TSTP Solution File: ITP083^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP083^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n015.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 03:18:05 EDT 2023
% Result : Theorem 0.83s 1.04s
% Output : Proof 0.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.19 % Problem : ITP083^1 : TPTP v8.1.2. Released v7.5.0.
% 0.13/0.20 % Command : do_cvc5 %s %d
% 0.20/0.41 % Computer : n015.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 14:50:54 EDT 2023
% 0.20/0.41 % CPUTime :
% 0.26/0.60 %----Proving TH0
% 0.26/0.61 %------------------------------------------------------------------------------
% 0.26/0.61 % File : ITP083^1 : TPTP v8.1.2. Released v7.5.0.
% 0.26/0.61 % Domain : Interactive Theorem Proving
% 0.26/0.61 % Problem : Sledgehammer Irreducible problem prob_641__6629180_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 : Irreducible/prob_641__6629180_1 [Des21]
% 0.26/0.61
% 0.26/0.61 % Status : Theorem
% 0.26/0.61 % Rating : 0.23 v8.1.0, 0.18 v7.5.0
% 0.26/0.61 % Syntax : Number of formulae : 541 ( 183 unt; 187 typ; 0 def)
% 0.26/0.61 % Number of atoms : 948 ( 275 equ; 0 cnn)
% 0.26/0.61 % Maximal formula atoms : 7 ( 2 avg)
% 0.26/0.61 % Number of connectives : 3285 ( 114 ~; 12 |; 66 &;2729 @)
% 0.26/0.61 % ( 0 <=>; 364 =>; 0 <=; 0 <~>)
% 0.26/0.61 % Maximal formula depth : 22 ( 6 avg)
% 0.26/0.61 % Number of types : 53 ( 52 usr)
% 0.26/0.61 % Number of type conns : 511 ( 511 >; 0 *; 0 +; 0 <<)
% 0.26/0.61 % Number of symbols : 136 ( 135 usr; 10 con; 0-8 aty)
% 0.26/0.61 % Number of variables : 937 ( 98 ^; 800 !; 39 ?; 937 :)
% 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 15:43:41.217
% 0.26/0.61 %------------------------------------------------------------------------------
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% 0.26/0.61 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_Itf__val_Mtf__node_J,type,
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% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_Itf__val_Mtf__val_J,type,
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% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set_OCollect_001t__Set__Oset_Itf__val_J,type,
% 0.26/0.61 collect_set_val: ( set_val > $o ) > set_set_val ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set_OCollect_001tf__node,type,
% 0.26/0.61 collect_node: ( node > $o ) > set_node ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set_OCollect_001tf__val,type,
% 0.26/0.61 collect_val: ( val > $o ) > set_val ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J,type,
% 0.26/0.61 insert1846469495et_val: produc1324971431et_val > set_Pr1311924359et_val > set_Pr1311924359et_val ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_Itf__node_Mtf__val_J,type,
% 0.26/0.61 insert869443870de_val: produc1432036078de_val > set_Pr699757092de_val > set_Pr699757092de_val ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set_Oinsert_001t__Set__Oset_Itf__val_J,type,
% 0.26/0.61 insert_set_val: set_val > set_set_val > set_set_val ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set_Oinsert_001tf__node,type,
% 0.26/0.61 insert_node: node > set_node > set_node ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set_Oinsert_001tf__val,type,
% 0.26/0.61 insert_val: val > set_val > set_val ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Transitive__Closure_Oacyclic_001t__Set__Oset_Itf__val_J,type,
% 0.26/0.61 transi1953622797et_val: set_Pr1311924359et_val > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Transitive__Closure_Otranclp_001tf__val,type,
% 0.26/0.61 transi1991289355lp_val: ( val > val > $o ) > val > val > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J_Mt__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J_J,type,
% 0.26/0.61 member1254968080et_val: produc1904584935et_val > set_Pr1587248327et_val > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__node_Mtf__val_J_Mt__Product____Type__Oprod_Itf__node_Mtf__val_J_J,type,
% 0.26/0.61 member698732390de_val: produc452075965de_val > set_Pr819703837de_val > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J,type,
% 0.26/0.61 member1711426256et_val: produc1324971431et_val > set_Pr1311924359et_val > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mtf__node_J,type,
% 0.26/0.61 member76372137l_node: produc1013974930l_node > set_Pr574789832l_node > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mtf__val_J,type,
% 0.26/0.61 member1110026224al_val: produc782216903al_val > set_Pr1157324199al_val > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__node_Mtf__val_J_J,type,
% 0.26/0.61 member562853661de_val: produc1615737844de_val > set_Pr1245322836de_val > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_Itf__node_Mt__Set__Oset_Itf__val_J_J,type,
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% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_Itf__node_Mtf__node_J,type,
% 0.26/0.61 member2110109140e_node: produc951622955e_node > set_Pr9085835e_node > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_Itf__node_Mtf__val_J,type,
% 0.26/0.61 member313544709de_val: produc1432036078de_val > set_Pr699757092de_val > $o ).
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% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_Itf__val_Mt__Product____Type__Oprod_Itf__node_Mtf__val_J_J,type,
% 0.26/0.61 member1894062994de_val: produc1664334075de_val > set_Pr701036849de_val > $o ).
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% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Product____Type__Oprod_Itf__val_Mtf__val_J,type,
% 0.26/0.61 member1680438992al_val: product_prod_val_val > set_Pr700443783al_val > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Set__Oset_Itf__val_J,type,
% 0.26/0.61 member_set_val: set_val > set_set_val > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001tf__node,type,
% 0.26/0.61 member_node: node > set_node > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001tf__val,type,
% 0.26/0.61 member_val: val > set_val > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_v__092_060alpha_062n,type,
% 0.26/0.61 alpha_n: g > list_node ).
% 0.26/0.61
% 0.26/0.61 thf(sy_v__092_060phi_062,type,
% 0.26/0.61 phi: val ).
% 0.26/0.61
% 0.26/0.61 thf(sy_v__092_060phi_062_092_060_094sub_062s,type,
% 0.26/0.61 phi_s: val ).
% 0.26/0.61
% 0.26/0.61 thf(sy_v__092_060phi_062_H____,type,
% 0.26/0.61 phi2: val ).
% 0.26/0.61
% 0.26/0.61 thf(sy_v_defs,type,
% 0.26/0.61 defs: g > node > set_val ).
% 0.26/0.61
% 0.26/0.61 thf(sy_v_g,type,
% 0.26/0.61 g2: g ).
% 0.26/0.61
% 0.26/0.61 thf(sy_v_inEdges_H,type,
% 0.26/0.61 inEdges: g > node > list_P561207620_edgeD ).
% 0.26/0.61
% 0.26/0.61 thf(sy_v_phis,type,
% 0.26/0.61 phis: g > produc1432036078de_val > option_list_val ).
% 0.26/0.61
% 0.26/0.61 thf(sy_v_s,type,
% 0.26/0.61 s: val ).
% 0.26/0.61
% 0.26/0.61 thf(sy_v_uses,type,
% 0.26/0.61 uses: g > node > set_val ).
% 0.26/0.61
% 0.26/0.61 thf(sy_v_var,type,
% 0.26/0.61 var2: g > val > var ).
% 0.26/0.61
% 0.26/0.61 % Relevant facts (353)
% 0.26/0.61 thf(fact_0_assms_I4_J,axiom,
% 0.26/0.61 phi_s != s ).
% 0.26/0.61
% 0.26/0.61 % assms(4)
% 0.26/0.61 thf(fact_1_False,axiom,
% 0.26/0.61 phi != phi_s ).
% 0.26/0.61
% 0.26/0.61 % False
% 0.26/0.61 thf(fact_2__092_060open_062phiArg_Ag_A_092_060phi_062_H_A_092_060phi_062_092_060_094sub_062s_092_060close_062,axiom,
% 0.26/0.61 sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ phi2 @ phi_s ).
% 0.26/0.61
% 0.26/0.61 % \<open>phiArg g \<phi>' \<phi>\<^sub>s\<close>
% 0.26/0.61 thf(fact_3_assms_I3_J,axiom,
% 0.26/0.61 member_val @ s @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ) ).
% 0.26/0.61
% 0.26/0.61 % assms(3)
% 0.26/0.61 thf(fact_4_assms_I2_J,axiom,
% 0.26/0.61 member_val @ phi @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ) ).
% 0.26/0.61
% 0.26/0.61 % assms(2)
% 0.26/0.61 thf(fact_5__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062_092_060phi_062_H_O_AphiArg_Ag_A_092_060phi_062_H_A_092_060phi_062_092_060_094sub_062s_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.26/0.61 ~ ! [Phi: val] :
% 0.26/0.61 ~ ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ Phi @ phi_s ) ).
% 0.26/0.61
% 0.26/0.61 % \<open>\<And>thesis. (\<And>\<phi>'. phiArg g \<phi>' \<phi>\<^sub>s \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.26/0.61 thf(fact_6_phiArg__in__allVars,axiom,
% 0.26/0.61 ! [G: g,V: val,V2: val] :
% 0.26/0.61 ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ V @ V2 )
% 0.26/0.61 => ( member_val @ V2 @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % phiArg_in_allVars
% 0.26/0.61 thf(fact_7_uses__in__vars,axiom,
% 0.26/0.61 ! [V: val,G: g,N: node] :
% 0.26/0.61 ( ( member_val @ V @ ( uses @ G @ N ) )
% 0.26/0.61 => ( member_val @ V @ ( sSA_CF655860150de_val @ alpha_n @ uses @ G ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % uses_in_vars
% 0.26/0.61 thf(fact_8_trivial__in__allVars,axiom,
% 0.26/0.61 ! [G: g,V: val] :
% 0.26/0.61 ( ( sSA_CF1899243830eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G @ V )
% 0.26/0.61 => ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % trivial_in_allVars
% 0.26/0.61 thf(fact_9_liveVal__in__allVars,axiom,
% 0.26/0.61 ! [G: g,V: val] :
% 0.26/0.61 ( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ V )
% 0.26/0.61 => ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % liveVal_in_allVars
% 0.26/0.61 thf(fact_10_allVars__finite,axiom,
% 0.26/0.61 ! [G: g] : ( finite_finite_val @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) ) ).
% 0.26/0.61
% 0.26/0.61 % allVars_finite
% 0.26/0.61 thf(fact_11_uses__in__allUses,axiom,
% 0.26/0.61 ! [V: val,G: g,N: node] :
% 0.26/0.61 ( ( member_val @ V @ ( uses @ G @ N ) )
% 0.26/0.61 => ( member_val @ V @ ( sSA_CF178745443eD_val @ alpha_n @ inEdges @ uses @ phis @ G @ N ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % uses_in_allUses
% 0.26/0.61 thf(fact_12_redundant__def,axiom,
% 0.26/0.61 ! [G: g] :
% 0.26/0.61 ( ( sSA_CF1660885746eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G )
% 0.26/0.61 = ( ? [X: val] :
% 0.26/0.61 ( ( member_val @ X @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.26/0.61 & ( sSA_CF1899243830eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G @ X ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % redundant_def
% 0.26/0.61 thf(fact_13_trivial__def,axiom,
% 0.26/0.61 ! [G: g,V: val] :
% 0.26/0.61 ( ( sSA_CF1899243830eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G @ V )
% 0.26/0.61 = ( ? [X: val] :
% 0.26/0.61 ( ( member_val @ X @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.26/0.61 & ( sSA_CF1909049442de_val @ alpha_n @ defs @ phis @ G @ V @ X ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % trivial_def
% 0.26/0.61 thf(fact_14__092_060open_062_092_060not_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062s_A_092_060noteq_062_AdefNode_Ag_As_092_060close_062,axiom,
% 0.26/0.61 ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_s )
% 0.26/0.61 = ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ s ) ) ).
% 0.26/0.61
% 0.26/0.61 % \<open>\<not> defNode g \<phi>\<^sub>s \<noteq> defNode g s\<close>
% 0.26/0.61 thf(fact_15_defs__uses__disjoint_H,axiom,
% 0.26/0.61 ! [N: node,G: g,V: val] :
% 0.26/0.61 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.26/0.61 => ( ( member_val @ V @ ( defs @ G @ N ) )
% 0.26/0.61 => ~ ( member_val @ V @ ( uses @ G @ N ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % defs_uses_disjoint'
% 0.26/0.61 thf(fact_16_livePhi,axiom,
% 0.26/0.61 ! [G: g,V: val,V2: val] :
% 0.26/0.61 ( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ V )
% 0.26/0.61 => ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ V @ V2 )
% 0.26/0.61 => ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ V2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % livePhi
% 0.26/0.61 thf(fact_17_phiArg__distinct__nodes,axiom,
% 0.26/0.61 ! [G: g,P: val,Q: val] :
% 0.26/0.61 ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ P @ Q )
% 0.26/0.61 => ( ( P != Q )
% 0.26/0.61 => ( ( member_val @ P @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.26/0.61 => ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ P )
% 0.26/0.61 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ Q ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % phiArg_distinct_nodes
% 0.26/0.61 thf(fact_18_phiArgs__def__distinct,axiom,
% 0.26/0.61 ! [G: g,P: val,Q: val,R: val] :
% 0.26/0.61 ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ P @ Q )
% 0.26/0.61 => ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ P @ R )
% 0.26/0.61 => ( ( Q != R )
% 0.26/0.61 => ( ( member_val @ P @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.26/0.61 => ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ Q )
% 0.26/0.61 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ R ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % phiArgs_def_distinct
% 0.26/0.61 thf(fact_19_uses__in___092_060alpha_062n,axiom,
% 0.26/0.61 ! [V: val,G: g,N: node] :
% 0.26/0.61 ( ( member_val @ V @ ( uses @ G @ N ) )
% 0.26/0.61 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % uses_in_\<alpha>n
% 0.26/0.61 thf(fact_20_defs__finite,axiom,
% 0.26/0.61 ! [G: g,N: node] : ( finite_finite_val @ ( defs @ G @ N ) ) ).
% 0.26/0.61
% 0.26/0.61 % defs_finite
% 0.26/0.61 thf(fact_21_varsE,axiom,
% 0.26/0.61 ! [V: val,G: g] :
% 0.26/0.61 ( ( member_val @ V @ ( sSA_CF655860150de_val @ alpha_n @ uses @ G ) )
% 0.26/0.61 => ~ ! [N2: node] :
% 0.26/0.61 ( ( member_node @ N2 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.26/0.61 => ~ ( member_val @ V @ ( uses @ G @ N2 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % varsE
% 0.26/0.61 thf(fact_22_vars__finite,axiom,
% 0.26/0.61 ! [G: g] : ( finite_finite_val @ ( sSA_CF655860150de_val @ alpha_n @ uses @ G ) ) ).
% 0.26/0.61
% 0.26/0.61 % vars_finite
% 0.26/0.61 thf(fact_23_liveSimple,axiom,
% 0.26/0.61 ! [N: node,G: g,Val: val] :
% 0.26/0.61 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.26/0.61 => ( ( member_val @ Val @ ( uses @ G @ N ) )
% 0.26/0.61 => ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ Val ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % liveSimple
% 0.26/0.61 thf(fact_24_liveVal_Osimps,axiom,
% 0.26/0.61 ! [G: g,A: val] :
% 0.26/0.61 ( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ A )
% 0.26/0.61 = ( ? [N3: node,Val2: val] :
% 0.26/0.61 ( ( A = Val2 )
% 0.26/0.61 & ( member_node @ N3 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.26/0.61 & ( member_val @ Val2 @ ( uses @ G @ N3 ) ) )
% 0.26/0.61 | ? [V3: val,V4: val] :
% 0.26/0.61 ( ( A = V4 )
% 0.26/0.61 & ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ V3 )
% 0.26/0.61 & ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ V3 @ V4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % liveVal.simps
% 0.26/0.61 thf(fact_25_liveVal_Oinducts,axiom,
% 0.26/0.61 ! [G: g,X2: val,P2: val > $o] :
% 0.26/0.61 ( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ X2 )
% 0.26/0.61 => ( ! [N2: node,Val3: val] :
% 0.26/0.61 ( ( member_node @ N2 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.26/0.61 => ( ( member_val @ Val3 @ ( uses @ G @ N2 ) )
% 0.26/0.61 => ( P2 @ Val3 ) ) )
% 0.26/0.61 => ( ! [V5: val,V6: val] :
% 0.26/0.61 ( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ V5 )
% 0.26/0.61 => ( ( P2 @ V5 )
% 0.26/0.61 => ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ V5 @ V6 )
% 0.26/0.61 => ( P2 @ V6 ) ) ) )
% 0.26/0.61 => ( P2 @ X2 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % liveVal.inducts
% 0.26/0.61 thf(fact_26_liveVal_Ocases,axiom,
% 0.26/0.61 ! [G: g,A: val] :
% 0.26/0.61 ( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ A )
% 0.26/0.61 => ( ! [N2: node] :
% 0.26/0.61 ( ( member_node @ N2 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.26/0.61 => ~ ( member_val @ A @ ( uses @ G @ N2 ) ) )
% 0.26/0.61 => ~ ! [V5: val] :
% 0.26/0.61 ( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ V5 )
% 0.26/0.61 => ~ ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ V5 @ A ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % liveVal.cases
% 0.26/0.61 thf(fact_27_allUses__finite,axiom,
% 0.26/0.61 ! [N: node,G: g] :
% 0.26/0.61 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.26/0.61 => ( finite_finite_val @ ( sSA_CF178745443eD_val @ alpha_n @ inEdges @ uses @ phis @ G @ N ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % allUses_finite
% 0.26/0.61 thf(fact_28_defNode_I1_J,axiom,
% 0.26/0.61 ! [V: val,G: g] :
% 0.26/0.61 ( ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.26/0.61 => ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ V ) @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % defNode(1)
% 0.26/0.61 thf(fact_29_uses__finite,axiom,
% 0.26/0.61 ! [G: g,N: node] : ( finite_finite_val @ ( uses @ G @ N ) ) ).
% 0.26/0.61
% 0.26/0.61 % uses_finite
% 0.26/0.61 thf(fact_30_eq,axiom,
% 0.26/0.61 ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_s )
% 0.26/0.61 = ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ s ) ) ).
% 0.26/0.61
% 0.26/0.61 % eq
% 0.26/0.61 thf(fact_31_allUses__in__allVars,axiom,
% 0.26/0.61 ! [V: val,G: g,N: node] :
% 0.26/0.61 ( ( member_val @ V @ ( sSA_CF178745443eD_val @ alpha_n @ inEdges @ uses @ phis @ G @ N ) )
% 0.26/0.61 => ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.26/0.61 => ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % allUses_in_allVars
% 0.26/0.61 thf(fact_32_phiUses__in__allUses,axiom,
% 0.26/0.61 ! [V: val,G: g,N: node] :
% 0.26/0.61 ( ( member_val @ V @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ N ) )
% 0.26/0.61 => ( member_val @ V @ ( sSA_CF178745443eD_val @ alpha_n @ inEdges @ uses @ phis @ G @ N ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % phiUses_in_allUses
% 0.26/0.61 thf(fact_33_phiUses__finite,axiom,
% 0.26/0.61 ! [N: node,G: g] :
% 0.26/0.61 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.26/0.61 => ( finite_finite_val @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ N ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % phiUses_finite
% 0.26/0.61 thf(fact_34_defNode_I2_J,axiom,
% 0.26/0.61 ! [V: val,G: g] :
% 0.26/0.61 ( ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.26/0.61 => ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ V ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % defNode(2)
% 0.26/0.61 thf(fact_35_defNode__ex1,axiom,
% 0.26/0.61 ! [V: val,G: g] :
% 0.26/0.61 ( ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.26/0.61 => ? [X3: node] :
% 0.26/0.61 ( ( member_node @ X3 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.26/0.61 & ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ X3 ) )
% 0.26/0.61 & ! [Y: node] :
% 0.26/0.61 ( ( ( member_node @ Y @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.26/0.61 & ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ Y ) ) )
% 0.26/0.61 => ( Y = X3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % defNode_ex1
% 0.26/0.61 thf(fact_36_allVars__in__allDefs,axiom,
% 0.26/0.61 ! [V: val,G: g] :
% 0.26/0.61 ( ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.26/0.61 => ? [X3: node] :
% 0.26/0.61 ( ( member_node @ X3 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.26/0.61 & ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ X3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % allVars_in_allDefs
% 0.26/0.61 thf(fact_37_List_Ofinite__set,axiom,
% 0.26/0.61 ! [Xs: list_P844977291de_val] : ( finite781217938de_val @ ( set_Pr434939430de_val @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % List.finite_set
% 0.26/0.61 thf(fact_38_List_Ofinite__set,axiom,
% 0.26/0.61 ! [Xs: list_P761482893et_val] : ( finite1581417648et_val @ ( set_Pr2104310812et_val @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % List.finite_set
% 0.26/0.61 thf(fact_39_List_Ofinite__set,axiom,
% 0.26/0.61 ! [Xs: list_P1078858818l_node] : ( finite423892681l_node @ ( set_Pr1600883293l_node @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % List.finite_set
% 0.26/0.61 thf(fact_40_List_Ofinite__set,axiom,
% 0.26/0.61 ! [Xs: list_P1811375021al_val] : ( finite759259600al_val @ ( set_Pr102746428al_val @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % List.finite_set
% 0.26/0.61 thf(fact_41_List_Ofinite__set,axiom,
% 0.26/0.61 ! [Xs: list_set_val] : ( finite1265617511et_val @ ( set_set_val2 @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % List.finite_set
% 0.26/0.61 thf(fact_42_List_Ofinite__set,axiom,
% 0.26/0.61 ! [Xs: list_node] : ( finite_finite_node @ ( set_node2 @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % List.finite_set
% 0.26/0.61 thf(fact_43_List_Ofinite__set,axiom,
% 0.26/0.61 ! [Xs: list_val] : ( finite_finite_val @ ( set_val2 @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % List.finite_set
% 0.26/0.61 thf(fact_44_List_Ofinite__set,axiom,
% 0.26/0.61 ! [Xs: list_P2089461677et_val] : ( finite79836624et_val @ ( set_Pr284769596et_val @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % List.finite_set
% 0.26/0.61 thf(fact_45_List_Ofinite__set,axiom,
% 0.26/0.61 ! [Xs: list_P1820443774de_val] : ( finite2056463621de_val @ ( set_Pr1085970585de_val @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % List.finite_set
% 0.26/0.61 thf(fact_46_phiDefs__finite,axiom,
% 0.26/0.61 ! [G: g,N: node] : ( finite_finite_val @ ( sSA_CF370335846de_val @ phis @ G @ N ) ) ).
% 0.26/0.61
% 0.26/0.61 % phiDefs_finite
% 0.26/0.61 thf(fact_47_allDefs__finite,axiom,
% 0.26/0.61 ! [N: node,G: g] :
% 0.26/0.61 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.26/0.61 => ( finite_finite_val @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % allDefs_finite
% 0.26/0.61 thf(fact_48_assms_I5_J,axiom,
% 0.26/0.61 ( ( var2 @ g2 @ phi )
% 0.26/0.61 = ( var2 @ g2 @ s ) ) ).
% 0.26/0.61
% 0.26/0.61 % assms(5)
% 0.26/0.61 thf(fact_49_CFG__SSA__wf__base_Oredundant__def,axiom,
% 0.26/0.61 ( sSA_CF1660885746eD_val
% 0.26/0.61 = ( ^ [Alpha_n: g > list_node,InEdges: g > node > list_P561207620_edgeD,Defs: g > node > set_val,Uses: g > node > set_val,Phis: g > produc1432036078de_val > option_list_val,G2: g] :
% 0.26/0.61 ? [X: val] :
% 0.26/0.61 ( ( member_val @ X @ ( sSA_CF1517915011eD_val @ Alpha_n @ InEdges @ Defs @ Uses @ Phis @ G2 ) )
% 0.26/0.61 & ( sSA_CF1899243830eD_val @ Alpha_n @ InEdges @ Defs @ Uses @ Phis @ G2 @ X ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_wf_base.redundant_def
% 0.26/0.61 thf(fact_50_defs__in__allDefs,axiom,
% 0.26/0.61 ! [V: val,G: g,N: node] :
% 0.26/0.61 ( ( member_val @ V @ ( defs @ G @ N ) )
% 0.26/0.61 => ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % defs_in_allDefs
% 0.26/0.61 thf(fact_51_phiDefs__in__allDefs,axiom,
% 0.26/0.61 ! [V: val,G: g,N: node] :
% 0.26/0.61 ( ( member_val @ V @ ( sSA_CF370335846de_val @ phis @ G @ N ) )
% 0.26/0.61 => ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % phiDefs_in_allDefs
% 0.26/0.61 thf(fact_52_allDefs__disjoint_H,axiom,
% 0.26/0.61 ! [N: node,G: g,M: node,V: val] :
% 0.26/0.61 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.26/0.61 => ( ( member_node @ M @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.26/0.61 => ( ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) )
% 0.26/0.61 => ( ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ M ) )
% 0.26/0.61 => ( N = M ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % allDefs_disjoint'
% 0.26/0.61 thf(fact_53_mem__Collect__eq,axiom,
% 0.26/0.61 ! [A: produc1946948786l_node,P2: produc1946948786l_node > $o] :
% 0.26/0.61 ( ( member828457417l_node @ A @ ( collec885255687l_node @ P2 ) )
% 0.26/0.61 = ( P2 @ A ) ) ).
% 0.26/0.61
% 0.26/0.61 % mem_Collect_eq
% 0.26/0.61 thf(fact_54_mem__Collect__eq,axiom,
% 0.26/0.61 ! [A: product_prod_val_val,P2: product_prod_val_val > $o] :
% 0.26/0.61 ( ( member1680438992al_val @ A @ ( collec52550418al_val @ P2 ) )
% 0.26/0.61 = ( P2 @ A ) ) ).
% 0.26/0.61
% 0.26/0.61 % mem_Collect_eq
% 0.26/0.61 thf(fact_55_mem__Collect__eq,axiom,
% 0.26/0.61 ! [A: val,P2: val > $o] :
% 0.26/0.61 ( ( member_val @ A @ ( collect_val @ P2 ) )
% 0.26/0.61 = ( P2 @ A ) ) ).
% 0.26/0.61
% 0.26/0.61 % mem_Collect_eq
% 0.26/0.61 thf(fact_56_mem__Collect__eq,axiom,
% 0.26/0.61 ! [A: node,P2: node > $o] :
% 0.26/0.61 ( ( member_node @ A @ ( collect_node @ P2 ) )
% 0.26/0.61 = ( P2 @ A ) ) ).
% 0.26/0.61
% 0.26/0.61 % mem_Collect_eq
% 0.26/0.61 thf(fact_57_mem__Collect__eq,axiom,
% 0.26/0.61 ! [A: set_val,P2: set_val > $o] :
% 0.26/0.61 ( ( member_set_val @ A @ ( collect_set_val @ P2 ) )
% 0.26/0.61 = ( P2 @ A ) ) ).
% 0.26/0.61
% 0.26/0.61 % mem_Collect_eq
% 0.26/0.61 thf(fact_58_mem__Collect__eq,axiom,
% 0.26/0.61 ! [A: produc1432036078de_val,P2: produc1432036078de_val > $o] :
% 0.26/0.61 ( ( member313544709de_val @ A @ ( collec370342979de_val @ P2 ) )
% 0.26/0.61 = ( P2 @ A ) ) ).
% 0.26/0.61
% 0.26/0.61 % mem_Collect_eq
% 0.26/0.61 thf(fact_59_mem__Collect__eq,axiom,
% 0.26/0.61 ! [A: produc1324971431et_val,P2: produc1324971431et_val > $o] :
% 0.26/0.61 ( ( member1711426256et_val @ A @ ( collec1117167378et_val @ P2 ) )
% 0.26/0.61 = ( P2 @ A ) ) ).
% 0.26/0.61
% 0.26/0.61 % mem_Collect_eq
% 0.26/0.61 thf(fact_60_Collect__mem__eq,axiom,
% 0.26/0.61 ! [A2: set_val] :
% 0.26/0.61 ( ( collect_val
% 0.26/0.61 @ ^ [X: val] : ( member_val @ X @ A2 ) )
% 0.26/0.61 = A2 ) ).
% 0.26/0.61
% 0.26/0.61 % Collect_mem_eq
% 0.26/0.61 thf(fact_61_Collect__mem__eq,axiom,
% 0.26/0.61 ! [A2: set_node] :
% 0.26/0.61 ( ( collect_node
% 0.26/0.61 @ ^ [X: node] : ( member_node @ X @ A2 ) )
% 0.26/0.61 = A2 ) ).
% 0.26/0.61
% 0.26/0.61 % Collect_mem_eq
% 0.26/0.61 thf(fact_62_Collect__mem__eq,axiom,
% 0.26/0.61 ! [A2: set_set_val] :
% 0.26/0.61 ( ( collect_set_val
% 0.26/0.61 @ ^ [X: set_val] : ( member_set_val @ X @ A2 ) )
% 0.26/0.61 = A2 ) ).
% 0.26/0.61
% 0.26/0.61 % Collect_mem_eq
% 0.26/0.61 thf(fact_63_Collect__mem__eq,axiom,
% 0.26/0.61 ! [A2: set_Pr699757092de_val] :
% 0.26/0.61 ( ( collec370342979de_val
% 0.26/0.61 @ ^ [X: produc1432036078de_val] : ( member313544709de_val @ X @ A2 ) )
% 0.26/0.61 = A2 ) ).
% 0.26/0.61
% 0.26/0.61 % Collect_mem_eq
% 0.26/0.61 thf(fact_64_Collect__mem__eq,axiom,
% 0.26/0.61 ! [A2: set_Pr1311924359et_val] :
% 0.26/0.61 ( ( collec1117167378et_val
% 0.26/0.61 @ ^ [X: produc1324971431et_val] : ( member1711426256et_val @ X @ A2 ) )
% 0.26/0.61 = A2 ) ).
% 0.26/0.61
% 0.26/0.61 % Collect_mem_eq
% 0.26/0.61 thf(fact_65_phiArg__same__var,axiom,
% 0.26/0.61 ! [G: g,P: val,Q: val] :
% 0.26/0.61 ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ P @ Q )
% 0.26/0.61 => ( ( var2 @ G @ Q )
% 0.26/0.61 = ( var2 @ G @ P ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % phiArg_same_var
% 0.26/0.61 thf(fact_66_vars__eq,axiom,
% 0.26/0.61 ( ( var2 @ g2 @ phi )
% 0.26/0.61 = ( var2 @ g2 @ phi_s ) ) ).
% 0.26/0.61
% 0.26/0.61 % vars_eq
% 0.26/0.61 thf(fact_67_allDefs__var__disjoint,axiom,
% 0.26/0.61 ! [N: node,G: g,V: val,V2: val] :
% 0.26/0.61 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.26/0.61 => ( ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) )
% 0.26/0.61 => ( ( member_val @ V2 @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) )
% 0.26/0.61 => ( ( V != V2 )
% 0.26/0.61 => ( ( var2 @ G @ V2 )
% 0.26/0.61 != ( var2 @ G @ V ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % allDefs_var_disjoint
% 0.26/0.61 thf(fact_68_defNode__var__disjoint,axiom,
% 0.26/0.61 ! [P: val,G: g,Q: val] :
% 0.26/0.61 ( ( member_val @ P @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.26/0.61 => ( ( member_val @ Q @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.26/0.61 => ( ( P != Q )
% 0.26/0.61 => ( ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ P )
% 0.26/0.61 = ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ Q ) )
% 0.26/0.61 => ( ( var2 @ G @ P )
% 0.26/0.61 != ( var2 @ G @ Q ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % defNode_var_disjoint
% 0.26/0.61 thf(fact_69_defNode__eq,axiom,
% 0.26/0.61 ! [N: node,G: g,V: val] :
% 0.26/0.61 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.26/0.61 => ( ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) )
% 0.26/0.61 => ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ V )
% 0.26/0.61 = N ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % defNode_eq
% 0.26/0.61 thf(fact_70_allDefs__in__allVars,axiom,
% 0.26/0.61 ! [V: val,G: g,N: node] :
% 0.26/0.61 ( ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) )
% 0.26/0.61 => ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.26/0.61 => ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % allDefs_in_allVars
% 0.26/0.61 thf(fact_71_pruned__def,axiom,
% 0.26/0.61 ! [G: g] :
% 0.26/0.61 ( ( sSA_CF2074824714de_val @ alpha_n @ defs @ uses @ phis @ G )
% 0.26/0.61 = ( ! [X: node] :
% 0.26/0.61 ( ( member_node @ X @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.26/0.61 => ! [Val2: val] :
% 0.26/0.61 ( ( member_val @ Val2 @ ( sSA_CF370335846de_val @ phis @ G @ X ) )
% 0.26/0.61 => ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ Val2 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % pruned_def
% 0.26/0.61 thf(fact_72_CFG__SSA__base_OphiUses_Ocong,axiom,
% 0.26/0.61 sSA_CF848637139eD_val = sSA_CF848637139eD_val ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_base.phiUses.cong
% 0.26/0.61 thf(fact_73_CFG__SSA__base_OphiDefs_Ocong,axiom,
% 0.26/0.61 sSA_CF370335846de_val = sSA_CF370335846de_val ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_base.phiDefs.cong
% 0.26/0.61 thf(fact_74_CFG__SSA__base_OallDefs_Ocong,axiom,
% 0.26/0.61 sSA_CF139593942de_val = sSA_CF139593942de_val ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_base.allDefs.cong
% 0.26/0.61 thf(fact_75_CFG__SSA__wf__base_OdefNode_Ocong,axiom,
% 0.26/0.61 sSA_CF551432799de_val = sSA_CF551432799de_val ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_wf_base.defNode.cong
% 0.26/0.61 thf(fact_76_CFG__SSA__base_OallVars_Ocong,axiom,
% 0.26/0.61 sSA_CF1517915011eD_val = sSA_CF1517915011eD_val ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_base.allVars.cong
% 0.26/0.61 thf(fact_77_CFG__SSA__wf__base_OphiArg_Ocong,axiom,
% 0.26/0.61 sSA_CF1252180629de_val = sSA_CF1252180629de_val ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_wf_base.phiArg.cong
% 0.26/0.61 thf(fact_78_CFG__SSA__base_OallUses_Ocong,axiom,
% 0.26/0.61 sSA_CF178745443eD_val = sSA_CF178745443eD_val ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_base.allUses.cong
% 0.26/0.61 thf(fact_79_CFG__SSA__wf__base_OliveVal_Ocong,axiom,
% 0.26/0.61 sSA_CF794421325de_val = sSA_CF794421325de_val ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_wf_base.liveVal.cong
% 0.26/0.61 thf(fact_80_CFG__SSA__wf__base_Otrivial_Ocong,axiom,
% 0.26/0.61 sSA_CF1899243830eD_val = sSA_CF1899243830eD_val ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_wf_base.trivial.cong
% 0.26/0.61 thf(fact_81_CFG__base_Ovars_Ocong,axiom,
% 0.26/0.61 sSA_CF655860150de_val = sSA_CF655860150de_val ).
% 0.26/0.61
% 0.26/0.61 % CFG_base.vars.cong
% 0.26/0.61 thf(fact_82_CFG__SSA__wf__base_OisTrivialPhi_Ocong,axiom,
% 0.26/0.61 sSA_CF1909049442de_val = sSA_CF1909049442de_val ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_wf_base.isTrivialPhi.cong
% 0.26/0.61 thf(fact_83_CFG__SSA__wf__base_Oredundant_Ocong,axiom,
% 0.26/0.61 sSA_CF1660885746eD_val = sSA_CF1660885746eD_val ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_wf_base.redundant.cong
% 0.26/0.61 thf(fact_84_finite__list,axiom,
% 0.26/0.61 ! [A2: set_node] :
% 0.26/0.61 ( ( finite_finite_node @ A2 )
% 0.26/0.61 => ? [Xs2: list_node] :
% 0.26/0.61 ( ( set_node2 @ Xs2 )
% 0.26/0.61 = A2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % finite_list
% 0.26/0.61 thf(fact_85_finite__list,axiom,
% 0.26/0.61 ! [A2: set_val] :
% 0.26/0.61 ( ( finite_finite_val @ A2 )
% 0.26/0.61 => ? [Xs2: list_val] :
% 0.26/0.61 ( ( set_val2 @ Xs2 )
% 0.26/0.61 = A2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % finite_list
% 0.26/0.61 thf(fact_86_finite__list,axiom,
% 0.26/0.61 ! [A2: set_Pr1311924359et_val] :
% 0.26/0.61 ( ( finite79836624et_val @ A2 )
% 0.26/0.61 => ? [Xs2: list_P2089461677et_val] :
% 0.26/0.61 ( ( set_Pr284769596et_val @ Xs2 )
% 0.26/0.61 = A2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % finite_list
% 0.26/0.61 thf(fact_87_finite__list,axiom,
% 0.26/0.61 ! [A2: set_Pr699757092de_val] :
% 0.26/0.61 ( ( finite2056463621de_val @ A2 )
% 0.26/0.61 => ? [Xs2: list_P1820443774de_val] :
% 0.26/0.61 ( ( set_Pr1085970585de_val @ Xs2 )
% 0.26/0.61 = A2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % finite_list
% 0.26/0.61 thf(fact_88_CFG__SSA__wf__base_OliveSimple,axiom,
% 0.26/0.61 ! [N: node,Alpha_n2: g > list_node,G: g,Val: val,Uses2: g > node > set_val,Defs2: g > node > set_val,Phis2: g > produc1432036078de_val > option_list_val] :
% 0.26/0.61 ( ( member_node @ N @ ( set_node2 @ ( Alpha_n2 @ G ) ) )
% 0.26/0.61 => ( ( member_val @ Val @ ( Uses2 @ G @ N ) )
% 0.26/0.61 => ( sSA_CF794421325de_val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G @ Val ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_wf_base.liveSimple
% 0.26/0.61 thf(fact_89_CFG__SSA__wf__base_OlivePhi,axiom,
% 0.26/0.61 ! [Alpha_n2: g > list_node,Defs2: g > node > set_val,Uses2: g > node > set_val,Phis2: g > produc1432036078de_val > option_list_val,G: g,V: val,V2: val] :
% 0.26/0.61 ( ( sSA_CF794421325de_val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G @ V )
% 0.26/0.61 => ( ( sSA_CF1252180629de_val @ Alpha_n2 @ Defs2 @ Phis2 @ G @ V @ V2 )
% 0.26/0.61 => ( sSA_CF794421325de_val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G @ V2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_wf_base.livePhi
% 0.26/0.61 thf(fact_90_CFG__SSA__wf__base_OliveVal_Oinducts,axiom,
% 0.26/0.61 ! [Alpha_n2: g > list_node,Defs2: g > node > set_val,Uses2: g > node > set_val,Phis2: g > produc1432036078de_val > option_list_val,G: g,X2: val,P2: val > $o] :
% 0.26/0.61 ( ( sSA_CF794421325de_val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G @ X2 )
% 0.26/0.61 => ( ! [N2: node,Val3: val] :
% 0.26/0.61 ( ( member_node @ N2 @ ( set_node2 @ ( Alpha_n2 @ G ) ) )
% 0.26/0.61 => ( ( member_val @ Val3 @ ( Uses2 @ G @ N2 ) )
% 0.26/0.61 => ( P2 @ Val3 ) ) )
% 0.26/0.61 => ( ! [V5: val,V6: val] :
% 0.26/0.61 ( ( sSA_CF794421325de_val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G @ V5 )
% 0.26/0.61 => ( ( P2 @ V5 )
% 0.26/0.61 => ( ( sSA_CF1252180629de_val @ Alpha_n2 @ Defs2 @ Phis2 @ G @ V5 @ V6 )
% 0.26/0.61 => ( P2 @ V6 ) ) ) )
% 0.26/0.61 => ( P2 @ X2 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_wf_base.liveVal.inducts
% 0.26/0.61 thf(fact_91_CFG__SSA__wf__base_OliveVal_Osimps,axiom,
% 0.26/0.61 ( sSA_CF794421325de_val
% 0.26/0.61 = ( ^ [Alpha_n: g > list_node,Defs: g > node > set_val,Uses: g > node > set_val,Phis: g > produc1432036078de_val > option_list_val,G2: g,A3: val] :
% 0.26/0.61 ( ? [N3: node,Val2: val] :
% 0.26/0.61 ( ( A3 = Val2 )
% 0.26/0.61 & ( member_node @ N3 @ ( set_node2 @ ( Alpha_n @ G2 ) ) )
% 0.26/0.61 & ( member_val @ Val2 @ ( Uses @ G2 @ N3 ) ) )
% 0.26/0.61 | ? [V3: val,V4: val] :
% 0.26/0.61 ( ( A3 = V4 )
% 0.26/0.61 & ( sSA_CF794421325de_val @ Alpha_n @ Defs @ Uses @ Phis @ G2 @ V3 )
% 0.26/0.61 & ( sSA_CF1252180629de_val @ Alpha_n @ Defs @ Phis @ G2 @ V3 @ V4 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_wf_base.liveVal.simps
% 0.26/0.61 thf(fact_92_CFG__SSA__wf__base_OliveVal_Ocases,axiom,
% 0.26/0.61 ! [Alpha_n2: g > list_node,Defs2: g > node > set_val,Uses2: g > node > set_val,Phis2: g > produc1432036078de_val > option_list_val,G: g,A: val] :
% 0.26/0.61 ( ( sSA_CF794421325de_val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G @ A )
% 0.26/0.61 => ( ! [N2: node] :
% 0.26/0.61 ( ( member_node @ N2 @ ( set_node2 @ ( Alpha_n2 @ G ) ) )
% 0.26/0.61 => ~ ( member_val @ A @ ( Uses2 @ G @ N2 ) ) )
% 0.26/0.61 => ~ ! [V5: val] :
% 0.26/0.61 ( ( sSA_CF794421325de_val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G @ V5 )
% 0.26/0.61 => ~ ( sSA_CF1252180629de_val @ Alpha_n2 @ Defs2 @ Phis2 @ G @ V5 @ A ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_wf_base.liveVal.cases
% 0.26/0.61 thf(fact_93_CFG__SSA__wf__base_Otrivial__def,axiom,
% 0.26/0.61 ( sSA_CF1899243830eD_val
% 0.26/0.61 = ( ^ [Alpha_n: g > list_node,InEdges: g > node > list_P561207620_edgeD,Defs: g > node > set_val,Uses: g > node > set_val,Phis: g > produc1432036078de_val > option_list_val,G2: g,V3: val] :
% 0.26/0.61 ? [X: val] :
% 0.26/0.61 ( ( member_val @ X @ ( sSA_CF1517915011eD_val @ Alpha_n @ InEdges @ Defs @ Uses @ Phis @ G2 ) )
% 0.26/0.61 & ( sSA_CF1909049442de_val @ Alpha_n @ Defs @ Phis @ G2 @ V3 @ X ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_wf_base.trivial_def
% 0.26/0.61 thf(fact_94_condensation__finite,axiom,
% 0.26/0.61 ! [G: g,P2: set_val] : ( finite79836624et_val @ ( irredu893086079de_val @ alpha_n @ defs @ phis @ G @ P2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % condensation_finite
% 0.26/0.61 thf(fact_95_phiUses__exI_H,axiom,
% 0.26/0.61 ! [G: g,P: val,Q: val] :
% 0.26/0.61 ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ P @ Q )
% 0.26/0.61 => ( ( member_val @ P @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.26/0.61 => ~ ! [M2: node] :
% 0.26/0.61 ( ( member_val @ Q @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ M2 ) )
% 0.26/0.61 => ~ ( member_node @ M2 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ P ) ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % phiUses_exI'
% 0.26/0.61 thf(fact_96_allUses__def,axiom,
% 0.26/0.61 ! [G: g,N: node] :
% 0.26/0.61 ( ( sSA_CF178745443eD_val @ alpha_n @ inEdges @ uses @ phis @ G @ N )
% 0.26/0.61 = ( sup_sup_set_val @ ( uses @ G @ N ) @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ N ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % allUses_def
% 0.26/0.61 thf(fact_97_phiArg__trancl__same__var,axiom,
% 0.26/0.61 ! [G: g,Phi2: val,N: val] :
% 0.26/0.61 ( ( transi1991289355lp_val @ ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G ) @ Phi2 @ N )
% 0.26/0.61 => ( ( var2 @ G @ Phi2 )
% 0.26/0.61 = ( var2 @ G @ N ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % phiArg_trancl_same_var
% 0.26/0.61 thf(fact_98_allDefs__def,axiom,
% 0.26/0.61 ! [G: g,N: node] :
% 0.26/0.61 ( ( sSA_CF139593942de_val @ defs @ phis @ G @ N )
% 0.26/0.61 = ( sup_sup_set_val @ ( defs @ G @ N ) @ ( sSA_CF370335846de_val @ phis @ G @ N ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % allDefs_def
% 0.26/0.61 thf(fact_99_CFG__SSA__wf__base_Opruned__def,axiom,
% 0.26/0.61 ( sSA_CF2074824714de_val
% 0.26/0.61 = ( ^ [Alpha_n: g > list_node,Defs: g > node > set_val,Uses: g > node > set_val,Phis: g > produc1432036078de_val > option_list_val,G2: g] :
% 0.26/0.61 ! [X: node] :
% 0.26/0.61 ( ( member_node @ X @ ( set_node2 @ ( Alpha_n @ G2 ) ) )
% 0.26/0.61 => ! [Val2: val] :
% 0.26/0.61 ( ( member_val @ Val2 @ ( sSA_CF370335846de_val @ Phis @ G2 @ X ) )
% 0.26/0.61 => ( sSA_CF794421325de_val @ Alpha_n @ Defs @ Uses @ Phis @ G2 @ Val2 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_wf_base.pruned_def
% 0.26/0.61 thf(fact_100_defNode__cases,axiom,
% 0.26/0.61 ! [V: val,G: g] :
% 0.26/0.61 ( ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.26/0.61 => ( ~ ( member_val @ V @ ( defs @ G @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ V ) ) )
% 0.26/0.61 => ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ V )
% 0.26/0.61 != none_list_val ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % defNode_cases
% 0.26/0.61 thf(fact_101_simpleDef__not__phi,axiom,
% 0.26/0.61 ! [N: node,G: g,V: val] :
% 0.26/0.61 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.26/0.61 => ( ( member_val @ V @ ( defs @ G @ N ) )
% 0.26/0.61 => ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ V )
% 0.26/0.61 = none_list_val ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % simpleDef_not_phi
% 0.26/0.61 thf(fact_102_finite__Un,axiom,
% 0.26/0.61 ! [F: set_Pr1311924359et_val,G3: set_Pr1311924359et_val] :
% 0.26/0.61 ( ( finite79836624et_val @ ( sup_su2005730907et_val @ F @ G3 ) )
% 0.26/0.61 = ( ( finite79836624et_val @ F )
% 0.26/0.61 & ( finite79836624et_val @ G3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % finite_Un
% 0.26/0.61 thf(fact_103_finite__Un,axiom,
% 0.26/0.61 ! [F: set_Pr699757092de_val,G3: set_Pr699757092de_val] :
% 0.26/0.61 ( ( finite2056463621de_val @ ( sup_su2138939728de_val @ F @ G3 ) )
% 0.26/0.61 = ( ( finite2056463621de_val @ F )
% 0.26/0.61 & ( finite2056463621de_val @ G3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % finite_Un
% 0.26/0.61 thf(fact_104_finite__Un,axiom,
% 0.26/0.61 ! [F: set_val,G3: set_val] :
% 0.26/0.61 ( ( finite_finite_val @ ( sup_sup_set_val @ F @ G3 ) )
% 0.26/0.61 = ( ( finite_finite_val @ F )
% 0.26/0.61 & ( finite_finite_val @ G3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % finite_Un
% 0.26/0.61 thf(fact_105_trivial__phi,axiom,
% 0.26/0.61 ! [G: g,V: val] :
% 0.26/0.61 ( ( sSA_CF1899243830eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G @ V )
% 0.26/0.61 => ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ V )
% 0.26/0.61 != none_list_val ) ) ).
% 0.26/0.61
% 0.26/0.61 % trivial_phi
% 0.26/0.61 thf(fact_106_phiArg__exI,axiom,
% 0.26/0.61 ! [M: node,G: g,V: val] :
% 0.26/0.61 ( ( member_node @ M @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ V ) ) ) )
% 0.26/0.61 => ( ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ V )
% 0.26/0.61 != none_list_val )
% 0.26/0.61 => ( ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.26/0.61 => ~ ! [V6: val] :
% 0.26/0.61 ( ( member_val @ V6 @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ M ) )
% 0.26/0.61 => ~ ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ V @ V6 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % phiArg_exI
% 0.26/0.61 thf(fact_107_CFG__SSA__wf__base_Ophi_Ocong,axiom,
% 0.26/0.61 sSA_CF262257161de_val = sSA_CF262257161de_val ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_wf_base.phi.cong
% 0.26/0.61 thf(fact_108_infinite__Un,axiom,
% 0.26/0.61 ! [S: set_Pr1311924359et_val,T: set_Pr1311924359et_val] :
% 0.26/0.61 ( ( ~ ( finite79836624et_val @ ( sup_su2005730907et_val @ S @ T ) ) )
% 0.26/0.61 = ( ~ ( finite79836624et_val @ S )
% 0.26/0.61 | ~ ( finite79836624et_val @ T ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % infinite_Un
% 0.26/0.61 thf(fact_109_infinite__Un,axiom,
% 0.26/0.61 ! [S: set_Pr699757092de_val,T: set_Pr699757092de_val] :
% 0.26/0.61 ( ( ~ ( finite2056463621de_val @ ( sup_su2138939728de_val @ S @ T ) ) )
% 0.26/0.61 = ( ~ ( finite2056463621de_val @ S )
% 0.26/0.61 | ~ ( finite2056463621de_val @ T ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % infinite_Un
% 0.26/0.61 thf(fact_110_infinite__Un,axiom,
% 0.26/0.61 ! [S: set_val,T: set_val] :
% 0.26/0.61 ( ( ~ ( finite_finite_val @ ( sup_sup_set_val @ S @ T ) ) )
% 0.26/0.61 = ( ~ ( finite_finite_val @ S )
% 0.26/0.61 | ~ ( finite_finite_val @ T ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % infinite_Un
% 0.26/0.61 thf(fact_111_Un__infinite,axiom,
% 0.26/0.61 ! [S: set_Pr1311924359et_val,T: set_Pr1311924359et_val] :
% 0.26/0.61 ( ~ ( finite79836624et_val @ S )
% 0.26/0.61 => ~ ( finite79836624et_val @ ( sup_su2005730907et_val @ S @ T ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Un_infinite
% 0.26/0.61 thf(fact_112_Un__infinite,axiom,
% 0.26/0.61 ! [S: set_Pr699757092de_val,T: set_Pr699757092de_val] :
% 0.26/0.61 ( ~ ( finite2056463621de_val @ S )
% 0.26/0.61 => ~ ( finite2056463621de_val @ ( sup_su2138939728de_val @ S @ T ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Un_infinite
% 0.26/0.61 thf(fact_113_Un__infinite,axiom,
% 0.26/0.61 ! [S: set_val,T: set_val] :
% 0.26/0.61 ( ~ ( finite_finite_val @ S )
% 0.26/0.61 => ~ ( finite_finite_val @ ( sup_sup_set_val @ S @ T ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Un_infinite
% 0.26/0.61 thf(fact_114_finite__UnI,axiom,
% 0.26/0.61 ! [F: set_Pr1311924359et_val,G3: set_Pr1311924359et_val] :
% 0.26/0.61 ( ( finite79836624et_val @ F )
% 0.26/0.61 => ( ( finite79836624et_val @ G3 )
% 0.26/0.61 => ( finite79836624et_val @ ( sup_su2005730907et_val @ F @ G3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % finite_UnI
% 0.26/0.61 thf(fact_115_finite__UnI,axiom,
% 0.26/0.61 ! [F: set_Pr699757092de_val,G3: set_Pr699757092de_val] :
% 0.26/0.61 ( ( finite2056463621de_val @ F )
% 0.26/0.61 => ( ( finite2056463621de_val @ G3 )
% 0.26/0.61 => ( finite2056463621de_val @ ( sup_su2138939728de_val @ F @ G3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % finite_UnI
% 0.26/0.61 thf(fact_116_finite__UnI,axiom,
% 0.26/0.61 ! [F: set_val,G3: set_val] :
% 0.26/0.61 ( ( finite_finite_val @ F )
% 0.26/0.61 => ( ( finite_finite_val @ G3 )
% 0.26/0.61 => ( finite_finite_val @ ( sup_sup_set_val @ F @ G3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % finite_UnI
% 0.26/0.61 thf(fact_117_CFG__SSA__Transformed_Ocondensation__edges_Ocong,axiom,
% 0.26/0.61 irredu893086079de_val = irredu893086079de_val ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_Transformed.condensation_edges.cong
% 0.26/0.61 thf(fact_118_CFG__SSA__wf__base_Opruned_Ocong,axiom,
% 0.26/0.61 sSA_CF2074824714de_val = sSA_CF2074824714de_val ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_wf_base.pruned.cong
% 0.26/0.61 thf(fact_119_CFG__SSA__base_OallDefs__def,axiom,
% 0.26/0.61 ( sSA_CF139593942de_val
% 0.26/0.61 = ( ^ [Defs: g > node > set_val,Phis: g > produc1432036078de_val > option_list_val,G2: g,N3: node] : ( sup_sup_set_val @ ( Defs @ G2 @ N3 ) @ ( sSA_CF370335846de_val @ Phis @ G2 @ N3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_base.allDefs_def
% 0.26/0.61 thf(fact_120_CFG__SSA__base_OallUses__def,axiom,
% 0.26/0.61 ( sSA_CF178745443eD_val
% 0.26/0.61 = ( ^ [Alpha_n: g > list_node,InEdges: g > node > list_P561207620_edgeD,Uses: g > node > set_val,Phis: g > produc1432036078de_val > option_list_val,G2: g,N3: node] : ( sup_sup_set_val @ ( Uses @ G2 @ N3 ) @ ( sSA_CF848637139eD_val @ Alpha_n @ InEdges @ Phis @ G2 @ N3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_base.allUses_def
% 0.26/0.61 thf(fact_121_phi__phiDefs,axiom,
% 0.26/0.61 ! [G: g,V: val,Vs: list_val] :
% 0.26/0.61 ( ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ V )
% 0.26/0.61 = ( some_list_val @ Vs ) )
% 0.26/0.61 => ( member_val @ V @ ( sSA_CF370335846de_val @ phis @ G @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ V ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % phi_phiDefs
% 0.26/0.61 thf(fact_122_condensation__acyclic,axiom,
% 0.26/0.61 ! [G: g,P2: set_val] : ( transi1953622797et_val @ ( irredu893086079de_val @ alpha_n @ defs @ phis @ G @ P2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % condensation_acyclic
% 0.26/0.61 thf(fact_123_phi__def,axiom,
% 0.26/0.61 ! [G: g,V: val] :
% 0.26/0.61 ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ V )
% 0.26/0.61 = ( phis @ G @ ( produc1470527136de_val @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ V ) @ V ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % phi_def
% 0.26/0.61 thf(fact_124_phiArg__def,axiom,
% 0.26/0.61 ! [G: g,V: val,V2: val] :
% 0.26/0.61 ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ V @ V2 )
% 0.26/0.61 = ( ? [Vs2: list_val] :
% 0.26/0.61 ( ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ V )
% 0.26/0.61 = ( some_list_val @ Vs2 ) )
% 0.26/0.61 & ( member_val @ V2 @ ( set_val2 @ Vs2 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % phiArg_def
% 0.26/0.61 thf(fact_125_phi__finite,axiom,
% 0.26/0.61 ! [G: g] : ( finite_finite_val @ ( dom_val_list_val @ ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % phi_finite
% 0.26/0.61 thf(fact_126_redundant__scc__phis,axiom,
% 0.26/0.61 ! [G: g,P2: set_val,Scc: set_val,X2: val] :
% 0.26/0.61 ( ( irredu224829488eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G @ P2 )
% 0.26/0.61 => ( ( member_set_val @ Scc @ ( irredu681226810de_val @ alpha_n @ defs @ phis @ G @ P2 ) )
% 0.26/0.61 => ( ( member_val @ X2 @ Scc )
% 0.26/0.61 => ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ X2 )
% 0.26/0.61 != none_list_val ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % redundant_scc_phis
% 0.26/0.61 thf(fact_127_phis__disj_I2_J,axiom,
% 0.26/0.61 ! [G: g,N: node,V: val,Vs: list_val,N4: node,Vs3: list_val] :
% 0.26/0.61 ( ( ( phis @ G @ ( produc1470527136de_val @ N @ V ) )
% 0.26/0.61 = ( some_list_val @ Vs ) )
% 0.26/0.61 => ( ( ( phis @ G @ ( produc1470527136de_val @ N4 @ V ) )
% 0.26/0.61 = ( some_list_val @ Vs3 ) )
% 0.26/0.61 => ( Vs = Vs3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % phis_disj(2)
% 0.26/0.61 thf(fact_128_phis__disj_I1_J,axiom,
% 0.26/0.61 ! [G: g,N: node,V: val,Vs: list_val,N4: node,Vs3: list_val] :
% 0.26/0.61 ( ( ( phis @ G @ ( produc1470527136de_val @ N @ V ) )
% 0.26/0.61 = ( some_list_val @ Vs ) )
% 0.26/0.61 => ( ( ( phis @ G @ ( produc1470527136de_val @ N4 @ V ) )
% 0.26/0.61 = ( some_list_val @ Vs3 ) )
% 0.26/0.61 => ( N = N4 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % phis_disj(1)
% 0.26/0.61 thf(fact_129_phis__in___092_060alpha_062n,axiom,
% 0.26/0.61 ! [G: g,N: node,V: val,Vs: list_val] :
% 0.26/0.61 ( ( ( phis @ G @ ( produc1470527136de_val @ N @ V ) )
% 0.26/0.61 = ( some_list_val @ Vs ) )
% 0.26/0.61 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % phis_in_\<alpha>n
% 0.26/0.61 thf(fact_130_phis__same__var,axiom,
% 0.26/0.61 ! [G: g,N: node,V: val,Vs: list_val,V2: val] :
% 0.26/0.61 ( ( ( phis @ G @ ( produc1470527136de_val @ N @ V ) )
% 0.26/0.61 = ( some_list_val @ Vs ) )
% 0.26/0.61 => ( ( member_val @ V2 @ ( set_val2 @ Vs ) )
% 0.26/0.61 => ( ( var2 @ G @ V2 )
% 0.26/0.61 = ( var2 @ G @ V ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % phis_same_var
% 0.26/0.61 thf(fact_131_phis__phi,axiom,
% 0.26/0.61 ! [G: g,N: node,V: val,Vs: list_val] :
% 0.26/0.61 ( ( ( phis @ G @ ( produc1470527136de_val @ N @ V ) )
% 0.26/0.61 = ( some_list_val @ Vs ) )
% 0.26/0.61 => ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ V )
% 0.26/0.61 = ( some_list_val @ Vs ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % phis_phi
% 0.26/0.61 thf(fact_132_phiUses__exI,axiom,
% 0.26/0.61 ! [M: node,G: g,N: node,V: val,Vs: list_val] :
% 0.26/0.61 ( ( member_node @ M @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N ) ) )
% 0.26/0.61 => ( ( ( phis @ G @ ( produc1470527136de_val @ N @ V ) )
% 0.26/0.61 = ( some_list_val @ Vs ) )
% 0.26/0.61 => ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.26/0.61 => ~ ! [V6: val] :
% 0.26/0.61 ( ( member_val @ V6 @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ M ) )
% 0.26/0.61 => ~ ( member_val @ V6 @ ( set_val2 @ Vs ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % phiUses_exI
% 0.26/0.61 thf(fact_133_CFG__SSA__Transformed_Ocondensation__nodes_Ocong,axiom,
% 0.26/0.61 irredu681226810de_val = irredu681226810de_val ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_Transformed.condensation_nodes.cong
% 0.26/0.61 thf(fact_134_CFG__SSA__Transformed_Oredundant__set_Ocong,axiom,
% 0.26/0.61 irredu224829488eD_val = irredu224829488eD_val ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_Transformed.redundant_set.cong
% 0.26/0.61 thf(fact_135_CFG__SSA__wf__base_Ophi__def,axiom,
% 0.26/0.61 ( sSA_CF262257161de_val
% 0.26/0.61 = ( ^ [Alpha_n: g > list_node,Defs: g > node > set_val,Phis: g > produc1432036078de_val > option_list_val,G2: g,V3: val] : ( Phis @ G2 @ ( produc1470527136de_val @ ( sSA_CF551432799de_val @ Alpha_n @ Defs @ Phis @ G2 @ V3 ) @ V3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_wf_base.phi_def
% 0.26/0.61 thf(fact_136_CFG__SSA__wf__base_OphiArg__def,axiom,
% 0.26/0.61 ( sSA_CF1252180629de_val
% 0.26/0.61 = ( ^ [Alpha_n: g > list_node,Defs: g > node > set_val,Phis: g > produc1432036078de_val > option_list_val,G2: g,V3: val,V4: val] :
% 0.26/0.61 ? [Vs2: list_val] :
% 0.26/0.61 ( ( ( sSA_CF262257161de_val @ Alpha_n @ Defs @ Phis @ G2 @ V3 )
% 0.26/0.61 = ( some_list_val @ Vs2 ) )
% 0.26/0.61 & ( member_val @ V4 @ ( set_val2 @ Vs2 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_wf_base.phiArg_def
% 0.26/0.61 thf(fact_137_phiUsesI,axiom,
% 0.26/0.61 ! [N4: node,G: g,V2: val,Vs: list_val,N: node,V: val] :
% 0.26/0.61 ( ( member_node @ N4 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.26/0.61 => ( ( ( phis @ G @ ( produc1470527136de_val @ N4 @ V2 ) )
% 0.26/0.61 = ( some_list_val @ Vs ) )
% 0.26/0.61 => ( ( member313544709de_val @ ( produc1470527136de_val @ N @ V ) @ ( set_Pr1085970585de_val @ ( zip_node_val @ ( graph_272749361_edgeD @ inEdges @ G @ N4 ) @ Vs ) ) )
% 0.26/0.61 => ( member_val @ V @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ N ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % phiUsesI
% 0.26/0.61 thf(fact_138_scc__in__P,axiom,
% 0.26/0.61 ! [Scc: set_val,G: g,P2: set_val] :
% 0.26/0.61 ( ( member_set_val @ Scc @ ( irredu681226810de_val @ alpha_n @ defs @ phis @ G @ P2 ) )
% 0.26/0.61 => ( ord_less_eq_set_val @ Scc @ P2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % scc_in_P
% 0.26/0.61 thf(fact_139_not__None__eq,axiom,
% 0.26/0.61 ! [X2: option_list_val] :
% 0.26/0.61 ( ( X2 != none_list_val )
% 0.26/0.61 = ( ? [Y2: list_val] :
% 0.26/0.61 ( X2
% 0.26/0.61 = ( some_list_val @ Y2 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % not_None_eq
% 0.26/0.61 thf(fact_140_not__Some__eq,axiom,
% 0.26/0.61 ! [X2: option_list_val] :
% 0.26/0.61 ( ( ! [Y2: list_val] :
% 0.26/0.61 ( X2
% 0.26/0.61 != ( some_list_val @ Y2 ) ) )
% 0.26/0.61 = ( X2 = none_list_val ) ) ).
% 0.26/0.61
% 0.26/0.61 % not_Some_eq
% 0.26/0.61 thf(fact_141_sup__Some,axiom,
% 0.26/0.61 ! [X2: set_val,Y3: set_val] :
% 0.26/0.61 ( ( sup_su1487070040et_val @ ( some_set_val @ X2 ) @ ( some_set_val @ Y3 ) )
% 0.26/0.61 = ( some_set_val @ ( sup_sup_set_val @ X2 @ Y3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % sup_Some
% 0.26/0.61 thf(fact_142_option_Oinject,axiom,
% 0.26/0.61 ! [X22: list_val,Y22: list_val] :
% 0.26/0.61 ( ( ( some_list_val @ X22 )
% 0.26/0.61 = ( some_list_val @ Y22 ) )
% 0.26/0.61 = ( X22 = Y22 ) ) ).
% 0.26/0.61
% 0.26/0.61 % option.inject
% 0.26/0.61 thf(fact_143_less__eq__option__Some,axiom,
% 0.26/0.61 ! [X2: set_val,Y3: set_val] :
% 0.26/0.61 ( ( ord_le596993316et_val @ ( some_set_val @ X2 ) @ ( some_set_val @ Y3 ) )
% 0.26/0.61 = ( ord_less_eq_set_val @ X2 @ Y3 ) ) ).
% 0.26/0.61
% 0.26/0.61 % less_eq_option_Some
% 0.26/0.61 thf(fact_144_zip__same,axiom,
% 0.26/0.61 ! [A: produc1324971431et_val,B: produc1324971431et_val,Xs: list_P2089461677et_val] :
% 0.26/0.61 ( ( member1254968080et_val @ ( produc1377626967et_val @ A @ B ) @ ( set_Pr1006393724et_val @ ( zip_Pr21865079et_val @ Xs @ Xs ) ) )
% 0.26/0.61 = ( ( member1711426256et_val @ A @ ( set_Pr284769596et_val @ Xs ) )
% 0.26/0.61 & ( A = B ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % zip_same
% 0.26/0.61 thf(fact_145_zip__same,axiom,
% 0.26/0.61 ! [A: node,B: node,Xs: list_node] :
% 0.26/0.61 ( ( member2110109140e_node @ ( produc457016035e_node @ A @ B ) @ ( set_Pr450990656e_node @ ( zip_node_node @ Xs @ Xs ) ) )
% 0.26/0.61 = ( ( member_node @ A @ ( set_node2 @ Xs ) )
% 0.26/0.61 & ( A = B ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % zip_same
% 0.26/0.61 thf(fact_146_zip__same,axiom,
% 0.26/0.61 ! [A: val,B: val,Xs: list_val] :
% 0.26/0.61 ( ( member1680438992al_val @ ( product_Pair_val_val @ A @ B ) @ ( set_Pr102746428al_val @ ( zip_val_val @ Xs @ Xs ) ) )
% 0.26/0.61 = ( ( member_val @ A @ ( set_val2 @ Xs ) )
% 0.26/0.61 & ( A = B ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % zip_same
% 0.26/0.61 thf(fact_147_zip__same,axiom,
% 0.26/0.61 ! [A: produc1432036078de_val,B: produc1432036078de_val,Xs: list_P1820443774de_val] :
% 0.26/0.61 ( ( member698732390de_val @ ( produc453318901de_val @ A @ B ) @ ( set_Pr482027474de_val @ ( zip_Pr1472086037de_val @ Xs @ Xs ) ) )
% 0.26/0.61 = ( ( member313544709de_val @ A @ ( set_Pr1085970585de_val @ Xs ) )
% 0.26/0.61 & ( A = B ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % zip_same
% 0.26/0.61 thf(fact_148_zip__same,axiom,
% 0.26/0.61 ! [A: set_val,B: set_val,Xs: list_set_val] :
% 0.26/0.61 ( ( member1711426256et_val @ ( produc1041633943et_val @ A @ B ) @ ( set_Pr284769596et_val @ ( zip_set_val_set_val @ Xs @ Xs ) ) )
% 0.26/0.61 = ( ( member_set_val @ A @ ( set_set_val2 @ Xs ) )
% 0.26/0.61 & ( A = B ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % zip_same
% 0.26/0.61 thf(fact_149__C1_C,axiom,
% 0.26/0.61 ! [G: g,P2: set_val] :
% 0.26/0.61 ( ( irredu224829488eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G @ P2 )
% 0.26/0.61 => ? [Scc2: set_val] :
% 0.26/0.61 ( ( ord_less_eq_set_val @ Scc2 @ P2 )
% 0.26/0.61 & ( irredu1955035135eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G @ P2 @ Scc2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % "1"
% 0.26/0.61 thf(fact_150_phiUsesE,axiom,
% 0.26/0.61 ! [V: val,G: g,N: node] :
% 0.26/0.61 ( ( member_val @ V @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ N ) )
% 0.26/0.61 => ~ ! [N5: node] :
% 0.26/0.61 ( ( member_node @ N5 @ ( set_node2 @ ( graph_1037173556_edgeD @ alpha_n @ inEdges @ G @ N ) ) )
% 0.26/0.61 => ! [V6: val,Vs4: list_val] :
% 0.26/0.61 ( ( member313544709de_val @ ( produc1470527136de_val @ N @ V ) @ ( set_Pr1085970585de_val @ ( zip_node_val @ ( graph_272749361_edgeD @ inEdges @ G @ N5 ) @ Vs4 ) ) )
% 0.26/0.61 => ( ( phis @ G @ ( produc1470527136de_val @ N5 @ V6 ) )
% 0.26/0.61 != ( some_list_val @ Vs4 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % phiUsesE
% 0.26/0.61 thf(fact_151_finite__has__minimal2,axiom,
% 0.26/0.61 ! [A2: set_node,A: node] :
% 0.26/0.61 ( ( finite_finite_node @ A2 )
% 0.26/0.61 => ( ( member_node @ A @ A2 )
% 0.26/0.61 => ? [X3: node] :
% 0.26/0.61 ( ( member_node @ X3 @ A2 )
% 0.26/0.61 & ( ord_less_eq_node @ X3 @ A )
% 0.26/0.61 & ! [Xa: node] :
% 0.26/0.61 ( ( member_node @ Xa @ A2 )
% 0.26/0.61 => ( ( ord_less_eq_node @ Xa @ X3 )
% 0.26/0.61 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % finite_has_minimal2
% 0.26/0.61 thf(fact_152_finite__has__minimal2,axiom,
% 0.26/0.61 ! [A2: set_val,A: val] :
% 0.26/0.61 ( ( finite_finite_val @ A2 )
% 0.26/0.61 => ( ( member_val @ A @ A2 )
% 0.26/0.61 => ? [X3: val] :
% 0.26/0.61 ( ( member_val @ X3 @ A2 )
% 0.26/0.61 & ( ord_less_eq_val @ X3 @ A )
% 0.26/0.61 & ! [Xa: val] :
% 0.26/0.61 ( ( member_val @ Xa @ A2 )
% 0.26/0.61 => ( ( ord_less_eq_val @ Xa @ X3 )
% 0.26/0.61 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % finite_has_minimal2
% 0.26/0.61 thf(fact_153_finite__has__minimal2,axiom,
% 0.26/0.61 ! [A2: set_set_val,A: set_val] :
% 0.26/0.61 ( ( finite1265617511et_val @ A2 )
% 0.26/0.61 => ( ( member_set_val @ A @ A2 )
% 0.26/0.61 => ? [X3: set_val] :
% 0.26/0.61 ( ( member_set_val @ X3 @ A2 )
% 0.26/0.61 & ( ord_less_eq_set_val @ X3 @ A )
% 0.26/0.61 & ! [Xa: set_val] :
% 0.26/0.61 ( ( member_set_val @ Xa @ A2 )
% 0.26/0.61 => ( ( ord_less_eq_set_val @ Xa @ X3 )
% 0.26/0.61 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % finite_has_minimal2
% 0.26/0.61 thf(fact_154_finite__has__maximal2,axiom,
% 0.26/0.61 ! [A2: set_node,A: node] :
% 0.26/0.61 ( ( finite_finite_node @ A2 )
% 0.26/0.61 => ( ( member_node @ A @ A2 )
% 0.26/0.61 => ? [X3: node] :
% 0.26/0.61 ( ( member_node @ X3 @ A2 )
% 0.26/0.61 & ( ord_less_eq_node @ A @ X3 )
% 0.26/0.61 & ! [Xa: node] :
% 0.26/0.61 ( ( member_node @ Xa @ A2 )
% 0.26/0.61 => ( ( ord_less_eq_node @ X3 @ Xa )
% 0.26/0.61 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % finite_has_maximal2
% 0.26/0.61 thf(fact_155_finite__has__maximal2,axiom,
% 0.26/0.61 ! [A2: set_val,A: val] :
% 0.26/0.61 ( ( finite_finite_val @ A2 )
% 0.26/0.61 => ( ( member_val @ A @ A2 )
% 0.26/0.61 => ? [X3: val] :
% 0.26/0.61 ( ( member_val @ X3 @ A2 )
% 0.26/0.61 & ( ord_less_eq_val @ A @ X3 )
% 0.26/0.61 & ! [Xa: val] :
% 0.26/0.61 ( ( member_val @ Xa @ A2 )
% 0.26/0.61 => ( ( ord_less_eq_val @ X3 @ Xa )
% 0.26/0.61 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % finite_has_maximal2
% 0.26/0.61 thf(fact_156_finite__has__maximal2,axiom,
% 0.26/0.61 ! [A2: set_set_val,A: set_val] :
% 0.26/0.61 ( ( finite1265617511et_val @ A2 )
% 0.26/0.61 => ( ( member_set_val @ A @ A2 )
% 0.26/0.61 => ? [X3: set_val] :
% 0.26/0.61 ( ( member_set_val @ X3 @ A2 )
% 0.26/0.61 & ( ord_less_eq_set_val @ A @ X3 )
% 0.26/0.61 & ! [Xa: set_val] :
% 0.26/0.61 ( ( member_set_val @ Xa @ A2 )
% 0.26/0.61 => ( ( ord_less_eq_set_val @ X3 @ Xa )
% 0.26/0.61 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % finite_has_maximal2
% 0.26/0.61 thf(fact_157_subset__code_I1_J,axiom,
% 0.26/0.61 ! [Xs: list_set_val,B2: set_set_val] :
% 0.26/0.61 ( ( ord_le1742111550et_val @ ( set_set_val2 @ Xs ) @ B2 )
% 0.26/0.61 = ( ! [X: set_val] :
% 0.26/0.61 ( ( member_set_val @ X @ ( set_set_val2 @ Xs ) )
% 0.26/0.61 => ( member_set_val @ X @ B2 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % subset_code(1)
% 0.26/0.61 thf(fact_158_subset__code_I1_J,axiom,
% 0.26/0.61 ! [Xs: list_P2089461677et_val,B2: set_Pr1311924359et_val] :
% 0.26/0.61 ( ( ord_le299366439et_val @ ( set_Pr284769596et_val @ Xs ) @ B2 )
% 0.26/0.61 = ( ! [X: produc1324971431et_val] :
% 0.26/0.61 ( ( member1711426256et_val @ X @ ( set_Pr284769596et_val @ Xs ) )
% 0.26/0.61 => ( member1711426256et_val @ X @ B2 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % subset_code(1)
% 0.26/0.61 thf(fact_159_subset__code_I1_J,axiom,
% 0.26/0.61 ! [Xs: list_node,B2: set_node] :
% 0.26/0.61 ( ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ B2 )
% 0.26/0.61 = ( ! [X: node] :
% 0.26/0.61 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.26/0.61 => ( member_node @ X @ B2 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % subset_code(1)
% 0.26/0.61 thf(fact_160_subset__code_I1_J,axiom,
% 0.26/0.61 ! [Xs: list_P1820443774de_val,B2: set_Pr699757092de_val] :
% 0.26/0.61 ( ( ord_le1643692676de_val @ ( set_Pr1085970585de_val @ Xs ) @ B2 )
% 0.26/0.61 = ( ! [X: produc1432036078de_val] :
% 0.26/0.61 ( ( member313544709de_val @ X @ ( set_Pr1085970585de_val @ Xs ) )
% 0.26/0.61 => ( member313544709de_val @ X @ B2 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % subset_code(1)
% 0.26/0.61 thf(fact_161_subset__code_I1_J,axiom,
% 0.26/0.61 ! [Xs: list_val,B2: set_val] :
% 0.26/0.61 ( ( ord_less_eq_set_val @ ( set_val2 @ Xs ) @ B2 )
% 0.26/0.61 = ( ! [X: val] :
% 0.26/0.61 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.26/0.61 => ( member_val @ X @ B2 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % subset_code(1)
% 0.26/0.61 thf(fact_162_rev__finite__subset,axiom,
% 0.26/0.61 ! [B2: set_Pr1311924359et_val,A2: set_Pr1311924359et_val] :
% 0.26/0.61 ( ( finite79836624et_val @ B2 )
% 0.26/0.61 => ( ( ord_le299366439et_val @ A2 @ B2 )
% 0.26/0.61 => ( finite79836624et_val @ A2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % rev_finite_subset
% 0.26/0.61 thf(fact_163_rev__finite__subset,axiom,
% 0.26/0.61 ! [B2: set_Pr699757092de_val,A2: set_Pr699757092de_val] :
% 0.26/0.61 ( ( finite2056463621de_val @ B2 )
% 0.26/0.61 => ( ( ord_le1643692676de_val @ A2 @ B2 )
% 0.26/0.61 => ( finite2056463621de_val @ A2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % rev_finite_subset
% 0.26/0.61 thf(fact_164_rev__finite__subset,axiom,
% 0.26/0.61 ! [B2: set_val,A2: set_val] :
% 0.26/0.61 ( ( finite_finite_val @ B2 )
% 0.26/0.61 => ( ( ord_less_eq_set_val @ A2 @ B2 )
% 0.26/0.61 => ( finite_finite_val @ A2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % rev_finite_subset
% 0.26/0.61 thf(fact_165_infinite__super,axiom,
% 0.26/0.61 ! [S: set_Pr1311924359et_val,T: set_Pr1311924359et_val] :
% 0.26/0.61 ( ( ord_le299366439et_val @ S @ T )
% 0.26/0.61 => ( ~ ( finite79836624et_val @ S )
% 0.26/0.61 => ~ ( finite79836624et_val @ T ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % infinite_super
% 0.26/0.61 thf(fact_166_infinite__super,axiom,
% 0.26/0.61 ! [S: set_Pr699757092de_val,T: set_Pr699757092de_val] :
% 0.26/0.61 ( ( ord_le1643692676de_val @ S @ T )
% 0.26/0.61 => ( ~ ( finite2056463621de_val @ S )
% 0.26/0.61 => ~ ( finite2056463621de_val @ T ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % infinite_super
% 0.26/0.61 thf(fact_167_infinite__super,axiom,
% 0.26/0.61 ! [S: set_val,T: set_val] :
% 0.26/0.61 ( ( ord_less_eq_set_val @ S @ T )
% 0.26/0.61 => ( ~ ( finite_finite_val @ S )
% 0.26/0.61 => ~ ( finite_finite_val @ T ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % infinite_super
% 0.26/0.61 thf(fact_168_finite__subset,axiom,
% 0.26/0.61 ! [A2: set_Pr1311924359et_val,B2: set_Pr1311924359et_val] :
% 0.26/0.61 ( ( ord_le299366439et_val @ A2 @ B2 )
% 0.26/0.61 => ( ( finite79836624et_val @ B2 )
% 0.26/0.61 => ( finite79836624et_val @ A2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % finite_subset
% 0.26/0.61 thf(fact_169_finite__subset,axiom,
% 0.26/0.61 ! [A2: set_Pr699757092de_val,B2: set_Pr699757092de_val] :
% 0.26/0.61 ( ( ord_le1643692676de_val @ A2 @ B2 )
% 0.26/0.61 => ( ( finite2056463621de_val @ B2 )
% 0.26/0.61 => ( finite2056463621de_val @ A2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % finite_subset
% 0.26/0.61 thf(fact_170_finite__subset,axiom,
% 0.26/0.61 ! [A2: set_val,B2: set_val] :
% 0.26/0.61 ( ( ord_less_eq_set_val @ A2 @ B2 )
% 0.26/0.61 => ( ( finite_finite_val @ B2 )
% 0.26/0.61 => ( finite_finite_val @ A2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % finite_subset
% 0.26/0.61 thf(fact_171_in__set__zipE,axiom,
% 0.26/0.61 ! [X2: node,Y3: node,Xs: list_node,Ys: list_node] :
% 0.26/0.61 ( ( member2110109140e_node @ ( produc457016035e_node @ X2 @ Y3 ) @ ( set_Pr450990656e_node @ ( zip_node_node @ Xs @ Ys ) ) )
% 0.26/0.61 => ~ ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 0.26/0.61 => ~ ( member_node @ Y3 @ ( set_node2 @ Ys ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % in_set_zipE
% 0.26/0.61 thf(fact_172_in__set__zipE,axiom,
% 0.26/0.61 ! [X2: val,Y3: node,Xs: list_val,Ys: list_node] :
% 0.26/0.61 ( ( member828457417l_node @ ( produc1074923692l_node @ X2 @ Y3 ) @ ( set_Pr1600883293l_node @ ( zip_val_node @ Xs @ Ys ) ) )
% 0.26/0.61 => ~ ( ( member_val @ X2 @ ( set_val2 @ Xs ) )
% 0.26/0.61 => ~ ( member_node @ Y3 @ ( set_node2 @ Ys ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % in_set_zipE
% 0.26/0.61 thf(fact_173_in__set__zipE,axiom,
% 0.26/0.61 ! [X2: val,Y3: val,Xs: list_val,Ys: list_val] :
% 0.26/0.61 ( ( member1680438992al_val @ ( product_Pair_val_val @ X2 @ Y3 ) @ ( set_Pr102746428al_val @ ( zip_val_val @ Xs @ Ys ) ) )
% 0.26/0.61 => ~ ( ( member_val @ X2 @ ( set_val2 @ Xs ) )
% 0.26/0.61 => ~ ( member_val @ Y3 @ ( set_val2 @ Ys ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % in_set_zipE
% 0.26/0.61 thf(fact_174_in__set__zipE,axiom,
% 0.26/0.61 ! [X2: node,Y3: val,Xs: list_node,Ys: list_val] :
% 0.26/0.61 ( ( member313544709de_val @ ( produc1470527136de_val @ X2 @ Y3 ) @ ( set_Pr1085970585de_val @ ( zip_node_val @ Xs @ Ys ) ) )
% 0.26/0.61 => ~ ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 0.26/0.61 => ~ ( member_val @ Y3 @ ( set_val2 @ Ys ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % in_set_zipE
% 0.26/0.61 thf(fact_175_in__set__zipE,axiom,
% 0.26/0.61 ! [X2: set_val,Y3: node,Xs: list_set_val,Ys: list_node] :
% 0.26/0.61 ( ( member76372137l_node @ ( produc2052093836l_node @ X2 @ Y3 ) @ ( set_Pr1904955709l_node @ ( zip_set_val_node @ Xs @ Ys ) ) )
% 0.26/0.61 => ~ ( ( member_set_val @ X2 @ ( set_set_val2 @ Xs ) )
% 0.26/0.61 => ~ ( member_node @ Y3 @ ( set_node2 @ Ys ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % in_set_zipE
% 0.26/0.61 thf(fact_176_in__set__zipE,axiom,
% 0.26/0.61 ! [X2: set_val,Y3: val,Xs: list_set_val,Ys: list_val] :
% 0.26/0.61 ( ( member1110026224al_val @ ( produc1337903031al_val @ X2 @ Y3 ) @ ( set_Pr1027623516al_val @ ( zip_set_val_val @ Xs @ Ys ) ) )
% 0.26/0.61 => ~ ( ( member_set_val @ X2 @ ( set_set_val2 @ Xs ) )
% 0.26/0.61 => ~ ( member_val @ Y3 @ ( set_val2 @ Ys ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % in_set_zipE
% 0.26/0.61 thf(fact_177_in__set__zipE,axiom,
% 0.26/0.61 ! [X2: node,Y3: set_val,Xs: list_node,Ys: list_set_val] :
% 0.26/0.61 ( ( member125181669et_val @ ( produc2042994048et_val @ X2 @ Y3 ) @ ( set_Pr1953765241et_val @ ( zip_node_set_val @ Xs @ Ys ) ) )
% 0.26/0.61 => ~ ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 0.26/0.61 => ~ ( member_set_val @ Y3 @ ( set_set_val2 @ Ys ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % in_set_zipE
% 0.26/0.61 thf(fact_178_in__set__zipE,axiom,
% 0.26/0.61 ! [X2: val,Y3: set_val,Xs: list_val,Ys: list_set_val] :
% 0.26/0.61 ( ( member39229872et_val @ ( produc1446164855et_val @ X2 @ Y3 ) @ ( set_Pr2104310812et_val @ ( zip_val_set_val @ Xs @ Ys ) ) )
% 0.26/0.61 => ~ ( ( member_val @ X2 @ ( set_val2 @ Xs ) )
% 0.26/0.61 => ~ ( member_set_val @ Y3 @ ( set_set_val2 @ Ys ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % in_set_zipE
% 0.26/0.61 thf(fact_179_in__set__zipE,axiom,
% 0.26/0.61 ! [X2: node,Y3: produc1432036078de_val,Xs: list_node,Ys: list_P1820443774de_val] :
% 0.26/0.61 ( ( member562853661de_val @ ( produc1162531244de_val @ X2 @ Y3 ) @ ( set_Pr1157337481de_val @ ( zip_no263301324de_val @ Xs @ Ys ) ) )
% 0.26/0.61 => ~ ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 0.26/0.61 => ~ ( member313544709de_val @ Y3 @ ( set_Pr1085970585de_val @ Ys ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % in_set_zipE
% 0.26/0.61 thf(fact_180_in__set__zipE,axiom,
% 0.26/0.61 ! [X2: val,Y3: produc1432036078de_val,Xs: list_val,Ys: list_P1820443774de_val] :
% 0.26/0.61 ( ( member1894062994de_val @ ( produc1571934709de_val @ X2 @ Y3 ) @ ( set_Pr434939430de_val @ ( zip_va679686869de_val @ Xs @ Ys ) ) )
% 0.26/0.61 => ~ ( ( member_val @ X2 @ ( set_val2 @ Xs ) )
% 0.26/0.61 => ~ ( member313544709de_val @ Y3 @ ( set_Pr1085970585de_val @ Ys ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % in_set_zipE
% 0.26/0.61 thf(fact_181_set__zip__leftD,axiom,
% 0.26/0.61 ! [X2: node,Y3: val,Xs: list_node,Ys: list_val] :
% 0.26/0.61 ( ( member313544709de_val @ ( produc1470527136de_val @ X2 @ Y3 ) @ ( set_Pr1085970585de_val @ ( zip_node_val @ Xs @ Ys ) ) )
% 0.26/0.61 => ( member_node @ X2 @ ( set_node2 @ Xs ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % set_zip_leftD
% 0.26/0.61 thf(fact_182_set__zip__leftD,axiom,
% 0.26/0.61 ! [X2: set_val,Y3: set_val,Xs: list_set_val,Ys: list_set_val] :
% 0.26/0.61 ( ( member1711426256et_val @ ( produc1041633943et_val @ X2 @ Y3 ) @ ( set_Pr284769596et_val @ ( zip_set_val_set_val @ Xs @ Ys ) ) )
% 0.26/0.61 => ( member_set_val @ X2 @ ( set_set_val2 @ Xs ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % set_zip_leftD
% 0.26/0.61 thf(fact_183_set__zip__rightD,axiom,
% 0.26/0.61 ! [X2: node,Y3: val,Xs: list_node,Ys: list_val] :
% 0.26/0.61 ( ( member313544709de_val @ ( produc1470527136de_val @ X2 @ Y3 ) @ ( set_Pr1085970585de_val @ ( zip_node_val @ Xs @ Ys ) ) )
% 0.26/0.61 => ( member_val @ Y3 @ ( set_val2 @ Ys ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % set_zip_rightD
% 0.26/0.61 thf(fact_184_set__zip__rightD,axiom,
% 0.26/0.61 ! [X2: set_val,Y3: set_val,Xs: list_set_val,Ys: list_set_val] :
% 0.26/0.61 ( ( member1711426256et_val @ ( produc1041633943et_val @ X2 @ Y3 ) @ ( set_Pr284769596et_val @ ( zip_set_val_set_val @ Xs @ Ys ) ) )
% 0.26/0.61 => ( member_set_val @ Y3 @ ( set_set_val2 @ Ys ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % set_zip_rightD
% 0.26/0.61 thf(fact_185_combine__options__cases,axiom,
% 0.26/0.61 ! [X2: option_list_val,P2: option_list_val > option_list_val > $o,Y3: option_list_val] :
% 0.26/0.61 ( ( ( X2 = none_list_val )
% 0.26/0.61 => ( P2 @ X2 @ Y3 ) )
% 0.26/0.61 => ( ( ( Y3 = none_list_val )
% 0.26/0.61 => ( P2 @ X2 @ Y3 ) )
% 0.26/0.61 => ( ! [A4: list_val,B3: list_val] :
% 0.26/0.61 ( ( X2
% 0.26/0.61 = ( some_list_val @ A4 ) )
% 0.26/0.61 => ( ( Y3
% 0.26/0.61 = ( some_list_val @ B3 ) )
% 0.26/0.61 => ( P2 @ X2 @ Y3 ) ) )
% 0.26/0.61 => ( P2 @ X2 @ Y3 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % combine_options_cases
% 0.26/0.61 thf(fact_186_split__option__all,axiom,
% 0.26/0.61 ( ( ^ [P3: option_list_val > $o] :
% 0.26/0.61 ! [X4: option_list_val] : ( P3 @ X4 ) )
% 0.26/0.61 = ( ^ [P4: option_list_val > $o] :
% 0.26/0.61 ( ( P4 @ none_list_val )
% 0.26/0.61 & ! [X: list_val] : ( P4 @ ( some_list_val @ X ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % split_option_all
% 0.26/0.61 thf(fact_187_split__option__ex,axiom,
% 0.26/0.61 ( ( ^ [P3: option_list_val > $o] :
% 0.26/0.61 ? [X4: option_list_val] : ( P3 @ X4 ) )
% 0.26/0.61 = ( ^ [P4: option_list_val > $o] :
% 0.26/0.61 ( ( P4 @ none_list_val )
% 0.26/0.61 | ? [X: list_val] : ( P4 @ ( some_list_val @ X ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % split_option_ex
% 0.26/0.61 thf(fact_188_option_Oinducts,axiom,
% 0.26/0.61 ! [P2: option_list_val > $o,Option: option_list_val] :
% 0.26/0.61 ( ( P2 @ none_list_val )
% 0.26/0.61 => ( ! [X3: list_val] : ( P2 @ ( some_list_val @ X3 ) )
% 0.26/0.61 => ( P2 @ Option ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % option.inducts
% 0.26/0.61 thf(fact_189_option_Oexhaust,axiom,
% 0.26/0.61 ! [Y3: option_list_val] :
% 0.26/0.61 ( ( Y3 != none_list_val )
% 0.26/0.61 => ~ ! [X23: list_val] :
% 0.26/0.61 ( Y3
% 0.26/0.61 != ( some_list_val @ X23 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % option.exhaust
% 0.26/0.61 thf(fact_190_option_OdiscI,axiom,
% 0.26/0.61 ! [Option: option_list_val,X22: list_val] :
% 0.26/0.61 ( ( Option
% 0.26/0.61 = ( some_list_val @ X22 ) )
% 0.26/0.61 => ( Option != none_list_val ) ) ).
% 0.26/0.61
% 0.26/0.61 % option.discI
% 0.26/0.61 thf(fact_191_option_Odistinct_I1_J,axiom,
% 0.26/0.61 ! [X22: list_val] :
% 0.26/0.61 ( none_list_val
% 0.26/0.61 != ( some_list_val @ X22 ) ) ).
% 0.26/0.61
% 0.26/0.61 % option.distinct(1)
% 0.26/0.61 thf(fact_192_Ex__condensation__leaf,axiom,
% 0.26/0.61 ! [P2: set_val,G: g] :
% 0.26/0.61 ( ( P2 != bot_bot_set_val )
% 0.26/0.61 => ? [Leaf: set_val] :
% 0.26/0.61 ( ( member_set_val @ Leaf @ ( irredu681226810de_val @ alpha_n @ defs @ phis @ G @ P2 ) )
% 0.26/0.61 & ! [Scc3: set_val] :
% 0.26/0.61 ~ ( member1711426256et_val @ ( produc1041633943et_val @ Leaf @ Scc3 ) @ ( irredu893086079de_val @ alpha_n @ defs @ phis @ G @ P2 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Ex_condensation_leaf
% 0.26/0.61 thf(fact_193_Un__subset__iff,axiom,
% 0.26/0.61 ! [A2: set_val,B2: set_val,C: set_val] :
% 0.26/0.61 ( ( ord_less_eq_set_val @ ( sup_sup_set_val @ A2 @ B2 ) @ C )
% 0.26/0.61 = ( ( ord_less_eq_set_val @ A2 @ C )
% 0.26/0.61 & ( ord_less_eq_set_val @ B2 @ C ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Un_subset_iff
% 0.26/0.61 thf(fact_194_le__sup__iff,axiom,
% 0.26/0.61 ! [X2: set_val,Y3: set_val,Z: set_val] :
% 0.26/0.61 ( ( ord_less_eq_set_val @ ( sup_sup_set_val @ X2 @ Y3 ) @ Z )
% 0.26/0.61 = ( ( ord_less_eq_set_val @ X2 @ Z )
% 0.26/0.61 & ( ord_less_eq_set_val @ Y3 @ Z ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % le_sup_iff
% 0.26/0.61 thf(fact_195_sup_Obounded__iff,axiom,
% 0.26/0.61 ! [B: set_val,C2: set_val,A: set_val] :
% 0.26/0.61 ( ( ord_less_eq_set_val @ ( sup_sup_set_val @ B @ C2 ) @ A )
% 0.26/0.61 = ( ( ord_less_eq_set_val @ B @ A )
% 0.26/0.61 & ( ord_less_eq_set_val @ C2 @ A ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % sup.bounded_iff
% 0.26/0.61 thf(fact_196_subset__antisym,axiom,
% 0.26/0.61 ! [A2: set_val,B2: set_val] :
% 0.26/0.61 ( ( ord_less_eq_set_val @ A2 @ B2 )
% 0.26/0.61 => ( ( ord_less_eq_set_val @ B2 @ A2 )
% 0.26/0.61 => ( A2 = B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % subset_antisym
% 0.26/0.61 thf(fact_197_subsetI,axiom,
% 0.26/0.61 ! [A2: set_node,B2: set_node] :
% 0.26/0.61 ( ! [X3: node] :
% 0.26/0.61 ( ( member_node @ X3 @ A2 )
% 0.26/0.61 => ( member_node @ X3 @ B2 ) )
% 0.26/0.61 => ( ord_less_eq_set_node @ A2 @ B2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % subsetI
% 0.26/0.61 thf(fact_198_subsetI,axiom,
% 0.26/0.61 ! [A2: set_set_val,B2: set_set_val] :
% 0.26/0.61 ( ! [X3: set_val] :
% 0.26/0.61 ( ( member_set_val @ X3 @ A2 )
% 0.26/0.61 => ( member_set_val @ X3 @ B2 ) )
% 0.26/0.61 => ( ord_le1742111550et_val @ A2 @ B2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % subsetI
% 0.26/0.61 thf(fact_199_subsetI,axiom,
% 0.26/0.61 ! [A2: set_Pr699757092de_val,B2: set_Pr699757092de_val] :
% 0.26/0.61 ( ! [X3: produc1432036078de_val] :
% 0.26/0.61 ( ( member313544709de_val @ X3 @ A2 )
% 0.26/0.61 => ( member313544709de_val @ X3 @ B2 ) )
% 0.26/0.61 => ( ord_le1643692676de_val @ A2 @ B2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % subsetI
% 0.26/0.61 thf(fact_200_subsetI,axiom,
% 0.26/0.61 ! [A2: set_Pr1311924359et_val,B2: set_Pr1311924359et_val] :
% 0.26/0.61 ( ! [X3: produc1324971431et_val] :
% 0.26/0.61 ( ( member1711426256et_val @ X3 @ A2 )
% 0.26/0.61 => ( member1711426256et_val @ X3 @ B2 ) )
% 0.26/0.61 => ( ord_le299366439et_val @ A2 @ B2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % subsetI
% 0.26/0.61 thf(fact_201_subsetI,axiom,
% 0.26/0.61 ! [A2: set_val,B2: set_val] :
% 0.26/0.61 ( ! [X3: val] :
% 0.26/0.61 ( ( member_val @ X3 @ A2 )
% 0.26/0.61 => ( member_val @ X3 @ B2 ) )
% 0.26/0.61 => ( ord_less_eq_set_val @ A2 @ B2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % subsetI
% 0.26/0.61 thf(fact_202_sup_Oright__idem,axiom,
% 0.26/0.61 ! [A: set_val,B: set_val] :
% 0.26/0.61 ( ( sup_sup_set_val @ ( sup_sup_set_val @ A @ B ) @ B )
% 0.26/0.61 = ( sup_sup_set_val @ A @ B ) ) ).
% 0.26/0.61
% 0.26/0.61 % sup.right_idem
% 0.26/0.61 thf(fact_203_sup__left__idem,axiom,
% 0.26/0.61 ! [X2: set_val,Y3: set_val] :
% 0.26/0.61 ( ( sup_sup_set_val @ X2 @ ( sup_sup_set_val @ X2 @ Y3 ) )
% 0.26/0.61 = ( sup_sup_set_val @ X2 @ Y3 ) ) ).
% 0.26/0.61
% 0.26/0.61 % sup_left_idem
% 0.26/0.61 thf(fact_204_sup_Oleft__idem,axiom,
% 0.26/0.61 ! [A: set_val,B: set_val] :
% 0.26/0.61 ( ( sup_sup_set_val @ A @ ( sup_sup_set_val @ A @ B ) )
% 0.26/0.61 = ( sup_sup_set_val @ A @ B ) ) ).
% 0.26/0.61
% 0.26/0.61 % sup.left_idem
% 0.26/0.61 thf(fact_205_sup__idem,axiom,
% 0.26/0.61 ! [X2: set_val] :
% 0.26/0.61 ( ( sup_sup_set_val @ X2 @ X2 )
% 0.26/0.61 = X2 ) ).
% 0.26/0.61
% 0.26/0.61 % sup_idem
% 0.26/0.61 thf(fact_206_sup_Oidem,axiom,
% 0.26/0.61 ! [A: set_val] :
% 0.26/0.61 ( ( sup_sup_set_val @ A @ A )
% 0.26/0.61 = A ) ).
% 0.26/0.61
% 0.26/0.61 % sup.idem
% 0.26/0.61 thf(fact_207_Un__iff,axiom,
% 0.26/0.61 ! [C2: node,A2: set_node,B2: set_node] :
% 0.26/0.61 ( ( member_node @ C2 @ ( sup_sup_set_node @ A2 @ B2 ) )
% 0.26/0.61 = ( ( member_node @ C2 @ A2 )
% 0.26/0.61 | ( member_node @ C2 @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Un_iff
% 0.26/0.61 thf(fact_208_Un__iff,axiom,
% 0.26/0.61 ! [C2: set_val,A2: set_set_val,B2: set_set_val] :
% 0.26/0.61 ( ( member_set_val @ C2 @ ( sup_sup_set_set_val @ A2 @ B2 ) )
% 0.26/0.61 = ( ( member_set_val @ C2 @ A2 )
% 0.26/0.61 | ( member_set_val @ C2 @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Un_iff
% 0.26/0.61 thf(fact_209_Un__iff,axiom,
% 0.26/0.61 ! [C2: produc1432036078de_val,A2: set_Pr699757092de_val,B2: set_Pr699757092de_val] :
% 0.26/0.61 ( ( member313544709de_val @ C2 @ ( sup_su2138939728de_val @ A2 @ B2 ) )
% 0.26/0.61 = ( ( member313544709de_val @ C2 @ A2 )
% 0.26/0.61 | ( member313544709de_val @ C2 @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Un_iff
% 0.26/0.61 thf(fact_210_Un__iff,axiom,
% 0.26/0.61 ! [C2: produc1324971431et_val,A2: set_Pr1311924359et_val,B2: set_Pr1311924359et_val] :
% 0.26/0.61 ( ( member1711426256et_val @ C2 @ ( sup_su2005730907et_val @ A2 @ B2 ) )
% 0.26/0.61 = ( ( member1711426256et_val @ C2 @ A2 )
% 0.26/0.61 | ( member1711426256et_val @ C2 @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Un_iff
% 0.26/0.61 thf(fact_211_Un__iff,axiom,
% 0.26/0.61 ! [C2: val,A2: set_val,B2: set_val] :
% 0.26/0.61 ( ( member_val @ C2 @ ( sup_sup_set_val @ A2 @ B2 ) )
% 0.26/0.61 = ( ( member_val @ C2 @ A2 )
% 0.26/0.61 | ( member_val @ C2 @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Un_iff
% 0.26/0.61 thf(fact_212_UnCI,axiom,
% 0.26/0.61 ! [C2: node,B2: set_node,A2: set_node] :
% 0.26/0.61 ( ( ~ ( member_node @ C2 @ B2 )
% 0.26/0.61 => ( member_node @ C2 @ A2 ) )
% 0.26/0.61 => ( member_node @ C2 @ ( sup_sup_set_node @ A2 @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % UnCI
% 0.26/0.61 thf(fact_213_UnCI,axiom,
% 0.26/0.61 ! [C2: set_val,B2: set_set_val,A2: set_set_val] :
% 0.26/0.61 ( ( ~ ( member_set_val @ C2 @ B2 )
% 0.26/0.61 => ( member_set_val @ C2 @ A2 ) )
% 0.26/0.61 => ( member_set_val @ C2 @ ( sup_sup_set_set_val @ A2 @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % UnCI
% 0.26/0.61 thf(fact_214_UnCI,axiom,
% 0.26/0.61 ! [C2: produc1432036078de_val,B2: set_Pr699757092de_val,A2: set_Pr699757092de_val] :
% 0.26/0.61 ( ( ~ ( member313544709de_val @ C2 @ B2 )
% 0.26/0.61 => ( member313544709de_val @ C2 @ A2 ) )
% 0.26/0.61 => ( member313544709de_val @ C2 @ ( sup_su2138939728de_val @ A2 @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % UnCI
% 0.26/0.61 thf(fact_215_UnCI,axiom,
% 0.26/0.61 ! [C2: produc1324971431et_val,B2: set_Pr1311924359et_val,A2: set_Pr1311924359et_val] :
% 0.26/0.61 ( ( ~ ( member1711426256et_val @ C2 @ B2 )
% 0.26/0.61 => ( member1711426256et_val @ C2 @ A2 ) )
% 0.26/0.61 => ( member1711426256et_val @ C2 @ ( sup_su2005730907et_val @ A2 @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % UnCI
% 0.26/0.61 thf(fact_216_UnCI,axiom,
% 0.26/0.61 ! [C2: val,B2: set_val,A2: set_val] :
% 0.26/0.61 ( ( ~ ( member_val @ C2 @ B2 )
% 0.26/0.61 => ( member_val @ C2 @ A2 ) )
% 0.26/0.61 => ( member_val @ C2 @ ( sup_sup_set_val @ A2 @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % UnCI
% 0.26/0.61 thf(fact_217_subset__empty,axiom,
% 0.26/0.61 ! [A2: set_val] :
% 0.26/0.61 ( ( ord_less_eq_set_val @ A2 @ bot_bot_set_val )
% 0.26/0.61 = ( A2 = bot_bot_set_val ) ) ).
% 0.26/0.61
% 0.26/0.61 % subset_empty
% 0.26/0.61 thf(fact_218_empty__subsetI,axiom,
% 0.26/0.61 ! [A2: set_val] : ( ord_less_eq_set_val @ bot_bot_set_val @ A2 ) ).
% 0.26/0.61
% 0.26/0.61 % empty_subsetI
% 0.26/0.61 thf(fact_219_sup__bot__left,axiom,
% 0.26/0.61 ! [X2: set_val] :
% 0.26/0.61 ( ( sup_sup_set_val @ bot_bot_set_val @ X2 )
% 0.26/0.61 = X2 ) ).
% 0.26/0.61
% 0.26/0.61 % sup_bot_left
% 0.26/0.61 thf(fact_220_sup__bot__right,axiom,
% 0.26/0.61 ! [X2: set_val] :
% 0.26/0.61 ( ( sup_sup_set_val @ X2 @ bot_bot_set_val )
% 0.26/0.61 = X2 ) ).
% 0.26/0.61
% 0.26/0.61 % sup_bot_right
% 0.26/0.61 thf(fact_221_bot__eq__sup__iff,axiom,
% 0.26/0.61 ! [X2: set_val,Y3: set_val] :
% 0.26/0.61 ( ( bot_bot_set_val
% 0.26/0.61 = ( sup_sup_set_val @ X2 @ Y3 ) )
% 0.26/0.61 = ( ( X2 = bot_bot_set_val )
% 0.26/0.61 & ( Y3 = bot_bot_set_val ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % bot_eq_sup_iff
% 0.26/0.61 thf(fact_222_sup__eq__bot__iff,axiom,
% 0.26/0.61 ! [X2: set_val,Y3: set_val] :
% 0.26/0.61 ( ( ( sup_sup_set_val @ X2 @ Y3 )
% 0.26/0.61 = bot_bot_set_val )
% 0.26/0.61 = ( ( X2 = bot_bot_set_val )
% 0.26/0.61 & ( Y3 = bot_bot_set_val ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % sup_eq_bot_iff
% 0.26/0.61 thf(fact_223_sup__bot_Oeq__neutr__iff,axiom,
% 0.26/0.61 ! [A: set_val,B: set_val] :
% 0.26/0.61 ( ( ( sup_sup_set_val @ A @ B )
% 0.26/0.61 = bot_bot_set_val )
% 0.26/0.61 = ( ( A = bot_bot_set_val )
% 0.26/0.61 & ( B = bot_bot_set_val ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % sup_bot.eq_neutr_iff
% 0.26/0.61 thf(fact_224_sup__bot_Oleft__neutral,axiom,
% 0.26/0.61 ! [A: set_val] :
% 0.26/0.61 ( ( sup_sup_set_val @ bot_bot_set_val @ A )
% 0.26/0.61 = A ) ).
% 0.26/0.61
% 0.26/0.61 % sup_bot.left_neutral
% 0.26/0.61 thf(fact_225_sup__bot_Oneutr__eq__iff,axiom,
% 0.26/0.61 ! [A: set_val,B: set_val] :
% 0.26/0.61 ( ( bot_bot_set_val
% 0.26/0.61 = ( sup_sup_set_val @ A @ B ) )
% 0.26/0.61 = ( ( A = bot_bot_set_val )
% 0.26/0.61 & ( B = bot_bot_set_val ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % sup_bot.neutr_eq_iff
% 0.26/0.61 thf(fact_226_sup__bot_Oright__neutral,axiom,
% 0.26/0.61 ! [A: set_val] :
% 0.26/0.61 ( ( sup_sup_set_val @ A @ bot_bot_set_val )
% 0.26/0.61 = A ) ).
% 0.26/0.61
% 0.26/0.61 % sup_bot.right_neutral
% 0.26/0.61 thf(fact_227_Un__empty,axiom,
% 0.26/0.61 ! [A2: set_val,B2: set_val] :
% 0.26/0.61 ( ( ( sup_sup_set_val @ A2 @ B2 )
% 0.26/0.61 = bot_bot_set_val )
% 0.26/0.61 = ( ( A2 = bot_bot_set_val )
% 0.26/0.61 & ( B2 = bot_bot_set_val ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Un_empty
% 0.26/0.61 thf(fact_228_old_Osuccessors__predecessors,axiom,
% 0.26/0.61 ! [N: node,G: g,M: node] :
% 0.26/0.61 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.26/0.61 => ( ( member_node @ N @ ( set_node2 @ ( graph_1037173556_edgeD @ alpha_n @ inEdges @ G @ M ) ) )
% 0.26/0.61 = ( member_node @ M @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % old.successors_predecessors
% 0.26/0.61 thf(fact_229_Un__empty__left,axiom,
% 0.26/0.61 ! [B2: set_val] :
% 0.26/0.61 ( ( sup_sup_set_val @ bot_bot_set_val @ B2 )
% 0.26/0.61 = B2 ) ).
% 0.26/0.61
% 0.26/0.61 % Un_empty_left
% 0.26/0.61 thf(fact_230_Un__empty__right,axiom,
% 0.26/0.61 ! [A2: set_val] :
% 0.26/0.61 ( ( sup_sup_set_val @ A2 @ bot_bot_set_val )
% 0.26/0.61 = A2 ) ).
% 0.26/0.61
% 0.26/0.61 % Un_empty_right
% 0.26/0.61 thf(fact_231_infinite__imp__nonempty,axiom,
% 0.26/0.61 ! [S: set_Pr1311924359et_val] :
% 0.26/0.61 ( ~ ( finite79836624et_val @ S )
% 0.26/0.61 => ( S != bot_bo2078591731et_val ) ) ).
% 0.26/0.61
% 0.26/0.61 % infinite_imp_nonempty
% 0.26/0.61 thf(fact_232_infinite__imp__nonempty,axiom,
% 0.26/0.61 ! [S: set_Pr699757092de_val] :
% 0.26/0.61 ( ~ ( finite2056463621de_val @ S )
% 0.26/0.61 => ( S != bot_bo404898488de_val ) ) ).
% 0.26/0.61
% 0.26/0.61 % infinite_imp_nonempty
% 0.26/0.61 thf(fact_233_infinite__imp__nonempty,axiom,
% 0.26/0.61 ! [S: set_val] :
% 0.26/0.61 ( ~ ( finite_finite_val @ S )
% 0.26/0.61 => ( S != bot_bot_set_val ) ) ).
% 0.26/0.61
% 0.26/0.61 % infinite_imp_nonempty
% 0.26/0.61 thf(fact_234_finite_OemptyI,axiom,
% 0.26/0.61 finite79836624et_val @ bot_bo2078591731et_val ).
% 0.26/0.61
% 0.26/0.61 % finite.emptyI
% 0.26/0.61 thf(fact_235_finite_OemptyI,axiom,
% 0.26/0.61 finite2056463621de_val @ bot_bo404898488de_val ).
% 0.26/0.61
% 0.26/0.61 % finite.emptyI
% 0.26/0.61 thf(fact_236_finite_OemptyI,axiom,
% 0.26/0.61 finite_finite_val @ bot_bot_set_val ).
% 0.26/0.61
% 0.26/0.61 % finite.emptyI
% 0.26/0.61 thf(fact_237_CFG__SSA__Transformed_Oredundant__scc_Ocong,axiom,
% 0.26/0.61 irredu1955035135eD_val = irredu1955035135eD_val ).
% 0.26/0.61
% 0.26/0.61 % CFG_SSA_Transformed.redundant_scc.cong
% 0.26/0.61 thf(fact_238_finite__has__maximal,axiom,
% 0.26/0.61 ! [A2: set_val] :
% 0.26/0.61 ( ( finite_finite_val @ A2 )
% 0.26/0.61 => ( ( A2 != bot_bot_set_val )
% 0.26/0.61 => ? [X3: val] :
% 0.26/0.61 ( ( member_val @ X3 @ A2 )
% 0.26/0.61 & ! [Xa: val] :
% 0.26/0.61 ( ( member_val @ Xa @ A2 )
% 0.26/0.61 => ( ( ord_less_eq_val @ X3 @ Xa )
% 0.26/0.61 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % finite_has_maximal
% 0.26/0.61 thf(fact_239_finite__has__maximal,axiom,
% 0.26/0.61 ! [A2: set_set_val] :
% 0.26/0.61 ( ( finite1265617511et_val @ A2 )
% 0.26/0.61 => ( ( A2 != bot_bot_set_set_val )
% 0.26/0.61 => ? [X3: set_val] :
% 0.26/0.61 ( ( member_set_val @ X3 @ A2 )
% 0.26/0.61 & ! [Xa: set_val] :
% 0.26/0.61 ( ( member_set_val @ Xa @ A2 )
% 0.26/0.61 => ( ( ord_less_eq_set_val @ X3 @ Xa )
% 0.26/0.61 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % finite_has_maximal
% 0.26/0.61 thf(fact_240_finite__has__minimal,axiom,
% 0.26/0.61 ! [A2: set_val] :
% 0.26/0.61 ( ( finite_finite_val @ A2 )
% 0.26/0.61 => ( ( A2 != bot_bot_set_val )
% 0.26/0.61 => ? [X3: val] :
% 0.26/0.61 ( ( member_val @ X3 @ A2 )
% 0.26/0.61 & ! [Xa: val] :
% 0.26/0.61 ( ( member_val @ Xa @ A2 )
% 0.26/0.61 => ( ( ord_less_eq_val @ Xa @ X3 )
% 0.26/0.61 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % finite_has_minimal
% 0.26/0.61 thf(fact_241_finite__has__minimal,axiom,
% 0.26/0.61 ! [A2: set_set_val] :
% 0.26/0.61 ( ( finite1265617511et_val @ A2 )
% 0.26/0.61 => ( ( A2 != bot_bot_set_set_val )
% 0.26/0.61 => ? [X3: set_val] :
% 0.26/0.61 ( ( member_set_val @ X3 @ A2 )
% 0.26/0.61 & ! [Xa: set_val] :
% 0.26/0.61 ( ( member_set_val @ Xa @ A2 )
% 0.26/0.61 => ( ( ord_less_eq_set_val @ Xa @ X3 )
% 0.26/0.61 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % finite_has_minimal
% 0.26/0.61 thf(fact_242_Collect__mono__iff,axiom,
% 0.26/0.61 ! [P2: val > $o,Q2: val > $o] :
% 0.26/0.61 ( ( ord_less_eq_set_val @ ( collect_val @ P2 ) @ ( collect_val @ Q2 ) )
% 0.26/0.61 = ( ! [X: val] :
% 0.26/0.61 ( ( P2 @ X )
% 0.26/0.61 => ( Q2 @ X ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Collect_mono_iff
% 0.26/0.61 thf(fact_243_set__eq__subset,axiom,
% 0.26/0.61 ( ( ^ [Y4: set_val,Z2: set_val] : ( Y4 = Z2 ) )
% 0.26/0.61 = ( ^ [A5: set_val,B4: set_val] :
% 0.26/0.61 ( ( ord_less_eq_set_val @ A5 @ B4 )
% 0.26/0.61 & ( ord_less_eq_set_val @ B4 @ A5 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % set_eq_subset
% 0.26/0.61 thf(fact_244_subset__trans,axiom,
% 0.26/0.61 ! [A2: set_val,B2: set_val,C: set_val] :
% 0.26/0.61 ( ( ord_less_eq_set_val @ A2 @ B2 )
% 0.26/0.61 => ( ( ord_less_eq_set_val @ B2 @ C )
% 0.26/0.61 => ( ord_less_eq_set_val @ A2 @ C ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % subset_trans
% 0.26/0.61 thf(fact_245_Collect__mono,axiom,
% 0.26/0.61 ! [P2: val > $o,Q2: val > $o] :
% 0.26/0.61 ( ! [X3: val] :
% 0.26/0.61 ( ( P2 @ X3 )
% 0.26/0.61 => ( Q2 @ X3 ) )
% 0.26/0.61 => ( ord_less_eq_set_val @ ( collect_val @ P2 ) @ ( collect_val @ Q2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Collect_mono
% 0.26/0.61 thf(fact_246_subset__refl,axiom,
% 0.26/0.61 ! [A2: set_val] : ( ord_less_eq_set_val @ A2 @ A2 ) ).
% 0.26/0.61
% 0.26/0.61 % subset_refl
% 0.26/0.61 thf(fact_247_subset__iff,axiom,
% 0.26/0.61 ( ord_less_eq_set_node
% 0.26/0.61 = ( ^ [A5: set_node,B4: set_node] :
% 0.26/0.61 ! [T2: node] :
% 0.26/0.61 ( ( member_node @ T2 @ A5 )
% 0.26/0.61 => ( member_node @ T2 @ B4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % subset_iff
% 0.26/0.61 thf(fact_248_subset__iff,axiom,
% 0.26/0.61 ( ord_le1742111550et_val
% 0.26/0.61 = ( ^ [A5: set_set_val,B4: set_set_val] :
% 0.26/0.61 ! [T2: set_val] :
% 0.26/0.61 ( ( member_set_val @ T2 @ A5 )
% 0.26/0.61 => ( member_set_val @ T2 @ B4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % subset_iff
% 0.26/0.61 thf(fact_249_subset__iff,axiom,
% 0.26/0.61 ( ord_le1643692676de_val
% 0.26/0.61 = ( ^ [A5: set_Pr699757092de_val,B4: set_Pr699757092de_val] :
% 0.26/0.61 ! [T2: produc1432036078de_val] :
% 0.26/0.61 ( ( member313544709de_val @ T2 @ A5 )
% 0.26/0.61 => ( member313544709de_val @ T2 @ B4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % subset_iff
% 0.26/0.61 thf(fact_250_subset__iff,axiom,
% 0.26/0.61 ( ord_le299366439et_val
% 0.26/0.61 = ( ^ [A5: set_Pr1311924359et_val,B4: set_Pr1311924359et_val] :
% 0.26/0.61 ! [T2: produc1324971431et_val] :
% 0.26/0.61 ( ( member1711426256et_val @ T2 @ A5 )
% 0.26/0.61 => ( member1711426256et_val @ T2 @ B4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % subset_iff
% 0.26/0.61 thf(fact_251_subset__iff,axiom,
% 0.26/0.61 ( ord_less_eq_set_val
% 0.26/0.61 = ( ^ [A5: set_val,B4: set_val] :
% 0.26/0.61 ! [T2: val] :
% 0.26/0.61 ( ( member_val @ T2 @ A5 )
% 0.26/0.61 => ( member_val @ T2 @ B4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % subset_iff
% 0.26/0.61 thf(fact_252_equalityD2,axiom,
% 0.26/0.61 ! [A2: set_val,B2: set_val] :
% 0.26/0.61 ( ( A2 = B2 )
% 0.26/0.61 => ( ord_less_eq_set_val @ B2 @ A2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % equalityD2
% 0.26/0.61 thf(fact_253_equalityD1,axiom,
% 0.26/0.61 ! [A2: set_val,B2: set_val] :
% 0.26/0.61 ( ( A2 = B2 )
% 0.26/0.61 => ( ord_less_eq_set_val @ A2 @ B2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % equalityD1
% 0.26/0.61 thf(fact_254_subset__eq,axiom,
% 0.26/0.61 ( ord_less_eq_set_node
% 0.26/0.61 = ( ^ [A5: set_node,B4: set_node] :
% 0.26/0.61 ! [X: node] :
% 0.26/0.61 ( ( member_node @ X @ A5 )
% 0.26/0.61 => ( member_node @ X @ B4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % subset_eq
% 0.26/0.61 thf(fact_255_subset__eq,axiom,
% 0.26/0.61 ( ord_le1742111550et_val
% 0.26/0.61 = ( ^ [A5: set_set_val,B4: set_set_val] :
% 0.26/0.61 ! [X: set_val] :
% 0.26/0.61 ( ( member_set_val @ X @ A5 )
% 0.26/0.61 => ( member_set_val @ X @ B4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % subset_eq
% 0.26/0.61 thf(fact_256_subset__eq,axiom,
% 0.26/0.61 ( ord_le1643692676de_val
% 0.26/0.61 = ( ^ [A5: set_Pr699757092de_val,B4: set_Pr699757092de_val] :
% 0.26/0.61 ! [X: produc1432036078de_val] :
% 0.26/0.61 ( ( member313544709de_val @ X @ A5 )
% 0.26/0.61 => ( member313544709de_val @ X @ B4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % subset_eq
% 0.26/0.61 thf(fact_257_subset__eq,axiom,
% 0.26/0.61 ( ord_le299366439et_val
% 0.26/0.61 = ( ^ [A5: set_Pr1311924359et_val,B4: set_Pr1311924359et_val] :
% 0.26/0.61 ! [X: produc1324971431et_val] :
% 0.26/0.61 ( ( member1711426256et_val @ X @ A5 )
% 0.26/0.61 => ( member1711426256et_val @ X @ B4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % subset_eq
% 0.26/0.61 thf(fact_258_subset__eq,axiom,
% 0.26/0.61 ( ord_less_eq_set_val
% 0.26/0.61 = ( ^ [A5: set_val,B4: set_val] :
% 0.26/0.61 ! [X: val] :
% 0.26/0.61 ( ( member_val @ X @ A5 )
% 0.26/0.61 => ( member_val @ X @ B4 ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % subset_eq
% 0.26/0.61 thf(fact_259_equalityE,axiom,
% 0.26/0.61 ! [A2: set_val,B2: set_val] :
% 0.26/0.61 ( ( A2 = B2 )
% 0.26/0.61 => ~ ( ( ord_less_eq_set_val @ A2 @ B2 )
% 0.26/0.61 => ~ ( ord_less_eq_set_val @ B2 @ A2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % equalityE
% 0.26/0.61 thf(fact_260_subsetD,axiom,
% 0.26/0.61 ! [A2: set_node,B2: set_node,C2: node] :
% 0.26/0.61 ( ( ord_less_eq_set_node @ A2 @ B2 )
% 0.26/0.61 => ( ( member_node @ C2 @ A2 )
% 0.26/0.61 => ( member_node @ C2 @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % subsetD
% 0.26/0.61 thf(fact_261_subsetD,axiom,
% 0.26/0.61 ! [A2: set_set_val,B2: set_set_val,C2: set_val] :
% 0.26/0.61 ( ( ord_le1742111550et_val @ A2 @ B2 )
% 0.26/0.61 => ( ( member_set_val @ C2 @ A2 )
% 0.26/0.61 => ( member_set_val @ C2 @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % subsetD
% 0.26/0.61 thf(fact_262_subsetD,axiom,
% 0.26/0.61 ! [A2: set_Pr699757092de_val,B2: set_Pr699757092de_val,C2: produc1432036078de_val] :
% 0.26/0.61 ( ( ord_le1643692676de_val @ A2 @ B2 )
% 0.26/0.61 => ( ( member313544709de_val @ C2 @ A2 )
% 0.26/0.61 => ( member313544709de_val @ C2 @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % subsetD
% 0.26/0.61 thf(fact_263_subsetD,axiom,
% 0.26/0.61 ! [A2: set_Pr1311924359et_val,B2: set_Pr1311924359et_val,C2: produc1324971431et_val] :
% 0.26/0.61 ( ( ord_le299366439et_val @ A2 @ B2 )
% 0.26/0.61 => ( ( member1711426256et_val @ C2 @ A2 )
% 0.26/0.61 => ( member1711426256et_val @ C2 @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % subsetD
% 0.26/0.61 thf(fact_264_subsetD,axiom,
% 0.26/0.61 ! [A2: set_val,B2: set_val,C2: val] :
% 0.26/0.62 ( ( ord_less_eq_set_val @ A2 @ B2 )
% 0.26/0.62 => ( ( member_val @ C2 @ A2 )
% 0.26/0.62 => ( member_val @ C2 @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subsetD
% 0.26/0.62 thf(fact_265_in__mono,axiom,
% 0.26/0.62 ! [A2: set_node,B2: set_node,X2: node] :
% 0.26/0.62 ( ( ord_less_eq_set_node @ A2 @ B2 )
% 0.26/0.62 => ( ( member_node @ X2 @ A2 )
% 0.26/0.62 => ( member_node @ X2 @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % in_mono
% 0.26/0.62 thf(fact_266_in__mono,axiom,
% 0.26/0.62 ! [A2: set_set_val,B2: set_set_val,X2: set_val] :
% 0.26/0.62 ( ( ord_le1742111550et_val @ A2 @ B2 )
% 0.26/0.62 => ( ( member_set_val @ X2 @ A2 )
% 0.26/0.62 => ( member_set_val @ X2 @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % in_mono
% 0.26/0.62 thf(fact_267_in__mono,axiom,
% 0.26/0.62 ! [A2: set_Pr699757092de_val,B2: set_Pr699757092de_val,X2: produc1432036078de_val] :
% 0.26/0.62 ( ( ord_le1643692676de_val @ A2 @ B2 )
% 0.26/0.62 => ( ( member313544709de_val @ X2 @ A2 )
% 0.26/0.62 => ( member313544709de_val @ X2 @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % in_mono
% 0.26/0.62 thf(fact_268_in__mono,axiom,
% 0.26/0.62 ! [A2: set_Pr1311924359et_val,B2: set_Pr1311924359et_val,X2: produc1324971431et_val] :
% 0.26/0.62 ( ( ord_le299366439et_val @ A2 @ B2 )
% 0.26/0.62 => ( ( member1711426256et_val @ X2 @ A2 )
% 0.26/0.62 => ( member1711426256et_val @ X2 @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % in_mono
% 0.26/0.62 thf(fact_269_in__mono,axiom,
% 0.26/0.62 ! [A2: set_val,B2: set_val,X2: val] :
% 0.26/0.62 ( ( ord_less_eq_set_val @ A2 @ B2 )
% 0.26/0.62 => ( ( member_val @ X2 @ A2 )
% 0.26/0.62 => ( member_val @ X2 @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % in_mono
% 0.26/0.62 thf(fact_270_sup__left__commute,axiom,
% 0.26/0.62 ! [X2: set_val,Y3: set_val,Z: set_val] :
% 0.26/0.62 ( ( sup_sup_set_val @ X2 @ ( sup_sup_set_val @ Y3 @ Z ) )
% 0.26/0.62 = ( sup_sup_set_val @ Y3 @ ( sup_sup_set_val @ X2 @ Z ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % sup_left_commute
% 0.26/0.62 thf(fact_271_sup_Oleft__commute,axiom,
% 0.26/0.62 ! [B: set_val,A: set_val,C2: set_val] :
% 0.26/0.62 ( ( sup_sup_set_val @ B @ ( sup_sup_set_val @ A @ C2 ) )
% 0.26/0.62 = ( sup_sup_set_val @ A @ ( sup_sup_set_val @ B @ C2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % sup.left_commute
% 0.26/0.62 thf(fact_272_sup__commute,axiom,
% 0.26/0.62 ( sup_sup_set_val
% 0.26/0.62 = ( ^ [X: set_val,Y2: set_val] : ( sup_sup_set_val @ Y2 @ X ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % sup_commute
% 0.26/0.62 thf(fact_273_sup_Ocommute,axiom,
% 0.26/0.62 ( sup_sup_set_val
% 0.26/0.62 = ( ^ [A3: set_val,B5: set_val] : ( sup_sup_set_val @ B5 @ A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % sup.commute
% 0.26/0.62 thf(fact_274_sup__assoc,axiom,
% 0.26/0.62 ! [X2: set_val,Y3: set_val,Z: set_val] :
% 0.26/0.62 ( ( sup_sup_set_val @ ( sup_sup_set_val @ X2 @ Y3 ) @ Z )
% 0.26/0.62 = ( sup_sup_set_val @ X2 @ ( sup_sup_set_val @ Y3 @ Z ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % sup_assoc
% 0.26/0.62 thf(fact_275_sup_Oassoc,axiom,
% 0.26/0.62 ! [A: set_val,B: set_val,C2: set_val] :
% 0.26/0.62 ( ( sup_sup_set_val @ ( sup_sup_set_val @ A @ B ) @ C2 )
% 0.26/0.62 = ( sup_sup_set_val @ A @ ( sup_sup_set_val @ B @ C2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % sup.assoc
% 0.26/0.62 thf(fact_276_boolean__algebra__cancel_Osup2,axiom,
% 0.26/0.62 ! [B2: set_val,K: set_val,B: set_val,A: set_val] :
% 0.26/0.62 ( ( B2
% 0.26/0.62 = ( sup_sup_set_val @ K @ B ) )
% 0.26/0.62 => ( ( sup_sup_set_val @ A @ B2 )
% 0.26/0.62 = ( sup_sup_set_val @ K @ ( sup_sup_set_val @ A @ B ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % boolean_algebra_cancel.sup2
% 0.26/0.62 thf(fact_277_boolean__algebra__cancel_Osup1,axiom,
% 0.26/0.62 ! [A2: set_val,K: set_val,A: set_val,B: set_val] :
% 0.26/0.62 ( ( A2
% 0.26/0.62 = ( sup_sup_set_val @ K @ A ) )
% 0.26/0.62 => ( ( sup_sup_set_val @ A2 @ B )
% 0.26/0.62 = ( sup_sup_set_val @ K @ ( sup_sup_set_val @ A @ B ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % boolean_algebra_cancel.sup1
% 0.26/0.62 thf(fact_278_inf__sup__aci_I5_J,axiom,
% 0.26/0.62 ( sup_sup_set_val
% 0.26/0.62 = ( ^ [X: set_val,Y2: set_val] : ( sup_sup_set_val @ Y2 @ X ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % inf_sup_aci(5)
% 0.26/0.62 thf(fact_279_inf__sup__aci_I6_J,axiom,
% 0.26/0.62 ! [X2: set_val,Y3: set_val,Z: set_val] :
% 0.26/0.62 ( ( sup_sup_set_val @ ( sup_sup_set_val @ X2 @ Y3 ) @ Z )
% 0.26/0.62 = ( sup_sup_set_val @ X2 @ ( sup_sup_set_val @ Y3 @ Z ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % inf_sup_aci(6)
% 0.26/0.62 thf(fact_280_inf__sup__aci_I7_J,axiom,
% 0.26/0.62 ! [X2: set_val,Y3: set_val,Z: set_val] :
% 0.26/0.62 ( ( sup_sup_set_val @ X2 @ ( sup_sup_set_val @ Y3 @ Z ) )
% 0.26/0.62 = ( sup_sup_set_val @ Y3 @ ( sup_sup_set_val @ X2 @ Z ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % inf_sup_aci(7)
% 0.26/0.62 thf(fact_281_inf__sup__aci_I8_J,axiom,
% 0.26/0.62 ! [X2: set_val,Y3: set_val] :
% 0.26/0.62 ( ( sup_sup_set_val @ X2 @ ( sup_sup_set_val @ X2 @ Y3 ) )
% 0.26/0.62 = ( sup_sup_set_val @ X2 @ Y3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % inf_sup_aci(8)
% 0.26/0.62 thf(fact_282_Un__left__commute,axiom,
% 0.26/0.62 ! [A2: set_val,B2: set_val,C: set_val] :
% 0.26/0.62 ( ( sup_sup_set_val @ A2 @ ( sup_sup_set_val @ B2 @ C ) )
% 0.26/0.62 = ( sup_sup_set_val @ B2 @ ( sup_sup_set_val @ A2 @ C ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Un_left_commute
% 0.26/0.62 thf(fact_283_Un__left__absorb,axiom,
% 0.26/0.62 ! [A2: set_val,B2: set_val] :
% 0.26/0.62 ( ( sup_sup_set_val @ A2 @ ( sup_sup_set_val @ A2 @ B2 ) )
% 0.26/0.62 = ( sup_sup_set_val @ A2 @ B2 ) ) ).
% 0.26/0.62
% 0.26/0.62 % Un_left_absorb
% 0.26/0.62 thf(fact_284_Un__commute,axiom,
% 0.26/0.62 ( sup_sup_set_val
% 0.26/0.62 = ( ^ [A5: set_val,B4: set_val] : ( sup_sup_set_val @ B4 @ A5 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Un_commute
% 0.26/0.62 thf(fact_285_Un__absorb,axiom,
% 0.26/0.62 ! [A2: set_val] :
% 0.26/0.62 ( ( sup_sup_set_val @ A2 @ A2 )
% 0.26/0.62 = A2 ) ).
% 0.26/0.62
% 0.26/0.62 % Un_absorb
% 0.26/0.62 thf(fact_286_Un__assoc,axiom,
% 0.26/0.62 ! [A2: set_val,B2: set_val,C: set_val] :
% 0.26/0.62 ( ( sup_sup_set_val @ ( sup_sup_set_val @ A2 @ B2 ) @ C )
% 0.26/0.62 = ( sup_sup_set_val @ A2 @ ( sup_sup_set_val @ B2 @ C ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Un_assoc
% 0.26/0.62 thf(fact_287_ball__Un,axiom,
% 0.26/0.62 ! [A2: set_val,B2: set_val,P2: val > $o] :
% 0.26/0.62 ( ( ! [X: val] :
% 0.26/0.62 ( ( member_val @ X @ ( sup_sup_set_val @ A2 @ B2 ) )
% 0.26/0.62 => ( P2 @ X ) ) )
% 0.26/0.62 = ( ! [X: val] :
% 0.26/0.62 ( ( member_val @ X @ A2 )
% 0.26/0.62 => ( P2 @ X ) )
% 0.26/0.62 & ! [X: val] :
% 0.26/0.62 ( ( member_val @ X @ B2 )
% 0.26/0.62 => ( P2 @ X ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % ball_Un
% 0.26/0.62 thf(fact_288_bex__Un,axiom,
% 0.26/0.62 ! [A2: set_val,B2: set_val,P2: val > $o] :
% 0.26/0.62 ( ( ? [X: val] :
% 0.26/0.62 ( ( member_val @ X @ ( sup_sup_set_val @ A2 @ B2 ) )
% 0.26/0.62 & ( P2 @ X ) ) )
% 0.26/0.62 = ( ? [X: val] :
% 0.26/0.62 ( ( member_val @ X @ A2 )
% 0.26/0.62 & ( P2 @ X ) )
% 0.26/0.62 | ? [X: val] :
% 0.26/0.62 ( ( member_val @ X @ B2 )
% 0.26/0.62 & ( P2 @ X ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % bex_Un
% 0.26/0.62 thf(fact_289_UnI2,axiom,
% 0.26/0.62 ! [C2: node,B2: set_node,A2: set_node] :
% 0.26/0.62 ( ( member_node @ C2 @ B2 )
% 0.26/0.62 => ( member_node @ C2 @ ( sup_sup_set_node @ A2 @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % UnI2
% 0.26/0.62 thf(fact_290_UnI2,axiom,
% 0.26/0.62 ! [C2: set_val,B2: set_set_val,A2: set_set_val] :
% 0.26/0.62 ( ( member_set_val @ C2 @ B2 )
% 0.26/0.62 => ( member_set_val @ C2 @ ( sup_sup_set_set_val @ A2 @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % UnI2
% 0.26/0.62 thf(fact_291_UnI2,axiom,
% 0.26/0.62 ! [C2: produc1432036078de_val,B2: set_Pr699757092de_val,A2: set_Pr699757092de_val] :
% 0.26/0.62 ( ( member313544709de_val @ C2 @ B2 )
% 0.26/0.62 => ( member313544709de_val @ C2 @ ( sup_su2138939728de_val @ A2 @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % UnI2
% 0.26/0.62 thf(fact_292_UnI2,axiom,
% 0.26/0.62 ! [C2: produc1324971431et_val,B2: set_Pr1311924359et_val,A2: set_Pr1311924359et_val] :
% 0.26/0.62 ( ( member1711426256et_val @ C2 @ B2 )
% 0.26/0.62 => ( member1711426256et_val @ C2 @ ( sup_su2005730907et_val @ A2 @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % UnI2
% 0.26/0.62 thf(fact_293_UnI2,axiom,
% 0.26/0.62 ! [C2: val,B2: set_val,A2: set_val] :
% 0.26/0.62 ( ( member_val @ C2 @ B2 )
% 0.26/0.62 => ( member_val @ C2 @ ( sup_sup_set_val @ A2 @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % UnI2
% 0.26/0.62 thf(fact_294_UnI1,axiom,
% 0.26/0.62 ! [C2: node,A2: set_node,B2: set_node] :
% 0.26/0.62 ( ( member_node @ C2 @ A2 )
% 0.26/0.62 => ( member_node @ C2 @ ( sup_sup_set_node @ A2 @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % UnI1
% 0.26/0.62 thf(fact_295_UnI1,axiom,
% 0.26/0.62 ! [C2: set_val,A2: set_set_val,B2: set_set_val] :
% 0.26/0.62 ( ( member_set_val @ C2 @ A2 )
% 0.26/0.62 => ( member_set_val @ C2 @ ( sup_sup_set_set_val @ A2 @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % UnI1
% 0.26/0.62 thf(fact_296_UnI1,axiom,
% 0.26/0.62 ! [C2: produc1432036078de_val,A2: set_Pr699757092de_val,B2: set_Pr699757092de_val] :
% 0.26/0.62 ( ( member313544709de_val @ C2 @ A2 )
% 0.26/0.62 => ( member313544709de_val @ C2 @ ( sup_su2138939728de_val @ A2 @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % UnI1
% 0.26/0.62 thf(fact_297_UnI1,axiom,
% 0.26/0.62 ! [C2: produc1324971431et_val,A2: set_Pr1311924359et_val,B2: set_Pr1311924359et_val] :
% 0.26/0.62 ( ( member1711426256et_val @ C2 @ A2 )
% 0.26/0.62 => ( member1711426256et_val @ C2 @ ( sup_su2005730907et_val @ A2 @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % UnI1
% 0.26/0.62 thf(fact_298_UnI1,axiom,
% 0.26/0.62 ! [C2: val,A2: set_val,B2: set_val] :
% 0.26/0.62 ( ( member_val @ C2 @ A2 )
% 0.26/0.62 => ( member_val @ C2 @ ( sup_sup_set_val @ A2 @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % UnI1
% 0.26/0.62 thf(fact_299_UnE,axiom,
% 0.26/0.62 ! [C2: node,A2: set_node,B2: set_node] :
% 0.26/0.62 ( ( member_node @ C2 @ ( sup_sup_set_node @ A2 @ B2 ) )
% 0.26/0.62 => ( ~ ( member_node @ C2 @ A2 )
% 0.26/0.62 => ( member_node @ C2 @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % UnE
% 0.26/0.62 thf(fact_300_UnE,axiom,
% 0.26/0.62 ! [C2: set_val,A2: set_set_val,B2: set_set_val] :
% 0.26/0.62 ( ( member_set_val @ C2 @ ( sup_sup_set_set_val @ A2 @ B2 ) )
% 0.26/0.62 => ( ~ ( member_set_val @ C2 @ A2 )
% 0.26/0.62 => ( member_set_val @ C2 @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % UnE
% 0.26/0.62 thf(fact_301_UnE,axiom,
% 0.26/0.62 ! [C2: produc1432036078de_val,A2: set_Pr699757092de_val,B2: set_Pr699757092de_val] :
% 0.26/0.62 ( ( member313544709de_val @ C2 @ ( sup_su2138939728de_val @ A2 @ B2 ) )
% 0.26/0.62 => ( ~ ( member313544709de_val @ C2 @ A2 )
% 0.26/0.62 => ( member313544709de_val @ C2 @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % UnE
% 0.26/0.62 thf(fact_302_UnE,axiom,
% 0.26/0.62 ! [C2: produc1324971431et_val,A2: set_Pr1311924359et_val,B2: set_Pr1311924359et_val] :
% 0.26/0.62 ( ( member1711426256et_val @ C2 @ ( sup_su2005730907et_val @ A2 @ B2 ) )
% 0.26/0.62 => ( ~ ( member1711426256et_val @ C2 @ A2 )
% 0.26/0.62 => ( member1711426256et_val @ C2 @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % UnE
% 0.26/0.62 thf(fact_303_UnE,axiom,
% 0.26/0.62 ! [C2: val,A2: set_val,B2: set_val] :
% 0.26/0.62 ( ( member_val @ C2 @ ( sup_sup_set_val @ A2 @ B2 ) )
% 0.26/0.62 => ( ~ ( member_val @ C2 @ A2 )
% 0.26/0.62 => ( member_val @ C2 @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % UnE
% 0.26/0.62 thf(fact_304_sup_OcoboundedI2,axiom,
% 0.26/0.62 ! [C2: set_val,B: set_val,A: set_val] :
% 0.26/0.62 ( ( ord_less_eq_set_val @ C2 @ B )
% 0.26/0.62 => ( ord_less_eq_set_val @ C2 @ ( sup_sup_set_val @ A @ B ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % sup.coboundedI2
% 0.26/0.62 thf(fact_305_sup_OcoboundedI1,axiom,
% 0.26/0.62 ! [C2: set_val,A: set_val,B: set_val] :
% 0.26/0.62 ( ( ord_less_eq_set_val @ C2 @ A )
% 0.26/0.62 => ( ord_less_eq_set_val @ C2 @ ( sup_sup_set_val @ A @ B ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % sup.coboundedI1
% 0.26/0.62 thf(fact_306_sup_Oabsorb__iff2,axiom,
% 0.26/0.62 ( ord_less_eq_set_val
% 0.26/0.62 = ( ^ [A3: set_val,B5: set_val] :
% 0.26/0.62 ( ( sup_sup_set_val @ A3 @ B5 )
% 0.26/0.62 = B5 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % sup.absorb_iff2
% 0.26/0.62 thf(fact_307_sup_Oabsorb__iff1,axiom,
% 0.26/0.62 ( ord_less_eq_set_val
% 0.26/0.62 = ( ^ [B5: set_val,A3: set_val] :
% 0.26/0.62 ( ( sup_sup_set_val @ A3 @ B5 )
% 0.26/0.62 = A3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % sup.absorb_iff1
% 0.26/0.62 thf(fact_308_sup_Ocobounded2,axiom,
% 0.26/0.62 ! [B: set_val,A: set_val] : ( ord_less_eq_set_val @ B @ ( sup_sup_set_val @ A @ B ) ) ).
% 0.26/0.62
% 0.26/0.62 % sup.cobounded2
% 0.26/0.62 thf(fact_309_sup_Ocobounded1,axiom,
% 0.26/0.62 ! [A: set_val,B: set_val] : ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ A @ B ) ) ).
% 0.26/0.62
% 0.26/0.62 % sup.cobounded1
% 0.26/0.62 thf(fact_310_sup_Oorder__iff,axiom,
% 0.26/0.62 ( ord_less_eq_set_val
% 0.26/0.62 = ( ^ [B5: set_val,A3: set_val] :
% 0.26/0.62 ( A3
% 0.26/0.62 = ( sup_sup_set_val @ A3 @ B5 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % sup.order_iff
% 0.26/0.62 thf(fact_311_sup_OboundedI,axiom,
% 0.26/0.62 ! [B: set_val,A: set_val,C2: set_val] :
% 0.26/0.62 ( ( ord_less_eq_set_val @ B @ A )
% 0.26/0.62 => ( ( ord_less_eq_set_val @ C2 @ A )
% 0.26/0.62 => ( ord_less_eq_set_val @ ( sup_sup_set_val @ B @ C2 ) @ A ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % sup.boundedI
% 0.26/0.62 thf(fact_312_sup_OboundedE,axiom,
% 0.26/0.62 ! [B: set_val,C2: set_val,A: set_val] :
% 0.26/0.62 ( ( ord_less_eq_set_val @ ( sup_sup_set_val @ B @ C2 ) @ A )
% 0.26/0.62 => ~ ( ( ord_less_eq_set_val @ B @ A )
% 0.26/0.62 => ~ ( ord_less_eq_set_val @ C2 @ A ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % sup.boundedE
% 0.26/0.62 thf(fact_313_sup__absorb2,axiom,
% 0.26/0.62 ! [X2: set_val,Y3: set_val] :
% 0.26/0.62 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.26/0.62 => ( ( sup_sup_set_val @ X2 @ Y3 )
% 0.26/0.62 = Y3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % sup_absorb2
% 0.26/0.62 thf(fact_314_sup__absorb1,axiom,
% 0.26/0.62 ! [Y3: set_val,X2: set_val] :
% 0.26/0.62 ( ( ord_less_eq_set_val @ Y3 @ X2 )
% 0.26/0.62 => ( ( sup_sup_set_val @ X2 @ Y3 )
% 0.26/0.62 = X2 ) ) ).
% 0.26/0.62
% 0.26/0.62 % sup_absorb1
% 0.26/0.62 thf(fact_315_sup_Oabsorb2,axiom,
% 0.26/0.62 ! [A: set_val,B: set_val] :
% 0.26/0.62 ( ( ord_less_eq_set_val @ A @ B )
% 0.26/0.62 => ( ( sup_sup_set_val @ A @ B )
% 0.26/0.62 = B ) ) ).
% 0.26/0.62
% 0.26/0.62 % sup.absorb2
% 0.26/0.62 thf(fact_316_sup_Oabsorb1,axiom,
% 0.26/0.62 ! [B: set_val,A: set_val] :
% 0.26/0.62 ( ( ord_less_eq_set_val @ B @ A )
% 0.26/0.62 => ( ( sup_sup_set_val @ A @ B )
% 0.26/0.62 = A ) ) ).
% 0.26/0.62
% 0.26/0.62 % sup.absorb1
% 0.26/0.62 thf(fact_317_sup__unique,axiom,
% 0.26/0.62 ! [F2: set_val > set_val > set_val,X2: set_val,Y3: set_val] :
% 0.26/0.62 ( ! [X3: set_val,Y5: set_val] : ( ord_less_eq_set_val @ X3 @ ( F2 @ X3 @ Y5 ) )
% 0.26/0.62 => ( ! [X3: set_val,Y5: set_val] : ( ord_less_eq_set_val @ Y5 @ ( F2 @ X3 @ Y5 ) )
% 0.26/0.62 => ( ! [X3: set_val,Y5: set_val,Z3: set_val] :
% 0.26/0.62 ( ( ord_less_eq_set_val @ Y5 @ X3 )
% 0.26/0.62 => ( ( ord_less_eq_set_val @ Z3 @ X3 )
% 0.26/0.62 => ( ord_less_eq_set_val @ ( F2 @ Y5 @ Z3 ) @ X3 ) ) )
% 0.26/0.62 => ( ( sup_sup_set_val @ X2 @ Y3 )
% 0.26/0.62 = ( F2 @ X2 @ Y3 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % sup_unique
% 0.26/0.62 thf(fact_318_sup_OorderI,axiom,
% 0.26/0.62 ! [A: set_val,B: set_val] :
% 0.26/0.62 ( ( A
% 0.26/0.62 = ( sup_sup_set_val @ A @ B ) )
% 0.26/0.62 => ( ord_less_eq_set_val @ B @ A ) ) ).
% 0.26/0.62
% 0.26/0.62 % sup.orderI
% 0.26/0.62 thf(fact_319_sup_OorderE,axiom,
% 0.26/0.62 ! [B: set_val,A: set_val] :
% 0.26/0.62 ( ( ord_less_eq_set_val @ B @ A )
% 0.26/0.62 => ( A
% 0.26/0.62 = ( sup_sup_set_val @ A @ B ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % sup.orderE
% 0.26/0.62 thf(fact_320_le__iff__sup,axiom,
% 0.26/0.62 ( ord_less_eq_set_val
% 0.26/0.62 = ( ^ [X: set_val,Y2: set_val] :
% 0.26/0.62 ( ( sup_sup_set_val @ X @ Y2 )
% 0.26/0.62 = Y2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % le_iff_sup
% 0.26/0.62 thf(fact_321_sup__least,axiom,
% 0.26/0.62 ! [Y3: set_val,X2: set_val,Z: set_val] :
% 0.26/0.62 ( ( ord_less_eq_set_val @ Y3 @ X2 )
% 0.26/0.62 => ( ( ord_less_eq_set_val @ Z @ X2 )
% 0.26/0.62 => ( ord_less_eq_set_val @ ( sup_sup_set_val @ Y3 @ Z ) @ X2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % sup_least
% 0.26/0.62 thf(fact_322_sup__mono,axiom,
% 0.26/0.62 ! [A: set_val,C2: set_val,B: set_val,D: set_val] :
% 0.26/0.62 ( ( ord_less_eq_set_val @ A @ C2 )
% 0.26/0.62 => ( ( ord_less_eq_set_val @ B @ D )
% 0.26/0.62 => ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ B ) @ ( sup_sup_set_val @ C2 @ D ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % sup_mono
% 0.26/0.62 thf(fact_323_sup_Omono,axiom,
% 0.26/0.62 ! [C2: set_val,A: set_val,D: set_val,B: set_val] :
% 0.26/0.62 ( ( ord_less_eq_set_val @ C2 @ A )
% 0.26/0.62 => ( ( ord_less_eq_set_val @ D @ B )
% 0.26/0.62 => ( ord_less_eq_set_val @ ( sup_sup_set_val @ C2 @ D ) @ ( sup_sup_set_val @ A @ B ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % sup.mono
% 0.26/0.62 thf(fact_324_le__supI2,axiom,
% 0.26/0.62 ! [X2: set_val,B: set_val,A: set_val] :
% 0.26/0.62 ( ( ord_less_eq_set_val @ X2 @ B )
% 0.26/0.62 => ( ord_less_eq_set_val @ X2 @ ( sup_sup_set_val @ A @ B ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % le_supI2
% 0.26/0.62 thf(fact_325_le__supI1,axiom,
% 0.26/0.62 ! [X2: set_val,A: set_val,B: set_val] :
% 0.26/0.62 ( ( ord_less_eq_set_val @ X2 @ A )
% 0.26/0.62 => ( ord_less_eq_set_val @ X2 @ ( sup_sup_set_val @ A @ B ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % le_supI1
% 0.26/0.62 thf(fact_326_sup__ge2,axiom,
% 0.26/0.62 ! [Y3: set_val,X2: set_val] : ( ord_less_eq_set_val @ Y3 @ ( sup_sup_set_val @ X2 @ Y3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % sup_ge2
% 0.26/0.62 thf(fact_327_sup__ge1,axiom,
% 0.26/0.62 ! [X2: set_val,Y3: set_val] : ( ord_less_eq_set_val @ X2 @ ( sup_sup_set_val @ X2 @ Y3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % sup_ge1
% 0.26/0.62 thf(fact_328_le__supI,axiom,
% 0.26/0.62 ! [A: set_val,X2: set_val,B: set_val] :
% 0.26/0.62 ( ( ord_less_eq_set_val @ A @ X2 )
% 0.26/0.62 => ( ( ord_less_eq_set_val @ B @ X2 )
% 0.26/0.62 => ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ B ) @ X2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % le_supI
% 0.26/0.62 thf(fact_329_le__supE,axiom,
% 0.26/0.62 ! [A: set_val,B: set_val,X2: set_val] :
% 0.26/0.62 ( ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ B ) @ X2 )
% 0.26/0.62 => ~ ( ( ord_less_eq_set_val @ A @ X2 )
% 0.26/0.62 => ~ ( ord_less_eq_set_val @ B @ X2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % le_supE
% 0.26/0.62 thf(fact_330_inf__sup__ord_I3_J,axiom,
% 0.26/0.62 ! [X2: set_val,Y3: set_val] : ( ord_less_eq_set_val @ X2 @ ( sup_sup_set_val @ X2 @ Y3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % inf_sup_ord(3)
% 0.26/0.62 thf(fact_331_inf__sup__ord_I4_J,axiom,
% 0.26/0.62 ! [Y3: set_val,X2: set_val] : ( ord_less_eq_set_val @ Y3 @ ( sup_sup_set_val @ X2 @ Y3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % inf_sup_ord(4)
% 0.26/0.62 thf(fact_332_subset__Un__eq,axiom,
% 0.26/0.62 ( ord_less_eq_set_val
% 0.26/0.62 = ( ^ [A5: set_val,B4: set_val] :
% 0.26/0.62 ( ( sup_sup_set_val @ A5 @ B4 )
% 0.26/0.62 = B4 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_Un_eq
% 0.26/0.62 thf(fact_333_subset__UnE,axiom,
% 0.26/0.62 ! [C: set_val,A2: set_val,B2: set_val] :
% 0.26/0.62 ( ( ord_less_eq_set_val @ C @ ( sup_sup_set_val @ A2 @ B2 ) )
% 0.26/0.62 => ~ ! [A6: set_val] :
% 0.26/0.62 ( ( ord_less_eq_set_val @ A6 @ A2 )
% 0.26/0.62 => ! [B6: set_val] :
% 0.26/0.62 ( ( ord_less_eq_set_val @ B6 @ B2 )
% 0.26/0.62 => ( C
% 0.26/0.62 != ( sup_sup_set_val @ A6 @ B6 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_UnE
% 0.26/0.62 thf(fact_334_Un__absorb2,axiom,
% 0.26/0.62 ! [B2: set_val,A2: set_val] :
% 0.26/0.62 ( ( ord_less_eq_set_val @ B2 @ A2 )
% 0.26/0.62 => ( ( sup_sup_set_val @ A2 @ B2 )
% 0.26/0.62 = A2 ) ) ).
% 0.26/0.62
% 0.26/0.62 % Un_absorb2
% 0.26/0.62 thf(fact_335_Un__absorb1,axiom,
% 0.26/0.62 ! [A2: set_val,B2: set_val] :
% 0.26/0.62 ( ( ord_less_eq_set_val @ A2 @ B2 )
% 0.26/0.62 => ( ( sup_sup_set_val @ A2 @ B2 )
% 0.26/0.62 = B2 ) ) ).
% 0.26/0.62
% 0.26/0.62 % Un_absorb1
% 0.26/0.62 thf(fact_336_Un__upper2,axiom,
% 0.26/0.62 ! [B2: set_val,A2: set_val] : ( ord_less_eq_set_val @ B2 @ ( sup_sup_set_val @ A2 @ B2 ) ) ).
% 0.26/0.62
% 0.26/0.62 % Un_upper2
% 0.26/0.62 thf(fact_337_Un__upper1,axiom,
% 0.26/0.62 ! [A2: set_val,B2: set_val] : ( ord_less_eq_set_val @ A2 @ ( sup_sup_set_val @ A2 @ B2 ) ) ).
% 0.26/0.62
% 0.26/0.62 % Un_upper1
% 0.26/0.62 thf(fact_338_Un__least,axiom,
% 0.26/0.62 ! [A2: set_val,C: set_val,B2: set_val] :
% 0.26/0.62 ( ( ord_less_eq_set_val @ A2 @ C )
% 0.26/0.62 => ( ( ord_less_eq_set_val @ B2 @ C )
% 0.26/0.62 => ( ord_less_eq_set_val @ ( sup_sup_set_val @ A2 @ B2 ) @ C ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Un_least
% 0.26/0.62 thf(fact_339_Un__mono,axiom,
% 0.26/0.62 ! [A2: set_val,C: set_val,B2: set_val,D2: set_val] :
% 0.26/0.62 ( ( ord_less_eq_set_val @ A2 @ C )
% 0.26/0.62 => ( ( ord_less_eq_set_val @ B2 @ D2 )
% 0.26/0.62 => ( ord_less_eq_set_val @ ( sup_sup_set_val @ A2 @ B2 ) @ ( sup_sup_set_val @ C @ D2 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Un_mono
% 0.26/0.62 thf(fact_340_redundant__set__def,axiom,
% 0.26/0.62 ! [G: g,P2: set_val] :
% 0.26/0.62 ( ( irredu224829488eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G @ P2 )
% 0.26/0.62 = ( ( P2 != bot_bot_set_val )
% 0.26/0.62 & ( ord_less_eq_set_val @ P2 @ ( dom_val_list_val @ ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G ) ) )
% 0.26/0.62 & ? [X: val] :
% 0.26/0.62 ( ( member_val @ X @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.26/0.62 & ! [Y2: val] :
% 0.26/0.62 ( ( member_val @ Y2 @ P2 )
% 0.26/0.62 => ! [Phi3: val] :
% 0.26/0.62 ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ Y2 @ Phi3 )
% 0.26/0.62 => ( member_val @ Phi3 @ ( sup_sup_set_val @ P2 @ ( insert_val @ X @ bot_bot_set_val ) ) ) ) ) ) ) ) ).
% 0.26/0.70
% 0.26/0.70 % redundant_set_def
% 0.26/0.70 thf(fact_341_phi__no__closed__loop,axiom,
% 0.26/0.70 ! [P: val,G: g,Vs: list_val] :
% 0.26/0.70 ( ( member_val @ P @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.26/0.70 => ( ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ P )
% 0.26/0.70 = ( some_list_val @ Vs ) )
% 0.26/0.70 => ( ( set_val2 @ Vs )
% 0.26/0.70 != ( insert_val @ P @ bot_bot_set_val ) ) ) ) ).
% 0.26/0.70
% 0.26/0.70 % phi_no_closed_loop
% 0.26/0.70 thf(fact_342_dom__eq__empty__conv,axiom,
% 0.26/0.70 ! [F2: produc1432036078de_val > option_list_val] :
% 0.26/0.70 ( ( ( dom_Pr729677986st_val @ F2 )
% 0.26/0.70 = bot_bo404898488de_val )
% 0.26/0.70 = ( F2
% 0.26/0.70 = ( ^ [X: produc1432036078de_val] : none_list_val ) ) ) ).
% 0.26/0.70
% 0.26/0.70 % dom_eq_empty_conv
% 0.26/0.70 thf(fact_343_dom__eq__empty__conv,axiom,
% 0.26/0.70 ! [F2: val > option_list_val] :
% 0.26/0.70 ( ( ( dom_val_list_val @ F2 )
% 0.26/0.70 = bot_bot_set_val )
% 0.26/0.70 = ( F2
% 0.26/0.70 = ( ^ [X: val] : none_list_val ) ) ) ).
% 0.26/0.70
% 0.26/0.70 % dom_eq_empty_conv
% 0.26/0.70 thf(fact_344_phis__finite,axiom,
% 0.26/0.70 ! [G: g] : ( finite2056463621de_val @ ( dom_Pr729677986st_val @ ( phis @ G ) ) ) ).
% 0.26/0.70
% 0.26/0.70 % phis_finite
% 0.26/0.70 thf(fact_345_insert__subset,axiom,
% 0.26/0.70 ! [X2: node,A2: set_node,B2: set_node] :
% 0.26/0.70 ( ( ord_less_eq_set_node @ ( insert_node @ X2 @ A2 ) @ B2 )
% 0.26/0.70 = ( ( member_node @ X2 @ B2 )
% 0.26/0.70 & ( ord_less_eq_set_node @ A2 @ B2 ) ) ) ).
% 0.26/0.70
% 0.26/0.70 % insert_subset
% 0.26/0.70 thf(fact_346_insert__subset,axiom,
% 0.26/0.70 ! [X2: set_val,A2: set_set_val,B2: set_set_val] :
% 0.26/0.70 ( ( ord_le1742111550et_val @ ( insert_set_val @ X2 @ A2 ) @ B2 )
% 0.26/0.70 = ( ( member_set_val @ X2 @ B2 )
% 0.26/0.70 & ( ord_le1742111550et_val @ A2 @ B2 ) ) ) ).
% 0.26/0.70
% 0.26/0.70 % insert_subset
% 0.26/0.70 thf(fact_347_insert__subset,axiom,
% 0.26/0.70 ! [X2: produc1432036078de_val,A2: set_Pr699757092de_val,B2: set_Pr699757092de_val] :
% 0.26/0.70 ( ( ord_le1643692676de_val @ ( insert869443870de_val @ X2 @ A2 ) @ B2 )
% 0.26/0.70 = ( ( member313544709de_val @ X2 @ B2 )
% 0.26/0.70 & ( ord_le1643692676de_val @ A2 @ B2 ) ) ) ).
% 0.26/0.70
% 0.26/0.70 % insert_subset
% 0.26/0.70 thf(fact_348_insert__subset,axiom,
% 0.26/0.70 ! [X2: produc1324971431et_val,A2: set_Pr1311924359et_val,B2: set_Pr1311924359et_val] :
% 0.26/0.70 ( ( ord_le299366439et_val @ ( insert1846469495et_val @ X2 @ A2 ) @ B2 )
% 0.26/0.70 = ( ( member1711426256et_val @ X2 @ B2 )
% 0.26/0.70 & ( ord_le299366439et_val @ A2 @ B2 ) ) ) ).
% 0.26/0.70
% 0.26/0.70 % insert_subset
% 0.26/0.70 thf(fact_349_insert__subset,axiom,
% 0.26/0.70 ! [X2: val,A2: set_val,B2: set_val] :
% 0.26/0.70 ( ( ord_less_eq_set_val @ ( insert_val @ X2 @ A2 ) @ B2 )
% 0.26/0.70 = ( ( member_val @ X2 @ B2 )
% 0.26/0.70 & ( ord_less_eq_set_val @ A2 @ B2 ) ) ) ).
% 0.26/0.70
% 0.26/0.70 % insert_subset
% 0.26/0.70 thf(fact_350_finite__insert,axiom,
% 0.26/0.70 ! [A: val,A2: set_val] :
% 0.26/0.70 ( ( finite_finite_val @ ( insert_val @ A @ A2 ) )
% 0.26/0.70 = ( finite_finite_val @ A2 ) ) ).
% 0.26/0.70
% 0.26/0.70 % finite_insert
% 0.26/0.70 thf(fact_351_finite__insert,axiom,
% 0.26/0.70 ! [A: produc1324971431et_val,A2: set_Pr1311924359et_val] :
% 0.26/0.70 ( ( finite79836624et_val @ ( insert1846469495et_val @ A @ A2 ) )
% 0.26/0.70 = ( finite79836624et_val @ A2 ) ) ).
% 0.26/0.70
% 0.26/0.70 % finite_insert
% 0.26/0.70 thf(fact_352_finite__insert,axiom,
% 0.26/0.70 ! [A: produc1432036078de_val,A2: set_Pr699757092de_val] :
% 0.26/0.70 ( ( finite2056463621de_val @ ( insert869443870de_val @ A @ A2 ) )
% 0.26/0.70 = ( finite2056463621de_val @ A2 ) ) ).
% 0.26/0.70
% 0.26/0.70 % finite_insert
% 0.26/0.70
% 0.26/0.70 % Conjectures (1)
% 0.26/0.70 thf(conj_0,conjecture,
% 0.26/0.70 member_val @ phi_s @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ) ).
% 0.26/0.70
% 0.26/0.70 %------------------------------------------------------------------------------
% 0.26/0.70 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.Nk0Lg9V55l/cvc5---1.0.5_28802.p...
% 0.26/0.70 (declare-sort $$unsorted 0)
% 0.26/0.70 (declare-sort tptp.list_P88441325et_val 0)
% 0.26/0.70 (declare-sort tptp.set_Pr1587248327et_val 0)
% 0.26/0.70 (declare-sort tptp.produc1904584935et_val 0)
% 0.26/0.70 (declare-sort tptp.list_P729276995de_val 0)
% 0.26/0.70 (declare-sort tptp.set_Pr819703837de_val 0)
% 0.26/0.70 (declare-sort tptp.produc452075965de_val 0)
% 0.26/0.70 (declare-sort tptp.list_P1108777338de_val 0)
% 0.26/0.70 (declare-sort tptp.list_P844977291de_val 0)
% 0.26/0.70 (declare-sort tptp.set_Pr1245322836de_val 0)
% 0.26/0.70 (declare-sort tptp.set_Pr701036849de_val 0)
% 0.26/0.70 (declare-sort tptp.list_P2089461677et_val 0)
% 0.26/0.70 (declare-sort tptp.set_Pr1311924359et_val 0)
% 0.26/0.70 (declare-sort tptp.produc1615737844de_val 0)
% 0.26/0.70 (declare-sort tptp.produc1664334075de_val 0)
% 0.26/0.70 (declare-sort tptp.list_P12184414et_val 0)
% 0.26/0.70 (declare-sort tptp.list_P1414038306l_node 0)
% 0.26/0.70 (declare-sort tptp.list_P761482893et_val 0)
% 0.26/0.70 (declare-sort tptp.list_P940784845al_val 0)
% 0.26/0.70 (declare-sort tptp.set_Pr1320419588et_val 0)
% 0.26/0.70 (declare-sort tptp.set_Pr574789832l_node 0)
% 0.26/0.70 (declare-sort tptp.set_Pr978022247et_val 0)
% 0.26/0.70 (declare-sort tptp.set_Pr1157324199al_val 0)
% 0.26/0.70 (declare-sort tptp.produc1324971431et_val 0)
% 0.26/0.70 (declare-sort tptp.list_P561207620_edgeD 0)
% 0.26/0.70 (declare-sort tptp.list_P1127016369e_node 0)
% 0.26/0.70 (declare-sort tptp.list_P1078858818l_node 0)
% 0.26/0.70 (declare-sort tptp.list_P1820443774de_val 0)
% 0.26/0.70 (declare-sort tptp.set_Pr9085835e_node 0)
% 0.26/0.70 (declare-sort tptp.list_P1811375021al_val 0)
% 0.26/0.70 (declare-sort tptp.set_Pr2105655784l_node 0)
% 0.26/0.70 (declare-sort tptp.set_Pr699757092de_val 0)
% 0.26/0.70 (declare-sort tptp.produc1062784462et_val 0)
% 0.26/0.70 (declare-sort tptp.produc1013974930l_node 0)
% 0.26/0.70 (declare-sort tptp.set_Pr700443783al_val 0)
% 0.26/0.70 (declare-sort tptp.produc1858904199et_val 0)
% 0.26/0.70 (declare-sort tptp.produc782216903al_val 0)
% 0.26/0.70 (declare-sort tptp.produc951622955e_node 0)
% 0.26/0.70 (declare-sort tptp.option_list_val 0)
% 0.26/0.70 (declare-sort tptp.produc1946948786l_node 0)
% 0.26/0.70 (declare-sort tptp.produc1432036078de_val 0)
% 0.26/0.70 (declare-sort tptp.product_prod_val_val 0)
% 0.26/0.70 (declare-sort tptp.option_set_val 0)
% 0.26/0.70 (declare-sort tptp.list_set_val 0)
% 0.26/0.70 (declare-sort tptp.set_set_val 0)
% 0.26/0.70 (declare-sort tptp.list_node 0)
% 0.26/0.70 (declare-sort tptp.list_val 0)
% 0.26/0.70 (declare-sort tptp.set_node 0)
% 0.26/0.70 (declare-sort tptp.set_val 0)
% 0.26/0.70 (declare-sort tptp.node 0)
% 0.26/0.70 (declare-sort tptp.var 0)
% 0.26/0.70 (declare-sort tptp.val 0)
% 0.26/0.70 (declare-sort tptp.g 0)
% 0.26/0.70 (declare-fun tptp.finite79836624et_val (tptp.set_Pr1311924359et_val) Bool)
% 0.26/0.70 (declare-fun tptp.finite2056463621de_val (tptp.set_Pr699757092de_val) Bool)
% 0.26/0.70 (declare-fun tptp.finite781217938de_val (tptp.set_Pr701036849de_val) Bool)
% 0.26/0.70 (declare-fun tptp.finite1581417648et_val (tptp.set_Pr978022247et_val) Bool)
% 0.26/0.70 (declare-fun tptp.finite423892681l_node (tptp.set_Pr2105655784l_node) Bool)
% 0.26/0.70 (declare-fun tptp.finite759259600al_val (tptp.set_Pr700443783al_val) Bool)
% 0.26/0.70 (declare-fun tptp.finite1265617511et_val (tptp.set_set_val) Bool)
% 0.26/0.70 (declare-fun tptp.finite_finite_node (tptp.set_node) Bool)
% 0.26/0.70 (declare-fun tptp.finite_finite_val (tptp.set_val) Bool)
% 0.26/0.70 (declare-fun tptp.graph_272749361_edgeD ((-> tptp.g tptp.node tptp.list_P561207620_edgeD) tptp.g tptp.node) tptp.list_node)
% 0.26/0.70 (declare-fun tptp.graph_1037173556_edgeD ((-> tptp.g tptp.list_node) (-> tptp.g tptp.node tptp.list_P561207620_edgeD) tptp.g tptp.node) tptp.list_node)
% 0.26/0.70 (declare-fun tptp.irredu893086079de_val ((-> tptp.g tptp.list_node) (-> tptp.g tptp.node tptp.set_val) (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val) tptp.g tptp.set_val) tptp.set_Pr1311924359et_val)
% 0.26/0.70 (declare-fun tptp.irredu681226810de_val ((-> tptp.g tptp.list_node) (-> tptp.g tptp.node tptp.set_val) (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val) tptp.g tptp.set_val) tptp.set_set_val)
% 0.26/0.70 (declare-fun tptp.irredu1955035135eD_val ((-> tptp.g tptp.list_node) (-> tptp.g tptp.node tptp.list_P561207620_edgeD) (-> tptp.g tptp.node tptp.set_val) (-> tptp.g tptp.node tptp.set_val) (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val) tptp.g tptp.set_val tptp.set_val) Bool)
% 0.26/0.70 (declare-fun tptp.irredu224829488eD_val ((-> tptp.g tptp.list_node) (-> tptp.g tptp.node tptp.list_P561207620_edgeD) (-> tptp.g tptp.node tptp.set_val) (-> tptp.g tptp.node tptp.set_val) (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val) tptp.g tptp.set_val) Bool)
% 0.26/0.70 (declare-fun tptp.sup_su1487070040et_val (tptp.option_set_val tptp.option_set_val) tptp.option_set_val)
% 0.26/0.70 (declare-fun tptp.sup_su2005730907et_val (tptp.set_Pr1311924359et_val tptp.set_Pr1311924359et_val) tptp.set_Pr1311924359et_val)
% 0.26/0.70 (declare-fun tptp.sup_su2138939728de_val (tptp.set_Pr699757092de_val tptp.set_Pr699757092de_val) tptp.set_Pr699757092de_val)
% 0.26/0.70 (declare-fun tptp.sup_sup_set_set_val (tptp.set_set_val tptp.set_set_val) tptp.set_set_val)
% 0.26/0.70 (declare-fun tptp.sup_sup_set_node (tptp.set_node tptp.set_node) tptp.set_node)
% 0.26/0.70 (declare-fun tptp.sup_sup_set_val (tptp.set_val tptp.set_val) tptp.set_val)
% 0.26/0.70 (declare-fun tptp.set_Pr1006393724et_val (tptp.list_P88441325et_val) tptp.set_Pr1587248327et_val)
% 0.26/0.70 (declare-fun tptp.set_Pr482027474de_val (tptp.list_P729276995de_val) tptp.set_Pr819703837de_val)
% 0.26/0.70 (declare-fun tptp.set_Pr284769596et_val (tptp.list_P2089461677et_val) tptp.set_Pr1311924359et_val)
% 0.26/0.70 (declare-fun tptp.set_Pr1904955709l_node (tptp.list_P1414038306l_node) tptp.set_Pr574789832l_node)
% 0.26/0.70 (declare-fun tptp.set_Pr1027623516al_val (tptp.list_P940784845al_val) tptp.set_Pr1157324199al_val)
% 0.26/0.70 (declare-fun tptp.set_Pr1157337481de_val (tptp.list_P1108777338de_val) tptp.set_Pr1245322836de_val)
% 0.26/0.70 (declare-fun tptp.set_Pr1953765241et_val (tptp.list_P12184414et_val) tptp.set_Pr1320419588et_val)
% 0.26/0.70 (declare-fun tptp.set_Pr450990656e_node (tptp.list_P1127016369e_node) tptp.set_Pr9085835e_node)
% 0.26/0.70 (declare-fun tptp.set_Pr1085970585de_val (tptp.list_P1820443774de_val) tptp.set_Pr699757092de_val)
% 0.26/0.70 (declare-fun tptp.set_Pr434939430de_val (tptp.list_P844977291de_val) tptp.set_Pr701036849de_val)
% 0.26/0.70 (declare-fun tptp.set_Pr2104310812et_val (tptp.list_P761482893et_val) tptp.set_Pr978022247et_val)
% 0.26/0.70 (declare-fun tptp.set_Pr1600883293l_node (tptp.list_P1078858818l_node) tptp.set_Pr2105655784l_node)
% 0.26/0.70 (declare-fun tptp.set_Pr102746428al_val (tptp.list_P1811375021al_val) tptp.set_Pr700443783al_val)
% 0.26/0.70 (declare-fun tptp.set_set_val2 (tptp.list_set_val) tptp.set_set_val)
% 0.26/0.70 (declare-fun tptp.set_node2 (tptp.list_node) tptp.set_node)
% 0.26/0.70 (declare-fun tptp.set_val2 (tptp.list_val) tptp.set_val)
% 0.26/0.70 (declare-fun tptp.zip_Pr21865079et_val (tptp.list_P2089461677et_val tptp.list_P2089461677et_val) tptp.list_P88441325et_val)
% 0.26/0.70 (declare-fun tptp.zip_Pr1472086037de_val (tptp.list_P1820443774de_val tptp.list_P1820443774de_val) tptp.list_P729276995de_val)
% 0.26/0.70 (declare-fun tptp.zip_set_val_set_val (tptp.list_set_val tptp.list_set_val) tptp.list_P2089461677et_val)
% 0.26/0.70 (declare-fun tptp.zip_set_val_node (tptp.list_set_val tptp.list_node) tptp.list_P1414038306l_node)
% 0.26/0.70 (declare-fun tptp.zip_set_val_val (tptp.list_set_val tptp.list_val) tptp.list_P940784845al_val)
% 0.26/0.70 (declare-fun tptp.zip_no263301324de_val (tptp.list_node tptp.list_P1820443774de_val) tptp.list_P1108777338de_val)
% 0.26/0.70 (declare-fun tptp.zip_node_set_val (tptp.list_node tptp.list_set_val) tptp.list_P12184414et_val)
% 0.26/0.70 (declare-fun tptp.zip_node_node (tptp.list_node tptp.list_node) tptp.list_P1127016369e_node)
% 0.26/0.70 (declare-fun tptp.zip_node_val (tptp.list_node tptp.list_val) tptp.list_P1820443774de_val)
% 0.26/0.70 (declare-fun tptp.zip_va679686869de_val (tptp.list_val tptp.list_P1820443774de_val) tptp.list_P844977291de_val)
% 0.26/0.70 (declare-fun tptp.zip_val_set_val (tptp.list_val tptp.list_set_val) tptp.list_P761482893et_val)
% 0.26/0.70 (declare-fun tptp.zip_val_node (tptp.list_val tptp.list_node) tptp.list_P1078858818l_node)
% 0.26/0.70 (declare-fun tptp.zip_val_val (tptp.list_val tptp.list_val) tptp.list_P1811375021al_val)
% 0.26/0.70 (declare-fun tptp.dom_Pr729677986st_val ((-> tptp.produc1432036078de_val tptp.option_list_val)) tptp.set_Pr699757092de_val)
% 0.26/0.70 (declare-fun tptp.dom_val_list_val ((-> tptp.val tptp.option_list_val)) tptp.set_val)
% 0.26/0.70 (declare-fun tptp.none_list_val () tptp.option_list_val)
% 0.26/0.70 (declare-fun tptp.some_list_val (tptp.list_val) tptp.option_list_val)
% 0.26/0.70 (declare-fun tptp.some_set_val (tptp.set_val) tptp.option_set_val)
% 0.26/0.70 (declare-fun tptp.bot_bo2078591731et_val () tptp.set_Pr1311924359et_val)
% 0.26/0.70 (declare-fun tptp.bot_bo404898488de_val () tptp.set_Pr699757092de_val)
% 0.26/0.70 (declare-fun tptp.bot_bot_set_set_val () tptp.set_set_val)
% 0.26/0.70 (declare-fun tptp.bot_bot_set_val () tptp.set_val)
% 0.26/0.70 (declare-fun tptp.ord_le596993316et_val (tptp.option_set_val tptp.option_set_val) Bool)
% 0.26/0.70 (declare-fun tptp.ord_le299366439et_val (tptp.set_Pr1311924359et_val tptp.set_Pr1311924359et_val) Bool)
% 0.26/0.70 (declare-fun tptp.ord_le1643692676de_val (tptp.set_Pr699757092de_val tptp.set_Pr699757092de_val) Bool)
% 0.26/0.70 (declare-fun tptp.ord_le1742111550et_val (tptp.set_set_val tptp.set_set_val) Bool)
% 0.26/0.70 (declare-fun tptp.ord_less_eq_set_node (tptp.set_node tptp.set_node) Bool)
% 0.26/0.70 (declare-fun tptp.ord_less_eq_set_val (tptp.set_val tptp.set_val) Bool)
% 0.26/0.70 (declare-fun tptp.ord_less_eq_node (tptp.node tptp.node) Bool)
% 0.26/0.70 (declare-fun tptp.ord_less_eq_val (tptp.val tptp.val) Bool)
% 0.26/0.70 (declare-fun tptp.produc1377626967et_val (tptp.produc1324971431et_val tptp.produc1324971431et_val) tptp.produc1904584935et_val)
% 0.26/0.70 (declare-fun tptp.produc453318901de_val (tptp.produc1432036078de_val tptp.produc1432036078de_val) tptp.produc452075965de_val)
% 0.26/0.70 (declare-fun tptp.produc1041633943et_val (tptp.set_val tptp.set_val) tptp.produc1324971431et_val)
% 0.26/0.70 (declare-fun tptp.produc2052093836l_node (tptp.set_val tptp.node) tptp.produc1013974930l_node)
% 0.26/0.70 (declare-fun tptp.produc1337903031al_val (tptp.set_val tptp.val) tptp.produc782216903al_val)
% 0.26/0.70 (declare-fun tptp.produc1162531244de_val (tptp.node tptp.produc1432036078de_val) tptp.produc1615737844de_val)
% 0.26/0.70 (declare-fun tptp.produc2042994048et_val (tptp.node tptp.set_val) tptp.produc1062784462et_val)
% 0.26/0.70 (declare-fun tptp.produc457016035e_node (tptp.node tptp.node) tptp.produc951622955e_node)
% 0.26/0.70 (declare-fun tptp.produc1470527136de_val (tptp.node tptp.val) tptp.produc1432036078de_val)
% 0.26/0.70 (declare-fun tptp.produc1571934709de_val (tptp.val tptp.produc1432036078de_val) tptp.produc1664334075de_val)
% 0.26/0.70 (declare-fun tptp.produc1446164855et_val (tptp.val tptp.set_val) tptp.produc1858904199et_val)
% 0.26/0.70 (declare-fun tptp.produc1074923692l_node (tptp.val tptp.node) tptp.produc1946948786l_node)
% 0.26/0.70 (declare-fun tptp.product_Pair_val_val (tptp.val tptp.val) tptp.product_prod_val_val)
% 0.26/0.70 (declare-fun tptp.sSA_CF139593942de_val ((-> tptp.g tptp.node tptp.set_val) (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val) tptp.g tptp.node) tptp.set_val)
% 0.26/0.70 (declare-fun tptp.sSA_CF178745443eD_val ((-> tptp.g tptp.list_node) (-> tptp.g tptp.node tptp.list_P561207620_edgeD) (-> tptp.g tptp.node tptp.set_val) (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val) tptp.g tptp.node) tptp.set_val)
% 0.26/0.70 (declare-fun tptp.sSA_CF1517915011eD_val ((-> tptp.g tptp.list_node) (-> tptp.g tptp.node tptp.list_P561207620_edgeD) (-> tptp.g tptp.node tptp.set_val) (-> tptp.g tptp.node tptp.set_val) (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val) tptp.g) tptp.set_val)
% 0.26/0.70 (declare-fun tptp.sSA_CF370335846de_val ((-> tptp.g tptp.produc1432036078de_val tptp.option_list_val) tptp.g tptp.node) tptp.set_val)
% 0.26/0.70 (declare-fun tptp.sSA_CF848637139eD_val ((-> tptp.g tptp.list_node) (-> tptp.g tptp.node tptp.list_P561207620_edgeD) (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val) tptp.g tptp.node) tptp.set_val)
% 0.26/0.70 (declare-fun tptp.sSA_CF551432799de_val ((-> tptp.g tptp.list_node) (-> tptp.g tptp.node tptp.set_val) (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val) tptp.g tptp.val) tptp.node)
% 0.26/0.70 (declare-fun tptp.sSA_CF1909049442de_val ((-> tptp.g tptp.list_node) (-> tptp.g tptp.node tptp.set_val) (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val) tptp.g tptp.val tptp.val) Bool)
% 0.26/0.70 (declare-fun tptp.sSA_CF794421325de_val ((-> tptp.g tptp.list_node) (-> tptp.g tptp.node tptp.set_val) (-> tptp.g tptp.node tptp.set_val) (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val) tptp.g tptp.val) Bool)
% 0.26/0.70 (declare-fun tptp.sSA_CF1252180629de_val ((-> tptp.g tptp.list_node) (-> tptp.g tptp.node tptp.set_val) (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val) tptp.g tptp.val tptp.val) Bool)
% 0.26/0.70 (declare-fun tptp.sSA_CF262257161de_val ((-> tptp.g tptp.list_node) (-> tptp.g tptp.node tptp.set_val) (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val) tptp.g tptp.val) tptp.option_list_val)
% 0.26/0.70 (declare-fun tptp.sSA_CF2074824714de_val ((-> tptp.g tptp.list_node) (-> tptp.g tptp.node tptp.set_val) (-> tptp.g tptp.node tptp.set_val) (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val) tptp.g) Bool)
% 0.26/0.70 (declare-fun tptp.sSA_CF1660885746eD_val ((-> tptp.g tptp.list_node) (-> tptp.g tptp.node tptp.list_P561207620_edgeD) (-> tptp.g tptp.node tptp.set_val) (-> tptp.g tptp.node tptp.set_val) (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val) tptp.g) Bool)
% 0.26/0.70 (declare-fun tptp.sSA_CF1899243830eD_val ((-> tptp.g tptp.list_node) (-> tptp.g tptp.node tptp.list_P561207620_edgeD) (-> tptp.g tptp.node tptp.set_val) (-> tptp.g tptp.node tptp.set_val) (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val) tptp.g tptp.val) Bool)
% 0.26/0.70 (declare-fun tptp.sSA_CF655860150de_val ((-> tptp.g tptp.list_node) (-> tptp.g tptp.node tptp.set_val) tptp.g) tptp.set_val)
% 0.26/0.70 (declare-fun tptp.collec1117167378et_val ((-> tptp.produc1324971431et_val Bool)) tptp.set_Pr1311924359et_val)
% 0.26/0.70 (declare-fun tptp.collec370342979de_val ((-> tptp.produc1432036078de_val Bool)) tptp.set_Pr699757092de_val)
% 0.26/0.70 (declare-fun tptp.collec885255687l_node ((-> tptp.produc1946948786l_node Bool)) tptp.set_Pr2105655784l_node)
% 0.26/0.70 (declare-fun tptp.collec52550418al_val ((-> tptp.product_prod_val_val Bool)) tptp.set_Pr700443783al_val)
% 0.26/0.70 (declare-fun tptp.collect_set_val ((-> tptp.set_val Bool)) tptp.set_set_val)
% 0.26/0.70 (declare-fun tptp.collect_node ((-> tptp.node Bool)) tptp.set_node)
% 0.26/0.70 (declare-fun tptp.collect_val ((-> tptp.val Bool)) tptp.set_val)
% 0.26/0.70 (declare-fun tptp.insert1846469495et_val (tptp.produc1324971431et_val tptp.set_Pr1311924359et_val) tptp.set_Pr1311924359et_val)
% 0.26/0.70 (declare-fun tptp.insert869443870de_val (tptp.produc1432036078de_val tptp.set_Pr699757092de_val) tptp.set_Pr699757092de_val)
% 0.26/0.70 (declare-fun tptp.insert_set_val (tptp.set_val tptp.set_set_val) tptp.set_set_val)
% 0.26/0.70 (declare-fun tptp.insert_node (tptp.node tptp.set_node) tptp.set_node)
% 0.26/0.70 (declare-fun tptp.insert_val (tptp.val tptp.set_val) tptp.set_val)
% 0.26/0.70 (declare-fun tptp.transi1953622797et_val (tptp.set_Pr1311924359et_val) Bool)
% 0.26/0.70 (declare-fun tptp.transi1991289355lp_val ((-> tptp.val tptp.val Bool) tptp.val tptp.val) Bool)
% 0.26/0.70 (declare-fun tptp.member1254968080et_val (tptp.produc1904584935et_val tptp.set_Pr1587248327et_val) Bool)
% 0.26/0.70 (declare-fun tptp.member698732390de_val (tptp.produc452075965de_val tptp.set_Pr819703837de_val) Bool)
% 0.26/0.70 (declare-fun tptp.member1711426256et_val (tptp.produc1324971431et_val tptp.set_Pr1311924359et_val) Bool)
% 0.26/0.70 (declare-fun tptp.member76372137l_node (tptp.produc1013974930l_node tptp.set_Pr574789832l_node) Bool)
% 0.26/0.70 (declare-fun tptp.member1110026224al_val (tptp.produc782216903al_val tptp.set_Pr1157324199al_val) Bool)
% 0.26/0.70 (declare-fun tptp.member562853661de_val (tptp.produc1615737844de_val tptp.set_Pr1245322836de_val) Bool)
% 0.26/0.70 (declare-fun tptp.member125181669et_val (tptp.produc1062784462et_val tptp.set_Pr1320419588et_val) Bool)
% 0.26/0.70 (declare-fun tptp.member2110109140e_node (tptp.produc951622955e_node tptp.set_Pr9085835e_node) Bool)
% 0.26/0.70 (declare-fun tptp.member313544709de_val (tptp.produc1432036078de_val tptp.set_Pr699757092de_val) Bool)
% 0.26/0.70 (declare-fun tptp.member1894062994de_val (tptp.produc1664334075de_val tptp.set_Pr701036849de_val) Bool)
% 0.26/0.70 (declare-fun tptp.member39229872et_val (tptp.produc1858904199et_val tptp.set_Pr978022247et_val) Bool)
% 0.26/0.70 (declare-fun tptp.member828457417l_node (tptp.produc1946948786l_node tptp.set_Pr2105655784l_node) Bool)
% 0.26/0.70 (declare-fun tptp.member1680438992al_val (tptp.product_prod_val_val tptp.set_Pr700443783al_val) Bool)
% 0.26/0.70 (declare-fun tptp.member_set_val (tptp.set_val tptp.set_set_val) Bool)
% 0.26/0.70 (declare-fun tptp.member_node (tptp.node tptp.set_node) Bool)
% 0.26/0.70 (declare-fun tptp.member_val (tptp.val tptp.set_val) Bool)
% 0.26/0.70 (declare-fun tptp.alpha_n (tptp.g) tptp.list_node)
% 0.26/0.70 (declare-fun tptp.phi () tptp.val)
% 0.26/0.70 (declare-fun tptp.phi_s () tptp.val)
% 0.26/0.70 (declare-fun tptp.phi2 () tptp.val)
% 0.26/0.70 (declare-fun tptp.defs (tptp.g tptp.node) tptp.set_val)
% 0.26/0.70 (declare-fun tptp.g2 () tptp.g)
% 0.26/0.70 (declare-fun tptp.inEdges (tptp.g tptp.node) tptp.list_P561207620_edgeD)
% 0.26/0.70 (declare-fun tptp.phis (tptp.g tptp.produc1432036078de_val) tptp.option_list_val)
% 0.26/0.70 (declare-fun tptp.s () tptp.val)
% 0.26/0.70 (declare-fun tptp.uses (tptp.g tptp.node) tptp.set_val)
% 0.26/0.70 (declare-fun tptp.var2 (tptp.g tptp.val) tptp.var)
% 0.26/0.70 (assert (not (= tptp.phi_s tptp.s)))
% 0.26/0.70 (assert (not (= tptp.phi tptp.phi_s)))
% 0.26/0.70 (assert (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) tptp.g2) tptp.phi2) tptp.phi_s))
% 0.26/0.70 (assert (@ (@ tptp.member_val tptp.s) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) tptp.g2)))
% 0.26/0.70 (assert (@ (@ tptp.member_val tptp.phi) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) tptp.g2)))
% 0.26/0.70 (assert (not (forall ((Phi tptp.val)) (not (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) tptp.g2) Phi) tptp.phi_s)))))
% 0.26/0.70 (assert (forall ((G tptp.g) (V tptp.val) (V2 tptp.val)) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) V2) (@ (@ tptp.member_val V2) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)))))
% 0.26/0.70 (assert (forall ((V tptp.val) (G tptp.g) (N tptp.node)) (let ((_let_1 (@ tptp.member_val V))) (=> (@ _let_1 (@ (@ tptp.uses G) N)) (@ _let_1 (@ (@ (@ tptp.sSA_CF655860150de_val tptp.alpha_n) tptp.uses) G))))))
% 0.26/0.70 (assert (forall ((G tptp.g) (V tptp.val)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.sSA_CF1899243830eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G) V) (@ (@ tptp.member_val V) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)))))
% 0.26/0.70 (assert (forall ((G tptp.g) (V tptp.val)) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val tptp.alpha_n) tptp.defs) tptp.uses) tptp.phis) G) V) (@ (@ tptp.member_val V) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)))))
% 0.26/0.70 (assert (forall ((G tptp.g)) (@ tptp.finite_finite_val (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G))))
% 0.26/0.70 (assert (forall ((V tptp.val) (G tptp.g) (N tptp.node)) (let ((_let_1 (@ tptp.member_val V))) (=> (@ _let_1 (@ (@ tptp.uses G) N)) (@ _let_1 (@ (@ (@ (@ (@ (@ tptp.sSA_CF178745443eD_val tptp.alpha_n) tptp.inEdges) tptp.uses) tptp.phis) G) N))))))
% 0.26/0.70 (assert (forall ((G tptp.g)) (= (@ (@ (@ (@ (@ (@ tptp.sSA_CF1660885746eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G) (exists ((X tptp.val)) (and (@ (@ tptp.member_val X) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)) (@ (@ (@ (@ (@ (@ (@ tptp.sSA_CF1899243830eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G) X))))))
% 0.26/0.70 (assert (forall ((G tptp.g) (V tptp.val)) (= (@ (@ (@ (@ (@ (@ (@ tptp.sSA_CF1899243830eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G) V) (exists ((X tptp.val)) (and (@ (@ tptp.member_val X) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1909049442de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) X))))))
% 0.26/0.70 (assert (let ((_let_1 (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) tptp.g2))) (= (@ _let_1 tptp.phi_s) (@ _let_1 tptp.s))))
% 0.26/0.70 (assert (forall ((N tptp.node) (G tptp.g) (V tptp.val)) (let ((_let_1 (@ tptp.member_val V))) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (=> (@ _let_1 (@ (@ tptp.defs G) N)) (not (@ _let_1 (@ (@ tptp.uses G) N))))))))
% 0.26/0.70 (assert (forall ((G tptp.g) (V tptp.val) (V2 tptp.val)) (let ((_let_1 (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val tptp.alpha_n) tptp.defs) tptp.uses) tptp.phis) G))) (=> (@ _let_1 V) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) V2) (@ _let_1 V2))))))
% 0.26/0.70 (assert (forall ((G tptp.g) (P tptp.val) (Q tptp.val)) (let ((_let_1 (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) G))) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) G) P) Q) (=> (not (= P Q)) (=> (@ (@ tptp.member_val P) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)) (not (= (@ _let_1 P) (@ _let_1 Q)))))))))
% 0.26/0.70 (assert (forall ((G tptp.g) (P tptp.val) (Q tptp.val) (R tptp.val)) (let ((_let_1 (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) G))) (let ((_let_2 (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) G) P))) (=> (@ _let_2 Q) (=> (@ _let_2 R) (=> (not (= Q R)) (=> (@ (@ tptp.member_val P) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)) (not (= (@ _let_1 Q) (@ _let_1 R)))))))))))
% 0.26/0.70 (assert (forall ((V tptp.val) (G tptp.g) (N tptp.node)) (=> (@ (@ tptp.member_val V) (@ (@ tptp.uses G) N)) (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))))))
% 0.26/0.70 (assert (forall ((G tptp.g) (N tptp.node)) (@ tptp.finite_finite_val (@ (@ tptp.defs G) N))))
% 0.26/0.70 (assert (forall ((V tptp.val) (G tptp.g)) (=> (@ (@ tptp.member_val V) (@ (@ (@ tptp.sSA_CF655860150de_val tptp.alpha_n) tptp.uses) G)) (not (forall ((N2 tptp.node)) (=> (@ (@ tptp.member_node N2) (@ tptp.set_node2 (@ tptp.alpha_n G))) (not (@ (@ tptp.member_val V) (@ (@ tptp.uses G) N2)))))))))
% 0.26/0.70 (assert (forall ((G tptp.g)) (@ tptp.finite_finite_val (@ (@ (@ tptp.sSA_CF655860150de_val tptp.alpha_n) tptp.uses) G))))
% 0.26/0.70 (assert (forall ((N tptp.node) (G tptp.g) (Val tptp.val)) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (=> (@ (@ tptp.member_val Val) (@ (@ tptp.uses G) N)) (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val tptp.alpha_n) tptp.defs) tptp.uses) tptp.phis) G) Val)))))
% 0.26/0.70 (assert (forall ((G tptp.g) (A tptp.val)) (= (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val tptp.alpha_n) tptp.defs) tptp.uses) tptp.phis) G) A) (or (exists ((N3 tptp.node) (Val2 tptp.val)) (and (= A Val2) (@ (@ tptp.member_node N3) (@ tptp.set_node2 (@ tptp.alpha_n G))) (@ (@ tptp.member_val Val2) (@ (@ tptp.uses G) N3)))) (exists ((V3 tptp.val) (V4 tptp.val)) (and (= A V4) (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val tptp.alpha_n) tptp.defs) tptp.uses) tptp.phis) G) V3) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V3) V4)))))))
% 0.26/0.70 (assert (forall ((G tptp.g) (X2 tptp.val) (P2 (-> tptp.val Bool))) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val tptp.alpha_n) tptp.defs) tptp.uses) tptp.phis) G) X2) (=> (forall ((N2 tptp.node) (Val3 tptp.val)) (=> (@ (@ tptp.member_node N2) (@ tptp.set_node2 (@ tptp.alpha_n G))) (=> (@ (@ tptp.member_val Val3) (@ (@ tptp.uses G) N2)) (@ P2 Val3)))) (=> (forall ((V5 tptp.val) (V6 tptp.val)) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val tptp.alpha_n) tptp.defs) tptp.uses) tptp.phis) G) V5) (=> (@ P2 V5) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V5) V6) (@ P2 V6))))) (@ P2 X2))))))
% 0.26/0.70 (assert (forall ((G tptp.g) (A tptp.val)) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val tptp.alpha_n) tptp.defs) tptp.uses) tptp.phis) G) A) (=> (forall ((N2 tptp.node)) (=> (@ (@ tptp.member_node N2) (@ tptp.set_node2 (@ tptp.alpha_n G))) (not (@ (@ tptp.member_val A) (@ (@ tptp.uses G) N2))))) (not (forall ((V5 tptp.val)) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val tptp.alpha_n) tptp.defs) tptp.uses) tptp.phis) G) V5) (not (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V5) A)))))))))
% 0.26/0.70 (assert (forall ((N tptp.node) (G tptp.g)) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (@ tptp.finite_finite_val (@ (@ (@ (@ (@ (@ tptp.sSA_CF178745443eD_val tptp.alpha_n) tptp.inEdges) tptp.uses) tptp.phis) G) N)))))
% 0.26/0.70 (assert (forall ((V tptp.val) (G tptp.g)) (=> (@ (@ tptp.member_val V) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)) (@ (@ tptp.member_node (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V)) (@ tptp.set_node2 (@ tptp.alpha_n G))))))
% 0.26/0.70 (assert (forall ((G tptp.g) (N tptp.node)) (@ tptp.finite_finite_val (@ (@ tptp.uses G) N))))
% 0.26/0.70 (assert (let ((_let_1 (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) tptp.g2))) (= (@ _let_1 tptp.phi_s) (@ _let_1 tptp.s))))
% 0.26/0.70 (assert (forall ((V tptp.val) (G tptp.g) (N tptp.node)) (let ((_let_1 (@ tptp.member_val V))) (=> (@ _let_1 (@ (@ (@ (@ (@ (@ tptp.sSA_CF178745443eD_val tptp.alpha_n) tptp.inEdges) tptp.uses) tptp.phis) G) N)) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (@ _let_1 (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)))))))
% 0.26/0.70 (assert (forall ((V tptp.val) (G tptp.g) (N tptp.node)) (let ((_let_1 (@ tptp.member_val V))) (=> (@ _let_1 (@ (@ (@ (@ (@ tptp.sSA_CF848637139eD_val tptp.alpha_n) tptp.inEdges) tptp.phis) G) N)) (@ _let_1 (@ (@ (@ (@ (@ (@ tptp.sSA_CF178745443eD_val tptp.alpha_n) tptp.inEdges) tptp.uses) tptp.phis) G) N))))))
% 0.26/0.70 (assert (forall ((N tptp.node) (G tptp.g)) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (@ tptp.finite_finite_val (@ (@ (@ (@ (@ tptp.sSA_CF848637139eD_val tptp.alpha_n) tptp.inEdges) tptp.phis) G) N)))))
% 0.26/0.70 (assert (forall ((V tptp.val) (G tptp.g)) (let ((_let_1 (@ tptp.member_val V))) (=> (@ _let_1 (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)) (@ _let_1 (@ (@ (@ (@ tptp.sSA_CF139593942de_val tptp.defs) tptp.phis) G) (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V)))))))
% 0.26/0.70 (assert (forall ((V tptp.val) (G tptp.g)) (=> (@ (@ tptp.member_val V) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)) (exists ((X3 tptp.node)) (and (@ (@ tptp.member_node X3) (@ tptp.set_node2 (@ tptp.alpha_n G))) (@ (@ tptp.member_val V) (@ (@ (@ (@ tptp.sSA_CF139593942de_val tptp.defs) tptp.phis) G) X3)) (forall ((Y tptp.node)) (=> (and (@ (@ tptp.member_node Y) (@ tptp.set_node2 (@ tptp.alpha_n G))) (@ (@ tptp.member_val V) (@ (@ (@ (@ tptp.sSA_CF139593942de_val tptp.defs) tptp.phis) G) Y))) (= Y X3))))))))
% 0.26/0.70 (assert (forall ((V tptp.val) (G tptp.g)) (=> (@ (@ tptp.member_val V) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)) (exists ((X3 tptp.node)) (and (@ (@ tptp.member_node X3) (@ tptp.set_node2 (@ tptp.alpha_n G))) (@ (@ tptp.member_val V) (@ (@ (@ (@ tptp.sSA_CF139593942de_val tptp.defs) tptp.phis) G) X3)))))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_P844977291de_val)) (@ tptp.finite781217938de_val (@ tptp.set_Pr434939430de_val Xs))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_P761482893et_val)) (@ tptp.finite1581417648et_val (@ tptp.set_Pr2104310812et_val Xs))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_P1078858818l_node)) (@ tptp.finite423892681l_node (@ tptp.set_Pr1600883293l_node Xs))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_P1811375021al_val)) (@ tptp.finite759259600al_val (@ tptp.set_Pr102746428al_val Xs))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_val)) (@ tptp.finite1265617511et_val (@ tptp.set_set_val2 Xs))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_node)) (@ tptp.finite_finite_node (@ tptp.set_node2 Xs))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_val)) (@ tptp.finite_finite_val (@ tptp.set_val2 Xs))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_P2089461677et_val)) (@ tptp.finite79836624et_val (@ tptp.set_Pr284769596et_val Xs))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_P1820443774de_val)) (@ tptp.finite2056463621de_val (@ tptp.set_Pr1085970585de_val Xs))))
% 0.26/0.70 (assert (forall ((G tptp.g) (N tptp.node)) (@ tptp.finite_finite_val (@ (@ (@ tptp.sSA_CF370335846de_val tptp.phis) G) N))))
% 0.26/0.70 (assert (forall ((N tptp.node) (G tptp.g)) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (@ tptp.finite_finite_val (@ (@ (@ (@ tptp.sSA_CF139593942de_val tptp.defs) tptp.phis) G) N)))))
% 0.26/0.70 (assert (let ((_let_1 (@ tptp.var2 tptp.g2))) (= (@ _let_1 tptp.phi) (@ _let_1 tptp.s))))
% 0.26/0.70 (assert (= tptp.sSA_CF1660885746eD_val (lambda ((Alpha_n (-> tptp.g tptp.list_node)) (InEdges (-> tptp.g tptp.node tptp.list_P561207620_edgeD)) (Defs (-> tptp.g tptp.node tptp.set_val)) (Uses (-> tptp.g tptp.node tptp.set_val)) (Phis (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val)) (G2 tptp.g)) (exists ((X tptp.val)) (and (@ (@ tptp.member_val X) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val Alpha_n) InEdges) Defs) Uses) Phis) G2)) (@ (@ (@ (@ (@ (@ (@ tptp.sSA_CF1899243830eD_val Alpha_n) InEdges) Defs) Uses) Phis) G2) X))))))
% 0.26/0.70 (assert (forall ((V tptp.val) (G tptp.g) (N tptp.node)) (let ((_let_1 (@ tptp.member_val V))) (=> (@ _let_1 (@ (@ tptp.defs G) N)) (@ _let_1 (@ (@ (@ (@ tptp.sSA_CF139593942de_val tptp.defs) tptp.phis) G) N))))))
% 0.26/0.70 (assert (forall ((V tptp.val) (G tptp.g) (N tptp.node)) (let ((_let_1 (@ tptp.member_val V))) (=> (@ _let_1 (@ (@ (@ tptp.sSA_CF370335846de_val tptp.phis) G) N)) (@ _let_1 (@ (@ (@ (@ tptp.sSA_CF139593942de_val tptp.defs) tptp.phis) G) N))))))
% 0.26/0.70 (assert (forall ((N tptp.node) (G tptp.g) (M tptp.node) (V tptp.val)) (let ((_let_1 (@ (@ (@ tptp.sSA_CF139593942de_val tptp.defs) tptp.phis) G))) (let ((_let_2 (@ tptp.member_val V))) (let ((_let_3 (@ tptp.set_node2 (@ tptp.alpha_n G)))) (=> (@ (@ tptp.member_node N) _let_3) (=> (@ (@ tptp.member_node M) _let_3) (=> (@ _let_2 (@ _let_1 N)) (=> (@ _let_2 (@ _let_1 M)) (= N M))))))))))
% 0.26/0.70 (assert (forall ((A tptp.produc1946948786l_node) (P2 (-> tptp.produc1946948786l_node Bool))) (= (@ (@ tptp.member828457417l_node A) (@ tptp.collec885255687l_node P2)) (@ P2 A))))
% 0.26/0.70 (assert (forall ((A tptp.product_prod_val_val) (P2 (-> tptp.product_prod_val_val Bool))) (= (@ (@ tptp.member1680438992al_val A) (@ tptp.collec52550418al_val P2)) (@ P2 A))))
% 0.26/0.70 (assert (forall ((A tptp.val) (P2 (-> tptp.val Bool))) (= (@ (@ tptp.member_val A) (@ tptp.collect_val P2)) (@ P2 A))))
% 0.26/0.70 (assert (forall ((A tptp.node) (P2 (-> tptp.node Bool))) (= (@ (@ tptp.member_node A) (@ tptp.collect_node P2)) (@ P2 A))))
% 0.26/0.70 (assert (forall ((A tptp.set_val) (P2 (-> tptp.set_val Bool))) (= (@ (@ tptp.member_set_val A) (@ tptp.collect_set_val P2)) (@ P2 A))))
% 0.26/0.70 (assert (forall ((A tptp.produc1432036078de_val) (P2 (-> tptp.produc1432036078de_val Bool))) (= (@ (@ tptp.member313544709de_val A) (@ tptp.collec370342979de_val P2)) (@ P2 A))))
% 0.26/0.70 (assert (forall ((A tptp.produc1324971431et_val) (P2 (-> tptp.produc1324971431et_val Bool))) (= (@ (@ tptp.member1711426256et_val A) (@ tptp.collec1117167378et_val P2)) (@ P2 A))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val)) (= (@ tptp.collect_val (lambda ((X tptp.val)) (@ (@ tptp.member_val X) A2))) A2)))
% 0.26/0.70 (assert (forall ((A2 tptp.set_node)) (= (@ tptp.collect_node (lambda ((X tptp.node)) (@ (@ tptp.member_node X) A2))) A2)))
% 0.26/0.70 (assert (forall ((A2 tptp.set_set_val)) (= (@ tptp.collect_set_val (lambda ((X tptp.set_val)) (@ (@ tptp.member_set_val X) A2))) A2)))
% 0.26/0.70 (assert (forall ((A2 tptp.set_Pr699757092de_val)) (= (@ tptp.collec370342979de_val (lambda ((X tptp.produc1432036078de_val)) (@ (@ tptp.member313544709de_val X) A2))) A2)))
% 0.26/0.70 (assert (forall ((A2 tptp.set_Pr1311924359et_val)) (= (@ tptp.collec1117167378et_val (lambda ((X tptp.produc1324971431et_val)) (@ (@ tptp.member1711426256et_val X) A2))) A2)))
% 0.26/0.70 (assert (forall ((G tptp.g) (P tptp.val) (Q tptp.val)) (let ((_let_1 (@ tptp.var2 G))) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) G) P) Q) (= (@ _let_1 Q) (@ _let_1 P))))))
% 0.26/0.70 (assert (let ((_let_1 (@ tptp.var2 tptp.g2))) (= (@ _let_1 tptp.phi) (@ _let_1 tptp.phi_s))))
% 0.26/0.70 (assert (forall ((N tptp.node) (G tptp.g) (V tptp.val) (V2 tptp.val)) (let ((_let_1 (@ tptp.var2 G))) (let ((_let_2 (@ (@ (@ (@ tptp.sSA_CF139593942de_val tptp.defs) tptp.phis) G) N))) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (=> (@ (@ tptp.member_val V) _let_2) (=> (@ (@ tptp.member_val V2) _let_2) (=> (not (= V V2)) (not (= (@ _let_1 V2) (@ _let_1 V)))))))))))
% 0.26/0.70 (assert (forall ((P tptp.val) (G tptp.g) (Q tptp.val)) (let ((_let_1 (@ tptp.var2 G))) (let ((_let_2 (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) G))) (let ((_let_3 (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G))) (=> (@ (@ tptp.member_val P) _let_3) (=> (@ (@ tptp.member_val Q) _let_3) (=> (not (= P Q)) (=> (= (@ _let_2 P) (@ _let_2 Q)) (not (= (@ _let_1 P) (@ _let_1 Q))))))))))))
% 0.26/0.70 (assert (forall ((N tptp.node) (G tptp.g) (V tptp.val)) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (=> (@ (@ tptp.member_val V) (@ (@ (@ (@ tptp.sSA_CF139593942de_val tptp.defs) tptp.phis) G) N)) (= (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) N)))))
% 0.26/0.70 (assert (forall ((V tptp.val) (G tptp.g) (N tptp.node)) (let ((_let_1 (@ tptp.member_val V))) (=> (@ _let_1 (@ (@ (@ (@ tptp.sSA_CF139593942de_val tptp.defs) tptp.phis) G) N)) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (@ _let_1 (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)))))))
% 0.26/0.70 (assert (forall ((G tptp.g)) (= (@ (@ (@ (@ (@ tptp.sSA_CF2074824714de_val tptp.alpha_n) tptp.defs) tptp.uses) tptp.phis) G) (forall ((X tptp.node)) (=> (@ (@ tptp.member_node X) (@ tptp.set_node2 (@ tptp.alpha_n G))) (forall ((Val2 tptp.val)) (=> (@ (@ tptp.member_val Val2) (@ (@ (@ tptp.sSA_CF370335846de_val tptp.phis) G) X)) (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val tptp.alpha_n) tptp.defs) tptp.uses) tptp.phis) G) Val2))))))))
% 0.26/0.70 (assert (= tptp.sSA_CF848637139eD_val tptp.sSA_CF848637139eD_val))
% 0.26/0.70 (assert (= tptp.sSA_CF370335846de_val tptp.sSA_CF370335846de_val))
% 0.26/0.70 (assert (= tptp.sSA_CF139593942de_val tptp.sSA_CF139593942de_val))
% 0.26/0.70 (assert (= tptp.sSA_CF551432799de_val tptp.sSA_CF551432799de_val))
% 0.26/0.70 (assert (= tptp.sSA_CF1517915011eD_val tptp.sSA_CF1517915011eD_val))
% 0.26/0.70 (assert (= tptp.sSA_CF1252180629de_val tptp.sSA_CF1252180629de_val))
% 0.26/0.70 (assert (= tptp.sSA_CF178745443eD_val tptp.sSA_CF178745443eD_val))
% 0.26/0.70 (assert (= tptp.sSA_CF794421325de_val tptp.sSA_CF794421325de_val))
% 0.26/0.70 (assert (= tptp.sSA_CF1899243830eD_val tptp.sSA_CF1899243830eD_val))
% 0.26/0.70 (assert (= tptp.sSA_CF655860150de_val tptp.sSA_CF655860150de_val))
% 0.26/0.70 (assert (= tptp.sSA_CF1909049442de_val tptp.sSA_CF1909049442de_val))
% 0.26/0.70 (assert (= tptp.sSA_CF1660885746eD_val tptp.sSA_CF1660885746eD_val))
% 0.26/0.70 (assert (forall ((A2 tptp.set_node)) (=> (@ tptp.finite_finite_node A2) (exists ((Xs2 tptp.list_node)) (= (@ tptp.set_node2 Xs2) A2)))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val)) (=> (@ tptp.finite_finite_val A2) (exists ((Xs2 tptp.list_val)) (= (@ tptp.set_val2 Xs2) A2)))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_Pr1311924359et_val)) (=> (@ tptp.finite79836624et_val A2) (exists ((Xs2 tptp.list_P2089461677et_val)) (= (@ tptp.set_Pr284769596et_val Xs2) A2)))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_Pr699757092de_val)) (=> (@ tptp.finite2056463621de_val A2) (exists ((Xs2 tptp.list_P1820443774de_val)) (= (@ tptp.set_Pr1085970585de_val Xs2) A2)))))
% 0.26/0.70 (assert (forall ((N tptp.node) (Alpha_n2 (-> tptp.g tptp.list_node)) (G tptp.g) (Val tptp.val) (Uses2 (-> tptp.g tptp.node tptp.set_val)) (Defs2 (-> tptp.g tptp.node tptp.set_val)) (Phis2 (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val))) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ Alpha_n2 G))) (=> (@ (@ tptp.member_val Val) (@ (@ Uses2 G) N)) (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val Alpha_n2) Defs2) Uses2) Phis2) G) Val)))))
% 0.26/0.70 (assert (forall ((Alpha_n2 (-> tptp.g tptp.list_node)) (Defs2 (-> tptp.g tptp.node tptp.set_val)) (Uses2 (-> tptp.g tptp.node tptp.set_val)) (Phis2 (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val)) (G tptp.g) (V tptp.val) (V2 tptp.val)) (let ((_let_1 (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val Alpha_n2) Defs2) Uses2) Phis2) G))) (=> (@ _let_1 V) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val Alpha_n2) Defs2) Phis2) G) V) V2) (@ _let_1 V2))))))
% 0.26/0.70 (assert (forall ((Alpha_n2 (-> tptp.g tptp.list_node)) (Defs2 (-> tptp.g tptp.node tptp.set_val)) (Uses2 (-> tptp.g tptp.node tptp.set_val)) (Phis2 (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val)) (G tptp.g) (X2 tptp.val) (P2 (-> tptp.val Bool))) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val Alpha_n2) Defs2) Uses2) Phis2) G) X2) (=> (forall ((N2 tptp.node) (Val3 tptp.val)) (=> (@ (@ tptp.member_node N2) (@ tptp.set_node2 (@ Alpha_n2 G))) (=> (@ (@ tptp.member_val Val3) (@ (@ Uses2 G) N2)) (@ P2 Val3)))) (=> (forall ((V5 tptp.val) (V6 tptp.val)) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val Alpha_n2) Defs2) Uses2) Phis2) G) V5) (=> (@ P2 V5) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val Alpha_n2) Defs2) Phis2) G) V5) V6) (@ P2 V6))))) (@ P2 X2))))))
% 0.26/0.70 (assert (= tptp.sSA_CF794421325de_val (lambda ((Alpha_n (-> tptp.g tptp.list_node)) (Defs (-> tptp.g tptp.node tptp.set_val)) (Uses (-> tptp.g tptp.node tptp.set_val)) (Phis (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val)) (G2 tptp.g) (A3 tptp.val)) (or (exists ((N3 tptp.node) (Val2 tptp.val)) (and (= A3 Val2) (@ (@ tptp.member_node N3) (@ tptp.set_node2 (@ Alpha_n G2))) (@ (@ tptp.member_val Val2) (@ (@ Uses G2) N3)))) (exists ((V3 tptp.val) (V4 tptp.val)) (and (= A3 V4) (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val Alpha_n) Defs) Uses) Phis) G2) V3) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val Alpha_n) Defs) Phis) G2) V3) V4)))))))
% 0.26/0.70 (assert (forall ((Alpha_n2 (-> tptp.g tptp.list_node)) (Defs2 (-> tptp.g tptp.node tptp.set_val)) (Uses2 (-> tptp.g tptp.node tptp.set_val)) (Phis2 (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val)) (G tptp.g) (A tptp.val)) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val Alpha_n2) Defs2) Uses2) Phis2) G) A) (=> (forall ((N2 tptp.node)) (=> (@ (@ tptp.member_node N2) (@ tptp.set_node2 (@ Alpha_n2 G))) (not (@ (@ tptp.member_val A) (@ (@ Uses2 G) N2))))) (not (forall ((V5 tptp.val)) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val Alpha_n2) Defs2) Uses2) Phis2) G) V5) (not (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val Alpha_n2) Defs2) Phis2) G) V5) A)))))))))
% 0.26/0.70 (assert (= tptp.sSA_CF1899243830eD_val (lambda ((Alpha_n (-> tptp.g tptp.list_node)) (InEdges (-> tptp.g tptp.node tptp.list_P561207620_edgeD)) (Defs (-> tptp.g tptp.node tptp.set_val)) (Uses (-> tptp.g tptp.node tptp.set_val)) (Phis (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val)) (G2 tptp.g) (V3 tptp.val)) (exists ((X tptp.val)) (and (@ (@ tptp.member_val X) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val Alpha_n) InEdges) Defs) Uses) Phis) G2)) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1909049442de_val Alpha_n) Defs) Phis) G2) V3) X))))))
% 0.26/0.70 (assert (forall ((G tptp.g) (P2 tptp.set_val)) (@ tptp.finite79836624et_val (@ (@ (@ (@ (@ tptp.irredu893086079de_val tptp.alpha_n) tptp.defs) tptp.phis) G) P2))))
% 0.26/0.70 (assert (forall ((G tptp.g) (P tptp.val) (Q tptp.val)) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) G) P) Q) (=> (@ (@ tptp.member_val P) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)) (not (forall ((M2 tptp.node)) (=> (@ (@ tptp.member_val Q) (@ (@ (@ (@ (@ tptp.sSA_CF848637139eD_val tptp.alpha_n) tptp.inEdges) tptp.phis) G) M2)) (not (@ (@ tptp.member_node M2) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) G) P))))))))))))
% 0.26/0.70 (assert (forall ((G tptp.g) (N tptp.node)) (= (@ (@ (@ (@ (@ (@ tptp.sSA_CF178745443eD_val tptp.alpha_n) tptp.inEdges) tptp.uses) tptp.phis) G) N) (@ (@ tptp.sup_sup_set_val (@ (@ tptp.uses G) N)) (@ (@ (@ (@ (@ tptp.sSA_CF848637139eD_val tptp.alpha_n) tptp.inEdges) tptp.phis) G) N)))))
% 0.26/0.70 (assert (forall ((G tptp.g) (Phi2 tptp.val) (N tptp.val)) (let ((_let_1 (@ tptp.var2 G))) (=> (@ (@ (@ tptp.transi1991289355lp_val (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) G)) Phi2) N) (= (@ _let_1 Phi2) (@ _let_1 N))))))
% 0.26/0.70 (assert (forall ((G tptp.g) (N tptp.node)) (= (@ (@ (@ (@ tptp.sSA_CF139593942de_val tptp.defs) tptp.phis) G) N) (@ (@ tptp.sup_sup_set_val (@ (@ tptp.defs G) N)) (@ (@ (@ tptp.sSA_CF370335846de_val tptp.phis) G) N)))))
% 0.26/0.70 (assert (= tptp.sSA_CF2074824714de_val (lambda ((Alpha_n (-> tptp.g tptp.list_node)) (Defs (-> tptp.g tptp.node tptp.set_val)) (Uses (-> tptp.g tptp.node tptp.set_val)) (Phis (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val)) (G2 tptp.g)) (forall ((X tptp.node)) (=> (@ (@ tptp.member_node X) (@ tptp.set_node2 (@ Alpha_n G2))) (forall ((Val2 tptp.val)) (=> (@ (@ tptp.member_val Val2) (@ (@ (@ tptp.sSA_CF370335846de_val Phis) G2) X)) (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val Alpha_n) Defs) Uses) Phis) G2) Val2))))))))
% 0.26/0.70 (assert (forall ((V tptp.val) (G tptp.g)) (let ((_let_1 (@ tptp.member_val V))) (=> (@ _let_1 (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)) (=> (not (@ _let_1 (@ (@ tptp.defs G) (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V)))) (not (= (@ (@ (@ (@ (@ tptp.sSA_CF262257161de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) tptp.none_list_val)))))))
% 0.26/0.70 (assert (forall ((N tptp.node) (G tptp.g) (V tptp.val)) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (=> (@ (@ tptp.member_val V) (@ (@ tptp.defs G) N)) (= (@ (@ (@ (@ (@ tptp.sSA_CF262257161de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) tptp.none_list_val)))))
% 0.26/0.70 (assert (forall ((F tptp.set_Pr1311924359et_val) (G3 tptp.set_Pr1311924359et_val)) (= (@ tptp.finite79836624et_val (@ (@ tptp.sup_su2005730907et_val F) G3)) (and (@ tptp.finite79836624et_val F) (@ tptp.finite79836624et_val G3)))))
% 0.26/0.70 (assert (forall ((F tptp.set_Pr699757092de_val) (G3 tptp.set_Pr699757092de_val)) (= (@ tptp.finite2056463621de_val (@ (@ tptp.sup_su2138939728de_val F) G3)) (and (@ tptp.finite2056463621de_val F) (@ tptp.finite2056463621de_val G3)))))
% 0.26/0.70 (assert (forall ((F tptp.set_val) (G3 tptp.set_val)) (= (@ tptp.finite_finite_val (@ (@ tptp.sup_sup_set_val F) G3)) (and (@ tptp.finite_finite_val F) (@ tptp.finite_finite_val G3)))))
% 0.26/0.70 (assert (forall ((G tptp.g) (V tptp.val)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.sSA_CF1899243830eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G) V) (not (= (@ (@ (@ (@ (@ tptp.sSA_CF262257161de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) tptp.none_list_val)))))
% 0.26/0.70 (assert (forall ((M tptp.node) (G tptp.g) (V tptp.val)) (=> (@ (@ tptp.member_node M) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V)))) (=> (not (= (@ (@ (@ (@ (@ tptp.sSA_CF262257161de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) tptp.none_list_val)) (=> (@ (@ tptp.member_val V) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)) (not (forall ((V6 tptp.val)) (=> (@ (@ tptp.member_val V6) (@ (@ (@ (@ (@ tptp.sSA_CF848637139eD_val tptp.alpha_n) tptp.inEdges) tptp.phis) G) M)) (not (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) V6))))))))))
% 0.26/0.70 (assert (= tptp.sSA_CF262257161de_val tptp.sSA_CF262257161de_val))
% 0.26/0.70 (assert (forall ((S tptp.set_Pr1311924359et_val) (T tptp.set_Pr1311924359et_val)) (= (not (@ tptp.finite79836624et_val (@ (@ tptp.sup_su2005730907et_val S) T))) (or (not (@ tptp.finite79836624et_val S)) (not (@ tptp.finite79836624et_val T))))))
% 0.26/0.70 (assert (forall ((S tptp.set_Pr699757092de_val) (T tptp.set_Pr699757092de_val)) (= (not (@ tptp.finite2056463621de_val (@ (@ tptp.sup_su2138939728de_val S) T))) (or (not (@ tptp.finite2056463621de_val S)) (not (@ tptp.finite2056463621de_val T))))))
% 0.26/0.70 (assert (forall ((S tptp.set_val) (T tptp.set_val)) (= (not (@ tptp.finite_finite_val (@ (@ tptp.sup_sup_set_val S) T))) (or (not (@ tptp.finite_finite_val S)) (not (@ tptp.finite_finite_val T))))))
% 0.26/0.70 (assert (forall ((S tptp.set_Pr1311924359et_val) (T tptp.set_Pr1311924359et_val)) (=> (not (@ tptp.finite79836624et_val S)) (not (@ tptp.finite79836624et_val (@ (@ tptp.sup_su2005730907et_val S) T))))))
% 0.26/0.70 (assert (forall ((S tptp.set_Pr699757092de_val) (T tptp.set_Pr699757092de_val)) (=> (not (@ tptp.finite2056463621de_val S)) (not (@ tptp.finite2056463621de_val (@ (@ tptp.sup_su2138939728de_val S) T))))))
% 0.26/0.70 (assert (forall ((S tptp.set_val) (T tptp.set_val)) (=> (not (@ tptp.finite_finite_val S)) (not (@ tptp.finite_finite_val (@ (@ tptp.sup_sup_set_val S) T))))))
% 0.26/0.70 (assert (forall ((F tptp.set_Pr1311924359et_val) (G3 tptp.set_Pr1311924359et_val)) (=> (@ tptp.finite79836624et_val F) (=> (@ tptp.finite79836624et_val G3) (@ tptp.finite79836624et_val (@ (@ tptp.sup_su2005730907et_val F) G3))))))
% 0.26/0.70 (assert (forall ((F tptp.set_Pr699757092de_val) (G3 tptp.set_Pr699757092de_val)) (=> (@ tptp.finite2056463621de_val F) (=> (@ tptp.finite2056463621de_val G3) (@ tptp.finite2056463621de_val (@ (@ tptp.sup_su2138939728de_val F) G3))))))
% 0.26/0.70 (assert (forall ((F tptp.set_val) (G3 tptp.set_val)) (=> (@ tptp.finite_finite_val F) (=> (@ tptp.finite_finite_val G3) (@ tptp.finite_finite_val (@ (@ tptp.sup_sup_set_val F) G3))))))
% 0.26/0.70 (assert (= tptp.irredu893086079de_val tptp.irredu893086079de_val))
% 0.26/0.70 (assert (= tptp.sSA_CF2074824714de_val tptp.sSA_CF2074824714de_val))
% 0.26/0.70 (assert (= tptp.sSA_CF139593942de_val (lambda ((Defs (-> tptp.g tptp.node tptp.set_val)) (Phis (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val)) (G2 tptp.g) (N3 tptp.node)) (@ (@ tptp.sup_sup_set_val (@ (@ Defs G2) N3)) (@ (@ (@ tptp.sSA_CF370335846de_val Phis) G2) N3)))))
% 0.26/0.70 (assert (= tptp.sSA_CF178745443eD_val (lambda ((Alpha_n (-> tptp.g tptp.list_node)) (InEdges (-> tptp.g tptp.node tptp.list_P561207620_edgeD)) (Uses (-> tptp.g tptp.node tptp.set_val)) (Phis (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val)) (G2 tptp.g) (N3 tptp.node)) (@ (@ tptp.sup_sup_set_val (@ (@ Uses G2) N3)) (@ (@ (@ (@ (@ tptp.sSA_CF848637139eD_val Alpha_n) InEdges) Phis) G2) N3)))))
% 0.26/0.70 (assert (forall ((G tptp.g) (V tptp.val) (Vs tptp.list_val)) (=> (= (@ (@ (@ (@ (@ tptp.sSA_CF262257161de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) (@ tptp.some_list_val Vs)) (@ (@ tptp.member_val V) (@ (@ (@ tptp.sSA_CF370335846de_val tptp.phis) G) (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V))))))
% 0.26/0.70 (assert (forall ((G tptp.g) (P2 tptp.set_val)) (@ tptp.transi1953622797et_val (@ (@ (@ (@ (@ tptp.irredu893086079de_val tptp.alpha_n) tptp.defs) tptp.phis) G) P2))))
% 0.26/0.70 (assert (forall ((G tptp.g) (V tptp.val)) (= (@ (@ (@ (@ (@ tptp.sSA_CF262257161de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) (@ (@ tptp.phis G) (@ (@ tptp.produc1470527136de_val (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V)) V)))))
% 0.26/0.70 (assert (forall ((G tptp.g) (V tptp.val) (V2 tptp.val)) (= (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) V2) (exists ((Vs2 tptp.list_val)) (and (= (@ (@ (@ (@ (@ tptp.sSA_CF262257161de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) (@ tptp.some_list_val Vs2)) (@ (@ tptp.member_val V2) (@ tptp.set_val2 Vs2)))))))
% 0.26/0.70 (assert (forall ((G tptp.g)) (@ tptp.finite_finite_val (@ tptp.dom_val_list_val (@ (@ (@ (@ tptp.sSA_CF262257161de_val tptp.alpha_n) tptp.defs) tptp.phis) G)))))
% 0.26/0.70 (assert (forall ((G tptp.g) (P2 tptp.set_val) (Scc tptp.set_val) (X2 tptp.val)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.irredu224829488eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G) P2) (=> (@ (@ tptp.member_set_val Scc) (@ (@ (@ (@ (@ tptp.irredu681226810de_val tptp.alpha_n) tptp.defs) tptp.phis) G) P2)) (=> (@ (@ tptp.member_val X2) Scc) (not (= (@ (@ (@ (@ (@ tptp.sSA_CF262257161de_val tptp.alpha_n) tptp.defs) tptp.phis) G) X2) tptp.none_list_val)))))))
% 0.26/0.70 (assert (forall ((G tptp.g) (N tptp.node) (V tptp.val) (Vs tptp.list_val) (N4 tptp.node) (Vs3 tptp.list_val)) (let ((_let_1 (@ tptp.phis G))) (=> (= (@ _let_1 (@ (@ tptp.produc1470527136de_val N) V)) (@ tptp.some_list_val Vs)) (=> (= (@ _let_1 (@ (@ tptp.produc1470527136de_val N4) V)) (@ tptp.some_list_val Vs3)) (= Vs Vs3))))))
% 0.26/0.70 (assert (forall ((G tptp.g) (N tptp.node) (V tptp.val) (Vs tptp.list_val) (N4 tptp.node) (Vs3 tptp.list_val)) (let ((_let_1 (@ tptp.phis G))) (=> (= (@ _let_1 (@ (@ tptp.produc1470527136de_val N) V)) (@ tptp.some_list_val Vs)) (=> (= (@ _let_1 (@ (@ tptp.produc1470527136de_val N4) V)) (@ tptp.some_list_val Vs3)) (= N N4))))))
% 0.26/0.70 (assert (forall ((G tptp.g) (N tptp.node) (V tptp.val) (Vs tptp.list_val)) (=> (= (@ (@ tptp.phis G) (@ (@ tptp.produc1470527136de_val N) V)) (@ tptp.some_list_val Vs)) (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))))))
% 0.26/0.70 (assert (forall ((G tptp.g) (N tptp.node) (V tptp.val) (Vs tptp.list_val) (V2 tptp.val)) (let ((_let_1 (@ tptp.var2 G))) (=> (= (@ (@ tptp.phis G) (@ (@ tptp.produc1470527136de_val N) V)) (@ tptp.some_list_val Vs)) (=> (@ (@ tptp.member_val V2) (@ tptp.set_val2 Vs)) (= (@ _let_1 V2) (@ _let_1 V)))))))
% 0.26/0.70 (assert (forall ((G tptp.g) (N tptp.node) (V tptp.val) (Vs tptp.list_val)) (let ((_let_1 (@ tptp.some_list_val Vs))) (=> (= (@ (@ tptp.phis G) (@ (@ tptp.produc1470527136de_val N) V)) _let_1) (= (@ (@ (@ (@ (@ tptp.sSA_CF262257161de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) _let_1)))))
% 0.26/0.70 (assert (forall ((M tptp.node) (G tptp.g) (N tptp.node) (V tptp.val) (Vs tptp.list_val)) (=> (@ (@ tptp.member_node M) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) N))) (=> (= (@ (@ tptp.phis G) (@ (@ tptp.produc1470527136de_val N) V)) (@ tptp.some_list_val Vs)) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (not (forall ((V6 tptp.val)) (let ((_let_1 (@ tptp.member_val V6))) (=> (@ _let_1 (@ (@ (@ (@ (@ tptp.sSA_CF848637139eD_val tptp.alpha_n) tptp.inEdges) tptp.phis) G) M)) (not (@ _let_1 (@ tptp.set_val2 Vs))))))))))))
% 0.26/0.70 (assert (= tptp.irredu681226810de_val tptp.irredu681226810de_val))
% 0.26/0.70 (assert (= tptp.irredu224829488eD_val tptp.irredu224829488eD_val))
% 0.26/0.70 (assert (= tptp.sSA_CF262257161de_val (lambda ((Alpha_n (-> tptp.g tptp.list_node)) (Defs (-> tptp.g tptp.node tptp.set_val)) (Phis (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val)) (G2 tptp.g) (V3 tptp.val)) (@ (@ Phis G2) (@ (@ tptp.produc1470527136de_val (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val Alpha_n) Defs) Phis) G2) V3)) V3)))))
% 0.26/0.70 (assert (= tptp.sSA_CF1252180629de_val (lambda ((Alpha_n (-> tptp.g tptp.list_node)) (Defs (-> tptp.g tptp.node tptp.set_val)) (Phis (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val)) (G2 tptp.g) (V3 tptp.val) (V4 tptp.val)) (exists ((Vs2 tptp.list_val)) (and (= (@ (@ (@ (@ (@ tptp.sSA_CF262257161de_val Alpha_n) Defs) Phis) G2) V3) (@ tptp.some_list_val Vs2)) (@ (@ tptp.member_val V4) (@ tptp.set_val2 Vs2)))))))
% 0.26/0.70 (assert (forall ((N4 tptp.node) (G tptp.g) (V2 tptp.val) (Vs tptp.list_val) (N tptp.node) (V tptp.val)) (=> (@ (@ tptp.member_node N4) (@ tptp.set_node2 (@ tptp.alpha_n G))) (=> (= (@ (@ tptp.phis G) (@ (@ tptp.produc1470527136de_val N4) V2)) (@ tptp.some_list_val Vs)) (=> (@ (@ tptp.member313544709de_val (@ (@ tptp.produc1470527136de_val N) V)) (@ tptp.set_Pr1085970585de_val (@ (@ tptp.zip_node_val (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) N4)) Vs))) (@ (@ tptp.member_val V) (@ (@ (@ (@ (@ tptp.sSA_CF848637139eD_val tptp.alpha_n) tptp.inEdges) tptp.phis) G) N)))))))
% 0.26/0.70 (assert (forall ((Scc tptp.set_val) (G tptp.g) (P2 tptp.set_val)) (=> (@ (@ tptp.member_set_val Scc) (@ (@ (@ (@ (@ tptp.irredu681226810de_val tptp.alpha_n) tptp.defs) tptp.phis) G) P2)) (@ (@ tptp.ord_less_eq_set_val Scc) P2))))
% 0.26/0.70 (assert (forall ((X2 tptp.option_list_val)) (= (not (= X2 tptp.none_list_val)) (exists ((Y2 tptp.list_val)) (= X2 (@ tptp.some_list_val Y2))))))
% 0.26/0.70 (assert (forall ((X2 tptp.option_list_val)) (= (forall ((Y2 tptp.list_val)) (not (= X2 (@ tptp.some_list_val Y2)))) (= X2 tptp.none_list_val))))
% 0.26/0.70 (assert (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (= (@ (@ tptp.sup_su1487070040et_val (@ tptp.some_set_val X2)) (@ tptp.some_set_val Y3)) (@ tptp.some_set_val (@ (@ tptp.sup_sup_set_val X2) Y3)))))
% 0.26/0.70 (assert (forall ((X22 tptp.list_val) (Y22 tptp.list_val)) (= (= (@ tptp.some_list_val X22) (@ tptp.some_list_val Y22)) (= X22 Y22))))
% 0.26/0.70 (assert (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (= (@ (@ tptp.ord_le596993316et_val (@ tptp.some_set_val X2)) (@ tptp.some_set_val Y3)) (@ (@ tptp.ord_less_eq_set_val X2) Y3))))
% 0.26/0.70 (assert (forall ((A tptp.produc1324971431et_val) (B tptp.produc1324971431et_val) (Xs tptp.list_P2089461677et_val)) (= (@ (@ tptp.member1254968080et_val (@ (@ tptp.produc1377626967et_val A) B)) (@ tptp.set_Pr1006393724et_val (@ (@ tptp.zip_Pr21865079et_val Xs) Xs))) (and (@ (@ tptp.member1711426256et_val A) (@ tptp.set_Pr284769596et_val Xs)) (= A B)))))
% 0.26/0.70 (assert (forall ((A tptp.node) (B tptp.node) (Xs tptp.list_node)) (= (@ (@ tptp.member2110109140e_node (@ (@ tptp.produc457016035e_node A) B)) (@ tptp.set_Pr450990656e_node (@ (@ tptp.zip_node_node Xs) Xs))) (and (@ (@ tptp.member_node A) (@ tptp.set_node2 Xs)) (= A B)))))
% 0.26/0.70 (assert (forall ((A tptp.val) (B tptp.val) (Xs tptp.list_val)) (= (@ (@ tptp.member1680438992al_val (@ (@ tptp.product_Pair_val_val A) B)) (@ tptp.set_Pr102746428al_val (@ (@ tptp.zip_val_val Xs) Xs))) (and (@ (@ tptp.member_val A) (@ tptp.set_val2 Xs)) (= A B)))))
% 0.26/0.70 (assert (forall ((A tptp.produc1432036078de_val) (B tptp.produc1432036078de_val) (Xs tptp.list_P1820443774de_val)) (= (@ (@ tptp.member698732390de_val (@ (@ tptp.produc453318901de_val A) B)) (@ tptp.set_Pr482027474de_val (@ (@ tptp.zip_Pr1472086037de_val Xs) Xs))) (and (@ (@ tptp.member313544709de_val A) (@ tptp.set_Pr1085970585de_val Xs)) (= A B)))))
% 0.26/0.70 (assert (forall ((A tptp.set_val) (B tptp.set_val) (Xs tptp.list_set_val)) (= (@ (@ tptp.member1711426256et_val (@ (@ tptp.produc1041633943et_val A) B)) (@ tptp.set_Pr284769596et_val (@ (@ tptp.zip_set_val_set_val Xs) Xs))) (and (@ (@ tptp.member_set_val A) (@ tptp.set_set_val2 Xs)) (= A B)))))
% 0.26/0.70 (assert (forall ((G tptp.g) (P2 tptp.set_val)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.irredu224829488eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G) P2) (exists ((Scc2 tptp.set_val)) (and (@ (@ tptp.ord_less_eq_set_val Scc2) P2) (@ (@ (@ (@ (@ (@ (@ (@ tptp.irredu1955035135eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G) P2) Scc2))))))
% 0.26/0.70 (assert (forall ((V tptp.val) (G tptp.g) (N tptp.node)) (=> (@ (@ tptp.member_val V) (@ (@ (@ (@ (@ tptp.sSA_CF848637139eD_val tptp.alpha_n) tptp.inEdges) tptp.phis) G) N)) (not (forall ((N5 tptp.node)) (=> (@ (@ tptp.member_node N5) (@ tptp.set_node2 (@ (@ (@ (@ tptp.graph_1037173556_edgeD tptp.alpha_n) tptp.inEdges) G) N))) (forall ((V6 tptp.val) (Vs4 tptp.list_val)) (=> (@ (@ tptp.member313544709de_val (@ (@ tptp.produc1470527136de_val N) V)) (@ tptp.set_Pr1085970585de_val (@ (@ tptp.zip_node_val (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) N5)) Vs4))) (not (= (@ (@ tptp.phis G) (@ (@ tptp.produc1470527136de_val N5) V6)) (@ tptp.some_list_val Vs4)))))))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_node) (A tptp.node)) (=> (@ tptp.finite_finite_node A2) (=> (@ (@ tptp.member_node A) A2) (exists ((X3 tptp.node)) (and (@ (@ tptp.member_node X3) A2) (@ (@ tptp.ord_less_eq_node X3) A) (forall ((Xa tptp.node)) (=> (@ (@ tptp.member_node Xa) A2) (=> (@ (@ tptp.ord_less_eq_node Xa) X3) (= X3 Xa))))))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val) (A tptp.val)) (=> (@ tptp.finite_finite_val A2) (=> (@ (@ tptp.member_val A) A2) (exists ((X3 tptp.val)) (and (@ (@ tptp.member_val X3) A2) (@ (@ tptp.ord_less_eq_val X3) A) (forall ((Xa tptp.val)) (=> (@ (@ tptp.member_val Xa) A2) (=> (@ (@ tptp.ord_less_eq_val Xa) X3) (= X3 Xa))))))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_set_val) (A tptp.set_val)) (=> (@ tptp.finite1265617511et_val A2) (=> (@ (@ tptp.member_set_val A) A2) (exists ((X3 tptp.set_val)) (and (@ (@ tptp.member_set_val X3) A2) (@ (@ tptp.ord_less_eq_set_val X3) A) (forall ((Xa tptp.set_val)) (=> (@ (@ tptp.member_set_val Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_val Xa) X3) (= X3 Xa))))))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_node) (A tptp.node)) (=> (@ tptp.finite_finite_node A2) (=> (@ (@ tptp.member_node A) A2) (exists ((X3 tptp.node)) (and (@ (@ tptp.member_node X3) A2) (@ (@ tptp.ord_less_eq_node A) X3) (forall ((Xa tptp.node)) (=> (@ (@ tptp.member_node Xa) A2) (=> (@ (@ tptp.ord_less_eq_node X3) Xa) (= X3 Xa))))))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val) (A tptp.val)) (=> (@ tptp.finite_finite_val A2) (=> (@ (@ tptp.member_val A) A2) (exists ((X3 tptp.val)) (and (@ (@ tptp.member_val X3) A2) (@ (@ tptp.ord_less_eq_val A) X3) (forall ((Xa tptp.val)) (=> (@ (@ tptp.member_val Xa) A2) (=> (@ (@ tptp.ord_less_eq_val X3) Xa) (= X3 Xa))))))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_set_val) (A tptp.set_val)) (=> (@ tptp.finite1265617511et_val A2) (=> (@ (@ tptp.member_set_val A) A2) (exists ((X3 tptp.set_val)) (and (@ (@ tptp.member_set_val X3) A2) (@ (@ tptp.ord_less_eq_set_val A) X3) (forall ((Xa tptp.set_val)) (=> (@ (@ tptp.member_set_val Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_val X3) Xa) (= X3 Xa))))))))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_val) (B2 tptp.set_set_val)) (= (@ (@ tptp.ord_le1742111550et_val (@ tptp.set_set_val2 Xs)) B2) (forall ((X tptp.set_val)) (let ((_let_1 (@ tptp.member_set_val X))) (=> (@ _let_1 (@ tptp.set_set_val2 Xs)) (@ _let_1 B2)))))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_P2089461677et_val) (B2 tptp.set_Pr1311924359et_val)) (= (@ (@ tptp.ord_le299366439et_val (@ tptp.set_Pr284769596et_val Xs)) B2) (forall ((X tptp.produc1324971431et_val)) (let ((_let_1 (@ tptp.member1711426256et_val X))) (=> (@ _let_1 (@ tptp.set_Pr284769596et_val Xs)) (@ _let_1 B2)))))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_node) (B2 tptp.set_node)) (= (@ (@ tptp.ord_less_eq_set_node (@ tptp.set_node2 Xs)) B2) (forall ((X tptp.node)) (let ((_let_1 (@ tptp.member_node X))) (=> (@ _let_1 (@ tptp.set_node2 Xs)) (@ _let_1 B2)))))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_P1820443774de_val) (B2 tptp.set_Pr699757092de_val)) (= (@ (@ tptp.ord_le1643692676de_val (@ tptp.set_Pr1085970585de_val Xs)) B2) (forall ((X tptp.produc1432036078de_val)) (let ((_let_1 (@ tptp.member313544709de_val X))) (=> (@ _let_1 (@ tptp.set_Pr1085970585de_val Xs)) (@ _let_1 B2)))))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_val) (B2 tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val (@ tptp.set_val2 Xs)) B2) (forall ((X tptp.val)) (let ((_let_1 (@ tptp.member_val X))) (=> (@ _let_1 (@ tptp.set_val2 Xs)) (@ _let_1 B2)))))))
% 0.26/0.70 (assert (forall ((B2 tptp.set_Pr1311924359et_val) (A2 tptp.set_Pr1311924359et_val)) (=> (@ tptp.finite79836624et_val B2) (=> (@ (@ tptp.ord_le299366439et_val A2) B2) (@ tptp.finite79836624et_val A2)))))
% 0.26/0.70 (assert (forall ((B2 tptp.set_Pr699757092de_val) (A2 tptp.set_Pr699757092de_val)) (=> (@ tptp.finite2056463621de_val B2) (=> (@ (@ tptp.ord_le1643692676de_val A2) B2) (@ tptp.finite2056463621de_val A2)))))
% 0.26/0.70 (assert (forall ((B2 tptp.set_val) (A2 tptp.set_val)) (=> (@ tptp.finite_finite_val B2) (=> (@ (@ tptp.ord_less_eq_set_val A2) B2) (@ tptp.finite_finite_val A2)))))
% 0.26/0.70 (assert (forall ((S tptp.set_Pr1311924359et_val) (T tptp.set_Pr1311924359et_val)) (=> (@ (@ tptp.ord_le299366439et_val S) T) (=> (not (@ tptp.finite79836624et_val S)) (not (@ tptp.finite79836624et_val T))))))
% 0.26/0.70 (assert (forall ((S tptp.set_Pr699757092de_val) (T tptp.set_Pr699757092de_val)) (=> (@ (@ tptp.ord_le1643692676de_val S) T) (=> (not (@ tptp.finite2056463621de_val S)) (not (@ tptp.finite2056463621de_val T))))))
% 0.26/0.70 (assert (forall ((S tptp.set_val) (T tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val S) T) (=> (not (@ tptp.finite_finite_val S)) (not (@ tptp.finite_finite_val T))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_Pr1311924359et_val) (B2 tptp.set_Pr1311924359et_val)) (=> (@ (@ tptp.ord_le299366439et_val A2) B2) (=> (@ tptp.finite79836624et_val B2) (@ tptp.finite79836624et_val A2)))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_Pr699757092de_val) (B2 tptp.set_Pr699757092de_val)) (=> (@ (@ tptp.ord_le1643692676de_val A2) B2) (=> (@ tptp.finite2056463621de_val B2) (@ tptp.finite2056463621de_val A2)))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val) (B2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A2) B2) (=> (@ tptp.finite_finite_val B2) (@ tptp.finite_finite_val A2)))))
% 0.26/0.70 (assert (forall ((X2 tptp.node) (Y3 tptp.node) (Xs tptp.list_node) (Ys tptp.list_node)) (=> (@ (@ tptp.member2110109140e_node (@ (@ tptp.produc457016035e_node X2) Y3)) (@ tptp.set_Pr450990656e_node (@ (@ tptp.zip_node_node Xs) Ys))) (not (=> (@ (@ tptp.member_node X2) (@ tptp.set_node2 Xs)) (not (@ (@ tptp.member_node Y3) (@ tptp.set_node2 Ys))))))))
% 0.26/0.70 (assert (forall ((X2 tptp.val) (Y3 tptp.node) (Xs tptp.list_val) (Ys tptp.list_node)) (=> (@ (@ tptp.member828457417l_node (@ (@ tptp.produc1074923692l_node X2) Y3)) (@ tptp.set_Pr1600883293l_node (@ (@ tptp.zip_val_node Xs) Ys))) (not (=> (@ (@ tptp.member_val X2) (@ tptp.set_val2 Xs)) (not (@ (@ tptp.member_node Y3) (@ tptp.set_node2 Ys))))))))
% 0.26/0.70 (assert (forall ((X2 tptp.val) (Y3 tptp.val) (Xs tptp.list_val) (Ys tptp.list_val)) (=> (@ (@ tptp.member1680438992al_val (@ (@ tptp.product_Pair_val_val X2) Y3)) (@ tptp.set_Pr102746428al_val (@ (@ tptp.zip_val_val Xs) Ys))) (not (=> (@ (@ tptp.member_val X2) (@ tptp.set_val2 Xs)) (not (@ (@ tptp.member_val Y3) (@ tptp.set_val2 Ys))))))))
% 0.26/0.70 (assert (forall ((X2 tptp.node) (Y3 tptp.val) (Xs tptp.list_node) (Ys tptp.list_val)) (=> (@ (@ tptp.member313544709de_val (@ (@ tptp.produc1470527136de_val X2) Y3)) (@ tptp.set_Pr1085970585de_val (@ (@ tptp.zip_node_val Xs) Ys))) (not (=> (@ (@ tptp.member_node X2) (@ tptp.set_node2 Xs)) (not (@ (@ tptp.member_val Y3) (@ tptp.set_val2 Ys))))))))
% 0.26/0.70 (assert (forall ((X2 tptp.set_val) (Y3 tptp.node) (Xs tptp.list_set_val) (Ys tptp.list_node)) (=> (@ (@ tptp.member76372137l_node (@ (@ tptp.produc2052093836l_node X2) Y3)) (@ tptp.set_Pr1904955709l_node (@ (@ tptp.zip_set_val_node Xs) Ys))) (not (=> (@ (@ tptp.member_set_val X2) (@ tptp.set_set_val2 Xs)) (not (@ (@ tptp.member_node Y3) (@ tptp.set_node2 Ys))))))))
% 0.26/0.70 (assert (forall ((X2 tptp.set_val) (Y3 tptp.val) (Xs tptp.list_set_val) (Ys tptp.list_val)) (=> (@ (@ tptp.member1110026224al_val (@ (@ tptp.produc1337903031al_val X2) Y3)) (@ tptp.set_Pr1027623516al_val (@ (@ tptp.zip_set_val_val Xs) Ys))) (not (=> (@ (@ tptp.member_set_val X2) (@ tptp.set_set_val2 Xs)) (not (@ (@ tptp.member_val Y3) (@ tptp.set_val2 Ys))))))))
% 0.26/0.70 (assert (forall ((X2 tptp.node) (Y3 tptp.set_val) (Xs tptp.list_node) (Ys tptp.list_set_val)) (=> (@ (@ tptp.member125181669et_val (@ (@ tptp.produc2042994048et_val X2) Y3)) (@ tptp.set_Pr1953765241et_val (@ (@ tptp.zip_node_set_val Xs) Ys))) (not (=> (@ (@ tptp.member_node X2) (@ tptp.set_node2 Xs)) (not (@ (@ tptp.member_set_val Y3) (@ tptp.set_set_val2 Ys))))))))
% 0.26/0.70 (assert (forall ((X2 tptp.val) (Y3 tptp.set_val) (Xs tptp.list_val) (Ys tptp.list_set_val)) (=> (@ (@ tptp.member39229872et_val (@ (@ tptp.produc1446164855et_val X2) Y3)) (@ tptp.set_Pr2104310812et_val (@ (@ tptp.zip_val_set_val Xs) Ys))) (not (=> (@ (@ tptp.member_val X2) (@ tptp.set_val2 Xs)) (not (@ (@ tptp.member_set_val Y3) (@ tptp.set_set_val2 Ys))))))))
% 0.26/0.70 (assert (forall ((X2 tptp.node) (Y3 tptp.produc1432036078de_val) (Xs tptp.list_node) (Ys tptp.list_P1820443774de_val)) (=> (@ (@ tptp.member562853661de_val (@ (@ tptp.produc1162531244de_val X2) Y3)) (@ tptp.set_Pr1157337481de_val (@ (@ tptp.zip_no263301324de_val Xs) Ys))) (not (=> (@ (@ tptp.member_node X2) (@ tptp.set_node2 Xs)) (not (@ (@ tptp.member313544709de_val Y3) (@ tptp.set_Pr1085970585de_val Ys))))))))
% 0.26/0.70 (assert (forall ((X2 tptp.val) (Y3 tptp.produc1432036078de_val) (Xs tptp.list_val) (Ys tptp.list_P1820443774de_val)) (=> (@ (@ tptp.member1894062994de_val (@ (@ tptp.produc1571934709de_val X2) Y3)) (@ tptp.set_Pr434939430de_val (@ (@ tptp.zip_va679686869de_val Xs) Ys))) (not (=> (@ (@ tptp.member_val X2) (@ tptp.set_val2 Xs)) (not (@ (@ tptp.member313544709de_val Y3) (@ tptp.set_Pr1085970585de_val Ys))))))))
% 0.26/0.70 (assert (forall ((X2 tptp.node) (Y3 tptp.val) (Xs tptp.list_node) (Ys tptp.list_val)) (=> (@ (@ tptp.member313544709de_val (@ (@ tptp.produc1470527136de_val X2) Y3)) (@ tptp.set_Pr1085970585de_val (@ (@ tptp.zip_node_val Xs) Ys))) (@ (@ tptp.member_node X2) (@ tptp.set_node2 Xs)))))
% 0.26/0.70 (assert (forall ((X2 tptp.set_val) (Y3 tptp.set_val) (Xs tptp.list_set_val) (Ys tptp.list_set_val)) (=> (@ (@ tptp.member1711426256et_val (@ (@ tptp.produc1041633943et_val X2) Y3)) (@ tptp.set_Pr284769596et_val (@ (@ tptp.zip_set_val_set_val Xs) Ys))) (@ (@ tptp.member_set_val X2) (@ tptp.set_set_val2 Xs)))))
% 0.26/0.70 (assert (forall ((X2 tptp.node) (Y3 tptp.val) (Xs tptp.list_node) (Ys tptp.list_val)) (=> (@ (@ tptp.member313544709de_val (@ (@ tptp.produc1470527136de_val X2) Y3)) (@ tptp.set_Pr1085970585de_val (@ (@ tptp.zip_node_val Xs) Ys))) (@ (@ tptp.member_val Y3) (@ tptp.set_val2 Ys)))))
% 0.26/0.70 (assert (forall ((X2 tptp.set_val) (Y3 tptp.set_val) (Xs tptp.list_set_val) (Ys tptp.list_set_val)) (=> (@ (@ tptp.member1711426256et_val (@ (@ tptp.produc1041633943et_val X2) Y3)) (@ tptp.set_Pr284769596et_val (@ (@ tptp.zip_set_val_set_val Xs) Ys))) (@ (@ tptp.member_set_val Y3) (@ tptp.set_set_val2 Ys)))))
% 0.26/0.70 (assert (forall ((X2 tptp.option_list_val) (P2 (-> tptp.option_list_val tptp.option_list_val Bool)) (Y3 tptp.option_list_val)) (let ((_let_1 (@ (@ P2 X2) Y3))) (=> (=> (= X2 tptp.none_list_val) _let_1) (=> (=> (= Y3 tptp.none_list_val) _let_1) (=> (forall ((A4 tptp.list_val) (B3 tptp.list_val)) (=> (= X2 (@ tptp.some_list_val A4)) (=> (= Y3 (@ tptp.some_list_val B3)) (@ (@ P2 X2) Y3)))) _let_1))))))
% 0.26/0.70 (assert (= (lambda ((P3 (-> tptp.option_list_val Bool))) (forall ((X4 tptp.option_list_val)) (@ P3 X4))) (lambda ((P4 (-> tptp.option_list_val Bool))) (and (@ P4 tptp.none_list_val) (forall ((X tptp.list_val)) (@ P4 (@ tptp.some_list_val X)))))))
% 0.26/0.70 (assert (= (lambda ((P3 (-> tptp.option_list_val Bool))) (exists ((X4 tptp.option_list_val)) (@ P3 X4))) (lambda ((P4 (-> tptp.option_list_val Bool))) (or (@ P4 tptp.none_list_val) (exists ((X tptp.list_val)) (@ P4 (@ tptp.some_list_val X)))))))
% 0.26/0.70 (assert (forall ((P2 (-> tptp.option_list_val Bool)) (Option tptp.option_list_val)) (=> (@ P2 tptp.none_list_val) (=> (forall ((X3 tptp.list_val)) (@ P2 (@ tptp.some_list_val X3))) (@ P2 Option)))))
% 0.26/0.70 (assert (forall ((Y3 tptp.option_list_val)) (=> (not (= Y3 tptp.none_list_val)) (not (forall ((X23 tptp.list_val)) (not (= Y3 (@ tptp.some_list_val X23))))))))
% 0.26/0.70 (assert (forall ((Option tptp.option_list_val) (X22 tptp.list_val)) (=> (= Option (@ tptp.some_list_val X22)) (not (= Option tptp.none_list_val)))))
% 0.26/0.70 (assert (forall ((X22 tptp.list_val)) (not (= tptp.none_list_val (@ tptp.some_list_val X22)))))
% 0.26/0.70 (assert (forall ((P2 tptp.set_val) (G tptp.g)) (=> (not (= P2 tptp.bot_bot_set_val)) (exists ((Leaf tptp.set_val)) (and (@ (@ tptp.member_set_val Leaf) (@ (@ (@ (@ (@ tptp.irredu681226810de_val tptp.alpha_n) tptp.defs) tptp.phis) G) P2)) (forall ((Scc3 tptp.set_val)) (not (@ (@ tptp.member1711426256et_val (@ (@ tptp.produc1041633943et_val Leaf) Scc3)) (@ (@ (@ (@ (@ tptp.irredu893086079de_val tptp.alpha_n) tptp.defs) tptp.phis) G) P2)))))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val) (B2 tptp.set_val) (C tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val A2) B2)) C) (and (@ (@ tptp.ord_less_eq_set_val A2) C) (@ (@ tptp.ord_less_eq_set_val B2) C)))))
% 0.26/0.70 (assert (forall ((X2 tptp.set_val) (Y3 tptp.set_val) (Z tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val X2) Y3)) Z) (and (@ (@ tptp.ord_less_eq_set_val X2) Z) (@ (@ tptp.ord_less_eq_set_val Y3) Z)))))
% 0.26/0.70 (assert (forall ((B tptp.set_val) (C2 tptp.set_val) (A tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val B) C2)) A) (and (@ (@ tptp.ord_less_eq_set_val B) A) (@ (@ tptp.ord_less_eq_set_val C2) A)))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val) (B2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A2) B2) (=> (@ (@ tptp.ord_less_eq_set_val B2) A2) (= A2 B2)))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_node) (B2 tptp.set_node)) (=> (forall ((X3 tptp.node)) (let ((_let_1 (@ tptp.member_node X3))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_less_eq_set_node A2) B2))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_set_val) (B2 tptp.set_set_val)) (=> (forall ((X3 tptp.set_val)) (let ((_let_1 (@ tptp.member_set_val X3))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_le1742111550et_val A2) B2))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_Pr699757092de_val) (B2 tptp.set_Pr699757092de_val)) (=> (forall ((X3 tptp.produc1432036078de_val)) (let ((_let_1 (@ tptp.member313544709de_val X3))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_le1643692676de_val A2) B2))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_Pr1311924359et_val) (B2 tptp.set_Pr1311924359et_val)) (=> (forall ((X3 tptp.produc1324971431et_val)) (let ((_let_1 (@ tptp.member1711426256et_val X3))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_le299366439et_val A2) B2))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val) (B2 tptp.set_val)) (=> (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_less_eq_set_val A2) B2))))
% 0.26/0.70 (assert (forall ((A tptp.set_val) (B tptp.set_val)) (let ((_let_1 (@ (@ tptp.sup_sup_set_val A) B))) (= (@ (@ tptp.sup_sup_set_val _let_1) B) _let_1))))
% 0.26/0.70 (assert (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val X2))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2)))))
% 0.26/0.70 (assert (forall ((A tptp.set_val) (B tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 0.26/0.70 (assert (forall ((X2 tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val X2) X2) X2)))
% 0.26/0.70 (assert (forall ((A tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val A) A) A)))
% 0.26/0.70 (assert (forall ((C2 tptp.node) (A2 tptp.set_node) (B2 tptp.set_node)) (let ((_let_1 (@ tptp.member_node C2))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_node A2) B2)) (or (@ _let_1 A2) (@ _let_1 B2))))))
% 0.26/0.70 (assert (forall ((C2 tptp.set_val) (A2 tptp.set_set_val) (B2 tptp.set_set_val)) (let ((_let_1 (@ tptp.member_set_val C2))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_set_val A2) B2)) (or (@ _let_1 A2) (@ _let_1 B2))))))
% 0.26/0.70 (assert (forall ((C2 tptp.produc1432036078de_val) (A2 tptp.set_Pr699757092de_val) (B2 tptp.set_Pr699757092de_val)) (let ((_let_1 (@ tptp.member313544709de_val C2))) (= (@ _let_1 (@ (@ tptp.sup_su2138939728de_val A2) B2)) (or (@ _let_1 A2) (@ _let_1 B2))))))
% 0.26/0.70 (assert (forall ((C2 tptp.produc1324971431et_val) (A2 tptp.set_Pr1311924359et_val) (B2 tptp.set_Pr1311924359et_val)) (let ((_let_1 (@ tptp.member1711426256et_val C2))) (= (@ _let_1 (@ (@ tptp.sup_su2005730907et_val A2) B2)) (or (@ _let_1 A2) (@ _let_1 B2))))))
% 0.26/0.70 (assert (forall ((C2 tptp.val) (A2 tptp.set_val) (B2 tptp.set_val)) (let ((_let_1 (@ tptp.member_val C2))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_val A2) B2)) (or (@ _let_1 A2) (@ _let_1 B2))))))
% 0.26/0.70 (assert (forall ((C2 tptp.node) (B2 tptp.set_node) (A2 tptp.set_node)) (let ((_let_1 (@ tptp.member_node C2))) (=> (=> (not (@ _let_1 B2)) (@ _let_1 A2)) (@ _let_1 (@ (@ tptp.sup_sup_set_node A2) B2))))))
% 0.26/0.70 (assert (forall ((C2 tptp.set_val) (B2 tptp.set_set_val) (A2 tptp.set_set_val)) (let ((_let_1 (@ tptp.member_set_val C2))) (=> (=> (not (@ _let_1 B2)) (@ _let_1 A2)) (@ _let_1 (@ (@ tptp.sup_sup_set_set_val A2) B2))))))
% 0.26/0.70 (assert (forall ((C2 tptp.produc1432036078de_val) (B2 tptp.set_Pr699757092de_val) (A2 tptp.set_Pr699757092de_val)) (let ((_let_1 (@ tptp.member313544709de_val C2))) (=> (=> (not (@ _let_1 B2)) (@ _let_1 A2)) (@ _let_1 (@ (@ tptp.sup_su2138939728de_val A2) B2))))))
% 0.26/0.70 (assert (forall ((C2 tptp.produc1324971431et_val) (B2 tptp.set_Pr1311924359et_val) (A2 tptp.set_Pr1311924359et_val)) (let ((_let_1 (@ tptp.member1711426256et_val C2))) (=> (=> (not (@ _let_1 B2)) (@ _let_1 A2)) (@ _let_1 (@ (@ tptp.sup_su2005730907et_val A2) B2))))))
% 0.26/0.70 (assert (forall ((C2 tptp.val) (B2 tptp.set_val) (A2 tptp.set_val)) (let ((_let_1 (@ tptp.member_val C2))) (=> (=> (not (@ _let_1 B2)) (@ _let_1 A2)) (@ _let_1 (@ (@ tptp.sup_sup_set_val A2) B2))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val A2) tptp.bot_bot_set_val) (= A2 tptp.bot_bot_set_val))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val tptp.bot_bot_set_val) A2)))
% 0.26/0.70 (assert (forall ((X2 tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val tptp.bot_bot_set_val) X2) X2)))
% 0.26/0.70 (assert (forall ((X2 tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val X2) tptp.bot_bot_set_val) X2)))
% 0.26/0.70 (assert (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (= (= tptp.bot_bot_set_val (@ (@ tptp.sup_sup_set_val X2) Y3)) (and (= X2 tptp.bot_bot_set_val) (= Y3 tptp.bot_bot_set_val)))))
% 0.26/0.70 (assert (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (= (= (@ (@ tptp.sup_sup_set_val X2) Y3) tptp.bot_bot_set_val) (and (= X2 tptp.bot_bot_set_val) (= Y3 tptp.bot_bot_set_val)))))
% 0.26/0.70 (assert (forall ((A tptp.set_val) (B tptp.set_val)) (= (= (@ (@ tptp.sup_sup_set_val A) B) tptp.bot_bot_set_val) (and (= A tptp.bot_bot_set_val) (= B tptp.bot_bot_set_val)))))
% 0.26/0.70 (assert (forall ((A tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val tptp.bot_bot_set_val) A) A)))
% 0.26/0.70 (assert (forall ((A tptp.set_val) (B tptp.set_val)) (= (= tptp.bot_bot_set_val (@ (@ tptp.sup_sup_set_val A) B)) (and (= A tptp.bot_bot_set_val) (= B tptp.bot_bot_set_val)))))
% 0.26/0.70 (assert (forall ((A tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val A) tptp.bot_bot_set_val) A)))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val) (B2 tptp.set_val)) (= (= (@ (@ tptp.sup_sup_set_val A2) B2) tptp.bot_bot_set_val) (and (= A2 tptp.bot_bot_set_val) (= B2 tptp.bot_bot_set_val)))))
% 0.26/0.70 (assert (forall ((N tptp.node) (G tptp.g) (M tptp.node)) (let ((_let_1 (@ tptp.member_node N))) (=> (@ _let_1 (@ tptp.set_node2 (@ tptp.alpha_n G))) (= (@ _let_1 (@ tptp.set_node2 (@ (@ (@ (@ tptp.graph_1037173556_edgeD tptp.alpha_n) tptp.inEdges) G) M))) (@ (@ tptp.member_node M) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) N))))))))
% 0.26/0.70 (assert (forall ((B2 tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val tptp.bot_bot_set_val) B2) B2)))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val A2) tptp.bot_bot_set_val) A2)))
% 0.26/0.70 (assert (forall ((S tptp.set_Pr1311924359et_val)) (=> (not (@ tptp.finite79836624et_val S)) (not (= S tptp.bot_bo2078591731et_val)))))
% 0.26/0.70 (assert (forall ((S tptp.set_Pr699757092de_val)) (=> (not (@ tptp.finite2056463621de_val S)) (not (= S tptp.bot_bo404898488de_val)))))
% 0.26/0.70 (assert (forall ((S tptp.set_val)) (=> (not (@ tptp.finite_finite_val S)) (not (= S tptp.bot_bot_set_val)))))
% 0.26/0.70 (assert (@ tptp.finite79836624et_val tptp.bot_bo2078591731et_val))
% 0.26/0.70 (assert (@ tptp.finite2056463621de_val tptp.bot_bo404898488de_val))
% 0.26/0.70 (assert (@ tptp.finite_finite_val tptp.bot_bot_set_val))
% 0.26/0.70 (assert (= tptp.irredu1955035135eD_val tptp.irredu1955035135eD_val))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val)) (=> (@ tptp.finite_finite_val A2) (=> (not (= A2 tptp.bot_bot_set_val)) (exists ((X3 tptp.val)) (and (@ (@ tptp.member_val X3) A2) (forall ((Xa tptp.val)) (=> (@ (@ tptp.member_val Xa) A2) (=> (@ (@ tptp.ord_less_eq_val X3) Xa) (= X3 Xa))))))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_set_val)) (=> (@ tptp.finite1265617511et_val A2) (=> (not (= A2 tptp.bot_bot_set_set_val)) (exists ((X3 tptp.set_val)) (and (@ (@ tptp.member_set_val X3) A2) (forall ((Xa tptp.set_val)) (=> (@ (@ tptp.member_set_val Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_val X3) Xa) (= X3 Xa))))))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val)) (=> (@ tptp.finite_finite_val A2) (=> (not (= A2 tptp.bot_bot_set_val)) (exists ((X3 tptp.val)) (and (@ (@ tptp.member_val X3) A2) (forall ((Xa tptp.val)) (=> (@ (@ tptp.member_val Xa) A2) (=> (@ (@ tptp.ord_less_eq_val Xa) X3) (= X3 Xa))))))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_set_val)) (=> (@ tptp.finite1265617511et_val A2) (=> (not (= A2 tptp.bot_bot_set_set_val)) (exists ((X3 tptp.set_val)) (and (@ (@ tptp.member_set_val X3) A2) (forall ((Xa tptp.set_val)) (=> (@ (@ tptp.member_set_val Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_val Xa) X3) (= X3 Xa))))))))))
% 0.26/0.70 (assert (forall ((P2 (-> tptp.val Bool)) (Q2 (-> tptp.val Bool))) (= (@ (@ tptp.ord_less_eq_set_val (@ tptp.collect_val P2)) (@ tptp.collect_val Q2)) (forall ((X tptp.val)) (=> (@ P2 X) (@ Q2 X))))))
% 0.26/0.70 (assert (= (lambda ((Y4 tptp.set_val) (Z2 tptp.set_val)) (= Y4 Z2)) (lambda ((A5 tptp.set_val) (B4 tptp.set_val)) (and (@ (@ tptp.ord_less_eq_set_val A5) B4) (@ (@ tptp.ord_less_eq_set_val B4) A5)))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val) (B2 tptp.set_val) (C tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_val B2) C) (@ _let_1 C))))))
% 0.26/0.70 (assert (forall ((P2 (-> tptp.val Bool)) (Q2 (-> tptp.val Bool))) (=> (forall ((X3 tptp.val)) (=> (@ P2 X3) (@ Q2 X3))) (@ (@ tptp.ord_less_eq_set_val (@ tptp.collect_val P2)) (@ tptp.collect_val Q2)))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val A2) A2)))
% 0.26/0.70 (assert (= tptp.ord_less_eq_set_node (lambda ((A5 tptp.set_node) (B4 tptp.set_node)) (forall ((T2 tptp.node)) (let ((_let_1 (@ tptp.member_node T2))) (=> (@ _let_1 A5) (@ _let_1 B4)))))))
% 0.26/0.70 (assert (= tptp.ord_le1742111550et_val (lambda ((A5 tptp.set_set_val) (B4 tptp.set_set_val)) (forall ((T2 tptp.set_val)) (let ((_let_1 (@ tptp.member_set_val T2))) (=> (@ _let_1 A5) (@ _let_1 B4)))))))
% 0.26/0.70 (assert (= tptp.ord_le1643692676de_val (lambda ((A5 tptp.set_Pr699757092de_val) (B4 tptp.set_Pr699757092de_val)) (forall ((T2 tptp.produc1432036078de_val)) (let ((_let_1 (@ tptp.member313544709de_val T2))) (=> (@ _let_1 A5) (@ _let_1 B4)))))))
% 0.26/0.70 (assert (= tptp.ord_le299366439et_val (lambda ((A5 tptp.set_Pr1311924359et_val) (B4 tptp.set_Pr1311924359et_val)) (forall ((T2 tptp.produc1324971431et_val)) (let ((_let_1 (@ tptp.member1711426256et_val T2))) (=> (@ _let_1 A5) (@ _let_1 B4)))))))
% 0.26/0.70 (assert (= tptp.ord_less_eq_set_val (lambda ((A5 tptp.set_val) (B4 tptp.set_val)) (forall ((T2 tptp.val)) (let ((_let_1 (@ tptp.member_val T2))) (=> (@ _let_1 A5) (@ _let_1 B4)))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val) (B2 tptp.set_val)) (=> (= A2 B2) (@ (@ tptp.ord_less_eq_set_val B2) A2))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val) (B2 tptp.set_val)) (=> (= A2 B2) (@ (@ tptp.ord_less_eq_set_val A2) B2))))
% 0.26/0.70 (assert (= tptp.ord_less_eq_set_node (lambda ((A5 tptp.set_node) (B4 tptp.set_node)) (forall ((X tptp.node)) (let ((_let_1 (@ tptp.member_node X))) (=> (@ _let_1 A5) (@ _let_1 B4)))))))
% 0.26/0.70 (assert (= tptp.ord_le1742111550et_val (lambda ((A5 tptp.set_set_val) (B4 tptp.set_set_val)) (forall ((X tptp.set_val)) (let ((_let_1 (@ tptp.member_set_val X))) (=> (@ _let_1 A5) (@ _let_1 B4)))))))
% 0.26/0.70 (assert (= tptp.ord_le1643692676de_val (lambda ((A5 tptp.set_Pr699757092de_val) (B4 tptp.set_Pr699757092de_val)) (forall ((X tptp.produc1432036078de_val)) (let ((_let_1 (@ tptp.member313544709de_val X))) (=> (@ _let_1 A5) (@ _let_1 B4)))))))
% 0.26/0.70 (assert (= tptp.ord_le299366439et_val (lambda ((A5 tptp.set_Pr1311924359et_val) (B4 tptp.set_Pr1311924359et_val)) (forall ((X tptp.produc1324971431et_val)) (let ((_let_1 (@ tptp.member1711426256et_val X))) (=> (@ _let_1 A5) (@ _let_1 B4)))))))
% 0.26/0.70 (assert (= tptp.ord_less_eq_set_val (lambda ((A5 tptp.set_val) (B4 tptp.set_val)) (forall ((X tptp.val)) (let ((_let_1 (@ tptp.member_val X))) (=> (@ _let_1 A5) (@ _let_1 B4)))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val) (B2 tptp.set_val)) (=> (= A2 B2) (not (=> (@ (@ tptp.ord_less_eq_set_val A2) B2) (not (@ (@ tptp.ord_less_eq_set_val B2) A2)))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_node) (B2 tptp.set_node) (C2 tptp.node)) (let ((_let_1 (@ tptp.member_node C2))) (=> (@ (@ tptp.ord_less_eq_set_node A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_set_val) (B2 tptp.set_set_val) (C2 tptp.set_val)) (let ((_let_1 (@ tptp.member_set_val C2))) (=> (@ (@ tptp.ord_le1742111550et_val A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_Pr699757092de_val) (B2 tptp.set_Pr699757092de_val) (C2 tptp.produc1432036078de_val)) (let ((_let_1 (@ tptp.member313544709de_val C2))) (=> (@ (@ tptp.ord_le1643692676de_val A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_Pr1311924359et_val) (B2 tptp.set_Pr1311924359et_val) (C2 tptp.produc1324971431et_val)) (let ((_let_1 (@ tptp.member1711426256et_val C2))) (=> (@ (@ tptp.ord_le299366439et_val A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val) (B2 tptp.set_val) (C2 tptp.val)) (let ((_let_1 (@ tptp.member_val C2))) (=> (@ (@ tptp.ord_less_eq_set_val A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_node) (B2 tptp.set_node) (X2 tptp.node)) (let ((_let_1 (@ tptp.member_node X2))) (=> (@ (@ tptp.ord_less_eq_set_node A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_set_val) (B2 tptp.set_set_val) (X2 tptp.set_val)) (let ((_let_1 (@ tptp.member_set_val X2))) (=> (@ (@ tptp.ord_le1742111550et_val A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_Pr699757092de_val) (B2 tptp.set_Pr699757092de_val) (X2 tptp.produc1432036078de_val)) (let ((_let_1 (@ tptp.member313544709de_val X2))) (=> (@ (@ tptp.ord_le1643692676de_val A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_Pr1311924359et_val) (B2 tptp.set_Pr1311924359et_val) (X2 tptp.produc1324971431et_val)) (let ((_let_1 (@ tptp.member1711426256et_val X2))) (=> (@ (@ tptp.ord_le299366439et_val A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val) (B2 tptp.set_val) (X2 tptp.val)) (let ((_let_1 (@ tptp.member_val X2))) (=> (@ (@ tptp.ord_less_eq_set_val A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 0.26/0.70 (assert (forall ((X2 tptp.set_val) (Y3 tptp.set_val) (Z tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val X2))) (let ((_let_2 (@ tptp.sup_sup_set_val Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.26/0.70 (assert (forall ((B tptp.set_val) (A tptp.set_val) (C2 tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val B))) (let ((_let_2 (@ tptp.sup_sup_set_val A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 0.26/0.70 (assert (= tptp.sup_sup_set_val (lambda ((X tptp.set_val) (Y2 tptp.set_val)) (@ (@ tptp.sup_sup_set_val Y2) X))))
% 0.26/0.70 (assert (= tptp.sup_sup_set_val (lambda ((A3 tptp.set_val) (B5 tptp.set_val)) (@ (@ tptp.sup_sup_set_val B5) A3))))
% 0.26/0.70 (assert (forall ((X2 tptp.set_val) (Y3 tptp.set_val) (Z tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val X2))) (= (@ (@ tptp.sup_sup_set_val (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.sup_sup_set_val Y3) Z))))))
% 0.26/0.70 (assert (forall ((A tptp.set_val) (B tptp.set_val) (C2 tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val A))) (= (@ (@ tptp.sup_sup_set_val (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.sup_sup_set_val B) C2))))))
% 0.26/0.70 (assert (forall ((B2 tptp.set_val) (K tptp.set_val) (B tptp.set_val) (A tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val A))) (let ((_let_2 (@ tptp.sup_sup_set_val K))) (=> (= B2 (@ _let_2 B)) (= (@ _let_1 B2) (@ _let_2 (@ _let_1 B))))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val) (K tptp.set_val) (A tptp.set_val) (B tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.sup_sup_set_val A2) B) (@ _let_1 (@ (@ tptp.sup_sup_set_val A) B)))))))
% 0.26/0.70 (assert (= tptp.sup_sup_set_val (lambda ((X tptp.set_val) (Y2 tptp.set_val)) (@ (@ tptp.sup_sup_set_val Y2) X))))
% 0.26/0.70 (assert (forall ((X2 tptp.set_val) (Y3 tptp.set_val) (Z tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val X2))) (= (@ (@ tptp.sup_sup_set_val (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.sup_sup_set_val Y3) Z))))))
% 0.26/0.70 (assert (forall ((X2 tptp.set_val) (Y3 tptp.set_val) (Z tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val X2))) (let ((_let_2 (@ tptp.sup_sup_set_val Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.26/0.70 (assert (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val X2))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2)))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val) (B2 tptp.set_val) (C tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val A2))) (let ((_let_2 (@ tptp.sup_sup_set_val B2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val) (B2 tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val A2))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))))
% 0.26/0.70 (assert (= tptp.sup_sup_set_val (lambda ((A5 tptp.set_val) (B4 tptp.set_val)) (@ (@ tptp.sup_sup_set_val B4) A5))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val A2) A2) A2)))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val) (B2 tptp.set_val) (C tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val A2))) (= (@ (@ tptp.sup_sup_set_val (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.sup_sup_set_val B2) C))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val) (B2 tptp.set_val) (P2 (-> tptp.val Bool))) (= (forall ((X tptp.val)) (=> (@ (@ tptp.member_val X) (@ (@ tptp.sup_sup_set_val A2) B2)) (@ P2 X))) (and (forall ((X tptp.val)) (=> (@ (@ tptp.member_val X) A2) (@ P2 X))) (forall ((X tptp.val)) (=> (@ (@ tptp.member_val X) B2) (@ P2 X)))))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val) (B2 tptp.set_val) (P2 (-> tptp.val Bool))) (= (exists ((X tptp.val)) (and (@ (@ tptp.member_val X) (@ (@ tptp.sup_sup_set_val A2) B2)) (@ P2 X))) (or (exists ((X tptp.val)) (and (@ (@ tptp.member_val X) A2) (@ P2 X))) (exists ((X tptp.val)) (and (@ (@ tptp.member_val X) B2) (@ P2 X)))))))
% 0.26/0.70 (assert (forall ((C2 tptp.node) (B2 tptp.set_node) (A2 tptp.set_node)) (let ((_let_1 (@ tptp.member_node C2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_set_node A2) B2))))))
% 0.26/0.70 (assert (forall ((C2 tptp.set_val) (B2 tptp.set_set_val) (A2 tptp.set_set_val)) (let ((_let_1 (@ tptp.member_set_val C2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_set_set_val A2) B2))))))
% 0.26/0.70 (assert (forall ((C2 tptp.produc1432036078de_val) (B2 tptp.set_Pr699757092de_val) (A2 tptp.set_Pr699757092de_val)) (let ((_let_1 (@ tptp.member313544709de_val C2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_su2138939728de_val A2) B2))))))
% 0.26/0.70 (assert (forall ((C2 tptp.produc1324971431et_val) (B2 tptp.set_Pr1311924359et_val) (A2 tptp.set_Pr1311924359et_val)) (let ((_let_1 (@ tptp.member1711426256et_val C2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_su2005730907et_val A2) B2))))))
% 0.26/0.70 (assert (forall ((C2 tptp.val) (B2 tptp.set_val) (A2 tptp.set_val)) (let ((_let_1 (@ tptp.member_val C2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_set_val A2) B2))))))
% 0.26/0.70 (assert (forall ((C2 tptp.node) (A2 tptp.set_node) (B2 tptp.set_node)) (let ((_let_1 (@ tptp.member_node C2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_set_node A2) B2))))))
% 0.26/0.70 (assert (forall ((C2 tptp.set_val) (A2 tptp.set_set_val) (B2 tptp.set_set_val)) (let ((_let_1 (@ tptp.member_set_val C2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_set_set_val A2) B2))))))
% 0.26/0.70 (assert (forall ((C2 tptp.produc1432036078de_val) (A2 tptp.set_Pr699757092de_val) (B2 tptp.set_Pr699757092de_val)) (let ((_let_1 (@ tptp.member313544709de_val C2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_su2138939728de_val A2) B2))))))
% 0.26/0.70 (assert (forall ((C2 tptp.produc1324971431et_val) (A2 tptp.set_Pr1311924359et_val) (B2 tptp.set_Pr1311924359et_val)) (let ((_let_1 (@ tptp.member1711426256et_val C2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_su2005730907et_val A2) B2))))))
% 0.26/0.70 (assert (forall ((C2 tptp.val) (A2 tptp.set_val) (B2 tptp.set_val)) (let ((_let_1 (@ tptp.member_val C2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_set_val A2) B2))))))
% 0.26/0.70 (assert (forall ((C2 tptp.node) (A2 tptp.set_node) (B2 tptp.set_node)) (let ((_let_1 (@ tptp.member_node C2))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_node A2) B2)) (=> (not (@ _let_1 A2)) (@ _let_1 B2))))))
% 0.26/0.70 (assert (forall ((C2 tptp.set_val) (A2 tptp.set_set_val) (B2 tptp.set_set_val)) (let ((_let_1 (@ tptp.member_set_val C2))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_set_val A2) B2)) (=> (not (@ _let_1 A2)) (@ _let_1 B2))))))
% 0.26/0.70 (assert (forall ((C2 tptp.produc1432036078de_val) (A2 tptp.set_Pr699757092de_val) (B2 tptp.set_Pr699757092de_val)) (let ((_let_1 (@ tptp.member313544709de_val C2))) (=> (@ _let_1 (@ (@ tptp.sup_su2138939728de_val A2) B2)) (=> (not (@ _let_1 A2)) (@ _let_1 B2))))))
% 0.26/0.70 (assert (forall ((C2 tptp.produc1324971431et_val) (A2 tptp.set_Pr1311924359et_val) (B2 tptp.set_Pr1311924359et_val)) (let ((_let_1 (@ tptp.member1711426256et_val C2))) (=> (@ _let_1 (@ (@ tptp.sup_su2005730907et_val A2) B2)) (=> (not (@ _let_1 A2)) (@ _let_1 B2))))))
% 0.26/0.70 (assert (forall ((C2 tptp.val) (A2 tptp.set_val) (B2 tptp.set_val)) (let ((_let_1 (@ tptp.member_val C2))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_val A2) B2)) (=> (not (@ _let_1 A2)) (@ _let_1 B2))))))
% 0.26/0.70 (assert (forall ((C2 tptp.set_val) (B tptp.set_val) (A tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_set_val A) B))))))
% 0.26/0.70 (assert (forall ((C2 tptp.set_val) (A tptp.set_val) (B tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_val A) B))))))
% 0.26/0.70 (assert (= tptp.ord_less_eq_set_val (lambda ((A3 tptp.set_val) (B5 tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val A3) B5) B5))))
% 0.26/0.70 (assert (= tptp.ord_less_eq_set_val (lambda ((B5 tptp.set_val) (A3 tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val A3) B5) A3))))
% 0.26/0.70 (assert (forall ((B tptp.set_val) (A tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val B) (@ (@ tptp.sup_sup_set_val A) B))))
% 0.26/0.70 (assert (forall ((A tptp.set_val) (B tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val A) (@ (@ tptp.sup_sup_set_val A) B))))
% 0.26/0.70 (assert (= tptp.ord_less_eq_set_val (lambda ((B5 tptp.set_val) (A3 tptp.set_val)) (= A3 (@ (@ tptp.sup_sup_set_val A3) B5)))))
% 0.26/0.70 (assert (forall ((B tptp.set_val) (A tptp.set_val) (C2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val B) A) (=> (@ (@ tptp.ord_less_eq_set_val C2) A) (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val B) C2)) A)))))
% 0.26/0.70 (assert (forall ((B tptp.set_val) (C2 tptp.set_val) (A tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val B) C2)) A) (not (=> (@ (@ tptp.ord_less_eq_set_val B) A) (not (@ (@ tptp.ord_less_eq_set_val C2) A)))))))
% 0.26/0.70 (assert (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (= (@ (@ tptp.sup_sup_set_val X2) Y3) Y3))))
% 0.26/0.70 (assert (forall ((Y3 tptp.set_val) (X2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val Y3) X2) (= (@ (@ tptp.sup_sup_set_val X2) Y3) X2))))
% 0.26/0.70 (assert (forall ((A tptp.set_val) (B tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A) B) (= (@ (@ tptp.sup_sup_set_val A) B) B))))
% 0.26/0.70 (assert (forall ((B tptp.set_val) (A tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val B) A) (= (@ (@ tptp.sup_sup_set_val A) B) A))))
% 0.26/0.70 (assert (forall ((F2 (-> tptp.set_val tptp.set_val tptp.set_val)) (X2 tptp.set_val) (Y3 tptp.set_val)) (=> (forall ((X3 tptp.set_val) (Y5 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val X3) (@ (@ F2 X3) Y5))) (=> (forall ((X3 tptp.set_val) (Y5 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val Y5) (@ (@ F2 X3) Y5))) (=> (forall ((X3 tptp.set_val) (Y5 tptp.set_val) (Z3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val Y5) X3) (=> (@ (@ tptp.ord_less_eq_set_val Z3) X3) (@ (@ tptp.ord_less_eq_set_val (@ (@ F2 Y5) Z3)) X3)))) (= (@ (@ tptp.sup_sup_set_val X2) Y3) (@ (@ F2 X2) Y3)))))))
% 0.26/0.70 (assert (forall ((A tptp.set_val) (B tptp.set_val)) (=> (= A (@ (@ tptp.sup_sup_set_val A) B)) (@ (@ tptp.ord_less_eq_set_val B) A))))
% 0.26/0.70 (assert (forall ((B tptp.set_val) (A tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val B) A) (= A (@ (@ tptp.sup_sup_set_val A) B)))))
% 0.26/0.70 (assert (= tptp.ord_less_eq_set_val (lambda ((X tptp.set_val) (Y2 tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val X) Y2) Y2))))
% 0.26/0.70 (assert (forall ((Y3 tptp.set_val) (X2 tptp.set_val) (Z tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val Y3) X2) (=> (@ (@ tptp.ord_less_eq_set_val Z) X2) (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val Y3) Z)) X2)))))
% 0.26/0.70 (assert (forall ((A tptp.set_val) (C2 tptp.set_val) (B tptp.set_val) (D tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A) C2) (=> (@ (@ tptp.ord_less_eq_set_val B) D) (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val A) B)) (@ (@ tptp.sup_sup_set_val C2) D))))))
% 0.26/0.70 (assert (forall ((C2 tptp.set_val) (A tptp.set_val) (D tptp.set_val) (B tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val C2) A) (=> (@ (@ tptp.ord_less_eq_set_val D) B) (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val C2) D)) (@ (@ tptp.sup_sup_set_val A) B))))))
% 0.26/0.70 (assert (forall ((X2 tptp.set_val) (B tptp.set_val) (A tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val X2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_set_val A) B))))))
% 0.26/0.70 (assert (forall ((X2 tptp.set_val) (A tptp.set_val) (B tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val X2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_val A) B))))))
% 0.26/0.70 (assert (forall ((Y3 tptp.set_val) (X2 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val Y3) (@ (@ tptp.sup_sup_set_val X2) Y3))))
% 0.26/0.70 (assert (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val X2) (@ (@ tptp.sup_sup_set_val X2) Y3))))
% 0.26/0.70 (assert (forall ((A tptp.set_val) (X2 tptp.set_val) (B tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A) X2) (=> (@ (@ tptp.ord_less_eq_set_val B) X2) (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val A) B)) X2)))))
% 0.26/0.70 (assert (forall ((A tptp.set_val) (B tptp.set_val) (X2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val A) B)) X2) (not (=> (@ (@ tptp.ord_less_eq_set_val A) X2) (not (@ (@ tptp.ord_less_eq_set_val B) X2)))))))
% 0.26/0.70 (assert (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val X2) (@ (@ tptp.sup_sup_set_val X2) Y3))))
% 0.26/0.70 (assert (forall ((Y3 tptp.set_val) (X2 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val Y3) (@ (@ tptp.sup_sup_set_val X2) Y3))))
% 0.26/0.70 (assert (= tptp.ord_less_eq_set_val (lambda ((A5 tptp.set_val) (B4 tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val A5) B4) B4))))
% 0.26/0.70 (assert (forall ((C tptp.set_val) (A2 tptp.set_val) (B2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val C) (@ (@ tptp.sup_sup_set_val A2) B2)) (not (forall ((A6 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A6) A2) (forall ((B6 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val B6) B2) (not (= C (@ (@ tptp.sup_sup_set_val A6) B6)))))))))))
% 0.26/0.70 (assert (forall ((B2 tptp.set_val) (A2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val B2) A2) (= (@ (@ tptp.sup_sup_set_val A2) B2) A2))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val) (B2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A2) B2) (= (@ (@ tptp.sup_sup_set_val A2) B2) B2))))
% 0.26/0.70 (assert (forall ((B2 tptp.set_val) (A2 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val B2) (@ (@ tptp.sup_sup_set_val A2) B2))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val) (B2 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val A2) (@ (@ tptp.sup_sup_set_val A2) B2))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val) (C tptp.set_val) (B2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A2) C) (=> (@ (@ tptp.ord_less_eq_set_val B2) C) (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val A2) B2)) C)))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_val) (C tptp.set_val) (B2 tptp.set_val) (D2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A2) C) (=> (@ (@ tptp.ord_less_eq_set_val B2) D2) (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val A2) B2)) (@ (@ tptp.sup_sup_set_val C) D2))))))
% 0.83/1.04 (assert (forall ((G tptp.g) (P2 tptp.set_val)) (= (@ (@ (@ (@ (@ (@ (@ tptp.irredu224829488eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G) P2) (and (not (= P2 tptp.bot_bot_set_val)) (@ (@ tptp.ord_less_eq_set_val P2) (@ tptp.dom_val_list_val (@ (@ (@ (@ tptp.sSA_CF262257161de_val tptp.alpha_n) tptp.defs) tptp.phis) G))) (exists ((X tptp.val)) (and (@ (@ tptp.member_val X) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)) (forall ((Y2 tptp.val)) (=> (@ (@ tptp.member_val Y2) P2) (forall ((Phi3 tptp.val)) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) G) Y2) Phi3) (@ (@ tptp.member_val Phi3) (@ (@ tptp.sup_sup_set_val P2) (@ (@ tptp.insert_val X) tptp.bot_bot_set_val)))))))))))))
% 0.83/1.04 (assert (forall ((P tptp.val) (G tptp.g) (Vs tptp.list_val)) (=> (@ (@ tptp.member_val P) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)) (=> (= (@ (@ (@ (@ (@ tptp.sSA_CF262257161de_val tptp.alpha_n) tptp.defs) tptp.phis) G) P) (@ tptp.some_list_val Vs)) (not (= (@ tptp.set_val2 Vs) (@ (@ tptp.insert_val P) tptp.bot_bot_set_val)))))))
% 0.83/1.04 (assert (forall ((F2 (-> tptp.produc1432036078de_val tptp.option_list_val))) (= (= (@ tptp.dom_Pr729677986st_val F2) tptp.bot_bo404898488de_val) (= F2 (lambda ((X tptp.produc1432036078de_val)) tptp.none_list_val)))))
% 0.83/1.04 (assert (forall ((F2 (-> tptp.val tptp.option_list_val))) (= (= (@ tptp.dom_val_list_val F2) tptp.bot_bot_set_val) (= F2 (lambda ((X tptp.val)) tptp.none_list_val)))))
% 0.83/1.04 (assert (forall ((G tptp.g)) (@ tptp.finite2056463621de_val (@ tptp.dom_Pr729677986st_val (@ tptp.phis G)))))
% 0.83/1.04 (assert (forall ((X2 tptp.node) (A2 tptp.set_node) (B2 tptp.set_node)) (= (@ (@ tptp.ord_less_eq_set_node (@ (@ tptp.insert_node X2) A2)) B2) (and (@ (@ tptp.member_node X2) B2) (@ (@ tptp.ord_less_eq_set_node A2) B2)))))
% 0.83/1.04 (assert (forall ((X2 tptp.set_val) (A2 tptp.set_set_val) (B2 tptp.set_set_val)) (= (@ (@ tptp.ord_le1742111550et_val (@ (@ tptp.insert_set_val X2) A2)) B2) (and (@ (@ tptp.member_set_val X2) B2) (@ (@ tptp.ord_le1742111550et_val A2) B2)))))
% 0.83/1.04 (assert (forall ((X2 tptp.produc1432036078de_val) (A2 tptp.set_Pr699757092de_val) (B2 tptp.set_Pr699757092de_val)) (= (@ (@ tptp.ord_le1643692676de_val (@ (@ tptp.insert869443870de_val X2) A2)) B2) (and (@ (@ tptp.member313544709de_val X2) B2) (@ (@ tptp.ord_le1643692676de_val A2) B2)))))
% 0.83/1.04 (assert (forall ((X2 tptp.produc1324971431et_val) (A2 tptp.set_Pr1311924359et_val) (B2 tptp.set_Pr1311924359et_val)) (= (@ (@ tptp.ord_le299366439et_val (@ (@ tptp.insert1846469495et_val X2) A2)) B2) (and (@ (@ tptp.member1711426256et_val X2) B2) (@ (@ tptp.ord_le299366439et_val A2) B2)))))
% 0.83/1.04 (assert (forall ((X2 tptp.val) (A2 tptp.set_val) (B2 tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.insert_val X2) A2)) B2) (and (@ (@ tptp.member_val X2) B2) (@ (@ tptp.ord_less_eq_set_val A2) B2)))))
% 0.83/1.04 (assert (forall ((A tptp.val) (A2 tptp.set_val)) (= (@ tptp.finite_finite_val (@ (@ tptp.insert_val A) A2)) (@ tptp.finite_finite_val A2))))
% 0.83/1.04 (assert (forall ((A tptp.produc1324971431et_val) (A2 tptp.set_Pr1311924359et_val)) (= (@ tptp.finite79836624et_val (@ (@ tptp.insert1846469495et_val A) A2)) (@ tptp.finite79836624et_val A2))))
% 0.83/1.04 (assert (forall ((A tptp.produc1432036078de_val) (A2 tptp.set_Pr699757092de_val)) (= (@ tptp.finite2056463621de_val (@ (@ tptp.insert869443870de_val A) A2)) (@ tptp.finite2056463621de_val A2))))
% 0.83/1.04 (assert (not (@ (@ tptp.member_val tptp.phi_s) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) tptp.g2))))
% 0.83/1.04 (set-info :filename cvc5---1.0.5_28802)
% 0.83/1.04 (check-sat-assuming ( true ))
% 0.83/1.04 ------- get file name : TPTP file name is ITP083^1
% 0.83/1.04 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_28802.smt2...
% 0.83/1.04 --- Run --ho-elim --full-saturate-quant at 10...
% 0.83/1.04 % SZS status Theorem for ITP083^1
% 0.83/1.04 % SZS output start Proof for ITP083^1
% 0.83/1.04 (
% 0.83/1.04 (let ((_let_1 (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) tptp.g2))) (let ((_let_2 (not (@ (@ tptp.member_val tptp.phi_s) _let_1)))) (let ((_let_3 (= tptp.ord_less_eq_set_val (lambda ((A5 tptp.set_val) (B4 tptp.set_val)) (forall ((T2 tptp.val)) (let ((_let_1 (@ tptp.member_val T2))) (=> (@ _let_1 A5) (@ _let_1 B4)))))))) (let ((_let_4 (= tptp.ord_le299366439et_val (lambda ((A5 tptp.set_Pr1311924359et_val) (B4 tptp.set_Pr1311924359et_val)) (forall ((T2 tptp.produc1324971431et_val)) (let ((_let_1 (@ tptp.member1711426256et_val T2))) (=> (@ _let_1 A5) (@ _let_1 B4)))))))) (let ((_let_5 (= tptp.ord_le1643692676de_val (lambda ((A5 tptp.set_Pr699757092de_val) (B4 tptp.set_Pr699757092de_val)) (forall ((T2 tptp.produc1432036078de_val)) (let ((_let_1 (@ tptp.member313544709de_val T2))) (=> (@ _let_1 A5) (@ _let_1 B4)))))))) (let ((_let_6 (= tptp.ord_le1742111550et_val (lambda ((A5 tptp.set_set_val) (B4 tptp.set_set_val)) (forall ((T2 tptp.set_val)) (let ((_let_1 (@ tptp.member_set_val T2))) (=> (@ _let_1 A5) (@ _let_1 B4)))))))) (let ((_let_7 (= tptp.ord_less_eq_set_node (lambda ((A5 tptp.set_node) (B4 tptp.set_node)) (forall ((T2 tptp.node)) (let ((_let_1 (@ tptp.member_node T2))) (=> (@ _let_1 A5) (@ _let_1 B4)))))))) (let ((_let_8 (= tptp.sSA_CF1252180629de_val (lambda ((Alpha_n (-> tptp.g tptp.list_node)) (Defs (-> tptp.g tptp.node tptp.set_val)) (Phis (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val)) (G2 tptp.g) (V3 tptp.val) (V4 tptp.val)) (exists ((Vs2 tptp.list_val)) (and (= (@ (@ (@ (@ (@ tptp.sSA_CF262257161de_val Alpha_n) Defs) Phis) G2) V3) (@ tptp.some_list_val Vs2)) (@ (@ tptp.member_val V4) (@ tptp.set_val2 Vs2)))))))) (let ((_let_9 (= tptp.sSA_CF262257161de_val (lambda ((Alpha_n (-> tptp.g tptp.list_node)) (Defs (-> tptp.g tptp.node tptp.set_val)) (Phis (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val)) (G2 tptp.g) (V3 tptp.val)) (@ (@ Phis G2) (@ (@ tptp.produc1470527136de_val (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val Alpha_n) Defs) Phis) G2) V3)) V3)))))) (let ((_let_10 (= tptp.sSA_CF178745443eD_val (lambda ((Alpha_n (-> tptp.g tptp.list_node)) (InEdges (-> tptp.g tptp.node tptp.list_P561207620_edgeD)) (Uses (-> tptp.g tptp.node tptp.set_val)) (Phis (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val)) (G2 tptp.g) (N3 tptp.node)) (@ (@ tptp.sup_sup_set_val (@ (@ Uses G2) N3)) (@ (@ (@ (@ (@ tptp.sSA_CF848637139eD_val Alpha_n) InEdges) Phis) G2) N3)))))) (let ((_let_11 (= tptp.sSA_CF139593942de_val (lambda ((Defs (-> tptp.g tptp.node tptp.set_val)) (Phis (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val)) (G2 tptp.g) (N3 tptp.node)) (@ (@ tptp.sup_sup_set_val (@ (@ Defs G2) N3)) (@ (@ (@ tptp.sSA_CF370335846de_val Phis) G2) N3)))))) (let ((_let_12 (= tptp.sSA_CF2074824714de_val (lambda ((Alpha_n (-> tptp.g tptp.list_node)) (Defs (-> tptp.g tptp.node tptp.set_val)) (Uses (-> tptp.g tptp.node tptp.set_val)) (Phis (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val)) (G2 tptp.g)) (forall ((X tptp.node)) (=> (@ (@ tptp.member_node X) (@ tptp.set_node2 (@ Alpha_n G2))) (forall ((Val2 tptp.val)) (=> (@ (@ tptp.member_val Val2) (@ (@ (@ tptp.sSA_CF370335846de_val Phis) G2) X)) (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val Alpha_n) Defs) Uses) Phis) G2) Val2))))))))) (let ((_let_13 (= tptp.sSA_CF1899243830eD_val (lambda ((Alpha_n (-> tptp.g tptp.list_node)) (InEdges (-> tptp.g tptp.node tptp.list_P561207620_edgeD)) (Defs (-> tptp.g tptp.node tptp.set_val)) (Uses (-> tptp.g tptp.node tptp.set_val)) (Phis (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val)) (G2 tptp.g) (V3 tptp.val)) (exists ((X tptp.val)) (and (@ (@ tptp.member_val X) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val Alpha_n) InEdges) Defs) Uses) Phis) G2)) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1909049442de_val Alpha_n) Defs) Phis) G2) V3) X))))))) (let ((_let_14 (@ tptp.var2 tptp.g2))) (let ((_let_15 (@ _let_14 tptp.phi))) (let ((_let_16 (= tptp.sSA_CF1660885746eD_val (lambda ((Alpha_n (-> tptp.g tptp.list_node)) (InEdges (-> tptp.g tptp.node tptp.list_P561207620_edgeD)) (Defs (-> tptp.g tptp.node tptp.set_val)) (Uses (-> tptp.g tptp.node tptp.set_val)) (Phis (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val)) (G2 tptp.g)) (exists ((X tptp.val)) (and (@ (@ tptp.member_val X) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val Alpha_n) InEdges) Defs) Uses) Phis) G2)) (@ (@ (@ (@ (@ (@ (@ tptp.sSA_CF1899243830eD_val Alpha_n) InEdges) Defs) Uses) Phis) G2) X))))))) (let ((_let_17 (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) tptp.g2))) (let ((_let_18 (= (@ _let_17 tptp.phi_s) (@ _let_17 tptp.s)))) (let ((_let_19 (forall ((G tptp.g) (V tptp.val) (V2 tptp.val)) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) V2) (@ (@ tptp.member_val V2) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)))))) (let ((_let_20 (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) tptp.g2) tptp.phi2) tptp.phi_s))) (let ((_let_21 (forall ((G tptp.g) (V tptp.val) (V2 tptp.val) (BOUND_VARIABLE_9768 tptp.list_val)) (let ((_let_1 (ho_75 k_74 V2))) (or (ho_61 _let_1 (ho_150 (ho_149 (ho_148 (ho_147 (ho_146 (ho_145 k_144 k_48) k_142) k_46) k_141) k_44) G)) (not (= (ho_108 k_107 BOUND_VARIABLE_9768) (ho_41 (ho_45 k_44 G) (ho_58 (ho_57 k_56 (ho_55 (ho_54 (ho_53 (ho_52 (ho_51 k_50 k_48) k_46) k_44) G) V)) V)))) (not (ho_61 _let_1 (ho_117 k_116 BOUND_VARIABLE_9768)))))))) (let ((_let_22 (ho_75 k_74 tptp.phi_s))) (let ((_let_23 (ho_61 _let_22 (ho_117 k_116 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_400)))) (let ((_let_24 (not _let_23))) (let ((_let_25 (ho_108 k_107 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_400))) (let ((_let_26 (ho_41 (ho_45 k_44 tptp.g2) (ho_58 (ho_57 k_56 (ho_55 (ho_54 (ho_53 (ho_52 (ho_51 k_50 k_48) k_46) k_44) tptp.g2) tptp.phi2)) tptp.phi2)))) (let ((_let_27 (= _let_26 _let_25))) (let ((_let_28 (not _let_27))) (let ((_let_29 (ho_61 _let_22 (ho_150 (ho_149 (ho_148 (ho_147 (ho_146 (ho_145 k_144 k_48) k_142) k_46) k_141) k_44) tptp.g2)))) (let ((_let_30 (or _let_29 _let_28 _let_24))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (ASSUME :args (_let_11)))) (let ((_let_35 (ASSUME :args (_let_10)))) (let ((_let_36 (ASSUME :args (_let_9)))) (let ((_let_37 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_36 _let_35 _let_34 _let_33 _let_32 _let_31) :args ((= tptp.sSA_CF1252180629de_val (lambda ((Alpha_n (-> tptp.g tptp.list_node)) (Defs (-> tptp.g tptp.node tptp.set_val)) (Phis (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val)) (G2 tptp.g) (V3 tptp.val) (V4 tptp.val)) (not (forall ((Vs2 tptp.list_val)) (or (not (= (@ (@ (@ (@ (@ tptp.sSA_CF262257161de_val Alpha_n) Defs) Phis) G2) V3) (@ tptp.some_list_val Vs2))) (not (@ (@ tptp.member_val V4) (@ tptp.set_val2 Vs2)))))))) SB_DEFAULT SBA_FIXPOINT))) _let_36 _let_35 _let_34 _let_33 _let_32 _let_31))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_19)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_37 :args ((forall ((G tptp.g) (V tptp.val) (V2 tptp.val)) (or (not (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) V2)) (@ (@ tptp.member_val V2) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((G tptp.g) (V tptp.val) (V2 tptp.val) (BOUND_VARIABLE_9768 tptp.list_val)) (let ((_let_1 (@ tptp.member_val V2))) (or (@ _let_1 (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)) (not (= (@ (@ tptp.phis G) (@ (@ tptp.produc1470527136de_val (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V)) V)) (@ tptp.some_list_val BOUND_VARIABLE_9768))) (not (@ _let_1 (@ tptp.set_val2 BOUND_VARIABLE_9768)))))) _let_21))))))) (let ((_let_39 (not _let_30))) (let ((_let_40 (or _let_28 _let_24))) (let ((_let_41 (forall ((Vs2 tptp.list_val)) (or (not (= (ho_108 k_107 Vs2) (ho_41 (ho_45 k_44 tptp.g2) (ho_58 (ho_57 k_56 (ho_55 (ho_54 (ho_53 (ho_52 (ho_51 k_50 k_48) k_46) k_44) tptp.g2) tptp.phi2)) tptp.phi2)))) (not (ho_61 (ho_75 k_74 tptp.phi_s) (ho_117 k_116 Vs2))))))) (let ((_let_42 (not _let_40))) (let ((_let_43 (not _let_41))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_20)) (TRANS (MACRO_SR_EQ_INTRO _let_37 :args (_let_20 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((Vs2 tptp.list_val)) (or (not (= (@ tptp.some_list_val Vs2) (@ (@ tptp.phis tptp.g2) (@ (@ tptp.produc1470527136de_val (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) tptp.g2) tptp.phi2)) tptp.phi2)))) (not (@ (@ tptp.member_val tptp.phi_s) (@ tptp.set_val2 Vs2)))))) _let_43))))))) (let ((_let_45 (or))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_44) :args (_let_43)) (REWRITE :args ((=> _let_43 (not (or (not (= _let_25 _let_26)) _let_24))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_41))) (REFL :args (_let_42)) :args _let_45)) _let_44 :args (_let_42 true _let_41)))) (let ((_let_47 (REFL :args (_let_40)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_38 :args (tptp.g2 tptp.phi2 tptp.phi_s SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_400 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_21)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_30)) :args ((or _let_29 _let_24 _let_28 _let_39))) (EQ_RESOLVE (ASSUME :args (_let_2)) (PREPROCESS :args ((= _let_2 (not _let_29))))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 1)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_45)) :args ((or _let_23 _let_40))) _let_46 :args (_let_23 true _let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 0)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) :args _let_45)) :args ((or _let_27 _let_40))) _let_46 :args (_let_27 true _let_40)) :args (_let_39 true _let_29 false _let_23 false _let_27)) _let_38 :args (false true _let_30 false _let_21)) :args ((not (= tptp.phi_s tptp.s)) (not (= tptp.phi tptp.phi_s)) _let_20 (@ (@ tptp.member_val tptp.s) _let_1) (@ (@ tptp.member_val tptp.phi) _let_1) (not (forall ((Phi tptp.val)) (not (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) tptp.g2) Phi) tptp.phi_s)))) _let_19 (forall ((V tptp.val) (G tptp.g) (N tptp.node)) (let ((_let_1 (@ tptp.member_val V))) (=> (@ _let_1 (@ (@ tptp.uses G) N)) (@ _let_1 (@ (@ (@ tptp.sSA_CF655860150de_val tptp.alpha_n) tptp.uses) G))))) (forall ((G tptp.g) (V tptp.val)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.sSA_CF1899243830eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G) V) (@ (@ tptp.member_val V) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)))) (forall ((G tptp.g) (V tptp.val)) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val tptp.alpha_n) tptp.defs) tptp.uses) tptp.phis) G) V) (@ (@ tptp.member_val V) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)))) (forall ((G tptp.g)) (@ tptp.finite_finite_val (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G))) (forall ((V tptp.val) (G tptp.g) (N tptp.node)) (let ((_let_1 (@ tptp.member_val V))) (=> (@ _let_1 (@ (@ tptp.uses G) N)) (@ _let_1 (@ (@ (@ (@ (@ (@ tptp.sSA_CF178745443eD_val tptp.alpha_n) tptp.inEdges) tptp.uses) tptp.phis) G) N))))) (forall ((G tptp.g)) (= (@ (@ (@ (@ (@ (@ tptp.sSA_CF1660885746eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G) (exists ((X tptp.val)) (and (@ (@ tptp.member_val X) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)) (@ (@ (@ (@ (@ (@ (@ tptp.sSA_CF1899243830eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G) X))))) (forall ((G tptp.g) (V tptp.val)) (= (@ (@ (@ (@ (@ (@ (@ tptp.sSA_CF1899243830eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G) V) (exists ((X tptp.val)) (and (@ (@ tptp.member_val X) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1909049442de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) X))))) _let_18 (forall ((N tptp.node) (G tptp.g) (V tptp.val)) (let ((_let_1 (@ tptp.member_val V))) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (=> (@ _let_1 (@ (@ tptp.defs G) N)) (not (@ _let_1 (@ (@ tptp.uses G) N))))))) (forall ((G tptp.g) (V tptp.val) (V2 tptp.val)) (let ((_let_1 (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val tptp.alpha_n) tptp.defs) tptp.uses) tptp.phis) G))) (=> (@ _let_1 V) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) V2) (@ _let_1 V2))))) (forall ((G tptp.g) (P tptp.val) (Q tptp.val)) (let ((_let_1 (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) G))) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) G) P) Q) (=> (not (= P Q)) (=> (@ (@ tptp.member_val P) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)) (not (= (@ _let_1 P) (@ _let_1 Q)))))))) (forall ((G tptp.g) (P tptp.val) (Q tptp.val) (R tptp.val)) (let ((_let_1 (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) G))) (let ((_let_2 (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) G) P))) (=> (@ _let_2 Q) (=> (@ _let_2 R) (=> (not (= Q R)) (=> (@ (@ tptp.member_val P) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)) (not (= (@ _let_1 Q) (@ _let_1 R)))))))))) (forall ((V tptp.val) (G tptp.g) (N tptp.node)) (=> (@ (@ tptp.member_val V) (@ (@ tptp.uses G) N)) (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))))) (forall ((G tptp.g) (N tptp.node)) (@ tptp.finite_finite_val (@ (@ tptp.defs G) N))) (forall ((V tptp.val) (G tptp.g)) (=> (@ (@ tptp.member_val V) (@ (@ (@ tptp.sSA_CF655860150de_val tptp.alpha_n) tptp.uses) G)) (not (forall ((N2 tptp.node)) (=> (@ (@ tptp.member_node N2) (@ tptp.set_node2 (@ tptp.alpha_n G))) (not (@ (@ tptp.member_val V) (@ (@ tptp.uses G) N2)))))))) (forall ((G tptp.g)) (@ tptp.finite_finite_val (@ (@ (@ tptp.sSA_CF655860150de_val tptp.alpha_n) tptp.uses) G))) (forall ((N tptp.node) (G tptp.g) (Val tptp.val)) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (=> (@ (@ tptp.member_val Val) (@ (@ tptp.uses G) N)) (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val tptp.alpha_n) tptp.defs) tptp.uses) tptp.phis) G) Val)))) (forall ((G tptp.g) (A tptp.val)) (= (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val tptp.alpha_n) tptp.defs) tptp.uses) tptp.phis) G) A) (or (exists ((N3 tptp.node) (Val2 tptp.val)) (and (= A Val2) (@ (@ tptp.member_node N3) (@ tptp.set_node2 (@ tptp.alpha_n G))) (@ (@ tptp.member_val Val2) (@ (@ tptp.uses G) N3)))) (exists ((V3 tptp.val) (V4 tptp.val)) (and (= A V4) (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val tptp.alpha_n) tptp.defs) tptp.uses) tptp.phis) G) V3) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V3) V4)))))) (forall ((G tptp.g) (X2 tptp.val) (P2 (-> tptp.val Bool))) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val tptp.alpha_n) tptp.defs) tptp.uses) tptp.phis) G) X2) (=> (forall ((N2 tptp.node) (Val3 tptp.val)) (=> (@ (@ tptp.member_node N2) (@ tptp.set_node2 (@ tptp.alpha_n G))) (=> (@ (@ tptp.member_val Val3) (@ (@ tptp.uses G) N2)) (@ P2 Val3)))) (=> (forall ((V5 tptp.val) (V6 tptp.val)) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val tptp.alpha_n) tptp.defs) tptp.uses) tptp.phis) G) V5) (=> (@ P2 V5) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V5) V6) (@ P2 V6))))) (@ P2 X2))))) (forall ((G tptp.g) (A tptp.val)) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val tptp.alpha_n) tptp.defs) tptp.uses) tptp.phis) G) A) (=> (forall ((N2 tptp.node)) (=> (@ (@ tptp.member_node N2) (@ tptp.set_node2 (@ tptp.alpha_n G))) (not (@ (@ tptp.member_val A) (@ (@ tptp.uses G) N2))))) (not (forall ((V5 tptp.val)) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val tptp.alpha_n) tptp.defs) tptp.uses) tptp.phis) G) V5) (not (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V5) A)))))))) (forall ((N tptp.node) (G tptp.g)) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (@ tptp.finite_finite_val (@ (@ (@ (@ (@ (@ tptp.sSA_CF178745443eD_val tptp.alpha_n) tptp.inEdges) tptp.uses) tptp.phis) G) N)))) (forall ((V tptp.val) (G tptp.g)) (=> (@ (@ tptp.member_val V) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)) (@ (@ tptp.member_node (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V)) (@ tptp.set_node2 (@ tptp.alpha_n G))))) (forall ((G tptp.g) (N tptp.node)) (@ tptp.finite_finite_val (@ (@ tptp.uses G) N))) _let_18 (forall ((V tptp.val) (G tptp.g) (N tptp.node)) (let ((_let_1 (@ tptp.member_val V))) (=> (@ _let_1 (@ (@ (@ (@ (@ (@ tptp.sSA_CF178745443eD_val tptp.alpha_n) tptp.inEdges) tptp.uses) tptp.phis) G) N)) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (@ _let_1 (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)))))) (forall ((V tptp.val) (G tptp.g) (N tptp.node)) (let ((_let_1 (@ tptp.member_val V))) (=> (@ _let_1 (@ (@ (@ (@ (@ tptp.sSA_CF848637139eD_val tptp.alpha_n) tptp.inEdges) tptp.phis) G) N)) (@ _let_1 (@ (@ (@ (@ (@ (@ tptp.sSA_CF178745443eD_val tptp.alpha_n) tptp.inEdges) tptp.uses) tptp.phis) G) N))))) (forall ((N tptp.node) (G tptp.g)) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (@ tptp.finite_finite_val (@ (@ (@ (@ (@ tptp.sSA_CF848637139eD_val tptp.alpha_n) tptp.inEdges) tptp.phis) G) N)))) (forall ((V tptp.val) (G tptp.g)) (let ((_let_1 (@ tptp.member_val V))) (=> (@ _let_1 (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)) (@ _let_1 (@ (@ (@ (@ tptp.sSA_CF139593942de_val tptp.defs) tptp.phis) G) (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V)))))) (forall ((V tptp.val) (G tptp.g)) (=> (@ (@ tptp.member_val V) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)) (exists ((X3 tptp.node)) (and (@ (@ tptp.member_node X3) (@ tptp.set_node2 (@ tptp.alpha_n G))) (@ (@ tptp.member_val V) (@ (@ (@ (@ tptp.sSA_CF139593942de_val tptp.defs) tptp.phis) G) X3)) (forall ((Y tptp.node)) (=> (and (@ (@ tptp.member_node Y) (@ tptp.set_node2 (@ tptp.alpha_n G))) (@ (@ tptp.member_val V) (@ (@ (@ (@ tptp.sSA_CF139593942de_val tptp.defs) tptp.phis) G) Y))) (= Y X3))))))) (forall ((V tptp.val) (G tptp.g)) (=> (@ (@ tptp.member_val V) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)) (exists ((X3 tptp.node)) (and (@ (@ tptp.member_node X3) (@ tptp.set_node2 (@ tptp.alpha_n G))) (@ (@ tptp.member_val V) (@ (@ (@ (@ tptp.sSA_CF139593942de_val tptp.defs) tptp.phis) G) X3)))))) (forall ((Xs tptp.list_P844977291de_val)) (@ tptp.finite781217938de_val (@ tptp.set_Pr434939430de_val Xs))) (forall ((Xs tptp.list_P761482893et_val)) (@ tptp.finite1581417648et_val (@ tptp.set_Pr2104310812et_val Xs))) (forall ((Xs tptp.list_P1078858818l_node)) (@ tptp.finite423892681l_node (@ tptp.set_Pr1600883293l_node Xs))) (forall ((Xs tptp.list_P1811375021al_val)) (@ tptp.finite759259600al_val (@ tptp.set_Pr102746428al_val Xs))) (forall ((Xs tptp.list_set_val)) (@ tptp.finite1265617511et_val (@ tptp.set_set_val2 Xs))) (forall ((Xs tptp.list_node)) (@ tptp.finite_finite_node (@ tptp.set_node2 Xs))) (forall ((Xs tptp.list_val)) (@ tptp.finite_finite_val (@ tptp.set_val2 Xs))) (forall ((Xs tptp.list_P2089461677et_val)) (@ tptp.finite79836624et_val (@ tptp.set_Pr284769596et_val Xs))) (forall ((Xs tptp.list_P1820443774de_val)) (@ tptp.finite2056463621de_val (@ tptp.set_Pr1085970585de_val Xs))) (forall ((G tptp.g) (N tptp.node)) (@ tptp.finite_finite_val (@ (@ (@ tptp.sSA_CF370335846de_val tptp.phis) G) N))) (forall ((N tptp.node) (G tptp.g)) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (@ tptp.finite_finite_val (@ (@ (@ (@ tptp.sSA_CF139593942de_val tptp.defs) tptp.phis) G) N)))) (= _let_15 (@ _let_14 tptp.s)) _let_16 (forall ((V tptp.val) (G tptp.g) (N tptp.node)) (let ((_let_1 (@ tptp.member_val V))) (=> (@ _let_1 (@ (@ tptp.defs G) N)) (@ _let_1 (@ (@ (@ (@ tptp.sSA_CF139593942de_val tptp.defs) tptp.phis) G) N))))) (forall ((V tptp.val) (G tptp.g) (N tptp.node)) (let ((_let_1 (@ tptp.member_val V))) (=> (@ _let_1 (@ (@ (@ tptp.sSA_CF370335846de_val tptp.phis) G) N)) (@ _let_1 (@ (@ (@ (@ tptp.sSA_CF139593942de_val tptp.defs) tptp.phis) G) N))))) (forall ((N tptp.node) (G tptp.g) (M tptp.node) (V tptp.val)) (let ((_let_1 (@ (@ (@ tptp.sSA_CF139593942de_val tptp.defs) tptp.phis) G))) (let ((_let_2 (@ tptp.member_val V))) (let ((_let_3 (@ tptp.set_node2 (@ tptp.alpha_n G)))) (=> (@ (@ tptp.member_node N) _let_3) (=> (@ (@ tptp.member_node M) _let_3) (=> (@ _let_2 (@ _let_1 N)) (=> (@ _let_2 (@ _let_1 M)) (= N M))))))))) (forall ((A tptp.produc1946948786l_node) (P2 (-> tptp.produc1946948786l_node Bool))) (= (@ (@ tptp.member828457417l_node A) (@ tptp.collec885255687l_node P2)) (@ P2 A))) (forall ((A tptp.product_prod_val_val) (P2 (-> tptp.product_prod_val_val Bool))) (= (@ (@ tptp.member1680438992al_val A) (@ tptp.collec52550418al_val P2)) (@ P2 A))) (forall ((A tptp.val) (P2 (-> tptp.val Bool))) (= (@ (@ tptp.member_val A) (@ tptp.collect_val P2)) (@ P2 A))) (forall ((A tptp.node) (P2 (-> tptp.node Bool))) (= (@ (@ tptp.member_node A) (@ tptp.collect_node P2)) (@ P2 A))) (forall ((A tptp.set_val) (P2 (-> tptp.set_val Bool))) (= (@ (@ tptp.member_set_val A) (@ tptp.collect_set_val P2)) (@ P2 A))) (forall ((A tptp.produc1432036078de_val) (P2 (-> tptp.produc1432036078de_val Bool))) (= (@ (@ tptp.member313544709de_val A) (@ tptp.collec370342979de_val P2)) (@ P2 A))) (forall ((A tptp.produc1324971431et_val) (P2 (-> tptp.produc1324971431et_val Bool))) (= (@ (@ tptp.member1711426256et_val A) (@ tptp.collec1117167378et_val P2)) (@ P2 A))) (forall ((A2 tptp.set_val)) (= (@ tptp.collect_val (lambda ((X tptp.val)) (@ (@ tptp.member_val X) A2))) A2)) (forall ((A2 tptp.set_node)) (= (@ tptp.collect_node (lambda ((X tptp.node)) (@ (@ tptp.member_node X) A2))) A2)) (forall ((A2 tptp.set_set_val)) (= (@ tptp.collect_set_val (lambda ((X tptp.set_val)) (@ (@ tptp.member_set_val X) A2))) A2)) (forall ((A2 tptp.set_Pr699757092de_val)) (= (@ tptp.collec370342979de_val (lambda ((X tptp.produc1432036078de_val)) (@ (@ tptp.member313544709de_val X) A2))) A2)) (forall ((A2 tptp.set_Pr1311924359et_val)) (= (@ tptp.collec1117167378et_val (lambda ((X tptp.produc1324971431et_val)) (@ (@ tptp.member1711426256et_val X) A2))) A2)) (forall ((G tptp.g) (P tptp.val) (Q tptp.val)) (let ((_let_1 (@ tptp.var2 G))) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) G) P) Q) (= (@ _let_1 Q) (@ _let_1 P))))) (= _let_15 (@ _let_14 tptp.phi_s)) (forall ((N tptp.node) (G tptp.g) (V tptp.val) (V2 tptp.val)) (let ((_let_1 (@ tptp.var2 G))) (let ((_let_2 (@ (@ (@ (@ tptp.sSA_CF139593942de_val tptp.defs) tptp.phis) G) N))) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (=> (@ (@ tptp.member_val V) _let_2) (=> (@ (@ tptp.member_val V2) _let_2) (=> (not (= V V2)) (not (= (@ _let_1 V2) (@ _let_1 V)))))))))) (forall ((P tptp.val) (G tptp.g) (Q tptp.val)) (let ((_let_1 (@ tptp.var2 G))) (let ((_let_2 (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) G))) (let ((_let_3 (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G))) (=> (@ (@ tptp.member_val P) _let_3) (=> (@ (@ tptp.member_val Q) _let_3) (=> (not (= P Q)) (=> (= (@ _let_2 P) (@ _let_2 Q)) (not (= (@ _let_1 P) (@ _let_1 Q))))))))))) (forall ((N tptp.node) (G tptp.g) (V tptp.val)) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (=> (@ (@ tptp.member_val V) (@ (@ (@ (@ tptp.sSA_CF139593942de_val tptp.defs) tptp.phis) G) N)) (= (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) N)))) (forall ((V tptp.val) (G tptp.g) (N tptp.node)) (let ((_let_1 (@ tptp.member_val V))) (=> (@ _let_1 (@ (@ (@ (@ tptp.sSA_CF139593942de_val tptp.defs) tptp.phis) G) N)) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (@ _let_1 (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)))))) (forall ((G tptp.g)) (= (@ (@ (@ (@ (@ tptp.sSA_CF2074824714de_val tptp.alpha_n) tptp.defs) tptp.uses) tptp.phis) G) (forall ((X tptp.node)) (=> (@ (@ tptp.member_node X) (@ tptp.set_node2 (@ tptp.alpha_n G))) (forall ((Val2 tptp.val)) (=> (@ (@ tptp.member_val Val2) (@ (@ (@ tptp.sSA_CF370335846de_val tptp.phis) G) X)) (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val tptp.alpha_n) tptp.defs) tptp.uses) tptp.phis) G) Val2))))))) (= tptp.sSA_CF848637139eD_val tptp.sSA_CF848637139eD_val) (= tptp.sSA_CF370335846de_val tptp.sSA_CF370335846de_val) (= tptp.sSA_CF139593942de_val tptp.sSA_CF139593942de_val) (= tptp.sSA_CF551432799de_val tptp.sSA_CF551432799de_val) (= tptp.sSA_CF1517915011eD_val tptp.sSA_CF1517915011eD_val) (= tptp.sSA_CF1252180629de_val tptp.sSA_CF1252180629de_val) (= tptp.sSA_CF178745443eD_val tptp.sSA_CF178745443eD_val) (= tptp.sSA_CF794421325de_val tptp.sSA_CF794421325de_val) (= tptp.sSA_CF1899243830eD_val tptp.sSA_CF1899243830eD_val) (= tptp.sSA_CF655860150de_val tptp.sSA_CF655860150de_val) (= tptp.sSA_CF1909049442de_val tptp.sSA_CF1909049442de_val) (= tptp.sSA_CF1660885746eD_val tptp.sSA_CF1660885746eD_val) (forall ((A2 tptp.set_node)) (=> (@ tptp.finite_finite_node A2) (exists ((Xs2 tptp.list_node)) (= (@ tptp.set_node2 Xs2) A2)))) (forall ((A2 tptp.set_val)) (=> (@ tptp.finite_finite_val A2) (exists ((Xs2 tptp.list_val)) (= (@ tptp.set_val2 Xs2) A2)))) (forall ((A2 tptp.set_Pr1311924359et_val)) (=> (@ tptp.finite79836624et_val A2) (exists ((Xs2 tptp.list_P2089461677et_val)) (= (@ tptp.set_Pr284769596et_val Xs2) A2)))) (forall ((A2 tptp.set_Pr699757092de_val)) (=> (@ tptp.finite2056463621de_val A2) (exists ((Xs2 tptp.list_P1820443774de_val)) (= (@ tptp.set_Pr1085970585de_val Xs2) A2)))) (forall ((N tptp.node) (Alpha_n2 (-> tptp.g tptp.list_node)) (G tptp.g) (Val tptp.val) (Uses2 (-> tptp.g tptp.node tptp.set_val)) (Defs2 (-> tptp.g tptp.node tptp.set_val)) (Phis2 (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val))) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ Alpha_n2 G))) (=> (@ (@ tptp.member_val Val) (@ (@ Uses2 G) N)) (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val Alpha_n2) Defs2) Uses2) Phis2) G) Val)))) (forall ((Alpha_n2 (-> tptp.g tptp.list_node)) (Defs2 (-> tptp.g tptp.node tptp.set_val)) (Uses2 (-> tptp.g tptp.node tptp.set_val)) (Phis2 (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val)) (G tptp.g) (V tptp.val) (V2 tptp.val)) (let ((_let_1 (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val Alpha_n2) Defs2) Uses2) Phis2) G))) (=> (@ _let_1 V) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val Alpha_n2) Defs2) Phis2) G) V) V2) (@ _let_1 V2))))) (forall ((Alpha_n2 (-> tptp.g tptp.list_node)) (Defs2 (-> tptp.g tptp.node tptp.set_val)) (Uses2 (-> tptp.g tptp.node tptp.set_val)) (Phis2 (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val)) (G tptp.g) (X2 tptp.val) (P2 (-> tptp.val Bool))) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val Alpha_n2) Defs2) Uses2) Phis2) G) X2) (=> (forall ((N2 tptp.node) (Val3 tptp.val)) (=> (@ (@ tptp.member_node N2) (@ tptp.set_node2 (@ Alpha_n2 G))) (=> (@ (@ tptp.member_val Val3) (@ (@ Uses2 G) N2)) (@ P2 Val3)))) (=> (forall ((V5 tptp.val) (V6 tptp.val)) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val Alpha_n2) Defs2) Uses2) Phis2) G) V5) (=> (@ P2 V5) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val Alpha_n2) Defs2) Phis2) G) V5) V6) (@ P2 V6))))) (@ P2 X2))))) (= tptp.sSA_CF794421325de_val (lambda ((Alpha_n (-> tptp.g tptp.list_node)) (Defs (-> tptp.g tptp.node tptp.set_val)) (Uses (-> tptp.g tptp.node tptp.set_val)) (Phis (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val)) (G2 tptp.g) (A3 tptp.val)) (or (exists ((N3 tptp.node) (Val2 tptp.val)) (and (= A3 Val2) (@ (@ tptp.member_node N3) (@ tptp.set_node2 (@ Alpha_n G2))) (@ (@ tptp.member_val Val2) (@ (@ Uses G2) N3)))) (exists ((V3 tptp.val) (V4 tptp.val)) (and (= A3 V4) (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val Alpha_n) Defs) Uses) Phis) G2) V3) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val Alpha_n) Defs) Phis) G2) V3) V4)))))) (forall ((Alpha_n2 (-> tptp.g tptp.list_node)) (Defs2 (-> tptp.g tptp.node tptp.set_val)) (Uses2 (-> tptp.g tptp.node tptp.set_val)) (Phis2 (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val)) (G tptp.g) (A tptp.val)) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val Alpha_n2) Defs2) Uses2) Phis2) G) A) (=> (forall ((N2 tptp.node)) (=> (@ (@ tptp.member_node N2) (@ tptp.set_node2 (@ Alpha_n2 G))) (not (@ (@ tptp.member_val A) (@ (@ Uses2 G) N2))))) (not (forall ((V5 tptp.val)) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF794421325de_val Alpha_n2) Defs2) Uses2) Phis2) G) V5) (not (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val Alpha_n2) Defs2) Phis2) G) V5) A)))))))) _let_13 (forall ((G tptp.g) (P2 tptp.set_val)) (@ tptp.finite79836624et_val (@ (@ (@ (@ (@ tptp.irredu893086079de_val tptp.alpha_n) tptp.defs) tptp.phis) G) P2))) (forall ((G tptp.g) (P tptp.val) (Q tptp.val)) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) G) P) Q) (=> (@ (@ tptp.member_val P) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)) (not (forall ((M2 tptp.node)) (=> (@ (@ tptp.member_val Q) (@ (@ (@ (@ (@ tptp.sSA_CF848637139eD_val tptp.alpha_n) tptp.inEdges) tptp.phis) G) M2)) (not (@ (@ tptp.member_node M2) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) G) P))))))))))) (forall ((G tptp.g) (N tptp.node)) (= (@ (@ (@ (@ (@ (@ tptp.sSA_CF178745443eD_val tptp.alpha_n) tptp.inEdges) tptp.uses) tptp.phis) G) N) (@ (@ tptp.sup_sup_set_val (@ (@ tptp.uses G) N)) (@ (@ (@ (@ (@ tptp.sSA_CF848637139eD_val tptp.alpha_n) tptp.inEdges) tptp.phis) G) N)))) (forall ((G tptp.g) (Phi2 tptp.val) (N tptp.val)) (let ((_let_1 (@ tptp.var2 G))) (=> (@ (@ (@ tptp.transi1991289355lp_val (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) G)) Phi2) N) (= (@ _let_1 Phi2) (@ _let_1 N))))) (forall ((G tptp.g) (N tptp.node)) (= (@ (@ (@ (@ tptp.sSA_CF139593942de_val tptp.defs) tptp.phis) G) N) (@ (@ tptp.sup_sup_set_val (@ (@ tptp.defs G) N)) (@ (@ (@ tptp.sSA_CF370335846de_val tptp.phis) G) N)))) _let_12 (forall ((V tptp.val) (G tptp.g)) (let ((_let_1 (@ tptp.member_val V))) (=> (@ _let_1 (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)) (=> (not (@ _let_1 (@ (@ tptp.defs G) (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V)))) (not (= (@ (@ (@ (@ (@ tptp.sSA_CF262257161de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) tptp.none_list_val)))))) (forall ((N tptp.node) (G tptp.g) (V tptp.val)) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (=> (@ (@ tptp.member_val V) (@ (@ tptp.defs G) N)) (= (@ (@ (@ (@ (@ tptp.sSA_CF262257161de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) tptp.none_list_val)))) (forall ((F tptp.set_Pr1311924359et_val) (G3 tptp.set_Pr1311924359et_val)) (= (@ tptp.finite79836624et_val (@ (@ tptp.sup_su2005730907et_val F) G3)) (and (@ tptp.finite79836624et_val F) (@ tptp.finite79836624et_val G3)))) (forall ((F tptp.set_Pr699757092de_val) (G3 tptp.set_Pr699757092de_val)) (= (@ tptp.finite2056463621de_val (@ (@ tptp.sup_su2138939728de_val F) G3)) (and (@ tptp.finite2056463621de_val F) (@ tptp.finite2056463621de_val G3)))) (forall ((F tptp.set_val) (G3 tptp.set_val)) (= (@ tptp.finite_finite_val (@ (@ tptp.sup_sup_set_val F) G3)) (and (@ tptp.finite_finite_val F) (@ tptp.finite_finite_val G3)))) (forall ((G tptp.g) (V tptp.val)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.sSA_CF1899243830eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G) V) (not (= (@ (@ (@ (@ (@ tptp.sSA_CF262257161de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) tptp.none_list_val)))) (forall ((M tptp.node) (G tptp.g) (V tptp.val)) (=> (@ (@ tptp.member_node M) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V)))) (=> (not (= (@ (@ (@ (@ (@ tptp.sSA_CF262257161de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) tptp.none_list_val)) (=> (@ (@ tptp.member_val V) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)) (not (forall ((V6 tptp.val)) (=> (@ (@ tptp.member_val V6) (@ (@ (@ (@ (@ tptp.sSA_CF848637139eD_val tptp.alpha_n) tptp.inEdges) tptp.phis) G) M)) (not (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) V6))))))))) (= tptp.sSA_CF262257161de_val tptp.sSA_CF262257161de_val) (forall ((S tptp.set_Pr1311924359et_val) (T tptp.set_Pr1311924359et_val)) (= (not (@ tptp.finite79836624et_val (@ (@ tptp.sup_su2005730907et_val S) T))) (or (not (@ tptp.finite79836624et_val S)) (not (@ tptp.finite79836624et_val T))))) (forall ((S tptp.set_Pr699757092de_val) (T tptp.set_Pr699757092de_val)) (= (not (@ tptp.finite2056463621de_val (@ (@ tptp.sup_su2138939728de_val S) T))) (or (not (@ tptp.finite2056463621de_val S)) (not (@ tptp.finite2056463621de_val T))))) (forall ((S tptp.set_val) (T tptp.set_val)) (= (not (@ tptp.finite_finite_val (@ (@ tptp.sup_sup_set_val S) T))) (or (not (@ tptp.finite_finite_val S)) (not (@ tptp.finite_finite_val T))))) (forall ((S tptp.set_Pr1311924359et_val) (T tptp.set_Pr1311924359et_val)) (=> (not (@ tptp.finite79836624et_val S)) (not (@ tptp.finite79836624et_val (@ (@ tptp.sup_su2005730907et_val S) T))))) (forall ((S tptp.set_Pr699757092de_val) (T tptp.set_Pr699757092de_val)) (=> (not (@ tptp.finite2056463621de_val S)) (not (@ tptp.finite2056463621de_val (@ (@ tptp.sup_su2138939728de_val S) T))))) (forall ((S tptp.set_val) (T tptp.set_val)) (=> (not (@ tptp.finite_finite_val S)) (not (@ tptp.finite_finite_val (@ (@ tptp.sup_sup_set_val S) T))))) (forall ((F tptp.set_Pr1311924359et_val) (G3 tptp.set_Pr1311924359et_val)) (=> (@ tptp.finite79836624et_val F) (=> (@ tptp.finite79836624et_val G3) (@ tptp.finite79836624et_val (@ (@ tptp.sup_su2005730907et_val F) G3))))) (forall ((F tptp.set_Pr699757092de_val) (G3 tptp.set_Pr699757092de_val)) (=> (@ tptp.finite2056463621de_val F) (=> (@ tptp.finite2056463621de_val G3) (@ tptp.finite2056463621de_val (@ (@ tptp.sup_su2138939728de_val F) G3))))) (forall ((F tptp.set_val) (G3 tptp.set_val)) (=> (@ tptp.finite_finite_val F) (=> (@ tptp.finite_finite_val G3) (@ tptp.finite_finite_val (@ (@ tptp.sup_sup_set_val F) G3))))) (= tptp.irredu893086079de_val tptp.irredu893086079de_val) (= tptp.sSA_CF2074824714de_val tptp.sSA_CF2074824714de_val) _let_11 _let_10 (forall ((G tptp.g) (V tptp.val) (Vs tptp.list_val)) (=> (= (@ (@ (@ (@ (@ tptp.sSA_CF262257161de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) (@ tptp.some_list_val Vs)) (@ (@ tptp.member_val V) (@ (@ (@ tptp.sSA_CF370335846de_val tptp.phis) G) (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V))))) (forall ((G tptp.g) (P2 tptp.set_val)) (@ tptp.transi1953622797et_val (@ (@ (@ (@ (@ tptp.irredu893086079de_val tptp.alpha_n) tptp.defs) tptp.phis) G) P2))) (forall ((G tptp.g) (V tptp.val)) (= (@ (@ (@ (@ (@ tptp.sSA_CF262257161de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) (@ (@ tptp.phis G) (@ (@ tptp.produc1470527136de_val (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V)) V)))) (forall ((G tptp.g) (V tptp.val) (V2 tptp.val)) (= (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) V2) (exists ((Vs2 tptp.list_val)) (and (= (@ (@ (@ (@ (@ tptp.sSA_CF262257161de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) (@ tptp.some_list_val Vs2)) (@ (@ tptp.member_val V2) (@ tptp.set_val2 Vs2)))))) (forall ((G tptp.g)) (@ tptp.finite_finite_val (@ tptp.dom_val_list_val (@ (@ (@ (@ tptp.sSA_CF262257161de_val tptp.alpha_n) tptp.defs) tptp.phis) G)))) (forall ((G tptp.g) (P2 tptp.set_val) (Scc tptp.set_val) (X2 tptp.val)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.irredu224829488eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G) P2) (=> (@ (@ tptp.member_set_val Scc) (@ (@ (@ (@ (@ tptp.irredu681226810de_val tptp.alpha_n) tptp.defs) tptp.phis) G) P2)) (=> (@ (@ tptp.member_val X2) Scc) (not (= (@ (@ (@ (@ (@ tptp.sSA_CF262257161de_val tptp.alpha_n) tptp.defs) tptp.phis) G) X2) tptp.none_list_val)))))) (forall ((G tptp.g) (N tptp.node) (V tptp.val) (Vs tptp.list_val) (N4 tptp.node) (Vs3 tptp.list_val)) (let ((_let_1 (@ tptp.phis G))) (=> (= (@ _let_1 (@ (@ tptp.produc1470527136de_val N) V)) (@ tptp.some_list_val Vs)) (=> (= (@ _let_1 (@ (@ tptp.produc1470527136de_val N4) V)) (@ tptp.some_list_val Vs3)) (= Vs Vs3))))) (forall ((G tptp.g) (N tptp.node) (V tptp.val) (Vs tptp.list_val) (N4 tptp.node) (Vs3 tptp.list_val)) (let ((_let_1 (@ tptp.phis G))) (=> (= (@ _let_1 (@ (@ tptp.produc1470527136de_val N) V)) (@ tptp.some_list_val Vs)) (=> (= (@ _let_1 (@ (@ tptp.produc1470527136de_val N4) V)) (@ tptp.some_list_val Vs3)) (= N N4))))) (forall ((G tptp.g) (N tptp.node) (V tptp.val) (Vs tptp.list_val)) (=> (= (@ (@ tptp.phis G) (@ (@ tptp.produc1470527136de_val N) V)) (@ tptp.some_list_val Vs)) (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))))) (forall ((G tptp.g) (N tptp.node) (V tptp.val) (Vs tptp.list_val) (V2 tptp.val)) (let ((_let_1 (@ tptp.var2 G))) (=> (= (@ (@ tptp.phis G) (@ (@ tptp.produc1470527136de_val N) V)) (@ tptp.some_list_val Vs)) (=> (@ (@ tptp.member_val V2) (@ tptp.set_val2 Vs)) (= (@ _let_1 V2) (@ _let_1 V)))))) (forall ((G tptp.g) (N tptp.node) (V tptp.val) (Vs tptp.list_val)) (let ((_let_1 (@ tptp.some_list_val Vs))) (=> (= (@ (@ tptp.phis G) (@ (@ tptp.produc1470527136de_val N) V)) _let_1) (= (@ (@ (@ (@ (@ tptp.sSA_CF262257161de_val tptp.alpha_n) tptp.defs) tptp.phis) G) V) _let_1)))) (forall ((M tptp.node) (G tptp.g) (N tptp.node) (V tptp.val) (Vs tptp.list_val)) (=> (@ (@ tptp.member_node M) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) N))) (=> (= (@ (@ tptp.phis G) (@ (@ tptp.produc1470527136de_val N) V)) (@ tptp.some_list_val Vs)) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (not (forall ((V6 tptp.val)) (let ((_let_1 (@ tptp.member_val V6))) (=> (@ _let_1 (@ (@ (@ (@ (@ tptp.sSA_CF848637139eD_val tptp.alpha_n) tptp.inEdges) tptp.phis) G) M)) (not (@ _let_1 (@ tptp.set_val2 Vs))))))))))) (= tptp.irredu681226810de_val tptp.irredu681226810de_val) (= tptp.irredu224829488eD_val tptp.irredu224829488eD_val) _let_9 _let_8 (forall ((N4 tptp.node) (G tptp.g) (V2 tptp.val) (Vs tptp.list_val) (N tptp.node) (V tptp.val)) (=> (@ (@ tptp.member_node N4) (@ tptp.set_node2 (@ tptp.alpha_n G))) (=> (= (@ (@ tptp.phis G) (@ (@ tptp.produc1470527136de_val N4) V2)) (@ tptp.some_list_val Vs)) (=> (@ (@ tptp.member313544709de_val (@ (@ tptp.produc1470527136de_val N) V)) (@ tptp.set_Pr1085970585de_val (@ (@ tptp.zip_node_val (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) N4)) Vs))) (@ (@ tptp.member_val V) (@ (@ (@ (@ (@ tptp.sSA_CF848637139eD_val tptp.alpha_n) tptp.inEdges) tptp.phis) G) N)))))) (forall ((Scc tptp.set_val) (G tptp.g) (P2 tptp.set_val)) (=> (@ (@ tptp.member_set_val Scc) (@ (@ (@ (@ (@ tptp.irredu681226810de_val tptp.alpha_n) tptp.defs) tptp.phis) G) P2)) (@ (@ tptp.ord_less_eq_set_val Scc) P2))) (forall ((X2 tptp.option_list_val)) (= (not (= X2 tptp.none_list_val)) (exists ((Y2 tptp.list_val)) (= X2 (@ tptp.some_list_val Y2))))) (forall ((X2 tptp.option_list_val)) (= (forall ((Y2 tptp.list_val)) (not (= X2 (@ tptp.some_list_val Y2)))) (= X2 tptp.none_list_val))) (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (= (@ (@ tptp.sup_su1487070040et_val (@ tptp.some_set_val X2)) (@ tptp.some_set_val Y3)) (@ tptp.some_set_val (@ (@ tptp.sup_sup_set_val X2) Y3)))) (forall ((X22 tptp.list_val) (Y22 tptp.list_val)) (= (= (@ tptp.some_list_val X22) (@ tptp.some_list_val Y22)) (= X22 Y22))) (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (= (@ (@ tptp.ord_le596993316et_val (@ tptp.some_set_val X2)) (@ tptp.some_set_val Y3)) (@ (@ tptp.ord_less_eq_set_val X2) Y3))) (forall ((A tptp.produc1324971431et_val) (B tptp.produc1324971431et_val) (Xs tptp.list_P2089461677et_val)) (= (@ (@ tptp.member1254968080et_val (@ (@ tptp.produc1377626967et_val A) B)) (@ tptp.set_Pr1006393724et_val (@ (@ tptp.zip_Pr21865079et_val Xs) Xs))) (and (@ (@ tptp.member1711426256et_val A) (@ tptp.set_Pr284769596et_val Xs)) (= A B)))) (forall ((A tptp.node) (B tptp.node) (Xs tptp.list_node)) (= (@ (@ tptp.member2110109140e_node (@ (@ tptp.produc457016035e_node A) B)) (@ tptp.set_Pr450990656e_node (@ (@ tptp.zip_node_node Xs) Xs))) (and (@ (@ tptp.member_node A) (@ tptp.set_node2 Xs)) (= A B)))) (forall ((A tptp.val) (B tptp.val) (Xs tptp.list_val)) (= (@ (@ tptp.member1680438992al_val (@ (@ tptp.product_Pair_val_val A) B)) (@ tptp.set_Pr102746428al_val (@ (@ tptp.zip_val_val Xs) Xs))) (and (@ (@ tptp.member_val A) (@ tptp.set_val2 Xs)) (= A B)))) (forall ((A tptp.produc1432036078de_val) (B tptp.produc1432036078de_val) (Xs tptp.list_P1820443774de_val)) (= (@ (@ tptp.member698732390de_val (@ (@ tptp.produc453318901de_val A) B)) (@ tptp.set_Pr482027474de_val (@ (@ tptp.zip_Pr1472086037de_val Xs) Xs))) (and (@ (@ tptp.member313544709de_val A) (@ tptp.set_Pr1085970585de_val Xs)) (= A B)))) (forall ((A tptp.set_val) (B tptp.set_val) (Xs tptp.list_set_val)) (= (@ (@ tptp.member1711426256et_val (@ (@ tptp.produc1041633943et_val A) B)) (@ tptp.set_Pr284769596et_val (@ (@ tptp.zip_set_val_set_val Xs) Xs))) (and (@ (@ tptp.member_set_val A) (@ tptp.set_set_val2 Xs)) (= A B)))) (forall ((G tptp.g) (P2 tptp.set_val)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.irredu224829488eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G) P2) (exists ((Scc2 tptp.set_val)) (and (@ (@ tptp.ord_less_eq_set_val Scc2) P2) (@ (@ (@ (@ (@ (@ (@ (@ tptp.irredu1955035135eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G) P2) Scc2))))) (forall ((V tptp.val) (G tptp.g) (N tptp.node)) (=> (@ (@ tptp.member_val V) (@ (@ (@ (@ (@ tptp.sSA_CF848637139eD_val tptp.alpha_n) tptp.inEdges) tptp.phis) G) N)) (not (forall ((N5 tptp.node)) (=> (@ (@ tptp.member_node N5) (@ tptp.set_node2 (@ (@ (@ (@ tptp.graph_1037173556_edgeD tptp.alpha_n) tptp.inEdges) G) N))) (forall ((V6 tptp.val) (Vs4 tptp.list_val)) (=> (@ (@ tptp.member313544709de_val (@ (@ tptp.produc1470527136de_val N) V)) (@ tptp.set_Pr1085970585de_val (@ (@ tptp.zip_node_val (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) N5)) Vs4))) (not (= (@ (@ tptp.phis G) (@ (@ tptp.produc1470527136de_val N5) V6)) (@ tptp.some_list_val Vs4)))))))))) (forall ((A2 tptp.set_node) (A tptp.node)) (=> (@ tptp.finite_finite_node A2) (=> (@ (@ tptp.member_node A) A2) (exists ((X3 tptp.node)) (and (@ (@ tptp.member_node X3) A2) (@ (@ tptp.ord_less_eq_node X3) A) (forall ((Xa tptp.node)) (=> (@ (@ tptp.member_node Xa) A2) (=> (@ (@ tptp.ord_less_eq_node Xa) X3) (= X3 Xa))))))))) (forall ((A2 tptp.set_val) (A tptp.val)) (=> (@ tptp.finite_finite_val A2) (=> (@ (@ tptp.member_val A) A2) (exists ((X3 tptp.val)) (and (@ (@ tptp.member_val X3) A2) (@ (@ tptp.ord_less_eq_val X3) A) (forall ((Xa tptp.val)) (=> (@ (@ tptp.member_val Xa) A2) (=> (@ (@ tptp.ord_less_eq_val Xa) X3) (= X3 Xa))))))))) (forall ((A2 tptp.set_set_val) (A tptp.set_val)) (=> (@ tptp.finite1265617511et_val A2) (=> (@ (@ tptp.member_set_val A) A2) (exists ((X3 tptp.set_val)) (and (@ (@ tptp.member_set_val X3) A2) (@ (@ tptp.ord_less_eq_set_val X3) A) (forall ((Xa tptp.set_val)) (=> (@ (@ tptp.member_set_val Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_val Xa) X3) (= X3 Xa))))))))) (forall ((A2 tptp.set_node) (A tptp.node)) (=> (@ tptp.finite_finite_node A2) (=> (@ (@ tptp.member_node A) A2) (exists ((X3 tptp.node)) (and (@ (@ tptp.member_node X3) A2) (@ (@ tptp.ord_less_eq_node A) X3) (forall ((Xa tptp.node)) (=> (@ (@ tptp.member_node Xa) A2) (=> (@ (@ tptp.ord_less_eq_node X3) Xa) (= X3 Xa))))))))) (forall ((A2 tptp.set_val) (A tptp.val)) (=> (@ tptp.finite_finite_val A2) (=> (@ (@ tptp.member_val A) A2) (exists ((X3 tptp.val)) (and (@ (@ tptp.member_val X3) A2) (@ (@ tptp.ord_less_eq_val A) X3) (forall ((Xa tptp.val)) (=> (@ (@ tptp.member_val Xa) A2) (=> (@ (@ tptp.ord_less_eq_val X3) Xa) (= X3 Xa))))))))) (forall ((A2 tptp.set_set_val) (A tptp.set_val)) (=> (@ tptp.finite1265617511et_val A2) (=> (@ (@ tptp.member_set_val A) A2) (exists ((X3 tptp.set_val)) (and (@ (@ tptp.member_set_val X3) A2) (@ (@ tptp.ord_less_eq_set_val A) X3) (forall ((Xa tptp.set_val)) (=> (@ (@ tptp.member_set_val Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_val X3) Xa) (= X3 Xa))))))))) (forall ((Xs tptp.list_set_val) (B2 tptp.set_set_val)) (= (@ (@ tptp.ord_le1742111550et_val (@ tptp.set_set_val2 Xs)) B2) (forall ((X tptp.set_val)) (let ((_let_1 (@ tptp.member_set_val X))) (=> (@ _let_1 (@ tptp.set_set_val2 Xs)) (@ _let_1 B2)))))) (forall ((Xs tptp.list_P2089461677et_val) (B2 tptp.set_Pr1311924359et_val)) (= (@ (@ tptp.ord_le299366439et_val (@ tptp.set_Pr284769596et_val Xs)) B2) (forall ((X tptp.produc1324971431et_val)) (let ((_let_1 (@ tptp.member1711426256et_val X))) (=> (@ _let_1 (@ tptp.set_Pr284769596et_val Xs)) (@ _let_1 B2)))))) (forall ((Xs tptp.list_node) (B2 tptp.set_node)) (= (@ (@ tptp.ord_less_eq_set_node (@ tptp.set_node2 Xs)) B2) (forall ((X tptp.node)) (let ((_let_1 (@ tptp.member_node X))) (=> (@ _let_1 (@ tptp.set_node2 Xs)) (@ _let_1 B2)))))) (forall ((Xs tptp.list_P1820443774de_val) (B2 tptp.set_Pr699757092de_val)) (= (@ (@ tptp.ord_le1643692676de_val (@ tptp.set_Pr1085970585de_val Xs)) B2) (forall ((X tptp.produc1432036078de_val)) (let ((_let_1 (@ tptp.member313544709de_val X))) (=> (@ _let_1 (@ tptp.set_Pr1085970585de_val Xs)) (@ _let_1 B2)))))) (forall ((Xs tptp.list_val) (B2 tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val (@ tptp.set_val2 Xs)) B2) (forall ((X tptp.val)) (let ((_let_1 (@ tptp.member_val X))) (=> (@ _let_1 (@ tptp.set_val2 Xs)) (@ _let_1 B2)))))) (forall ((B2 tptp.set_Pr1311924359et_val) (A2 tptp.set_Pr1311924359et_val)) (=> (@ tptp.finite79836624et_val B2) (=> (@ (@ tptp.ord_le299366439et_val A2) B2) (@ tptp.finite79836624et_val A2)))) (forall ((B2 tptp.set_Pr699757092de_val) (A2 tptp.set_Pr699757092de_val)) (=> (@ tptp.finite2056463621de_val B2) (=> (@ (@ tptp.ord_le1643692676de_val A2) B2) (@ tptp.finite2056463621de_val A2)))) (forall ((B2 tptp.set_val) (A2 tptp.set_val)) (=> (@ tptp.finite_finite_val B2) (=> (@ (@ tptp.ord_less_eq_set_val A2) B2) (@ tptp.finite_finite_val A2)))) (forall ((S tptp.set_Pr1311924359et_val) (T tptp.set_Pr1311924359et_val)) (=> (@ (@ tptp.ord_le299366439et_val S) T) (=> (not (@ tptp.finite79836624et_val S)) (not (@ tptp.finite79836624et_val T))))) (forall ((S tptp.set_Pr699757092de_val) (T tptp.set_Pr699757092de_val)) (=> (@ (@ tptp.ord_le1643692676de_val S) T) (=> (not (@ tptp.finite2056463621de_val S)) (not (@ tptp.finite2056463621de_val T))))) (forall ((S tptp.set_val) (T tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val S) T) (=> (not (@ tptp.finite_finite_val S)) (not (@ tptp.finite_finite_val T))))) (forall ((A2 tptp.set_Pr1311924359et_val) (B2 tptp.set_Pr1311924359et_val)) (=> (@ (@ tptp.ord_le299366439et_val A2) B2) (=> (@ tptp.finite79836624et_val B2) (@ tptp.finite79836624et_val A2)))) (forall ((A2 tptp.set_Pr699757092de_val) (B2 tptp.set_Pr699757092de_val)) (=> (@ (@ tptp.ord_le1643692676de_val A2) B2) (=> (@ tptp.finite2056463621de_val B2) (@ tptp.finite2056463621de_val A2)))) (forall ((A2 tptp.set_val) (B2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A2) B2) (=> (@ tptp.finite_finite_val B2) (@ tptp.finite_finite_val A2)))) (forall ((X2 tptp.node) (Y3 tptp.node) (Xs tptp.list_node) (Ys tptp.list_node)) (=> (@ (@ tptp.member2110109140e_node (@ (@ tptp.produc457016035e_node X2) Y3)) (@ tptp.set_Pr450990656e_node (@ (@ tptp.zip_node_node Xs) Ys))) (not (=> (@ (@ tptp.member_node X2) (@ tptp.set_node2 Xs)) (not (@ (@ tptp.member_node Y3) (@ tptp.set_node2 Ys))))))) (forall ((X2 tptp.val) (Y3 tptp.node) (Xs tptp.list_val) (Ys tptp.list_node)) (=> (@ (@ tptp.member828457417l_node (@ (@ tptp.produc1074923692l_node X2) Y3)) (@ tptp.set_Pr1600883293l_node (@ (@ tptp.zip_val_node Xs) Ys))) (not (=> (@ (@ tptp.member_val X2) (@ tptp.set_val2 Xs)) (not (@ (@ tptp.member_node Y3) (@ tptp.set_node2 Ys))))))) (forall ((X2 tptp.val) (Y3 tptp.val) (Xs tptp.list_val) (Ys tptp.list_val)) (=> (@ (@ tptp.member1680438992al_val (@ (@ tptp.product_Pair_val_val X2) Y3)) (@ tptp.set_Pr102746428al_val (@ (@ tptp.zip_val_val Xs) Ys))) (not (=> (@ (@ tptp.member_val X2) (@ tptp.set_val2 Xs)) (not (@ (@ tptp.member_val Y3) (@ tptp.set_val2 Ys))))))) (forall ((X2 tptp.node) (Y3 tptp.val) (Xs tptp.list_node) (Ys tptp.list_val)) (=> (@ (@ tptp.member313544709de_val (@ (@ tptp.produc1470527136de_val X2) Y3)) (@ tptp.set_Pr1085970585de_val (@ (@ tptp.zip_node_val Xs) Ys))) (not (=> (@ (@ tptp.member_node X2) (@ tptp.set_node2 Xs)) (not (@ (@ tptp.member_val Y3) (@ tptp.set_val2 Ys))))))) (forall ((X2 tptp.set_val) (Y3 tptp.node) (Xs tptp.list_set_val) (Ys tptp.list_node)) (=> (@ (@ tptp.member76372137l_node (@ (@ tptp.produc2052093836l_node X2) Y3)) (@ tptp.set_Pr1904955709l_node (@ (@ tptp.zip_set_val_node Xs) Ys))) (not (=> (@ (@ tptp.member_set_val X2) (@ tptp.set_set_val2 Xs)) (not (@ (@ tptp.member_node Y3) (@ tptp.set_node2 Ys))))))) (forall ((X2 tptp.set_val) (Y3 tptp.val) (Xs tptp.list_set_val) (Ys tptp.list_val)) (=> (@ (@ tptp.member1110026224al_val (@ (@ tptp.produc1337903031al_val X2) Y3)) (@ tptp.set_Pr1027623516al_val (@ (@ tptp.zip_set_val_val Xs) Ys))) (not (=> (@ (@ tptp.member_set_val X2) (@ tptp.set_set_val2 Xs)) (not (@ (@ tptp.member_val Y3) (@ tptp.set_val2 Ys))))))) (forall ((X2 tptp.node) (Y3 tptp.set_val) (Xs tptp.list_node) (Ys tptp.list_set_val)) (=> (@ (@ tptp.member125181669et_val (@ (@ tptp.produc2042994048et_val X2) Y3)) (@ tptp.set_Pr1953765241et_val (@ (@ tptp.zip_node_set_val Xs) Ys))) (not (=> (@ (@ tptp.member_node X2) (@ tptp.set_node2 Xs)) (not (@ (@ tptp.member_set_val Y3) (@ tptp.set_set_val2 Ys))))))) (forall ((X2 tptp.val) (Y3 tptp.set_val) (Xs tptp.list_val) (Ys tptp.list_set_val)) (=> (@ (@ tptp.member39229872et_val (@ (@ tptp.produc1446164855et_val X2) Y3)) (@ tptp.set_Pr2104310812et_val (@ (@ tptp.zip_val_set_val Xs) Ys))) (not (=> (@ (@ tptp.member_val X2) (@ tptp.set_val2 Xs)) (not (@ (@ tptp.member_set_val Y3) (@ tptp.set_set_val2 Ys))))))) (forall ((X2 tptp.node) (Y3 tptp.produc1432036078de_val) (Xs tptp.list_node) (Ys tptp.list_P1820443774de_val)) (=> (@ (@ tptp.member562853661de_val (@ (@ tptp.produc1162531244de_val X2) Y3)) (@ tptp.set_Pr1157337481de_val (@ (@ tptp.zip_no263301324de_val Xs) Ys))) (not (=> (@ (@ tptp.member_node X2) (@ tptp.set_node2 Xs)) (not (@ (@ tptp.member313544709de_val Y3) (@ tptp.set_Pr1085970585de_val Ys))))))) (forall ((X2 tptp.val) (Y3 tptp.produc1432036078de_val) (Xs tptp.list_val) (Ys tptp.list_P1820443774de_val)) (=> (@ (@ tptp.member1894062994de_val (@ (@ tptp.produc1571934709de_val X2) Y3)) (@ tptp.set_Pr434939430de_val (@ (@ tptp.zip_va679686869de_val Xs) Ys))) (not (=> (@ (@ tptp.member_val X2) (@ tptp.set_val2 Xs)) (not (@ (@ tptp.member313544709de_val Y3) (@ tptp.set_Pr1085970585de_val Ys))))))) (forall ((X2 tptp.node) (Y3 tptp.val) (Xs tptp.list_node) (Ys tptp.list_val)) (=> (@ (@ tptp.member313544709de_val (@ (@ tptp.produc1470527136de_val X2) Y3)) (@ tptp.set_Pr1085970585de_val (@ (@ tptp.zip_node_val Xs) Ys))) (@ (@ tptp.member_node X2) (@ tptp.set_node2 Xs)))) (forall ((X2 tptp.set_val) (Y3 tptp.set_val) (Xs tptp.list_set_val) (Ys tptp.list_set_val)) (=> (@ (@ tptp.member1711426256et_val (@ (@ tptp.produc1041633943et_val X2) Y3)) (@ tptp.set_Pr284769596et_val (@ (@ tptp.zip_set_val_set_val Xs) Ys))) (@ (@ tptp.member_set_val X2) (@ tptp.set_set_val2 Xs)))) (forall ((X2 tptp.node) (Y3 tptp.val) (Xs tptp.list_node) (Ys tptp.list_val)) (=> (@ (@ tptp.member313544709de_val (@ (@ tptp.produc1470527136de_val X2) Y3)) (@ tptp.set_Pr1085970585de_val (@ (@ tptp.zip_node_val Xs) Ys))) (@ (@ tptp.member_val Y3) (@ tptp.set_val2 Ys)))) (forall ((X2 tptp.set_val) (Y3 tptp.set_val) (Xs tptp.list_set_val) (Ys tptp.list_set_val)) (=> (@ (@ tptp.member1711426256et_val (@ (@ tptp.produc1041633943et_val X2) Y3)) (@ tptp.set_Pr284769596et_val (@ (@ tptp.zip_set_val_set_val Xs) Ys))) (@ (@ tptp.member_set_val Y3) (@ tptp.set_set_val2 Ys)))) (forall ((X2 tptp.option_list_val) (P2 (-> tptp.option_list_val tptp.option_list_val Bool)) (Y3 tptp.option_list_val)) (let ((_let_1 (@ (@ P2 X2) Y3))) (=> (=> (= X2 tptp.none_list_val) _let_1) (=> (=> (= Y3 tptp.none_list_val) _let_1) (=> (forall ((A4 tptp.list_val) (B3 tptp.list_val)) (=> (= X2 (@ tptp.some_list_val A4)) (=> (= Y3 (@ tptp.some_list_val B3)) (@ (@ P2 X2) Y3)))) _let_1))))) (= (lambda ((P3 (-> tptp.option_list_val Bool))) (forall ((X4 tptp.option_list_val)) (@ P3 X4))) (lambda ((P4 (-> tptp.option_list_val Bool))) (and (@ P4 tptp.none_list_val) (forall ((X tptp.list_val)) (@ P4 (@ tptp.some_list_val X)))))) (= (lambda ((P3 (-> tptp.option_list_val Bool))) (exists ((X4 tptp.option_list_val)) (@ P3 X4))) (lambda ((P4 (-> tptp.option_list_val Bool))) (or (@ P4 tptp.none_list_val) (exists ((X tptp.list_val)) (@ P4 (@ tptp.some_list_val X)))))) (forall ((P2 (-> tptp.option_list_val Bool)) (Option tptp.option_list_val)) (=> (@ P2 tptp.none_list_val) (=> (forall ((X3 tptp.list_val)) (@ P2 (@ tptp.some_list_val X3))) (@ P2 Option)))) (forall ((Y3 tptp.option_list_val)) (=> (not (= Y3 tptp.none_list_val)) (not (forall ((X23 tptp.list_val)) (not (= Y3 (@ tptp.some_list_val X23))))))) (forall ((Option tptp.option_list_val) (X22 tptp.list_val)) (=> (= Option (@ tptp.some_list_val X22)) (not (= Option tptp.none_list_val)))) (forall ((X22 tptp.list_val)) (not (= tptp.none_list_val (@ tptp.some_list_val X22)))) (forall ((P2 tptp.set_val) (G tptp.g)) (=> (not (= P2 tptp.bot_bot_set_val)) (exists ((Leaf tptp.set_val)) (and (@ (@ tptp.member_set_val Leaf) (@ (@ (@ (@ (@ tptp.irredu681226810de_val tptp.alpha_n) tptp.defs) tptp.phis) G) P2)) (forall ((Scc3 tptp.set_val)) (not (@ (@ tptp.member1711426256et_val (@ (@ tptp.produc1041633943et_val Leaf) Scc3)) (@ (@ (@ (@ (@ tptp.irredu893086079de_val tptp.alpha_n) tptp.defs) tptp.phis) G) P2)))))))) (forall ((A2 tptp.set_val) (B2 tptp.set_val) (C tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val A2) B2)) C) (and (@ (@ tptp.ord_less_eq_set_val A2) C) (@ (@ tptp.ord_less_eq_set_val B2) C)))) (forall ((X2 tptp.set_val) (Y3 tptp.set_val) (Z tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val X2) Y3)) Z) (and (@ (@ tptp.ord_less_eq_set_val X2) Z) (@ (@ tptp.ord_less_eq_set_val Y3) Z)))) (forall ((B tptp.set_val) (C2 tptp.set_val) (A tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val B) C2)) A) (and (@ (@ tptp.ord_less_eq_set_val B) A) (@ (@ tptp.ord_less_eq_set_val C2) A)))) (forall ((A2 tptp.set_val) (B2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A2) B2) (=> (@ (@ tptp.ord_less_eq_set_val B2) A2) (= A2 B2)))) (forall ((A2 tptp.set_node) (B2 tptp.set_node)) (=> (forall ((X3 tptp.node)) (let ((_let_1 (@ tptp.member_node X3))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_less_eq_set_node A2) B2))) (forall ((A2 tptp.set_set_val) (B2 tptp.set_set_val)) (=> (forall ((X3 tptp.set_val)) (let ((_let_1 (@ tptp.member_set_val X3))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_le1742111550et_val A2) B2))) (forall ((A2 tptp.set_Pr699757092de_val) (B2 tptp.set_Pr699757092de_val)) (=> (forall ((X3 tptp.produc1432036078de_val)) (let ((_let_1 (@ tptp.member313544709de_val X3))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_le1643692676de_val A2) B2))) (forall ((A2 tptp.set_Pr1311924359et_val) (B2 tptp.set_Pr1311924359et_val)) (=> (forall ((X3 tptp.produc1324971431et_val)) (let ((_let_1 (@ tptp.member1711426256et_val X3))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_le299366439et_val A2) B2))) (forall ((A2 tptp.set_val) (B2 tptp.set_val)) (=> (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_less_eq_set_val A2) B2))) (forall ((A tptp.set_val) (B tptp.set_val)) (let ((_let_1 (@ (@ tptp.sup_sup_set_val A) B))) (= (@ (@ tptp.sup_sup_set_val _let_1) B) _let_1))) (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val X2))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.set_val) (B tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X2 tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val X2) X2) X2)) (forall ((A tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val A) A) A)) (forall ((C2 tptp.node) (A2 tptp.set_node) (B2 tptp.set_node)) (let ((_let_1 (@ tptp.member_node C2))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_node A2) B2)) (or (@ _let_1 A2) (@ _let_1 B2))))) (forall ((C2 tptp.set_val) (A2 tptp.set_set_val) (B2 tptp.set_set_val)) (let ((_let_1 (@ tptp.member_set_val C2))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_set_val A2) B2)) (or (@ _let_1 A2) (@ _let_1 B2))))) (forall ((C2 tptp.produc1432036078de_val) (A2 tptp.set_Pr699757092de_val) (B2 tptp.set_Pr699757092de_val)) (let ((_let_1 (@ tptp.member313544709de_val C2))) (= (@ _let_1 (@ (@ tptp.sup_su2138939728de_val A2) B2)) (or (@ _let_1 A2) (@ _let_1 B2))))) (forall ((C2 tptp.produc1324971431et_val) (A2 tptp.set_Pr1311924359et_val) (B2 tptp.set_Pr1311924359et_val)) (let ((_let_1 (@ tptp.member1711426256et_val C2))) (= (@ _let_1 (@ (@ tptp.sup_su2005730907et_val A2) B2)) (or (@ _let_1 A2) (@ _let_1 B2))))) (forall ((C2 tptp.val) (A2 tptp.set_val) (B2 tptp.set_val)) (let ((_let_1 (@ tptp.member_val C2))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_val A2) B2)) (or (@ _let_1 A2) (@ _let_1 B2))))) (forall ((C2 tptp.node) (B2 tptp.set_node) (A2 tptp.set_node)) (let ((_let_1 (@ tptp.member_node C2))) (=> (=> (not (@ _let_1 B2)) (@ _let_1 A2)) (@ _let_1 (@ (@ tptp.sup_sup_set_node A2) B2))))) (forall ((C2 tptp.set_val) (B2 tptp.set_set_val) (A2 tptp.set_set_val)) (let ((_let_1 (@ tptp.member_set_val C2))) (=> (=> (not (@ _let_1 B2)) (@ _let_1 A2)) (@ _let_1 (@ (@ tptp.sup_sup_set_set_val A2) B2))))) (forall ((C2 tptp.produc1432036078de_val) (B2 tptp.set_Pr699757092de_val) (A2 tptp.set_Pr699757092de_val)) (let ((_let_1 (@ tptp.member313544709de_val C2))) (=> (=> (not (@ _let_1 B2)) (@ _let_1 A2)) (@ _let_1 (@ (@ tptp.sup_su2138939728de_val A2) B2))))) (forall ((C2 tptp.produc1324971431et_val) (B2 tptp.set_Pr1311924359et_val) (A2 tptp.set_Pr1311924359et_val)) (let ((_let_1 (@ tptp.member1711426256et_val C2))) (=> (=> (not (@ _let_1 B2)) (@ _let_1 A2)) (@ _let_1 (@ (@ tptp.sup_su2005730907et_val A2) B2))))) (forall ((C2 tptp.val) (B2 tptp.set_val) (A2 tptp.set_val)) (let ((_let_1 (@ tptp.member_val C2))) (=> (=> (not (@ _let_1 B2)) (@ _let_1 A2)) (@ _let_1 (@ (@ tptp.sup_sup_set_val A2) B2))))) (forall ((A2 tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val A2) tptp.bot_bot_set_val) (= A2 tptp.bot_bot_set_val))) (forall ((A2 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val tptp.bot_bot_set_val) A2)) (forall ((X2 tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val tptp.bot_bot_set_val) X2) X2)) (forall ((X2 tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val X2) tptp.bot_bot_set_val) X2)) (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (= (= tptp.bot_bot_set_val (@ (@ tptp.sup_sup_set_val X2) Y3)) (and (= X2 tptp.bot_bot_set_val) (= Y3 tptp.bot_bot_set_val)))) (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (= (= (@ (@ tptp.sup_sup_set_val X2) Y3) tptp.bot_bot_set_val) (and (= X2 tptp.bot_bot_set_val) (= Y3 tptp.bot_bot_set_val)))) (forall ((A tptp.set_val) (B tptp.set_val)) (= (= (@ (@ tptp.sup_sup_set_val A) B) tptp.bot_bot_set_val) (and (= A tptp.bot_bot_set_val) (= B tptp.bot_bot_set_val)))) (forall ((A tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val tptp.bot_bot_set_val) A) A)) (forall ((A tptp.set_val) (B tptp.set_val)) (= (= tptp.bot_bot_set_val (@ (@ tptp.sup_sup_set_val A) B)) (and (= A tptp.bot_bot_set_val) (= B tptp.bot_bot_set_val)))) (forall ((A tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val A) tptp.bot_bot_set_val) A)) (forall ((A2 tptp.set_val) (B2 tptp.set_val)) (= (= (@ (@ tptp.sup_sup_set_val A2) B2) tptp.bot_bot_set_val) (and (= A2 tptp.bot_bot_set_val) (= B2 tptp.bot_bot_set_val)))) (forall ((N tptp.node) (G tptp.g) (M tptp.node)) (let ((_let_1 (@ tptp.member_node N))) (=> (@ _let_1 (@ tptp.set_node2 (@ tptp.alpha_n G))) (= (@ _let_1 (@ tptp.set_node2 (@ (@ (@ (@ tptp.graph_1037173556_edgeD tptp.alpha_n) tptp.inEdges) G) M))) (@ (@ tptp.member_node M) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) N))))))) (forall ((B2 tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val tptp.bot_bot_set_val) B2) B2)) (forall ((A2 tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val A2) tptp.bot_bot_set_val) A2)) (forall ((S tptp.set_Pr1311924359et_val)) (=> (not (@ tptp.finite79836624et_val S)) (not (= S tptp.bot_bo2078591731et_val)))) (forall ((S tptp.set_Pr699757092de_val)) (=> (not (@ tptp.finite2056463621de_val S)) (not (= S tptp.bot_bo404898488de_val)))) (forall ((S tptp.set_val)) (=> (not (@ tptp.finite_finite_val S)) (not (= S tptp.bot_bot_set_val)))) (@ tptp.finite79836624et_val tptp.bot_bo2078591731et_val) (@ tptp.finite2056463621de_val tptp.bot_bo404898488de_val) (@ tptp.finite_finite_val tptp.bot_bot_set_val) (= tptp.irredu1955035135eD_val tptp.irredu1955035135eD_val) (forall ((A2 tptp.set_val)) (=> (@ tptp.finite_finite_val A2) (=> (not (= A2 tptp.bot_bot_set_val)) (exists ((X3 tptp.val)) (and (@ (@ tptp.member_val X3) A2) (forall ((Xa tptp.val)) (=> (@ (@ tptp.member_val Xa) A2) (=> (@ (@ tptp.ord_less_eq_val X3) Xa) (= X3 Xa))))))))) (forall ((A2 tptp.set_set_val)) (=> (@ tptp.finite1265617511et_val A2) (=> (not (= A2 tptp.bot_bot_set_set_val)) (exists ((X3 tptp.set_val)) (and (@ (@ tptp.member_set_val X3) A2) (forall ((Xa tptp.set_val)) (=> (@ (@ tptp.member_set_val Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_val X3) Xa) (= X3 Xa))))))))) (forall ((A2 tptp.set_val)) (=> (@ tptp.finite_finite_val A2) (=> (not (= A2 tptp.bot_bot_set_val)) (exists ((X3 tptp.val)) (and (@ (@ tptp.member_val X3) A2) (forall ((Xa tptp.val)) (=> (@ (@ tptp.member_val Xa) A2) (=> (@ (@ tptp.ord_less_eq_val Xa) X3) (= X3 Xa))))))))) (forall ((A2 tptp.set_set_val)) (=> (@ tptp.finite1265617511et_val A2) (=> (not (= A2 tptp.bot_bot_set_set_val)) (exists ((X3 tptp.set_val)) (and (@ (@ tptp.member_set_val X3) A2) (forall ((Xa tptp.set_val)) (=> (@ (@ tptp.member_set_val Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_val Xa) X3) (= X3 Xa))))))))) (forall ((P2 (-> tptp.val Bool)) (Q2 (-> tptp.val Bool))) (= (@ (@ tptp.ord_less_eq_set_val (@ tptp.collect_val P2)) (@ tptp.collect_val Q2)) (forall ((X tptp.val)) (=> (@ P2 X) (@ Q2 X))))) (= (lambda ((Y4 tptp.set_val) (Z2 tptp.set_val)) (= Y4 Z2)) (lambda ((A5 tptp.set_val) (B4 tptp.set_val)) (and (@ (@ tptp.ord_less_eq_set_val A5) B4) (@ (@ tptp.ord_less_eq_set_val B4) A5)))) (forall ((A2 tptp.set_val) (B2 tptp.set_val) (C tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_val B2) C) (@ _let_1 C))))) (forall ((P2 (-> tptp.val Bool)) (Q2 (-> tptp.val Bool))) (=> (forall ((X3 tptp.val)) (=> (@ P2 X3) (@ Q2 X3))) (@ (@ tptp.ord_less_eq_set_val (@ tptp.collect_val P2)) (@ tptp.collect_val Q2)))) (forall ((A2 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val A2) A2)) _let_7 _let_6 _let_5 _let_4 _let_3 (forall ((A2 tptp.set_val) (B2 tptp.set_val)) (=> (= A2 B2) (@ (@ tptp.ord_less_eq_set_val B2) A2))) (forall ((A2 tptp.set_val) (B2 tptp.set_val)) (=> (= A2 B2) (@ (@ tptp.ord_less_eq_set_val A2) B2))) (= tptp.ord_less_eq_set_node (lambda ((A5 tptp.set_node) (B4 tptp.set_node)) (forall ((X tptp.node)) (let ((_let_1 (@ tptp.member_node X))) (=> (@ _let_1 A5) (@ _let_1 B4)))))) (= tptp.ord_le1742111550et_val (lambda ((A5 tptp.set_set_val) (B4 tptp.set_set_val)) (forall ((X tptp.set_val)) (let ((_let_1 (@ tptp.member_set_val X))) (=> (@ _let_1 A5) (@ _let_1 B4)))))) (= tptp.ord_le1643692676de_val (lambda ((A5 tptp.set_Pr699757092de_val) (B4 tptp.set_Pr699757092de_val)) (forall ((X tptp.produc1432036078de_val)) (let ((_let_1 (@ tptp.member313544709de_val X))) (=> (@ _let_1 A5) (@ _let_1 B4)))))) (= tptp.ord_le299366439et_val (lambda ((A5 tptp.set_Pr1311924359et_val) (B4 tptp.set_Pr1311924359et_val)) (forall ((X tptp.produc1324971431et_val)) (let ((_let_1 (@ tptp.member1711426256et_val X))) (=> (@ _let_1 A5) (@ _let_1 B4)))))) (= tptp.ord_less_eq_set_val (lambda ((A5 tptp.set_val) (B4 tptp.set_val)) (forall ((X tptp.val)) (let ((_let_1 (@ tptp.member_val X))) (=> (@ _let_1 A5) (@ _let_1 B4)))))) (forall ((A2 tptp.set_val) (B2 tptp.set_val)) (=> (= A2 B2) (not (=> (@ (@ tptp.ord_less_eq_set_val A2) B2) (not (@ (@ tptp.ord_less_eq_set_val B2) A2)))))) (forall ((A2 tptp.set_node) (B2 tptp.set_node) (C2 tptp.node)) (let ((_let_1 (@ tptp.member_node C2))) (=> (@ (@ tptp.ord_less_eq_set_node A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_set_val) (B2 tptp.set_set_val) (C2 tptp.set_val)) (let ((_let_1 (@ tptp.member_set_val C2))) (=> (@ (@ tptp.ord_le1742111550et_val A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_Pr699757092de_val) (B2 tptp.set_Pr699757092de_val) (C2 tptp.produc1432036078de_val)) (let ((_let_1 (@ tptp.member313544709de_val C2))) (=> (@ (@ tptp.ord_le1643692676de_val A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_Pr1311924359et_val) (B2 tptp.set_Pr1311924359et_val) (C2 tptp.produc1324971431et_val)) (let ((_let_1 (@ tptp.member1711426256et_val C2))) (=> (@ (@ tptp.ord_le299366439et_val A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_val) (B2 tptp.set_val) (C2 tptp.val)) (let ((_let_1 (@ tptp.member_val C2))) (=> (@ (@ tptp.ord_less_eq_set_val A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_node) (B2 tptp.set_node) (X2 tptp.node)) (let ((_let_1 (@ tptp.member_node X2))) (=> (@ (@ tptp.ord_less_eq_set_node A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_set_val) (B2 tptp.set_set_val) (X2 tptp.set_val)) (let ((_let_1 (@ tptp.member_set_val X2))) (=> (@ (@ tptp.ord_le1742111550et_val A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_Pr699757092de_val) (B2 tptp.set_Pr699757092de_val) (X2 tptp.produc1432036078de_val)) (let ((_let_1 (@ tptp.member313544709de_val X2))) (=> (@ (@ tptp.ord_le1643692676de_val A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_Pr1311924359et_val) (B2 tptp.set_Pr1311924359et_val) (X2 tptp.produc1324971431et_val)) (let ((_let_1 (@ tptp.member1711426256et_val X2))) (=> (@ (@ tptp.ord_le299366439et_val A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_val) (B2 tptp.set_val) (X2 tptp.val)) (let ((_let_1 (@ tptp.member_val X2))) (=> (@ (@ tptp.ord_less_eq_set_val A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((X2 tptp.set_val) (Y3 tptp.set_val) (Z tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val X2))) (let ((_let_2 (@ tptp.sup_sup_set_val Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((B tptp.set_val) (A tptp.set_val) (C2 tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val B))) (let ((_let_2 (@ tptp.sup_sup_set_val A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))) (= tptp.sup_sup_set_val (lambda ((X tptp.set_val) (Y2 tptp.set_val)) (@ (@ tptp.sup_sup_set_val Y2) X))) (= tptp.sup_sup_set_val (lambda ((A3 tptp.set_val) (B5 tptp.set_val)) (@ (@ tptp.sup_sup_set_val B5) A3))) (forall ((X2 tptp.set_val) (Y3 tptp.set_val) (Z tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val X2))) (= (@ (@ tptp.sup_sup_set_val (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.sup_sup_set_val Y3) Z))))) (forall ((A tptp.set_val) (B tptp.set_val) (C2 tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val A))) (= (@ (@ tptp.sup_sup_set_val (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.sup_sup_set_val B) C2))))) (forall ((B2 tptp.set_val) (K tptp.set_val) (B tptp.set_val) (A tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val A))) (let ((_let_2 (@ tptp.sup_sup_set_val K))) (=> (= B2 (@ _let_2 B)) (= (@ _let_1 B2) (@ _let_2 (@ _let_1 B))))))) (forall ((A2 tptp.set_val) (K tptp.set_val) (A tptp.set_val) (B tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.sup_sup_set_val A2) B) (@ _let_1 (@ (@ tptp.sup_sup_set_val A) B)))))) (= tptp.sup_sup_set_val (lambda ((X tptp.set_val) (Y2 tptp.set_val)) (@ (@ tptp.sup_sup_set_val Y2) X))) (forall ((X2 tptp.set_val) (Y3 tptp.set_val) (Z tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val X2))) (= (@ (@ tptp.sup_sup_set_val (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ tptp.sup_sup_set_val Y3) Z))))) (forall ((X2 tptp.set_val) (Y3 tptp.set_val) (Z tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val X2))) (let ((_let_2 (@ tptp.sup_sup_set_val Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val X2))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A2 tptp.set_val) (B2 tptp.set_val) (C tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val A2))) (let ((_let_2 (@ tptp.sup_sup_set_val B2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((A2 tptp.set_val) (B2 tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val A2))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))) (= tptp.sup_sup_set_val (lambda ((A5 tptp.set_val) (B4 tptp.set_val)) (@ (@ tptp.sup_sup_set_val B4) A5))) (forall ((A2 tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val A2) A2) A2)) (forall ((A2 tptp.set_val) (B2 tptp.set_val) (C tptp.set_val)) (let ((_let_1 (@ tptp.sup_sup_set_val A2))) (= (@ (@ tptp.sup_sup_set_val (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.sup_sup_set_val B2) C))))) (forall ((A2 tptp.set_val) (B2 tptp.set_val) (P2 (-> tptp.val Bool))) (= (forall ((X tptp.val)) (=> (@ (@ tptp.member_val X) (@ (@ tptp.sup_sup_set_val A2) B2)) (@ P2 X))) (and (forall ((X tptp.val)) (=> (@ (@ tptp.member_val X) A2) (@ P2 X))) (forall ((X tptp.val)) (=> (@ (@ tptp.member_val X) B2) (@ P2 X)))))) (forall ((A2 tptp.set_val) (B2 tptp.set_val) (P2 (-> tptp.val Bool))) (= (exists ((X tptp.val)) (and (@ (@ tptp.member_val X) (@ (@ tptp.sup_sup_set_val A2) B2)) (@ P2 X))) (or (exists ((X tptp.val)) (and (@ (@ tptp.member_val X) A2) (@ P2 X))) (exists ((X tptp.val)) (and (@ (@ tptp.member_val X) B2) (@ P2 X)))))) (forall ((C2 tptp.node) (B2 tptp.set_node) (A2 tptp.set_node)) (let ((_let_1 (@ tptp.member_node C2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_set_node A2) B2))))) (forall ((C2 tptp.set_val) (B2 tptp.set_set_val) (A2 tptp.set_set_val)) (let ((_let_1 (@ tptp.member_set_val C2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_set_set_val A2) B2))))) (forall ((C2 tptp.produc1432036078de_val) (B2 tptp.set_Pr699757092de_val) (A2 tptp.set_Pr699757092de_val)) (let ((_let_1 (@ tptp.member313544709de_val C2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_su2138939728de_val A2) B2))))) (forall ((C2 tptp.produc1324971431et_val) (B2 tptp.set_Pr1311924359et_val) (A2 tptp.set_Pr1311924359et_val)) (let ((_let_1 (@ tptp.member1711426256et_val C2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_su2005730907et_val A2) B2))))) (forall ((C2 tptp.val) (B2 tptp.set_val) (A2 tptp.set_val)) (let ((_let_1 (@ tptp.member_val C2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_set_val A2) B2))))) (forall ((C2 tptp.node) (A2 tptp.set_node) (B2 tptp.set_node)) (let ((_let_1 (@ tptp.member_node C2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_set_node A2) B2))))) (forall ((C2 tptp.set_val) (A2 tptp.set_set_val) (B2 tptp.set_set_val)) (let ((_let_1 (@ tptp.member_set_val C2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_set_set_val A2) B2))))) (forall ((C2 tptp.produc1432036078de_val) (A2 tptp.set_Pr699757092de_val) (B2 tptp.set_Pr699757092de_val)) (let ((_let_1 (@ tptp.member313544709de_val C2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_su2138939728de_val A2) B2))))) (forall ((C2 tptp.produc1324971431et_val) (A2 tptp.set_Pr1311924359et_val) (B2 tptp.set_Pr1311924359et_val)) (let ((_let_1 (@ tptp.member1711426256et_val C2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_su2005730907et_val A2) B2))))) (forall ((C2 tptp.val) (A2 tptp.set_val) (B2 tptp.set_val)) (let ((_let_1 (@ tptp.member_val C2))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_set_val A2) B2))))) (forall ((C2 tptp.node) (A2 tptp.set_node) (B2 tptp.set_node)) (let ((_let_1 (@ tptp.member_node C2))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_node A2) B2)) (=> (not (@ _let_1 A2)) (@ _let_1 B2))))) (forall ((C2 tptp.set_val) (A2 tptp.set_set_val) (B2 tptp.set_set_val)) (let ((_let_1 (@ tptp.member_set_val C2))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_set_val A2) B2)) (=> (not (@ _let_1 A2)) (@ _let_1 B2))))) (forall ((C2 tptp.produc1432036078de_val) (A2 tptp.set_Pr699757092de_val) (B2 tptp.set_Pr699757092de_val)) (let ((_let_1 (@ tptp.member313544709de_val C2))) (=> (@ _let_1 (@ (@ tptp.sup_su2138939728de_val A2) B2)) (=> (not (@ _let_1 A2)) (@ _let_1 B2))))) (forall ((C2 tptp.produc1324971431et_val) (A2 tptp.set_Pr1311924359et_val) (B2 tptp.set_Pr1311924359et_val)) (let ((_let_1 (@ tptp.member1711426256et_val C2))) (=> (@ _let_1 (@ (@ tptp.sup_su2005730907et_val A2) B2)) (=> (not (@ _let_1 A2)) (@ _let_1 B2))))) (forall ((C2 tptp.val) (A2 tptp.set_val) (B2 tptp.set_val)) (let ((_let_1 (@ tptp.member_val C2))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_val A2) B2)) (=> (not (@ _let_1 A2)) (@ _let_1 B2))))) (forall ((C2 tptp.set_val) (B tptp.set_val) (A tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_set_val A) B))))) (forall ((C2 tptp.set_val) (A tptp.set_val) (B tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_val A) B))))) (= tptp.ord_less_eq_set_val (lambda ((A3 tptp.set_val) (B5 tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val A3) B5) B5))) (= tptp.ord_less_eq_set_val (lambda ((B5 tptp.set_val) (A3 tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val A3) B5) A3))) (forall ((B tptp.set_val) (A tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val B) (@ (@ tptp.sup_sup_set_val A) B))) (forall ((A tptp.set_val) (B tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val A) (@ (@ tptp.sup_sup_set_val A) B))) (= tptp.ord_less_eq_set_val (lambda ((B5 tptp.set_val) (A3 tptp.set_val)) (= A3 (@ (@ tptp.sup_sup_set_val A3) B5)))) (forall ((B tptp.set_val) (A tptp.set_val) (C2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val B) A) (=> (@ (@ tptp.ord_less_eq_set_val C2) A) (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val B) C2)) A)))) (forall ((B tptp.set_val) (C2 tptp.set_val) (A tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val B) C2)) A) (not (=> (@ (@ tptp.ord_less_eq_set_val B) A) (not (@ (@ tptp.ord_less_eq_set_val C2) A)))))) (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val X2) Y3) (= (@ (@ tptp.sup_sup_set_val X2) Y3) Y3))) (forall ((Y3 tptp.set_val) (X2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val Y3) X2) (= (@ (@ tptp.sup_sup_set_val X2) Y3) X2))) (forall ((A tptp.set_val) (B tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A) B) (= (@ (@ tptp.sup_sup_set_val A) B) B))) (forall ((B tptp.set_val) (A tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val B) A) (= (@ (@ tptp.sup_sup_set_val A) B) A))) (forall ((F2 (-> tptp.set_val tptp.set_val tptp.set_val)) (X2 tptp.set_val) (Y3 tptp.set_val)) (=> (forall ((X3 tptp.set_val) (Y5 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val X3) (@ (@ F2 X3) Y5))) (=> (forall ((X3 tptp.set_val) (Y5 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val Y5) (@ (@ F2 X3) Y5))) (=> (forall ((X3 tptp.set_val) (Y5 tptp.set_val) (Z3 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val Y5) X3) (=> (@ (@ tptp.ord_less_eq_set_val Z3) X3) (@ (@ tptp.ord_less_eq_set_val (@ (@ F2 Y5) Z3)) X3)))) (= (@ (@ tptp.sup_sup_set_val X2) Y3) (@ (@ F2 X2) Y3)))))) (forall ((A tptp.set_val) (B tptp.set_val)) (=> (= A (@ (@ tptp.sup_sup_set_val A) B)) (@ (@ tptp.ord_less_eq_set_val B) A))) (forall ((B tptp.set_val) (A tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val B) A) (= A (@ (@ tptp.sup_sup_set_val A) B)))) (= tptp.ord_less_eq_set_val (lambda ((X tptp.set_val) (Y2 tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val X) Y2) Y2))) (forall ((Y3 tptp.set_val) (X2 tptp.set_val) (Z tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val Y3) X2) (=> (@ (@ tptp.ord_less_eq_set_val Z) X2) (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val Y3) Z)) X2)))) (forall ((A tptp.set_val) (C2 tptp.set_val) (B tptp.set_val) (D tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A) C2) (=> (@ (@ tptp.ord_less_eq_set_val B) D) (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val A) B)) (@ (@ tptp.sup_sup_set_val C2) D))))) (forall ((C2 tptp.set_val) (A tptp.set_val) (D tptp.set_val) (B tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val C2) A) (=> (@ (@ tptp.ord_less_eq_set_val D) B) (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val C2) D)) (@ (@ tptp.sup_sup_set_val A) B))))) (forall ((X2 tptp.set_val) (B tptp.set_val) (A tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val X2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_set_val A) B))))) (forall ((X2 tptp.set_val) (A tptp.set_val) (B tptp.set_val)) (let ((_let_1 (@ tptp.ord_less_eq_set_val X2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_val A) B))))) (forall ((Y3 tptp.set_val) (X2 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val Y3) (@ (@ tptp.sup_sup_set_val X2) Y3))) (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val X2) (@ (@ tptp.sup_sup_set_val X2) Y3))) (forall ((A tptp.set_val) (X2 tptp.set_val) (B tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A) X2) (=> (@ (@ tptp.ord_less_eq_set_val B) X2) (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val A) B)) X2)))) (forall ((A tptp.set_val) (B tptp.set_val) (X2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val A) B)) X2) (not (=> (@ (@ tptp.ord_less_eq_set_val A) X2) (not (@ (@ tptp.ord_less_eq_set_val B) X2)))))) (forall ((X2 tptp.set_val) (Y3 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val X2) (@ (@ tptp.sup_sup_set_val X2) Y3))) (forall ((Y3 tptp.set_val) (X2 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val Y3) (@ (@ tptp.sup_sup_set_val X2) Y3))) (= tptp.ord_less_eq_set_val (lambda ((A5 tptp.set_val) (B4 tptp.set_val)) (= (@ (@ tptp.sup_sup_set_val A5) B4) B4))) (forall ((C tptp.set_val) (A2 tptp.set_val) (B2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val C) (@ (@ tptp.sup_sup_set_val A2) B2)) (not (forall ((A6 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A6) A2) (forall ((B6 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val B6) B2) (not (= C (@ (@ tptp.sup_sup_set_val A6) B6)))))))))) (forall ((B2 tptp.set_val) (A2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val B2) A2) (= (@ (@ tptp.sup_sup_set_val A2) B2) A2))) (forall ((A2 tptp.set_val) (B2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A2) B2) (= (@ (@ tptp.sup_sup_set_val A2) B2) B2))) (forall ((B2 tptp.set_val) (A2 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val B2) (@ (@ tptp.sup_sup_set_val A2) B2))) (forall ((A2 tptp.set_val) (B2 tptp.set_val)) (@ (@ tptp.ord_less_eq_set_val A2) (@ (@ tptp.sup_sup_set_val A2) B2))) (forall ((A2 tptp.set_val) (C tptp.set_val) (B2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A2) C) (=> (@ (@ tptp.ord_less_eq_set_val B2) C) (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val A2) B2)) C)))) (forall ((A2 tptp.set_val) (C tptp.set_val) (B2 tptp.set_val) (D2 tptp.set_val)) (=> (@ (@ tptp.ord_less_eq_set_val A2) C) (=> (@ (@ tptp.ord_less_eq_set_val B2) D2) (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.sup_sup_set_val A2) B2)) (@ (@ tptp.sup_sup_set_val C) D2))))) (forall ((G tptp.g) (P2 tptp.set_val)) (= (@ (@ (@ (@ (@ (@ (@ tptp.irredu224829488eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G) P2) (and (not (= P2 tptp.bot_bot_set_val)) (@ (@ tptp.ord_less_eq_set_val P2) (@ tptp.dom_val_list_val (@ (@ (@ (@ tptp.sSA_CF262257161de_val tptp.alpha_n) tptp.defs) tptp.phis) G))) (exists ((X tptp.val)) (and (@ (@ tptp.member_val X) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)) (forall ((Y2 tptp.val)) (=> (@ (@ tptp.member_val Y2) P2) (forall ((Phi3 tptp.val)) (=> (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) G) Y2) Phi3) (@ (@ tptp.member_val Phi3) (@ (@ tptp.sup_sup_set_val P2) (@ (@ tptp.insert_val X) tptp.bot_bot_set_val)))))))))))) (forall ((P tptp.val) (G tptp.g) (Vs tptp.list_val)) (=> (@ (@ tptp.member_val P) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1517915011eD_val tptp.alpha_n) tptp.inEdges) tptp.defs) tptp.uses) tptp.phis) G)) (=> (= (@ (@ (@ (@ (@ tptp.sSA_CF262257161de_val tptp.alpha_n) tptp.defs) tptp.phis) G) P) (@ tptp.some_list_val Vs)) (not (= (@ tptp.set_val2 Vs) (@ (@ tptp.insert_val P) tptp.bot_bot_set_val)))))) (forall ((F2 (-> tptp.produc1432036078de_val tptp.option_list_val))) (= (= (@ tptp.dom_Pr729677986st_val F2) tptp.bot_bo404898488de_val) (= F2 (lambda ((X tptp.produc1432036078de_val)) tptp.none_list_val)))) (forall ((F2 (-> tptp.val tptp.option_list_val))) (= (= (@ tptp.dom_val_list_val F2) tptp.bot_bot_set_val) (= F2 (lambda ((X tptp.val)) tptp.none_list_val)))) (forall ((G tptp.g)) (@ tptp.finite2056463621de_val (@ tptp.dom_Pr729677986st_val (@ tptp.phis G)))) (forall ((X2 tptp.node) (A2 tptp.set_node) (B2 tptp.set_node)) (= (@ (@ tptp.ord_less_eq_set_node (@ (@ tptp.insert_node X2) A2)) B2) (and (@ (@ tptp.member_node X2) B2) (@ (@ tptp.ord_less_eq_set_node A2) B2)))) (forall ((X2 tptp.set_val) (A2 tptp.set_set_val) (B2 tptp.set_set_val)) (= (@ (@ tptp.ord_le1742111550et_val (@ (@ tptp.insert_set_val X2) A2)) B2) (and (@ (@ tptp.member_set_val X2) B2) (@ (@ tptp.ord_le1742111550et_val A2) B2)))) (forall ((X2 tptp.produc1432036078de_val) (A2 tptp.set_Pr699757092de_val) (B2 tptp.set_Pr699757092de_val)) (= (@ (@ tptp.ord_le1643692676de_val (@ (@ tptp.insert869443870de_val X2) A2)) B2) (and (@ (@ tptp.member313544709de_val X2) B2) (@ (@ tptp.ord_le1643692676de_val A2) B2)))) (forall ((X2 tptp.produc1324971431et_val) (A2 tptp.set_Pr1311924359et_val) (B2 tptp.set_Pr1311924359et_val)) (= (@ (@ tptp.ord_le299366439et_val (@ (@ tptp.insert1846469495et_val X2) A2)) B2) (and (@ (@ tptp.member1711426256et_val X2) B2) (@ (@ tptp.ord_le299366439et_val A2) B2)))) (forall ((X2 tptp.val) (A2 tptp.set_val) (B2 tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val (@ (@ tptp.insert_val X2) A2)) B2) (and (@ (@ tptp.member_val X2) B2) (@ (@ tptp.ord_less_eq_set_val A2) B2)))) (forall ((A tptp.val) (A2 tptp.set_val)) (= (@ tptp.finite_finite_val (@ (@ tptp.insert_val A) A2)) (@ tptp.finite_finite_val A2))) (forall ((A tptp.produc1324971431et_val) (A2 tptp.set_Pr1311924359et_val)) (= (@ tptp.finite79836624et_val (@ (@ tptp.insert1846469495et_val A) A2)) (@ tptp.finite79836624et_val A2))) (forall ((A tptp.produc1432036078de_val) (A2 tptp.set_Pr699757092de_val)) (= (@ tptp.finite2056463621de_val (@ (@ tptp.insert869443870de_val A) A2)) (@ tptp.finite2056463621de_val A2))) _let_2 true))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.83/1.05 )
% 0.83/1.05 % SZS output end Proof for ITP083^1
% 0.83/1.05 % cvc5---1.0.5 exiting
% 0.83/1.05 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------