))))).
% 2.86/1.53 thf(fact_77_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A8:(set @ A),B7:(set @ A)]: ((! [X4:A]: (((((member @ A) @ X4) @ A8) => (((member @ A) @ X4) @ B7)))))))))).
% 2.86/1.53 thf(fact_78_equalityD1, axiom, (! [A:$tType,A4:(set @ A),B6:(set @ A)]: (((A4 = B6) => (((ord_less_eq @ (set @ A)) @ A4) @ B6))))).
% 2.86/1.53 thf(fact_79_equalityD2, axiom, (! [A:$tType,A4:(set @ A),B6:(set @ A)]: (((A4 = B6) => (((ord_less_eq @ (set @ A)) @ B6) @ A4))))).
% 2.86/1.53 thf(fact_80_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A8:(set @ A),B7:(set @ A)]: ((! [T2:A]: (((((member @ A) @ T2) @ A8) => (((member @ A) @ T2) @ B7)))))))))).
% 2.86/1.53 thf(fact_81_subset__refl, axiom, (! [A:$tType,A4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A4) @ A4)))).
% 2.86/1.53 thf(fact_82_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X5:A]: (((P @ X5) => (Q @ X5)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 2.86/1.53 thf(fact_83_subset__trans, axiom, (! [A:$tType,A4:(set @ A),B6:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B6) => ((((ord_less_eq @ (set @ A)) @ B6) @ C4) => (((ord_less_eq @ (set @ A)) @ A4) @ C4)))))).
% 2.86/1.53 thf(fact_84_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y5:(set @ A),Z:(set @ A)]: ((Y5 = Z))) = (^ [A8:(set @ A),B7:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A8) @ B7) & (((ord_less_eq @ (set @ A)) @ B7) @ A8)))))))).
% 2.86/1.53 thf(fact_85_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X4:A]: (((P @ X4) => (Q @ X4)))))))).
% 2.86/1.53 thf(fact_86_insertE, axiom, (! [A:$tType,A2:A,B2:A,A4:(set @ A)]: (((((member @ A) @ A2) @ (((insert @ A) @ B2) @ A4)) => ((A2 != B2) => (((member @ A) @ A2) @ A4)))))).
% 2.86/1.53 thf(fact_87_insertI1, axiom, (! [A:$tType,A2:A,B6:(set @ A)]: ((((member @ A) @ A2) @ (((insert @ A) @ A2) @ B6))))).
% 2.86/1.53 thf(fact_88_insertI2, axiom, (! [A:$tType,A2:A,B6:(set @ A),B2:A]: (((((member @ A) @ A2) @ B6) => (((member @ A) @ A2) @ (((insert @ A) @ B2) @ B6)))))).
% 2.86/1.53 thf(fact_89_Set_Oset__insert, axiom, (! [A:$tType,X3:A,A4:(set @ A)]: (((((member @ A) @ X3) @ A4) => (~ ((! [B8:(set @ A)]: (((A4 = (((insert @ A) @ X3) @ B8)) => (((member @ A) @ X3) @ B8)))))))))).
% 2.86/1.53 thf(fact_90_insert__ident, axiom, (! [A:$tType,X3:A,A4:(set @ A),B6:(set @ A)]: (((~ ((((member @ A) @ X3) @ A4))) => ((~ ((((member @ A) @ X3) @ B6))) => (((((insert @ A) @ X3) @ A4) = (((insert @ A) @ X3) @ B6)) = (A4 = B6))))))).
% 2.86/1.53 thf(fact_91_insert__absorb, axiom, (! [A:$tType,A2:A,A4:(set @ A)]: (((((member @ A) @ A2) @ A4) => ((((insert @ A) @ A2) @ A4) = A4))))).
% 2.86/1.53 thf(fact_92_insert__eq__iff, axiom, (! [A:$tType,A2:A,A4:(set @ A),B2:A,B6:(set @ A)]: (((~ ((((member @ A) @ A2) @ A4))) => ((~ ((((member @ A) @ B2) @ B6))) => (((((insert @ A) @ A2) @ A4) = (((insert @ A) @ B2) @ B6)) = (((A2 = B2) => (A4 = B6)) & ((A2 != B2) => (? [C5:(set @ A)]: (((A4 = (((insert @ A) @ B2) @ C5)) & ((~ ((((member @ A) @ B2) @ C5))) & ((B6 = (((insert @ A) @ A2) @ C5)) & (~ ((((member @ A) @ A2) @ C5)))))))))))))))).
% 2.86/1.53 thf(fact_93_insert__commute, axiom, (! [A:$tType,X3:A,Y:A,A4:(set @ A)]: (((((insert @ A) @ X3) @ (((insert @ A) @ Y) @ A4)) = (((insert @ A) @ Y) @ (((insert @ A) @ X3) @ A4)))))).
% 2.86/1.53 thf(fact_94_mk__disjoint__insert, axiom, (! [A:$tType,A2:A,A4:(set @ A)]: (((((member @ A) @ A2) @ A4) => (? [B8:(set @ A)]: (((A4 = (((insert @ A) @ A2) @ B8)) & (~ ((((member @ A) @ A2) @ B8)))))))))).
% 2.86/1.53 thf(fact_95_zero__le, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [X3:A]: ((((ord_less_eq @ A) @ (zero_zero @ A)) @ X3))))))).
% 2.86/1.53 thf(fact_96_singletonD, axiom, (! [A:$tType,B2:A,A2:A]: (((((member @ A) @ B2) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))) => (B2 = A2))))).
% 2.86/1.53 thf(fact_97_singleton__iff, axiom, (! [A:$tType,B2:A,A2:A]: (((((member @ A) @ B2) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))) = (B2 = A2))))).
% 2.86/1.53 thf(fact_98_doubleton__eq__iff, axiom, (! [A:$tType,A2:A,B2:A,C3:A,D:A]: ((((((insert @ A) @ A2) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) = (((insert @ A) @ C3) @ (((insert @ A) @ D) @ (bot_bot @ (set @ A))))) = (((A2 = C3) & (B2 = D)) | ((A2 = D) & (B2 = C3))))))).
% 2.86/1.53 thf(fact_99_insert__not__empty, axiom, (! [A:$tType,A2:A,A4:(set @ A)]: (((((insert @ A) @ A2) @ A4) != (bot_bot @ (set @ A)))))).
% 2.86/1.53 thf(fact_100_singleton__inject, axiom, (! [A:$tType,A2:A,B2:A]: ((((((insert @ A) @ A2) @ (bot_bot @ (set @ A))) = (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) => (A2 = B2))))).
% 2.86/1.53 thf(fact_101_insert__mono, axiom, (! [A:$tType,C4:(set @ A),D2:(set @ A),A2:A]: (((((ord_less_eq @ (set @ A)) @ C4) @ D2) => (((ord_less_eq @ (set @ A)) @ (((insert @ A) @ A2) @ C4)) @ (((insert @ A) @ A2) @ D2)))))).
% 2.86/1.53 thf(fact_102_subset__insert, axiom, (! [A:$tType,X3:A,A4:(set @ A),B6:(set @ A)]: (((~ ((((member @ A) @ X3) @ A4))) => ((((ord_less_eq @ (set @ A)) @ A4) @ (((insert @ A) @ X3) @ B6)) = (((ord_less_eq @ (set @ A)) @ A4) @ B6)))))).
% 2.86/1.53 thf(fact_103_subset__insertI, axiom, (! [A:$tType,B6:(set @ A),A2:A]: ((((ord_less_eq @ (set @ A)) @ B6) @ (((insert @ A) @ A2) @ B6))))).
% 2.86/1.53 thf(fact_104_subset__insertI2, axiom, (! [A:$tType,A4:(set @ A),B6:(set @ A),B2:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B6) => (((ord_less_eq @ (set @ A)) @ A4) @ (((insert @ A) @ B2) @ B6)))))).
% 2.86/1.53 thf(fact_105_univalentD, axiom, (! [A:$tType,B:$tType,R2:(set @ ((product_prod @ A) @ B)),X3:A,Y:B,Z2:B]: (((((univalent @ A) @ B) @ R2) => ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y)) @ R2) => ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Z2)) @ R2) => (Z2 = Y))))))).
% 2.86/1.53 thf(fact_106_univalent__def, axiom, (! [B:$tType,A:$tType]: ((((univalent @ A) @ B) = (^ [R4:(set @ ((product_prod @ A) @ B))]: ((! [X4:A,Y3:B,Z3:B]: ((((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X4) @ Y3)) @ R4) & (((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X4) @ Z3)) @ R4)) => (Z3 = Y3)))))))))).
% 2.86/1.53 thf(fact_107_graph__homomorphismI, axiom, (! [B:$tType,C:$tType,A:$tType,S:((labeled_graph @ B) @ A),H:(set @ ((product_prod @ A) @ C)),T3:((labeled_graph @ B) @ C)]: ((((((labeled_vertices @ B) @ A) @ S) = (((domain @ A) @ C) @ H)) => ((((ord_less_eq @ (set @ C)) @ ((((image @ A) @ C) @ H) @ (((labeled_vertices @ B) @ A) @ S))) @ (((labeled_vertices @ B) @ C) @ T3)) => ((((univalent @ A) @ C) @ H) => (((((((edge_preserving @ A) @ C) @ B) @ H) @ (((labeled_edges @ B) @ A) @ S)) @ (((labeled_edges @ B) @ C) @ T3)) => ((S = (((restrict @ B) @ A) @ S)) => ((T3 = (((restrict @ B) @ C) @ T3)) => ((((((graph_homomorphism @ B) @ A) @ C) @ S) @ T3) @ H)))))))))).
% 2.86/1.53 thf(fact_108_graph__homomorphism__def, axiom, (! [C:$tType,B:$tType,A:$tType]: (((((graph_homomorphism @ A) @ B) @ C) = (^ [G_1:((labeled_graph @ A) @ B),G_2:((labeled_graph @ A) @ C),F2:(set @ ((product_prod @ B) @ C))]: ((((((labeled_vertices @ A) @ B) @ G_1) = (((domain @ B) @ C) @ F2)) & ((G_1 = (((restrict @ A) @ B) @ G_1)) & ((G_2 = (((restrict @ A) @ C) @ G_2)) & ((((ord_less_eq @ (set @ C)) @ ((((image @ B) @ C) @ F2) @ (((labeled_vertices @ A) @ B) @ G_1))) @ (((labeled_vertices @ A) @ C) @ G_2)) & ((((univalent @ B) @ C) @ F2) & ((((((edge_preserving @ B) @ C) @ A) @ F2) @ (((labeled_edges @ A) @ B) @ G_1)) @ (((labeled_edges @ A) @ C) @ G_2))))))))))))).
% 2.86/1.53 thf(fact_109_subset__singletonD, axiom, (! [A:$tType,A4:(set @ A),X3:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))) => ((A4 = (bot_bot @ (set @ A))) | (A4 = (((insert @ A) @ X3) @ (bot_bot @ (set @ A))))))))).
% 2.86/1.53 thf(fact_110_subset__singleton__iff, axiom, (! [A:$tType,X2:(set @ A),A2:A]: (((((ord_less_eq @ (set @ A)) @ X2) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))) = ((X2 = (bot_bot @ (set @ A))) | (X2 = (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))))))).
% 2.86/1.53 thf(fact_111_univalent__insert, axiom, (! [A:$tType,B:$tType,A2:B,R2:(set @ ((product_prod @ B) @ A)),B2:A]: (((! [C6:A]: ((~ ((((member @ ((product_prod @ B) @ A)) @ ((((product_Pair @ B) @ A) @ A2) @ C6)) @ R2))))) => ((((univalent @ B) @ A) @ (((insert @ ((product_prod @ B) @ A)) @ ((((product_Pair @ B) @ A) @ A2) @ B2)) @ R2)) = (((univalent @ B) @ A) @ R2)))))).
% 2.86/1.53 thf(fact_112_graph__homomorphism__concr__graph, axiom, (! [A:$tType,B:$tType,C:$tType,G:((labeled_graph @ A) @ B),E:(set @ ((product_prod @ A) @ ((product_prod @ C) @ C))),V3:(set @ C),X3:(set @ ((product_prod @ C) @ B))]: (((G = (((restrict @ A) @ B) @ G)) => ((((((labeled_LG @ A) @ C) @ E) @ V3) = (((restrict @ A) @ C) @ ((((labeled_LG @ A) @ C) @ E) @ V3))) => (((((((graph_homomorphism @ A) @ C) @ B) @ ((((labeled_LG @ A) @ C) @ E) @ V3)) @ G) @ X3) = ((((ord_less_eq @ (set @ B)) @ ((((image @ C) @ B) @ X3) @ V3)) @ (((labeled_vertices @ A) @ B) @ G)) & ((((ord_less_eq @ (set @ ((product_prod @ A) @ ((product_prod @ B) @ B)))) @ ((((image @ ((product_prod @ A) @ ((product_prod @ C) @ C))) @ ((product_prod @ A) @ ((product_prod @ B) @ B))) @ ((((on_triple @ C) @ B) @ A) @ X3)) @ E)) @ (((labeled_edges @ A) @ B) @ G)) & ((((univalent @ C) @ B) @ X3) & ((((domain @ C) @ B) @ X3) = V3)))))))))).
% 2.86/1.53 thf(fact_113_le0, axiom, (! [N:nat]: ((((ord_less_eq @ nat) @ (zero_zero @ nat)) @ N)))).
% 2.86/1.53 thf(fact_114_bot__nat__0_Oextremum, axiom, (! [A2:nat]: ((((ord_less_eq @ nat) @ (zero_zero @ nat)) @ A2)))).
% 2.86/1.53 thf(fact_115_the__elem__eq, axiom, (! [A:$tType,X3:A]: ((((the_elem @ A) @ (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))) = X3)))).
% 2.86/1.53 thf(fact_116_bot__apply, axiom, (! [C:$tType,D3:$tType]: (((bot @ C) => ((bot_bot @ (D3 > C)) = (^ [X4:D3]: ((bot_bot @ C)))))))).
% 2.86/1.53 thf(fact_117_prod_Oinject, axiom, (! [A:$tType,B:$tType,X1:A,X22:B,Y1:A,Y2:B]: (((((((product_Pair @ A) @ B) @ X1) @ X22) = ((((product_Pair @ A) @ B) @ Y1) @ Y2)) = ((X1 = Y1) & (X22 = Y2)))))).
% 2.86/1.53 thf(fact_118_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A9:A,B9:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A9) @ B9)) = ((A2 = A9) & (B2 = B9)))))).
% 2.86/1.53 thf(fact_119_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A]: ((((ord_less_eq @ A) @ X3) @ X3))))))).
% 2.86/1.53 thf(fact_120_on__triple__univ, axiom, (! [C:$tType,B:$tType,A:$tType,F:(set @ ((product_prod @ A) @ B))]: (((((univalent @ A) @ B) @ F) => (((univalent @ ((product_prod @ C) @ ((product_prod @ A) @ A))) @ ((product_prod @ C) @ ((product_prod @ B) @ B))) @ ((((on_triple @ A) @ B) @ C) @ F)))))).
% 2.86/1.53 thf(fact_121_on__triple, axiom, (! [B:$tType,C:$tType,A:$tType,L1:A,V1:B,V22:B,L2:A,V32:C,V4:C,R2:(set @ ((product_prod @ B) @ C))]: (((((member @ ((product_prod @ ((product_prod @ A) @ ((product_prod @ B) @ B))) @ ((product_prod @ A) @ ((product_prod @ C) @ C)))) @ ((((product_Pair @ ((product_prod @ A) @ ((product_prod @ B) @ B))) @ ((product_prod @ A) @ ((product_prod @ C) @ C))) @ ((((product_Pair @ A) @ ((product_prod @ B) @ B)) @ L1) @ ((((product_Pair @ B) @ B) @ V1) @ V22))) @ ((((product_Pair @ A) @ ((product_prod @ C) @ C)) @ L2) @ ((((product_Pair @ C) @ C) @ V32) @ V4)))) @ ((((on_triple @ B) @ C) @ A) @ R2)) = ((((member @ ((product_prod @ B) @ C)) @ ((((product_Pair @ B) @ C) @ V1) @ V32)) @ R2) & ((((member @ ((product_prod @ B) @ C)) @ ((((product_Pair @ B) @ C) @ V22) @ V4)) @ R2) & (L1 = L2))))))).
% 2.86/1.53 thf(fact_122_edge__preservingI, axiom, (! [C:$tType,B:$tType,A:$tType,R2:(set @ ((product_prod @ C) @ B)),E3:(set @ ((product_prod @ A) @ ((product_prod @ C) @ C))),G:(set @ ((product_prod @ A) @ ((product_prod @ B) @ B)))]: (((((ord_less_eq @ (set @ ((product_prod @ A) @ ((product_prod @ B) @ B)))) @ ((((image @ ((product_prod @ A) @ ((product_prod @ C) @ C))) @ ((product_prod @ A) @ ((product_prod @ B) @ B))) @ ((((on_triple @ C) @ B) @ A) @ R2)) @ E3)) @ G) => ((((((edge_preserving @ C) @ B) @ A) @ R2) @ E3) @ G))))).
% 2.86/1.53 thf(fact_123_Nat_Oex__has__greatest__nat, axiom, (! [P:(nat > $o),K:nat,B2:nat]: (((P @ K) => ((! [Y4:nat]: (((P @ Y4) => (((ord_less_eq @ nat) @ Y4) @ B2)))) => (? [X5:nat]: (((P @ X5) & (! [Y6:nat]: (((P @ Y6) => (((ord_less_eq @ nat) @ Y6) @ X5)))))))))))).
% 2.86/1.53 thf(fact_124_nat__le__linear, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) | (((ord_less_eq @ nat) @ N) @ M))))).
% 2.86/1.53 thf(fact_125_le__antisym, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((((ord_less_eq @ nat) @ N) @ M) => (M = N)))))).
% 2.86/1.53 thf(fact_126_eq__imp__le, axiom, (! [M:nat,N:nat]: (((M = N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 2.86/1.53 thf(fact_127_le__trans, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less_eq @ nat) @ I) @ J) => ((((ord_less_eq @ nat) @ J) @ K) => (((ord_less_eq @ nat) @ I) @ K)))))).
% 2.86/1.53 thf(fact_128_le__refl, axiom, (! [N:nat]: ((((ord_less_eq @ nat) @ N) @ N)))).
% 2.86/1.53 thf(fact_129_bot__nat__def, axiom, ((bot_bot @ nat) = (zero_zero @ nat))).
% 2.86/1.53 thf(fact_130_bot__empty__eq, axiom, (! [A:$tType]: (((bot_bot @ (A > $o)) = (^ [X4:A]: ((((member @ A) @ X4) @ (bot_bot @ (set @ A))))))))).
% 2.86/1.53 thf(fact_131_bot__set__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (bot_bot @ (A > $o))))))).
% 2.86/1.53 thf(fact_132_edge__preserving, axiom, (! [C:$tType,B:$tType,A:$tType]: (((((edge_preserving @ A) @ B) @ C) = (^ [R4:(set @ ((product_prod @ A) @ B)),E4:(set @ ((product_prod @ C) @ ((product_prod @ A) @ A)))]: (((ord_less_eq @ (set @ ((product_prod @ C) @ ((product_prod @ B) @ B)))) @ ((((image @ ((product_prod @ C) @ ((product_prod @ A) @ A))) @ ((product_prod @ C) @ ((product_prod @ B) @ B))) @ ((((on_triple @ A) @ B) @ C) @ R4)) @ E4)))))))).
% 2.86/1.53 thf(fact_133_on__tripleD_I1_J, axiom, (! [B:$tType,C:$tType,A:$tType,L1:A,V1:B,V22:B,L2:A,V32:C,V4:C,R2:(set @ ((product_prod @ B) @ C))]: (((((member @ ((product_prod @ ((product_prod @ A) @ ((product_prod @ B) @ B))) @ ((product_prod @ A) @ ((product_prod @ C) @ C)))) @ ((((product_Pair @ ((product_prod @ A) @ ((product_prod @ B) @ B))) @ ((product_prod @ A) @ ((product_prod @ C) @ C))) @ ((((product_Pair @ A) @ ((product_prod @ B) @ B)) @ L1) @ ((((product_Pair @ B) @ B) @ V1) @ V22))) @ ((((product_Pair @ A) @ ((product_prod @ C) @ C)) @ L2) @ ((((product_Pair @ C) @ C) @ V32) @ V4)))) @ ((((on_triple @ B) @ C) @ A) @ R2)) => (L2 = L1))))).
% 2.86/1.53 thf(fact_134_on__tripleD_I2_J, axiom, (! [A:$tType,C:$tType,B:$tType,L1:A,V1:B,V22:B,L2:A,V32:C,V4:C,R2:(set @ ((product_prod @ B) @ C))]: (((((member @ ((product_prod @ ((product_prod @ A) @ ((product_prod @ B) @ B))) @ ((product_prod @ A) @ ((product_prod @ C) @ C)))) @ ((((product_Pair @ ((product_prod @ A) @ ((product_prod @ B) @ B))) @ ((product_prod @ A) @ ((product_prod @ C) @ C))) @ ((((product_Pair @ A) @ ((product_prod @ B) @ B)) @ L1) @ ((((product_Pair @ B) @ B) @ V1) @ V22))) @ ((((product_Pair @ A) @ ((product_prod @ C) @ C)) @ L2) @ ((((product_Pair @ C) @ C) @ V32) @ V4)))) @ ((((on_triple @ B) @ C) @ A) @ R2)) => (((member @ ((product_prod @ B) @ C)) @ ((((product_Pair @ B) @ C) @ V1) @ V32)) @ R2))))).
% 2.86/1.53 thf(fact_135_on__tripleD_I3_J, axiom, (! [A:$tType,C:$tType,B:$tType,L1:A,V1:B,V22:B,L2:A,V32:C,V4:C,R2:(set @ ((product_prod @ B) @ C))]: (((((member @ ((product_prod @ ((product_prod @ A) @ ((product_prod @ B) @ B))) @ ((product_prod @ A) @ ((product_prod @ C) @ C)))) @ ((((product_Pair @ ((product_prod @ A) @ ((product_prod @ B) @ B))) @ ((product_prod @ A) @ ((product_prod @ C) @ C))) @ ((((product_Pair @ A) @ ((product_prod @ B) @ B)) @ L1) @ ((((product_Pair @ B) @ B) @ V1) @ V22))) @ ((((product_Pair @ A) @ ((product_prod @ C) @ C)) @ L2) @ ((((product_Pair @ C) @ C) @ V32) @ V4)))) @ ((((on_triple @ B) @ C) @ A) @ R2)) => (((member @ ((product_prod @ B) @ C)) @ ((((product_Pair @ B) @ C) @ V22) @ V4)) @ R2))))).
% 2.86/1.53 thf(fact_136_on__triple__dest, axiom, (! [C:$tType,B:$tType,A:$tType,R2:(set @ ((product_prod @ C) @ B)),E3:(set @ ((product_prod @ A) @ ((product_prod @ C) @ C))),G:(set @ ((product_prod @ A) @ ((product_prod @ B) @ B))),L3:A,X3:C,Y:C,Xx:B,Yy:B]: (((((ord_less_eq @ (set @ ((product_prod @ A) @ ((product_prod @ B) @ B)))) @ ((((image @ ((product_prod @ A) @ ((product_prod @ C) @ C))) @ ((product_prod @ A) @ ((product_prod @ B) @ B))) @ ((((on_triple @ C) @ B) @ A) @ R2)) @ E3)) @ G) => ((((member @ ((product_prod @ A) @ ((product_prod @ C) @ C))) @ ((((product_Pair @ A) @ ((product_prod @ C) @ C)) @ L3) @ ((((product_Pair @ C) @ C) @ X3) @ Y))) @ E3) => ((((member @ ((product_prod @ C) @ B)) @ ((((product_Pair @ C) @ B) @ X3) @ Xx)) @ R2) => ((((member @ ((product_prod @ C) @ B)) @ ((((product_Pair @ C) @ B) @ Y) @ Yy)) @ R2) => (((member @ ((product_prod @ A) @ ((product_prod @ B) @ B))) @ ((((product_Pair @ A) @ ((product_prod @ B) @ B)) @ L3) @ ((((product_Pair @ B) @ B) @ Xx) @ Yy))) @ G)))))))).
% 2.86/1.53 thf(fact_137_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ A2) @ B2) => (A2 = B2))))))))).
% 2.86/1.53 thf(fact_138_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y5:A,Z:A]: ((Y5 = Z))) = (^ [A7:A,B5:A]: (((((ord_less_eq @ A) @ B5) @ A7) & (((ord_less_eq @ A) @ A7) @ B5))))))))).
% 2.86/1.53 thf(fact_139_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C3:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C3) @ B2) => (((ord_less_eq @ A) @ C3) @ A2))))))))).
% 2.86/1.53 thf(fact_140_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A2:A,B2:A]: (((! [A6:A,B4:A]: (((((ord_less_eq @ A) @ A6) @ B4) => ((P @ A6) @ B4)))) => ((! [A6:A,B4:A]: ((((P @ B4) @ A6) => ((P @ A6) @ B4)))) => ((P @ A2) @ B2))))))))).
% 2.86/1.53 thf(fact_141_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 2.86/1.53 thf(fact_142_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y:A,Z2:A]: (((((ord_less_eq @ A) @ X3) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z2) => (((ord_less_eq @ A) @ X3) @ Z2))))))))).
% 2.86/1.53 thf(fact_143_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ A2) => (A2 = B2))))))))).
% 2.86/1.53 thf(fact_144_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C3:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((B2 = C3) => (((ord_less_eq @ A) @ A2) @ C3))))))))).
% 2.86/1.53 thf(fact_145_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C3:A]: (((A2 = B2) => ((((ord_less_eq @ A) @ B2) @ C3) => (((ord_less_eq @ A) @ A2) @ C3))))))))).
% 2.86/1.53 thf(fact_146_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y5:A,Z:A]: ((Y5 = Z))) = (^ [A7:A,B5:A]: (((((ord_less_eq @ A) @ A7) @ B5) & (((ord_less_eq @ A) @ B5) @ A7))))))))).
% 2.86/1.53 thf(fact_147_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y:A,X3:A]: (((((ord_less_eq @ A) @ Y) @ X3) => ((((ord_less_eq @ A) @ X3) @ Y) = (X3 = Y))))))))).
% 2.86/1.53 thf(fact_148_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y:A,Z2:A]: ((((((ord_less_eq @ A) @ X3) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ Z2)))) => (((((ord_less_eq @ A) @ Y) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Z2)))) => (((((ord_less_eq @ A) @ X3) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ Y)))) => (((((ord_less_eq @ A) @ Z2) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ X3)))) => (((((ord_less_eq @ A) @ Y) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ X3)))) => (~ (((((ord_less_eq @ A) @ Z2) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Y))))))))))))))))).
% 2.86/1.53 thf(fact_149_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C3:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ C3) => (((ord_less_eq @ A) @ A2) @ C3))))))))).
% 2.86/1.53 thf(fact_150_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X3) @ Y))) => (((ord_less_eq @ A) @ Y) @ X3)))))))).
% 2.86/1.53 thf(fact_151_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y:A]: (((X3 = Y) => (((ord_less_eq @ A) @ X3) @ Y)))))))).
% 2.86/1.53 thf(fact_152_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y:A]: (((((ord_less_eq @ A) @ X3) @ Y) | (((ord_less_eq @ A) @ Y) @ X3)))))))).
% 2.86/1.53 thf(fact_153_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y:A]: (((((ord_less_eq @ A) @ X3) @ Y) => ((((ord_less_eq @ A) @ Y) @ X3) => (X3 = Y))))))))).
% 2.86/1.53 thf(fact_154_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y5:A,Z:A]: ((Y5 = Z))) = (^ [X4:A,Y3:A]: (((((ord_less_eq @ A) @ X4) @ Y3) & (((ord_less_eq @ A) @ Y3) @ X4))))))))).
% 2.86/1.53 thf(fact_155_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,B2:A,F:(A > B),C3:B]: (((((ord_less_eq @ A) @ A2) @ B2) => (((F @ B2) = C3) => ((! [X5:A,Y4:A]: (((((ord_less_eq @ A) @ X5) @ Y4) => (((ord_less_eq @ B) @ (F @ X5)) @ (F @ Y4))))) => (((ord_less_eq @ B) @ (F @ A2)) @ C3)))))))))).
% 2.86/1.53 thf(fact_156_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,F:(B > A),B2:B,C3:B]: (((A2 = (F @ B2)) => ((((ord_less_eq @ B) @ B2) @ C3) => ((! [X5:B,Y4:B]: (((((ord_less_eq @ B) @ X5) @ Y4) => (((ord_less_eq @ A) @ (F @ X5)) @ (F @ Y4))))) => (((ord_less_eq @ A) @ A2) @ (F @ C3))))))))))).
% 2.86/1.53 thf(fact_157_order__subst2, axiom, (! [A:$tType,C:$tType]: ((((order @ C) & (order @ A)) => (! [A2:A,B2:A,F:(A > C),C3:C]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ C) @ (F @ B2)) @ C3) => ((! [X5:A,Y4:A]: (((((ord_less_eq @ A) @ X5) @ Y4) => (((ord_less_eq @ C) @ (F @ X5)) @ (F @ Y4))))) => (((ord_less_eq @ C) @ (F @ A2)) @ C3)))))))))).
% 2.86/1.53 thf(fact_158_order__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F:(B > A),B2:B,C3:B]: (((((ord_less_eq @ A) @ A2) @ (F @ B2)) => ((((ord_less_eq @ B) @ B2) @ C3) => ((! [X5:B,Y4:B]: (((((ord_less_eq @ B) @ X5) @ Y4) => (((ord_less_eq @ A) @ (F @ X5)) @ (F @ Y4))))) => (((ord_less_eq @ A) @ A2) @ (F @ C3))))))))))).
% 2.86/1.53 thf(fact_159_le__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less_eq @ (A > B)) = (^ [F2:(A > B),G3:(A > B)]: ((! [X4:A]: ((((ord_less_eq @ B) @ (F2 @ X4)) @ (G3 @ X4))))))))))).
% 2.86/1.53 thf(fact_160_le__funI, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G2:(A > B)]: (((! [X5:A]: ((((ord_less_eq @ B) @ (F @ X5)) @ (G2 @ X5)))) => (((ord_less_eq @ (A > B)) @ F) @ G2)))))))).
% 2.86/1.53 thf(fact_161_le__funE, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G2:(A > B),X3:A]: (((((ord_less_eq @ (A > B)) @ F) @ G2) => (((ord_less_eq @ B) @ (F @ X3)) @ (G2 @ X3))))))))).
% 2.86/1.53 thf(fact_162_le__funD, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G2:(A > B),X3:A]: (((((ord_less_eq @ (A > B)) @ F) @ G2) => (((ord_less_eq @ B) @ (F @ X3)) @ (G2 @ X3))))))))).
% 2.86/1.53 thf(fact_163_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A6:A,B4:B]: ((P @ ((((product_Pair @ A) @ B) @ A6) @ B4)))) => (P @ Prod))))).
% 2.86/1.53 thf(fact_164_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y:((product_prod @ A) @ B)]: ((~ ((! [A6:A,B4:B]: ((Y != ((((product_Pair @ A) @ B) @ A6) @ B4))))))))).
% 2.86/1.53 thf(fact_165_Pair__inject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A9:A,B9:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A9) @ B9)) => (~ (((A2 = A9) => (B2 != B9)))))))).
% 2.86/1.53 thf(fact_166_prod__cases, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),P2:((product_prod @ A) @ B)]: (((! [A6:A,B4:B]: ((P @ ((((product_Pair @ A) @ B) @ A6) @ B4)))) => (P @ P2))))).
% 2.86/1.53 thf(fact_167_surj__pair, axiom, (! [A:$tType,B:$tType,P2:((product_prod @ A) @ B)]: ((? [X5:A,Y4:B]: ((P2 = ((((product_Pair @ A) @ B) @ X5) @ Y4))))))).
% 2.86/1.53 thf(fact_168_bot__fun__def, axiom, (! [B:$tType,A:$tType]: (((bot @ B) => ((bot_bot @ (A > B)) = (^ [X4:A]: ((bot_bot @ B)))))))).
% 2.86/1.53 thf(fact_169_bot__nat__0_Oextremum__uniqueI, axiom, (! [A2:nat]: (((((ord_less_eq @ nat) @ A2) @ (zero_zero @ nat)) => (A2 = (zero_zero @ nat)))))).
% 2.86/1.53 thf(fact_170_bot__nat__0_Oextremum__unique, axiom, (! [A2:nat]: (((((ord_less_eq @ nat) @ A2) @ (zero_zero @ nat)) = (A2 = (zero_zero @ nat)))))).
% 2.86/1.53 thf(fact_171_le__0__eq, axiom, (! [N:nat]: (((((ord_less_eq @ nat) @ N) @ (zero_zero @ nat)) = (N = (zero_zero @ nat)))))).
% 2.86/1.53 thf(fact_172_less__eq__nat_Osimps_I1_J, axiom, (! [N:nat]: ((((ord_less_eq @ nat) @ (zero_zero @ nat)) @ N)))).
% 2.86/1.53 thf(fact_173_bot_Oextremum__uniqueI, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A2:A]: (((((ord_less_eq @ A) @ A2) @ (bot_bot @ A)) => (A2 = (bot_bot @ A))))))))).
% 2.86/1.53 thf(fact_174_bot_Oextremum__unique, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A2:A]: (((((ord_less_eq @ A) @ A2) @ (bot_bot @ A)) = (A2 = (bot_bot @ A))))))))).
% 2.86/1.53 thf(fact_175_bot_Oextremum, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ (bot_bot @ A)) @ A2))))))).
% 2.86/1.53 thf(fact_176_prod__induct7, axiom, (! [G4:$tType,F3:$tType,E5:$tType,D3:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D3) @ ((product_prod @ E5) @ ((product_prod @ F3) @ G4)))))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D3) @ ((product_prod @ E5) @ ((product_prod @ F3) @ G4))))))]: (((! [A6:A,B4:B,C6:C,D4:D3,E6:E5,F4:F3,G5:G4]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D3) @ ((product_prod @ E5) @ ((product_prod @ F3) @ G4)))))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D3) @ ((product_prod @ E5) @ ((product_prod @ F3) @ G4))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D3) @ ((product_prod @ E5) @ ((product_prod @ F3) @ G4)))) @ C6) @ ((((product_Pair @ D3) @ ((product_prod @ E5) @ ((product_prod @ F3) @ G4))) @ D4) @ ((((product_Pair @ E5) @ ((product_prod @ F3) @ G4)) @ E6) @ ((((product_Pair @ F3) @ G4) @ F4) @ G5))))))))) => (P @ X3))))).
% 2.86/1.53 thf(fact_177_prod__induct6, axiom, (! [F3:$tType,E5:$tType,D3:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D3) @ ((product_prod @ E5) @ F3))))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D3) @ ((product_prod @ E5) @ F3)))))]: (((! [A6:A,B4:B,C6:C,D4:D3,E6:E5,F4:F3]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D3) @ ((product_prod @ E5) @ F3))))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D3) @ ((product_prod @ E5) @ F3)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D3) @ ((product_prod @ E5) @ F3))) @ C6) @ ((((product_Pair @ D3) @ ((product_prod @ E5) @ F3)) @ D4) @ ((((product_Pair @ E5) @ F3) @ E6) @ F4)))))))) => (P @ X3))))).
% 2.86/1.53 thf(fact_178_prod__induct5, axiom, (! [E5:$tType,D3:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D3) @ E5)))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D3) @ E5))))]: (((! [A6:A,B4:B,C6:C,D4:D3,E6:E5]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D3) @ E5)))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D3) @ E5))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D3) @ E5)) @ C6) @ ((((product_Pair @ D3) @ E5) @ D4) @ E6))))))) => (P @ X3))))).
% 2.86/1.53 thf(fact_179_prod__induct4, axiom, (! [D3:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D3))) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D3)))]: (((! [A6:A,B4:B,C6:C,D4:D3]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D3))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D3)) @ B4) @ ((((product_Pair @ C) @ D3) @ C6) @ D4)))))) => (P @ X3))))).
% 2.86/1.53 thf(fact_180_prod__induct3, axiom, (! [C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ C)) > $o),X3:((product_prod @ A) @ ((product_prod @ B) @ C))]: (((! [A6:A,B4:B,C6:C]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A6) @ ((((product_Pair @ B) @ C) @ B4) @ C6))))) => (P @ X3))))).
% 2.86/1.53 thf(fact_181_prod__cases7, axiom, (! [A:$tType,B:$tType,C:$tType,D3:$tType,E5:$tType,F3:$tType,G4:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D3) @ ((product_prod @ E5) @ ((product_prod @ F3) @ G4))))))]: ((~ ((! [A6:A,B4:B,C6:C,D4:D3,E6:E5,F4:F3,G5:G4]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D3) @ ((product_prod @ E5) @ ((product_prod @ F3) @ G4)))))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D3) @ ((product_prod @ E5) @ ((product_prod @ F3) @ G4))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D3) @ ((product_prod @ E5) @ ((product_prod @ F3) @ G4)))) @ C6) @ ((((product_Pair @ D3) @ ((product_prod @ E5) @ ((product_prod @ F3) @ G4))) @ D4) @ ((((product_Pair @ E5) @ ((product_prod @ F3) @ G4)) @ E6) @ ((((product_Pair @ F3) @ G4) @ F4) @ G5)))))))))))))).
% 2.86/1.53 thf(fact_182_prod__cases6, axiom, (! [A:$tType,B:$tType,C:$tType,D3:$tType,E5:$tType,F3:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D3) @ ((product_prod @ E5) @ F3)))))]: ((~ ((! [A6:A,B4:B,C6:C,D4:D3,E6:E5,F4:F3]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D3) @ ((product_prod @ E5) @ F3))))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D3) @ ((product_prod @ E5) @ F3)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D3) @ ((product_prod @ E5) @ F3))) @ C6) @ ((((product_Pair @ D3) @ ((product_prod @ E5) @ F3)) @ D4) @ ((((product_Pair @ E5) @ F3) @ E6) @ F4))))))))))))).
% 2.86/1.53 thf(fact_183_prod__cases5, axiom, (! [A:$tType,B:$tType,C:$tType,D3:$tType,E5:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D3) @ E5))))]: ((~ ((! [A6:A,B4:B,C6:C,D4:D3,E6:E5]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D3) @ E5)))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D3) @ E5))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D3) @ E5)) @ C6) @ ((((product_Pair @ D3) @ E5) @ D4) @ E6)))))))))))).
% 2.86/1.53 thf(fact_184_prod__cases4, axiom, (! [A:$tType,B:$tType,C:$tType,D3:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D3)))]: ((~ ((! [A6:A,B4:B,C6:C,D4:D3]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D3))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D3)) @ B4) @ ((((product_Pair @ C) @ D3) @ C6) @ D4))))))))))).
% 2.86/1.53 thf(fact_185_prod__cases3, axiom, (! [A:$tType,B:$tType,C:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ C))]: ((~ ((! [A6:A,B4:B,C6:C]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A6) @ ((((product_Pair @ B) @ C) @ B4) @ C6)))))))))).
% 2.86/1.53 thf(fact_186_old_Oprod_Orec, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > (B > T)),A2:A,B2:B]: (((((((product_rec_prod @ A) @ B) @ T) @ F1) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) = ((F1 @ A2) @ B2))))).
% 2.86/1.53 thf(fact_187_is__singleton__the__elem, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A8:(set @ A)]: ((A8 = (((insert @ A) @ ((the_elem @ A) @ A8)) @ (bot_bot @ (set @ A)))))))))).
% 2.86/1.53 thf(fact_188_top__rule__def, axiom, (! [L:$tType]: (((standa400804411p_rule @ L) = (^ [T2:L]: (((((product_Pair @ ((labeled_graph @ L) @ nat)) @ ((labeled_graph @ L) @ nat)) @ ((((labeled_LG @ L) @ nat) @ (bot_bot @ (set @ ((product_prod @ L) @ ((product_prod @ nat) @ nat))))) @ (((insert @ nat) @ (zero_zero @ nat)) @ (((insert @ nat) @ (one_one @ nat)) @ (bot_bot @ (set @ nat)))))) @ ((((labeled_LG @ L) @ nat) @ (((insert @ ((product_prod @ L) @ ((product_prod @ nat) @ nat))) @ ((((product_Pair @ L) @ ((product_prod @ nat) @ nat)) @ T2) @ ((((product_Pair @ nat) @ nat) @ (zero_zero @ nat)) @ (one_one @ nat)))) @ (bot_bot @ (set @ ((product_prod @ L) @ ((product_prod @ nat) @ nat)))))) @ (((insert @ nat) @ (zero_zero @ nat)) @ (((insert @ nat) @ (one_one @ nat)) @ (bot_bot @ (set @ nat)))))))))))).
% 2.86/1.53 thf(fact_189_map__graph__def, axiom, (! [A:$tType,B:$tType,C:$tType]: (((((map_graph @ C) @ B) @ A) = (^ [F2:(set @ ((product_prod @ C) @ B)),G6:((labeled_graph @ A) @ C)]: (((((labeled_LG @ A) @ B) @ ((((image @ ((product_prod @ A) @ ((product_prod @ C) @ C))) @ ((product_prod @ A) @ ((product_prod @ B) @ B))) @ ((((on_triple @ C) @ B) @ A) @ F2)) @ (((labeled_edges @ A) @ C) @ G6))) @ ((((image @ C) @ B) @ F2) @ (((labeled_vertices @ A) @ C) @ G6))))))))).
% 2.86/1.53 thf(fact_190_map__graph__preserves__restricted, axiom, (! [C:$tType,B:$tType,A:$tType,G:((labeled_graph @ A) @ B),F:(set @ ((product_prod @ B) @ C))]: (((G = (((restrict @ A) @ B) @ G)) => ((((((map_graph @ B) @ C) @ A) @ F) @ G) = (((restrict @ A) @ C) @ (((((map_graph @ B) @ C) @ A) @ F) @ G))))))).
% 2.86/1.53 thf(fact_191_map__graph__selectors_I1_J, axiom, (! [A:$tType,C:$tType,B:$tType,F:(set @ ((product_prod @ C) @ A)),G:((labeled_graph @ B) @ C)]: (((((labeled_vertices @ B) @ A) @ (((((map_graph @ C) @ A) @ B) @ F) @ G)) = ((((image @ C) @ A) @ F) @ (((labeled_vertices @ B) @ C) @ G)))))).
% 2.86/1.53 thf(fact_192_is__singletonI, axiom, (! [A:$tType,X3:A]: (((is_singleton @ A) @ (((insert @ A) @ X3) @ (bot_bot @ (set @ A))))))).
% 2.86/1.53 thf(fact_193_map__graph__edge__preserving, axiom, (! [B:$tType,A:$tType,C:$tType,F:(set @ ((product_prod @ A) @ B)),G:((labeled_graph @ C) @ A)]: (((((((edge_preserving @ A) @ B) @ C) @ F) @ (((labeled_edges @ C) @ A) @ G)) @ (((labeled_edges @ C) @ B) @ (((((map_graph @ A) @ B) @ C) @ F) @ G)))))).
% 2.86/1.53 thf(fact_194_map__graph__selectors_I2_J, axiom, (! [A:$tType,C:$tType,B:$tType,F:(set @ ((product_prod @ C) @ A)),G:((labeled_graph @ B) @ C)]: (((((labeled_edges @ B) @ A) @ (((((map_graph @ C) @ A) @ B) @ F) @ G)) = ((((image @ ((product_prod @ B) @ ((product_prod @ C) @ C))) @ ((product_prod @ B) @ ((product_prod @ A) @ A))) @ ((((on_triple @ C) @ A) @ B) @ F)) @ (((labeled_edges @ B) @ C) @ G)))))).
% 2.86/1.53 thf(fact_195_map__graph__homo, axiom, (! [C:$tType,B:$tType,A:$tType,F:(set @ ((product_prod @ A) @ B)),G:((labeled_graph @ C) @ A)]: (((((univalent @ A) @ B) @ F) => (((((labeled_vertices @ C) @ A) @ G) = (((domain @ A) @ B) @ F)) => ((G = (((restrict @ C) @ A) @ G)) => ((((((graph_homomorphism @ C) @ A) @ B) @ G) @ (((((map_graph @ A) @ B) @ C) @ F) @ G)) @ F))))))).
% 2.86/1.53 thf(fact_196_one__reorient, axiom, (! [A:$tType]: (((one @ A) => (! [X3:A]: ((((one_one @ A) = X3) = (X3 = (one_one @ A))))))))).
% 2.86/1.53 thf(fact_197_is__singletonI_H, axiom, (! [A:$tType,A4:(set @ A)]: (((A4 != (bot_bot @ (set @ A))) => ((! [X5:A,Y4:A]: (((((member @ A) @ X5) @ A4) => ((((member @ A) @ Y4) @ A4) => (X5 = Y4))))) => ((is_singleton @ A) @ A4)))))).
% 2.86/1.53 thf(fact_198_map__graph__returns__restricted, axiom, (! [C:$tType,A:$tType,B:$tType,G:((labeled_graph @ B) @ A),F:(set @ ((product_prod @ A) @ C))]: ((((((labeled_vertices @ B) @ A) @ G) = (((domain @ A) @ C) @ F)) => ((((((map_graph @ A) @ C) @ B) @ F) @ G) = (((restrict @ B) @ C) @ (((((map_graph @ A) @ C) @ B) @ F) @ G))))))).
% 2.86/1.53 thf(fact_199_is__singletonE, axiom, (! [A:$tType,A4:(set @ A)]: ((((is_singleton @ A) @ A4) => (~ ((! [X5:A]: ((A4 != (((insert @ A) @ X5) @ (bot_bot @ (set @ A)))))))))))).
% 2.86/1.53 thf(fact_200_is__singleton__def, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A8:(set @ A)]: ((? [X4:A]: ((A8 = (((insert @ A) @ X4) @ (bot_bot @ (set @ A)))))))))))).
% 2.86/1.53 thf(fact_201_map__graph__homo__simp, axiom, (! [C:$tType,B:$tType,A:$tType,G:((labeled_graph @ A) @ B),F:(set @ ((product_prod @ B) @ C))]: ((((((((graph_homomorphism @ A) @ B) @ C) @ G) @ (((((map_graph @ B) @ C) @ A) @ F) @ G)) @ F) = ((((univalent @ B) @ C) @ F) & (((((labeled_vertices @ A) @ B) @ G) = (((domain @ B) @ C) @ F)) & (G = (((restrict @ A) @ B) @ G)))))))).
% 2.86/1.53 thf(fact_202_not__one__le__zero, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less_eq @ A) @ (one_one @ A)) @ (zero_zero @ A)))))))).
% 2.86/1.53 thf(fact_203_zero__le__one, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (one_one @ A)))))).
% 2.86/1.53 thf(fact_204_zero__neq__one, axiom, (! [A:$tType]: (((zero_neq_one @ A) => ((zero_zero @ A) != (one_one @ A)))))).
% 2.86/1.53 thf(fact_205_graph__homomorphism__def2, axiom, (! [C:$tType,B:$tType,A:$tType]: (((((graph_homomorphism @ A) @ B) @ C) = (^ [G_1:((labeled_graph @ A) @ B),G_2:((labeled_graph @ A) @ C),F2:(set @ ((product_prod @ B) @ C))]: ((((((labeled_vertices @ A) @ B) @ G_1) = (((domain @ B) @ C) @ F2)) & ((((univalent @ B) @ C) @ F2) & ((G_1 = (((restrict @ A) @ B) @ G_1)) & ((G_2 = (((restrict @ A) @ C) @ G_2)) & (((((graph_union @ A) @ C) @ (((((map_graph @ B) @ C) @ A) @ F2) @ G_1)) @ G_2) = G_2))))))))))).
% 2.86/1.53 thf(fact_206_Collect__empty__eq__bot, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (P = (bot_bot @ (A > $o))))))).
% 2.86/1.53 thf(fact_207_graph__union__idemp_I3_J, axiom, (! [B:$tType,A:$tType,A4:((labeled_graph @ A) @ B),B6:((labeled_graph @ A) @ B)]: ((((((graph_union @ A) @ B) @ A4) @ ((((graph_union @ A) @ B) @ B6) @ A4)) = ((((graph_union @ A) @ B) @ B6) @ A4))))).
% 2.86/1.53 thf(fact_208_graph__union__idemp_I2_J, axiom, (! [B:$tType,A:$tType,A4:((labeled_graph @ A) @ B),B6:((labeled_graph @ A) @ B)]: ((((((graph_union @ A) @ B) @ A4) @ ((((graph_union @ A) @ B) @ A4) @ B6)) = ((((graph_union @ A) @ B) @ A4) @ B6))))).
% 2.86/1.53 thf(fact_209_graph__union__idemp_I1_J, axiom, (! [B:$tType,A:$tType,A4:((labeled_graph @ A) @ B)]: ((((((graph_union @ A) @ B) @ A4) @ A4) = A4)))).
% 2.86/1.53 thf(fact_210_graph__union__preserves__restrict, axiom, (! [B:$tType,A:$tType,G_12:((labeled_graph @ A) @ B),G_22:((labeled_graph @ A) @ B)]: (((G_12 = (((restrict @ A) @ B) @ G_12)) => ((G_22 = (((restrict @ A) @ B) @ G_22)) => (((((graph_union @ A) @ B) @ G_12) @ G_22) = (((restrict @ A) @ B) @ ((((graph_union @ A) @ B) @ G_12) @ G_22)))))))).
% 2.86/1.53 thf(fact_211_graph__unionI, axiom, (! [B:$tType,A:$tType,G_12:((labeled_graph @ A) @ B),G_22:((labeled_graph @ A) @ B)]: (((((ord_less_eq @ (set @ ((product_prod @ A) @ ((product_prod @ B) @ B)))) @ (((labeled_edges @ A) @ B) @ G_12)) @ (((labeled_edges @ A) @ B) @ G_22)) => ((((ord_less_eq @ (set @ B)) @ (((labeled_vertices @ A) @ B) @ G_12)) @ (((labeled_vertices @ A) @ B) @ G_22)) => (((((graph_union @ A) @ B) @ G_12) @ G_22) = G_22)))))).
% 2.86/1.53 thf(fact_212_graph__union__iff, axiom, (! [B:$tType,A:$tType,G_12:((labeled_graph @ A) @ B),G_22:((labeled_graph @ A) @ B)]: (((((((graph_union @ A) @ B) @ G_12) @ G_22) = G_22) = ((((ord_less_eq @ (set @ ((product_prod @ A) @ ((product_prod @ B) @ B)))) @ (((labeled_edges @ A) @ B) @ G_12)) @ (((labeled_edges @ A) @ B) @ G_22)) & (((ord_less_eq @ (set @ B)) @ (((labeled_vertices @ A) @ B) @ G_12)) @ (((labeled_vertices @ A) @ B) @ G_22))))))).
% 2.86/1.53 thf(fact_213_less__by__empty, axiom, (! [A:$tType,A4:(set @ ((product_prod @ A) @ A)),B6:(set @ ((product_prod @ A) @ A))]: (((A4 = (bot_bot @ (set @ ((product_prod @ A) @ A)))) => (((ord_less_eq @ (set @ ((product_prod @ A) @ A))) @ A4) @ B6))))).
% 2.86/1.53 thf(fact_214_on__triple__ID__restrict, axiom, (! [B:$tType,A:$tType,G:((labeled_graph @ A) @ B)]: ((((((image @ ((product_prod @ A) @ ((product_prod @ B) @ B))) @ ((product_prod @ A) @ ((product_prod @ B) @ B))) @ ((((on_triple @ B) @ B) @ A) @ ((id_on @ B) @ (((labeled_vertices @ A) @ B) @ G)))) @ (((labeled_edges @ A) @ B) @ G)) = (((labeled_edges @ A) @ B) @ (((restrict @ A) @ B) @ G)))))).
% 2.86/1.53 thf(fact_215_Id__onI, axiom, (! [A:$tType,A2:A,A4:(set @ A)]: (((((member @ A) @ A2) @ A4) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ A2)) @ ((id_on @ A) @ A4)))))).
% 2.86/1.53 thf(fact_216_Domain__Id__on, axiom, (! [A:$tType,A4:(set @ A)]: (((((domain @ A) @ A) @ ((id_on @ A) @ A4)) = A4)))).
% 2.86/1.53 thf(fact_217_id__univalent, axiom, (! [A:$tType,X3:(set @ A)]: ((((univalent @ A) @ A) @ ((id_on @ A) @ X3))))).
% 2.86/1.53 thf(fact_218_edge__preserving__Id, axiom, (! [A:$tType,B:$tType,Y:(set @ A),X3:(set @ ((product_prod @ B) @ ((product_prod @ A) @ A)))]: (((((((edge_preserving @ A) @ A) @ B) @ ((id_on @ A) @ Y)) @ X3) @ X3)))).
% 2.86/1.53 thf(fact_219_Id__on__empty, axiom, (! [A:$tType]: ((((id_on @ A) @ (bot_bot @ (set @ A))) = (bot_bot @ (set @ ((product_prod @ A) @ A))))))).
% 2.86/1.53 thf(fact_220_graph__homomorphism__Id, axiom, (! [B:$tType,A:$tType,A2:((labeled_graph @ A) @ B)]: (((((((graph_homomorphism @ A) @ B) @ B) @ (((restrict @ A) @ B) @ A2)) @ (((restrict @ A) @ B) @ A2)) @ ((id_on @ B) @ (((labeled_vertices @ A) @ B) @ A2)))))).
% 2.86/1.53 thf(fact_221_subgraph__restrict, axiom, (! [B:$tType,A:$tType,G:((labeled_graph @ A) @ B)]: ((((((((graph_homomorphism @ A) @ B) @ B) @ G) @ (((restrict @ A) @ B) @ G)) @ ((id_on @ B) @ (((labeled_vertices @ A) @ B) @ G))) = (G = (((restrict @ A) @ B) @ G)))))).
% 2.86/1.53 thf(fact_222_subgraph__refl, axiom, (! [B:$tType,A:$tType,G:((labeled_graph @ A) @ B)]: ((((((((graph_homomorphism @ A) @ B) @ B) @ G) @ G) @ ((id_on @ B) @ (((labeled_vertices @ A) @ B) @ G))) = (G = (((restrict @ A) @ B) @ G)))))).
% 2.86/1.53 thf(fact_223_map__graph__preserves__subgraph, axiom, (! [C:$tType,B:$tType,A:$tType,A4:((labeled_graph @ A) @ B),B6:((labeled_graph @ A) @ B),F:(set @ ((product_prod @ B) @ C))]: ((((((((graph_homomorphism @ A) @ B) @ B) @ A4) @ B6) @ ((id_on @ B) @ (((labeled_vertices @ A) @ B) @ A4))) => ((((((graph_homomorphism @ A) @ C) @ C) @ (((((map_graph @ B) @ C) @ A) @ F) @ A4)) @ (((((map_graph @ B) @ C) @ A) @ F) @ B6)) @ ((id_on @ C) @ (((labeled_vertices @ A) @ C) @ (((((map_graph @ B) @ C) @ A) @ F) @ A4)))))))).
% 2.86/1.53 thf(fact_224_map__graph__fn__id_I2_J, axiom, (! [B:$tType,A:$tType,X2:((labeled_graph @ A) @ B)]: (((((((map_graph @ B) @ B) @ A) @ ((id_on @ B) @ (((labeled_vertices @ A) @ B) @ X2))) @ X2) = (((restrict @ A) @ B) @ X2))))).
% 2.86/1.53 thf(fact_225_Id__on__iff, axiom, (! [A:$tType,X3:A,Y:A,A4:(set @ A)]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ Y)) @ ((id_on @ A) @ A4)) = ((X3 = Y) & (((member @ A) @ X3) @ A4)))))).
% 2.86/1.53 thf(fact_226_Id__on__eqI, axiom, (! [A:$tType,A2:A,B2:A,A4:(set @ A)]: (((A2 = B2) => ((((member @ A) @ A2) @ A4) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ ((id_on @ A) @ A4))))))).
% 2.86/1.53 thf(fact_227_Id__onE, axiom, (! [A:$tType,C3:((product_prod @ A) @ A),A4:(set @ A)]: (((((member @ ((product_prod @ A) @ A)) @ C3) @ ((id_on @ A) @ A4)) => (~ ((! [X5:A]: (((((member @ A) @ X5) @ A4) => (C3 != ((((product_Pair @ A) @ A) @ X5) @ X5))))))))))).
% 2.86/1.53 thf(fact_228_subgraph__preserves__hom, axiom, (! [A:$tType,B:$tType,C:$tType,A4:((labeled_graph @ A) @ B),B6:((labeled_graph @ A) @ B),X2:((labeled_graph @ A) @ C),H:(set @ ((product_prod @ C) @ B))]: ((((((((graph_homomorphism @ A) @ B) @ B) @ A4) @ B6) @ ((id_on @ B) @ (((labeled_vertices @ A) @ B) @ A4))) => (((((((graph_homomorphism @ A) @ C) @ B) @ X2) @ A4) @ H) => ((((((graph_homomorphism @ A) @ C) @ B) @ X2) @ B6) @ H)))))).
% 2.86/1.53 thf(fact_229_subgraph__trans, axiom, (! [B:$tType,A:$tType,G_12:((labeled_graph @ A) @ B),G_22:((labeled_graph @ A) @ B),G_3:((labeled_graph @ A) @ B)]: ((((((((graph_homomorphism @ A) @ B) @ B) @ G_12) @ G_22) @ ((id_on @ B) @ (((labeled_vertices @ A) @ B) @ G_12))) => (((((((graph_homomorphism @ A) @ B) @ B) @ G_22) @ G_3) @ ((id_on @ B) @ (((labeled_vertices @ A) @ B) @ G_22))) => ((((((graph_homomorphism @ A) @ B) @ B) @ G_12) @ G_3) @ ((id_on @ B) @ (((labeled_vertices @ A) @ B) @ G_12)))))))).
% 2.86/1.53 thf(fact_230_subgraph__subset_I1_J, axiom, (! [B:$tType,A:$tType,G_12:((labeled_graph @ A) @ B),G_22:((labeled_graph @ A) @ B)]: ((((((((graph_homomorphism @ A) @ B) @ B) @ G_12) @ G_22) @ ((id_on @ B) @ (((labeled_vertices @ A) @ B) @ G_12))) => (((ord_less_eq @ (set @ B)) @ (((labeled_vertices @ A) @ B) @ G_12)) @ (((labeled_vertices @ A) @ B) @ G_22)))))).
% 2.86/1.53 thf(fact_231_subgraph__def, axiom, (! [B:$tType,A:$tType,G_12:((labeled_graph @ A) @ B),G_22:((labeled_graph @ A) @ B)]: ((((((((graph_homomorphism @ A) @ B) @ B) @ G_12) @ G_22) @ ((id_on @ B) @ (((labeled_vertices @ A) @ B) @ G_12))) = ((G_12 = (((restrict @ A) @ B) @ G_12)) & ((G_22 = (((restrict @ A) @ B) @ G_22)) & (((((graph_union @ A) @ B) @ G_12) @ G_22) = G_22))))))).
% 2.86/1.53 thf(fact_232_subgraph__subset_I2_J, axiom, (! [B:$tType,A:$tType,G_12:((labeled_graph @ A) @ B),G_22:((labeled_graph @ A) @ B)]: ((((((((graph_homomorphism @ A) @ B) @ B) @ G_12) @ G_22) @ ((id_on @ B) @ (((labeled_vertices @ A) @ B) @ G_12))) => (((ord_less_eq @ (set @ ((product_prod @ A) @ ((product_prod @ B) @ B)))) @ (((labeled_edges @ A) @ B) @ (((restrict @ A) @ B) @ G_12))) @ (((labeled_edges @ A) @ B) @ G_22)))))).
% 2.86/1.53 thf(fact_233_subgraph__def2, axiom, (! [B:$tType,A:$tType,G_12:((labeled_graph @ A) @ B),G_22:((labeled_graph @ A) @ B)]: (((G_12 = (((restrict @ A) @ B) @ G_12)) => ((G_22 = (((restrict @ A) @ B) @ G_22)) => (((((((graph_homomorphism @ A) @ B) @ B) @ G_12) @ G_22) @ ((id_on @ B) @ (((labeled_vertices @ A) @ B) @ G_12))) = ((((ord_less_eq @ (set @ B)) @ (((labeled_vertices @ A) @ B) @ G_12)) @ (((labeled_vertices @ A) @ B) @ G_22)) & (((ord_less_eq @ (set @ ((product_prod @ A) @ ((product_prod @ B) @ B)))) @ (((labeled_edges @ A) @ B) @ G_12)) @ (((labeled_edges @ A) @ B) @ G_22))))))))).
% 2.86/1.53 thf(fact_234_gr_I1_J, axiom, (((((getRel @ (standard_Constant @ a)) @ ((sum_sum @ a) @ b)) @ (standard_S_Idt @ a)) @ g) = ((id_on @ ((sum_sum @ a) @ b)) @ (((labeled_vertices @ (standard_Constant @ a)) @ ((sum_sum @ a) @ b)) @ g)))).
% 2.86/1.53 thf(fact_235_insert__subsetI, axiom, (! [A:$tType,X3:A,A4:(set @ A),X2:(set @ A)]: (((((member @ A) @ X3) @ A4) => ((((ord_less_eq @ (set @ A)) @ X2) @ A4) => (((ord_less_eq @ (set @ A)) @ (((insert @ A) @ X3) @ X2)) @ A4)))))).
% 2.86/1.53 thf(fact_236_ssubst__Pair__rhs, axiom, (! [B:$tType,A:$tType,R:A,S:B,R2:(set @ ((product_prod @ A) @ B)),S2:B]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ R) @ S)) @ R2) => ((S2 = S) => (((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ R) @ S2)) @ R2)))))).
% 2.86/1.53 thf(fact_237_subset__emptyI, axiom, (! [A:$tType,A4:(set @ A)]: (((! [X5:A]: ((~ ((((member @ A) @ X5) @ A4))))) => (((ord_less_eq @ (set @ A)) @ A4) @ (bot_bot @ (set @ A))))))).
% 2.86/1.53 thf(fact_238_getRel__subgraph, axiom, (! [A:$tType,B:$tType,Y:A,Z2:A,L3:B,G:((labeled_graph @ B) @ A),G7:((labeled_graph @ B) @ A)]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y) @ Z2)) @ ((((getRel @ B) @ A) @ L3) @ G)) => (((((((graph_homomorphism @ B) @ A) @ A) @ G) @ G7) @ ((id_on @ A) @ (((labeled_vertices @ B) @ A) @ G))) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y) @ Z2)) @ ((((getRel @ B) @ A) @ L3) @ G7))))))).
% 2.86/1.53 thf(fact_239_gr_I2_J, axiom, (((((getRel @ (standard_Constant @ a)) @ ((sum_sum @ a) @ b)) @ (standard_S_Bot @ a)) @ g) = (bot_bot @ (set @ ((product_prod @ ((sum_sum @ a) @ b)) @ ((sum_sum @ a) @ b)))))).
% 2.86/1.53 thf(fact_240_Standard__Constant_Odistinct_I7_J, axiom, (! [V:$tType]: (((standard_S_Bot @ V) != (standard_S_Idt @ V))))).
% 2.86/1.53 thf(fact_241_getRel__homR, axiom, (! [C:$tType,A:$tType,B:$tType,Y:A,Z2:A,L3:B,G:((labeled_graph @ B) @ A),U:C,F:(set @ ((product_prod @ A) @ C)),V3:C]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y) @ Z2)) @ ((((getRel @ B) @ A) @ L3) @ G)) => ((((member @ ((product_prod @ A) @ C)) @ ((((product_Pair @ A) @ C) @ Y) @ U)) @ F) => ((((member @ ((product_prod @ A) @ C)) @ ((((product_Pair @ A) @ C) @ Z2) @ V3)) @ F) => (((member @ ((product_prod @ C) @ C)) @ ((((product_Pair @ C) @ C) @ U) @ V3)) @ ((((getRel @ B) @ C) @ L3) @ (((((map_graph @ A) @ C) @ B) @ F) @ G))))))))).
% 2.86/1.53 thf(fact_242_getRel__dom_I2_J, axiom, (! [B:$tType,A:$tType,G:((labeled_graph @ A) @ B),A2:B,B2:B,L3:A]: (((G = (((restrict @ A) @ B) @ G)) => ((((member @ ((product_prod @ B) @ B)) @ ((((product_Pair @ B) @ B) @ A2) @ B2)) @ ((((getRel @ A) @ B) @ L3) @ G)) => (((member @ B) @ B2) @ (((labeled_vertices @ A) @ B) @ G))))))).
% 2.86/1.53 thf(fact_243_getRel__dom_I1_J, axiom, (! [B:$tType,A:$tType,G:((labeled_graph @ A) @ B),A2:B,B2:B,L3:A]: (((G = (((restrict @ A) @ B) @ G)) => ((((member @ ((product_prod @ B) @ B)) @ ((((product_Pair @ B) @ B) @ A2) @ B2)) @ ((((getRel @ A) @ B) @ L3) @ G)) => (((member @ B) @ A2) @ (((labeled_vertices @ A) @ B) @ G))))))).
% 2.86/1.53 thf(fact_244_nonempty__rule, axiom, (! [A:$tType,B:$tType,G:((labeled_graph @ A) @ B)]: (((G = (((restrict @ A) @ B) @ G)) => ((((((maintained @ A) @ nat) @ B) @ (standa244753842y_rule @ A)) @ G) = ((((labeled_vertices @ A) @ B) @ G) != (bot_bot @ (set @ B)))))))).
% 2.86/1.53 thf(fact_245_le__numeral__extra_I4_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (one_one @ A)) @ (one_one @ A)))))).
% 2.86/1.53 thf(fact_246__092_060open_062maintained_A_Isymmetry__rule_AS__Idt_J_AG_092_060close_062, axiom, (((((maintained @ (standard_Constant @ a)) @ nat) @ ((sum_sum @ a) @ b)) @ ((standa1805702094y_rule @ (standard_Constant @ a)) @ (standard_S_Idt @ a))) @ g)).
% 2.86/1.53 thf(fact_247__092_060open_062maintained_A_Itransitive__rule_AS__Idt_J_AG_092_060close_062, axiom, (((((maintained @ (standard_Constant @ a)) @ nat) @ ((sum_sum @ a) @ b)) @ ((standa2114124375e_rule @ (standard_Constant @ a)) @ (standard_S_Idt @ a))) @ g)).
% 2.86/1.53 thf(fact_248_le__numeral__extra_I3_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (zero_zero @ A)))))).
% 2.86/1.53 thf(fact_249__092_060open_062maintained_A_Icongruence__rule_AS__Idt_Al_J_AG_092_060close_062, axiom, (((((maintained @ (standard_Constant @ a)) @ nat) @ ((sum_sum @ a) @ b)) @ (((standa1068660421e_rule @ (standard_Constant @ a)) @ (standard_S_Idt @ a)) @ l)) @ g)).
% 2.86/1.53 thf(fact_250_maintained__refl, axiom, (! [B:$tType,C:$tType,A:$tType,R2:((labeled_graph @ A) @ B),G:((labeled_graph @ A) @ C)]: ((((((maintained @ A) @ B) @ C) @ ((((product_Pair @ ((labeled_graph @ A) @ B)) @ ((labeled_graph @ A) @ B)) @ R2) @ R2)) @ G)))).
% 2.86/1.53 thf(fact_251_maintainedD2, axiom, (! [A:$tType,C:$tType,B:$tType,A4:((labeled_graph @ A) @ B),B6:((labeled_graph @ A) @ B),G:((labeled_graph @ A) @ C),F:(set @ ((product_prod @ B) @ C))]: (((((((maintained @ A) @ B) @ C) @ ((((product_Pair @ ((labeled_graph @ A) @ B)) @ ((labeled_graph @ A) @ B)) @ A4) @ B6)) @ G) => (((((((graph_homomorphism @ A) @ B) @ C) @ A4) @ G) @ F) => (~ ((! [G5:(set @ ((product_prod @ B) @ C))]: ((((((((graph_homomorphism @ A) @ B) @ C) @ B6) @ G) @ G5) => (~ ((((ord_less_eq @ (set @ ((product_prod @ B) @ C))) @ F) @ G5))))))))))))).
% 2.86/1.53 thf(fact_252_equivalence, axiom, (! [B:$tType,A:$tType,G:((labeled_graph @ A) @ B),I2:A]: (((G = (((restrict @ A) @ B) @ G)) => ((! [X5:((product_prod @ ((labeled_graph @ A) @ nat)) @ ((labeled_graph @ A) @ nat))]: (((((member @ ((product_prod @ ((labeled_graph @ A) @ nat)) @ ((labeled_graph @ A) @ nat))) @ X5) @ (((insert @ ((product_prod @ ((labeled_graph @ A) @ nat)) @ ((labeled_graph @ A) @ nat))) @ ((standa245363227y_rule @ A) @ I2)) @ (((insert @ ((product_prod @ ((labeled_graph @ A) @ nat)) @ ((labeled_graph @ A) @ nat))) @ ((standa2114124375e_rule @ A) @ I2)) @ (((insert @ ((product_prod @ ((labeled_graph @ A) @ nat)) @ ((labeled_graph @ A) @ nat))) @ ((standa1805702094y_rule @ A) @ I2)) @ (bot_bot @ (set @ ((product_prod @ ((labeled_graph @ A) @ nat)) @ ((labeled_graph @ A) @ nat)))))))) => (((((maintained @ A) @ nat) @ B) @ X5) @ G)))) => (((equiv_equiv @ B) @ (((labeled_vertices @ A) @ B) @ G)) @ ((((getRel @ A) @ B) @ I2) @ G))))))).
% 2.86/1.53 thf(tcon_fun___Orderings_Oorder__bot, axiom, (! [A10:$tType,A11:$tType]: (((order_bot @ A11) => (order_bot @ (A10 > A11)))))).
% 2.86/1.53 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A10:$tType,A11:$tType]: (((preorder @ A11) => (preorder @ (A10 > A11)))))).
% 2.86/1.53 thf(tcon_fun___Orderings_Oorder, axiom, (! [A10:$tType,A11:$tType]: (((order @ A11) => (order @ (A10 > A11)))))).
% 2.86/1.53 thf(tcon_fun___Orderings_Oord, axiom, (! [A10:$tType,A11:$tType]: (((ord @ A11) => (ord @ (A10 > A11)))))).
% 2.86/1.53 thf(tcon_fun___Orderings_Obot, axiom, (! [A10:$tType,A11:$tType]: (((bot @ A11) => (bot @ (A10 > A11)))))).
% 2.86/1.53 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, axiom, (canoni770627133id_add @ nat)).
% 2.86/1.53 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring, axiom, (linord1659791738miring @ nat)).
% 2.86/1.53 thf(tcon_Nat_Onat___Orderings_Oorder__bot_1, axiom, (order_bot @ nat)).
% 2.86/1.53 thf(tcon_Nat_Onat___Rings_Ozero__neq__one, axiom, (zero_neq_one @ nat)).
% 2.86/1.53 thf(tcon_Nat_Onat___Orderings_Opreorder_2, axiom, (preorder @ nat)).
% 2.86/1.53 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, (linorder @ nat)).
% 2.86/1.53 thf(tcon_Nat_Onat___Orderings_Oorder_3, axiom, (order @ nat)).
% 2.86/1.53 thf(tcon_Nat_Onat___Orderings_Oord_4, axiom, (ord @ nat)).
% 2.86/1.53 thf(tcon_Nat_Onat___Orderings_Obot_5, axiom, (bot @ nat)).
% 2.86/1.53 thf(tcon_Nat_Onat___Groups_Ozero, axiom, (zero @ nat)).
% 2.86/1.53 thf(tcon_Nat_Onat___Groups_Oone, axiom, (one @ nat)).
% 2.86/1.53 thf(tcon_Set_Oset___Orderings_Oorder__bot_6, axiom, (! [A10:$tType]: ((order_bot @ (set @ A10))))).
% 2.86/1.53 thf(tcon_Set_Oset___Orderings_Opreorder_7, axiom, (! [A10:$tType]: ((preorder @ (set @ A10))))).
% 2.86/1.53 thf(tcon_Set_Oset___Orderings_Oorder_8, axiom, (! [A10:$tType]: ((order @ (set @ A10))))).
% 2.86/1.53 thf(tcon_Set_Oset___Orderings_Oord_9, axiom, (! [A10:$tType]: ((ord @ (set @ A10))))).
% 2.86/1.53 thf(tcon_Set_Oset___Orderings_Obot_10, axiom, (! [A10:$tType]: ((bot @ (set @ A10))))).
% 2.86/1.53 thf(tcon_HOL_Obool___Orderings_Oorder__bot_11, axiom, (order_bot @ $o)).
% 2.86/1.53 thf(tcon_HOL_Obool___Orderings_Opreorder_12, axiom, (preorder @ $o)).
% 2.86/1.53 thf(tcon_HOL_Obool___Orderings_Olinorder_13, axiom, (linorder @ $o)).
% 2.86/1.53 thf(tcon_HOL_Obool___Orderings_Oorder_14, axiom, (order @ $o)).
% 2.86/1.53 thf(tcon_HOL_Obool___Orderings_Oord_15, axiom, (ord @ $o)).
% 2.86/1.53 thf(tcon_HOL_Obool___Orderings_Obot_16, axiom, (bot @ $o)).
% 2.86/1.53 thf(conj_0, conjecture, (((((labeled_vertices @ (standard_Constant @ a)) @ nat) @ ((((labeled_LG @ (standard_Constant @ a)) @ nat) @ (((insert @ ((product_prod @ (standard_Constant @ a)) @ ((product_prod @ nat) @ nat))) @ ((((product_Pair @ (standard_Constant @ a)) @ ((product_prod @ nat) @ nat)) @ (standard_S_Idt @ a)) @ ((((product_Pair @ nat) @ nat) @ (zero_zero @ nat)) @ (zero_zero @ nat)))) @ (bot_bot @ (set @ ((product_prod @ (standard_Constant @ a)) @ ((product_prod @ nat) @ nat)))))) @ (((insert @ nat) @ (zero_zero @ nat)) @ (bot_bot @ (set @ nat))))) = (((domain @ nat) @ ((sum_sum @ a) @ b)) @ (((insert @ ((product_prod @ nat) @ ((sum_sum @ a) @ b))) @ ((((product_Pair @ nat) @ ((sum_sum @ a) @ b)) @ (zero_zero @ nat)) @ v)) @ (bot_bot @ (set @ ((product_prod @ nat) @ ((sum_sum @ a) @ b))))))) & ((((((labeled_LG @ (standard_Constant @ a)) @ nat) @ (((insert @ ((product_prod @ (standard_Constant @ a)) @ ((product_prod @ nat) @ nat))) @ ((((product_Pair @ (standard_Constant @ a)) @ ((product_prod @ nat) @ nat)) @ (standard_S_Idt @ a)) @ ((((product_Pair @ nat) @ nat) @ (zero_zero @ nat)) @ (zero_zero @ nat)))) @ (bot_bot @ (set @ ((product_prod @ (standard_Constant @ a)) @ ((product_prod @ nat) @ nat)))))) @ (((insert @ nat) @ (zero_zero @ nat)) @ (bot_bot @ (set @ nat)))) = (((restrict @ (standard_Constant @ a)) @ nat) @ ((((labeled_LG @ (standard_Constant @ a)) @ nat) @ (((insert @ ((product_prod @ (standard_Constant @ a)) @ ((product_prod @ nat) @ nat))) @ ((((product_Pair @ (standard_Constant @ a)) @ ((product_prod @ nat) @ nat)) @ (standard_S_Idt @ a)) @ ((((product_Pair @ nat) @ nat) @ (zero_zero @ nat)) @ (zero_zero @ nat)))) @ (bot_bot @ (set @ ((product_prod @ (standard_Constant @ a)) @ ((product_prod @ nat) @ nat)))))) @ (((insert @ nat) @ (zero_zero @ nat)) @ (bot_bot @ (set @ nat)))))) & ((g = (((restrict @ (standard_Constant @ a)) @ ((sum_sum @ a) @ b)) @ g)) & ((((ord_less_eq @ (set @ ((sum_sum @ a) @ b))) @ ((((image @ nat) @ ((sum_sum @ a) @ b)) @ (((insert @ ((product_prod @ nat) @ ((sum_sum @ a) @ b))) @ ((((product_Pair @ nat) @ ((sum_sum @ a) @ b)) @ (zero_zero @ nat)) @ v)) @ (bot_bot @ (set @ ((product_prod @ nat) @ ((sum_sum @ a) @ b)))))) @ (((labeled_vertices @ (standard_Constant @ a)) @ nat) @ ((((labeled_LG @ (standard_Constant @ a)) @ nat) @ (((insert @ ((product_prod @ (standard_Constant @ a)) @ ((product_prod @ nat) @ nat))) @ ((((product_Pair @ (standard_Constant @ a)) @ ((product_prod @ nat) @ nat)) @ (standard_S_Idt @ a)) @ ((((product_Pair @ nat) @ nat) @ (zero_zero @ nat)) @ (zero_zero @ nat)))) @ (bot_bot @ (set @ ((product_prod @ (standard_Constant @ a)) @ ((product_prod @ nat) @ nat)))))) @ (((insert @ nat) @ (zero_zero @ nat)) @ (bot_bot @ (set @ nat))))))) @ (((labeled_vertices @ (standard_Constant @ a)) @ ((sum_sum @ a) @ b)) @ g)) & ((((univalent @ nat) @ ((sum_sum @ a) @ b)) @ (((insert @ ((product_prod @ nat) @ ((sum_sum @ a) @ b))) @ ((((product_Pair @ nat) @ ((sum_sum @ a) @ b)) @ (zero_zero @ nat)) @ v)) @ (bot_bot @ (set @ ((product_prod @ nat) @ ((sum_sum @ a) @ b)))))) & ((((((edge_preserving @ nat) @ ((sum_sum @ a) @ b)) @ (standard_Constant @ a)) @ (((insert @ ((product_prod @ nat) @ ((sum_sum @ a) @ b))) @ ((((product_Pair @ nat) @ ((sum_sum @ a) @ b)) @ (zero_zero @ nat)) @ v)) @ (bot_bot @ (set @ ((product_prod @ nat) @ ((sum_sum @ a) @ b)))))) @ (((labeled_edges @ (standard_Constant @ a)) @ nat) @ ((((labeled_LG @ (standard_Constant @ a)) @ nat) @ (((insert @ ((product_prod @ (standard_Constant @ a)) @ ((product_prod @ nat) @ nat))) @ ((((product_Pair @ (standard_Constant @ a)) @ ((product_prod @ nat) @ nat)) @ (standard_S_Idt @ a)) @ ((((product_Pair @ nat) @ nat) @ (zero_zero @ nat)) @ (zero_zero @ nat)))) @ (bot_bot @ (set @ ((product_prod @ (standard_Constant @ a)) @ ((product_prod @ nat) @ nat)))))) @ (((insert @ nat) @ (zero_zero @ nat)) @ (bot_bot @ (set @ nat)))))) @ (((labeled_edges @ (standard_Constant @ a)) @ ((sum_sum @ a) @ b)) @ g)))))))).
% 2.86/1.53 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.L5LtdenOSc/DTF2DTF15863.p
% 2.86/1.53 ------------------------
% 2.86/1.59 ---- Cleaned THF ---
% 2.86/1.59 thf(ty_t_LabeledGraphSemantics_OStandard__Constant,type,
% 2.86/1.59 standard_Constant: $tType > $tType ).
% 2.86/1.59
% 2.86/1.59 thf(ty_t_LabeledGraphs_Olabeled__graph,type,
% 2.86/1.59 labeled_graph: $tType > $tType > $tType ).
% 2.86/1.59
% 2.86/1.59 thf(ty_t_Product__Type_Oprod,type,
% 2.86/1.59 product_prod: $tType > $tType > $tType ).
% 2.86/1.59
% 2.86/1.59 thf(ty_t_Sum__Type_Osum,type,
% 2.86/1.59 sum_sum: $tType > $tType > $tType ).
% 2.86/1.59
% 2.86/1.59 thf(ty_t_Set_Oset,type,
% 2.86/1.59 set: $tType > $tType ).
% 2.86/1.59
% 2.86/1.59 thf(ty_t_Nat_Onat,type,
% 2.86/1.59 nat: $tType ).
% 2.86/1.59
% 2.86/1.59 thf(ty_tf_b,type,
% 2.86/1.59 b: $tType ).
% 2.86/1.59
% 2.86/1.59 thf(ty_tf_a,type,
% 2.86/1.59 a: $tType ).
% 2.86/1.59
% 2.86/1.59 thf(sy_cl_HOL_Otype,type,
% 2.86/1.59 type:
% 2.86/1.59 !>[A: $tType] : $o ).
% 2.86/1.59
% 2.86/1.59 thf(sy_cl_Groups_Oone,type,
% 2.86/1.59 one:
% 2.86/1.59 !>[A: $tType] : $o ).
% 2.86/1.59
% 2.86/1.59 thf(sy_cl_Groups_Ozero,type,
% 2.86/1.59 zero:
% 2.86/1.59 !>[A: $tType] : $o ).
% 2.86/1.59
% 2.86/1.59 thf(sy_cl_Orderings_Obot,type,
% 2.86/1.59 bot:
% 2.86/1.59 !>[A: $tType] : $o ).
% 2.86/1.59
% 2.86/1.59 thf(sy_cl_Orderings_Oord,type,
% 2.86/1.59 ord:
% 2.86/1.59 !>[A: $tType] : $o ).
% 2.86/1.59
% 2.86/1.59 thf(sy_cl_Orderings_Oorder,type,
% 2.86/1.59 order:
% 2.86/1.59 !>[A: $tType] : $o ).
% 2.86/1.59
% 2.86/1.59 thf(sy_cl_Orderings_Olinorder,type,
% 2.86/1.59 linorder:
% 2.86/1.59 !>[A: $tType] : $o ).
% 2.86/1.59
% 2.86/1.59 thf(sy_cl_Orderings_Opreorder,type,
% 2.86/1.59 preorder:
% 2.86/1.59 !>[A: $tType] : $o ).
% 2.86/1.59
% 2.86/1.59 thf(sy_cl_Rings_Ozero__neq__one,type,
% 2.86/1.59 zero_neq_one:
% 2.86/1.59 !>[A: $tType] : $o ).
% 2.86/1.59
% 2.86/1.59 thf(sy_cl_Orderings_Oorder__bot,type,
% 2.86/1.59 order_bot:
% 2.86/1.59 !>[A: $tType] : $o ).
% 2.86/1.59
% 2.86/1.59 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 2.86/1.59 linord1659791738miring:
% 2.86/1.59 !>[A: $tType] : $o ).
% 2.86/1.59
% 2.86/1.59 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 2.86/1.59 canoni770627133id_add:
% 2.86/1.59 !>[A: $tType] : $o ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_Equiv__Relations_Oequiv,type,
% 2.86/1.59 equiv_equiv:
% 2.86/1.59 !>[A: $tType] : ( ( set @ A ) > ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_Groups_Oone__class_Oone,type,
% 2.86/1.59 one_one:
% 2.86/1.59 !>[A: $tType] : A ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 2.86/1.59 zero_zero:
% 2.86/1.59 !>[A: $tType] : A ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_LabeledGraphSemantics_OStandard__Constant_OS__Bot,type,
% 2.86/1.59 standard_S_Bot:
% 2.86/1.59 !>[V: $tType] : ( standard_Constant @ V ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_LabeledGraphSemantics_OStandard__Constant_OS__Idt,type,
% 2.86/1.59 standard_S_Idt:
% 2.86/1.59 !>[V: $tType] : ( standard_Constant @ V ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_LabeledGraphSemantics_OgetRel,type,
% 2.86/1.59 getRel:
% 2.86/1.59 !>[B: $tType,A: $tType] : ( B > ( labeled_graph @ B @ A ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_LabeledGraphs_Oedge__preserving,type,
% 2.86/1.59 edge_preserving:
% 2.86/1.59 !>[A: $tType,B: $tType,C: $tType] : ( ( set @ ( product_prod @ A @ B ) ) > ( set @ ( product_prod @ C @ ( product_prod @ A @ A ) ) ) > ( set @ ( product_prod @ C @ ( product_prod @ B @ B ) ) ) > $o ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_LabeledGraphs_Ograph__homomorphism,type,
% 2.86/1.59 graph_homomorphism:
% 2.86/1.59 !>[A: $tType,B: $tType,C: $tType] : ( ( labeled_graph @ A @ B ) > ( labeled_graph @ A @ C ) > ( set @ ( product_prod @ B @ C ) ) > $o ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_LabeledGraphs_Ograph__union,type,
% 2.86/1.59 graph_union:
% 2.86/1.59 !>[A: $tType,B: $tType] : ( ( labeled_graph @ A @ B ) > ( labeled_graph @ A @ B ) > ( labeled_graph @ A @ B ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_LabeledGraphs_Olabeled__graph_OLG,type,
% 2.86/1.59 labeled_LG:
% 2.86/1.59 !>[L: $tType,V: $tType] : ( ( set @ ( product_prod @ L @ ( product_prod @ V @ V ) ) ) > ( set @ V ) > ( labeled_graph @ L @ V ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_LabeledGraphs_Olabeled__graph_Oedges,type,
% 2.86/1.59 labeled_edges:
% 2.86/1.59 !>[L: $tType,V: $tType] : ( ( labeled_graph @ L @ V ) > ( set @ ( product_prod @ L @ ( product_prod @ V @ V ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_LabeledGraphs_Olabeled__graph_Overtices,type,
% 2.86/1.59 labeled_vertices:
% 2.86/1.59 !>[L: $tType,V: $tType] : ( ( labeled_graph @ L @ V ) > ( set @ V ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_LabeledGraphs_Omap__graph,type,
% 2.86/1.59 map_graph:
% 2.86/1.59 !>[C: $tType,B: $tType,A: $tType] : ( ( set @ ( product_prod @ C @ B ) ) > ( labeled_graph @ A @ C ) > ( labeled_graph @ A @ B ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_LabeledGraphs_Oon__triple,type,
% 2.86/1.59 on_triple:
% 2.86/1.59 !>[B: $tType,C: $tType,A: $tType] : ( ( set @ ( product_prod @ B @ C ) ) > ( set @ ( product_prod @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( product_prod @ A @ ( product_prod @ C @ C ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_LabeledGraphs_Orestrict,type,
% 2.86/1.59 restrict:
% 2.86/1.59 !>[A: $tType,B: $tType] : ( ( labeled_graph @ A @ B ) > ( labeled_graph @ A @ B ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_MissingRelation_Ounivalent,type,
% 2.86/1.59 univalent:
% 2.86/1.59 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ B ) ) > $o ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_Orderings_Obot__class_Obot,type,
% 2.86/1.59 bot_bot:
% 2.86/1.59 !>[A: $tType] : A ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.86/1.59 ord_less_eq:
% 2.86/1.59 !>[A: $tType] : ( A > A > $o ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_Product__Type_OPair,type,
% 2.86/1.59 product_Pair:
% 2.86/1.59 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 2.86/1.59 product_rec_prod:
% 2.86/1.59 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_Relation_ODomain,type,
% 2.86/1.59 domain:
% 2.86/1.59 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ B ) ) > ( set @ A ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_Relation_OId__on,type,
% 2.86/1.59 id_on:
% 2.86/1.59 !>[A: $tType] : ( ( set @ A ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_Relation_OImage,type,
% 2.86/1.59 image:
% 2.86/1.59 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ B ) ) > ( set @ A ) > ( set @ B ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_RulesAndChains_Omaintained,type,
% 2.86/1.59 maintained:
% 2.86/1.59 !>[L: $tType,X: $tType,V: $tType] : ( ( product_prod @ ( labeled_graph @ L @ X ) @ ( labeled_graph @ L @ X ) ) > ( labeled_graph @ L @ V ) > $o ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_Set_OCollect,type,
% 2.86/1.59 collect:
% 2.86/1.59 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_Set_Oinsert,type,
% 2.86/1.59 insert:
% 2.86/1.59 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_Set_Ois__singleton,type,
% 2.86/1.59 is_singleton:
% 2.86/1.59 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_Set_Othe__elem,type,
% 2.86/1.59 the_elem:
% 2.86/1.59 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_StandardRules__Mirabelle__xlrcbcygrg_Ocongruence__rule,type,
% 2.86/1.59 standa1068660421e_rule:
% 2.86/1.59 !>[L: $tType] : ( L > L > ( product_prod @ ( labeled_graph @ L @ nat ) @ ( labeled_graph @ L @ nat ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_StandardRules__Mirabelle__xlrcbcygrg_Ononempty__rule,type,
% 2.86/1.59 standa244753842y_rule:
% 2.86/1.59 !>[L: $tType] : ( product_prod @ ( labeled_graph @ L @ nat ) @ ( labeled_graph @ L @ nat ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_StandardRules__Mirabelle__xlrcbcygrg_Oreflexivity__rule,type,
% 2.86/1.59 standa245363227y_rule:
% 2.86/1.59 !>[L: $tType] : ( L > ( product_prod @ ( labeled_graph @ L @ nat ) @ ( labeled_graph @ L @ nat ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_StandardRules__Mirabelle__xlrcbcygrg_Osymmetry__rule,type,
% 2.86/1.59 standa1805702094y_rule:
% 2.86/1.59 !>[L: $tType] : ( L > ( product_prod @ ( labeled_graph @ L @ nat ) @ ( labeled_graph @ L @ nat ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_StandardRules__Mirabelle__xlrcbcygrg_Otop__rule,type,
% 2.86/1.59 standa400804411p_rule:
% 2.86/1.59 !>[L: $tType] : ( L > ( product_prod @ ( labeled_graph @ L @ nat ) @ ( labeled_graph @ L @ nat ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_StandardRules__Mirabelle__xlrcbcygrg_Otransitive__rule,type,
% 2.86/1.59 standa2114124375e_rule:
% 2.86/1.59 !>[L: $tType] : ( L > ( product_prod @ ( labeled_graph @ L @ nat ) @ ( labeled_graph @ L @ nat ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_c_member,type,
% 2.86/1.59 member:
% 2.86/1.59 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_v_G,type,
% 2.86/1.59 g: labeled_graph @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_v_f____,type,
% 2.86/1.59 f: set @ ( product_prod @ nat @ ( sum_sum @ a @ b ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(sy_v_l,type,
% 2.86/1.59 l: standard_Constant @ a ).
% 2.86/1.59
% 2.86/1.59 thf(sy_v_v____,type,
% 2.86/1.59 v: sum_sum @ a @ b ).
% 2.86/1.59
% 2.86/1.59 thf(fact_0_g,axiom,
% 2.86/1.59 ( g
% 2.86/1.59 = ( restrict @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) @ g ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_1_v,axiom,
% 2.86/1.59 member @ ( sum_sum @ a @ b ) @ v @ ( labeled_vertices @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) @ g ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_2__092_060open_062edge__preserving_A_123_I0_058_058_063_Hc1_M_Av_J_125_A_123_IS__Idt_M_A0_058_058_063_Hc1_M_A0_058_058_063_Hc1_J_125_A_Iedges_AG_J_092_060close_062,axiom,
% 2.86/1.59 ! [C2: $tType] :
% 2.86/1.59 ( ( zero @ C2 )
% 2.86/1.59 => ( edge_preserving @ C2 @ ( sum_sum @ a @ b ) @ ( standard_Constant @ a ) @ ( insert @ ( product_prod @ C2 @ ( sum_sum @ a @ b ) ) @ ( product_Pair @ C2 @ ( sum_sum @ a @ b ) @ ( zero_zero @ C2 ) @ v ) @ ( bot_bot @ ( set @ ( product_prod @ C2 @ ( sum_sum @ a @ b ) ) ) ) ) @ ( insert @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ C2 @ C2 ) ) @ ( product_Pair @ ( standard_Constant @ a ) @ ( product_prod @ C2 @ C2 ) @ ( standard_S_Idt @ a ) @ ( product_Pair @ C2 @ C2 @ ( zero_zero @ C2 ) @ ( zero_zero @ C2 ) ) ) @ ( bot_bot @ ( set @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ C2 @ C2 ) ) ) ) ) @ ( labeled_edges @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) @ g ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_3_r,axiom,
% 2.86/1.59 ord_less_eq @ ( set @ ( sum_sum @ a @ b ) ) @ ( image @ nat @ ( sum_sum @ a @ b ) @ f @ ( insert @ nat @ ( zero_zero @ nat ) @ ( bot_bot @ ( set @ nat ) ) ) ) @ ( labeled_vertices @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) @ g ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_4_f,axiom,
% 2.86/1.59 ( f
% 2.86/1.59 = ( insert @ ( product_prod @ nat @ ( sum_sum @ a @ b ) ) @ ( product_Pair @ nat @ ( sum_sum @ a @ b ) @ ( zero_zero @ nat ) @ v ) @ ( bot_bot @ ( set @ ( product_prod @ nat @ ( sum_sum @ a @ b ) ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_5_d,axiom,
% 2.86/1.59 ( ( domain @ nat @ ( sum_sum @ a @ b ) @ f )
% 2.86/1.59 = ( insert @ nat @ ( zero_zero @ nat ) @ ( bot_bot @ ( set @ nat ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_6_graph__single,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType,A2: A,B2: B,C3: B] :
% 2.86/1.59 ( ( labeled_LG @ A @ B @ ( insert @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( product_Pair @ A @ ( product_prod @ B @ B ) @ A2 @ ( product_Pair @ B @ B @ B2 @ C3 ) ) @ ( bot_bot @ ( set @ ( product_prod @ A @ ( product_prod @ B @ B ) ) ) ) ) @ ( insert @ B @ B2 @ ( insert @ B @ C3 @ ( bot_bot @ ( set @ B ) ) ) ) )
% 2.86/1.59 = ( restrict @ A @ B @ ( labeled_LG @ A @ B @ ( insert @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( product_Pair @ A @ ( product_prod @ B @ B ) @ A2 @ ( product_Pair @ B @ B @ B2 @ C3 ) ) @ ( bot_bot @ ( set @ ( product_prod @ A @ ( product_prod @ B @ B ) ) ) ) ) @ ( insert @ B @ B2 @ ( insert @ B @ C3 @ ( bot_bot @ ( set @ B ) ) ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_7__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062v_O_A_I0_M_Av_J_A_092_060in_062_Af_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.86/1.59 ~ ! [V2: sum_sum @ a @ b] :
% 2.86/1.59 ~ ( member @ ( product_prod @ nat @ ( sum_sum @ a @ b ) ) @ ( product_Pair @ nat @ ( sum_sum @ a @ b ) @ ( zero_zero @ nat ) @ V2 ) @ f ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_8_u,axiom,
% 2.86/1.59 univalent @ nat @ ( sum_sum @ a @ b ) @ f ).
% 2.86/1.59
% 2.86/1.59 thf(fact_9_Domain__insert,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,A2: A,B2: B,R: set @ ( product_prod @ A @ B )] :
% 2.86/1.59 ( ( domain @ A @ B @ ( insert @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ B2 ) @ R ) )
% 2.86/1.59 = ( insert @ A @ A2 @ ( domain @ A @ B @ R ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_10_Image__singleton__iff,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType,B2: A,R: set @ ( product_prod @ B @ A ),A2: B] :
% 2.86/1.59 ( ( member @ A @ B2 @ ( image @ B @ A @ R @ ( insert @ B @ A2 @ ( bot_bot @ ( set @ B ) ) ) ) )
% 2.86/1.59 = ( member @ ( product_prod @ B @ A ) @ ( product_Pair @ B @ A @ A2 @ B2 ) @ R ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_11_graph__empty__e,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType,V3: set @ B] :
% 2.86/1.59 ( ( labeled_LG @ A @ B @ ( bot_bot @ ( set @ ( product_prod @ A @ ( product_prod @ B @ B ) ) ) ) @ V3 )
% 2.86/1.59 = ( restrict @ A @ B @ ( labeled_LG @ A @ B @ ( bot_bot @ ( set @ ( product_prod @ A @ ( product_prod @ B @ B ) ) ) ) @ V3 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_12_labeled__graph_Ocollapse,axiom,
% 2.86/1.59 ! [V: $tType,L: $tType,Labeled_graph: labeled_graph @ L @ V] :
% 2.86/1.59 ( ( labeled_LG @ L @ V @ ( labeled_edges @ L @ V @ Labeled_graph ) @ ( labeled_vertices @ L @ V @ Labeled_graph ) )
% 2.86/1.59 = Labeled_graph ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_13_Domain__empty,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType] :
% 2.86/1.59 ( ( domain @ A @ B @ ( bot_bot @ ( set @ ( product_prod @ A @ B ) ) ) )
% 2.86/1.59 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_14_Image__empty1,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,X2: set @ B] :
% 2.86/1.59 ( ( image @ B @ A @ ( bot_bot @ ( set @ ( product_prod @ B @ A ) ) ) @ X2 )
% 2.86/1.59 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_15_restrict__idemp,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,X3: labeled_graph @ A @ B] :
% 2.86/1.59 ( ( restrict @ A @ B @ ( restrict @ A @ B @ X3 ) )
% 2.86/1.59 = ( restrict @ A @ B @ X3 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_16_labeled__graph_Oinject,axiom,
% 2.86/1.59 ! [L: $tType,V: $tType,X1: set @ ( product_prod @ L @ ( product_prod @ V @ V ) ),X22: set @ V,Y1: set @ ( product_prod @ L @ ( product_prod @ V @ V ) ),Y2: set @ V] :
% 2.86/1.59 ( ( ( labeled_LG @ L @ V @ X1 @ X22 )
% 2.86/1.59 = ( labeled_LG @ L @ V @ Y1 @ Y2 ) )
% 2.86/1.59 = ( ( X1 = Y1 )
% 2.86/1.59 & ( X22 = Y2 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_17_v__gr,axiom,
% 2.86/1.59 ! [A3: sum_sum @ a @ b,B3: sum_sum @ a @ b] :
% 2.86/1.59 ( ( member @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ ( sum_sum @ a @ b ) @ ( sum_sum @ a @ b ) ) ) @ ( product_Pair @ ( standard_Constant @ a ) @ ( product_prod @ ( sum_sum @ a @ b ) @ ( sum_sum @ a @ b ) ) @ ( standard_S_Idt @ a ) @ ( product_Pair @ ( sum_sum @ a @ b ) @ ( sum_sum @ a @ b ) @ A3 @ B3 ) ) @ ( labeled_edges @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) @ g ) )
% 2.86/1.59 = ( ( member @ ( sum_sum @ a @ b ) @ A3 @ ( labeled_vertices @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) @ g ) )
% 2.86/1.59 & ( B3 = A3 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_18__092_060open_062_IS__Idt_M_Av_M_Av_J_A_092_060in_062_Aedges_AG_092_060close_062,axiom,
% 2.86/1.59 member @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ ( sum_sum @ a @ b ) @ ( sum_sum @ a @ b ) ) ) @ ( product_Pair @ ( standard_Constant @ a ) @ ( product_prod @ ( sum_sum @ a @ b ) @ ( sum_sum @ a @ b ) ) @ ( standard_S_Idt @ a ) @ ( product_Pair @ ( sum_sum @ a @ b ) @ ( sum_sum @ a @ b ) @ v @ v ) ) @ ( labeled_edges @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) @ g ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_19_ImageI,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,A2: A,B2: B,R: set @ ( product_prod @ A @ B ),A4: set @ A] :
% 2.86/1.59 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ B2 ) @ R )
% 2.86/1.59 => ( ( member @ A @ A2 @ A4 )
% 2.86/1.59 => ( member @ B @ B2 @ ( image @ A @ B @ R @ A4 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_20_Image__empty2,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,R2: set @ ( product_prod @ B @ A )] :
% 2.86/1.59 ( ( image @ B @ A @ R2 @ ( bot_bot @ ( set @ B ) ) )
% 2.86/1.59 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_21_vertices__restrict,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType,G: labeled_graph @ B @ A] :
% 2.86/1.59 ( ( labeled_vertices @ B @ A @ ( restrict @ B @ A @ G ) )
% 2.86/1.59 = ( labeled_vertices @ B @ A @ G ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_22__092_060open_062graph__homomorphism_A_ILG_A_123_125_A_1230_125_J_AG_Af_092_060close_062,axiom,
% 2.86/1.59 graph_homomorphism @ ( standard_Constant @ a ) @ nat @ ( sum_sum @ a @ b ) @ ( labeled_LG @ ( standard_Constant @ a ) @ nat @ ( bot_bot @ ( set @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) ) ) ) @ ( insert @ nat @ ( zero_zero @ nat ) @ ( bot_bot @ ( set @ nat ) ) ) ) @ g @ f ).
% 2.86/1.59
% 2.86/1.59 thf(fact_23_labeled__graph_Oexhaust,axiom,
% 2.86/1.59 ! [L: $tType,V: $tType,Y: labeled_graph @ L @ V] :
% 2.86/1.59 ~ ! [X12: set @ ( product_prod @ L @ ( product_prod @ V @ V ) ),X23: set @ V] :
% 2.86/1.59 ( Y
% 2.86/1.59 != ( labeled_LG @ L @ V @ X12 @ X23 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_24_labeled__graph_Oinduct,axiom,
% 2.86/1.59 ! [V: $tType,L: $tType,P: ( labeled_graph @ L @ V ) > $o,Labeled_graph: labeled_graph @ L @ V] :
% 2.86/1.59 ( ! [X1a: set @ ( product_prod @ L @ ( product_prod @ V @ V ) ),X2a: set @ V] : ( P @ ( labeled_LG @ L @ V @ X1a @ X2a ) )
% 2.86/1.59 => ( P @ Labeled_graph ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_25_rev__ImageI,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,A2: A,A4: set @ A,B2: B,R: set @ ( product_prod @ A @ B )] :
% 2.86/1.59 ( ( member @ A @ A2 @ A4 )
% 2.86/1.59 => ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ B2 ) @ R )
% 2.86/1.59 => ( member @ B @ B2 @ ( image @ A @ B @ R @ A4 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_26_Image__iff,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType,B2: A,R: set @ ( product_prod @ B @ A ),A4: set @ B] :
% 2.86/1.59 ( ( member @ A @ B2 @ ( image @ B @ A @ R @ A4 ) )
% 2.86/1.59 = ( ? [X4: B] :
% 2.86/1.59 ( ( member @ B @ X4 @ A4 )
% 2.86/1.59 & ( member @ ( product_prod @ B @ A ) @ ( product_Pair @ B @ A @ X4 @ B2 ) @ R ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_27_ImageE,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType,B2: A,R: set @ ( product_prod @ B @ A ),A4: set @ B] :
% 2.86/1.59 ( ( member @ A @ B2 @ ( image @ B @ A @ R @ A4 ) )
% 2.86/1.59 => ~ ! [X5: B] :
% 2.86/1.59 ( ( member @ ( product_prod @ B @ A ) @ ( product_Pair @ B @ A @ X5 @ B2 ) @ R )
% 2.86/1.59 => ~ ( member @ B @ X5 @ A4 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_28_Image__mono,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,R3: set @ ( product_prod @ A @ B ),R: set @ ( product_prod @ A @ B ),A5: set @ A,A4: set @ A] :
% 2.86/1.59 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R3 @ R )
% 2.86/1.59 => ( ( ord_less_eq @ ( set @ A ) @ A5 @ A4 )
% 2.86/1.59 => ( ord_less_eq @ ( set @ B ) @ ( image @ A @ B @ R3 @ A5 ) @ ( image @ A @ B @ R @ A4 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_29_Domain_Oinducts,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,X3: A,R: set @ ( product_prod @ A @ B ),P: A > $o] :
% 2.86/1.59 ( ( member @ A @ X3 @ ( domain @ A @ B @ R ) )
% 2.86/1.59 => ( ! [A6: A,B4: B] :
% 2.86/1.59 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A6 @ B4 ) @ R )
% 2.86/1.59 => ( P @ A6 ) )
% 2.86/1.59 => ( P @ X3 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_30_Domain_ODomainI,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,A2: A,B2: B,R: set @ ( product_prod @ A @ B )] :
% 2.86/1.59 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ B2 ) @ R )
% 2.86/1.59 => ( member @ A @ A2 @ ( domain @ A @ B @ R ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_31_Domain_Osimps,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,A2: A,R: set @ ( product_prod @ A @ B )] :
% 2.86/1.59 ( ( member @ A @ A2 @ ( domain @ A @ B @ R ) )
% 2.86/1.59 = ( ? [A7: A,B5: B] :
% 2.86/1.59 ( ( A2 = A7 )
% 2.86/1.59 & ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A7 @ B5 ) @ R ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_32_Domain_Ocases,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,A2: A,R: set @ ( product_prod @ A @ B )] :
% 2.86/1.59 ( ( member @ A @ A2 @ ( domain @ A @ B @ R ) )
% 2.86/1.59 => ~ ! [B4: B] :
% 2.86/1.59 ~ ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ B4 ) @ R ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_33_Domain__iff,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType,A2: A,R: set @ ( product_prod @ A @ B )] :
% 2.86/1.59 ( ( member @ A @ A2 @ ( domain @ A @ B @ R ) )
% 2.86/1.59 = ( ? [Y3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ Y3 ) @ R ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_34_DomainE,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,A2: A,R: set @ ( product_prod @ A @ B )] :
% 2.86/1.59 ( ( member @ A @ A2 @ ( domain @ A @ B @ R ) )
% 2.86/1.59 => ~ ! [B4: B] :
% 2.86/1.59 ~ ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ B4 ) @ R ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_35_Domain__mono,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 2.86/1.59 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R @ S )
% 2.86/1.59 => ( ord_less_eq @ ( set @ A ) @ ( domain @ A @ B @ R ) @ ( domain @ A @ B @ S ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_36_labeled__graph_Oexpand,axiom,
% 2.86/1.59 ! [V: $tType,L: $tType,Labeled_graph: labeled_graph @ L @ V,Labeled_graph2: labeled_graph @ L @ V] :
% 2.86/1.59 ( ( ( ( labeled_edges @ L @ V @ Labeled_graph )
% 2.86/1.59 = ( labeled_edges @ L @ V @ Labeled_graph2 ) )
% 2.86/1.59 & ( ( labeled_vertices @ L @ V @ Labeled_graph )
% 2.86/1.59 = ( labeled_vertices @ L @ V @ Labeled_graph2 ) ) )
% 2.86/1.59 => ( Labeled_graph = Labeled_graph2 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_37_labeled__graph_Osel_I2_J,axiom,
% 2.86/1.59 ! [L: $tType,V: $tType,X1: set @ ( product_prod @ L @ ( product_prod @ V @ V ) ),X22: set @ V] :
% 2.86/1.59 ( ( labeled_vertices @ L @ V @ ( labeled_LG @ L @ V @ X1 @ X22 ) )
% 2.86/1.59 = X22 ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_38_labeled__graph_Osel_I1_J,axiom,
% 2.86/1.59 ! [V: $tType,L: $tType,X1: set @ ( product_prod @ L @ ( product_prod @ V @ V ) ),X22: set @ V] :
% 2.86/1.59 ( ( labeled_edges @ L @ V @ ( labeled_LG @ L @ V @ X1 @ X22 ) )
% 2.86/1.59 = X1 ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_39_Domain__empty__iff,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B )] :
% 2.86/1.59 ( ( ( domain @ A @ B @ R )
% 2.86/1.59 = ( bot_bot @ ( set @ A ) ) )
% 2.86/1.59 = ( R
% 2.86/1.59 = ( bot_bot @ ( set @ ( product_prod @ A @ B ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_40_edge__preserving__atomic,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType,C: $tType,H1: set @ ( product_prod @ A @ B ),E1: set @ ( product_prod @ C @ ( product_prod @ A @ A ) ),E2: set @ ( product_prod @ C @ ( product_prod @ B @ B ) ),V1: A,V12: B,V22: A,V23: B,K: C] :
% 2.86/1.59 ( ( edge_preserving @ A @ B @ C @ H1 @ E1 @ E2 )
% 2.86/1.59 => ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ V1 @ V12 ) @ H1 )
% 2.86/1.59 => ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ V22 @ V23 ) @ H1 )
% 2.86/1.59 => ( ( member @ ( product_prod @ C @ ( product_prod @ A @ A ) ) @ ( product_Pair @ C @ ( product_prod @ A @ A ) @ K @ ( product_Pair @ A @ A @ V1 @ V22 ) ) @ E1 )
% 2.86/1.59 => ( member @ ( product_prod @ C @ ( product_prod @ B @ B ) ) @ ( product_Pair @ C @ ( product_prod @ B @ B ) @ K @ ( product_Pair @ B @ B @ V12 @ V23 ) ) @ E2 ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_41_labeled__graph_Oexhaust__sel,axiom,
% 2.86/1.59 ! [V: $tType,L: $tType,Labeled_graph: labeled_graph @ L @ V] :
% 2.86/1.59 ( Labeled_graph
% 2.86/1.59 = ( labeled_LG @ L @ V @ ( labeled_edges @ L @ V @ Labeled_graph ) @ ( labeled_vertices @ L @ V @ Labeled_graph ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_42_singleton__insert__inj__eq_H,axiom,
% 2.86/1.59 ! [A: $tType,A2: A,A4: set @ A,B2: A] :
% 2.86/1.59 ( ( ( insert @ A @ A2 @ A4 )
% 2.86/1.59 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.86/1.59 = ( ( A2 = B2 )
% 2.86/1.59 & ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_43_singleton__insert__inj__eq,axiom,
% 2.86/1.59 ! [A: $tType,B2: A,A2: A,A4: set @ A] :
% 2.86/1.59 ( ( ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) )
% 2.86/1.59 = ( insert @ A @ A2 @ A4 ) )
% 2.86/1.59 = ( ( A2 = B2 )
% 2.86/1.59 & ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_44_univalent__empty,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType] : ( univalent @ A @ B @ ( bot_bot @ ( set @ ( product_prod @ A @ B ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_45_mem__Collect__eq,axiom,
% 2.86/1.59 ! [A: $tType,A2: A,P: A > $o] :
% 2.86/1.59 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.86/1.59 = ( P @ A2 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_46_Collect__mem__eq,axiom,
% 2.86/1.59 ! [A: $tType,A4: set @ A] :
% 2.86/1.59 ( ( collect @ A
% 2.86/1.59 @ ^ [X4: A] : ( member @ A @ X4 @ A4 ) )
% 2.86/1.59 = A4 ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_47_Collect__cong,axiom,
% 2.86/1.59 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.86/1.59 ( ! [X5: A] :
% 2.86/1.59 ( ( P @ X5 )
% 2.86/1.59 = ( Q @ X5 ) )
% 2.86/1.59 => ( ( collect @ A @ P )
% 2.86/1.59 = ( collect @ A @ Q ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_48_ext,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,F: A > B,G2: A > B] :
% 2.86/1.59 ( ! [X5: A] :
% 2.86/1.59 ( ( F @ X5 )
% 2.86/1.59 = ( G2 @ X5 ) )
% 2.86/1.59 => ( F = G2 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_49_insert__subset,axiom,
% 2.86/1.59 ! [A: $tType,X3: A,A4: set @ A,B6: set @ A] :
% 2.86/1.59 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X3 @ A4 ) @ B6 )
% 2.86/1.59 = ( ( member @ A @ X3 @ B6 )
% 2.86/1.59 & ( ord_less_eq @ ( set @ A ) @ A4 @ B6 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_50_singletonI,axiom,
% 2.86/1.59 ! [A: $tType,A2: A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_51_empty__subsetI,axiom,
% 2.86/1.59 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A4 ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_52_subset__empty,axiom,
% 2.86/1.59 ! [A: $tType,A4: set @ A] :
% 2.86/1.59 ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 2.86/1.59 = ( A4
% 2.86/1.59 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_53_le__zero__eq,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( canoni770627133id_add @ A )
% 2.86/1.59 => ! [N: A] :
% 2.86/1.59 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 2.86/1.59 = ( N
% 2.86/1.59 = ( zero_zero @ A ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_54_reflexivity__rule__def,axiom,
% 2.86/1.59 ! [L: $tType] :
% 2.86/1.59 ( ( standa245363227y_rule @ L )
% 2.86/1.59 = ( ^ [T2: L] : ( product_Pair @ ( labeled_graph @ L @ nat ) @ ( labeled_graph @ L @ nat ) @ ( labeled_LG @ L @ nat @ ( bot_bot @ ( set @ ( product_prod @ L @ ( product_prod @ nat @ nat ) ) ) ) @ ( insert @ nat @ ( zero_zero @ nat ) @ ( bot_bot @ ( set @ nat ) ) ) ) @ ( labeled_LG @ L @ nat @ ( insert @ ( product_prod @ L @ ( product_prod @ nat @ nat ) ) @ ( product_Pair @ L @ ( product_prod @ nat @ nat ) @ T2 @ ( product_Pair @ nat @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ) @ ( bot_bot @ ( set @ ( product_prod @ L @ ( product_prod @ nat @ nat ) ) ) ) ) @ ( insert @ nat @ ( zero_zero @ nat ) @ ( bot_bot @ ( set @ nat ) ) ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_55_nonempty__rule__def,axiom,
% 2.86/1.59 ! [L: $tType] :
% 2.86/1.59 ( ( standa244753842y_rule @ L )
% 2.86/1.59 = ( product_Pair @ ( labeled_graph @ L @ nat ) @ ( labeled_graph @ L @ nat ) @ ( labeled_LG @ L @ nat @ ( bot_bot @ ( set @ ( product_prod @ L @ ( product_prod @ nat @ nat ) ) ) ) @ ( bot_bot @ ( set @ nat ) ) ) @ ( labeled_LG @ L @ nat @ ( bot_bot @ ( set @ ( product_prod @ L @ ( product_prod @ nat @ nat ) ) ) ) @ ( insert @ nat @ ( zero_zero @ nat ) @ ( bot_bot @ ( set @ nat ) ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_56_empty__iff,axiom,
% 2.86/1.59 ! [A: $tType,C3: A] :
% 2.86/1.59 ~ ( member @ A @ C3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_57_all__not__in__conv,axiom,
% 2.86/1.59 ! [A: $tType,A4: set @ A] :
% 2.86/1.59 ( ( ! [X4: A] :
% 2.86/1.59 ~ ( member @ A @ X4 @ A4 ) )
% 2.86/1.59 = ( A4
% 2.86/1.59 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_58_Collect__empty__eq,axiom,
% 2.86/1.59 ! [A: $tType,P: A > $o] :
% 2.86/1.59 ( ( ( collect @ A @ P )
% 2.86/1.59 = ( bot_bot @ ( set @ A ) ) )
% 2.86/1.59 = ( ! [X4: A] :
% 2.86/1.59 ~ ( P @ X4 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_59_empty__Collect__eq,axiom,
% 2.86/1.59 ! [A: $tType,P: A > $o] :
% 2.86/1.59 ( ( ( bot_bot @ ( set @ A ) )
% 2.86/1.59 = ( collect @ A @ P ) )
% 2.86/1.59 = ( ! [X4: A] :
% 2.86/1.59 ~ ( P @ X4 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_60_subsetI,axiom,
% 2.86/1.59 ! [A: $tType,A4: set @ A,B6: set @ A] :
% 2.86/1.59 ( ! [X5: A] :
% 2.86/1.59 ( ( member @ A @ X5 @ A4 )
% 2.86/1.59 => ( member @ A @ X5 @ B6 ) )
% 2.86/1.59 => ( ord_less_eq @ ( set @ A ) @ A4 @ B6 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_61_subset__antisym,axiom,
% 2.86/1.59 ! [A: $tType,A4: set @ A,B6: set @ A] :
% 2.86/1.59 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B6 )
% 2.86/1.59 => ( ( ord_less_eq @ ( set @ A ) @ B6 @ A4 )
% 2.86/1.59 => ( A4 = B6 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_62_insertCI,axiom,
% 2.86/1.59 ! [A: $tType,A2: A,B6: set @ A,B2: A] :
% 2.86/1.59 ( ( ~ ( member @ A @ A2 @ B6 )
% 2.86/1.59 => ( A2 = B2 ) )
% 2.86/1.59 => ( member @ A @ A2 @ ( insert @ A @ B2 @ B6 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_63_insert__iff,axiom,
% 2.86/1.59 ! [A: $tType,A2: A,B2: A,A4: set @ A] :
% 2.86/1.59 ( ( member @ A @ A2 @ ( insert @ A @ B2 @ A4 ) )
% 2.86/1.59 = ( ( A2 = B2 )
% 2.86/1.59 | ( member @ A @ A2 @ A4 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_64_insert__absorb2,axiom,
% 2.86/1.59 ! [A: $tType,X3: A,A4: set @ A] :
% 2.86/1.59 ( ( insert @ A @ X3 @ ( insert @ A @ X3 @ A4 ) )
% 2.86/1.59 = ( insert @ A @ X3 @ A4 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_65_graph__homomorphism__empty,axiom,
% 2.86/1.59 ! [B: $tType,C: $tType,A: $tType,G: labeled_graph @ A @ C,F: set @ ( product_prod @ B @ C )] :
% 2.86/1.59 ( ( graph_homomorphism @ A @ B @ C @ ( labeled_LG @ A @ B @ ( bot_bot @ ( set @ ( product_prod @ A @ ( product_prod @ B @ B ) ) ) ) @ ( bot_bot @ ( set @ B ) ) ) @ G @ F )
% 2.86/1.59 = ( ( F
% 2.86/1.59 = ( bot_bot @ ( set @ ( product_prod @ B @ C ) ) ) )
% 2.86/1.59 & ( G
% 2.86/1.59 = ( restrict @ A @ C @ G ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_66_edge__preserving__subset,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType,C: $tType,R_1: set @ ( product_prod @ A @ B ),R_2: set @ ( product_prod @ A @ B ),E_1: set @ ( product_prod @ C @ ( product_prod @ A @ A ) ),E_2: set @ ( product_prod @ C @ ( product_prod @ A @ A ) ),G: set @ ( product_prod @ C @ ( product_prod @ B @ B ) )] :
% 2.86/1.59 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R_1 @ R_2 )
% 2.86/1.59 => ( ( ord_less_eq @ ( set @ ( product_prod @ C @ ( product_prod @ A @ A ) ) ) @ E_1 @ E_2 )
% 2.86/1.59 => ( ( edge_preserving @ A @ B @ C @ R_2 @ E_2 @ G )
% 2.86/1.59 => ( edge_preserving @ A @ B @ C @ R_1 @ E_1 @ G ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_67_subrelI,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 2.86/1.59 ( ! [X5: A,Y4: B] :
% 2.86/1.59 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X5 @ Y4 ) @ R )
% 2.86/1.59 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X5 @ Y4 ) @ S ) )
% 2.86/1.59 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R @ S ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_68_restrict__subsD,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,G: labeled_graph @ A @ B] :
% 2.86/1.59 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ ( product_prod @ B @ B ) ) ) @ ( labeled_edges @ A @ B @ G ) @ ( labeled_edges @ A @ B @ ( restrict @ A @ B @ G ) ) )
% 2.86/1.59 => ( G
% 2.86/1.59 = ( restrict @ A @ B @ G ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_69_zero__reorient,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( zero @ A )
% 2.86/1.59 => ! [X3: A] :
% 2.86/1.59 ( ( ( zero_zero @ A )
% 2.86/1.59 = X3 )
% 2.86/1.59 = ( X3
% 2.86/1.59 = ( zero_zero @ A ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_70_emptyE,axiom,
% 2.86/1.59 ! [A: $tType,A2: A] :
% 2.86/1.59 ~ ( member @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_71_equals0D,axiom,
% 2.86/1.59 ! [A: $tType,A4: set @ A,A2: A] :
% 2.86/1.59 ( ( A4
% 2.86/1.59 = ( bot_bot @ ( set @ A ) ) )
% 2.86/1.59 => ~ ( member @ A @ A2 @ A4 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_72_equals0I,axiom,
% 2.86/1.59 ! [A: $tType,A4: set @ A] :
% 2.86/1.59 ( ! [Y4: A] :
% 2.86/1.59 ~ ( member @ A @ Y4 @ A4 )
% 2.86/1.59 => ( A4
% 2.86/1.59 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_73_ex__in__conv,axiom,
% 2.86/1.59 ! [A: $tType,A4: set @ A] :
% 2.86/1.59 ( ( ? [X4: A] : ( member @ A @ X4 @ A4 ) )
% 2.86/1.59 = ( A4
% 2.86/1.59 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_74_in__mono,axiom,
% 2.86/1.59 ! [A: $tType,A4: set @ A,B6: set @ A,X3: A] :
% 2.86/1.59 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B6 )
% 2.86/1.59 => ( ( member @ A @ X3 @ A4 )
% 2.86/1.59 => ( member @ A @ X3 @ B6 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_75_subsetD,axiom,
% 2.86/1.59 ! [A: $tType,A4: set @ A,B6: set @ A,C3: A] :
% 2.86/1.59 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B6 )
% 2.86/1.59 => ( ( member @ A @ C3 @ A4 )
% 2.86/1.59 => ( member @ A @ C3 @ B6 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_76_equalityE,axiom,
% 2.86/1.59 ! [A: $tType,A4: set @ A,B6: set @ A] :
% 2.86/1.59 ( ( A4 = B6 )
% 2.86/1.59 => ~ ( ( ord_less_eq @ ( set @ A ) @ A4 @ B6 )
% 2.86/1.59 => ~ ( ord_less_eq @ ( set @ A ) @ B6 @ A4 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_77_subset__eq,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( ord_less_eq @ ( set @ A ) )
% 2.86/1.59 = ( ^ [A8: set @ A,B7: set @ A] :
% 2.86/1.59 ! [X4: A] :
% 2.86/1.59 ( ( member @ A @ X4 @ A8 )
% 2.86/1.59 => ( member @ A @ X4 @ B7 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_78_equalityD1,axiom,
% 2.86/1.59 ! [A: $tType,A4: set @ A,B6: set @ A] :
% 2.86/1.59 ( ( A4 = B6 )
% 2.86/1.59 => ( ord_less_eq @ ( set @ A ) @ A4 @ B6 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_79_equalityD2,axiom,
% 2.86/1.59 ! [A: $tType,A4: set @ A,B6: set @ A] :
% 2.86/1.59 ( ( A4 = B6 )
% 2.86/1.59 => ( ord_less_eq @ ( set @ A ) @ B6 @ A4 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_80_subset__iff,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( ord_less_eq @ ( set @ A ) )
% 2.86/1.59 = ( ^ [A8: set @ A,B7: set @ A] :
% 2.86/1.59 ! [T2: A] :
% 2.86/1.59 ( ( member @ A @ T2 @ A8 )
% 2.86/1.59 => ( member @ A @ T2 @ B7 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_81_subset__refl,axiom,
% 2.86/1.59 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ A4 ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_82_Collect__mono,axiom,
% 2.86/1.59 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.86/1.59 ( ! [X5: A] :
% 2.86/1.59 ( ( P @ X5 )
% 2.86/1.59 => ( Q @ X5 ) )
% 2.86/1.59 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_83_subset__trans,axiom,
% 2.86/1.59 ! [A: $tType,A4: set @ A,B6: set @ A,C4: set @ A] :
% 2.86/1.59 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B6 )
% 2.86/1.59 => ( ( ord_less_eq @ ( set @ A ) @ B6 @ C4 )
% 2.86/1.59 => ( ord_less_eq @ ( set @ A ) @ A4 @ C4 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_84_set__eq__subset,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( ^ [Y5: set @ A,Z: set @ A] : ( Y5 = Z ) )
% 2.86/1.59 = ( ^ [A8: set @ A,B7: set @ A] :
% 2.86/1.59 ( ( ord_less_eq @ ( set @ A ) @ A8 @ B7 )
% 2.86/1.59 & ( ord_less_eq @ ( set @ A ) @ B7 @ A8 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_85_Collect__mono__iff,axiom,
% 2.86/1.59 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.86/1.59 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 2.86/1.59 = ( ! [X4: A] :
% 2.86/1.59 ( ( P @ X4 )
% 2.86/1.59 => ( Q @ X4 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_86_insertE,axiom,
% 2.86/1.59 ! [A: $tType,A2: A,B2: A,A4: set @ A] :
% 2.86/1.59 ( ( member @ A @ A2 @ ( insert @ A @ B2 @ A4 ) )
% 2.86/1.59 => ( ( A2 != B2 )
% 2.86/1.59 => ( member @ A @ A2 @ A4 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_87_insertI1,axiom,
% 2.86/1.59 ! [A: $tType,A2: A,B6: set @ A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ B6 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_88_insertI2,axiom,
% 2.86/1.59 ! [A: $tType,A2: A,B6: set @ A,B2: A] :
% 2.86/1.59 ( ( member @ A @ A2 @ B6 )
% 2.86/1.59 => ( member @ A @ A2 @ ( insert @ A @ B2 @ B6 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_89_Set_Oset__insert,axiom,
% 2.86/1.59 ! [A: $tType,X3: A,A4: set @ A] :
% 2.86/1.59 ( ( member @ A @ X3 @ A4 )
% 2.86/1.59 => ~ ! [B8: set @ A] :
% 2.86/1.59 ( ( A4
% 2.86/1.59 = ( insert @ A @ X3 @ B8 ) )
% 2.86/1.59 => ( member @ A @ X3 @ B8 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_90_insert__ident,axiom,
% 2.86/1.59 ! [A: $tType,X3: A,A4: set @ A,B6: set @ A] :
% 2.86/1.59 ( ~ ( member @ A @ X3 @ A4 )
% 2.86/1.59 => ( ~ ( member @ A @ X3 @ B6 )
% 2.86/1.59 => ( ( ( insert @ A @ X3 @ A4 )
% 2.86/1.59 = ( insert @ A @ X3 @ B6 ) )
% 2.86/1.59 = ( A4 = B6 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_91_insert__absorb,axiom,
% 2.86/1.59 ! [A: $tType,A2: A,A4: set @ A] :
% 2.86/1.59 ( ( member @ A @ A2 @ A4 )
% 2.86/1.59 => ( ( insert @ A @ A2 @ A4 )
% 2.86/1.59 = A4 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_92_insert__eq__iff,axiom,
% 2.86/1.59 ! [A: $tType,A2: A,A4: set @ A,B2: A,B6: set @ A] :
% 2.86/1.59 ( ~ ( member @ A @ A2 @ A4 )
% 2.86/1.59 => ( ~ ( member @ A @ B2 @ B6 )
% 2.86/1.59 => ( ( ( insert @ A @ A2 @ A4 )
% 2.86/1.59 = ( insert @ A @ B2 @ B6 ) )
% 2.86/1.59 = ( ( ( A2 = B2 )
% 2.86/1.59 => ( A4 = B6 ) )
% 2.86/1.59 & ( ( A2 != B2 )
% 2.86/1.59 => ? [C5: set @ A] :
% 2.86/1.59 ( ( A4
% 2.86/1.59 = ( insert @ A @ B2 @ C5 ) )
% 2.86/1.59 & ~ ( member @ A @ B2 @ C5 )
% 2.86/1.59 & ( B6
% 2.86/1.59 = ( insert @ A @ A2 @ C5 ) )
% 2.86/1.59 & ~ ( member @ A @ A2 @ C5 ) ) ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_93_insert__commute,axiom,
% 2.86/1.59 ! [A: $tType,X3: A,Y: A,A4: set @ A] :
% 2.86/1.59 ( ( insert @ A @ X3 @ ( insert @ A @ Y @ A4 ) )
% 2.86/1.59 = ( insert @ A @ Y @ ( insert @ A @ X3 @ A4 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_94_mk__disjoint__insert,axiom,
% 2.86/1.59 ! [A: $tType,A2: A,A4: set @ A] :
% 2.86/1.59 ( ( member @ A @ A2 @ A4 )
% 2.86/1.59 => ? [B8: set @ A] :
% 2.86/1.59 ( ( A4
% 2.86/1.59 = ( insert @ A @ A2 @ B8 ) )
% 2.86/1.59 & ~ ( member @ A @ A2 @ B8 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_95_zero__le,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( canoni770627133id_add @ A )
% 2.86/1.59 => ! [X3: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X3 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_96_singletonD,axiom,
% 2.86/1.59 ! [A: $tType,B2: A,A2: A] :
% 2.86/1.59 ( ( member @ A @ B2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.86/1.59 => ( B2 = A2 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_97_singleton__iff,axiom,
% 2.86/1.59 ! [A: $tType,B2: A,A2: A] :
% 2.86/1.59 ( ( member @ A @ B2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.86/1.59 = ( B2 = A2 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_98_doubleton__eq__iff,axiom,
% 2.86/1.59 ! [A: $tType,A2: A,B2: A,C3: A,D: A] :
% 2.86/1.59 ( ( ( insert @ A @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.86/1.59 = ( insert @ A @ C3 @ ( insert @ A @ D @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.86/1.59 = ( ( ( A2 = C3 )
% 2.86/1.59 & ( B2 = D ) )
% 2.86/1.59 | ( ( A2 = D )
% 2.86/1.59 & ( B2 = C3 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_99_insert__not__empty,axiom,
% 2.86/1.59 ! [A: $tType,A2: A,A4: set @ A] :
% 2.86/1.59 ( ( insert @ A @ A2 @ A4 )
% 2.86/1.59 != ( bot_bot @ ( set @ A ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_100_singleton__inject,axiom,
% 2.86/1.59 ! [A: $tType,A2: A,B2: A] :
% 2.86/1.59 ( ( ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 2.86/1.59 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.86/1.59 => ( A2 = B2 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_101_insert__mono,axiom,
% 2.86/1.59 ! [A: $tType,C4: set @ A,D2: set @ A,A2: A] :
% 2.86/1.59 ( ( ord_less_eq @ ( set @ A ) @ C4 @ D2 )
% 2.86/1.59 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ A2 @ C4 ) @ ( insert @ A @ A2 @ D2 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_102_subset__insert,axiom,
% 2.86/1.59 ! [A: $tType,X3: A,A4: set @ A,B6: set @ A] :
% 2.86/1.59 ( ~ ( member @ A @ X3 @ A4 )
% 2.86/1.59 => ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ X3 @ B6 ) )
% 2.86/1.59 = ( ord_less_eq @ ( set @ A ) @ A4 @ B6 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_103_subset__insertI,axiom,
% 2.86/1.59 ! [A: $tType,B6: set @ A,A2: A] : ( ord_less_eq @ ( set @ A ) @ B6 @ ( insert @ A @ A2 @ B6 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_104_subset__insertI2,axiom,
% 2.86/1.59 ! [A: $tType,A4: set @ A,B6: set @ A,B2: A] :
% 2.86/1.59 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B6 )
% 2.86/1.59 => ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ B2 @ B6 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_105_univalentD,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType,R2: set @ ( product_prod @ A @ B ),X3: A,Y: B,Z2: B] :
% 2.86/1.59 ( ( univalent @ A @ B @ R2 )
% 2.86/1.59 => ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y ) @ R2 )
% 2.86/1.59 => ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Z2 ) @ R2 )
% 2.86/1.59 => ( Z2 = Y ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_106_univalent__def,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType] :
% 2.86/1.59 ( ( univalent @ A @ B )
% 2.86/1.59 = ( ^ [R4: set @ ( product_prod @ A @ B )] :
% 2.86/1.59 ! [X4: A,Y3: B,Z3: B] :
% 2.86/1.59 ( ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y3 ) @ R4 )
% 2.86/1.59 & ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Z3 ) @ R4 ) )
% 2.86/1.59 => ( Z3 = Y3 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_107_graph__homomorphismI,axiom,
% 2.86/1.59 ! [B: $tType,C: $tType,A: $tType,S: labeled_graph @ B @ A,H: set @ ( product_prod @ A @ C ),T3: labeled_graph @ B @ C] :
% 2.86/1.59 ( ( ( labeled_vertices @ B @ A @ S )
% 2.86/1.59 = ( domain @ A @ C @ H ) )
% 2.86/1.59 => ( ( ord_less_eq @ ( set @ C ) @ ( image @ A @ C @ H @ ( labeled_vertices @ B @ A @ S ) ) @ ( labeled_vertices @ B @ C @ T3 ) )
% 2.86/1.59 => ( ( univalent @ A @ C @ H )
% 2.86/1.59 => ( ( edge_preserving @ A @ C @ B @ H @ ( labeled_edges @ B @ A @ S ) @ ( labeled_edges @ B @ C @ T3 ) )
% 2.86/1.59 => ( ( S
% 2.86/1.59 = ( restrict @ B @ A @ S ) )
% 2.86/1.59 => ( ( T3
% 2.86/1.59 = ( restrict @ B @ C @ T3 ) )
% 2.86/1.59 => ( graph_homomorphism @ B @ A @ C @ S @ T3 @ H ) ) ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_108_graph__homomorphism__def,axiom,
% 2.86/1.59 ! [C: $tType,B: $tType,A: $tType] :
% 2.86/1.59 ( ( graph_homomorphism @ A @ B @ C )
% 2.86/1.59 = ( ^ [G_1: labeled_graph @ A @ B,G_2: labeled_graph @ A @ C,F2: set @ ( product_prod @ B @ C )] :
% 2.86/1.59 ( ( ( labeled_vertices @ A @ B @ G_1 )
% 2.86/1.59 = ( domain @ B @ C @ F2 ) )
% 2.86/1.59 & ( G_1
% 2.86/1.59 = ( restrict @ A @ B @ G_1 ) )
% 2.86/1.59 & ( G_2
% 2.86/1.59 = ( restrict @ A @ C @ G_2 ) )
% 2.86/1.59 & ( ord_less_eq @ ( set @ C ) @ ( image @ B @ C @ F2 @ ( labeled_vertices @ A @ B @ G_1 ) ) @ ( labeled_vertices @ A @ C @ G_2 ) )
% 2.86/1.59 & ( univalent @ B @ C @ F2 )
% 2.86/1.59 & ( edge_preserving @ B @ C @ A @ F2 @ ( labeled_edges @ A @ B @ G_1 ) @ ( labeled_edges @ A @ C @ G_2 ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_109_subset__singletonD,axiom,
% 2.86/1.59 ! [A: $tType,A4: set @ A,X3: A] :
% 2.86/1.59 ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.86/1.59 => ( ( A4
% 2.86/1.59 = ( bot_bot @ ( set @ A ) ) )
% 2.86/1.59 | ( A4
% 2.86/1.59 = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_110_subset__singleton__iff,axiom,
% 2.86/1.59 ! [A: $tType,X2: set @ A,A2: A] :
% 2.86/1.59 ( ( ord_less_eq @ ( set @ A ) @ X2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.86/1.59 = ( ( X2
% 2.86/1.59 = ( bot_bot @ ( set @ A ) ) )
% 2.86/1.59 | ( X2
% 2.86/1.59 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_111_univalent__insert,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType,A2: B,R2: set @ ( product_prod @ B @ A ),B2: A] :
% 2.86/1.59 ( ! [C6: A] :
% 2.86/1.59 ~ ( member @ ( product_prod @ B @ A ) @ ( product_Pair @ B @ A @ A2 @ C6 ) @ R2 )
% 2.86/1.59 => ( ( univalent @ B @ A @ ( insert @ ( product_prod @ B @ A ) @ ( product_Pair @ B @ A @ A2 @ B2 ) @ R2 ) )
% 2.86/1.59 = ( univalent @ B @ A @ R2 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_112_graph__homomorphism__concr__graph,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType,C: $tType,G: labeled_graph @ A @ B,E: set @ ( product_prod @ A @ ( product_prod @ C @ C ) ),V3: set @ C,X3: set @ ( product_prod @ C @ B )] :
% 2.86/1.59 ( ( G
% 2.86/1.59 = ( restrict @ A @ B @ G ) )
% 2.86/1.59 => ( ( ( labeled_LG @ A @ C @ E @ V3 )
% 2.86/1.59 = ( restrict @ A @ C @ ( labeled_LG @ A @ C @ E @ V3 ) ) )
% 2.86/1.59 => ( ( graph_homomorphism @ A @ C @ B @ ( labeled_LG @ A @ C @ E @ V3 ) @ G @ X3 )
% 2.86/1.59 = ( ( ord_less_eq @ ( set @ B ) @ ( image @ C @ B @ X3 @ V3 ) @ ( labeled_vertices @ A @ B @ G ) )
% 2.86/1.59 & ( ord_less_eq @ ( set @ ( product_prod @ A @ ( product_prod @ B @ B ) ) ) @ ( image @ ( product_prod @ A @ ( product_prod @ C @ C ) ) @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( on_triple @ C @ B @ A @ X3 ) @ E ) @ ( labeled_edges @ A @ B @ G ) )
% 2.86/1.59 & ( univalent @ C @ B @ X3 )
% 2.86/1.59 & ( ( domain @ C @ B @ X3 )
% 2.86/1.59 = V3 ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_113_le0,axiom,
% 2.86/1.59 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_114_bot__nat__0_Oextremum,axiom,
% 2.86/1.59 ! [A2: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A2 ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_115_the__elem__eq,axiom,
% 2.86/1.59 ! [A: $tType,X3: A] :
% 2.86/1.59 ( ( the_elem @ A @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.86/1.59 = X3 ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_116_bot__apply,axiom,
% 2.86/1.59 ! [C: $tType,D3: $tType] :
% 2.86/1.59 ( ( bot @ C )
% 2.86/1.59 => ( ( bot_bot @ ( D3 > C ) )
% 2.86/1.59 = ( ^ [X4: D3] : ( bot_bot @ C ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_117_prod_Oinject,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType,X1: A,X22: B,Y1: A,Y2: B] :
% 2.86/1.59 ( ( ( product_Pair @ A @ B @ X1 @ X22 )
% 2.86/1.59 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 2.86/1.59 = ( ( X1 = Y1 )
% 2.86/1.59 & ( X22 = Y2 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_118_old_Oprod_Oinject,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType,A2: A,B2: B,A9: A,B9: B] :
% 2.86/1.59 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 2.86/1.59 = ( product_Pair @ A @ B @ A9 @ B9 ) )
% 2.86/1.59 = ( ( A2 = A9 )
% 2.86/1.59 & ( B2 = B9 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_119_order__refl,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( preorder @ A )
% 2.86/1.59 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_120_on__triple__univ,axiom,
% 2.86/1.59 ! [C: $tType,B: $tType,A: $tType,F: set @ ( product_prod @ A @ B )] :
% 2.86/1.59 ( ( univalent @ A @ B @ F )
% 2.86/1.59 => ( univalent @ ( product_prod @ C @ ( product_prod @ A @ A ) ) @ ( product_prod @ C @ ( product_prod @ B @ B ) ) @ ( on_triple @ A @ B @ C @ F ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_121_on__triple,axiom,
% 2.86/1.59 ! [B: $tType,C: $tType,A: $tType,L1: A,V1: B,V22: B,L2: A,V32: C,V4: C,R2: set @ ( product_prod @ B @ C )] :
% 2.86/1.59 ( ( member @ ( product_prod @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( product_prod @ A @ ( product_prod @ C @ C ) ) ) @ ( product_Pair @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( product_prod @ A @ ( product_prod @ C @ C ) ) @ ( product_Pair @ A @ ( product_prod @ B @ B ) @ L1 @ ( product_Pair @ B @ B @ V1 @ V22 ) ) @ ( product_Pair @ A @ ( product_prod @ C @ C ) @ L2 @ ( product_Pair @ C @ C @ V32 @ V4 ) ) ) @ ( on_triple @ B @ C @ A @ R2 ) )
% 2.86/1.59 = ( ( member @ ( product_prod @ B @ C ) @ ( product_Pair @ B @ C @ V1 @ V32 ) @ R2 )
% 2.86/1.59 & ( member @ ( product_prod @ B @ C ) @ ( product_Pair @ B @ C @ V22 @ V4 ) @ R2 )
% 2.86/1.59 & ( L1 = L2 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_122_edge__preservingI,axiom,
% 2.86/1.59 ! [C: $tType,B: $tType,A: $tType,R2: set @ ( product_prod @ C @ B ),E3: set @ ( product_prod @ A @ ( product_prod @ C @ C ) ),G: set @ ( product_prod @ A @ ( product_prod @ B @ B ) )] :
% 2.86/1.59 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ ( product_prod @ B @ B ) ) ) @ ( image @ ( product_prod @ A @ ( product_prod @ C @ C ) ) @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( on_triple @ C @ B @ A @ R2 ) @ E3 ) @ G )
% 2.86/1.59 => ( edge_preserving @ C @ B @ A @ R2 @ E3 @ G ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_123_Nat_Oex__has__greatest__nat,axiom,
% 2.86/1.59 ! [P: nat > $o,K: nat,B2: nat] :
% 2.86/1.59 ( ( P @ K )
% 2.86/1.59 => ( ! [Y4: nat] :
% 2.86/1.59 ( ( P @ Y4 )
% 2.86/1.59 => ( ord_less_eq @ nat @ Y4 @ B2 ) )
% 2.86/1.59 => ? [X5: nat] :
% 2.86/1.59 ( ( P @ X5 )
% 2.86/1.59 & ! [Y6: nat] :
% 2.86/1.59 ( ( P @ Y6 )
% 2.86/1.59 => ( ord_less_eq @ nat @ Y6 @ X5 ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_124_nat__le__linear,axiom,
% 2.86/1.59 ! [M: nat,N: nat] :
% 2.86/1.59 ( ( ord_less_eq @ nat @ M @ N )
% 2.86/1.59 | ( ord_less_eq @ nat @ N @ M ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_125_le__antisym,axiom,
% 2.86/1.59 ! [M: nat,N: nat] :
% 2.86/1.59 ( ( ord_less_eq @ nat @ M @ N )
% 2.86/1.59 => ( ( ord_less_eq @ nat @ N @ M )
% 2.86/1.59 => ( M = N ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_126_eq__imp__le,axiom,
% 2.86/1.59 ! [M: nat,N: nat] :
% 2.86/1.59 ( ( M = N )
% 2.86/1.59 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_127_le__trans,axiom,
% 2.86/1.59 ! [I: nat,J: nat,K: nat] :
% 2.86/1.59 ( ( ord_less_eq @ nat @ I @ J )
% 2.86/1.59 => ( ( ord_less_eq @ nat @ J @ K )
% 2.86/1.59 => ( ord_less_eq @ nat @ I @ K ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_128_le__refl,axiom,
% 2.86/1.59 ! [N: nat] : ( ord_less_eq @ nat @ N @ N ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_129_bot__nat__def,axiom,
% 2.86/1.59 ( ( bot_bot @ nat )
% 2.86/1.59 = ( zero_zero @ nat ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_130_bot__empty__eq,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( bot_bot @ ( A > $o ) )
% 2.86/1.59 = ( ^ [X4: A] : ( member @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_131_bot__set__def,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( bot_bot @ ( set @ A ) )
% 2.86/1.59 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_132_edge__preserving,axiom,
% 2.86/1.59 ! [C: $tType,B: $tType,A: $tType] :
% 2.86/1.59 ( ( edge_preserving @ A @ B @ C )
% 2.86/1.59 = ( ^ [R4: set @ ( product_prod @ A @ B ),E4: set @ ( product_prod @ C @ ( product_prod @ A @ A ) )] : ( ord_less_eq @ ( set @ ( product_prod @ C @ ( product_prod @ B @ B ) ) ) @ ( image @ ( product_prod @ C @ ( product_prod @ A @ A ) ) @ ( product_prod @ C @ ( product_prod @ B @ B ) ) @ ( on_triple @ A @ B @ C @ R4 ) @ E4 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_133_on__tripleD_I1_J,axiom,
% 2.86/1.59 ! [B: $tType,C: $tType,A: $tType,L1: A,V1: B,V22: B,L2: A,V32: C,V4: C,R2: set @ ( product_prod @ B @ C )] :
% 2.86/1.59 ( ( member @ ( product_prod @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( product_prod @ A @ ( product_prod @ C @ C ) ) ) @ ( product_Pair @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( product_prod @ A @ ( product_prod @ C @ C ) ) @ ( product_Pair @ A @ ( product_prod @ B @ B ) @ L1 @ ( product_Pair @ B @ B @ V1 @ V22 ) ) @ ( product_Pair @ A @ ( product_prod @ C @ C ) @ L2 @ ( product_Pair @ C @ C @ V32 @ V4 ) ) ) @ ( on_triple @ B @ C @ A @ R2 ) )
% 2.86/1.59 => ( L2 = L1 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_134_on__tripleD_I2_J,axiom,
% 2.86/1.59 ! [A: $tType,C: $tType,B: $tType,L1: A,V1: B,V22: B,L2: A,V32: C,V4: C,R2: set @ ( product_prod @ B @ C )] :
% 2.86/1.59 ( ( member @ ( product_prod @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( product_prod @ A @ ( product_prod @ C @ C ) ) ) @ ( product_Pair @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( product_prod @ A @ ( product_prod @ C @ C ) ) @ ( product_Pair @ A @ ( product_prod @ B @ B ) @ L1 @ ( product_Pair @ B @ B @ V1 @ V22 ) ) @ ( product_Pair @ A @ ( product_prod @ C @ C ) @ L2 @ ( product_Pair @ C @ C @ V32 @ V4 ) ) ) @ ( on_triple @ B @ C @ A @ R2 ) )
% 2.86/1.59 => ( member @ ( product_prod @ B @ C ) @ ( product_Pair @ B @ C @ V1 @ V32 ) @ R2 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_135_on__tripleD_I3_J,axiom,
% 2.86/1.59 ! [A: $tType,C: $tType,B: $tType,L1: A,V1: B,V22: B,L2: A,V32: C,V4: C,R2: set @ ( product_prod @ B @ C )] :
% 2.86/1.59 ( ( member @ ( product_prod @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( product_prod @ A @ ( product_prod @ C @ C ) ) ) @ ( product_Pair @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( product_prod @ A @ ( product_prod @ C @ C ) ) @ ( product_Pair @ A @ ( product_prod @ B @ B ) @ L1 @ ( product_Pair @ B @ B @ V1 @ V22 ) ) @ ( product_Pair @ A @ ( product_prod @ C @ C ) @ L2 @ ( product_Pair @ C @ C @ V32 @ V4 ) ) ) @ ( on_triple @ B @ C @ A @ R2 ) )
% 2.86/1.59 => ( member @ ( product_prod @ B @ C ) @ ( product_Pair @ B @ C @ V22 @ V4 ) @ R2 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_136_on__triple__dest,axiom,
% 2.86/1.59 ! [C: $tType,B: $tType,A: $tType,R2: set @ ( product_prod @ C @ B ),E3: set @ ( product_prod @ A @ ( product_prod @ C @ C ) ),G: set @ ( product_prod @ A @ ( product_prod @ B @ B ) ),L3: A,X3: C,Y: C,Xx: B,Yy: B] :
% 2.86/1.59 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ ( product_prod @ B @ B ) ) ) @ ( image @ ( product_prod @ A @ ( product_prod @ C @ C ) ) @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( on_triple @ C @ B @ A @ R2 ) @ E3 ) @ G )
% 2.86/1.59 => ( ( member @ ( product_prod @ A @ ( product_prod @ C @ C ) ) @ ( product_Pair @ A @ ( product_prod @ C @ C ) @ L3 @ ( product_Pair @ C @ C @ X3 @ Y ) ) @ E3 )
% 2.86/1.59 => ( ( member @ ( product_prod @ C @ B ) @ ( product_Pair @ C @ B @ X3 @ Xx ) @ R2 )
% 2.86/1.59 => ( ( member @ ( product_prod @ C @ B ) @ ( product_Pair @ C @ B @ Y @ Yy ) @ R2 )
% 2.86/1.59 => ( member @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( product_Pair @ A @ ( product_prod @ B @ B ) @ L3 @ ( product_Pair @ B @ B @ Xx @ Yy ) ) @ G ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_137_dual__order_Oantisym,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( order @ A )
% 2.86/1.59 => ! [B2: A,A2: A] :
% 2.86/1.59 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.86/1.59 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.86/1.59 => ( A2 = B2 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_138_dual__order_Oeq__iff,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( order @ A )
% 2.86/1.59 => ( ( ^ [Y5: A,Z: A] : ( Y5 = Z ) )
% 2.86/1.59 = ( ^ [A7: A,B5: A] :
% 2.86/1.59 ( ( ord_less_eq @ A @ B5 @ A7 )
% 2.86/1.59 & ( ord_less_eq @ A @ A7 @ B5 ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_139_dual__order_Otrans,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( order @ A )
% 2.86/1.59 => ! [B2: A,A2: A,C3: A] :
% 2.86/1.59 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.86/1.59 => ( ( ord_less_eq @ A @ C3 @ B2 )
% 2.86/1.59 => ( ord_less_eq @ A @ C3 @ A2 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_140_linorder__wlog,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( linorder @ A )
% 2.86/1.59 => ! [P: A > A > $o,A2: A,B2: A] :
% 2.86/1.59 ( ! [A6: A,B4: A] :
% 2.86/1.59 ( ( ord_less_eq @ A @ A6 @ B4 )
% 2.86/1.59 => ( P @ A6 @ B4 ) )
% 2.86/1.59 => ( ! [A6: A,B4: A] :
% 2.86/1.59 ( ( P @ B4 @ A6 )
% 2.86/1.59 => ( P @ A6 @ B4 ) )
% 2.86/1.59 => ( P @ A2 @ B2 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_141_dual__order_Orefl,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( order @ A )
% 2.86/1.59 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_142_order__trans,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( preorder @ A )
% 2.86/1.59 => ! [X3: A,Y: A,Z2: A] :
% 2.86/1.59 ( ( ord_less_eq @ A @ X3 @ Y )
% 2.86/1.59 => ( ( ord_less_eq @ A @ Y @ Z2 )
% 2.86/1.59 => ( ord_less_eq @ A @ X3 @ Z2 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_143_order__class_Oorder_Oantisym,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( order @ A )
% 2.86/1.59 => ! [A2: A,B2: A] :
% 2.86/1.59 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.86/1.59 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.86/1.59 => ( A2 = B2 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_144_ord__le__eq__trans,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( ord @ A )
% 2.86/1.59 => ! [A2: A,B2: A,C3: A] :
% 2.86/1.59 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.86/1.59 => ( ( B2 = C3 )
% 2.86/1.59 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_145_ord__eq__le__trans,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( ord @ A )
% 2.86/1.59 => ! [A2: A,B2: A,C3: A] :
% 2.86/1.59 ( ( A2 = B2 )
% 2.86/1.59 => ( ( ord_less_eq @ A @ B2 @ C3 )
% 2.86/1.59 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_146_order__class_Oorder_Oeq__iff,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( order @ A )
% 2.86/1.59 => ( ( ^ [Y5: A,Z: A] : ( Y5 = Z ) )
% 2.86/1.59 = ( ^ [A7: A,B5: A] :
% 2.86/1.59 ( ( ord_less_eq @ A @ A7 @ B5 )
% 2.86/1.59 & ( ord_less_eq @ A @ B5 @ A7 ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_147_antisym__conv,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( order @ A )
% 2.86/1.59 => ! [Y: A,X3: A] :
% 2.86/1.59 ( ( ord_less_eq @ A @ Y @ X3 )
% 2.86/1.59 => ( ( ord_less_eq @ A @ X3 @ Y )
% 2.86/1.59 = ( X3 = Y ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_148_le__cases3,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( linorder @ A )
% 2.86/1.59 => ! [X3: A,Y: A,Z2: A] :
% 2.86/1.59 ( ( ( ord_less_eq @ A @ X3 @ Y )
% 2.86/1.59 => ~ ( ord_less_eq @ A @ Y @ Z2 ) )
% 2.86/1.59 => ( ( ( ord_less_eq @ A @ Y @ X3 )
% 2.86/1.59 => ~ ( ord_less_eq @ A @ X3 @ Z2 ) )
% 2.86/1.59 => ( ( ( ord_less_eq @ A @ X3 @ Z2 )
% 2.86/1.59 => ~ ( ord_less_eq @ A @ Z2 @ Y ) )
% 2.86/1.59 => ( ( ( ord_less_eq @ A @ Z2 @ Y )
% 2.86/1.59 => ~ ( ord_less_eq @ A @ Y @ X3 ) )
% 2.86/1.59 => ( ( ( ord_less_eq @ A @ Y @ Z2 )
% 2.86/1.59 => ~ ( ord_less_eq @ A @ Z2 @ X3 ) )
% 2.86/1.59 => ~ ( ( ord_less_eq @ A @ Z2 @ X3 )
% 2.86/1.59 => ~ ( ord_less_eq @ A @ X3 @ Y ) ) ) ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_149_order_Otrans,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( order @ A )
% 2.86/1.59 => ! [A2: A,B2: A,C3: A] :
% 2.86/1.59 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.86/1.59 => ( ( ord_less_eq @ A @ B2 @ C3 )
% 2.86/1.59 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_150_le__cases,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( linorder @ A )
% 2.86/1.59 => ! [X3: A,Y: A] :
% 2.86/1.59 ( ~ ( ord_less_eq @ A @ X3 @ Y )
% 2.86/1.59 => ( ord_less_eq @ A @ Y @ X3 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_151_eq__refl,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( preorder @ A )
% 2.86/1.59 => ! [X3: A,Y: A] :
% 2.86/1.59 ( ( X3 = Y )
% 2.86/1.59 => ( ord_less_eq @ A @ X3 @ Y ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_152_linear,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( linorder @ A )
% 2.86/1.59 => ! [X3: A,Y: A] :
% 2.86/1.59 ( ( ord_less_eq @ A @ X3 @ Y )
% 2.86/1.59 | ( ord_less_eq @ A @ Y @ X3 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_153_antisym,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( order @ A )
% 2.86/1.59 => ! [X3: A,Y: A] :
% 2.86/1.59 ( ( ord_less_eq @ A @ X3 @ Y )
% 2.86/1.59 => ( ( ord_less_eq @ A @ Y @ X3 )
% 2.86/1.59 => ( X3 = Y ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_154_eq__iff,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( order @ A )
% 2.86/1.59 => ( ( ^ [Y5: A,Z: A] : ( Y5 = Z ) )
% 2.86/1.59 = ( ^ [X4: A,Y3: A] :
% 2.86/1.59 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 2.86/1.59 & ( ord_less_eq @ A @ Y3 @ X4 ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_155_ord__le__eq__subst,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType] :
% 2.86/1.59 ( ( ( ord @ B )
% 2.86/1.59 & ( ord @ A ) )
% 2.86/1.59 => ! [A2: A,B2: A,F: A > B,C3: B] :
% 2.86/1.59 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.86/1.59 => ( ( ( F @ B2 )
% 2.86/1.59 = C3 )
% 2.86/1.59 => ( ! [X5: A,Y4: A] :
% 2.86/1.59 ( ( ord_less_eq @ A @ X5 @ Y4 )
% 2.86/1.59 => ( ord_less_eq @ B @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.86/1.59 => ( ord_less_eq @ B @ ( F @ A2 ) @ C3 ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_156_ord__eq__le__subst,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType] :
% 2.86/1.59 ( ( ( ord @ B )
% 2.86/1.59 & ( ord @ A ) )
% 2.86/1.59 => ! [A2: A,F: B > A,B2: B,C3: B] :
% 2.86/1.59 ( ( A2
% 2.86/1.59 = ( F @ B2 ) )
% 2.86/1.59 => ( ( ord_less_eq @ B @ B2 @ C3 )
% 2.86/1.59 => ( ! [X5: B,Y4: B] :
% 2.86/1.59 ( ( ord_less_eq @ B @ X5 @ Y4 )
% 2.86/1.59 => ( ord_less_eq @ A @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.86/1.59 => ( ord_less_eq @ A @ A2 @ ( F @ C3 ) ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_157_order__subst2,axiom,
% 2.86/1.59 ! [A: $tType,C: $tType] :
% 2.86/1.59 ( ( ( order @ C )
% 2.86/1.59 & ( order @ A ) )
% 2.86/1.59 => ! [A2: A,B2: A,F: A > C,C3: C] :
% 2.86/1.59 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.86/1.59 => ( ( ord_less_eq @ C @ ( F @ B2 ) @ C3 )
% 2.86/1.59 => ( ! [X5: A,Y4: A] :
% 2.86/1.59 ( ( ord_less_eq @ A @ X5 @ Y4 )
% 2.86/1.59 => ( ord_less_eq @ C @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.86/1.59 => ( ord_less_eq @ C @ ( F @ A2 ) @ C3 ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_158_order__subst1,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType] :
% 2.86/1.59 ( ( ( order @ B )
% 2.86/1.59 & ( order @ A ) )
% 2.86/1.59 => ! [A2: A,F: B > A,B2: B,C3: B] :
% 2.86/1.59 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 2.86/1.59 => ( ( ord_less_eq @ B @ B2 @ C3 )
% 2.86/1.59 => ( ! [X5: B,Y4: B] :
% 2.86/1.59 ( ( ord_less_eq @ B @ X5 @ Y4 )
% 2.86/1.59 => ( ord_less_eq @ A @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.86/1.59 => ( ord_less_eq @ A @ A2 @ ( F @ C3 ) ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_159_le__fun__def,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType] :
% 2.86/1.59 ( ( ord @ B )
% 2.86/1.59 => ( ( ord_less_eq @ ( A > B ) )
% 2.86/1.59 = ( ^ [F2: A > B,G3: A > B] :
% 2.86/1.59 ! [X4: A] : ( ord_less_eq @ B @ ( F2 @ X4 ) @ ( G3 @ X4 ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_160_le__funI,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType] :
% 2.86/1.59 ( ( ord @ B )
% 2.86/1.59 => ! [F: A > B,G2: A > B] :
% 2.86/1.59 ( ! [X5: A] : ( ord_less_eq @ B @ ( F @ X5 ) @ ( G2 @ X5 ) )
% 2.86/1.59 => ( ord_less_eq @ ( A > B ) @ F @ G2 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_161_le__funE,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType] :
% 2.86/1.59 ( ( ord @ B )
% 2.86/1.59 => ! [F: A > B,G2: A > B,X3: A] :
% 2.86/1.59 ( ( ord_less_eq @ ( A > B ) @ F @ G2 )
% 2.86/1.59 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( G2 @ X3 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_162_le__funD,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType] :
% 2.86/1.59 ( ( ord @ B )
% 2.86/1.59 => ! [F: A > B,G2: A > B,X3: A] :
% 2.86/1.59 ( ( ord_less_eq @ ( A > B ) @ F @ G2 )
% 2.86/1.59 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( G2 @ X3 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_163_old_Oprod_Oinducts,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 2.86/1.59 ( ! [A6: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A6 @ B4 ) )
% 2.86/1.59 => ( P @ Prod ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_164_old_Oprod_Oexhaust,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 2.86/1.59 ~ ! [A6: A,B4: B] :
% 2.86/1.59 ( Y
% 2.86/1.59 != ( product_Pair @ A @ B @ A6 @ B4 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_165_Pair__inject,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType,A2: A,B2: B,A9: A,B9: B] :
% 2.86/1.59 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 2.86/1.59 = ( product_Pair @ A @ B @ A9 @ B9 ) )
% 2.86/1.59 => ~ ( ( A2 = A9 )
% 2.86/1.59 => ( B2 != B9 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_166_prod__cases,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P2: product_prod @ A @ B] :
% 2.86/1.59 ( ! [A6: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A6 @ B4 ) )
% 2.86/1.59 => ( P @ P2 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_167_surj__pair,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType,P2: product_prod @ A @ B] :
% 2.86/1.59 ? [X5: A,Y4: B] :
% 2.86/1.59 ( P2
% 2.86/1.59 = ( product_Pair @ A @ B @ X5 @ Y4 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_168_bot__fun__def,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType] :
% 2.86/1.59 ( ( bot @ B )
% 2.86/1.59 => ( ( bot_bot @ ( A > B ) )
% 2.86/1.59 = ( ^ [X4: A] : ( bot_bot @ B ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_169_bot__nat__0_Oextremum__uniqueI,axiom,
% 2.86/1.59 ! [A2: nat] :
% 2.86/1.59 ( ( ord_less_eq @ nat @ A2 @ ( zero_zero @ nat ) )
% 2.86/1.59 => ( A2
% 2.86/1.59 = ( zero_zero @ nat ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_170_bot__nat__0_Oextremum__unique,axiom,
% 2.86/1.59 ! [A2: nat] :
% 2.86/1.59 ( ( ord_less_eq @ nat @ A2 @ ( zero_zero @ nat ) )
% 2.86/1.59 = ( A2
% 2.86/1.59 = ( zero_zero @ nat ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_171_le__0__eq,axiom,
% 2.86/1.59 ! [N: nat] :
% 2.86/1.59 ( ( ord_less_eq @ nat @ N @ ( zero_zero @ nat ) )
% 2.86/1.59 = ( N
% 2.86/1.59 = ( zero_zero @ nat ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_172_less__eq__nat_Osimps_I1_J,axiom,
% 2.86/1.59 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_173_bot_Oextremum__uniqueI,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( order_bot @ A )
% 2.86/1.59 => ! [A2: A] :
% 2.86/1.59 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 2.86/1.59 => ( A2
% 2.86/1.59 = ( bot_bot @ A ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_174_bot_Oextremum__unique,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( order_bot @ A )
% 2.86/1.59 => ! [A2: A] :
% 2.86/1.59 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 2.86/1.59 = ( A2
% 2.86/1.59 = ( bot_bot @ A ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_175_bot_Oextremum,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( order_bot @ A )
% 2.86/1.59 => ! [A2: A] : ( ord_less_eq @ A @ ( bot_bot @ A ) @ A2 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_176_prod__induct7,axiom,
% 2.86/1.59 ! [G4: $tType,F3: $tType,E5: $tType,D3: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ ( product_prod @ F3 @ G4 ) ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ ( product_prod @ F3 @ G4 ) ) ) ) )] :
% 2.86/1.59 ( ! [A6: A,B4: B,C6: C,D4: D3,E6: E5,F4: F3,G5: G4] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ ( product_prod @ F3 @ G4 ) ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ ( product_prod @ F3 @ G4 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ ( product_prod @ F3 @ G4 ) ) ) @ C6 @ ( product_Pair @ D3 @ ( product_prod @ E5 @ ( product_prod @ F3 @ G4 ) ) @ D4 @ ( product_Pair @ E5 @ ( product_prod @ F3 @ G4 ) @ E6 @ ( product_Pair @ F3 @ G4 @ F4 @ G5 ) ) ) ) ) ) )
% 2.86/1.59 => ( P @ X3 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_177_prod__induct6,axiom,
% 2.86/1.59 ! [F3: $tType,E5: $tType,D3: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ F3 ) ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ F3 ) ) ) )] :
% 2.86/1.59 ( ! [A6: A,B4: B,C6: C,D4: D3,E6: E5,F4: F3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ F3 ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ F3 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ F3 ) ) @ C6 @ ( product_Pair @ D3 @ ( product_prod @ E5 @ F3 ) @ D4 @ ( product_Pair @ E5 @ F3 @ E6 @ F4 ) ) ) ) ) )
% 2.86/1.59 => ( P @ X3 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_178_prod__induct5,axiom,
% 2.86/1.59 ! [E5: $tType,D3: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ E5 ) ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ E5 ) ) )] :
% 2.86/1.59 ( ! [A6: A,B4: B,C6: C,D4: D3,E6: E5] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ E5 ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D3 @ E5 ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D3 @ E5 ) @ C6 @ ( product_Pair @ D3 @ E5 @ D4 @ E6 ) ) ) ) )
% 2.86/1.59 => ( P @ X3 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_179_prod__induct4,axiom,
% 2.86/1.59 ! [D3: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D3 ) ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D3 ) )] :
% 2.86/1.59 ( ! [A6: A,B4: B,C6: C,D4: D3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D3 ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ D3 ) @ B4 @ ( product_Pair @ C @ D3 @ C6 @ D4 ) ) ) )
% 2.86/1.59 => ( P @ X3 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_180_prod__induct3,axiom,
% 2.86/1.59 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X3: product_prod @ A @ ( product_prod @ B @ C )] :
% 2.86/1.59 ( ! [A6: A,B4: B,C6: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A6 @ ( product_Pair @ B @ C @ B4 @ C6 ) ) )
% 2.86/1.59 => ( P @ X3 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_181_prod__cases7,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType,C: $tType,D3: $tType,E5: $tType,F3: $tType,G4: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ ( product_prod @ F3 @ G4 ) ) ) ) )] :
% 2.86/1.59 ~ ! [A6: A,B4: B,C6: C,D4: D3,E6: E5,F4: F3,G5: G4] :
% 2.86/1.59 ( Y
% 2.86/1.59 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ ( product_prod @ F3 @ G4 ) ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ ( product_prod @ F3 @ G4 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ ( product_prod @ F3 @ G4 ) ) ) @ C6 @ ( product_Pair @ D3 @ ( product_prod @ E5 @ ( product_prod @ F3 @ G4 ) ) @ D4 @ ( product_Pair @ E5 @ ( product_prod @ F3 @ G4 ) @ E6 @ ( product_Pair @ F3 @ G4 @ F4 @ G5 ) ) ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_182_prod__cases6,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType,C: $tType,D3: $tType,E5: $tType,F3: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ F3 ) ) ) )] :
% 2.86/1.59 ~ ! [A6: A,B4: B,C6: C,D4: D3,E6: E5,F4: F3] :
% 2.86/1.59 ( Y
% 2.86/1.59 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ F3 ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ F3 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D3 @ ( product_prod @ E5 @ F3 ) ) @ C6 @ ( product_Pair @ D3 @ ( product_prod @ E5 @ F3 ) @ D4 @ ( product_Pair @ E5 @ F3 @ E6 @ F4 ) ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_183_prod__cases5,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType,C: $tType,D3: $tType,E5: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ E5 ) ) )] :
% 2.86/1.59 ~ ! [A6: A,B4: B,C6: C,D4: D3,E6: E5] :
% 2.86/1.59 ( Y
% 2.86/1.59 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D3 @ E5 ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D3 @ E5 ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D3 @ E5 ) @ C6 @ ( product_Pair @ D3 @ E5 @ D4 @ E6 ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_184_prod__cases4,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType,C: $tType,D3: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D3 ) )] :
% 2.86/1.59 ~ ! [A6: A,B4: B,C6: C,D4: D3] :
% 2.86/1.59 ( Y
% 2.86/1.59 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D3 ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ D3 ) @ B4 @ ( product_Pair @ C @ D3 @ C6 @ D4 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_185_prod__cases3,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 2.86/1.59 ~ ! [A6: A,B4: B,C6: C] :
% 2.86/1.59 ( Y
% 2.86/1.59 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A6 @ ( product_Pair @ B @ C @ B4 @ C6 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_186_old_Oprod_Orec,axiom,
% 2.86/1.59 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 2.86/1.59 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 2.86/1.59 = ( F1 @ A2 @ B2 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_187_is__singleton__the__elem,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( is_singleton @ A )
% 2.86/1.59 = ( ^ [A8: set @ A] :
% 2.86/1.59 ( A8
% 2.86/1.59 = ( insert @ A @ ( the_elem @ A @ A8 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_188_top__rule__def,axiom,
% 2.86/1.59 ! [L: $tType] :
% 2.86/1.59 ( ( standa400804411p_rule @ L )
% 2.86/1.59 = ( ^ [T2: L] : ( product_Pair @ ( labeled_graph @ L @ nat ) @ ( labeled_graph @ L @ nat ) @ ( labeled_LG @ L @ nat @ ( bot_bot @ ( set @ ( product_prod @ L @ ( product_prod @ nat @ nat ) ) ) ) @ ( insert @ nat @ ( zero_zero @ nat ) @ ( insert @ nat @ ( one_one @ nat ) @ ( bot_bot @ ( set @ nat ) ) ) ) ) @ ( labeled_LG @ L @ nat @ ( insert @ ( product_prod @ L @ ( product_prod @ nat @ nat ) ) @ ( product_Pair @ L @ ( product_prod @ nat @ nat ) @ T2 @ ( product_Pair @ nat @ nat @ ( zero_zero @ nat ) @ ( one_one @ nat ) ) ) @ ( bot_bot @ ( set @ ( product_prod @ L @ ( product_prod @ nat @ nat ) ) ) ) ) @ ( insert @ nat @ ( zero_zero @ nat ) @ ( insert @ nat @ ( one_one @ nat ) @ ( bot_bot @ ( set @ nat ) ) ) ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_189_map__graph__def,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType,C: $tType] :
% 2.86/1.59 ( ( map_graph @ C @ B @ A )
% 2.86/1.59 = ( ^ [F2: set @ ( product_prod @ C @ B ),G6: labeled_graph @ A @ C] : ( labeled_LG @ A @ B @ ( image @ ( product_prod @ A @ ( product_prod @ C @ C ) ) @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( on_triple @ C @ B @ A @ F2 ) @ ( labeled_edges @ A @ C @ G6 ) ) @ ( image @ C @ B @ F2 @ ( labeled_vertices @ A @ C @ G6 ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_190_map__graph__preserves__restricted,axiom,
% 2.86/1.59 ! [C: $tType,B: $tType,A: $tType,G: labeled_graph @ A @ B,F: set @ ( product_prod @ B @ C )] :
% 2.86/1.59 ( ( G
% 2.86/1.59 = ( restrict @ A @ B @ G ) )
% 2.86/1.59 => ( ( map_graph @ B @ C @ A @ F @ G )
% 2.86/1.59 = ( restrict @ A @ C @ ( map_graph @ B @ C @ A @ F @ G ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_191_map__graph__selectors_I1_J,axiom,
% 2.86/1.59 ! [A: $tType,C: $tType,B: $tType,F: set @ ( product_prod @ C @ A ),G: labeled_graph @ B @ C] :
% 2.86/1.59 ( ( labeled_vertices @ B @ A @ ( map_graph @ C @ A @ B @ F @ G ) )
% 2.86/1.59 = ( image @ C @ A @ F @ ( labeled_vertices @ B @ C @ G ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_192_is__singletonI,axiom,
% 2.86/1.59 ! [A: $tType,X3: A] : ( is_singleton @ A @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_193_map__graph__edge__preserving,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,C: $tType,F: set @ ( product_prod @ A @ B ),G: labeled_graph @ C @ A] : ( edge_preserving @ A @ B @ C @ F @ ( labeled_edges @ C @ A @ G ) @ ( labeled_edges @ C @ B @ ( map_graph @ A @ B @ C @ F @ G ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_194_map__graph__selectors_I2_J,axiom,
% 2.86/1.59 ! [A: $tType,C: $tType,B: $tType,F: set @ ( product_prod @ C @ A ),G: labeled_graph @ B @ C] :
% 2.86/1.59 ( ( labeled_edges @ B @ A @ ( map_graph @ C @ A @ B @ F @ G ) )
% 2.86/1.59 = ( image @ ( product_prod @ B @ ( product_prod @ C @ C ) ) @ ( product_prod @ B @ ( product_prod @ A @ A ) ) @ ( on_triple @ C @ A @ B @ F ) @ ( labeled_edges @ B @ C @ G ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_195_map__graph__homo,axiom,
% 2.86/1.59 ! [C: $tType,B: $tType,A: $tType,F: set @ ( product_prod @ A @ B ),G: labeled_graph @ C @ A] :
% 2.86/1.59 ( ( univalent @ A @ B @ F )
% 2.86/1.59 => ( ( ( labeled_vertices @ C @ A @ G )
% 2.86/1.59 = ( domain @ A @ B @ F ) )
% 2.86/1.59 => ( ( G
% 2.86/1.59 = ( restrict @ C @ A @ G ) )
% 2.86/1.59 => ( graph_homomorphism @ C @ A @ B @ G @ ( map_graph @ A @ B @ C @ F @ G ) @ F ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_196_one__reorient,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( one @ A )
% 2.86/1.59 => ! [X3: A] :
% 2.86/1.59 ( ( ( one_one @ A )
% 2.86/1.59 = X3 )
% 2.86/1.59 = ( X3
% 2.86/1.59 = ( one_one @ A ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_197_is__singletonI_H,axiom,
% 2.86/1.59 ! [A: $tType,A4: set @ A] :
% 2.86/1.59 ( ( A4
% 2.86/1.59 != ( bot_bot @ ( set @ A ) ) )
% 2.86/1.59 => ( ! [X5: A,Y4: A] :
% 2.86/1.59 ( ( member @ A @ X5 @ A4 )
% 2.86/1.59 => ( ( member @ A @ Y4 @ A4 )
% 2.86/1.59 => ( X5 = Y4 ) ) )
% 2.86/1.59 => ( is_singleton @ A @ A4 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_198_map__graph__returns__restricted,axiom,
% 2.86/1.59 ! [C: $tType,A: $tType,B: $tType,G: labeled_graph @ B @ A,F: set @ ( product_prod @ A @ C )] :
% 2.86/1.59 ( ( ( labeled_vertices @ B @ A @ G )
% 2.86/1.59 = ( domain @ A @ C @ F ) )
% 2.86/1.59 => ( ( map_graph @ A @ C @ B @ F @ G )
% 2.86/1.59 = ( restrict @ B @ C @ ( map_graph @ A @ C @ B @ F @ G ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_199_is__singletonE,axiom,
% 2.86/1.59 ! [A: $tType,A4: set @ A] :
% 2.86/1.59 ( ( is_singleton @ A @ A4 )
% 2.86/1.59 => ~ ! [X5: A] :
% 2.86/1.59 ( A4
% 2.86/1.59 != ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_200_is__singleton__def,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( is_singleton @ A )
% 2.86/1.59 = ( ^ [A8: set @ A] :
% 2.86/1.59 ? [X4: A] :
% 2.86/1.59 ( A8
% 2.86/1.59 = ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_201_map__graph__homo__simp,axiom,
% 2.86/1.59 ! [C: $tType,B: $tType,A: $tType,G: labeled_graph @ A @ B,F: set @ ( product_prod @ B @ C )] :
% 2.86/1.59 ( ( graph_homomorphism @ A @ B @ C @ G @ ( map_graph @ B @ C @ A @ F @ G ) @ F )
% 2.86/1.59 = ( ( univalent @ B @ C @ F )
% 2.86/1.59 & ( ( labeled_vertices @ A @ B @ G )
% 2.86/1.59 = ( domain @ B @ C @ F ) )
% 2.86/1.59 & ( G
% 2.86/1.59 = ( restrict @ A @ B @ G ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_202_not__one__le__zero,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( linord1659791738miring @ A )
% 2.86/1.59 => ~ ( ord_less_eq @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_203_zero__le__one,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( linord1659791738miring @ A )
% 2.86/1.59 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_204_zero__neq__one,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( zero_neq_one @ A )
% 2.86/1.59 => ( ( zero_zero @ A )
% 2.86/1.59 != ( one_one @ A ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_205_graph__homomorphism__def2,axiom,
% 2.86/1.59 ! [C: $tType,B: $tType,A: $tType] :
% 2.86/1.59 ( ( graph_homomorphism @ A @ B @ C )
% 2.86/1.59 = ( ^ [G_1: labeled_graph @ A @ B,G_2: labeled_graph @ A @ C,F2: set @ ( product_prod @ B @ C )] :
% 2.86/1.59 ( ( ( labeled_vertices @ A @ B @ G_1 )
% 2.86/1.59 = ( domain @ B @ C @ F2 ) )
% 2.86/1.59 & ( univalent @ B @ C @ F2 )
% 2.86/1.59 & ( G_1
% 2.86/1.59 = ( restrict @ A @ B @ G_1 ) )
% 2.86/1.59 & ( G_2
% 2.86/1.59 = ( restrict @ A @ C @ G_2 ) )
% 2.86/1.59 & ( ( graph_union @ A @ C @ ( map_graph @ B @ C @ A @ F2 @ G_1 ) @ G_2 )
% 2.86/1.59 = G_2 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_206_Collect__empty__eq__bot,axiom,
% 2.86/1.59 ! [A: $tType,P: A > $o] :
% 2.86/1.59 ( ( ( collect @ A @ P )
% 2.86/1.59 = ( bot_bot @ ( set @ A ) ) )
% 2.86/1.59 = ( P
% 2.86/1.59 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_207_graph__union__idemp_I3_J,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,A4: labeled_graph @ A @ B,B6: labeled_graph @ A @ B] :
% 2.86/1.59 ( ( graph_union @ A @ B @ A4 @ ( graph_union @ A @ B @ B6 @ A4 ) )
% 2.86/1.59 = ( graph_union @ A @ B @ B6 @ A4 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_208_graph__union__idemp_I2_J,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,A4: labeled_graph @ A @ B,B6: labeled_graph @ A @ B] :
% 2.86/1.59 ( ( graph_union @ A @ B @ A4 @ ( graph_union @ A @ B @ A4 @ B6 ) )
% 2.86/1.59 = ( graph_union @ A @ B @ A4 @ B6 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_209_graph__union__idemp_I1_J,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,A4: labeled_graph @ A @ B] :
% 2.86/1.59 ( ( graph_union @ A @ B @ A4 @ A4 )
% 2.86/1.59 = A4 ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_210_graph__union__preserves__restrict,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,G_12: labeled_graph @ A @ B,G_22: labeled_graph @ A @ B] :
% 2.86/1.59 ( ( G_12
% 2.86/1.59 = ( restrict @ A @ B @ G_12 ) )
% 2.86/1.59 => ( ( G_22
% 2.86/1.59 = ( restrict @ A @ B @ G_22 ) )
% 2.86/1.59 => ( ( graph_union @ A @ B @ G_12 @ G_22 )
% 2.86/1.59 = ( restrict @ A @ B @ ( graph_union @ A @ B @ G_12 @ G_22 ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_211_graph__unionI,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,G_12: labeled_graph @ A @ B,G_22: labeled_graph @ A @ B] :
% 2.86/1.59 ( ( ord_less_eq @ ( set @ ( product_prod @ A @ ( product_prod @ B @ B ) ) ) @ ( labeled_edges @ A @ B @ G_12 ) @ ( labeled_edges @ A @ B @ G_22 ) )
% 2.86/1.59 => ( ( ord_less_eq @ ( set @ B ) @ ( labeled_vertices @ A @ B @ G_12 ) @ ( labeled_vertices @ A @ B @ G_22 ) )
% 2.86/1.59 => ( ( graph_union @ A @ B @ G_12 @ G_22 )
% 2.86/1.59 = G_22 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_212_graph__union__iff,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,G_12: labeled_graph @ A @ B,G_22: labeled_graph @ A @ B] :
% 2.86/1.59 ( ( ( graph_union @ A @ B @ G_12 @ G_22 )
% 2.86/1.59 = G_22 )
% 2.86/1.59 = ( ( ord_less_eq @ ( set @ ( product_prod @ A @ ( product_prod @ B @ B ) ) ) @ ( labeled_edges @ A @ B @ G_12 ) @ ( labeled_edges @ A @ B @ G_22 ) )
% 2.86/1.59 & ( ord_less_eq @ ( set @ B ) @ ( labeled_vertices @ A @ B @ G_12 ) @ ( labeled_vertices @ A @ B @ G_22 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_213_less__by__empty,axiom,
% 2.86/1.59 ! [A: $tType,A4: set @ ( product_prod @ A @ A ),B6: set @ ( product_prod @ A @ A )] :
% 2.86/1.59 ( ( A4
% 2.86/1.59 = ( bot_bot @ ( set @ ( product_prod @ A @ A ) ) ) )
% 2.86/1.59 => ( ord_less_eq @ ( set @ ( product_prod @ A @ A ) ) @ A4 @ B6 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_214_on__triple__ID__restrict,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,G: labeled_graph @ A @ B] :
% 2.86/1.59 ( ( image @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( product_prod @ A @ ( product_prod @ B @ B ) ) @ ( on_triple @ B @ B @ A @ ( id_on @ B @ ( labeled_vertices @ A @ B @ G ) ) ) @ ( labeled_edges @ A @ B @ G ) )
% 2.86/1.59 = ( labeled_edges @ A @ B @ ( restrict @ A @ B @ G ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_215_Id__onI,axiom,
% 2.86/1.59 ! [A: $tType,A2: A,A4: set @ A] :
% 2.86/1.59 ( ( member @ A @ A2 @ A4 )
% 2.86/1.59 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ A2 ) @ ( id_on @ A @ A4 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_216_Domain__Id__on,axiom,
% 2.86/1.59 ! [A: $tType,A4: set @ A] :
% 2.86/1.59 ( ( domain @ A @ A @ ( id_on @ A @ A4 ) )
% 2.86/1.59 = A4 ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_217_id__univalent,axiom,
% 2.86/1.59 ! [A: $tType,X3: set @ A] : ( univalent @ A @ A @ ( id_on @ A @ X3 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_218_edge__preserving__Id,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType,Y: set @ A,X3: set @ ( product_prod @ B @ ( product_prod @ A @ A ) )] : ( edge_preserving @ A @ A @ B @ ( id_on @ A @ Y ) @ X3 @ X3 ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_219_Id__on__empty,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( id_on @ A @ ( bot_bot @ ( set @ A ) ) )
% 2.86/1.59 = ( bot_bot @ ( set @ ( product_prod @ A @ A ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_220_graph__homomorphism__Id,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,A2: labeled_graph @ A @ B] : ( graph_homomorphism @ A @ B @ B @ ( restrict @ A @ B @ A2 ) @ ( restrict @ A @ B @ A2 ) @ ( id_on @ B @ ( labeled_vertices @ A @ B @ A2 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_221_subgraph__restrict,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,G: labeled_graph @ A @ B] :
% 2.86/1.59 ( ( graph_homomorphism @ A @ B @ B @ G @ ( restrict @ A @ B @ G ) @ ( id_on @ B @ ( labeled_vertices @ A @ B @ G ) ) )
% 2.86/1.59 = ( G
% 2.86/1.59 = ( restrict @ A @ B @ G ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_222_subgraph__refl,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,G: labeled_graph @ A @ B] :
% 2.86/1.59 ( ( graph_homomorphism @ A @ B @ B @ G @ G @ ( id_on @ B @ ( labeled_vertices @ A @ B @ G ) ) )
% 2.86/1.59 = ( G
% 2.86/1.59 = ( restrict @ A @ B @ G ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_223_map__graph__preserves__subgraph,axiom,
% 2.86/1.59 ! [C: $tType,B: $tType,A: $tType,A4: labeled_graph @ A @ B,B6: labeled_graph @ A @ B,F: set @ ( product_prod @ B @ C )] :
% 2.86/1.59 ( ( graph_homomorphism @ A @ B @ B @ A4 @ B6 @ ( id_on @ B @ ( labeled_vertices @ A @ B @ A4 ) ) )
% 2.86/1.59 => ( graph_homomorphism @ A @ C @ C @ ( map_graph @ B @ C @ A @ F @ A4 ) @ ( map_graph @ B @ C @ A @ F @ B6 ) @ ( id_on @ C @ ( labeled_vertices @ A @ C @ ( map_graph @ B @ C @ A @ F @ A4 ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_224_map__graph__fn__id_I2_J,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,X2: labeled_graph @ A @ B] :
% 2.86/1.59 ( ( map_graph @ B @ B @ A @ ( id_on @ B @ ( labeled_vertices @ A @ B @ X2 ) ) @ X2 )
% 2.86/1.59 = ( restrict @ A @ B @ X2 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_225_Id__on__iff,axiom,
% 2.86/1.59 ! [A: $tType,X3: A,Y: A,A4: set @ A] :
% 2.86/1.59 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y ) @ ( id_on @ A @ A4 ) )
% 2.86/1.59 = ( ( X3 = Y )
% 2.86/1.59 & ( member @ A @ X3 @ A4 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_226_Id__on__eqI,axiom,
% 2.86/1.59 ! [A: $tType,A2: A,B2: A,A4: set @ A] :
% 2.86/1.59 ( ( A2 = B2 )
% 2.86/1.59 => ( ( member @ A @ A2 @ A4 )
% 2.86/1.59 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( id_on @ A @ A4 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_227_Id__onE,axiom,
% 2.86/1.59 ! [A: $tType,C3: product_prod @ A @ A,A4: set @ A] :
% 2.86/1.59 ( ( member @ ( product_prod @ A @ A ) @ C3 @ ( id_on @ A @ A4 ) )
% 2.86/1.59 => ~ ! [X5: A] :
% 2.86/1.59 ( ( member @ A @ X5 @ A4 )
% 2.86/1.59 => ( C3
% 2.86/1.59 != ( product_Pair @ A @ A @ X5 @ X5 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_228_subgraph__preserves__hom,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType,C: $tType,A4: labeled_graph @ A @ B,B6: labeled_graph @ A @ B,X2: labeled_graph @ A @ C,H: set @ ( product_prod @ C @ B )] :
% 2.86/1.59 ( ( graph_homomorphism @ A @ B @ B @ A4 @ B6 @ ( id_on @ B @ ( labeled_vertices @ A @ B @ A4 ) ) )
% 2.86/1.59 => ( ( graph_homomorphism @ A @ C @ B @ X2 @ A4 @ H )
% 2.86/1.59 => ( graph_homomorphism @ A @ C @ B @ X2 @ B6 @ H ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_229_subgraph__trans,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,G_12: labeled_graph @ A @ B,G_22: labeled_graph @ A @ B,G_3: labeled_graph @ A @ B] :
% 2.86/1.59 ( ( graph_homomorphism @ A @ B @ B @ G_12 @ G_22 @ ( id_on @ B @ ( labeled_vertices @ A @ B @ G_12 ) ) )
% 2.86/1.59 => ( ( graph_homomorphism @ A @ B @ B @ G_22 @ G_3 @ ( id_on @ B @ ( labeled_vertices @ A @ B @ G_22 ) ) )
% 2.86/1.59 => ( graph_homomorphism @ A @ B @ B @ G_12 @ G_3 @ ( id_on @ B @ ( labeled_vertices @ A @ B @ G_12 ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_230_subgraph__subset_I1_J,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,G_12: labeled_graph @ A @ B,G_22: labeled_graph @ A @ B] :
% 2.86/1.59 ( ( graph_homomorphism @ A @ B @ B @ G_12 @ G_22 @ ( id_on @ B @ ( labeled_vertices @ A @ B @ G_12 ) ) )
% 2.86/1.59 => ( ord_less_eq @ ( set @ B ) @ ( labeled_vertices @ A @ B @ G_12 ) @ ( labeled_vertices @ A @ B @ G_22 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_231_subgraph__def,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,G_12: labeled_graph @ A @ B,G_22: labeled_graph @ A @ B] :
% 2.86/1.59 ( ( graph_homomorphism @ A @ B @ B @ G_12 @ G_22 @ ( id_on @ B @ ( labeled_vertices @ A @ B @ G_12 ) ) )
% 2.86/1.59 = ( ( G_12
% 2.86/1.59 = ( restrict @ A @ B @ G_12 ) )
% 2.86/1.59 & ( G_22
% 2.86/1.59 = ( restrict @ A @ B @ G_22 ) )
% 2.86/1.59 & ( ( graph_union @ A @ B @ G_12 @ G_22 )
% 2.86/1.59 = G_22 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_232_subgraph__subset_I2_J,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,G_12: labeled_graph @ A @ B,G_22: labeled_graph @ A @ B] :
% 2.86/1.59 ( ( graph_homomorphism @ A @ B @ B @ G_12 @ G_22 @ ( id_on @ B @ ( labeled_vertices @ A @ B @ G_12 ) ) )
% 2.86/1.59 => ( ord_less_eq @ ( set @ ( product_prod @ A @ ( product_prod @ B @ B ) ) ) @ ( labeled_edges @ A @ B @ ( restrict @ A @ B @ G_12 ) ) @ ( labeled_edges @ A @ B @ G_22 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_233_subgraph__def2,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,G_12: labeled_graph @ A @ B,G_22: labeled_graph @ A @ B] :
% 2.86/1.59 ( ( G_12
% 2.86/1.59 = ( restrict @ A @ B @ G_12 ) )
% 2.86/1.59 => ( ( G_22
% 2.86/1.59 = ( restrict @ A @ B @ G_22 ) )
% 2.86/1.59 => ( ( graph_homomorphism @ A @ B @ B @ G_12 @ G_22 @ ( id_on @ B @ ( labeled_vertices @ A @ B @ G_12 ) ) )
% 2.86/1.59 = ( ( ord_less_eq @ ( set @ B ) @ ( labeled_vertices @ A @ B @ G_12 ) @ ( labeled_vertices @ A @ B @ G_22 ) )
% 2.86/1.59 & ( ord_less_eq @ ( set @ ( product_prod @ A @ ( product_prod @ B @ B ) ) ) @ ( labeled_edges @ A @ B @ G_12 ) @ ( labeled_edges @ A @ B @ G_22 ) ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_234_gr_I1_J,axiom,
% 2.86/1.59 ( ( getRel @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) @ ( standard_S_Idt @ a ) @ g )
% 2.86/1.59 = ( id_on @ ( sum_sum @ a @ b ) @ ( labeled_vertices @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) @ g ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_235_insert__subsetI,axiom,
% 2.86/1.59 ! [A: $tType,X3: A,A4: set @ A,X2: set @ A] :
% 2.86/1.59 ( ( member @ A @ X3 @ A4 )
% 2.86/1.59 => ( ( ord_less_eq @ ( set @ A ) @ X2 @ A4 )
% 2.86/1.59 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X3 @ X2 ) @ A4 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_236_ssubst__Pair__rhs,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,R: A,S: B,R2: set @ ( product_prod @ A @ B ),S2: B] :
% 2.86/1.59 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R @ S ) @ R2 )
% 2.86/1.59 => ( ( S2 = S )
% 2.86/1.59 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R @ S2 ) @ R2 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_237_subset__emptyI,axiom,
% 2.86/1.59 ! [A: $tType,A4: set @ A] :
% 2.86/1.59 ( ! [X5: A] :
% 2.86/1.59 ~ ( member @ A @ X5 @ A4 )
% 2.86/1.59 => ( ord_less_eq @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_238_getRel__subgraph,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType,Y: A,Z2: A,L3: B,G: labeled_graph @ B @ A,G7: labeled_graph @ B @ A] :
% 2.86/1.59 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y @ Z2 ) @ ( getRel @ B @ A @ L3 @ G ) )
% 2.86/1.59 => ( ( graph_homomorphism @ B @ A @ A @ G @ G7 @ ( id_on @ A @ ( labeled_vertices @ B @ A @ G ) ) )
% 2.86/1.59 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y @ Z2 ) @ ( getRel @ B @ A @ L3 @ G7 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_239_gr_I2_J,axiom,
% 2.86/1.59 ( ( getRel @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) @ ( standard_S_Bot @ a ) @ g )
% 2.86/1.59 = ( bot_bot @ ( set @ ( product_prod @ ( sum_sum @ a @ b ) @ ( sum_sum @ a @ b ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_240_Standard__Constant_Odistinct_I7_J,axiom,
% 2.86/1.59 ! [V: $tType] :
% 2.86/1.59 ( ( standard_S_Bot @ V )
% 2.86/1.59 != ( standard_S_Idt @ V ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_241_getRel__homR,axiom,
% 2.86/1.59 ! [C: $tType,A: $tType,B: $tType,Y: A,Z2: A,L3: B,G: labeled_graph @ B @ A,U: C,F: set @ ( product_prod @ A @ C ),V3: C] :
% 2.86/1.59 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y @ Z2 ) @ ( getRel @ B @ A @ L3 @ G ) )
% 2.86/1.59 => ( ( member @ ( product_prod @ A @ C ) @ ( product_Pair @ A @ C @ Y @ U ) @ F )
% 2.86/1.59 => ( ( member @ ( product_prod @ A @ C ) @ ( product_Pair @ A @ C @ Z2 @ V3 ) @ F )
% 2.86/1.59 => ( member @ ( product_prod @ C @ C ) @ ( product_Pair @ C @ C @ U @ V3 ) @ ( getRel @ B @ C @ L3 @ ( map_graph @ A @ C @ B @ F @ G ) ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_242_getRel__dom_I2_J,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,G: labeled_graph @ A @ B,A2: B,B2: B,L3: A] :
% 2.86/1.59 ( ( G
% 2.86/1.59 = ( restrict @ A @ B @ G ) )
% 2.86/1.59 => ( ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ A2 @ B2 ) @ ( getRel @ A @ B @ L3 @ G ) )
% 2.86/1.59 => ( member @ B @ B2 @ ( labeled_vertices @ A @ B @ G ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_243_getRel__dom_I1_J,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,G: labeled_graph @ A @ B,A2: B,B2: B,L3: A] :
% 2.86/1.59 ( ( G
% 2.86/1.59 = ( restrict @ A @ B @ G ) )
% 2.86/1.59 => ( ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ A2 @ B2 ) @ ( getRel @ A @ B @ L3 @ G ) )
% 2.86/1.59 => ( member @ B @ A2 @ ( labeled_vertices @ A @ B @ G ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_244_nonempty__rule,axiom,
% 2.86/1.59 ! [A: $tType,B: $tType,G: labeled_graph @ A @ B] :
% 2.86/1.59 ( ( G
% 2.86/1.59 = ( restrict @ A @ B @ G ) )
% 2.86/1.59 => ( ( maintained @ A @ nat @ B @ ( standa244753842y_rule @ A ) @ G )
% 2.86/1.59 = ( ( labeled_vertices @ A @ B @ G )
% 2.86/1.59 != ( bot_bot @ ( set @ B ) ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_245_le__numeral__extra_I4_J,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( linord1659791738miring @ A )
% 2.86/1.59 => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_246__092_060open_062maintained_A_Isymmetry__rule_AS__Idt_J_AG_092_060close_062,axiom,
% 2.86/1.59 maintained @ ( standard_Constant @ a ) @ nat @ ( sum_sum @ a @ b ) @ ( standa1805702094y_rule @ ( standard_Constant @ a ) @ ( standard_S_Idt @ a ) ) @ g ).
% 2.86/1.59
% 2.86/1.59 thf(fact_247__092_060open_062maintained_A_Itransitive__rule_AS__Idt_J_AG_092_060close_062,axiom,
% 2.86/1.59 maintained @ ( standard_Constant @ a ) @ nat @ ( sum_sum @ a @ b ) @ ( standa2114124375e_rule @ ( standard_Constant @ a ) @ ( standard_S_Idt @ a ) ) @ g ).
% 2.86/1.59
% 2.86/1.59 thf(fact_248_le__numeral__extra_I3_J,axiom,
% 2.86/1.59 ! [A: $tType] :
% 2.86/1.59 ( ( linord1659791738miring @ A )
% 2.86/1.59 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_249__092_060open_062maintained_A_Icongruence__rule_AS__Idt_Al_J_AG_092_060close_062,axiom,
% 2.86/1.59 maintained @ ( standard_Constant @ a ) @ nat @ ( sum_sum @ a @ b ) @ ( standa1068660421e_rule @ ( standard_Constant @ a ) @ ( standard_S_Idt @ a ) @ l ) @ g ).
% 2.86/1.59
% 2.86/1.59 thf(fact_250_maintained__refl,axiom,
% 2.86/1.59 ! [B: $tType,C: $tType,A: $tType,R2: labeled_graph @ A @ B,G: labeled_graph @ A @ C] : ( maintained @ A @ B @ C @ ( product_Pair @ ( labeled_graph @ A @ B ) @ ( labeled_graph @ A @ B ) @ R2 @ R2 ) @ G ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_251_maintainedD2,axiom,
% 2.86/1.59 ! [A: $tType,C: $tType,B: $tType,A4: labeled_graph @ A @ B,B6: labeled_graph @ A @ B,G: labeled_graph @ A @ C,F: set @ ( product_prod @ B @ C )] :
% 2.86/1.59 ( ( maintained @ A @ B @ C @ ( product_Pair @ ( labeled_graph @ A @ B ) @ ( labeled_graph @ A @ B ) @ A4 @ B6 ) @ G )
% 2.86/1.59 => ( ( graph_homomorphism @ A @ B @ C @ A4 @ G @ F )
% 2.86/1.59 => ~ ! [G5: set @ ( product_prod @ B @ C )] :
% 2.86/1.59 ( ( graph_homomorphism @ A @ B @ C @ B6 @ G @ G5 )
% 2.86/1.59 => ~ ( ord_less_eq @ ( set @ ( product_prod @ B @ C ) ) @ F @ G5 ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(fact_252_equivalence,axiom,
% 2.86/1.59 ! [B: $tType,A: $tType,G: labeled_graph @ A @ B,I2: A] :
% 2.86/1.59 ( ( G
% 2.86/1.59 = ( restrict @ A @ B @ G ) )
% 2.86/1.59 => ( ! [X5: product_prod @ ( labeled_graph @ A @ nat ) @ ( labeled_graph @ A @ nat )] :
% 2.86/1.59 ( ( member @ ( product_prod @ ( labeled_graph @ A @ nat ) @ ( labeled_graph @ A @ nat ) ) @ X5 @ ( insert @ ( product_prod @ ( labeled_graph @ A @ nat ) @ ( labeled_graph @ A @ nat ) ) @ ( standa245363227y_rule @ A @ I2 ) @ ( insert @ ( product_prod @ ( labeled_graph @ A @ nat ) @ ( labeled_graph @ A @ nat ) ) @ ( standa2114124375e_rule @ A @ I2 ) @ ( insert @ ( product_prod @ ( labeled_graph @ A @ nat ) @ ( labeled_graph @ A @ nat ) ) @ ( standa1805702094y_rule @ A @ I2 ) @ ( bot_bot @ ( set @ ( product_prod @ ( labeled_graph @ A @ nat ) @ ( labeled_graph @ A @ nat ) ) ) ) ) ) ) )
% 2.86/1.59 => ( maintained @ A @ nat @ B @ X5 @ G ) )
% 2.86/1.59 => ( equiv_equiv @ B @ ( labeled_vertices @ A @ B @ G ) @ ( getRel @ A @ B @ I2 @ G ) ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 2.86/1.59 ! [A10: $tType,A11: $tType] :
% 2.86/1.59 ( ( order_bot @ A11 )
% 2.86/1.59 => ( order_bot @ ( A10 > A11 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.86/1.59 ! [A10: $tType,A11: $tType] :
% 2.86/1.59 ( ( preorder @ A11 )
% 2.86/1.59 => ( preorder @ ( A10 > A11 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.86/1.59 ! [A10: $tType,A11: $tType] :
% 2.86/1.59 ( ( order @ A11 )
% 2.86/1.59 => ( order @ ( A10 > A11 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(tcon_fun___Orderings_Oord,axiom,
% 2.86/1.59 ! [A10: $tType,A11: $tType] :
% 2.86/1.59 ( ( ord @ A11 )
% 2.86/1.59 => ( ord @ ( A10 > A11 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(tcon_fun___Orderings_Obot,axiom,
% 2.86/1.59 ! [A10: $tType,A11: $tType] :
% 2.86/1.59 ( ( bot @ A11 )
% 2.86/1.59 => ( bot @ ( A10 > A11 ) ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 2.86/1.59 canoni770627133id_add @ nat ).
% 2.86/1.59
% 2.86/1.59 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring,axiom,
% 2.86/1.59 linord1659791738miring @ nat ).
% 2.86/1.59
% 2.86/1.59 thf(tcon_Nat_Onat___Orderings_Oorder__bot_1,axiom,
% 2.86/1.59 order_bot @ nat ).
% 2.86/1.59
% 2.86/1.59 thf(tcon_Nat_Onat___Rings_Ozero__neq__one,axiom,
% 2.86/1.59 zero_neq_one @ nat ).
% 2.86/1.59
% 2.86/1.59 thf(tcon_Nat_Onat___Orderings_Opreorder_2,axiom,
% 2.86/1.59 preorder @ nat ).
% 2.86/1.59
% 2.86/1.59 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 2.86/1.59 linorder @ nat ).
% 2.86/1.59
% 2.86/1.59 thf(tcon_Nat_Onat___Orderings_Oorder_3,axiom,
% 2.86/1.59 order @ nat ).
% 2.86/1.59
% 2.86/1.59 thf(tcon_Nat_Onat___Orderings_Oord_4,axiom,
% 2.86/1.59 ord @ nat ).
% 2.86/1.59
% 2.86/1.59 thf(tcon_Nat_Onat___Orderings_Obot_5,axiom,
% 2.86/1.59 bot @ nat ).
% 2.86/1.59
% 2.86/1.59 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 2.86/1.59 zero @ nat ).
% 2.86/1.59
% 2.86/1.59 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 2.86/1.59 one @ nat ).
% 2.86/1.59
% 2.86/1.59 thf(tcon_Set_Oset___Orderings_Oorder__bot_6,axiom,
% 2.86/1.59 ! [A10: $tType] : ( order_bot @ ( set @ A10 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(tcon_Set_Oset___Orderings_Opreorder_7,axiom,
% 2.86/1.59 ! [A10: $tType] : ( preorder @ ( set @ A10 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(tcon_Set_Oset___Orderings_Oorder_8,axiom,
% 2.86/1.59 ! [A10: $tType] : ( order @ ( set @ A10 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(tcon_Set_Oset___Orderings_Oord_9,axiom,
% 2.86/1.59 ! [A10: $tType] : ( ord @ ( set @ A10 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(tcon_Set_Oset___Orderings_Obot_10,axiom,
% 2.86/1.59 ! [A10: $tType] : ( bot @ ( set @ A10 ) ) ).
% 2.86/1.59
% 2.86/1.59 thf(tcon_HOL_Obool___Orderings_Oorder__bot_11,axiom,
% 2.86/1.59 order_bot @ $o ).
% 2.86/1.59
% 2.86/1.59 thf(tcon_HOL_Obool___Orderings_Opreorder_12,axiom,
% 2.86/1.59 preorder @ $o ).
% 2.86/1.59
% 2.86/1.59 thf(tcon_HOL_Obool___Orderings_Olinorder_13,axiom,
% 2.86/1.59 linorder @ $o ).
% 2.86/1.59
% 2.86/1.59 thf(tcon_HOL_Obool___Orderings_Oorder_14,axiom,
% 2.86/1.59 order @ $o ).
% 2.86/1.59
% 2.86/1.59 thf(tcon_HOL_Obool___Orderings_Oord_15,axiom,
% 2.86/1.59 ord @ $o ).
% 2.86/1.59
% 2.86/1.59 thf(tcon_HOL_Obool___Orderings_Obot_16,axiom,
% 2.86/1.59 bot @ $o ).
% 2.86/1.59
% 2.86/1.59 thf(conj_0,conjecture,
% 2.86/1.59 ( ( ( labeled_vertices @ ( standard_Constant @ a ) @ nat @ ( labeled_LG @ ( standard_Constant @ a ) @ nat @ ( insert @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) ) @ ( product_Pair @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) @ ( standard_S_Idt @ a ) @ ( product_Pair @ nat @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ) @ ( bot_bot @ ( set @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) ) ) ) ) @ ( insert @ nat @ ( zero_zero @ nat ) @ ( bot_bot @ ( set @ nat ) ) ) ) )
% 2.86/1.59 = ( domain @ nat @ ( sum_sum @ a @ b ) @ ( insert @ ( product_prod @ nat @ ( sum_sum @ a @ b ) ) @ ( product_Pair @ nat @ ( sum_sum @ a @ b ) @ ( zero_zero @ nat ) @ v ) @ ( bot_bot @ ( set @ ( product_prod @ nat @ ( sum_sum @ a @ b ) ) ) ) ) ) )
% 2.86/1.59 & ( ( labeled_LG @ ( standard_Constant @ a ) @ nat @ ( insert @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) ) @ ( product_Pair @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) @ ( standard_S_Idt @ a ) @ ( product_Pair @ nat @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ) @ ( bot_bot @ ( set @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) ) ) ) ) @ ( insert @ nat @ ( zero_zero @ nat ) @ ( bot_bot @ ( set @ nat ) ) ) )
% 2.86/1.59 = ( restrict @ ( standard_Constant @ a ) @ nat @ ( labeled_LG @ ( standard_Constant @ a ) @ nat @ ( insert @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) ) @ ( product_Pair @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) @ ( standard_S_Idt @ a ) @ ( product_Pair @ nat @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ) @ ( bot_bot @ ( set @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) ) ) ) ) @ ( insert @ nat @ ( zero_zero @ nat ) @ ( bot_bot @ ( set @ nat ) ) ) ) ) )
% 2.86/1.59 & ( g
% 2.86/1.59 = ( restrict @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) @ g ) )
% 2.86/1.59 & ( ord_less_eq @ ( set @ ( sum_sum @ a @ b ) ) @ ( image @ nat @ ( sum_sum @ a @ b ) @ ( insert @ ( product_prod @ nat @ ( sum_sum @ a @ b ) ) @ ( product_Pair @ nat @ ( sum_sum @ a @ b ) @ ( zero_zero @ nat ) @ v ) @ ( bot_bot @ ( set @ ( product_prod @ nat @ ( sum_sum @ a @ b ) ) ) ) ) @ ( labeled_vertices @ ( standard_Constant @ a ) @ nat @ ( labeled_LG @ ( standard_Constant @ a ) @ nat @ ( insert @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) ) @ ( product_Pair @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) @ ( standard_S_Idt @ a ) @ ( product_Pair @ nat @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ) @ ( bot_bot @ ( set @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) ) ) ) ) @ ( insert @ nat @ ( zero_zero @ nat ) @ ( bot_bot @ ( set @ nat ) ) ) ) ) ) @ ( labeled_vertices @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) @ g ) )
% 2.86/1.59 & ( univalent @ nat @ ( sum_sum @ a @ b ) @ ( insert @ ( product_prod @ nat @ ( sum_sum @ a @ b ) ) @ ( product_Pair @ nat @ ( sum_sum @ a @ b ) @ ( zero_zero @ nat ) @ v ) @ ( bot_bot @ ( set @ ( product_prod @ nat @ ( sum_sum @ a @ b ) ) ) ) ) )
% 2.86/1.59 & ( edge_preserving @ nat @ ( sum_sum @ a @ b ) @ ( standard_Constant @ a ) @ ( insert @ ( product_prod @ nat @ ( sum_sum @ a @ b ) ) @ ( product_Pair @ nat @ ( sum_sum @ a @ b ) @ ( zero_zero @ nat ) @ v ) @ ( bot_bot @ ( set @ ( product_prod @ nat @ ( sum_sum @ a @ b ) ) ) ) ) @ ( labeled_edges @ ( standard_Constant @ a ) @ nat @ ( labeled_LG @ ( standard_Constant @ a ) @ nat @ ( insert @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) ) @ ( product_Pair @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) @ ( standard_S_Idt @ a ) @ ( product_Pair @ nat @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ) @ ( bot_bot @ ( set @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ nat @ nat ) ) ) ) ) @ ( insert @ nat @ ( zero_zero @ nat ) @ ( bot_bot @ ( set @ nat ) ) ) ) ) @ ( labeled_edges @ ( standard_Constant @ a ) @ ( sum_sum @ a @ b ) @ g ) ) ) ).
% 2.86/1.59 ------------------------
% 2.97/1.61 % (16146)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15863 for (2999ds/18Mi)
% 2.97/1.62 % (16146)Instruction limit reached!
% 2.97/1.62 % (16146)------------------------------
% 2.97/1.62 % (16146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.62 % (16146)Termination reason: Unknown
% 2.97/1.62 % (16146)Termination phase: shuffling
% 2.97/1.62
% 2.97/1.62 % (16146)Memory used [KB]: 1791
% 2.97/1.62 % (16146)Time elapsed: 0.008 s
% 2.97/1.62 % (16146)Instructions burned: 19 (million)
% 2.97/1.62 % (16146)------------------------------
% 2.97/1.62 % (16146)------------------------------
% 2.97/1.62 % (16140)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15863 for (2999ds/183Mi)
% 2.97/1.62 % (16141)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_15863 for (2999ds/4Mi)
% 2.97/1.62 % (16142)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_15863 for (2999ds/27Mi)
% 2.97/1.62 % (16143)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15863 for (2999ds/2Mi)
% 2.97/1.62 % (16144)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_15863 for (2999ds/2Mi)
% 2.97/1.62 % (16145)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_15863 for (2999ds/275Mi)
% 2.97/1.62 % (16143)Instruction limit reached!
% 2.97/1.62 % (16143)------------------------------
% 2.97/1.62 % (16143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.62 % (16143)Termination reason: Unknown
% 2.97/1.62 % (16143)Termination phase: shuffling
% 2.97/1.62
% 2.97/1.62 % (16143)Memory used [KB]: 1407
% 2.97/1.62 % (16143)Time elapsed: 0.004 s
% 2.97/1.62 % (16143)Instructions burned: 3 (million)
% 2.97/1.62 % (16143)------------------------------
% 2.97/1.62 % (16143)------------------------------
% 2.97/1.62 % (16144)Instruction limit reached!
% 2.97/1.62 % (16144)------------------------------
% 2.97/1.62 % (16144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.62 % (16144)Termination reason: Unknown
% 2.97/1.62 % (16144)Termination phase: shuffling
% 2.97/1.62
% 2.97/1.62 % (16144)Memory used [KB]: 1407
% 2.97/1.62 % (16144)Time elapsed: 0.004 s
% 2.97/1.62 % (16144)Instructions burned: 3 (million)
% 2.97/1.62 % (16144)------------------------------
% 2.97/1.62 % (16144)------------------------------
% 2.97/1.62 % (16141)Instruction limit reached!
% 2.97/1.62 % (16141)------------------------------
% 2.97/1.62 % (16141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.62 % (16141)Termination reason: Unknown
% 2.97/1.62 % (16141)Termination phase: shuffling
% 2.97/1.62
% 2.97/1.62 % (16141)Memory used [KB]: 1535
% 2.97/1.62 % (16141)Time elapsed: 0.005 s
% 2.97/1.62 % (16141)Instructions burned: 5 (million)
% 2.97/1.62 % (16141)------------------------------
% 2.97/1.62 % (16141)------------------------------
% 2.97/1.63 % (16147)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15863 for (2999ds/3Mi)
% 2.97/1.63 % (16147)Instruction limit reached!
% 2.97/1.63 % (16147)------------------------------
% 2.97/1.63 % (16147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.63 % (16147)Termination reason: Unknown
% 2.97/1.63 % (16147)Termination phase: shuffling
% 2.97/1.63
% 2.97/1.63 % (16147)Memory used [KB]: 1407
% 2.97/1.63 % (16147)Time elapsed: 0.003 s
% 2.97/1.63 % (16147)Instructions burned: 5 (million)
% 2.97/1.63 % (16147)------------------------------
% 2.97/1.63 % (16147)------------------------------
% 2.97/1.64 % (16142)Instruction limit reached!
% 2.97/1.64 % (16142)------------------------------
% 2.97/1.64 % (16142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.64 % (16142)Termination reason: Unknown
% 2.97/1.64 % (16142)Termination phase: shuffling
% 2.97/1.64
% 2.97/1.64 % (16142)Memory used [KB]: 1918
% 2.97/1.64 % (16142)Time elapsed: 0.019 s
% 2.97/1.64 % (16142)Instructions burned: 27 (million)
% 2.97/1.64 % (16142)------------------------------
% 2.97/1.64 % (16142)------------------------------
% 2.97/1.64 % (16148)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_15863 for (2999ds/37Mi)
% 2.97/1.64 % (16149)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_15863 for (2999ds/15Mi)
% 2.97/1.64 % (16152)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_15863 for (2999ds/1041Mi)
% 2.97/1.64 % (16151)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15863 for (2999ds/3Mi)
% 2.97/1.64 % (16151)Instruction limit reached!
% 2.97/1.64 % (16151)------------------------------
% 2.97/1.64 % (16151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.64 % (16151)Termination reason: Unknown
% 2.97/1.64 % (16151)Termination phase: shuffling
% 2.97/1.64
% 2.97/1.64 % (16151)Memory used [KB]: 1407
% 2.97/1.64 % (16151)Time elapsed: 0.004 s
% 2.97/1.64 % (16151)Instructions burned: 3 (million)
% 2.97/1.64 % (16151)------------------------------
% 2.97/1.64 % (16151)------------------------------
% 2.97/1.65 % (16149)Instruction limit reached!
% 2.97/1.65 % (16149)------------------------------
% 2.97/1.65 % (16149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.65 % (16149)Termination reason: Unknown
% 2.97/1.65 % (16149)Termination phase: shuffling
% 2.97/1.65
% 2.97/1.65 % (16149)Memory used [KB]: 1663
% 2.97/1.65 % (16149)Time elapsed: 0.012 s
% 2.97/1.65 % (16149)Instructions burned: 16 (million)
% 2.97/1.65 % (16149)------------------------------
% 2.97/1.65 % (16149)------------------------------
% 2.97/1.66 % (16153)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_15863 for (2999ds/7Mi)
% 2.97/1.66 % (16153)Instruction limit reached!
% 2.97/1.66 % (16153)------------------------------
% 2.97/1.66 % (16153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.66 % (16153)Termination reason: Unknown
% 2.97/1.66 % (16153)Termination phase: shuffling
% 2.97/1.66
% 2.97/1.66 % (16153)Memory used [KB]: 1535
% 2.97/1.66 % (16153)Time elapsed: 0.006 s
% 2.97/1.66 % (16153)Instructions burned: 8 (million)
% 2.97/1.66 % (16153)------------------------------
% 2.97/1.66 % (16153)------------------------------
% 2.97/1.66 % (16148)Instruction limit reached!
% 2.97/1.66 % (16148)------------------------------
% 2.97/1.66 % (16148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.66 % (16148)Termination reason: Unknown
% 2.97/1.66 % (16148)Termination phase: shuffling
% 2.97/1.66
% 2.97/1.66 % (16148)Memory used [KB]: 2174
% 2.97/1.66 % (16148)Time elapsed: 0.022 s
% 2.97/1.66 % (16148)Instructions burned: 38 (million)
% 2.97/1.66 % (16148)------------------------------
% 2.97/1.66 % (16148)------------------------------
% 2.97/1.66 % (16154)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_15863 for (2999ds/16Mi)
% 2.97/1.67 % (16155)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_15863 for (2999ds/3Mi)
% 2.97/1.67 % (16155)Instruction limit reached!
% 2.97/1.67 % (16155)------------------------------
% 2.97/1.67 % (16155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.67 % (16155)Termination reason: Unknown
% 2.97/1.67 % (16155)Termination phase: shuffling
% 2.97/1.67
% 2.97/1.67 % (16155)Memory used [KB]: 1407
% 2.97/1.67 % (16155)Time elapsed: 0.004 s
% 2.97/1.67 % (16155)Instructions burned: 4 (million)
% 2.97/1.67 % (16155)------------------------------
% 2.97/1.67 % (16155)------------------------------
% 2.97/1.67 % (16154)Instruction limit reached!
% 2.97/1.67 % (16154)------------------------------
% 2.97/1.67 % (16154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.67 % (16154)Termination reason: Unknown
% 2.97/1.67 % (16154)Termination phase: shuffling
% 2.97/1.67
% 2.97/1.67 % (16154)Memory used [KB]: 1663
% 2.97/1.67 % (16154)Time elapsed: 0.012 s
% 2.97/1.67 % (16154)Instructions burned: 17 (million)
% 2.97/1.67 % (16154)------------------------------
% 2.97/1.67 % (16154)------------------------------
% 2.97/1.67 % (16156)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_15863 for (2999ds/3Mi)
% 2.97/1.67 % (16156)Instruction limit reached!
% 2.97/1.67 % (16156)------------------------------
% 2.97/1.67 % (16156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.67 % (16156)Termination reason: Unknown
% 2.97/1.67 % (16156)Termination phase: shuffling
% 2.97/1.67
% 2.97/1.67 % (16156)Memory used [KB]: 1407
% 2.97/1.67 % (16156)Time elapsed: 0.003 s
% 2.97/1.67 % (16156)Instructions burned: 4 (million)
% 2.97/1.67 % (16156)------------------------------
% 2.97/1.67 % (16156)------------------------------
% 2.97/1.68 % (16157)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_15863 for (2999ds/7Mi)
% 2.97/1.68 % (16157)Instruction limit reached!
% 2.97/1.68 % (16157)------------------------------
% 2.97/1.68 % (16157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.68 % (16157)Termination reason: Unknown
% 2.97/1.68 % (16157)Termination phase: shuffling
% 2.97/1.68
% 2.97/1.68 % (16157)Memory used [KB]: 1535
% 2.97/1.68 % (16157)Time elapsed: 0.006 s
% 2.97/1.68 % (16157)Instructions burned: 7 (million)
% 2.97/1.68 % (16157)------------------------------
% 2.97/1.68 % (16157)------------------------------
% 2.97/1.68 % (16160)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_15863 for (2999ds/18Mi)
% 2.97/1.69 % (16158)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_15863 for (2999ds/3Mi)
% 2.97/1.69 % (16159)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_15863 for (2999ds/4Mi)
% 2.97/1.69 % (16158)Instruction limit reached!
% 2.97/1.69 % (16158)------------------------------
% 2.97/1.69 % (16158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.69 % (16158)Termination reason: Unknown
% 2.97/1.69 % (16158)Termination phase: shuffling
% 2.97/1.69
% 2.97/1.69 % (16158)Memory used [KB]: 1407
% 2.97/1.69 % (16158)Time elapsed: 0.003 s
% 2.97/1.69 % (16158)Instructions burned: 3 (million)
% 2.97/1.69 % (16158)------------------------------
% 2.97/1.69 % (16158)------------------------------
% 2.97/1.69 % (16159)Instruction limit reached!
% 2.97/1.69 % (16159)------------------------------
% 2.97/1.69 % (16159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.69 % (16159)Termination reason: Unknown
% 2.97/1.69 % (16159)Termination phase: shuffling
% 2.97/1.69
% 2.97/1.69 % (16159)Memory used [KB]: 1407
% 2.97/1.69 % (16159)Time elapsed: 0.004 s
% 2.97/1.69 % (16159)Instructions burned: 4 (million)
% 2.97/1.69 % (16159)------------------------------
% 2.97/1.69 % (16159)------------------------------
% 2.97/1.69 % (16160)Instruction limit reached!
% 2.97/1.69 % (16160)------------------------------
% 2.97/1.69 % (16160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.69 % (16160)Termination reason: Unknown
% 2.97/1.69 % (16160)Termination phase: shuffling
% 2.97/1.69
% 2.97/1.69 % (16160)Memory used [KB]: 1791
% 2.97/1.69 % (16160)Time elapsed: 0.008 s
% 2.97/1.69 % (16160)Instructions burned: 20 (million)
% 2.97/1.69 % (16160)------------------------------
% 2.97/1.69 % (16160)------------------------------
% 2.97/1.70 % (16163)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_15863 for (2999ds/902Mi)
% 2.97/1.70 % (16162)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_15863 for (2999ds/6Mi)
% 2.97/1.70 % (16161)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_15863 for (2999ds/710Mi)
% 2.97/1.70 % (16140)Instruction limit reached!
% 2.97/1.70 % (16140)------------------------------
% 2.97/1.70 % (16140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.70 % (16140)Termination reason: Unknown
% 2.97/1.70 % (16140)Termination phase: Saturation
% 2.97/1.70
% 2.97/1.70 % (16140)Memory used [KB]: 7164
% 2.97/1.70 % (16140)Time elapsed: 0.082 s
% 2.97/1.70 % (16140)Instructions burned: 185 (million)
% 2.97/1.70 % (16140)------------------------------
% 2.97/1.70 % (16140)------------------------------
% 2.97/1.70 % (16164)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_15863 for (2999ds/21Mi)
% 2.97/1.70 % (16162)Instruction limit reached!
% 2.97/1.70 % (16162)------------------------------
% 2.97/1.70 % (16162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.70 % (16162)Termination reason: Unknown
% 2.97/1.70 % (16162)Termination phase: shuffling
% 2.97/1.70
% 2.97/1.70 % (16162)Memory used [KB]: 1535
% 2.97/1.70 % (16162)Time elapsed: 0.004 s
% 2.97/1.70 % (16162)Instructions burned: 8 (million)
% 2.97/1.70 % (16162)------------------------------
% 2.97/1.70 % (16162)------------------------------
% 2.97/1.71 % (16164)Instruction limit reached!
% 2.97/1.71 % (16164)------------------------------
% 2.97/1.71 % (16164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.71 % (16164)Termination reason: Unknown
% 2.97/1.71 % (16164)Termination phase: shuffling
% 2.97/1.71
% 2.97/1.71 % (16164)Memory used [KB]: 1791
% 2.97/1.71 % (16164)Time elapsed: 0.009 s
% 2.97/1.71 % (16164)Instructions burned: 21 (million)
% 2.97/1.71 % (16164)------------------------------
% 2.97/1.71 % (16164)------------------------------
% 2.97/1.71 % (16165)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_15863 for (2998ds/5Mi)
% 2.97/1.71 % (16166)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_15863 for (2998ds/6Mi)
% 2.97/1.71 % (16165)Instruction limit reached!
% 2.97/1.71 % (16165)------------------------------
% 2.97/1.71 % (16165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.71 % (16165)Termination reason: Unknown
% 2.97/1.71 % (16165)Termination phase: shuffling
% 2.97/1.71
% 2.97/1.71 % (16165)Memory used [KB]: 1535
% 2.97/1.71 % (16165)Time elapsed: 0.004 s
% 2.97/1.71 % (16165)Instructions burned: 7 (million)
% 2.97/1.71 % (16165)------------------------------
% 2.97/1.71 % (16165)------------------------------
% 2.97/1.71 % (16166)Instruction limit reached!
% 2.97/1.71 % (16166)------------------------------
% 2.97/1.71 % (16166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.71 % (16166)Termination reason: Unknown
% 2.97/1.71 % (16166)Termination phase: shuffling
% 2.97/1.71
% 2.97/1.71 % (16166)Memory used [KB]: 1535
% 2.97/1.71 % (16166)Time elapsed: 0.003 s
% 2.97/1.71 % (16166)Instructions burned: 7 (million)
% 2.97/1.71 % (16166)------------------------------
% 2.97/1.71 % (16166)------------------------------
% 2.97/1.72 % (16167)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_15863 for (2998ds/377Mi)
% 2.97/1.72 % (16168)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_15863 for (2998ds/779Mi)
% 2.97/1.73 % (16169)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_15863 for (2998ds/19Mi)
% 2.97/1.73 % (16169)Instruction limit reached!
% 2.97/1.73 % (16169)------------------------------
% 2.97/1.73 % (16169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.73 % (16169)Termination reason: Unknown
% 2.97/1.73 % (16169)Termination phase: shuffling
% 2.97/1.73
% 2.97/1.73 % (16169)Memory used [KB]: 1918
% 2.97/1.73 % (16169)Time elapsed: 0.008 s
% 2.97/1.73 % (16169)Instructions burned: 20 (million)
% 2.97/1.73 % (16169)------------------------------
% 2.97/1.73 % (16169)------------------------------
% 2.97/1.74 % (16170)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_15863 for (2998ds/879Mi)
% 2.97/1.75 % (16145)Instruction limit reached!
% 2.97/1.75 % (16145)------------------------------
% 2.97/1.75 % (16145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.75 % (16145)Termination reason: Unknown
% 2.97/1.75 % (16145)Termination phase: Saturation
% 2.97/1.75
% 2.97/1.75 % (16145)Memory used [KB]: 7675
% 2.97/1.75 % (16145)Time elapsed: 0.135 s
% 2.97/1.75 % (16145)Instructions burned: 275 (million)
% 2.97/1.75 % (16145)------------------------------
% 2.97/1.75 % (16145)------------------------------
% 2.97/1.77 % (16171)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_15863 for (2998ds/17Mi)
% 2.97/1.77 % (16171)Instruction limit reached!
% 2.97/1.77 % (16171)------------------------------
% 2.97/1.77 % (16171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.77 % (16171)Termination reason: Unknown
% 2.97/1.77 % (16171)Termination phase: shuffling
% 2.97/1.77
% 2.97/1.77 % (16171)Memory used [KB]: 1791
% 2.97/1.77 % (16171)Time elapsed: 0.008 s
% 2.97/1.77 % (16171)Instructions burned: 17 (million)
% 2.97/1.77 % (16171)------------------------------
% 2.97/1.77 % (16171)------------------------------
% 2.97/1.78 % (16172)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_15863 for (2998ds/3Mi)
% 2.97/1.78 % (16172)Instruction limit reached!
% 2.97/1.78 % (16172)------------------------------
% 2.97/1.78 % (16172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.78 % (16172)Termination reason: Unknown
% 2.97/1.78 % (16172)Termination phase: shuffling
% 2.97/1.78
% 2.97/1.78 % (16172)Memory used [KB]: 1407
% 2.97/1.78 % (16172)Time elapsed: 0.003 s
% 2.97/1.78 % (16172)Instructions burned: 4 (million)
% 2.97/1.78 % (16172)------------------------------
% 2.97/1.78 % (16172)------------------------------
% 2.97/1.79 % (16173)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_15863 for (2998ds/30Mi)
% 2.97/1.80 % (16173)Instruction limit reached!
% 2.97/1.80 % (16173)------------------------------
% 2.97/1.80 % (16173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.80 % (16173)Termination reason: Unknown
% 2.97/1.80 % (16173)Termination phase: shuffling
% 2.97/1.80
% 2.97/1.80 % (16173)Memory used [KB]: 2046
% 2.97/1.80 % (16173)Time elapsed: 0.013 s
% 2.97/1.80 % (16173)Instructions burned: 32 (million)
% 2.97/1.80 % (16173)------------------------------
% 2.97/1.80 % (16173)------------------------------
% 2.97/1.81 % (16174)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_15863 for (2998ds/127Mi)
% 2.97/1.83 % (16167)Instruction limit reached!
% 2.97/1.83 % (16167)------------------------------
% 2.97/1.83 % (16167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.83 % (16167)Termination reason: Unknown
% 2.97/1.83 % (16167)Termination phase: Saturation
% 2.97/1.83
% 2.97/1.83 % (16167)Memory used [KB]: 7675
% 2.97/1.83 % (16167)Time elapsed: 0.115 s
% 2.97/1.83 % (16167)Instructions burned: 380 (million)
% 2.97/1.83 % (16167)------------------------------
% 2.97/1.83 % (16167)------------------------------
% 2.97/1.84 % (16175)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_15863 for (2997ds/100Mi)
% 2.97/1.85 % (16174)Instruction limit reached!
% 2.97/1.85 % (16174)------------------------------
% 2.97/1.85 % (16174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.85 % (16174)Termination reason: Unknown
% 2.97/1.85 % (16174)Termination phase: Saturation
% 2.97/1.85
% 2.97/1.85 % (16174)Memory used [KB]: 6908
% 2.97/1.85 % (16174)Time elapsed: 0.042 s
% 2.97/1.85 % (16174)Instructions burned: 128 (million)
% 2.97/1.85 % (16174)------------------------------
% 2.97/1.85 % (16174)------------------------------
% 2.97/1.86 % (16176)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_15863 for (2997ds/3Mi)
% 2.97/1.87 % (16176)Instruction limit reached!
% 2.97/1.87 % (16176)------------------------------
% 2.97/1.87 % (16176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.87 % (16176)Termination reason: Unknown
% 2.97/1.87 % (16176)Termination phase: shuffling
% 2.97/1.87
% 2.97/1.87 % (16176)Memory used [KB]: 1535
% 2.97/1.87 % (16176)Time elapsed: 0.003 s
% 2.97/1.87 % (16176)Instructions burned: 4 (million)
% 2.97/1.87 % (16176)------------------------------
% 2.97/1.87 % (16176)------------------------------
% 2.97/1.87 % (16175)Instruction limit reached!
% 2.97/1.87 % (16175)------------------------------
% 2.97/1.87 % (16175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.87 % (16175)Termination reason: Unknown
% 2.97/1.87 % (16175)Termination phase: Property scanning
% 2.97/1.87
% 2.97/1.87 % (16175)Memory used [KB]: 2686
% 2.97/1.87 % (16175)Time elapsed: 0.032 s
% 2.97/1.87 % (16175)Instructions burned: 100 (million)
% 2.97/1.87 % (16175)------------------------------
% 2.97/1.87 % (16175)------------------------------
% 2.97/1.88 % (16177)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_15863 for (2997ds/20Mi)
% 2.97/1.88 % (16177)Instruction limit reached!
% 2.97/1.88 % (16177)------------------------------
% 2.97/1.88 % (16177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.88 % (16177)Termination reason: Unknown
% 2.97/1.88 % (16177)Termination phase: shuffling
% 2.97/1.88
% 2.97/1.88 % (16177)Memory used [KB]: 1918
% 2.97/1.88 % (16177)Time elapsed: 0.009 s
% 2.97/1.88 % (16177)Instructions burned: 21 (million)
% 2.97/1.88 % (16177)------------------------------
% 2.97/1.88 % (16177)------------------------------
% 2.97/1.88 % (16178)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_15863 for (2997ds/86Mi)
% 2.97/1.89 % (16179)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_15863 for (2997ds/107Mi)
% 2.97/1.91 % (16178)Instruction limit reached!
% 2.97/1.91 % (16178)------------------------------
% 2.97/1.91 % (16178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.91 % (16178)Termination reason: Unknown
% 2.97/1.91 % (16178)Termination phase: Property scanning
% 2.97/1.91
% 2.97/1.91 % (16178)Memory used [KB]: 2430
% 2.97/1.91 % (16178)Time elapsed: 0.030 s
% 2.97/1.91 % (16178)Instructions burned: 87 (million)
% 2.97/1.91 % (16178)------------------------------
% 2.97/1.91 % (16178)------------------------------
% 2.97/1.92 % (16180)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_15863 for (2996ds/39Mi)
% 2.97/1.93 % (16179)Instruction limit reached!
% 2.97/1.93 % (16179)------------------------------
% 2.97/1.93 % (16179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.93 % (16179)Termination reason: Unknown
% 2.97/1.93 % (16179)Termination phase: Saturation
% 2.97/1.93
% 2.97/1.93 % (16179)Memory used [KB]: 6908
% 2.97/1.93 % (16179)Time elapsed: 0.036 s
% 2.97/1.93 % (16179)Instructions burned: 107 (million)
% 2.97/1.93 % (16179)------------------------------
% 2.97/1.93 % (16179)------------------------------
% 2.97/1.93 % (16180)Instruction limit reached!
% 2.97/1.93 % (16180)------------------------------
% 2.97/1.93 % (16180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.93 % (16180)Termination reason: Unknown
% 2.97/1.93 % (16180)Termination phase: shuffling
% 2.97/1.93
% 2.97/1.93 % (16180)Memory used [KB]: 2174
% 2.97/1.93 % (16180)Time elapsed: 0.014 s
% 2.97/1.93 % (16180)Instructions burned: 41 (million)
% 2.97/1.93 % (16180)------------------------------
% 2.97/1.93 % (16180)------------------------------
% 2.97/1.94 % (16181)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_15863 for (2996ds/448Mi)
% 2.97/1.94 % (16182)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_15863 for (2996ds/46Mi)
% 2.97/1.96 % (16182)Instruction limit reached!
% 2.97/1.96 % (16182)------------------------------
% 2.97/1.96 % (16182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.96 % (16182)Termination reason: Unknown
% 2.97/1.96 % (16182)Termination phase: SInE selection
% 2.97/1.96
% 2.97/1.96 % (16182)Memory used [KB]: 1918
% 2.97/1.96 % (16182)Time elapsed: 0.017 s
% 2.97/1.96 % (16182)Instructions burned: 46 (million)
% 2.97/1.96 % (16182)------------------------------
% 2.97/1.96 % (16182)------------------------------
% 2.97/1.96 % (16152)Instruction limit reached!
% 2.97/1.96 % (16152)------------------------------
% 2.97/1.96 % (16152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.96 % (16152)Termination reason: Unknown
% 2.97/1.96 % (16152)Termination phase: Saturation
% 2.97/1.96
% 2.97/1.96 % (16152)Memory used [KB]: 10234
% 2.97/1.96 % (16152)Time elapsed: 0.322 s
% 2.97/1.96 % (16152)Instructions burned: 1041 (million)
% 2.97/1.96 % (16152)------------------------------
% 2.97/1.96 % (16152)------------------------------
% 2.97/1.97 % (16163)Instruction limit reached!
% 2.97/1.97 % (16163)------------------------------
% 2.97/1.97 % (16163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.97 % (16163)Termination reason: Unknown
% 2.97/1.97 % (16163)Termination phase: Saturation
% 2.97/1.97
% 2.97/1.97 % (16163)Memory used [KB]: 8699
% 2.97/1.97 % (16163)Time elapsed: 0.268 s
% 2.97/1.97 % (16163)Instructions burned: 903 (million)
% 2.97/1.97 % (16163)------------------------------
% 2.97/1.97 % (16163)------------------------------
% 2.97/1.97 % (16183)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_15863 for (2996ds/98Mi)
% 2.97/1.97 % (16184)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_15863 for (2996ds/507Mi)
% 2.97/1.98 % (16185)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_15863 for (2996ds/149Mi)
% 2.97/1.98 % (16161)Instruction limit reached!
% 2.97/1.98 % (16161)------------------------------
% 2.97/1.98 % (16161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.98 % (16161)Termination reason: Unknown
% 2.97/1.98 % (16161)Termination phase: Saturation
% 2.97/1.98
% 2.97/1.98 % (16161)Memory used [KB]: 8443
% 2.97/1.98 % (16161)Time elapsed: 0.279 s
% 2.97/1.98 % (16161)Instructions burned: 710 (million)
% 2.97/1.98 % (16161)------------------------------
% 2.97/1.98 % (16161)------------------------------
% 2.97/1.98 % (16168)Instruction limit reached!
% 2.97/1.98 % (16168)------------------------------
% 2.97/1.98 % (16168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.98 % (16168)Termination reason: Unknown
% 2.97/1.98 % (16168)Termination phase: Saturation
% 2.97/1.98
% 2.97/1.98 % (16168)Memory used [KB]: 9083
% 2.97/1.98 % (16168)Time elapsed: 0.259 s
% 2.97/1.98 % (16168)Instructions burned: 779 (million)
% 2.97/1.98 % (16168)------------------------------
% 2.97/1.98 % (16168)------------------------------
% 2.97/1.99 % (16186)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_15863 for (2996ds/39Mi)
% 2.97/1.99 % (16187)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_15863 for (2996ds/6Mi)
% 2.97/1.99 % (16187)Instruction limit reached!
% 2.97/1.99 % (16187)------------------------------
% 2.97/1.99 % (16187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.99 % (16187)Termination reason: Unknown
% 2.97/1.99 % (16187)Termination phase: shuffling
% 2.97/1.99
% 2.97/1.99 % (16187)Memory used [KB]: 1535
% 2.97/1.99 % (16187)Time elapsed: 0.004 s
% 2.97/1.99 % (16187)Instructions burned: 7 (million)
% 2.97/1.99 % (16187)------------------------------
% 2.97/1.99 % (16187)------------------------------
% 2.97/2.00 % (16183)Instruction limit reached!
% 2.97/2.00 % (16183)------------------------------
% 2.97/2.00 % (16183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/2.00 % (16183)Termination reason: Unknown
% 2.97/2.00 % (16183)Termination phase: Property scanning
% 2.97/2.00
% 2.97/2.00 % (16183)Memory used [KB]: 2686
% 2.97/2.00 % (16183)Time elapsed: 0.029 s
% 2.97/2.00 % (16183)Instructions burned: 99 (million)
% 2.97/2.00 % (16183)------------------------------
% 2.97/2.00 % (16183)------------------------------
% 2.97/2.00 % (16186)Instruction limit reached!
% 2.97/2.00 % (16186)------------------------------
% 2.97/2.00 % (16186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/2.00 % (16186)Termination reason: Unknown
% 2.97/2.00 % (16186)Termination phase: Property scanning
% 2.97/2.00
% 2.97/2.00 % (16186)Memory used [KB]: 1918
% 2.97/2.00 % (16186)Time elapsed: 0.015 s
% 2.97/2.00 % (16186)Instructions burned: 39 (million)
% 2.97/2.00 % (16186)------------------------------
% 2.97/2.00 % (16186)------------------------------
% 2.97/2.00 % (16188)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_15863 for (2995ds/1087Mi)
% 2.97/2.01 % (16189)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_15863 for (2995ds/47Mi)
% 2.97/2.01 % (16190)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_15863 for (2995ds/44Mi)
% 2.97/2.02 % (16185)Instruction limit reached!
% 2.97/2.02 % (16185)------------------------------
% 2.97/2.02 % (16185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/2.02 % (16185)Termination reason: Unknown
% 2.97/2.02 % (16185)Termination phase: Saturation
% 2.97/2.02
% 2.97/2.02 % (16185)Memory used [KB]: 7036
% 2.97/2.02 % (16185)Time elapsed: 0.043 s
% 2.97/2.02 % (16185)Instructions burned: 149 (million)
% 2.97/2.02 % (16185)------------------------------
% 2.97/2.02 % (16185)------------------------------
% 2.97/2.02 % (16170)Instruction limit reached!
% 2.97/2.02 % (16170)------------------------------
% 2.97/2.02 % (16170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/2.02 % (16170)Termination reason: Unknown
% 2.97/2.02 % (16170)Termination phase: Saturation
% 2.97/2.02
% 2.97/2.02 % (16170)Memory used [KB]: 8315
% 2.97/2.02 % (16170)Time elapsed: 0.281 s
% 2.97/2.02 % (16170)Instructions burned: 881 (million)
% 2.97/2.02 % (16170)------------------------------
% 2.97/2.02 % (16170)------------------------------
% 2.97/2.02 % (16189)Instruction limit reached!
% 2.97/2.02 % (16189)------------------------------
% 2.97/2.02 % (16189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/2.02 % (16189)Termination reason: Unknown
% 2.97/2.02 % (16189)Termination phase: Preprocessing 3
% 2.97/2.02
% 2.97/2.02 % (16189)Memory used [KB]: 2046
% 2.97/2.02 % (16189)Time elapsed: 0.016 s
% 2.97/2.02 % (16189)Instructions burned: 49 (million)
% 2.97/2.02 % (16189)------------------------------
% 2.97/2.02 % (16189)------------------------------
% 5.81/2.03 % (16190)Instruction limit reached!
% 5.81/2.03 % (16190)------------------------------
% 5.81/2.03 % (16190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.81/2.03 % (16190)Termination reason: Unknown
% 5.81/2.03 % (16190)Termination phase: Property scanning
% 5.81/2.03
% 5.81/2.03 % (16190)Memory used [KB]: 2302
% 5.81/2.03 % (16190)Time elapsed: 0.016 s
% 5.81/2.03 % (16190)Instructions burned: 47 (million)
% 5.81/2.03 % (16190)------------------------------
% 5.81/2.03 % (16190)------------------------------
% 5.81/2.03 % (16191)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_15863 for (2995ds/432Mi)
% 5.81/2.03 % (16193)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_15863 for (2995ds/31Mi)
% 5.81/2.03 % (16192)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_15863 for (2995ds/62Mi)
% 5.81/2.03 % (16184)Refutation not found, incomplete strategy
% 5.81/2.03 % (16184)------------------------------
% 5.81/2.03 % (16184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.81/2.03 % (16184)Termination reason: Refutation not found, incomplete strategy
% 5.81/2.03
% 5.81/2.03
% 5.81/2.03 % (16184)Memory used [KB]: 8443
% 5.81/2.03 % (16184)Time elapsed: 0.063 s
% 5.81/2.03 % (16184)Instructions burned: 209 (million)
% 5.81/2.03 % (16184)------------------------------
% 5.81/2.03 % (16184)------------------------------
% 5.81/2.04 % (16194)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_15863 for (2995ds/96Mi)
% 5.81/2.04 % (16193)Instruction limit reached!
% 5.81/2.04 % (16193)------------------------------
% 5.81/2.04 % (16193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.81/2.04 % (16193)Termination reason: Unknown
% 5.81/2.04 % (16193)Termination phase: Property scanning
% 5.81/2.04
% 5.81/2.04 % (16193)Memory used [KB]: 1918
% 5.81/2.04 % (16193)Time elapsed: 0.011 s
% 5.81/2.04 % (16193)Instructions burned: 31 (million)
% 5.81/2.04 % (16193)------------------------------
% 5.81/2.04 % (16193)------------------------------
% 5.81/2.04 % (16195)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_15863 for (2995ds/453Mi)
% 5.81/2.05 % (16196)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_15863 for (2995ds/71Mi)
% 5.81/2.05 % (16192)Instruction limit reached!
% 5.81/2.05 % (16192)------------------------------
% 5.81/2.05 % (16192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.81/2.05 % (16192)Termination reason: Unknown
% 5.81/2.05 % (16192)Termination phase: Property scanning
% 5.81/2.05
% 5.81/2.05 % (16192)Memory used [KB]: 2302
% 5.81/2.05 % (16192)Time elapsed: 0.021 s
% 5.81/2.05 % (16192)Instructions burned: 65 (million)
% 5.81/2.05 % (16192)------------------------------
% 5.81/2.05 % (16192)------------------------------
% 5.81/2.06 % (16197)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_15863 for (2995ds/83Mi)
% 5.81/2.07 % (16194)Instruction limit reached!
% 5.81/2.07 % (16194)------------------------------
% 5.81/2.07 % (16194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.81/2.07 % (16194)Termination reason: Unknown
% 5.81/2.07 % (16194)Termination phase: Property scanning
% 5.81/2.07
% 5.81/2.07 % (16194)Memory used [KB]: 2430
% 5.81/2.07 % (16194)Time elapsed: 0.033 s
% 5.81/2.07 % (16194)Instructions burned: 98 (million)
% 5.81/2.07 % (16194)------------------------------
% 5.81/2.07 % (16194)------------------------------
% 5.81/2.07 % (16196)Instruction limit reached!
% 5.81/2.07 % (16196)------------------------------
% 5.81/2.07 % (16196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.81/2.07 % (16196)Termination reason: Unknown
% 5.81/2.07 % (16196)Termination phase: Property scanning
% 5.81/2.07
% 5.81/2.07 % (16196)Memory used [KB]: 2302
% 5.81/2.07 % (16196)Time elapsed: 0.023 s
% 5.81/2.07 % (16196)Instructions burned: 73 (million)
% 5.81/2.07 % (16196)------------------------------
% 5.81/2.07 % (16196)------------------------------
% 5.81/2.08 % (16198)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_15863 for (2995ds/11Mi)
% 5.81/2.08 % (16198)Instruction limit reached!
% 5.81/2.08 % (16198)------------------------------
% 5.81/2.08 % (16198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.81/2.08 % (16198)Termination reason: Unknown
% 5.81/2.08 % (16198)Termination phase: shuffling
% 5.81/2.08
% 5.81/2.08 % (16198)Memory used [KB]: 1663
% 5.81/2.08 % (16198)Time elapsed: 0.005 s
% 5.81/2.08 % (16198)Instructions burned: 11 (million)
% 5.81/2.08 % (16198)------------------------------
% 5.81/2.08 % (16198)------------------------------
% 5.81/2.08 % (16199)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_15863 for (2995ds/41Mi)
% 5.81/2.08 % (16181)Instruction limit reached!
% 5.81/2.08 % (16181)------------------------------
% 5.81/2.08 % (16181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.81/2.08 % (16181)Termination reason: Unknown
% 5.81/2.08 % (16181)Termination phase: Saturation
% 5.81/2.08
% 5.81/2.08 % (16181)Memory used [KB]: 8827
% 5.81/2.08 % (16181)Time elapsed: 0.169 s
% 5.81/2.08 % (16181)Instructions burned: 448 (million)
% 5.81/2.08 % (16181)------------------------------
% 5.81/2.08 % (16181)------------------------------
% 5.81/2.09 % (16197)Instruction limit reached!
% 5.81/2.09 % (16197)------------------------------
% 5.81/2.09 % (16197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.81/2.09 % (16197)Termination reason: Unknown
% 5.81/2.09 % (16197)Termination phase: Property scanning
% 5.81/2.09
% 5.81/2.09 % (16197)Memory used [KB]: 2174
% 5.81/2.09 % (16197)Time elapsed: 0.029 s
% 5.81/2.09 % (16197)Instructions burned: 85 (million)
% 5.81/2.09 % (16197)------------------------------
% 5.81/2.09 % (16197)------------------------------
% 5.81/2.09 % (16200)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_15863 for (2995ds/6Mi)
% 5.81/2.09 % (16200)Instruction limit reached!
% 5.81/2.09 % (16200)------------------------------
% 5.81/2.09 % (16200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.81/2.09 % (16200)Termination reason: Unknown
% 5.81/2.09 % (16200)Termination phase: shuffling
% 5.81/2.09
% 5.81/2.09 % (16200)Memory used [KB]: 1535
% 5.81/2.09 % (16200)Time elapsed: 0.004 s
% 5.81/2.09 % (16200)Instructions burned: 6 (million)
% 5.81/2.09 % (16200)------------------------------
% 5.81/2.09 % (16200)------------------------------
% 5.81/2.09 % (16201)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_15863 for (2995ds/150Mi)
% 5.81/2.09 % (16199)Instruction limit reached!
% 5.81/2.09 % (16199)------------------------------
% 5.81/2.09 % (16199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.81/2.09 % (16199)Termination reason: Unknown
% 5.81/2.09 % (16199)Termination phase: shuffling
% 5.81/2.09
% 5.81/2.09 % (16199)Memory used [KB]: 2302
% 5.81/2.09 % (16199)Time elapsed: 0.013 s
% 5.81/2.09 % (16199)Instructions burned: 42 (million)
% 5.81/2.09 % (16199)------------------------------
% 5.81/2.09 % (16199)------------------------------
% 5.81/2.10 % (16202)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_15863 for (2995ds/343Mi)
% 5.81/2.10 % (16203)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_15863 for (2995ds/109Mi)
% 5.81/2.10 % (16204)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_15863 for (2995ds/253Mi)
% 6.28/2.14 % (16201)Instruction limit reached!
% 6.28/2.14 % (16201)------------------------------
% 6.28/2.14 % (16201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.14 % (16201)Termination reason: Unknown
% 6.28/2.14 % (16201)Termination phase: Saturation
% 6.28/2.14
% 6.28/2.14 % (16201)Memory used [KB]: 7164
% 6.28/2.14 % (16201)Time elapsed: 0.045 s
% 6.28/2.14 % (16201)Instructions burned: 150 (million)
% 6.28/2.14 % (16201)------------------------------
% 6.28/2.14 % (16201)------------------------------
% 6.28/2.14 % (16203)Instruction limit reached!
% 6.28/2.14 % (16203)------------------------------
% 6.28/2.14 % (16203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.14 % (16203)Termination reason: Unknown
% 6.28/2.14 % (16203)Termination phase: Property scanning
% 6.28/2.14
% 6.28/2.14 % (16203)Memory used [KB]: 2430
% 6.28/2.14 % (16203)Time elapsed: 0.037 s
% 6.28/2.14 % (16203)Instructions burned: 112 (million)
% 6.28/2.14 % (16203)------------------------------
% 6.28/2.14 % (16203)------------------------------
% 6.28/2.15 % (16205)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_15863 for (2994ds/140Mi)
% 6.28/2.15 % (16206)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_15863 for (2994ds/614Mi)
% 6.28/2.16 % (16191)Instruction limit reached!
% 6.28/2.16 % (16191)------------------------------
% 6.28/2.16 % (16191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.16 % (16191)Termination reason: Unknown
% 6.28/2.16 % (16191)Termination phase: Saturation
% 6.28/2.16
% 6.28/2.16 % (16191)Memory used [KB]: 3965
% 6.28/2.16 % (16191)Time elapsed: 0.133 s
% 6.28/2.16 % (16191)Instructions burned: 432 (million)
% 6.28/2.16 % (16191)------------------------------
% 6.28/2.16 % (16191)------------------------------
% 6.28/2.17 % (16207)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_15863 for (2994ds/202Mi)
% 6.28/2.17 % (16195)Instruction limit reached!
% 6.28/2.17 % (16195)------------------------------
% 6.28/2.17 % (16195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.17 % (16195)Termination reason: Unknown
% 6.28/2.17 % (16195)Termination phase: Saturation
% 6.28/2.17
% 6.28/2.17 % (16195)Memory used [KB]: 8699
% 6.28/2.17 % (16195)Time elapsed: 0.131 s
% 6.28/2.17 % (16195)Instructions burned: 454 (million)
% 6.28/2.17 % (16195)------------------------------
% 6.28/2.17 % (16195)------------------------------
% 6.28/2.18 % (16204)Instruction limit reached!
% 6.28/2.18 % (16204)------------------------------
% 6.28/2.18 % (16204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.18 % (16204)Termination reason: Unknown
% 6.28/2.18 % (16204)Termination phase: Saturation
% 6.28/2.18
% 6.28/2.18 % (16204)Memory used [KB]: 7931
% 6.28/2.18 % (16204)Time elapsed: 0.077 s
% 6.28/2.18 % (16204)Instructions burned: 253 (million)
% 6.28/2.18 % (16204)------------------------------
% 6.28/2.18 % (16204)------------------------------
% 6.28/2.18 % (16208)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_15863 for (2994ds/339Mi)
% 6.28/2.19 % (16209)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_15863 for (2994ds/283Mi)
% 6.28/2.19 % (16205)Instruction limit reached!
% 6.28/2.19 % (16205)------------------------------
% 6.28/2.19 % (16205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.19 % (16205)Termination reason: Unknown
% 6.28/2.19 % (16205)Termination phase: Saturation
% 6.28/2.19
% 6.28/2.19 % (16205)Memory used [KB]: 7291
% 6.28/2.19 % (16205)Time elapsed: 0.044 s
% 6.28/2.19 % (16205)Instructions burned: 140 (million)
% 6.28/2.19 % (16205)------------------------------
% 6.28/2.19 % (16205)------------------------------
% 6.87/2.20 % (16210)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_15863 for (2994ds/134Mi)
% 6.87/2.21 % (16202)Instruction limit reached!
% 6.87/2.21 % (16202)------------------------------
% 6.87/2.21 % (16202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.21 % (16202)Termination reason: Unknown
% 6.87/2.21 % (16202)Termination phase: Saturation
% 6.87/2.21
% 6.87/2.21 % (16202)Memory used [KB]: 8059
% 6.87/2.21 % (16202)Time elapsed: 0.110 s
% 6.87/2.21 % (16202)Instructions burned: 345 (million)
% 6.87/2.21 % (16202)------------------------------
% 6.87/2.21 % (16202)------------------------------
% 6.87/2.22 % (16211)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_15863 for (2993ds/298Mi)
% 6.87/2.23 % (16207)Instruction limit reached!
% 6.87/2.23 % (16207)------------------------------
% 6.87/2.23 % (16207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.23 % (16207)Termination reason: Unknown
% 6.87/2.23 % (16207)Termination phase: Saturation
% 6.87/2.23
% 6.87/2.23 % (16207)Memory used [KB]: 7931
% 6.87/2.23 % (16207)Time elapsed: 0.063 s
% 6.87/2.23 % (16207)Instructions burned: 204 (million)
% 6.87/2.23 % (16207)------------------------------
% 6.87/2.23 % (16207)------------------------------
% 6.87/2.24 % (16210)Instruction limit reached!
% 6.87/2.24 % (16210)------------------------------
% 6.87/2.24 % (16210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.24 % (16210)Termination reason: Unknown
% 6.87/2.24 % (16210)Termination phase: Saturation
% 6.87/2.24
% 6.87/2.24 % (16210)Memory used [KB]: 7036
% 6.87/2.24 % (16210)Time elapsed: 0.040 s
% 6.87/2.24 % (16210)Instructions burned: 135 (million)
% 6.87/2.24 % (16210)------------------------------
% 6.87/2.24 % (16210)------------------------------
% 6.87/2.24 % (16212)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_15863 for (2993ds/192Mi)
% 6.87/2.25 % (16213)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_15863 for (2993ds/258Mi)
% 6.87/2.27 % (16209)Instruction limit reached!
% 6.87/2.27 % (16209)------------------------------
% 6.87/2.27 % (16209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.27 % (16209)Termination reason: Unknown
% 6.87/2.27 % (16209)Termination phase: Saturation
% 6.87/2.27
% 6.87/2.27 % (16209)Memory used [KB]: 7675
% 6.87/2.27 % (16209)Time elapsed: 0.087 s
% 6.87/2.27 % (16209)Instructions burned: 284 (million)
% 6.87/2.27 % (16209)------------------------------
% 6.87/2.27 % (16209)------------------------------
% 6.87/2.28 % (16208)Instruction limit reached!
% 6.87/2.28 % (16208)------------------------------
% 6.87/2.28 % (16208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.28 % (16208)Termination reason: Unknown
% 6.87/2.28 % (16208)Termination phase: Saturation
% 6.87/2.28
% 6.87/2.28 % (16208)Memory used [KB]: 7291
% 6.87/2.28 % (16208)Time elapsed: 0.096 s
% 6.87/2.28 % (16208)Instructions burned: 339 (million)
% 6.87/2.28 % (16208)------------------------------
% 6.87/2.28 % (16208)------------------------------
% 6.87/2.28 % (16214)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_15863 for (2993ds/90Mi)
% 6.87/2.29 % (16215)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_15863 for (2993ds/231Mi)
% 7.41/2.30 % (16212)Instruction limit reached!
% 7.41/2.30 % (16212)------------------------------
% 7.41/2.30 % (16212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.30 % (16212)Termination reason: Unknown
% 7.41/2.30 % (16212)Termination phase: Saturation
% 7.41/2.30
% 7.41/2.30 % (16212)Memory used [KB]: 3326
% 7.41/2.30 % (16212)Time elapsed: 0.057 s
% 7.41/2.30 % (16212)Instructions burned: 194 (million)
% 7.41/2.30 % (16212)------------------------------
% 7.41/2.30 % (16212)------------------------------
% 7.41/2.30 % (16211)Instruction limit reached!
% 7.41/2.30 % (16211)------------------------------
% 7.41/2.30 % (16211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.30 % (16211)Termination reason: Unknown
% 7.41/2.30 % (16211)Termination phase: Saturation
% 7.41/2.30
% 7.41/2.30 % (16211)Memory used [KB]: 8699
% 7.41/2.30 % (16211)Time elapsed: 0.085 s
% 7.41/2.30 % (16211)Instructions burned: 301 (million)
% 7.41/2.30 % (16211)------------------------------
% 7.41/2.30 % (16211)------------------------------
% 7.41/2.31 % (16216)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_15863 for (2993ds/458Mi)
% 7.41/2.31 % (16217)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_15863 for (2993ds/31Mi)
% 7.41/2.31 % (16214)Instruction limit reached!
% 7.41/2.31 % (16214)------------------------------
% 7.41/2.31 % (16214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.31 % (16214)Termination reason: Unknown
% 7.41/2.31 % (16214)Termination phase: Property scanning
% 7.41/2.31
% 7.41/2.31 % (16214)Memory used [KB]: 2558
% 7.41/2.31 % (16214)Time elapsed: 0.029 s
% 7.41/2.31 % (16214)Instructions burned: 92 (million)
% 7.41/2.31 % (16214)------------------------------
% 7.41/2.31 % (16214)------------------------------
% 7.41/2.32 % (16206)Instruction limit reached!
% 7.41/2.32 % (16206)------------------------------
% 7.41/2.32 % (16206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.32 % (16206)Termination reason: Unknown
% 7.41/2.32 % (16206)Termination phase: Saturation
% 7.41/2.32
% 7.41/2.32 % (16206)Memory used [KB]: 8571
% 7.41/2.32 % (16206)Time elapsed: 0.173 s
% 7.41/2.32 % (16206)Instructions burned: 615 (million)
% 7.41/2.32 % (16206)------------------------------
% 7.41/2.32 % (16206)------------------------------
% 7.41/2.32 % (16217)Instruction limit reached!
% 7.41/2.32 % (16217)------------------------------
% 7.41/2.32 % (16217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.32 % (16217)Termination reason: Unknown
% 7.41/2.32 % (16217)Termination phase: Property scanning
% 7.41/2.32
% 7.41/2.32 % (16217)Memory used [KB]: 1918
% 7.41/2.32 % (16217)Time elapsed: 0.012 s
% 7.41/2.32 % (16217)Instructions burned: 32 (million)
% 7.41/2.32 % (16217)------------------------------
% 7.41/2.32 % (16217)------------------------------
% 7.41/2.32 % (16218)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_15863 for (2992ds/297Mi)
% 7.41/2.33 % (16213)Instruction limit reached!
% 7.41/2.33 % (16213)------------------------------
% 7.41/2.33 % (16213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.33 % (16213)Termination reason: Unknown
% 7.41/2.33 % (16213)Termination phase: Saturation
% 7.41/2.33
% 7.41/2.33 % (16213)Memory used [KB]: 8315
% 7.41/2.33 % (16213)Time elapsed: 0.079 s
% 7.41/2.33 % (16213)Instructions burned: 260 (million)
% 7.41/2.33 % (16213)------------------------------
% 7.41/2.33 % (16213)------------------------------
% 7.41/2.33 % (16219)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_15863 for (2992ds/987Mi)
% 7.41/2.33 % (16220)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_15863 for (2992ds/182Mi)
% 7.41/2.33 % (16221)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_15863 for (2992ds/182Mi)
% 7.41/2.35 % (16188)Instruction limit reached!
% 7.41/2.35 % (16188)------------------------------
% 7.41/2.35 % (16188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.35 % (16188)Termination reason: Unknown
% 7.41/2.35 % (16188)Termination phase: Saturation
% 7.41/2.35
% 7.41/2.35 % (16188)Memory used [KB]: 8443
% 7.41/2.35 % (16188)Time elapsed: 0.347 s
% 7.41/2.35 % (16188)Instructions burned: 1087 (million)
% 7.41/2.35 % (16188)------------------------------
% 7.41/2.35 % (16188)------------------------------
% 7.41/2.35 % (16215)Instruction limit reached!
% 7.41/2.35 % (16215)------------------------------
% 7.41/2.35 % (16215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.35 % (16215)Termination reason: Unknown
% 7.41/2.35 % (16215)Termination phase: Saturation
% 7.41/2.35
% 7.41/2.35 % (16215)Memory used [KB]: 7547
% 7.41/2.35 % (16215)Time elapsed: 0.066 s
% 7.41/2.35 % (16215)Instructions burned: 232 (million)
% 7.41/2.35 % (16215)------------------------------
% 7.41/2.35 % (16215)------------------------------
% 7.41/2.36 % (16222)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_15863 for (2992ds/154Mi)
% 7.41/2.36 % (16223)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_15863 for (2992ds/79Mi)
% 7.41/2.38 % (16220)Instruction limit reached!
% 7.41/2.38 % (16220)------------------------------
% 7.41/2.38 % (16220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.38 % (16220)Termination reason: Unknown
% 7.41/2.38 % (16220)Termination phase: Saturation
% 7.41/2.38
% 7.41/2.38 % (16220)Memory used [KB]: 7164
% 7.41/2.38 % (16220)Time elapsed: 0.053 s
% 7.41/2.38 % (16220)Instructions burned: 182 (million)
% 7.41/2.38 % (16220)------------------------------
% 7.41/2.38 % (16220)------------------------------
% 7.41/2.39 % (16223)Instruction limit reached!
% 7.41/2.39 % (16223)------------------------------
% 7.41/2.39 % (16223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.39 % (16223)Termination reason: Unknown
% 7.41/2.39 % (16223)Termination phase: Function definition elimination
% 7.41/2.39
% 7.41/2.39 % (16223)Memory used [KB]: 2430
% 7.41/2.39 % (16223)Time elapsed: 0.026 s
% 7.41/2.39 % (16223)Instructions burned: 81 (million)
% 7.41/2.39 % (16223)------------------------------
% 7.41/2.39 % (16223)------------------------------
% 7.41/2.39 % (16224)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_15863 for (2992ds/216Mi)
% 7.41/2.39 % (16221)Instruction limit reached!
% 7.41/2.39 % (16221)------------------------------
% 7.41/2.39 % (16221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.39 % (16221)Termination reason: Unknown
% 7.41/2.39 % (16221)Termination phase: Saturation
% 7.41/2.39
% 7.41/2.39 % (16221)Memory used [KB]: 7419
% 7.41/2.39 % (16221)Time elapsed: 0.081 s
% 7.41/2.39 % (16221)Instructions burned: 184 (million)
% 7.41/2.39 % (16221)------------------------------
% 7.41/2.39 % (16221)------------------------------
% 8.20/2.40 % (16225)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_15863 for (2992ds/114Mi)
% 8.20/2.40 % (16222)Instruction limit reached!
% 8.20/2.40 % (16222)------------------------------
% 8.20/2.40 % (16222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.20/2.40 % (16222)Termination reason: Unknown
% 8.20/2.40 % (16222)Termination phase: Saturation
% 8.20/2.40
% 8.20/2.40 % (16222)Memory used [KB]: 2814
% 8.20/2.40 % (16222)Time elapsed: 0.044 s
% 8.20/2.40 % (16222)Instructions burned: 155 (million)
% 8.20/2.40 % (16222)------------------------------
% 8.20/2.40 % (16222)------------------------------
% 8.20/2.40 % (16226)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_15863 for (2991ds/922Mi)
% 8.20/2.41 % (16218)Instruction limit reached!
% 8.20/2.41 % (16218)------------------------------
% 8.20/2.41 % (16218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.20/2.41 % (16218)Termination reason: Unknown
% 8.20/2.41 % (16218)Termination phase: Saturation
% 8.20/2.41
% 8.20/2.41 % (16218)Memory used [KB]: 7675
% 8.20/2.41 % (16218)Time elapsed: 0.109 s
% 8.20/2.41 % (16218)Instructions burned: 298 (million)
% 8.20/2.41 % (16218)------------------------------
% 8.20/2.41 % (16218)------------------------------
% 8.20/2.41 % (16227)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_15863 for (2991ds/182Mi)
% 8.20/2.42 % (16228)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_15863 for (2991ds/164Mi)
% 8.20/2.43 % (16225)Instruction limit reached!
% 8.20/2.43 % (16225)------------------------------
% 8.20/2.43 % (16225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.20/2.43 % (16225)Termination reason: Unknown
% 8.20/2.43 % (16225)Termination phase: Saturation
% 8.20/2.43
% 8.20/2.43 % (16225)Memory used [KB]: 6908
% 8.20/2.43 % (16225)Time elapsed: 0.034 s
% 8.20/2.43 % (16225)Instructions burned: 114 (million)
% 8.20/2.43 % (16225)------------------------------
% 8.20/2.43 % (16225)------------------------------
% 8.20/2.44 % (16216)Instruction limit reached!
% 8.20/2.44 % (16216)------------------------------
% 8.20/2.44 % (16216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.20/2.44 % (16216)Termination reason: Unknown
% 8.20/2.44 % (16216)Termination phase: Saturation
% 8.20/2.44
% 8.20/2.44 % (16216)Memory used [KB]: 7931
% 8.20/2.44 % (16216)Time elapsed: 0.131 s
% 8.20/2.44 % (16216)Instructions burned: 459 (million)
% 8.20/2.44 % (16216)------------------------------
% 8.20/2.44 % (16216)------------------------------
% 8.20/2.44 % (16229)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_15863 for (2991ds/50Mi)
% 8.20/2.45 % (16230)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_15863 for (2991ds/368Mi)
% 8.20/2.45 % (16224)Instruction limit reached!
% 8.20/2.45 % (16224)------------------------------
% 8.20/2.45 % (16224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.20/2.45 % (16224)Termination reason: Unknown
% 8.20/2.45 % (16224)Termination phase: Saturation
% 8.20/2.45
% 8.20/2.45 % (16224)Memory used [KB]: 7547
% 8.20/2.45 % (16224)Time elapsed: 0.061 s
% 8.20/2.45 % (16224)Instructions burned: 216 (million)
% 8.20/2.45 % (16224)------------------------------
% 8.20/2.45 % (16224)------------------------------
% 8.20/2.45 % (16229)Instruction limit reached!
% 8.20/2.45 % (16229)------------------------------
% 8.20/2.45 % (16229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.20/2.45 % (16229)Termination reason: Unknown
% 8.20/2.45 % (16229)Termination phase: Property scanning
% 8.20/2.45
% 8.20/2.45 % (16229)Memory used [KB]: 2302
% 8.20/2.45 % (16229)Time elapsed: 0.015 s
% 8.20/2.45 % (16229)Instructions burned: 51 (million)
% 8.20/2.45 % (16229)------------------------------
% 8.20/2.45 % (16229)------------------------------
% 8.20/2.46 % (16231)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_15863 for (2991ds/1021Mi)
% 8.20/2.46 % (16227)Instruction limit reached!
% 8.20/2.46 % (16227)------------------------------
% 8.20/2.46 % (16227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.20/2.46 % (16227)Termination reason: Unknown
% 8.20/2.46 % (16227)Termination phase: Saturation
% 8.20/2.46
% 8.20/2.46 % (16227)Memory used [KB]: 7291
% 8.20/2.46 % (16227)Time elapsed: 0.051 s
% 8.20/2.46 % (16227)Instructions burned: 182 (million)
% 8.20/2.46 % (16227)------------------------------
% 8.20/2.46 % (16227)------------------------------
% 8.20/2.46 % (16232)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_15863 for (2991ds/267Mi)
% 8.20/2.46 % (16228)Instruction limit reached!
% 8.20/2.46 % (16228)------------------------------
% 8.20/2.46 % (16228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.20/2.46 % (16228)Termination reason: Unknown
% 8.20/2.46 % (16228)Termination phase: Saturation
% 8.20/2.46
% 8.20/2.46 % (16228)Memory used [KB]: 2686
% 8.20/2.46 % (16228)Time elapsed: 0.047 s
% 8.20/2.46 % (16228)Instructions burned: 164 (million)
% 8.20/2.46 % (16228)------------------------------
% 8.20/2.46 % (16228)------------------------------
% 8.20/2.47 % (16233)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_15863 for (2991ds/204Mi)
% 8.20/2.47 % (16234)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_15863 for (2991ds/26Mi)
% 8.20/2.48 % (16234)Instruction limit reached!
% 8.20/2.48 % (16234)------------------------------
% 8.20/2.48 % (16234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.20/2.48 % (16234)Termination reason: Unknown
% 8.20/2.48 % (16234)Termination phase: shuffling
% 8.20/2.48
% 8.20/2.48 % (16234)Memory used [KB]: 2046
% 8.20/2.48 % (16234)Time elapsed: 0.009 s
% 8.20/2.48 % (16234)Instructions burned: 26 (million)
% 8.20/2.48 % (16234)------------------------------
% 8.20/2.48 % (16234)------------------------------
% 8.20/2.49 % (16235)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_15863 for (2991ds/53Mi)
% 8.76/2.51 % (16235)Instruction limit reached!
% 8.76/2.51 % (16235)------------------------------
% 8.76/2.51 % (16235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.76/2.51 % (16235)Termination reason: Unknown
% 8.76/2.51 % (16235)Termination phase: Property scanning
% 8.76/2.51
% 8.76/2.51 % (16235)Memory used [KB]: 2302
% 8.76/2.51 % (16235)Time elapsed: 0.016 s
% 8.76/2.51 % (16235)Instructions burned: 56 (million)
% 8.76/2.51 % (16235)------------------------------
% 8.76/2.51 % (16235)------------------------------
% 8.76/2.52 % (16236)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_15863 for (2990ds/4436Mi)
% 8.76/2.53 % (16233)Instruction limit reached!
% 8.76/2.53 % (16233)------------------------------
% 8.76/2.53 % (16233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.76/2.53 % (16233)Termination reason: Unknown
% 8.76/2.53 % (16233)Termination phase: Saturation
% 8.76/2.53
% 8.76/2.53 % (16233)Memory used [KB]: 7036
% 8.76/2.53 % (16233)Time elapsed: 0.060 s
% 8.76/2.53 % (16233)Instructions burned: 207 (million)
% 8.76/2.53 % (16233)------------------------------
% 8.76/2.53 % (16233)------------------------------
% 8.76/2.54 % (16237)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_15863 for (2990ds/1539Mi)
% 8.76/2.54 % (16232)Instruction limit reached!
% 8.76/2.54 % (16232)------------------------------
% 8.76/2.54 % (16232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.76/2.54 % (16232)Termination reason: Unknown
% 8.76/2.54 % (16232)Termination phase: Saturation
% 8.76/2.54
% 8.76/2.54 % (16232)Memory used [KB]: 7675
% 8.76/2.54 % (16232)Time elapsed: 0.082 s
% 8.76/2.54 % (16232)Instructions burned: 267 (million)
% 8.76/2.54 % (16232)------------------------------
% 8.76/2.54 % (16232)------------------------------
% 8.76/2.55 % (16230)Instruction limit reached!
% 8.76/2.55 % (16230)------------------------------
% 8.76/2.55 % (16230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.76/2.55 % (16230)Termination reason: Unknown
% 8.76/2.55 % (16230)Termination phase: Saturation
% 8.76/2.55
% 8.76/2.55 % (16230)Memory used [KB]: 7675
% 8.76/2.55 % (16230)Time elapsed: 0.104 s
% 8.76/2.55 % (16230)Instructions burned: 370 (million)
% 8.76/2.55 % (16230)------------------------------
% 8.76/2.55 % (16230)------------------------------
% 8.76/2.55 % (16238)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_15863 for (2990ds/408Mi)
% 8.76/2.56 % (16239)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_15863 for (2990ds/5205Mi)
% 9.06/2.61 % (16238)Refutation not found, incomplete strategy
% 9.06/2.61 % (16238)------------------------------
% 9.06/2.61 % (16238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.06/2.61 % (16238)Termination reason: Refutation not found, incomplete strategy
% 9.06/2.61
% 9.06/2.61
% 9.06/2.61 % (16238)Memory used [KB]: 7803
% 9.06/2.61 % (16238)Time elapsed: 0.057 s
% 9.06/2.61 % (16238)Instructions burned: 179 (million)
% 9.06/2.61 % (16238)------------------------------
% 9.06/2.61 % (16238)------------------------------
% 9.06/2.62 % (16240)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_15863 for (2989ds/1913Mi)
% 9.06/2.63 % (16219)Instruction limit reached!
% 9.06/2.63 % (16219)------------------------------
% 9.06/2.63 % (16219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.06/2.63 % (16219)Termination reason: Unknown
% 9.06/2.63 % (16219)Termination phase: Saturation
% 9.06/2.63
% 9.06/2.63 % (16219)Memory used [KB]: 9850
% 9.06/2.63 % (16219)Time elapsed: 0.326 s
% 9.06/2.63 % (16219)Instructions burned: 989 (million)
% 9.06/2.63 % (16219)------------------------------
% 9.06/2.63 % (16219)------------------------------
% 9.06/2.64 % (16241)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_15863 for (2989ds/4350Mi)
% 9.06/2.69 % (16226)Instruction limit reached!
% 9.06/2.69 % (16226)------------------------------
% 9.06/2.69 % (16226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.06/2.69 % (16226)Termination reason: Unknown
% 9.06/2.69 % (16226)Termination phase: Saturation
% 9.06/2.69
% 9.06/2.69 % (16226)Memory used [KB]: 8059
% 9.06/2.69 % (16226)Time elapsed: 0.291 s
% 9.06/2.69 % (16226)Instructions burned: 923 (million)
% 9.06/2.69 % (16226)------------------------------
% 9.06/2.69 % (16226)------------------------------
% 9.74/2.70 % (16242)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_15863 for (2989ds/68Mi)
% 9.74/2.72 % (16242)Instruction limit reached!
% 9.74/2.72 % (16242)------------------------------
% 9.74/2.72 % (16242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.74/2.72 % (16242)Termination reason: Unknown
% 9.74/2.72 % (16242)Termination phase: Property scanning
% 9.74/2.72
% 9.74/2.72 % (16242)Memory used [KB]: 2174
% 9.74/2.72 % (16242)Time elapsed: 0.023 s
% 9.74/2.72 % (16242)Instructions burned: 71 (million)
% 9.74/2.72 % (16242)------------------------------
% 9.74/2.72 % (16242)------------------------------
% 9.74/2.73 % (16243)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_15863 for (2988ds/358Mi)
% 9.74/2.77 % (16231)Instruction limit reached!
% 9.74/2.77 % (16231)------------------------------
% 9.74/2.77 % (16231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.74/2.77 % (16231)Termination reason: Unknown
% 9.74/2.77 % (16231)Termination phase: Saturation
% 9.74/2.77
% 9.74/2.77 % (16231)Memory used [KB]: 9594
% 9.74/2.77 % (16231)Time elapsed: 0.307 s
% 9.74/2.77 % (16231)Instructions burned: 1021 (million)
% 9.74/2.77 % (16231)------------------------------
% 9.74/2.77 % (16231)------------------------------
% 9.74/2.78 % (16244)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_15863 for (2988ds/31Mi)
% 9.74/2.79 % (16244)Instruction limit reached!
% 9.74/2.79 % (16244)------------------------------
% 9.74/2.79 % (16244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.74/2.79 % (16244)Termination reason: Unknown
% 9.74/2.79 % (16244)Termination phase: Property scanning
% 9.74/2.79
% 9.74/2.79 % (16244)Memory used [KB]: 1918
% 9.74/2.79 % (16244)Time elapsed: 0.012 s
% 9.74/2.79 % (16244)Instructions burned: 31 (million)
% 9.74/2.79 % (16244)------------------------------
% 9.74/2.79 % (16244)------------------------------
% 10.12/2.80 % (16245)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_15863 for (2988ds/279Mi)
% 10.12/2.85 % (16243)Instruction limit reached!
% 10.12/2.85 % (16243)------------------------------
% 10.12/2.85 % (16243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.12/2.85 % (16243)Termination reason: Unknown
% 10.12/2.85 % (16243)Termination phase: Saturation
% 10.12/2.85
% 10.12/2.85 % (16243)Memory used [KB]: 7931
% 10.12/2.85 % (16243)Time elapsed: 0.112 s
% 10.12/2.85 % (16243)Instructions burned: 358 (million)
% 10.12/2.85 % (16243)------------------------------
% 10.12/2.85 % (16243)------------------------------
% 10.12/2.85 % (16245)Refutation not found, incomplete strategy
% 10.12/2.85 % (16245)------------------------------
% 10.12/2.85 % (16245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.12/2.85 % (16245)Termination reason: Refutation not found, incomplete strategy
% 10.12/2.85
% 10.12/2.85
% 10.12/2.85 % (16245)Memory used [KB]: 7547
% 10.12/2.85 % (16245)Time elapsed: 0.050 s
% 10.12/2.85 % (16245)Instructions burned: 178 (million)
% 10.12/2.85 % (16245)------------------------------
% 10.12/2.85 % (16245)------------------------------
% 10.12/2.86 % (16246)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_15863 for (2987ds/258Mi)
% 10.12/2.86 % (16247)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_15863 for (2987ds/26Mi)
% 10.12/2.86 % (16247)Instruction limit reached!
% 10.12/2.86 % (16247)------------------------------
% 10.12/2.86 % (16247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.12/2.86 % (16247)Termination reason: Unknown
% 10.12/2.86 % (16247)Termination phase: shuffling
% 10.12/2.86
% 10.12/2.86 % (16247)Memory used [KB]: 2046
% 10.12/2.86 % (16247)Time elapsed: 0.009 s
% 10.12/2.86 % (16247)Instructions burned: 27 (million)
% 10.12/2.86 % (16247)------------------------------
% 10.12/2.86 % (16247)------------------------------
% 10.12/2.87 % (16248)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_15863 for (2987ds/995Mi)
% 10.31/2.93 % (16246)Instruction limit reached!
% 10.31/2.93 % (16246)------------------------------
% 10.31/2.93 % (16246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.31/2.93 % (16246)Termination reason: Unknown
% 10.31/2.93 % (16246)Termination phase: Saturation
% 10.31/2.93
% 10.31/2.93 % (16246)Memory used [KB]: 7803
% 10.31/2.93 % (16246)Time elapsed: 0.080 s
% 10.31/2.93 % (16246)Instructions burned: 259 (million)
% 10.31/2.93 % (16246)------------------------------
% 10.31/2.93 % (16246)------------------------------
% 10.31/2.94 % (16249)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_15863 for (2986ds/373Mi)
% 10.31/3.01 % (16237)Instruction limit reached!
% 10.31/3.01 % (16237)------------------------------
% 10.31/3.01 % (16237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.31/3.01 % (16237)Termination reason: Unknown
% 10.31/3.01 % (16237)Termination phase: Saturation
% 10.31/3.01
% 10.31/3.01 % (16237)Memory used [KB]: 12665
% 10.31/3.01 % (16237)Time elapsed: 0.470 s
% 10.31/3.01 % (16237)Instructions burned: 1540 (million)
% 10.31/3.01 % (16237)------------------------------
% 10.31/3.01 % (16237)------------------------------
% 10.31/3.02 % (16250)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_15863 for (2985ds/253Mi)
% 12.86/3.05 % (16249)Instruction limit reached!
% 12.86/3.05 % (16249)------------------------------
% 12.86/3.05 % (16249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.86/3.05 % (16249)Termination reason: Unknown
% 12.86/3.05 % (16249)Termination phase: Saturation
% 12.86/3.05
% 12.86/3.05 % (16249)Memory used [KB]: 7675
% 12.86/3.05 % (16249)Time elapsed: 0.107 s
% 12.86/3.05 % (16249)Instructions burned: 373 (million)
% 12.86/3.05 % (16249)------------------------------
% 12.86/3.05 % (16249)------------------------------
% 12.86/3.06 % (16251)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_15863 for (2985ds/832Mi)
% 12.86/3.09 % (16250)Instruction limit reached!
% 12.86/3.09 % (16250)------------------------------
% 12.86/3.09 % (16250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.86/3.09 % (16250)Termination reason: Unknown
% 12.86/3.09 % (16250)Termination phase: Saturation
% 12.86/3.09
% 12.86/3.09 % (16250)Memory used [KB]: 7675
% 12.86/3.09 % (16250)Time elapsed: 0.073 s
% 12.86/3.09 % (16250)Instructions burned: 255 (million)
% 12.86/3.09 % (16250)------------------------------
% 12.86/3.09 % (16250)------------------------------
% 12.86/3.10 % (16252)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_15863 for (2985ds/668Mi)
% 13.51/3.17 % (16248)Instruction limit reached!
% 13.51/3.17 % (16248)------------------------------
% 13.51/3.17 % (16248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.51/3.17 % (16248)Termination reason: Unknown
% 13.51/3.17 % (16248)Termination phase: Saturation
% 13.51/3.17
% 13.51/3.17 % (16248)Memory used [KB]: 10106
% 13.51/3.17 % (16248)Time elapsed: 0.298 s
% 13.51/3.17 % (16248)Instructions burned: 997 (million)
% 13.51/3.17 % (16248)------------------------------
% 13.51/3.17 % (16248)------------------------------
% 13.51/3.18 % (16253)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_15863 for (2984ds/40Mi)
% 13.51/3.19 % (16253)Instruction limit reached!
% 13.51/3.19 % (16253)------------------------------
% 13.51/3.19 % (16253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.51/3.19 % (16253)Termination reason: Unknown
% 13.51/3.19 % (16253)Termination phase: shuffling
% 13.51/3.19
% 13.51/3.19 % (16253)Memory used [KB]: 2302
% 13.51/3.19 % (16253)Time elapsed: 0.013 s
% 13.51/3.19 % (16253)Instructions burned: 42 (million)
% 13.51/3.19 % (16253)------------------------------
% 13.51/3.19 % (16253)------------------------------
% 13.86/3.20 % (16254)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_15863 for (2983ds/294Mi)
% 13.86/3.22 % (16240)Instruction limit reached!
% 13.86/3.22 % (16240)------------------------------
% 13.86/3.22 % (16240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.86/3.22 % (16240)Termination reason: Unknown
% 13.86/3.22 % (16240)Termination phase: Saturation
% 13.86/3.22
% 13.86/3.22 % (16240)Memory used [KB]: 4477
% 13.86/3.22 % (16240)Time elapsed: 0.599 s
% 13.86/3.22 % (16240)Instructions burned: 1915 (million)
% 13.86/3.22 % (16240)------------------------------
% 13.86/3.22 % (16240)------------------------------
% 13.86/3.23 % (16255)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_15863 for (2983ds/187Mi)
% 13.86/3.25 % (16254)Refutation not found, incomplete strategy
% 13.86/3.25 % (16254)------------------------------
% 13.86/3.25 % (16254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.86/3.25 % (16254)Termination reason: Refutation not found, incomplete strategy
% 13.86/3.25
% 13.86/3.25
% 13.86/3.25 % (16254)Memory used [KB]: 7547
% 13.86/3.25 % (16254)Time elapsed: 0.049 s
% 13.86/3.25 % (16254)Instructions burned: 173 (million)
% 13.86/3.25 % (16254)------------------------------
% 13.86/3.25 % (16254)------------------------------
% 13.86/3.26 % (16256)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_15863 for (2983ds/371Mi)
% 13.86/3.28 % (16255)Instruction limit reached!
% 13.86/3.28 % (16255)------------------------------
% 13.86/3.28 % (16255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.86/3.28 % (16255)Termination reason: Unknown
% 13.86/3.28 % (16255)Termination phase: Saturation
% 13.86/3.28
% 13.86/3.28 % (16255)Memory used [KB]: 7164
% 13.86/3.28 % (16255)Time elapsed: 0.055 s
% 13.86/3.28 % (16255)Instructions burned: 187 (million)
% 13.86/3.28 % (16255)------------------------------
% 13.86/3.28 % (16255)------------------------------
% 13.86/3.29 % (16257)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_15863 for (2983ds/1827Mi)
% 14.31/3.30 % (16252)Instruction limit reached!
% 14.31/3.30 % (16252)------------------------------
% 14.31/3.30 % (16252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.31/3.30 % (16252)Termination reason: Unknown
% 14.31/3.30 % (16252)Termination phase: Saturation
% 14.31/3.30
% 14.31/3.30 % (16252)Memory used [KB]: 14328
% 14.31/3.30 % (16252)Time elapsed: 0.200 s
% 14.31/3.30 % (16252)Instructions burned: 670 (million)
% 14.31/3.30 % (16252)------------------------------
% 14.31/3.30 % (16252)------------------------------
% 14.31/3.31 % (16258)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_15863 for (2982ds/70Mi)
% 14.31/3.32 % (16251)Instruction limit reached!
% 14.31/3.32 % (16251)------------------------------
% 14.31/3.32 % (16251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.31/3.32 % (16251)Termination reason: Unknown
% 14.31/3.32 % (16251)Termination phase: Saturation
% 14.31/3.32
% 14.31/3.32 % (16251)Memory used [KB]: 8443
% 14.31/3.32 % (16251)Time elapsed: 0.261 s
% 14.31/3.32 % (16251)Instructions burned: 832 (million)
% 14.31/3.32 % (16251)------------------------------
% 14.31/3.32 % (16251)------------------------------
% 14.31/3.33 % (16258)Instruction limit reached!
% 14.31/3.33 % (16258)------------------------------
% 14.31/3.33 % (16258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.31/3.33 % (16258)Termination reason: Unknown
% 14.31/3.33 % (16258)Termination phase: Preprocessing 1
% 14.31/3.33
% 14.31/3.33 % (16258)Memory used [KB]: 2302
% 14.31/3.33 % (16258)Time elapsed: 0.020 s
% 14.31/3.33 % (16258)Instructions burned: 70 (million)
% 14.31/3.33 % (16258)------------------------------
% 14.31/3.33 % (16258)------------------------------
% 14.31/3.33 % (16259)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_15863 for (2982ds/316Mi)
% 14.31/3.34 % (16260)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_15863 for (2982ds/932Mi)
% 14.31/3.38 % (16256)Instruction limit reached!
% 14.31/3.38 % (16256)------------------------------
% 14.31/3.38 % (16256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.31/3.38 % (16256)Termination reason: Unknown
% 14.31/3.38 % (16256)Termination phase: Saturation
% 14.31/3.38
% 14.31/3.38 % (16256)Memory used [KB]: 8571
% 14.31/3.38 % (16256)Time elapsed: 0.121 s
% 14.31/3.38 % (16256)Instructions burned: 372 (million)
% 14.31/3.38 % (16256)------------------------------
% 14.31/3.38 % (16256)------------------------------
% 14.31/3.39 % (16261)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_15863 for (2982ds/4714Mi)
% 14.31/3.39 % (16259)Refutation not found, incomplete strategy
% 14.31/3.39 % (16259)------------------------------
% 14.31/3.39 % (16259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.31/3.39 % (16259)Termination reason: Refutation not found, incomplete strategy
% 14.31/3.39
% 14.31/3.39
% 14.31/3.39 % (16259)Memory used [KB]: 7803
% 14.31/3.39 % (16259)Time elapsed: 0.064 s
% 14.31/3.39 % (16259)Instructions burned: 226 (million)
% 14.31/3.39 % (16259)------------------------------
% 14.31/3.39 % (16259)------------------------------
% 15.32/3.40 % (16262)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_15863 for (2982ds/8250Mi)
% 15.32/3.46 % (16261)Refutation not found, incomplete strategy
% 15.32/3.46 % (16261)------------------------------
% 15.32/3.46 % (16261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.32/3.46 % (16261)Termination reason: Refutation not found, incomplete strategy
% 15.32/3.46
% 15.32/3.46
% 15.32/3.46 % (16261)Memory used [KB]: 7931
% 15.32/3.46 % (16261)Time elapsed: 0.072 s
% 15.32/3.46 % (16261)Instructions burned: 252 (million)
% 15.32/3.46 % (16261)------------------------------
% 15.32/3.46 % (16261)------------------------------
% 15.32/3.47 % (16263)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_15863 for (2981ds/770Mi)
% 15.71/3.51 % (16263)Refutation not found, incomplete strategy
% 15.71/3.51 % (16263)------------------------------
% 15.71/3.51 % (16263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.71/3.51 % (16263)Termination reason: Refutation not found, incomplete strategy
% 15.71/3.51
% 15.71/3.51
% 15.71/3.51 % (16263)Memory used [KB]: 7547
% 15.71/3.51 % (16263)Time elapsed: 0.037 s
% 15.71/3.51 % (16263)Instructions burned: 114 (million)
% 15.71/3.51 % (16263)------------------------------
% 15.71/3.51 % (16263)------------------------------
% 15.71/3.52 % (16264)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_15863 for (2980ds/794Mi)
% 16.06/3.62 % (16260)Instruction limit reached!
% 16.06/3.62 % (16260)------------------------------
% 16.06/3.62 % (16260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.06/3.62 % (16260)Termination reason: Unknown
% 16.06/3.62 % (16260)Termination phase: Saturation
% 16.06/3.62
% 16.06/3.62 % (16260)Memory used [KB]: 9978
% 16.06/3.62 % (16260)Time elapsed: 0.283 s
% 16.06/3.62 % (16260)Instructions burned: 932 (million)
% 16.06/3.62 % (16260)------------------------------
% 16.06/3.62 % (16260)------------------------------
% 16.06/3.63 % (16265)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_15863 for (2979ds/464Mi)
% 16.65/3.75 % (16264)Instruction limit reached!
% 16.65/3.75 % (16264)------------------------------
% 16.65/3.75 % (16264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.65/3.75 % (16264)Termination reason: Unknown
% 16.65/3.75 % (16264)Termination phase: Saturation
% 16.65/3.75
% 16.65/3.75 % (16264)Memory used [KB]: 4733
% 16.65/3.75 % (16264)Time elapsed: 0.233 s
% 16.65/3.75 % (16264)Instructions burned: 796 (million)
% 16.65/3.75 % (16264)------------------------------
% 16.65/3.75 % (16264)------------------------------
% 16.65/3.76 % (16266)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_15863 for (2978ds/1376Mi)
% 16.65/3.76 % (16265)Instruction limit reached!
% 16.65/3.76 % (16265)------------------------------
% 16.65/3.76 % (16265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.65/3.76 % (16265)Termination reason: Unknown
% 16.65/3.76 % (16265)Termination phase: Saturation
% 16.65/3.76
% 16.65/3.76 % (16265)Memory used [KB]: 7291
% 16.65/3.76 % (16265)Time elapsed: 0.134 s
% 16.65/3.76 % (16265)Instructions burned: 465 (million)
% 16.65/3.76 % (16265)------------------------------
% 16.65/3.76 % (16265)------------------------------
% 16.65/3.77 % (16267)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_15863 for (2978ds/906Mi)
% 17.33/3.85 % (16236)Instruction limit reached!
% 17.33/3.85 % (16236)------------------------------
% 17.33/3.85 % (16236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.33/3.85 % (16236)Termination reason: Unknown
% 17.33/3.85 % (16236)Termination phase: Saturation
% 17.33/3.85
% 17.33/3.85 % (16236)Memory used [KB]: 11385
% 17.33/3.85 % (16236)Time elapsed: 1.331 s
% 17.33/3.85 % (16236)Instructions burned: 4438 (million)
% 17.33/3.85 % (16236)------------------------------
% 17.33/3.85 % (16236)------------------------------
% 17.33/3.86 % (16268)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_15863 for (2977ds/434Mi)
% 17.33/3.86 % (16257)Instruction limit reached!
% 17.33/3.86 % (16257)------------------------------
% 17.33/3.86 % (16257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.33/3.86 % (16257)Termination reason: Unknown
% 17.33/3.86 % (16257)Termination phase: Saturation
% 17.33/3.86
% 17.33/3.86 % (16257)Memory used [KB]: 10874
% 17.33/3.86 % (16257)Time elapsed: 0.566 s
% 17.33/3.86 % (16257)Instructions burned: 1828 (million)
% 17.33/3.86 % (16257)------------------------------
% 17.33/3.86 % (16257)------------------------------
% 17.33/3.87 % (16269)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_15863 for (2977ds/865Mi)
% 18.18/3.93 % (16241)Instruction limit reached!
% 18.18/3.93 % (16241)------------------------------
% 18.18/3.93 % (16241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.18/3.93 % (16241)Termination reason: Unknown
% 18.18/3.93 % (16241)Termination phase: Saturation
% 18.18/3.93
% 18.18/3.93 % (16241)Memory used [KB]: 11513
% 18.18/3.93 % (16241)Time elapsed: 1.291 s
% 18.18/3.93 % (16241)Instructions burned: 4351 (million)
% 18.18/3.93 % (16241)------------------------------
% 18.18/3.93 % (16241)------------------------------
% 18.18/3.94 % (16270)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_15863 for (2976ds/593Mi)
% 18.18/3.99 % (16268)Instruction limit reached!
% 18.18/3.99 % (16268)------------------------------
% 18.18/3.99 % (16268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.18/3.99 % (16268)Termination reason: Unknown
% 18.18/3.99 % (16268)Termination phase: Saturation
% 18.18/3.99
% 18.18/3.99 % (16268)Memory used [KB]: 7675
% 18.18/3.99 % (16268)Time elapsed: 0.137 s
% 18.18/3.99 % (16268)Instructions burned: 436 (million)
% 18.18/3.99 % (16268)------------------------------
% 18.18/3.99 % (16268)------------------------------
% 18.18/4.00 % (16271)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_15863 for (2976ds/443Mi)
% 19.88/4.08 % (16239)Instruction limit reached!
% 19.88/4.08 % (16239)------------------------------
% 19.88/4.08 % (16239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.88/4.08 % (16239)Termination reason: Unknown
% 19.88/4.08 % (16239)Termination phase: Saturation
% 19.88/4.08
% 19.88/4.08 % (16239)Memory used [KB]: 15863
% 19.88/4.08 % (16239)Time elapsed: 1.525 s
% 19.88/4.08 % (16239)Instructions burned: 5207 (million)
% 19.88/4.08 % (16239)------------------------------
% 19.88/4.08 % (16239)------------------------------
% 19.88/4.09 % (16272)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_15863 for (2975ds/594Mi)
% 19.88/4.09 % (16267)Instruction limit reached!
% 19.88/4.09 % (16267)------------------------------
% 19.88/4.09 % (16267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.88/4.09 % (16267)Termination reason: Unknown
% 19.88/4.09 % (16267)Termination phase: Saturation
% 19.88/4.09
% 19.88/4.09 % (16267)Memory used [KB]: 12281
% 19.88/4.09 % (16267)Time elapsed: 0.323 s
% 19.88/4.09 % (16267)Instructions burned: 907 (million)
% 19.88/4.09 % (16267)------------------------------
% 19.88/4.09 % (16267)------------------------------
% 19.88/4.10 % (16273)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_15863 for (2975ds/327Mi)
% 19.88/4.12 % (16270)Instruction limit reached!
% 19.88/4.12 % (16270)------------------------------
% 19.88/4.12 % (16270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.88/4.12 % (16270)Termination reason: Unknown
% 19.88/4.12 % (16270)Termination phase: Saturation
% 19.88/4.12
% 19.88/4.12 % (16270)Memory used [KB]: 9594
% 19.88/4.12 % (16270)Time elapsed: 0.180 s
% 19.88/4.12 % (16270)Instructions burned: 595 (million)
% 19.88/4.12 % (16270)------------------------------
% 19.88/4.12 % (16270)------------------------------
% 20.55/4.12 % (16271)Instruction limit reached!
% 20.55/4.12 % (16271)------------------------------
% 20.55/4.12 % (16271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.55/4.12 % (16271)Termination reason: Unknown
% 20.55/4.12 % (16271)Termination phase: Saturation
% 20.55/4.12
% 20.55/4.12 % (16271)Memory used [KB]: 7803
% 20.55/4.12 % (16271)Time elapsed: 0.124 s
% 20.55/4.12 % (16271)Instructions burned: 443 (million)
% 20.55/4.12 % (16271)------------------------------
% 20.55/4.12 % (16271)------------------------------
% 20.55/4.13 % (16269)Instruction limit reached!
% 20.55/4.13 % (16269)------------------------------
% 20.55/4.13 % (16269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.55/4.13 % (16269)Termination reason: Unknown
% 20.55/4.13 % (16269)Termination phase: Saturation
% 20.55/4.13
% 20.55/4.13 % (16269)Memory used [KB]: 9594
% 20.55/4.13 % (16269)Time elapsed: 0.263 s
% 20.55/4.13 % (16269)Instructions burned: 867 (million)
% 20.55/4.13 % (16269)------------------------------
% 20.55/4.13 % (16269)------------------------------
% 20.55/4.13 % (16274)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_15863 for (2974ds/5411Mi)
% 20.55/4.13 % (16275)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_15863 for (2974ds/1762Mi)
% 20.55/4.14 % (16276)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_15863 for (2974ds/96Mi)
% 20.55/4.17 % (16276)Instruction limit reached!
% 20.55/4.17 % (16276)------------------------------
% 20.55/4.17 % (16276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.55/4.17 % (16276)Termination reason: Unknown
% 20.55/4.17 % (16276)Termination phase: Property scanning
% 20.55/4.17
% 20.55/4.17 % (16276)Memory used [KB]: 2686
% 20.55/4.17 % (16276)Time elapsed: 0.028 s
% 20.55/4.17 % (16276)Instructions burned: 97 (million)
% 20.55/4.17 % (16276)------------------------------
% 20.55/4.17 % (16276)------------------------------
% 20.55/4.17 % (16266)Instruction limit reached!
% 20.55/4.17 % (16266)------------------------------
% 20.55/4.17 % (16266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.55/4.17 % (16266)Termination reason: Unknown
% 20.55/4.17 % (16266)Termination phase: Saturation
% 20.55/4.17
% 20.55/4.17 % (16266)Memory used [KB]: 13944
% 20.55/4.17 % (16266)Time elapsed: 0.413 s
% 20.55/4.17 % (16266)Instructions burned: 1376 (million)
% 20.55/4.17 % (16266)------------------------------
% 20.55/4.17 % (16266)------------------------------
% 20.55/4.17 % (16277)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_15863 for (2974ds/503Mi)
% 20.55/4.18 % (16278)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_15863 for (2974ds/90Mi)
% 20.75/4.21 % (16273)Instruction limit reached!
% 20.75/4.21 % (16273)------------------------------
% 20.75/4.21 % (16273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.75/4.21 % (16273)Termination reason: Unknown
% 20.75/4.21 % (16273)Termination phase: Saturation
% 20.75/4.21
% 20.75/4.21 % (16273)Memory used [KB]: 8187
% 20.75/4.21 % (16273)Time elapsed: 0.105 s
% 20.75/4.21 % (16273)Instructions burned: 328 (million)
% 20.75/4.21 % (16273)------------------------------
% 20.75/4.21 % (16273)------------------------------
% 20.75/4.21 % (16278)Instruction limit reached!
% 20.75/4.21 % (16278)------------------------------
% 20.75/4.21 % (16278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.75/4.21 % (16278)Termination reason: Unknown
% 20.75/4.21 % (16278)Termination phase: Property scanning
% 20.75/4.21
% 20.75/4.21 % (16278)Memory used [KB]: 2558
% 20.75/4.21 % (16278)Time elapsed: 0.028 s
% 20.75/4.21 % (16278)Instructions burned: 90 (million)
% 20.75/4.21 % (16278)------------------------------
% 20.75/4.21 % (16278)------------------------------
% 20.75/4.22 % (16279)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_15863 for (2973ds/593Mi)
% 20.75/4.22 % (16280)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_15863 for (2973ds/1512Mi)
% 20.75/4.23 % (16277)Refutation not found, incomplete strategy
% 20.75/4.23 % (16277)------------------------------
% 20.75/4.23 % (16277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.75/4.23 % (16277)Termination reason: Refutation not found, incomplete strategy
% 20.75/4.23
% 20.75/4.23
% 20.75/4.23 % (16277)Memory used [KB]: 7803
% 20.75/4.23 % (16277)Time elapsed: 0.052 s
% 20.75/4.23 % (16277)Instructions burned: 164 (million)
% 20.75/4.23 % (16277)------------------------------
% 20.75/4.23 % (16277)------------------------------
% 20.75/4.24 % (16281)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_15863 for (2973ds/569Mi)
% 20.75/4.28 % (16272)Instruction limit reached!
% 20.75/4.28 % (16272)------------------------------
% 20.75/4.28 % (16272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.75/4.28 % (16272)Termination reason: Unknown
% 20.75/4.28 % (16272)Termination phase: Saturation
% 20.75/4.28
% 20.75/4.28 % (16272)Memory used [KB]: 8571
% 20.75/4.28 % (16272)Time elapsed: 0.183 s
% 20.75/4.28 % (16272)Instructions burned: 594 (million)
% 20.75/4.28 % (16272)------------------------------
% 20.75/4.28 % (16272)------------------------------
% 20.75/4.29 % (16282)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_15863 for (2973ds/501Mi)
% 21.27/4.32 % (16280)First to succeed.
% 21.27/4.33 % (16280)Refutation found. Thanks to Tanya!
% 21.27/4.33 % SZS status Theorem for DTF2THF_15863
% 21.27/4.33 % SZS output start Proof for DTF2THF_15863
% 21.27/4.33 thf(type_def_5, type, set: ($tType) > $tType).
% 21.27/4.33 thf(type_def_6, type, product_prod: ($tType * $tType) > $tType).
% 21.27/4.33 thf(type_def_8, type, standard_Constant: ($tType) > $tType).
% 21.27/4.33 thf(type_def_9, type, labeled_graph: ($tType * $tType) > $tType).
% 21.27/4.33 thf(type_def_10, type, nat: $tType).
% 21.27/4.33 thf(type_def_11, type, a: $tType).
% 21.27/4.33 thf(type_def_12, type, b: $tType).
% 21.27/4.33 thf(type_def_13, type, sum_sum: ($tType * $tType) > $tType).
% 21.27/4.33 thf(func_def_0, type, standard_Constant: ($tType) > $tType).
% 21.27/4.33 thf(func_def_1, type, labeled_graph: ($tType * $tType) > $tType).
% 21.27/4.33 thf(func_def_2, type, product_prod: ($tType * $tType) > $tType).
% 21.27/4.33 thf(func_def_3, type, sum_sum: ($tType * $tType) > $tType).
% 21.27/4.33 thf(func_def_4, type, set: ($tType) > $tType).
% 21.27/4.33 thf(func_def_5, type, nat: $tType).
% 21.27/4.33 thf(func_def_6, type, b: $tType).
% 21.27/4.33 thf(func_def_7, type, a: $tType).
% 21.27/4.33 thf(func_def_8, type, type: !>[X0: $tType]:($o)).
% 21.27/4.33 thf(func_def_9, type, one: !>[X0: $tType]:($o)).
% 21.27/4.33 thf(func_def_10, type, zero: !>[X0: $tType]:($o)).
% 21.27/4.33 thf(func_def_11, type, bot: !>[X0: $tType]:($o)).
% 21.27/4.33 thf(func_def_12, type, ord: !>[X0: $tType]:($o)).
% 21.27/4.33 thf(func_def_13, type, order: !>[X0: $tType]:($o)).
% 21.27/4.33 thf(func_def_14, type, linorder: !>[X0: $tType]:($o)).
% 21.27/4.33 thf(func_def_15, type, preorder: !>[X0: $tType]:($o)).
% 21.27/4.33 thf(func_def_16, type, zero_neq_one: !>[X0: $tType]:($o)).
% 21.27/4.33 thf(func_def_17, type, order_bot: !>[X0: $tType]:($o)).
% 21.27/4.33 thf(func_def_18, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 21.27/4.33 thf(func_def_19, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 21.27/4.33 thf(func_def_20, type, equiv_equiv: !>[X0: $tType]:(set @ X0 > set @ product_prod @ X0 @ X0 > $o)).
% 21.27/4.33 thf(func_def_21, type, one_one: !>[X0: $tType]:(X0)).
% 21.27/4.33 thf(func_def_22, type, zero_zero: !>[X0: $tType]:(X0)).
% 21.27/4.33 thf(func_def_23, type, standard_S_Bot: !>[X0: $tType]:(standard_Constant @ X0)).
% 21.27/4.33 thf(func_def_24, type, standard_S_Idt: !>[X0: $tType]:(standard_Constant @ X0)).
% 21.27/4.33 thf(func_def_25, type, getRel: !>[X0: $tType, X1: $tType]:(X0 > labeled_graph @ X0 @ X1 > set @ product_prod @ X1 @ X1)).
% 21.27/4.33 thf(func_def_26, type, edge_preserving: !>[X0: $tType, X1: $tType, X2: $tType]:(set @ product_prod @ X0 @ X1 > set @ product_prod @ X2 @ product_prod @ X0 @ X0 > set @ product_prod @ X2 @ product_prod @ X1 @ X1 > $o)).
% 21.27/4.33 thf(func_def_27, type, graph_homomorphism: !>[X0: $tType, X1: $tType, X2: $tType]:(labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X2 > set @ product_prod @ X1 @ X2 > $o)).
% 21.27/4.33 thf(func_def_28, type, graph_union: !>[X0: $tType, X1: $tType]:(labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X1)).
% 21.27/4.33 thf(func_def_29, type, labeled_LG: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X0 @ product_prod @ X1 @ X1 > set @ X1 > labeled_graph @ X0 @ X1)).
% 21.27/4.33 thf(func_def_30, type, labeled_edges: !>[X0: $tType, X1: $tType]:(labeled_graph @ X0 @ X1 > set @ product_prod @ X0 @ product_prod @ X1 @ X1)).
% 21.27/4.33 thf(func_def_31, type, labeled_vertices: !>[X0: $tType, X1: $tType]:(labeled_graph @ X0 @ X1 > set @ X1)).
% 21.27/4.33 thf(func_def_32, type, map_graph: !>[X0: $tType, X1: $tType, X2: $tType]:(set @ product_prod @ X0 @ X1 > labeled_graph @ X2 @ X0 > labeled_graph @ X2 @ X1)).
% 21.27/4.33 thf(func_def_33, type, on_triple: !>[X0: $tType, X1: $tType, X2: $tType]:(set @ product_prod @ X0 @ X1 > set @ product_prod @ product_prod @ X2 @ product_prod @ X0 @ X0 @ product_prod @ X2 @ product_prod @ X1 @ X1)).
% 21.27/4.33 thf(func_def_34, type, restrict: !>[X0: $tType, X1: $tType]:(labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X1)).
% 21.27/4.33 thf(func_def_35, type, univalent: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X0 @ X1 > $o)).
% 21.27/4.33 thf(func_def_36, type, bot_bot: !>[X0: $tType]:(X0)).
% 21.27/4.33 thf(func_def_37, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 21.27/4.33 thf(func_def_38, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 21.27/4.33 thf(func_def_39, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 21.27/4.33 thf(func_def_40, type, domain: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X0 @ X1 > set @ X0)).
% 21.27/4.33 thf(func_def_41, type, id_on: !>[X0: $tType]:(set @ X0 > set @ product_prod @ X0 @ X0)).
% 21.27/4.33 thf(func_def_42, type, image: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X0 @ X1 > set @ X0 > set @ X1)).
% 21.27/4.33 thf(func_def_43, type, maintained: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ labeled_graph @ X0 @ X1 @ labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X2 > $o)).
% 21.27/4.33 thf(func_def_44, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 21.27/4.33 thf(func_def_45, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 21.27/4.33 thf(func_def_46, type, is_singleton: !>[X0: $tType]:(set @ X0 > $o)).
% 21.27/4.33 thf(func_def_47, type, the_elem: !>[X0: $tType]:(set @ X0 > X0)).
% 21.27/4.33 thf(func_def_48, type, standa1068660421e_rule: !>[X0: $tType]:(X0 > X0 > product_prod @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat)).
% 21.27/4.33 thf(func_def_49, type, standa244753842y_rule: !>[X0: $tType]:(product_prod @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat)).
% 21.27/4.33 thf(func_def_50, type, standa245363227y_rule: !>[X0: $tType]:(X0 > product_prod @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat)).
% 21.27/4.33 thf(func_def_51, type, standa1805702094y_rule: !>[X0: $tType]:(X0 > product_prod @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat)).
% 21.27/4.33 thf(func_def_52, type, standa400804411p_rule: !>[X0: $tType]:(X0 > product_prod @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat)).
% 21.27/4.33 thf(func_def_53, type, standa2114124375e_rule: !>[X0: $tType]:(X0 > product_prod @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat)).
% 21.27/4.33 thf(func_def_54, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 21.27/4.33 thf(func_def_55, type, g: labeled_graph @ standard_Constant @ a @ sum_sum @ a @ b).
% 21.27/4.33 thf(func_def_56, type, f: set @ product_prod @ nat @ sum_sum @ a @ b).
% 21.27/4.33 thf(func_def_57, type, l: standard_Constant @ a).
% 21.27/4.33 thf(func_def_58, type, v: sum_sum @ a @ b).
% 21.27/4.33 thf(func_def_72, type, sK0: !>[X0: $tType]:((X0 > $o) > X0)).
% 21.27/4.33 thf(func_def_73, type, sK1: !>[X0: $tType]:((X0 > $o) > X0)).
% 21.27/4.33 thf(func_def_76, type, sP2: !>[X0: $tType]:(set @ X0 > set @ X0 > X0 > X0 > $o)).
% 21.27/4.33 thf(func_def_77, type, sP3: !>[X0: $tType]:(X0 > set @ X0 > X0 > set @ X0 > $o)).
% 21.27/4.33 thf(func_def_78, type, sP4: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 21.27/4.33 thf(func_def_79, type, sP5: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 21.27/4.33 thf(func_def_80, type, sP6: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 21.27/4.33 thf(func_def_81, type, sK7: !>[X0: $tType]:((X0 > $o) > X0)).
% 21.27/4.33 thf(func_def_82, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType]:(set @ product_prod @ X2 @ X1 > labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X2 > set @ product_prod @ X2 @ X1)).
% 21.27/4.33 thf(func_def_83, type, sK9: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 21.27/4.33 thf(func_def_84, type, sK10: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 21.27/4.33 thf(func_def_85, type, sK11: !>[X0: $tType]:(set @ X0 > X0 > set @ X0)).
% 21.27/4.33 thf(func_def_86, type, sK12: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 21.27/4.33 thf(func_def_87, type, sK13: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 21.27/4.33 thf(func_def_88, type, sK14: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 21.27/4.33 thf(func_def_89, type, sK15: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 21.27/4.33 thf(func_def_90, type, sK16: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > X1 > X0)).
% 21.27/4.33 thf(func_def_91, type, sK17: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 21.27/4.33 thf(func_def_92, type, sK18: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 21.27/4.33 thf(func_def_93, type, sK19: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > X1 > X0)).
% 21.27/4.33 thf(func_def_94, type, sK20: !>[X0: $tType]:(set @ X0 > X0)).
% 21.27/4.33 thf(func_def_95, type, sK21: !>[X0: $tType]:(set @ X0 > X0)).
% 21.27/4.33 thf(func_def_96, type, sK22: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 21.27/4.33 thf(func_def_97, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0)).
% 21.27/4.33 thf(func_def_98, type, sK24: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1)).
% 21.27/4.33 thf(func_def_99, type, sK25: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2)).
% 21.27/4.33 thf(func_def_100, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3)).
% 21.27/4.33 thf(func_def_101, type, sK27: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 21.27/4.33 thf(func_def_102, type, sK28: nat > (nat > $o) > nat).
% 21.27/4.33 thf(func_def_103, type, sK29: (nat > $o) > nat).
% 21.27/4.33 thf(func_def_104, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X0)).
% 21.27/4.33 thf(func_def_105, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X1)).
% 21.27/4.33 thf(func_def_106, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X2)).
% 21.27/4.33 thf(func_def_107, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X3)).
% 21.27/4.33 thf(func_def_108, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X4)).
% 21.27/4.33 thf(func_def_109, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X5)).
% 21.27/4.33 thf(func_def_110, type, sK36: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 21.27/4.33 thf(func_def_111, type, sK37: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 21.27/4.33 thf(func_def_112, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 21.27/4.33 thf(func_def_113, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 21.27/4.33 thf(func_def_114, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 21.27/4.33 thf(func_def_115, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 21.27/4.33 thf(func_def_116, type, sK42: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1)).
% 21.27/4.33 thf(func_def_117, type, sK43: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0)).
% 21.27/4.33 thf(func_def_118, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0)).
% 21.27/4.33 thf(func_def_119, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1)).
% 21.27/4.33 thf(func_def_120, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2)).
% 21.27/4.33 thf(func_def_121, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3)).
% 21.27/4.33 thf(func_def_122, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4)).
% 21.27/4.33 thf(func_def_123, type, sK49: !>[X0: $tType]:(set @ X0 > X0)).
% 21.27/4.33 thf(func_def_124, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X6)).
% 21.27/4.33 thf(func_def_125, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 21.27/4.33 thf(func_def_126, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 21.27/4.33 thf(func_def_127, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 21.27/4.33 thf(func_def_128, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 21.27/4.33 thf(func_def_129, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 21.27/4.33 thf(func_def_130, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 21.27/4.33 thf(func_def_131, type, sK57: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 21.27/4.33 thf(func_def_132, type, sK58: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 21.27/4.33 thf(func_def_133, type, sK59: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 21.27/4.33 thf(func_def_134, type, sK60: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 21.27/4.33 thf(func_def_135, type, sK61: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 21.27/4.33 thf(func_def_136, type, sK62: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 21.27/4.33 thf(func_def_137, type, sK63: !>[X0: $tType]:(set @ X0 > X0)).
% 21.27/4.33 thf(func_def_138, type, sK64: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 21.27/4.33 thf(func_def_139, type, sK65: !>[X0: $tType, X1: $tType]:(set @ X1 > set @ product_prod @ X1 @ X0 > X0 > X1)).
% 21.27/4.33 thf(func_def_140, type, sK66: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 21.27/4.33 thf(func_def_141, type, sK67: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 21.27/4.33 thf(func_def_142, type, sK68: !>[X0: $tType]:(set @ X0 > set @ X0 > X0 > X0 > set @ X0)).
% 21.27/4.33 thf(func_def_143, type, sK69: !>[X0: $tType, X1: $tType]:(labeled_graph @ X0 @ X1 > set @ product_prod @ X0 @ product_prod @ X1 @ X1)).
% 21.27/4.33 thf(func_def_144, type, sK70: !>[X0: $tType, X1: $tType]:(labeled_graph @ X0 @ X1 > set @ X1)).
% 21.27/4.33 thf(func_def_145, type, sK71: !>[X0: $tType, X1: $tType]:((X1 > $o) > set @ product_prod @ X1 @ X0 > X1)).
% 21.27/4.33 thf(func_def_146, type, sK72: !>[X0: $tType, X1: $tType]:((X1 > $o) > set @ product_prod @ X1 @ X0 > X0)).
% 21.27/4.33 thf(func_def_147, type, sK73: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > X1 > X0)).
% 21.27/4.33 thf(func_def_148, type, sK74: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > X1 > X1)).
% 21.27/4.33 thf(func_def_149, type, sK75: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > X1 > X0)).
% 21.27/4.33 thf(func_def_150, type, sK76: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 21.27/4.33 thf(func_def_151, type, sK77: !>[X0: $tType]:((X0 > $o) > X0)).
% 21.27/4.33 thf(func_def_152, type, sK78: !>[X0: $tType]:(set @ X0 > X0)).
% 21.27/4.33 thf(func_def_153, type, sK79: !>[X0: $tType]:(set @ X0 > X0)).
% 21.27/4.33 thf(func_def_154, type, sK80: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 21.27/4.33 thf(func_def_155, type, sK81: !>[X0: $tType, X1: $tType]:(set @ X1 > set @ product_prod @ X1 @ X0 > X0 > X1)).
% 21.27/4.33 thf(func_def_156, type, sK82: !>[X0: $tType]:(set @ X0 > X0)).
% 21.27/4.33 thf(func_def_157, type, sK83: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X0 @ X1 > X0 > X1)).
% 21.27/4.33 thf(func_def_158, type, sK84: !>[X0: $tType]:(set @ X0 > X0 > set @ X0)).
% 21.27/4.33 thf(func_def_159, type, sK85: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 21.27/4.33 thf(func_def_160, type, sK86: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 21.27/4.33 thf(func_def_161, type, sK87: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 21.27/4.33 thf(func_def_162, type, sK88: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 21.27/4.33 thf(func_def_163, type, sK89: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 21.27/4.33 thf(func_def_164, type, sK90: !>[X0: $tType, X1: $tType]:(X1 > labeled_graph @ X1 @ X0 > product_prod @ labeled_graph @ X1 @ nat @ labeled_graph @ X1 @ nat)).
% 21.27/4.33 thf(func_def_165, type, sK91: !>[X0: $tType]:(set @ X0 > product_prod @ X0 @ X0 > X0)).
% 21.27/4.33 thf(func_def_166, type, sK92: !>[X0: $tType, X1: $tType]:((labeled_graph @ X1 @ X0 > $o) > set @ product_prod @ X1 @ product_prod @ X0 @ X0)).
% 21.27/4.33 thf(func_def_167, type, sK93: !>[X0: $tType, X1: $tType]:((labeled_graph @ X1 @ X0 > $o) > set @ X0)).
% 21.27/4.33 thf(func_def_168, type, sK94: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X0)).
% 21.27/4.33 thf(func_def_169, type, sK95: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X1)).
% 21.27/4.33 thf(func_def_170, type, sK96: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X2)).
% 21.27/4.33 thf(func_def_171, type, sK97: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 21.27/4.33 thf(func_def_172, type, sK98: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 21.27/4.33 thf(func_def_173, type, sK99: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 21.27/4.33 thf(func_def_174, type, sK100: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 21.27/4.33 thf(func_def_175, type, sK101: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 21.27/4.33 thf(func_def_176, type, sK102: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 21.27/4.33 thf(func_def_177, type, sK103: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 21.27/4.33 thf(func_def_178, type, sK104: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 21.27/4.33 thf(func_def_179, type, sK105: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 21.27/4.33 thf(func_def_180, type, sK106: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X0)).
% 21.27/4.33 thf(func_def_181, type, sK107: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X1)).
% 21.27/4.33 thf(func_def_182, type, sK108: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X2)).
% 21.27/4.33 thf(func_def_183, type, sK109: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X3)).
% 21.27/4.33 thf(func_def_184, type, sK110: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X4)).
% 21.27/4.33 thf(func_def_185, type, sK111: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X5)).
% 21.27/4.33 thf(func_def_186, type, sK112: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X6)).
% 21.27/4.33 thf(func_def_187, type, sK113: sum_sum @ a @ b).
% 21.27/4.33 thf(func_def_188, type, sK114: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 21.27/4.33 thf(func_def_189, type, sK115: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 21.27/4.33 thf(func_def_190, type, sK116: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 21.27/4.33 thf(func_def_192, type, ph118: !>[X0: $tType]:(X0)).
% 21.27/4.33 thf(f1907,plain,(
% 21.27/4.33 $false),
% 21.27/4.33 inference(avatar_sat_refutation,[status(thm)],[f1763,f1792,f1906])).
% 21.27/4.33 thf(f1906,plain,(
% 21.27/4.33 spl117_1),
% 21.27/4.33 inference(avatar_contradiction_clause,[status(thm)],[f1905])).
% 21.27/4.33 thf(f1905,plain,(
% 21.27/4.33 $false | spl117_1),
% 21.27/4.33 inference(subsumption_resolution,[status(thm)],[f1904,f1687])).
% 21.27/4.33 thf(f1687,plain,(
% 21.27/4.33 ( ! [X0 : $tType,X2 : X0] : (((member @ X0 @ X2 @ (insert @ X0 @ X2 @ bot_bot @ set @ X0)) = $true)) )),
% 21.27/4.33 inference(equality_resolution,[status(thm)],[f1427])).
% 21.27/4.33 thf(f1427,plain,(
% 21.27/4.33 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (((member @ X0 @ X1 @ (insert @ X0 @ X2 @ bot_bot @ set @ X0)) = $true) | (X1 != X2)) )),
% 21.27/4.33 inference(cnf_transformation,[status(thm)],[f1162])).
% 21.27/4.33 thf(f1162,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : X0,X2 : X0] : (((X1 = X2) | ((member @ X0 @ X1 @ (insert @ X0 @ X2 @ bot_bot @ set @ X0)) != $true)) & (((member @ X0 @ X1 @ (insert @ X0 @ X2 @ bot_bot @ set @ X0)) = $true) | (X1 != X2)))),
% 21.27/4.33 inference(nnf_transformation,[status(thm)],[f406])).
% 21.27/4.33 thf(f406,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : X0,X2 : X0] : ((X1 = X2) <=> ((member @ X0 @ X1 @ (insert @ X0 @ X2 @ bot_bot @ set @ X0)) = $true))),
% 21.27/4.33 inference(fool_elimination,[status(thm)],[f405])).
% 21.27/4.33 thf(f405,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : X0,X2 : X0] : ((X1 = X2) = (member @ X0 @ X1 @ (insert @ X0 @ X2 @ bot_bot @ set @ X0)))),
% 21.27/4.33 inference(rectify,[status(thm)],[f98])).
% 21.27/4.33 thf(f98,axiom,(
% 21.27/4.33 ! [X0 : $tType,X9 : X0,X8 : X0] : ((X8 = X9) = (member @ X0 @ X9 @ (insert @ X0 @ X8 @ bot_bot @ set @ X0)))),
% 21.27/4.33 file('/export/starexec/sandbox/tmp/tmp.L5LtdenOSc/DTF2THF_15863.p',fact_97_singleton__iff)).
% 21.27/4.33 thf(f1904,plain,(
% 21.27/4.33 ((member @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat)) != $true) | spl117_1),
% 21.27/4.33 inference(forward_demodulation,[status(thm)],[f1903,f1575])).
% 21.27/4.33 thf(f1575,plain,(
% 21.27/4.33 (zero_zero @ nat = bot_bot @ nat)),
% 21.27/4.33 inference(cnf_transformation,[status(thm)],[f754])).
% 21.27/4.33 thf(f754,plain,(
% 21.27/4.33 (zero_zero @ nat = bot_bot @ nat)),
% 21.27/4.33 inference(fool_elimination,[status(thm)],[f130])).
% 21.27/4.33 thf(f130,axiom,(
% 21.27/4.33 (zero_zero @ nat = bot_bot @ nat)),
% 21.27/4.33 file('/export/starexec/sandbox/tmp/tmp.L5LtdenOSc/DTF2THF_15863.p',fact_129_bot__nat__def)).
% 21.27/4.33 thf(f1903,plain,(
% 21.27/4.33 ($true != (member @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat))) | spl117_1),
% 21.27/4.33 inference(subsumption_resolution,[status(thm)],[f1902,f1351])).
% 21.27/4.33 thf(f1351,plain,(
% 21.27/4.33 ( ! [X0 : $tType,X1 : set @ X0] : (($true = (ord_less_eq @ set @ X0 @ X1 @ X1))) )),
% 21.27/4.33 inference(cnf_transformation,[status(thm)],[f789])).
% 21.27/4.33 thf(f789,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : set @ X0] : ($true = (ord_less_eq @ set @ X0 @ X1 @ X1))),
% 21.27/4.33 inference(fool_elimination,[status(thm)],[f788])).
% 21.27/4.33 thf(f788,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : set @ X0] : (ord_less_eq @ set @ X0 @ X1 @ X1)),
% 21.27/4.33 inference(rectify,[status(thm)],[f82])).
% 21.27/4.33 thf(f82,axiom,(
% 21.27/4.33 ! [X0 : $tType,X23 : set @ X0] : (ord_less_eq @ set @ X0 @ X23 @ X23)),
% 21.27/4.33 file('/export/starexec/sandbox/tmp/tmp.L5LtdenOSc/DTF2THF_15863.p',fact_81_subset__refl)).
% 21.27/4.33 thf(f1902,plain,(
% 21.27/4.33 ($true != (member @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat))) | ((ord_less_eq @ set @ product_prod @ nat @ sum_sum @ a @ b @ f @ f) != $true) | spl117_1),
% 21.27/4.33 inference(forward_demodulation,[status(thm)],[f1901,f1415])).
% 21.27/4.33 thf(f1415,plain,(
% 21.27/4.33 (f = (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b))),
% 21.27/4.33 inference(cnf_transformation,[status(thm)],[f525])).
% 21.27/4.33 thf(f525,plain,(
% 21.27/4.33 (f = (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b))),
% 21.27/4.33 inference(fool_elimination,[status(thm)],[f5])).
% 21.27/4.33 thf(f5,axiom,(
% 21.27/4.33 (f = (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b))),
% 21.27/4.33 file('/export/starexec/sandbox/tmp/tmp.L5LtdenOSc/DTF2THF_15863.p',fact_4_f)).
% 21.27/4.33 thf(f1901,plain,(
% 21.27/4.33 ((ord_less_eq @ set @ product_prod @ nat @ sum_sum @ a @ b @ f @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b)) != $true) | ($true != (member @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat))) | spl117_1),
% 21.27/4.33 inference(subsumption_resolution,[status(thm)],[f1899,f1303])).
% 21.27/4.33 thf(f1303,plain,(
% 21.27/4.33 (zero @ nat = $true)),
% 21.27/4.33 inference(cnf_transformation,[status(thm)],[f305])).
% 21.27/4.33 thf(f305,plain,(
% 21.27/4.33 (zero @ nat = $true)),
% 21.27/4.33 inference(fool_elimination,[status(thm)],[f304])).
% 21.27/4.33 thf(f304,plain,(
% 21.27/4.33 zero @ nat),
% 21.27/4.33 inference(rectify,[status(thm)],[f268])).
% 21.27/4.33 thf(f268,axiom,(
% 21.27/4.33 zero @ nat),
% 21.27/4.33 file('/export/starexec/sandbox/tmp/tmp.L5LtdenOSc/DTF2THF_15863.p',tcon_Nat_Onat___Groups_Ozero)).
% 21.27/4.33 thf(f1899,plain,(
% 21.27/4.33 (zero @ nat != $true) | ((ord_less_eq @ set @ product_prod @ nat @ sum_sum @ a @ b @ f @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b)) != $true) | ($true != (member @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat))) | spl117_1),
% 21.27/4.33 inference(trivial_inequality_removal,[status(thm)],[f1897])).
% 21.27/4.33 thf(f1897,plain,(
% 21.27/4.33 ($true != (member @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat))) | ((ord_less_eq @ set @ product_prod @ nat @ sum_sum @ a @ b @ f @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b)) != $true) | (zero @ nat != $true) | ($true != $true) | spl117_1),
% 21.27/4.33 inference(superposition,[status(thm)],[f1855,f1630])).
% 21.27/4.33 thf(f1630,plain,(
% 21.27/4.33 ( ! [X0 : $tType] : (($true = (edge_preserving @ X0 @ sum_sum @ a @ b @ standard_Constant @ a @ (insert @ product_prod @ X0 @ sum_sum @ a @ b @ (product_Pair @ X0 @ sum_sum @ a @ b @ zero_zero @ X0 @ v) @ bot_bot @ set @ product_prod @ X0 @ sum_sum @ a @ b) @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ X0 @ X0 @ (product_Pair @ standard_Constant @ a @ product_prod @ X0 @ X0 @ standard_S_Idt @ a @ (product_Pair @ X0 @ X0 @ zero_zero @ X0 @ zero_zero @ X0)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ X0 @ X0) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g))) | (zero @ X0 != $true)) )),
% 21.27/4.33 inference(cnf_transformation,[status(thm)],[f925])).
% 21.27/4.33 thf(f925,plain,(
% 21.27/4.33 ! [X0 : $tType] : ((zero @ X0 != $true) | ($true = (edge_preserving @ X0 @ sum_sum @ a @ b @ standard_Constant @ a @ (insert @ product_prod @ X0 @ sum_sum @ a @ b @ (product_Pair @ X0 @ sum_sum @ a @ b @ zero_zero @ X0 @ v) @ bot_bot @ set @ product_prod @ X0 @ sum_sum @ a @ b) @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ X0 @ X0 @ (product_Pair @ standard_Constant @ a @ product_prod @ X0 @ X0 @ standard_S_Idt @ a @ (product_Pair @ X0 @ X0 @ zero_zero @ X0 @ zero_zero @ X0)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ X0 @ X0) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g))))),
% 21.27/4.33 inference(ennf_transformation,[status(thm)],[f529])).
% 21.27/4.33 thf(f529,plain,(
% 21.27/4.33 ! [X0 : $tType] : ((zero @ X0 = $true) => ($true = (edge_preserving @ X0 @ sum_sum @ a @ b @ standard_Constant @ a @ (insert @ product_prod @ X0 @ sum_sum @ a @ b @ (product_Pair @ X0 @ sum_sum @ a @ b @ zero_zero @ X0 @ v) @ bot_bot @ set @ product_prod @ X0 @ sum_sum @ a @ b) @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ X0 @ X0 @ (product_Pair @ standard_Constant @ a @ product_prod @ X0 @ X0 @ standard_S_Idt @ a @ (product_Pair @ X0 @ X0 @ zero_zero @ X0 @ zero_zero @ X0)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ X0 @ X0) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g))))),
% 21.27/4.33 inference(fool_elimination,[status(thm)],[f528])).
% 21.27/4.33 thf(f528,plain,(
% 21.27/4.33 ! [X0 : $tType] : (zero @ X0 => (edge_preserving @ X0 @ sum_sum @ a @ b @ standard_Constant @ a @ (insert @ product_prod @ X0 @ sum_sum @ a @ b @ (product_Pair @ X0 @ sum_sum @ a @ b @ zero_zero @ X0 @ v) @ bot_bot @ set @ product_prod @ X0 @ sum_sum @ a @ b) @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ X0 @ X0 @ (product_Pair @ standard_Constant @ a @ product_prod @ X0 @ X0 @ standard_S_Idt @ a @ (product_Pair @ X0 @ X0 @ zero_zero @ X0 @ zero_zero @ X0)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ X0 @ X0) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)))),
% 21.27/4.33 inference(rectify,[status(thm)],[f3])).
% 21.27/4.33 thf(f3,axiom,(
% 21.27/4.33 ! [X7 : $tType] : (zero @ X7 => (edge_preserving @ X7 @ sum_sum @ a @ b @ standard_Constant @ a @ (insert @ product_prod @ X7 @ sum_sum @ a @ b @ (product_Pair @ X7 @ sum_sum @ a @ b @ zero_zero @ X7 @ v) @ bot_bot @ set @ product_prod @ X7 @ sum_sum @ a @ b) @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ X7 @ X7 @ (product_Pair @ standard_Constant @ a @ product_prod @ X7 @ X7 @ standard_S_Idt @ a @ (product_Pair @ X7 @ X7 @ zero_zero @ X7 @ zero_zero @ X7)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ X7 @ X7) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)))),
% 21.27/4.33 file('/export/starexec/sandbox/tmp/tmp.L5LtdenOSc/DTF2THF_15863.p',fact_2__092_060open_062edge__preserving_A_123_I0_058_058_063_Hc1_M_Av_J_125_A_123_IS__Idt_M_A0_058_058_063_Hc1_M_A0_058_058_063_Hc1_J_125_A_Iedges_AG_J_092_060close_062)).
% 21.27/4.33 thf(f1855,plain,(
% 21.27/4.33 ( ! [X0 : set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat,X1 : set @ product_prod @ nat @ sum_sum @ a @ b] : (((edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ X1 @ X0 @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true) | ($true != (member @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ X0)) | ((ord_less_eq @ set @ product_prod @ nat @ sum_sum @ a @ b @ f @ X1) != $true)) ) | spl117_1),
% 21.27/4.33 inference(subsumption_resolution,[status(thm)],[f1846,f1423])).
% 21.27/4.33 thf(f1423,plain,(
% 21.27/4.33 ( ! [X0 : $tType,X1 : set @ X0] : (((ord_less_eq @ set @ X0 @ bot_bot @ set @ X0 @ X1) = $true)) )),
% 21.27/4.33 inference(cnf_transformation,[status(thm)],[f817])).
% 21.27/4.33 thf(f817,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : set @ X0] : ((ord_less_eq @ set @ X0 @ bot_bot @ set @ X0 @ X1) = $true)),
% 21.27/4.33 inference(fool_elimination,[status(thm)],[f816])).
% 21.27/4.33 thf(f816,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : set @ X0] : (ord_less_eq @ set @ X0 @ bot_bot @ set @ X0 @ X1)),
% 21.27/4.33 inference(rectify,[status(thm)],[f52])).
% 21.27/4.33 thf(f52,axiom,(
% 21.27/4.33 ! [X0 : $tType,X23 : set @ X0] : (ord_less_eq @ set @ X0 @ bot_bot @ set @ X0 @ X23)),
% 21.27/4.33 file('/export/starexec/sandbox/tmp/tmp.L5LtdenOSc/DTF2THF_15863.p',fact_51_empty__subsetI)).
% 21.27/4.33 thf(f1846,plain,(
% 21.27/4.33 ( ! [X0 : set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat,X1 : set @ product_prod @ nat @ sum_sum @ a @ b] : (($true != (member @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ X0)) | ((edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ X1 @ X0 @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true) | ((ord_less_eq @ set @ product_prod @ nat @ sum_sum @ a @ b @ f @ X1) != $true) | ((ord_less_eq @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ X0) != $true)) ) | spl117_1),
% 21.27/4.33 inference(trivial_inequality_removal,[status(thm)],[f1808])).
% 21.27/4.33 thf(f1808,plain,(
% 21.27/4.33 ( ! [X0 : set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat,X1 : set @ product_prod @ nat @ sum_sum @ a @ b] : (($true != (member @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ X0)) | ($true != $true) | ((edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ X1 @ X0 @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true) | ((ord_less_eq @ set @ product_prod @ nat @ sum_sum @ a @ b @ f @ X1) != $true) | ((ord_less_eq @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ X0) != $true)) ) | spl117_1),
% 21.27/4.33 inference(superposition,[status(thm)],[f1797,f1296])).
% 21.27/4.33 thf(f1296,plain,(
% 21.27/4.33 ( ! [X0 : $tType,X2 : set @ X0,X3 : set @ X0,X1 : X0] : (((ord_less_eq @ set @ X0 @ (insert @ X0 @ X1 @ X3) @ X2) = $true) | ((ord_less_eq @ set @ X0 @ X3 @ X2) != $true) | ((member @ X0 @ X1 @ X2) != $true)) )),
% 21.27/4.33 inference(cnf_transformation,[status(thm)],[f963])).
% 21.27/4.33 thf(f963,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : X0,X2 : set @ X0,X3 : set @ X0] : (((member @ X0 @ X1 @ X2) != $true) | ((ord_less_eq @ set @ X0 @ (insert @ X0 @ X1 @ X3) @ X2) = $true) | ((ord_less_eq @ set @ X0 @ X3 @ X2) != $true))),
% 21.27/4.33 inference(flattening,[status(thm)],[f962])).
% 21.27/4.33 thf(f962,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : X0,X2 : set @ X0,X3 : set @ X0] : ((((ord_less_eq @ set @ X0 @ (insert @ X0 @ X1 @ X3) @ X2) = $true) | ((ord_less_eq @ set @ X0 @ X3 @ X2) != $true)) | ((member @ X0 @ X1 @ X2) != $true))),
% 21.27/4.33 inference(ennf_transformation,[status(thm)],[f561])).
% 21.27/4.33 thf(f561,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : X0,X2 : set @ X0,X3 : set @ X0] : (((member @ X0 @ X1 @ X2) = $true) => (((ord_less_eq @ set @ X0 @ X3 @ X2) = $true) => ((ord_less_eq @ set @ X0 @ (insert @ X0 @ X1 @ X3) @ X2) = $true)))),
% 21.27/4.33 inference(fool_elimination,[status(thm)],[f560])).
% 21.27/4.33 thf(f560,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : X0,X2 : set @ X0,X3 : set @ X0] : ((member @ X0 @ X1 @ X2) => ((ord_less_eq @ set @ X0 @ X3 @ X2) => (ord_less_eq @ set @ X0 @ (insert @ X0 @ X1 @ X3) @ X2)))),
% 21.27/4.33 inference(rectify,[status(thm)],[f236])).
% 21.27/4.33 thf(f236,axiom,(
% 21.27/4.33 ! [X0 : $tType,X16 : X0,X23 : set @ X0,X15 : set @ X0] : ((member @ X0 @ X16 @ X23) => ((ord_less_eq @ set @ X0 @ X15 @ X23) => (ord_less_eq @ set @ X0 @ (insert @ X0 @ X16 @ X15) @ X23)))),
% 21.27/4.33 file('/export/starexec/sandbox/tmp/tmp.L5LtdenOSc/DTF2THF_15863.p',fact_235_insert__subsetI)).
% 21.27/4.33 thf(f1797,plain,(
% 21.27/4.33 ( ! [X0 : set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat,X1 : set @ product_prod @ nat @ sum_sum @ a @ b] : (($true != (ord_less_eq @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ X0)) | ((ord_less_eq @ set @ product_prod @ nat @ sum_sum @ a @ b @ f @ X1) != $true) | ((edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ X1 @ X0 @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true)) ) | spl117_1),
% 21.27/4.33 inference(trivial_inequality_removal,[status(thm)],[f1796])).
% 21.27/4.33 thf(f1796,plain,(
% 21.27/4.33 ( ! [X0 : set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat,X1 : set @ product_prod @ nat @ sum_sum @ a @ b] : (((edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ X1 @ X0 @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true) | ($true != (ord_less_eq @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ X0)) | ($true != $true) | ((ord_less_eq @ set @ product_prod @ nat @ sum_sum @ a @ b @ f @ X1) != $true)) ) | spl117_1),
% 21.27/4.33 inference(superposition,[status(thm)],[f1758,f1639])).
% 21.27/4.33 thf(f1639,plain,(
% 21.27/4.33 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : set @ product_prod @ X0 @ X1,X6 : set @ product_prod @ X2 @ product_prod @ X0 @ X0,X7 : set @ product_prod @ X2 @ product_prod @ X1 @ X1,X4 : set @ product_prod @ X0 @ X1,X5 : set @ product_prod @ X2 @ product_prod @ X0 @ X0] : (((edge_preserving @ X0 @ X1 @ X2 @ X3 @ X5 @ X7) = $true) | ((ord_less_eq @ set @ product_prod @ X2 @ product_prod @ X0 @ X0 @ X5 @ X6) != $true) | ((ord_less_eq @ set @ product_prod @ X0 @ X1 @ X3 @ X4) != $true) | ((edge_preserving @ X0 @ X1 @ X2 @ X4 @ X6 @ X7) != $true)) )),
% 21.27/4.33 inference(cnf_transformation,[status(thm)],[f1042])).
% 21.27/4.33 thf(f1042,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : set @ product_prod @ X0 @ X1,X4 : set @ product_prod @ X0 @ X1,X5 : set @ product_prod @ X2 @ product_prod @ X0 @ X0,X6 : set @ product_prod @ X2 @ product_prod @ X0 @ X0,X7 : set @ product_prod @ X2 @ product_prod @ X1 @ X1] : (((edge_preserving @ X0 @ X1 @ X2 @ X3 @ X5 @ X7) = $true) | ((edge_preserving @ X0 @ X1 @ X2 @ X4 @ X6 @ X7) != $true) | ((ord_less_eq @ set @ product_prod @ X0 @ X1 @ X3 @ X4) != $true) | ((ord_less_eq @ set @ product_prod @ X2 @ product_prod @ X0 @ X0 @ X5 @ X6) != $true))),
% 21.27/4.33 inference(flattening,[status(thm)],[f1041])).
% 21.27/4.33 thf(f1041,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : set @ product_prod @ X0 @ X1,X4 : set @ product_prod @ X0 @ X1,X5 : set @ product_prod @ X2 @ product_prod @ X0 @ X0,X6 : set @ product_prod @ X2 @ product_prod @ X0 @ X0,X7 : set @ product_prod @ X2 @ product_prod @ X1 @ X1] : (((((edge_preserving @ X0 @ X1 @ X2 @ X3 @ X5 @ X7) = $true) | ((edge_preserving @ X0 @ X1 @ X2 @ X4 @ X6 @ X7) != $true)) | ((ord_less_eq @ set @ product_prod @ X2 @ product_prod @ X0 @ X0 @ X5 @ X6) != $true)) | ((ord_less_eq @ set @ product_prod @ X0 @ X1 @ X3 @ X4) != $true))),
% 21.27/4.33 inference(ennf_transformation,[status(thm)],[f772])).
% 21.27/4.33 thf(f772,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : set @ product_prod @ X0 @ X1,X4 : set @ product_prod @ X0 @ X1,X5 : set @ product_prod @ X2 @ product_prod @ X0 @ X0,X6 : set @ product_prod @ X2 @ product_prod @ X0 @ X0,X7 : set @ product_prod @ X2 @ product_prod @ X1 @ X1] : (((ord_less_eq @ set @ product_prod @ X0 @ X1 @ X3 @ X4) = $true) => (((ord_less_eq @ set @ product_prod @ X2 @ product_prod @ X0 @ X0 @ X5 @ X6) = $true) => (((edge_preserving @ X0 @ X1 @ X2 @ X4 @ X6 @ X7) = $true) => ((edge_preserving @ X0 @ X1 @ X2 @ X3 @ X5 @ X7) = $true))))),
% 21.27/4.33 inference(fool_elimination,[status(thm)],[f771])).
% 21.27/4.33 thf(f771,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : set @ product_prod @ X0 @ X1,X4 : set @ product_prod @ X0 @ X1,X5 : set @ product_prod @ X2 @ product_prod @ X0 @ X0,X6 : set @ product_prod @ X2 @ product_prod @ X0 @ X0,X7 : set @ product_prod @ X2 @ product_prod @ X1 @ X1] : ((ord_less_eq @ set @ product_prod @ X0 @ X1 @ X3 @ X4) => ((ord_less_eq @ set @ product_prod @ X2 @ product_prod @ X0 @ X0 @ X5 @ X6) => ((edge_preserving @ X0 @ X1 @ X2 @ X4 @ X6 @ X7) => (edge_preserving @ X0 @ X1 @ X2 @ X3 @ X5 @ X7))))),
% 21.27/4.33 inference(rectify,[status(thm)],[f67])).
% 21.27/4.33 thf(f67,axiom,(
% 21.27/4.33 ! [X0 : $tType,X2 : $tType,X3 : $tType,X57 : set @ product_prod @ X0 @ X2,X58 : set @ product_prod @ X0 @ X2,X59 : set @ product_prod @ X3 @ product_prod @ X0 @ X0,X60 : set @ product_prod @ X3 @ product_prod @ X0 @ X0,X25 : set @ product_prod @ X3 @ product_prod @ X2 @ X2] : ((ord_less_eq @ set @ product_prod @ X0 @ X2 @ X57 @ X58) => ((ord_less_eq @ set @ product_prod @ X3 @ product_prod @ X0 @ X0 @ X59 @ X60) => ((edge_preserving @ X0 @ X2 @ X3 @ X58 @ X60 @ X25) => (edge_preserving @ X0 @ X2 @ X3 @ X57 @ X59 @ X25))))),
% 21.27/4.33 file('/export/starexec/sandbox/tmp/tmp.L5LtdenOSc/DTF2THF_15863.p',fact_66_edge__preserving__subset)).
% 21.27/4.33 thf(f1758,plain,(
% 21.27/4.33 ((edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ f @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true) | spl117_1),
% 21.27/4.33 inference(avatar_component_clause,[status(thm)],[f1756])).
% 21.27/4.33 thf(f1756,definition,(
% 21.27/4.33 spl117_1 <=> ((edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ f @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)) = $true)),
% 21.27/4.33 introduced(definition,[new_symbols(naming,[spl117_1])],[avatar_definition])).
% 21.27/4.33 thf(f1792,plain,(
% 21.27/4.33 spl117_2),
% 21.27/4.33 inference(avatar_contradiction_clause,[status(thm)],[f1791])).
% 21.27/4.33 thf(f1791,plain,(
% 21.27/4.33 $false | spl117_2),
% 21.27/4.33 inference(subsumption_resolution,[status(thm)],[f1790,f1351])).
% 21.27/4.33 thf(f1790,plain,(
% 21.27/4.33 ((ord_less_eq @ set @ nat @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat)) != $true) | spl117_2),
% 21.27/4.33 inference(trivial_inequality_removal,[status(thm)],[f1787])).
% 21.27/4.33 thf(f1787,plain,(
% 21.27/4.33 ((ord_less_eq @ set @ nat @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat)) != $true) | ((labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) != (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat)))) | spl117_2),
% 21.27/4.33 inference(superposition,[status(thm)],[f1764,f1435])).
% 21.27/4.33 thf(f1435,plain,(
% 21.27/4.33 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1,X4 : X1] : (((restrict @ X0 @ X1 @ (labeled_LG @ X0 @ X1 @ (insert @ product_prod @ X0 @ product_prod @ X1 @ X1 @ (product_Pair @ X0 @ product_prod @ X1 @ X1 @ X2 @ (product_Pair @ X1 @ X1 @ X3 @ X4)) @ bot_bot @ set @ product_prod @ X0 @ product_prod @ X1 @ X1) @ (insert @ X1 @ X3 @ (insert @ X1 @ X4 @ bot_bot @ set @ X1)))) = (labeled_LG @ X0 @ X1 @ (insert @ product_prod @ X0 @ product_prod @ X1 @ X1 @ (product_Pair @ X0 @ product_prod @ X1 @ X1 @ X2 @ (product_Pair @ X1 @ X1 @ X3 @ X4)) @ bot_bot @ set @ product_prod @ X0 @ product_prod @ X1 @ X1) @ (insert @ X1 @ X3 @ (insert @ X1 @ X4 @ bot_bot @ set @ X1))))) )),
% 21.27/4.33 inference(cnf_transformation,[status(thm)],[f404])).
% 21.27/4.33 thf(f404,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X1,X4 : X1] : ((restrict @ X0 @ X1 @ (labeled_LG @ X0 @ X1 @ (insert @ product_prod @ X0 @ product_prod @ X1 @ X1 @ (product_Pair @ X0 @ product_prod @ X1 @ X1 @ X2 @ (product_Pair @ X1 @ X1 @ X3 @ X4)) @ bot_bot @ set @ product_prod @ X0 @ product_prod @ X1 @ X1) @ (insert @ X1 @ X3 @ (insert @ X1 @ X4 @ bot_bot @ set @ X1)))) = (labeled_LG @ X0 @ X1 @ (insert @ product_prod @ X0 @ product_prod @ X1 @ X1 @ (product_Pair @ X0 @ product_prod @ X1 @ X1 @ X2 @ (product_Pair @ X1 @ X1 @ X3 @ X4)) @ bot_bot @ set @ product_prod @ X0 @ product_prod @ X1 @ X1) @ (insert @ X1 @ X3 @ (insert @ X1 @ X4 @ bot_bot @ set @ X1))))),
% 21.27/4.33 inference(fool_elimination,[status(thm)],[f403])).
% 21.27/4.33 thf(f403,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X1,X4 : X1] : ((restrict @ X0 @ X1 @ (labeled_LG @ X0 @ X1 @ (insert @ product_prod @ X0 @ product_prod @ X1 @ X1 @ (product_Pair @ X0 @ product_prod @ X1 @ X1 @ X2 @ (product_Pair @ X1 @ X1 @ X3 @ X4)) @ bot_bot @ set @ product_prod @ X0 @ product_prod @ X1 @ X1) @ (insert @ X1 @ X3 @ (insert @ X1 @ X4 @ bot_bot @ set @ X1)))) = (labeled_LG @ X0 @ X1 @ (insert @ product_prod @ X0 @ product_prod @ X1 @ X1 @ (product_Pair @ X0 @ product_prod @ X1 @ X1 @ X2 @ (product_Pair @ X1 @ X1 @ X3 @ X4)) @ bot_bot @ set @ product_prod @ X0 @ product_prod @ X1 @ X1) @ (insert @ X1 @ X3 @ (insert @ X1 @ X4 @ bot_bot @ set @ X1))))),
% 21.27/4.33 inference(rectify,[status(thm)],[f7])).
% 21.27/4.33 thf(f7,axiom,(
% 21.27/4.33 ! [X0 : $tType,X2 : $tType,X8 : X0,X9 : X2,X10 : X2] : ((labeled_LG @ X0 @ X2 @ (insert @ product_prod @ X0 @ product_prod @ X2 @ X2 @ (product_Pair @ X0 @ product_prod @ X2 @ X2 @ X8 @ (product_Pair @ X2 @ X2 @ X9 @ X10)) @ bot_bot @ set @ product_prod @ X0 @ product_prod @ X2 @ X2) @ (insert @ X2 @ X9 @ (insert @ X2 @ X10 @ bot_bot @ set @ X2))) = (restrict @ X0 @ X2 @ (labeled_LG @ X0 @ X2 @ (insert @ product_prod @ X0 @ product_prod @ X2 @ X2 @ (product_Pair @ X0 @ product_prod @ X2 @ X2 @ X8 @ (product_Pair @ X2 @ X2 @ X9 @ X10)) @ bot_bot @ set @ product_prod @ X0 @ product_prod @ X2 @ X2) @ (insert @ X2 @ X9 @ (insert @ X2 @ X10 @ bot_bot @ set @ X2)))))),
% 21.27/4.33 file('/export/starexec/sandbox/tmp/tmp.L5LtdenOSc/DTF2THF_15863.p',fact_6_graph__single)).
% 21.27/4.33 thf(f1764,plain,(
% 21.27/4.33 ( ! [X0 : set @ nat] : (((labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ X0)) != (restrict @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ X0)))) | ($true != (ord_less_eq @ set @ nat @ X0 @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat)))) ) | spl117_2),
% 21.27/4.33 inference(superposition,[status(thm)],[f1762,f1683])).
% 21.27/4.33 thf(f1683,plain,(
% 21.27/4.33 ( ! [X0 : $tType,X2 : set @ X0,X3 : X0] : (((insert @ X0 @ X3 @ bot_bot @ set @ X0) = (insert @ X0 @ X3 @ X2)) | ($true != (ord_less_eq @ set @ X0 @ X2 @ (insert @ X0 @ X3 @ bot_bot @ set @ X0)))) )),
% 21.27/4.33 inference(equality_resolution,[status(thm)],[f1355])).
% 21.27/4.33 thf(f1355,plain,(
% 21.27/4.33 ( ! [X0 : $tType,X2 : set @ X0,X3 : X0,X1 : X0] : (((insert @ X0 @ X3 @ bot_bot @ set @ X0) = (insert @ X0 @ X1 @ X2)) | ($true != (ord_less_eq @ set @ X0 @ X2 @ (insert @ X0 @ X3 @ bot_bot @ set @ X0))) | (X1 != X3)) )),
% 21.27/4.33 inference(cnf_transformation,[status(thm)],[f1124])).
% 21.27/4.33 thf(f1124,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : X0,X2 : set @ X0,X3 : X0] : ((((insert @ X0 @ X3 @ bot_bot @ set @ X0) = (insert @ X0 @ X1 @ X2)) | ($true != (ord_less_eq @ set @ X0 @ X2 @ (insert @ X0 @ X3 @ bot_bot @ set @ X0))) | (X1 != X3)) & ((($true = (ord_less_eq @ set @ X0 @ X2 @ (insert @ X0 @ X3 @ bot_bot @ set @ X0))) & (X1 = X3)) | ((insert @ X0 @ X3 @ bot_bot @ set @ X0) != (insert @ X0 @ X1 @ X2))))),
% 21.27/4.33 inference(flattening,[status(thm)],[f1123])).
% 21.27/4.33 thf(f1123,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : X0,X2 : set @ X0,X3 : X0] : ((((insert @ X0 @ X3 @ bot_bot @ set @ X0) = (insert @ X0 @ X1 @ X2)) | (($true != (ord_less_eq @ set @ X0 @ X2 @ (insert @ X0 @ X3 @ bot_bot @ set @ X0))) | (X1 != X3))) & ((($true = (ord_less_eq @ set @ X0 @ X2 @ (insert @ X0 @ X3 @ bot_bot @ set @ X0))) & (X1 = X3)) | ((insert @ X0 @ X3 @ bot_bot @ set @ X0) != (insert @ X0 @ X1 @ X2))))),
% 21.27/4.33 inference(nnf_transformation,[status(thm)],[f833])).
% 21.27/4.33 thf(f833,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : X0,X2 : set @ X0,X3 : X0] : (((insert @ X0 @ X3 @ bot_bot @ set @ X0) = (insert @ X0 @ X1 @ X2)) <=> (($true = (ord_less_eq @ set @ X0 @ X2 @ (insert @ X0 @ X3 @ bot_bot @ set @ X0))) & (X1 = X3)))),
% 21.27/4.33 inference(fool_elimination,[status(thm)],[f832])).
% 21.27/4.33 thf(f832,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : X0,X2 : set @ X0,X3 : X0] : (((insert @ X0 @ X3 @ bot_bot @ set @ X0) = (insert @ X0 @ X1 @ X2)) = (ord_less_eq @ set @ X0 @ X2 @ (insert @ X0 @ X3 @ bot_bot @ set @ X0)) & (X1 = X3))),
% 21.27/4.33 inference(rectify,[status(thm)],[f43])).
% 21.27/4.33 thf(f43,axiom,(
% 21.27/4.33 ! [X0 : $tType,X8 : X0,X23 : set @ X0,X9 : X0] : (((insert @ X0 @ X8 @ X23) = (insert @ X0 @ X9 @ bot_bot @ set @ X0)) = (ord_less_eq @ set @ X0 @ X23 @ (insert @ X0 @ X9 @ bot_bot @ set @ X0)) & (X8 = X9))),
% 21.27/4.33 file('/export/starexec/sandbox/tmp/tmp.L5LtdenOSc/DTF2THF_15863.p',fact_42_singleton__insert__inj__eq_H)).
% 21.27/4.33 thf(f1762,plain,(
% 21.27/4.33 ((restrict @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) != (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) | spl117_2),
% 21.27/4.33 inference(avatar_component_clause,[status(thm)],[f1760])).
% 21.27/4.33 thf(f1760,definition,(
% 21.27/4.33 spl117_2 <=> ((restrict @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) = (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat)))),
% 21.27/4.33 introduced(definition,[new_symbols(naming,[spl117_2])],[avatar_definition])).
% 21.27/4.33 thf(f1763,plain,(
% 21.27/4.33 ~spl117_1 | ~spl117_2),
% 21.27/4.33 inference(avatar_split_clause,[status(thm)],[f1754,f1760,f1756])).
% 21.27/4.33 thf(f1754,plain,(
% 21.27/4.33 ((restrict @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) != (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) | ((edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ f @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true)),
% 21.27/4.33 inference(forward_demodulation,[status(thm)],[f1753,f1575])).
% 21.27/4.33 thf(f1753,plain,(
% 21.27/4.33 ((restrict @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) != (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) | ($true != (edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ f @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)))),
% 21.27/4.33 inference(forward_demodulation,[status(thm)],[f1752,f1494])).
% 21.27/4.33 thf(f1494,plain,(
% 21.27/4.33 ( ! [X1 : $tType,X0 : $tType,X2 : set @ product_prod @ X1 @ product_prod @ X0 @ X0,X3 : set @ X0] : (((labeled_edges @ X1 @ X0 @ (labeled_LG @ X1 @ X0 @ X2 @ X3)) = X2)) )),
% 21.27/4.33 inference(cnf_transformation,[status(thm)],[f339])).
% 21.27/4.33 thf(f339,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : $tType,X2 : set @ product_prod @ X1 @ product_prod @ X0 @ X0,X3 : set @ X0] : ((labeled_edges @ X1 @ X0 @ (labeled_LG @ X1 @ X0 @ X2 @ X3)) = X2)),
% 21.27/4.33 inference(fool_elimination,[status(thm)],[f338])).
% 21.27/4.33 thf(f338,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : $tType,X2 : set @ product_prod @ X1 @ product_prod @ X0 @ X0,X3 : set @ X0] : ((labeled_edges @ X1 @ X0 @ (labeled_LG @ X1 @ X0 @ X2 @ X3)) = X2)),
% 21.27/4.33 inference(rectify,[status(thm)],[f39])).
% 21.27/4.33 thf(f39,axiom,(
% 21.27/4.33 ! [X1 : $tType,X4 : $tType,X17 : set @ product_prod @ X4 @ product_prod @ X1 @ X1,X18 : set @ X1] : ((labeled_edges @ X4 @ X1 @ (labeled_LG @ X4 @ X1 @ X17 @ X18)) = X17)),
% 21.27/4.33 file('/export/starexec/sandbox/tmp/tmp.L5LtdenOSc/DTF2THF_15863.p',fact_38_labeled__graph_Osel_I1_J)).
% 21.27/4.33 thf(f1752,plain,(
% 21.27/4.33 ((restrict @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) != (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) | ((edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ f @ (labeled_edges @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true)),
% 21.27/4.33 inference(forward_demodulation,[status(thm)],[f1751,f1415])).
% 21.27/4.33 thf(f1751,plain,(
% 21.27/4.33 ((restrict @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) != (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) | ((edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_edges @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true)),
% 21.27/4.33 inference(trivial_inequality_removal,[status(thm)],[f1750])).
% 21.27/4.33 thf(f1750,plain,(
% 21.27/4.33 ((insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat) != (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat)) | ((restrict @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) != (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) | ((edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_edges @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true)),
% 21.27/4.33 inference(forward_demodulation,[status(thm)],[f1749,f1274])).
% 21.27/4.33 thf(f1274,plain,(
% 21.27/4.33 ( ! [X1 : $tType,X0 : $tType] : ((bot_bot @ set @ X1 = (domain @ X1 @ X0 @ bot_bot @ set @ product_prod @ X1 @ X0))) )),
% 21.27/4.33 inference(cnf_transformation,[status(thm)],[f588])).
% 21.27/4.33 thf(f588,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : $tType] : (bot_bot @ set @ X1 = (domain @ X1 @ X0 @ bot_bot @ set @ product_prod @ X1 @ X0))),
% 21.27/4.33 inference(fool_elimination,[status(thm)],[f587])).
% 21.27/4.33 thf(f587,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : $tType] : (bot_bot @ set @ X1 = (domain @ X1 @ X0 @ bot_bot @ set @ product_prod @ X1 @ X0))),
% 21.27/4.33 inference(rectify,[status(thm)],[f14])).
% 21.27/4.33 thf(f14,axiom,(
% 21.27/4.33 ! [X2 : $tType,X0 : $tType] : ((domain @ X0 @ X2 @ bot_bot @ set @ product_prod @ X0 @ X2) = bot_bot @ set @ X0)),
% 21.27/4.33 file('/export/starexec/sandbox/tmp/tmp.L5LtdenOSc/DTF2THF_15863.p',fact_13_Domain__empty)).
% 21.27/4.33 thf(f1749,plain,(
% 21.27/4.33 ((insert @ nat @ bot_bot @ nat @ (domain @ nat @ sum_sum @ a @ b @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b)) != (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat)) | ((edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_edges @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true) | ((restrict @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) != (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat)))),
% 21.27/4.33 inference(forward_demodulation,[status(thm)],[f1748,f1457])).
% 21.27/4.33 thf(f1457,plain,(
% 21.27/4.33 ( ! [X1 : $tType,X0 : $tType,X2 : set @ product_prod @ X0 @ product_prod @ X1 @ X1,X3 : set @ X1] : (((labeled_vertices @ X0 @ X1 @ (labeled_LG @ X0 @ X1 @ X2 @ X3)) = X3)) )),
% 21.27/4.33 inference(cnf_transformation,[status(thm)],[f472])).
% 21.27/4.33 thf(f472,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : $tType,X2 : set @ product_prod @ X0 @ product_prod @ X1 @ X1,X3 : set @ X1] : ((labeled_vertices @ X0 @ X1 @ (labeled_LG @ X0 @ X1 @ X2 @ X3)) = X3)),
% 21.27/4.33 inference(fool_elimination,[status(thm)],[f471])).
% 21.27/4.33 thf(f471,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : $tType,X2 : set @ product_prod @ X0 @ product_prod @ X1 @ X1,X3 : set @ X1] : ((labeled_vertices @ X0 @ X1 @ (labeled_LG @ X0 @ X1 @ X2 @ X3)) = X3)),
% 21.27/4.33 inference(rectify,[status(thm)],[f38])).
% 21.27/4.33 thf(f38,axiom,(
% 21.27/4.33 ! [X4 : $tType,X1 : $tType,X17 : set @ product_prod @ X4 @ product_prod @ X1 @ X1,X18 : set @ X1] : ((labeled_vertices @ X4 @ X1 @ (labeled_LG @ X4 @ X1 @ X17 @ X18)) = X18)),
% 21.27/4.33 file('/export/starexec/sandbox/tmp/tmp.L5LtdenOSc/DTF2THF_15863.p',fact_37_labeled__graph_Osel_I2_J)).
% 21.27/4.33 thf(f1748,plain,(
% 21.27/4.33 ((insert @ nat @ bot_bot @ nat @ (domain @ nat @ sum_sum @ a @ b @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b)) != (labeled_vertices @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat)))) | ((restrict @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) != (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) | ((edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_edges @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true)),
% 21.27/4.33 inference(forward_demodulation,[status(thm)],[f1747,f1575])).
% 21.27/4.33 thf(f1747,plain,(
% 21.27/4.33 ((labeled_vertices @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) != (insert @ nat @ zero_zero @ nat @ (domain @ nat @ sum_sum @ a @ b @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b))) | ((edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_edges @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true) | ((restrict @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) != (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat)))),
% 21.27/4.33 inference(forward_demodulation,[status(thm)],[f1746,f1475])).
% 21.27/4.33 thf(f1475,plain,(
% 21.27/4.33 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : X0,X4 : set @ product_prod @ X1 @ X0] : (((insert @ X1 @ X2 @ (domain @ X1 @ X0 @ X4)) = (domain @ X1 @ X0 @ (insert @ product_prod @ X1 @ X0 @ (product_Pair @ X1 @ X0 @ X2 @ X3) @ X4)))) )),
% 21.27/4.33 inference(cnf_transformation,[status(thm)],[f630])).
% 21.27/4.33 thf(f630,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : X0,X4 : set @ product_prod @ X1 @ X0] : ((insert @ X1 @ X2 @ (domain @ X1 @ X0 @ X4)) = (domain @ X1 @ X0 @ (insert @ product_prod @ X1 @ X0 @ (product_Pair @ X1 @ X0 @ X2 @ X3) @ X4)))),
% 21.27/4.33 inference(fool_elimination,[status(thm)],[f629])).
% 21.27/4.33 thf(f629,plain,(
% 21.27/4.33 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : X0,X4 : set @ product_prod @ X1 @ X0] : ((insert @ X1 @ X2 @ (domain @ X1 @ X0 @ X4)) = (domain @ X1 @ X0 @ (insert @ product_prod @ X1 @ X0 @ (product_Pair @ X1 @ X0 @ X2 @ X3) @ X4)))),
% 21.27/4.33 inference(rectify,[status(thm)],[f10])).
% 21.27/4.33 thf(f10,axiom,(
% 21.27/4.33 ! [X2 : $tType,X0 : $tType,X8 : X0,X9 : X2,X12 : set @ product_prod @ X0 @ X2] : ((domain @ X0 @ X2 @ (insert @ product_prod @ X0 @ X2 @ (product_Pair @ X0 @ X2 @ X8 @ X9) @ X12)) = (insert @ X0 @ X8 @ (domain @ X0 @ X2 @ X12)))),
% 21.27/4.33 file('/export/starexec/sandbox/tmp/tmp.L5LtdenOSc/DTF2THF_15863.p',fact_9_Domain__insert)).
% 21.27/4.33 thf(f1746,plain,(
% 21.27/4.33 ((labeled_vertices @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) != (domain @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b))) | ((restrict @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) != (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) | ((edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_edges @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true)),
% 21.27/4.33 inference(subsumption_resolution,[status(thm)],[f1745,f1609])).
% 21.27/4.33 thf(f1609,plain,(
% 21.27/4.33 ((ord_less_eq @ set @ sum_sum @ a @ b @ (image @ nat @ sum_sum @ a @ b @ f @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)) @ (labeled_vertices @ standard_Constant @ a @ sum_sum @ a @ b @ g)) = $true)),
% 21.27/4.33 inference(cnf_transformation,[status(thm)],[f508])).
% 21.27/4.33 thf(f508,plain,(
% 21.27/4.33 ((ord_less_eq @ set @ sum_sum @ a @ b @ (image @ nat @ sum_sum @ a @ b @ f @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)) @ (labeled_vertices @ standard_Constant @ a @ sum_sum @ a @ b @ g)) = $true)),
% 21.27/4.33 inference(fool_elimination,[status(thm)],[f507])).
% 21.27/4.33 thf(f507,plain,(
% 21.27/4.33 (ord_less_eq @ set @ sum_sum @ a @ b @ (image @ nat @ sum_sum @ a @ b @ f @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)) @ (labeled_vertices @ standard_Constant @ a @ sum_sum @ a @ b @ g))),
% 21.27/4.33 inference(rectify,[status(thm)],[f4])).
% 21.27/4.33 thf(f4,axiom,(
% 21.27/4.33 (ord_less_eq @ set @ sum_sum @ a @ b @ (image @ nat @ sum_sum @ a @ b @ f @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)) @ (labeled_vertices @ standard_Constant @ a @ sum_sum @ a @ b @ g))),
% 21.27/4.33 file('/export/starexec/sandbox/tmp/tmp.L5LtdenOSc/DTF2THF_15863.p',fact_3_r)).
% 21.27/4.33 thf(f1745,plain,(
% 21.27/4.33 ((labeled_vertices @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) != (domain @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b))) | ((ord_less_eq @ set @ sum_sum @ a @ b @ (image @ nat @ sum_sum @ a @ b @ f @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)) @ (labeled_vertices @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true) | ((edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_edges @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true) | ((restrict @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) != (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat)))),
% 21.27/4.33 inference(forward_demodulation,[status(thm)],[f1744,f1457])).
% 21.27/4.33 thf(f1744,plain,(
% 21.27/4.33 ((restrict @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) != (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) | ((ord_less_eq @ set @ sum_sum @ a @ b @ (image @ nat @ sum_sum @ a @ b @ f @ (labeled_vertices @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)))) @ (labeled_vertices @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true) | ((labeled_vertices @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) != (domain @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b))) | ((edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_edges @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true)),
% 21.27/4.33 inference(forward_demodulation,[status(thm)],[f1743,f1415])).
% 21.27/4.33 thf(f1743,plain,(
% 21.27/4.33 ((ord_less_eq @ set @ sum_sum @ a @ b @ (image @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_vertices @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)))) @ (labeled_vertices @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true) | ((edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_edges @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true) | ((restrict @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) != (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) | ((labeled_vertices @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) != (domain @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b)))),
% 21.27/4.33 inference(subsumption_resolution,[status(thm)],[f1742,f1535])).
% 21.27/4.33 thf(f1535,plain,(
% 21.27/4.33 ((univalent @ nat @ sum_sum @ a @ b @ f) = $true)),
% 21.27/4.33 inference(cnf_transformation,[status(thm)],[f337])).
% 21.27/4.33 thf(f337,plain,(
% 21.27/4.33 ((univalent @ nat @ sum_sum @ a @ b @ f) = $true)),
% 21.27/4.33 inference(fool_elimination,[status(thm)],[f336])).
% 21.27/4.33 thf(f336,plain,(
% 21.27/4.33 (univalent @ nat @ sum_sum @ a @ b @ f)),
% 21.27/4.33 inference(rectify,[status(thm)],[f9])).
% 21.27/4.33 thf(f9,axiom,(
% 21.27/4.33 (univalent @ nat @ sum_sum @ a @ b @ f)),
% 21.27/4.33 file('/export/starexec/sandbox/tmp/tmp.L5LtdenOSc/DTF2THF_15863.p',fact_8_u)).
% 21.27/4.33 thf(f1742,plain,(
% 21.27/4.33 ((labeled_vertices @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) != (domain @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b))) | ((edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_edges @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true) | ((ord_less_eq @ set @ sum_sum @ a @ b @ (image @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_vertices @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)))) @ (labeled_vertices @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true) | ((univalent @ nat @ sum_sum @ a @ b @ f) != $true) | ((restrict @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) != (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat)))),
% 21.27/4.33 inference(forward_demodulation,[status(thm)],[f1741,f1415])).
% 21.27/4.33 thf(f1741,plain,(
% 21.27/4.33 ((univalent @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b)) != $true) | ((restrict @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) != (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ bot_bot @ nat @ bot_bot @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ bot_bot @ nat @ bot_bot @ set @ nat))) | ((ord_less_eq @ set @ sum_sum @ a @ b @ (image @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_vertices @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)))) @ (labeled_vertices @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true) | ((labeled_vertices @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) != (domain @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b))) | ((edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_edges @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true)),
% 21.27/4.33 inference(forward_demodulation,[status(thm)],[f1740,f1575])).
% 21.27/4.33 thf(f1740,plain,(
% 21.27/4.33 ((labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)) != (restrict @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)))) | ((labeled_vertices @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) != (domain @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b))) | ((edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_edges @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true) | ((univalent @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b)) != $true) | ((ord_less_eq @ set @ sum_sum @ a @ b @ (image @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_vertices @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)))) @ (labeled_vertices @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true)),
% 21.27/4.33 inference(subsumption_resolution,[status(thm)],[f1629,f1666])).
% 21.27/4.33 thf(f1666,plain,(
% 21.27/4.33 (g = (restrict @ standard_Constant @ a @ sum_sum @ a @ b @ g))),
% 21.27/4.33 inference(cnf_transformation,[status(thm)],[f382])).
% 21.27/4.33 thf(f382,plain,(
% 21.27/4.33 (g = (restrict @ standard_Constant @ a @ sum_sum @ a @ b @ g))),
% 21.27/4.33 inference(fool_elimination,[status(thm)],[f1])).
% 21.27/4.33 thf(f1,axiom,(
% 21.27/4.33 (g = (restrict @ standard_Constant @ a @ sum_sum @ a @ b @ g))),
% 21.27/4.33 file('/export/starexec/sandbox/tmp/tmp.L5LtdenOSc/DTF2THF_15863.p',fact_0_g)).
% 21.27/4.33 thf(f1629,plain,(
% 21.27/4.33 ((ord_less_eq @ set @ sum_sum @ a @ b @ (image @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_vertices @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)))) @ (labeled_vertices @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true) | ((univalent @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b)) != $true) | ((labeled_vertices @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) != (domain @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b))) | ((labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)) != (restrict @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)))) | (g != (restrict @ standard_Constant @ a @ sum_sum @ a @ b @ g)) | ((edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_edges @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true)),
% 21.27/4.33 inference(cnf_transformation,[status(thm)],[f990])).
% 21.27/4.33 thf(f990,plain,(
% 21.27/4.33 ((labeled_vertices @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) != (domain @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b))) | ((ord_less_eq @ set @ sum_sum @ a @ b @ (image @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_vertices @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)))) @ (labeled_vertices @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true) | (g != (restrict @ standard_Constant @ a @ sum_sum @ a @ b @ g)) | ((labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)) != (restrict @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)))) | ((edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_edges @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)) != $true) | ((univalent @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b)) != $true)),
% 21.27/4.33 inference(ennf_transformation,[status(thm)],[f735])).
% 21.27/4.33 thf(f735,plain,(
% 21.27/4.33 ~(((labeled_vertices @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) = (domain @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b))) & (g = (restrict @ standard_Constant @ a @ sum_sum @ a @ b @ g)) & ((edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_edges @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)) = $true) & ((labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)) = (restrict @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)))) & ((ord_less_eq @ set @ sum_sum @ a @ b @ (image @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_vertices @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)))) @ (labeled_vertices @ standard_Constant @ a @ sum_sum @ a @ b @ g)) = $true) & ((univalent @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b)) = $true))),
% 21.27/4.33 inference(fool_elimination,[status(thm)],[f734])).
% 21.27/4.33 thf(f734,plain,(
% 21.27/4.33 ~((ord_less_eq @ set @ sum_sum @ a @ b @ (image @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_vertices @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)))) @ (labeled_vertices @ standard_Constant @ a @ sum_sum @ a @ b @ g)) & (edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_edges @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)) & ((labeled_vertices @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) = (domain @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b))) & ((labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)) = (restrict @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)))) & (g = (restrict @ standard_Constant @ a @ sum_sum @ a @ b @ g)) & (univalent @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b)))),
% 21.27/4.33 inference(rectify,[status(thm)],[f282])).
% 21.27/4.33 thf(f282,negated_conjecture,(
% 21.27/4.33 ~((ord_less_eq @ set @ sum_sum @ a @ b @ (image @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_vertices @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)))) @ (labeled_vertices @ standard_Constant @ a @ sum_sum @ a @ b @ g)) & (edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_edges @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)) & ((labeled_vertices @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) = (domain @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b))) & ((labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)) = (restrict @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)))) & (g = (restrict @ standard_Constant @ a @ sum_sum @ a @ b @ g)) & (univalent @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b)))),
% 21.27/4.33 inference(negated_conjecture,[status(cth)],[f281])).
% 21.27/4.33 thf(f281,conjecture,(
% 21.27/4.33 (ord_less_eq @ set @ sum_sum @ a @ b @ (image @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_vertices @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)))) @ (labeled_vertices @ standard_Constant @ a @ sum_sum @ a @ b @ g)) & (edge_preserving @ nat @ sum_sum @ a @ b @ standard_Constant @ a @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b) @ (labeled_edges @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) @ (labeled_edges @ standard_Constant @ a @ sum_sum @ a @ b @ g)) & ((labeled_vertices @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat))) = (domain @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b))) & ((labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)) = (restrict @ standard_Constant @ a @ nat @ (labeled_LG @ standard_Constant @ a @ nat @ (insert @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat @ (product_Pair @ standard_Constant @ a @ product_prod @ nat @ nat @ standard_S_Idt @ a @ (product_Pair @ nat @ nat @ zero_zero @ nat @ zero_zero @ nat)) @ bot_bot @ set @ product_prod @ standard_Constant @ a @ product_prod @ nat @ nat) @ (insert @ nat @ zero_zero @ nat @ bot_bot @ set @ nat)))) & (g = (restrict @ standard_Constant @ a @ sum_sum @ a @ b @ g)) & (univalent @ nat @ sum_sum @ a @ b @ (insert @ product_prod @ nat @ sum_sum @ a @ b @ (product_Pair @ nat @ sum_sum @ a @ b @ zero_zero @ nat @ v) @ bot_bot @ set @ product_prod @ nat @ sum_sum @ a @ b))),
% 21.27/4.33 file('/export/starexec/sandbox/tmp/tmp.L5LtdenOSc/DTF2THF_15863.p',conj_0)).
% 21.27/4.33 % SZS output end Proof for DTF2THF_15863
% 21.27/4.33 % (16280)------------------------------
% 21.27/4.33 % (16280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.27/4.33 % (16280)Termination reason: Refutation
% 21.27/4.33
% 21.27/4.33 % (16280)Memory used [KB]: 8315
% 21.27/4.33 % (16280)Time elapsed: 0.109 s
% 21.27/4.33 % (16280)Instructions burned: 329 (million)
% 21.27/4.33 % (16280)------------------------------
% 21.27/4.33 % (16280)------------------------------
% 21.27/4.33 % (16139)Success in time 2.73 s
%------------------------------------------------------------------------------