TSTP Solution File: ITP179^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP179^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 03:18:56 EDT 2023
% Result : Theorem 0.52s 1.11s
% Output : Proof 0.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.18 % Problem : ITP179^1 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.19 % Command : do_cvc5 %s %d
% 0.20/0.41 % Computer : n006.cluster.edu
% 0.20/0.41 % Model : x86_64 x86_64
% 0.20/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.41 % Memory : 8042.1875MB
% 0.20/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.41 % CPULimit : 300
% 0.20/0.41 % WCLimit : 300
% 0.20/0.41 % DateTime : Sun Aug 27 14:58:52 EDT 2023
% 0.20/0.41 % CPUTime :
% 0.26/0.60 %----Proving TH0
% 0.26/0.61 %------------------------------------------------------------------------------
% 0.26/0.61 % File : ITP179^1 : TPTP v8.1.2. Released v7.5.0.
% 0.26/0.61 % Domain : Interactive Theorem Proving
% 0.26/0.61 % Problem : Sledgehammer StandardRules problem prob_555__5392816_1
% 0.26/0.61 % Version : Especial.
% 0.26/0.61 % English :
% 0.26/0.61
% 0.26/0.61 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.26/0.61 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.26/0.61 % Source : [Des21]
% 0.26/0.61 % Names : StandardRules/prob_555__5392816_1 [Des21]
% 0.26/0.61
% 0.26/0.61 % Status : Theorem
% 0.26/0.61 % Rating : 0.15 v8.1.0, 0.18 v7.5.0
% 0.26/0.61 % Syntax : Number of formulae : 554 ( 231 unt; 201 typ; 0 def)
% 0.26/0.61 % Number of atoms : 847 ( 345 equ; 0 cnn)
% 0.26/0.61 % Maximal formula atoms : 6 ( 2 avg)
% 0.26/0.61 % Number of connectives : 2464 ( 112 ~; 9 |; 56 &;2064 @)
% 0.26/0.61 % ( 0 <=>; 223 =>; 0 <=; 0 <~>)
% 0.26/0.61 % Maximal formula depth : 18 ( 5 avg)
% 0.26/0.61 % Number of types : 55 ( 54 usr)
% 0.26/0.61 % Number of type conns : 262 ( 262 >; 0 *; 0 +; 0 <<)
% 0.26/0.61 % Number of symbols : 148 ( 147 usr; 27 con; 0-3 aty)
% 0.26/0.61 % Number of variables : 835 ( 20 ^; 788 !; 27 ?; 835 :)
% 0.26/0.61 % SPC : TH0_THM_EQU_NAR
% 0.26/0.61
% 0.26/0.61 % Comments : This file was generated by Sledgehammer 2021-02-23 15:38:59.416
% 0.26/0.61 %------------------------------------------------------------------------------
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% 0.26/0.61 insert271595217at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J,type,
% 0.26/0.61 insert983991207um_a_b: produc1124793815um_a_b > set_Pr1174980151um_a_b > set_Pr1174980151um_a_b ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J,type,
% 0.26/0.61 insert1435405693um_a_b: produc1548871597um_a_b > set_Pr1916610317um_a_b > set_Pr1916610317um_a_b ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set_Oinsert_001t__Sum____Type__Osum_Itf__a_Mtf__b_J,type,
% 0.26/0.61 insert_Sum_sum_a_b: sum_sum_a_b > set_Sum_sum_a_b > set_Sum_sum_a_b ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Ocongruence__rule_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
% 0.26/0.61 standa1343274079tant_a: standard_Constant_a > standard_Constant_a > produc1871334759_a_nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Ononempty__rule_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
% 0.26/0.61 standa1410829644tant_a: produc1871334759_a_nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Oreflexivity__rule_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
% 0.26/0.61 standa63370785tant_a: standard_Constant_a > produc1871334759_a_nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Osymmetry__rule_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
% 0.26/0.61 standa997693288tant_a: standard_Constant_a > produc1871334759_a_nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Otransitive__rule_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
% 0.26/0.61 standa1795879409tant_a: standard_Constant_a > produc1871334759_a_nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
% 0.26/0.61 member1632892294tant_a: standard_Constant_a > set_St761939237tant_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Nat__Onat,type,
% 0.26/0.61 member_nat: nat > set_nat > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.26/0.61 member1696759390at_nat: produc1032616263at_nat > set_Pr1647387645at_nat > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J,type,
% 0.26/0.61 member1502344244um_a_b: produc1003469085um_a_b > set_Pr326391507um_a_b > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J,type,
% 0.26/0.61 member1998628618um_a_b: produc1963079155um_a_b > set_Pr409224873um_a_b > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J,type,
% 0.26/0.61 member1641046175um_a_b: produc1394389750um_a_b > set_Pr1994339542um_a_b > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.26/0.61 member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J,type,
% 0.26/0.61 member1139034387um_a_b: produc204140796um_a_b > set_Pr1618094130um_a_b > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J,type,
% 0.26/0.61 member1294585472um_a_b: produc1124793815um_a_b > set_Pr1174980151um_a_b > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J,type,
% 0.26/0.61 member1590479267um_a_b: produc1681803642um_a_b > set_Pr1121389018um_a_b > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J,type,
% 0.26/0.61 member834135910um_a_b: produc1546082365um_a_b > set_Pr386468381um_a_b > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J,type,
% 0.26/0.61 member585880557um_a_b: produc1798470614um_a_b > set_Pr195945996um_a_b > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J,type,
% 0.26/0.61 member429827856um_a_b: produc1918750183um_a_b > set_Pr45173959um_a_b > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J,type,
% 0.26/0.61 member748122307um_a_b: produc585753260um_a_b > set_Pr653770722um_a_b > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Nat__Onat_J,type,
% 0.26/0.61 member1249152_b_nat: produc1978941143_b_nat > set_Pr375490359_b_nat > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J_J,type,
% 0.26/0.61 member1641922979um_a_b: produc1733247354um_a_b > set_Pr1558970842um_a_b > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J,type,
% 0.26/0.61 member485470653um_a_b: produc323101606um_a_b > set_Pr1783309276um_a_b > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J,type,
% 0.26/0.61 member947389014um_a_b: produc1548871597um_a_b > set_Pr1916610317um_a_b > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Sum____Type__Osum_Itf__a_Mtf__b_J,type,
% 0.26/0.61 member_Sum_sum_a_b: sum_sum_a_b > set_Sum_sum_a_b > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_v_G,type,
% 0.26/0.61 g: labele431970251um_a_b ).
% 0.26/0.61
% 0.26/0.61 thf(sy_v_f____,type,
% 0.26/0.61 f: set_Pr1174980151um_a_b ).
% 0.26/0.61
% 0.26/0.61 thf(sy_v_l,type,
% 0.26/0.61 l: standard_Constant_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_v_v____,type,
% 0.26/0.61 v: sum_sum_a_b ).
% 0.26/0.61
% 0.26/0.61 % Relevant facts (352)
% 0.26/0.61 thf(fact_0_g,axiom,
% 0.26/0.61 ( g
% 0.26/0.61 = ( restri1162247455um_a_b @ g ) ) ).
% 0.26/0.61
% 0.26/0.61 % g
% 0.26/0.61 thf(fact_1_v,axiom,
% 0.26/0.61 member_Sum_sum_a_b @ v @ ( labele577278695um_a_b @ g ) ).
% 0.26/0.61
% 0.26/0.61 % v
% 0.26/0.61 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,
% 0.26/0.61 edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( labele1939049654um_a_b @ g ) ).
% 0.26/0.61
% 0.26/0.61 % \<open>edge_preserving {(0::?'c1, v)} {(S_Idt, 0::?'c1, 0::?'c1)} (edges G)\<close>
% 0.26/0.61 thf(fact_3_r,axiom,
% 0.26/0.61 ord_le192794300um_a_b @ ( image_256773707um_a_b @ f @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ ( labele577278695um_a_b @ g ) ).
% 0.26/0.61
% 0.26/0.61 % r
% 0.26/0.61 thf(fact_4_f,axiom,
% 0.26/0.61 ( f
% 0.26/0.61 = ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) ).
% 0.26/0.61
% 0.26/0.61 % f
% 0.26/0.61 thf(fact_5_d,axiom,
% 0.26/0.61 ( ( domain1368163076um_a_b @ f )
% 0.26/0.61 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 0.26/0.61
% 0.26/0.61 % d
% 0.26/0.61 thf(fact_6_graph__single,axiom,
% 0.26/0.61 ! [A: standard_Constant_a,B: sum_sum_a_b,C: sum_sum_a_b] :
% 0.26/0.61 ( ( labele1729654377um_a_b @ ( insert323157027um_a_b @ ( produc1697725733um_a_b @ A @ ( produc176426981um_a_b @ B @ C ) ) @ bot_bo1262634813um_a_b ) @ ( insert_Sum_sum_a_b @ B @ ( insert_Sum_sum_a_b @ C @ bot_bo1491243248um_a_b ) ) )
% 0.26/0.61 = ( restri1162247455um_a_b @ ( labele1729654377um_a_b @ ( insert323157027um_a_b @ ( produc1697725733um_a_b @ A @ ( produc176426981um_a_b @ B @ C ) ) @ bot_bo1262634813um_a_b ) @ ( insert_Sum_sum_a_b @ B @ ( insert_Sum_sum_a_b @ C @ bot_bo1491243248um_a_b ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % graph_single
% 0.26/0.61 thf(fact_7_graph__single,axiom,
% 0.26/0.61 ! [A: standard_Constant_a,B: nat,C: nat] :
% 0.26/0.61 ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ A @ ( product_Pair_nat_nat @ B @ C ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ B @ ( insert_nat @ C @ bot_bot_set_nat ) ) )
% 0.26/0.61 = ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ A @ ( product_Pair_nat_nat @ B @ C ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ B @ ( insert_nat @ C @ bot_bot_set_nat ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % graph_single
% 0.26/0.61 thf(fact_8__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,
% 0.26/0.61 ~ ! [V: sum_sum_a_b] :
% 0.26/0.61 ~ ( member1294585472um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ V ) @ f ) ).
% 0.26/0.61
% 0.26/0.61 % \<open>\<And>thesis. (\<And>v. (0, v) \<in> f \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.26/0.61 thf(fact_9_u,axiom,
% 0.26/0.61 unival2092813468um_a_b @ f ).
% 0.26/0.61
% 0.26/0.61 % u
% 0.26/0.61 thf(fact_10_Domain__insert,axiom,
% 0.26/0.61 ! [A: standard_Constant_a,B: product_prod_nat_nat,R: set_Pr1647387645at_nat] :
% 0.26/0.61 ( ( domain1060562500at_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ A @ B ) @ R ) )
% 0.26/0.61 = ( insert1909710879tant_a @ A @ ( domain1060562500at_nat @ R ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Domain_insert
% 0.26/0.61 thf(fact_11_Domain__insert,axiom,
% 0.26/0.61 ! [A: nat,B: nat,R: set_Pr1986765409at_nat] :
% 0.26/0.61 ( ( domain_nat_nat @ ( insert271595217at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R ) )
% 0.26/0.61 = ( insert_nat @ A @ ( domain_nat_nat @ R ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Domain_insert
% 0.26/0.61 thf(fact_12_Domain__insert,axiom,
% 0.26/0.61 ! [A: nat,B: sum_sum_a_b,R: set_Pr1174980151um_a_b] :
% 0.26/0.61 ( ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ A @ B ) @ R ) )
% 0.26/0.61 = ( insert_nat @ A @ ( domain1368163076um_a_b @ R ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Domain_insert
% 0.26/0.61 thf(fact_13_Domain__insert,axiom,
% 0.26/0.61 ! [A: standard_Constant_a,B: produc1548871597um_a_b,R: set_Pr409224873um_a_b] :
% 0.26/0.61 ( ( domain1362581744um_a_b @ ( insert323157027um_a_b @ ( produc1697725733um_a_b @ A @ B ) @ R ) )
% 0.26/0.61 = ( insert1909710879tant_a @ A @ ( domain1362581744um_a_b @ R ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Domain_insert
% 0.26/0.61 thf(fact_14_Domain__insert,axiom,
% 0.26/0.61 ! [A: sum_sum_a_b,B: sum_sum_a_b,R: set_Pr1916610317um_a_b] :
% 0.26/0.61 ( ( domain2069673178um_a_b @ ( insert1435405693um_a_b @ ( produc176426981um_a_b @ A @ B ) @ R ) )
% 0.26/0.61 = ( insert_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ R ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Domain_insert
% 0.26/0.61 thf(fact_15_Image__singleton__iff,axiom,
% 0.26/0.61 ! [B: nat,R: set_Pr1986765409at_nat,A: nat] :
% 0.26/0.61 ( ( member_nat @ B @ ( image_nat_nat @ R @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.26/0.61 = ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R ) ) ).
% 0.26/0.61
% 0.26/0.61 % Image_singleton_iff
% 0.26/0.61 thf(fact_16_Image__singleton__iff,axiom,
% 0.26/0.61 ! [B: sum_sum_a_b,R: set_Pr1174980151um_a_b,A: nat] :
% 0.26/0.61 ( ( member_Sum_sum_a_b @ B @ ( image_256773707um_a_b @ R @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.26/0.61 = ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ B ) @ R ) ) ).
% 0.26/0.61
% 0.26/0.61 % Image_singleton_iff
% 0.26/0.61 thf(fact_17_Image__singleton__iff,axiom,
% 0.26/0.61 ! [B: sum_sum_a_b,R: set_Pr1994339542um_a_b,A: standard_Constant_a] :
% 0.26/0.61 ( ( member_Sum_sum_a_b @ B @ ( image_2129435242um_a_b @ R @ ( insert1909710879tant_a @ A @ bot_bo1160111033tant_a ) ) )
% 0.26/0.61 = ( member1641046175um_a_b @ ( produc584843310um_a_b @ A @ B ) @ R ) ) ).
% 0.26/0.61
% 0.26/0.61 % Image_singleton_iff
% 0.26/0.61 thf(fact_18_Image__singleton__iff,axiom,
% 0.26/0.61 ! [B: product_prod_nat_nat,R: set_Pr1647387645at_nat,A: standard_Constant_a] :
% 0.26/0.61 ( ( member701585322at_nat @ B @ ( image_127502653at_nat @ R @ ( insert1909710879tant_a @ A @ bot_bo1160111033tant_a ) ) )
% 0.26/0.61 = ( member1696759390at_nat @ ( produc407553657at_nat @ A @ B ) @ R ) ) ).
% 0.26/0.61
% 0.26/0.61 % Image_singleton_iff
% 0.26/0.61 thf(fact_19_Image__singleton__iff,axiom,
% 0.26/0.61 ! [B: sum_sum_a_b,R: set_Pr195945996um_a_b,A: product_prod_nat_nat] :
% 0.26/0.61 ( ( member_Sum_sum_a_b @ B @ ( image_1754351636um_a_b @ R @ ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) ) )
% 0.26/0.61 = ( member585880557um_a_b @ ( produc1872245072um_a_b @ A @ B ) @ R ) ) ).
% 0.26/0.61
% 0.26/0.61 % Image_singleton_iff
% 0.26/0.61 thf(fact_20_Image__singleton__iff,axiom,
% 0.26/0.61 ! [B: produc1124793815um_a_b,R: set_Pr1618094130um_a_b,A: nat] :
% 0.26/0.61 ( ( member1294585472um_a_b @ B @ ( image_1228479730um_a_b @ R @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.26/0.61 = ( member1139034387um_a_b @ ( produc1346373166um_a_b @ A @ B ) @ R ) ) ).
% 0.26/0.61
% 0.26/0.61 % Image_singleton_iff
% 0.26/0.61 thf(fact_21_Image__singleton__iff,axiom,
% 0.26/0.61 ! [B: sum_sum_a_b,R: set_Pr1916610317um_a_b,A: sum_sum_a_b] :
% 0.26/0.61 ( ( member_Sum_sum_a_b @ B @ ( image_1918588449um_a_b @ R @ ( insert_Sum_sum_a_b @ A @ bot_bo1491243248um_a_b ) ) )
% 0.26/0.61 = ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ B ) @ R ) ) ).
% 0.26/0.61
% 0.26/0.61 % Image_singleton_iff
% 0.26/0.61 thf(fact_22_Image__singleton__iff,axiom,
% 0.26/0.61 ! [B: produc1124793815um_a_b,R: set_Pr326391507um_a_b,A: standard_Constant_a] :
% 0.26/0.61 ( ( member1294585472um_a_b @ B @ ( image_1179143699um_a_b @ R @ ( insert1909710879tant_a @ A @ bot_bo1160111033tant_a ) ) )
% 0.26/0.61 = ( member1502344244um_a_b @ ( produc414524239um_a_b @ A @ B ) @ R ) ) ).
% 0.26/0.61
% 0.26/0.61 % Image_singleton_iff
% 0.26/0.61 thf(fact_23_Image__singleton__iff,axiom,
% 0.26/0.61 ! [B: produc1124793815um_a_b,R: set_Pr386468381um_a_b,A: product_prod_nat_nat] :
% 0.26/0.61 ( ( member1294585472um_a_b @ B @ ( image_320480233um_a_b @ R @ ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) ) )
% 0.26/0.61 = ( member834135910um_a_b @ ( produc335036333um_a_b @ A @ B ) @ R ) ) ).
% 0.26/0.61
% 0.26/0.61 % Image_singleton_iff
% 0.26/0.61 thf(fact_24_Image__singleton__iff,axiom,
% 0.26/0.61 ! [B: sum_sum_a_b,R: set_Pr653770722um_a_b,A: produc1124793815um_a_b] :
% 0.26/0.61 ( ( member_Sum_sum_a_b @ B @ ( image_869585130um_a_b @ R @ ( insert983991207um_a_b @ A @ bot_bo575978147um_a_b ) ) )
% 0.26/0.61 = ( member748122307um_a_b @ ( produc831476262um_a_b @ A @ B ) @ R ) ) ).
% 0.26/0.61
% 0.26/0.61 % Image_singleton_iff
% 0.26/0.61 thf(fact_25_graph__empty__e,axiom,
% 0.26/0.61 ! [V2: set_nat] :
% 0.26/0.61 ( ( labele16114835_a_nat @ bot_bo810816657at_nat @ V2 )
% 0.26/0.61 = ( restri572569417_a_nat @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ V2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % graph_empty_e
% 0.26/0.61 thf(fact_26_graph__empty__e,axiom,
% 0.26/0.61 ! [V2: set_Sum_sum_a_b] :
% 0.26/0.61 ( ( labele1729654377um_a_b @ bot_bo1262634813um_a_b @ V2 )
% 0.26/0.61 = ( restri1162247455um_a_b @ ( labele1729654377um_a_b @ bot_bo1262634813um_a_b @ V2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % graph_empty_e
% 0.26/0.61 thf(fact_27_labeled__graph_Ocollapse,axiom,
% 0.26/0.61 ! [Labeled_graph: labele935650037_a_nat] :
% 0.26/0.61 ( ( labele16114835_a_nat @ ( labele195203296_a_nat @ Labeled_graph ) @ ( labele1810595089_a_nat @ Labeled_graph ) )
% 0.26/0.61 = Labeled_graph ) ).
% 0.26/0.61
% 0.26/0.61 % labeled_graph.collapse
% 0.26/0.61 thf(fact_28_labeled__graph_Ocollapse,axiom,
% 0.26/0.61 ! [Labeled_graph: labele431970251um_a_b] :
% 0.26/0.61 ( ( labele1729654377um_a_b @ ( labele1939049654um_a_b @ Labeled_graph ) @ ( labele577278695um_a_b @ Labeled_graph ) )
% 0.26/0.61 = Labeled_graph ) ).
% 0.26/0.61
% 0.26/0.61 % labeled_graph.collapse
% 0.26/0.61 thf(fact_29_Domain__empty,axiom,
% 0.26/0.61 ( ( domain_nat_nat @ bot_bo2130386637at_nat )
% 0.26/0.61 = bot_bot_set_nat ) ).
% 0.26/0.61
% 0.26/0.61 % Domain_empty
% 0.26/0.61 thf(fact_30_Domain__empty,axiom,
% 0.26/0.61 ( ( domain1060562500at_nat @ bot_bo810816657at_nat )
% 0.26/0.61 = bot_bo1160111033tant_a ) ).
% 0.26/0.61
% 0.26/0.61 % Domain_empty
% 0.26/0.61 thf(fact_31_Domain__empty,axiom,
% 0.26/0.61 ( ( domain1368163076um_a_b @ bot_bo575978147um_a_b )
% 0.26/0.61 = bot_bot_set_nat ) ).
% 0.26/0.61
% 0.26/0.61 % Domain_empty
% 0.26/0.61 thf(fact_32_Domain__empty,axiom,
% 0.26/0.61 ( ( domain2069673178um_a_b @ bot_bo225809273um_a_b )
% 0.26/0.61 = bot_bo1491243248um_a_b ) ).
% 0.26/0.61
% 0.26/0.61 % Domain_empty
% 0.26/0.61 thf(fact_33_Domain__empty,axiom,
% 0.26/0.61 ( ( domain1362581744um_a_b @ bot_bo1262634813um_a_b )
% 0.26/0.61 = bot_bo1160111033tant_a ) ).
% 0.26/0.61
% 0.26/0.61 % Domain_empty
% 0.26/0.61 thf(fact_34_Image__empty1,axiom,
% 0.26/0.61 ! [X: set_St761939237tant_a] :
% 0.26/0.61 ( ( image_127502653at_nat @ bot_bo810816657at_nat @ X )
% 0.26/0.61 = bot_bo2130386637at_nat ) ).
% 0.26/0.61
% 0.26/0.61 % Image_empty1
% 0.26/0.61 thf(fact_35_Image__empty1,axiom,
% 0.26/0.61 ! [X: set_nat] :
% 0.26/0.61 ( ( image_256773707um_a_b @ bot_bo575978147um_a_b @ X )
% 0.26/0.61 = bot_bo1491243248um_a_b ) ).
% 0.26/0.61
% 0.26/0.61 % Image_empty1
% 0.26/0.61 thf(fact_36_Image__empty1,axiom,
% 0.26/0.61 ! [X: set_Sum_sum_a_b] :
% 0.26/0.61 ( ( image_1918588449um_a_b @ bot_bo225809273um_a_b @ X )
% 0.26/0.61 = bot_bo1491243248um_a_b ) ).
% 0.26/0.61
% 0.26/0.61 % Image_empty1
% 0.26/0.61 thf(fact_37_Image__empty1,axiom,
% 0.26/0.61 ! [X: set_St761939237tant_a] :
% 0.26/0.61 ( ( image_2023280617um_a_b @ bot_bo1262634813um_a_b @ X )
% 0.26/0.61 = bot_bo225809273um_a_b ) ).
% 0.26/0.61
% 0.26/0.61 % Image_empty1
% 0.26/0.61 thf(fact_38_restrict__idemp,axiom,
% 0.26/0.61 ! [X2: labele935650037_a_nat] :
% 0.26/0.61 ( ( restri572569417_a_nat @ ( restri572569417_a_nat @ X2 ) )
% 0.26/0.61 = ( restri572569417_a_nat @ X2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % restrict_idemp
% 0.26/0.61 thf(fact_39_restrict__idemp,axiom,
% 0.26/0.61 ! [X2: labele431970251um_a_b] :
% 0.26/0.61 ( ( restri1162247455um_a_b @ ( restri1162247455um_a_b @ X2 ) )
% 0.26/0.61 = ( restri1162247455um_a_b @ X2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % restrict_idemp
% 0.26/0.61 thf(fact_40_labeled__graph_Oinject,axiom,
% 0.26/0.61 ! [X1: set_Pr1647387645at_nat,X22: set_nat,Y1: set_Pr1647387645at_nat,Y2: set_nat] :
% 0.26/0.61 ( ( ( labele16114835_a_nat @ X1 @ X22 )
% 0.26/0.61 = ( labele16114835_a_nat @ Y1 @ Y2 ) )
% 0.26/0.61 = ( ( X1 = Y1 )
% 0.26/0.61 & ( X22 = Y2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % labeled_graph.inject
% 0.26/0.61 thf(fact_41_labeled__graph_Oinject,axiom,
% 0.26/0.61 ! [X1: set_Pr409224873um_a_b,X22: set_Sum_sum_a_b,Y1: set_Pr409224873um_a_b,Y2: set_Sum_sum_a_b] :
% 0.26/0.61 ( ( ( labele1729654377um_a_b @ X1 @ X22 )
% 0.26/0.61 = ( labele1729654377um_a_b @ Y1 @ Y2 ) )
% 0.26/0.61 = ( ( X1 = Y1 )
% 0.26/0.61 & ( X22 = Y2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % labeled_graph.inject
% 0.26/0.61 thf(fact_42_v__gr,axiom,
% 0.26/0.61 ! [A2: sum_sum_a_b,B2: sum_sum_a_b] :
% 0.26/0.61 ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ standard_S_Idt_a @ ( produc176426981um_a_b @ A2 @ B2 ) ) @ ( labele1939049654um_a_b @ g ) )
% 0.26/0.61 = ( ( member_Sum_sum_a_b @ A2 @ ( labele577278695um_a_b @ g ) )
% 0.26/0.61 & ( B2 = A2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % v_gr
% 0.26/0.61 thf(fact_43__092_060open_062_IS__Idt_M_Av_M_Av_J_A_092_060in_062_Aedges_AG_092_060close_062,axiom,
% 0.26/0.61 member1998628618um_a_b @ ( produc1697725733um_a_b @ standard_S_Idt_a @ ( produc176426981um_a_b @ v @ v ) ) @ ( labele1939049654um_a_b @ g ) ).
% 0.26/0.61
% 0.26/0.61 % \<open>(S_Idt, v, v) \<in> edges G\<close>
% 0.26/0.61 thf(fact_44_ImageI,axiom,
% 0.26/0.61 ! [A: nat,B: nat,R: set_Pr1986765409at_nat,A3: set_nat] :
% 0.26/0.61 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
% 0.26/0.61 => ( ( member_nat @ A @ A3 )
% 0.26/0.61 => ( member_nat @ B @ ( image_nat_nat @ R @ A3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % ImageI
% 0.26/0.61 thf(fact_45_ImageI,axiom,
% 0.26/0.61 ! [A: nat,B: sum_sum_a_b,R: set_Pr1174980151um_a_b,A3: set_nat] :
% 0.26/0.61 ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ B ) @ R )
% 0.26/0.61 => ( ( member_nat @ A @ A3 )
% 0.26/0.61 => ( member_Sum_sum_a_b @ B @ ( image_256773707um_a_b @ R @ A3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % ImageI
% 0.26/0.61 thf(fact_46_ImageI,axiom,
% 0.26/0.61 ! [A: standard_Constant_a,B: product_prod_nat_nat,R: set_Pr1647387645at_nat,A3: set_St761939237tant_a] :
% 0.26/0.61 ( ( member1696759390at_nat @ ( produc407553657at_nat @ A @ B ) @ R )
% 0.26/0.61 => ( ( member1632892294tant_a @ A @ A3 )
% 0.26/0.61 => ( member701585322at_nat @ B @ ( image_127502653at_nat @ R @ A3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % ImageI
% 0.26/0.61 thf(fact_47_ImageI,axiom,
% 0.26/0.61 ! [A: sum_sum_a_b,B: sum_sum_a_b,R: set_Pr1916610317um_a_b,A3: set_Sum_sum_a_b] :
% 0.26/0.61 ( ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ B ) @ R )
% 0.26/0.61 => ( ( member_Sum_sum_a_b @ A @ A3 )
% 0.26/0.61 => ( member_Sum_sum_a_b @ B @ ( image_1918588449um_a_b @ R @ A3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % ImageI
% 0.26/0.61 thf(fact_48_ImageI,axiom,
% 0.26/0.61 ! [A: sum_sum_a_b,B: produc1124793815um_a_b,R: set_Pr1783309276um_a_b,A3: set_Sum_sum_a_b] :
% 0.26/0.61 ( ( member485470653um_a_b @ ( produc1637282520um_a_b @ A @ B ) @ R )
% 0.26/0.61 => ( ( member_Sum_sum_a_b @ A @ A3 )
% 0.26/0.61 => ( member1294585472um_a_b @ B @ ( image_1675391388um_a_b @ R @ A3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % ImageI
% 0.26/0.61 thf(fact_49_ImageI,axiom,
% 0.26/0.61 ! [A: produc1124793815um_a_b,B: sum_sum_a_b,R: set_Pr653770722um_a_b,A3: set_Pr1174980151um_a_b] :
% 0.26/0.61 ( ( member748122307um_a_b @ ( produc831476262um_a_b @ A @ B ) @ R )
% 0.26/0.61 => ( ( member1294585472um_a_b @ A @ A3 )
% 0.26/0.61 => ( member_Sum_sum_a_b @ B @ ( image_869585130um_a_b @ R @ A3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % ImageI
% 0.26/0.61 thf(fact_50_ImageI,axiom,
% 0.26/0.61 ! [A: standard_Constant_a,B: produc1548871597um_a_b,R: set_Pr409224873um_a_b,A3: set_St761939237tant_a] :
% 0.26/0.61 ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ B ) @ R )
% 0.26/0.61 => ( ( member1632892294tant_a @ A @ A3 )
% 0.26/0.61 => ( member947389014um_a_b @ B @ ( image_2023280617um_a_b @ R @ A3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % ImageI
% 0.26/0.61 thf(fact_51_ImageI,axiom,
% 0.26/0.61 ! [A: produc1124793815um_a_b,B: produc1124793815um_a_b,R: set_Pr45173959um_a_b,A3: set_Pr1174980151um_a_b] :
% 0.26/0.61 ( ( member429827856um_a_b @ ( produc27163479um_a_b @ A @ B ) @ R )
% 0.26/0.61 => ( ( member1294585472um_a_b @ A @ A3 )
% 0.26/0.61 => ( member1294585472um_a_b @ B @ ( image_1464989587um_a_b @ R @ A3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % ImageI
% 0.26/0.61 thf(fact_52_ImageI,axiom,
% 0.26/0.61 ! [A: sum_sum_a_b,B: produc1963079155um_a_b,R: set_Pr1558970842um_a_b,A3: set_Sum_sum_a_b] :
% 0.26/0.61 ( ( member1641922979um_a_b @ ( produc230853810um_a_b @ A @ B ) @ R )
% 0.26/0.61 => ( ( member_Sum_sum_a_b @ A @ A3 )
% 0.26/0.61 => ( member1998628618um_a_b @ B @ ( image_1482984686um_a_b @ R @ A3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % ImageI
% 0.26/0.61 thf(fact_53_ImageI,axiom,
% 0.26/0.61 ! [A: produc1963079155um_a_b,B: sum_sum_a_b,R: set_Pr1121389018um_a_b,A3: set_Pr409224873um_a_b] :
% 0.26/0.61 ( ( member1590479267um_a_b @ ( produc522766386um_a_b @ A @ B ) @ R )
% 0.26/0.61 => ( ( member1998628618um_a_b @ A @ A3 )
% 0.26/0.61 => ( member_Sum_sum_a_b @ B @ ( image_1774897262um_a_b @ R @ A3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % ImageI
% 0.26/0.61 thf(fact_54_Image__empty2,axiom,
% 0.26/0.61 ! [R2: set_Pr1986765409at_nat] :
% 0.26/0.61 ( ( image_nat_nat @ R2 @ bot_bot_set_nat )
% 0.26/0.61 = bot_bot_set_nat ) ).
% 0.26/0.61
% 0.26/0.61 % Image_empty2
% 0.26/0.61 thf(fact_55_Image__empty2,axiom,
% 0.26/0.61 ! [R2: set_Pr1174980151um_a_b] :
% 0.26/0.61 ( ( image_256773707um_a_b @ R2 @ bot_bot_set_nat )
% 0.26/0.61 = bot_bo1491243248um_a_b ) ).
% 0.26/0.61
% 0.26/0.61 % Image_empty2
% 0.26/0.61 thf(fact_56_Image__empty2,axiom,
% 0.26/0.61 ! [R2: set_Pr375490359_b_nat] :
% 0.26/0.61 ( ( image_1117854795_b_nat @ R2 @ bot_bo1491243248um_a_b )
% 0.26/0.61 = bot_bot_set_nat ) ).
% 0.26/0.61
% 0.26/0.61 % Image_empty2
% 0.26/0.61 thf(fact_57_Image__empty2,axiom,
% 0.26/0.61 ! [R2: set_Pr1618094130um_a_b] :
% 0.26/0.61 ( ( image_1228479730um_a_b @ R2 @ bot_bot_set_nat )
% 0.26/0.61 = bot_bo575978147um_a_b ) ).
% 0.26/0.61
% 0.26/0.61 % Image_empty2
% 0.26/0.61 thf(fact_58_Image__empty2,axiom,
% 0.26/0.61 ! [R2: set_Pr1902304780_b_nat] :
% 0.26/0.61 ( ( image_128716052_b_nat @ R2 @ bot_bo575978147um_a_b )
% 0.26/0.61 = bot_bot_set_nat ) ).
% 0.26/0.61
% 0.26/0.61 % Image_empty2
% 0.26/0.61 thf(fact_59_Image__empty2,axiom,
% 0.26/0.61 ! [R2: set_Pr1916610317um_a_b] :
% 0.26/0.61 ( ( image_1918588449um_a_b @ R2 @ bot_bo1491243248um_a_b )
% 0.26/0.61 = bot_bo1491243248um_a_b ) ).
% 0.26/0.61
% 0.26/0.61 % Image_empty2
% 0.26/0.61 thf(fact_60_Image__empty2,axiom,
% 0.26/0.61 ! [R2: set_Pr689416536at_nat] :
% 0.26/0.61 ( ( image_452296684at_nat @ R2 @ bot_bo810816657at_nat )
% 0.26/0.61 = bot_bot_set_nat ) ).
% 0.26/0.61
% 0.26/0.61 % Image_empty2
% 0.26/0.61 thf(fact_61_Image__empty2,axiom,
% 0.26/0.61 ! [R2: set_Pr1134469976at_nat] :
% 0.26/0.61 ( ( image_489788268at_nat @ R2 @ bot_bot_set_nat )
% 0.26/0.61 = bot_bo810816657at_nat ) ).
% 0.26/0.61
% 0.26/0.61 % Image_empty2
% 0.26/0.61 thf(fact_62_Image__empty2,axiom,
% 0.26/0.61 ! [R2: set_Pr1155046920um_a_b] :
% 0.26/0.61 ( ( image_166667464um_a_b @ R2 @ bot_bot_set_nat )
% 0.26/0.61 = bot_bo225809273um_a_b ) ).
% 0.26/0.61
% 0.26/0.61 % Image_empty2
% 0.26/0.61 thf(fact_63_Image__empty2,axiom,
% 0.26/0.61 ! [R2: set_Pr653770722um_a_b] :
% 0.26/0.61 ( ( image_869585130um_a_b @ R2 @ bot_bo575978147um_a_b )
% 0.26/0.61 = bot_bo1491243248um_a_b ) ).
% 0.26/0.61
% 0.26/0.61 % Image_empty2
% 0.26/0.61 thf(fact_64_vertices__restrict,axiom,
% 0.26/0.61 ! [G: labele935650037_a_nat] :
% 0.26/0.61 ( ( labele1810595089_a_nat @ ( restri572569417_a_nat @ G ) )
% 0.26/0.61 = ( labele1810595089_a_nat @ G ) ) ).
% 0.26/0.61
% 0.26/0.61 % vertices_restrict
% 0.26/0.61 thf(fact_65_vertices__restrict,axiom,
% 0.26/0.61 ! [G: labele431970251um_a_b] :
% 0.26/0.61 ( ( labele577278695um_a_b @ ( restri1162247455um_a_b @ G ) )
% 0.26/0.61 = ( labele577278695um_a_b @ G ) ) ).
% 0.26/0.61
% 0.26/0.61 % vertices_restrict
% 0.26/0.61 thf(fact_66__092_060open_062graph__homomorphism_A_ILG_A_123_125_A_1230_125_J_AG_Af_092_060close_062,axiom,
% 0.26/0.61 graph_1452133198um_a_b @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ g @ f ).
% 0.26/0.61
% 0.26/0.61 % \<open>graph_homomorphism (LG {} {0}) G f\<close>
% 0.26/0.61 thf(fact_67_labeled__graph_Oexhaust,axiom,
% 0.26/0.61 ! [Y: labele935650037_a_nat] :
% 0.26/0.61 ~ ! [X12: set_Pr1647387645at_nat,X23: set_nat] :
% 0.26/0.61 ( Y
% 0.26/0.61 != ( labele16114835_a_nat @ X12 @ X23 ) ) ).
% 0.26/0.61
% 0.26/0.61 % labeled_graph.exhaust
% 0.26/0.61 thf(fact_68_labeled__graph_Oexhaust,axiom,
% 0.26/0.61 ! [Y: labele431970251um_a_b] :
% 0.26/0.61 ~ ! [X12: set_Pr409224873um_a_b,X23: set_Sum_sum_a_b] :
% 0.26/0.61 ( Y
% 0.26/0.61 != ( labele1729654377um_a_b @ X12 @ X23 ) ) ).
% 0.26/0.61
% 0.26/0.61 % labeled_graph.exhaust
% 0.26/0.61 thf(fact_69_labeled__graph_Oinduct,axiom,
% 0.26/0.61 ! [P: labele935650037_a_nat > $o,Labeled_graph: labele935650037_a_nat] :
% 0.26/0.62 ( ! [X1a: set_Pr1647387645at_nat,X2a: set_nat] : ( P @ ( labele16114835_a_nat @ X1a @ X2a ) )
% 0.26/0.62 => ( P @ Labeled_graph ) ) ).
% 0.26/0.62
% 0.26/0.62 % labeled_graph.induct
% 0.26/0.62 thf(fact_70_labeled__graph_Oinduct,axiom,
% 0.26/0.62 ! [P: labele431970251um_a_b > $o,Labeled_graph: labele431970251um_a_b] :
% 0.26/0.62 ( ! [X1a: set_Pr409224873um_a_b,X2a: set_Sum_sum_a_b] : ( P @ ( labele1729654377um_a_b @ X1a @ X2a ) )
% 0.26/0.62 => ( P @ Labeled_graph ) ) ).
% 0.26/0.62
% 0.26/0.62 % labeled_graph.induct
% 0.26/0.62 thf(fact_71_rev__ImageI,axiom,
% 0.26/0.62 ! [A: nat,A3: set_nat,B: nat,R: set_Pr1986765409at_nat] :
% 0.26/0.62 ( ( member_nat @ A @ A3 )
% 0.26/0.62 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
% 0.26/0.62 => ( member_nat @ B @ ( image_nat_nat @ R @ A3 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % rev_ImageI
% 0.26/0.62 thf(fact_72_rev__ImageI,axiom,
% 0.26/0.62 ! [A: nat,A3: set_nat,B: sum_sum_a_b,R: set_Pr1174980151um_a_b] :
% 0.26/0.62 ( ( member_nat @ A @ A3 )
% 0.26/0.62 => ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ B ) @ R )
% 0.26/0.62 => ( member_Sum_sum_a_b @ B @ ( image_256773707um_a_b @ R @ A3 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % rev_ImageI
% 0.26/0.62 thf(fact_73_rev__ImageI,axiom,
% 0.26/0.62 ! [A: standard_Constant_a,A3: set_St761939237tant_a,B: product_prod_nat_nat,R: set_Pr1647387645at_nat] :
% 0.26/0.62 ( ( member1632892294tant_a @ A @ A3 )
% 0.26/0.62 => ( ( member1696759390at_nat @ ( produc407553657at_nat @ A @ B ) @ R )
% 0.26/0.62 => ( member701585322at_nat @ B @ ( image_127502653at_nat @ R @ A3 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % rev_ImageI
% 0.26/0.62 thf(fact_74_rev__ImageI,axiom,
% 0.26/0.62 ! [A: sum_sum_a_b,A3: set_Sum_sum_a_b,B: sum_sum_a_b,R: set_Pr1916610317um_a_b] :
% 0.26/0.62 ( ( member_Sum_sum_a_b @ A @ A3 )
% 0.26/0.62 => ( ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ B ) @ R )
% 0.26/0.62 => ( member_Sum_sum_a_b @ B @ ( image_1918588449um_a_b @ R @ A3 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % rev_ImageI
% 0.26/0.62 thf(fact_75_rev__ImageI,axiom,
% 0.26/0.62 ! [A: sum_sum_a_b,A3: set_Sum_sum_a_b,B: produc1124793815um_a_b,R: set_Pr1783309276um_a_b] :
% 0.26/0.62 ( ( member_Sum_sum_a_b @ A @ A3 )
% 0.26/0.62 => ( ( member485470653um_a_b @ ( produc1637282520um_a_b @ A @ B ) @ R )
% 0.26/0.62 => ( member1294585472um_a_b @ B @ ( image_1675391388um_a_b @ R @ A3 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % rev_ImageI
% 0.26/0.62 thf(fact_76_rev__ImageI,axiom,
% 0.26/0.62 ! [A: produc1124793815um_a_b,A3: set_Pr1174980151um_a_b,B: sum_sum_a_b,R: set_Pr653770722um_a_b] :
% 0.26/0.62 ( ( member1294585472um_a_b @ A @ A3 )
% 0.26/0.62 => ( ( member748122307um_a_b @ ( produc831476262um_a_b @ A @ B ) @ R )
% 0.26/0.62 => ( member_Sum_sum_a_b @ B @ ( image_869585130um_a_b @ R @ A3 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % rev_ImageI
% 0.26/0.62 thf(fact_77_rev__ImageI,axiom,
% 0.26/0.62 ! [A: standard_Constant_a,A3: set_St761939237tant_a,B: produc1548871597um_a_b,R: set_Pr409224873um_a_b] :
% 0.26/0.62 ( ( member1632892294tant_a @ A @ A3 )
% 0.26/0.62 => ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ B ) @ R )
% 0.26/0.62 => ( member947389014um_a_b @ B @ ( image_2023280617um_a_b @ R @ A3 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % rev_ImageI
% 0.26/0.62 thf(fact_78_rev__ImageI,axiom,
% 0.26/0.62 ! [A: produc1124793815um_a_b,A3: set_Pr1174980151um_a_b,B: produc1124793815um_a_b,R: set_Pr45173959um_a_b] :
% 0.26/0.62 ( ( member1294585472um_a_b @ A @ A3 )
% 0.26/0.62 => ( ( member429827856um_a_b @ ( produc27163479um_a_b @ A @ B ) @ R )
% 0.26/0.62 => ( member1294585472um_a_b @ B @ ( image_1464989587um_a_b @ R @ A3 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % rev_ImageI
% 0.26/0.62 thf(fact_79_rev__ImageI,axiom,
% 0.26/0.62 ! [A: sum_sum_a_b,A3: set_Sum_sum_a_b,B: produc1963079155um_a_b,R: set_Pr1558970842um_a_b] :
% 0.26/0.62 ( ( member_Sum_sum_a_b @ A @ A3 )
% 0.26/0.62 => ( ( member1641922979um_a_b @ ( produc230853810um_a_b @ A @ B ) @ R )
% 0.26/0.62 => ( member1998628618um_a_b @ B @ ( image_1482984686um_a_b @ R @ A3 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % rev_ImageI
% 0.26/0.62 thf(fact_80_rev__ImageI,axiom,
% 0.26/0.62 ! [A: produc1963079155um_a_b,A3: set_Pr409224873um_a_b,B: sum_sum_a_b,R: set_Pr1121389018um_a_b] :
% 0.26/0.62 ( ( member1998628618um_a_b @ A @ A3 )
% 0.26/0.62 => ( ( member1590479267um_a_b @ ( produc522766386um_a_b @ A @ B ) @ R )
% 0.26/0.62 => ( member_Sum_sum_a_b @ B @ ( image_1774897262um_a_b @ R @ A3 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % rev_ImageI
% 0.26/0.62 thf(fact_81_Image__iff,axiom,
% 0.26/0.62 ! [B: product_prod_nat_nat,R: set_Pr1647387645at_nat,A3: set_St761939237tant_a] :
% 0.26/0.62 ( ( member701585322at_nat @ B @ ( image_127502653at_nat @ R @ A3 ) )
% 0.26/0.62 = ( ? [X3: standard_Constant_a] :
% 0.26/0.62 ( ( member1632892294tant_a @ X3 @ A3 )
% 0.26/0.62 & ( member1696759390at_nat @ ( produc407553657at_nat @ X3 @ B ) @ R ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Image_iff
% 0.26/0.62 thf(fact_82_Image__iff,axiom,
% 0.26/0.62 ! [B: nat,R: set_Pr1986765409at_nat,A3: set_nat] :
% 0.26/0.62 ( ( member_nat @ B @ ( image_nat_nat @ R @ A3 ) )
% 0.26/0.62 = ( ? [X3: nat] :
% 0.26/0.62 ( ( member_nat @ X3 @ A3 )
% 0.26/0.62 & ( member701585322at_nat @ ( product_Pair_nat_nat @ X3 @ B ) @ R ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Image_iff
% 0.26/0.62 thf(fact_83_Image__iff,axiom,
% 0.26/0.62 ! [B: sum_sum_a_b,R: set_Pr1174980151um_a_b,A3: set_nat] :
% 0.26/0.62 ( ( member_Sum_sum_a_b @ B @ ( image_256773707um_a_b @ R @ A3 ) )
% 0.26/0.62 = ( ? [X3: nat] :
% 0.26/0.62 ( ( member_nat @ X3 @ A3 )
% 0.26/0.62 & ( member1294585472um_a_b @ ( produc1808556047um_a_b @ X3 @ B ) @ R ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Image_iff
% 0.26/0.62 thf(fact_84_Image__iff,axiom,
% 0.26/0.62 ! [B: produc1548871597um_a_b,R: set_Pr409224873um_a_b,A3: set_St761939237tant_a] :
% 0.26/0.62 ( ( member947389014um_a_b @ B @ ( image_2023280617um_a_b @ R @ A3 ) )
% 0.26/0.62 = ( ? [X3: standard_Constant_a] :
% 0.26/0.62 ( ( member1632892294tant_a @ X3 @ A3 )
% 0.26/0.62 & ( member1998628618um_a_b @ ( produc1697725733um_a_b @ X3 @ B ) @ R ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Image_iff
% 0.26/0.62 thf(fact_85_Image__iff,axiom,
% 0.26/0.62 ! [B: sum_sum_a_b,R: set_Pr1916610317um_a_b,A3: set_Sum_sum_a_b] :
% 0.26/0.62 ( ( member_Sum_sum_a_b @ B @ ( image_1918588449um_a_b @ R @ A3 ) )
% 0.26/0.62 = ( ? [X3: sum_sum_a_b] :
% 0.26/0.62 ( ( member_Sum_sum_a_b @ X3 @ A3 )
% 0.26/0.62 & ( member947389014um_a_b @ ( produc176426981um_a_b @ X3 @ B ) @ R ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Image_iff
% 0.26/0.62 thf(fact_86_ImageE,axiom,
% 0.26/0.62 ! [B: nat,R: set_Pr1986765409at_nat,A3: set_nat] :
% 0.26/0.62 ( ( member_nat @ B @ ( image_nat_nat @ R @ A3 ) )
% 0.26/0.62 => ~ ! [X4: nat] :
% 0.26/0.62 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X4 @ B ) @ R )
% 0.26/0.62 => ~ ( member_nat @ X4 @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % ImageE
% 0.26/0.62 thf(fact_87_ImageE,axiom,
% 0.26/0.62 ! [B: sum_sum_a_b,R: set_Pr1174980151um_a_b,A3: set_nat] :
% 0.26/0.62 ( ( member_Sum_sum_a_b @ B @ ( image_256773707um_a_b @ R @ A3 ) )
% 0.26/0.62 => ~ ! [X4: nat] :
% 0.26/0.62 ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ X4 @ B ) @ R )
% 0.26/0.62 => ~ ( member_nat @ X4 @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % ImageE
% 0.26/0.62 thf(fact_88_ImageE,axiom,
% 0.26/0.62 ! [B: product_prod_nat_nat,R: set_Pr1647387645at_nat,A3: set_St761939237tant_a] :
% 0.26/0.62 ( ( member701585322at_nat @ B @ ( image_127502653at_nat @ R @ A3 ) )
% 0.26/0.62 => ~ ! [X4: standard_Constant_a] :
% 0.26/0.62 ( ( member1696759390at_nat @ ( produc407553657at_nat @ X4 @ B ) @ R )
% 0.26/0.62 => ~ ( member1632892294tant_a @ X4 @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % ImageE
% 0.26/0.62 thf(fact_89_ImageE,axiom,
% 0.26/0.62 ! [B: sum_sum_a_b,R: set_Pr1916610317um_a_b,A3: set_Sum_sum_a_b] :
% 0.26/0.62 ( ( member_Sum_sum_a_b @ B @ ( image_1918588449um_a_b @ R @ A3 ) )
% 0.26/0.62 => ~ ! [X4: sum_sum_a_b] :
% 0.26/0.62 ( ( member947389014um_a_b @ ( produc176426981um_a_b @ X4 @ B ) @ R )
% 0.26/0.62 => ~ ( member_Sum_sum_a_b @ X4 @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % ImageE
% 0.26/0.62 thf(fact_90_ImageE,axiom,
% 0.26/0.62 ! [B: sum_sum_a_b,R: set_Pr653770722um_a_b,A3: set_Pr1174980151um_a_b] :
% 0.26/0.62 ( ( member_Sum_sum_a_b @ B @ ( image_869585130um_a_b @ R @ A3 ) )
% 0.26/0.62 => ~ ! [X4: produc1124793815um_a_b] :
% 0.26/0.62 ( ( member748122307um_a_b @ ( produc831476262um_a_b @ X4 @ B ) @ R )
% 0.26/0.62 => ~ ( member1294585472um_a_b @ X4 @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % ImageE
% 0.26/0.62 thf(fact_91_ImageE,axiom,
% 0.26/0.62 ! [B: produc1124793815um_a_b,R: set_Pr1783309276um_a_b,A3: set_Sum_sum_a_b] :
% 0.26/0.62 ( ( member1294585472um_a_b @ B @ ( image_1675391388um_a_b @ R @ A3 ) )
% 0.26/0.62 => ~ ! [X4: sum_sum_a_b] :
% 0.26/0.62 ( ( member485470653um_a_b @ ( produc1637282520um_a_b @ X4 @ B ) @ R )
% 0.26/0.62 => ~ ( member_Sum_sum_a_b @ X4 @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % ImageE
% 0.26/0.62 thf(fact_92_ImageE,axiom,
% 0.26/0.62 ! [B: produc1548871597um_a_b,R: set_Pr409224873um_a_b,A3: set_St761939237tant_a] :
% 0.26/0.62 ( ( member947389014um_a_b @ B @ ( image_2023280617um_a_b @ R @ A3 ) )
% 0.26/0.62 => ~ ! [X4: standard_Constant_a] :
% 0.26/0.62 ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ X4 @ B ) @ R )
% 0.26/0.62 => ~ ( member1632892294tant_a @ X4 @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % ImageE
% 0.26/0.62 thf(fact_93_ImageE,axiom,
% 0.26/0.62 ! [B: produc1124793815um_a_b,R: set_Pr45173959um_a_b,A3: set_Pr1174980151um_a_b] :
% 0.26/0.62 ( ( member1294585472um_a_b @ B @ ( image_1464989587um_a_b @ R @ A3 ) )
% 0.26/0.62 => ~ ! [X4: produc1124793815um_a_b] :
% 0.26/0.62 ( ( member429827856um_a_b @ ( produc27163479um_a_b @ X4 @ B ) @ R )
% 0.26/0.62 => ~ ( member1294585472um_a_b @ X4 @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % ImageE
% 0.26/0.62 thf(fact_94_ImageE,axiom,
% 0.26/0.62 ! [B: sum_sum_a_b,R: set_Pr1121389018um_a_b,A3: set_Pr409224873um_a_b] :
% 0.26/0.62 ( ( member_Sum_sum_a_b @ B @ ( image_1774897262um_a_b @ R @ A3 ) )
% 0.26/0.62 => ~ ! [X4: produc1963079155um_a_b] :
% 0.26/0.62 ( ( member1590479267um_a_b @ ( produc522766386um_a_b @ X4 @ B ) @ R )
% 0.26/0.62 => ~ ( member1998628618um_a_b @ X4 @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % ImageE
% 0.26/0.62 thf(fact_95_ImageE,axiom,
% 0.26/0.62 ! [B: produc1963079155um_a_b,R: set_Pr1558970842um_a_b,A3: set_Sum_sum_a_b] :
% 0.26/0.62 ( ( member1998628618um_a_b @ B @ ( image_1482984686um_a_b @ R @ A3 ) )
% 0.26/0.62 => ~ ! [X4: sum_sum_a_b] :
% 0.26/0.62 ( ( member1641922979um_a_b @ ( produc230853810um_a_b @ X4 @ B ) @ R )
% 0.26/0.62 => ~ ( member_Sum_sum_a_b @ X4 @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % ImageE
% 0.26/0.62 thf(fact_96_Image__mono,axiom,
% 0.26/0.62 ! [R3: set_Pr1174980151um_a_b,R: set_Pr1174980151um_a_b,A4: set_nat,A3: set_nat] :
% 0.26/0.62 ( ( ord_le823954903um_a_b @ R3 @ R )
% 0.26/0.62 => ( ( ord_less_eq_set_nat @ A4 @ A3 )
% 0.26/0.62 => ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ R3 @ A4 ) @ ( image_256773707um_a_b @ R @ A3 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Image_mono
% 0.26/0.62 thf(fact_97_Image__mono,axiom,
% 0.26/0.62 ! [R3: set_Pr1916610317um_a_b,R: set_Pr1916610317um_a_b,A4: set_Sum_sum_a_b,A3: set_Sum_sum_a_b] :
% 0.26/0.62 ( ( ord_le1059794605um_a_b @ R3 @ R )
% 0.26/0.62 => ( ( ord_le192794300um_a_b @ A4 @ A3 )
% 0.26/0.62 => ( ord_le192794300um_a_b @ ( image_1918588449um_a_b @ R3 @ A4 ) @ ( image_1918588449um_a_b @ R @ A3 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Image_mono
% 0.26/0.62 thf(fact_98_Domain_Oinducts,axiom,
% 0.26/0.62 ! [X2: standard_Constant_a,R: set_Pr1647387645at_nat,P: standard_Constant_a > $o] :
% 0.26/0.62 ( ( member1632892294tant_a @ X2 @ ( domain1060562500at_nat @ R ) )
% 0.26/0.62 => ( ! [A5: standard_Constant_a,B3: product_prod_nat_nat] :
% 0.26/0.62 ( ( member1696759390at_nat @ ( produc407553657at_nat @ A5 @ B3 ) @ R )
% 0.26/0.62 => ( P @ A5 ) )
% 0.26/0.62 => ( P @ X2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain.inducts
% 0.26/0.62 thf(fact_99_Domain_Oinducts,axiom,
% 0.26/0.62 ! [X2: nat,R: set_Pr1986765409at_nat,P: nat > $o] :
% 0.26/0.62 ( ( member_nat @ X2 @ ( domain_nat_nat @ R ) )
% 0.26/0.62 => ( ! [A5: nat,B3: nat] :
% 0.26/0.62 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A5 @ B3 ) @ R )
% 0.26/0.62 => ( P @ A5 ) )
% 0.26/0.62 => ( P @ X2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain.inducts
% 0.26/0.62 thf(fact_100_Domain_Oinducts,axiom,
% 0.26/0.62 ! [X2: nat,R: set_Pr1174980151um_a_b,P: nat > $o] :
% 0.26/0.62 ( ( member_nat @ X2 @ ( domain1368163076um_a_b @ R ) )
% 0.26/0.62 => ( ! [A5: nat,B3: sum_sum_a_b] :
% 0.26/0.62 ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A5 @ B3 ) @ R )
% 0.26/0.62 => ( P @ A5 ) )
% 0.26/0.62 => ( P @ X2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain.inducts
% 0.26/0.62 thf(fact_101_Domain_Oinducts,axiom,
% 0.26/0.62 ! [X2: standard_Constant_a,R: set_Pr409224873um_a_b,P: standard_Constant_a > $o] :
% 0.26/0.62 ( ( member1632892294tant_a @ X2 @ ( domain1362581744um_a_b @ R ) )
% 0.26/0.62 => ( ! [A5: standard_Constant_a,B3: produc1548871597um_a_b] :
% 0.26/0.62 ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A5 @ B3 ) @ R )
% 0.26/0.62 => ( P @ A5 ) )
% 0.26/0.62 => ( P @ X2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain.inducts
% 0.26/0.62 thf(fact_102_Domain_Oinducts,axiom,
% 0.26/0.62 ! [X2: sum_sum_a_b,R: set_Pr1916610317um_a_b,P: sum_sum_a_b > $o] :
% 0.26/0.62 ( ( member_Sum_sum_a_b @ X2 @ ( domain2069673178um_a_b @ R ) )
% 0.26/0.62 => ( ! [A5: sum_sum_a_b,B3: sum_sum_a_b] :
% 0.26/0.62 ( ( member947389014um_a_b @ ( produc176426981um_a_b @ A5 @ B3 ) @ R )
% 0.26/0.62 => ( P @ A5 ) )
% 0.26/0.62 => ( P @ X2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain.inducts
% 0.26/0.62 thf(fact_103_Domain_ODomainI,axiom,
% 0.26/0.62 ! [A: standard_Constant_a,B: product_prod_nat_nat,R: set_Pr1647387645at_nat] :
% 0.26/0.62 ( ( member1696759390at_nat @ ( produc407553657at_nat @ A @ B ) @ R )
% 0.26/0.62 => ( member1632892294tant_a @ A @ ( domain1060562500at_nat @ R ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain.DomainI
% 0.26/0.62 thf(fact_104_Domain_ODomainI,axiom,
% 0.26/0.62 ! [A: nat,B: nat,R: set_Pr1986765409at_nat] :
% 0.26/0.62 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
% 0.26/0.62 => ( member_nat @ A @ ( domain_nat_nat @ R ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain.DomainI
% 0.26/0.62 thf(fact_105_Domain_ODomainI,axiom,
% 0.26/0.62 ! [A: nat,B: sum_sum_a_b,R: set_Pr1174980151um_a_b] :
% 0.26/0.62 ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ B ) @ R )
% 0.26/0.62 => ( member_nat @ A @ ( domain1368163076um_a_b @ R ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain.DomainI
% 0.26/0.62 thf(fact_106_Domain_ODomainI,axiom,
% 0.26/0.62 ! [A: standard_Constant_a,B: produc1548871597um_a_b,R: set_Pr409224873um_a_b] :
% 0.26/0.62 ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ B ) @ R )
% 0.26/0.62 => ( member1632892294tant_a @ A @ ( domain1362581744um_a_b @ R ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain.DomainI
% 0.26/0.62 thf(fact_107_Domain_ODomainI,axiom,
% 0.26/0.62 ! [A: sum_sum_a_b,B: sum_sum_a_b,R: set_Pr1916610317um_a_b] :
% 0.26/0.62 ( ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ B ) @ R )
% 0.26/0.62 => ( member_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ R ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain.DomainI
% 0.26/0.62 thf(fact_108_Domain_Osimps,axiom,
% 0.26/0.62 ! [A: standard_Constant_a,R: set_Pr1647387645at_nat] :
% 0.26/0.62 ( ( member1632892294tant_a @ A @ ( domain1060562500at_nat @ R ) )
% 0.26/0.62 = ( ? [A6: standard_Constant_a,B4: product_prod_nat_nat] :
% 0.26/0.62 ( ( A = A6 )
% 0.26/0.62 & ( member1696759390at_nat @ ( produc407553657at_nat @ A6 @ B4 ) @ R ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain.simps
% 0.26/0.62 thf(fact_109_Domain_Osimps,axiom,
% 0.26/0.62 ! [A: nat,R: set_Pr1986765409at_nat] :
% 0.26/0.62 ( ( member_nat @ A @ ( domain_nat_nat @ R ) )
% 0.26/0.62 = ( ? [A6: nat,B4: nat] :
% 0.26/0.62 ( ( A = A6 )
% 0.26/0.62 & ( member701585322at_nat @ ( product_Pair_nat_nat @ A6 @ B4 ) @ R ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain.simps
% 0.26/0.62 thf(fact_110_Domain_Osimps,axiom,
% 0.26/0.62 ! [A: nat,R: set_Pr1174980151um_a_b] :
% 0.26/0.62 ( ( member_nat @ A @ ( domain1368163076um_a_b @ R ) )
% 0.26/0.62 = ( ? [A6: nat,B4: sum_sum_a_b] :
% 0.26/0.62 ( ( A = A6 )
% 0.26/0.62 & ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A6 @ B4 ) @ R ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain.simps
% 0.26/0.62 thf(fact_111_Domain_Osimps,axiom,
% 0.26/0.62 ! [A: standard_Constant_a,R: set_Pr409224873um_a_b] :
% 0.26/0.62 ( ( member1632892294tant_a @ A @ ( domain1362581744um_a_b @ R ) )
% 0.26/0.62 = ( ? [A6: standard_Constant_a,B4: produc1548871597um_a_b] :
% 0.26/0.62 ( ( A = A6 )
% 0.26/0.62 & ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A6 @ B4 ) @ R ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain.simps
% 0.26/0.62 thf(fact_112_Domain_Osimps,axiom,
% 0.26/0.62 ! [A: sum_sum_a_b,R: set_Pr1916610317um_a_b] :
% 0.26/0.62 ( ( member_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ R ) )
% 0.26/0.62 = ( ? [A6: sum_sum_a_b,B4: sum_sum_a_b] :
% 0.26/0.62 ( ( A = A6 )
% 0.26/0.62 & ( member947389014um_a_b @ ( produc176426981um_a_b @ A6 @ B4 ) @ R ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain.simps
% 0.26/0.62 thf(fact_113_Domain_Ocases,axiom,
% 0.26/0.62 ! [A: standard_Constant_a,R: set_Pr1647387645at_nat] :
% 0.26/0.62 ( ( member1632892294tant_a @ A @ ( domain1060562500at_nat @ R ) )
% 0.26/0.62 => ~ ! [B3: product_prod_nat_nat] :
% 0.26/0.62 ~ ( member1696759390at_nat @ ( produc407553657at_nat @ A @ B3 ) @ R ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain.cases
% 0.26/0.62 thf(fact_114_Domain_Ocases,axiom,
% 0.26/0.62 ! [A: nat,R: set_Pr1986765409at_nat] :
% 0.26/0.62 ( ( member_nat @ A @ ( domain_nat_nat @ R ) )
% 0.26/0.62 => ~ ! [B3: nat] :
% 0.26/0.62 ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B3 ) @ R ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain.cases
% 0.26/0.62 thf(fact_115_Domain_Ocases,axiom,
% 0.26/0.62 ! [A: nat,R: set_Pr1174980151um_a_b] :
% 0.26/0.62 ( ( member_nat @ A @ ( domain1368163076um_a_b @ R ) )
% 0.26/0.62 => ~ ! [B3: sum_sum_a_b] :
% 0.26/0.62 ~ ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ B3 ) @ R ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain.cases
% 0.26/0.62 thf(fact_116_Domain_Ocases,axiom,
% 0.26/0.62 ! [A: standard_Constant_a,R: set_Pr409224873um_a_b] :
% 0.26/0.62 ( ( member1632892294tant_a @ A @ ( domain1362581744um_a_b @ R ) )
% 0.26/0.62 => ~ ! [B3: produc1548871597um_a_b] :
% 0.26/0.62 ~ ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ B3 ) @ R ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain.cases
% 0.26/0.62 thf(fact_117_Domain_Ocases,axiom,
% 0.26/0.62 ! [A: sum_sum_a_b,R: set_Pr1916610317um_a_b] :
% 0.26/0.62 ( ( member_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ R ) )
% 0.26/0.62 => ~ ! [B3: sum_sum_a_b] :
% 0.26/0.62 ~ ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ B3 ) @ R ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain.cases
% 0.26/0.62 thf(fact_118_Domain__iff,axiom,
% 0.26/0.62 ! [A: standard_Constant_a,R: set_Pr1647387645at_nat] :
% 0.26/0.62 ( ( member1632892294tant_a @ A @ ( domain1060562500at_nat @ R ) )
% 0.26/0.62 = ( ? [Y3: product_prod_nat_nat] : ( member1696759390at_nat @ ( produc407553657at_nat @ A @ Y3 ) @ R ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain_iff
% 0.26/0.62 thf(fact_119_Domain__iff,axiom,
% 0.26/0.62 ! [A: nat,R: set_Pr1986765409at_nat] :
% 0.26/0.62 ( ( member_nat @ A @ ( domain_nat_nat @ R ) )
% 0.26/0.62 = ( ? [Y3: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ Y3 ) @ R ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain_iff
% 0.26/0.62 thf(fact_120_Domain__iff,axiom,
% 0.26/0.62 ! [A: nat,R: set_Pr1174980151um_a_b] :
% 0.26/0.62 ( ( member_nat @ A @ ( domain1368163076um_a_b @ R ) )
% 0.26/0.62 = ( ? [Y3: sum_sum_a_b] : ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ Y3 ) @ R ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain_iff
% 0.26/0.62 thf(fact_121_Domain__iff,axiom,
% 0.26/0.62 ! [A: standard_Constant_a,R: set_Pr409224873um_a_b] :
% 0.26/0.62 ( ( member1632892294tant_a @ A @ ( domain1362581744um_a_b @ R ) )
% 0.26/0.62 = ( ? [Y3: produc1548871597um_a_b] : ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ Y3 ) @ R ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain_iff
% 0.26/0.62 thf(fact_122_Domain__iff,axiom,
% 0.26/0.62 ! [A: sum_sum_a_b,R: set_Pr1916610317um_a_b] :
% 0.26/0.62 ( ( member_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ R ) )
% 0.26/0.62 = ( ? [Y3: sum_sum_a_b] : ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ Y3 ) @ R ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain_iff
% 0.26/0.62 thf(fact_123_DomainE,axiom,
% 0.26/0.62 ! [A: standard_Constant_a,R: set_Pr1647387645at_nat] :
% 0.26/0.62 ( ( member1632892294tant_a @ A @ ( domain1060562500at_nat @ R ) )
% 0.26/0.62 => ~ ! [B3: product_prod_nat_nat] :
% 0.26/0.62 ~ ( member1696759390at_nat @ ( produc407553657at_nat @ A @ B3 ) @ R ) ) ).
% 0.26/0.62
% 0.26/0.62 % DomainE
% 0.26/0.62 thf(fact_124_DomainE,axiom,
% 0.26/0.62 ! [A: nat,R: set_Pr1986765409at_nat] :
% 0.26/0.62 ( ( member_nat @ A @ ( domain_nat_nat @ R ) )
% 0.26/0.62 => ~ ! [B3: nat] :
% 0.26/0.62 ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B3 ) @ R ) ) ).
% 0.26/0.62
% 0.26/0.62 % DomainE
% 0.26/0.62 thf(fact_125_DomainE,axiom,
% 0.26/0.62 ! [A: nat,R: set_Pr1174980151um_a_b] :
% 0.26/0.62 ( ( member_nat @ A @ ( domain1368163076um_a_b @ R ) )
% 0.26/0.62 => ~ ! [B3: sum_sum_a_b] :
% 0.26/0.62 ~ ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ B3 ) @ R ) ) ).
% 0.26/0.62
% 0.26/0.62 % DomainE
% 0.26/0.62 thf(fact_126_DomainE,axiom,
% 0.26/0.62 ! [A: standard_Constant_a,R: set_Pr409224873um_a_b] :
% 0.26/0.62 ( ( member1632892294tant_a @ A @ ( domain1362581744um_a_b @ R ) )
% 0.26/0.62 => ~ ! [B3: produc1548871597um_a_b] :
% 0.26/0.62 ~ ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ B3 ) @ R ) ) ).
% 0.26/0.62
% 0.26/0.62 % DomainE
% 0.26/0.62 thf(fact_127_DomainE,axiom,
% 0.26/0.62 ! [A: sum_sum_a_b,R: set_Pr1916610317um_a_b] :
% 0.26/0.62 ( ( member_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ R ) )
% 0.26/0.62 => ~ ! [B3: sum_sum_a_b] :
% 0.26/0.62 ~ ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ B3 ) @ R ) ) ).
% 0.26/0.62
% 0.26/0.62 % DomainE
% 0.26/0.62 thf(fact_128_Domain__mono,axiom,
% 0.26/0.62 ! [R: set_Pr1174980151um_a_b,S: set_Pr1174980151um_a_b] :
% 0.26/0.62 ( ( ord_le823954903um_a_b @ R @ S )
% 0.26/0.62 => ( ord_less_eq_set_nat @ ( domain1368163076um_a_b @ R ) @ ( domain1368163076um_a_b @ S ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain_mono
% 0.26/0.62 thf(fact_129_Domain__mono,axiom,
% 0.26/0.62 ! [R: set_Pr409224873um_a_b,S: set_Pr409224873um_a_b] :
% 0.26/0.62 ( ( ord_le615126793um_a_b @ R @ S )
% 0.26/0.62 => ( ord_le1739761029tant_a @ ( domain1362581744um_a_b @ R ) @ ( domain1362581744um_a_b @ S ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain_mono
% 0.26/0.62 thf(fact_130_Domain__mono,axiom,
% 0.26/0.62 ! [R: set_Pr1986765409at_nat,S: set_Pr1986765409at_nat] :
% 0.26/0.62 ( ( ord_le841296385at_nat @ R @ S )
% 0.26/0.62 => ( ord_less_eq_set_nat @ ( domain_nat_nat @ R ) @ ( domain_nat_nat @ S ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain_mono
% 0.26/0.62 thf(fact_131_Domain__mono,axiom,
% 0.26/0.62 ! [R: set_Pr1647387645at_nat,S: set_Pr1647387645at_nat] :
% 0.26/0.62 ( ( ord_le1909159005at_nat @ R @ S )
% 0.26/0.62 => ( ord_le1739761029tant_a @ ( domain1060562500at_nat @ R ) @ ( domain1060562500at_nat @ S ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain_mono
% 0.26/0.62 thf(fact_132_Domain__mono,axiom,
% 0.26/0.62 ! [R: set_Pr1916610317um_a_b,S: set_Pr1916610317um_a_b] :
% 0.26/0.62 ( ( ord_le1059794605um_a_b @ R @ S )
% 0.26/0.62 => ( ord_le192794300um_a_b @ ( domain2069673178um_a_b @ R ) @ ( domain2069673178um_a_b @ S ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain_mono
% 0.26/0.62 thf(fact_133_labeled__graph_Oexpand,axiom,
% 0.26/0.62 ! [Labeled_graph: labele935650037_a_nat,Labeled_graph2: labele935650037_a_nat] :
% 0.26/0.62 ( ( ( ( labele195203296_a_nat @ Labeled_graph )
% 0.26/0.62 = ( labele195203296_a_nat @ Labeled_graph2 ) )
% 0.26/0.62 & ( ( labele1810595089_a_nat @ Labeled_graph )
% 0.26/0.62 = ( labele1810595089_a_nat @ Labeled_graph2 ) ) )
% 0.26/0.62 => ( Labeled_graph = Labeled_graph2 ) ) ).
% 0.26/0.62
% 0.26/0.62 % labeled_graph.expand
% 0.26/0.62 thf(fact_134_labeled__graph_Oexpand,axiom,
% 0.26/0.62 ! [Labeled_graph: labele431970251um_a_b,Labeled_graph2: labele431970251um_a_b] :
% 0.26/0.62 ( ( ( ( labele1939049654um_a_b @ Labeled_graph )
% 0.26/0.62 = ( labele1939049654um_a_b @ Labeled_graph2 ) )
% 0.26/0.62 & ( ( labele577278695um_a_b @ Labeled_graph )
% 0.26/0.62 = ( labele577278695um_a_b @ Labeled_graph2 ) ) )
% 0.26/0.62 => ( Labeled_graph = Labeled_graph2 ) ) ).
% 0.26/0.62
% 0.26/0.62 % labeled_graph.expand
% 0.26/0.62 thf(fact_135_labeled__graph_Osel_I2_J,axiom,
% 0.26/0.62 ! [X1: set_Pr1647387645at_nat,X22: set_nat] :
% 0.26/0.62 ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ X1 @ X22 ) )
% 0.26/0.62 = X22 ) ).
% 0.26/0.62
% 0.26/0.62 % labeled_graph.sel(2)
% 0.26/0.62 thf(fact_136_labeled__graph_Osel_I2_J,axiom,
% 0.26/0.62 ! [X1: set_Pr409224873um_a_b,X22: set_Sum_sum_a_b] :
% 0.26/0.62 ( ( labele577278695um_a_b @ ( labele1729654377um_a_b @ X1 @ X22 ) )
% 0.26/0.62 = X22 ) ).
% 0.26/0.62
% 0.26/0.62 % labeled_graph.sel(2)
% 0.26/0.62 thf(fact_137_labeled__graph_Osel_I1_J,axiom,
% 0.26/0.62 ! [X1: set_Pr1647387645at_nat,X22: set_nat] :
% 0.26/0.62 ( ( labele195203296_a_nat @ ( labele16114835_a_nat @ X1 @ X22 ) )
% 0.26/0.62 = X1 ) ).
% 0.26/0.62
% 0.26/0.62 % labeled_graph.sel(1)
% 0.26/0.62 thf(fact_138_labeled__graph_Osel_I1_J,axiom,
% 0.26/0.62 ! [X1: set_Pr409224873um_a_b,X22: set_Sum_sum_a_b] :
% 0.26/0.62 ( ( labele1939049654um_a_b @ ( labele1729654377um_a_b @ X1 @ X22 ) )
% 0.26/0.62 = X1 ) ).
% 0.26/0.62
% 0.26/0.62 % labeled_graph.sel(1)
% 0.26/0.62 thf(fact_139_Domain__empty__iff,axiom,
% 0.26/0.62 ! [R: set_Pr1647387645at_nat] :
% 0.26/0.62 ( ( ( domain1060562500at_nat @ R )
% 0.26/0.62 = bot_bo1160111033tant_a )
% 0.26/0.62 = ( R = bot_bo810816657at_nat ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain_empty_iff
% 0.26/0.62 thf(fact_140_Domain__empty__iff,axiom,
% 0.26/0.62 ! [R: set_Pr409224873um_a_b] :
% 0.26/0.62 ( ( ( domain1362581744um_a_b @ R )
% 0.26/0.62 = bot_bo1160111033tant_a )
% 0.26/0.62 = ( R = bot_bo1262634813um_a_b ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain_empty_iff
% 0.26/0.62 thf(fact_141_Domain__empty__iff,axiom,
% 0.26/0.62 ! [R: set_Pr1986765409at_nat] :
% 0.26/0.62 ( ( ( domain_nat_nat @ R )
% 0.26/0.62 = bot_bot_set_nat )
% 0.26/0.62 = ( R = bot_bo2130386637at_nat ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain_empty_iff
% 0.26/0.62 thf(fact_142_Domain__empty__iff,axiom,
% 0.26/0.62 ! [R: set_Pr1174980151um_a_b] :
% 0.26/0.62 ( ( ( domain1368163076um_a_b @ R )
% 0.26/0.62 = bot_bot_set_nat )
% 0.26/0.62 = ( R = bot_bo575978147um_a_b ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain_empty_iff
% 0.26/0.62 thf(fact_143_Domain__empty__iff,axiom,
% 0.26/0.62 ! [R: set_Pr1916610317um_a_b] :
% 0.26/0.62 ( ( ( domain2069673178um_a_b @ R )
% 0.26/0.62 = bot_bo1491243248um_a_b )
% 0.26/0.62 = ( R = bot_bo225809273um_a_b ) ) ).
% 0.26/0.62
% 0.26/0.62 % Domain_empty_iff
% 0.26/0.62 thf(fact_144_edge__preserving__atomic,axiom,
% 0.26/0.62 ! [H1: set_Pr375490359_b_nat,E1: set_Pr409224873um_a_b,E2: set_Pr1647387645at_nat,V1: sum_sum_a_b,V12: nat,V22: sum_sum_a_b,V23: nat,K: standard_Constant_a] :
% 0.26/0.62 ( ( edge_p749155930tant_a @ H1 @ E1 @ E2 )
% 0.26/0.62 => ( ( member1249152_b_nat @ ( produc522153487_b_nat @ V1 @ V12 ) @ H1 )
% 0.26/0.62 => ( ( member1249152_b_nat @ ( produc522153487_b_nat @ V22 @ V23 ) @ H1 )
% 0.26/0.62 => ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ K @ ( produc176426981um_a_b @ V1 @ V22 ) ) @ E1 )
% 0.26/0.62 => ( member1696759390at_nat @ ( produc407553657at_nat @ K @ ( product_Pair_nat_nat @ V12 @ V23 ) ) @ E2 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % edge_preserving_atomic
% 0.26/0.62 thf(fact_145_edge__preserving__atomic,axiom,
% 0.26/0.62 ! [H1: set_Pr1986765409at_nat,E1: set_Pr1647387645at_nat,E2: set_Pr1647387645at_nat,V1: nat,V12: nat,V22: nat,V23: nat,K: standard_Constant_a] :
% 0.26/0.62 ( ( edge_p170421892tant_a @ H1 @ E1 @ E2 )
% 0.26/0.62 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ V1 @ V12 ) @ H1 )
% 0.26/0.62 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ V22 @ V23 ) @ H1 )
% 0.26/0.62 => ( ( member1696759390at_nat @ ( produc407553657at_nat @ K @ ( product_Pair_nat_nat @ V1 @ V22 ) ) @ E1 )
% 0.26/0.62 => ( member1696759390at_nat @ ( produc407553657at_nat @ K @ ( product_Pair_nat_nat @ V12 @ V23 ) ) @ E2 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % edge_preserving_atomic
% 0.26/0.62 thf(fact_146_edge__preserving__atomic,axiom,
% 0.26/0.62 ! [H1: set_Pr1916610317um_a_b,E1: set_Pr409224873um_a_b,E2: set_Pr409224873um_a_b,V1: sum_sum_a_b,V12: sum_sum_a_b,V22: sum_sum_a_b,V23: sum_sum_a_b,K: standard_Constant_a] :
% 0.26/0.62 ( ( edge_p1871801392tant_a @ H1 @ E1 @ E2 )
% 0.26/0.62 => ( ( member947389014um_a_b @ ( produc176426981um_a_b @ V1 @ V12 ) @ H1 )
% 0.26/0.62 => ( ( member947389014um_a_b @ ( produc176426981um_a_b @ V22 @ V23 ) @ H1 )
% 0.26/0.62 => ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ K @ ( produc176426981um_a_b @ V1 @ V22 ) ) @ E1 )
% 0.26/0.62 => ( member1998628618um_a_b @ ( produc1697725733um_a_b @ K @ ( produc176426981um_a_b @ V12 @ V23 ) ) @ E2 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % edge_preserving_atomic
% 0.26/0.62 thf(fact_147_edge__preserving__atomic,axiom,
% 0.26/0.62 ! [H1: set_Pr1174980151um_a_b,E1: set_Pr1647387645at_nat,E2: set_Pr409224873um_a_b,V1: nat,V12: sum_sum_a_b,V22: nat,V23: sum_sum_a_b,K: standard_Constant_a] :
% 0.26/0.62 ( ( edge_p1382426714tant_a @ H1 @ E1 @ E2 )
% 0.26/0.62 => ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ V1 @ V12 ) @ H1 )
% 0.26/0.62 => ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ V22 @ V23 ) @ H1 )
% 0.26/0.62 => ( ( member1696759390at_nat @ ( produc407553657at_nat @ K @ ( product_Pair_nat_nat @ V1 @ V22 ) ) @ E1 )
% 0.26/0.62 => ( member1998628618um_a_b @ ( produc1697725733um_a_b @ K @ ( produc176426981um_a_b @ V12 @ V23 ) ) @ E2 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % edge_preserving_atomic
% 0.26/0.62 thf(fact_148_labeled__graph_Oexhaust__sel,axiom,
% 0.26/0.62 ! [Labeled_graph: labele935650037_a_nat] :
% 0.26/0.62 ( Labeled_graph
% 0.26/0.62 = ( labele16114835_a_nat @ ( labele195203296_a_nat @ Labeled_graph ) @ ( labele1810595089_a_nat @ Labeled_graph ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % labeled_graph.exhaust_sel
% 0.26/0.62 thf(fact_149_labeled__graph_Oexhaust__sel,axiom,
% 0.26/0.62 ! [Labeled_graph: labele431970251um_a_b] :
% 0.26/0.62 ( Labeled_graph
% 0.26/0.62 = ( labele1729654377um_a_b @ ( labele1939049654um_a_b @ Labeled_graph ) @ ( labele577278695um_a_b @ Labeled_graph ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % labeled_graph.exhaust_sel
% 0.26/0.62 thf(fact_150_singleton__insert__inj__eq_H,axiom,
% 0.26/0.62 ! [A: standard_Constant_a,A3: set_St761939237tant_a,B: standard_Constant_a] :
% 0.26/0.62 ( ( ( insert1909710879tant_a @ A @ A3 )
% 0.26/0.62 = ( insert1909710879tant_a @ B @ bot_bo1160111033tant_a ) )
% 0.26/0.62 = ( ( A = B )
% 0.26/0.62 & ( ord_le1739761029tant_a @ A3 @ ( insert1909710879tant_a @ B @ bot_bo1160111033tant_a ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % singleton_insert_inj_eq'
% 0.26/0.62 thf(fact_151_singleton__insert__inj__eq_H,axiom,
% 0.26/0.62 ! [A: product_prod_nat_nat,A3: set_Pr1986765409at_nat,B: product_prod_nat_nat] :
% 0.26/0.62 ( ( ( insert271595217at_nat @ A @ A3 )
% 0.26/0.62 = ( insert271595217at_nat @ B @ bot_bo2130386637at_nat ) )
% 0.26/0.62 = ( ( A = B )
% 0.26/0.62 & ( ord_le841296385at_nat @ A3 @ ( insert271595217at_nat @ B @ bot_bo2130386637at_nat ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % singleton_insert_inj_eq'
% 0.26/0.62 thf(fact_152_singleton__insert__inj__eq_H,axiom,
% 0.26/0.62 ! [A: produc1032616263at_nat,A3: set_Pr1647387645at_nat,B: produc1032616263at_nat] :
% 0.26/0.62 ( ( ( insert1625259895at_nat @ A @ A3 )
% 0.26/0.62 = ( insert1625259895at_nat @ B @ bot_bo810816657at_nat ) )
% 0.26/0.62 = ( ( A = B )
% 0.26/0.62 & ( ord_le1909159005at_nat @ A3 @ ( insert1625259895at_nat @ B @ bot_bo810816657at_nat ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % singleton_insert_inj_eq'
% 0.26/0.62 thf(fact_153_singleton__insert__inj__eq_H,axiom,
% 0.26/0.62 ! [A: nat,A3: set_nat,B: nat] :
% 0.26/0.62 ( ( ( insert_nat @ A @ A3 )
% 0.26/0.62 = ( insert_nat @ B @ bot_bot_set_nat ) )
% 0.26/0.62 = ( ( A = B )
% 0.26/0.62 & ( ord_less_eq_set_nat @ A3 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % singleton_insert_inj_eq'
% 0.26/0.62 thf(fact_154_singleton__insert__inj__eq_H,axiom,
% 0.26/0.62 ! [A: produc1124793815um_a_b,A3: set_Pr1174980151um_a_b,B: produc1124793815um_a_b] :
% 0.26/0.62 ( ( ( insert983991207um_a_b @ A @ A3 )
% 0.26/0.62 = ( insert983991207um_a_b @ B @ bot_bo575978147um_a_b ) )
% 0.26/0.62 = ( ( A = B )
% 0.26/0.62 & ( ord_le823954903um_a_b @ A3 @ ( insert983991207um_a_b @ B @ bot_bo575978147um_a_b ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % singleton_insert_inj_eq'
% 0.26/0.62 thf(fact_155_singleton__insert__inj__eq_H,axiom,
% 0.26/0.62 ! [A: produc1548871597um_a_b,A3: set_Pr1916610317um_a_b,B: produc1548871597um_a_b] :
% 0.26/0.62 ( ( ( insert1435405693um_a_b @ A @ A3 )
% 0.26/0.62 = ( insert1435405693um_a_b @ B @ bot_bo225809273um_a_b ) )
% 0.26/0.62 = ( ( A = B )
% 0.26/0.62 & ( ord_le1059794605um_a_b @ A3 @ ( insert1435405693um_a_b @ B @ bot_bo225809273um_a_b ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % singleton_insert_inj_eq'
% 0.26/0.62 thf(fact_156_singleton__insert__inj__eq_H,axiom,
% 0.26/0.62 ! [A: produc1963079155um_a_b,A3: set_Pr409224873um_a_b,B: produc1963079155um_a_b] :
% 0.26/0.62 ( ( ( insert323157027um_a_b @ A @ A3 )
% 0.26/0.62 = ( insert323157027um_a_b @ B @ bot_bo1262634813um_a_b ) )
% 0.26/0.62 = ( ( A = B )
% 0.26/0.62 & ( ord_le615126793um_a_b @ A3 @ ( insert323157027um_a_b @ B @ bot_bo1262634813um_a_b ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % singleton_insert_inj_eq'
% 0.26/0.62 thf(fact_157_singleton__insert__inj__eq_H,axiom,
% 0.26/0.62 ! [A: sum_sum_a_b,A3: set_Sum_sum_a_b,B: sum_sum_a_b] :
% 0.26/0.62 ( ( ( insert_Sum_sum_a_b @ A @ A3 )
% 0.26/0.62 = ( insert_Sum_sum_a_b @ B @ bot_bo1491243248um_a_b ) )
% 0.26/0.62 = ( ( A = B )
% 0.26/0.62 & ( ord_le192794300um_a_b @ A3 @ ( insert_Sum_sum_a_b @ B @ bot_bo1491243248um_a_b ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % singleton_insert_inj_eq'
% 0.26/0.62 thf(fact_158_singleton__insert__inj__eq,axiom,
% 0.26/0.62 ! [B: standard_Constant_a,A: standard_Constant_a,A3: set_St761939237tant_a] :
% 0.26/0.62 ( ( ( insert1909710879tant_a @ B @ bot_bo1160111033tant_a )
% 0.26/0.62 = ( insert1909710879tant_a @ A @ A3 ) )
% 0.26/0.62 = ( ( A = B )
% 0.26/0.62 & ( ord_le1739761029tant_a @ A3 @ ( insert1909710879tant_a @ B @ bot_bo1160111033tant_a ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % singleton_insert_inj_eq
% 0.26/0.62 thf(fact_159_singleton__insert__inj__eq,axiom,
% 0.26/0.62 ! [B: product_prod_nat_nat,A: product_prod_nat_nat,A3: set_Pr1986765409at_nat] :
% 0.26/0.62 ( ( ( insert271595217at_nat @ B @ bot_bo2130386637at_nat )
% 0.26/0.62 = ( insert271595217at_nat @ A @ A3 ) )
% 0.26/0.62 = ( ( A = B )
% 0.26/0.62 & ( ord_le841296385at_nat @ A3 @ ( insert271595217at_nat @ B @ bot_bo2130386637at_nat ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % singleton_insert_inj_eq
% 0.26/0.62 thf(fact_160_singleton__insert__inj__eq,axiom,
% 0.26/0.62 ! [B: produc1032616263at_nat,A: produc1032616263at_nat,A3: set_Pr1647387645at_nat] :
% 0.26/0.62 ( ( ( insert1625259895at_nat @ B @ bot_bo810816657at_nat )
% 0.26/0.62 = ( insert1625259895at_nat @ A @ A3 ) )
% 0.26/0.62 = ( ( A = B )
% 0.26/0.62 & ( ord_le1909159005at_nat @ A3 @ ( insert1625259895at_nat @ B @ bot_bo810816657at_nat ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % singleton_insert_inj_eq
% 0.26/0.62 thf(fact_161_singleton__insert__inj__eq,axiom,
% 0.26/0.62 ! [B: nat,A: nat,A3: set_nat] :
% 0.26/0.62 ( ( ( insert_nat @ B @ bot_bot_set_nat )
% 0.26/0.62 = ( insert_nat @ A @ A3 ) )
% 0.26/0.62 = ( ( A = B )
% 0.26/0.62 & ( ord_less_eq_set_nat @ A3 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % singleton_insert_inj_eq
% 0.26/0.62 thf(fact_162_singleton__insert__inj__eq,axiom,
% 0.26/0.62 ! [B: produc1124793815um_a_b,A: produc1124793815um_a_b,A3: set_Pr1174980151um_a_b] :
% 0.26/0.62 ( ( ( insert983991207um_a_b @ B @ bot_bo575978147um_a_b )
% 0.26/0.62 = ( insert983991207um_a_b @ A @ A3 ) )
% 0.26/0.62 = ( ( A = B )
% 0.26/0.62 & ( ord_le823954903um_a_b @ A3 @ ( insert983991207um_a_b @ B @ bot_bo575978147um_a_b ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % singleton_insert_inj_eq
% 0.26/0.62 thf(fact_163_singleton__insert__inj__eq,axiom,
% 0.26/0.62 ! [B: produc1548871597um_a_b,A: produc1548871597um_a_b,A3: set_Pr1916610317um_a_b] :
% 0.26/0.62 ( ( ( insert1435405693um_a_b @ B @ bot_bo225809273um_a_b )
% 0.26/0.62 = ( insert1435405693um_a_b @ A @ A3 ) )
% 0.26/0.62 = ( ( A = B )
% 0.26/0.62 & ( ord_le1059794605um_a_b @ A3 @ ( insert1435405693um_a_b @ B @ bot_bo225809273um_a_b ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % singleton_insert_inj_eq
% 0.26/0.62 thf(fact_164_singleton__insert__inj__eq,axiom,
% 0.26/0.62 ! [B: produc1963079155um_a_b,A: produc1963079155um_a_b,A3: set_Pr409224873um_a_b] :
% 0.26/0.62 ( ( ( insert323157027um_a_b @ B @ bot_bo1262634813um_a_b )
% 0.26/0.62 = ( insert323157027um_a_b @ A @ A3 ) )
% 0.26/0.62 = ( ( A = B )
% 0.26/0.62 & ( ord_le615126793um_a_b @ A3 @ ( insert323157027um_a_b @ B @ bot_bo1262634813um_a_b ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % singleton_insert_inj_eq
% 0.26/0.62 thf(fact_165_singleton__insert__inj__eq,axiom,
% 0.26/0.62 ! [B: sum_sum_a_b,A: sum_sum_a_b,A3: set_Sum_sum_a_b] :
% 0.26/0.62 ( ( ( insert_Sum_sum_a_b @ B @ bot_bo1491243248um_a_b )
% 0.26/0.62 = ( insert_Sum_sum_a_b @ A @ A3 ) )
% 0.26/0.62 = ( ( A = B )
% 0.26/0.62 & ( ord_le192794300um_a_b @ A3 @ ( insert_Sum_sum_a_b @ B @ bot_bo1491243248um_a_b ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % singleton_insert_inj_eq
% 0.26/0.62 thf(fact_166_univalent__empty,axiom,
% 0.26/0.62 unival860567212at_nat @ bot_bo810816657at_nat ).
% 0.26/0.62
% 0.26/0.62 % univalent_empty
% 0.26/0.62 thf(fact_167_univalent__empty,axiom,
% 0.26/0.62 unival118648434um_a_b @ bot_bo225809273um_a_b ).
% 0.26/0.62
% 0.26/0.62 % univalent_empty
% 0.26/0.62 thf(fact_168_univalent__empty,axiom,
% 0.26/0.62 unival1487587672um_a_b @ bot_bo1262634813um_a_b ).
% 0.26/0.62
% 0.26/0.62 % univalent_empty
% 0.26/0.62 thf(fact_169_univalent__empty,axiom,
% 0.26/0.62 unival2092813468um_a_b @ bot_bo575978147um_a_b ).
% 0.26/0.62
% 0.26/0.62 % univalent_empty
% 0.26/0.62 thf(fact_170_mem__Collect__eq,axiom,
% 0.26/0.62 ! [A: sum_sum_a_b,P: sum_sum_a_b > $o] :
% 0.26/0.62 ( ( member_Sum_sum_a_b @ A @ ( collect_Sum_sum_a_b @ P ) )
% 0.26/0.62 = ( P @ A ) ) ).
% 0.26/0.62
% 0.26/0.62 % mem_Collect_eq
% 0.26/0.62 thf(fact_171_mem__Collect__eq,axiom,
% 0.26/0.62 ! [A: produc1124793815um_a_b,P: produc1124793815um_a_b > $o] :
% 0.26/0.62 ( ( member1294585472um_a_b @ A @ ( collec492052930um_a_b @ P ) )
% 0.26/0.62 = ( P @ A ) ) ).
% 0.26/0.62
% 0.26/0.62 % mem_Collect_eq
% 0.26/0.62 thf(fact_172_mem__Collect__eq,axiom,
% 0.26/0.62 ! [A: produc1963079155um_a_b,P: produc1963079155um_a_b > $o] :
% 0.26/0.62 ( ( member1998628618um_a_b @ A @ ( collec1254333256um_a_b @ P ) )
% 0.26/0.62 = ( P @ A ) ) ).
% 0.26/0.62
% 0.26/0.62 % mem_Collect_eq
% 0.26/0.62 thf(fact_173_Collect__mem__eq,axiom,
% 0.26/0.62 ! [A3: set_Sum_sum_a_b] :
% 0.26/0.62 ( ( collect_Sum_sum_a_b
% 0.26/0.62 @ ^ [X3: sum_sum_a_b] : ( member_Sum_sum_a_b @ X3 @ A3 ) )
% 0.26/0.62 = A3 ) ).
% 0.26/0.62
% 0.26/0.62 % Collect_mem_eq
% 0.26/0.62 thf(fact_174_Collect__mem__eq,axiom,
% 0.26/0.62 ! [A3: set_Pr1174980151um_a_b] :
% 0.26/0.62 ( ( collec492052930um_a_b
% 0.26/0.62 @ ^ [X3: produc1124793815um_a_b] : ( member1294585472um_a_b @ X3 @ A3 ) )
% 0.26/0.62 = A3 ) ).
% 0.26/0.62
% 0.26/0.62 % Collect_mem_eq
% 0.26/0.62 thf(fact_175_Collect__mem__eq,axiom,
% 0.26/0.62 ! [A3: set_Pr409224873um_a_b] :
% 0.26/0.62 ( ( collec1254333256um_a_b
% 0.26/0.62 @ ^ [X3: produc1963079155um_a_b] : ( member1998628618um_a_b @ X3 @ A3 ) )
% 0.26/0.62 = A3 ) ).
% 0.26/0.62
% 0.26/0.62 % Collect_mem_eq
% 0.26/0.62 thf(fact_176_insert__subset,axiom,
% 0.26/0.62 ! [X2: produc1032616263at_nat,A3: set_Pr1647387645at_nat,B5: set_Pr1647387645at_nat] :
% 0.26/0.62 ( ( ord_le1909159005at_nat @ ( insert1625259895at_nat @ X2 @ A3 ) @ B5 )
% 0.26/0.62 = ( ( member1696759390at_nat @ X2 @ B5 )
% 0.26/0.62 & ( ord_le1909159005at_nat @ A3 @ B5 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insert_subset
% 0.26/0.62 thf(fact_177_insert__subset,axiom,
% 0.26/0.62 ! [X2: nat,A3: set_nat,B5: set_nat] :
% 0.26/0.62 ( ( ord_less_eq_set_nat @ ( insert_nat @ X2 @ A3 ) @ B5 )
% 0.26/0.62 = ( ( member_nat @ X2 @ B5 )
% 0.26/0.62 & ( ord_less_eq_set_nat @ A3 @ B5 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insert_subset
% 0.26/0.62 thf(fact_178_insert__subset,axiom,
% 0.26/0.62 ! [X2: produc1548871597um_a_b,A3: set_Pr1916610317um_a_b,B5: set_Pr1916610317um_a_b] :
% 0.26/0.62 ( ( ord_le1059794605um_a_b @ ( insert1435405693um_a_b @ X2 @ A3 ) @ B5 )
% 0.26/0.62 = ( ( member947389014um_a_b @ X2 @ B5 )
% 0.26/0.62 & ( ord_le1059794605um_a_b @ A3 @ B5 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insert_subset
% 0.26/0.62 thf(fact_179_insert__subset,axiom,
% 0.26/0.62 ! [X2: standard_Constant_a,A3: set_St761939237tant_a,B5: set_St761939237tant_a] :
% 0.26/0.62 ( ( ord_le1739761029tant_a @ ( insert1909710879tant_a @ X2 @ A3 ) @ B5 )
% 0.26/0.62 = ( ( member1632892294tant_a @ X2 @ B5 )
% 0.26/0.62 & ( ord_le1739761029tant_a @ A3 @ B5 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insert_subset
% 0.26/0.62 thf(fact_180_insert__subset,axiom,
% 0.26/0.62 ! [X2: product_prod_nat_nat,A3: set_Pr1986765409at_nat,B5: set_Pr1986765409at_nat] :
% 0.26/0.62 ( ( ord_le841296385at_nat @ ( insert271595217at_nat @ X2 @ A3 ) @ B5 )
% 0.26/0.62 = ( ( member701585322at_nat @ X2 @ B5 )
% 0.26/0.62 & ( ord_le841296385at_nat @ A3 @ B5 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insert_subset
% 0.26/0.62 thf(fact_181_insert__subset,axiom,
% 0.26/0.62 ! [X2: produc1124793815um_a_b,A3: set_Pr1174980151um_a_b,B5: set_Pr1174980151um_a_b] :
% 0.26/0.62 ( ( ord_le823954903um_a_b @ ( insert983991207um_a_b @ X2 @ A3 ) @ B5 )
% 0.26/0.62 = ( ( member1294585472um_a_b @ X2 @ B5 )
% 0.26/0.62 & ( ord_le823954903um_a_b @ A3 @ B5 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insert_subset
% 0.26/0.62 thf(fact_182_insert__subset,axiom,
% 0.26/0.62 ! [X2: produc1963079155um_a_b,A3: set_Pr409224873um_a_b,B5: set_Pr409224873um_a_b] :
% 0.26/0.62 ( ( ord_le615126793um_a_b @ ( insert323157027um_a_b @ X2 @ A3 ) @ B5 )
% 0.26/0.62 = ( ( member1998628618um_a_b @ X2 @ B5 )
% 0.26/0.62 & ( ord_le615126793um_a_b @ A3 @ B5 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insert_subset
% 0.26/0.62 thf(fact_183_insert__subset,axiom,
% 0.26/0.62 ! [X2: sum_sum_a_b,A3: set_Sum_sum_a_b,B5: set_Sum_sum_a_b] :
% 0.26/0.62 ( ( ord_le192794300um_a_b @ ( insert_Sum_sum_a_b @ X2 @ A3 ) @ B5 )
% 0.26/0.62 = ( ( member_Sum_sum_a_b @ X2 @ B5 )
% 0.26/0.62 & ( ord_le192794300um_a_b @ A3 @ B5 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insert_subset
% 0.26/0.62 thf(fact_184_singletonI,axiom,
% 0.26/0.62 ! [A: standard_Constant_a] : ( member1632892294tant_a @ A @ ( insert1909710879tant_a @ A @ bot_bo1160111033tant_a ) ) ).
% 0.26/0.62
% 0.26/0.62 % singletonI
% 0.26/0.62 thf(fact_185_singletonI,axiom,
% 0.26/0.62 ! [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) ) ).
% 0.26/0.62
% 0.26/0.62 % singletonI
% 0.26/0.62 thf(fact_186_singletonI,axiom,
% 0.26/0.62 ! [A: produc1032616263at_nat] : ( member1696759390at_nat @ A @ ( insert1625259895at_nat @ A @ bot_bo810816657at_nat ) ) ).
% 0.26/0.62
% 0.26/0.62 % singletonI
% 0.26/0.62 thf(fact_187_singletonI,axiom,
% 0.26/0.62 ! [A: nat] : ( member_nat @ A @ ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 0.26/0.62
% 0.26/0.62 % singletonI
% 0.26/0.62 thf(fact_188_singletonI,axiom,
% 0.26/0.62 ! [A: produc1124793815um_a_b] : ( member1294585472um_a_b @ A @ ( insert983991207um_a_b @ A @ bot_bo575978147um_a_b ) ) ).
% 0.26/0.62
% 0.26/0.62 % singletonI
% 0.26/0.62 thf(fact_189_singletonI,axiom,
% 0.26/0.62 ! [A: produc1548871597um_a_b] : ( member947389014um_a_b @ A @ ( insert1435405693um_a_b @ A @ bot_bo225809273um_a_b ) ) ).
% 0.26/0.62
% 0.26/0.62 % singletonI
% 0.26/0.62 thf(fact_190_singletonI,axiom,
% 0.26/0.62 ! [A: produc1963079155um_a_b] : ( member1998628618um_a_b @ A @ ( insert323157027um_a_b @ A @ bot_bo1262634813um_a_b ) ) ).
% 0.26/0.62
% 0.26/0.62 % singletonI
% 0.26/0.62 thf(fact_191_singletonI,axiom,
% 0.26/0.62 ! [A: sum_sum_a_b] : ( member_Sum_sum_a_b @ A @ ( insert_Sum_sum_a_b @ A @ bot_bo1491243248um_a_b ) ) ).
% 0.26/0.62
% 0.26/0.62 % singletonI
% 0.26/0.62 thf(fact_192_empty__subsetI,axiom,
% 0.26/0.62 ! [A3: set_Pr1647387645at_nat] : ( ord_le1909159005at_nat @ bot_bo810816657at_nat @ A3 ) ).
% 0.26/0.62
% 0.26/0.62 % empty_subsetI
% 0.26/0.62 thf(fact_193_empty__subsetI,axiom,
% 0.26/0.62 ! [A3: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A3 ) ).
% 0.26/0.62
% 0.26/0.62 % empty_subsetI
% 0.26/0.62 thf(fact_194_empty__subsetI,axiom,
% 0.26/0.62 ! [A3: set_Pr1174980151um_a_b] : ( ord_le823954903um_a_b @ bot_bo575978147um_a_b @ A3 ) ).
% 0.26/0.62
% 0.26/0.62 % empty_subsetI
% 0.26/0.62 thf(fact_195_empty__subsetI,axiom,
% 0.26/0.62 ! [A3: set_Pr1916610317um_a_b] : ( ord_le1059794605um_a_b @ bot_bo225809273um_a_b @ A3 ) ).
% 0.26/0.62
% 0.26/0.62 % empty_subsetI
% 0.26/0.62 thf(fact_196_empty__subsetI,axiom,
% 0.26/0.62 ! [A3: set_Pr409224873um_a_b] : ( ord_le615126793um_a_b @ bot_bo1262634813um_a_b @ A3 ) ).
% 0.26/0.62
% 0.26/0.62 % empty_subsetI
% 0.26/0.62 thf(fact_197_empty__subsetI,axiom,
% 0.26/0.62 ! [A3: set_Sum_sum_a_b] : ( ord_le192794300um_a_b @ bot_bo1491243248um_a_b @ A3 ) ).
% 0.26/0.62
% 0.26/0.62 % empty_subsetI
% 0.26/0.62 thf(fact_198_subset__empty,axiom,
% 0.26/0.62 ! [A3: set_Pr1647387645at_nat] :
% 0.26/0.62 ( ( ord_le1909159005at_nat @ A3 @ bot_bo810816657at_nat )
% 0.26/0.62 = ( A3 = bot_bo810816657at_nat ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_empty
% 0.26/0.62 thf(fact_199_subset__empty,axiom,
% 0.26/0.62 ! [A3: set_nat] :
% 0.26/0.62 ( ( ord_less_eq_set_nat @ A3 @ bot_bot_set_nat )
% 0.26/0.62 = ( A3 = bot_bot_set_nat ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_empty
% 0.26/0.62 thf(fact_200_subset__empty,axiom,
% 0.26/0.62 ! [A3: set_Pr1174980151um_a_b] :
% 0.26/0.62 ( ( ord_le823954903um_a_b @ A3 @ bot_bo575978147um_a_b )
% 0.26/0.62 = ( A3 = bot_bo575978147um_a_b ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_empty
% 0.26/0.62 thf(fact_201_subset__empty,axiom,
% 0.26/0.62 ! [A3: set_Pr1916610317um_a_b] :
% 0.26/0.62 ( ( ord_le1059794605um_a_b @ A3 @ bot_bo225809273um_a_b )
% 0.26/0.62 = ( A3 = bot_bo225809273um_a_b ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_empty
% 0.26/0.62 thf(fact_202_subset__empty,axiom,
% 0.26/0.62 ! [A3: set_Pr409224873um_a_b] :
% 0.26/0.62 ( ( ord_le615126793um_a_b @ A3 @ bot_bo1262634813um_a_b )
% 0.26/0.62 = ( A3 = bot_bo1262634813um_a_b ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_empty
% 0.26/0.62 thf(fact_203_subset__empty,axiom,
% 0.26/0.62 ! [A3: set_Sum_sum_a_b] :
% 0.26/0.62 ( ( ord_le192794300um_a_b @ A3 @ bot_bo1491243248um_a_b )
% 0.26/0.62 = ( A3 = bot_bo1491243248um_a_b ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_empty
% 0.26/0.62 thf(fact_204_le__zero__eq,axiom,
% 0.26/0.62 ! [N: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.26/0.62 = ( N = zero_zero_nat ) ) ).
% 0.26/0.62
% 0.26/0.62 % le_zero_eq
% 0.26/0.62 thf(fact_205_reflexivity__rule__def,axiom,
% 0.26/0.62 ( standa63370785tant_a
% 0.26/0.62 = ( ^ [T: standard_Constant_a] : ( produc1676969687_a_nat @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ T @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % reflexivity_rule_def
% 0.26/0.62 thf(fact_206_nonempty__rule__def,axiom,
% 0.26/0.62 ( standa1410829644tant_a
% 0.26/0.62 = ( produc1676969687_a_nat @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ bot_bot_set_nat ) @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % nonempty_rule_def
% 0.26/0.62 thf(fact_207_empty__iff,axiom,
% 0.26/0.62 ! [C: produc1032616263at_nat] :
% 0.26/0.62 ~ ( member1696759390at_nat @ C @ bot_bo810816657at_nat ) ).
% 0.26/0.62
% 0.26/0.62 % empty_iff
% 0.26/0.62 thf(fact_208_empty__iff,axiom,
% 0.26/0.62 ! [C: nat] :
% 0.26/0.62 ~ ( member_nat @ C @ bot_bot_set_nat ) ).
% 0.26/0.62
% 0.26/0.62 % empty_iff
% 0.26/0.62 thf(fact_209_empty__iff,axiom,
% 0.26/0.62 ! [C: produc1124793815um_a_b] :
% 0.26/0.62 ~ ( member1294585472um_a_b @ C @ bot_bo575978147um_a_b ) ).
% 0.26/0.62
% 0.26/0.62 % empty_iff
% 0.26/0.62 thf(fact_210_empty__iff,axiom,
% 0.26/0.62 ! [C: produc1548871597um_a_b] :
% 0.26/0.62 ~ ( member947389014um_a_b @ C @ bot_bo225809273um_a_b ) ).
% 0.26/0.62
% 0.26/0.62 % empty_iff
% 0.26/0.62 thf(fact_211_empty__iff,axiom,
% 0.26/0.62 ! [C: produc1963079155um_a_b] :
% 0.26/0.62 ~ ( member1998628618um_a_b @ C @ bot_bo1262634813um_a_b ) ).
% 0.26/0.62
% 0.26/0.62 % empty_iff
% 0.26/0.62 thf(fact_212_empty__iff,axiom,
% 0.26/0.62 ! [C: sum_sum_a_b] :
% 0.26/0.62 ~ ( member_Sum_sum_a_b @ C @ bot_bo1491243248um_a_b ) ).
% 0.26/0.62
% 0.26/0.62 % empty_iff
% 0.26/0.62 thf(fact_213_all__not__in__conv,axiom,
% 0.26/0.62 ! [A3: set_Pr1647387645at_nat] :
% 0.26/0.62 ( ( ! [X3: produc1032616263at_nat] :
% 0.26/0.62 ~ ( member1696759390at_nat @ X3 @ A3 ) )
% 0.26/0.62 = ( A3 = bot_bo810816657at_nat ) ) ).
% 0.26/0.62
% 0.26/0.62 % all_not_in_conv
% 0.26/0.62 thf(fact_214_all__not__in__conv,axiom,
% 0.26/0.62 ! [A3: set_nat] :
% 0.26/0.62 ( ( ! [X3: nat] :
% 0.26/0.62 ~ ( member_nat @ X3 @ A3 ) )
% 0.26/0.62 = ( A3 = bot_bot_set_nat ) ) ).
% 0.26/0.62
% 0.26/0.62 % all_not_in_conv
% 0.26/0.62 thf(fact_215_all__not__in__conv,axiom,
% 0.26/0.62 ! [A3: set_Pr1174980151um_a_b] :
% 0.26/0.62 ( ( ! [X3: produc1124793815um_a_b] :
% 0.26/0.62 ~ ( member1294585472um_a_b @ X3 @ A3 ) )
% 0.26/0.62 = ( A3 = bot_bo575978147um_a_b ) ) ).
% 0.26/0.62
% 0.26/0.62 % all_not_in_conv
% 0.26/0.62 thf(fact_216_all__not__in__conv,axiom,
% 0.26/0.62 ! [A3: set_Pr1916610317um_a_b] :
% 0.26/0.62 ( ( ! [X3: produc1548871597um_a_b] :
% 0.26/0.62 ~ ( member947389014um_a_b @ X3 @ A3 ) )
% 0.26/0.62 = ( A3 = bot_bo225809273um_a_b ) ) ).
% 0.26/0.62
% 0.26/0.62 % all_not_in_conv
% 0.26/0.62 thf(fact_217_all__not__in__conv,axiom,
% 0.26/0.62 ! [A3: set_Pr409224873um_a_b] :
% 0.26/0.62 ( ( ! [X3: produc1963079155um_a_b] :
% 0.26/0.62 ~ ( member1998628618um_a_b @ X3 @ A3 ) )
% 0.26/0.62 = ( A3 = bot_bo1262634813um_a_b ) ) ).
% 0.26/0.62
% 0.26/0.62 % all_not_in_conv
% 0.26/0.62 thf(fact_218_all__not__in__conv,axiom,
% 0.26/0.62 ! [A3: set_Sum_sum_a_b] :
% 0.26/0.62 ( ( ! [X3: sum_sum_a_b] :
% 0.26/0.62 ~ ( member_Sum_sum_a_b @ X3 @ A3 ) )
% 0.26/0.62 = ( A3 = bot_bo1491243248um_a_b ) ) ).
% 0.26/0.62
% 0.26/0.62 % all_not_in_conv
% 0.26/0.62 thf(fact_219_Collect__empty__eq,axiom,
% 0.26/0.62 ! [P: produc1032616263at_nat > $o] :
% 0.26/0.62 ( ( ( collec52779676at_nat @ P )
% 0.26/0.62 = bot_bo810816657at_nat )
% 0.26/0.62 = ( ! [X3: produc1032616263at_nat] :
% 0.26/0.62 ~ ( P @ X3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Collect_empty_eq
% 0.26/0.62 thf(fact_220_Collect__empty__eq,axiom,
% 0.26/0.62 ! [P: nat > $o] :
% 0.26/0.62 ( ( ( collect_nat @ P )
% 0.26/0.62 = bot_bot_set_nat )
% 0.26/0.62 = ( ! [X3: nat] :
% 0.26/0.62 ~ ( P @ X3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Collect_empty_eq
% 0.26/0.62 thf(fact_221_Collect__empty__eq,axiom,
% 0.26/0.62 ! [P: produc1124793815um_a_b > $o] :
% 0.26/0.62 ( ( ( collec492052930um_a_b @ P )
% 0.26/0.62 = bot_bo575978147um_a_b )
% 0.26/0.62 = ( ! [X3: produc1124793815um_a_b] :
% 0.26/0.62 ~ ( P @ X3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Collect_empty_eq
% 0.26/0.62 thf(fact_222_Collect__empty__eq,axiom,
% 0.26/0.62 ! [P: produc1548871597um_a_b > $o] :
% 0.26/0.62 ( ( ( collec1769032088um_a_b @ P )
% 0.26/0.62 = bot_bo225809273um_a_b )
% 0.26/0.62 = ( ! [X3: produc1548871597um_a_b] :
% 0.26/0.62 ~ ( P @ X3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Collect_empty_eq
% 0.26/0.62 thf(fact_223_Collect__empty__eq,axiom,
% 0.26/0.62 ! [P: produc1963079155um_a_b > $o] :
% 0.26/0.62 ( ( ( collec1254333256um_a_b @ P )
% 0.26/0.62 = bot_bo1262634813um_a_b )
% 0.26/0.62 = ( ! [X3: produc1963079155um_a_b] :
% 0.26/0.62 ~ ( P @ X3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Collect_empty_eq
% 0.26/0.62 thf(fact_224_Collect__empty__eq,axiom,
% 0.26/0.62 ! [P: sum_sum_a_b > $o] :
% 0.26/0.62 ( ( ( collect_Sum_sum_a_b @ P )
% 0.26/0.62 = bot_bo1491243248um_a_b )
% 0.26/0.62 = ( ! [X3: sum_sum_a_b] :
% 0.26/0.62 ~ ( P @ X3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Collect_empty_eq
% 0.26/0.62 thf(fact_225_empty__Collect__eq,axiom,
% 0.26/0.62 ! [P: produc1032616263at_nat > $o] :
% 0.26/0.62 ( ( bot_bo810816657at_nat
% 0.26/0.62 = ( collec52779676at_nat @ P ) )
% 0.26/0.62 = ( ! [X3: produc1032616263at_nat] :
% 0.26/0.62 ~ ( P @ X3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % empty_Collect_eq
% 0.26/0.62 thf(fact_226_empty__Collect__eq,axiom,
% 0.26/0.62 ! [P: nat > $o] :
% 0.26/0.62 ( ( bot_bot_set_nat
% 0.26/0.62 = ( collect_nat @ P ) )
% 0.26/0.62 = ( ! [X3: nat] :
% 0.26/0.62 ~ ( P @ X3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % empty_Collect_eq
% 0.26/0.62 thf(fact_227_empty__Collect__eq,axiom,
% 0.26/0.62 ! [P: produc1124793815um_a_b > $o] :
% 0.26/0.62 ( ( bot_bo575978147um_a_b
% 0.26/0.62 = ( collec492052930um_a_b @ P ) )
% 0.26/0.62 = ( ! [X3: produc1124793815um_a_b] :
% 0.26/0.62 ~ ( P @ X3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % empty_Collect_eq
% 0.26/0.62 thf(fact_228_empty__Collect__eq,axiom,
% 0.26/0.62 ! [P: produc1548871597um_a_b > $o] :
% 0.26/0.62 ( ( bot_bo225809273um_a_b
% 0.26/0.62 = ( collec1769032088um_a_b @ P ) )
% 0.26/0.62 = ( ! [X3: produc1548871597um_a_b] :
% 0.26/0.62 ~ ( P @ X3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % empty_Collect_eq
% 0.26/0.62 thf(fact_229_empty__Collect__eq,axiom,
% 0.26/0.62 ! [P: produc1963079155um_a_b > $o] :
% 0.26/0.62 ( ( bot_bo1262634813um_a_b
% 0.26/0.62 = ( collec1254333256um_a_b @ P ) )
% 0.26/0.62 = ( ! [X3: produc1963079155um_a_b] :
% 0.26/0.62 ~ ( P @ X3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % empty_Collect_eq
% 0.26/0.62 thf(fact_230_empty__Collect__eq,axiom,
% 0.26/0.62 ! [P: sum_sum_a_b > $o] :
% 0.26/0.62 ( ( bot_bo1491243248um_a_b
% 0.26/0.62 = ( collect_Sum_sum_a_b @ P ) )
% 0.26/0.62 = ( ! [X3: sum_sum_a_b] :
% 0.26/0.62 ~ ( P @ X3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % empty_Collect_eq
% 0.26/0.62 thf(fact_231_subsetI,axiom,
% 0.26/0.62 ! [A3: set_Pr1174980151um_a_b,B5: set_Pr1174980151um_a_b] :
% 0.26/0.62 ( ! [X4: produc1124793815um_a_b] :
% 0.26/0.62 ( ( member1294585472um_a_b @ X4 @ A3 )
% 0.26/0.62 => ( member1294585472um_a_b @ X4 @ B5 ) )
% 0.26/0.62 => ( ord_le823954903um_a_b @ A3 @ B5 ) ) ).
% 0.26/0.62
% 0.26/0.62 % subsetI
% 0.26/0.62 thf(fact_232_subsetI,axiom,
% 0.26/0.62 ! [A3: set_Pr409224873um_a_b,B5: set_Pr409224873um_a_b] :
% 0.26/0.62 ( ! [X4: produc1963079155um_a_b] :
% 0.26/0.62 ( ( member1998628618um_a_b @ X4 @ A3 )
% 0.26/0.62 => ( member1998628618um_a_b @ X4 @ B5 ) )
% 0.26/0.62 => ( ord_le615126793um_a_b @ A3 @ B5 ) ) ).
% 0.26/0.62
% 0.26/0.62 % subsetI
% 0.26/0.62 thf(fact_233_subsetI,axiom,
% 0.26/0.62 ! [A3: set_Sum_sum_a_b,B5: set_Sum_sum_a_b] :
% 0.26/0.62 ( ! [X4: sum_sum_a_b] :
% 0.26/0.62 ( ( member_Sum_sum_a_b @ X4 @ A3 )
% 0.26/0.62 => ( member_Sum_sum_a_b @ X4 @ B5 ) )
% 0.26/0.62 => ( ord_le192794300um_a_b @ A3 @ B5 ) ) ).
% 0.26/0.62
% 0.26/0.62 % subsetI
% 0.26/0.62 thf(fact_234_subset__antisym,axiom,
% 0.26/0.62 ! [A3: set_Sum_sum_a_b,B5: set_Sum_sum_a_b] :
% 0.26/0.62 ( ( ord_le192794300um_a_b @ A3 @ B5 )
% 0.26/0.62 => ( ( ord_le192794300um_a_b @ B5 @ A3 )
% 0.26/0.62 => ( A3 = B5 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_antisym
% 0.26/0.62 thf(fact_235_insertCI,axiom,
% 0.26/0.62 ! [A: produc1032616263at_nat,B5: set_Pr1647387645at_nat,B: produc1032616263at_nat] :
% 0.26/0.62 ( ( ~ ( member1696759390at_nat @ A @ B5 )
% 0.26/0.62 => ( A = B ) )
% 0.26/0.62 => ( member1696759390at_nat @ A @ ( insert1625259895at_nat @ B @ B5 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insertCI
% 0.26/0.62 thf(fact_236_insertCI,axiom,
% 0.26/0.62 ! [A: nat,B5: set_nat,B: nat] :
% 0.26/0.62 ( ( ~ ( member_nat @ A @ B5 )
% 0.26/0.62 => ( A = B ) )
% 0.26/0.62 => ( member_nat @ A @ ( insert_nat @ B @ B5 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insertCI
% 0.26/0.62 thf(fact_237_insertCI,axiom,
% 0.26/0.62 ! [A: produc1548871597um_a_b,B5: set_Pr1916610317um_a_b,B: produc1548871597um_a_b] :
% 0.26/0.62 ( ( ~ ( member947389014um_a_b @ A @ B5 )
% 0.26/0.62 => ( A = B ) )
% 0.26/0.62 => ( member947389014um_a_b @ A @ ( insert1435405693um_a_b @ B @ B5 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insertCI
% 0.26/0.62 thf(fact_238_insertCI,axiom,
% 0.26/0.62 ! [A: standard_Constant_a,B5: set_St761939237tant_a,B: standard_Constant_a] :
% 0.26/0.62 ( ( ~ ( member1632892294tant_a @ A @ B5 )
% 0.26/0.62 => ( A = B ) )
% 0.26/0.62 => ( member1632892294tant_a @ A @ ( insert1909710879tant_a @ B @ B5 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insertCI
% 0.26/0.62 thf(fact_239_insertCI,axiom,
% 0.26/0.62 ! [A: product_prod_nat_nat,B5: set_Pr1986765409at_nat,B: product_prod_nat_nat] :
% 0.26/0.62 ( ( ~ ( member701585322at_nat @ A @ B5 )
% 0.26/0.62 => ( A = B ) )
% 0.26/0.62 => ( member701585322at_nat @ A @ ( insert271595217at_nat @ B @ B5 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insertCI
% 0.26/0.62 thf(fact_240_insertCI,axiom,
% 0.26/0.62 ! [A: sum_sum_a_b,B5: set_Sum_sum_a_b,B: sum_sum_a_b] :
% 0.26/0.62 ( ( ~ ( member_Sum_sum_a_b @ A @ B5 )
% 0.26/0.62 => ( A = B ) )
% 0.26/0.62 => ( member_Sum_sum_a_b @ A @ ( insert_Sum_sum_a_b @ B @ B5 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insertCI
% 0.26/0.62 thf(fact_241_insertCI,axiom,
% 0.26/0.62 ! [A: produc1124793815um_a_b,B5: set_Pr1174980151um_a_b,B: produc1124793815um_a_b] :
% 0.26/0.62 ( ( ~ ( member1294585472um_a_b @ A @ B5 )
% 0.26/0.62 => ( A = B ) )
% 0.26/0.62 => ( member1294585472um_a_b @ A @ ( insert983991207um_a_b @ B @ B5 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insertCI
% 0.26/0.62 thf(fact_242_insertCI,axiom,
% 0.26/0.62 ! [A: produc1963079155um_a_b,B5: set_Pr409224873um_a_b,B: produc1963079155um_a_b] :
% 0.26/0.62 ( ( ~ ( member1998628618um_a_b @ A @ B5 )
% 0.26/0.62 => ( A = B ) )
% 0.26/0.62 => ( member1998628618um_a_b @ A @ ( insert323157027um_a_b @ B @ B5 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insertCI
% 0.26/0.62 thf(fact_243_insert__iff,axiom,
% 0.26/0.62 ! [A: produc1032616263at_nat,B: produc1032616263at_nat,A3: set_Pr1647387645at_nat] :
% 0.26/0.62 ( ( member1696759390at_nat @ A @ ( insert1625259895at_nat @ B @ A3 ) )
% 0.26/0.62 = ( ( A = B )
% 0.26/0.62 | ( member1696759390at_nat @ A @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insert_iff
% 0.26/0.62 thf(fact_244_insert__iff,axiom,
% 0.26/0.62 ! [A: nat,B: nat,A3: set_nat] :
% 0.26/0.62 ( ( member_nat @ A @ ( insert_nat @ B @ A3 ) )
% 0.26/0.62 = ( ( A = B )
% 0.26/0.62 | ( member_nat @ A @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insert_iff
% 0.26/0.62 thf(fact_245_insert__iff,axiom,
% 0.26/0.62 ! [A: produc1548871597um_a_b,B: produc1548871597um_a_b,A3: set_Pr1916610317um_a_b] :
% 0.26/0.62 ( ( member947389014um_a_b @ A @ ( insert1435405693um_a_b @ B @ A3 ) )
% 0.26/0.62 = ( ( A = B )
% 0.26/0.62 | ( member947389014um_a_b @ A @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insert_iff
% 0.26/0.62 thf(fact_246_insert__iff,axiom,
% 0.26/0.62 ! [A: standard_Constant_a,B: standard_Constant_a,A3: set_St761939237tant_a] :
% 0.26/0.62 ( ( member1632892294tant_a @ A @ ( insert1909710879tant_a @ B @ A3 ) )
% 0.26/0.62 = ( ( A = B )
% 0.26/0.62 | ( member1632892294tant_a @ A @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insert_iff
% 0.26/0.62 thf(fact_247_insert__iff,axiom,
% 0.26/0.62 ! [A: product_prod_nat_nat,B: product_prod_nat_nat,A3: set_Pr1986765409at_nat] :
% 0.26/0.62 ( ( member701585322at_nat @ A @ ( insert271595217at_nat @ B @ A3 ) )
% 0.26/0.62 = ( ( A = B )
% 0.26/0.62 | ( member701585322at_nat @ A @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insert_iff
% 0.26/0.62 thf(fact_248_insert__iff,axiom,
% 0.26/0.62 ! [A: sum_sum_a_b,B: sum_sum_a_b,A3: set_Sum_sum_a_b] :
% 0.26/0.62 ( ( member_Sum_sum_a_b @ A @ ( insert_Sum_sum_a_b @ B @ A3 ) )
% 0.26/0.62 = ( ( A = B )
% 0.26/0.62 | ( member_Sum_sum_a_b @ A @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insert_iff
% 0.26/0.62 thf(fact_249_insert__iff,axiom,
% 0.26/0.62 ! [A: produc1124793815um_a_b,B: produc1124793815um_a_b,A3: set_Pr1174980151um_a_b] :
% 0.26/0.62 ( ( member1294585472um_a_b @ A @ ( insert983991207um_a_b @ B @ A3 ) )
% 0.26/0.62 = ( ( A = B )
% 0.26/0.62 | ( member1294585472um_a_b @ A @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insert_iff
% 0.26/0.62 thf(fact_250_insert__iff,axiom,
% 0.26/0.62 ! [A: produc1963079155um_a_b,B: produc1963079155um_a_b,A3: set_Pr409224873um_a_b] :
% 0.26/0.62 ( ( member1998628618um_a_b @ A @ ( insert323157027um_a_b @ B @ A3 ) )
% 0.26/0.62 = ( ( A = B )
% 0.26/0.62 | ( member1998628618um_a_b @ A @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insert_iff
% 0.26/0.62 thf(fact_251_insert__absorb2,axiom,
% 0.26/0.62 ! [X2: produc1032616263at_nat,A3: set_Pr1647387645at_nat] :
% 0.26/0.62 ( ( insert1625259895at_nat @ X2 @ ( insert1625259895at_nat @ X2 @ A3 ) )
% 0.26/0.62 = ( insert1625259895at_nat @ X2 @ A3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % insert_absorb2
% 0.26/0.62 thf(fact_252_insert__absorb2,axiom,
% 0.26/0.62 ! [X2: nat,A3: set_nat] :
% 0.26/0.62 ( ( insert_nat @ X2 @ ( insert_nat @ X2 @ A3 ) )
% 0.26/0.62 = ( insert_nat @ X2 @ A3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % insert_absorb2
% 0.26/0.62 thf(fact_253_insert__absorb2,axiom,
% 0.26/0.62 ! [X2: produc1124793815um_a_b,A3: set_Pr1174980151um_a_b] :
% 0.26/0.62 ( ( insert983991207um_a_b @ X2 @ ( insert983991207um_a_b @ X2 @ A3 ) )
% 0.26/0.62 = ( insert983991207um_a_b @ X2 @ A3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % insert_absorb2
% 0.26/0.62 thf(fact_254_insert__absorb2,axiom,
% 0.26/0.62 ! [X2: produc1963079155um_a_b,A3: set_Pr409224873um_a_b] :
% 0.26/0.62 ( ( insert323157027um_a_b @ X2 @ ( insert323157027um_a_b @ X2 @ A3 ) )
% 0.26/0.62 = ( insert323157027um_a_b @ X2 @ A3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % insert_absorb2
% 0.26/0.62 thf(fact_255_insert__absorb2,axiom,
% 0.26/0.62 ! [X2: sum_sum_a_b,A3: set_Sum_sum_a_b] :
% 0.26/0.62 ( ( insert_Sum_sum_a_b @ X2 @ ( insert_Sum_sum_a_b @ X2 @ A3 ) )
% 0.26/0.62 = ( insert_Sum_sum_a_b @ X2 @ A3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % insert_absorb2
% 0.26/0.62 thf(fact_256_insert__absorb2,axiom,
% 0.26/0.62 ! [X2: produc1548871597um_a_b,A3: set_Pr1916610317um_a_b] :
% 0.26/0.62 ( ( insert1435405693um_a_b @ X2 @ ( insert1435405693um_a_b @ X2 @ A3 ) )
% 0.26/0.62 = ( insert1435405693um_a_b @ X2 @ A3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % insert_absorb2
% 0.26/0.62 thf(fact_257_insert__absorb2,axiom,
% 0.26/0.62 ! [X2: standard_Constant_a,A3: set_St761939237tant_a] :
% 0.26/0.62 ( ( insert1909710879tant_a @ X2 @ ( insert1909710879tant_a @ X2 @ A3 ) )
% 0.26/0.62 = ( insert1909710879tant_a @ X2 @ A3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % insert_absorb2
% 0.26/0.62 thf(fact_258_insert__absorb2,axiom,
% 0.26/0.62 ! [X2: product_prod_nat_nat,A3: set_Pr1986765409at_nat] :
% 0.26/0.62 ( ( insert271595217at_nat @ X2 @ ( insert271595217at_nat @ X2 @ A3 ) )
% 0.26/0.62 = ( insert271595217at_nat @ X2 @ A3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % insert_absorb2
% 0.26/0.62 thf(fact_259_graph__homomorphism__empty,axiom,
% 0.26/0.62 ! [G: labele935650037_a_nat,F: set_Pr1986765409at_nat] :
% 0.26/0.62 ( ( graph_2130075512at_nat @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ bot_bot_set_nat ) @ G @ F )
% 0.26/0.62 = ( ( F = bot_bo2130386637at_nat )
% 0.26/0.62 & ( G
% 0.26/0.62 = ( restri572569417_a_nat @ G ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % graph_homomorphism_empty
% 0.26/0.62 thf(fact_260_graph__homomorphism__empty,axiom,
% 0.26/0.62 ! [G: labele935650037_a_nat,F: set_Pr375490359_b_nat] :
% 0.26/0.62 ( ( graph_165730638_b_nat @ ( labele1729654377um_a_b @ bot_bo1262634813um_a_b @ bot_bo1491243248um_a_b ) @ G @ F )
% 0.26/0.62 = ( ( F = bot_bo1923972003_b_nat )
% 0.26/0.62 & ( G
% 0.26/0.62 = ( restri572569417_a_nat @ G ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % graph_homomorphism_empty
% 0.26/0.62 thf(fact_261_graph__homomorphism__empty,axiom,
% 0.26/0.62 ! [G: labele431970251um_a_b,F: set_Pr1174980151um_a_b] :
% 0.26/0.62 ( ( graph_1452133198um_a_b @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ bot_bot_set_nat ) @ G @ F )
% 0.26/0.62 = ( ( F = bot_bo575978147um_a_b )
% 0.26/0.62 & ( G
% 0.26/0.62 = ( restri1162247455um_a_b @ G ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % graph_homomorphism_empty
% 0.26/0.62 thf(fact_262_graph__homomorphism__empty,axiom,
% 0.26/0.62 ! [G: labele935650037_a_nat,F: set_Pr1902304780_b_nat] :
% 0.26/0.62 ( ( graph_1203757137_b_nat @ ( labele2034032468um_a_b @ bot_bo1208513655um_a_b @ bot_bo575978147um_a_b ) @ G @ F )
% 0.26/0.62 = ( ( F = bot_bo949957280_b_nat )
% 0.26/0.62 & ( G
% 0.26/0.62 = ( restri572569417_a_nat @ G ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % graph_homomorphism_empty
% 0.26/0.62 thf(fact_263_graph__homomorphism__empty,axiom,
% 0.26/0.62 ! [G: labele431970251um_a_b,F: set_Pr1916610317um_a_b] :
% 0.26/0.62 ( ( graph_611893540um_a_b @ ( labele1729654377um_a_b @ bot_bo1262634813um_a_b @ bot_bo1491243248um_a_b ) @ G @ F )
% 0.26/0.62 = ( ( F = bot_bo225809273um_a_b )
% 0.26/0.62 & ( G
% 0.26/0.62 = ( restri1162247455um_a_b @ G ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % graph_homomorphism_empty
% 0.26/0.62 thf(fact_264_graph__homomorphism__empty,axiom,
% 0.26/0.62 ! [G: labele935650037_a_nat,F: set_Pr689416536at_nat] :
% 0.26/0.62 ( ( graph_149544303at_nat @ ( labele1813985418at_nat @ bot_bo1524397311at_nat @ bot_bo810816657at_nat ) @ G @ F )
% 0.26/0.62 = ( ( F = bot_bo1582968772at_nat )
% 0.26/0.62 & ( G
% 0.26/0.62 = ( restri572569417_a_nat @ G ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % graph_homomorphism_empty
% 0.26/0.62 thf(fact_265_graph__homomorphism__empty,axiom,
% 0.26/0.62 ! [G: labele431970251um_a_b,F: set_Pr653770722um_a_b] :
% 0.26/0.62 ( ( graph_502887975um_a_b @ ( labele2034032468um_a_b @ bot_bo1208513655um_a_b @ bot_bo575978147um_a_b ) @ G @ F )
% 0.26/0.62 = ( ( F = bot_bo1892785270um_a_b )
% 0.26/0.62 & ( G
% 0.26/0.62 = ( restri1162247455um_a_b @ G ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % graph_homomorphism_empty
% 0.26/0.62 thf(fact_266_graph__homomorphism__empty,axiom,
% 0.26/0.62 ! [G: labele935650037_a_nat,F: set_Pr507214050_b_nat] :
% 0.26/0.62 ( ( graph_1815313447_b_nat @ ( labele989994um_a_b @ bot_bo1262778871um_a_b @ bot_bo225809273um_a_b ) @ G @ F )
% 0.26/0.62 = ( ( F = bot_bo1746228598_b_nat )
% 0.26/0.62 & ( G
% 0.26/0.62 = ( restri572569417_a_nat @ G ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % graph_homomorphism_empty
% 0.26/0.62 thf(fact_267_graph__homomorphism__empty,axiom,
% 0.26/0.62 ! [G: labele431970251um_a_b,F: set_Pr304595758um_a_b] :
% 0.26/0.62 ( ( graph_166346565um_a_b @ ( labele1813985418at_nat @ bot_bo1524397311at_nat @ bot_bo810816657at_nat ) @ G @ F )
% 0.26/0.62 = ( ( F = bot_bo627753370um_a_b )
% 0.26/0.62 & ( G
% 0.26/0.62 = ( restri1162247455um_a_b @ G ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % graph_homomorphism_empty
% 0.26/0.62 thf(fact_268_graph__homomorphism__empty,axiom,
% 0.26/0.62 ! [G: labele431970251um_a_b,F: set_Pr55236280um_a_b] :
% 0.26/0.62 ( ( graph_1763806717um_a_b @ ( labele989994um_a_b @ bot_bo1262778871um_a_b @ bot_bo225809273um_a_b ) @ G @ F )
% 0.26/0.62 = ( ( F = bot_bo1217542988um_a_b )
% 0.26/0.62 & ( G
% 0.26/0.62 = ( restri1162247455um_a_b @ G ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % graph_homomorphism_empty
% 0.26/0.62 thf(fact_269_edge__preserving__subset,axiom,
% 0.26/0.62 ! [R_1: set_Pr1174980151um_a_b,R_2: set_Pr1174980151um_a_b,E_1: set_Pr1647387645at_nat,E_2: set_Pr1647387645at_nat,G: set_Pr409224873um_a_b] :
% 0.26/0.62 ( ( ord_le823954903um_a_b @ R_1 @ R_2 )
% 0.26/0.62 => ( ( ord_le1909159005at_nat @ E_1 @ E_2 )
% 0.26/0.62 => ( ( edge_p1382426714tant_a @ R_2 @ E_2 @ G )
% 0.26/0.62 => ( edge_p1382426714tant_a @ R_1 @ E_1 @ G ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % edge_preserving_subset
% 0.26/0.62 thf(fact_270_subrelI,axiom,
% 0.26/0.62 ! [R: set_Pr1647387645at_nat,S: set_Pr1647387645at_nat] :
% 0.26/0.62 ( ! [X4: standard_Constant_a,Y4: product_prod_nat_nat] :
% 0.26/0.62 ( ( member1696759390at_nat @ ( produc407553657at_nat @ X4 @ Y4 ) @ R )
% 0.26/0.62 => ( member1696759390at_nat @ ( produc407553657at_nat @ X4 @ Y4 ) @ S ) )
% 0.26/0.62 => ( ord_le1909159005at_nat @ R @ S ) ) ).
% 0.26/0.62
% 0.26/0.62 % subrelI
% 0.26/0.62 thf(fact_271_subrelI,axiom,
% 0.26/0.62 ! [R: set_Pr1986765409at_nat,S: set_Pr1986765409at_nat] :
% 0.26/0.62 ( ! [X4: nat,Y4: nat] :
% 0.26/0.62 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ R )
% 0.26/0.62 => ( member701585322at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ S ) )
% 0.26/0.62 => ( ord_le841296385at_nat @ R @ S ) ) ).
% 0.26/0.62
% 0.26/0.62 % subrelI
% 0.26/0.62 thf(fact_272_subrelI,axiom,
% 0.26/0.62 ! [R: set_Pr1174980151um_a_b,S: set_Pr1174980151um_a_b] :
% 0.26/0.62 ( ! [X4: nat,Y4: sum_sum_a_b] :
% 0.26/0.62 ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ X4 @ Y4 ) @ R )
% 0.26/0.62 => ( member1294585472um_a_b @ ( produc1808556047um_a_b @ X4 @ Y4 ) @ S ) )
% 0.26/0.62 => ( ord_le823954903um_a_b @ R @ S ) ) ).
% 0.26/0.62
% 0.26/0.62 % subrelI
% 0.26/0.62 thf(fact_273_subrelI,axiom,
% 0.26/0.62 ! [R: set_Pr409224873um_a_b,S: set_Pr409224873um_a_b] :
% 0.26/0.62 ( ! [X4: standard_Constant_a,Y4: produc1548871597um_a_b] :
% 0.26/0.62 ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ X4 @ Y4 ) @ R )
% 0.26/0.62 => ( member1998628618um_a_b @ ( produc1697725733um_a_b @ X4 @ Y4 ) @ S ) )
% 0.26/0.62 => ( ord_le615126793um_a_b @ R @ S ) ) ).
% 0.26/0.62
% 0.26/0.62 % subrelI
% 0.26/0.62 thf(fact_274_subrelI,axiom,
% 0.26/0.62 ! [R: set_Pr1916610317um_a_b,S: set_Pr1916610317um_a_b] :
% 0.26/0.62 ( ! [X4: sum_sum_a_b,Y4: sum_sum_a_b] :
% 0.26/0.62 ( ( member947389014um_a_b @ ( produc176426981um_a_b @ X4 @ Y4 ) @ R )
% 0.26/0.62 => ( member947389014um_a_b @ ( produc176426981um_a_b @ X4 @ Y4 ) @ S ) )
% 0.26/0.62 => ( ord_le1059794605um_a_b @ R @ S ) ) ).
% 0.26/0.62
% 0.26/0.62 % subrelI
% 0.26/0.62 thf(fact_275_restrict__subsD,axiom,
% 0.26/0.62 ! [G: labele935650037_a_nat] :
% 0.26/0.62 ( ( ord_le1909159005at_nat @ ( labele195203296_a_nat @ G ) @ ( labele195203296_a_nat @ ( restri572569417_a_nat @ G ) ) )
% 0.26/0.62 => ( G
% 0.26/0.62 = ( restri572569417_a_nat @ G ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % restrict_subsD
% 0.26/0.62 thf(fact_276_restrict__subsD,axiom,
% 0.26/0.62 ! [G: labele431970251um_a_b] :
% 0.26/0.62 ( ( ord_le615126793um_a_b @ ( labele1939049654um_a_b @ G ) @ ( labele1939049654um_a_b @ ( restri1162247455um_a_b @ G ) ) )
% 0.26/0.62 => ( G
% 0.26/0.62 = ( restri1162247455um_a_b @ G ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % restrict_subsD
% 0.26/0.62 thf(fact_277_zero__reorient,axiom,
% 0.26/0.62 ! [X2: nat] :
% 0.26/0.62 ( ( zero_zero_nat = X2 )
% 0.26/0.62 = ( X2 = zero_zero_nat ) ) ).
% 0.26/0.62
% 0.26/0.62 % zero_reorient
% 0.26/0.62 thf(fact_278_emptyE,axiom,
% 0.26/0.62 ! [A: produc1032616263at_nat] :
% 0.26/0.62 ~ ( member1696759390at_nat @ A @ bot_bo810816657at_nat ) ).
% 0.26/0.62
% 0.26/0.62 % emptyE
% 0.26/0.62 thf(fact_279_emptyE,axiom,
% 0.26/0.62 ! [A: nat] :
% 0.26/0.62 ~ ( member_nat @ A @ bot_bot_set_nat ) ).
% 0.26/0.62
% 0.26/0.62 % emptyE
% 0.26/0.62 thf(fact_280_emptyE,axiom,
% 0.26/0.62 ! [A: produc1124793815um_a_b] :
% 0.26/0.62 ~ ( member1294585472um_a_b @ A @ bot_bo575978147um_a_b ) ).
% 0.26/0.62
% 0.26/0.62 % emptyE
% 0.26/0.62 thf(fact_281_emptyE,axiom,
% 0.26/0.62 ! [A: produc1548871597um_a_b] :
% 0.26/0.62 ~ ( member947389014um_a_b @ A @ bot_bo225809273um_a_b ) ).
% 0.26/0.62
% 0.26/0.62 % emptyE
% 0.26/0.62 thf(fact_282_emptyE,axiom,
% 0.26/0.62 ! [A: produc1963079155um_a_b] :
% 0.26/0.62 ~ ( member1998628618um_a_b @ A @ bot_bo1262634813um_a_b ) ).
% 0.26/0.62
% 0.26/0.62 % emptyE
% 0.26/0.62 thf(fact_283_emptyE,axiom,
% 0.26/0.62 ! [A: sum_sum_a_b] :
% 0.26/0.62 ~ ( member_Sum_sum_a_b @ A @ bot_bo1491243248um_a_b ) ).
% 0.26/0.62
% 0.26/0.62 % emptyE
% 0.26/0.62 thf(fact_284_equals0D,axiom,
% 0.26/0.62 ! [A3: set_Pr1647387645at_nat,A: produc1032616263at_nat] :
% 0.26/0.62 ( ( A3 = bot_bo810816657at_nat )
% 0.26/0.62 => ~ ( member1696759390at_nat @ A @ A3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % equals0D
% 0.26/0.62 thf(fact_285_equals0D,axiom,
% 0.26/0.62 ! [A3: set_nat,A: nat] :
% 0.26/0.62 ( ( A3 = bot_bot_set_nat )
% 0.26/0.62 => ~ ( member_nat @ A @ A3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % equals0D
% 0.26/0.62 thf(fact_286_equals0D,axiom,
% 0.26/0.62 ! [A3: set_Pr1174980151um_a_b,A: produc1124793815um_a_b] :
% 0.26/0.62 ( ( A3 = bot_bo575978147um_a_b )
% 0.26/0.62 => ~ ( member1294585472um_a_b @ A @ A3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % equals0D
% 0.26/0.62 thf(fact_287_equals0D,axiom,
% 0.26/0.62 ! [A3: set_Pr1916610317um_a_b,A: produc1548871597um_a_b] :
% 0.26/0.62 ( ( A3 = bot_bo225809273um_a_b )
% 0.26/0.62 => ~ ( member947389014um_a_b @ A @ A3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % equals0D
% 0.26/0.62 thf(fact_288_equals0D,axiom,
% 0.26/0.62 ! [A3: set_Pr409224873um_a_b,A: produc1963079155um_a_b] :
% 0.26/0.62 ( ( A3 = bot_bo1262634813um_a_b )
% 0.26/0.62 => ~ ( member1998628618um_a_b @ A @ A3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % equals0D
% 0.26/0.62 thf(fact_289_equals0D,axiom,
% 0.26/0.62 ! [A3: set_Sum_sum_a_b,A: sum_sum_a_b] :
% 0.26/0.62 ( ( A3 = bot_bo1491243248um_a_b )
% 0.26/0.62 => ~ ( member_Sum_sum_a_b @ A @ A3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % equals0D
% 0.26/0.62 thf(fact_290_equals0I,axiom,
% 0.26/0.62 ! [A3: set_Pr1647387645at_nat] :
% 0.26/0.62 ( ! [Y4: produc1032616263at_nat] :
% 0.26/0.62 ~ ( member1696759390at_nat @ Y4 @ A3 )
% 0.26/0.62 => ( A3 = bot_bo810816657at_nat ) ) ).
% 0.26/0.62
% 0.26/0.62 % equals0I
% 0.26/0.62 thf(fact_291_equals0I,axiom,
% 0.26/0.62 ! [A3: set_nat] :
% 0.26/0.62 ( ! [Y4: nat] :
% 0.26/0.62 ~ ( member_nat @ Y4 @ A3 )
% 0.26/0.62 => ( A3 = bot_bot_set_nat ) ) ).
% 0.26/0.62
% 0.26/0.62 % equals0I
% 0.26/0.62 thf(fact_292_equals0I,axiom,
% 0.26/0.62 ! [A3: set_Pr1174980151um_a_b] :
% 0.26/0.62 ( ! [Y4: produc1124793815um_a_b] :
% 0.26/0.62 ~ ( member1294585472um_a_b @ Y4 @ A3 )
% 0.26/0.62 => ( A3 = bot_bo575978147um_a_b ) ) ).
% 0.26/0.62
% 0.26/0.62 % equals0I
% 0.26/0.62 thf(fact_293_equals0I,axiom,
% 0.26/0.62 ! [A3: set_Pr1916610317um_a_b] :
% 0.26/0.62 ( ! [Y4: produc1548871597um_a_b] :
% 0.26/0.62 ~ ( member947389014um_a_b @ Y4 @ A3 )
% 0.26/0.62 => ( A3 = bot_bo225809273um_a_b ) ) ).
% 0.26/0.62
% 0.26/0.62 % equals0I
% 0.26/0.62 thf(fact_294_equals0I,axiom,
% 0.26/0.62 ! [A3: set_Pr409224873um_a_b] :
% 0.26/0.62 ( ! [Y4: produc1963079155um_a_b] :
% 0.26/0.62 ~ ( member1998628618um_a_b @ Y4 @ A3 )
% 0.26/0.62 => ( A3 = bot_bo1262634813um_a_b ) ) ).
% 0.26/0.62
% 0.26/0.62 % equals0I
% 0.26/0.62 thf(fact_295_equals0I,axiom,
% 0.26/0.62 ! [A3: set_Sum_sum_a_b] :
% 0.26/0.62 ( ! [Y4: sum_sum_a_b] :
% 0.26/0.62 ~ ( member_Sum_sum_a_b @ Y4 @ A3 )
% 0.26/0.62 => ( A3 = bot_bo1491243248um_a_b ) ) ).
% 0.26/0.62
% 0.26/0.62 % equals0I
% 0.26/0.62 thf(fact_296_ex__in__conv,axiom,
% 0.26/0.62 ! [A3: set_Pr1647387645at_nat] :
% 0.26/0.62 ( ( ? [X3: produc1032616263at_nat] : ( member1696759390at_nat @ X3 @ A3 ) )
% 0.26/0.62 = ( A3 != bot_bo810816657at_nat ) ) ).
% 0.26/0.62
% 0.26/0.62 % ex_in_conv
% 0.26/0.62 thf(fact_297_ex__in__conv,axiom,
% 0.26/0.62 ! [A3: set_nat] :
% 0.26/0.62 ( ( ? [X3: nat] : ( member_nat @ X3 @ A3 ) )
% 0.26/0.62 = ( A3 != bot_bot_set_nat ) ) ).
% 0.26/0.62
% 0.26/0.62 % ex_in_conv
% 0.26/0.62 thf(fact_298_ex__in__conv,axiom,
% 0.26/0.62 ! [A3: set_Pr1174980151um_a_b] :
% 0.26/0.62 ( ( ? [X3: produc1124793815um_a_b] : ( member1294585472um_a_b @ X3 @ A3 ) )
% 0.26/0.62 = ( A3 != bot_bo575978147um_a_b ) ) ).
% 0.26/0.62
% 0.26/0.62 % ex_in_conv
% 0.26/0.62 thf(fact_299_ex__in__conv,axiom,
% 0.26/0.62 ! [A3: set_Pr1916610317um_a_b] :
% 0.26/0.62 ( ( ? [X3: produc1548871597um_a_b] : ( member947389014um_a_b @ X3 @ A3 ) )
% 0.26/0.62 = ( A3 != bot_bo225809273um_a_b ) ) ).
% 0.26/0.62
% 0.26/0.62 % ex_in_conv
% 0.26/0.62 thf(fact_300_ex__in__conv,axiom,
% 0.26/0.62 ! [A3: set_Pr409224873um_a_b] :
% 0.26/0.62 ( ( ? [X3: produc1963079155um_a_b] : ( member1998628618um_a_b @ X3 @ A3 ) )
% 0.26/0.62 = ( A3 != bot_bo1262634813um_a_b ) ) ).
% 0.26/0.62
% 0.26/0.62 % ex_in_conv
% 0.26/0.62 thf(fact_301_ex__in__conv,axiom,
% 0.26/0.62 ! [A3: set_Sum_sum_a_b] :
% 0.26/0.62 ( ( ? [X3: sum_sum_a_b] : ( member_Sum_sum_a_b @ X3 @ A3 ) )
% 0.26/0.62 = ( A3 != bot_bo1491243248um_a_b ) ) ).
% 0.26/0.62
% 0.26/0.62 % ex_in_conv
% 0.26/0.62 thf(fact_302_in__mono,axiom,
% 0.26/0.62 ! [A3: set_Pr1174980151um_a_b,B5: set_Pr1174980151um_a_b,X2: produc1124793815um_a_b] :
% 0.26/0.62 ( ( ord_le823954903um_a_b @ A3 @ B5 )
% 0.26/0.62 => ( ( member1294585472um_a_b @ X2 @ A3 )
% 0.26/0.62 => ( member1294585472um_a_b @ X2 @ B5 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % in_mono
% 0.26/0.62 thf(fact_303_in__mono,axiom,
% 0.26/0.62 ! [A3: set_Pr409224873um_a_b,B5: set_Pr409224873um_a_b,X2: produc1963079155um_a_b] :
% 0.26/0.62 ( ( ord_le615126793um_a_b @ A3 @ B5 )
% 0.26/0.62 => ( ( member1998628618um_a_b @ X2 @ A3 )
% 0.26/0.62 => ( member1998628618um_a_b @ X2 @ B5 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % in_mono
% 0.26/0.62 thf(fact_304_in__mono,axiom,
% 0.26/0.62 ! [A3: set_Sum_sum_a_b,B5: set_Sum_sum_a_b,X2: sum_sum_a_b] :
% 0.26/0.62 ( ( ord_le192794300um_a_b @ A3 @ B5 )
% 0.26/0.62 => ( ( member_Sum_sum_a_b @ X2 @ A3 )
% 0.26/0.62 => ( member_Sum_sum_a_b @ X2 @ B5 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % in_mono
% 0.26/0.62 thf(fact_305_subsetD,axiom,
% 0.26/0.62 ! [A3: set_Pr1174980151um_a_b,B5: set_Pr1174980151um_a_b,C: produc1124793815um_a_b] :
% 0.26/0.62 ( ( ord_le823954903um_a_b @ A3 @ B5 )
% 0.26/0.62 => ( ( member1294585472um_a_b @ C @ A3 )
% 0.26/0.62 => ( member1294585472um_a_b @ C @ B5 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subsetD
% 0.26/0.62 thf(fact_306_subsetD,axiom,
% 0.26/0.62 ! [A3: set_Pr409224873um_a_b,B5: set_Pr409224873um_a_b,C: produc1963079155um_a_b] :
% 0.26/0.62 ( ( ord_le615126793um_a_b @ A3 @ B5 )
% 0.26/0.62 => ( ( member1998628618um_a_b @ C @ A3 )
% 0.26/0.62 => ( member1998628618um_a_b @ C @ B5 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subsetD
% 0.26/0.62 thf(fact_307_subsetD,axiom,
% 0.26/0.62 ! [A3: set_Sum_sum_a_b,B5: set_Sum_sum_a_b,C: sum_sum_a_b] :
% 0.26/0.62 ( ( ord_le192794300um_a_b @ A3 @ B5 )
% 0.26/0.62 => ( ( member_Sum_sum_a_b @ C @ A3 )
% 0.26/0.62 => ( member_Sum_sum_a_b @ C @ B5 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subsetD
% 0.26/0.62 thf(fact_308_equalityE,axiom,
% 0.26/0.62 ! [A3: set_Sum_sum_a_b,B5: set_Sum_sum_a_b] :
% 0.26/0.62 ( ( A3 = B5 )
% 0.26/0.62 => ~ ( ( ord_le192794300um_a_b @ A3 @ B5 )
% 0.26/0.62 => ~ ( ord_le192794300um_a_b @ B5 @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % equalityE
% 0.26/0.62 thf(fact_309_subset__eq,axiom,
% 0.26/0.62 ( ord_le823954903um_a_b
% 0.26/0.62 = ( ^ [A7: set_Pr1174980151um_a_b,B6: set_Pr1174980151um_a_b] :
% 0.26/0.62 ! [X3: produc1124793815um_a_b] :
% 0.26/0.62 ( ( member1294585472um_a_b @ X3 @ A7 )
% 0.26/0.62 => ( member1294585472um_a_b @ X3 @ B6 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_eq
% 0.26/0.62 thf(fact_310_subset__eq,axiom,
% 0.26/0.62 ( ord_le615126793um_a_b
% 0.26/0.62 = ( ^ [A7: set_Pr409224873um_a_b,B6: set_Pr409224873um_a_b] :
% 0.26/0.62 ! [X3: produc1963079155um_a_b] :
% 0.26/0.62 ( ( member1998628618um_a_b @ X3 @ A7 )
% 0.26/0.62 => ( member1998628618um_a_b @ X3 @ B6 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_eq
% 0.26/0.62 thf(fact_311_subset__eq,axiom,
% 0.26/0.62 ( ord_le192794300um_a_b
% 0.26/0.62 = ( ^ [A7: set_Sum_sum_a_b,B6: set_Sum_sum_a_b] :
% 0.26/0.62 ! [X3: sum_sum_a_b] :
% 0.26/0.62 ( ( member_Sum_sum_a_b @ X3 @ A7 )
% 0.26/0.62 => ( member_Sum_sum_a_b @ X3 @ B6 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_eq
% 0.26/0.62 thf(fact_312_equalityD1,axiom,
% 0.26/0.62 ! [A3: set_Sum_sum_a_b,B5: set_Sum_sum_a_b] :
% 0.26/0.62 ( ( A3 = B5 )
% 0.26/0.62 => ( ord_le192794300um_a_b @ A3 @ B5 ) ) ).
% 0.26/0.62
% 0.26/0.62 % equalityD1
% 0.26/0.62 thf(fact_313_equalityD2,axiom,
% 0.26/0.62 ! [A3: set_Sum_sum_a_b,B5: set_Sum_sum_a_b] :
% 0.26/0.62 ( ( A3 = B5 )
% 0.26/0.62 => ( ord_le192794300um_a_b @ B5 @ A3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % equalityD2
% 0.26/0.62 thf(fact_314_subset__iff,axiom,
% 0.26/0.62 ( ord_le823954903um_a_b
% 0.26/0.62 = ( ^ [A7: set_Pr1174980151um_a_b,B6: set_Pr1174980151um_a_b] :
% 0.26/0.62 ! [T: produc1124793815um_a_b] :
% 0.26/0.62 ( ( member1294585472um_a_b @ T @ A7 )
% 0.26/0.62 => ( member1294585472um_a_b @ T @ B6 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_iff
% 0.26/0.62 thf(fact_315_subset__iff,axiom,
% 0.26/0.62 ( ord_le615126793um_a_b
% 0.26/0.62 = ( ^ [A7: set_Pr409224873um_a_b,B6: set_Pr409224873um_a_b] :
% 0.26/0.62 ! [T: produc1963079155um_a_b] :
% 0.26/0.62 ( ( member1998628618um_a_b @ T @ A7 )
% 0.26/0.62 => ( member1998628618um_a_b @ T @ B6 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_iff
% 0.26/0.62 thf(fact_316_subset__iff,axiom,
% 0.26/0.62 ( ord_le192794300um_a_b
% 0.26/0.62 = ( ^ [A7: set_Sum_sum_a_b,B6: set_Sum_sum_a_b] :
% 0.26/0.62 ! [T: sum_sum_a_b] :
% 0.26/0.62 ( ( member_Sum_sum_a_b @ T @ A7 )
% 0.26/0.62 => ( member_Sum_sum_a_b @ T @ B6 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_iff
% 0.26/0.62 thf(fact_317_subset__refl,axiom,
% 0.26/0.62 ! [A3: set_Sum_sum_a_b] : ( ord_le192794300um_a_b @ A3 @ A3 ) ).
% 0.26/0.62
% 0.26/0.62 % subset_refl
% 0.26/0.62 thf(fact_318_Collect__mono,axiom,
% 0.26/0.62 ! [P: sum_sum_a_b > $o,Q: sum_sum_a_b > $o] :
% 0.26/0.62 ( ! [X4: sum_sum_a_b] :
% 0.26/0.62 ( ( P @ X4 )
% 0.26/0.62 => ( Q @ X4 ) )
% 0.26/0.62 => ( ord_le192794300um_a_b @ ( collect_Sum_sum_a_b @ P ) @ ( collect_Sum_sum_a_b @ Q ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Collect_mono
% 0.26/0.62 thf(fact_319_subset__trans,axiom,
% 0.26/0.62 ! [A3: set_Sum_sum_a_b,B5: set_Sum_sum_a_b,C2: set_Sum_sum_a_b] :
% 0.26/0.62 ( ( ord_le192794300um_a_b @ A3 @ B5 )
% 0.26/0.62 => ( ( ord_le192794300um_a_b @ B5 @ C2 )
% 0.26/0.62 => ( ord_le192794300um_a_b @ A3 @ C2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_trans
% 0.26/0.62 thf(fact_320_set__eq__subset,axiom,
% 0.26/0.62 ( ( ^ [Y5: set_Sum_sum_a_b,Z: set_Sum_sum_a_b] : ( Y5 = Z ) )
% 0.26/0.62 = ( ^ [A7: set_Sum_sum_a_b,B6: set_Sum_sum_a_b] :
% 0.26/0.62 ( ( ord_le192794300um_a_b @ A7 @ B6 )
% 0.26/0.62 & ( ord_le192794300um_a_b @ B6 @ A7 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % set_eq_subset
% 0.26/0.62 thf(fact_321_Collect__mono__iff,axiom,
% 0.26/0.62 ! [P: sum_sum_a_b > $o,Q: sum_sum_a_b > $o] :
% 0.26/0.62 ( ( ord_le192794300um_a_b @ ( collect_Sum_sum_a_b @ P ) @ ( collect_Sum_sum_a_b @ Q ) )
% 0.26/0.62 = ( ! [X3: sum_sum_a_b] :
% 0.26/0.62 ( ( P @ X3 )
% 0.26/0.62 => ( Q @ X3 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Collect_mono_iff
% 0.26/0.62 thf(fact_322_insertE,axiom,
% 0.26/0.62 ! [A: produc1032616263at_nat,B: produc1032616263at_nat,A3: set_Pr1647387645at_nat] :
% 0.26/0.62 ( ( member1696759390at_nat @ A @ ( insert1625259895at_nat @ B @ A3 ) )
% 0.26/0.62 => ( ( A != B )
% 0.26/0.62 => ( member1696759390at_nat @ A @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insertE
% 0.26/0.62 thf(fact_323_insertE,axiom,
% 0.26/0.62 ! [A: nat,B: nat,A3: set_nat] :
% 0.26/0.62 ( ( member_nat @ A @ ( insert_nat @ B @ A3 ) )
% 0.26/0.62 => ( ( A != B )
% 0.26/0.62 => ( member_nat @ A @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insertE
% 0.26/0.62 thf(fact_324_insertE,axiom,
% 0.26/0.62 ! [A: produc1548871597um_a_b,B: produc1548871597um_a_b,A3: set_Pr1916610317um_a_b] :
% 0.26/0.62 ( ( member947389014um_a_b @ A @ ( insert1435405693um_a_b @ B @ A3 ) )
% 0.26/0.62 => ( ( A != B )
% 0.26/0.62 => ( member947389014um_a_b @ A @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insertE
% 0.26/0.62 thf(fact_325_insertE,axiom,
% 0.26/0.62 ! [A: standard_Constant_a,B: standard_Constant_a,A3: set_St761939237tant_a] :
% 0.26/0.62 ( ( member1632892294tant_a @ A @ ( insert1909710879tant_a @ B @ A3 ) )
% 0.26/0.62 => ( ( A != B )
% 0.26/0.62 => ( member1632892294tant_a @ A @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insertE
% 0.26/0.62 thf(fact_326_insertE,axiom,
% 0.26/0.62 ! [A: product_prod_nat_nat,B: product_prod_nat_nat,A3: set_Pr1986765409at_nat] :
% 0.26/0.62 ( ( member701585322at_nat @ A @ ( insert271595217at_nat @ B @ A3 ) )
% 0.26/0.62 => ( ( A != B )
% 0.26/0.62 => ( member701585322at_nat @ A @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insertE
% 0.26/0.62 thf(fact_327_insertE,axiom,
% 0.26/0.62 ! [A: sum_sum_a_b,B: sum_sum_a_b,A3: set_Sum_sum_a_b] :
% 0.26/0.62 ( ( member_Sum_sum_a_b @ A @ ( insert_Sum_sum_a_b @ B @ A3 ) )
% 0.26/0.62 => ( ( A != B )
% 0.26/0.62 => ( member_Sum_sum_a_b @ A @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insertE
% 0.26/0.62 thf(fact_328_insertE,axiom,
% 0.26/0.62 ! [A: produc1124793815um_a_b,B: produc1124793815um_a_b,A3: set_Pr1174980151um_a_b] :
% 0.26/0.62 ( ( member1294585472um_a_b @ A @ ( insert983991207um_a_b @ B @ A3 ) )
% 0.26/0.62 => ( ( A != B )
% 0.26/0.62 => ( member1294585472um_a_b @ A @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insertE
% 0.26/0.62 thf(fact_329_insertE,axiom,
% 0.26/0.62 ! [A: produc1963079155um_a_b,B: produc1963079155um_a_b,A3: set_Pr409224873um_a_b] :
% 0.26/0.62 ( ( member1998628618um_a_b @ A @ ( insert323157027um_a_b @ B @ A3 ) )
% 0.26/0.62 => ( ( A != B )
% 0.26/0.62 => ( member1998628618um_a_b @ A @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % insertE
% 0.26/0.62 thf(fact_330_insertI1,axiom,
% 0.26/0.62 ! [A: product_prod_nat_nat,B5: set_Pr1986765409at_nat] : ( member701585322at_nat @ A @ ( insert271595217at_nat @ A @ B5 ) ) ).
% 0.26/0.62
% 0.26/0.62 % insertI1
% 0.26/0.62 thf(fact_331_insertI1,axiom,
% 0.26/0.62 ! [A: sum_sum_a_b,B5: set_Sum_sum_a_b] : ( member_Sum_sum_a_b @ A @ ( insert_Sum_sum_a_b @ A @ B5 ) ) ).
% 0.26/0.62
% 0.26/0.62 % insertI1
% 0.26/0.62 thf(fact_332_insertI1,axiom,
% 0.26/0.62 ! [A: produc1124793815um_a_b,B5: set_Pr1174980151um_a_b] : ( member1294585472um_a_b @ A @ ( insert983991207um_a_b @ A @ B5 ) ) ).
% 0.26/0.62
% 0.26/0.62 % insertI1
% 0.26/0.62 thf(fact_333_insertI1,axiom,
% 0.26/0.62 ! [A: produc1963079155um_a_b,B5: set_Pr409224873um_a_b] : ( member1998628618um_a_b @ A @ ( insert323157027um_a_b @ A @ B5 ) ) ).
% 0.26/0.62
% 0.26/0.62 % insertI1
% 0.26/0.62 thf(fact_334_le0,axiom,
% 0.26/0.62 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.26/0.62
% 0.26/0.62 % le0
% 0.26/0.62 thf(fact_335_bot__nat__0_Oextremum,axiom,
% 0.26/0.62 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 0.26/0.62
% 0.26/0.62 % bot_nat_0.extremum
% 0.26/0.62 thf(fact_336_Nat_Oex__has__greatest__nat,axiom,
% 0.26/0.62 ! [P: nat > $o,K: nat,B: nat] :
% 0.26/0.62 ( ( P @ K )
% 0.26/0.62 => ( ! [Y4: nat] :
% 0.26/0.62 ( ( P @ Y4 )
% 0.26/0.62 => ( ord_less_eq_nat @ Y4 @ B ) )
% 0.26/0.62 => ? [X4: nat] :
% 0.26/0.62 ( ( P @ X4 )
% 0.26/0.62 & ! [Y6: nat] :
% 0.26/0.62 ( ( P @ Y6 )
% 0.26/0.62 => ( ord_less_eq_nat @ Y6 @ X4 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Nat.ex_has_greatest_nat
% 0.26/0.62 thf(fact_337_nat__le__linear,axiom,
% 0.26/0.62 ! [M: nat,N: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.62 | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.26/0.62
% 0.26/0.62 % nat_le_linear
% 0.26/0.62 thf(fact_338_le__antisym,axiom,
% 0.26/0.62 ! [M: nat,N: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ M @ N )
% 0.26/0.62 => ( ( ord_less_eq_nat @ N @ M )
% 0.26/0.62 => ( M = N ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % le_antisym
% 0.26/0.62 thf(fact_339_eq__imp__le,axiom,
% 0.26/0.62 ! [M: nat,N: nat] :
% 0.26/0.62 ( ( M = N )
% 0.26/0.62 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.26/0.62
% 0.26/0.62 % eq_imp_le
% 0.26/0.62 thf(fact_340_le__trans,axiom,
% 0.26/0.62 ! [I: nat,J: nat,K: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ I @ J )
% 0.26/0.62 => ( ( ord_less_eq_nat @ J @ K )
% 0.26/0.62 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % le_trans
% 0.26/0.62 thf(fact_341_le__refl,axiom,
% 0.26/0.62 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.26/0.62
% 0.26/0.62 % le_refl
% 0.26/0.62 thf(fact_342_bot__nat__def,axiom,
% 0.26/0.62 bot_bot_nat = zero_zero_nat ).
% 0.26/0.62
% 0.26/0.62 % bot_nat_def
% 0.26/0.62 thf(fact_343_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.26/0.62 ! [A: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.26/0.62 => ( A = zero_zero_nat ) ) ).
% 0.26/0.62
% 0.26/0.62 % bot_nat_0.extremum_uniqueI
% 0.26/0.62 thf(fact_344_bot__nat__0_Oextremum__unique,axiom,
% 0.26/0.62 ! [A: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.26/0.62 = ( A = zero_zero_nat ) ) ).
% 0.26/0.62
% 0.26/0.62 % bot_nat_0.extremum_unique
% 0.26/0.62 thf(fact_345_le__0__eq,axiom,
% 0.26/0.62 ! [N: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.26/0.62 = ( N = zero_zero_nat ) ) ).
% 0.26/0.62
% 0.26/0.62 % le_0_eq
% 0.26/0.62 thf(fact_346_less__eq__nat_Osimps_I1_J,axiom,
% 0.26/0.62 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.26/0.62
% 0.26/0.62 % less_eq_nat.simps(1)
% 0.26/0.62 thf(fact_347_gr_I1_J,axiom,
% 0.26/0.62 ( ( getRel1465196352um_a_b @ standard_S_Idt_a @ g )
% 0.26/0.62 = ( id_on_Sum_sum_a_b @ ( labele577278695um_a_b @ g ) ) ) ).
% 0.26/0.62
% 0.26/0.70 % gr(1)
% 0.26/0.70 thf(fact_348_gr_I2_J,axiom,
% 0.26/0.70 ( ( getRel1465196352um_a_b @ standard_S_Bot_a @ g )
% 0.26/0.70 = bot_bo225809273um_a_b ) ).
% 0.26/0.70
% 0.26/0.70 % gr(2)
% 0.26/0.70 thf(fact_349__092_060open_062maintained_A_Isymmetry__rule_AS__Idt_J_AG_092_060close_062,axiom,
% 0.26/0.70 mainta522127984um_a_b @ ( standa997693288tant_a @ standard_S_Idt_a ) @ g ).
% 0.26/0.70
% 0.26/0.70 % \<open>maintained (symmetry_rule S_Idt) G\<close>
% 0.26/0.70 thf(fact_350__092_060open_062maintained_A_Itransitive__rule_AS__Idt_J_AG_092_060close_062,axiom,
% 0.26/0.70 mainta522127984um_a_b @ ( standa1795879409tant_a @ standard_S_Idt_a ) @ g ).
% 0.26/0.70
% 0.26/0.70 % \<open>maintained (transitive_rule S_Idt) G\<close>
% 0.26/0.70 thf(fact_351__092_060open_062maintained_A_Icongruence__rule_AS__Idt_Al_J_AG_092_060close_062,axiom,
% 0.26/0.70 mainta522127984um_a_b @ ( standa1343274079tant_a @ standard_S_Idt_a @ l ) @ g ).
% 0.26/0.70
% 0.26/0.70 % \<open>maintained (congruence_rule S_Idt l) G\<close>
% 0.26/0.70
% 0.26/0.70 % Conjectures (1)
% 0.26/0.70 thf(conj_0,conjecture,
% 0.26/0.70 ( ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 0.26/0.70 = ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) )
% 0.26/0.70 & ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
% 0.26/0.70 = ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) )
% 0.26/0.70 & ( g
% 0.26/0.70 = ( restri1162247455um_a_b @ g ) )
% 0.26/0.70 & ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) )
% 0.26/0.70 & ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
% 0.26/0.70 & ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) ) ) ).
% 0.26/0.70
% 0.26/0.70 %------------------------------------------------------------------------------
% 0.26/0.70 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.ba3FMSBoxx/cvc5---1.0.5_15148.p...
% 0.26/0.70 (declare-sort $$unsorted 0)
% 0.26/0.70 (declare-sort tptp.set_Pr1355257963at_nat 0)
% 0.26/0.70 (declare-sort tptp.set_Pr1429673827um_a_b 0)
% 0.26/0.70 (declare-sort tptp.set_Pr2065572323um_a_b 0)
% 0.26/0.70 (declare-sort tptp.set_Pr1558970842um_a_b 0)
% 0.26/0.70 (declare-sort tptp.set_Pr1121389018um_a_b 0)
% 0.26/0.70 (declare-sort tptp.produc1733247354um_a_b 0)
% 0.26/0.70 (declare-sort tptp.produc1681803642um_a_b 0)
% 0.26/0.70 (declare-sort tptp.produc1871334759_a_nat 0)
% 0.26/0.70 (declare-sort tptp.labele498606060at_nat 0)
% 0.26/0.70 (declare-sort tptp.set_Pr304595758um_a_b 0)
% 0.26/0.70 (declare-sort tptp.set_Pr409224873um_a_b 0)
% 0.26/0.70 (declare-sort tptp.set_Pr45173959um_a_b 0)
% 0.26/0.70 (declare-sort tptp.set_Pr689416536at_nat 0)
% 0.26/0.70 (declare-sort tptp.set_Pr1134469976at_nat 0)
% 0.26/0.70 (declare-sort tptp.labele1191284958um_a_b 0)
% 0.26/0.70 (declare-sort tptp.produc1963079155um_a_b 0)
% 0.26/0.70 (declare-sort tptp.produc1918750183um_a_b 0)
% 0.26/0.70 (declare-sort tptp.set_Pr55236280um_a_b 0)
% 0.26/0.70 (declare-sort tptp.set_Pr326391507um_a_b 0)
% 0.26/0.70 (declare-sort tptp.set_Pr386468381um_a_b 0)
% 0.26/0.70 (declare-sort tptp.labele261019144um_a_b 0)
% 0.26/0.70 (declare-sort tptp.produc1003469085um_a_b 0)
% 0.26/0.70 (declare-sort tptp.produc1546082365um_a_b 0)
% 0.26/0.70 (declare-sort tptp.set_Pr1783309276um_a_b 0)
% 0.26/0.70 (declare-sort tptp.set_Pr507214050_b_nat 0)
% 0.26/0.70 (declare-sort tptp.set_Pr653770722um_a_b 0)
% 0.26/0.70 (declare-sort tptp.set_Pr1155046920um_a_b 0)
% 0.26/0.70 (declare-sort tptp.set_Pr1647387645at_nat 0)
% 0.26/0.70 (declare-sort tptp.produc323101606um_a_b 0)
% 0.26/0.70 (declare-sort tptp.produc585753260um_a_b 0)
% 0.26/0.70 (declare-sort tptp.produc1032616263at_nat 0)
% 0.26/0.70 (declare-sort tptp.set_Pr1994339542um_a_b 0)
% 0.26/0.70 (declare-sort tptp.set_Pr1902304780_b_nat 0)
% 0.26/0.70 (declare-sort tptp.set_Pr195945996um_a_b 0)
% 0.26/0.70 (declare-sort tptp.set_Pr1618094130um_a_b 0)
% 0.26/0.70 (declare-sort tptp.labele431970251um_a_b 0)
% 0.26/0.70 (declare-sort tptp.produc1394389750um_a_b 0)
% 0.26/0.70 (declare-sort tptp.produc1798470614um_a_b 0)
% 0.26/0.70 (declare-sort tptp.produc204140796um_a_b 0)
% 0.26/0.70 (declare-sort tptp.set_Pr1916610317um_a_b 0)
% 0.26/0.70 (declare-sort tptp.labele935650037_a_nat 0)
% 0.26/0.70 (declare-sort tptp.produc1548871597um_a_b 0)
% 0.26/0.70 (declare-sort tptp.set_Pr375490359_b_nat 0)
% 0.26/0.70 (declare-sort tptp.set_Pr1174980151um_a_b 0)
% 0.26/0.70 (declare-sort tptp.produc1978941143_b_nat 0)
% 0.26/0.70 (declare-sort tptp.produc1124793815um_a_b 0)
% 0.26/0.70 (declare-sort tptp.set_St761939237tant_a 0)
% 0.26/0.70 (declare-sort tptp.set_Pr1986765409at_nat 0)
% 0.26/0.70 (declare-sort tptp.standard_Constant_a 0)
% 0.26/0.70 (declare-sort tptp.product_prod_nat_nat 0)
% 0.26/0.70 (declare-sort tptp.set_Sum_sum_a_b 0)
% 0.26/0.70 (declare-sort tptp.sum_sum_a_b 0)
% 0.26/0.70 (declare-sort tptp.set_nat 0)
% 0.26/0.70 (declare-sort tptp.nat 0)
% 0.26/0.70 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 0.26/0.70 (declare-fun tptp.standard_S_Bot_a () tptp.standard_Constant_a)
% 0.26/0.70 (declare-fun tptp.standard_S_Idt_a () tptp.standard_Constant_a)
% 0.26/0.70 (declare-fun tptp.getRel1465196352um_a_b (tptp.standard_Constant_a tptp.labele431970251um_a_b) tptp.set_Pr1916610317um_a_b)
% 0.26/0.70 (declare-fun tptp.edge_p170421892tant_a (tptp.set_Pr1986765409at_nat tptp.set_Pr1647387645at_nat tptp.set_Pr1647387645at_nat) Bool)
% 0.26/0.70 (declare-fun tptp.edge_p1382426714tant_a (tptp.set_Pr1174980151um_a_b tptp.set_Pr1647387645at_nat tptp.set_Pr409224873um_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.edge_p749155930tant_a (tptp.set_Pr375490359_b_nat tptp.set_Pr409224873um_a_b tptp.set_Pr1647387645at_nat) Bool)
% 0.26/0.70 (declare-fun tptp.edge_p1871801392tant_a (tptp.set_Pr1916610317um_a_b tptp.set_Pr409224873um_a_b tptp.set_Pr409224873um_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.graph_2130075512at_nat (tptp.labele935650037_a_nat tptp.labele935650037_a_nat tptp.set_Pr1986765409at_nat) Bool)
% 0.26/0.70 (declare-fun tptp.graph_1452133198um_a_b (tptp.labele935650037_a_nat tptp.labele431970251um_a_b tptp.set_Pr1174980151um_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.graph_149544303at_nat (tptp.labele498606060at_nat tptp.labele935650037_a_nat tptp.set_Pr689416536at_nat) Bool)
% 0.26/0.70 (declare-fun tptp.graph_166346565um_a_b (tptp.labele498606060at_nat tptp.labele431970251um_a_b tptp.set_Pr304595758um_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.graph_1203757137_b_nat (tptp.labele261019144um_a_b tptp.labele935650037_a_nat tptp.set_Pr1902304780_b_nat) Bool)
% 0.26/0.70 (declare-fun tptp.graph_502887975um_a_b (tptp.labele261019144um_a_b tptp.labele431970251um_a_b tptp.set_Pr653770722um_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.graph_1815313447_b_nat (tptp.labele1191284958um_a_b tptp.labele935650037_a_nat tptp.set_Pr507214050_b_nat) Bool)
% 0.26/0.70 (declare-fun tptp.graph_1763806717um_a_b (tptp.labele1191284958um_a_b tptp.labele431970251um_a_b tptp.set_Pr55236280um_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.graph_165730638_b_nat (tptp.labele431970251um_a_b tptp.labele935650037_a_nat tptp.set_Pr375490359_b_nat) Bool)
% 0.26/0.70 (declare-fun tptp.graph_611893540um_a_b (tptp.labele431970251um_a_b tptp.labele431970251um_a_b tptp.set_Pr1916610317um_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.labele16114835_a_nat (tptp.set_Pr1647387645at_nat tptp.set_nat) tptp.labele935650037_a_nat)
% 0.26/0.70 (declare-fun tptp.labele1813985418at_nat (tptp.set_Pr1355257963at_nat tptp.set_Pr1647387645at_nat) tptp.labele498606060at_nat)
% 0.26/0.70 (declare-fun tptp.labele2034032468um_a_b (tptp.set_Pr2065572323um_a_b tptp.set_Pr1174980151um_a_b) tptp.labele261019144um_a_b)
% 0.26/0.70 (declare-fun tptp.labele989994um_a_b (tptp.set_Pr1429673827um_a_b tptp.set_Pr1916610317um_a_b) tptp.labele1191284958um_a_b)
% 0.26/0.70 (declare-fun tptp.labele1729654377um_a_b (tptp.set_Pr409224873um_a_b tptp.set_Sum_sum_a_b) tptp.labele431970251um_a_b)
% 0.26/0.70 (declare-fun tptp.labele195203296_a_nat (tptp.labele935650037_a_nat) tptp.set_Pr1647387645at_nat)
% 0.26/0.70 (declare-fun tptp.labele1939049654um_a_b (tptp.labele431970251um_a_b) tptp.set_Pr409224873um_a_b)
% 0.26/0.70 (declare-fun tptp.labele1810595089_a_nat (tptp.labele935650037_a_nat) tptp.set_nat)
% 0.26/0.70 (declare-fun tptp.labele577278695um_a_b (tptp.labele431970251um_a_b) tptp.set_Sum_sum_a_b)
% 0.26/0.70 (declare-fun tptp.restri572569417_a_nat (tptp.labele935650037_a_nat) tptp.labele935650037_a_nat)
% 0.26/0.70 (declare-fun tptp.restri1162247455um_a_b (tptp.labele431970251um_a_b) tptp.labele431970251um_a_b)
% 0.26/0.70 (declare-fun tptp.unival860567212at_nat (tptp.set_Pr1647387645at_nat) Bool)
% 0.26/0.70 (declare-fun tptp.unival1487587672um_a_b (tptp.set_Pr409224873um_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.unival2092813468um_a_b (tptp.set_Pr1174980151um_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.unival118648434um_a_b (tptp.set_Pr1916610317um_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 0.26/0.70 (declare-fun tptp.bot_bo1160111033tant_a () tptp.set_St761939237tant_a)
% 0.26/0.70 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 0.26/0.70 (declare-fun tptp.bot_bo810816657at_nat () tptp.set_Pr1647387645at_nat)
% 0.26/0.70 (declare-fun tptp.bot_bo1524397311at_nat () tptp.set_Pr1355257963at_nat)
% 0.26/0.70 (declare-fun tptp.bot_bo1208513655um_a_b () tptp.set_Pr2065572323um_a_b)
% 0.26/0.70 (declare-fun tptp.bot_bo1262778871um_a_b () tptp.set_Pr1429673827um_a_b)
% 0.26/0.70 (declare-fun tptp.bot_bo1262634813um_a_b () tptp.set_Pr409224873um_a_b)
% 0.26/0.70 (declare-fun tptp.bot_bo2130386637at_nat () tptp.set_Pr1986765409at_nat)
% 0.26/0.70 (declare-fun tptp.bot_bo575978147um_a_b () tptp.set_Pr1174980151um_a_b)
% 0.26/0.70 (declare-fun tptp.bot_bo1582968772at_nat () tptp.set_Pr689416536at_nat)
% 0.26/0.70 (declare-fun tptp.bot_bo627753370um_a_b () tptp.set_Pr304595758um_a_b)
% 0.26/0.70 (declare-fun tptp.bot_bo949957280_b_nat () tptp.set_Pr1902304780_b_nat)
% 0.26/0.70 (declare-fun tptp.bot_bo1892785270um_a_b () tptp.set_Pr653770722um_a_b)
% 0.26/0.70 (declare-fun tptp.bot_bo1746228598_b_nat () tptp.set_Pr507214050_b_nat)
% 0.26/0.70 (declare-fun tptp.bot_bo1217542988um_a_b () tptp.set_Pr55236280um_a_b)
% 0.26/0.70 (declare-fun tptp.bot_bo1923972003_b_nat () tptp.set_Pr375490359_b_nat)
% 0.26/0.70 (declare-fun tptp.bot_bo225809273um_a_b () tptp.set_Pr1916610317um_a_b)
% 0.26/0.70 (declare-fun tptp.bot_bo1491243248um_a_b () tptp.set_Sum_sum_a_b)
% 0.26/0.70 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 0.26/0.70 (declare-fun tptp.ord_le1739761029tant_a (tptp.set_St761939237tant_a tptp.set_St761939237tant_a) Bool)
% 0.26/0.70 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 0.26/0.70 (declare-fun tptp.ord_le1909159005at_nat (tptp.set_Pr1647387645at_nat tptp.set_Pr1647387645at_nat) Bool)
% 0.26/0.70 (declare-fun tptp.ord_le615126793um_a_b (tptp.set_Pr409224873um_a_b tptp.set_Pr409224873um_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.ord_le841296385at_nat (tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat) Bool)
% 0.26/0.70 (declare-fun tptp.ord_le823954903um_a_b (tptp.set_Pr1174980151um_a_b tptp.set_Pr1174980151um_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.ord_le1059794605um_a_b (tptp.set_Pr1916610317um_a_b tptp.set_Pr1916610317um_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.ord_le192794300um_a_b (tptp.set_Sum_sum_a_b tptp.set_Sum_sum_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.produc407553657at_nat (tptp.standard_Constant_a tptp.product_prod_nat_nat) tptp.produc1032616263at_nat)
% 0.26/0.70 (declare-fun tptp.produc414524239um_a_b (tptp.standard_Constant_a tptp.produc1124793815um_a_b) tptp.produc1003469085um_a_b)
% 0.26/0.70 (declare-fun tptp.produc1697725733um_a_b (tptp.standard_Constant_a tptp.produc1548871597um_a_b) tptp.produc1963079155um_a_b)
% 0.26/0.70 (declare-fun tptp.produc584843310um_a_b (tptp.standard_Constant_a tptp.sum_sum_a_b) tptp.produc1394389750um_a_b)
% 0.26/0.70 (declare-fun tptp.produc1676969687_a_nat (tptp.labele935650037_a_nat tptp.labele935650037_a_nat) tptp.produc1871334759_a_nat)
% 0.26/0.70 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 0.26/0.70 (declare-fun tptp.produc1346373166um_a_b (tptp.nat tptp.produc1124793815um_a_b) tptp.produc204140796um_a_b)
% 0.26/0.70 (declare-fun tptp.produc1808556047um_a_b (tptp.nat tptp.sum_sum_a_b) tptp.produc1124793815um_a_b)
% 0.26/0.70 (declare-fun tptp.produc522766386um_a_b (tptp.produc1963079155um_a_b tptp.sum_sum_a_b) tptp.produc1681803642um_a_b)
% 0.26/0.70 (declare-fun tptp.produc335036333um_a_b (tptp.product_prod_nat_nat tptp.produc1124793815um_a_b) tptp.produc1546082365um_a_b)
% 0.26/0.70 (declare-fun tptp.produc1872245072um_a_b (tptp.product_prod_nat_nat tptp.sum_sum_a_b) tptp.produc1798470614um_a_b)
% 0.26/0.70 (declare-fun tptp.produc27163479um_a_b (tptp.produc1124793815um_a_b tptp.produc1124793815um_a_b) tptp.produc1918750183um_a_b)
% 0.26/0.70 (declare-fun tptp.produc831476262um_a_b (tptp.produc1124793815um_a_b tptp.sum_sum_a_b) tptp.produc585753260um_a_b)
% 0.26/0.70 (declare-fun tptp.produc522153487_b_nat (tptp.sum_sum_a_b tptp.nat) tptp.produc1978941143_b_nat)
% 0.26/0.70 (declare-fun tptp.produc230853810um_a_b (tptp.sum_sum_a_b tptp.produc1963079155um_a_b) tptp.produc1733247354um_a_b)
% 0.26/0.70 (declare-fun tptp.produc1637282520um_a_b (tptp.sum_sum_a_b tptp.produc1124793815um_a_b) tptp.produc323101606um_a_b)
% 0.26/0.70 (declare-fun tptp.produc176426981um_a_b (tptp.sum_sum_a_b tptp.sum_sum_a_b) tptp.produc1548871597um_a_b)
% 0.26/0.70 (declare-fun tptp.domain1060562500at_nat (tptp.set_Pr1647387645at_nat) tptp.set_St761939237tant_a)
% 0.26/0.70 (declare-fun tptp.domain1362581744um_a_b (tptp.set_Pr409224873um_a_b) tptp.set_St761939237tant_a)
% 0.26/0.70 (declare-fun tptp.domain_nat_nat (tptp.set_Pr1986765409at_nat) tptp.set_nat)
% 0.26/0.70 (declare-fun tptp.domain1368163076um_a_b (tptp.set_Pr1174980151um_a_b) tptp.set_nat)
% 0.26/0.70 (declare-fun tptp.domain2069673178um_a_b (tptp.set_Pr1916610317um_a_b) tptp.set_Sum_sum_a_b)
% 0.26/0.70 (declare-fun tptp.id_on_Sum_sum_a_b (tptp.set_Sum_sum_a_b) tptp.set_Pr1916610317um_a_b)
% 0.26/0.70 (declare-fun tptp.image_127502653at_nat (tptp.set_Pr1647387645at_nat tptp.set_St761939237tant_a) tptp.set_Pr1986765409at_nat)
% 0.26/0.70 (declare-fun tptp.image_1179143699um_a_b (tptp.set_Pr326391507um_a_b tptp.set_St761939237tant_a) tptp.set_Pr1174980151um_a_b)
% 0.26/0.70 (declare-fun tptp.image_2023280617um_a_b (tptp.set_Pr409224873um_a_b tptp.set_St761939237tant_a) tptp.set_Pr1916610317um_a_b)
% 0.26/0.70 (declare-fun tptp.image_2129435242um_a_b (tptp.set_Pr1994339542um_a_b tptp.set_St761939237tant_a) tptp.set_Sum_sum_a_b)
% 0.26/0.70 (declare-fun tptp.image_nat_nat (tptp.set_Pr1986765409at_nat tptp.set_nat) tptp.set_nat)
% 0.26/0.70 (declare-fun tptp.image_489788268at_nat (tptp.set_Pr1134469976at_nat tptp.set_nat) tptp.set_Pr1647387645at_nat)
% 0.26/0.70 (declare-fun tptp.image_1228479730um_a_b (tptp.set_Pr1618094130um_a_b tptp.set_nat) tptp.set_Pr1174980151um_a_b)
% 0.26/0.70 (declare-fun tptp.image_166667464um_a_b (tptp.set_Pr1155046920um_a_b tptp.set_nat) tptp.set_Pr1916610317um_a_b)
% 0.26/0.70 (declare-fun tptp.image_256773707um_a_b (tptp.set_Pr1174980151um_a_b tptp.set_nat) tptp.set_Sum_sum_a_b)
% 0.26/0.70 (declare-fun tptp.image_452296684at_nat (tptp.set_Pr689416536at_nat tptp.set_Pr1647387645at_nat) tptp.set_nat)
% 0.26/0.70 (declare-fun tptp.image_1774897262um_a_b (tptp.set_Pr1121389018um_a_b tptp.set_Pr409224873um_a_b) tptp.set_Sum_sum_a_b)
% 0.26/0.70 (declare-fun tptp.image_320480233um_a_b (tptp.set_Pr386468381um_a_b tptp.set_Pr1986765409at_nat) tptp.set_Pr1174980151um_a_b)
% 0.26/0.70 (declare-fun tptp.image_1754351636um_a_b (tptp.set_Pr195945996um_a_b tptp.set_Pr1986765409at_nat) tptp.set_Sum_sum_a_b)
% 0.26/0.70 (declare-fun tptp.image_128716052_b_nat (tptp.set_Pr1902304780_b_nat tptp.set_Pr1174980151um_a_b) tptp.set_nat)
% 0.26/0.70 (declare-fun tptp.image_1464989587um_a_b (tptp.set_Pr45173959um_a_b tptp.set_Pr1174980151um_a_b) tptp.set_Pr1174980151um_a_b)
% 0.26/0.70 (declare-fun tptp.image_869585130um_a_b (tptp.set_Pr653770722um_a_b tptp.set_Pr1174980151um_a_b) tptp.set_Sum_sum_a_b)
% 0.26/0.70 (declare-fun tptp.image_1117854795_b_nat (tptp.set_Pr375490359_b_nat tptp.set_Sum_sum_a_b) tptp.set_nat)
% 0.26/0.70 (declare-fun tptp.image_1482984686um_a_b (tptp.set_Pr1558970842um_a_b tptp.set_Sum_sum_a_b) tptp.set_Pr409224873um_a_b)
% 0.26/0.70 (declare-fun tptp.image_1675391388um_a_b (tptp.set_Pr1783309276um_a_b tptp.set_Sum_sum_a_b) tptp.set_Pr1174980151um_a_b)
% 0.26/0.70 (declare-fun tptp.image_1918588449um_a_b (tptp.set_Pr1916610317um_a_b tptp.set_Sum_sum_a_b) tptp.set_Sum_sum_a_b)
% 0.26/0.70 (declare-fun tptp.mainta522127984um_a_b (tptp.produc1871334759_a_nat tptp.labele431970251um_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 0.26/0.70 (declare-fun tptp.collec52779676at_nat ((-> tptp.produc1032616263at_nat Bool)) tptp.set_Pr1647387645at_nat)
% 0.26/0.70 (declare-fun tptp.collec1254333256um_a_b ((-> tptp.produc1963079155um_a_b Bool)) tptp.set_Pr409224873um_a_b)
% 0.26/0.70 (declare-fun tptp.collec492052930um_a_b ((-> tptp.produc1124793815um_a_b Bool)) tptp.set_Pr1174980151um_a_b)
% 0.26/0.70 (declare-fun tptp.collec1769032088um_a_b ((-> tptp.produc1548871597um_a_b Bool)) tptp.set_Pr1916610317um_a_b)
% 0.26/0.70 (declare-fun tptp.collect_Sum_sum_a_b ((-> tptp.sum_sum_a_b Bool)) tptp.set_Sum_sum_a_b)
% 0.26/0.70 (declare-fun tptp.insert1909710879tant_a (tptp.standard_Constant_a tptp.set_St761939237tant_a) tptp.set_St761939237tant_a)
% 0.26/0.70 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 0.26/0.70 (declare-fun tptp.insert1625259895at_nat (tptp.produc1032616263at_nat tptp.set_Pr1647387645at_nat) tptp.set_Pr1647387645at_nat)
% 0.26/0.70 (declare-fun tptp.insert323157027um_a_b (tptp.produc1963079155um_a_b tptp.set_Pr409224873um_a_b) tptp.set_Pr409224873um_a_b)
% 0.26/0.70 (declare-fun tptp.insert271595217at_nat (tptp.product_prod_nat_nat tptp.set_Pr1986765409at_nat) tptp.set_Pr1986765409at_nat)
% 0.26/0.70 (declare-fun tptp.insert983991207um_a_b (tptp.produc1124793815um_a_b tptp.set_Pr1174980151um_a_b) tptp.set_Pr1174980151um_a_b)
% 0.26/0.70 (declare-fun tptp.insert1435405693um_a_b (tptp.produc1548871597um_a_b tptp.set_Pr1916610317um_a_b) tptp.set_Pr1916610317um_a_b)
% 0.26/0.70 (declare-fun tptp.insert_Sum_sum_a_b (tptp.sum_sum_a_b tptp.set_Sum_sum_a_b) tptp.set_Sum_sum_a_b)
% 0.26/0.70 (declare-fun tptp.standa1343274079tant_a (tptp.standard_Constant_a tptp.standard_Constant_a) tptp.produc1871334759_a_nat)
% 0.26/0.70 (declare-fun tptp.standa1410829644tant_a () tptp.produc1871334759_a_nat)
% 0.26/0.70 (declare-fun tptp.standa63370785tant_a (tptp.standard_Constant_a) tptp.produc1871334759_a_nat)
% 0.26/0.70 (declare-fun tptp.standa997693288tant_a (tptp.standard_Constant_a) tptp.produc1871334759_a_nat)
% 0.26/0.70 (declare-fun tptp.standa1795879409tant_a (tptp.standard_Constant_a) tptp.produc1871334759_a_nat)
% 0.26/0.70 (declare-fun tptp.member1632892294tant_a (tptp.standard_Constant_a tptp.set_St761939237tant_a) Bool)
% 0.26/0.70 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 0.26/0.70 (declare-fun tptp.member1696759390at_nat (tptp.produc1032616263at_nat tptp.set_Pr1647387645at_nat) Bool)
% 0.26/0.70 (declare-fun tptp.member1502344244um_a_b (tptp.produc1003469085um_a_b tptp.set_Pr326391507um_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.member1998628618um_a_b (tptp.produc1963079155um_a_b tptp.set_Pr409224873um_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.member1641046175um_a_b (tptp.produc1394389750um_a_b tptp.set_Pr1994339542um_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.member701585322at_nat (tptp.product_prod_nat_nat tptp.set_Pr1986765409at_nat) Bool)
% 0.26/0.70 (declare-fun tptp.member1139034387um_a_b (tptp.produc204140796um_a_b tptp.set_Pr1618094130um_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.member1294585472um_a_b (tptp.produc1124793815um_a_b tptp.set_Pr1174980151um_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.member1590479267um_a_b (tptp.produc1681803642um_a_b tptp.set_Pr1121389018um_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.member834135910um_a_b (tptp.produc1546082365um_a_b tptp.set_Pr386468381um_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.member585880557um_a_b (tptp.produc1798470614um_a_b tptp.set_Pr195945996um_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.member429827856um_a_b (tptp.produc1918750183um_a_b tptp.set_Pr45173959um_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.member748122307um_a_b (tptp.produc585753260um_a_b tptp.set_Pr653770722um_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.member1249152_b_nat (tptp.produc1978941143_b_nat tptp.set_Pr375490359_b_nat) Bool)
% 0.26/0.70 (declare-fun tptp.member1641922979um_a_b (tptp.produc1733247354um_a_b tptp.set_Pr1558970842um_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.member485470653um_a_b (tptp.produc323101606um_a_b tptp.set_Pr1783309276um_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.member947389014um_a_b (tptp.produc1548871597um_a_b tptp.set_Pr1916610317um_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.member_Sum_sum_a_b (tptp.sum_sum_a_b tptp.set_Sum_sum_a_b) Bool)
% 0.26/0.70 (declare-fun tptp.g () tptp.labele431970251um_a_b)
% 0.26/0.70 (declare-fun tptp.f () tptp.set_Pr1174980151um_a_b)
% 0.26/0.70 (declare-fun tptp.l () tptp.standard_Constant_a)
% 0.26/0.70 (declare-fun tptp.v () tptp.sum_sum_a_b)
% 0.26/0.70 (assert (= tptp.g (@ tptp.restri1162247455um_a_b tptp.g)))
% 0.26/0.70 (assert (@ (@ tptp.member_Sum_sum_a_b tptp.v) (@ tptp.labele577278695um_a_b tptp.g)))
% 0.26/0.70 (assert (@ (@ (@ tptp.edge_p1382426714tant_a (@ (@ tptp.insert983991207um_a_b (@ (@ tptp.produc1808556047um_a_b tptp.zero_zero_nat) tptp.v)) tptp.bot_bo575978147um_a_b)) (@ (@ tptp.insert1625259895at_nat (@ (@ tptp.produc407553657at_nat tptp.standard_S_Idt_a) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))) tptp.bot_bo810816657at_nat)) (@ tptp.labele1939049654um_a_b tptp.g)))
% 0.26/0.70 (assert (@ (@ tptp.ord_le192794300um_a_b (@ (@ tptp.image_256773707um_a_b tptp.f) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (@ tptp.labele577278695um_a_b tptp.g)))
% 0.26/0.70 (assert (= tptp.f (@ (@ tptp.insert983991207um_a_b (@ (@ tptp.produc1808556047um_a_b tptp.zero_zero_nat) tptp.v)) tptp.bot_bo575978147um_a_b)))
% 0.26/0.70 (assert (= (@ tptp.domain1368163076um_a_b tptp.f) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 0.26/0.70 (assert (forall ((A tptp.standard_Constant_a) (B tptp.sum_sum_a_b) (C tptp.sum_sum_a_b)) (let ((_let_1 (@ (@ tptp.labele1729654377um_a_b (@ (@ tptp.insert323157027um_a_b (@ (@ tptp.produc1697725733um_a_b A) (@ (@ tptp.produc176426981um_a_b B) C))) tptp.bot_bo1262634813um_a_b)) (@ (@ tptp.insert_Sum_sum_a_b B) (@ (@ tptp.insert_Sum_sum_a_b C) tptp.bot_bo1491243248um_a_b))))) (= _let_1 (@ tptp.restri1162247455um_a_b _let_1)))))
% 0.26/0.70 (assert (forall ((A tptp.standard_Constant_a) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ (@ tptp.labele16114835_a_nat (@ (@ tptp.insert1625259895at_nat (@ (@ tptp.produc407553657at_nat A) (@ (@ tptp.product_Pair_nat_nat B) C))) tptp.bot_bo810816657at_nat)) (@ (@ tptp.insert_nat B) (@ (@ tptp.insert_nat C) tptp.bot_bot_set_nat))))) (= _let_1 (@ tptp.restri572569417_a_nat _let_1)))))
% 0.26/0.70 (assert (not (forall ((V tptp.sum_sum_a_b)) (not (@ (@ tptp.member1294585472um_a_b (@ (@ tptp.produc1808556047um_a_b tptp.zero_zero_nat) V)) tptp.f)))))
% 0.26/0.70 (assert (@ tptp.unival2092813468um_a_b tptp.f))
% 0.26/0.70 (assert (forall ((A tptp.standard_Constant_a) (B tptp.product_prod_nat_nat) (R tptp.set_Pr1647387645at_nat)) (= (@ tptp.domain1060562500at_nat (@ (@ tptp.insert1625259895at_nat (@ (@ tptp.produc407553657at_nat A) B)) R)) (@ (@ tptp.insert1909710879tant_a A) (@ tptp.domain1060562500at_nat R)))))
% 0.26/0.70 (assert (forall ((A tptp.nat) (B tptp.nat) (R tptp.set_Pr1986765409at_nat)) (= (@ tptp.domain_nat_nat (@ (@ tptp.insert271595217at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) R)) (@ (@ tptp.insert_nat A) (@ tptp.domain_nat_nat R)))))
% 0.26/0.70 (assert (forall ((A tptp.nat) (B tptp.sum_sum_a_b) (R tptp.set_Pr1174980151um_a_b)) (= (@ tptp.domain1368163076um_a_b (@ (@ tptp.insert983991207um_a_b (@ (@ tptp.produc1808556047um_a_b A) B)) R)) (@ (@ tptp.insert_nat A) (@ tptp.domain1368163076um_a_b R)))))
% 0.26/0.70 (assert (forall ((A tptp.standard_Constant_a) (B tptp.produc1548871597um_a_b) (R tptp.set_Pr409224873um_a_b)) (= (@ tptp.domain1362581744um_a_b (@ (@ tptp.insert323157027um_a_b (@ (@ tptp.produc1697725733um_a_b A) B)) R)) (@ (@ tptp.insert1909710879tant_a A) (@ tptp.domain1362581744um_a_b R)))))
% 0.26/0.70 (assert (forall ((A tptp.sum_sum_a_b) (B tptp.sum_sum_a_b) (R tptp.set_Pr1916610317um_a_b)) (= (@ tptp.domain2069673178um_a_b (@ (@ tptp.insert1435405693um_a_b (@ (@ tptp.produc176426981um_a_b A) B)) R)) (@ (@ tptp.insert_Sum_sum_a_b A) (@ tptp.domain2069673178um_a_b R)))))
% 0.26/0.70 (assert (forall ((B tptp.nat) (R tptp.set_Pr1986765409at_nat) (A tptp.nat)) (= (@ (@ tptp.member_nat B) (@ (@ tptp.image_nat_nat R) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) R))))
% 0.26/0.70 (assert (forall ((B tptp.sum_sum_a_b) (R tptp.set_Pr1174980151um_a_b) (A tptp.nat)) (= (@ (@ tptp.member_Sum_sum_a_b B) (@ (@ tptp.image_256773707um_a_b R) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (@ (@ tptp.member1294585472um_a_b (@ (@ tptp.produc1808556047um_a_b A) B)) R))))
% 0.26/0.70 (assert (forall ((B tptp.sum_sum_a_b) (R tptp.set_Pr1994339542um_a_b) (A tptp.standard_Constant_a)) (= (@ (@ tptp.member_Sum_sum_a_b B) (@ (@ tptp.image_2129435242um_a_b R) (@ (@ tptp.insert1909710879tant_a A) tptp.bot_bo1160111033tant_a))) (@ (@ tptp.member1641046175um_a_b (@ (@ tptp.produc584843310um_a_b A) B)) R))))
% 0.26/0.70 (assert (forall ((B tptp.product_prod_nat_nat) (R tptp.set_Pr1647387645at_nat) (A tptp.standard_Constant_a)) (= (@ (@ tptp.member701585322at_nat B) (@ (@ tptp.image_127502653at_nat R) (@ (@ tptp.insert1909710879tant_a A) tptp.bot_bo1160111033tant_a))) (@ (@ tptp.member1696759390at_nat (@ (@ tptp.produc407553657at_nat A) B)) R))))
% 0.26/0.70 (assert (forall ((B tptp.sum_sum_a_b) (R tptp.set_Pr195945996um_a_b) (A tptp.product_prod_nat_nat)) (= (@ (@ tptp.member_Sum_sum_a_b B) (@ (@ tptp.image_1754351636um_a_b R) (@ (@ tptp.insert271595217at_nat A) tptp.bot_bo2130386637at_nat))) (@ (@ tptp.member585880557um_a_b (@ (@ tptp.produc1872245072um_a_b A) B)) R))))
% 0.26/0.70 (assert (forall ((B tptp.produc1124793815um_a_b) (R tptp.set_Pr1618094130um_a_b) (A tptp.nat)) (= (@ (@ tptp.member1294585472um_a_b B) (@ (@ tptp.image_1228479730um_a_b R) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (@ (@ tptp.member1139034387um_a_b (@ (@ tptp.produc1346373166um_a_b A) B)) R))))
% 0.26/0.70 (assert (forall ((B tptp.sum_sum_a_b) (R tptp.set_Pr1916610317um_a_b) (A tptp.sum_sum_a_b)) (= (@ (@ tptp.member_Sum_sum_a_b B) (@ (@ tptp.image_1918588449um_a_b R) (@ (@ tptp.insert_Sum_sum_a_b A) tptp.bot_bo1491243248um_a_b))) (@ (@ tptp.member947389014um_a_b (@ (@ tptp.produc176426981um_a_b A) B)) R))))
% 0.26/0.70 (assert (forall ((B tptp.produc1124793815um_a_b) (R tptp.set_Pr326391507um_a_b) (A tptp.standard_Constant_a)) (= (@ (@ tptp.member1294585472um_a_b B) (@ (@ tptp.image_1179143699um_a_b R) (@ (@ tptp.insert1909710879tant_a A) tptp.bot_bo1160111033tant_a))) (@ (@ tptp.member1502344244um_a_b (@ (@ tptp.produc414524239um_a_b A) B)) R))))
% 0.26/0.70 (assert (forall ((B tptp.produc1124793815um_a_b) (R tptp.set_Pr386468381um_a_b) (A tptp.product_prod_nat_nat)) (= (@ (@ tptp.member1294585472um_a_b B) (@ (@ tptp.image_320480233um_a_b R) (@ (@ tptp.insert271595217at_nat A) tptp.bot_bo2130386637at_nat))) (@ (@ tptp.member834135910um_a_b (@ (@ tptp.produc335036333um_a_b A) B)) R))))
% 0.26/0.70 (assert (forall ((B tptp.sum_sum_a_b) (R tptp.set_Pr653770722um_a_b) (A tptp.produc1124793815um_a_b)) (= (@ (@ tptp.member_Sum_sum_a_b B) (@ (@ tptp.image_869585130um_a_b R) (@ (@ tptp.insert983991207um_a_b A) tptp.bot_bo575978147um_a_b))) (@ (@ tptp.member748122307um_a_b (@ (@ tptp.produc831476262um_a_b A) B)) R))))
% 0.26/0.70 (assert (forall ((V2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.labele16114835_a_nat tptp.bot_bo810816657at_nat) V2))) (= _let_1 (@ tptp.restri572569417_a_nat _let_1)))))
% 0.26/0.70 (assert (forall ((V2 tptp.set_Sum_sum_a_b)) (let ((_let_1 (@ (@ tptp.labele1729654377um_a_b tptp.bot_bo1262634813um_a_b) V2))) (= _let_1 (@ tptp.restri1162247455um_a_b _let_1)))))
% 0.26/0.70 (assert (forall ((Labeled_graph tptp.labele935650037_a_nat)) (= (@ (@ tptp.labele16114835_a_nat (@ tptp.labele195203296_a_nat Labeled_graph)) (@ tptp.labele1810595089_a_nat Labeled_graph)) Labeled_graph)))
% 0.26/0.70 (assert (forall ((Labeled_graph tptp.labele431970251um_a_b)) (= (@ (@ tptp.labele1729654377um_a_b (@ tptp.labele1939049654um_a_b Labeled_graph)) (@ tptp.labele577278695um_a_b Labeled_graph)) Labeled_graph)))
% 0.26/0.70 (assert (= (@ tptp.domain_nat_nat tptp.bot_bo2130386637at_nat) tptp.bot_bot_set_nat))
% 0.26/0.70 (assert (= (@ tptp.domain1060562500at_nat tptp.bot_bo810816657at_nat) tptp.bot_bo1160111033tant_a))
% 0.26/0.70 (assert (= (@ tptp.domain1368163076um_a_b tptp.bot_bo575978147um_a_b) tptp.bot_bot_set_nat))
% 0.26/0.70 (assert (= (@ tptp.domain2069673178um_a_b tptp.bot_bo225809273um_a_b) tptp.bot_bo1491243248um_a_b))
% 0.26/0.70 (assert (= (@ tptp.domain1362581744um_a_b tptp.bot_bo1262634813um_a_b) tptp.bot_bo1160111033tant_a))
% 0.26/0.70 (assert (forall ((X tptp.set_St761939237tant_a)) (= (@ (@ tptp.image_127502653at_nat tptp.bot_bo810816657at_nat) X) tptp.bot_bo2130386637at_nat)))
% 0.26/0.70 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.image_256773707um_a_b tptp.bot_bo575978147um_a_b) X) tptp.bot_bo1491243248um_a_b)))
% 0.26/0.70 (assert (forall ((X tptp.set_Sum_sum_a_b)) (= (@ (@ tptp.image_1918588449um_a_b tptp.bot_bo225809273um_a_b) X) tptp.bot_bo1491243248um_a_b)))
% 0.26/0.70 (assert (forall ((X tptp.set_St761939237tant_a)) (= (@ (@ tptp.image_2023280617um_a_b tptp.bot_bo1262634813um_a_b) X) tptp.bot_bo225809273um_a_b)))
% 0.26/0.70 (assert (forall ((X2 tptp.labele935650037_a_nat)) (let ((_let_1 (@ tptp.restri572569417_a_nat X2))) (= (@ tptp.restri572569417_a_nat _let_1) _let_1))))
% 0.26/0.70 (assert (forall ((X2 tptp.labele431970251um_a_b)) (let ((_let_1 (@ tptp.restri1162247455um_a_b X2))) (= (@ tptp.restri1162247455um_a_b _let_1) _let_1))))
% 0.26/0.70 (assert (forall ((X1 tptp.set_Pr1647387645at_nat) (X22 tptp.set_nat) (Y1 tptp.set_Pr1647387645at_nat) (Y2 tptp.set_nat)) (= (= (@ (@ tptp.labele16114835_a_nat X1) X22) (@ (@ tptp.labele16114835_a_nat Y1) Y2)) (and (= X1 Y1) (= X22 Y2)))))
% 0.26/0.70 (assert (forall ((X1 tptp.set_Pr409224873um_a_b) (X22 tptp.set_Sum_sum_a_b) (Y1 tptp.set_Pr409224873um_a_b) (Y2 tptp.set_Sum_sum_a_b)) (= (= (@ (@ tptp.labele1729654377um_a_b X1) X22) (@ (@ tptp.labele1729654377um_a_b Y1) Y2)) (and (= X1 Y1) (= X22 Y2)))))
% 0.26/0.70 (assert (forall ((A2 tptp.sum_sum_a_b) (B2 tptp.sum_sum_a_b)) (= (@ (@ tptp.member1998628618um_a_b (@ (@ tptp.produc1697725733um_a_b tptp.standard_S_Idt_a) (@ (@ tptp.produc176426981um_a_b A2) B2))) (@ tptp.labele1939049654um_a_b tptp.g)) (and (@ (@ tptp.member_Sum_sum_a_b A2) (@ tptp.labele577278695um_a_b tptp.g)) (= B2 A2)))))
% 0.26/0.70 (assert (@ (@ tptp.member1998628618um_a_b (@ (@ tptp.produc1697725733um_a_b tptp.standard_S_Idt_a) (@ (@ tptp.produc176426981um_a_b tptp.v) tptp.v))) (@ tptp.labele1939049654um_a_b tptp.g)))
% 0.26/0.70 (assert (forall ((A tptp.nat) (B tptp.nat) (R tptp.set_Pr1986765409at_nat) (A3 tptp.set_nat)) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) R) (=> (@ (@ tptp.member_nat A) A3) (@ (@ tptp.member_nat B) (@ (@ tptp.image_nat_nat R) A3))))))
% 0.26/0.70 (assert (forall ((A tptp.nat) (B tptp.sum_sum_a_b) (R tptp.set_Pr1174980151um_a_b) (A3 tptp.set_nat)) (=> (@ (@ tptp.member1294585472um_a_b (@ (@ tptp.produc1808556047um_a_b A) B)) R) (=> (@ (@ tptp.member_nat A) A3) (@ (@ tptp.member_Sum_sum_a_b B) (@ (@ tptp.image_256773707um_a_b R) A3))))))
% 0.26/0.70 (assert (forall ((A tptp.standard_Constant_a) (B tptp.product_prod_nat_nat) (R tptp.set_Pr1647387645at_nat) (A3 tptp.set_St761939237tant_a)) (=> (@ (@ tptp.member1696759390at_nat (@ (@ tptp.produc407553657at_nat A) B)) R) (=> (@ (@ tptp.member1632892294tant_a A) A3) (@ (@ tptp.member701585322at_nat B) (@ (@ tptp.image_127502653at_nat R) A3))))))
% 0.26/0.70 (assert (forall ((A tptp.sum_sum_a_b) (B tptp.sum_sum_a_b) (R tptp.set_Pr1916610317um_a_b) (A3 tptp.set_Sum_sum_a_b)) (=> (@ (@ tptp.member947389014um_a_b (@ (@ tptp.produc176426981um_a_b A) B)) R) (=> (@ (@ tptp.member_Sum_sum_a_b A) A3) (@ (@ tptp.member_Sum_sum_a_b B) (@ (@ tptp.image_1918588449um_a_b R) A3))))))
% 0.26/0.70 (assert (forall ((A tptp.sum_sum_a_b) (B tptp.produc1124793815um_a_b) (R tptp.set_Pr1783309276um_a_b) (A3 tptp.set_Sum_sum_a_b)) (=> (@ (@ tptp.member485470653um_a_b (@ (@ tptp.produc1637282520um_a_b A) B)) R) (=> (@ (@ tptp.member_Sum_sum_a_b A) A3) (@ (@ tptp.member1294585472um_a_b B) (@ (@ tptp.image_1675391388um_a_b R) A3))))))
% 0.26/0.70 (assert (forall ((A tptp.produc1124793815um_a_b) (B tptp.sum_sum_a_b) (R tptp.set_Pr653770722um_a_b) (A3 tptp.set_Pr1174980151um_a_b)) (=> (@ (@ tptp.member748122307um_a_b (@ (@ tptp.produc831476262um_a_b A) B)) R) (=> (@ (@ tptp.member1294585472um_a_b A) A3) (@ (@ tptp.member_Sum_sum_a_b B) (@ (@ tptp.image_869585130um_a_b R) A3))))))
% 0.26/0.70 (assert (forall ((A tptp.standard_Constant_a) (B tptp.produc1548871597um_a_b) (R tptp.set_Pr409224873um_a_b) (A3 tptp.set_St761939237tant_a)) (=> (@ (@ tptp.member1998628618um_a_b (@ (@ tptp.produc1697725733um_a_b A) B)) R) (=> (@ (@ tptp.member1632892294tant_a A) A3) (@ (@ tptp.member947389014um_a_b B) (@ (@ tptp.image_2023280617um_a_b R) A3))))))
% 0.26/0.70 (assert (forall ((A tptp.produc1124793815um_a_b) (B tptp.produc1124793815um_a_b) (R tptp.set_Pr45173959um_a_b) (A3 tptp.set_Pr1174980151um_a_b)) (=> (@ (@ tptp.member429827856um_a_b (@ (@ tptp.produc27163479um_a_b A) B)) R) (=> (@ (@ tptp.member1294585472um_a_b A) A3) (@ (@ tptp.member1294585472um_a_b B) (@ (@ tptp.image_1464989587um_a_b R) A3))))))
% 0.26/0.70 (assert (forall ((A tptp.sum_sum_a_b) (B tptp.produc1963079155um_a_b) (R tptp.set_Pr1558970842um_a_b) (A3 tptp.set_Sum_sum_a_b)) (=> (@ (@ tptp.member1641922979um_a_b (@ (@ tptp.produc230853810um_a_b A) B)) R) (=> (@ (@ tptp.member_Sum_sum_a_b A) A3) (@ (@ tptp.member1998628618um_a_b B) (@ (@ tptp.image_1482984686um_a_b R) A3))))))
% 0.26/0.70 (assert (forall ((A tptp.produc1963079155um_a_b) (B tptp.sum_sum_a_b) (R tptp.set_Pr1121389018um_a_b) (A3 tptp.set_Pr409224873um_a_b)) (=> (@ (@ tptp.member1590479267um_a_b (@ (@ tptp.produc522766386um_a_b A) B)) R) (=> (@ (@ tptp.member1998628618um_a_b A) A3) (@ (@ tptp.member_Sum_sum_a_b B) (@ (@ tptp.image_1774897262um_a_b R) A3))))))
% 0.26/0.70 (assert (forall ((R2 tptp.set_Pr1986765409at_nat)) (= (@ (@ tptp.image_nat_nat R2) tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)))
% 0.26/0.70 (assert (forall ((R2 tptp.set_Pr1174980151um_a_b)) (= (@ (@ tptp.image_256773707um_a_b R2) tptp.bot_bot_set_nat) tptp.bot_bo1491243248um_a_b)))
% 0.26/0.70 (assert (forall ((R2 tptp.set_Pr375490359_b_nat)) (= (@ (@ tptp.image_1117854795_b_nat R2) tptp.bot_bo1491243248um_a_b) tptp.bot_bot_set_nat)))
% 0.26/0.70 (assert (forall ((R2 tptp.set_Pr1618094130um_a_b)) (= (@ (@ tptp.image_1228479730um_a_b R2) tptp.bot_bot_set_nat) tptp.bot_bo575978147um_a_b)))
% 0.26/0.70 (assert (forall ((R2 tptp.set_Pr1902304780_b_nat)) (= (@ (@ tptp.image_128716052_b_nat R2) tptp.bot_bo575978147um_a_b) tptp.bot_bot_set_nat)))
% 0.26/0.70 (assert (forall ((R2 tptp.set_Pr1916610317um_a_b)) (= (@ (@ tptp.image_1918588449um_a_b R2) tptp.bot_bo1491243248um_a_b) tptp.bot_bo1491243248um_a_b)))
% 0.26/0.70 (assert (forall ((R2 tptp.set_Pr689416536at_nat)) (= (@ (@ tptp.image_452296684at_nat R2) tptp.bot_bo810816657at_nat) tptp.bot_bot_set_nat)))
% 0.26/0.70 (assert (forall ((R2 tptp.set_Pr1134469976at_nat)) (= (@ (@ tptp.image_489788268at_nat R2) tptp.bot_bot_set_nat) tptp.bot_bo810816657at_nat)))
% 0.26/0.70 (assert (forall ((R2 tptp.set_Pr1155046920um_a_b)) (= (@ (@ tptp.image_166667464um_a_b R2) tptp.bot_bot_set_nat) tptp.bot_bo225809273um_a_b)))
% 0.26/0.70 (assert (forall ((R2 tptp.set_Pr653770722um_a_b)) (= (@ (@ tptp.image_869585130um_a_b R2) tptp.bot_bo575978147um_a_b) tptp.bot_bo1491243248um_a_b)))
% 0.26/0.70 (assert (forall ((G tptp.labele935650037_a_nat)) (= (@ tptp.labele1810595089_a_nat (@ tptp.restri572569417_a_nat G)) (@ tptp.labele1810595089_a_nat G))))
% 0.26/0.70 (assert (forall ((G tptp.labele431970251um_a_b)) (= (@ tptp.labele577278695um_a_b (@ tptp.restri1162247455um_a_b G)) (@ tptp.labele577278695um_a_b G))))
% 0.26/0.70 (assert (@ (@ (@ tptp.graph_1452133198um_a_b (@ (@ tptp.labele16114835_a_nat tptp.bot_bo810816657at_nat) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) tptp.g) tptp.f))
% 0.26/0.70 (assert (forall ((Y tptp.labele935650037_a_nat)) (not (forall ((X12 tptp.set_Pr1647387645at_nat) (X23 tptp.set_nat)) (not (= Y (@ (@ tptp.labele16114835_a_nat X12) X23)))))))
% 0.26/0.70 (assert (forall ((Y tptp.labele431970251um_a_b)) (not (forall ((X12 tptp.set_Pr409224873um_a_b) (X23 tptp.set_Sum_sum_a_b)) (not (= Y (@ (@ tptp.labele1729654377um_a_b X12) X23)))))))
% 0.26/0.70 (assert (forall ((P (-> tptp.labele935650037_a_nat Bool)) (Labeled_graph tptp.labele935650037_a_nat)) (=> (forall ((X1a tptp.set_Pr1647387645at_nat) (X2a tptp.set_nat)) (@ P (@ (@ tptp.labele16114835_a_nat X1a) X2a))) (@ P Labeled_graph))))
% 0.26/0.70 (assert (forall ((P (-> tptp.labele431970251um_a_b Bool)) (Labeled_graph tptp.labele431970251um_a_b)) (=> (forall ((X1a tptp.set_Pr409224873um_a_b) (X2a tptp.set_Sum_sum_a_b)) (@ P (@ (@ tptp.labele1729654377um_a_b X1a) X2a))) (@ P Labeled_graph))))
% 0.26/0.70 (assert (forall ((A tptp.nat) (A3 tptp.set_nat) (B tptp.nat) (R tptp.set_Pr1986765409at_nat)) (=> (@ (@ tptp.member_nat A) A3) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) R) (@ (@ tptp.member_nat B) (@ (@ tptp.image_nat_nat R) A3))))))
% 0.26/0.70 (assert (forall ((A tptp.nat) (A3 tptp.set_nat) (B tptp.sum_sum_a_b) (R tptp.set_Pr1174980151um_a_b)) (=> (@ (@ tptp.member_nat A) A3) (=> (@ (@ tptp.member1294585472um_a_b (@ (@ tptp.produc1808556047um_a_b A) B)) R) (@ (@ tptp.member_Sum_sum_a_b B) (@ (@ tptp.image_256773707um_a_b R) A3))))))
% 0.26/0.70 (assert (forall ((A tptp.standard_Constant_a) (A3 tptp.set_St761939237tant_a) (B tptp.product_prod_nat_nat) (R tptp.set_Pr1647387645at_nat)) (=> (@ (@ tptp.member1632892294tant_a A) A3) (=> (@ (@ tptp.member1696759390at_nat (@ (@ tptp.produc407553657at_nat A) B)) R) (@ (@ tptp.member701585322at_nat B) (@ (@ tptp.image_127502653at_nat R) A3))))))
% 0.26/0.70 (assert (forall ((A tptp.sum_sum_a_b) (A3 tptp.set_Sum_sum_a_b) (B tptp.sum_sum_a_b) (R tptp.set_Pr1916610317um_a_b)) (=> (@ (@ tptp.member_Sum_sum_a_b A) A3) (=> (@ (@ tptp.member947389014um_a_b (@ (@ tptp.produc176426981um_a_b A) B)) R) (@ (@ tptp.member_Sum_sum_a_b B) (@ (@ tptp.image_1918588449um_a_b R) A3))))))
% 0.26/0.70 (assert (forall ((A tptp.sum_sum_a_b) (A3 tptp.set_Sum_sum_a_b) (B tptp.produc1124793815um_a_b) (R tptp.set_Pr1783309276um_a_b)) (=> (@ (@ tptp.member_Sum_sum_a_b A) A3) (=> (@ (@ tptp.member485470653um_a_b (@ (@ tptp.produc1637282520um_a_b A) B)) R) (@ (@ tptp.member1294585472um_a_b B) (@ (@ tptp.image_1675391388um_a_b R) A3))))))
% 0.26/0.70 (assert (forall ((A tptp.produc1124793815um_a_b) (A3 tptp.set_Pr1174980151um_a_b) (B tptp.sum_sum_a_b) (R tptp.set_Pr653770722um_a_b)) (=> (@ (@ tptp.member1294585472um_a_b A) A3) (=> (@ (@ tptp.member748122307um_a_b (@ (@ tptp.produc831476262um_a_b A) B)) R) (@ (@ tptp.member_Sum_sum_a_b B) (@ (@ tptp.image_869585130um_a_b R) A3))))))
% 0.26/0.70 (assert (forall ((A tptp.standard_Constant_a) (A3 tptp.set_St761939237tant_a) (B tptp.produc1548871597um_a_b) (R tptp.set_Pr409224873um_a_b)) (=> (@ (@ tptp.member1632892294tant_a A) A3) (=> (@ (@ tptp.member1998628618um_a_b (@ (@ tptp.produc1697725733um_a_b A) B)) R) (@ (@ tptp.member947389014um_a_b B) (@ (@ tptp.image_2023280617um_a_b R) A3))))))
% 0.26/0.70 (assert (forall ((A tptp.produc1124793815um_a_b) (A3 tptp.set_Pr1174980151um_a_b) (B tptp.produc1124793815um_a_b) (R tptp.set_Pr45173959um_a_b)) (=> (@ (@ tptp.member1294585472um_a_b A) A3) (=> (@ (@ tptp.member429827856um_a_b (@ (@ tptp.produc27163479um_a_b A) B)) R) (@ (@ tptp.member1294585472um_a_b B) (@ (@ tptp.image_1464989587um_a_b R) A3))))))
% 0.26/0.70 (assert (forall ((A tptp.sum_sum_a_b) (A3 tptp.set_Sum_sum_a_b) (B tptp.produc1963079155um_a_b) (R tptp.set_Pr1558970842um_a_b)) (=> (@ (@ tptp.member_Sum_sum_a_b A) A3) (=> (@ (@ tptp.member1641922979um_a_b (@ (@ tptp.produc230853810um_a_b A) B)) R) (@ (@ tptp.member1998628618um_a_b B) (@ (@ tptp.image_1482984686um_a_b R) A3))))))
% 0.26/0.70 (assert (forall ((A tptp.produc1963079155um_a_b) (A3 tptp.set_Pr409224873um_a_b) (B tptp.sum_sum_a_b) (R tptp.set_Pr1121389018um_a_b)) (=> (@ (@ tptp.member1998628618um_a_b A) A3) (=> (@ (@ tptp.member1590479267um_a_b (@ (@ tptp.produc522766386um_a_b A) B)) R) (@ (@ tptp.member_Sum_sum_a_b B) (@ (@ tptp.image_1774897262um_a_b R) A3))))))
% 0.26/0.70 (assert (forall ((B tptp.product_prod_nat_nat) (R tptp.set_Pr1647387645at_nat) (A3 tptp.set_St761939237tant_a)) (= (@ (@ tptp.member701585322at_nat B) (@ (@ tptp.image_127502653at_nat R) A3)) (exists ((X3 tptp.standard_Constant_a)) (and (@ (@ tptp.member1632892294tant_a X3) A3) (@ (@ tptp.member1696759390at_nat (@ (@ tptp.produc407553657at_nat X3) B)) R))))))
% 0.26/0.70 (assert (forall ((B tptp.nat) (R tptp.set_Pr1986765409at_nat) (A3 tptp.set_nat)) (= (@ (@ tptp.member_nat B) (@ (@ tptp.image_nat_nat R) A3)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X3) B)) R))))))
% 0.26/0.70 (assert (forall ((B tptp.sum_sum_a_b) (R tptp.set_Pr1174980151um_a_b) (A3 tptp.set_nat)) (= (@ (@ tptp.member_Sum_sum_a_b B) (@ (@ tptp.image_256773707um_a_b R) A3)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.member1294585472um_a_b (@ (@ tptp.produc1808556047um_a_b X3) B)) R))))))
% 0.26/0.70 (assert (forall ((B tptp.produc1548871597um_a_b) (R tptp.set_Pr409224873um_a_b) (A3 tptp.set_St761939237tant_a)) (= (@ (@ tptp.member947389014um_a_b B) (@ (@ tptp.image_2023280617um_a_b R) A3)) (exists ((X3 tptp.standard_Constant_a)) (and (@ (@ tptp.member1632892294tant_a X3) A3) (@ (@ tptp.member1998628618um_a_b (@ (@ tptp.produc1697725733um_a_b X3) B)) R))))))
% 0.26/0.70 (assert (forall ((B tptp.sum_sum_a_b) (R tptp.set_Pr1916610317um_a_b) (A3 tptp.set_Sum_sum_a_b)) (= (@ (@ tptp.member_Sum_sum_a_b B) (@ (@ tptp.image_1918588449um_a_b R) A3)) (exists ((X3 tptp.sum_sum_a_b)) (and (@ (@ tptp.member_Sum_sum_a_b X3) A3) (@ (@ tptp.member947389014um_a_b (@ (@ tptp.produc176426981um_a_b X3) B)) R))))))
% 0.26/0.70 (assert (forall ((B tptp.nat) (R tptp.set_Pr1986765409at_nat) (A3 tptp.set_nat)) (=> (@ (@ tptp.member_nat B) (@ (@ tptp.image_nat_nat R) A3)) (not (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X4) B)) R) (not (@ (@ tptp.member_nat X4) A3))))))))
% 0.26/0.70 (assert (forall ((B tptp.sum_sum_a_b) (R tptp.set_Pr1174980151um_a_b) (A3 tptp.set_nat)) (=> (@ (@ tptp.member_Sum_sum_a_b B) (@ (@ tptp.image_256773707um_a_b R) A3)) (not (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member1294585472um_a_b (@ (@ tptp.produc1808556047um_a_b X4) B)) R) (not (@ (@ tptp.member_nat X4) A3))))))))
% 0.26/0.70 (assert (forall ((B tptp.product_prod_nat_nat) (R tptp.set_Pr1647387645at_nat) (A3 tptp.set_St761939237tant_a)) (=> (@ (@ tptp.member701585322at_nat B) (@ (@ tptp.image_127502653at_nat R) A3)) (not (forall ((X4 tptp.standard_Constant_a)) (=> (@ (@ tptp.member1696759390at_nat (@ (@ tptp.produc407553657at_nat X4) B)) R) (not (@ (@ tptp.member1632892294tant_a X4) A3))))))))
% 0.26/0.70 (assert (forall ((B tptp.sum_sum_a_b) (R tptp.set_Pr1916610317um_a_b) (A3 tptp.set_Sum_sum_a_b)) (=> (@ (@ tptp.member_Sum_sum_a_b B) (@ (@ tptp.image_1918588449um_a_b R) A3)) (not (forall ((X4 tptp.sum_sum_a_b)) (=> (@ (@ tptp.member947389014um_a_b (@ (@ tptp.produc176426981um_a_b X4) B)) R) (not (@ (@ tptp.member_Sum_sum_a_b X4) A3))))))))
% 0.26/0.70 (assert (forall ((B tptp.sum_sum_a_b) (R tptp.set_Pr653770722um_a_b) (A3 tptp.set_Pr1174980151um_a_b)) (=> (@ (@ tptp.member_Sum_sum_a_b B) (@ (@ tptp.image_869585130um_a_b R) A3)) (not (forall ((X4 tptp.produc1124793815um_a_b)) (=> (@ (@ tptp.member748122307um_a_b (@ (@ tptp.produc831476262um_a_b X4) B)) R) (not (@ (@ tptp.member1294585472um_a_b X4) A3))))))))
% 0.26/0.70 (assert (forall ((B tptp.produc1124793815um_a_b) (R tptp.set_Pr1783309276um_a_b) (A3 tptp.set_Sum_sum_a_b)) (=> (@ (@ tptp.member1294585472um_a_b B) (@ (@ tptp.image_1675391388um_a_b R) A3)) (not (forall ((X4 tptp.sum_sum_a_b)) (=> (@ (@ tptp.member485470653um_a_b (@ (@ tptp.produc1637282520um_a_b X4) B)) R) (not (@ (@ tptp.member_Sum_sum_a_b X4) A3))))))))
% 0.26/0.70 (assert (forall ((B tptp.produc1548871597um_a_b) (R tptp.set_Pr409224873um_a_b) (A3 tptp.set_St761939237tant_a)) (=> (@ (@ tptp.member947389014um_a_b B) (@ (@ tptp.image_2023280617um_a_b R) A3)) (not (forall ((X4 tptp.standard_Constant_a)) (=> (@ (@ tptp.member1998628618um_a_b (@ (@ tptp.produc1697725733um_a_b X4) B)) R) (not (@ (@ tptp.member1632892294tant_a X4) A3))))))))
% 0.26/0.70 (assert (forall ((B tptp.produc1124793815um_a_b) (R tptp.set_Pr45173959um_a_b) (A3 tptp.set_Pr1174980151um_a_b)) (=> (@ (@ tptp.member1294585472um_a_b B) (@ (@ tptp.image_1464989587um_a_b R) A3)) (not (forall ((X4 tptp.produc1124793815um_a_b)) (=> (@ (@ tptp.member429827856um_a_b (@ (@ tptp.produc27163479um_a_b X4) B)) R) (not (@ (@ tptp.member1294585472um_a_b X4) A3))))))))
% 0.26/0.70 (assert (forall ((B tptp.sum_sum_a_b) (R tptp.set_Pr1121389018um_a_b) (A3 tptp.set_Pr409224873um_a_b)) (=> (@ (@ tptp.member_Sum_sum_a_b B) (@ (@ tptp.image_1774897262um_a_b R) A3)) (not (forall ((X4 tptp.produc1963079155um_a_b)) (=> (@ (@ tptp.member1590479267um_a_b (@ (@ tptp.produc522766386um_a_b X4) B)) R) (not (@ (@ tptp.member1998628618um_a_b X4) A3))))))))
% 0.26/0.70 (assert (forall ((B tptp.produc1963079155um_a_b) (R tptp.set_Pr1558970842um_a_b) (A3 tptp.set_Sum_sum_a_b)) (=> (@ (@ tptp.member1998628618um_a_b B) (@ (@ tptp.image_1482984686um_a_b R) A3)) (not (forall ((X4 tptp.sum_sum_a_b)) (=> (@ (@ tptp.member1641922979um_a_b (@ (@ tptp.produc230853810um_a_b X4) B)) R) (not (@ (@ tptp.member_Sum_sum_a_b X4) A3))))))))
% 0.26/0.70 (assert (forall ((R3 tptp.set_Pr1174980151um_a_b) (R tptp.set_Pr1174980151um_a_b) (A4 tptp.set_nat) (A3 tptp.set_nat)) (=> (@ (@ tptp.ord_le823954903um_a_b R3) R) (=> (@ (@ tptp.ord_less_eq_set_nat A4) A3) (@ (@ tptp.ord_le192794300um_a_b (@ (@ tptp.image_256773707um_a_b R3) A4)) (@ (@ tptp.image_256773707um_a_b R) A3))))))
% 0.26/0.70 (assert (forall ((R3 tptp.set_Pr1916610317um_a_b) (R tptp.set_Pr1916610317um_a_b) (A4 tptp.set_Sum_sum_a_b) (A3 tptp.set_Sum_sum_a_b)) (=> (@ (@ tptp.ord_le1059794605um_a_b R3) R) (=> (@ (@ tptp.ord_le192794300um_a_b A4) A3) (@ (@ tptp.ord_le192794300um_a_b (@ (@ tptp.image_1918588449um_a_b R3) A4)) (@ (@ tptp.image_1918588449um_a_b R) A3))))))
% 0.26/0.70 (assert (forall ((X2 tptp.standard_Constant_a) (R tptp.set_Pr1647387645at_nat) (P (-> tptp.standard_Constant_a Bool))) (=> (@ (@ tptp.member1632892294tant_a X2) (@ tptp.domain1060562500at_nat R)) (=> (forall ((A5 tptp.standard_Constant_a) (B3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member1696759390at_nat (@ (@ tptp.produc407553657at_nat A5) B3)) R) (@ P A5))) (@ P X2)))))
% 0.26/0.70 (assert (forall ((X2 tptp.nat) (R tptp.set_Pr1986765409at_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X2) (@ tptp.domain_nat_nat R)) (=> (forall ((A5 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A5) B3)) R) (@ P A5))) (@ P X2)))))
% 0.26/0.70 (assert (forall ((X2 tptp.nat) (R tptp.set_Pr1174980151um_a_b) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X2) (@ tptp.domain1368163076um_a_b R)) (=> (forall ((A5 tptp.nat) (B3 tptp.sum_sum_a_b)) (=> (@ (@ tptp.member1294585472um_a_b (@ (@ tptp.produc1808556047um_a_b A5) B3)) R) (@ P A5))) (@ P X2)))))
% 0.26/0.70 (assert (forall ((X2 tptp.standard_Constant_a) (R tptp.set_Pr409224873um_a_b) (P (-> tptp.standard_Constant_a Bool))) (=> (@ (@ tptp.member1632892294tant_a X2) (@ tptp.domain1362581744um_a_b R)) (=> (forall ((A5 tptp.standard_Constant_a) (B3 tptp.produc1548871597um_a_b)) (=> (@ (@ tptp.member1998628618um_a_b (@ (@ tptp.produc1697725733um_a_b A5) B3)) R) (@ P A5))) (@ P X2)))))
% 0.26/0.70 (assert (forall ((X2 tptp.sum_sum_a_b) (R tptp.set_Pr1916610317um_a_b) (P (-> tptp.sum_sum_a_b Bool))) (=> (@ (@ tptp.member_Sum_sum_a_b X2) (@ tptp.domain2069673178um_a_b R)) (=> (forall ((A5 tptp.sum_sum_a_b) (B3 tptp.sum_sum_a_b)) (=> (@ (@ tptp.member947389014um_a_b (@ (@ tptp.produc176426981um_a_b A5) B3)) R) (@ P A5))) (@ P X2)))))
% 0.26/0.70 (assert (forall ((A tptp.standard_Constant_a) (B tptp.product_prod_nat_nat) (R tptp.set_Pr1647387645at_nat)) (=> (@ (@ tptp.member1696759390at_nat (@ (@ tptp.produc407553657at_nat A) B)) R) (@ (@ tptp.member1632892294tant_a A) (@ tptp.domain1060562500at_nat R)))))
% 0.26/0.70 (assert (forall ((A tptp.nat) (B tptp.nat) (R tptp.set_Pr1986765409at_nat)) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) R) (@ (@ tptp.member_nat A) (@ tptp.domain_nat_nat R)))))
% 0.26/0.70 (assert (forall ((A tptp.nat) (B tptp.sum_sum_a_b) (R tptp.set_Pr1174980151um_a_b)) (=> (@ (@ tptp.member1294585472um_a_b (@ (@ tptp.produc1808556047um_a_b A) B)) R) (@ (@ tptp.member_nat A) (@ tptp.domain1368163076um_a_b R)))))
% 0.26/0.70 (assert (forall ((A tptp.standard_Constant_a) (B tptp.produc1548871597um_a_b) (R tptp.set_Pr409224873um_a_b)) (=> (@ (@ tptp.member1998628618um_a_b (@ (@ tptp.produc1697725733um_a_b A) B)) R) (@ (@ tptp.member1632892294tant_a A) (@ tptp.domain1362581744um_a_b R)))))
% 0.26/0.70 (assert (forall ((A tptp.sum_sum_a_b) (B tptp.sum_sum_a_b) (R tptp.set_Pr1916610317um_a_b)) (=> (@ (@ tptp.member947389014um_a_b (@ (@ tptp.produc176426981um_a_b A) B)) R) (@ (@ tptp.member_Sum_sum_a_b A) (@ tptp.domain2069673178um_a_b R)))))
% 0.26/0.70 (assert (forall ((A tptp.standard_Constant_a) (R tptp.set_Pr1647387645at_nat)) (= (@ (@ tptp.member1632892294tant_a A) (@ tptp.domain1060562500at_nat R)) (exists ((A6 tptp.standard_Constant_a) (B4 tptp.product_prod_nat_nat)) (and (= A A6) (@ (@ tptp.member1696759390at_nat (@ (@ tptp.produc407553657at_nat A6) B4)) R))))))
% 0.26/0.70 (assert (forall ((A tptp.nat) (R tptp.set_Pr1986765409at_nat)) (= (@ (@ tptp.member_nat A) (@ tptp.domain_nat_nat R)) (exists ((A6 tptp.nat) (B4 tptp.nat)) (and (= A A6) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A6) B4)) R))))))
% 0.26/0.70 (assert (forall ((A tptp.nat) (R tptp.set_Pr1174980151um_a_b)) (= (@ (@ tptp.member_nat A) (@ tptp.domain1368163076um_a_b R)) (exists ((A6 tptp.nat) (B4 tptp.sum_sum_a_b)) (and (= A A6) (@ (@ tptp.member1294585472um_a_b (@ (@ tptp.produc1808556047um_a_b A6) B4)) R))))))
% 0.26/0.70 (assert (forall ((A tptp.standard_Constant_a) (R tptp.set_Pr409224873um_a_b)) (= (@ (@ tptp.member1632892294tant_a A) (@ tptp.domain1362581744um_a_b R)) (exists ((A6 tptp.standard_Constant_a) (B4 tptp.produc1548871597um_a_b)) (and (= A A6) (@ (@ tptp.member1998628618um_a_b (@ (@ tptp.produc1697725733um_a_b A6) B4)) R))))))
% 0.26/0.70 (assert (forall ((A tptp.sum_sum_a_b) (R tptp.set_Pr1916610317um_a_b)) (= (@ (@ tptp.member_Sum_sum_a_b A) (@ tptp.domain2069673178um_a_b R)) (exists ((A6 tptp.sum_sum_a_b) (B4 tptp.sum_sum_a_b)) (and (= A A6) (@ (@ tptp.member947389014um_a_b (@ (@ tptp.produc176426981um_a_b A6) B4)) R))))))
% 0.26/0.70 (assert (forall ((A tptp.standard_Constant_a) (R tptp.set_Pr1647387645at_nat)) (=> (@ (@ tptp.member1632892294tant_a A) (@ tptp.domain1060562500at_nat R)) (not (forall ((B3 tptp.product_prod_nat_nat)) (not (@ (@ tptp.member1696759390at_nat (@ (@ tptp.produc407553657at_nat A) B3)) R)))))))
% 0.26/0.70 (assert (forall ((A tptp.nat) (R tptp.set_Pr1986765409at_nat)) (=> (@ (@ tptp.member_nat A) (@ tptp.domain_nat_nat R)) (not (forall ((B3 tptp.nat)) (not (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) B3)) R)))))))
% 0.26/0.70 (assert (forall ((A tptp.nat) (R tptp.set_Pr1174980151um_a_b)) (=> (@ (@ tptp.member_nat A) (@ tptp.domain1368163076um_a_b R)) (not (forall ((B3 tptp.sum_sum_a_b)) (not (@ (@ tptp.member1294585472um_a_b (@ (@ tptp.produc1808556047um_a_b A) B3)) R)))))))
% 0.26/0.70 (assert (forall ((A tptp.standard_Constant_a) (R tptp.set_Pr409224873um_a_b)) (=> (@ (@ tptp.member1632892294tant_a A) (@ tptp.domain1362581744um_a_b R)) (not (forall ((B3 tptp.produc1548871597um_a_b)) (not (@ (@ tptp.member1998628618um_a_b (@ (@ tptp.produc1697725733um_a_b A) B3)) R)))))))
% 0.26/0.70 (assert (forall ((A tptp.sum_sum_a_b) (R tptp.set_Pr1916610317um_a_b)) (=> (@ (@ tptp.member_Sum_sum_a_b A) (@ tptp.domain2069673178um_a_b R)) (not (forall ((B3 tptp.sum_sum_a_b)) (not (@ (@ tptp.member947389014um_a_b (@ (@ tptp.produc176426981um_a_b A) B3)) R)))))))
% 0.26/0.70 (assert (forall ((A tptp.standard_Constant_a) (R tptp.set_Pr1647387645at_nat)) (= (@ (@ tptp.member1632892294tant_a A) (@ tptp.domain1060562500at_nat R)) (exists ((Y3 tptp.product_prod_nat_nat)) (@ (@ tptp.member1696759390at_nat (@ (@ tptp.produc407553657at_nat A) Y3)) R)))))
% 0.26/0.70 (assert (forall ((A tptp.nat) (R tptp.set_Pr1986765409at_nat)) (= (@ (@ tptp.member_nat A) (@ tptp.domain_nat_nat R)) (exists ((Y3 tptp.nat)) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) Y3)) R)))))
% 0.26/0.70 (assert (forall ((A tptp.nat) (R tptp.set_Pr1174980151um_a_b)) (= (@ (@ tptp.member_nat A) (@ tptp.domain1368163076um_a_b R)) (exists ((Y3 tptp.sum_sum_a_b)) (@ (@ tptp.member1294585472um_a_b (@ (@ tptp.produc1808556047um_a_b A) Y3)) R)))))
% 0.26/0.70 (assert (forall ((A tptp.standard_Constant_a) (R tptp.set_Pr409224873um_a_b)) (= (@ (@ tptp.member1632892294tant_a A) (@ tptp.domain1362581744um_a_b R)) (exists ((Y3 tptp.produc1548871597um_a_b)) (@ (@ tptp.member1998628618um_a_b (@ (@ tptp.produc1697725733um_a_b A) Y3)) R)))))
% 0.26/0.70 (assert (forall ((A tptp.sum_sum_a_b) (R tptp.set_Pr1916610317um_a_b)) (= (@ (@ tptp.member_Sum_sum_a_b A) (@ tptp.domain2069673178um_a_b R)) (exists ((Y3 tptp.sum_sum_a_b)) (@ (@ tptp.member947389014um_a_b (@ (@ tptp.produc176426981um_a_b A) Y3)) R)))))
% 0.26/0.70 (assert (forall ((A tptp.standard_Constant_a) (R tptp.set_Pr1647387645at_nat)) (=> (@ (@ tptp.member1632892294tant_a A) (@ tptp.domain1060562500at_nat R)) (not (forall ((B3 tptp.product_prod_nat_nat)) (not (@ (@ tptp.member1696759390at_nat (@ (@ tptp.produc407553657at_nat A) B3)) R)))))))
% 0.26/0.70 (assert (forall ((A tptp.nat) (R tptp.set_Pr1986765409at_nat)) (=> (@ (@ tptp.member_nat A) (@ tptp.domain_nat_nat R)) (not (forall ((B3 tptp.nat)) (not (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) B3)) R)))))))
% 0.26/0.70 (assert (forall ((A tptp.nat) (R tptp.set_Pr1174980151um_a_b)) (=> (@ (@ tptp.member_nat A) (@ tptp.domain1368163076um_a_b R)) (not (forall ((B3 tptp.sum_sum_a_b)) (not (@ (@ tptp.member1294585472um_a_b (@ (@ tptp.produc1808556047um_a_b A) B3)) R)))))))
% 0.26/0.70 (assert (forall ((A tptp.standard_Constant_a) (R tptp.set_Pr409224873um_a_b)) (=> (@ (@ tptp.member1632892294tant_a A) (@ tptp.domain1362581744um_a_b R)) (not (forall ((B3 tptp.produc1548871597um_a_b)) (not (@ (@ tptp.member1998628618um_a_b (@ (@ tptp.produc1697725733um_a_b A) B3)) R)))))))
% 0.26/0.70 (assert (forall ((A tptp.sum_sum_a_b) (R tptp.set_Pr1916610317um_a_b)) (=> (@ (@ tptp.member_Sum_sum_a_b A) (@ tptp.domain2069673178um_a_b R)) (not (forall ((B3 tptp.sum_sum_a_b)) (not (@ (@ tptp.member947389014um_a_b (@ (@ tptp.produc176426981um_a_b A) B3)) R)))))))
% 0.26/0.70 (assert (forall ((R tptp.set_Pr1174980151um_a_b) (S tptp.set_Pr1174980151um_a_b)) (=> (@ (@ tptp.ord_le823954903um_a_b R) S) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.domain1368163076um_a_b R)) (@ tptp.domain1368163076um_a_b S)))))
% 0.26/0.70 (assert (forall ((R tptp.set_Pr409224873um_a_b) (S tptp.set_Pr409224873um_a_b)) (=> (@ (@ tptp.ord_le615126793um_a_b R) S) (@ (@ tptp.ord_le1739761029tant_a (@ tptp.domain1362581744um_a_b R)) (@ tptp.domain1362581744um_a_b S)))))
% 0.26/0.70 (assert (forall ((R tptp.set_Pr1986765409at_nat) (S tptp.set_Pr1986765409at_nat)) (=> (@ (@ tptp.ord_le841296385at_nat R) S) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.domain_nat_nat R)) (@ tptp.domain_nat_nat S)))))
% 0.26/0.70 (assert (forall ((R tptp.set_Pr1647387645at_nat) (S tptp.set_Pr1647387645at_nat)) (=> (@ (@ tptp.ord_le1909159005at_nat R) S) (@ (@ tptp.ord_le1739761029tant_a (@ tptp.domain1060562500at_nat R)) (@ tptp.domain1060562500at_nat S)))))
% 0.26/0.70 (assert (forall ((R tptp.set_Pr1916610317um_a_b) (S tptp.set_Pr1916610317um_a_b)) (=> (@ (@ tptp.ord_le1059794605um_a_b R) S) (@ (@ tptp.ord_le192794300um_a_b (@ tptp.domain2069673178um_a_b R)) (@ tptp.domain2069673178um_a_b S)))))
% 0.26/0.70 (assert (forall ((Labeled_graph tptp.labele935650037_a_nat) (Labeled_graph2 tptp.labele935650037_a_nat)) (=> (and (= (@ tptp.labele195203296_a_nat Labeled_graph) (@ tptp.labele195203296_a_nat Labeled_graph2)) (= (@ tptp.labele1810595089_a_nat Labeled_graph) (@ tptp.labele1810595089_a_nat Labeled_graph2))) (= Labeled_graph Labeled_graph2))))
% 0.26/0.70 (assert (forall ((Labeled_graph tptp.labele431970251um_a_b) (Labeled_graph2 tptp.labele431970251um_a_b)) (=> (and (= (@ tptp.labele1939049654um_a_b Labeled_graph) (@ tptp.labele1939049654um_a_b Labeled_graph2)) (= (@ tptp.labele577278695um_a_b Labeled_graph) (@ tptp.labele577278695um_a_b Labeled_graph2))) (= Labeled_graph Labeled_graph2))))
% 0.26/0.70 (assert (forall ((X1 tptp.set_Pr1647387645at_nat) (X22 tptp.set_nat)) (= (@ tptp.labele1810595089_a_nat (@ (@ tptp.labele16114835_a_nat X1) X22)) X22)))
% 0.26/0.70 (assert (forall ((X1 tptp.set_Pr409224873um_a_b) (X22 tptp.set_Sum_sum_a_b)) (= (@ tptp.labele577278695um_a_b (@ (@ tptp.labele1729654377um_a_b X1) X22)) X22)))
% 0.26/0.70 (assert (forall ((X1 tptp.set_Pr1647387645at_nat) (X22 tptp.set_nat)) (= (@ tptp.labele195203296_a_nat (@ (@ tptp.labele16114835_a_nat X1) X22)) X1)))
% 0.26/0.70 (assert (forall ((X1 tptp.set_Pr409224873um_a_b) (X22 tptp.set_Sum_sum_a_b)) (= (@ tptp.labele1939049654um_a_b (@ (@ tptp.labele1729654377um_a_b X1) X22)) X1)))
% 0.26/0.70 (assert (forall ((R tptp.set_Pr1647387645at_nat)) (= (= (@ tptp.domain1060562500at_nat R) tptp.bot_bo1160111033tant_a) (= R tptp.bot_bo810816657at_nat))))
% 0.26/0.70 (assert (forall ((R tptp.set_Pr409224873um_a_b)) (= (= (@ tptp.domain1362581744um_a_b R) tptp.bot_bo1160111033tant_a) (= R tptp.bot_bo1262634813um_a_b))))
% 0.26/0.70 (assert (forall ((R tptp.set_Pr1986765409at_nat)) (= (= (@ tptp.domain_nat_nat R) tptp.bot_bot_set_nat) (= R tptp.bot_bo2130386637at_nat))))
% 0.26/0.70 (assert (forall ((R tptp.set_Pr1174980151um_a_b)) (= (= (@ tptp.domain1368163076um_a_b R) tptp.bot_bot_set_nat) (= R tptp.bot_bo575978147um_a_b))))
% 0.26/0.70 (assert (forall ((R tptp.set_Pr1916610317um_a_b)) (= (= (@ tptp.domain2069673178um_a_b R) tptp.bot_bo1491243248um_a_b) (= R tptp.bot_bo225809273um_a_b))))
% 0.26/0.70 (assert (forall ((H1 tptp.set_Pr375490359_b_nat) (E1 tptp.set_Pr409224873um_a_b) (E2 tptp.set_Pr1647387645at_nat) (V1 tptp.sum_sum_a_b) (V12 tptp.nat) (V22 tptp.sum_sum_a_b) (V23 tptp.nat) (K tptp.standard_Constant_a)) (=> (@ (@ (@ tptp.edge_p749155930tant_a H1) E1) E2) (=> (@ (@ tptp.member1249152_b_nat (@ (@ tptp.produc522153487_b_nat V1) V12)) H1) (=> (@ (@ tptp.member1249152_b_nat (@ (@ tptp.produc522153487_b_nat V22) V23)) H1) (=> (@ (@ tptp.member1998628618um_a_b (@ (@ tptp.produc1697725733um_a_b K) (@ (@ tptp.produc176426981um_a_b V1) V22))) E1) (@ (@ tptp.member1696759390at_nat (@ (@ tptp.produc407553657at_nat K) (@ (@ tptp.product_Pair_nat_nat V12) V23))) E2)))))))
% 0.26/0.70 (assert (forall ((H1 tptp.set_Pr1986765409at_nat) (E1 tptp.set_Pr1647387645at_nat) (E2 tptp.set_Pr1647387645at_nat) (V1 tptp.nat) (V12 tptp.nat) (V22 tptp.nat) (V23 tptp.nat) (K tptp.standard_Constant_a)) (let ((_let_1 (@ tptp.produc407553657at_nat K))) (let ((_let_2 (@ tptp.product_Pair_nat_nat V1))) (=> (@ (@ (@ tptp.edge_p170421892tant_a H1) E1) E2) (=> (@ (@ tptp.member701585322at_nat (@ _let_2 V12)) H1) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat V22) V23)) H1) (=> (@ (@ tptp.member1696759390at_nat (@ _let_1 (@ _let_2 V22))) E1) (@ (@ tptp.member1696759390at_nat (@ _let_1 (@ (@ tptp.product_Pair_nat_nat V12) V23))) E2)))))))))
% 0.26/0.70 (assert (forall ((H1 tptp.set_Pr1916610317um_a_b) (E1 tptp.set_Pr409224873um_a_b) (E2 tptp.set_Pr409224873um_a_b) (V1 tptp.sum_sum_a_b) (V12 tptp.sum_sum_a_b) (V22 tptp.sum_sum_a_b) (V23 tptp.sum_sum_a_b) (K tptp.standard_Constant_a)) (let ((_let_1 (@ tptp.produc1697725733um_a_b K))) (let ((_let_2 (@ tptp.produc176426981um_a_b V1))) (=> (@ (@ (@ tptp.edge_p1871801392tant_a H1) E1) E2) (=> (@ (@ tptp.member947389014um_a_b (@ _let_2 V12)) H1) (=> (@ (@ tptp.member947389014um_a_b (@ (@ tptp.produc176426981um_a_b V22) V23)) H1) (=> (@ (@ tptp.member1998628618um_a_b (@ _let_1 (@ _let_2 V22))) E1) (@ (@ tptp.member1998628618um_a_b (@ _let_1 (@ (@ tptp.produc176426981um_a_b V12) V23))) E2)))))))))
% 0.26/0.70 (assert (forall ((H1 tptp.set_Pr1174980151um_a_b) (E1 tptp.set_Pr1647387645at_nat) (E2 tptp.set_Pr409224873um_a_b) (V1 tptp.nat) (V12 tptp.sum_sum_a_b) (V22 tptp.nat) (V23 tptp.sum_sum_a_b) (K tptp.standard_Constant_a)) (=> (@ (@ (@ tptp.edge_p1382426714tant_a H1) E1) E2) (=> (@ (@ tptp.member1294585472um_a_b (@ (@ tptp.produc1808556047um_a_b V1) V12)) H1) (=> (@ (@ tptp.member1294585472um_a_b (@ (@ tptp.produc1808556047um_a_b V22) V23)) H1) (=> (@ (@ tptp.member1696759390at_nat (@ (@ tptp.produc407553657at_nat K) (@ (@ tptp.product_Pair_nat_nat V1) V22))) E1) (@ (@ tptp.member1998628618um_a_b (@ (@ tptp.produc1697725733um_a_b K) (@ (@ tptp.produc176426981um_a_b V12) V23))) E2)))))))
% 0.26/0.70 (assert (forall ((Labeled_graph tptp.labele935650037_a_nat)) (= Labeled_graph (@ (@ tptp.labele16114835_a_nat (@ tptp.labele195203296_a_nat Labeled_graph)) (@ tptp.labele1810595089_a_nat Labeled_graph)))))
% 0.26/0.70 (assert (forall ((Labeled_graph tptp.labele431970251um_a_b)) (= Labeled_graph (@ (@ tptp.labele1729654377um_a_b (@ tptp.labele1939049654um_a_b Labeled_graph)) (@ tptp.labele577278695um_a_b Labeled_graph)))))
% 0.26/0.70 (assert (forall ((A tptp.standard_Constant_a) (A3 tptp.set_St761939237tant_a) (B tptp.standard_Constant_a)) (let ((_let_1 (@ (@ tptp.insert1909710879tant_a B) tptp.bot_bo1160111033tant_a))) (= (= (@ (@ tptp.insert1909710879tant_a A) A3) _let_1) (and (= A B) (@ (@ tptp.ord_le1739761029tant_a A3) _let_1))))))
% 0.26/0.70 (assert (forall ((A tptp.product_prod_nat_nat) (A3 tptp.set_Pr1986765409at_nat) (B tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.insert271595217at_nat B) tptp.bot_bo2130386637at_nat))) (= (= (@ (@ tptp.insert271595217at_nat A) A3) _let_1) (and (= A B) (@ (@ tptp.ord_le841296385at_nat A3) _let_1))))))
% 0.26/0.70 (assert (forall ((A tptp.produc1032616263at_nat) (A3 tptp.set_Pr1647387645at_nat) (B tptp.produc1032616263at_nat)) (let ((_let_1 (@ (@ tptp.insert1625259895at_nat B) tptp.bot_bo810816657at_nat))) (= (= (@ (@ tptp.insert1625259895at_nat A) A3) _let_1) (and (= A B) (@ (@ tptp.ord_le1909159005at_nat A3) _let_1))))))
% 0.26/0.70 (assert (forall ((A tptp.nat) (A3 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (= (= (@ (@ tptp.insert_nat A) A3) _let_1) (and (= A B) (@ (@ tptp.ord_less_eq_set_nat A3) _let_1))))))
% 0.26/0.70 (assert (forall ((A tptp.produc1124793815um_a_b) (A3 tptp.set_Pr1174980151um_a_b) (B tptp.produc1124793815um_a_b)) (let ((_let_1 (@ (@ tptp.insert983991207um_a_b B) tptp.bot_bo575978147um_a_b))) (= (= (@ (@ tptp.insert983991207um_a_b A) A3) _let_1) (and (= A B) (@ (@ tptp.ord_le823954903um_a_b A3) _let_1))))))
% 0.26/0.70 (assert (forall ((A tptp.produc1548871597um_a_b) (A3 tptp.set_Pr1916610317um_a_b) (B tptp.produc1548871597um_a_b)) (let ((_let_1 (@ (@ tptp.insert1435405693um_a_b B) tptp.bot_bo225809273um_a_b))) (= (= (@ (@ tptp.insert1435405693um_a_b A) A3) _let_1) (and (= A B) (@ (@ tptp.ord_le1059794605um_a_b A3) _let_1))))))
% 0.26/0.70 (assert (forall ((A tptp.produc1963079155um_a_b) (A3 tptp.set_Pr409224873um_a_b) (B tptp.produc1963079155um_a_b)) (let ((_let_1 (@ (@ tptp.insert323157027um_a_b B) tptp.bot_bo1262634813um_a_b))) (= (= (@ (@ tptp.insert323157027um_a_b A) A3) _let_1) (and (= A B) (@ (@ tptp.ord_le615126793um_a_b A3) _let_1))))))
% 0.26/0.70 (assert (forall ((A tptp.sum_sum_a_b) (A3 tptp.set_Sum_sum_a_b) (B tptp.sum_sum_a_b)) (let ((_let_1 (@ (@ tptp.insert_Sum_sum_a_b B) tptp.bot_bo1491243248um_a_b))) (= (= (@ (@ tptp.insert_Sum_sum_a_b A) A3) _let_1) (and (= A B) (@ (@ tptp.ord_le192794300um_a_b A3) _let_1))))))
% 0.26/0.70 (assert (forall ((B tptp.standard_Constant_a) (A tptp.standard_Constant_a) (A3 tptp.set_St761939237tant_a)) (let ((_let_1 (@ (@ tptp.insert1909710879tant_a B) tptp.bot_bo1160111033tant_a))) (= (= _let_1 (@ (@ tptp.insert1909710879tant_a A) A3)) (and (= A B) (@ (@ tptp.ord_le1739761029tant_a A3) _let_1))))))
% 0.26/0.70 (assert (forall ((B tptp.product_prod_nat_nat) (A tptp.product_prod_nat_nat) (A3 tptp.set_Pr1986765409at_nat)) (let ((_let_1 (@ (@ tptp.insert271595217at_nat B) tptp.bot_bo2130386637at_nat))) (= (= _let_1 (@ (@ tptp.insert271595217at_nat A) A3)) (and (= A B) (@ (@ tptp.ord_le841296385at_nat A3) _let_1))))))
% 0.26/0.70 (assert (forall ((B tptp.produc1032616263at_nat) (A tptp.produc1032616263at_nat) (A3 tptp.set_Pr1647387645at_nat)) (let ((_let_1 (@ (@ tptp.insert1625259895at_nat B) tptp.bot_bo810816657at_nat))) (= (= _let_1 (@ (@ tptp.insert1625259895at_nat A) A3)) (and (= A B) (@ (@ tptp.ord_le1909159005at_nat A3) _let_1))))))
% 0.26/0.70 (assert (forall ((B tptp.nat) (A tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (= (= _let_1 (@ (@ tptp.insert_nat A) A3)) (and (= A B) (@ (@ tptp.ord_less_eq_set_nat A3) _let_1))))))
% 0.26/0.70 (assert (forall ((B tptp.produc1124793815um_a_b) (A tptp.produc1124793815um_a_b) (A3 tptp.set_Pr1174980151um_a_b)) (let ((_let_1 (@ (@ tptp.insert983991207um_a_b B) tptp.bot_bo575978147um_a_b))) (= (= _let_1 (@ (@ tptp.insert983991207um_a_b A) A3)) (and (= A B) (@ (@ tptp.ord_le823954903um_a_b A3) _let_1))))))
% 0.26/0.70 (assert (forall ((B tptp.produc1548871597um_a_b) (A tptp.produc1548871597um_a_b) (A3 tptp.set_Pr1916610317um_a_b)) (let ((_let_1 (@ (@ tptp.insert1435405693um_a_b B) tptp.bot_bo225809273um_a_b))) (= (= _let_1 (@ (@ tptp.insert1435405693um_a_b A) A3)) (and (= A B) (@ (@ tptp.ord_le1059794605um_a_b A3) _let_1))))))
% 0.26/0.70 (assert (forall ((B tptp.produc1963079155um_a_b) (A tptp.produc1963079155um_a_b) (A3 tptp.set_Pr409224873um_a_b)) (let ((_let_1 (@ (@ tptp.insert323157027um_a_b B) tptp.bot_bo1262634813um_a_b))) (= (= _let_1 (@ (@ tptp.insert323157027um_a_b A) A3)) (and (= A B) (@ (@ tptp.ord_le615126793um_a_b A3) _let_1))))))
% 0.26/0.70 (assert (forall ((B tptp.sum_sum_a_b) (A tptp.sum_sum_a_b) (A3 tptp.set_Sum_sum_a_b)) (let ((_let_1 (@ (@ tptp.insert_Sum_sum_a_b B) tptp.bot_bo1491243248um_a_b))) (= (= _let_1 (@ (@ tptp.insert_Sum_sum_a_b A) A3)) (and (= A B) (@ (@ tptp.ord_le192794300um_a_b A3) _let_1))))))
% 0.26/0.70 (assert (@ tptp.unival860567212at_nat tptp.bot_bo810816657at_nat))
% 0.26/0.70 (assert (@ tptp.unival118648434um_a_b tptp.bot_bo225809273um_a_b))
% 0.26/0.70 (assert (@ tptp.unival1487587672um_a_b tptp.bot_bo1262634813um_a_b))
% 0.26/0.70 (assert (@ tptp.unival2092813468um_a_b tptp.bot_bo575978147um_a_b))
% 0.26/0.70 (assert (forall ((A tptp.sum_sum_a_b) (P (-> tptp.sum_sum_a_b Bool))) (= (@ (@ tptp.member_Sum_sum_a_b A) (@ tptp.collect_Sum_sum_a_b P)) (@ P A))))
% 0.26/0.70 (assert (forall ((A tptp.produc1124793815um_a_b) (P (-> tptp.produc1124793815um_a_b Bool))) (= (@ (@ tptp.member1294585472um_a_b A) (@ tptp.collec492052930um_a_b P)) (@ P A))))
% 0.26/0.70 (assert (forall ((A tptp.produc1963079155um_a_b) (P (-> tptp.produc1963079155um_a_b Bool))) (= (@ (@ tptp.member1998628618um_a_b A) (@ tptp.collec1254333256um_a_b P)) (@ P A))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Sum_sum_a_b)) (= (@ tptp.collect_Sum_sum_a_b (lambda ((X3 tptp.sum_sum_a_b)) (@ (@ tptp.member_Sum_sum_a_b X3) A3))) A3)))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr1174980151um_a_b)) (= (@ tptp.collec492052930um_a_b (lambda ((X3 tptp.produc1124793815um_a_b)) (@ (@ tptp.member1294585472um_a_b X3) A3))) A3)))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr409224873um_a_b)) (= (@ tptp.collec1254333256um_a_b (lambda ((X3 tptp.produc1963079155um_a_b)) (@ (@ tptp.member1998628618um_a_b X3) A3))) A3)))
% 0.26/0.70 (assert (forall ((X2 tptp.produc1032616263at_nat) (A3 tptp.set_Pr1647387645at_nat) (B5 tptp.set_Pr1647387645at_nat)) (= (@ (@ tptp.ord_le1909159005at_nat (@ (@ tptp.insert1625259895at_nat X2) A3)) B5) (and (@ (@ tptp.member1696759390at_nat X2) B5) (@ (@ tptp.ord_le1909159005at_nat A3) B5)))))
% 0.26/0.70 (assert (forall ((X2 tptp.nat) (A3 tptp.set_nat) (B5 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat X2) A3)) B5) (and (@ (@ tptp.member_nat X2) B5) (@ (@ tptp.ord_less_eq_set_nat A3) B5)))))
% 0.26/0.70 (assert (forall ((X2 tptp.produc1548871597um_a_b) (A3 tptp.set_Pr1916610317um_a_b) (B5 tptp.set_Pr1916610317um_a_b)) (= (@ (@ tptp.ord_le1059794605um_a_b (@ (@ tptp.insert1435405693um_a_b X2) A3)) B5) (and (@ (@ tptp.member947389014um_a_b X2) B5) (@ (@ tptp.ord_le1059794605um_a_b A3) B5)))))
% 0.26/0.70 (assert (forall ((X2 tptp.standard_Constant_a) (A3 tptp.set_St761939237tant_a) (B5 tptp.set_St761939237tant_a)) (= (@ (@ tptp.ord_le1739761029tant_a (@ (@ tptp.insert1909710879tant_a X2) A3)) B5) (and (@ (@ tptp.member1632892294tant_a X2) B5) (@ (@ tptp.ord_le1739761029tant_a A3) B5)))))
% 0.26/0.70 (assert (forall ((X2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1986765409at_nat) (B5 tptp.set_Pr1986765409at_nat)) (= (@ (@ tptp.ord_le841296385at_nat (@ (@ tptp.insert271595217at_nat X2) A3)) B5) (and (@ (@ tptp.member701585322at_nat X2) B5) (@ (@ tptp.ord_le841296385at_nat A3) B5)))))
% 0.26/0.70 (assert (forall ((X2 tptp.produc1124793815um_a_b) (A3 tptp.set_Pr1174980151um_a_b) (B5 tptp.set_Pr1174980151um_a_b)) (= (@ (@ tptp.ord_le823954903um_a_b (@ (@ tptp.insert983991207um_a_b X2) A3)) B5) (and (@ (@ tptp.member1294585472um_a_b X2) B5) (@ (@ tptp.ord_le823954903um_a_b A3) B5)))))
% 0.26/0.70 (assert (forall ((X2 tptp.produc1963079155um_a_b) (A3 tptp.set_Pr409224873um_a_b) (B5 tptp.set_Pr409224873um_a_b)) (= (@ (@ tptp.ord_le615126793um_a_b (@ (@ tptp.insert323157027um_a_b X2) A3)) B5) (and (@ (@ tptp.member1998628618um_a_b X2) B5) (@ (@ tptp.ord_le615126793um_a_b A3) B5)))))
% 0.26/0.70 (assert (forall ((X2 tptp.sum_sum_a_b) (A3 tptp.set_Sum_sum_a_b) (B5 tptp.set_Sum_sum_a_b)) (= (@ (@ tptp.ord_le192794300um_a_b (@ (@ tptp.insert_Sum_sum_a_b X2) A3)) B5) (and (@ (@ tptp.member_Sum_sum_a_b X2) B5) (@ (@ tptp.ord_le192794300um_a_b A3) B5)))))
% 0.26/0.70 (assert (forall ((A tptp.standard_Constant_a)) (@ (@ tptp.member1632892294tant_a A) (@ (@ tptp.insert1909710879tant_a A) tptp.bot_bo1160111033tant_a))))
% 0.26/0.70 (assert (forall ((A tptp.product_prod_nat_nat)) (@ (@ tptp.member701585322at_nat A) (@ (@ tptp.insert271595217at_nat A) tptp.bot_bo2130386637at_nat))))
% 0.26/0.70 (assert (forall ((A tptp.produc1032616263at_nat)) (@ (@ tptp.member1696759390at_nat A) (@ (@ tptp.insert1625259895at_nat A) tptp.bot_bo810816657at_nat))))
% 0.26/0.70 (assert (forall ((A tptp.nat)) (@ (@ tptp.member_nat A) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))
% 0.26/0.70 (assert (forall ((A tptp.produc1124793815um_a_b)) (@ (@ tptp.member1294585472um_a_b A) (@ (@ tptp.insert983991207um_a_b A) tptp.bot_bo575978147um_a_b))))
% 0.26/0.70 (assert (forall ((A tptp.produc1548871597um_a_b)) (@ (@ tptp.member947389014um_a_b A) (@ (@ tptp.insert1435405693um_a_b A) tptp.bot_bo225809273um_a_b))))
% 0.26/0.70 (assert (forall ((A tptp.produc1963079155um_a_b)) (@ (@ tptp.member1998628618um_a_b A) (@ (@ tptp.insert323157027um_a_b A) tptp.bot_bo1262634813um_a_b))))
% 0.26/0.70 (assert (forall ((A tptp.sum_sum_a_b)) (@ (@ tptp.member_Sum_sum_a_b A) (@ (@ tptp.insert_Sum_sum_a_b A) tptp.bot_bo1491243248um_a_b))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr1647387645at_nat)) (@ (@ tptp.ord_le1909159005at_nat tptp.bot_bo810816657at_nat) A3)))
% 0.26/0.70 (assert (forall ((A3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A3)))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr1174980151um_a_b)) (@ (@ tptp.ord_le823954903um_a_b tptp.bot_bo575978147um_a_b) A3)))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr1916610317um_a_b)) (@ (@ tptp.ord_le1059794605um_a_b tptp.bot_bo225809273um_a_b) A3)))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr409224873um_a_b)) (@ (@ tptp.ord_le615126793um_a_b tptp.bot_bo1262634813um_a_b) A3)))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Sum_sum_a_b)) (@ (@ tptp.ord_le192794300um_a_b tptp.bot_bo1491243248um_a_b) A3)))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr1647387645at_nat)) (= (@ (@ tptp.ord_le1909159005at_nat A3) tptp.bot_bo810816657at_nat) (= A3 tptp.bot_bo810816657at_nat))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A3) tptp.bot_bot_set_nat) (= A3 tptp.bot_bot_set_nat))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr1174980151um_a_b)) (= (@ (@ tptp.ord_le823954903um_a_b A3) tptp.bot_bo575978147um_a_b) (= A3 tptp.bot_bo575978147um_a_b))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr1916610317um_a_b)) (= (@ (@ tptp.ord_le1059794605um_a_b A3) tptp.bot_bo225809273um_a_b) (= A3 tptp.bot_bo225809273um_a_b))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr409224873um_a_b)) (= (@ (@ tptp.ord_le615126793um_a_b A3) tptp.bot_bo1262634813um_a_b) (= A3 tptp.bot_bo1262634813um_a_b))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Sum_sum_a_b)) (= (@ (@ tptp.ord_le192794300um_a_b A3) tptp.bot_bo1491243248um_a_b) (= A3 tptp.bot_bo1491243248um_a_b))))
% 0.26/0.70 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 0.26/0.70 (assert (= tptp.standa63370785tant_a (lambda ((T tptp.standard_Constant_a)) (let ((_let_1 (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (@ (@ tptp.produc1676969687_a_nat (@ (@ tptp.labele16114835_a_nat tptp.bot_bo810816657at_nat) _let_1)) (@ (@ tptp.labele16114835_a_nat (@ (@ tptp.insert1625259895at_nat (@ (@ tptp.produc407553657at_nat T) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))) tptp.bot_bo810816657at_nat)) _let_1))))))
% 0.26/0.70 (assert (let ((_let_1 (@ tptp.labele16114835_a_nat tptp.bot_bo810816657at_nat))) (= tptp.standa1410829644tant_a (@ (@ tptp.produc1676969687_a_nat (@ _let_1 tptp.bot_bot_set_nat)) (@ _let_1 (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))))))
% 0.26/0.70 (assert (forall ((C tptp.produc1032616263at_nat)) (not (@ (@ tptp.member1696759390at_nat C) tptp.bot_bo810816657at_nat))))
% 0.26/0.70 (assert (forall ((C tptp.nat)) (not (@ (@ tptp.member_nat C) tptp.bot_bot_set_nat))))
% 0.26/0.70 (assert (forall ((C tptp.produc1124793815um_a_b)) (not (@ (@ tptp.member1294585472um_a_b C) tptp.bot_bo575978147um_a_b))))
% 0.26/0.70 (assert (forall ((C tptp.produc1548871597um_a_b)) (not (@ (@ tptp.member947389014um_a_b C) tptp.bot_bo225809273um_a_b))))
% 0.26/0.70 (assert (forall ((C tptp.produc1963079155um_a_b)) (not (@ (@ tptp.member1998628618um_a_b C) tptp.bot_bo1262634813um_a_b))))
% 0.26/0.70 (assert (forall ((C tptp.sum_sum_a_b)) (not (@ (@ tptp.member_Sum_sum_a_b C) tptp.bot_bo1491243248um_a_b))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr1647387645at_nat)) (= (forall ((X3 tptp.produc1032616263at_nat)) (not (@ (@ tptp.member1696759390at_nat X3) A3))) (= A3 tptp.bot_bo810816657at_nat))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_nat)) (= (forall ((X3 tptp.nat)) (not (@ (@ tptp.member_nat X3) A3))) (= A3 tptp.bot_bot_set_nat))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr1174980151um_a_b)) (= (forall ((X3 tptp.produc1124793815um_a_b)) (not (@ (@ tptp.member1294585472um_a_b X3) A3))) (= A3 tptp.bot_bo575978147um_a_b))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr1916610317um_a_b)) (= (forall ((X3 tptp.produc1548871597um_a_b)) (not (@ (@ tptp.member947389014um_a_b X3) A3))) (= A3 tptp.bot_bo225809273um_a_b))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr409224873um_a_b)) (= (forall ((X3 tptp.produc1963079155um_a_b)) (not (@ (@ tptp.member1998628618um_a_b X3) A3))) (= A3 tptp.bot_bo1262634813um_a_b))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Sum_sum_a_b)) (= (forall ((X3 tptp.sum_sum_a_b)) (not (@ (@ tptp.member_Sum_sum_a_b X3) A3))) (= A3 tptp.bot_bo1491243248um_a_b))))
% 0.26/0.70 (assert (forall ((P (-> tptp.produc1032616263at_nat Bool))) (= (= (@ tptp.collec52779676at_nat P) tptp.bot_bo810816657at_nat) (forall ((X3 tptp.produc1032616263at_nat)) (not (@ P X3))))))
% 0.26/0.70 (assert (forall ((P (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P) tptp.bot_bot_set_nat) (forall ((X3 tptp.nat)) (not (@ P X3))))))
% 0.26/0.70 (assert (forall ((P (-> tptp.produc1124793815um_a_b Bool))) (= (= (@ tptp.collec492052930um_a_b P) tptp.bot_bo575978147um_a_b) (forall ((X3 tptp.produc1124793815um_a_b)) (not (@ P X3))))))
% 0.26/0.70 (assert (forall ((P (-> tptp.produc1548871597um_a_b Bool))) (= (= (@ tptp.collec1769032088um_a_b P) tptp.bot_bo225809273um_a_b) (forall ((X3 tptp.produc1548871597um_a_b)) (not (@ P X3))))))
% 0.26/0.70 (assert (forall ((P (-> tptp.produc1963079155um_a_b Bool))) (= (= (@ tptp.collec1254333256um_a_b P) tptp.bot_bo1262634813um_a_b) (forall ((X3 tptp.produc1963079155um_a_b)) (not (@ P X3))))))
% 0.26/0.70 (assert (forall ((P (-> tptp.sum_sum_a_b Bool))) (= (= (@ tptp.collect_Sum_sum_a_b P) tptp.bot_bo1491243248um_a_b) (forall ((X3 tptp.sum_sum_a_b)) (not (@ P X3))))))
% 0.26/0.70 (assert (forall ((P (-> tptp.produc1032616263at_nat Bool))) (= (= tptp.bot_bo810816657at_nat (@ tptp.collec52779676at_nat P)) (forall ((X3 tptp.produc1032616263at_nat)) (not (@ P X3))))))
% 0.26/0.70 (assert (forall ((P (-> tptp.nat Bool))) (= (= tptp.bot_bot_set_nat (@ tptp.collect_nat P)) (forall ((X3 tptp.nat)) (not (@ P X3))))))
% 0.26/0.70 (assert (forall ((P (-> tptp.produc1124793815um_a_b Bool))) (= (= tptp.bot_bo575978147um_a_b (@ tptp.collec492052930um_a_b P)) (forall ((X3 tptp.produc1124793815um_a_b)) (not (@ P X3))))))
% 0.26/0.70 (assert (forall ((P (-> tptp.produc1548871597um_a_b Bool))) (= (= tptp.bot_bo225809273um_a_b (@ tptp.collec1769032088um_a_b P)) (forall ((X3 tptp.produc1548871597um_a_b)) (not (@ P X3))))))
% 0.26/0.70 (assert (forall ((P (-> tptp.produc1963079155um_a_b Bool))) (= (= tptp.bot_bo1262634813um_a_b (@ tptp.collec1254333256um_a_b P)) (forall ((X3 tptp.produc1963079155um_a_b)) (not (@ P X3))))))
% 0.26/0.70 (assert (forall ((P (-> tptp.sum_sum_a_b Bool))) (= (= tptp.bot_bo1491243248um_a_b (@ tptp.collect_Sum_sum_a_b P)) (forall ((X3 tptp.sum_sum_a_b)) (not (@ P X3))))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr1174980151um_a_b) (B5 tptp.set_Pr1174980151um_a_b)) (=> (forall ((X4 tptp.produc1124793815um_a_b)) (let ((_let_1 (@ tptp.member1294585472um_a_b X4))) (=> (@ _let_1 A3) (@ _let_1 B5)))) (@ (@ tptp.ord_le823954903um_a_b A3) B5))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr409224873um_a_b) (B5 tptp.set_Pr409224873um_a_b)) (=> (forall ((X4 tptp.produc1963079155um_a_b)) (let ((_let_1 (@ tptp.member1998628618um_a_b X4))) (=> (@ _let_1 A3) (@ _let_1 B5)))) (@ (@ tptp.ord_le615126793um_a_b A3) B5))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Sum_sum_a_b) (B5 tptp.set_Sum_sum_a_b)) (=> (forall ((X4 tptp.sum_sum_a_b)) (let ((_let_1 (@ tptp.member_Sum_sum_a_b X4))) (=> (@ _let_1 A3) (@ _let_1 B5)))) (@ (@ tptp.ord_le192794300um_a_b A3) B5))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Sum_sum_a_b) (B5 tptp.set_Sum_sum_a_b)) (=> (@ (@ tptp.ord_le192794300um_a_b A3) B5) (=> (@ (@ tptp.ord_le192794300um_a_b B5) A3) (= A3 B5)))))
% 0.26/0.70 (assert (forall ((A tptp.produc1032616263at_nat) (B5 tptp.set_Pr1647387645at_nat) (B tptp.produc1032616263at_nat)) (let ((_let_1 (@ tptp.member1696759390at_nat A))) (=> (=> (not (@ _let_1 B5)) (= A B)) (@ _let_1 (@ (@ tptp.insert1625259895at_nat B) B5))))))
% 0.26/0.70 (assert (forall ((A tptp.nat) (B5 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ tptp.member_nat A))) (=> (=> (not (@ _let_1 B5)) (= A B)) (@ _let_1 (@ (@ tptp.insert_nat B) B5))))))
% 0.26/0.70 (assert (forall ((A tptp.produc1548871597um_a_b) (B5 tptp.set_Pr1916610317um_a_b) (B tptp.produc1548871597um_a_b)) (let ((_let_1 (@ tptp.member947389014um_a_b A))) (=> (=> (not (@ _let_1 B5)) (= A B)) (@ _let_1 (@ (@ tptp.insert1435405693um_a_b B) B5))))))
% 0.26/0.70 (assert (forall ((A tptp.standard_Constant_a) (B5 tptp.set_St761939237tant_a) (B tptp.standard_Constant_a)) (let ((_let_1 (@ tptp.member1632892294tant_a A))) (=> (=> (not (@ _let_1 B5)) (= A B)) (@ _let_1 (@ (@ tptp.insert1909710879tant_a B) B5))))))
% 0.26/0.70 (assert (forall ((A tptp.product_prod_nat_nat) (B5 tptp.set_Pr1986765409at_nat) (B tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member701585322at_nat A))) (=> (=> (not (@ _let_1 B5)) (= A B)) (@ _let_1 (@ (@ tptp.insert271595217at_nat B) B5))))))
% 0.26/0.70 (assert (forall ((A tptp.sum_sum_a_b) (B5 tptp.set_Sum_sum_a_b) (B tptp.sum_sum_a_b)) (let ((_let_1 (@ tptp.member_Sum_sum_a_b A))) (=> (=> (not (@ _let_1 B5)) (= A B)) (@ _let_1 (@ (@ tptp.insert_Sum_sum_a_b B) B5))))))
% 0.26/0.70 (assert (forall ((A tptp.produc1124793815um_a_b) (B5 tptp.set_Pr1174980151um_a_b) (B tptp.produc1124793815um_a_b)) (let ((_let_1 (@ tptp.member1294585472um_a_b A))) (=> (=> (not (@ _let_1 B5)) (= A B)) (@ _let_1 (@ (@ tptp.insert983991207um_a_b B) B5))))))
% 0.26/0.70 (assert (forall ((A tptp.produc1963079155um_a_b) (B5 tptp.set_Pr409224873um_a_b) (B tptp.produc1963079155um_a_b)) (let ((_let_1 (@ tptp.member1998628618um_a_b A))) (=> (=> (not (@ _let_1 B5)) (= A B)) (@ _let_1 (@ (@ tptp.insert323157027um_a_b B) B5))))))
% 0.26/0.70 (assert (forall ((A tptp.produc1032616263at_nat) (B tptp.produc1032616263at_nat) (A3 tptp.set_Pr1647387645at_nat)) (let ((_let_1 (@ tptp.member1696759390at_nat A))) (= (@ _let_1 (@ (@ tptp.insert1625259895at_nat B) A3)) (or (= A B) (@ _let_1 A3))))))
% 0.26/0.70 (assert (forall ((A tptp.nat) (B tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A))) (= (@ _let_1 (@ (@ tptp.insert_nat B) A3)) (or (= A B) (@ _let_1 A3))))))
% 0.26/0.70 (assert (forall ((A tptp.produc1548871597um_a_b) (B tptp.produc1548871597um_a_b) (A3 tptp.set_Pr1916610317um_a_b)) (let ((_let_1 (@ tptp.member947389014um_a_b A))) (= (@ _let_1 (@ (@ tptp.insert1435405693um_a_b B) A3)) (or (= A B) (@ _let_1 A3))))))
% 0.26/0.70 (assert (forall ((A tptp.standard_Constant_a) (B tptp.standard_Constant_a) (A3 tptp.set_St761939237tant_a)) (let ((_let_1 (@ tptp.member1632892294tant_a A))) (= (@ _let_1 (@ (@ tptp.insert1909710879tant_a B) A3)) (or (= A B) (@ _let_1 A3))))))
% 0.26/0.70 (assert (forall ((A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat) (A3 tptp.set_Pr1986765409at_nat)) (let ((_let_1 (@ tptp.member701585322at_nat A))) (= (@ _let_1 (@ (@ tptp.insert271595217at_nat B) A3)) (or (= A B) (@ _let_1 A3))))))
% 0.26/0.70 (assert (forall ((A tptp.sum_sum_a_b) (B tptp.sum_sum_a_b) (A3 tptp.set_Sum_sum_a_b)) (let ((_let_1 (@ tptp.member_Sum_sum_a_b A))) (= (@ _let_1 (@ (@ tptp.insert_Sum_sum_a_b B) A3)) (or (= A B) (@ _let_1 A3))))))
% 0.26/0.70 (assert (forall ((A tptp.produc1124793815um_a_b) (B tptp.produc1124793815um_a_b) (A3 tptp.set_Pr1174980151um_a_b)) (let ((_let_1 (@ tptp.member1294585472um_a_b A))) (= (@ _let_1 (@ (@ tptp.insert983991207um_a_b B) A3)) (or (= A B) (@ _let_1 A3))))))
% 0.26/0.70 (assert (forall ((A tptp.produc1963079155um_a_b) (B tptp.produc1963079155um_a_b) (A3 tptp.set_Pr409224873um_a_b)) (let ((_let_1 (@ tptp.member1998628618um_a_b A))) (= (@ _let_1 (@ (@ tptp.insert323157027um_a_b B) A3)) (or (= A B) (@ _let_1 A3))))))
% 0.26/0.70 (assert (forall ((X2 tptp.produc1032616263at_nat) (A3 tptp.set_Pr1647387645at_nat)) (let ((_let_1 (@ tptp.insert1625259895at_nat X2))) (let ((_let_2 (@ _let_1 A3))) (= (@ _let_1 _let_2) _let_2)))))
% 0.26/0.70 (assert (forall ((X2 tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X2))) (let ((_let_2 (@ _let_1 A3))) (= (@ _let_1 _let_2) _let_2)))))
% 0.26/0.70 (assert (forall ((X2 tptp.produc1124793815um_a_b) (A3 tptp.set_Pr1174980151um_a_b)) (let ((_let_1 (@ tptp.insert983991207um_a_b X2))) (let ((_let_2 (@ _let_1 A3))) (= (@ _let_1 _let_2) _let_2)))))
% 0.26/0.70 (assert (forall ((X2 tptp.produc1963079155um_a_b) (A3 tptp.set_Pr409224873um_a_b)) (let ((_let_1 (@ tptp.insert323157027um_a_b X2))) (let ((_let_2 (@ _let_1 A3))) (= (@ _let_1 _let_2) _let_2)))))
% 0.26/0.70 (assert (forall ((X2 tptp.sum_sum_a_b) (A3 tptp.set_Sum_sum_a_b)) (let ((_let_1 (@ tptp.insert_Sum_sum_a_b X2))) (let ((_let_2 (@ _let_1 A3))) (= (@ _let_1 _let_2) _let_2)))))
% 0.26/0.70 (assert (forall ((X2 tptp.produc1548871597um_a_b) (A3 tptp.set_Pr1916610317um_a_b)) (let ((_let_1 (@ tptp.insert1435405693um_a_b X2))) (let ((_let_2 (@ _let_1 A3))) (= (@ _let_1 _let_2) _let_2)))))
% 0.26/0.70 (assert (forall ((X2 tptp.standard_Constant_a) (A3 tptp.set_St761939237tant_a)) (let ((_let_1 (@ tptp.insert1909710879tant_a X2))) (let ((_let_2 (@ _let_1 A3))) (= (@ _let_1 _let_2) _let_2)))))
% 0.26/0.70 (assert (forall ((X2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1986765409at_nat)) (let ((_let_1 (@ tptp.insert271595217at_nat X2))) (let ((_let_2 (@ _let_1 A3))) (= (@ _let_1 _let_2) _let_2)))))
% 0.26/0.70 (assert (forall ((G tptp.labele935650037_a_nat) (F tptp.set_Pr1986765409at_nat)) (= (@ (@ (@ tptp.graph_2130075512at_nat (@ (@ tptp.labele16114835_a_nat tptp.bot_bo810816657at_nat) tptp.bot_bot_set_nat)) G) F) (and (= F tptp.bot_bo2130386637at_nat) (= G (@ tptp.restri572569417_a_nat G))))))
% 0.26/0.70 (assert (forall ((G tptp.labele935650037_a_nat) (F tptp.set_Pr375490359_b_nat)) (= (@ (@ (@ tptp.graph_165730638_b_nat (@ (@ tptp.labele1729654377um_a_b tptp.bot_bo1262634813um_a_b) tptp.bot_bo1491243248um_a_b)) G) F) (and (= F tptp.bot_bo1923972003_b_nat) (= G (@ tptp.restri572569417_a_nat G))))))
% 0.26/0.70 (assert (forall ((G tptp.labele431970251um_a_b) (F tptp.set_Pr1174980151um_a_b)) (= (@ (@ (@ tptp.graph_1452133198um_a_b (@ (@ tptp.labele16114835_a_nat tptp.bot_bo810816657at_nat) tptp.bot_bot_set_nat)) G) F) (and (= F tptp.bot_bo575978147um_a_b) (= G (@ tptp.restri1162247455um_a_b G))))))
% 0.26/0.70 (assert (forall ((G tptp.labele935650037_a_nat) (F tptp.set_Pr1902304780_b_nat)) (= (@ (@ (@ tptp.graph_1203757137_b_nat (@ (@ tptp.labele2034032468um_a_b tptp.bot_bo1208513655um_a_b) tptp.bot_bo575978147um_a_b)) G) F) (and (= F tptp.bot_bo949957280_b_nat) (= G (@ tptp.restri572569417_a_nat G))))))
% 0.26/0.70 (assert (forall ((G tptp.labele431970251um_a_b) (F tptp.set_Pr1916610317um_a_b)) (= (@ (@ (@ tptp.graph_611893540um_a_b (@ (@ tptp.labele1729654377um_a_b tptp.bot_bo1262634813um_a_b) tptp.bot_bo1491243248um_a_b)) G) F) (and (= F tptp.bot_bo225809273um_a_b) (= G (@ tptp.restri1162247455um_a_b G))))))
% 0.26/0.70 (assert (forall ((G tptp.labele935650037_a_nat) (F tptp.set_Pr689416536at_nat)) (= (@ (@ (@ tptp.graph_149544303at_nat (@ (@ tptp.labele1813985418at_nat tptp.bot_bo1524397311at_nat) tptp.bot_bo810816657at_nat)) G) F) (and (= F tptp.bot_bo1582968772at_nat) (= G (@ tptp.restri572569417_a_nat G))))))
% 0.26/0.70 (assert (forall ((G tptp.labele431970251um_a_b) (F tptp.set_Pr653770722um_a_b)) (= (@ (@ (@ tptp.graph_502887975um_a_b (@ (@ tptp.labele2034032468um_a_b tptp.bot_bo1208513655um_a_b) tptp.bot_bo575978147um_a_b)) G) F) (and (= F tptp.bot_bo1892785270um_a_b) (= G (@ tptp.restri1162247455um_a_b G))))))
% 0.26/0.70 (assert (forall ((G tptp.labele935650037_a_nat) (F tptp.set_Pr507214050_b_nat)) (= (@ (@ (@ tptp.graph_1815313447_b_nat (@ (@ tptp.labele989994um_a_b tptp.bot_bo1262778871um_a_b) tptp.bot_bo225809273um_a_b)) G) F) (and (= F tptp.bot_bo1746228598_b_nat) (= G (@ tptp.restri572569417_a_nat G))))))
% 0.26/0.70 (assert (forall ((G tptp.labele431970251um_a_b) (F tptp.set_Pr304595758um_a_b)) (= (@ (@ (@ tptp.graph_166346565um_a_b (@ (@ tptp.labele1813985418at_nat tptp.bot_bo1524397311at_nat) tptp.bot_bo810816657at_nat)) G) F) (and (= F tptp.bot_bo627753370um_a_b) (= G (@ tptp.restri1162247455um_a_b G))))))
% 0.26/0.70 (assert (forall ((G tptp.labele431970251um_a_b) (F tptp.set_Pr55236280um_a_b)) (= (@ (@ (@ tptp.graph_1763806717um_a_b (@ (@ tptp.labele989994um_a_b tptp.bot_bo1262778871um_a_b) tptp.bot_bo225809273um_a_b)) G) F) (and (= F tptp.bot_bo1217542988um_a_b) (= G (@ tptp.restri1162247455um_a_b G))))))
% 0.26/0.70 (assert (forall ((R_1 tptp.set_Pr1174980151um_a_b) (R_2 tptp.set_Pr1174980151um_a_b) (E_1 tptp.set_Pr1647387645at_nat) (E_2 tptp.set_Pr1647387645at_nat) (G tptp.set_Pr409224873um_a_b)) (=> (@ (@ tptp.ord_le823954903um_a_b R_1) R_2) (=> (@ (@ tptp.ord_le1909159005at_nat E_1) E_2) (=> (@ (@ (@ tptp.edge_p1382426714tant_a R_2) E_2) G) (@ (@ (@ tptp.edge_p1382426714tant_a R_1) E_1) G))))))
% 0.26/0.70 (assert (forall ((R tptp.set_Pr1647387645at_nat) (S tptp.set_Pr1647387645at_nat)) (=> (forall ((X4 tptp.standard_Constant_a) (Y4 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member1696759390at_nat (@ (@ tptp.produc407553657at_nat X4) Y4)))) (=> (@ _let_1 R) (@ _let_1 S)))) (@ (@ tptp.ord_le1909159005at_nat R) S))))
% 0.26/0.70 (assert (forall ((R tptp.set_Pr1986765409at_nat) (S tptp.set_Pr1986765409at_nat)) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y4)))) (=> (@ _let_1 R) (@ _let_1 S)))) (@ (@ tptp.ord_le841296385at_nat R) S))))
% 0.26/0.70 (assert (forall ((R tptp.set_Pr1174980151um_a_b) (S tptp.set_Pr1174980151um_a_b)) (=> (forall ((X4 tptp.nat) (Y4 tptp.sum_sum_a_b)) (let ((_let_1 (@ tptp.member1294585472um_a_b (@ (@ tptp.produc1808556047um_a_b X4) Y4)))) (=> (@ _let_1 R) (@ _let_1 S)))) (@ (@ tptp.ord_le823954903um_a_b R) S))))
% 0.26/0.70 (assert (forall ((R tptp.set_Pr409224873um_a_b) (S tptp.set_Pr409224873um_a_b)) (=> (forall ((X4 tptp.standard_Constant_a) (Y4 tptp.produc1548871597um_a_b)) (let ((_let_1 (@ tptp.member1998628618um_a_b (@ (@ tptp.produc1697725733um_a_b X4) Y4)))) (=> (@ _let_1 R) (@ _let_1 S)))) (@ (@ tptp.ord_le615126793um_a_b R) S))))
% 0.26/0.70 (assert (forall ((R tptp.set_Pr1916610317um_a_b) (S tptp.set_Pr1916610317um_a_b)) (=> (forall ((X4 tptp.sum_sum_a_b) (Y4 tptp.sum_sum_a_b)) (let ((_let_1 (@ tptp.member947389014um_a_b (@ (@ tptp.produc176426981um_a_b X4) Y4)))) (=> (@ _let_1 R) (@ _let_1 S)))) (@ (@ tptp.ord_le1059794605um_a_b R) S))))
% 0.26/0.70 (assert (forall ((G tptp.labele935650037_a_nat)) (let ((_let_1 (@ tptp.restri572569417_a_nat G))) (=> (@ (@ tptp.ord_le1909159005at_nat (@ tptp.labele195203296_a_nat G)) (@ tptp.labele195203296_a_nat _let_1)) (= G _let_1)))))
% 0.26/0.70 (assert (forall ((G tptp.labele431970251um_a_b)) (let ((_let_1 (@ tptp.restri1162247455um_a_b G))) (=> (@ (@ tptp.ord_le615126793um_a_b (@ tptp.labele1939049654um_a_b G)) (@ tptp.labele1939049654um_a_b _let_1)) (= G _let_1)))))
% 0.26/0.70 (assert (forall ((X2 tptp.nat)) (= (= tptp.zero_zero_nat X2) (= X2 tptp.zero_zero_nat))))
% 0.26/0.70 (assert (forall ((A tptp.produc1032616263at_nat)) (not (@ (@ tptp.member1696759390at_nat A) tptp.bot_bo810816657at_nat))))
% 0.26/0.70 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.member_nat A) tptp.bot_bot_set_nat))))
% 0.26/0.70 (assert (forall ((A tptp.produc1124793815um_a_b)) (not (@ (@ tptp.member1294585472um_a_b A) tptp.bot_bo575978147um_a_b))))
% 0.26/0.70 (assert (forall ((A tptp.produc1548871597um_a_b)) (not (@ (@ tptp.member947389014um_a_b A) tptp.bot_bo225809273um_a_b))))
% 0.26/0.70 (assert (forall ((A tptp.produc1963079155um_a_b)) (not (@ (@ tptp.member1998628618um_a_b A) tptp.bot_bo1262634813um_a_b))))
% 0.26/0.70 (assert (forall ((A tptp.sum_sum_a_b)) (not (@ (@ tptp.member_Sum_sum_a_b A) tptp.bot_bo1491243248um_a_b))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr1647387645at_nat) (A tptp.produc1032616263at_nat)) (=> (= A3 tptp.bot_bo810816657at_nat) (not (@ (@ tptp.member1696759390at_nat A) A3)))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_nat) (A tptp.nat)) (=> (= A3 tptp.bot_bot_set_nat) (not (@ (@ tptp.member_nat A) A3)))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr1174980151um_a_b) (A tptp.produc1124793815um_a_b)) (=> (= A3 tptp.bot_bo575978147um_a_b) (not (@ (@ tptp.member1294585472um_a_b A) A3)))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr1916610317um_a_b) (A tptp.produc1548871597um_a_b)) (=> (= A3 tptp.bot_bo225809273um_a_b) (not (@ (@ tptp.member947389014um_a_b A) A3)))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr409224873um_a_b) (A tptp.produc1963079155um_a_b)) (=> (= A3 tptp.bot_bo1262634813um_a_b) (not (@ (@ tptp.member1998628618um_a_b A) A3)))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Sum_sum_a_b) (A tptp.sum_sum_a_b)) (=> (= A3 tptp.bot_bo1491243248um_a_b) (not (@ (@ tptp.member_Sum_sum_a_b A) A3)))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr1647387645at_nat)) (=> (forall ((Y4 tptp.produc1032616263at_nat)) (not (@ (@ tptp.member1696759390at_nat Y4) A3))) (= A3 tptp.bot_bo810816657at_nat))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_nat)) (=> (forall ((Y4 tptp.nat)) (not (@ (@ tptp.member_nat Y4) A3))) (= A3 tptp.bot_bot_set_nat))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr1174980151um_a_b)) (=> (forall ((Y4 tptp.produc1124793815um_a_b)) (not (@ (@ tptp.member1294585472um_a_b Y4) A3))) (= A3 tptp.bot_bo575978147um_a_b))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr1916610317um_a_b)) (=> (forall ((Y4 tptp.produc1548871597um_a_b)) (not (@ (@ tptp.member947389014um_a_b Y4) A3))) (= A3 tptp.bot_bo225809273um_a_b))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr409224873um_a_b)) (=> (forall ((Y4 tptp.produc1963079155um_a_b)) (not (@ (@ tptp.member1998628618um_a_b Y4) A3))) (= A3 tptp.bot_bo1262634813um_a_b))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Sum_sum_a_b)) (=> (forall ((Y4 tptp.sum_sum_a_b)) (not (@ (@ tptp.member_Sum_sum_a_b Y4) A3))) (= A3 tptp.bot_bo1491243248um_a_b))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr1647387645at_nat)) (= (exists ((X3 tptp.produc1032616263at_nat)) (@ (@ tptp.member1696759390at_nat X3) A3)) (not (= A3 tptp.bot_bo810816657at_nat)))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_nat)) (= (exists ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) A3)) (not (= A3 tptp.bot_bot_set_nat)))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr1174980151um_a_b)) (= (exists ((X3 tptp.produc1124793815um_a_b)) (@ (@ tptp.member1294585472um_a_b X3) A3)) (not (= A3 tptp.bot_bo575978147um_a_b)))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr1916610317um_a_b)) (= (exists ((X3 tptp.produc1548871597um_a_b)) (@ (@ tptp.member947389014um_a_b X3) A3)) (not (= A3 tptp.bot_bo225809273um_a_b)))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr409224873um_a_b)) (= (exists ((X3 tptp.produc1963079155um_a_b)) (@ (@ tptp.member1998628618um_a_b X3) A3)) (not (= A3 tptp.bot_bo1262634813um_a_b)))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Sum_sum_a_b)) (= (exists ((X3 tptp.sum_sum_a_b)) (@ (@ tptp.member_Sum_sum_a_b X3) A3)) (not (= A3 tptp.bot_bo1491243248um_a_b)))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr1174980151um_a_b) (B5 tptp.set_Pr1174980151um_a_b) (X2 tptp.produc1124793815um_a_b)) (let ((_let_1 (@ tptp.member1294585472um_a_b X2))) (=> (@ (@ tptp.ord_le823954903um_a_b A3) B5) (=> (@ _let_1 A3) (@ _let_1 B5))))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr409224873um_a_b) (B5 tptp.set_Pr409224873um_a_b) (X2 tptp.produc1963079155um_a_b)) (let ((_let_1 (@ tptp.member1998628618um_a_b X2))) (=> (@ (@ tptp.ord_le615126793um_a_b A3) B5) (=> (@ _let_1 A3) (@ _let_1 B5))))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Sum_sum_a_b) (B5 tptp.set_Sum_sum_a_b) (X2 tptp.sum_sum_a_b)) (let ((_let_1 (@ tptp.member_Sum_sum_a_b X2))) (=> (@ (@ tptp.ord_le192794300um_a_b A3) B5) (=> (@ _let_1 A3) (@ _let_1 B5))))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr1174980151um_a_b) (B5 tptp.set_Pr1174980151um_a_b) (C tptp.produc1124793815um_a_b)) (let ((_let_1 (@ tptp.member1294585472um_a_b C))) (=> (@ (@ tptp.ord_le823954903um_a_b A3) B5) (=> (@ _let_1 A3) (@ _let_1 B5))))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Pr409224873um_a_b) (B5 tptp.set_Pr409224873um_a_b) (C tptp.produc1963079155um_a_b)) (let ((_let_1 (@ tptp.member1998628618um_a_b C))) (=> (@ (@ tptp.ord_le615126793um_a_b A3) B5) (=> (@ _let_1 A3) (@ _let_1 B5))))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Sum_sum_a_b) (B5 tptp.set_Sum_sum_a_b) (C tptp.sum_sum_a_b)) (let ((_let_1 (@ tptp.member_Sum_sum_a_b C))) (=> (@ (@ tptp.ord_le192794300um_a_b A3) B5) (=> (@ _let_1 A3) (@ _let_1 B5))))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Sum_sum_a_b) (B5 tptp.set_Sum_sum_a_b)) (=> (= A3 B5) (not (=> (@ (@ tptp.ord_le192794300um_a_b A3) B5) (not (@ (@ tptp.ord_le192794300um_a_b B5) A3)))))))
% 0.26/0.70 (assert (= tptp.ord_le823954903um_a_b (lambda ((A7 tptp.set_Pr1174980151um_a_b) (B6 tptp.set_Pr1174980151um_a_b)) (forall ((X3 tptp.produc1124793815um_a_b)) (let ((_let_1 (@ tptp.member1294585472um_a_b X3))) (=> (@ _let_1 A7) (@ _let_1 B6)))))))
% 0.26/0.70 (assert (= tptp.ord_le615126793um_a_b (lambda ((A7 tptp.set_Pr409224873um_a_b) (B6 tptp.set_Pr409224873um_a_b)) (forall ((X3 tptp.produc1963079155um_a_b)) (let ((_let_1 (@ tptp.member1998628618um_a_b X3))) (=> (@ _let_1 A7) (@ _let_1 B6)))))))
% 0.26/0.70 (assert (= tptp.ord_le192794300um_a_b (lambda ((A7 tptp.set_Sum_sum_a_b) (B6 tptp.set_Sum_sum_a_b)) (forall ((X3 tptp.sum_sum_a_b)) (let ((_let_1 (@ tptp.member_Sum_sum_a_b X3))) (=> (@ _let_1 A7) (@ _let_1 B6)))))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Sum_sum_a_b) (B5 tptp.set_Sum_sum_a_b)) (=> (= A3 B5) (@ (@ tptp.ord_le192794300um_a_b A3) B5))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Sum_sum_a_b) (B5 tptp.set_Sum_sum_a_b)) (=> (= A3 B5) (@ (@ tptp.ord_le192794300um_a_b B5) A3))))
% 0.26/0.70 (assert (= tptp.ord_le823954903um_a_b (lambda ((A7 tptp.set_Pr1174980151um_a_b) (B6 tptp.set_Pr1174980151um_a_b)) (forall ((T tptp.produc1124793815um_a_b)) (let ((_let_1 (@ tptp.member1294585472um_a_b T))) (=> (@ _let_1 A7) (@ _let_1 B6)))))))
% 0.26/0.70 (assert (= tptp.ord_le615126793um_a_b (lambda ((A7 tptp.set_Pr409224873um_a_b) (B6 tptp.set_Pr409224873um_a_b)) (forall ((T tptp.produc1963079155um_a_b)) (let ((_let_1 (@ tptp.member1998628618um_a_b T))) (=> (@ _let_1 A7) (@ _let_1 B6)))))))
% 0.26/0.70 (assert (= tptp.ord_le192794300um_a_b (lambda ((A7 tptp.set_Sum_sum_a_b) (B6 tptp.set_Sum_sum_a_b)) (forall ((T tptp.sum_sum_a_b)) (let ((_let_1 (@ tptp.member_Sum_sum_a_b T))) (=> (@ _let_1 A7) (@ _let_1 B6)))))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Sum_sum_a_b)) (@ (@ tptp.ord_le192794300um_a_b A3) A3)))
% 0.26/0.70 (assert (forall ((P (-> tptp.sum_sum_a_b Bool)) (Q (-> tptp.sum_sum_a_b Bool))) (=> (forall ((X4 tptp.sum_sum_a_b)) (=> (@ P X4) (@ Q X4))) (@ (@ tptp.ord_le192794300um_a_b (@ tptp.collect_Sum_sum_a_b P)) (@ tptp.collect_Sum_sum_a_b Q)))))
% 0.26/0.70 (assert (forall ((A3 tptp.set_Sum_sum_a_b) (B5 tptp.set_Sum_sum_a_b) (C2 tptp.set_Sum_sum_a_b)) (let ((_let_1 (@ tptp.ord_le192794300um_a_b A3))) (=> (@ _let_1 B5) (=> (@ (@ tptp.ord_le192794300um_a_b B5) C2) (@ _let_1 C2))))))
% 0.26/0.70 (assert (= (lambda ((Y5 tptp.set_Sum_sum_a_b) (Z tptp.set_Sum_sum_a_b)) (= Y5 Z)) (lambda ((A7 tptp.set_Sum_sum_a_b) (B6 tptp.set_Sum_sum_a_b)) (and (@ (@ tptp.ord_le192794300um_a_b A7) B6) (@ (@ tptp.ord_le192794300um_a_b B6) A7)))))
% 0.26/0.70 (assert (forall ((P (-> tptp.sum_sum_a_b Bool)) (Q (-> tptp.sum_sum_a_b Bool))) (= (@ (@ tptp.ord_le192794300um_a_b (@ tptp.collect_Sum_sum_a_b P)) (@ tptp.collect_Sum_sum_a_b Q)) (forall ((X3 tptp.sum_sum_a_b)) (=> (@ P X3) (@ Q X3))))))
% 0.26/0.70 (assert (forall ((A tptp.produc1032616263at_nat) (B tptp.produc1032616263at_nat) (A3 tptp.set_Pr1647387645at_nat)) (let ((_let_1 (@ tptp.member1696759390at_nat A))) (=> (@ _let_1 (@ (@ tptp.insert1625259895at_nat B) A3)) (=> (not (= A B)) (@ _let_1 A3))))))
% 0.26/0.70 (assert (forall ((A tptp.nat) (B tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A))) (=> (@ _let_1 (@ (@ tptp.insert_nat B) A3)) (=> (not (= A B)) (@ _let_1 A3))))))
% 0.26/0.70 (assert (forall ((A tptp.produc1548871597um_a_b) (B tptp.produc1548871597um_a_b) (A3 tptp.set_Pr1916610317um_a_b)) (let ((_let_1 (@ tptp.member947389014um_a_b A))) (=> (@ _let_1 (@ (@ tptp.insert1435405693um_a_b B) A3)) (=> (not (= A B)) (@ _let_1 A3))))))
% 0.26/0.70 (assert (forall ((A tptp.standard_Constant_a) (B tptp.standard_Constant_a) (A3 tptp.set_St761939237tant_a)) (let ((_let_1 (@ tptp.member1632892294tant_a A))) (=> (@ _let_1 (@ (@ tptp.insert1909710879tant_a B) A3)) (=> (not (= A B)) (@ _let_1 A3))))))
% 0.26/0.70 (assert (forall ((A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat) (A3 tptp.set_Pr1986765409at_nat)) (let ((_let_1 (@ tptp.member701585322at_nat A))) (=> (@ _let_1 (@ (@ tptp.insert271595217at_nat B) A3)) (=> (not (= A B)) (@ _let_1 A3))))))
% 0.26/0.70 (assert (forall ((A tptp.sum_sum_a_b) (B tptp.sum_sum_a_b) (A3 tptp.set_Sum_sum_a_b)) (let ((_let_1 (@ tptp.member_Sum_sum_a_b A))) (=> (@ _let_1 (@ (@ tptp.insert_Sum_sum_a_b B) A3)) (=> (not (= A B)) (@ _let_1 A3))))))
% 0.26/0.70 (assert (forall ((A tptp.produc1124793815um_a_b) (B tptp.produc1124793815um_a_b) (A3 tptp.set_Pr1174980151um_a_b)) (let ((_let_1 (@ tptp.member1294585472um_a_b A))) (=> (@ _let_1 (@ (@ tptp.insert983991207um_a_b B) A3)) (=> (not (= A B)) (@ _let_1 A3))))))
% 0.26/0.70 (assert (forall ((A tptp.produc1963079155um_a_b) (B tptp.produc1963079155um_a_b) (A3 tptp.set_Pr409224873um_a_b)) (let ((_let_1 (@ tptp.member1998628618um_a_b A))) (=> (@ _let_1 (@ (@ tptp.insert323157027um_a_b B) A3)) (=> (not (= A B)) (@ _let_1 A3))))))
% 0.26/0.70 (assert (forall ((A tptp.product_prod_nat_nat) (B5 tptp.set_Pr1986765409at_nat)) (@ (@ tptp.member701585322at_nat A) (@ (@ tptp.insert271595217at_nat A) B5))))
% 0.26/0.70 (assert (forall ((A tptp.sum_sum_a_b) (B5 tptp.set_Sum_sum_a_b)) (@ (@ tptp.member_Sum_sum_a_b A) (@ (@ tptp.insert_Sum_sum_a_b A) B5))))
% 0.26/0.70 (assert (forall ((A tptp.produc1124793815um_a_b) (B5 tptp.set_Pr1174980151um_a_b)) (@ (@ tptp.member1294585472um_a_b A) (@ (@ tptp.insert983991207um_a_b A) B5))))
% 0.26/0.70 (assert (forall ((A tptp.produc1963079155um_a_b) (B5 tptp.set_Pr409224873um_a_b)) (@ (@ tptp.member1998628618um_a_b A) (@ (@ tptp.insert323157027um_a_b A) B5))))
% 0.26/0.70 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 0.26/0.70 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)))
% 0.26/0.70 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) B))) (exists ((X4 tptp.nat)) (and (@ P X4) (forall ((Y6 tptp.nat)) (=> (@ P Y6) (@ (@ tptp.ord_less_eq_nat Y6) X4)))))))))
% 0.26/0.70 (assert (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))))
% 0.26/0.70 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))))
% 0.52/1.11 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.52/1.11 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))))
% 0.52/1.11 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 0.52/1.11 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 0.52/1.11 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 0.52/1.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 0.52/1.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 0.52/1.11 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 0.52/1.11 (assert (= (@ (@ tptp.getRel1465196352um_a_b tptp.standard_S_Idt_a) tptp.g) (@ tptp.id_on_Sum_sum_a_b (@ tptp.labele577278695um_a_b tptp.g))))
% 0.52/1.11 (assert (= (@ (@ tptp.getRel1465196352um_a_b tptp.standard_S_Bot_a) tptp.g) tptp.bot_bo225809273um_a_b))
% 0.52/1.11 (assert (@ (@ tptp.mainta522127984um_a_b (@ tptp.standa997693288tant_a tptp.standard_S_Idt_a)) tptp.g))
% 0.52/1.11 (assert (@ (@ tptp.mainta522127984um_a_b (@ tptp.standa1795879409tant_a tptp.standard_S_Idt_a)) tptp.g))
% 0.52/1.11 (assert (@ (@ tptp.mainta522127984um_a_b (@ (@ tptp.standa1343274079tant_a tptp.standard_S_Idt_a) tptp.l)) tptp.g))
% 0.52/1.11 (assert (let ((_let_1 (@ (@ tptp.labele16114835_a_nat (@ (@ tptp.insert1625259895at_nat (@ (@ tptp.produc407553657at_nat tptp.standard_S_Idt_a) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))) tptp.bot_bo810816657at_nat)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))) (let ((_let_2 (@ (@ tptp.insert983991207um_a_b (@ (@ tptp.produc1808556047um_a_b tptp.zero_zero_nat) tptp.v)) tptp.bot_bo575978147um_a_b))) (let ((_let_3 (@ tptp.labele1810595089_a_nat _let_1))) (not (and (= _let_3 (@ tptp.domain1368163076um_a_b _let_2)) (= _let_1 (@ tptp.restri572569417_a_nat _let_1)) (= tptp.g (@ tptp.restri1162247455um_a_b tptp.g)) (@ (@ tptp.ord_le192794300um_a_b (@ (@ tptp.image_256773707um_a_b _let_2) _let_3)) (@ tptp.labele577278695um_a_b tptp.g)) (@ tptp.unival2092813468um_a_b _let_2) (@ (@ (@ tptp.edge_p1382426714tant_a _let_2) (@ tptp.labele195203296_a_nat _let_1)) (@ tptp.labele1939049654um_a_b tptp.g))))))))
% 0.52/1.11 (set-info :filename cvc5---1.0.5_15148)
% 0.52/1.11 (check-sat-assuming ( true ))
% 0.52/1.11 ------- get file name : TPTP file name is ITP179^1
% 0.52/1.11 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_15148.smt2...
% 0.52/1.11 --- Run --ho-elim --full-saturate-quant at 10...
% 0.52/1.11 % SZS status Theorem for ITP179^1
% 0.52/1.11 % SZS output start Proof for ITP179^1
% 0.52/1.11 (
% 0.52/1.11 (let ((_let_1 (@ tptp.labele1939049654um_a_b tptp.g))) (let ((_let_2 (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (let ((_let_3 (@ tptp.produc407553657at_nat tptp.standard_S_Idt_a))) (let ((_let_4 (@ (@ tptp.insert1625259895at_nat (@ _let_3 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))) tptp.bot_bo810816657at_nat))) (let ((_let_5 (@ (@ tptp.labele16114835_a_nat _let_4) _let_2))) (let ((_let_6 (@ (@ tptp.insert983991207um_a_b (@ (@ tptp.produc1808556047um_a_b tptp.zero_zero_nat) tptp.v)) tptp.bot_bo575978147um_a_b))) (let ((_let_7 (@ tptp.edge_p1382426714tant_a _let_6))) (let ((_let_8 (@ tptp.labele577278695um_a_b tptp.g))) (let ((_let_9 (@ tptp.labele1810595089_a_nat _let_5))) (let ((_let_10 (= tptp.g (@ tptp.restri1162247455um_a_b tptp.g)))) (let ((_let_11 (not (and (= _let_9 (@ tptp.domain1368163076um_a_b _let_6)) (= _let_5 (@ tptp.restri572569417_a_nat _let_5)) _let_10 (@ (@ tptp.ord_le192794300um_a_b (@ (@ tptp.image_256773707um_a_b _let_6) _let_9)) _let_8) (@ tptp.unival2092813468um_a_b _let_6) (@ (@ _let_7 (@ tptp.labele195203296_a_nat _let_5)) _let_1))))) (let ((_let_12 (= (@ (@ tptp.getRel1465196352um_a_b tptp.standard_S_Bot_a) tptp.g) tptp.bot_bo225809273um_a_b))) (let ((_let_13 (= tptp.bot_bot_nat tptp.zero_zero_nat))) (let ((_let_14 (= tptp.ord_le192794300um_a_b (lambda ((A7 tptp.set_Sum_sum_a_b) (B6 tptp.set_Sum_sum_a_b)) (forall ((X3 tptp.sum_sum_a_b)) (let ((_let_1 (@ tptp.member_Sum_sum_a_b X3))) (=> (@ _let_1 A7) (@ _let_1 B6)))))))) (let ((_let_15 (= tptp.ord_le615126793um_a_b (lambda ((A7 tptp.set_Pr409224873um_a_b) (B6 tptp.set_Pr409224873um_a_b)) (forall ((X3 tptp.produc1963079155um_a_b)) (let ((_let_1 (@ tptp.member1998628618um_a_b X3))) (=> (@ _let_1 A7) (@ _let_1 B6)))))))) (let ((_let_16 (= tptp.ord_le823954903um_a_b (lambda ((A7 tptp.set_Pr1174980151um_a_b) (B6 tptp.set_Pr1174980151um_a_b)) (forall ((X3 tptp.produc1124793815um_a_b)) (let ((_let_1 (@ tptp.member1294585472um_a_b X3))) (=> (@ _let_1 A7) (@ _let_1 B6)))))))) (let ((_let_17 (forall ((X2 tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X2))) (let ((_let_2 (@ _let_1 A3))) (= (@ _let_1 _let_2) _let_2)))))) (let ((_let_18 (@ tptp.labele16114835_a_nat tptp.bot_bo810816657at_nat))) (let ((_let_19 (@ _let_18 _let_2))) (let ((_let_20 (= tptp.standa1410829644tant_a (@ (@ tptp.produc1676969687_a_nat (@ _let_18 tptp.bot_bot_set_nat)) _let_19)))) (let ((_let_21 (= tptp.standa63370785tant_a (lambda ((T tptp.standard_Constant_a)) (let ((_let_1 (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (@ (@ tptp.produc1676969687_a_nat (@ (@ tptp.labele16114835_a_nat tptp.bot_bo810816657at_nat) _let_1)) (@ (@ tptp.labele16114835_a_nat (@ (@ tptp.insert1625259895at_nat (@ (@ tptp.produc407553657at_nat T) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))) tptp.bot_bo810816657at_nat)) _let_1))))))) (let ((_let_22 (forall ((X1 tptp.set_Pr1647387645at_nat) (X22 tptp.set_nat)) (= (@ tptp.labele195203296_a_nat (@ (@ tptp.labele16114835_a_nat X1) X22)) X1)))) (let ((_let_23 (forall ((X1 tptp.set_Pr1647387645at_nat) (X22 tptp.set_nat)) (= (@ tptp.labele1810595089_a_nat (@ (@ tptp.labele16114835_a_nat X1) X22)) X22)))) (let ((_let_24 (= (@ tptp.domain2069673178um_a_b tptp.bot_bo225809273um_a_b) tptp.bot_bo1491243248um_a_b))) (let ((_let_25 (= (@ tptp.domain1060562500at_nat tptp.bot_bo810816657at_nat) tptp.bot_bo1160111033tant_a))) (let ((_let_26 (@ tptp.domain_nat_nat tptp.bot_bo2130386637at_nat))) (let ((_let_27 (= _let_26 tptp.bot_bot_set_nat))) (let ((_let_28 (@ tptp.unival2092813468um_a_b tptp.f))) (let ((_let_29 (forall ((A tptp.standard_Constant_a) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ (@ tptp.labele16114835_a_nat (@ (@ tptp.insert1625259895at_nat (@ (@ tptp.produc407553657at_nat A) (@ (@ tptp.product_Pair_nat_nat B) C))) tptp.bot_bo810816657at_nat)) (@ (@ tptp.insert_nat B) (@ (@ tptp.insert_nat C) tptp.bot_bot_set_nat))))) (= _let_1 (@ tptp.restri572569417_a_nat _let_1)))))) (let ((_let_30 (@ tptp.domain1368163076um_a_b tptp.f))) (let ((_let_31 (= _let_30 _let_2))) (let ((_let_32 (= tptp.f _let_6))) (let ((_let_33 (@ (@ tptp.ord_le192794300um_a_b (@ (@ tptp.image_256773707um_a_b tptp.f) _let_2)) _let_8))) (let ((_let_34 (@ (@ _let_7 _let_4) _let_1))) (let ((_let_35 (ho_67 k_66 tptp.bot_bo2130386637at_nat))) (let ((_let_36 (ho_69 k_68 tptp.bot_bot_nat))) (let ((_let_37 (ho_70 _let_36 _let_35))) (let ((_let_38 (ho_56 (ho_55 k_54 (ho_53 (ho_52 k_51 tptp.standard_S_Idt_a) (ho_50 (ho_49 k_48 tptp.bot_bot_nat) tptp.bot_bot_nat))) tptp.bot_bo810816657at_nat))) (let ((_let_39 (ho_97 k_96 _let_38))) (let ((_let_40 (ho_98 _let_39 _let_37))) (let ((_let_41 (ho_189 k_188 _let_40))) (let ((_let_42 (= _let_37 _let_41))) (let ((_let_43 (ho_62 (ho_61 k_60 (ho_59 (ho_58 k_57 tptp.bot_bot_nat) tptp.v)) tptp.bot_bo575978147um_a_b))) (let ((_let_44 (ho_72 k_71 _let_43))) (let ((_let_45 (ho_18 k_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_372))) (let ((_let_46 (ho_15 _let_45 (ho_73 _let_44 _let_41)))) (let ((_let_47 (ho_15 _let_45 (ho_73 _let_44 _let_37)))) (let ((_let_48 (forall ((X1 tptp.set_Pr1647387645at_nat) (X22 tptp.set_nat)) (= X22 (ho_189 k_188 (ho_98 (ho_97 k_96 X1) X22)))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_23)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((X1 tptp.set_Pr1647387645at_nat) (X22 tptp.set_nat)) (= X22 (@ tptp.labele1810595089_a_nat (@ (@ tptp.labele16114835_a_nat X1) X22)))) _let_48))))))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (_let_38 _let_37 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_48))) _let_49 :args (_let_42 false _let_48)))) (let ((_let_51 (ho_15 _let_45 (ho_45 k_44 tptp.g)))) (let ((_let_52 (not _let_46))) (let ((_let_53 (or _let_52 _let_51))) (let ((_let_54 (forall ((X3 tptp.sum_sum_a_b)) (let ((_let_1 (ho_18 k_17 X3))) (or (not (ho_15 _let_1 (ho_73 (ho_72 k_71 (ho_62 (ho_61 k_60 (ho_59 (ho_58 k_57 tptp.bot_bot_nat) tptp.v)) tptp.bot_bo575978147um_a_b)) (ho_189 k_188 (ho_98 (ho_97 k_96 (ho_56 (ho_55 k_54 (ho_53 (ho_52 k_51 tptp.standard_S_Idt_a) (ho_50 (ho_49 k_48 tptp.bot_bot_nat) tptp.bot_bot_nat))) tptp.bot_bo810816657at_nat)) (ho_70 (ho_69 k_68 tptp.bot_bot_nat) (ho_67 k_66 tptp.bot_bo2130386637at_nat))))))) (ho_15 _let_1 (ho_45 k_44 tptp.g))))))) (let ((_let_55 (not _let_53))) (let ((_let_56 (ho_47 k_46 tptp.g))) (let ((_let_57 (ho_191 k_190 _let_40))) (let ((_let_58 (ho_64 k_63 _let_43))) (let ((_let_59 (ho_23 (ho_65 _let_58 _let_57) _let_56))) (let ((_let_60 (= _let_40 (ho_100 k_99 _let_40)))) (let ((_let_61 (ho_75 k_74 _let_43))) (let ((_let_62 (= _let_61 _let_41))) (let ((_let_63 (ho_29 k_101 _let_43))) (let ((_let_64 (= tptp.g (ho_43 k_42 tptp.g)))) (let ((_let_65 (not _let_54))) (let ((_let_66 (= _let_38 _let_57))) (let ((_let_67 (ho_23 (ho_65 _let_58 _let_38) _let_56))) (let ((_let_68 (forall ((X1 tptp.set_Pr1647387645at_nat) (X22 tptp.set_nat)) (= X1 (ho_191 k_190 (ho_98 (ho_97 k_96 X1) X22)))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_22)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((X1 tptp.set_Pr1647387645at_nat) (X22 tptp.set_nat)) (= X1 (@ tptp.labele195203296_a_nat (@ (@ tptp.labele16114835_a_nat X1) X22)))) _let_68))))))) (let ((_let_70 (@ (@ tptp.insert1625259895at_nat (@ _let_3 (@ (@ tptp.product_Pair_nat_nat tptp.bot_bot_nat) tptp.bot_bot_nat))) tptp.bot_bo810816657at_nat))) (let ((_let_71 (@ (@ tptp.insert983991207um_a_b (@ (@ tptp.produc1808556047um_a_b tptp.bot_bot_nat) tptp.v)) tptp.bot_bo575978147um_a_b))) (let ((_let_72 (@ tptp.edge_p1382426714tant_a _let_71))) (let ((_let_73 (ASSUME :args (_let_32)))) (let ((_let_74 (SYMM (ASSUME :args (_let_27))))) (let ((_let_75 (SYMM (ASSUME :args (_let_25))))) (let ((_let_76 (SYMM (ASSUME :args (_let_24))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_76 _let_75 _let_74 _let_73) :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (AND_INTRO (SYMM (ASSUME :args (_let_12))) (SYMM (ASSUME :args (_let_13))) (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_77 _let_76 _let_75 _let_74 _let_73) :args (_let_20 SB_DEFAULT SBA_FIXPOINT))) _let_77 _let_76 _let_75 _let_74 _let_73))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_34)) (TRANS (MACRO_SR_EQ_INTRO _let_78 :args (_let_34 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (@ (@ _let_72 _let_70) _let_1) _let_67))))))) (let ((_let_80 (and _let_67 _let_66))) (let ((_let_81 (_let_67 _let_66))) (let ((_let_82 (ASSUME :args (_let_66)))) (let ((_let_83 (ho_70 _let_36 _let_37))) (let ((_let_84 (= _let_37 _let_83))) (let ((_let_85 (ho_98 _let_39 _let_83))) (let ((_let_86 (= _let_85 (ho_100 k_99 _let_85)))) (let ((_let_87 (forall ((X2 tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (ho_69 k_68 X2))) (let ((_let_2 (ho_70 _let_1 A3))) (= _let_2 (ho_70 _let_1 _let_2))))))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_17)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((X2 tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X2))) (let ((_let_2 (@ _let_1 A3))) (= _let_2 (@ _let_1 _let_2))))) _let_87))))))) (let ((_let_89 (forall ((A tptp.standard_Constant_a) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (ho_98 (ho_97 k_96 (ho_56 (ho_55 k_54 (ho_53 (ho_52 k_51 A) (ho_50 (ho_49 k_48 B) C))) tptp.bot_bo810816657at_nat)) (ho_70 (ho_69 k_68 B) (ho_70 (ho_69 k_68 C) (ho_67 k_66 tptp.bot_bo2130386637at_nat)))))) (= _let_1 (ho_100 k_99 _let_1)))))) (let ((_let_90 (EQ_RESOLVE (ASSUME :args (_let_29)) (TRANS (MACRO_SR_EQ_INTRO _let_78 :args (_let_29 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((A tptp.standard_Constant_a) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ (@ tptp.labele16114835_a_nat (@ (@ tptp.insert1625259895at_nat (@ (@ tptp.produc407553657at_nat A) (@ (@ tptp.product_Pair_nat_nat B) C))) tptp.bot_bo810816657at_nat)) (@ (@ tptp.insert_nat B) (@ (@ tptp.insert_nat C) (@ tptp.domain_nat_nat tptp.bot_bo2130386637at_nat)))))) (= _let_1 (@ tptp.restri572569417_a_nat _let_1)))) _let_89))))))) (let ((_let_91 (and _let_86 _let_84))) (let ((_let_92 (ASSUME :args (_let_84)))) (let ((_let_93 (CONG (REFL :args (_let_39)) (SYMM _let_92) :args (APPLY_UF ho_98)))) (let ((_let_94 (ASSUME :args (_let_86)))) (let ((_let_95 (= _let_37 _let_61))) (let ((_let_96 (@ tptp.domain1368163076um_a_b _let_71))) (let ((_let_97 (@ (@ tptp.insert_nat tptp.bot_bot_nat) _let_26))) (let ((_let_98 (EQ_RESOLVE (ASSUME :args (_let_31)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_31 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_78 :args ((= _let_2 _let_30) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (= _let_97 _let_96) _let_95))))))) (let ((_let_99 (not _let_42))) (let ((_let_100 (and _let_95 _let_42))) (let ((_let_101 (ASSUME :args (_let_42)))) (let ((_let_102 (SYMM _let_101))) (let ((_let_103 (@ tptp.unival2092813468um_a_b _let_71))) (let ((_let_104 (forall ((u |u_(-> tptp.set_Sum_sum_a_b tptp.set_Pr409224873um_a_b)|) (e tptp.set_Pr409224873um_a_b) (i tptp.set_Sum_sum_a_b)) (not (forall ((v |u_(-> tptp.set_Sum_sum_a_b tptp.set_Pr409224873um_a_b)|)) (not (forall ((ii tptp.set_Sum_sum_a_b)) (= (ho_217 v ii) (ite (= i ii) e (ho_217 u ii)))))))))) (let ((_let_105 (forall ((x |u_(-> tptp.set_Sum_sum_a_b tptp.set_Pr409224873um_a_b)|) (y |u_(-> tptp.set_Sum_sum_a_b tptp.set_Pr409224873um_a_b)|)) (or (not (forall ((z tptp.set_Sum_sum_a_b)) (= (ho_217 x z) (ho_217 y z)))) (= x y))))) (let ((_let_106 (forall ((u |u_(-> tptp.produc1918750183um_a_b tptp.set_Pr45173959um_a_b Bool)|) (e |u_(-> tptp.set_Pr45173959um_a_b Bool)|) (i tptp.produc1918750183um_a_b)) (not (forall ((v |u_(-> tptp.produc1918750183um_a_b tptp.set_Pr45173959um_a_b Bool)|)) (not (forall ((ii tptp.produc1918750183um_a_b)) (= (ho_213 v ii) (ite (= i ii) e (ho_213 u ii)))))))))) (let ((_let_107 (forall ((x |u_(-> tptp.produc1918750183um_a_b tptp.set_Pr45173959um_a_b Bool)|) (y |u_(-> tptp.produc1918750183um_a_b tptp.set_Pr45173959um_a_b Bool)|)) (or (not (forall ((z tptp.produc1918750183um_a_b)) (= (ho_213 x z) (ho_213 y z)))) (= x y))))) (let ((_let_108 (forall ((u |u_(-> tptp.set_nat tptp.set_Pr1174980151um_a_b)|) (e tptp.set_Pr1174980151um_a_b) (i tptp.set_nat)) (not (forall ((v |u_(-> tptp.set_nat tptp.set_Pr1174980151um_a_b)|)) (not (forall ((ii tptp.set_nat)) (= (ho_149 v ii) (ite (= i ii) e (ho_149 u ii)))))))))) (let ((_let_109 (forall ((x |u_(-> tptp.set_nat tptp.set_Pr1174980151um_a_b)|) (y |u_(-> tptp.set_nat tptp.set_Pr1174980151um_a_b)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_149 x z) (ho_149 y z)))) (= x y))))) (let ((_let_110 (forall ((u |u_(-> tptp.set_Pr45173959um_a_b Bool)|) (e Bool) (i tptp.set_Pr45173959um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr45173959um_a_b Bool)|)) (not (forall ((ii tptp.set_Pr45173959um_a_b)) (= (ho_214 v ii) (ite (= i ii) e (ho_214 u ii)))))))))) (let ((_let_111 (forall ((x |u_(-> tptp.set_Pr45173959um_a_b Bool)|) (y |u_(-> tptp.set_Pr45173959um_a_b Bool)|)) (or (not (forall ((z tptp.set_Pr45173959um_a_b)) (= (ho_214 x z) (ho_214 y z)))) (= x y))))) (let ((_let_112 (forall ((u |u_(-> tptp.set_Pr409224873um_a_b tptp.set_St761939237tant_a tptp.set_Pr1916610317um_a_b)|) (e |u_(-> tptp.set_St761939237tant_a tptp.set_Pr1916610317um_a_b)|) (i tptp.set_Pr409224873um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr409224873um_a_b tptp.set_St761939237tant_a tptp.set_Pr1916610317um_a_b)|)) (not (forall ((ii tptp.set_Pr409224873um_a_b)) (= (ho_193 v ii) (ite (= i ii) e (ho_193 u ii)))))))))) (let ((_let_113 (forall ((x |u_(-> tptp.set_Pr409224873um_a_b tptp.set_St761939237tant_a tptp.set_Pr1916610317um_a_b)|) (y |u_(-> tptp.set_Pr409224873um_a_b tptp.set_St761939237tant_a tptp.set_Pr1916610317um_a_b)|)) (or (not (forall ((z tptp.set_Pr409224873um_a_b)) (= (ho_193 x z) (ho_193 y z)))) (= x y))))) (let ((_let_114 (forall ((u |u_(-> tptp.set_Pr1916610317um_a_b tptp.set_Pr1916610317um_a_b)|) (e tptp.set_Pr1916610317um_a_b) (i tptp.set_Pr1916610317um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1916610317um_a_b tptp.set_Pr1916610317um_a_b)|)) (not (forall ((ii tptp.set_Pr1916610317um_a_b)) (= (ho_114 v ii) (ite (= i ii) e (ho_114 u ii)))))))))) (let ((_let_115 (forall ((x |u_(-> tptp.set_Pr1916610317um_a_b tptp.set_Pr1916610317um_a_b)|) (y |u_(-> tptp.set_Pr1916610317um_a_b tptp.set_Pr1916610317um_a_b)|)) (or (not (forall ((z tptp.set_Pr1916610317um_a_b)) (= (ho_114 x z) (ho_114 y z)))) (= x y))))) (let ((_let_116 (forall ((u |u_(-> tptp.set_Pr45173959um_a_b tptp.set_Pr1174980151um_a_b tptp.set_Pr1174980151um_a_b)|) (e |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_Pr1174980151um_a_b)|) (i tptp.set_Pr45173959um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr45173959um_a_b tptp.set_Pr1174980151um_a_b tptp.set_Pr1174980151um_a_b)|)) (not (forall ((ii tptp.set_Pr45173959um_a_b)) (= (ho_208 v ii) (ite (= i ii) e (ho_208 u ii)))))))))) (let ((_let_117 (forall ((x |u_(-> tptp.set_Pr45173959um_a_b tptp.set_Pr1174980151um_a_b tptp.set_Pr1174980151um_a_b)|) (y |u_(-> tptp.set_Pr45173959um_a_b tptp.set_Pr1174980151um_a_b tptp.set_Pr1174980151um_a_b)|)) (or (not (forall ((z tptp.set_Pr45173959um_a_b)) (= (ho_208 x z) (ho_208 y z)))) (= x y))))) (let ((_let_118 (forall ((u |u_(-> tptp.labele935650037_a_nat tptp.set_nat)|) (e tptp.set_nat) (i tptp.labele935650037_a_nat)) (not (forall ((v |u_(-> tptp.labele935650037_a_nat tptp.set_nat)|)) (not (forall ((ii tptp.labele935650037_a_nat)) (= (ho_189 v ii) (ite (= i ii) e (ho_189 u ii)))))))))) (let ((_let_119 (forall ((x |u_(-> tptp.labele935650037_a_nat tptp.set_nat)|) (y |u_(-> tptp.labele935650037_a_nat tptp.set_nat)|)) (or (not (forall ((z tptp.labele935650037_a_nat)) (= (ho_189 x z) (ho_189 y z)))) (= x y))))) (let ((_let_120 (forall ((u |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_Sum_sum_a_b)|) (e tptp.set_Sum_sum_a_b) (i tptp.set_Pr1174980151um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_Sum_sum_a_b)|)) (not (forall ((ii tptp.set_Pr1174980151um_a_b)) (= (ho_187 v ii) (ite (= i ii) e (ho_187 u ii)))))))))) (let ((_let_121 (forall ((x |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_Sum_sum_a_b)|) (y |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_Sum_sum_a_b)|)) (or (not (forall ((z tptp.set_Pr1174980151um_a_b)) (= (ho_187 x z) (ho_187 y z)))) (= x y))))) (let ((_let_122 (forall ((u |u_(-> tptp.produc585753260um_a_b tptp.set_Pr653770722um_a_b Bool)|) (e |u_(-> tptp.set_Pr653770722um_a_b Bool)|) (i tptp.produc585753260um_a_b)) (not (forall ((v |u_(-> tptp.produc585753260um_a_b tptp.set_Pr653770722um_a_b Bool)|)) (not (forall ((ii tptp.produc585753260um_a_b)) (= (ho_183 v ii) (ite (= i ii) e (ho_183 u ii)))))))))) (let ((_let_123 (forall ((x |u_(-> tptp.produc585753260um_a_b tptp.set_Pr653770722um_a_b Bool)|) (y |u_(-> tptp.produc585753260um_a_b tptp.set_Pr653770722um_a_b Bool)|)) (or (not (forall ((z tptp.produc585753260um_a_b)) (= (ho_183 x z) (ho_183 y z)))) (= x y))))) (let ((_let_124 (forall ((u |u_(-> tptp.set_St761939237tant_a Bool)|) (e Bool) (i tptp.set_St761939237tant_a)) (not (forall ((v |u_(-> tptp.set_St761939237tant_a Bool)|)) (not (forall ((ii tptp.set_St761939237tant_a)) (= (ho_197 v ii) (ite (= i ii) e (ho_197 u ii)))))))))) (let ((_let_125 (forall ((x |u_(-> tptp.set_St761939237tant_a Bool)|) (y |u_(-> tptp.set_St761939237tant_a Bool)|)) (or (not (forall ((z tptp.set_St761939237tant_a)) (= (ho_197 x z) (ho_197 y z)))) (= x y))))) (let ((_let_126 (forall ((u |u_(-> tptp.sum_sum_a_b tptp.produc585753260um_a_b)|) (e tptp.produc585753260um_a_b) (i tptp.sum_sum_a_b)) (not (forall ((v |u_(-> tptp.sum_sum_a_b tptp.produc585753260um_a_b)|)) (not (forall ((ii tptp.sum_sum_a_b)) (= (ho_181 v ii) (ite (= i ii) e (ho_181 u ii)))))))))) (let ((_let_127 (forall ((x |u_(-> tptp.sum_sum_a_b tptp.produc585753260um_a_b)|) (y |u_(-> tptp.sum_sum_a_b tptp.produc585753260um_a_b)|)) (or (not (forall ((z tptp.sum_sum_a_b)) (= (ho_181 x z) (ho_181 y z)))) (= x y))))) (let ((_let_128 (forall ((u |u_(-> tptp.set_Pr386468381um_a_b Bool)|) (e Bool) (i tptp.set_Pr386468381um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr386468381um_a_b Bool)|)) (not (forall ((ii tptp.set_Pr386468381um_a_b)) (= (ho_175 v ii) (ite (= i ii) e (ho_175 u ii)))))))))) (let ((_let_129 (forall ((x |u_(-> tptp.set_Pr386468381um_a_b Bool)|) (y |u_(-> tptp.set_Pr386468381um_a_b Bool)|)) (or (not (forall ((z tptp.set_Pr386468381um_a_b)) (= (ho_175 x z) (ho_175 y z)))) (= x y))))) (let ((_let_130 (forall ((u |u_(-> tptp.set_Pr1174980151um_a_b Bool)|) (e Bool) (i tptp.set_Pr1174980151um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1174980151um_a_b Bool)|)) (not (forall ((ii tptp.set_Pr1174980151um_a_b)) (= (ho_29 v ii) (ite (= i ii) e (ho_29 u ii)))))))))) (let ((_let_131 (forall ((x |u_(-> tptp.set_Pr1174980151um_a_b Bool)|) (y |u_(-> tptp.set_Pr1174980151um_a_b Bool)|)) (or (not (forall ((z tptp.set_Pr1174980151um_a_b)) (= (ho_29 x z) (ho_29 y z)))) (= x y))))) (let ((_let_132 (forall ((u |u_(-> tptp.produc1003469085um_a_b tptp.set_Pr326391507um_a_b Bool)|) (e |u_(-> tptp.set_Pr326391507um_a_b Bool)|) (i tptp.produc1003469085um_a_b)) (not (forall ((v |u_(-> tptp.produc1003469085um_a_b tptp.set_Pr326391507um_a_b Bool)|)) (not (forall ((ii tptp.produc1003469085um_a_b)) (= (ho_168 v ii) (ite (= i ii) e (ho_168 u ii)))))))))) (let ((_let_133 (forall ((x |u_(-> tptp.produc1003469085um_a_b tptp.set_Pr326391507um_a_b Bool)|) (y |u_(-> tptp.produc1003469085um_a_b tptp.set_Pr326391507um_a_b Bool)|)) (or (not (forall ((z tptp.produc1003469085um_a_b)) (= (ho_168 x z) (ho_168 y z)))) (= x y))))) (let ((_let_134 (forall ((u |u_(-> tptp.standard_Constant_a tptp.set_St761939237tant_a Bool)|) (e |u_(-> tptp.set_St761939237tant_a Bool)|) (i tptp.standard_Constant_a)) (not (forall ((v |u_(-> tptp.standard_Constant_a tptp.set_St761939237tant_a Bool)|)) (not (forall ((ii tptp.standard_Constant_a)) (= (ho_196 v ii) (ite (= i ii) e (ho_196 u ii)))))))))) (let ((_let_135 (forall ((x |u_(-> tptp.standard_Constant_a tptp.set_St761939237tant_a Bool)|) (y |u_(-> tptp.standard_Constant_a tptp.set_St761939237tant_a Bool)|)) (or (not (forall ((z tptp.standard_Constant_a)) (= (ho_196 x z) (ho_196 y z)))) (= x y))))) (let ((_let_136 (forall ((u |u_(-> tptp.standard_Constant_a tptp.produc1124793815um_a_b tptp.produc1003469085um_a_b)|) (e |u_(-> tptp.produc1124793815um_a_b tptp.produc1003469085um_a_b)|) (i tptp.standard_Constant_a)) (not (forall ((v |u_(-> tptp.standard_Constant_a tptp.produc1124793815um_a_b tptp.produc1003469085um_a_b)|)) (not (forall ((ii tptp.standard_Constant_a)) (= (ho_165 v ii) (ite (= i ii) e (ho_165 u ii)))))))))) (let ((_let_137 (forall ((x |u_(-> tptp.standard_Constant_a tptp.produc1124793815um_a_b tptp.produc1003469085um_a_b)|) (y |u_(-> tptp.standard_Constant_a tptp.produc1124793815um_a_b tptp.produc1003469085um_a_b)|)) (or (not (forall ((z tptp.standard_Constant_a)) (= (ho_165 x z) (ho_165 y z)))) (= x y))))) (let ((_let_138 (forall ((u |u_(-> tptp.set_Pr1783309276um_a_b Bool)|) (e Bool) (i tptp.set_Pr1783309276um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1783309276um_a_b Bool)|)) (not (forall ((ii tptp.set_Pr1783309276um_a_b)) (= (ho_206 v ii) (ite (= i ii) e (ho_206 u ii)))))))))) (let ((_let_139 (forall ((x |u_(-> tptp.set_Pr1783309276um_a_b Bool)|) (y |u_(-> tptp.set_Pr1783309276um_a_b Bool)|)) (or (not (forall ((z tptp.set_Pr1783309276um_a_b)) (= (ho_206 x z) (ho_206 y z)))) (= x y))))) (let ((_let_140 (forall ((u |u_(-> tptp.produc1124793815um_a_b tptp.produc1003469085um_a_b)|) (e tptp.produc1003469085um_a_b) (i tptp.produc1124793815um_a_b)) (not (forall ((v |u_(-> tptp.produc1124793815um_a_b tptp.produc1003469085um_a_b)|)) (not (forall ((ii tptp.produc1124793815um_a_b)) (= (ho_166 v ii) (ite (= i ii) e (ho_166 u ii)))))))))) (let ((_let_141 (forall ((x |u_(-> tptp.produc1124793815um_a_b tptp.produc1003469085um_a_b)|) (y |u_(-> tptp.produc1124793815um_a_b tptp.produc1003469085um_a_b)|)) (or (not (forall ((z tptp.produc1124793815um_a_b)) (= (ho_166 x z) (ho_166 y z)))) (= x y))))) (let ((_let_142 (forall ((u |u_(-> tptp.produc1548871597um_a_b tptp.produc1963079155um_a_b)|) (e tptp.produc1963079155um_a_b) (i tptp.produc1548871597um_a_b)) (not (forall ((v |u_(-> tptp.produc1548871597um_a_b tptp.produc1963079155um_a_b)|)) (not (forall ((ii tptp.produc1548871597um_a_b)) (= (ho_89 v ii) (ite (= i ii) e (ho_89 u ii)))))))))) (let ((_let_143 (forall ((x |u_(-> tptp.produc1548871597um_a_b tptp.produc1963079155um_a_b)|) (y |u_(-> tptp.produc1548871597um_a_b tptp.produc1963079155um_a_b)|)) (or (not (forall ((z tptp.produc1548871597um_a_b)) (= (ho_89 x z) (ho_89 y z)))) (= x y))))) (let ((_let_144 (forall ((u |u_(-> tptp.set_Pr2065572323um_a_b tptp.set_Pr1174980151um_a_b tptp.labele261019144um_a_b)|) (e |u_(-> tptp.set_Pr1174980151um_a_b tptp.labele261019144um_a_b)|) (i tptp.set_Pr2065572323um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr2065572323um_a_b tptp.set_Pr1174980151um_a_b tptp.labele261019144um_a_b)|)) (not (forall ((ii tptp.set_Pr2065572323um_a_b)) (= (ho_303 v ii) (ite (= i ii) e (ho_303 u ii)))))))))) (let ((_let_145 (forall ((x |u_(-> tptp.set_Pr2065572323um_a_b tptp.set_Pr1174980151um_a_b tptp.labele261019144um_a_b)|) (y |u_(-> tptp.set_Pr2065572323um_a_b tptp.set_Pr1174980151um_a_b tptp.labele261019144um_a_b)|)) (or (not (forall ((z tptp.set_Pr2065572323um_a_b)) (= (ho_303 x z) (ho_303 y z)))) (= x y))))) (let ((_let_146 (forall ((u |u_(-> tptp.set_St761939237tant_a tptp.set_Pr1174980151um_a_b)|) (e tptp.set_Pr1174980151um_a_b) (i tptp.set_St761939237tant_a)) (not (forall ((v |u_(-> tptp.set_St761939237tant_a tptp.set_Pr1174980151um_a_b)|)) (not (forall ((ii tptp.set_St761939237tant_a)) (= (ho_163 v ii) (ite (= i ii) e (ho_163 u ii)))))))))) (let ((_let_147 (forall ((x |u_(-> tptp.set_St761939237tant_a tptp.set_Pr1174980151um_a_b)|) (y |u_(-> tptp.set_St761939237tant_a tptp.set_Pr1174980151um_a_b)|)) (or (not (forall ((z tptp.set_St761939237tant_a)) (= (ho_163 x z) (ho_163 y z)))) (= x y))))) (let ((_let_148 (forall ((u |u_(-> tptp.produc1124793815um_a_b tptp.produc323101606um_a_b)|) (e tptp.produc323101606um_a_b) (i tptp.produc1124793815um_a_b)) (not (forall ((v |u_(-> tptp.produc1124793815um_a_b tptp.produc323101606um_a_b)|)) (not (forall ((ii tptp.produc1124793815um_a_b)) (= (ho_203 v ii) (ite (= i ii) e (ho_203 u ii)))))))))) (let ((_let_149 (forall ((x |u_(-> tptp.produc1124793815um_a_b tptp.produc323101606um_a_b)|) (y |u_(-> tptp.produc1124793815um_a_b tptp.produc323101606um_a_b)|)) (or (not (forall ((z tptp.produc1124793815um_a_b)) (= (ho_203 x z) (ho_203 y z)))) (= x y))))) (let ((_let_150 (forall ((u |u_(-> tptp.labele431970251um_a_b tptp.labele431970251um_a_b tptp.set_Pr1916610317um_a_b Bool)|) (e |u_(-> tptp.labele431970251um_a_b tptp.set_Pr1916610317um_a_b Bool)|) (i tptp.labele431970251um_a_b)) (not (forall ((v |u_(-> tptp.labele431970251um_a_b tptp.labele431970251um_a_b tptp.set_Pr1916610317um_a_b Bool)|)) (not (forall ((ii tptp.labele431970251um_a_b)) (= (ho_310 v ii) (ite (= i ii) e (ho_310 u ii)))))))))) (let ((_let_151 (forall ((x |u_(-> tptp.labele431970251um_a_b tptp.labele431970251um_a_b tptp.set_Pr1916610317um_a_b Bool)|) (y |u_(-> tptp.labele431970251um_a_b tptp.labele431970251um_a_b tptp.set_Pr1916610317um_a_b Bool)|)) (or (not (forall ((z tptp.labele431970251um_a_b)) (= (ho_310 x z) (ho_310 y z)))) (= x y))))) (let ((_let_152 (forall ((u |u_(-> tptp.set_Pr1916610317um_a_b Bool)|) (e Bool) (i tptp.set_Pr1916610317um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1916610317um_a_b Bool)|)) (not (forall ((ii tptp.set_Pr1916610317um_a_b)) (= (ho_160 v ii) (ite (= i ii) e (ho_160 u ii)))))))))) (let ((_let_153 (forall ((x |u_(-> tptp.set_Pr1916610317um_a_b Bool)|) (y |u_(-> tptp.set_Pr1916610317um_a_b Bool)|)) (or (not (forall ((z tptp.set_Pr1916610317um_a_b)) (= (ho_160 x z) (ho_160 y z)))) (= x y))))) (let ((_let_154 (forall ((u |u_(-> tptp.produc204140796um_a_b tptp.set_Pr1618094130um_a_b Bool)|) (e |u_(-> tptp.set_Pr1618094130um_a_b Bool)|) (i tptp.produc204140796um_a_b)) (not (forall ((v |u_(-> tptp.produc204140796um_a_b tptp.set_Pr1618094130um_a_b Bool)|)) (not (forall ((ii tptp.produc204140796um_a_b)) (= (ho_154 v ii) (ite (= i ii) e (ho_154 u ii)))))))))) (let ((_let_155 (forall ((x |u_(-> tptp.produc204140796um_a_b tptp.set_Pr1618094130um_a_b Bool)|) (y |u_(-> tptp.produc204140796um_a_b tptp.set_Pr1618094130um_a_b Bool)|)) (or (not (forall ((z tptp.produc204140796um_a_b)) (= (ho_154 x z) (ho_154 y z)))) (= x y))))) (let ((_let_156 (forall ((u |u_(-> tptp.set_Pr195945996um_a_b Bool)|) (e Bool) (i tptp.set_Pr195945996um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr195945996um_a_b Bool)|)) (not (forall ((ii tptp.set_Pr195945996um_a_b)) (= (ho_143 v ii) (ite (= i ii) e (ho_143 u ii)))))))))) (let ((_let_157 (forall ((x |u_(-> tptp.set_Pr195945996um_a_b Bool)|) (y |u_(-> tptp.set_Pr195945996um_a_b Bool)|)) (or (not (forall ((z tptp.set_Pr195945996um_a_b)) (= (ho_143 x z) (ho_143 y z)))) (= x y))))) (let ((_let_158 (forall ((u |u_(-> tptp.set_Pr1618094130um_a_b Bool)|) (e Bool) (i tptp.set_Pr1618094130um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1618094130um_a_b Bool)|)) (not (forall ((ii tptp.set_Pr1618094130um_a_b)) (= (ho_155 v ii) (ite (= i ii) e (ho_155 u ii)))))))))) (let ((_let_159 (forall ((x |u_(-> tptp.set_Pr1618094130um_a_b Bool)|) (y |u_(-> tptp.set_Pr1618094130um_a_b Bool)|)) (or (not (forall ((z tptp.set_Pr1618094130um_a_b)) (= (ho_155 x z) (ho_155 y z)))) (= x y))))) (let ((_let_160 (forall ((u |u_(-> tptp.set_Pr1986765409at_nat tptp.set_Pr1647387645at_nat tptp.set_Pr1647387645at_nat Bool)|) (e |u_(-> tptp.set_Pr1647387645at_nat tptp.set_Pr1647387645at_nat Bool)|) (i tptp.set_Pr1986765409at_nat)) (not (forall ((v |u_(-> tptp.set_Pr1986765409at_nat tptp.set_Pr1647387645at_nat tptp.set_Pr1647387645at_nat Bool)|)) (not (forall ((ii tptp.set_Pr1986765409at_nat)) (= (ho_274 v ii) (ite (= i ii) e (ho_274 u ii)))))))))) (let ((_let_161 (forall ((x |u_(-> tptp.set_Pr1986765409at_nat tptp.set_Pr1647387645at_nat tptp.set_Pr1647387645at_nat Bool)|) (y |u_(-> tptp.set_Pr1986765409at_nat tptp.set_Pr1647387645at_nat tptp.set_Pr1647387645at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1986765409at_nat)) (= (ho_274 x z) (ho_274 y z)))) (= x y))))) (let ((_let_162 (forall ((u |u_(-> tptp.labele431970251um_a_b tptp.set_Pr1916610317um_a_b Bool)|) (e |u_(-> tptp.set_Pr1916610317um_a_b Bool)|) (i tptp.labele431970251um_a_b)) (not (forall ((v |u_(-> tptp.labele431970251um_a_b tptp.set_Pr1916610317um_a_b Bool)|)) (not (forall ((ii tptp.labele431970251um_a_b)) (= (ho_311 v ii) (ite (= i ii) e (ho_311 u ii)))))))))) (let ((_let_163 (forall ((x |u_(-> tptp.labele431970251um_a_b tptp.set_Pr1916610317um_a_b Bool)|) (y |u_(-> tptp.labele431970251um_a_b tptp.set_Pr1916610317um_a_b Bool)|)) (or (not (forall ((z tptp.labele431970251um_a_b)) (= (ho_311 x z) (ho_311 y z)))) (= x y))))) (let ((_let_164 (forall ((u |u_(-> tptp.set_Pr1618094130um_a_b tptp.set_nat tptp.set_Pr1174980151um_a_b)|) (e |u_(-> tptp.set_nat tptp.set_Pr1174980151um_a_b)|) (i tptp.set_Pr1618094130um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1618094130um_a_b tptp.set_nat tptp.set_Pr1174980151um_a_b)|)) (not (forall ((ii tptp.set_Pr1618094130um_a_b)) (= (ho_148 v ii) (ite (= i ii) e (ho_148 u ii)))))))))) (let ((_let_165 (forall ((x |u_(-> tptp.set_Pr1618094130um_a_b tptp.set_nat tptp.set_Pr1174980151um_a_b)|) (y |u_(-> tptp.set_Pr1618094130um_a_b tptp.set_nat tptp.set_Pr1174980151um_a_b)|)) (or (not (forall ((z tptp.set_Pr1618094130um_a_b)) (= (ho_148 x z) (ho_148 y z)))) (= x y))))) (let ((_let_166 (forall ((u |u_(-> tptp.labele431970251um_a_b tptp.set_Pr1916610317um_a_b)|) (e tptp.set_Pr1916610317um_a_b) (i tptp.labele431970251um_a_b)) (not (forall ((v |u_(-> tptp.labele431970251um_a_b tptp.set_Pr1916610317um_a_b)|)) (not (forall ((ii tptp.labele431970251um_a_b)) (= (ho_78 v ii) (ite (= i ii) e (ho_78 u ii)))))))))) (let ((_let_167 (forall ((x |u_(-> tptp.labele431970251um_a_b tptp.set_Pr1916610317um_a_b)|) (y |u_(-> tptp.labele431970251um_a_b tptp.set_Pr1916610317um_a_b)|)) (or (not (forall ((z tptp.labele431970251um_a_b)) (= (ho_78 x z) (ho_78 y z)))) (= x y))))) (let ((_let_168 (forall ((u |u_(-> tptp.produc1124793815um_a_b tptp.sum_sum_a_b tptp.produc585753260um_a_b)|) (e |u_(-> tptp.sum_sum_a_b tptp.produc585753260um_a_b)|) (i tptp.produc1124793815um_a_b)) (not (forall ((v |u_(-> tptp.produc1124793815um_a_b tptp.sum_sum_a_b tptp.produc585753260um_a_b)|)) (not (forall ((ii tptp.produc1124793815um_a_b)) (= (ho_180 v ii) (ite (= i ii) e (ho_180 u ii)))))))))) (let ((_let_169 (forall ((x |u_(-> tptp.produc1124793815um_a_b tptp.sum_sum_a_b tptp.produc585753260um_a_b)|) (y |u_(-> tptp.produc1124793815um_a_b tptp.sum_sum_a_b tptp.produc585753260um_a_b)|)) (or (not (forall ((z tptp.produc1124793815um_a_b)) (= (ho_180 x z) (ho_180 y z)))) (= x y))))) (let ((_let_170 (forall ((u |u_(-> tptp.produc1798470614um_a_b tptp.set_Pr195945996um_a_b Bool)|) (e |u_(-> tptp.set_Pr195945996um_a_b Bool)|) (i tptp.produc1798470614um_a_b)) (not (forall ((v |u_(-> tptp.produc1798470614um_a_b tptp.set_Pr195945996um_a_b Bool)|)) (not (forall ((ii tptp.produc1798470614um_a_b)) (= (ho_142 v ii) (ite (= i ii) e (ho_142 u ii)))))))))) (let ((_let_171 (forall ((x |u_(-> tptp.produc1798470614um_a_b tptp.set_Pr195945996um_a_b Bool)|) (y |u_(-> tptp.produc1798470614um_a_b tptp.set_Pr195945996um_a_b Bool)|)) (or (not (forall ((z tptp.produc1798470614um_a_b)) (= (ho_142 x z) (ho_142 y z)))) (= x y))))) (let ((_let_172 (forall ((u |u_(-> tptp.labele935650037_a_nat Bool)|) (e Bool) (i tptp.labele935650037_a_nat)) (not (forall ((v |u_(-> tptp.labele935650037_a_nat Bool)|)) (not (forall ((ii tptp.labele935650037_a_nat)) (= (ho_250 v ii) (ite (= i ii) e (ho_250 u ii)))))))))) (let ((_let_173 (forall ((x |u_(-> tptp.labele935650037_a_nat Bool)|) (y |u_(-> tptp.labele935650037_a_nat Bool)|)) (or (not (forall ((z tptp.labele935650037_a_nat)) (= (ho_250 x z) (ho_250 y z)))) (= x y))))) (let ((_let_174 (forall ((u |u_(-> tptp.product_prod_nat_nat tptp.sum_sum_a_b tptp.produc1798470614um_a_b)|) (e |u_(-> tptp.sum_sum_a_b tptp.produc1798470614um_a_b)|) (i tptp.product_prod_nat_nat)) (not (forall ((v |u_(-> tptp.product_prod_nat_nat tptp.sum_sum_a_b tptp.produc1798470614um_a_b)|)) (not (forall ((ii tptp.product_prod_nat_nat)) (= (ho_139 v ii) (ite (= i ii) e (ho_139 u ii)))))))))) (let ((_let_175 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.sum_sum_a_b tptp.produc1798470614um_a_b)|) (y |u_(-> tptp.product_prod_nat_nat tptp.sum_sum_a_b tptp.produc1798470614um_a_b)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_139 x z) (ho_139 y z)))) (= x y))))) (let ((_let_176 (forall ((u |u_(-> tptp.sum_sum_a_b tptp.produc1798470614um_a_b)|) (e tptp.produc1798470614um_a_b) (i tptp.sum_sum_a_b)) (not (forall ((v |u_(-> tptp.sum_sum_a_b tptp.produc1798470614um_a_b)|)) (not (forall ((ii tptp.sum_sum_a_b)) (= (ho_140 v ii) (ite (= i ii) e (ho_140 u ii)))))))))) (let ((_let_177 (forall ((x |u_(-> tptp.sum_sum_a_b tptp.produc1798470614um_a_b)|) (y |u_(-> tptp.sum_sum_a_b tptp.produc1798470614um_a_b)|)) (or (not (forall ((z tptp.sum_sum_a_b)) (= (ho_140 x z) (ho_140 y z)))) (= x y))))) (let ((_let_178 (forall ((u |u_(-> tptp.produc1124793815um_a_b tptp.produc1124793815um_a_b tptp.produc1918750183um_a_b)|) (e |u_(-> tptp.produc1124793815um_a_b tptp.produc1918750183um_a_b)|) (i tptp.produc1124793815um_a_b)) (not (forall ((v |u_(-> tptp.produc1124793815um_a_b tptp.produc1124793815um_a_b tptp.produc1918750183um_a_b)|)) (not (forall ((ii tptp.produc1124793815um_a_b)) (= (ho_210 v ii) (ite (= i ii) e (ho_210 u ii)))))))))) (let ((_let_179 (forall ((x |u_(-> tptp.produc1124793815um_a_b tptp.produc1124793815um_a_b tptp.produc1918750183um_a_b)|) (y |u_(-> tptp.produc1124793815um_a_b tptp.produc1124793815um_a_b tptp.produc1918750183um_a_b)|)) (or (not (forall ((z tptp.produc1124793815um_a_b)) (= (ho_210 x z) (ho_210 y z)))) (= x y))))) (let ((_let_180 (forall ((u |u_(-> tptp.produc1546082365um_a_b tptp.set_Pr386468381um_a_b Bool)|) (e |u_(-> tptp.set_Pr386468381um_a_b Bool)|) (i tptp.produc1546082365um_a_b)) (not (forall ((v |u_(-> tptp.produc1546082365um_a_b tptp.set_Pr386468381um_a_b Bool)|)) (not (forall ((ii tptp.produc1546082365um_a_b)) (= (ho_174 v ii) (ite (= i ii) e (ho_174 u ii)))))))))) (let ((_let_181 (forall ((x |u_(-> tptp.produc1546082365um_a_b tptp.set_Pr386468381um_a_b Bool)|) (y |u_(-> tptp.produc1546082365um_a_b tptp.set_Pr386468381um_a_b Bool)|)) (or (not (forall ((z tptp.produc1546082365um_a_b)) (= (ho_174 x z) (ho_174 y z)))) (= x y))))) (let ((_let_182 (forall ((u |u_(-> tptp.set_Pr1783309276um_a_b tptp.set_Sum_sum_a_b tptp.set_Pr1174980151um_a_b)|) (e |u_(-> tptp.set_Sum_sum_a_b tptp.set_Pr1174980151um_a_b)|) (i tptp.set_Pr1783309276um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1783309276um_a_b tptp.set_Sum_sum_a_b tptp.set_Pr1174980151um_a_b)|)) (not (forall ((ii tptp.set_Pr1783309276um_a_b)) (= (ho_199 v ii) (ite (= i ii) e (ho_199 u ii)))))))))) (let ((_let_183 (forall ((x |u_(-> tptp.set_Pr1783309276um_a_b tptp.set_Sum_sum_a_b tptp.set_Pr1174980151um_a_b)|) (y |u_(-> tptp.set_Pr1783309276um_a_b tptp.set_Sum_sum_a_b tptp.set_Pr1174980151um_a_b)|)) (or (not (forall ((z tptp.set_Pr1783309276um_a_b)) (= (ho_199 x z) (ho_199 y z)))) (= x y))))) (let ((_let_184 (forall ((u |u_(-> tptp.set_Pr1647387645at_nat Bool)|) (e Bool) (i tptp.set_Pr1647387645at_nat)) (not (forall ((v |u_(-> tptp.set_Pr1647387645at_nat Bool)|)) (not (forall ((ii tptp.set_Pr1647387645at_nat)) (= (ho_137 v ii) (ite (= i ii) e (ho_137 u ii)))))))))) (let ((_let_185 (forall ((x |u_(-> tptp.set_Pr1647387645at_nat Bool)|) (y |u_(-> tptp.set_Pr1647387645at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1647387645at_nat)) (= (ho_137 x z) (ho_137 y z)))) (= x y))))) (let ((_let_186 (forall ((u |u_(-> tptp.set_Pr1647387645at_nat tptp.set_St761939237tant_a tptp.set_Pr1986765409at_nat)|) (e |u_(-> tptp.set_St761939237tant_a tptp.set_Pr1986765409at_nat)|) (i tptp.set_Pr1647387645at_nat)) (not (forall ((v |u_(-> tptp.set_Pr1647387645at_nat tptp.set_St761939237tant_a tptp.set_Pr1986765409at_nat)|)) (not (forall ((ii tptp.set_Pr1647387645at_nat)) (= (ho_133 v ii) (ite (= i ii) e (ho_133 u ii)))))))))) (let ((_let_187 (forall ((x |u_(-> tptp.set_Pr1647387645at_nat tptp.set_St761939237tant_a tptp.set_Pr1986765409at_nat)|) (y |u_(-> tptp.set_Pr1647387645at_nat tptp.set_St761939237tant_a tptp.set_Pr1986765409at_nat)|)) (or (not (forall ((z tptp.set_Pr1647387645at_nat)) (= (ho_133 x z) (ho_133 y z)))) (= x y))))) (let ((_let_188 (forall ((u |u_(-> tptp.set_St761939237tant_a tptp.set_Pr1986765409at_nat)|) (e tptp.set_Pr1986765409at_nat) (i tptp.set_St761939237tant_a)) (not (forall ((v |u_(-> tptp.set_St761939237tant_a tptp.set_Pr1986765409at_nat)|)) (not (forall ((ii tptp.set_St761939237tant_a)) (= (ho_134 v ii) (ite (= i ii) e (ho_134 u ii)))))))))) (let ((_let_189 (forall ((x |u_(-> tptp.set_St761939237tant_a tptp.set_Pr1986765409at_nat)|) (y |u_(-> tptp.set_St761939237tant_a tptp.set_Pr1986765409at_nat)|)) (or (not (forall ((z tptp.set_St761939237tant_a)) (= (ho_134 x z) (ho_134 y z)))) (= x y))))) (let ((_let_190 (forall ((u |u_(-> tptp.nat tptp.produc1124793815um_a_b tptp.produc204140796um_a_b)|) (e |u_(-> tptp.produc1124793815um_a_b tptp.produc204140796um_a_b)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.produc1124793815um_a_b tptp.produc204140796um_a_b)|)) (not (forall ((ii tptp.nat)) (= (ho_151 v ii) (ite (= i ii) e (ho_151 u ii)))))))))) (let ((_let_191 (forall ((x |u_(-> tptp.nat tptp.produc1124793815um_a_b tptp.produc204140796um_a_b)|) (y |u_(-> tptp.nat tptp.produc1124793815um_a_b tptp.produc204140796um_a_b)|)) (or (not (forall ((z tptp.nat)) (= (ho_151 x z) (ho_151 y z)))) (= x y))))) (let ((_let_192 (forall ((u |u_(-> tptp.produc1394389750um_a_b tptp.set_Pr1994339542um_a_b Bool)|) (e |u_(-> tptp.set_Pr1994339542um_a_b Bool)|) (i tptp.produc1394389750um_a_b)) (not (forall ((v |u_(-> tptp.produc1394389750um_a_b tptp.set_Pr1994339542um_a_b Bool)|)) (not (forall ((ii tptp.produc1394389750um_a_b)) (= (ho_130 v ii) (ite (= i ii) e (ho_130 u ii)))))))))) (let ((_let_193 (forall ((x |u_(-> tptp.produc1394389750um_a_b tptp.set_Pr1994339542um_a_b Bool)|) (y |u_(-> tptp.produc1394389750um_a_b tptp.set_Pr1994339542um_a_b Bool)|)) (or (not (forall ((z tptp.produc1394389750um_a_b)) (= (ho_130 x z) (ho_130 y z)))) (= x y))))) (let ((_let_194 (forall ((u |u_(-> tptp.produc1032616263at_nat tptp.set_Pr1647387645at_nat Bool)|) (e |u_(-> tptp.set_Pr1647387645at_nat Bool)|) (i tptp.produc1032616263at_nat)) (not (forall ((v |u_(-> tptp.produc1032616263at_nat tptp.set_Pr1647387645at_nat Bool)|)) (not (forall ((ii tptp.produc1032616263at_nat)) (= (ho_136 v ii) (ite (= i ii) e (ho_136 u ii)))))))))) (let ((_let_195 (forall ((x |u_(-> tptp.produc1032616263at_nat tptp.set_Pr1647387645at_nat Bool)|) (y |u_(-> tptp.produc1032616263at_nat tptp.set_Pr1647387645at_nat Bool)|)) (or (not (forall ((z tptp.produc1032616263at_nat)) (= (ho_136 x z) (ho_136 y z)))) (= x y))))) (let ((_let_196 (forall ((u |u_(-> tptp.standard_Constant_a tptp.sum_sum_a_b tptp.produc1394389750um_a_b)|) (e |u_(-> tptp.sum_sum_a_b tptp.produc1394389750um_a_b)|) (i tptp.standard_Constant_a)) (not (forall ((v |u_(-> tptp.standard_Constant_a tptp.sum_sum_a_b tptp.produc1394389750um_a_b)|)) (not (forall ((ii tptp.standard_Constant_a)) (= (ho_127 v ii) (ite (= i ii) e (ho_127 u ii)))))))))) (let ((_let_197 (forall ((x |u_(-> tptp.standard_Constant_a tptp.sum_sum_a_b tptp.produc1394389750um_a_b)|) (y |u_(-> tptp.standard_Constant_a tptp.sum_sum_a_b tptp.produc1394389750um_a_b)|)) (or (not (forall ((z tptp.standard_Constant_a)) (= (ho_127 x z) (ho_127 y z)))) (= x y))))) (let ((_let_198 (forall ((u |u_(-> tptp.set_Pr1994339542um_a_b Bool)|) (e Bool) (i tptp.set_Pr1994339542um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1994339542um_a_b Bool)|)) (not (forall ((ii tptp.set_Pr1994339542um_a_b)) (= (ho_131 v ii) (ite (= i ii) e (ho_131 u ii)))))))))) (let ((_let_199 (forall ((x |u_(-> tptp.set_Pr1994339542um_a_b Bool)|) (y |u_(-> tptp.set_Pr1994339542um_a_b Bool)|)) (or (not (forall ((z tptp.set_Pr1994339542um_a_b)) (= (ho_131 x z) (ho_131 y z)))) (= x y))))) (let ((_let_200 (forall ((u |u_(-> tptp.set_St761939237tant_a tptp.set_Pr1916610317um_a_b)|) (e tptp.set_Pr1916610317um_a_b) (i tptp.set_St761939237tant_a)) (not (forall ((v |u_(-> tptp.set_St761939237tant_a tptp.set_Pr1916610317um_a_b)|)) (not (forall ((ii tptp.set_St761939237tant_a)) (= (ho_194 v ii) (ite (= i ii) e (ho_194 u ii)))))))))) (let ((_let_201 (forall ((x |u_(-> tptp.set_St761939237tant_a tptp.set_Pr1916610317um_a_b)|) (y |u_(-> tptp.set_St761939237tant_a tptp.set_Pr1916610317um_a_b)|)) (or (not (forall ((z tptp.set_St761939237tant_a)) (= (ho_194 x z) (ho_194 y z)))) (= x y))))) (let ((_let_202 (forall ((u |u_(-> tptp.set_Pr1994339542um_a_b tptp.set_St761939237tant_a tptp.set_Sum_sum_a_b)|) (e |u_(-> tptp.set_St761939237tant_a tptp.set_Sum_sum_a_b)|) (i tptp.set_Pr1994339542um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1994339542um_a_b tptp.set_St761939237tant_a tptp.set_Sum_sum_a_b)|)) (not (forall ((ii tptp.set_Pr1994339542um_a_b)) (= (ho_124 v ii) (ite (= i ii) e (ho_124 u ii)))))))))) (let ((_let_203 (forall ((x |u_(-> tptp.set_Pr1994339542um_a_b tptp.set_St761939237tant_a tptp.set_Sum_sum_a_b)|) (y |u_(-> tptp.set_Pr1994339542um_a_b tptp.set_St761939237tant_a tptp.set_Sum_sum_a_b)|)) (or (not (forall ((z tptp.set_Pr1994339542um_a_b)) (= (ho_124 x z) (ho_124 y z)))) (= x y))))) (let ((_let_204 (forall ((u |u_(-> tptp.set_St761939237tant_a tptp.set_Sum_sum_a_b)|) (e tptp.set_Sum_sum_a_b) (i tptp.set_St761939237tant_a)) (not (forall ((v |u_(-> tptp.set_St761939237tant_a tptp.set_Sum_sum_a_b)|)) (not (forall ((ii tptp.set_St761939237tant_a)) (= (ho_125 v ii) (ite (= i ii) e (ho_125 u ii)))))))))) (let ((_let_205 (forall ((x |u_(-> tptp.set_St761939237tant_a tptp.set_Sum_sum_a_b)|) (y |u_(-> tptp.set_St761939237tant_a tptp.set_Sum_sum_a_b)|)) (or (not (forall ((z tptp.set_St761939237tant_a)) (= (ho_125 x z) (ho_125 y z)))) (= x y))))) (let ((_let_206 (forall ((u |u_(-> tptp.set_nat tptp.set_Pr1916610317um_a_b)|) (e tptp.set_Pr1916610317um_a_b) (i tptp.set_nat)) (not (forall ((v |u_(-> tptp.set_nat tptp.set_Pr1916610317um_a_b)|)) (not (forall ((ii tptp.set_nat)) (= (ho_246 v ii) (ite (= i ii) e (ho_246 u ii)))))))))) (let ((_let_207 (forall ((x |u_(-> tptp.set_nat tptp.set_Pr1916610317um_a_b)|) (y |u_(-> tptp.set_nat tptp.set_Pr1916610317um_a_b)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_246 x z) (ho_246 y z)))) (= x y))))) (let ((_let_208 (forall ((u |u_(-> tptp.nat tptp.produc1978941143_b_nat)|) (e tptp.produc1978941143_b_nat) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.produc1978941143_b_nat)|)) (not (forall ((ii tptp.nat)) (= (ho_266 v ii) (ite (= i ii) e (ho_266 u ii)))))))))) (let ((_let_209 (forall ((x |u_(-> tptp.nat tptp.produc1978941143_b_nat)|) (y |u_(-> tptp.nat tptp.produc1978941143_b_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_266 x z) (ho_266 y z)))) (= x y))))) (let ((_let_210 (forall ((u |u_(-> _u_(-> tptp.produc1124793815um_a_b Bool)_ tptp.set_Pr1174980151um_a_b)|) (e tptp.set_Pr1174980151um_a_b) (i |u_(-> tptp.produc1124793815um_a_b Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1124793815um_a_b Bool)_ tptp.set_Pr1174980151um_a_b)|)) (not (forall ((ii |u_(-> tptp.produc1124793815um_a_b Bool)|)) (= (ho_283 v ii) (ite (= i ii) e (ho_283 u ii)))))))))) (let ((_let_211 (forall ((x |u_(-> _u_(-> tptp.produc1124793815um_a_b Bool)_ tptp.set_Pr1174980151um_a_b)|) (y |u_(-> _u_(-> tptp.produc1124793815um_a_b Bool)_ tptp.set_Pr1174980151um_a_b)|)) (or (not (forall ((z |u_(-> tptp.produc1124793815um_a_b Bool)|)) (= (ho_283 x z) (ho_283 y z)))) (= x y))))) (let ((_let_212 (forall ((u |u_(-> tptp.set_nat Bool)|) (e Bool) (i tptp.set_nat)) (not (forall ((v |u_(-> tptp.set_nat Bool)|)) (not (forall ((ii tptp.set_nat)) (= (ho_119 v ii) (ite (= i ii) e (ho_119 u ii)))))))))) (let ((_let_213 (forall ((x |u_(-> tptp.set_nat Bool)|) (y |u_(-> tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_119 x z) (ho_119 y z)))) (= x y))))) (let ((_let_214 (forall ((u |u_(-> tptp.produc1548871597um_a_b tptp.set_Pr1916610317um_a_b tptp.set_Pr1916610317um_a_b)|) (e |u_(-> tptp.set_Pr1916610317um_a_b tptp.set_Pr1916610317um_a_b)|) (i tptp.produc1548871597um_a_b)) (not (forall ((v |u_(-> tptp.produc1548871597um_a_b tptp.set_Pr1916610317um_a_b tptp.set_Pr1916610317um_a_b)|)) (not (forall ((ii tptp.produc1548871597um_a_b)) (= (ho_113 v ii) (ite (= i ii) e (ho_113 u ii)))))))))) (let ((_let_215 (forall ((x |u_(-> tptp.produc1548871597um_a_b tptp.set_Pr1916610317um_a_b tptp.set_Pr1916610317um_a_b)|) (y |u_(-> tptp.produc1548871597um_a_b tptp.set_Pr1916610317um_a_b tptp.set_Pr1916610317um_a_b)|)) (or (not (forall ((z tptp.produc1548871597um_a_b)) (= (ho_113 x z) (ho_113 y z)))) (= x y))))) (let ((_let_216 (forall ((u |u_(-> tptp.product_prod_nat_nat tptp.set_Pr1986765409at_nat Bool)|) (e |u_(-> tptp.set_Pr1986765409at_nat Bool)|) (i tptp.product_prod_nat_nat)) (not (forall ((v |u_(-> tptp.product_prod_nat_nat tptp.set_Pr1986765409at_nat Bool)|)) (not (forall ((ii tptp.product_prod_nat_nat)) (= (ho_121 v ii) (ite (= i ii) e (ho_121 u ii)))))))))) (let ((_let_217 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.set_Pr1986765409at_nat Bool)|) (y |u_(-> tptp.product_prod_nat_nat tptp.set_Pr1986765409at_nat Bool)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_121 x z) (ho_121 y z)))) (= x y))))) (let ((_let_218 (forall ((u |u_(-> tptp.nat tptp.sum_sum_a_b tptp.produc1124793815um_a_b)|) (e |u_(-> tptp.sum_sum_a_b tptp.produc1124793815um_a_b)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.sum_sum_a_b tptp.produc1124793815um_a_b)|)) (not (forall ((ii tptp.nat)) (= (ho_58 v ii) (ite (= i ii) e (ho_58 u ii)))))))))) (let ((_let_219 (forall ((x |u_(-> tptp.nat tptp.sum_sum_a_b tptp.produc1124793815um_a_b)|) (y |u_(-> tptp.nat tptp.sum_sum_a_b tptp.produc1124793815um_a_b)|)) (or (not (forall ((z tptp.nat)) (= (ho_58 x z) (ho_58 y z)))) (= x y))))) (let ((_let_220 (forall ((u |u_(-> tptp.sum_sum_a_b tptp.set_Sum_sum_a_b tptp.set_Sum_sum_a_b)|) (e |u_(-> tptp.set_Sum_sum_a_b tptp.set_Sum_sum_a_b)|) (i tptp.sum_sum_a_b)) (not (forall ((v |u_(-> tptp.sum_sum_a_b tptp.set_Sum_sum_a_b tptp.set_Sum_sum_a_b)|)) (not (forall ((ii tptp.sum_sum_a_b)) (= (ho_82 v ii) (ite (= i ii) e (ho_82 u ii)))))))))) (let ((_let_221 (forall ((x |u_(-> tptp.sum_sum_a_b tptp.set_Sum_sum_a_b tptp.set_Sum_sum_a_b)|) (y |u_(-> tptp.sum_sum_a_b tptp.set_Sum_sum_a_b tptp.set_Sum_sum_a_b)|)) (or (not (forall ((z tptp.sum_sum_a_b)) (= (ho_82 x z) (ho_82 y z)))) (= x y))))) (let ((_let_222 (forall ((u |u_(-> tptp.labele935650037_a_nat tptp.set_Pr375490359_b_nat Bool)|) (e |u_(-> tptp.set_Pr375490359_b_nat Bool)|) (i tptp.labele935650037_a_nat)) (not (forall ((v |u_(-> tptp.labele935650037_a_nat tptp.set_Pr375490359_b_nat Bool)|)) (not (forall ((ii tptp.labele935650037_a_nat)) (= (ho_301 v ii) (ite (= i ii) e (ho_301 u ii)))))))))) (let ((_let_223 (forall ((x |u_(-> tptp.labele935650037_a_nat tptp.set_Pr375490359_b_nat Bool)|) (y |u_(-> tptp.labele935650037_a_nat tptp.set_Pr375490359_b_nat Bool)|)) (or (not (forall ((z tptp.labele935650037_a_nat)) (= (ho_301 x z) (ho_301 y z)))) (= x y))))) (let ((_let_224 (forall ((u |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_Pr1174980151um_a_b)|) (e tptp.set_Pr1174980151um_a_b) (i tptp.set_Pr1174980151um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_Pr1174980151um_a_b)|)) (not (forall ((ii tptp.set_Pr1174980151um_a_b)) (= (ho_62 v ii) (ite (= i ii) e (ho_62 u ii)))))))))) (let ((_let_225 (forall ((x |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_Pr1174980151um_a_b)|) (y |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_Pr1174980151um_a_b)|)) (or (not (forall ((z tptp.set_Pr1174980151um_a_b)) (= (ho_62 x z) (ho_62 y z)))) (= x y))))) (let ((_let_226 (forall ((u |u_(-> tptp.produc323101606um_a_b tptp.set_Pr1783309276um_a_b Bool)|) (e |u_(-> tptp.set_Pr1783309276um_a_b Bool)|) (i tptp.produc323101606um_a_b)) (not (forall ((v |u_(-> tptp.produc323101606um_a_b tptp.set_Pr1783309276um_a_b Bool)|)) (not (forall ((ii tptp.produc323101606um_a_b)) (= (ho_205 v ii) (ite (= i ii) e (ho_205 u ii)))))))))) (let ((_let_227 (forall ((x |u_(-> tptp.produc323101606um_a_b tptp.set_Pr1783309276um_a_b Bool)|) (y |u_(-> tptp.produc323101606um_a_b tptp.set_Pr1783309276um_a_b Bool)|)) (or (not (forall ((z tptp.produc323101606um_a_b)) (= (ho_205 x z) (ho_205 y z)))) (= x y))))) (let ((_let_228 (forall ((u |u_(-> tptp.nat tptp.set_nat Bool)|) (e |u_(-> tptp.set_nat Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.set_nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_118 v ii) (ite (= i ii) e (ho_118 u ii)))))))))) (let ((_let_229 (forall ((x |u_(-> tptp.nat tptp.set_nat Bool)|) (y |u_(-> tptp.nat tptp.set_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_118 x z) (ho_118 y z)))) (= x y))))) (let ((_let_230 (forall ((u |u_(-> tptp.standard_Constant_a tptp.produc1548871597um_a_b tptp.produc1963079155um_a_b)|) (e |u_(-> tptp.produc1548871597um_a_b tptp.produc1963079155um_a_b)|) (i tptp.standard_Constant_a)) (not (forall ((v |u_(-> tptp.standard_Constant_a tptp.produc1548871597um_a_b tptp.produc1963079155um_a_b)|)) (not (forall ((ii tptp.standard_Constant_a)) (= (ho_88 v ii) (ite (= i ii) e (ho_88 u ii)))))))))) (let ((_let_231 (forall ((x |u_(-> tptp.standard_Constant_a tptp.produc1548871597um_a_b tptp.produc1963079155um_a_b)|) (y |u_(-> tptp.standard_Constant_a tptp.produc1548871597um_a_b tptp.produc1963079155um_a_b)|)) (or (not (forall ((z tptp.standard_Constant_a)) (= (ho_88 x z) (ho_88 y z)))) (= x y))))) (let ((_let_232 (forall ((u |u_(-> tptp.set_Pr1558970842um_a_b tptp.set_Sum_sum_a_b tptp.set_Pr409224873um_a_b)|) (e |u_(-> tptp.set_Sum_sum_a_b tptp.set_Pr409224873um_a_b)|) (i tptp.set_Pr1558970842um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1558970842um_a_b tptp.set_Sum_sum_a_b tptp.set_Pr409224873um_a_b)|)) (not (forall ((ii tptp.set_Pr1558970842um_a_b)) (= (ho_216 v ii) (ite (= i ii) e (ho_216 u ii)))))))))) (let ((_let_233 (forall ((x |u_(-> tptp.set_Pr1558970842um_a_b tptp.set_Sum_sum_a_b tptp.set_Pr409224873um_a_b)|) (y |u_(-> tptp.set_Pr1558970842um_a_b tptp.set_Sum_sum_a_b tptp.set_Pr409224873um_a_b)|)) (or (not (forall ((z tptp.set_Pr1558970842um_a_b)) (= (ho_216 x z) (ho_216 y z)))) (= x y))))) (let ((_let_234 (forall ((u |u_(-> tptp.labele431970251um_a_b tptp.labele431970251um_a_b)|) (e tptp.labele431970251um_a_b) (i tptp.labele431970251um_a_b)) (not (forall ((v |u_(-> tptp.labele431970251um_a_b tptp.labele431970251um_a_b)|)) (not (forall ((ii tptp.labele431970251um_a_b)) (= (ho_43 v ii) (ite (= i ii) e (ho_43 u ii)))))))))) (let ((_let_235 (forall ((x |u_(-> tptp.labele431970251um_a_b tptp.labele431970251um_a_b)|) (y |u_(-> tptp.labele431970251um_a_b tptp.labele431970251um_a_b)|)) (or (not (forall ((z tptp.labele431970251um_a_b)) (= (ho_43 x z) (ho_43 y z)))) (= x y))))) (let ((_let_236 (forall ((u |u_(-> tptp.set_Pr507214050_b_nat Bool)|) (e Bool) (i tptp.set_Pr507214050_b_nat)) (not (forall ((v |u_(-> tptp.set_Pr507214050_b_nat Bool)|)) (not (forall ((ii tptp.set_Pr507214050_b_nat)) (= (ho_328 v ii) (ite (= i ii) e (ho_328 u ii)))))))))) (let ((_let_237 (forall ((x |u_(-> tptp.set_Pr507214050_b_nat Bool)|) (y |u_(-> tptp.set_Pr507214050_b_nat Bool)|)) (or (not (forall ((z tptp.set_Pr507214050_b_nat)) (= (ho_328 x z) (ho_328 y z)))) (= x y))))) (let ((_let_238 (forall ((u |u_(-> tptp.nat tptp.product_prod_nat_nat)|) (e tptp.product_prod_nat_nat) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.product_prod_nat_nat)|)) (not (forall ((ii tptp.nat)) (= (ho_50 v ii) (ite (= i ii) e (ho_50 u ii)))))))))) (let ((_let_239 (forall ((x |u_(-> tptp.nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_50 x z) (ho_50 y z)))) (= x y))))) (let ((_let_240 (forall ((u |u_(-> tptp.set_Pr1916610317um_a_b tptp.set_Pr409224873um_a_b tptp.set_Pr409224873um_a_b Bool)|) (e |u_(-> tptp.set_Pr409224873um_a_b tptp.set_Pr409224873um_a_b Bool)|) (i tptp.set_Pr1916610317um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1916610317um_a_b tptp.set_Pr409224873um_a_b tptp.set_Pr409224873um_a_b Bool)|)) (not (forall ((ii tptp.set_Pr1916610317um_a_b)) (= (ho_276 v ii) (ite (= i ii) e (ho_276 u ii)))))))))) (let ((_let_241 (forall ((x |u_(-> tptp.set_Pr1916610317um_a_b tptp.set_Pr409224873um_a_b tptp.set_Pr409224873um_a_b Bool)|) (y |u_(-> tptp.set_Pr1916610317um_a_b tptp.set_Pr409224873um_a_b tptp.set_Pr409224873um_a_b Bool)|)) (or (not (forall ((z tptp.set_Pr1916610317um_a_b)) (= (ho_276 x z) (ho_276 y z)))) (= x y))))) (let ((_let_242 (forall ((u |u_(-> tptp.produc1124793815um_a_b tptp.produc1546082365um_a_b)|) (e tptp.produc1546082365um_a_b) (i tptp.produc1124793815um_a_b)) (not (forall ((v |u_(-> tptp.produc1124793815um_a_b tptp.produc1546082365um_a_b)|)) (not (forall ((ii tptp.produc1124793815um_a_b)) (= (ho_172 v ii) (ite (= i ii) e (ho_172 u ii)))))))))) (let ((_let_243 (forall ((x |u_(-> tptp.produc1124793815um_a_b tptp.produc1546082365um_a_b)|) (y |u_(-> tptp.produc1124793815um_a_b tptp.produc1546082365um_a_b)|)) (or (not (forall ((z tptp.produc1124793815um_a_b)) (= (ho_172 x z) (ho_172 y z)))) (= x y))))) (let ((_let_244 (forall ((u |u_(-> tptp.set_Sum_sum_a_b tptp.sum_sum_a_b Bool)|) (e |u_(-> tptp.sum_sum_a_b Bool)|) (i tptp.set_Sum_sum_a_b)) (not (forall ((v |u_(-> tptp.set_Sum_sum_a_b tptp.sum_sum_a_b Bool)|)) (not (forall ((ii tptp.set_Sum_sum_a_b)) (= (ho_40 v ii) (ite (= i ii) e (ho_40 u ii)))))))))) (let ((_let_245 (forall ((x |u_(-> tptp.set_Sum_sum_a_b tptp.sum_sum_a_b Bool)|) (y |u_(-> tptp.set_Sum_sum_a_b tptp.sum_sum_a_b Bool)|)) (or (not (forall ((z tptp.set_Sum_sum_a_b)) (= (ho_40 x z) (ho_40 y z)))) (= x y))))) (let ((_let_246 (forall ((u |u_(-> tptp.set_Sum_sum_a_b tptp.set_Sum_sum_a_b Bool)|) (e |u_(-> tptp.set_Sum_sum_a_b Bool)|) (i tptp.set_Sum_sum_a_b)) (not (forall ((v |u_(-> tptp.set_Sum_sum_a_b tptp.set_Sum_sum_a_b Bool)|)) (not (forall ((ii tptp.set_Sum_sum_a_b)) (= (ho_14 v ii) (ite (= i ii) e (ho_14 u ii)))))))))) (let ((_let_247 (forall ((x |u_(-> tptp.set_Sum_sum_a_b tptp.set_Sum_sum_a_b Bool)|) (y |u_(-> tptp.set_Sum_sum_a_b tptp.set_Sum_sum_a_b Bool)|)) (or (not (forall ((z tptp.set_Sum_sum_a_b)) (= (ho_14 x z) (ho_14 y z)))) (= x y))))) (let ((_let_248 (forall ((u |u_(-> tptp.produc1124793815um_a_b tptp.set_Pr1174980151um_a_b tptp.set_Pr1174980151um_a_b)|) (e |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_Pr1174980151um_a_b)|) (i tptp.produc1124793815um_a_b)) (not (forall ((v |u_(-> tptp.produc1124793815um_a_b tptp.set_Pr1174980151um_a_b tptp.set_Pr1174980151um_a_b)|)) (not (forall ((ii tptp.produc1124793815um_a_b)) (= (ho_61 v ii) (ite (= i ii) e (ho_61 u ii)))))))))) (let ((_let_249 (forall ((x |u_(-> tptp.produc1124793815um_a_b tptp.set_Pr1174980151um_a_b tptp.set_Pr1174980151um_a_b)|) (y |u_(-> tptp.produc1124793815um_a_b tptp.set_Pr1174980151um_a_b tptp.set_Pr1174980151um_a_b)|)) (or (not (forall ((z tptp.produc1124793815um_a_b)) (= (ho_61 x z) (ho_61 y z)))) (= x y))))) (let ((_let_250 (forall ((u |u_(-> tptp.set_Sum_sum_a_b tptp.set_Pr1174980151um_a_b)|) (e tptp.set_Pr1174980151um_a_b) (i tptp.set_Sum_sum_a_b)) (not (forall ((v |u_(-> tptp.set_Sum_sum_a_b tptp.set_Pr1174980151um_a_b)|)) (not (forall ((ii tptp.set_Sum_sum_a_b)) (= (ho_200 v ii) (ite (= i ii) e (ho_200 u ii)))))))))) (let ((_let_251 (forall ((x |u_(-> tptp.set_Sum_sum_a_b tptp.set_Pr1174980151um_a_b)|) (y |u_(-> tptp.set_Sum_sum_a_b tptp.set_Pr1174980151um_a_b)|)) (or (not (forall ((z tptp.set_Sum_sum_a_b)) (= (ho_200 x z) (ho_200 y z)))) (= x y))))) (let ((_let_252 (forall ((u |u_(-> tptp.set_Pr326391507um_a_b Bool)|) (e Bool) (i tptp.set_Pr326391507um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr326391507um_a_b Bool)|)) (not (forall ((ii tptp.set_Pr326391507um_a_b)) (= (ho_169 v ii) (ite (= i ii) e (ho_169 u ii)))))))))) (let ((_let_253 (forall ((x |u_(-> tptp.set_Pr326391507um_a_b Bool)|) (y |u_(-> tptp.set_Pr326391507um_a_b Bool)|)) (or (not (forall ((z tptp.set_Pr326391507um_a_b)) (= (ho_169 x z) (ho_169 y z)))) (= x y))))) (let ((_let_254 (forall ((u |u_(-> tptp.set_Sum_sum_a_b tptp.labele431970251um_a_b)|) (e tptp.labele431970251um_a_b) (i tptp.set_Sum_sum_a_b)) (not (forall ((v |u_(-> tptp.set_Sum_sum_a_b tptp.labele431970251um_a_b)|)) (not (forall ((ii tptp.set_Sum_sum_a_b)) (= (ho_95 v ii) (ite (= i ii) e (ho_95 u ii)))))))))) (let ((_let_255 (forall ((x |u_(-> tptp.set_Sum_sum_a_b tptp.labele431970251um_a_b)|) (y |u_(-> tptp.set_Sum_sum_a_b tptp.labele431970251um_a_b)|)) (or (not (forall ((z tptp.set_Sum_sum_a_b)) (= (ho_95 x z) (ho_95 y z)))) (= x y))))) (let ((_let_256 (forall ((u |u_(-> tptp.standard_Constant_a tptp.set_St761939237tant_a tptp.set_St761939237tant_a)|) (e |u_(-> tptp.set_St761939237tant_a tptp.set_St761939237tant_a)|) (i tptp.standard_Constant_a)) (not (forall ((v |u_(-> tptp.standard_Constant_a tptp.set_St761939237tant_a tptp.set_St761939237tant_a)|)) (not (forall ((ii tptp.standard_Constant_a)) (= (ho_105 v ii) (ite (= i ii) e (ho_105 u ii)))))))))) (let ((_let_257 (forall ((x |u_(-> tptp.standard_Constant_a tptp.set_St761939237tant_a tptp.set_St761939237tant_a)|) (y |u_(-> tptp.standard_Constant_a tptp.set_St761939237tant_a tptp.set_St761939237tant_a)|)) (or (not (forall ((z tptp.standard_Constant_a)) (= (ho_105 x z) (ho_105 y z)))) (= x y))))) (let ((_let_258 (forall ((u |u_(-> tptp.labele935650037_a_nat tptp.set_Pr1986765409at_nat Bool)|) (e |u_(-> tptp.set_Pr1986765409at_nat Bool)|) (i tptp.labele935650037_a_nat)) (not (forall ((v |u_(-> tptp.labele935650037_a_nat tptp.set_Pr1986765409at_nat Bool)|)) (not (forall ((ii tptp.labele935650037_a_nat)) (= (ho_298 v ii) (ite (= i ii) e (ho_298 u ii)))))))))) (let ((_let_259 (forall ((x |u_(-> tptp.labele935650037_a_nat tptp.set_Pr1986765409at_nat Bool)|) (y |u_(-> tptp.labele935650037_a_nat tptp.set_Pr1986765409at_nat Bool)|)) (or (not (forall ((z tptp.labele935650037_a_nat)) (= (ho_298 x z) (ho_298 y z)))) (= x y))))) (let ((_let_260 (forall ((u |u_(-> tptp.set_Pr653770722um_a_b tptp.set_Pr1174980151um_a_b tptp.set_Sum_sum_a_b)|) (e |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_Sum_sum_a_b)|) (i tptp.set_Pr653770722um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr653770722um_a_b tptp.set_Pr1174980151um_a_b tptp.set_Sum_sum_a_b)|)) (not (forall ((ii tptp.set_Pr653770722um_a_b)) (= (ho_186 v ii) (ite (= i ii) e (ho_186 u ii)))))))))) (let ((_let_261 (forall ((x |u_(-> tptp.set_Pr653770722um_a_b tptp.set_Pr1174980151um_a_b tptp.set_Sum_sum_a_b)|) (y |u_(-> tptp.set_Pr653770722um_a_b tptp.set_Pr1174980151um_a_b tptp.set_Sum_sum_a_b)|)) (or (not (forall ((z tptp.set_Pr653770722um_a_b)) (= (ho_186 x z) (ho_186 y z)))) (= x y))))) (let ((_let_262 (forall ((u |u_(-> tptp.set_Pr409224873um_a_b tptp.set_Pr409224873um_a_b)|) (e tptp.set_Pr409224873um_a_b) (i tptp.set_Pr409224873um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr409224873um_a_b tptp.set_Pr409224873um_a_b)|)) (not (forall ((ii tptp.set_Pr409224873um_a_b)) (= (ho_92 v ii) (ite (= i ii) e (ho_92 u ii)))))))))) (let ((_let_263 (forall ((x |u_(-> tptp.set_Pr409224873um_a_b tptp.set_Pr409224873um_a_b)|) (y |u_(-> tptp.set_Pr409224873um_a_b tptp.set_Pr409224873um_a_b)|)) (or (not (forall ((z tptp.set_Pr409224873um_a_b)) (= (ho_92 x z) (ho_92 y z)))) (= x y))))) (let ((_let_264 (forall ((u |u_(-> tptp.labele935650037_a_nat tptp.set_Pr1647387645at_nat)|) (e tptp.set_Pr1647387645at_nat) (i tptp.labele935650037_a_nat)) (not (forall ((v |u_(-> tptp.labele935650037_a_nat tptp.set_Pr1647387645at_nat)|)) (not (forall ((ii tptp.labele935650037_a_nat)) (= (ho_191 v ii) (ite (= i ii) e (ho_191 u ii)))))))))) (let ((_let_265 (forall ((x |u_(-> tptp.labele935650037_a_nat tptp.set_Pr1647387645at_nat)|) (y |u_(-> tptp.labele935650037_a_nat tptp.set_Pr1647387645at_nat)|)) (or (not (forall ((z tptp.labele935650037_a_nat)) (= (ho_191 x z) (ho_191 y z)))) (= x y))))) (let ((_let_266 (forall ((u |u_(-> tptp.labele431970251um_a_b tptp.set_Sum_sum_a_b)|) (e tptp.set_Sum_sum_a_b) (i tptp.labele431970251um_a_b)) (not (forall ((v |u_(-> tptp.labele431970251um_a_b tptp.set_Sum_sum_a_b)|)) (not (forall ((ii tptp.labele431970251um_a_b)) (= (ho_45 v ii) (ite (= i ii) e (ho_45 u ii)))))))))) (let ((_let_267 (forall ((x |u_(-> tptp.labele431970251um_a_b tptp.set_Sum_sum_a_b)|) (y |u_(-> tptp.labele431970251um_a_b tptp.set_Sum_sum_a_b)|)) (or (not (forall ((z tptp.labele431970251um_a_b)) (= (ho_45 x z) (ho_45 y z)))) (= x y))))) (let ((_let_268 (forall ((u |u_(-> tptp.set_Pr1916610317um_a_b tptp.set_Sum_sum_a_b tptp.set_Sum_sum_a_b)|) (e |u_(-> tptp.set_Sum_sum_a_b tptp.set_Sum_sum_a_b)|) (i tptp.set_Pr1916610317um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1916610317um_a_b tptp.set_Sum_sum_a_b tptp.set_Sum_sum_a_b)|)) (not (forall ((ii tptp.set_Pr1916610317um_a_b)) (= (ho_157 v ii) (ite (= i ii) e (ho_157 u ii)))))))))) (let ((_let_269 (forall ((x |u_(-> tptp.set_Pr1916610317um_a_b tptp.set_Sum_sum_a_b tptp.set_Sum_sum_a_b)|) (y |u_(-> tptp.set_Pr1916610317um_a_b tptp.set_Sum_sum_a_b tptp.set_Sum_sum_a_b)|)) (or (not (forall ((z tptp.set_Pr1916610317um_a_b)) (= (ho_157 x z) (ho_157 y z)))) (= x y))))) (let ((_let_270 (forall ((u |u_(-> tptp.set_Pr1647387645at_nat tptp.set_nat)|) (e tptp.set_nat) (i tptp.set_Pr1647387645at_nat)) (not (forall ((v |u_(-> tptp.set_Pr1647387645at_nat tptp.set_nat)|)) (not (forall ((ii tptp.set_Pr1647387645at_nat)) (= (ho_240 v ii) (ite (= i ii) e (ho_240 u ii)))))))))) (let ((_let_271 (forall ((x |u_(-> tptp.set_Pr1647387645at_nat tptp.set_nat)|) (y |u_(-> tptp.set_Pr1647387645at_nat tptp.set_nat)|)) (or (not (forall ((z tptp.set_Pr1647387645at_nat)) (= (ho_240 x z) (ho_240 y z)))) (= x y))))) (let ((_let_272 (forall ((u |u_(-> tptp.set_Pr409224873um_a_b Bool)|) (e Bool) (i tptp.set_Pr409224873um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr409224873um_a_b Bool)|)) (not (forall ((ii tptp.set_Pr409224873um_a_b)) (= (ho_23 v ii) (ite (= i ii) e (ho_23 u ii)))))))))) (let ((_let_273 (forall ((x |u_(-> tptp.set_Pr409224873um_a_b Bool)|) (y |u_(-> tptp.set_Pr409224873um_a_b Bool)|)) (or (not (forall ((z tptp.set_Pr409224873um_a_b)) (= (ho_23 x z) (ho_23 y z)))) (= x y))))) (let ((_let_274 (forall ((u |u_(-> tptp.set_Pr326391507um_a_b tptp.set_St761939237tant_a tptp.set_Pr1174980151um_a_b)|) (e |u_(-> tptp.set_St761939237tant_a tptp.set_Pr1174980151um_a_b)|) (i tptp.set_Pr326391507um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr326391507um_a_b tptp.set_St761939237tant_a tptp.set_Pr1174980151um_a_b)|)) (not (forall ((ii tptp.set_Pr326391507um_a_b)) (= (ho_162 v ii) (ite (= i ii) e (ho_162 u ii)))))))))) (let ((_let_275 (forall ((x |u_(-> tptp.set_Pr326391507um_a_b tptp.set_St761939237tant_a tptp.set_Pr1174980151um_a_b)|) (y |u_(-> tptp.set_Pr326391507um_a_b tptp.set_St761939237tant_a tptp.set_Pr1174980151um_a_b)|)) (or (not (forall ((z tptp.set_Pr326391507um_a_b)) (= (ho_162 x z) (ho_162 y z)))) (= x y))))) (let ((_let_276 (forall ((u |u_(-> tptp.set_Pr1647387645at_nat tptp.set_Pr1647387645at_nat)|) (e tptp.set_Pr1647387645at_nat) (i tptp.set_Pr1647387645at_nat)) (not (forall ((v |u_(-> tptp.set_Pr1647387645at_nat tptp.set_Pr1647387645at_nat)|)) (not (forall ((ii tptp.set_Pr1647387645at_nat)) (= (ho_56 v ii) (ite (= i ii) e (ho_56 u ii)))))))))) (let ((_let_277 (forall ((x |u_(-> tptp.set_Pr1647387645at_nat tptp.set_Pr1647387645at_nat)|) (y |u_(-> tptp.set_Pr1647387645at_nat tptp.set_Pr1647387645at_nat)|)) (or (not (forall ((z tptp.set_Pr1647387645at_nat)) (= (ho_56 x z) (ho_56 y z)))) (= x y))))) (let ((_let_278 (forall ((u |u_(-> tptp.labele935650037_a_nat tptp.labele431970251um_a_b tptp.set_Pr1174980151um_a_b Bool)|) (e |u_(-> tptp.labele431970251um_a_b tptp.set_Pr1174980151um_a_b Bool)|) (i tptp.labele935650037_a_nat)) (not (forall ((v |u_(-> tptp.labele935650037_a_nat tptp.labele431970251um_a_b tptp.set_Pr1174980151um_a_b Bool)|)) (not (forall ((ii tptp.labele935650037_a_nat)) (= (ho_248 v ii) (ite (= i ii) e (ho_248 u ii)))))))))) (let ((_let_279 (forall ((x |u_(-> tptp.labele935650037_a_nat tptp.labele431970251um_a_b tptp.set_Pr1174980151um_a_b Bool)|) (y |u_(-> tptp.labele935650037_a_nat tptp.labele431970251um_a_b tptp.set_Pr1174980151um_a_b Bool)|)) (or (not (forall ((z tptp.labele935650037_a_nat)) (= (ho_248 x z) (ho_248 y z)))) (= x y))))) (let ((_let_280 (forall ((u |u_(-> tptp.set_Pr409224873um_a_b tptp.set_Pr409224873um_a_b Bool)|) (e |u_(-> tptp.set_Pr409224873um_a_b Bool)|) (i tptp.set_Pr409224873um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr409224873um_a_b tptp.set_Pr409224873um_a_b Bool)|)) (not (forall ((ii tptp.set_Pr409224873um_a_b)) (= (ho_22 v ii) (ite (= i ii) e (ho_22 u ii)))))))))) (let ((_let_281 (forall ((x |u_(-> tptp.set_Pr409224873um_a_b tptp.set_Pr409224873um_a_b Bool)|) (y |u_(-> tptp.set_Pr409224873um_a_b tptp.set_Pr409224873um_a_b Bool)|)) (or (not (forall ((z tptp.set_Pr409224873um_a_b)) (= (ho_22 x z) (ho_22 y z)))) (= x y))))) (let ((_let_282 (forall ((u |u_(-> tptp.nat tptp.set_nat tptp.set_nat)|) (e |u_(-> tptp.set_nat tptp.set_nat)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.set_nat tptp.set_nat)|)) (not (forall ((ii tptp.nat)) (= (ho_69 v ii) (ite (= i ii) e (ho_69 u ii)))))))))) (let ((_let_283 (forall ((x |u_(-> tptp.nat tptp.set_nat tptp.set_nat)|) (y |u_(-> tptp.nat tptp.set_nat tptp.set_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_69 x z) (ho_69 y z)))) (= x y))))) (let ((_let_284 (forall ((u |u_(-> tptp.set_Sum_sum_a_b tptp.set_Sum_sum_a_b)|) (e tptp.set_Sum_sum_a_b) (i tptp.set_Sum_sum_a_b)) (not (forall ((v |u_(-> tptp.set_Sum_sum_a_b tptp.set_Sum_sum_a_b)|)) (not (forall ((ii tptp.set_Sum_sum_a_b)) (= (ho_83 v ii) (ite (= i ii) e (ho_83 u ii)))))))))) (let ((_let_285 (forall ((x |u_(-> tptp.set_Sum_sum_a_b tptp.set_Sum_sum_a_b)|) (y |u_(-> tptp.set_Sum_sum_a_b tptp.set_Sum_sum_a_b)|)) (or (not (forall ((z tptp.set_Sum_sum_a_b)) (= (ho_83 x z) (ho_83 y z)))) (= x y))))) (let ((_let_286 (forall ((u |u_(-> tptp.set_Pr1916610317um_a_b tptp.labele1191284958um_a_b)|) (e tptp.labele1191284958um_a_b) (i tptp.set_Pr1916610317um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1916610317um_a_b tptp.labele1191284958um_a_b)|)) (not (forall ((ii tptp.set_Pr1916610317um_a_b)) (= (ho_324 v ii) (ite (= i ii) e (ho_324 u ii)))))))))) (let ((_let_287 (forall ((x |u_(-> tptp.set_Pr1916610317um_a_b tptp.labele1191284958um_a_b)|) (y |u_(-> tptp.set_Pr1916610317um_a_b tptp.labele1191284958um_a_b)|)) (or (not (forall ((z tptp.set_Pr1916610317um_a_b)) (= (ho_324 x z) (ho_324 y z)))) (= x y))))) (let ((_let_288 (forall ((u |u_(-> tptp.set_Pr1986765409at_nat tptp.set_Sum_sum_a_b)|) (e tptp.set_Sum_sum_a_b) (i tptp.set_Pr1986765409at_nat)) (not (forall ((v |u_(-> tptp.set_Pr1986765409at_nat tptp.set_Sum_sum_a_b)|)) (not (forall ((ii tptp.set_Pr1986765409at_nat)) (= (ho_146 v ii) (ite (= i ii) e (ho_146 u ii)))))))))) (let ((_let_289 (forall ((x |u_(-> tptp.set_Pr1986765409at_nat tptp.set_Sum_sum_a_b)|) (y |u_(-> tptp.set_Pr1986765409at_nat tptp.set_Sum_sum_a_b)|)) (or (not (forall ((z tptp.set_Pr1986765409at_nat)) (= (ho_146 x z) (ho_146 y z)))) (= x y))))) (let ((_let_290 (forall ((u |u_(-> tptp.set_Pr1174980151um_a_b tptp.produc1124793815um_a_b Bool)|) (e |u_(-> tptp.produc1124793815um_a_b Bool)|) (i tptp.set_Pr1174980151um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1174980151um_a_b tptp.produc1124793815um_a_b Bool)|)) (not (forall ((ii tptp.set_Pr1174980151um_a_b)) (= (ho_37 v ii) (ite (= i ii) e (ho_37 u ii)))))))))) (let ((_let_291 (forall ((x |u_(-> tptp.set_Pr1174980151um_a_b tptp.produc1124793815um_a_b Bool)|) (y |u_(-> tptp.set_Pr1174980151um_a_b tptp.produc1124793815um_a_b Bool)|)) (or (not (forall ((z tptp.set_Pr1174980151um_a_b)) (= (ho_37 x z) (ho_37 y z)))) (= x y))))) (let ((_let_292 (forall ((u |u_(-> tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat)|) (e tptp.set_Pr1986765409at_nat) (i tptp.set_Pr1986765409at_nat)) (not (forall ((v |u_(-> tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat)|)) (not (forall ((ii tptp.set_Pr1986765409at_nat)) (= (ho_109 v ii) (ite (= i ii) e (ho_109 u ii)))))))))) (let ((_let_293 (forall ((x |u_(-> tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat)|) (y |u_(-> tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat)|)) (or (not (forall ((z tptp.set_Pr1986765409at_nat)) (= (ho_109 x z) (ho_109 y z)))) (= x y))))) (let ((_let_294 (forall ((u |u_(-> tptp.produc1963079155um_a_b Bool)|) (e Bool) (i tptp.produc1963079155um_a_b)) (not (forall ((v |u_(-> tptp.produc1963079155um_a_b Bool)|)) (not (forall ((ii tptp.produc1963079155um_a_b)) (= (ho_35 v ii) (ite (= i ii) e (ho_35 u ii)))))))))) (let ((_let_295 (forall ((x |u_(-> tptp.produc1963079155um_a_b Bool)|) (y |u_(-> tptp.produc1963079155um_a_b Bool)|)) (or (not (forall ((z tptp.produc1963079155um_a_b)) (= (ho_35 x z) (ho_35 y z)))) (= x y))))) (let ((_let_296 (forall ((u |u_(-> tptp.set_Pr409224873um_a_b tptp.set_Pr1647387645at_nat Bool)|) (e |u_(-> tptp.set_Pr1647387645at_nat Bool)|) (i tptp.set_Pr409224873um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr409224873um_a_b tptp.set_Pr1647387645at_nat Bool)|)) (not (forall ((ii tptp.set_Pr409224873um_a_b)) (= (ho_272 v ii) (ite (= i ii) e (ho_272 u ii)))))))))) (let ((_let_297 (forall ((x |u_(-> tptp.set_Pr409224873um_a_b tptp.set_Pr1647387645at_nat Bool)|) (y |u_(-> tptp.set_Pr409224873um_a_b tptp.set_Pr1647387645at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr409224873um_a_b)) (= (ho_272 x z) (ho_272 y z)))) (= x y))))) (let ((_let_298 (forall ((u |u_(-> tptp.sum_sum_a_b tptp.produc1394389750um_a_b)|) (e tptp.produc1394389750um_a_b) (i tptp.sum_sum_a_b)) (not (forall ((v |u_(-> tptp.sum_sum_a_b tptp.produc1394389750um_a_b)|)) (not (forall ((ii tptp.sum_sum_a_b)) (= (ho_128 v ii) (ite (= i ii) e (ho_128 u ii)))))))))) (let ((_let_299 (forall ((x |u_(-> tptp.sum_sum_a_b tptp.produc1394389750um_a_b)|) (y |u_(-> tptp.sum_sum_a_b tptp.produc1394389750um_a_b)|)) (or (not (forall ((z tptp.sum_sum_a_b)) (= (ho_128 x z) (ho_128 y z)))) (= x y))))) (let ((_let_300 (forall ((u |u_(-> _u_(-> tptp.sum_sum_a_b Bool)_ tptp.set_Sum_sum_a_b)|) (e tptp.set_Sum_sum_a_b) (i |u_(-> tptp.sum_sum_a_b Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.sum_sum_a_b Bool)_ tptp.set_Sum_sum_a_b)|)) (not (forall ((ii |u_(-> tptp.sum_sum_a_b Bool)|)) (= (ho_281 v ii) (ite (= i ii) e (ho_281 u ii)))))))))) (let ((_let_301 (forall ((x |u_(-> _u_(-> tptp.sum_sum_a_b Bool)_ tptp.set_Sum_sum_a_b)|) (y |u_(-> _u_(-> tptp.sum_sum_a_b Bool)_ tptp.set_Sum_sum_a_b)|)) (or (not (forall ((z |u_(-> tptp.sum_sum_a_b Bool)|)) (= (ho_281 x z) (ho_281 y z)))) (= x y))))) (let ((_let_302 (forall ((u |u_(-> tptp.produc1032616263at_nat tptp.set_Pr1647387645at_nat tptp.set_Pr1647387645at_nat)|) (e |u_(-> tptp.set_Pr1647387645at_nat tptp.set_Pr1647387645at_nat)|) (i tptp.produc1032616263at_nat)) (not (forall ((v |u_(-> tptp.produc1032616263at_nat tptp.set_Pr1647387645at_nat tptp.set_Pr1647387645at_nat)|)) (not (forall ((ii tptp.produc1032616263at_nat)) (= (ho_55 v ii) (ite (= i ii) e (ho_55 u ii)))))))))) (let ((_let_303 (forall ((x |u_(-> tptp.produc1032616263at_nat tptp.set_Pr1647387645at_nat tptp.set_Pr1647387645at_nat)|) (y |u_(-> tptp.produc1032616263at_nat tptp.set_Pr1647387645at_nat tptp.set_Pr1647387645at_nat)|)) (or (not (forall ((z tptp.produc1032616263at_nat)) (= (ho_55 x z) (ho_55 y z)))) (= x y))))) (let ((_let_304 (forall ((u |u_(-> tptp.set_Pr1647387645at_nat tptp.set_nat tptp.labele935650037_a_nat)|) (e |u_(-> tptp.set_nat tptp.labele935650037_a_nat)|) (i tptp.set_Pr1647387645at_nat)) (not (forall ((v |u_(-> tptp.set_Pr1647387645at_nat tptp.set_nat tptp.labele935650037_a_nat)|)) (not (forall ((ii tptp.set_Pr1647387645at_nat)) (= (ho_97 v ii) (ite (= i ii) e (ho_97 u ii)))))))))) (let ((_let_305 (forall ((x |u_(-> tptp.set_Pr1647387645at_nat tptp.set_nat tptp.labele935650037_a_nat)|) (y |u_(-> tptp.set_Pr1647387645at_nat tptp.set_nat tptp.labele935650037_a_nat)|)) (or (not (forall ((z tptp.set_Pr1647387645at_nat)) (= (ho_97 x z) (ho_97 y z)))) (= x y))))) (let ((_let_306 (forall ((u |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_Pr1174980151um_a_b Bool)|) (e |u_(-> tptp.set_Pr1174980151um_a_b Bool)|) (i tptp.set_Pr1174980151um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_Pr1174980151um_a_b Bool)|)) (not (forall ((ii tptp.set_Pr1174980151um_a_b)) (= (ho_28 v ii) (ite (= i ii) e (ho_28 u ii)))))))))) (let ((_let_307 (forall ((x |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_Pr1174980151um_a_b Bool)|) (y |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_Pr1174980151um_a_b Bool)|)) (or (not (forall ((z tptp.set_Pr1174980151um_a_b)) (= (ho_28 x z) (ho_28 y z)))) (= x y))))) (let ((_let_308 (forall ((u |u_(-> tptp.produc1124793815um_a_b tptp.produc1918750183um_a_b)|) (e tptp.produc1918750183um_a_b) (i tptp.produc1124793815um_a_b)) (not (forall ((v |u_(-> tptp.produc1124793815um_a_b tptp.produc1918750183um_a_b)|)) (not (forall ((ii tptp.produc1124793815um_a_b)) (= (ho_211 v ii) (ite (= i ii) e (ho_211 u ii)))))))))) (let ((_let_309 (forall ((x |u_(-> tptp.produc1124793815um_a_b tptp.produc1918750183um_a_b)|) (y |u_(-> tptp.produc1124793815um_a_b tptp.produc1918750183um_a_b)|)) (or (not (forall ((z tptp.produc1124793815um_a_b)) (= (ho_211 x z) (ho_211 y z)))) (= x y))))) (let ((_let_310 (forall ((u |u_(-> tptp.set_Pr1647387645at_nat tptp.set_Pr1647387645at_nat Bool)|) (e |u_(-> tptp.set_Pr1647387645at_nat Bool)|) (i tptp.set_Pr1647387645at_nat)) (not (forall ((v |u_(-> tptp.set_Pr1647387645at_nat tptp.set_Pr1647387645at_nat Bool)|)) (not (forall ((ii tptp.set_Pr1647387645at_nat)) (= (ho_263 v ii) (ite (= i ii) e (ho_263 u ii)))))))))) (let ((_let_311 (forall ((x |u_(-> tptp.set_Pr1647387645at_nat tptp.set_Pr1647387645at_nat Bool)|) (y |u_(-> tptp.set_Pr1647387645at_nat tptp.set_Pr1647387645at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1647387645at_nat)) (= (ho_263 x z) (ho_263 y z)))) (= x y))))) (let ((_let_312 (forall ((u |u_(-> tptp.standard_Constant_a tptp.product_prod_nat_nat tptp.produc1032616263at_nat)|) (e |u_(-> tptp.product_prod_nat_nat tptp.produc1032616263at_nat)|) (i tptp.standard_Constant_a)) (not (forall ((v |u_(-> tptp.standard_Constant_a tptp.product_prod_nat_nat tptp.produc1032616263at_nat)|)) (not (forall ((ii tptp.standard_Constant_a)) (= (ho_52 v ii) (ite (= i ii) e (ho_52 u ii)))))))))) (let ((_let_313 (forall ((x |u_(-> tptp.standard_Constant_a tptp.product_prod_nat_nat tptp.produc1032616263at_nat)|) (y |u_(-> tptp.standard_Constant_a tptp.product_prod_nat_nat tptp.produc1032616263at_nat)|)) (or (not (forall ((z tptp.standard_Constant_a)) (= (ho_52 x z) (ho_52 y z)))) (= x y))))) (let ((_let_314 (forall ((u |u_(-> tptp.set_Pr386468381um_a_b tptp.set_Pr1986765409at_nat tptp.set_Pr1174980151um_a_b)|) (e |u_(-> tptp.set_Pr1986765409at_nat tptp.set_Pr1174980151um_a_b)|) (i tptp.set_Pr386468381um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr386468381um_a_b tptp.set_Pr1986765409at_nat tptp.set_Pr1174980151um_a_b)|)) (not (forall ((ii tptp.set_Pr386468381um_a_b)) (= (ho_177 v ii) (ite (= i ii) e (ho_177 u ii)))))))))) (let ((_let_315 (forall ((x |u_(-> tptp.set_Pr386468381um_a_b tptp.set_Pr1986765409at_nat tptp.set_Pr1174980151um_a_b)|) (y |u_(-> tptp.set_Pr386468381um_a_b tptp.set_Pr1986765409at_nat tptp.set_Pr1174980151um_a_b)|)) (or (not (forall ((z tptp.set_Pr386468381um_a_b)) (= (ho_177 x z) (ho_177 y z)))) (= x y))))) (let ((_let_316 (forall ((u |u_(-> tptp.set_Pr409224873um_a_b tptp.set_Sum_sum_a_b tptp.labele431970251um_a_b)|) (e |u_(-> tptp.set_Sum_sum_a_b tptp.labele431970251um_a_b)|) (i tptp.set_Pr409224873um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr409224873um_a_b tptp.set_Sum_sum_a_b tptp.labele431970251um_a_b)|)) (not (forall ((ii tptp.set_Pr409224873um_a_b)) (= (ho_94 v ii) (ite (= i ii) e (ho_94 u ii)))))))))) (let ((_let_317 (forall ((x |u_(-> tptp.set_Pr409224873um_a_b tptp.set_Sum_sum_a_b tptp.labele431970251um_a_b)|) (y |u_(-> tptp.set_Pr409224873um_a_b tptp.set_Sum_sum_a_b tptp.labele431970251um_a_b)|)) (or (not (forall ((z tptp.set_Pr409224873um_a_b)) (= (ho_94 x z) (ho_94 y z)))) (= x y))))) (let ((_let_318 (forall ((u |u_(-> tptp.product_prod_nat_nat tptp.produc1124793815um_a_b tptp.produc1546082365um_a_b)|) (e |u_(-> tptp.produc1124793815um_a_b tptp.produc1546082365um_a_b)|) (i tptp.product_prod_nat_nat)) (not (forall ((v |u_(-> tptp.product_prod_nat_nat tptp.produc1124793815um_a_b tptp.produc1546082365um_a_b)|)) (not (forall ((ii tptp.product_prod_nat_nat)) (= (ho_171 v ii) (ite (= i ii) e (ho_171 u ii)))))))))) (let ((_let_319 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.produc1124793815um_a_b tptp.produc1546082365um_a_b)|) (y |u_(-> tptp.product_prod_nat_nat tptp.produc1124793815um_a_b tptp.produc1546082365um_a_b)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_171 x z) (ho_171 y z)))) (= x y))))) (let ((_let_320 (forall ((u |u_(-> tptp.produc1124793815um_a_b tptp.set_Pr1174980151um_a_b Bool)|) (e |u_(-> tptp.set_Pr1174980151um_a_b Bool)|) (i tptp.produc1124793815um_a_b)) (not (forall ((v |u_(-> tptp.produc1124793815um_a_b tptp.set_Pr1174980151um_a_b Bool)|)) (not (forall ((ii tptp.produc1124793815um_a_b)) (= (ho_31 v ii) (ite (= i ii) e (ho_31 u ii)))))))))) (let ((_let_321 (forall ((x |u_(-> tptp.produc1124793815um_a_b tptp.set_Pr1174980151um_a_b Bool)|) (y |u_(-> tptp.produc1124793815um_a_b tptp.set_Pr1174980151um_a_b Bool)|)) (or (not (forall ((z tptp.produc1124793815um_a_b)) (= (ho_31 x z) (ho_31 y z)))) (= x y))))) (let ((_let_322 (forall ((u |u_(-> tptp.set_Pr409224873um_a_b tptp.produc1963079155um_a_b Bool)|) (e |u_(-> tptp.produc1963079155um_a_b Bool)|) (i tptp.set_Pr409224873um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr409224873um_a_b tptp.produc1963079155um_a_b Bool)|)) (not (forall ((ii tptp.set_Pr409224873um_a_b)) (= (ho_34 v ii) (ite (= i ii) e (ho_34 u ii)))))))))) (let ((_let_323 (forall ((x |u_(-> tptp.set_Pr409224873um_a_b tptp.produc1963079155um_a_b Bool)|) (y |u_(-> tptp.set_Pr409224873um_a_b tptp.produc1963079155um_a_b Bool)|)) (or (not (forall ((z tptp.set_Pr409224873um_a_b)) (= (ho_34 x z) (ho_34 y z)))) (= x y))))) (let ((_let_324 (forall ((u |u_(-> tptp.set_Pr1174980151um_a_b tptp.labele261019144um_a_b)|) (e tptp.labele261019144um_a_b) (i tptp.set_Pr1174980151um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1174980151um_a_b tptp.labele261019144um_a_b)|)) (not (forall ((ii tptp.set_Pr1174980151um_a_b)) (= (ho_304 v ii) (ite (= i ii) e (ho_304 u ii)))))))))) (let ((_let_325 (forall ((x |u_(-> tptp.set_Pr1174980151um_a_b tptp.labele261019144um_a_b)|) (y |u_(-> tptp.set_Pr1174980151um_a_b tptp.labele261019144um_a_b)|)) (or (not (forall ((z tptp.set_Pr1174980151um_a_b)) (= (ho_304 x z) (ho_304 y z)))) (= x y))))) (let ((_let_326 (forall ((u |u_(-> tptp.produc1963079155um_a_b tptp.set_Pr409224873um_a_b Bool)|) (e |u_(-> tptp.set_Pr409224873um_a_b Bool)|) (i tptp.produc1963079155um_a_b)) (not (forall ((v |u_(-> tptp.produc1963079155um_a_b tptp.set_Pr409224873um_a_b Bool)|)) (not (forall ((ii tptp.produc1963079155um_a_b)) (= (ho_25 v ii) (ite (= i ii) e (ho_25 u ii)))))))))) (let ((_let_327 (forall ((x |u_(-> tptp.produc1963079155um_a_b tptp.set_Pr409224873um_a_b Bool)|) (y |u_(-> tptp.produc1963079155um_a_b tptp.set_Pr409224873um_a_b Bool)|)) (or (not (forall ((z tptp.produc1963079155um_a_b)) (= (ho_25 x z) (ho_25 y z)))) (= x y))))) (let ((_let_328 (forall ((u |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat)|) (e |u_(-> tptp.nat tptp.product_prod_nat_nat)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat)|)) (not (forall ((ii tptp.nat)) (= (ho_49 v ii) (ite (= i ii) e (ho_49 u ii)))))))))) (let ((_let_329 (forall ((x |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_49 x z) (ho_49 y z)))) (= x y))))) (let ((_let_330 (forall ((u |u_(-> tptp.set_Pr1986765409at_nat Bool)|) (e Bool) (i tptp.set_Pr1986765409at_nat)) (not (forall ((v |u_(-> tptp.set_Pr1986765409at_nat Bool)|)) (not (forall ((ii tptp.set_Pr1986765409at_nat)) (= (ho_122 v ii) (ite (= i ii) e (ho_122 u ii)))))))))) (let ((_let_331 (forall ((x |u_(-> tptp.set_Pr1986765409at_nat Bool)|) (y |u_(-> tptp.set_Pr1986765409at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1986765409at_nat)) (= (ho_122 x z) (ho_122 y z)))) (= x y))))) (let ((_let_332 (forall ((u |u_(-> tptp.set_Pr1902304780_b_nat tptp.set_Pr1174980151um_a_b tptp.set_nat)|) (e |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_nat)|) (i tptp.set_Pr1902304780_b_nat)) (not (forall ((v |u_(-> tptp.set_Pr1902304780_b_nat tptp.set_Pr1174980151um_a_b tptp.set_nat)|)) (not (forall ((ii tptp.set_Pr1902304780_b_nat)) (= (ho_237 v ii) (ite (= i ii) e (ho_237 u ii)))))))))) (let ((_let_333 (forall ((x |u_(-> tptp.set_Pr1902304780_b_nat tptp.set_Pr1174980151um_a_b tptp.set_nat)|) (y |u_(-> tptp.set_Pr1902304780_b_nat tptp.set_Pr1174980151um_a_b tptp.set_nat)|)) (or (not (forall ((z tptp.set_Pr1902304780_b_nat)) (= (ho_237 x z) (ho_237 y z)))) (= x y))))) (let ((_let_334 (forall ((u |u_(-> tptp.labele935650037_a_nat tptp.labele935650037_a_nat)|) (e tptp.labele935650037_a_nat) (i tptp.labele935650037_a_nat)) (not (forall ((v |u_(-> tptp.labele935650037_a_nat tptp.labele935650037_a_nat)|)) (not (forall ((ii tptp.labele935650037_a_nat)) (= (ho_100 v ii) (ite (= i ii) e (ho_100 u ii)))))))))) (let ((_let_335 (forall ((x |u_(-> tptp.labele935650037_a_nat tptp.labele935650037_a_nat)|) (y |u_(-> tptp.labele935650037_a_nat tptp.labele935650037_a_nat)|)) (or (not (forall ((z tptp.labele935650037_a_nat)) (= (ho_100 x z) (ho_100 y z)))) (= x y))))) (let ((_let_336 (forall ((u |u_(-> tptp.labele935650037_a_nat tptp.set_Pr507214050_b_nat Bool)|) (e |u_(-> tptp.set_Pr507214050_b_nat Bool)|) (i tptp.labele935650037_a_nat)) (not (forall ((v |u_(-> tptp.labele935650037_a_nat tptp.set_Pr507214050_b_nat Bool)|)) (not (forall ((ii tptp.labele935650037_a_nat)) (= (ho_327 v ii) (ite (= i ii) e (ho_327 u ii)))))))))) (let ((_let_337 (forall ((x |u_(-> tptp.labele935650037_a_nat tptp.set_Pr507214050_b_nat Bool)|) (y |u_(-> tptp.labele935650037_a_nat tptp.set_Pr507214050_b_nat Bool)|)) (or (not (forall ((z tptp.labele935650037_a_nat)) (= (ho_327 x z) (ho_327 y z)))) (= x y))))) (let ((_let_338 (forall ((u |u_(-> tptp.set_Pr1986765409at_nat tptp.set_Pr1174980151um_a_b)|) (e tptp.set_Pr1174980151um_a_b) (i tptp.set_Pr1986765409at_nat)) (not (forall ((v |u_(-> tptp.set_Pr1986765409at_nat tptp.set_Pr1174980151um_a_b)|)) (not (forall ((ii tptp.set_Pr1986765409at_nat)) (= (ho_178 v ii) (ite (= i ii) e (ho_178 u ii)))))))))) (let ((_let_339 (forall ((x |u_(-> tptp.set_Pr1986765409at_nat tptp.set_Pr1174980151um_a_b)|) (y |u_(-> tptp.set_Pr1986765409at_nat tptp.set_Pr1174980151um_a_b)|)) (or (not (forall ((z tptp.set_Pr1986765409at_nat)) (= (ho_178 x z) (ho_178 y z)))) (= x y))))) (let ((_let_340 (forall ((u |u_(-> tptp.produc1124793815um_a_b Bool)|) (e Bool) (i tptp.produc1124793815um_a_b)) (not (forall ((v |u_(-> tptp.produc1124793815um_a_b Bool)|)) (not (forall ((ii tptp.produc1124793815um_a_b)) (= (ho_38 v ii) (ite (= i ii) e (ho_38 u ii)))))))))) (let ((_let_341 (forall ((x |u_(-> tptp.produc1124793815um_a_b Bool)|) (y |u_(-> tptp.produc1124793815um_a_b Bool)|)) (or (not (forall ((z tptp.produc1124793815um_a_b)) (= (ho_38 x z) (ho_38 y z)))) (= x y))))) (let ((_let_342 (forall ((u |u_(-> tptp.produc1124793815um_a_b tptp.produc204140796um_a_b)|) (e tptp.produc204140796um_a_b) (i tptp.produc1124793815um_a_b)) (not (forall ((v |u_(-> tptp.produc1124793815um_a_b tptp.produc204140796um_a_b)|)) (not (forall ((ii tptp.produc1124793815um_a_b)) (= (ho_152 v ii) (ite (= i ii) e (ho_152 u ii)))))))))) (let ((_let_343 (forall ((x |u_(-> tptp.produc1124793815um_a_b tptp.produc204140796um_a_b)|) (y |u_(-> tptp.produc1124793815um_a_b tptp.produc204140796um_a_b)|)) (or (not (forall ((z tptp.produc1124793815um_a_b)) (= (ho_152 x z) (ho_152 y z)))) (= x y))))) (let ((_let_344 (forall ((u |u_(-> tptp.produc1733247354um_a_b tptp.set_Pr1558970842um_a_b Bool)|) (e |u_(-> tptp.set_Pr1558970842um_a_b Bool)|) (i tptp.produc1733247354um_a_b)) (not (forall ((v |u_(-> tptp.produc1733247354um_a_b tptp.set_Pr1558970842um_a_b Bool)|)) (not (forall ((ii tptp.produc1733247354um_a_b)) (= (ho_222 v ii) (ite (= i ii) e (ho_222 u ii)))))))))) (let ((_let_345 (forall ((x |u_(-> tptp.produc1733247354um_a_b tptp.set_Pr1558970842um_a_b Bool)|) (y |u_(-> tptp.produc1733247354um_a_b tptp.set_Pr1558970842um_a_b Bool)|)) (or (not (forall ((z tptp.produc1733247354um_a_b)) (= (ho_222 x z) (ho_222 y z)))) (= x y))))) (let ((_let_346 (forall ((u |u_(-> tptp.sum_sum_a_b tptp.set_Sum_sum_a_b Bool)|) (e |u_(-> tptp.set_Sum_sum_a_b Bool)|) (i tptp.sum_sum_a_b)) (not (forall ((v |u_(-> tptp.sum_sum_a_b tptp.set_Sum_sum_a_b Bool)|)) (not (forall ((ii tptp.sum_sum_a_b)) (= (ho_18 v ii) (ite (= i ii) e (ho_18 u ii)))))))))) (let ((_let_347 (forall ((x |u_(-> tptp.sum_sum_a_b tptp.set_Sum_sum_a_b Bool)|) (y |u_(-> tptp.sum_sum_a_b tptp.set_Sum_sum_a_b Bool)|)) (or (not (forall ((z tptp.sum_sum_a_b)) (= (ho_18 x z) (ho_18 y z)))) (= x y))))) (let ((_let_348 (forall ((u |u_(-> tptp.labele431970251um_a_b Bool)|) (e Bool) (i tptp.labele431970251um_a_b)) (not (forall ((v |u_(-> tptp.labele431970251um_a_b Bool)|)) (not (forall ((ii tptp.labele431970251um_a_b)) (= (ho_251 v ii) (ite (= i ii) e (ho_251 u ii)))))))))) (let ((_let_349 (forall ((x |u_(-> tptp.labele431970251um_a_b Bool)|) (y |u_(-> tptp.labele431970251um_a_b Bool)|)) (or (not (forall ((z tptp.labele431970251um_a_b)) (= (ho_251 x z) (ho_251 y z)))) (= x y))))) (let ((_let_350 (forall ((u |u_(-> tptp.set_Pr1986765409at_nat tptp.set_nat)|) (e tptp.set_nat) (i tptp.set_Pr1986765409at_nat)) (not (forall ((v |u_(-> tptp.set_Pr1986765409at_nat tptp.set_nat)|)) (not (forall ((ii tptp.set_Pr1986765409at_nat)) (= (ho_67 v ii) (ite (= i ii) e (ho_67 u ii)))))))))) (let ((_let_351 (forall ((x |u_(-> tptp.set_Pr1986765409at_nat tptp.set_nat)|) (y |u_(-> tptp.set_Pr1986765409at_nat tptp.set_nat)|)) (or (not (forall ((z tptp.set_Pr1986765409at_nat)) (= (ho_67 x z) (ho_67 y z)))) (= x y))))) (let ((_let_352 (forall ((u |u_(-> tptp.set_Pr409224873um_a_b tptp.set_Sum_sum_a_b)|) (e tptp.set_Sum_sum_a_b) (i tptp.set_Pr409224873um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr409224873um_a_b tptp.set_Sum_sum_a_b)|)) (not (forall ((ii tptp.set_Pr409224873um_a_b)) (= (ho_226 v ii) (ite (= i ii) e (ho_226 u ii)))))))))) (let ((_let_353 (forall ((x |u_(-> tptp.set_Pr409224873um_a_b tptp.set_Sum_sum_a_b)|) (y |u_(-> tptp.set_Pr409224873um_a_b tptp.set_Sum_sum_a_b)|)) (or (not (forall ((z tptp.set_Pr409224873um_a_b)) (= (ho_226 x z) (ho_226 y z)))) (= x y))))) (let ((_let_354 (forall ((u |u_(-> tptp.set_Pr195945996um_a_b tptp.set_Pr1986765409at_nat tptp.set_Sum_sum_a_b)|) (e |u_(-> tptp.set_Pr1986765409at_nat tptp.set_Sum_sum_a_b)|) (i tptp.set_Pr195945996um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr195945996um_a_b tptp.set_Pr1986765409at_nat tptp.set_Sum_sum_a_b)|)) (not (forall ((ii tptp.set_Pr195945996um_a_b)) (= (ho_145 v ii) (ite (= i ii) e (ho_145 u ii)))))))))) (let ((_let_355 (forall ((x |u_(-> tptp.set_Pr195945996um_a_b tptp.set_Pr1986765409at_nat tptp.set_Sum_sum_a_b)|) (y |u_(-> tptp.set_Pr195945996um_a_b tptp.set_Pr1986765409at_nat tptp.set_Sum_sum_a_b)|)) (or (not (forall ((z tptp.set_Pr195945996um_a_b)) (= (ho_145 x z) (ho_145 y z)))) (= x y))))) (let ((_let_356 (forall ((u |u_(-> tptp.sum_sum_a_b Bool)|) (e Bool) (i tptp.sum_sum_a_b)) (not (forall ((v |u_(-> tptp.sum_sum_a_b Bool)|)) (not (forall ((ii tptp.sum_sum_a_b)) (= (ho_41 v ii) (ite (= i ii) e (ho_41 u ii)))))))))) (let ((_let_357 (forall ((x |u_(-> tptp.sum_sum_a_b Bool)|) (y |u_(-> tptp.sum_sum_a_b Bool)|)) (or (not (forall ((z tptp.sum_sum_a_b)) (= (ho_41 x z) (ho_41 y z)))) (= x y))))) (let ((_let_358 (forall ((u |u_(-> tptp.set_Pr1986765409at_nat tptp.set_nat tptp.set_nat)|) (e |u_(-> tptp.set_nat tptp.set_nat)|) (i tptp.set_Pr1986765409at_nat)) (not (forall ((v |u_(-> tptp.set_Pr1986765409at_nat tptp.set_nat tptp.set_nat)|)) (not (forall ((ii tptp.set_Pr1986765409at_nat)) (= (ho_116 v ii) (ite (= i ii) e (ho_116 u ii)))))))))) (let ((_let_359 (forall ((x |u_(-> tptp.set_Pr1986765409at_nat tptp.set_nat tptp.set_nat)|) (y |u_(-> tptp.set_Pr1986765409at_nat tptp.set_nat tptp.set_nat)|)) (or (not (forall ((z tptp.set_Pr1986765409at_nat)) (= (ho_116 x z) (ho_116 y z)))) (= x y))))) (let ((_let_360 (forall ((u |u_(-> tptp.set_nat tptp.set_Sum_sum_a_b)|) (e tptp.set_Sum_sum_a_b) (i tptp.set_nat)) (not (forall ((v |u_(-> tptp.set_nat tptp.set_Sum_sum_a_b)|)) (not (forall ((ii tptp.set_nat)) (= (ho_73 v ii) (ite (= i ii) e (ho_73 u ii)))))))))) (let ((_let_361 (forall ((x |u_(-> tptp.set_nat tptp.set_Sum_sum_a_b)|) (y |u_(-> tptp.set_nat tptp.set_Sum_sum_a_b)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_73 x z) (ho_73 y z)))) (= x y))))) (let ((_let_362 (forall ((u |u_(-> tptp.labele261019144um_a_b tptp.labele935650037_a_nat tptp.set_Pr1902304780_b_nat Bool)|) (e |u_(-> tptp.labele935650037_a_nat tptp.set_Pr1902304780_b_nat Bool)|) (i tptp.labele261019144um_a_b)) (not (forall ((v |u_(-> tptp.labele261019144um_a_b tptp.labele935650037_a_nat tptp.set_Pr1902304780_b_nat Bool)|)) (not (forall ((ii tptp.labele261019144um_a_b)) (= (ho_306 v ii) (ite (= i ii) e (ho_306 u ii)))))))))) (let ((_let_363 (forall ((x |u_(-> tptp.labele261019144um_a_b tptp.labele935650037_a_nat tptp.set_Pr1902304780_b_nat Bool)|) (y |u_(-> tptp.labele261019144um_a_b tptp.labele935650037_a_nat tptp.set_Pr1902304780_b_nat Bool)|)) (or (not (forall ((z tptp.labele261019144um_a_b)) (= (ho_306 x z) (ho_306 y z)))) (= x y))))) (let ((_let_364 (forall ((u |u_(-> tptp.labele935650037_a_nat tptp.set_Pr689416536at_nat Bool)|) (e |u_(-> tptp.set_Pr689416536at_nat Bool)|) (i tptp.labele935650037_a_nat)) (not (forall ((v |u_(-> tptp.labele935650037_a_nat tptp.set_Pr689416536at_nat Bool)|)) (not (forall ((ii tptp.labele935650037_a_nat)) (= (ho_317 v ii) (ite (= i ii) e (ho_317 u ii)))))))))) (let ((_let_365 (forall ((x |u_(-> tptp.labele935650037_a_nat tptp.set_Pr689416536at_nat Bool)|) (y |u_(-> tptp.labele935650037_a_nat tptp.set_Pr689416536at_nat Bool)|)) (or (not (forall ((z tptp.labele935650037_a_nat)) (= (ho_317 x z) (ho_317 y z)))) (= x y))))) (let ((_let_366 (forall ((u |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_nat tptp.set_Sum_sum_a_b)|) (e |u_(-> tptp.set_nat tptp.set_Sum_sum_a_b)|) (i tptp.set_Pr1174980151um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_nat tptp.set_Sum_sum_a_b)|)) (not (forall ((ii tptp.set_Pr1174980151um_a_b)) (= (ho_72 v ii) (ite (= i ii) e (ho_72 u ii)))))))))) (let ((_let_367 (forall ((x |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_nat tptp.set_Sum_sum_a_b)|) (y |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_nat tptp.set_Sum_sum_a_b)|)) (or (not (forall ((z tptp.set_Pr1174980151um_a_b)) (= (ho_72 x z) (ho_72 y z)))) (= x y))))) (let ((_let_368 (forall ((u |u_(-> tptp.set_Pr1647387645at_nat tptp.set_Pr409224873um_a_b Bool)|) (e |u_(-> tptp.set_Pr409224873um_a_b Bool)|) (i tptp.set_Pr1647387645at_nat)) (not (forall ((v |u_(-> tptp.set_Pr1647387645at_nat tptp.set_Pr409224873um_a_b Bool)|)) (not (forall ((ii tptp.set_Pr1647387645at_nat)) (= (ho_65 v ii) (ite (= i ii) e (ho_65 u ii)))))))))) (let ((_let_369 (forall ((x |u_(-> tptp.set_Pr1647387645at_nat tptp.set_Pr409224873um_a_b Bool)|) (y |u_(-> tptp.set_Pr1647387645at_nat tptp.set_Pr409224873um_a_b Bool)|)) (or (not (forall ((z tptp.set_Pr1647387645at_nat)) (= (ho_65 x z) (ho_65 y z)))) (= x y))))) (let ((_let_370 (forall ((u |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_Pr1647387645at_nat tptp.set_Pr409224873um_a_b Bool)|) (e |u_(-> tptp.set_Pr1647387645at_nat tptp.set_Pr409224873um_a_b Bool)|) (i tptp.set_Pr1174980151um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_Pr1647387645at_nat tptp.set_Pr409224873um_a_b Bool)|)) (not (forall ((ii tptp.set_Pr1174980151um_a_b)) (= (ho_64 v ii) (ite (= i ii) e (ho_64 u ii)))))))))) (let ((_let_371 (forall ((x |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_Pr1647387645at_nat tptp.set_Pr409224873um_a_b Bool)|) (y |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_Pr1647387645at_nat tptp.set_Pr409224873um_a_b Bool)|)) (or (not (forall ((z tptp.set_Pr1174980151um_a_b)) (= (ho_64 x z) (ho_64 y z)))) (= x y))))) (let ((_let_372 (forall ((u |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_nat)|) (e tptp.set_nat) (i tptp.set_Pr1174980151um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_nat)|)) (not (forall ((ii tptp.set_Pr1174980151um_a_b)) (= (ho_75 v ii) (ite (= i ii) e (ho_75 u ii)))))))))) (let ((_let_373 (forall ((x |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_nat)|) (y |u_(-> tptp.set_Pr1174980151um_a_b tptp.set_nat)|)) (or (not (forall ((z tptp.set_Pr1174980151um_a_b)) (= (ho_75 x z) (ho_75 y z)))) (= x y))))) (let ((_let_374 (forall ((u |u_(-> tptp.labele431970251um_a_b tptp.set_Pr409224873um_a_b)|) (e tptp.set_Pr409224873um_a_b) (i tptp.labele431970251um_a_b)) (not (forall ((v |u_(-> tptp.labele431970251um_a_b tptp.set_Pr409224873um_a_b)|)) (not (forall ((ii tptp.labele431970251um_a_b)) (= (ho_47 v ii) (ite (= i ii) e (ho_47 u ii)))))))))) (let ((_let_375 (forall ((x |u_(-> tptp.labele431970251um_a_b tptp.set_Pr409224873um_a_b)|) (y |u_(-> tptp.labele431970251um_a_b tptp.set_Pr409224873um_a_b)|)) (or (not (forall ((z tptp.labele431970251um_a_b)) (= (ho_47 x z) (ho_47 y z)))) (= x y))))) (let ((_let_376 (forall ((u |u_(-> tptp.sum_sum_a_b tptp.produc1548871597um_a_b)|) (e tptp.produc1548871597um_a_b) (i tptp.sum_sum_a_b)) (not (forall ((v |u_(-> tptp.sum_sum_a_b tptp.produc1548871597um_a_b)|)) (not (forall ((ii tptp.sum_sum_a_b)) (= (ho_86 v ii) (ite (= i ii) e (ho_86 u ii)))))))))) (let ((_let_377 (forall ((x |u_(-> tptp.sum_sum_a_b tptp.produc1548871597um_a_b)|) (y |u_(-> tptp.sum_sum_a_b tptp.produc1548871597um_a_b)|)) (or (not (forall ((z tptp.sum_sum_a_b)) (= (ho_86 x z) (ho_86 y z)))) (= x y))))) (let ((_let_378 (forall ((u |u_(-> tptp.set_Pr1429673827um_a_b tptp.set_Pr1916610317um_a_b tptp.labele1191284958um_a_b)|) (e |u_(-> tptp.set_Pr1916610317um_a_b tptp.labele1191284958um_a_b)|) (i tptp.set_Pr1429673827um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1429673827um_a_b tptp.set_Pr1916610317um_a_b tptp.labele1191284958um_a_b)|)) (not (forall ((ii tptp.set_Pr1429673827um_a_b)) (= (ho_323 v ii) (ite (= i ii) e (ho_323 u ii)))))))))) (let ((_let_379 (forall ((x |u_(-> tptp.set_Pr1429673827um_a_b tptp.set_Pr1916610317um_a_b tptp.labele1191284958um_a_b)|) (y |u_(-> tptp.set_Pr1429673827um_a_b tptp.set_Pr1916610317um_a_b tptp.labele1191284958um_a_b)|)) (or (not (forall ((z tptp.set_Pr1429673827um_a_b)) (= (ho_323 x z) (ho_323 y z)))) (= x y))))) (let ((_let_380 (forall ((u |u_(-> tptp.produc1963079155um_a_b tptp.set_Pr409224873um_a_b tptp.set_Pr409224873um_a_b)|) (e |u_(-> tptp.set_Pr409224873um_a_b tptp.set_Pr409224873um_a_b)|) (i tptp.produc1963079155um_a_b)) (not (forall ((v |u_(-> tptp.produc1963079155um_a_b tptp.set_Pr409224873um_a_b tptp.set_Pr409224873um_a_b)|)) (not (forall ((ii tptp.produc1963079155um_a_b)) (= (ho_91 v ii) (ite (= i ii) e (ho_91 u ii)))))))))) (let ((_let_381 (forall ((x |u_(-> tptp.produc1963079155um_a_b tptp.set_Pr409224873um_a_b tptp.set_Pr409224873um_a_b)|) (y |u_(-> tptp.produc1963079155um_a_b tptp.set_Pr409224873um_a_b tptp.set_Pr409224873um_a_b)|)) (or (not (forall ((z tptp.produc1963079155um_a_b)) (= (ho_91 x z) (ho_91 y z)))) (= x y))))) (let ((_let_382 (forall ((u |u_(-> tptp.sum_sum_a_b tptp.produc1124793815um_a_b tptp.produc323101606um_a_b)|) (e |u_(-> tptp.produc1124793815um_a_b tptp.produc323101606um_a_b)|) (i tptp.sum_sum_a_b)) (not (forall ((v |u_(-> tptp.sum_sum_a_b tptp.produc1124793815um_a_b tptp.produc323101606um_a_b)|)) (not (forall ((ii tptp.sum_sum_a_b)) (= (ho_202 v ii) (ite (= i ii) e (ho_202 u ii)))))))))) (let ((_let_383 (forall ((x |u_(-> tptp.sum_sum_a_b tptp.produc1124793815um_a_b tptp.produc323101606um_a_b)|) (y |u_(-> tptp.sum_sum_a_b tptp.produc1124793815um_a_b tptp.produc323101606um_a_b)|)) (or (not (forall ((z tptp.sum_sum_a_b)) (= (ho_202 x z) (ho_202 y z)))) (= x y))))) (let ((_let_384 (forall ((u |u_(-> tptp.set_Sum_sum_a_b Bool)|) (e Bool) (i tptp.set_Sum_sum_a_b)) (not (forall ((v |u_(-> tptp.set_Sum_sum_a_b Bool)|)) (not (forall ((ii tptp.set_Sum_sum_a_b)) (= (ho_15 v ii) (ite (= i ii) e (ho_15 u ii)))))))))) (let ((_let_385 (forall ((x |u_(-> tptp.set_Sum_sum_a_b Bool)|) (y |u_(-> tptp.set_Sum_sum_a_b Bool)|)) (or (not (forall ((z tptp.set_Sum_sum_a_b)) (= (ho_15 x z) (ho_15 y z)))) (= x y))))) (let ((_let_386 (forall ((u |u_(-> tptp.standard_Constant_a tptp.labele431970251um_a_b tptp.set_Pr1916610317um_a_b)|) (e |u_(-> tptp.labele431970251um_a_b tptp.set_Pr1916610317um_a_b)|) (i tptp.standard_Constant_a)) (not (forall ((v |u_(-> tptp.standard_Constant_a tptp.labele431970251um_a_b tptp.set_Pr1916610317um_a_b)|)) (not (forall ((ii tptp.standard_Constant_a)) (= (ho_77 v ii) (ite (= i ii) e (ho_77 u ii)))))))))) (let ((_let_387 (forall ((x |u_(-> tptp.standard_Constant_a tptp.labele431970251um_a_b tptp.set_Pr1916610317um_a_b)|) (y |u_(-> tptp.standard_Constant_a tptp.labele431970251um_a_b tptp.set_Pr1916610317um_a_b)|)) (or (not (forall ((z tptp.standard_Constant_a)) (= (ho_77 x z) (ho_77 y z)))) (= x y))))) (let ((_let_388 (forall ((u |u_(-> tptp.product_prod_nat_nat tptp.produc1032616263at_nat)|) (e tptp.produc1032616263at_nat) (i tptp.product_prod_nat_nat)) (not (forall ((v |u_(-> tptp.product_prod_nat_nat tptp.produc1032616263at_nat)|)) (not (forall ((ii tptp.product_prod_nat_nat)) (= (ho_53 v ii) (ite (= i ii) e (ho_53 u ii)))))))))) (let ((_let_389 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.produc1032616263at_nat)|) (y |u_(-> tptp.product_prod_nat_nat tptp.produc1032616263at_nat)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_53 x z) (ho_53 y z)))) (= x y))))) (let ((_let_390 (forall ((u |u_(-> tptp.set_Pr375490359_b_nat tptp.set_Pr409224873um_a_b tptp.set_Pr1647387645at_nat Bool)|) (e |u_(-> tptp.set_Pr409224873um_a_b tptp.set_Pr1647387645at_nat Bool)|) (i tptp.set_Pr375490359_b_nat)) (not (forall ((v |u_(-> tptp.set_Pr375490359_b_nat tptp.set_Pr409224873um_a_b tptp.set_Pr1647387645at_nat Bool)|)) (not (forall ((ii tptp.set_Pr375490359_b_nat)) (= (ho_271 v ii) (ite (= i ii) e (ho_271 u ii)))))))))) (let ((_let_391 (forall ((x |u_(-> tptp.set_Pr375490359_b_nat tptp.set_Pr409224873um_a_b tptp.set_Pr1647387645at_nat Bool)|) (y |u_(-> tptp.set_Pr375490359_b_nat tptp.set_Pr409224873um_a_b tptp.set_Pr1647387645at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr375490359_b_nat)) (= (ho_271 x z) (ho_271 y z)))) (= x y))))) (let ((_let_392 (forall ((u |u_(-> tptp.set_Pr1916610317um_a_b tptp.set_Sum_sum_a_b)|) (e tptp.set_Sum_sum_a_b) (i tptp.set_Pr1916610317um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1916610317um_a_b tptp.set_Sum_sum_a_b)|)) (not (forall ((ii tptp.set_Pr1916610317um_a_b)) (= (ho_80 v ii) (ite (= i ii) e (ho_80 u ii)))))))))) (let ((_let_393 (forall ((x |u_(-> tptp.set_Pr1916610317um_a_b tptp.set_Sum_sum_a_b)|) (y |u_(-> tptp.set_Pr1916610317um_a_b tptp.set_Sum_sum_a_b)|)) (or (not (forall ((z tptp.set_Pr1916610317um_a_b)) (= (ho_80 x z) (ho_80 y z)))) (= x y))))) (let ((_let_394 (forall ((u |u_(-> tptp.sum_sum_a_b tptp.sum_sum_a_b tptp.produc1548871597um_a_b)|) (e |u_(-> tptp.sum_sum_a_b tptp.produc1548871597um_a_b)|) (i tptp.sum_sum_a_b)) (not (forall ((v |u_(-> tptp.sum_sum_a_b tptp.sum_sum_a_b tptp.produc1548871597um_a_b)|)) (not (forall ((ii tptp.sum_sum_a_b)) (= (ho_85 v ii) (ite (= i ii) e (ho_85 u ii)))))))))) (let ((_let_395 (forall ((x |u_(-> tptp.sum_sum_a_b tptp.sum_sum_a_b tptp.produc1548871597um_a_b)|) (y |u_(-> tptp.sum_sum_a_b tptp.sum_sum_a_b tptp.produc1548871597um_a_b)|)) (or (not (forall ((z tptp.sum_sum_a_b)) (= (ho_85 x z) (ho_85 y z)))) (= x y))))) (let ((_let_396 (forall ((u |u_(-> tptp.set_Pr1121389018um_a_b Bool)|) (e Bool) (i tptp.set_Pr1121389018um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1121389018um_a_b Bool)|)) (not (forall ((ii tptp.set_Pr1121389018um_a_b)) (= (ho_232 v ii) (ite (= i ii) e (ho_232 u ii)))))))))) (let ((_let_397 (forall ((x |u_(-> tptp.set_Pr1121389018um_a_b Bool)|) (y |u_(-> tptp.set_Pr1121389018um_a_b Bool)|)) (or (not (forall ((z tptp.set_Pr1121389018um_a_b)) (= (ho_232 x z) (ho_232 y z)))) (= x y))))) (let ((_let_398 (forall ((u |u_(-> tptp.set_nat tptp.labele935650037_a_nat)|) (e tptp.labele935650037_a_nat) (i tptp.set_nat)) (not (forall ((v |u_(-> tptp.set_nat tptp.labele935650037_a_nat)|)) (not (forall ((ii tptp.set_nat)) (= (ho_98 v ii) (ite (= i ii) e (ho_98 u ii)))))))))) (let ((_let_399 (forall ((x |u_(-> tptp.set_nat tptp.labele935650037_a_nat)|) (y |u_(-> tptp.set_nat tptp.labele935650037_a_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_98 x z) (ho_98 y z)))) (= x y))))) (let ((_let_400 (forall ((u |u_(-> tptp.set_Pr304595758um_a_b Bool)|) (e Bool) (i tptp.set_Pr304595758um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr304595758um_a_b Bool)|)) (not (forall ((ii tptp.set_Pr304595758um_a_b)) (= (ho_332 v ii) (ite (= i ii) e (ho_332 u ii)))))))))) (let ((_let_401 (forall ((x |u_(-> tptp.set_Pr304595758um_a_b Bool)|) (y |u_(-> tptp.set_Pr304595758um_a_b Bool)|)) (or (not (forall ((z tptp.set_Pr304595758um_a_b)) (= (ho_332 x z) (ho_332 y z)))) (= x y))))) (let ((_let_402 (forall ((u |u_(-> tptp.sum_sum_a_b tptp.produc1124793815um_a_b)|) (e tptp.produc1124793815um_a_b) (i tptp.sum_sum_a_b)) (not (forall ((v |u_(-> tptp.sum_sum_a_b tptp.produc1124793815um_a_b)|)) (not (forall ((ii tptp.sum_sum_a_b)) (= (ho_59 v ii) (ite (= i ii) e (ho_59 u ii)))))))))) (let ((_let_403 (forall ((x |u_(-> tptp.sum_sum_a_b tptp.produc1124793815um_a_b)|) (y |u_(-> tptp.sum_sum_a_b tptp.produc1124793815um_a_b)|)) (or (not (forall ((z tptp.sum_sum_a_b)) (= (ho_59 x z) (ho_59 y z)))) (= x y))))) (let ((_let_404 (forall ((u |u_(-> tptp.set_Pr1647387645at_nat tptp.set_St761939237tant_a)|) (e tptp.set_St761939237tant_a) (i tptp.set_Pr1647387645at_nat)) (not (forall ((v |u_(-> tptp.set_Pr1647387645at_nat tptp.set_St761939237tant_a)|)) (not (forall ((ii tptp.set_Pr1647387645at_nat)) (= (ho_103 v ii) (ite (= i ii) e (ho_103 u ii)))))))))) (let ((_let_405 (forall ((x |u_(-> tptp.set_Pr1647387645at_nat tptp.set_St761939237tant_a)|) (y |u_(-> tptp.set_Pr1647387645at_nat tptp.set_St761939237tant_a)|)) (or (not (forall ((z tptp.set_Pr1647387645at_nat)) (= (ho_103 x z) (ho_103 y z)))) (= x y))))) (let ((_let_406 (forall ((u |u_(-> tptp.set_St761939237tant_a tptp.set_St761939237tant_a)|) (e tptp.set_St761939237tant_a) (i tptp.set_St761939237tant_a)) (not (forall ((v |u_(-> tptp.set_St761939237tant_a tptp.set_St761939237tant_a)|)) (not (forall ((ii tptp.set_St761939237tant_a)) (= (ho_106 v ii) (ite (= i ii) e (ho_106 u ii)))))))))) (let ((_let_407 (forall ((x |u_(-> tptp.set_St761939237tant_a tptp.set_St761939237tant_a)|) (y |u_(-> tptp.set_St761939237tant_a tptp.set_St761939237tant_a)|)) (or (not (forall ((z tptp.set_St761939237tant_a)) (= (ho_106 x z) (ho_106 y z)))) (= x y))))) (let ((_let_408 (forall ((u |u_(-> tptp.set_Pr653770722um_a_b Bool)|) (e Bool) (i tptp.set_Pr653770722um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr653770722um_a_b Bool)|)) (not (forall ((ii tptp.set_Pr653770722um_a_b)) (= (ho_184 v ii) (ite (= i ii) e (ho_184 u ii)))))))))) (let ((_let_409 (forall ((x |u_(-> tptp.set_Pr653770722um_a_b Bool)|) (y |u_(-> tptp.set_Pr653770722um_a_b Bool)|)) (or (not (forall ((z tptp.set_Pr653770722um_a_b)) (= (ho_184 x z) (ho_184 y z)))) (= x y))))) (let ((_let_410 (forall ((u |u_(-> tptp.product_prod_nat_nat tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat)|) (e |u_(-> tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat)|) (i tptp.product_prod_nat_nat)) (not (forall ((v |u_(-> tptp.product_prod_nat_nat tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat)|)) (not (forall ((ii tptp.product_prod_nat_nat)) (= (ho_108 v ii) (ite (= i ii) e (ho_108 u ii)))))))))) (let ((_let_411 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat)|) (y |u_(-> tptp.product_prod_nat_nat tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_108 x z) (ho_108 y z)))) (= x y))))) (let ((_let_412 (forall ((u |u_(-> tptp.produc1548871597um_a_b tptp.set_Pr1916610317um_a_b Bool)|) (e |u_(-> tptp.set_Pr1916610317um_a_b Bool)|) (i tptp.produc1548871597um_a_b)) (not (forall ((v |u_(-> tptp.produc1548871597um_a_b tptp.set_Pr1916610317um_a_b Bool)|)) (not (forall ((ii tptp.produc1548871597um_a_b)) (= (ho_159 v ii) (ite (= i ii) e (ho_159 u ii)))))))))) (let ((_let_413 (forall ((x |u_(-> tptp.produc1548871597um_a_b tptp.set_Pr1916610317um_a_b Bool)|) (y |u_(-> tptp.produc1548871597um_a_b tptp.set_Pr1916610317um_a_b Bool)|)) (or (not (forall ((z tptp.produc1548871597um_a_b)) (= (ho_159 x z) (ho_159 y z)))) (= x y))))) (let ((_let_414 (forall ((u |u_(-> tptp.set_Pr409224873um_a_b tptp.set_St761939237tant_a)|) (e tptp.set_St761939237tant_a) (i tptp.set_Pr409224873um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr409224873um_a_b tptp.set_St761939237tant_a)|)) (not (forall ((ii tptp.set_Pr409224873um_a_b)) (= (ho_111 v ii) (ite (= i ii) e (ho_111 u ii)))))))))) (let ((_let_415 (forall ((x |u_(-> tptp.set_Pr409224873um_a_b tptp.set_St761939237tant_a)|) (y |u_(-> tptp.set_Pr409224873um_a_b tptp.set_St761939237tant_a)|)) (or (not (forall ((z tptp.set_Pr409224873um_a_b)) (= (ho_111 x z) (ho_111 y z)))) (= x y))))) (let ((_let_416 (forall ((u |u_(-> tptp.set_nat tptp.set_nat)|) (e tptp.set_nat) (i tptp.set_nat)) (not (forall ((v |u_(-> tptp.set_nat tptp.set_nat)|)) (not (forall ((ii tptp.set_nat)) (= (ho_70 v ii) (ite (= i ii) e (ho_70 u ii)))))))))) (let ((_let_417 (forall ((x |u_(-> tptp.set_nat tptp.set_nat)|) (y |u_(-> tptp.set_nat tptp.set_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_70 x z) (ho_70 y z)))) (= x y))))) (let ((_let_418 (forall ((u |u_(-> tptp.set_Pr689416536at_nat Bool)|) (e Bool) (i tptp.set_Pr689416536at_nat)) (not (forall ((v |u_(-> tptp.set_Pr689416536at_nat Bool)|)) (not (forall ((ii tptp.set_Pr689416536at_nat)) (= (ho_318 v ii) (ite (= i ii) e (ho_318 u ii)))))))))) (let ((_let_419 (forall ((x |u_(-> tptp.set_Pr689416536at_nat Bool)|) (y |u_(-> tptp.set_Pr689416536at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr689416536at_nat)) (= (ho_318 x z) (ho_318 y z)))) (= x y))))) (let ((_let_420 (forall ((u |u_(-> tptp.labele261019144um_a_b tptp.labele431970251um_a_b tptp.set_Pr653770722um_a_b Bool)|) (e |u_(-> tptp.labele431970251um_a_b tptp.set_Pr653770722um_a_b Bool)|) (i tptp.labele261019144um_a_b)) (not (forall ((v |u_(-> tptp.labele261019144um_a_b tptp.labele431970251um_a_b tptp.set_Pr653770722um_a_b Bool)|)) (not (forall ((ii tptp.labele261019144um_a_b)) (= (ho_320 v ii) (ite (= i ii) e (ho_320 u ii)))))))))) (let ((_let_421 (forall ((x |u_(-> tptp.labele261019144um_a_b tptp.labele431970251um_a_b tptp.set_Pr653770722um_a_b Bool)|) (y |u_(-> tptp.labele261019144um_a_b tptp.labele431970251um_a_b tptp.set_Pr653770722um_a_b Bool)|)) (or (not (forall ((z tptp.labele261019144um_a_b)) (= (ho_320 x z) (ho_320 y z)))) (= x y))))) (let ((_let_422 (forall ((u |u_(-> tptp.set_Pr1558970842um_a_b Bool)|) (e Bool) (i tptp.set_Pr1558970842um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1558970842um_a_b Bool)|)) (not (forall ((ii tptp.set_Pr1558970842um_a_b)) (= (ho_223 v ii) (ite (= i ii) e (ho_223 u ii)))))))))) (let ((_let_423 (forall ((x |u_(-> tptp.set_Pr1558970842um_a_b Bool)|) (y |u_(-> tptp.set_Pr1558970842um_a_b Bool)|)) (or (not (forall ((z tptp.set_Pr1558970842um_a_b)) (= (ho_223 x z) (ho_223 y z)))) (= x y))))) (let ((_let_424 (forall ((u |u_(-> tptp.produc1963079155um_a_b tptp.produc1733247354um_a_b)|) (e tptp.produc1733247354um_a_b) (i tptp.produc1963079155um_a_b)) (not (forall ((v |u_(-> tptp.produc1963079155um_a_b tptp.produc1733247354um_a_b)|)) (not (forall ((ii tptp.produc1963079155um_a_b)) (= (ho_220 v ii) (ite (= i ii) e (ho_220 u ii)))))))))) (let ((_let_425 (forall ((x |u_(-> tptp.produc1963079155um_a_b tptp.produc1733247354um_a_b)|) (y |u_(-> tptp.produc1963079155um_a_b tptp.produc1733247354um_a_b)|)) (or (not (forall ((z tptp.produc1963079155um_a_b)) (= (ho_220 x z) (ho_220 y z)))) (= x y))))) (let ((_let_426 (forall ((u |u_(-> tptp.sum_sum_a_b tptp.produc1963079155um_a_b tptp.produc1733247354um_a_b)|) (e |u_(-> tptp.produc1963079155um_a_b tptp.produc1733247354um_a_b)|) (i tptp.sum_sum_a_b)) (not (forall ((v |u_(-> tptp.sum_sum_a_b tptp.produc1963079155um_a_b tptp.produc1733247354um_a_b)|)) (not (forall ((ii tptp.sum_sum_a_b)) (= (ho_219 v ii) (ite (= i ii) e (ho_219 u ii)))))))))) (let ((_let_427 (forall ((x |u_(-> tptp.sum_sum_a_b tptp.produc1963079155um_a_b tptp.produc1733247354um_a_b)|) (y |u_(-> tptp.sum_sum_a_b tptp.produc1963079155um_a_b tptp.produc1733247354um_a_b)|)) (or (not (forall ((z tptp.sum_sum_a_b)) (= (ho_219 x z) (ho_219 y z)))) (= x y))))) (let ((_let_428 (forall ((u |u_(-> tptp.set_Pr1121389018um_a_b tptp.set_Pr409224873um_a_b tptp.set_Sum_sum_a_b)|) (e |u_(-> tptp.set_Pr409224873um_a_b tptp.set_Sum_sum_a_b)|) (i tptp.set_Pr1121389018um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1121389018um_a_b tptp.set_Pr409224873um_a_b tptp.set_Sum_sum_a_b)|)) (not (forall ((ii tptp.set_Pr1121389018um_a_b)) (= (ho_225 v ii) (ite (= i ii) e (ho_225 u ii)))))))))) (let ((_let_429 (forall ((x |u_(-> tptp.set_Pr1121389018um_a_b tptp.set_Pr409224873um_a_b tptp.set_Sum_sum_a_b)|) (y |u_(-> tptp.set_Pr1121389018um_a_b tptp.set_Pr409224873um_a_b tptp.set_Sum_sum_a_b)|)) (or (not (forall ((z tptp.set_Pr1121389018um_a_b)) (= (ho_225 x z) (ho_225 y z)))) (= x y))))) (let ((_let_430 (forall ((u |u_(-> tptp.sum_sum_a_b tptp.produc1681803642um_a_b)|) (e tptp.produc1681803642um_a_b) (i tptp.sum_sum_a_b)) (not (forall ((v |u_(-> tptp.sum_sum_a_b tptp.produc1681803642um_a_b)|)) (not (forall ((ii tptp.sum_sum_a_b)) (= (ho_229 v ii) (ite (= i ii) e (ho_229 u ii)))))))))) (let ((_let_431 (forall ((x |u_(-> tptp.sum_sum_a_b tptp.produc1681803642um_a_b)|) (y |u_(-> tptp.sum_sum_a_b tptp.produc1681803642um_a_b)|)) (or (not (forall ((z tptp.sum_sum_a_b)) (= (ho_229 x z) (ho_229 y z)))) (= x y))))) (let ((_let_432 (forall ((u |u_(-> tptp.produc1963079155um_a_b tptp.sum_sum_a_b tptp.produc1681803642um_a_b)|) (e |u_(-> tptp.sum_sum_a_b tptp.produc1681803642um_a_b)|) (i tptp.produc1963079155um_a_b)) (not (forall ((v |u_(-> tptp.produc1963079155um_a_b tptp.sum_sum_a_b tptp.produc1681803642um_a_b)|)) (not (forall ((ii tptp.produc1963079155um_a_b)) (= (ho_228 v ii) (ite (= i ii) e (ho_228 u ii)))))))))) (let ((_let_433 (forall ((x |u_(-> tptp.produc1963079155um_a_b tptp.sum_sum_a_b tptp.produc1681803642um_a_b)|) (y |u_(-> tptp.produc1963079155um_a_b tptp.sum_sum_a_b tptp.produc1681803642um_a_b)|)) (or (not (forall ((z tptp.produc1963079155um_a_b)) (= (ho_228 x z) (ho_228 y z)))) (= x y))))) (let ((_let_434 (forall ((u |u_(-> tptp.produc1681803642um_a_b tptp.set_Pr1121389018um_a_b Bool)|) (e |u_(-> tptp.set_Pr1121389018um_a_b Bool)|) (i tptp.produc1681803642um_a_b)) (not (forall ((v |u_(-> tptp.produc1681803642um_a_b tptp.set_Pr1121389018um_a_b Bool)|)) (not (forall ((ii tptp.produc1681803642um_a_b)) (= (ho_231 v ii) (ite (= i ii) e (ho_231 u ii)))))))))) (let ((_let_435 (forall ((x |u_(-> tptp.produc1681803642um_a_b tptp.set_Pr1121389018um_a_b Bool)|) (y |u_(-> tptp.produc1681803642um_a_b tptp.set_Pr1121389018um_a_b Bool)|)) (or (not (forall ((z tptp.produc1681803642um_a_b)) (= (ho_231 x z) (ho_231 y z)))) (= x y))))) (let ((_let_436 (forall ((u |u_(-> tptp.set_Sum_sum_a_b tptp.set_nat)|) (e tptp.set_nat) (i tptp.set_Sum_sum_a_b)) (not (forall ((v |u_(-> tptp.set_Sum_sum_a_b tptp.set_nat)|)) (not (forall ((ii tptp.set_Sum_sum_a_b)) (= (ho_235 v ii) (ite (= i ii) e (ho_235 u ii)))))))))) (let ((_let_437 (forall ((x |u_(-> tptp.set_Sum_sum_a_b tptp.set_nat)|) (y |u_(-> tptp.set_Sum_sum_a_b tptp.set_nat)|)) (or (not (forall ((z tptp.set_Sum_sum_a_b)) (= (ho_235 x z) (ho_235 y z)))) (= x y))))) (let ((_let_438 (forall ((u |u_(-> tptp.set_Pr375490359_b_nat tptp.set_Sum_sum_a_b tptp.set_nat)|) (e |u_(-> tptp.set_Sum_sum_a_b tptp.set_nat)|) (i tptp.set_Pr375490359_b_nat)) (not (forall ((v |u_(-> tptp.set_Pr375490359_b_nat tptp.set_Sum_sum_a_b tptp.set_nat)|)) (not (forall ((ii tptp.set_Pr375490359_b_nat)) (= (ho_234 v ii) (ite (= i ii) e (ho_234 u ii)))))))))) (let ((_let_439 (forall ((x |u_(-> tptp.set_Pr375490359_b_nat tptp.set_Sum_sum_a_b tptp.set_nat)|) (y |u_(-> tptp.set_Pr375490359_b_nat tptp.set_Sum_sum_a_b tptp.set_nat)|)) (or (not (forall ((z tptp.set_Pr375490359_b_nat)) (= (ho_234 x z) (ho_234 y z)))) (= x y))))) (let ((_let_440 (forall ((u |u_(-> tptp.set_Pr689416536at_nat tptp.set_Pr1647387645at_nat tptp.set_nat)|) (e |u_(-> tptp.set_Pr1647387645at_nat tptp.set_nat)|) (i tptp.set_Pr689416536at_nat)) (not (forall ((v |u_(-> tptp.set_Pr689416536at_nat tptp.set_Pr1647387645at_nat tptp.set_nat)|)) (not (forall ((ii tptp.set_Pr689416536at_nat)) (= (ho_239 v ii) (ite (= i ii) e (ho_239 u ii)))))))))) (let ((_let_441 (forall ((x |u_(-> tptp.set_Pr689416536at_nat tptp.set_Pr1647387645at_nat tptp.set_nat)|) (y |u_(-> tptp.set_Pr689416536at_nat tptp.set_Pr1647387645at_nat tptp.set_nat)|)) (or (not (forall ((z tptp.set_Pr689416536at_nat)) (= (ho_239 x z) (ho_239 y z)))) (= x y))))) (let ((_let_442 (forall ((u |u_(-> tptp.set_nat tptp.set_Pr1647387645at_nat)|) (e tptp.set_Pr1647387645at_nat) (i tptp.set_nat)) (not (forall ((v |u_(-> tptp.set_nat tptp.set_Pr1647387645at_nat)|)) (not (forall ((ii tptp.set_nat)) (= (ho_243 v ii) (ite (= i ii) e (ho_243 u ii)))))))))) (let ((_let_443 (forall ((x |u_(-> tptp.set_nat tptp.set_Pr1647387645at_nat)|) (y |u_(-> tptp.set_nat tptp.set_Pr1647387645at_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_243 x z) (ho_243 y z)))) (= x y))))) (let ((_let_444 (forall ((u |u_(-> tptp.produc1032616263at_nat Bool)|) (e Bool) (i tptp.produc1032616263at_nat)) (not (forall ((v |u_(-> tptp.produc1032616263at_nat Bool)|)) (not (forall ((ii tptp.produc1032616263at_nat)) (= (ho_288 v ii) (ite (= i ii) e (ho_288 u ii)))))))))) (let ((_let_445 (forall ((x |u_(-> tptp.produc1032616263at_nat Bool)|) (y |u_(-> tptp.produc1032616263at_nat Bool)|)) (or (not (forall ((z tptp.produc1032616263at_nat)) (= (ho_288 x z) (ho_288 y z)))) (= x y))))) (let ((_let_446 (forall ((u |u_(-> tptp.set_Pr1134469976at_nat tptp.set_nat tptp.set_Pr1647387645at_nat)|) (e |u_(-> tptp.set_nat tptp.set_Pr1647387645at_nat)|) (i tptp.set_Pr1134469976at_nat)) (not (forall ((v |u_(-> tptp.set_Pr1134469976at_nat tptp.set_nat tptp.set_Pr1647387645at_nat)|)) (not (forall ((ii tptp.set_Pr1134469976at_nat)) (= (ho_242 v ii) (ite (= i ii) e (ho_242 u ii)))))))))) (let ((_let_447 (forall ((x |u_(-> tptp.set_Pr1134469976at_nat tptp.set_nat tptp.set_Pr1647387645at_nat)|) (y |u_(-> tptp.set_Pr1134469976at_nat tptp.set_nat tptp.set_Pr1647387645at_nat)|)) (or (not (forall ((z tptp.set_Pr1134469976at_nat)) (= (ho_242 x z) (ho_242 y z)))) (= x y))))) (let ((_let_448 (forall ((u |u_(-> tptp.set_Pr1155046920um_a_b tptp.set_nat tptp.set_Pr1916610317um_a_b)|) (e |u_(-> tptp.set_nat tptp.set_Pr1916610317um_a_b)|) (i tptp.set_Pr1155046920um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1155046920um_a_b tptp.set_nat tptp.set_Pr1916610317um_a_b)|)) (not (forall ((ii tptp.set_Pr1155046920um_a_b)) (= (ho_245 v ii) (ite (= i ii) e (ho_245 u ii)))))))))) (let ((_let_449 (forall ((x |u_(-> tptp.set_Pr1155046920um_a_b tptp.set_nat tptp.set_Pr1916610317um_a_b)|) (y |u_(-> tptp.set_Pr1155046920um_a_b tptp.set_nat tptp.set_Pr1916610317um_a_b)|)) (or (not (forall ((z tptp.set_Pr1155046920um_a_b)) (= (ho_245 x z) (ho_245 y z)))) (= x y))))) (let ((_let_450 (forall ((u |u_(-> tptp.labele431970251um_a_b tptp.set_Pr1174980151um_a_b Bool)|) (e |u_(-> tptp.set_Pr1174980151um_a_b Bool)|) (i tptp.labele431970251um_a_b)) (not (forall ((v |u_(-> tptp.labele431970251um_a_b tptp.set_Pr1174980151um_a_b Bool)|)) (not (forall ((ii tptp.labele431970251um_a_b)) (= (ho_249 v ii) (ite (= i ii) e (ho_249 u ii)))))))))) (let ((_let_451 (forall ((x |u_(-> tptp.labele431970251um_a_b tptp.set_Pr1174980151um_a_b Bool)|) (y |u_(-> tptp.labele431970251um_a_b tptp.set_Pr1174980151um_a_b Bool)|)) (or (not (forall ((z tptp.labele431970251um_a_b)) (= (ho_249 x z) (ho_249 y z)))) (= x y))))) (let ((_let_452 (forall ((u |u_(-> tptp.set_nat tptp.set_nat Bool)|) (e |u_(-> tptp.set_nat Bool)|) (i tptp.set_nat)) (not (forall ((v |u_(-> tptp.set_nat tptp.set_nat Bool)|)) (not (forall ((ii tptp.set_nat)) (= (ho_253 v ii) (ite (= i ii) e (ho_253 u ii)))))))))) (let ((_let_453 (forall ((x |u_(-> tptp.set_nat tptp.set_nat Bool)|) (y |u_(-> tptp.set_nat tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_253 x z) (ho_253 y z)))) (= x y))))) (let ((_let_454 (forall ((u |u_(-> tptp.set_Pr1916610317um_a_b tptp.set_Pr1916610317um_a_b Bool)|) (e |u_(-> tptp.set_Pr1916610317um_a_b Bool)|) (i tptp.set_Pr1916610317um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr1916610317um_a_b tptp.set_Pr1916610317um_a_b Bool)|)) (not (forall ((ii tptp.set_Pr1916610317um_a_b)) (= (ho_255 v ii) (ite (= i ii) e (ho_255 u ii)))))))))) (let ((_let_455 (forall ((x |u_(-> tptp.set_Pr1916610317um_a_b tptp.set_Pr1916610317um_a_b Bool)|) (y |u_(-> tptp.set_Pr1916610317um_a_b tptp.set_Pr1916610317um_a_b Bool)|)) (or (not (forall ((z tptp.set_Pr1916610317um_a_b)) (= (ho_255 x z) (ho_255 y z)))) (= x y))))) (let ((_let_456 (forall ((u |u_(-> tptp.standard_Constant_a Bool)|) (e Bool) (i tptp.standard_Constant_a)) (not (forall ((v |u_(-> tptp.standard_Constant_a Bool)|)) (not (forall ((ii tptp.standard_Constant_a)) (= (ho_256 v ii) (ite (= i ii) e (ho_256 u ii)))))))))) (let ((_let_457 (forall ((x |u_(-> tptp.standard_Constant_a Bool)|) (y |u_(-> tptp.standard_Constant_a Bool)|)) (or (not (forall ((z tptp.standard_Constant_a)) (= (ho_256 x z) (ho_256 y z)))) (= x y))))) (let ((_let_458 (forall ((u |u_(-> tptp.nat Bool)|) (e Bool) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_257 v ii) (ite (= i ii) e (ho_257 u ii)))))))))) (let ((_let_459 (forall ((x |u_(-> tptp.nat Bool)|) (y |u_(-> tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_257 x z) (ho_257 y z)))) (= x y))))) (let ((_let_460 (forall ((u |u_(-> tptp.set_St761939237tant_a tptp.set_St761939237tant_a Bool)|) (e |u_(-> tptp.set_St761939237tant_a Bool)|) (i tptp.set_St761939237tant_a)) (not (forall ((v |u_(-> tptp.set_St761939237tant_a tptp.set_St761939237tant_a Bool)|)) (not (forall ((ii tptp.set_St761939237tant_a)) (= (ho_259 v ii) (ite (= i ii) e (ho_259 u ii)))))))))) (let ((_let_461 (forall ((x |u_(-> tptp.set_St761939237tant_a tptp.set_St761939237tant_a Bool)|) (y |u_(-> tptp.set_St761939237tant_a tptp.set_St761939237tant_a Bool)|)) (or (not (forall ((z tptp.set_St761939237tant_a)) (= (ho_259 x z) (ho_259 y z)))) (= x y))))) (let ((_let_462 (forall ((u |u_(-> tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat Bool)|) (e |u_(-> tptp.set_Pr1986765409at_nat Bool)|) (i tptp.set_Pr1986765409at_nat)) (not (forall ((v |u_(-> tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat Bool)|)) (not (forall ((ii tptp.set_Pr1986765409at_nat)) (= (ho_261 v ii) (ite (= i ii) e (ho_261 u ii)))))))))) (let ((_let_463 (forall ((x |u_(-> tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat Bool)|) (y |u_(-> tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1986765409at_nat)) (= (ho_261 x z) (ho_261 y z)))) (= x y))))) (let ((_let_464 (forall ((u |u_(-> tptp.set_Pr375490359_b_nat Bool)|) (e Bool) (i tptp.set_Pr375490359_b_nat)) (not (forall ((v |u_(-> tptp.set_Pr375490359_b_nat Bool)|)) (not (forall ((ii tptp.set_Pr375490359_b_nat)) (= (ho_269 v ii) (ite (= i ii) e (ho_269 u ii)))))))))) (let ((_let_465 (forall ((x |u_(-> tptp.set_Pr375490359_b_nat Bool)|) (y |u_(-> tptp.set_Pr375490359_b_nat Bool)|)) (or (not (forall ((z tptp.set_Pr375490359_b_nat)) (= (ho_269 x z) (ho_269 y z)))) (= x y))))) (let ((_let_466 (forall ((u |u_(-> _u_(-> tptp.produc1548871597um_a_b Bool)_ tptp.set_Pr1916610317um_a_b)|) (e tptp.set_Pr1916610317um_a_b) (i |u_(-> tptp.produc1548871597um_a_b Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1548871597um_a_b Bool)_ tptp.set_Pr1916610317um_a_b)|)) (not (forall ((ii |u_(-> tptp.produc1548871597um_a_b Bool)|)) (= (ho_295 v ii) (ite (= i ii) e (ho_295 u ii)))))))))) (let ((_let_467 (forall ((x |u_(-> _u_(-> tptp.produc1548871597um_a_b Bool)_ tptp.set_Pr1916610317um_a_b)|) (y |u_(-> _u_(-> tptp.produc1548871597um_a_b Bool)_ tptp.set_Pr1916610317um_a_b)|)) (or (not (forall ((z |u_(-> tptp.produc1548871597um_a_b Bool)|)) (= (ho_295 x z) (ho_295 y z)))) (= x y))))) (let ((_let_468 (forall ((u |u_(-> tptp.sum_sum_a_b tptp.nat tptp.produc1978941143_b_nat)|) (e |u_(-> tptp.nat tptp.produc1978941143_b_nat)|) (i tptp.sum_sum_a_b)) (not (forall ((v |u_(-> tptp.sum_sum_a_b tptp.nat tptp.produc1978941143_b_nat)|)) (not (forall ((ii tptp.sum_sum_a_b)) (= (ho_265 v ii) (ite (= i ii) e (ho_265 u ii)))))))))) (let ((_let_469 (forall ((x |u_(-> tptp.sum_sum_a_b tptp.nat tptp.produc1978941143_b_nat)|) (y |u_(-> tptp.sum_sum_a_b tptp.nat tptp.produc1978941143_b_nat)|)) (or (not (forall ((z tptp.sum_sum_a_b)) (= (ho_265 x z) (ho_265 y z)))) (= x y))))) (let ((_let_470 (forall ((u |u_(-> tptp.produc1978941143_b_nat tptp.set_Pr375490359_b_nat Bool)|) (e |u_(-> tptp.set_Pr375490359_b_nat Bool)|) (i tptp.produc1978941143_b_nat)) (not (forall ((v |u_(-> tptp.produc1978941143_b_nat tptp.set_Pr375490359_b_nat Bool)|)) (not (forall ((ii tptp.produc1978941143_b_nat)) (= (ho_268 v ii) (ite (= i ii) e (ho_268 u ii)))))))))) (let ((_let_471 (forall ((x |u_(-> tptp.produc1978941143_b_nat tptp.set_Pr375490359_b_nat Bool)|) (y |u_(-> tptp.produc1978941143_b_nat tptp.set_Pr375490359_b_nat Bool)|)) (or (not (forall ((z tptp.produc1978941143_b_nat)) (= (ho_268 x z) (ho_268 y z)))) (= x y))))) (let ((_let_472 (forall ((u |u_(-> _u_(-> tptp.produc1963079155um_a_b Bool)_ tptp.set_Pr409224873um_a_b)|) (e tptp.set_Pr409224873um_a_b) (i |u_(-> tptp.produc1963079155um_a_b Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1963079155um_a_b Bool)_ tptp.set_Pr409224873um_a_b)|)) (not (forall ((ii |u_(-> tptp.produc1963079155um_a_b Bool)|)) (= (ho_285 v ii) (ite (= i ii) e (ho_285 u ii)))))))))) (let ((_let_473 (forall ((x |u_(-> _u_(-> tptp.produc1963079155um_a_b Bool)_ tptp.set_Pr409224873um_a_b)|) (y |u_(-> _u_(-> tptp.produc1963079155um_a_b Bool)_ tptp.set_Pr409224873um_a_b)|)) (or (not (forall ((z |u_(-> tptp.produc1963079155um_a_b Bool)|)) (= (ho_285 x z) (ho_285 y z)))) (= x y))))) (let ((_let_474 (forall ((u |u_(-> tptp.nat tptp.nat Bool)|) (e |u_(-> tptp.nat Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_287 v ii) (ite (= i ii) e (ho_287 u ii)))))))))) (let ((_let_475 (forall ((x |u_(-> tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_287 x z) (ho_287 y z)))) (= x y))))) (let ((_let_476 (forall ((u |u_(-> _u_(-> tptp.produc1032616263at_nat Bool)_ tptp.set_Pr1647387645at_nat)|) (e tptp.set_Pr1647387645at_nat) (i |u_(-> tptp.produc1032616263at_nat Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.produc1032616263at_nat Bool)_ tptp.set_Pr1647387645at_nat)|)) (not (forall ((ii |u_(-> tptp.produc1032616263at_nat Bool)|)) (= (ho_290 v ii) (ite (= i ii) e (ho_290 u ii)))))))))) (let ((_let_477 (forall ((x |u_(-> _u_(-> tptp.produc1032616263at_nat Bool)_ tptp.set_Pr1647387645at_nat)|) (y |u_(-> _u_(-> tptp.produc1032616263at_nat Bool)_ tptp.set_Pr1647387645at_nat)|)) (or (not (forall ((z |u_(-> tptp.produc1032616263at_nat Bool)|)) (= (ho_290 x z) (ho_290 y z)))) (= x y))))) (let ((_let_478 (forall ((u |u_(-> _u_(-> tptp.nat Bool)_ tptp.set_nat)|) (e tptp.set_nat) (i |u_(-> tptp.nat Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.nat Bool)_ tptp.set_nat)|)) (not (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ho_292 v ii) (ite (= i ii) e (ho_292 u ii)))))))))) (let ((_let_479 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.set_nat)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.set_nat)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_292 x z) (ho_292 y z)))) (= x y))))) (let ((_let_480 (forall ((u |u_(-> tptp.produc1548871597um_a_b Bool)|) (e Bool) (i tptp.produc1548871597um_a_b)) (not (forall ((v |u_(-> tptp.produc1548871597um_a_b Bool)|)) (not (forall ((ii tptp.produc1548871597um_a_b)) (= (ho_293 v ii) (ite (= i ii) e (ho_293 u ii)))))))))) (let ((_let_481 (forall ((x |u_(-> tptp.produc1548871597um_a_b Bool)|) (y |u_(-> tptp.produc1548871597um_a_b Bool)|)) (or (not (forall ((z tptp.produc1548871597um_a_b)) (= (ho_293 x z) (ho_293 y z)))) (= x y))))) (let ((_let_482 (forall ((u |u_(-> tptp.labele935650037_a_nat tptp.labele935650037_a_nat tptp.set_Pr1986765409at_nat Bool)|) (e |u_(-> tptp.labele935650037_a_nat tptp.set_Pr1986765409at_nat Bool)|) (i tptp.labele935650037_a_nat)) (not (forall ((v |u_(-> tptp.labele935650037_a_nat tptp.labele935650037_a_nat tptp.set_Pr1986765409at_nat Bool)|)) (not (forall ((ii tptp.labele935650037_a_nat)) (= (ho_297 v ii) (ite (= i ii) e (ho_297 u ii)))))))))) (let ((_let_483 (forall ((x |u_(-> tptp.labele935650037_a_nat tptp.labele935650037_a_nat tptp.set_Pr1986765409at_nat Bool)|) (y |u_(-> tptp.labele935650037_a_nat tptp.labele935650037_a_nat tptp.set_Pr1986765409at_nat Bool)|)) (or (not (forall ((z tptp.labele935650037_a_nat)) (= (ho_297 x z) (ho_297 y z)))) (= x y))))) (let ((_let_484 (forall ((u |u_(-> tptp.labele431970251um_a_b tptp.labele935650037_a_nat tptp.set_Pr375490359_b_nat Bool)|) (e |u_(-> tptp.labele935650037_a_nat tptp.set_Pr375490359_b_nat Bool)|) (i tptp.labele431970251um_a_b)) (not (forall ((v |u_(-> tptp.labele431970251um_a_b tptp.labele935650037_a_nat tptp.set_Pr375490359_b_nat Bool)|)) (not (forall ((ii tptp.labele431970251um_a_b)) (= (ho_300 v ii) (ite (= i ii) e (ho_300 u ii)))))))))) (let ((_let_485 (forall ((x |u_(-> tptp.labele431970251um_a_b tptp.labele935650037_a_nat tptp.set_Pr375490359_b_nat Bool)|) (y |u_(-> tptp.labele431970251um_a_b tptp.labele935650037_a_nat tptp.set_Pr375490359_b_nat Bool)|)) (or (not (forall ((z tptp.labele431970251um_a_b)) (= (ho_300 x z) (ho_300 y z)))) (= x y))))) (let ((_let_486 (forall ((u |u_(-> tptp.set_Pr1902304780_b_nat Bool)|) (e Bool) (i tptp.set_Pr1902304780_b_nat)) (not (forall ((v |u_(-> tptp.set_Pr1902304780_b_nat Bool)|)) (not (forall ((ii tptp.set_Pr1902304780_b_nat)) (= (ho_308 v ii) (ite (= i ii) e (ho_308 u ii)))))))))) (let ((_let_487 (forall ((x |u_(-> tptp.set_Pr1902304780_b_nat Bool)|) (y |u_(-> tptp.set_Pr1902304780_b_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1902304780_b_nat)) (= (ho_308 x z) (ho_308 y z)))) (= x y))))) (let ((_let_488 (forall ((u |u_(-> tptp.labele935650037_a_nat tptp.set_Pr1902304780_b_nat Bool)|) (e |u_(-> tptp.set_Pr1902304780_b_nat Bool)|) (i tptp.labele935650037_a_nat)) (not (forall ((v |u_(-> tptp.labele935650037_a_nat tptp.set_Pr1902304780_b_nat Bool)|)) (not (forall ((ii tptp.labele935650037_a_nat)) (= (ho_307 v ii) (ite (= i ii) e (ho_307 u ii)))))))))) (let ((_let_489 (forall ((x |u_(-> tptp.labele935650037_a_nat tptp.set_Pr1902304780_b_nat Bool)|) (y |u_(-> tptp.labele935650037_a_nat tptp.set_Pr1902304780_b_nat Bool)|)) (or (not (forall ((z tptp.labele935650037_a_nat)) (= (ho_307 x z) (ho_307 y z)))) (= x y))))) (let ((_let_490 (forall ((u |u_(-> tptp.set_Pr1647387645at_nat tptp.labele498606060at_nat)|) (e tptp.labele498606060at_nat) (i tptp.set_Pr1647387645at_nat)) (not (forall ((v |u_(-> tptp.set_Pr1647387645at_nat tptp.labele498606060at_nat)|)) (not (forall ((ii tptp.set_Pr1647387645at_nat)) (= (ho_314 v ii) (ite (= i ii) e (ho_314 u ii)))))))))) (let ((_let_491 (forall ((x |u_(-> tptp.set_Pr1647387645at_nat tptp.labele498606060at_nat)|) (y |u_(-> tptp.set_Pr1647387645at_nat tptp.labele498606060at_nat)|)) (or (not (forall ((z tptp.set_Pr1647387645at_nat)) (= (ho_314 x z) (ho_314 y z)))) (= x y))))) (let ((_let_492 (forall ((u |u_(-> tptp.set_Pr1355257963at_nat tptp.set_Pr1647387645at_nat tptp.labele498606060at_nat)|) (e |u_(-> tptp.set_Pr1647387645at_nat tptp.labele498606060at_nat)|) (i tptp.set_Pr1355257963at_nat)) (not (forall ((v |u_(-> tptp.set_Pr1355257963at_nat tptp.set_Pr1647387645at_nat tptp.labele498606060at_nat)|)) (not (forall ((ii tptp.set_Pr1355257963at_nat)) (= (ho_313 v ii) (ite (= i ii) e (ho_313 u ii)))))))))) (let ((_let_493 (forall ((x |u_(-> tptp.set_Pr1355257963at_nat tptp.set_Pr1647387645at_nat tptp.labele498606060at_nat)|) (y |u_(-> tptp.set_Pr1355257963at_nat tptp.set_Pr1647387645at_nat tptp.labele498606060at_nat)|)) (or (not (forall ((z tptp.set_Pr1355257963at_nat)) (= (ho_313 x z) (ho_313 y z)))) (= x y))))) (let ((_let_494 (forall ((u |u_(-> tptp.labele431970251um_a_b tptp.set_Pr653770722um_a_b Bool)|) (e |u_(-> tptp.set_Pr653770722um_a_b Bool)|) (i tptp.labele431970251um_a_b)) (not (forall ((v |u_(-> tptp.labele431970251um_a_b tptp.set_Pr653770722um_a_b Bool)|)) (not (forall ((ii tptp.labele431970251um_a_b)) (= (ho_321 v ii) (ite (= i ii) e (ho_321 u ii)))))))))) (let ((_let_495 (forall ((x |u_(-> tptp.labele431970251um_a_b tptp.set_Pr653770722um_a_b Bool)|) (y |u_(-> tptp.labele431970251um_a_b tptp.set_Pr653770722um_a_b Bool)|)) (or (not (forall ((z tptp.labele431970251um_a_b)) (= (ho_321 x z) (ho_321 y z)))) (= x y))))) (let ((_let_496 (forall ((u |u_(-> tptp.labele498606060at_nat tptp.labele935650037_a_nat tptp.set_Pr689416536at_nat Bool)|) (e |u_(-> tptp.labele935650037_a_nat tptp.set_Pr689416536at_nat Bool)|) (i tptp.labele498606060at_nat)) (not (forall ((v |u_(-> tptp.labele498606060at_nat tptp.labele935650037_a_nat tptp.set_Pr689416536at_nat Bool)|)) (not (forall ((ii tptp.labele498606060at_nat)) (= (ho_316 v ii) (ite (= i ii) e (ho_316 u ii)))))))))) (let ((_let_497 (forall ((x |u_(-> tptp.labele498606060at_nat tptp.labele935650037_a_nat tptp.set_Pr689416536at_nat Bool)|) (y |u_(-> tptp.labele498606060at_nat tptp.labele935650037_a_nat tptp.set_Pr689416536at_nat Bool)|)) (or (not (forall ((z tptp.labele498606060at_nat)) (= (ho_316 x z) (ho_316 y z)))) (= x y))))) (let ((_let_498 (forall ((u |u_(-> tptp.labele1191284958um_a_b tptp.labele935650037_a_nat tptp.set_Pr507214050_b_nat Bool)|) (e |u_(-> tptp.labele935650037_a_nat tptp.set_Pr507214050_b_nat Bool)|) (i tptp.labele1191284958um_a_b)) (not (forall ((v |u_(-> tptp.labele1191284958um_a_b tptp.labele935650037_a_nat tptp.set_Pr507214050_b_nat Bool)|)) (not (forall ((ii tptp.labele1191284958um_a_b)) (= (ho_326 v ii) (ite (= i ii) e (ho_326 u ii)))))))))) (let ((_let_499 (forall ((x |u_(-> tptp.labele1191284958um_a_b tptp.labele935650037_a_nat tptp.set_Pr507214050_b_nat Bool)|) (y |u_(-> tptp.labele1191284958um_a_b tptp.labele935650037_a_nat tptp.set_Pr507214050_b_nat Bool)|)) (or (not (forall ((z tptp.labele1191284958um_a_b)) (= (ho_326 x z) (ho_326 y z)))) (= x y))))) (let ((_let_500 (forall ((u |u_(-> tptp.labele431970251um_a_b tptp.set_Pr304595758um_a_b Bool)|) (e |u_(-> tptp.set_Pr304595758um_a_b Bool)|) (i tptp.labele431970251um_a_b)) (not (forall ((v |u_(-> tptp.labele431970251um_a_b tptp.set_Pr304595758um_a_b Bool)|)) (not (forall ((ii tptp.labele431970251um_a_b)) (= (ho_331 v ii) (ite (= i ii) e (ho_331 u ii)))))))))) (let ((_let_501 (forall ((x |u_(-> tptp.labele431970251um_a_b tptp.set_Pr304595758um_a_b Bool)|) (y |u_(-> tptp.labele431970251um_a_b tptp.set_Pr304595758um_a_b Bool)|)) (or (not (forall ((z tptp.labele431970251um_a_b)) (= (ho_331 x z) (ho_331 y z)))) (= x y))))) (let ((_let_502 (forall ((u |u_(-> tptp.labele498606060at_nat tptp.labele431970251um_a_b tptp.set_Pr304595758um_a_b Bool)|) (e |u_(-> tptp.labele431970251um_a_b tptp.set_Pr304595758um_a_b Bool)|) (i tptp.labele498606060at_nat)) (not (forall ((v |u_(-> tptp.labele498606060at_nat tptp.labele431970251um_a_b tptp.set_Pr304595758um_a_b Bool)|)) (not (forall ((ii tptp.labele498606060at_nat)) (= (ho_330 v ii) (ite (= i ii) e (ho_330 u ii)))))))))) (let ((_let_503 (forall ((x |u_(-> tptp.labele498606060at_nat tptp.labele431970251um_a_b tptp.set_Pr304595758um_a_b Bool)|) (y |u_(-> tptp.labele498606060at_nat tptp.labele431970251um_a_b tptp.set_Pr304595758um_a_b Bool)|)) (or (not (forall ((z tptp.labele498606060at_nat)) (= (ho_330 x z) (ho_330 y z)))) (= x y))))) (let ((_let_504 (forall ((u |u_(-> tptp.set_Pr55236280um_a_b Bool)|) (e Bool) (i tptp.set_Pr55236280um_a_b)) (not (forall ((v |u_(-> tptp.set_Pr55236280um_a_b Bool)|)) (not (forall ((ii tptp.set_Pr55236280um_a_b)) (= (ho_336 v ii) (ite (= i ii) e (ho_336 u ii)))))))))) (let ((_let_505 (forall ((x |u_(-> tptp.set_Pr55236280um_a_b Bool)|) (y |u_(-> tptp.set_Pr55236280um_a_b Bool)|)) (or (not (forall ((z tptp.set_Pr55236280um_a_b)) (= (ho_336 x z) (ho_336 y z)))) (= x y))))) (let ((_let_506 (forall ((u |u_(-> tptp.labele431970251um_a_b tptp.set_Pr55236280um_a_b Bool)|) (e |u_(-> tptp.set_Pr55236280um_a_b Bool)|) (i tptp.labele431970251um_a_b)) (not (forall ((v |u_(-> tptp.labele431970251um_a_b tptp.set_Pr55236280um_a_b Bool)|)) (not (forall ((ii tptp.labele431970251um_a_b)) (= (ho_335 v ii) (ite (= i ii) e (ho_335 u ii)))))))))) (let ((_let_507 (forall ((x |u_(-> tptp.labele431970251um_a_b tptp.set_Pr55236280um_a_b Bool)|) (y |u_(-> tptp.labele431970251um_a_b tptp.set_Pr55236280um_a_b Bool)|)) (or (not (forall ((z tptp.labele431970251um_a_b)) (= (ho_335 x z) (ho_335 y z)))) (= x y))))) (let ((_let_508 (forall ((u |u_(-> tptp.labele1191284958um_a_b tptp.labele431970251um_a_b tptp.set_Pr55236280um_a_b Bool)|) (e |u_(-> tptp.labele431970251um_a_b tptp.set_Pr55236280um_a_b Bool)|) (i tptp.labele1191284958um_a_b)) (not (forall ((v |u_(-> tptp.labele1191284958um_a_b tptp.labele431970251um_a_b tptp.set_Pr55236280um_a_b Bool)|)) (not (forall ((ii tptp.labele1191284958um_a_b)) (= (ho_334 v ii) (ite (= i ii) e (ho_334 u ii)))))))))) (let ((_let_509 (forall ((x |u_(-> tptp.labele1191284958um_a_b tptp.labele431970251um_a_b tptp.set_Pr55236280um_a_b Bool)|) (y |u_(-> tptp.labele1191284958um_a_b tptp.labele431970251um_a_b tptp.set_Pr55236280um_a_b Bool)|)) (or (not (forall ((z tptp.labele1191284958um_a_b)) (= (ho_334 x z) (ho_334 y z)))) (= x y))))) (let ((_let_510 (forall ((u |u_(-> tptp.set_Sum_sum_a_b tptp.set_Pr1916610317um_a_b)|) (e tptp.set_Pr1916610317um_a_b) (i tptp.set_Sum_sum_a_b)) (not (forall ((v |u_(-> tptp.set_Sum_sum_a_b tptp.set_Pr1916610317um_a_b)|)) (not (forall ((ii tptp.set_Sum_sum_a_b)) (= (ho_338 v ii) (ite (= i ii) e (ho_338 u ii)))))))))) (let ((_let_511 (forall ((x |u_(-> tptp.set_Sum_sum_a_b tptp.set_Pr1916610317um_a_b)|) (y |u_(-> tptp.set_Sum_sum_a_b tptp.set_Pr1916610317um_a_b)|)) (or (not (forall ((z tptp.set_Sum_sum_a_b)) (= (ho_338 x z) (ho_338 y z)))) (= x y))))) (let ((_let_512 (forall ((u |u_(-> tptp.standard_Constant_a tptp.produc1871334759_a_nat)|) (e tptp.produc1871334759_a_nat) (i tptp.standard_Constant_a)) (not (forall ((v |u_(-> tptp.standard_Constant_a tptp.produc1871334759_a_nat)|)) (not (forall ((ii tptp.standard_Constant_a)) (= (ho_340 v ii) (ite (= i ii) e (ho_340 u ii)))))))))) (let ((_let_513 (forall ((x |u_(-> tptp.standard_Constant_a tptp.produc1871334759_a_nat)|) (y |u_(-> tptp.standard_Constant_a tptp.produc1871334759_a_nat)|)) (or (not (forall ((z tptp.standard_Constant_a)) (= (ho_340 x z) (ho_340 y z)))) (= x y))))) (let ((_let_514 (forall ((u |u_(-> tptp.produc1871334759_a_nat tptp.labele431970251um_a_b Bool)|) (e |u_(-> tptp.labele431970251um_a_b Bool)|) (i tptp.produc1871334759_a_nat)) (not (forall ((v |u_(-> tptp.produc1871334759_a_nat tptp.labele431970251um_a_b Bool)|)) (not (forall ((ii tptp.produc1871334759_a_nat)) (= (ho_342 v ii) (ite (= i ii) e (ho_342 u ii)))))))))) (let ((_let_515 (forall ((x |u_(-> tptp.produc1871334759_a_nat tptp.labele431970251um_a_b Bool)|) (y |u_(-> tptp.produc1871334759_a_nat tptp.labele431970251um_a_b Bool)|)) (or (not (forall ((z tptp.produc1871334759_a_nat)) (= (ho_342 x z) (ho_342 y z)))) (= x y))))) (let ((_let_516 (forall ((u |u_(-> tptp.standard_Constant_a tptp.standard_Constant_a tptp.produc1871334759_a_nat)|) (e |u_(-> tptp.standard_Constant_a tptp.produc1871334759_a_nat)|) (i tptp.standard_Constant_a)) (not (forall ((v |u_(-> tptp.standard_Constant_a tptp.standard_Constant_a tptp.produc1871334759_a_nat)|)) (not (forall ((ii tptp.standard_Constant_a)) (= (ho_345 v ii) (ite (= i ii) e (ho_345 u ii)))))))))) (let ((_let_517 (forall ((x |u_(-> tptp.standard_Constant_a tptp.standard_Constant_a tptp.produc1871334759_a_nat)|) (y |u_(-> tptp.standard_Constant_a tptp.standard_Constant_a tptp.produc1871334759_a_nat)|)) (or (not (forall ((z tptp.standard_Constant_a)) (= (ho_345 x z) (ho_345 y z)))) (= x y))))) (let ((_let_518 (forall ((BOUND_VARIABLE_8988 tptp.set_Sum_sum_a_b) (BOUND_VARIABLE_8989 tptp.set_Sum_sum_a_b)) (= (= BOUND_VARIABLE_8988 BOUND_VARIABLE_8989) (ho_15 (ho_14 k_13 BOUND_VARIABLE_8988) BOUND_VARIABLE_8989))))) (let ((_let_519 (forall ((BOUND_VARIABLE_8973 tptp.set_Sum_sum_a_b) (BOUND_VARIABLE_8974 tptp.set_Sum_sum_a_b)) (= (ho_15 (ho_14 k_16 BOUND_VARIABLE_8973) BOUND_VARIABLE_8974) (and (forall ((X3 tptp.sum_sum_a_b)) (let ((_let_1 (ho_18 k_17 X3))) (or (not (ho_15 _let_1 BOUND_VARIABLE_8973)) (ho_15 _let_1 BOUND_VARIABLE_8974)))) (forall ((X3 tptp.sum_sum_a_b)) (let ((_let_1 (ho_18 k_17 X3))) (or (not (ho_15 _let_1 BOUND_VARIABLE_8974)) (ho_15 _let_1 BOUND_VARIABLE_8973))))))))) (let ((_let_520 (forall ((BOUND_VARIABLE_8962 tptp.set_Sum_sum_a_b) (BOUND_VARIABLE_8963 tptp.set_Sum_sum_a_b)) (= (ho_15 (ho_14 k_19 BOUND_VARIABLE_8962) BOUND_VARIABLE_8963) (forall ((X3 tptp.sum_sum_a_b)) (let ((_let_1 (ho_18 k_17 X3))) (or (not (ho_15 _let_1 BOUND_VARIABLE_8962)) (ho_15 _let_1 BOUND_VARIABLE_8963)))))))) (let ((_let_521 (forall ((BOUND_VARIABLE_8951 tptp.set_Sum_sum_a_b) (BOUND_VARIABLE_8952 tptp.set_Sum_sum_a_b)) (= (ho_15 (ho_14 k_20 BOUND_VARIABLE_8951) BOUND_VARIABLE_8952) (forall ((T tptp.sum_sum_a_b)) (let ((_let_1 (ho_18 k_17 T))) (or (not (ho_15 _let_1 BOUND_VARIABLE_8951)) (ho_15 _let_1 BOUND_VARIABLE_8952)))))))) (let ((_let_522 (forall ((BOUND_VARIABLE_8940 tptp.set_Pr409224873um_a_b) (BOUND_VARIABLE_8941 tptp.set_Pr409224873um_a_b)) (= (ho_23 (ho_22 k_21 BOUND_VARIABLE_8940) BOUND_VARIABLE_8941) (forall ((X3 tptp.produc1963079155um_a_b)) (let ((_let_1 (ho_25 k_24 X3))) (or (not (ho_23 _let_1 BOUND_VARIABLE_8940)) (ho_23 _let_1 BOUND_VARIABLE_8941)))))))) (let ((_let_523 (forall ((BOUND_VARIABLE_8929 tptp.set_Pr409224873um_a_b) (BOUND_VARIABLE_8930 tptp.set_Pr409224873um_a_b)) (= (ho_23 (ho_22 k_26 BOUND_VARIABLE_8929) BOUND_VARIABLE_8930) (forall ((T tptp.produc1963079155um_a_b)) (let ((_let_1 (ho_25 k_24 T))) (or (not (ho_23 _let_1 BOUND_VARIABLE_8929)) (ho_23 _let_1 BOUND_VARIABLE_8930)))))))) (let ((_let_524 (forall ((BOUND_VARIABLE_8918 tptp.set_Pr1174980151um_a_b) (BOUND_VARIABLE_8919 tptp.set_Pr1174980151um_a_b)) (= (ho_29 (ho_28 k_27 BOUND_VARIABLE_8918) BOUND_VARIABLE_8919) (forall ((X3 tptp.produc1124793815um_a_b)) (let ((_let_1 (ho_31 k_30 X3))) (or (not (ho_29 _let_1 BOUND_VARIABLE_8918)) (ho_29 _let_1 BOUND_VARIABLE_8919)))))))) (let ((_let_525 (forall ((BOUND_VARIABLE_8907 tptp.set_Pr1174980151um_a_b) (BOUND_VARIABLE_8908 tptp.set_Pr1174980151um_a_b)) (= (ho_29 (ho_28 k_32 BOUND_VARIABLE_8907) BOUND_VARIABLE_8908) (forall ((T tptp.produc1124793815um_a_b)) (let ((_let_1 (ho_31 k_30 T))) (or (not (ho_29 _let_1 BOUND_VARIABLE_8907)) (ho_29 _let_1 BOUND_VARIABLE_8908)))))))) (let ((_let_526 (forall ((BOUND_VARIABLE_8899 tptp.set_Pr409224873um_a_b) (BOUND_VARIABLE_8900 tptp.produc1963079155um_a_b)) (= (ho_35 (ho_34 k_33 BOUND_VARIABLE_8899) BOUND_VARIABLE_8900) (ho_23 (ho_25 k_24 BOUND_VARIABLE_8900) BOUND_VARIABLE_8899))))) (let ((_let_527 (forall ((BOUND_VARIABLE_8891 tptp.set_Pr1174980151um_a_b) (BOUND_VARIABLE_8892 tptp.produc1124793815um_a_b)) (= (ho_38 (ho_37 k_36 BOUND_VARIABLE_8891) BOUND_VARIABLE_8892) (ho_29 (ho_31 k_30 BOUND_VARIABLE_8892) BOUND_VARIABLE_8891))))) (let ((_let_528 (forall ((BOUND_VARIABLE_8883 tptp.set_Sum_sum_a_b) (BOUND_VARIABLE_8884 tptp.sum_sum_a_b)) (= (ho_41 (ho_40 k_39 BOUND_VARIABLE_8883) BOUND_VARIABLE_8884) (ho_15 (ho_18 k_17 BOUND_VARIABLE_8884) BOUND_VARIABLE_8883))))) (let ((_let_529 (forall ((BOUND_VARIABLE_8988 tptp.set_Sum_sum_a_b) (BOUND_VARIABLE_8989 tptp.set_Sum_sum_a_b)) (= (= BOUND_VARIABLE_8988 BOUND_VARIABLE_8989) (ll_12 BOUND_VARIABLE_8988 BOUND_VARIABLE_8989))))) (let ((_let_530 (forall ((BOUND_VARIABLE_8973 tptp.set_Sum_sum_a_b) (BOUND_VARIABLE_8974 tptp.set_Sum_sum_a_b)) (= (and (forall ((X3 tptp.sum_sum_a_b)) (let ((_let_1 (@ tptp.member_Sum_sum_a_b X3))) (or (not (@ _let_1 BOUND_VARIABLE_8973)) (@ _let_1 BOUND_VARIABLE_8974)))) (forall ((X3 tptp.sum_sum_a_b)) (let ((_let_1 (@ tptp.member_Sum_sum_a_b X3))) (or (not (@ _let_1 BOUND_VARIABLE_8974)) (@ _let_1 BOUND_VARIABLE_8973))))) (ll_11 BOUND_VARIABLE_8973 BOUND_VARIABLE_8974))))) (let ((_let_531 (forall ((BOUND_VARIABLE_8962 tptp.set_Sum_sum_a_b) (BOUND_VARIABLE_8963 tptp.set_Sum_sum_a_b)) (= (forall ((X3 tptp.sum_sum_a_b)) (let ((_let_1 (@ tptp.member_Sum_sum_a_b X3))) (or (not (@ _let_1 BOUND_VARIABLE_8962)) (@ _let_1 BOUND_VARIABLE_8963)))) (ll_10 BOUND_VARIABLE_8962 BOUND_VARIABLE_8963))))) (let ((_let_532 (forall ((BOUND_VARIABLE_8951 tptp.set_Sum_sum_a_b) (BOUND_VARIABLE_8952 tptp.set_Sum_sum_a_b)) (= (forall ((T tptp.sum_sum_a_b)) (let ((_let_1 (@ tptp.member_Sum_sum_a_b T))) (or (not (@ _let_1 BOUND_VARIABLE_8951)) (@ _let_1 BOUND_VARIABLE_8952)))) (ll_9 BOUND_VARIABLE_8951 BOUND_VARIABLE_8952))))) (let ((_let_533 (forall ((BOUND_VARIABLE_8940 tptp.set_Pr409224873um_a_b) (BOUND_VARIABLE_8941 tptp.set_Pr409224873um_a_b)) (= (forall ((X3 tptp.produc1963079155um_a_b)) (let ((_let_1 (@ tptp.member1998628618um_a_b X3))) (or (not (@ _let_1 BOUND_VARIABLE_8940)) (@ _let_1 BOUND_VARIABLE_8941)))) (ll_8 BOUND_VARIABLE_8940 BOUND_VARIABLE_8941))))) (let ((_let_534 (forall ((BOUND_VARIABLE_8929 tptp.set_Pr409224873um_a_b) (BOUND_VARIABLE_8930 tptp.set_Pr409224873um_a_b)) (= (forall ((T tptp.produc1963079155um_a_b)) (let ((_let_1 (@ tptp.member1998628618um_a_b T))) (or (not (@ _let_1 BOUND_VARIABLE_8929)) (@ _let_1 BOUND_VARIABLE_8930)))) (ll_7 BOUND_VARIABLE_8929 BOUND_VARIABLE_8930))))) (let ((_let_535 (forall ((BOUND_VARIABLE_8918 tptp.set_Pr1174980151um_a_b) (BOUND_VARIABLE_8919 tptp.set_Pr1174980151um_a_b)) (= (forall ((X3 tptp.produc1124793815um_a_b)) (let ((_let_1 (@ tptp.member1294585472um_a_b X3))) (or (not (@ _let_1 BOUND_VARIABLE_8918)) (@ _let_1 BOUND_VARIABLE_8919)))) (ll_6 BOUND_VARIABLE_8918 BOUND_VARIABLE_8919))))) (let ((_let_536 (forall ((BOUND_VARIABLE_8907 tptp.set_Pr1174980151um_a_b) (BOUND_VARIABLE_8908 tptp.set_Pr1174980151um_a_b)) (= (forall ((T tptp.produc1124793815um_a_b)) (let ((_let_1 (@ tptp.member1294585472um_a_b T))) (or (not (@ _let_1 BOUND_VARIABLE_8907)) (@ _let_1 BOUND_VARIABLE_8908)))) (ll_5 BOUND_VARIABLE_8907 BOUND_VARIABLE_8908))))) (let ((_let_537 (forall ((BOUND_VARIABLE_8899 tptp.set_Pr409224873um_a_b) (BOUND_VARIABLE_8900 tptp.produc1963079155um_a_b)) (= (@ (@ tptp.member1998628618um_a_b BOUND_VARIABLE_8900) BOUND_VARIABLE_8899) (ll_4 BOUND_VARIABLE_8899 BOUND_VARIABLE_8900))))) (let ((_let_538 (forall ((BOUND_VARIABLE_8891 tptp.set_Pr1174980151um_a_b) (BOUND_VARIABLE_8892 tptp.produc1124793815um_a_b)) (= (@ (@ tptp.member1294585472um_a_b BOUND_VARIABLE_8892) BOUND_VARIABLE_8891) (ll_3 BOUND_VARIABLE_8891 BOUND_VARIABLE_8892))))) (let ((_let_539 (forall ((BOUND_VARIABLE_8883 tptp.set_Sum_sum_a_b) (BOUND_VARIABLE_8884 tptp.sum_sum_a_b)) (= (@ (@ tptp.member_Sum_sum_a_b BOUND_VARIABLE_8884) BOUND_VARIABLE_8883) (ll_2 BOUND_VARIABLE_8883 BOUND_VARIABLE_8884))))) (let ((_let_540 (and _let_10 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529))) (let ((_let_541 (@ (@ tptp.labele16114835_a_nat _let_70) _let_97))) (let ((_let_542 (or))) (let ((_let_543 (_let_65))) (let ((_let_544 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_543)) :args _let_543)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_54))) (REFL :args (_let_55)) :args _let_542)) (MACRO_RESOLUTION_TRUST (REORDERING (NOT_AND (EQ_RESOLVE (ASSUME :args (_let_11)) (TRANS (MACRO_SR_EQ_INTRO _let_78 :args (_let_11 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (and (= _let_96 (@ tptp.labele1810595089_a_nat _let_541)) (= _let_541 (@ tptp.restri572569417_a_nat _let_541)) _let_10 (forall ((X3 tptp.sum_sum_a_b)) (let ((_let_1 (@ tptp.member_Sum_sum_a_b X3))) (or (not (@ _let_1 (@ (@ 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_let_531 _let_530 _let_529)))) :args (_let_540)) (PREPROCESS :args ((= _let_540 (and _let_64 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518))))) (PREPROCESS :args ((and _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104)))) :args ((and _let_64 _let_528 _let_527 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(ASSUME :args (_let_545)))) (let ((_let_550 (ASSUME :args (_let_46)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_549 _let_101 _let_550) :args (_let_42 _let_46 _let_545)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_550)) (CONG (REFL :args (_let_45)) (CONG (REFL :args (_let_44)) _let_102 :args (APPLY_UF ho_73)) :args (APPLY_UF ho_15)) (FALSE_INTRO _let_549))) :args (_let_545 _let_42 _let_46)) :args ((not (and _let_42 _let_46 _let_545)) SB_LITERAL))) (CONG (REFL :args (_let_99)) (REFL :args (_let_52)) (MACRO_SR_PRED_INTRO :args ((= (not _let_545) _let_47))) :args _let_542)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_546)) :args ((or _let_51 _let_545 (not _let_546)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_53 1)) _let_544 :args ((not _let_51) true _let_53)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_548 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_372 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tptp.sum_sum_a_b)) (not (@ (@ tptp.member1294585472um_a_b (@ (@ tptp.produc1808556047um_a_b tptp.zero_zero_nat) V)) tptp.f)))) _let_28 (forall ((A tptp.standard_Constant_a) (B tptp.product_prod_nat_nat) (R tptp.set_Pr1647387645at_nat)) (= (@ tptp.domain1060562500at_nat (@ (@ tptp.insert1625259895at_nat (@ (@ tptp.produc407553657at_nat A) B)) R)) (@ (@ tptp.insert1909710879tant_a A) (@ tptp.domain1060562500at_nat R)))) (forall ((A tptp.nat) (B tptp.nat) (R tptp.set_Pr1986765409at_nat)) (= (@ tptp.domain_nat_nat (@ (@ tptp.insert271595217at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) R)) (@ (@ tptp.insert_nat A) (@ tptp.domain_nat_nat R)))) (forall ((A tptp.nat) (B tptp.sum_sum_a_b) (R tptp.set_Pr1174980151um_a_b)) (= (@ tptp.domain1368163076um_a_b (@ (@ tptp.insert983991207um_a_b (@ (@ tptp.produc1808556047um_a_b A) B)) R)) (@ (@ tptp.insert_nat A) (@ tptp.domain1368163076um_a_b R)))) (forall ((A tptp.standard_Constant_a) (B tptp.produc1548871597um_a_b) (R tptp.set_Pr409224873um_a_b)) (= (@ tptp.domain1362581744um_a_b (@ (@ tptp.insert323157027um_a_b (@ (@ tptp.produc1697725733um_a_b A) B)) R)) (@ (@ tptp.insert1909710879tant_a A) (@ tptp.domain1362581744um_a_b R)))) (forall ((A tptp.sum_sum_a_b) (B tptp.sum_sum_a_b) (R tptp.set_Pr1916610317um_a_b)) (= (@ tptp.domain2069673178um_a_b (@ (@ tptp.insert1435405693um_a_b (@ (@ tptp.produc176426981um_a_b A) B)) R)) (@ (@ tptp.insert_Sum_sum_a_b A) (@ tptp.domain2069673178um_a_b R)))) (forall ((B tptp.nat) (R tptp.set_Pr1986765409at_nat) (A tptp.nat)) (= (@ (@ tptp.member_nat B) (@ (@ tptp.image_nat_nat R) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) R))) (forall ((B tptp.sum_sum_a_b) (R tptp.set_Pr1174980151um_a_b) (A tptp.nat)) (= (@ (@ tptp.member_Sum_sum_a_b B) (@ (@ tptp.image_256773707um_a_b R) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (@ (@ tptp.member1294585472um_a_b (@ (@ tptp.produc1808556047um_a_b A) B)) R))) (forall ((B tptp.sum_sum_a_b) (R tptp.set_Pr1994339542um_a_b) (A tptp.standard_Constant_a)) (= (@ (@ tptp.member_Sum_sum_a_b B) (@ (@ tptp.image_2129435242um_a_b R) (@ (@ tptp.insert1909710879tant_a A) tptp.bot_bo1160111033tant_a))) (@ (@ tptp.member1641046175um_a_b (@ (@ tptp.produc584843310um_a_b A) B)) R))) (forall ((B tptp.product_prod_nat_nat) (R tptp.set_Pr1647387645at_nat) (A tptp.standard_Constant_a)) (= (@ (@ tptp.member701585322at_nat B) (@ (@ tptp.image_127502653at_nat R) (@ (@ tptp.insert1909710879tant_a A) tptp.bot_bo1160111033tant_a))) (@ (@ tptp.member1696759390at_nat (@ (@ tptp.produc407553657at_nat A) B)) R))) (forall ((B tptp.sum_sum_a_b) (R tptp.set_Pr195945996um_a_b) (A tptp.product_prod_nat_nat)) (= (@ (@ tptp.member_Sum_sum_a_b B) (@ (@ tptp.image_1754351636um_a_b R) (@ (@ tptp.insert271595217at_nat A) tptp.bot_bo2130386637at_nat))) (@ (@ tptp.member585880557um_a_b (@ (@ tptp.produc1872245072um_a_b A) B)) R))) (forall ((B tptp.produc1124793815um_a_b) (R 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tptp.labele1810595089_a_nat Labeled_graph)) Labeled_graph)) (forall ((Labeled_graph tptp.labele431970251um_a_b)) (= (@ (@ tptp.labele1729654377um_a_b (@ tptp.labele1939049654um_a_b Labeled_graph)) (@ tptp.labele577278695um_a_b Labeled_graph)) Labeled_graph)) _let_27 _let_25 (= (@ tptp.domain1368163076um_a_b tptp.bot_bo575978147um_a_b) tptp.bot_bot_set_nat) _let_24 (= (@ tptp.domain1362581744um_a_b tptp.bot_bo1262634813um_a_b) tptp.bot_bo1160111033tant_a) (forall ((X tptp.set_St761939237tant_a)) (= (@ (@ tptp.image_127502653at_nat tptp.bot_bo810816657at_nat) X) tptp.bot_bo2130386637at_nat)) (forall ((X tptp.set_nat)) (= (@ (@ tptp.image_256773707um_a_b tptp.bot_bo575978147um_a_b) X) tptp.bot_bo1491243248um_a_b)) (forall ((X tptp.set_Sum_sum_a_b)) (= (@ (@ tptp.image_1918588449um_a_b tptp.bot_bo225809273um_a_b) X) tptp.bot_bo1491243248um_a_b)) (forall ((X tptp.set_St761939237tant_a)) (= (@ (@ tptp.image_2023280617um_a_b tptp.bot_bo1262634813um_a_b) X) tptp.bot_bo225809273um_a_b)) (forall ((X2 tptp.labele935650037_a_nat)) (let ((_let_1 (@ tptp.restri572569417_a_nat X2))) (= (@ tptp.restri572569417_a_nat _let_1) _let_1))) (forall ((X2 tptp.labele431970251um_a_b)) (let ((_let_1 (@ tptp.restri1162247455um_a_b X2))) (= (@ tptp.restri1162247455um_a_b _let_1) _let_1))) (forall ((X1 tptp.set_Pr1647387645at_nat) (X22 tptp.set_nat) (Y1 tptp.set_Pr1647387645at_nat) (Y2 tptp.set_nat)) (= (= (@ (@ tptp.labele16114835_a_nat X1) X22) (@ (@ tptp.labele16114835_a_nat Y1) Y2)) (and (= X1 Y1) (= X22 Y2)))) (forall ((X1 tptp.set_Pr409224873um_a_b) (X22 tptp.set_Sum_sum_a_b) (Y1 tptp.set_Pr409224873um_a_b) (Y2 tptp.set_Sum_sum_a_b)) (= (= (@ (@ tptp.labele1729654377um_a_b X1) X22) (@ (@ tptp.labele1729654377um_a_b Y1) Y2)) (and (= X1 Y1) (= X22 Y2)))) (forall ((A2 tptp.sum_sum_a_b) (B2 tptp.sum_sum_a_b)) (= (@ (@ tptp.member1998628618um_a_b (@ (@ tptp.produc1697725733um_a_b tptp.standard_S_Idt_a) (@ (@ tptp.produc176426981um_a_b A2) B2))) (@ tptp.labele1939049654um_a_b tptp.g)) (and (@ (@ 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R)))) (forall ((A tptp.nat) (B tptp.sum_sum_a_b) (R tptp.set_Pr1174980151um_a_b)) (=> (@ (@ tptp.member1294585472um_a_b (@ (@ tptp.produc1808556047um_a_b A) B)) R) (@ (@ tptp.member_nat A) (@ tptp.domain1368163076um_a_b R)))) (forall ((A tptp.standard_Constant_a) (B tptp.produc1548871597um_a_b) (R tptp.set_Pr409224873um_a_b)) (=> (@ (@ tptp.member1998628618um_a_b (@ (@ tptp.produc1697725733um_a_b A) B)) R) (@ (@ tptp.member1632892294tant_a A) (@ tptp.domain1362581744um_a_b R)))) (forall ((A tptp.sum_sum_a_b) (B tptp.sum_sum_a_b) (R tptp.set_Pr1916610317um_a_b)) (=> (@ (@ tptp.member947389014um_a_b (@ (@ tptp.produc176426981um_a_b A) B)) R) (@ (@ tptp.member_Sum_sum_a_b A) (@ tptp.domain2069673178um_a_b R)))) (forall ((A tptp.standard_Constant_a) (R tptp.set_Pr1647387645at_nat)) (= (@ (@ tptp.member1632892294tant_a A) (@ tptp.domain1060562500at_nat R)) (exists ((A6 tptp.standard_Constant_a) (B4 tptp.product_prod_nat_nat)) (and (= A A6) (@ (@ tptp.member1696759390at_nat (@ (@ 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(exists ((A6 tptp.sum_sum_a_b) (B4 tptp.sum_sum_a_b)) (and (= A A6) (@ (@ tptp.member947389014um_a_b (@ (@ tptp.produc176426981um_a_b A6) B4)) R))))) (forall ((A tptp.standard_Constant_a) (R tptp.set_Pr1647387645at_nat)) (=> (@ (@ tptp.member1632892294tant_a A) (@ tptp.domain1060562500at_nat R)) (not (forall ((B3 tptp.product_prod_nat_nat)) (not (@ (@ tptp.member1696759390at_nat (@ (@ tptp.produc407553657at_nat A) B3)) R)))))) (forall ((A tptp.nat) (R tptp.set_Pr1986765409at_nat)) (=> (@ (@ tptp.member_nat A) (@ tptp.domain_nat_nat R)) (not (forall ((B3 tptp.nat)) (not (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) B3)) R)))))) (forall ((A tptp.nat) (R tptp.set_Pr1174980151um_a_b)) (=> (@ (@ tptp.member_nat A) (@ tptp.domain1368163076um_a_b R)) (not (forall ((B3 tptp.sum_sum_a_b)) (not (@ (@ tptp.member1294585472um_a_b (@ (@ tptp.produc1808556047um_a_b A) B3)) R)))))) (forall ((A tptp.standard_Constant_a) (R tptp.set_Pr409224873um_a_b)) (=> (@ (@ tptp.member1632892294tant_a A) (@ tptp.domain1362581744um_a_b R)) (not (forall ((B3 tptp.produc1548871597um_a_b)) (not (@ (@ tptp.member1998628618um_a_b (@ (@ tptp.produc1697725733um_a_b A) B3)) R)))))) (forall ((A tptp.sum_sum_a_b) (R tptp.set_Pr1916610317um_a_b)) (=> (@ (@ tptp.member_Sum_sum_a_b A) (@ tptp.domain2069673178um_a_b R)) (not (forall ((B3 tptp.sum_sum_a_b)) (not (@ (@ tptp.member947389014um_a_b (@ (@ tptp.produc176426981um_a_b A) B3)) R)))))) (forall ((A tptp.standard_Constant_a) (R tptp.set_Pr1647387645at_nat)) (= (@ (@ tptp.member1632892294tant_a A) (@ tptp.domain1060562500at_nat R)) (exists ((Y3 tptp.product_prod_nat_nat)) (@ (@ tptp.member1696759390at_nat (@ (@ tptp.produc407553657at_nat A) Y3)) R)))) (forall ((A tptp.nat) (R tptp.set_Pr1986765409at_nat)) (= (@ (@ tptp.member_nat A) (@ tptp.domain_nat_nat R)) (exists ((Y3 tptp.nat)) (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) Y3)) R)))) (forall ((A tptp.nat) (R tptp.set_Pr1174980151um_a_b)) (= (@ (@ tptp.member_nat A) (@ tptp.domain1368163076um_a_b R)) (exists ((Y3 tptp.sum_sum_a_b)) (@ (@ tptp.member1294585472um_a_b (@ (@ tptp.produc1808556047um_a_b A) Y3)) R)))) (forall ((A tptp.standard_Constant_a) (R tptp.set_Pr409224873um_a_b)) (= (@ (@ tptp.member1632892294tant_a A) (@ tptp.domain1362581744um_a_b R)) (exists ((Y3 tptp.produc1548871597um_a_b)) (@ (@ tptp.member1998628618um_a_b (@ (@ tptp.produc1697725733um_a_b A) Y3)) R)))) (forall ((A tptp.sum_sum_a_b) (R tptp.set_Pr1916610317um_a_b)) (= (@ (@ tptp.member_Sum_sum_a_b A) (@ tptp.domain2069673178um_a_b R)) (exists ((Y3 tptp.sum_sum_a_b)) (@ (@ tptp.member947389014um_a_b (@ (@ tptp.produc176426981um_a_b A) Y3)) R)))) (forall ((A tptp.standard_Constant_a) (R tptp.set_Pr1647387645at_nat)) (=> (@ (@ tptp.member1632892294tant_a A) (@ tptp.domain1060562500at_nat R)) (not (forall ((B3 tptp.product_prod_nat_nat)) (not (@ (@ tptp.member1696759390at_nat (@ (@ tptp.produc407553657at_nat A) B3)) R)))))) (forall ((A tptp.nat) (R tptp.set_Pr1986765409at_nat)) (=> (@ (@ tptp.member_nat A) (@ tptp.domain_nat_nat R)) (not (forall ((B3 tptp.nat)) (not (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat A) B3)) R)))))) (forall ((A tptp.nat) (R tptp.set_Pr1174980151um_a_b)) (=> (@ (@ tptp.member_nat A) (@ tptp.domain1368163076um_a_b R)) (not (forall ((B3 tptp.sum_sum_a_b)) (not (@ (@ tptp.member1294585472um_a_b (@ (@ tptp.produc1808556047um_a_b A) B3)) R)))))) (forall ((A tptp.standard_Constant_a) (R tptp.set_Pr409224873um_a_b)) (=> (@ (@ tptp.member1632892294tant_a A) (@ tptp.domain1362581744um_a_b R)) (not (forall ((B3 tptp.produc1548871597um_a_b)) (not (@ (@ tptp.member1998628618um_a_b (@ (@ tptp.produc1697725733um_a_b A) B3)) R)))))) (forall ((A tptp.sum_sum_a_b) (R tptp.set_Pr1916610317um_a_b)) (=> (@ (@ tptp.member_Sum_sum_a_b A) (@ tptp.domain2069673178um_a_b R)) (not (forall ((B3 tptp.sum_sum_a_b)) (not (@ (@ tptp.member947389014um_a_b (@ (@ tptp.produc176426981um_a_b A) B3)) R)))))) (forall ((R tptp.set_Pr1174980151um_a_b) (S tptp.set_Pr1174980151um_a_b)) (=> (@ (@ tptp.ord_le823954903um_a_b R) S) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.domain1368163076um_a_b R)) (@ tptp.domain1368163076um_a_b S)))) (forall ((R tptp.set_Pr409224873um_a_b) (S tptp.set_Pr409224873um_a_b)) (=> (@ (@ tptp.ord_le615126793um_a_b R) S) (@ (@ tptp.ord_le1739761029tant_a (@ tptp.domain1362581744um_a_b R)) (@ tptp.domain1362581744um_a_b S)))) (forall ((R tptp.set_Pr1986765409at_nat) (S tptp.set_Pr1986765409at_nat)) (=> (@ (@ tptp.ord_le841296385at_nat R) S) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.domain_nat_nat R)) (@ tptp.domain_nat_nat S)))) (forall ((R tptp.set_Pr1647387645at_nat) (S tptp.set_Pr1647387645at_nat)) (=> (@ (@ tptp.ord_le1909159005at_nat R) S) (@ (@ tptp.ord_le1739761029tant_a (@ tptp.domain1060562500at_nat R)) (@ tptp.domain1060562500at_nat S)))) (forall ((R tptp.set_Pr1916610317um_a_b) (S tptp.set_Pr1916610317um_a_b)) (=> (@ (@ tptp.ord_le1059794605um_a_b R) S) (@ (@ tptp.ord_le192794300um_a_b (@ tptp.domain2069673178um_a_b R)) (@ tptp.domain2069673178um_a_b S)))) (forall ((Labeled_graph tptp.labele935650037_a_nat) (Labeled_graph2 tptp.labele935650037_a_nat)) (=> (and (= (@ tptp.labele195203296_a_nat Labeled_graph) (@ tptp.labele195203296_a_nat Labeled_graph2)) (= (@ tptp.labele1810595089_a_nat Labeled_graph) (@ tptp.labele1810595089_a_nat Labeled_graph2))) (= Labeled_graph Labeled_graph2))) (forall ((Labeled_graph tptp.labele431970251um_a_b) (Labeled_graph2 tptp.labele431970251um_a_b)) (=> (and (= (@ tptp.labele1939049654um_a_b Labeled_graph) (@ tptp.labele1939049654um_a_b Labeled_graph2)) (= (@ tptp.labele577278695um_a_b Labeled_graph) (@ tptp.labele577278695um_a_b Labeled_graph2))) (= Labeled_graph Labeled_graph2))) _let_23 (forall ((X1 tptp.set_Pr409224873um_a_b) (X22 tptp.set_Sum_sum_a_b)) (= (@ tptp.labele577278695um_a_b (@ (@ tptp.labele1729654377um_a_b X1) X22)) X22)) _let_22 (forall ((X1 tptp.set_Pr409224873um_a_b) (X22 tptp.set_Sum_sum_a_b)) (= (@ tptp.labele1939049654um_a_b (@ (@ tptp.labele1729654377um_a_b X1) X22)) X1)) (forall ((R tptp.set_Pr1647387645at_nat)) (= (= (@ tptp.domain1060562500at_nat R) tptp.bot_bo1160111033tant_a) (= R tptp.bot_bo810816657at_nat))) (forall ((R tptp.set_Pr409224873um_a_b)) (= (= (@ tptp.domain1362581744um_a_b R) tptp.bot_bo1160111033tant_a) (= R tptp.bot_bo1262634813um_a_b))) (forall ((R tptp.set_Pr1986765409at_nat)) (= (= (@ tptp.domain_nat_nat R) tptp.bot_bot_set_nat) (= R tptp.bot_bo2130386637at_nat))) (forall ((R tptp.set_Pr1174980151um_a_b)) (= (= (@ tptp.domain1368163076um_a_b R) tptp.bot_bot_set_nat) (= R tptp.bot_bo575978147um_a_b))) (forall ((R tptp.set_Pr1916610317um_a_b)) (= (= (@ tptp.domain2069673178um_a_b R) tptp.bot_bo1491243248um_a_b) (= R tptp.bot_bo225809273um_a_b))) (forall ((H1 tptp.set_Pr375490359_b_nat) (E1 tptp.set_Pr409224873um_a_b) (E2 tptp.set_Pr1647387645at_nat) (V1 tptp.sum_sum_a_b) (V12 tptp.nat) (V22 tptp.sum_sum_a_b) (V23 tptp.nat) (K tptp.standard_Constant_a)) (=> (@ (@ (@ tptp.edge_p749155930tant_a H1) E1) E2) (=> (@ (@ tptp.member1249152_b_nat (@ (@ tptp.produc522153487_b_nat V1) V12)) H1) (=> (@ (@ tptp.member1249152_b_nat (@ (@ tptp.produc522153487_b_nat V22) V23)) H1) (=> (@ (@ tptp.member1998628618um_a_b (@ (@ tptp.produc1697725733um_a_b K) (@ (@ tptp.produc176426981um_a_b V1) V22))) E1) (@ (@ tptp.member1696759390at_nat (@ (@ tptp.produc407553657at_nat K) (@ (@ tptp.product_Pair_nat_nat V12) V23))) E2)))))) (forall ((H1 tptp.set_Pr1986765409at_nat) (E1 tptp.set_Pr1647387645at_nat) (E2 tptp.set_Pr1647387645at_nat) (V1 tptp.nat) (V12 tptp.nat) (V22 tptp.nat) (V23 tptp.nat) (K tptp.standard_Constant_a)) (let ((_let_1 (@ tptp.produc407553657at_nat K))) (let ((_let_2 (@ tptp.product_Pair_nat_nat V1))) (=> (@ (@ (@ tptp.edge_p170421892tant_a H1) E1) E2) (=> (@ (@ tptp.member701585322at_nat (@ _let_2 V12)) H1) (=> (@ (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat V22) V23)) H1) (=> (@ (@ tptp.member1696759390at_nat (@ _let_1 (@ _let_2 V22))) E1) (@ (@ tptp.member1696759390at_nat (@ _let_1 (@ (@ tptp.product_Pair_nat_nat V12) V23))) E2)))))))) (forall ((H1 tptp.set_Pr1916610317um_a_b) (E1 tptp.set_Pr409224873um_a_b) (E2 tptp.set_Pr409224873um_a_b) (V1 tptp.sum_sum_a_b) (V12 tptp.sum_sum_a_b) (V22 tptp.sum_sum_a_b) (V23 tptp.sum_sum_a_b) (K tptp.standard_Constant_a)) (let ((_let_1 (@ tptp.produc1697725733um_a_b K))) (let ((_let_2 (@ tptp.produc176426981um_a_b V1))) (=> (@ (@ (@ tptp.edge_p1871801392tant_a H1) E1) E2) (=> (@ (@ tptp.member947389014um_a_b (@ _let_2 V12)) H1) (=> (@ (@ tptp.member947389014um_a_b (@ (@ tptp.produc176426981um_a_b V22) V23)) H1) (=> (@ (@ tptp.member1998628618um_a_b (@ _let_1 (@ _let_2 V22))) E1) (@ (@ tptp.member1998628618um_a_b (@ _let_1 (@ (@ tptp.produc176426981um_a_b V12) V23))) E2)))))))) (forall ((H1 tptp.set_Pr1174980151um_a_b) (E1 tptp.set_Pr1647387645at_nat) (E2 tptp.set_Pr409224873um_a_b) (V1 tptp.nat) (V12 tptp.sum_sum_a_b) (V22 tptp.nat) (V23 tptp.sum_sum_a_b) (K tptp.standard_Constant_a)) (=> (@ (@ (@ tptp.edge_p1382426714tant_a H1) E1) E2) (=> (@ (@ tptp.member1294585472um_a_b (@ (@ tptp.produc1808556047um_a_b V1) V12)) H1) (=> (@ (@ tptp.member1294585472um_a_b (@ (@ tptp.produc1808556047um_a_b V22) V23)) H1) (=> (@ (@ tptp.member1696759390at_nat (@ (@ tptp.produc407553657at_nat K) (@ (@ tptp.product_Pair_nat_nat V1) V22))) E1) (@ (@ tptp.member1998628618um_a_b (@ (@ tptp.produc1697725733um_a_b K) (@ (@ tptp.produc176426981um_a_b V12) V23))) E2)))))) (forall ((Labeled_graph tptp.labele935650037_a_nat)) (= Labeled_graph (@ (@ tptp.labele16114835_a_nat (@ tptp.labele195203296_a_nat Labeled_graph)) (@ tptp.labele1810595089_a_nat Labeled_graph)))) (forall ((Labeled_graph tptp.labele431970251um_a_b)) (= Labeled_graph (@ (@ tptp.labele1729654377um_a_b (@ tptp.labele1939049654um_a_b Labeled_graph)) (@ tptp.labele577278695um_a_b Labeled_graph)))) (forall ((A tptp.standard_Constant_a) (A3 tptp.set_St761939237tant_a) (B tptp.standard_Constant_a)) (let ((_let_1 (@ (@ tptp.insert1909710879tant_a B) tptp.bot_bo1160111033tant_a))) (= (= (@ (@ tptp.insert1909710879tant_a A) A3) _let_1) (and (= A B) (@ (@ tptp.ord_le1739761029tant_a A3) _let_1))))) (forall ((A tptp.product_prod_nat_nat) (A3 tptp.set_Pr1986765409at_nat) (B tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.insert271595217at_nat B) tptp.bot_bo2130386637at_nat))) (= (= (@ (@ tptp.insert271595217at_nat A) A3) _let_1) (and (= A B) (@ (@ tptp.ord_le841296385at_nat A3) _let_1))))) (forall ((A tptp.produc1032616263at_nat) (A3 tptp.set_Pr1647387645at_nat) (B tptp.produc1032616263at_nat)) (let ((_let_1 (@ (@ tptp.insert1625259895at_nat B) tptp.bot_bo810816657at_nat))) (= (= (@ (@ tptp.insert1625259895at_nat A) A3) _let_1) (and (= A B) (@ (@ tptp.ord_le1909159005at_nat A3) _let_1))))) (forall ((A tptp.nat) (A3 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (= (= (@ (@ tptp.insert_nat A) A3) _let_1) (and (= A B) (@ (@ tptp.ord_less_eq_set_nat A3) _let_1))))) (forall ((A tptp.produc1124793815um_a_b) (A3 tptp.set_Pr1174980151um_a_b) (B tptp.produc1124793815um_a_b)) (let ((_let_1 (@ (@ tptp.insert983991207um_a_b B) tptp.bot_bo575978147um_a_b))) (= (= (@ (@ tptp.insert983991207um_a_b A) A3) _let_1) (and (= A B) (@ (@ tptp.ord_le823954903um_a_b A3) _let_1))))) (forall ((A tptp.produc1548871597um_a_b) (A3 tptp.set_Pr1916610317um_a_b) (B tptp.produc1548871597um_a_b)) (let ((_let_1 (@ (@ tptp.insert1435405693um_a_b B) tptp.bot_bo225809273um_a_b))) (= (= (@ (@ tptp.insert1435405693um_a_b A) A3) _let_1) (and (= A B) (@ (@ tptp.ord_le1059794605um_a_b A3) _let_1))))) (forall ((A tptp.produc1963079155um_a_b) (A3 tptp.set_Pr409224873um_a_b) (B tptp.produc1963079155um_a_b)) (let ((_let_1 (@ (@ tptp.insert323157027um_a_b B) tptp.bot_bo1262634813um_a_b))) (= (= (@ (@ tptp.insert323157027um_a_b A) A3) _let_1) (and (= A B) (@ (@ tptp.ord_le615126793um_a_b A3) _let_1))))) (forall ((A tptp.sum_sum_a_b) (A3 tptp.set_Sum_sum_a_b) (B tptp.sum_sum_a_b)) (let ((_let_1 (@ (@ tptp.insert_Sum_sum_a_b B) tptp.bot_bo1491243248um_a_b))) (= (= (@ (@ tptp.insert_Sum_sum_a_b A) A3) _let_1) (and (= A B) (@ (@ tptp.ord_le192794300um_a_b A3) _let_1))))) (forall ((B tptp.standard_Constant_a) (A tptp.standard_Constant_a) (A3 tptp.set_St761939237tant_a)) (let ((_let_1 (@ (@ tptp.insert1909710879tant_a B) tptp.bot_bo1160111033tant_a))) (= (= _let_1 (@ (@ tptp.insert1909710879tant_a A) A3)) (and (= A B) (@ (@ tptp.ord_le1739761029tant_a A3) _let_1))))) (forall ((B tptp.product_prod_nat_nat) (A tptp.product_prod_nat_nat) (A3 tptp.set_Pr1986765409at_nat)) (let ((_let_1 (@ (@ tptp.insert271595217at_nat B) tptp.bot_bo2130386637at_nat))) (= (= _let_1 (@ (@ tptp.insert271595217at_nat A) A3)) (and (= A B) (@ (@ tptp.ord_le841296385at_nat A3) _let_1))))) (forall ((B tptp.produc1032616263at_nat) (A tptp.produc1032616263at_nat) (A3 tptp.set_Pr1647387645at_nat)) (let ((_let_1 (@ (@ tptp.insert1625259895at_nat B) tptp.bot_bo810816657at_nat))) (= (= _let_1 (@ (@ tptp.insert1625259895at_nat A) A3)) (and (= A B) (@ (@ tptp.ord_le1909159005at_nat A3) _let_1))))) (forall ((B tptp.nat) (A tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (= (= _let_1 (@ (@ tptp.insert_nat A) A3)) (and (= A B) (@ (@ tptp.ord_less_eq_set_nat A3) _let_1))))) (forall ((B tptp.produc1124793815um_a_b) (A tptp.produc1124793815um_a_b) (A3 tptp.set_Pr1174980151um_a_b)) (let ((_let_1 (@ (@ tptp.insert983991207um_a_b B) tptp.bot_bo575978147um_a_b))) (= (= _let_1 (@ (@ tptp.insert983991207um_a_b A) A3)) (and (= A B) (@ (@ tptp.ord_le823954903um_a_b A3) _let_1))))) (forall ((B tptp.produc1548871597um_a_b) (A tptp.produc1548871597um_a_b) (A3 tptp.set_Pr1916610317um_a_b)) (let ((_let_1 (@ (@ tptp.insert1435405693um_a_b B) tptp.bot_bo225809273um_a_b))) (= (= _let_1 (@ (@ tptp.insert1435405693um_a_b A) A3)) (and (= A B) (@ (@ tptp.ord_le1059794605um_a_b A3) _let_1))))) (forall ((B tptp.produc1963079155um_a_b) (A tptp.produc1963079155um_a_b) (A3 tptp.set_Pr409224873um_a_b)) (let ((_let_1 (@ (@ tptp.insert323157027um_a_b B) tptp.bot_bo1262634813um_a_b))) (= (= _let_1 (@ (@ tptp.insert323157027um_a_b A) A3)) (and (= A B) (@ (@ tptp.ord_le615126793um_a_b A3) _let_1))))) (forall ((B tptp.sum_sum_a_b) (A tptp.sum_sum_a_b) (A3 tptp.set_Sum_sum_a_b)) (let ((_let_1 (@ (@ tptp.insert_Sum_sum_a_b B) tptp.bot_bo1491243248um_a_b))) (= (= _let_1 (@ (@ tptp.insert_Sum_sum_a_b A) A3)) (and (= A B) (@ (@ tptp.ord_le192794300um_a_b A3) _let_1))))) (@ tptp.unival860567212at_nat tptp.bot_bo810816657at_nat) (@ tptp.unival118648434um_a_b tptp.bot_bo225809273um_a_b) (@ tptp.unival1487587672um_a_b tptp.bot_bo1262634813um_a_b) (@ tptp.unival2092813468um_a_b tptp.bot_bo575978147um_a_b) (forall ((A tptp.sum_sum_a_b) (P (-> tptp.sum_sum_a_b Bool))) (= (@ (@ tptp.member_Sum_sum_a_b A) (@ tptp.collect_Sum_sum_a_b P)) (@ P A))) (forall ((A tptp.produc1124793815um_a_b) (P (-> tptp.produc1124793815um_a_b Bool))) (= (@ (@ tptp.member1294585472um_a_b A) (@ tptp.collec492052930um_a_b P)) (@ P A))) (forall ((A tptp.produc1963079155um_a_b) (P (-> tptp.produc1963079155um_a_b Bool))) (= (@ (@ tptp.member1998628618um_a_b A) (@ tptp.collec1254333256um_a_b P)) (@ P A))) (forall ((A3 tptp.set_Sum_sum_a_b)) (= (@ tptp.collect_Sum_sum_a_b (lambda ((X3 tptp.sum_sum_a_b)) (@ (@ tptp.member_Sum_sum_a_b X3) A3))) A3)) (forall ((A3 tptp.set_Pr1174980151um_a_b)) (= (@ tptp.collec492052930um_a_b (lambda ((X3 tptp.produc1124793815um_a_b)) (@ (@ tptp.member1294585472um_a_b X3) A3))) A3)) (forall ((A3 tptp.set_Pr409224873um_a_b)) (= (@ tptp.collec1254333256um_a_b (lambda ((X3 tptp.produc1963079155um_a_b)) (@ (@ tptp.member1998628618um_a_b X3) A3))) A3)) (forall ((X2 tptp.produc1032616263at_nat) (A3 tptp.set_Pr1647387645at_nat) (B5 tptp.set_Pr1647387645at_nat)) (= (@ (@ tptp.ord_le1909159005at_nat (@ (@ tptp.insert1625259895at_nat X2) A3)) B5) (and (@ (@ tptp.member1696759390at_nat X2) B5) (@ (@ tptp.ord_le1909159005at_nat A3) B5)))) (forall ((X2 tptp.nat) (A3 tptp.set_nat) (B5 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat X2) A3)) B5) (and (@ (@ tptp.member_nat X2) B5) (@ (@ tptp.ord_less_eq_set_nat A3) B5)))) (forall ((X2 tptp.produc1548871597um_a_b) (A3 tptp.set_Pr1916610317um_a_b) (B5 tptp.set_Pr1916610317um_a_b)) (= (@ (@ tptp.ord_le1059794605um_a_b (@ (@ tptp.insert1435405693um_a_b X2) A3)) B5) (and (@ (@ tptp.member947389014um_a_b X2) B5) (@ (@ tptp.ord_le1059794605um_a_b A3) B5)))) (forall ((X2 tptp.standard_Constant_a) (A3 tptp.set_St761939237tant_a) (B5 tptp.set_St761939237tant_a)) (= (@ (@ tptp.ord_le1739761029tant_a (@ (@ tptp.insert1909710879tant_a X2) A3)) B5) (and (@ (@ tptp.member1632892294tant_a X2) B5) (@ (@ tptp.ord_le1739761029tant_a A3) B5)))) (forall ((X2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1986765409at_nat) (B5 tptp.set_Pr1986765409at_nat)) (= (@ (@ tptp.ord_le841296385at_nat (@ (@ tptp.insert271595217at_nat X2) A3)) B5) (and (@ (@ tptp.member701585322at_nat X2) B5) (@ (@ tptp.ord_le841296385at_nat A3) B5)))) (forall ((X2 tptp.produc1124793815um_a_b) (A3 tptp.set_Pr1174980151um_a_b) (B5 tptp.set_Pr1174980151um_a_b)) (= (@ (@ tptp.ord_le823954903um_a_b (@ (@ tptp.insert983991207um_a_b X2) A3)) B5) (and (@ (@ tptp.member1294585472um_a_b X2) B5) (@ (@ tptp.ord_le823954903um_a_b A3) B5)))) (forall ((X2 tptp.produc1963079155um_a_b) (A3 tptp.set_Pr409224873um_a_b) (B5 tptp.set_Pr409224873um_a_b)) (= (@ (@ tptp.ord_le615126793um_a_b (@ (@ tptp.insert323157027um_a_b X2) A3)) B5) (and (@ (@ tptp.member1998628618um_a_b X2) B5) (@ (@ tptp.ord_le615126793um_a_b A3) B5)))) (forall ((X2 tptp.sum_sum_a_b) (A3 tptp.set_Sum_sum_a_b) (B5 tptp.set_Sum_sum_a_b)) (= (@ (@ tptp.ord_le192794300um_a_b (@ (@ tptp.insert_Sum_sum_a_b X2) A3)) B5) (and (@ (@ tptp.member_Sum_sum_a_b X2) B5) (@ (@ tptp.ord_le192794300um_a_b A3) B5)))) (forall ((A tptp.standard_Constant_a)) (@ (@ tptp.member1632892294tant_a A) (@ (@ tptp.insert1909710879tant_a A) tptp.bot_bo1160111033tant_a))) (forall ((A tptp.product_prod_nat_nat)) (@ (@ tptp.member701585322at_nat A) (@ (@ tptp.insert271595217at_nat A) tptp.bot_bo2130386637at_nat))) (forall ((A tptp.produc1032616263at_nat)) (@ (@ tptp.member1696759390at_nat A) (@ (@ tptp.insert1625259895at_nat A) tptp.bot_bo810816657at_nat))) (forall ((A tptp.nat)) (@ (@ tptp.member_nat A) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (forall ((A tptp.produc1124793815um_a_b)) (@ (@ tptp.member1294585472um_a_b A) (@ (@ tptp.insert983991207um_a_b A) tptp.bot_bo575978147um_a_b))) (forall ((A tptp.produc1548871597um_a_b)) (@ (@ tptp.member947389014um_a_b A) (@ (@ tptp.insert1435405693um_a_b A) tptp.bot_bo225809273um_a_b))) (forall ((A tptp.produc1963079155um_a_b)) (@ (@ tptp.member1998628618um_a_b A) (@ (@ tptp.insert323157027um_a_b A) tptp.bot_bo1262634813um_a_b))) (forall ((A tptp.sum_sum_a_b)) (@ (@ tptp.member_Sum_sum_a_b A) (@ (@ tptp.insert_Sum_sum_a_b A) tptp.bot_bo1491243248um_a_b))) (forall ((A3 tptp.set_Pr1647387645at_nat)) (@ (@ tptp.ord_le1909159005at_nat tptp.bot_bo810816657at_nat) A3)) (forall ((A3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A3)) (forall ((A3 tptp.set_Pr1174980151um_a_b)) (@ (@ tptp.ord_le823954903um_a_b tptp.bot_bo575978147um_a_b) A3)) (forall ((A3 tptp.set_Pr1916610317um_a_b)) (@ (@ tptp.ord_le1059794605um_a_b tptp.bot_bo225809273um_a_b) A3)) (forall ((A3 tptp.set_Pr409224873um_a_b)) (@ (@ tptp.ord_le615126793um_a_b tptp.bot_bo1262634813um_a_b) A3)) (forall ((A3 tptp.set_Sum_sum_a_b)) (@ (@ tptp.ord_le192794300um_a_b tptp.bot_bo1491243248um_a_b) A3)) (forall ((A3 tptp.set_Pr1647387645at_nat)) (= (@ (@ tptp.ord_le1909159005at_nat A3) tptp.bot_bo810816657at_nat) (= A3 tptp.bot_bo810816657at_nat))) (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A3) tptp.bot_bot_set_nat) (= A3 tptp.bot_bot_set_nat))) (forall ((A3 tptp.set_Pr1174980151um_a_b)) (= (@ (@ tptp.ord_le823954903um_a_b A3) tptp.bot_bo575978147um_a_b) (= A3 tptp.bot_bo575978147um_a_b))) (forall ((A3 tptp.set_Pr1916610317um_a_b)) (= (@ (@ tptp.ord_le1059794605um_a_b A3) tptp.bot_bo225809273um_a_b) (= A3 tptp.bot_bo225809273um_a_b))) (forall ((A3 tptp.set_Pr409224873um_a_b)) (= (@ (@ tptp.ord_le615126793um_a_b A3) tptp.bot_bo1262634813um_a_b) (= A3 tptp.bot_bo1262634813um_a_b))) (forall ((A3 tptp.set_Sum_sum_a_b)) (= (@ (@ tptp.ord_le192794300um_a_b A3) tptp.bot_bo1491243248um_a_b) (= A3 tptp.bot_bo1491243248um_a_b))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) _let_21 _let_20 (forall ((C tptp.produc1032616263at_nat)) (not (@ (@ tptp.member1696759390at_nat C) tptp.bot_bo810816657at_nat))) (forall ((C tptp.nat)) (not (@ (@ tptp.member_nat C) tptp.bot_bot_set_nat))) (forall ((C tptp.produc1124793815um_a_b)) (not (@ (@ tptp.member1294585472um_a_b C) tptp.bot_bo575978147um_a_b))) (forall ((C tptp.produc1548871597um_a_b)) (not (@ (@ tptp.member947389014um_a_b C) tptp.bot_bo225809273um_a_b))) (forall ((C tptp.produc1963079155um_a_b)) (not (@ (@ tptp.member1998628618um_a_b C) tptp.bot_bo1262634813um_a_b))) (forall ((C tptp.sum_sum_a_b)) (not (@ (@ tptp.member_Sum_sum_a_b C) tptp.bot_bo1491243248um_a_b))) (forall ((A3 tptp.set_Pr1647387645at_nat)) (= (forall ((X3 tptp.produc1032616263at_nat)) (not (@ (@ tptp.member1696759390at_nat X3) A3))) (= A3 tptp.bot_bo810816657at_nat))) (forall ((A3 tptp.set_nat)) (= (forall ((X3 tptp.nat)) (not (@ (@ tptp.member_nat X3) A3))) (= A3 tptp.bot_bot_set_nat))) (forall ((A3 tptp.set_Pr1174980151um_a_b)) (= (forall ((X3 tptp.produc1124793815um_a_b)) (not (@ (@ tptp.member1294585472um_a_b X3) A3))) (= A3 tptp.bot_bo575978147um_a_b))) (forall ((A3 tptp.set_Pr1916610317um_a_b)) (= (forall ((X3 tptp.produc1548871597um_a_b)) (not (@ (@ tptp.member947389014um_a_b X3) A3))) (= A3 tptp.bot_bo225809273um_a_b))) (forall ((A3 tptp.set_Pr409224873um_a_b)) (= (forall ((X3 tptp.produc1963079155um_a_b)) (not (@ (@ tptp.member1998628618um_a_b X3) A3))) (= A3 tptp.bot_bo1262634813um_a_b))) (forall ((A3 tptp.set_Sum_sum_a_b)) (= (forall ((X3 tptp.sum_sum_a_b)) (not (@ (@ tptp.member_Sum_sum_a_b X3) A3))) (= A3 tptp.bot_bo1491243248um_a_b))) (forall ((P (-> tptp.produc1032616263at_nat Bool))) (= (= (@ tptp.collec52779676at_nat P) tptp.bot_bo810816657at_nat) (forall ((X3 tptp.produc1032616263at_nat)) (not (@ P X3))))) (forall ((P (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P) tptp.bot_bot_set_nat) (forall ((X3 tptp.nat)) (not (@ P X3))))) (forall ((P (-> tptp.produc1124793815um_a_b Bool))) (= (= (@ tptp.collec492052930um_a_b P) tptp.bot_bo575978147um_a_b) (forall ((X3 tptp.produc1124793815um_a_b)) (not (@ P X3))))) (forall ((P (-> tptp.produc1548871597um_a_b Bool))) (= (= (@ tptp.collec1769032088um_a_b P) tptp.bot_bo225809273um_a_b) (forall ((X3 tptp.produc1548871597um_a_b)) (not (@ P X3))))) (forall ((P (-> tptp.produc1963079155um_a_b Bool))) (= (= (@ tptp.collec1254333256um_a_b P) tptp.bot_bo1262634813um_a_b) (forall ((X3 tptp.produc1963079155um_a_b)) (not (@ P X3))))) (forall ((P (-> tptp.sum_sum_a_b Bool))) (= (= (@ tptp.collect_Sum_sum_a_b P) tptp.bot_bo1491243248um_a_b) (forall ((X3 tptp.sum_sum_a_b)) (not (@ P X3))))) (forall ((P (-> tptp.produc1032616263at_nat Bool))) (= (= tptp.bot_bo810816657at_nat (@ tptp.collec52779676at_nat P)) (forall ((X3 tptp.produc1032616263at_nat)) (not (@ P X3))))) (forall ((P (-> tptp.nat Bool))) (= (= tptp.bot_bot_set_nat (@ tptp.collect_nat P)) (forall ((X3 tptp.nat)) (not (@ P X3))))) (forall ((P (-> tptp.produc1124793815um_a_b Bool))) (= (= tptp.bot_bo575978147um_a_b (@ tptp.collec492052930um_a_b P)) (forall ((X3 tptp.produc1124793815um_a_b)) (not (@ P X3))))) (forall ((P (-> tptp.produc1548871597um_a_b Bool))) (= (= tptp.bot_bo225809273um_a_b (@ tptp.collec1769032088um_a_b P)) (forall ((X3 tptp.produc1548871597um_a_b)) (not (@ P X3))))) (forall ((P (-> tptp.produc1963079155um_a_b Bool))) (= (= tptp.bot_bo1262634813um_a_b (@ tptp.collec1254333256um_a_b P)) (forall ((X3 tptp.produc1963079155um_a_b)) (not (@ P X3))))) (forall ((P (-> tptp.sum_sum_a_b Bool))) (= (= tptp.bot_bo1491243248um_a_b (@ tptp.collect_Sum_sum_a_b P)) (forall ((X3 tptp.sum_sum_a_b)) (not (@ P X3))))) (forall ((A3 tptp.set_Pr1174980151um_a_b) (B5 tptp.set_Pr1174980151um_a_b)) (=> (forall ((X4 tptp.produc1124793815um_a_b)) (let ((_let_1 (@ tptp.member1294585472um_a_b X4))) (=> (@ _let_1 A3) (@ _let_1 B5)))) (@ (@ tptp.ord_le823954903um_a_b A3) B5))) (forall ((A3 tptp.set_Pr409224873um_a_b) (B5 tptp.set_Pr409224873um_a_b)) (=> (forall ((X4 tptp.produc1963079155um_a_b)) (let ((_let_1 (@ tptp.member1998628618um_a_b X4))) (=> (@ _let_1 A3) (@ _let_1 B5)))) (@ (@ tptp.ord_le615126793um_a_b A3) B5))) (forall ((A3 tptp.set_Sum_sum_a_b) (B5 tptp.set_Sum_sum_a_b)) (=> (forall ((X4 tptp.sum_sum_a_b)) (let ((_let_1 (@ tptp.member_Sum_sum_a_b X4))) (=> (@ _let_1 A3) (@ _let_1 B5)))) (@ (@ tptp.ord_le192794300um_a_b A3) B5))) (forall ((A3 tptp.set_Sum_sum_a_b) (B5 tptp.set_Sum_sum_a_b)) (=> (@ (@ tptp.ord_le192794300um_a_b A3) B5) (=> (@ (@ tptp.ord_le192794300um_a_b B5) A3) (= A3 B5)))) (forall ((A tptp.produc1032616263at_nat) (B5 tptp.set_Pr1647387645at_nat) (B tptp.produc1032616263at_nat)) (let ((_let_1 (@ tptp.member1696759390at_nat A))) (=> (=> (not (@ _let_1 B5)) (= A B)) (@ _let_1 (@ (@ tptp.insert1625259895at_nat B) B5))))) (forall ((A tptp.nat) (B5 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ tptp.member_nat A))) (=> (=> (not (@ _let_1 B5)) (= A B)) (@ _let_1 (@ (@ tptp.insert_nat B) B5))))) (forall ((A tptp.produc1548871597um_a_b) (B5 tptp.set_Pr1916610317um_a_b) (B tptp.produc1548871597um_a_b)) (let ((_let_1 (@ tptp.member947389014um_a_b A))) (=> (=> (not (@ _let_1 B5)) (= A B)) (@ _let_1 (@ (@ tptp.insert1435405693um_a_b B) B5))))) (forall ((A tptp.standard_Constant_a) (B5 tptp.set_St761939237tant_a) (B tptp.standard_Constant_a)) (let ((_let_1 (@ tptp.member1632892294tant_a A))) (=> (=> (not (@ _let_1 B5)) (= A B)) (@ _let_1 (@ (@ tptp.insert1909710879tant_a B) B5))))) (forall ((A tptp.product_prod_nat_nat) (B5 tptp.set_Pr1986765409at_nat) (B tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member701585322at_nat A))) (=> (=> (not (@ _let_1 B5)) (= A B)) (@ _let_1 (@ (@ tptp.insert271595217at_nat B) B5))))) (forall ((A tptp.sum_sum_a_b) (B5 tptp.set_Sum_sum_a_b) (B tptp.sum_sum_a_b)) (let ((_let_1 (@ tptp.member_Sum_sum_a_b A))) (=> (=> (not (@ _let_1 B5)) (= A B)) (@ _let_1 (@ (@ tptp.insert_Sum_sum_a_b B) B5))))) (forall ((A tptp.produc1124793815um_a_b) (B5 tptp.set_Pr1174980151um_a_b) (B tptp.produc1124793815um_a_b)) (let ((_let_1 (@ tptp.member1294585472um_a_b A))) (=> (=> (not (@ _let_1 B5)) (= A B)) (@ _let_1 (@ (@ tptp.insert983991207um_a_b B) B5))))) (forall ((A tptp.produc1963079155um_a_b) (B5 tptp.set_Pr409224873um_a_b) (B tptp.produc1963079155um_a_b)) (let ((_let_1 (@ tptp.member1998628618um_a_b A))) (=> (=> (not (@ _let_1 B5)) (= A B)) (@ _let_1 (@ (@ tptp.insert323157027um_a_b B) B5))))) (forall ((A tptp.produc1032616263at_nat) (B tptp.produc1032616263at_nat) (A3 tptp.set_Pr1647387645at_nat)) (let ((_let_1 (@ tptp.member1696759390at_nat A))) (= (@ _let_1 (@ (@ tptp.insert1625259895at_nat B) A3)) (or (= A B) (@ _let_1 A3))))) (forall ((A tptp.nat) (B tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A))) (= (@ _let_1 (@ (@ tptp.insert_nat B) A3)) (or (= A B) (@ _let_1 A3))))) (forall ((A tptp.produc1548871597um_a_b) (B tptp.produc1548871597um_a_b) (A3 tptp.set_Pr1916610317um_a_b)) (let ((_let_1 (@ tptp.member947389014um_a_b A))) (= (@ _let_1 (@ (@ tptp.insert1435405693um_a_b B) A3)) (or (= A B) (@ _let_1 A3))))) (forall ((A tptp.standard_Constant_a) (B tptp.standard_Constant_a) (A3 tptp.set_St761939237tant_a)) (let ((_let_1 (@ tptp.member1632892294tant_a A))) (= (@ _let_1 (@ (@ tptp.insert1909710879tant_a B) A3)) (or (= A B) (@ _let_1 A3))))) (forall ((A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat) (A3 tptp.set_Pr1986765409at_nat)) (let ((_let_1 (@ tptp.member701585322at_nat A))) (= (@ _let_1 (@ (@ tptp.insert271595217at_nat B) A3)) (or (= A B) (@ _let_1 A3))))) (forall ((A tptp.sum_sum_a_b) (B tptp.sum_sum_a_b) (A3 tptp.set_Sum_sum_a_b)) (let ((_let_1 (@ tptp.member_Sum_sum_a_b A))) (= (@ _let_1 (@ (@ tptp.insert_Sum_sum_a_b B) A3)) (or (= A B) (@ _let_1 A3))))) (forall ((A tptp.produc1124793815um_a_b) (B tptp.produc1124793815um_a_b) (A3 tptp.set_Pr1174980151um_a_b)) (let ((_let_1 (@ tptp.member1294585472um_a_b A))) (= (@ _let_1 (@ (@ tptp.insert983991207um_a_b B) A3)) (or (= A B) (@ _let_1 A3))))) (forall ((A tptp.produc1963079155um_a_b) (B tptp.produc1963079155um_a_b) (A3 tptp.set_Pr409224873um_a_b)) (let ((_let_1 (@ tptp.member1998628618um_a_b A))) (= (@ _let_1 (@ (@ tptp.insert323157027um_a_b B) A3)) (or (= A B) (@ _let_1 A3))))) (forall ((X2 tptp.produc1032616263at_nat) (A3 tptp.set_Pr1647387645at_nat)) (let ((_let_1 (@ tptp.insert1625259895at_nat X2))) (let ((_let_2 (@ _let_1 A3))) (= (@ _let_1 _let_2) _let_2)))) _let_17 (forall ((X2 tptp.produc1124793815um_a_b) (A3 tptp.set_Pr1174980151um_a_b)) (let ((_let_1 (@ tptp.insert983991207um_a_b X2))) (let ((_let_2 (@ _let_1 A3))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X2 tptp.produc1963079155um_a_b) (A3 tptp.set_Pr409224873um_a_b)) (let ((_let_1 (@ tptp.insert323157027um_a_b X2))) (let ((_let_2 (@ _let_1 A3))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X2 tptp.sum_sum_a_b) (A3 tptp.set_Sum_sum_a_b)) (let ((_let_1 (@ tptp.insert_Sum_sum_a_b X2))) (let ((_let_2 (@ _let_1 A3))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X2 tptp.produc1548871597um_a_b) (A3 tptp.set_Pr1916610317um_a_b)) (let ((_let_1 (@ tptp.insert1435405693um_a_b X2))) (let ((_let_2 (@ _let_1 A3))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X2 tptp.standard_Constant_a) (A3 tptp.set_St761939237tant_a)) (let ((_let_1 (@ tptp.insert1909710879tant_a X2))) (let ((_let_2 (@ _let_1 A3))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X2 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1986765409at_nat)) (let ((_let_1 (@ tptp.insert271595217at_nat X2))) (let ((_let_2 (@ _let_1 A3))) (= (@ _let_1 _let_2) _let_2)))) (forall ((G tptp.labele935650037_a_nat) (F tptp.set_Pr1986765409at_nat)) (= (@ (@ (@ tptp.graph_2130075512at_nat (@ (@ tptp.labele16114835_a_nat tptp.bot_bo810816657at_nat) tptp.bot_bot_set_nat)) G) F) (and (= F tptp.bot_bo2130386637at_nat) (= G (@ tptp.restri572569417_a_nat G))))) (forall ((G tptp.labele935650037_a_nat) (F tptp.set_Pr375490359_b_nat)) (= (@ (@ (@ tptp.graph_165730638_b_nat (@ (@ tptp.labele1729654377um_a_b tptp.bot_bo1262634813um_a_b) tptp.bot_bo1491243248um_a_b)) G) F) (and (= F tptp.bot_bo1923972003_b_nat) (= G (@ tptp.restri572569417_a_nat G))))) (forall ((G tptp.labele431970251um_a_b) (F tptp.set_Pr1174980151um_a_b)) (= (@ (@ (@ tptp.graph_1452133198um_a_b (@ (@ tptp.labele16114835_a_nat tptp.bot_bo810816657at_nat) tptp.bot_bot_set_nat)) G) F) (and (= F tptp.bot_bo575978147um_a_b) (= G (@ tptp.restri1162247455um_a_b G))))) (forall ((G tptp.labele935650037_a_nat) (F tptp.set_Pr1902304780_b_nat)) (= (@ (@ (@ tptp.graph_1203757137_b_nat (@ (@ tptp.labele2034032468um_a_b tptp.bot_bo1208513655um_a_b) tptp.bot_bo575978147um_a_b)) G) F) (and (= F tptp.bot_bo949957280_b_nat) (= G (@ tptp.restri572569417_a_nat G))))) (forall ((G tptp.labele431970251um_a_b) (F tptp.set_Pr1916610317um_a_b)) (= (@ (@ (@ tptp.graph_611893540um_a_b (@ (@ tptp.labele1729654377um_a_b tptp.bot_bo1262634813um_a_b) tptp.bot_bo1491243248um_a_b)) G) F) (and (= F tptp.bot_bo225809273um_a_b) (= G (@ tptp.restri1162247455um_a_b G))))) (forall ((G tptp.labele935650037_a_nat) (F tptp.set_Pr689416536at_nat)) (= (@ (@ (@ tptp.graph_149544303at_nat (@ (@ tptp.labele1813985418at_nat tptp.bot_bo1524397311at_nat) tptp.bot_bo810816657at_nat)) G) F) (and (= F tptp.bot_bo1582968772at_nat) (= G (@ tptp.restri572569417_a_nat G))))) (forall ((G tptp.labele431970251um_a_b) (F tptp.set_Pr653770722um_a_b)) (= (@ (@ (@ tptp.graph_502887975um_a_b (@ (@ tptp.labele2034032468um_a_b tptp.bot_bo1208513655um_a_b) tptp.bot_bo575978147um_a_b)) G) F) (and (= F tptp.bot_bo1892785270um_a_b) (= G (@ tptp.restri1162247455um_a_b G))))) (forall ((G tptp.labele935650037_a_nat) (F tptp.set_Pr507214050_b_nat)) (= (@ (@ (@ tptp.graph_1815313447_b_nat (@ (@ tptp.labele989994um_a_b tptp.bot_bo1262778871um_a_b) tptp.bot_bo225809273um_a_b)) G) F) (and (= F tptp.bot_bo1746228598_b_nat) (= G (@ tptp.restri572569417_a_nat G))))) (forall ((G tptp.labele431970251um_a_b) (F tptp.set_Pr304595758um_a_b)) (= (@ (@ (@ tptp.graph_166346565um_a_b (@ (@ tptp.labele1813985418at_nat tptp.bot_bo1524397311at_nat) tptp.bot_bo810816657at_nat)) G) F) (and (= F tptp.bot_bo627753370um_a_b) (= G (@ tptp.restri1162247455um_a_b G))))) (forall ((G tptp.labele431970251um_a_b) (F tptp.set_Pr55236280um_a_b)) (= (@ (@ (@ tptp.graph_1763806717um_a_b (@ (@ tptp.labele989994um_a_b tptp.bot_bo1262778871um_a_b) tptp.bot_bo225809273um_a_b)) G) F) (and (= F tptp.bot_bo1217542988um_a_b) (= G (@ tptp.restri1162247455um_a_b G))))) (forall ((R_1 tptp.set_Pr1174980151um_a_b) (R_2 tptp.set_Pr1174980151um_a_b) (E_1 tptp.set_Pr1647387645at_nat) (E_2 tptp.set_Pr1647387645at_nat) (G tptp.set_Pr409224873um_a_b)) (=> (@ (@ tptp.ord_le823954903um_a_b R_1) R_2) (=> (@ (@ tptp.ord_le1909159005at_nat E_1) E_2) (=> (@ (@ (@ tptp.edge_p1382426714tant_a R_2) E_2) G) (@ (@ (@ tptp.edge_p1382426714tant_a R_1) E_1) G))))) (forall ((R tptp.set_Pr1647387645at_nat) (S tptp.set_Pr1647387645at_nat)) (=> (forall ((X4 tptp.standard_Constant_a) (Y4 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member1696759390at_nat (@ (@ tptp.produc407553657at_nat X4) Y4)))) (=> (@ _let_1 R) (@ _let_1 S)))) (@ (@ tptp.ord_le1909159005at_nat R) S))) (forall ((R tptp.set_Pr1986765409at_nat) (S tptp.set_Pr1986765409at_nat)) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.member701585322at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y4)))) (=> (@ _let_1 R) (@ _let_1 S)))) (@ (@ tptp.ord_le841296385at_nat R) S))) (forall ((R tptp.set_Pr1174980151um_a_b) (S tptp.set_Pr1174980151um_a_b)) (=> (forall ((X4 tptp.nat) (Y4 tptp.sum_sum_a_b)) (let ((_let_1 (@ tptp.member1294585472um_a_b (@ (@ tptp.produc1808556047um_a_b X4) Y4)))) (=> (@ _let_1 R) (@ _let_1 S)))) (@ (@ tptp.ord_le823954903um_a_b R) S))) (forall ((R tptp.set_Pr409224873um_a_b) (S tptp.set_Pr409224873um_a_b)) (=> (forall ((X4 tptp.standard_Constant_a) (Y4 tptp.produc1548871597um_a_b)) (let ((_let_1 (@ tptp.member1998628618um_a_b (@ (@ tptp.produc1697725733um_a_b X4) Y4)))) (=> (@ _let_1 R) (@ _let_1 S)))) (@ (@ tptp.ord_le615126793um_a_b R) S))) (forall ((R tptp.set_Pr1916610317um_a_b) (S tptp.set_Pr1916610317um_a_b)) (=> (forall ((X4 tptp.sum_sum_a_b) (Y4 tptp.sum_sum_a_b)) (let ((_let_1 (@ tptp.member947389014um_a_b (@ (@ tptp.produc176426981um_a_b X4) Y4)))) (=> (@ _let_1 R) (@ _let_1 S)))) (@ (@ tptp.ord_le1059794605um_a_b R) S))) (forall ((G tptp.labele935650037_a_nat)) (let ((_let_1 (@ tptp.restri572569417_a_nat G))) (=> (@ (@ tptp.ord_le1909159005at_nat (@ tptp.labele195203296_a_nat G)) (@ tptp.labele195203296_a_nat _let_1)) (= G _let_1)))) (forall ((G tptp.labele431970251um_a_b)) (let ((_let_1 (@ tptp.restri1162247455um_a_b G))) (=> (@ (@ tptp.ord_le615126793um_a_b (@ tptp.labele1939049654um_a_b G)) (@ tptp.labele1939049654um_a_b _let_1)) (= G _let_1)))) (forall ((X2 tptp.nat)) (= (= tptp.zero_zero_nat X2) (= X2 tptp.zero_zero_nat))) (forall ((A tptp.produc1032616263at_nat)) (not (@ (@ tptp.member1696759390at_nat A) tptp.bot_bo810816657at_nat))) (forall ((A tptp.nat)) (not (@ (@ tptp.member_nat A) tptp.bot_bot_set_nat))) (forall ((A tptp.produc1124793815um_a_b)) (not (@ (@ tptp.member1294585472um_a_b A) tptp.bot_bo575978147um_a_b))) (forall ((A tptp.produc1548871597um_a_b)) (not (@ (@ tptp.member947389014um_a_b A) tptp.bot_bo225809273um_a_b))) (forall ((A tptp.produc1963079155um_a_b)) (not (@ (@ tptp.member1998628618um_a_b A) tptp.bot_bo1262634813um_a_b))) (forall ((A tptp.sum_sum_a_b)) (not (@ (@ tptp.member_Sum_sum_a_b A) tptp.bot_bo1491243248um_a_b))) (forall ((A3 tptp.set_Pr1647387645at_nat) (A tptp.produc1032616263at_nat)) (=> (= A3 tptp.bot_bo810816657at_nat) (not (@ (@ tptp.member1696759390at_nat A) A3)))) (forall ((A3 tptp.set_nat) (A tptp.nat)) (=> (= A3 tptp.bot_bot_set_nat) (not (@ (@ tptp.member_nat A) A3)))) (forall ((A3 tptp.set_Pr1174980151um_a_b) (A tptp.produc1124793815um_a_b)) (=> (= A3 tptp.bot_bo575978147um_a_b) (not (@ (@ tptp.member1294585472um_a_b A) A3)))) (forall ((A3 tptp.set_Pr1916610317um_a_b) (A tptp.produc1548871597um_a_b)) (=> (= A3 tptp.bot_bo225809273um_a_b) (not (@ (@ tptp.member947389014um_a_b A) A3)))) (forall ((A3 tptp.set_Pr409224873um_a_b) (A tptp.produc1963079155um_a_b)) (=> (= A3 tptp.bot_bo1262634813um_a_b) (not (@ (@ tptp.member1998628618um_a_b A) A3)))) (forall ((A3 tptp.set_Sum_sum_a_b) (A tptp.sum_sum_a_b)) (=> (= A3 tptp.bot_bo1491243248um_a_b) (not (@ (@ tptp.member_Sum_sum_a_b A) A3)))) (forall ((A3 tptp.set_Pr1647387645at_nat)) (=> (forall ((Y4 tptp.produc1032616263at_nat)) (not (@ (@ tptp.member1696759390at_nat Y4) A3))) (= A3 tptp.bot_bo810816657at_nat))) (forall ((A3 tptp.set_nat)) (=> (forall ((Y4 tptp.nat)) (not (@ (@ tptp.member_nat Y4) A3))) (= A3 tptp.bot_bot_set_nat))) (forall ((A3 tptp.set_Pr1174980151um_a_b)) (=> (forall ((Y4 tptp.produc1124793815um_a_b)) (not (@ (@ tptp.member1294585472um_a_b Y4) A3))) (= A3 tptp.bot_bo575978147um_a_b))) (forall ((A3 tptp.set_Pr1916610317um_a_b)) (=> (forall ((Y4 tptp.produc1548871597um_a_b)) (not (@ (@ tptp.member947389014um_a_b Y4) A3))) (= A3 tptp.bot_bo225809273um_a_b))) (forall ((A3 tptp.set_Pr409224873um_a_b)) (=> (forall ((Y4 tptp.produc1963079155um_a_b)) (not (@ (@ tptp.member1998628618um_a_b Y4) A3))) (= A3 tptp.bot_bo1262634813um_a_b))) (forall ((A3 tptp.set_Sum_sum_a_b)) (=> (forall ((Y4 tptp.sum_sum_a_b)) (not (@ (@ tptp.member_Sum_sum_a_b Y4) A3))) (= A3 tptp.bot_bo1491243248um_a_b))) (forall ((A3 tptp.set_Pr1647387645at_nat)) (= (exists ((X3 tptp.produc1032616263at_nat)) (@ (@ tptp.member1696759390at_nat X3) A3)) (not (= A3 tptp.bot_bo810816657at_nat)))) (forall ((A3 tptp.set_nat)) (= (exists ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) A3)) (not (= A3 tptp.bot_bot_set_nat)))) (forall ((A3 tptp.set_Pr1174980151um_a_b)) (= (exists ((X3 tptp.produc1124793815um_a_b)) (@ (@ tptp.member1294585472um_a_b X3) A3)) (not (= A3 tptp.bot_bo575978147um_a_b)))) (forall ((A3 tptp.set_Pr1916610317um_a_b)) (= (exists ((X3 tptp.produc1548871597um_a_b)) (@ (@ tptp.member947389014um_a_b X3) A3)) (not (= A3 tptp.bot_bo225809273um_a_b)))) (forall ((A3 tptp.set_Pr409224873um_a_b)) (= (exists ((X3 tptp.produc1963079155um_a_b)) (@ (@ tptp.member1998628618um_a_b X3) A3)) (not (= A3 tptp.bot_bo1262634813um_a_b)))) (forall ((A3 tptp.set_Sum_sum_a_b)) (= (exists ((X3 tptp.sum_sum_a_b)) (@ (@ tptp.member_Sum_sum_a_b X3) A3)) (not (= A3 tptp.bot_bo1491243248um_a_b)))) (forall ((A3 tptp.set_Pr1174980151um_a_b) (B5 tptp.set_Pr1174980151um_a_b) (X2 tptp.produc1124793815um_a_b)) (let ((_let_1 (@ tptp.member1294585472um_a_b X2))) (=> (@ (@ tptp.ord_le823954903um_a_b A3) B5) (=> (@ _let_1 A3) (@ _let_1 B5))))) (forall ((A3 tptp.set_Pr409224873um_a_b) (B5 tptp.set_Pr409224873um_a_b) (X2 tptp.produc1963079155um_a_b)) (let ((_let_1 (@ tptp.member1998628618um_a_b X2))) (=> (@ (@ tptp.ord_le615126793um_a_b A3) B5) (=> (@ _let_1 A3) (@ _let_1 B5))))) (forall ((A3 tptp.set_Sum_sum_a_b) (B5 tptp.set_Sum_sum_a_b) (X2 tptp.sum_sum_a_b)) (let ((_let_1 (@ tptp.member_Sum_sum_a_b X2))) (=> (@ (@ tptp.ord_le192794300um_a_b A3) B5) (=> (@ _let_1 A3) (@ _let_1 B5))))) (forall ((A3 tptp.set_Pr1174980151um_a_b) (B5 tptp.set_Pr1174980151um_a_b) (C tptp.produc1124793815um_a_b)) (let ((_let_1 (@ tptp.member1294585472um_a_b C))) (=> (@ (@ tptp.ord_le823954903um_a_b A3) B5) (=> (@ _let_1 A3) (@ _let_1 B5))))) (forall ((A3 tptp.set_Pr409224873um_a_b) (B5 tptp.set_Pr409224873um_a_b) (C tptp.produc1963079155um_a_b)) (let ((_let_1 (@ tptp.member1998628618um_a_b C))) (=> (@ (@ tptp.ord_le615126793um_a_b A3) B5) (=> (@ _let_1 A3) (@ _let_1 B5))))) (forall ((A3 tptp.set_Sum_sum_a_b) (B5 tptp.set_Sum_sum_a_b) (C tptp.sum_sum_a_b)) (let ((_let_1 (@ tptp.member_Sum_sum_a_b C))) (=> (@ (@ tptp.ord_le192794300um_a_b A3) B5) (=> (@ _let_1 A3) (@ _let_1 B5))))) (forall ((A3 tptp.set_Sum_sum_a_b) (B5 tptp.set_Sum_sum_a_b)) (=> (= A3 B5) (not (=> (@ (@ tptp.ord_le192794300um_a_b A3) B5) (not (@ (@ tptp.ord_le192794300um_a_b B5) A3)))))) _let_16 _let_15 _let_14 (forall ((A3 tptp.set_Sum_sum_a_b) (B5 tptp.set_Sum_sum_a_b)) (=> (= A3 B5) (@ (@ tptp.ord_le192794300um_a_b A3) B5))) (forall ((A3 tptp.set_Sum_sum_a_b) (B5 tptp.set_Sum_sum_a_b)) (=> (= A3 B5) (@ (@ tptp.ord_le192794300um_a_b B5) A3))) (= tptp.ord_le823954903um_a_b (lambda ((A7 tptp.set_Pr1174980151um_a_b) (B6 tptp.set_Pr1174980151um_a_b)) (forall ((T tptp.produc1124793815um_a_b)) (let ((_let_1 (@ tptp.member1294585472um_a_b T))) (=> (@ _let_1 A7) (@ _let_1 B6)))))) (= tptp.ord_le615126793um_a_b (lambda ((A7 tptp.set_Pr409224873um_a_b) (B6 tptp.set_Pr409224873um_a_b)) (forall ((T tptp.produc1963079155um_a_b)) (let ((_let_1 (@ tptp.member1998628618um_a_b T))) (=> (@ _let_1 A7) (@ _let_1 B6)))))) (= tptp.ord_le192794300um_a_b (lambda ((A7 tptp.set_Sum_sum_a_b) (B6 tptp.set_Sum_sum_a_b)) (forall ((T tptp.sum_sum_a_b)) (let ((_let_1 (@ tptp.member_Sum_sum_a_b T))) (=> (@ _let_1 A7) (@ _let_1 B6)))))) (forall ((A3 tptp.set_Sum_sum_a_b)) (@ (@ tptp.ord_le192794300um_a_b A3) A3)) (forall ((P (-> tptp.sum_sum_a_b Bool)) (Q (-> tptp.sum_sum_a_b Bool))) (=> (forall ((X4 tptp.sum_sum_a_b)) (=> (@ P X4) (@ Q X4))) (@ (@ tptp.ord_le192794300um_a_b (@ tptp.collect_Sum_sum_a_b P)) (@ tptp.collect_Sum_sum_a_b Q)))) (forall ((A3 tptp.set_Sum_sum_a_b) (B5 tptp.set_Sum_sum_a_b) (C2 tptp.set_Sum_sum_a_b)) (let ((_let_1 (@ tptp.ord_le192794300um_a_b A3))) (=> (@ _let_1 B5) (=> (@ (@ tptp.ord_le192794300um_a_b B5) C2) (@ _let_1 C2))))) (= (lambda ((Y5 tptp.set_Sum_sum_a_b) (Z tptp.set_Sum_sum_a_b)) (= Y5 Z)) (lambda ((A7 tptp.set_Sum_sum_a_b) (B6 tptp.set_Sum_sum_a_b)) (and (@ (@ tptp.ord_le192794300um_a_b A7) B6) (@ (@ tptp.ord_le192794300um_a_b B6) A7)))) (forall ((P (-> tptp.sum_sum_a_b Bool)) (Q (-> tptp.sum_sum_a_b Bool))) (= (@ (@ tptp.ord_le192794300um_a_b (@ tptp.collect_Sum_sum_a_b P)) (@ tptp.collect_Sum_sum_a_b Q)) (forall ((X3 tptp.sum_sum_a_b)) (=> (@ P X3) (@ Q X3))))) (forall ((A tptp.produc1032616263at_nat) (B tptp.produc1032616263at_nat) (A3 tptp.set_Pr1647387645at_nat)) (let ((_let_1 (@ tptp.member1696759390at_nat A))) (=> (@ _let_1 (@ (@ tptp.insert1625259895at_nat B) A3)) (=> (not (= A B)) (@ _let_1 A3))))) (forall ((A tptp.nat) (B tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A))) (=> (@ _let_1 (@ (@ tptp.insert_nat B) A3)) (=> (not (= A B)) (@ _let_1 A3))))) (forall ((A tptp.produc1548871597um_a_b) (B tptp.produc1548871597um_a_b) (A3 tptp.set_Pr1916610317um_a_b)) (let ((_let_1 (@ tptp.member947389014um_a_b A))) (=> (@ _let_1 (@ (@ tptp.insert1435405693um_a_b B) A3)) (=> (not (= A B)) (@ _let_1 A3))))) (forall ((A tptp.standard_Constant_a) (B tptp.standard_Constant_a) (A3 tptp.set_St761939237tant_a)) (let ((_let_1 (@ tptp.member1632892294tant_a A))) (=> (@ _let_1 (@ (@ tptp.insert1909710879tant_a B) A3)) (=> (not (= A B)) (@ _let_1 A3))))) (forall ((A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat) (A3 tptp.set_Pr1986765409at_nat)) (let ((_let_1 (@ tptp.member701585322at_nat A))) (=> (@ _let_1 (@ (@ tptp.insert271595217at_nat B) A3)) (=> (not (= A B)) (@ _let_1 A3))))) (forall ((A tptp.sum_sum_a_b) (B tptp.sum_sum_a_b) (A3 tptp.set_Sum_sum_a_b)) (let ((_let_1 (@ tptp.member_Sum_sum_a_b A))) (=> (@ _let_1 (@ (@ tptp.insert_Sum_sum_a_b B) A3)) (=> (not (= A B)) (@ _let_1 A3))))) (forall ((A tptp.produc1124793815um_a_b) (B tptp.produc1124793815um_a_b) (A3 tptp.set_Pr1174980151um_a_b)) (let ((_let_1 (@ tptp.member1294585472um_a_b A))) (=> (@ _let_1 (@ (@ tptp.insert983991207um_a_b B) A3)) (=> (not (= A B)) (@ _let_1 A3))))) (forall ((A tptp.produc1963079155um_a_b) (B tptp.produc1963079155um_a_b) (A3 tptp.set_Pr409224873um_a_b)) (let ((_let_1 (@ tptp.member1998628618um_a_b A))) (=> (@ _let_1 (@ (@ tptp.insert323157027um_a_b B) A3)) (=> (not (= A B)) (@ _let_1 A3))))) (forall ((A tptp.product_prod_nat_nat) (B5 tptp.set_Pr1986765409at_nat)) (@ (@ tptp.member701585322at_nat A) (@ (@ tptp.insert271595217at_nat A) B5))) (forall ((A tptp.sum_sum_a_b) (B5 tptp.set_Sum_sum_a_b)) (@ (@ tptp.member_Sum_sum_a_b A) (@ (@ tptp.insert_Sum_sum_a_b A) B5))) (forall ((A tptp.produc1124793815um_a_b) (B5 tptp.set_Pr1174980151um_a_b)) (@ (@ tptp.member1294585472um_a_b A) (@ (@ tptp.insert983991207um_a_b A) B5))) (forall ((A tptp.produc1963079155um_a_b) (B5 tptp.set_Pr409224873um_a_b)) (@ (@ tptp.member1998628618um_a_b A) (@ (@ tptp.insert323157027um_a_b A) B5))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)) (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) B))) (exists ((X4 tptp.nat)) (and (@ P X4) (forall ((Y6 tptp.nat)) (=> (@ P Y6) (@ (@ tptp.ord_less_eq_nat Y6) X4)))))))) (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)) _let_13 (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))) (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)) (= (@ (@ tptp.getRel1465196352um_a_b tptp.standard_S_Idt_a) tptp.g) (@ tptp.id_on_Sum_sum_a_b _let_8)) _let_12 (@ (@ tptp.mainta522127984um_a_b (@ tptp.standa997693288tant_a tptp.standard_S_Idt_a)) tptp.g) (@ (@ tptp.mainta522127984um_a_b (@ tptp.standa1795879409tant_a tptp.standard_S_Idt_a)) tptp.g) (@ (@ tptp.mainta522127984um_a_b (@ (@ tptp.standa1343274079tant_a tptp.standard_S_Idt_a) tptp.l)) tptp.g) _let_11 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.52/1.12 )
% 0.52/1.12 % SZS output end Proof for ITP179^1
% 0.52/1.12 % cvc5---1.0.5 exiting
% 0.52/1.12 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------