%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV296-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n022.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 21:50:17 EDT 2023

% Result   : Unsatisfiable 27.56s 27.78s
% Output   : Proof 27.56s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.24  % Problem    : SWV296-1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.25  % Command    : do_cvc5 %s %d
% 0.24/0.46  % Computer : n022.cluster.edu
% 0.24/0.46  % Model    : x86_64 x86_64
% 0.24/0.46  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.46  % Memory   : 8042.1875MB
% 0.24/0.46  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.24/0.46  % CPULimit   : 300
% 0.24/0.46  % WCLimit    : 300
% 0.24/0.46  % DateTime   : Tue Aug 29 05:38:24 EDT 2023
% 0.24/0.47  % CPUTime    : 
% 0.58/0.75  %----Proving TF0_NAR, FOF, or CNF
% 0.58/0.76  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.x9iay7UHnN/cvc5---1.0.5_5953.p...
% 0.58/0.92  ------- get file name : TPTP file name is SWV296-1
% 0.58/0.92  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_5953.smt2...
% 0.58/0.92  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.84/11.08  --- Run --no-e-matching --full-saturate-quant at 5...
% 16.01/16.23  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 21.16/21.36  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 26.16/26.43  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 27.56/27.78  % SZS status Unsatisfiable for SWV296-1
% 27.56/27.78  % SZS output start Proof for SWV296-1
% 27.56/27.80  (
% 27.56/27.80  (let ((_let_1 (= tptp.v_A tptp.v_Aa))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (let ((_let_3 (= tptp.v_NA _let_2))) (let ((_let_4 (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs3))) (let ((_let_5 (tptp.c_Message_Oparts _let_4))) (let ((_let_6 (tptp.c_Message_Omsg_OKey tptp.v_K))) (let ((_let_7 (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_6))) (let ((_let_8 (tptp.c_Public_OshrK tptp.v_A))) (let ((_let_9 (tptp.c_Message_Omsg_OCrypt _let_8 _let_7))) (let ((_let_10 (tptp.c_in _let_9 _let_5 tptp.tc_Message_Omsg))) (let ((_let_11 (or _let_10 _let_3 _let_1))) (let ((_let_12 (= tptp.v_A tptp.v_Ba))) (let ((_let_13 (or _let_10 _let_12 _let_1))) (let ((_let_14 (forall ((V_BK $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey tptp.v_K))) (or (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_1)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_BK _let_1))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= tptp.v_K tptp.v_KAB)))))) (let ((_let_15 (= tptp.v_K tptp.v_KAB))) (let ((_let_16 (forall ((V_U $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (or (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OKey tptp.v_K))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs3)) tptp.tc_Message_Omsg) (= tptp.v_NA _let_1) (not (= V_U _let_1)) (not (= tptp.v_B tptp.v_Ba))))))) (let ((_let_17 (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent))) (let ((_let_18 (tptp.c_Message_Omsg_OAgent tptp.v_B))) (let ((_let_19 (tptp.c_Message_Omsg_OAgent tptp.v_A))) (let ((_let_20 (tptp.c_Message_Omsg_OMPair _let_19 _let_18))) (let ((_let_21 (tptp.c_Message_Omsg_OCrypt _let_8 (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_20)))) (let ((_let_22 (tptp.c_Message_Omsg_OMPair _let_18 _let_21))) (let ((_let_23 (tptp.c_Message_Omsg_OMPair _let_19 _let_22))) (let ((_let_24 (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_23))) (let ((_let_25 (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.v_A tptp.v_B _let_24) _let_17 tptp.tc_Event_Oevent))) (let ((_let_26 (forall ((V_U $$unsorted)) (or (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OKey tptp.v_K))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs3)) tptp.tc_Message_Omsg) (= tptp.v_A tptp.v_Ba) (not (= V_U (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (not (= tptp.v_B tptp.v_Ba)))))) (let ((_let_27 (not _let_25))) (let ((_let_28 (not _let_10))) (let ((_let_29 (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair _let_9 (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair tptp.v_x _let_6))))) _let_17 tptp.tc_Event_Oevent))) (let ((_let_30 (or _let_29 _let_28 _let_27))) (let ((_let_31 (tptp.c_Message_Omsg_OAgent tptp.v_Ba))) (let ((_let_32 (tptp.c_Message_Omsg_OAgent tptp.v_Aa))) (let ((_let_33 (tptp.c_Message_Omsg_OMPair _let_32 _let_31))) (let ((_let_34 (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (let ((_let_35 (tptp.c_Public_OshrK tptp.v_Ba))) (let ((_let_36 (tptp.c_Message_Omsg_OCrypt _let_35 (tptp.c_Message_Omsg_OMPair _let_34 (tptp.c_Message_Omsg_OMPair _let_2 _let_33))))) (let ((_let_37 (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair _let_34 _let_33)))) (let ((_let_38 (tptp.c_Message_Omsg_OMPair _let_37 _let_36))) (let ((_let_39 (tptp.c_Message_Omsg_OMPair _let_31 _let_38))) (let ((_let_40 (tptp.c_Message_Omsg_OMPair _let_32 _let_39))) (let ((_let_41 (tptp.c_Message_Omsg_OMPair _let_34 _let_40))) (let ((_let_42 (tptp.c_in (tptp.c_Event_Oevent_OGets tptp.c_Message_Oagent_OServer _let_41) _let_17 tptp.tc_Event_Oevent))) (let ((_let_43 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (let ((_let_44 (tptp.c_in _let_43 (tptp.c_Event_Oused tptp.v_evs3) tptp.tc_Message_Omsg))) (let ((_let_45 (not _let_44))) (let ((_let_46 (= tptp.v_NA _let_34))) (let ((_let_47 (or _let_10 _let_3 _let_46))) (let ((_let_48 (or _let_10 _let_12 _let_46))) (let ((_let_49 (tptp.c_in tptp.v_evs3 tptp.c_OtwayRees_Ootway (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (let ((_let_50 (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent))) (let ((_let_51 (not _let_50))) (let ((_let_52 (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_NA $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)))) (let ((_let_2 (tptp.c_Message_Omsg_OAgent V_A))) (let ((_let_3 (tptp.c_Public_OshrK V_A))) (or (not (tptp.c_in V_evs tptp.c_OtwayRees_Ootway (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt _let_3 (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OAgent V_C)))) _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt _let_3 (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OAgent V_B)))) _let_1 tptp.tc_Message_Omsg)) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (= V_B V_C)))))))) (let ((_let_53 (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_NA_H $$unsorted) (V_NA $$unsorted) (V_A_H $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)))) (let ((_let_2 (tptp.c_Message_Omsg_OAgent V_A))) (let ((_let_3 (tptp.c_Public_OshrK V_A))) (or (not (tptp.c_in V_evs tptp.c_OtwayRees_Ootway (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt _let_3 (tptp.c_Message_Omsg_OMPair V_NA_H (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A_H) _let_2)))) _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt _let_3 (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OAgent V_B)))) _let_1 tptp.tc_Message_Omsg)) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)))))))) (let ((_let_54 (forall ((V_evs $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (or (not (tptp.c_in V_evs tptp.c_OtwayRees_Ootway (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets V_B V_X) _let_1 tptp.tc_Event_Oevent)) (tptp.c_in (tptp.c_Event_Oevent_OSays (tptp.v_sko__usf V_B V_X V_evs) V_B V_X) _let_1 tptp.tc_Event_Oevent)))))) (let ((_let_55 (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) _let_1 tptp.tc_Message_Omsg)) (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))))) (let ((_let_56 (forall ((V_c $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg))))) (let ((_let_57 (forall ((V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (not (tptp.c_in (tptp.c_Event_Oevent_OSays V_A V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))))) (let ((_let_58 (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)) (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))))) (let ((_let_59 (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)) (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)))))) (let ((_let_60 (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)) (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)))))) (let ((_let_61 (forall ((V_c $$unsorted) (V_evs $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_c (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg))))) (let ((_let_62 (tptp.c_in _let_36 _let_5 tptp.tc_Message_Omsg))) (let ((_let_63 (tptp.c_in (tptp.c_Message_Omsg_OCrypt _let_8 (tptp.c_Message_Omsg_OMPair _let_34 (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair _let_32 _let_19)))) _let_5 tptp.tc_Message_Omsg))) (let ((_let_64 (tptp.c_in _let_38 _let_5 tptp.tc_Message_Omsg))) (let ((_let_65 (not _let_64))) (let ((_let_66 (or _let_65 _let_62))) (let ((_let_67 (_let_59))) (let ((_let_68 (ASSUME :args _let_67))) (let ((_let_69 (tptp.c_Message_Oparts V_H))) (let ((_let_70 (tptp.c_Message_Omsg_OMPair V_X V_Y))) (let ((_let_71 (_let_70 _let_69))) (let ((_let_72 (tptp.c_Message_Oanalz _let_4))) (let ((_let_73 (tptp.c_in _let_38 _let_72 tptp.tc_Message_Omsg))) (let ((_let_74 (not _let_73))) (let ((_let_75 (or _let_74 _let_64))) (let ((_let_76 (_let_56))) (let ((_let_77 (ASSUME :args _let_76))) (let ((_let_78 (tptp.c_in _let_39 _let_72 tptp.tc_Message_Omsg))) (let ((_let_79 (not _let_78))) (let ((_let_80 (or _let_79 _let_73))) (let ((_let_81 (_let_60))) (let ((_let_82 (ASSUME :args _let_81))) (let ((_let_83 (tptp.c_in _let_40 _let_72 tptp.tc_Message_Omsg))) (let ((_let_84 (not _let_83))) (let ((_let_85 (or _let_84 _let_78))) (let ((_let_86 ((not (= (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg) false))))) (let ((_let_87 (tptp.c_in _let_41 _let_72 tptp.tc_Message_Omsg))) (let ((_let_88 (not _let_87))) (let ((_let_89 (or _let_88 _let_83))) (let ((_let_90 (tptp.v_sko__usf tptp.c_Message_Oagent_OServer _let_41 tptp.v_evs3))) (let ((_let_91 (tptp.c_in (tptp.c_Event_Oevent_OSays _let_90 tptp.c_Message_Oagent_OServer _let_41) _let_17 tptp.tc_Event_Oevent))) (let ((_let_92 (not _let_91))) (let ((_let_93 (or _let_92 _let_87))) (let ((_let_94 (_let_57))) (let ((_let_95 (ASSUME :args _let_94))) (let ((_let_96 ((not (= (tptp.c_in (tptp.c_Event_Oevent_OSays V_A V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent) false))))) (let ((_let_97 (not _let_42))) (let ((_let_98 (not _let_49))) (let ((_let_99 (or _let_98 _let_97 _let_91))) (let ((_let_100 (_let_54))) (let ((_let_101 (ASSUME :args _let_100))) (let ((_let_102 (ASSUME :args (_let_49)))) (let ((_let_103 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_64 _let_74 (not _let_75)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_80)) :args ((or _let_73 _let_79 (not _let_80)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_85)) :args ((or _let_84 _let_78 (not _let_85)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_89)) :args ((or _let_88 _let_83 (not _let_89)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_93)) :args ((or _let_92 _let_87 (not _let_93)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_99)) :args ((or _let_98 _let_97 _let_91 (not _let_99)))) _let_102 (ASSUME :args (_let_42)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_101 :args (tptp.v_evs3 tptp.c_Message_Oagent_OServer _let_41 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_in (tptp.c_Event_Oevent_OGets V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent) false))))) :args _let_100)) _let_101 :args (_let_99 false _let_54)) :args (_let_91 false _let_49 false _let_42 false _let_99)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 :args (_let_90 tptp.c_Message_Oagent_OServer _let_41 tptp.v_evs3 QUANTIFIERS_INST_E_MATCHING _let_96)) :args _let_94)) _let_95 :args (_let_93 false _let_57)) :args (_let_87 false _let_91 false _let_93)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args (_let_34 _let_40 _let_4 QUANTIFIERS_INST_E_MATCHING _let_86)) :args _let_81)) _let_82 :args (_let_89 false _let_60)) :args (_let_83 false _let_87 false _let_89)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args (_let_32 _let_39 _let_4 QUANTIFIERS_INST_E_MATCHING _let_86)) :args _let_81)) _let_82 :args (_let_85 false _let_60)) :args (_let_78 false _let_83 false _let_85)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args (_let_31 _let_38 _let_4 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_81)) _let_82 :args (_let_80 false _let_60)) :args (_let_73 false _let_78 false _let_80)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_77 :args (_let_38 _let_4 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg) true))))) :args _let_76)) _let_77 :args (_let_75 false _let_56)) :args (_let_64 false _let_73 false _let_75)))) (let ((_let_104 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_62 _let_65 (not _let_66)))) _let_103 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args (_let_37 _let_36 _let_4 QUANTIFIERS_INST_E_MATCHING _let_71)) :args _let_67)) _let_68 :args (_let_66 false _let_59)) :args (_let_62 false _let_64 false _let_66)))) (let ((_let_105 (tptp.c_in _let_7 _let_5 tptp.tc_Message_Omsg))) (let ((_let_106 (or _let_28 _let_105))) (let ((_let_107 (forall ((V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey tptp.v_K))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA 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(TRANS (SYMM _let_186) (CONG (CONG (CONG _let_188 :args _let_151) (CONG _let_150 (CONG _let_196 (CONG (REFL :args (_let_32)) (CONG _let_188 :args _let_146) :args _let_144) :args _let_144) :args _let_144) :args _let_143) _let_124 _let_123 :args _let_122) (FALSE_INTRO _let_200))) :args (_let_198 _let_12 _let_3 _let_62)) :args ((not (and _let_3 _let_12 _let_62 _let_198)) SB_LITERAL))) (CONG (REFL :args (_let_183)) (REFL :args (_let_182)) (REFL :args (_let_181)) (MACRO_SR_PRED_INTRO :args ((= (not _let_198) _let_63))) :args _let_120)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_199)) :args ((or _let_50 _let_98 _let_176 _let_198 (not _let_199)))) _let_152 _let_102 _let_171 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_180 :args (tptp.v_evs3 tptp.v_A _let_34 tptp.v_NA tptp.v_Aa tptp.v_B QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_179)) _let_180 :args (_let_199 false _let_53)) :args (_let_198 true _let_50 false _let_49 false _let_132 false _let_199)) (MACRO_RESOLUTION_TRUST (REORDERING (ASSUME :args (_let_11)) :args ((or _let_3 _let_1 _let_10))) _let_197 _let_127 :args (_let_3 true _let_1 true _let_10)) (MACRO_RESOLUTION_TRUST (REORDERING (ASSUME :args (_let_13)) :args ((or _let_1 _let_10 _let_12))) _let_197 _let_127 :args (_let_12 true _let_1 true _let_10)) _let_104 :args (false true _let_63 false _let_3 false _let_12 false _let_62)) :args ((forall ((V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Datatype__Universe_OLeaf V_x T_a T_b) (tptp.c_Datatype__Universe_OLeaf V_y T_a T_b))) (= V_x V_y))) (forall ((V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Datatype__Universe_ONumb V_x T_a T_b) (tptp.c_Datatype__Universe_ONumb V_y T_a T_b))) (= V_x V_y))) (forall ((V_c $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (or (not (tptp.c_in V_c (tptp.c_Datatype__Universe_Odprod V_r V_s T_a T_b) (tptp.tc_prod _let_1 _let_1))) (= V_c (tptp.c_Pair (tptp.c_Datatype__Universe_OScons (tptp.c_Main_OdprodE__1 V_c V_r V_s T_a T_b) (tptp.c_Main_OdprodE__2 V_c V_r V_s T_a T_b) T_a T_b) (tptp.c_Datatype__Universe_OScons (tptp.c_Main_OdprodE__3 V_c V_r V_s T_a T_b) (tptp.c_Main_OdprodE__4 V_c V_r V_s T_a T_b) T_a T_b) _let_1 _let_1))))) (forall ((V_c $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (let ((_let_2 (tptp.tc_prod _let_1 _let_1))) (or (not (tptp.c_in V_c (tptp.c_Datatype__Universe_Odprod V_r V_s T_a T_b) _let_2)) (tptp.c_in (tptp.c_Pair (tptp.c_Main_OdprodE__2 V_c V_r V_s T_a T_b) (tptp.c_Main_OdprodE__4 V_c V_r V_s T_a T_b) _let_1 _let_1) V_s _let_2))))) (forall ((V_c $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (let ((_let_2 (tptp.tc_prod _let_1 _let_1))) (or (not (tptp.c_in V_c (tptp.c_Datatype__Universe_Odprod V_r V_s T_a T_b) _let_2)) (tptp.c_in (tptp.c_Pair (tptp.c_Main_OdprodE__1 V_c V_r V_s T_a T_b) (tptp.c_Main_OdprodE__3 V_c V_r V_s T_a T_b) _let_1 _let_1) V_r _let_2))))) (forall ((V_N $$unsorted) (V_N_H $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_s $$unsorted) (V_M $$unsorted) (V_M_H $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (let ((_let_2 (tptp.tc_prod _let_1 _let_1))) (or (not (tptp.c_in (tptp.c_Pair V_N V_N_H _let_1 _let_1) V_s _let_2)) (not (tptp.c_in (tptp.c_Pair V_M V_M_H _let_1 _let_1) V_r _let_2)) (tptp.c_in (tptp.c_Pair (tptp.c_Datatype__Universe_OScons V_M V_N T_a T_b) (tptp.c_Datatype__Universe_OScons V_M_H V_N_H T_a T_b) _let_1 _let_1) (tptp.c_Datatype__Universe_Odprod V_r V_s T_a T_b) _let_2))))) (forall ((V_w $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (or (not (tptp.c_in V_w (tptp.c_Datatype__Universe_Odsum V_r V_s T_a T_b) (tptp.tc_prod _let_1 _let_1))) (= V_w (tptp.c_Pair (tptp.c_Datatype__Universe_OIn0 (tptp.c_Main_OdsumE__1 V_r V_w T_a T_b) T_a T_b) (tptp.c_Datatype__Universe_OIn0 (tptp.c_Main_OdsumE__2 V_r V_w T_a T_b) T_a T_b) _let_1 _let_1)) (= V_w (tptp.c_Pair (tptp.c_Datatype__Universe_OIn1 (tptp.c_Main_OdsumE__3 V_s V_w T_a T_b) T_a T_b) (tptp.c_Datatype__Universe_OIn1 (tptp.c_Main_OdsumE__4 V_s V_w T_a T_b) T_a T_b) _let_1 _let_1))))) (forall ((V_w $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (let ((_let_2 (tptp.tc_prod _let_1 _let_1))) (or (not (tptp.c_in V_w (tptp.c_Datatype__Universe_Odsum V_r V_s T_a T_b) _let_2)) (tptp.c_in (tptp.c_Pair (tptp.c_Main_OdsumE__3 V_s V_w T_a T_b) (tptp.c_Main_OdsumE__4 V_s V_w T_a T_b) _let_1 _let_1) V_s _let_2) (= V_w (tptp.c_Pair (tptp.c_Datatype__Universe_OIn0 (tptp.c_Main_OdsumE__1 V_r V_w T_a T_b) T_a T_b) (tptp.c_Datatype__Universe_OIn0 (tptp.c_Main_OdsumE__2 V_r V_w T_a T_b) T_a T_b) _let_1 _let_1)))))) (forall ((V_w $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (let ((_let_2 (tptp.tc_prod _let_1 _let_1))) (or (not (tptp.c_in V_w (tptp.c_Datatype__Universe_Odsum V_r V_s T_a T_b) _let_2)) (tptp.c_in (tptp.c_Pair (tptp.c_Main_OdsumE__1 V_r V_w T_a T_b) (tptp.c_Main_OdsumE__2 V_r V_w T_a T_b) _let_1 _let_1) V_r _let_2) (= V_w (tptp.c_Pair (tptp.c_Datatype__Universe_OIn1 (tptp.c_Main_OdsumE__3 V_s V_w T_a T_b) T_a T_b) (tptp.c_Datatype__Universe_OIn1 (tptp.c_Main_OdsumE__4 V_s V_w T_a T_b) T_a T_b) _let_1 _let_1)))))) (forall ((V_w $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (let ((_let_2 (tptp.tc_prod _let_1 _let_1))) (or (not (tptp.c_in V_w (tptp.c_Datatype__Universe_Odsum V_r V_s T_a T_b) _let_2)) (tptp.c_in (tptp.c_Pair (tptp.c_Main_OdsumE__1 V_r V_w T_a T_b) (tptp.c_Main_OdsumE__2 V_r V_w T_a T_b) _let_1 _let_1) V_r _let_2) (tptp.c_in (tptp.c_Pair (tptp.c_Main_OdsumE__3 V_s V_w T_a T_b) (tptp.c_Main_OdsumE__4 V_s V_w T_a T_b) _let_1 _let_1) V_s _let_2))))) (forall ((V_M $$unsorted) (V_M_H $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_r $$unsorted) (V_s $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (let ((_let_2 (tptp.tc_prod _let_1 _let_1))) (or (not (tptp.c_in (tptp.c_Pair V_M V_M_H _let_1 _let_1) V_r _let_2)) (tptp.c_in (tptp.c_Pair (tptp.c_Datatype__Universe_OIn0 V_M T_a T_b) (tptp.c_Datatype__Universe_OIn0 V_M_H T_a T_b) _let_1 _let_1) (tptp.c_Datatype__Universe_Odsum V_r V_s T_a T_b) _let_2))))) (forall ((V_N $$unsorted) (V_N_H $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_s $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (let ((_let_2 (tptp.tc_prod _let_1 _let_1))) (or (not (tptp.c_in (tptp.c_Pair V_N V_N_H _let_1 _let_1) V_s _let_2)) (tptp.c_in (tptp.c_Pair (tptp.c_Datatype__Universe_OIn1 V_N T_a T_b) (tptp.c_Datatype__Universe_OIn1 V_N_H T_a T_b) _let_1 _let_1) (tptp.c_Datatype__Universe_Odsum V_r V_s T_a T_b) _let_2))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Datatype__Universe_Ouprod V_A V_B T_a T_b) (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (= V_c (tptp.c_Datatype__Universe_OScons (tptp.c_Main_OuprodE__1 V_A V_B V_c T_a T_b) (tptp.c_Main_OuprodE__2 V_A V_B V_c T_a T_b) T_a T_b)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (or (not (tptp.c_in V_c (tptp.c_Datatype__Universe_Ouprod V_A V_B T_a T_b) _let_1)) (tptp.c_in (tptp.c_Main_OuprodE__2 V_A V_B V_c T_a T_b) V_B _let_1)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (or (not (tptp.c_in V_c (tptp.c_Datatype__Universe_Ouprod V_A V_B T_a T_b) _let_1)) (tptp.c_in (tptp.c_Main_OuprodE__1 V_A V_B V_c T_a T_b) V_A _let_1)))) (forall ((V_N $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_M $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (or (not (tptp.c_in V_N V_B _let_1)) (not (tptp.c_in V_M V_A _let_1)) (tptp.c_in (tptp.c_Datatype__Universe_OScons V_M V_N T_a T_b) (tptp.c_Datatype__Universe_Ouprod V_A V_B T_a T_b) _let_1)))) (forall ((V_u $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (tptp.c_in V_u (tptp.c_Datatype__Universe_Ousum V_A V_B T_a T_b) (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (= V_u (tptp.c_Datatype__Universe_OIn0 (tptp.c_Main_OusumE__1 V_A V_u T_a T_b) T_a T_b)) (= V_u (tptp.c_Datatype__Universe_OIn1 (tptp.c_Main_OusumE__2 V_B V_u T_a T_b) T_a T_b)))) (forall ((V_u $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (or (not (tptp.c_in V_u (tptp.c_Datatype__Universe_Ousum V_A V_B T_a T_b) _let_1)) (tptp.c_in (tptp.c_Main_OusumE__2 V_B V_u T_a T_b) V_B _let_1) (= V_u (tptp.c_Datatype__Universe_OIn0 (tptp.c_Main_OusumE__1 V_A V_u T_a T_b) T_a T_b))))) (forall ((V_u $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (or (not (tptp.c_in V_u (tptp.c_Datatype__Universe_Ousum V_A V_B T_a T_b) _let_1)) (tptp.c_in (tptp.c_Main_OusumE__1 V_A V_u T_a T_b) V_A _let_1) (= V_u (tptp.c_Datatype__Universe_OIn1 (tptp.c_Main_OusumE__2 V_B V_u T_a T_b) T_a T_b))))) (forall ((V_u $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (or (not (tptp.c_in V_u (tptp.c_Datatype__Universe_Ousum V_A V_B T_a T_b) _let_1)) (tptp.c_in (tptp.c_Main_OusumE__1 V_A V_u T_a T_b) V_A _let_1) (tptp.c_in (tptp.c_Main_OusumE__2 V_B V_u T_a T_b) V_B _let_1)))) (forall ((V_M $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (or (not (tptp.c_in V_M V_A _let_1)) (tptp.c_in (tptp.c_Datatype__Universe_OIn0 V_M T_a T_b) (tptp.c_Datatype__Universe_Ousum V_A V_B T_a T_b) _let_1)))) (forall ((V_N $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (or (not (tptp.c_in V_N V_B _let_1)) (tptp.c_in (tptp.c_Datatype__Universe_OIn1 V_N T_a T_b) (tptp.c_Datatype__Universe_Ousum V_A V_B T_a T_b) _let_1)))) (forall ((V_m $$unsorted)) (tptp.c_Divides_Oop_Advd V_m tptp.c_0 tptp.tc_nat)) (forall ((V_k $$unsorted)) (tptp.c_Divides_Oop_Advd (tptp.c_Suc tptp.c_0) V_k tptp.tc_nat)) (forall ((V_k $$unsorted) (V_m $$unsorted)) (tptp.c_Divides_Oop_Advd V_k (tptp.c_times V_k V_m tptp.tc_nat) tptp.tc_nat)) (forall ((V_k $$unsorted) (V_m $$unsorted)) (tptp.c_Divides_Oop_Advd V_k (tptp.c_times V_m V_k tptp.tc_nat) tptp.tc_nat)) (forall ((V_m $$unsorted) (V_d $$unsorted)) (or (not (= (tptp.c_Divides_Oop_Amod V_m V_d tptp.tc_nat) tptp.c_0)) (= V_m (tptp.c_times V_d (tptp.c_Main_Omod__eq__0D__dest__1 V_d V_m) tptp.tc_nat)))) (forall ((T_a $$unsorted)) (tptp.c_in tptp.c_emptyset tptp.c_Finite__Set_OFinites (tptp.tc_set T_a))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites _let_1)) (tptp.c_in (tptp.c_insert V_a V_A T_a) tptp.c_Finite__Set_OFinites _let_1)))) (forall ((V_F $$unsorted) (T_a $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in V_F tptp.c_Finite__Set_OFinites _let_1)) (tptp.c_in (tptp.c_inter V_F V_G T_a) tptp.c_Finite__Set_OFinites _let_1)))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_F $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in V_G tptp.c_Finite__Set_OFinites _let_1)) (tptp.c_in (tptp.c_inter V_F V_G T_a) tptp.c_Finite__Set_OFinites _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set _let_1))) (tptp.c_in (tptp.c_Main_Ofinite__Union__1 V_A T_a) V_A _let_1) (tptp.c_in (tptp.c_Union V_A T_a) tptp.c_Finite__Set_OFinites _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set _let_1))) (not (tptp.c_in (tptp.c_Main_Ofinite__Union__1 V_A T_a) tptp.c_Finite__Set_OFinites _let_1)) (tptp.c_in (tptp.c_Union V_A T_a) tptp.c_Finite__Set_OFinites _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_Divides_Oop_Advd (tptp.c_GCD_Ogcd (tptp.c_Pair V_m V_n tptp.tc_nat tptp.tc_nat)) V_m tptp.tc_nat)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_Divides_Oop_Advd (tptp.c_GCD_Ogcd (tptp.c_Pair V_m V_n tptp.tc_nat tptp.tc_nat)) V_n tptp.tc_nat)) (forall ((V_S $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_Infinite__Set_Oatmost__one V_S T_a)) (not (tptp.c_in V_y V_S T_a)) (not (tptp.c_in V_x V_S T_a)) (= V_y V_x))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.c_lessequals (tptp.c_uminus (tptp.c_IntDef_Oint V_n) tptp.tc_IntDef_Oint) (tptp.c_IntDef_Oint V_m) tptp.tc_IntDef_Oint)) (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.c_less (tptp.c_uminus (tptp.c_IntDef_Oint (tptp.c_Suc V_n)) tptp.tc_IntDef_Oint) (tptp.c_IntDef_Oint V_m) tptp.tc_IntDef_Oint)) (forall ((V_m $$unsorted)) (tptp.c_Divides_Oop_Advd V_m tptp.c_0 tptp.tc_IntDef_Oint)) (forall ((V_m $$unsorted)) (tptp.c_Divides_Oop_Advd tptp.c_1 V_m tptp.tc_IntDef_Oint)) (forall ((V_k $$unsorted) (V_m $$unsorted)) (tptp.c_Divides_Oop_Advd V_k (tptp.c_times V_k V_m tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (forall ((V_k $$unsorted) (V_m $$unsorted)) (tptp.c_Divides_Oop_Advd V_k (tptp.c_times V_m V_k tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (forall ((V_m $$unsorted) (V_d $$unsorted)) (or (not (= (tptp.c_Divides_Oop_Amod V_m V_d tptp.tc_IntDef_Oint) tptp.c_0)) (= V_m (tptp.c_times V_d (tptp.c_Main_Ozmod__eq__0D__dest__1 V_d V_m) tptp.tc_IntDef_Oint)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (tptp.c_List_Odistinct (tptp.c_List_Oremdups V_xs T_a) T_a)) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (tptp.c_in (tptp.c_List_Oset V_xs T_a) tptp.c_Finite__Set_OFinites (tptp.tc_set T_a))) (forall ((V_xs $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_U $$unsorted)) (or (not (tptp.c_in V_xs (tptp.c_List_Olists V_A T_a) (tptp.tc_List_Olist T_a))) (not (tptp.c_in V_U (tptp.c_List_Oset V_xs T_a) T_a)) (tptp.c_in V_U V_A T_a))) (forall ((V_xs $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_xs (tptp.c_List_Olists V_A T_a) (tptp.tc_List_Olist T_a)) (tptp.c_in (tptp.c_Main_Oin__listsI__1 V_A V_xs T_a) (tptp.c_List_Oset V_xs T_a) T_a))) (forall ((V_A $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in (tptp.c_Main_Oin__listsI__1 V_A V_xs T_a) V_A T_a)) (tptp.c_in V_xs (tptp.c_List_Olists V_A T_a) (tptp.tc_List_Olist T_a)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (tptp.c_lessequals (tptp.c_Nat_Osize (tptp.c_List_Oremdups V_xs T_a) _let_1) (tptp.c_Nat_Osize V_xs _let_1) tptp.tc_nat))) (forall ((V_y $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_xs $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (not (tptp.c_in (tptp.c_Pair (tptp.c_List_Olist_OCons V_y V_ys T_a) V_xs _let_1 _let_1) (tptp.c_List_Olistrel V_r T_a) (tptp.tc_prod _let_1 _let_1))) (= V_xs (tptp.c_List_Olist_OCons (tptp.c_Main_Olistrel__Cons1__1 V_r V_xs V_y V_ys T_a) (tptp.c_Main_Olistrel__Cons1__2 V_r V_xs V_y V_ys T_a) T_a))))) (forall ((V_y $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_xs $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.tc_prod _let_1 _let_1))) (let ((_let_3 (tptp.c_List_Olistrel V_r T_a))) (or (not (tptp.c_in (tptp.c_Pair (tptp.c_List_Olist_OCons V_y V_ys T_a) V_xs _let_1 _let_1) _let_3 _let_2)) (tptp.c_in (tptp.c_Pair V_ys (tptp.c_Main_Olistrel__Cons1__2 V_r V_xs V_y V_ys T_a) _let_1 _let_1) _let_3 _let_2)))))) (forall ((V_y $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_xs $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (not (tptp.c_in (tptp.c_Pair (tptp.c_List_Olist_OCons V_y V_ys T_a) V_xs _let_1 _let_1) (tptp.c_List_Olistrel V_r T_a) (tptp.tc_prod _let_1 _let_1))) (tptp.c_in (tptp.c_Pair V_y (tptp.c_Main_Olistrel__Cons1__1 V_r V_xs V_y V_ys T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a))))) (forall ((V_xs $$unsorted) (V_y $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (not (tptp.c_in (tptp.c_Pair V_xs (tptp.c_List_Olist_OCons V_y V_ys T_a) _let_1 _let_1) (tptp.c_List_Olistrel V_r T_a) (tptp.tc_prod _let_1 _let_1))) (= V_xs (tptp.c_List_Olist_OCons (tptp.c_Main_Olistrel__Cons2__1 V_r V_xs V_y V_ys T_a) (tptp.c_Main_Olistrel__Cons2__2 V_r V_xs V_y V_ys T_a) T_a))))) (forall ((V_xs $$unsorted) (V_y $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.tc_prod _let_1 _let_1))) (let ((_let_3 (tptp.c_List_Olistrel V_r T_a))) (or (not (tptp.c_in (tptp.c_Pair V_xs (tptp.c_List_Olist_OCons V_y V_ys T_a) _let_1 _let_1) _let_3 _let_2)) (tptp.c_in (tptp.c_Pair (tptp.c_Main_Olistrel__Cons2__2 V_r V_xs V_y V_ys T_a) V_ys _let_1 _let_1) _let_3 _let_2)))))) (forall ((V_xs $$unsorted) (V_y $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (not (tptp.c_in (tptp.c_Pair V_xs (tptp.c_List_Olist_OCons V_y V_ys T_a) _let_1 _let_1) (tptp.c_List_Olistrel V_r T_a) (tptp.tc_prod _let_1 _let_1))) (tptp.c_in (tptp.c_Pair (tptp.c_Main_Olistrel__Cons2__1 V_r V_xs V_y V_ys T_a) V_y T_a T_a) V_r (tptp.tc_prod T_a T_a))))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (not (tptp.c_in (tptp.c_Pair tptp.c_List_Olist_ONil V_xs _let_1 _let_1) (tptp.c_List_Olistrel V_r T_a) (tptp.tc_prod _let_1 _let_1))) (= V_xs tptp.c_List_Olist_ONil)))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (not (tptp.c_in (tptp.c_Pair V_xs tptp.c_List_Olist_ONil _let_1 _let_1) (tptp.c_List_Olistrel V_r T_a) (tptp.tc_prod _let_1 _let_1))) (= V_xs tptp.c_List_Olist_ONil)))) (forall ((V_x $$unsorted) (V_l $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_List_Olists V_A T_a))) (or (not (tptp.c_in (tptp.c_List_Olist_OCons V_x V_l T_a) _let_2 _let_1)) (tptp.c_in V_l _let_2 _let_1))))) (forall ((V_x $$unsorted) (V_l $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.c_in (tptp.c_List_Olist_OCons V_x V_l T_a) (tptp.c_List_Olists V_A T_a) (tptp.tc_List_Olist T_a))) (tptp.c_in V_x V_A T_a))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_l $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_List_Olists V_A T_a))) (or (not (tptp.c_in V_a V_A T_a)) (not (tptp.c_in V_l _let_2 _let_1)) (tptp.c_in (tptp.c_List_Olist_OCons V_a V_l T_a) _let_2 _let_1))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_in tptp.c_List_Olist_ONil (tptp.c_List_Olists V_A T_a) (tptp.tc_List_Olist T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Wellfounded__Recursion_Owf V_r T_a)) (tptp.c_Wellfounded__Recursion_Owf (tptp.c_List_Olenlex V_r T_a) (tptp.tc_List_Olist T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Wellfounded__Recursion_Owf V_r T_a)) (tptp.c_Wellfounded__Recursion_Owf (tptp.c_List_Olex V_r T_a) (tptp.tc_List_Olist T_a)))) (forall ((V_n $$unsorted)) (tptp.c_lessequals tptp.c_0 V_n tptp.tc_nat)) (forall ((V_n $$unsorted)) (tptp.c_less V_n (tptp.c_Suc V_n) tptp.tc_nat)) (forall ((V_n $$unsorted)) (not (tptp.c_less V_n V_n tptp.tc_nat))) (forall ((V_n $$unsorted)) (tptp.c_less tptp.c_0 (tptp.c_Suc V_n) tptp.tc_nat)) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (tptp.c_in V_a (tptp.c_Relation_ODomain V_r T_a T_b) T_a)) (tptp.c_in (tptp.c_Pair V_a (tptp.c_Main_ODomainE__1 V_a V_r T_a T_b) T_a T_b) V_r (tptp.tc_prod T_a T_b)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_r $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) V_r (tptp.tc_prod T_a T_b))) (tptp.c_in V_a (tptp.c_Relation_ODomain V_r T_a T_b) T_a))) (forall ((V_p $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Main_OIdE__1 V_p T_a))) (or (not (tptp.c_in V_p tptp.c_Relation_OId (tptp.tc_prod T_a T_a))) (= V_p (tptp.c_Pair _let_1 _let_1 T_a T_a))))) (forall ((V_b $$unsorted) (V_r $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_b (tptp.c_Relation_OImage V_r V_A T_b T_a) T_a)) (tptp.c_in (tptp.c_Main_OImageE__1 V_A V_b V_r T_b T_a) V_A T_b))) (forall ((V_b $$unsorted) (V_r $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_b (tptp.c_Relation_OImage V_r V_A T_b T_a) T_a)) (tptp.c_in (tptp.c_Pair (tptp.c_Main_OImageE__1 V_A V_b V_r T_b T_a) V_b T_b T_a) V_r (tptp.tc_prod T_b T_a)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted) (V_r $$unsorted)) (or (not (tptp.c_in V_a V_A T_a)) (not (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) V_r (tptp.tc_prod T_a T_b))) (tptp.c_in V_b (tptp.c_Relation_OImage V_r V_A T_a T_b) T_b))) (forall ((V_b $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_b (tptp.c_Relation_ORange V_r T_b T_a) T_a)) (tptp.c_in (tptp.c_Pair (tptp.c_Main_ORangeE__1 V_b V_r T_a T_b) V_b T_b T_a) V_r (tptp.tc_prod T_b T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_r $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) V_r (tptp.tc_prod T_a T_b))) (tptp.c_in V_b (tptp.c_Relation_ORange V_r T_a T_b) T_b))) (forall ((V_yx $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_yx (tptp.c_Relation_Oconverse V_r T_b T_a) (tptp.tc_prod T_a T_b))) (tptp.c_in (tptp.c_Pair (tptp.c_Main_OconverseE__1 V_r V_yx T_b T_a) (tptp.c_Main_OconverseE__2 V_r V_yx T_b T_a) T_b T_a) V_r (tptp.tc_prod T_b T_a)))) (forall ((V_yx $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_yx (tptp.c_Relation_Oconverse V_r T_b T_a) (tptp.tc_prod T_a T_b))) (= V_yx (tptp.c_Pair (tptp.c_Main_OconverseE__2 V_r V_yx T_b T_a) (tptp.c_Main_OconverseE__1 V_r V_yx T_b T_a) T_a T_b)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Main_OdiagE__1 V_A V_c T_a))) (or (not (tptp.c_in V_c (tptp.c_Relation_Odiag V_A T_a) (tptp.tc_prod T_a T_a))) (= V_c (tptp.c_Pair _let_1 _let_1 T_a T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Relation_Odiag V_A T_a) (tptp.tc_prod T_a T_a))) (tptp.c_in (tptp.c_Main_OdiagE__1 V_A V_c T_a) V_A T_a))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_a V_A T_a)) (tptp.c_in (tptp.c_Pair V_a V_a T_a T_a) (tptp.c_Relation_Odiag V_A T_a) (tptp.tc_prod T_a T_a)))) (forall ((V_xz $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_xz (tptp.c_Relation_Orel__comp V_r V_s T_c T_b T_a) (tptp.tc_prod T_a T_b))) (tptp.c_in (tptp.c_Pair (tptp.c_Main_Orel__compE__2 V_r V_s V_xz T_c T_b T_a) (tptp.c_Main_Orel__compE__3 V_r V_s V_xz T_c T_b T_a) T_c T_b) V_r (tptp.tc_prod T_c T_b)))) (forall ((V_xz $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_xz (tptp.c_Relation_Orel__comp V_r V_s T_c T_b T_a) (tptp.tc_prod T_a T_b))) (tptp.c_in (tptp.c_Pair (tptp.c_Main_Orel__compE__1 V_r V_s V_xz T_c T_b T_a) (tptp.c_Main_Orel__compE__2 V_r V_s V_xz T_c T_b T_a) T_a T_c) V_s (tptp.tc_prod T_a T_c)))) (forall ((V_xz $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_xz (tptp.c_Relation_Orel__comp V_r V_s T_c T_b T_a) (tptp.tc_prod T_a T_b))) (= V_xz (tptp.c_Pair (tptp.c_Main_Orel__compE__1 V_r V_s V_xz T_c T_b T_a) (tptp.c_Main_Orel__compE__3 V_r V_s V_xz T_c T_b T_a) T_a T_b)))) (forall ((V_b $$unsorted) (V_c $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_r $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_s $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_b V_c T_b T_c) V_r (tptp.tc_prod T_b T_c))) (not (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) V_s (tptp.tc_prod T_a T_b))) (tptp.c_in (tptp.c_Pair V_a V_c T_a T_c) (tptp.c_Relation_Orel__comp V_r V_s T_b T_c T_a) (tptp.tc_prod T_a T_c)))) (forall ((V_l $$unsorted) (V_u $$unsorted)) (tptp.c_in (tptp.c_SetInterval_OatLeastAtMost V_l V_u tptp.tc_nat) tptp.c_Finite__Set_OFinites (tptp.tc_set tptp.tc_nat))) (forall ((V_l $$unsorted) (V_u $$unsorted)) (tptp.c_in (tptp.c_SetInterval_OatLeastAtMost V_l V_u tptp.tc_IntDef_Oint) tptp.c_Finite__Set_OFinites (tptp.tc_set tptp.tc_IntDef_Oint))) (forall ((V_l $$unsorted) (V_u $$unsorted)) (tptp.c_in (tptp.c_SetInterval_OatLeastLessThan V_l V_u tptp.tc_nat) tptp.c_Finite__Set_OFinites (tptp.tc_set tptp.tc_nat))) (forall ((V_l $$unsorted) (V_u $$unsorted)) (tptp.c_in (tptp.c_SetInterval_OatLeastLessThan V_l V_u tptp.tc_IntDef_Oint) tptp.c_Finite__Set_OFinites (tptp.tc_set tptp.tc_IntDef_Oint))) (forall ((V_k $$unsorted)) (tptp.c_in (tptp.c_SetInterval_OatMost V_k tptp.tc_nat) tptp.c_Finite__Set_OFinites (tptp.tc_set tptp.tc_nat))) (forall ((V_l $$unsorted) (V_u $$unsorted)) (tptp.c_in (tptp.c_SetInterval_OgreaterThanAtMost V_l V_u tptp.tc_nat) tptp.c_Finite__Set_OFinites (tptp.tc_set tptp.tc_nat))) (forall ((V_l $$unsorted) (V_u $$unsorted)) (tptp.c_in (tptp.c_SetInterval_OgreaterThanAtMost V_l V_u tptp.tc_IntDef_Oint) tptp.c_Finite__Set_OFinites (tptp.tc_set tptp.tc_IntDef_Oint))) (forall ((V_l $$unsorted) (V_u $$unsorted)) (tptp.c_in (tptp.c_SetInterval_OgreaterThanLessThan V_l V_u tptp.tc_nat) tptp.c_Finite__Set_OFinites (tptp.tc_set tptp.tc_nat))) (forall ((V_l $$unsorted) (V_u $$unsorted)) (tptp.c_in (tptp.c_SetInterval_OgreaterThanLessThan V_l V_u tptp.tc_IntDef_Oint) tptp.c_Finite__Set_OFinites (tptp.tc_set tptp.tc_IntDef_Oint))) (forall ((V_k $$unsorted)) (tptp.c_in (tptp.c_SetInterval_OlessThan V_k tptp.tc_nat) tptp.c_Finite__Set_OFinites (tptp.tc_set tptp.tc_nat))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_A (tptp.c_Inter V_C T_a) T_a) (tptp.c_in (tptp.c_Main_OInterI__1 V_A V_C T_a) V_C (tptp.tc_set T_a)))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_A (tptp.c_Main_OInterI__1 V_A V_C T_a) T_a)) (tptp.c_in V_A (tptp.c_Inter V_C T_a) T_a))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_in V_x tptp.c_UNIV T_a)) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_A (tptp.c_Union V_C T_a) T_a)) (tptp.c_in (tptp.c_Main_OUnionE__1 V_A V_C T_a) V_C (tptp.tc_set T_a)))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_A (tptp.c_Union V_C T_a) T_a)) (tptp.c_in V_A (tptp.c_Main_OUnionE__1 V_A V_C T_a) T_a))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals tptp.c_emptyset V_A (tptp.tc_set T_a))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_less V_A V_B _let_1)) (not (tptp.c_lessequals V_B V_A _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_less V_A V_B _let_1)) (tptp.c_lessequals V_A V_B _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.c_less V_A V_B _let_1) (= V_A V_B)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_b (tptp.c_insert V_a tptp.c_emptyset T_a) T_a)) (= V_b V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (tptp.c_in V_a (tptp.c_insert V_a tptp.c_emptyset T_a) T_a)) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (not (= (tptp.c_insert V_a tptp.c_emptyset T_a) (tptp.c_insert V_b tptp.c_emptyset T_a))) (= V_a V_b))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (tptp.c_in V_c V_A T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_set T_a))) (tptp.c_in V_c V_B T_a))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_in (tptp.c_Main_OsubsetI__1 V_A V_B T_a) V_A T_a) (tptp.c_lessequals V_A V_B (tptp.tc_set T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in (tptp.c_Main_OsubsetI__1 V_A V_B T_a) V_B T_a)) (tptp.c_lessequals V_A V_B (tptp.tc_set T_a)))) (forall ((V_B $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_lessequals V_A V_B _let_1)) (= V_A V_B)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_A V_A (tptp.tc_set T_a))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (not (tptp.c_in V_a V_A T_a)) (tptp.c_in (tptp.c_Sum__Type_OInl V_a T_a T_b) (tptp.c_Sum__Type_OPlus V_A V_B T_a T_b) (tptp.tc_sum T_a T_b)))) (forall ((V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (not (tptp.c_in V_b V_B T_a)) (tptp.c_in (tptp.c_Sum__Type_OInr V_b T_a T_b) (tptp.c_Sum__Type_OPlus V_A V_B T_b T_a) (tptp.tc_sum T_b T_a)))) (forall ((V_u $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (tptp.c_in V_u (tptp.c_Sum__Type_OPlus V_A V_B T_a T_b) (tptp.tc_sum T_a T_b))) (= V_u (tptp.c_Sum__Type_OInl (tptp.c_Main_OPlusE__1 V_A V_u T_a T_b) T_a T_b)) (= V_u (tptp.c_Sum__Type_OInr (tptp.c_Main_OPlusE__2 V_B V_u T_b T_a) T_b T_a)))) (forall ((V_u $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (tptp.c_in V_u (tptp.c_Sum__Type_OPlus V_A V_B T_a T_b) (tptp.tc_sum T_a T_b))) (tptp.c_in (tptp.c_Main_OPlusE__2 V_B V_u T_b T_a) V_B T_b) (= V_u (tptp.c_Sum__Type_OInl (tptp.c_Main_OPlusE__1 V_A V_u T_a T_b) T_a T_b)))) (forall ((V_u $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (tptp.c_in V_u (tptp.c_Sum__Type_OPlus V_A V_B T_a T_b) (tptp.tc_sum T_a T_b))) (tptp.c_in (tptp.c_Main_OPlusE__1 V_A V_u T_a T_b) V_A T_a) (= V_u (tptp.c_Sum__Type_OInr (tptp.c_Main_OPlusE__2 V_B V_u T_b T_a) T_b T_a)))) (forall ((V_u $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (tptp.c_in V_u (tptp.c_Sum__Type_OPlus V_A V_B T_a T_b) (tptp.tc_sum T_a T_b))) (tptp.c_in (tptp.c_Main_OPlusE__1 V_A V_u T_a T_b) V_A T_a) (tptp.c_in (tptp.c_Main_OPlusE__2 V_B V_u T_b T_a) V_B T_b))) (forall ((V_p $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (not (tptp.c_in V_p V_r _let_1)) (tptp.c_in V_p (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (tptp.c_in (tptp.c_Pair V_a V_a T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Pair V_a V_b T_a T_a))) (or (not (tptp.c_in _let_2 V_r _let_1)) (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a) _let_1))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Pair V_a V_b T_a T_a))) (or (not (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a) _let_1)) (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1))))) (forall ((T_a $$unsorted)) (tptp.c_Wellfounded__Recursion_Owf tptp.c_emptyset T_a)) (tptp.c_Relation_Otrans tptp.c_Wellfounded__Relations_Oless__than tptp.tc_nat) (forall ((V_R2 $$unsorted) (T_b $$unsorted) (V_R1 $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Relation_Otrans V_R2 T_b)) (not (tptp.c_Relation_Otrans V_R1 T_a)) (tptp.c_Relation_Otrans (tptp.c_Wellfounded__Relations_Olex__prod V_R1 V_R2 T_a T_b) (tptp.tc_prod T_a T_b)))) (tptp.c_Wellfounded__Recursion_Owf tptp.c_Wellfounded__Relations_Oless__than tptp.tc_nat) (forall ((V_rb $$unsorted) (T_b $$unsorted) (V_ra $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Wellfounded__Recursion_Owf V_rb T_b)) (not (tptp.c_Wellfounded__Recursion_Owf V_ra T_a)) (tptp.c_Wellfounded__Recursion_Owf (tptp.c_Wellfounded__Relations_Olex__prod V_ra V_rb T_a T_b) (tptp.tc_prod T_a T_b)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Finite__Set_Ofinite (tptp.tc_Datatype_Ooption T_1)) (not (tptp.class_Finite__Set_Ofinite T_1)))) (tptp.class_HOL_Ominus tptp.tc_IntDef_Oint) (tptp.class_HOL_Oone tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Osemiring tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Ocomm__semiring tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Ocomm__semiring__0 tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Oab__group__add tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Osemiring__0__cancel tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Oring tptp.tc_IntDef_Oint) (tptp.class_HOL_Oplus tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Ocomm__semiring__0__cancel tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Ocomm__ring tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Oaxclass__0__neq__1 tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Ocomm__monoid__mult tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Osemiring__1 tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Osemiring__1__cancel tptp.tc_IntDef_Oint) 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(tptp.class_Ring__and__Field_Opordered__cancel__semiring tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Oordered__semiring__strict tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Opordered__comm__semiring tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Opordered__cancel__comm__semiring tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Oaxclass__abs__if tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Opordered__ab__group__add tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Olordered__ab__group tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Opordered__ring tptp.tc_IntDef_Oint) (tptp.class_Orderings_Oord tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Olordered__ab__group__abs tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Olordered__ab__group__meet tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Olordered__ab__group__join tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Olordered__ring tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Oaxclass__no__zero__divisors tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Oordered__ring__strict tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Oidom tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Oordered__idom tptp.tc_IntDef_Oint) (tptp.class_Numeral_Onumber tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Osemigroup__add tptp.tc_IntDef_Oint) (tptp.class_Numeral_Onumber__ring tptp.tc_IntDef_Oint) (tptp.class_Divides_Odiv tptp.tc_IntDef_Oint) (tptp.class_Nat_Opower tptp.tc_IntDef_Oint) (tptp.class_Power_Orecpower tptp.tc_IntDef_Oint) (tptp.class_Parity_Oeven__odd tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Osemigroup__mult tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_IntDef_Oint) (tptp.class_Finite__Set_Ofinite tptp.tc_Product__Type_Ounit) (tptp.class_Finite__Set_Ofinite tptp.tc_bool) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Finite__Set_Ofinite (tptp.tc_fun T_2 T_1)) (not (tptp.class_Finite__Set_Ofinite T_1)) (not (tptp.class_Finite__Set_Ofinite T_2)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (tptp.class_Nat_Opower (tptp.tc_fun T_2 T_1))) (tptp.class_HOL_Oone tptp.tc_nat) (tptp.class_HOL_Ozero tptp.tc_nat) (tptp.class_HOL_Oplus tptp.tc_nat) (tptp.class_HOL_Otimes tptp.tc_nat) (tptp.class_Nat_Opower tptp.tc_nat) (tptp.class_Ring__and__Field_Oaxclass__0__neq__1 tptp.tc_nat) (tptp.class_OrderedGroup_Osemigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Osemigroup__mult tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring tptp.tc_nat) (tptp.class_Orderings_Oord tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring__0 tptp.tc_nat) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__mult tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__1 tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__0__cancel tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__1__cancel tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring__0__cancel tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring__1__cancel tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le tptp.tc_nat) (tptp.class_OrderedGroup_Oordered__cancel__ab__semigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_Opordered__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Opordered__cancel__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semiring__strict tptp.tc_nat) (tptp.class_LOrder_Omeet__semilorder tptp.tc_nat) (tptp.class_Ring__and__Field_Opordered__comm__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Opordered__cancel__comm__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_nat) (tptp.class_Divides_Odiv tptp.tc_nat) (tptp.class_Power_Orecpower tptp.tc_nat) (tptp.class_Numeral_Onumber tptp.tc_nat) (tptp.class_Parity_Oeven__odd tptp.tc_nat) (tptp.class_LOrder_Ojoin__semilorder tptp.tc_nat) (tptp.class_LOrder_Olorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Wellfounded__Recursion_Owellorder tptp.tc_nat) (tptp.class_HOL_Ominus tptp.tc_nat) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Finite__Set_Ofinite (tptp.tc_prod T_2 T_1)) (not (tptp.class_Finite__Set_Ofinite T_1)) (not (tptp.class_Finite__Set_Ofinite T_2)))) (forall ((T_1 $$unsorted)) (tptp.class_HOL_Ominus (tptp.tc_set T_1))) (forall ((T_1 $$unsorted)) (tptp.class_Orderings_Oord (tptp.tc_set T_1))) (forall ((T_1 $$unsorted)) (tptp.class_Orderings_Oorder (tptp.tc_set T_1))) (forall ((T_1 $$unsorted)) (or (tptp.class_Finite__Set_Ofinite (tptp.tc_set T_1)) (not (tptp.class_Finite__Set_Ofinite T_1)))) (forall ((T_1 $$unsorted)) (tptp.class_Nat_Opower (tptp.tc_set T_1))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Finite__Set_Ofinite (tptp.tc_sum T_2 T_1)) (not (tptp.class_Finite__Set_Ofinite T_1)) (not (tptp.class_Finite__Set_Ofinite T_2)))) (forall ((T $$unsorted)) (or (not (tptp.class_LOrder_Ojoin__semilorder T)) (tptp.class_Orderings_Oord T))) (forall ((T $$unsorted)) (or (not (tptp.class_LOrder_Ojoin__semilorder T)) 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(tptp.class_Ring__and__Field_Osemiring__1__cancel T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_Ring__and__Field_Oring__1 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_Ring__and__Field_Ocomm__semiring__1__cancel T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_Ring__and__Field_Ocomm__ring__1 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_HOL_Otimes T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_Numeral_Onumber T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_OrderedGroup_Osemigroup__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_OrderedGroup_Oab__semigroup__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_Ring__and__Field_Osemiring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_Ring__and__Field_Ocomm__semiring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_HOL_Ozero T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_OrderedGroup_Ocomm__monoid__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T)) (tptp.class_HOL_Ominus T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T)) (tptp.class_OrderedGroup_Ocomm__monoid__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T)) (tptp.class_HOL_Ozero T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T)) (tptp.class_OrderedGroup_Oab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T)) (tptp.class_OrderedGroup_Osemigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T)) (tptp.class_HOL_Oplus T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T)) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T)) (tptp.class_OrderedGroup_Ocancel__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__add T)) (tptp.class_OrderedGroup_Osemigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__add T)) (tptp.class_HOL_Oplus T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T)) (tptp.class_OrderedGroup_Osemigroup__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T)) (tptp.class_HOL_Otimes T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T)) (tptp.class_OrderedGroup_Oab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T)) (tptp.class_OrderedGroup_Osemigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T)) (tptp.class_HOL_Oplus T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T)) (tptp.class_OrderedGroup_Ocancel__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T)) (tptp.class_OrderedGroup_Osemigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T)) (tptp.class_HOL_Oplus T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T)) (tptp.class_HOL_Ozero T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T)) (tptp.class_OrderedGroup_Oab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T)) (tptp.class_OrderedGroup_Osemigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T)) (tptp.class_HOL_Oplus T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T)) (tptp.class_HOL_Oone T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T)) (tptp.class_OrderedGroup_Oab__semigroup__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T)) (tptp.class_OrderedGroup_Osemigroup__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T)) (tptp.class_HOL_Otimes T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T)) (tptp.class_OrderedGroup_Omonoid__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T)) (tptp.class_OrderedGroup_Opordered__ab__group__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T)) (tptp.class_OrderedGroup_Oab__group__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T)) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T)) (tptp.class_OrderedGroup_Oab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T)) (tptp.class_OrderedGroup_Ocancel__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T)) (tptp.class_OrderedGroup_Osemigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T)) (tptp.class_HOL_Oplus T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T)) (tptp.class_LOrder_Olorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T)) (tptp.class_LOrder_Ojoin__semilorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T)) 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$$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_k $$unsorted)) (not (= (tptp.c_Datatype__Universe_OScons V_M V_N T_a T_b) (tptp.c_Datatype__Universe_ONumb V_k T_a T_b)))) (forall ((V_m $$unsorted)) (or (not (tptp.c_Divides_Oop_Advd tptp.c_0 V_m tptp.tc_nat)) (= V_m tptp.c_0))) (tptp.c_Divides_Oop_Advd tptp.c_0 tptp.c_0 tptp.tc_nat) (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (not (= tptp.c_emptyset (tptp.c_Equiv__Relations_Oquotient V_A V_r T_a))) (= V_A tptp.c_emptyset))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= tptp.c_emptyset (tptp.c_Equiv__Relations_Oquotient tptp.c_emptyset V_r T_a))) (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Equiv__Relations_Oquotient V_A V_r T_a) tptp.c_emptyset)) (= V_A tptp.c_emptyset))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Equiv__Relations_Oquotient tptp.c_emptyset V_r T_a) tptp.c_emptyset)) (not (= tptp.c_Extraction_Osumbool_OLeft tptp.c_Extraction_Osumbool_ORight)) (not (= tptp.c_Extraction_Osumbool_ORight tptp.c_Extraction_Osumbool_OLeft)) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in (tptp.c_minus V_A (tptp.c_insert V_a V_B T_a) _let_1) tptp.c_Finite__Set_OFinites _let_1)) (tptp.c_in (tptp.c_minus V_A V_B _let_1) tptp.c_Finite__Set_OFinites _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in (tptp.c_minus V_A V_B _let_1) tptp.c_Finite__Set_OFinites _let_1)) (tptp.c_in (tptp.c_minus V_A (tptp.c_insert V_a V_B T_a) _let_1) tptp.c_Finite__Set_OFinites _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in (tptp.c_Pow V_A T_a) tptp.c_Finite__Set_OFinites (tptp.tc_set _let_1))) (tptp.c_in V_A tptp.c_Finite__Set_OFinites _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites _let_1)) (tptp.c_in (tptp.c_Pow V_A T_a) tptp.c_Finite__Set_OFinites (tptp.tc_set _let_1))))) (forall ((V_F $$unsorted) (V_G $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in (tptp.c_union V_F V_G T_a) tptp.c_Finite__Set_OFinites _let_1)) (tptp.c_in V_F tptp.c_Finite__Set_OFinites _let_1)))) (forall ((V_F $$unsorted) (V_G $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in (tptp.c_union V_F V_G T_a) tptp.c_Finite__Set_OFinites _let_1)) (tptp.c_in V_G tptp.c_Finite__Set_OFinites _let_1)))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_F $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in V_G tptp.c_Finite__Set_OFinites _let_1)) (not (tptp.c_in V_F tptp.c_Finite__Set_OFinites _let_1)) (tptp.c_in (tptp.c_union V_F V_G T_a) tptp.c_Finite__Set_OFinites _let_1)))) (forall ((V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in (tptp.c_Relation_Oconverse V_r T_b T_a) tptp.c_Finite__Set_OFinites (tptp.tc_set (tptp.tc_prod T_a T_b)))) (tptp.c_in V_r tptp.c_Finite__Set_OFinites (tptp.tc_set (tptp.tc_prod T_b T_a))))) (forall ((V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_r tptp.c_Finite__Set_OFinites (tptp.tc_set (tptp.tc_prod T_b T_a)))) (tptp.c_in (tptp.c_Relation_Oconverse V_r T_b T_a) tptp.c_Finite__Set_OFinites (tptp.tc_set (tptp.tc_prod T_a T_b))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_Divides_Oop_Advd V_k (tptp.c_GCD_Ogcd (tptp.c_Pair V_m V_n tptp.tc_nat tptp.tc_nat)) tptp.tc_nat)) (tptp.c_Divides_Oop_Advd V_k V_m tptp.tc_nat))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_Divides_Oop_Advd V_k (tptp.c_GCD_Ogcd (tptp.c_Pair V_m V_n tptp.tc_nat tptp.tc_nat)) tptp.tc_nat)) (tptp.c_Divides_Oop_Advd V_k V_n tptp.tc_nat))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (not (tptp.c_Divides_Oop_Advd V_k V_n tptp.tc_nat)) (not (tptp.c_Divides_Oop_Advd V_k V_m tptp.tc_nat)) (tptp.c_Divides_Oop_Advd V_k (tptp.c_GCD_Ogcd (tptp.c_Pair V_m V_n tptp.tc_nat tptp.tc_nat)) tptp.tc_nat))) (not (tptp.c_in tptp.c_UNIV tptp.c_Finite__Set_OFinites (tptp.tc_set tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_IntDef_Oint V_m) (tptp.c_IntDef_Oint V_n))) (= V_m V_n))) (forall ((V_z $$unsorted) (V_w $$unsorted)) (or (not (tptp.c_Divides_Oop_Advd V_z (tptp.c_uminus V_w tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (tptp.c_Divides_Oop_Advd V_z V_w tptp.tc_IntDef_Oint))) (forall ((V_z $$unsorted) (V_w $$unsorted)) (or (not (tptp.c_Divides_Oop_Advd V_z V_w tptp.tc_IntDef_Oint)) (tptp.c_Divides_Oop_Advd V_z (tptp.c_uminus V_w tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint))) (forall ((V_m $$unsorted)) (or (not (tptp.c_Divides_Oop_Advd tptp.c_0 V_m tptp.tc_IntDef_Oint)) (= V_m tptp.c_0))) (tptp.c_Divides_Oop_Advd tptp.c_0 tptp.c_0 tptp.tc_IntDef_Oint) (forall ((V_z $$unsorted) (V_w $$unsorted)) (or (not (tptp.c_Divides_Oop_Advd (tptp.c_uminus V_z tptp.tc_IntDef_Oint) V_w tptp.tc_IntDef_Oint)) (tptp.c_Divides_Oop_Advd V_z V_w tptp.tc_IntDef_Oint))) (forall ((V_z $$unsorted) (V_w $$unsorted)) (or (not (tptp.c_Divides_Oop_Advd V_z V_w tptp.tc_IntDef_Oint)) (tptp.c_Divides_Oop_Advd (tptp.c_uminus V_z tptp.tc_IntDef_Oint) V_w tptp.tc_IntDef_Oint))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (not (tptp.c_in (tptp.c_Pair V_xs tptp.c_List_Olist_ONil _let_1 _let_1) (tptp.c_List_Olex V_r T_a) (tptp.tc_prod _let_1 _let_1))))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= tptp.c_List_Olist_ONil (tptp.c_append V_xs V_ys T_a))) (= V_xs tptp.c_List_Olist_ONil))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= tptp.c_List_Olist_ONil (tptp.c_append V_xs V_ys T_a))) (= V_ys tptp.c_List_Olist_ONil))) (forall ((T_a $$unsorted)) (= tptp.c_List_Olist_ONil (tptp.c_append tptp.c_List_Olist_ONil tptp.c_List_Olist_ONil T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (not (= tptp.c_List_Olist_ONil (tptp.c_List_Orev V_xs T_a))) (= V_xs tptp.c_List_Olist_ONil))) (forall ((T_a $$unsorted)) (= tptp.c_List_Olist_ONil (tptp.c_List_Orev tptp.c_List_Olist_ONil T_a))) (forall ((V_ys $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (not (tptp.c_in (tptp.c_Pair tptp.c_List_Olist_ONil V_ys _let_1 _let_1) (tptp.c_List_Olex V_r T_a) (tptp.tc_prod _let_1 _let_1))))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_append V_xs (tptp.c_List_Olist_OCons V_x tptp.c_List_Olist_ONil T_a) T_a) (tptp.c_append V_ys (tptp.c_List_Olist_OCons V_y tptp.c_List_Olist_ONil T_a) T_a))) (= V_xs V_ys))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_append V_xs (tptp.c_List_Olist_OCons V_x tptp.c_List_Olist_ONil T_a) T_a) (tptp.c_append V_ys (tptp.c_List_Olist_OCons V_y tptp.c_List_Olist_ONil T_a) T_a))) (= V_x V_y))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_List_Olists V_A T_a))) (or (not (tptp.c_in (tptp.c_append V_xs V_ys T_a) _let_2 _let_1)) (tptp.c_in V_xs _let_2 _let_1))))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_List_Olists V_A T_a))) (or (not (tptp.c_in (tptp.c_append V_xs V_ys T_a) _let_2 _let_1)) (tptp.c_in V_ys _let_2 _let_1))))) (forall ((V_ys $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_List_Olists V_A T_a))) (or (not (tptp.c_in V_ys _let_2 _let_1)) (not (tptp.c_in V_xs _let_2 _let_1)) (tptp.c_in (tptp.c_append V_xs V_ys T_a) _let_2 _let_1))))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_append V_xs V_ys T_a) tptp.c_List_Olist_ONil)) (= V_xs tptp.c_List_Olist_ONil))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_append V_xs V_ys T_a) tptp.c_List_Olist_ONil)) (= V_ys tptp.c_List_Olist_ONil))) (forall ((T_a $$unsorted)) (= (tptp.c_append tptp.c_List_Olist_ONil tptp.c_List_Olist_ONil T_a) tptp.c_List_Olist_ONil)) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_append V_ys V_xs T_a) (tptp.c_append V_zs V_xs T_a))) (= V_ys V_zs))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_append V_xs V_ys T_a) V_ys)) (= V_xs tptp.c_List_Olist_ONil))) (forall ((V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.c_append tptp.c_List_Olist_ONil V_ys T_a) V_ys)) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_append V_xs V_ys T_a) V_xs)) (= V_ys tptp.c_List_Olist_ONil))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_append V_xs tptp.c_List_Olist_ONil T_a) V_xs)) (forall ((V_nibble1 $$unsorted) (V_nibble2 $$unsorted) (V_nibble1_H $$unsorted) (V_nibble2_H $$unsorted)) (or (not (= (tptp.c_List_Ochar_OChar V_nibble1 V_nibble2) (tptp.c_List_Ochar_OChar V_nibble1_H V_nibble2_H))) (= V_nibble1 V_nibble1_H))) (forall ((V_nibble1 $$unsorted) (V_nibble2 $$unsorted) (V_nibble1_H $$unsorted) (V_nibble2_H $$unsorted)) (or (not (= (tptp.c_List_Ochar_OChar V_nibble1 V_nibble2) (tptp.c_List_Ochar_OChar V_nibble1_H V_nibble2_H))) (= V_nibble2 V_nibble2_H))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Nat_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.c_0)) (= V_xs tptp.c_List_Olist_ONil))) (forall ((T_a $$unsorted)) (= (tptp.c_Nat_Osize tptp.c_List_Olist_ONil (tptp.tc_List_Olist T_a)) tptp.c_0)) (forall ((T_a $$unsorted)) (not (tptp.c_less tptp.c_0 (tptp.c_Nat_Osize tptp.c_List_Olist_ONil (tptp.tc_List_Olist T_a)) tptp.tc_nat))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_less tptp.c_0 (tptp.c_Nat_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat) (= V_xs tptp.c_List_Olist_ONil))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Oremdups V_xs T_a))) (let ((_let_2 (tptp.tc_List_Olist T_a))) (or (not (= (tptp.c_Nat_Osize _let_1 _let_2) (tptp.c_Nat_Osize V_xs _let_2))) (= _let_1 V_xs))))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_List_Oremdups V_xs T_a))) (or (not (= _let_2 V_xs)) (= (tptp.c_Nat_Osize _let_2 _let_1) (tptp.c_Nat_Osize V_xs _let_1)))))) (forall ((V_a_H $$unsorted) (V_list_H $$unsorted) (T_a $$unsorted)) (not (= tptp.c_List_Olist_ONil (tptp.c_List_Olist_OCons V_a_H V_list_H T_a)))) (forall ((V_a_H $$unsorted) (V_list_H $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_a_H V_list_H T_a) tptp.c_List_Olist_ONil))) (forall ((V_a $$unsorted) (V_list $$unsorted) (T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_a V_list T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a))) (= V_a V_a_H))) (forall ((V_a $$unsorted) (V_list $$unsorted) (T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_a V_list T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a))) (= V_list V_list_H))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Orev V_xs T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a))) (= V_xs (tptp.c_append (tptp.c_List_Orev V_ys T_a) (tptp.c_List_Olist_OCons V_y tptp.c_List_Olist_ONil T_a) T_a)))) (forall ((V_ys $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (= (tptp.c_List_Orev (tptp.c_append (tptp.c_List_Orev V_ys T_a) (tptp.c_List_Olist_OCons V_y tptp.c_List_Olist_ONil T_a) T_a) T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Orev V_xs T_a) tptp.c_List_Olist_ONil)) (= V_xs tptp.c_List_Olist_ONil))) (forall ((T_a $$unsorted)) (= (tptp.c_List_Orev tptp.c_List_Olist_ONil T_a) tptp.c_List_Olist_ONil)) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Orev V_xs T_a) (tptp.c_List_Orev V_ys T_a))) (= V_xs V_ys))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_append V_xs V_ys T_a) (tptp.c_append V_xs V_zs T_a))) (= V_ys V_zs))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (= V_ys (tptp.c_append V_xs V_ys T_a))) (= V_xs tptp.c_List_Olist_ONil))) (forall ((V_ys $$unsorted) (T_a $$unsorted)) (= V_ys (tptp.c_append tptp.c_List_Olist_ONil V_ys T_a))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= V_xs (tptp.c_append V_xs V_ys T_a))) (= V_ys tptp.c_List_Olist_ONil))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= V_xs (tptp.c_append V_xs tptp.c_List_Olist_ONil T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (not (= tptp.c_emptyset (tptp.c_List_Oset V_xs T_a))) (= V_xs tptp.c_List_Olist_ONil))) (forall ((T_a $$unsorted)) (= tptp.c_emptyset (tptp.c_List_Oset tptp.c_List_Olist_ONil T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oset V_xs T_a) tptp.c_emptyset)) (= V_xs tptp.c_List_Olist_ONil))) (forall ((T_a $$unsorted)) (= (tptp.c_List_Oset tptp.c_List_Olist_ONil T_a) tptp.c_emptyset)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_Suc V_m) (tptp.c_Suc V_n))) (= V_m V_n))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_Suc V_n) (tptp.c_Suc V_m) tptp.tc_nat)) (tptp.c_lessequals V_n V_m tptp.tc_nat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (not (tptp.c_lessequals V_n V_m tptp.tc_nat)) (tptp.c_lessequals (tptp.c_Suc V_n) (tptp.c_Suc V_m) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_less (tptp.c_Suc V_m) (tptp.c_Suc V_n) tptp.tc_nat)) (tptp.c_less V_m V_n tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_less V_m V_n tptp.tc_nat)) (tptp.c_less (tptp.c_Suc V_m) (tptp.c_Suc V_n) tptp.tc_nat))) (forall ((V_m $$unsorted)) (not (= (tptp.c_Suc V_m) tptp.c_0))) (forall ((V_m $$unsorted)) (not (= tptp.c_0 (tptp.c_Suc V_m)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_less tptp.c_0 (tptp.c_plus V_m V_n tptp.tc_nat) tptp.tc_nat)) (tptp.c_less tptp.c_0 V_n tptp.tc_nat) (tptp.c_less tptp.c_0 V_m tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_less tptp.c_0 V_m tptp.tc_nat)) (tptp.c_less tptp.c_0 (tptp.c_plus V_m V_n tptp.tc_nat) tptp.tc_nat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (not (tptp.c_less tptp.c_0 V_n tptp.tc_nat)) (tptp.c_less tptp.c_0 (tptp.c_plus V_m V_n tptp.tc_nat) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_plus V_m V_n tptp.tc_nat) tptp.c_0)) (= V_m tptp.c_0))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_plus V_m V_n tptp.tc_nat) tptp.c_0)) (= V_n tptp.c_0))) (= (tptp.c_plus tptp.c_0 tptp.c_0 tptp.tc_nat) tptp.c_0) (forall ((V_i $$unsorted)) (or (not (tptp.c_lessequals V_i tptp.c_0 tptp.tc_nat)) (= V_i tptp.c_0))) (tptp.c_lessequals tptp.c_0 tptp.c_0 tptp.tc_nat) (forall ((V_n $$unsorted)) (or (not (tptp.c_less V_n (tptp.c_Suc tptp.c_0) tptp.tc_nat)) (= V_n tptp.c_0))) (tptp.c_less tptp.c_0 (tptp.c_Suc tptp.c_0) tptp.tc_nat) (forall ((V_n $$unsorted)) (or (not (tptp.c_less V_n tptp.c_1 tptp.tc_nat)) (= V_n tptp.c_0))) (tptp.c_less tptp.c_0 tptp.c_1 tptp.tc_nat) (forall ((V_n $$unsorted)) (or (tptp.c_less tptp.c_0 V_n tptp.tc_nat) (= V_n tptp.c_0))) (not (tptp.c_less tptp.c_0 tptp.c_0 tptp.tc_nat)) (forall ((V_i $$unsorted) (V_j $$unsorted)) (not (tptp.c_less (tptp.c_plus V_i V_j tptp.tc_nat) V_i tptp.tc_nat))) (forall ((V_j $$unsorted) (V_i $$unsorted)) (not (tptp.c_less (tptp.c_plus V_j V_i tptp.tc_nat) V_i tptp.tc_nat))) (forall ((V_n $$unsorted)) (not (tptp.c_less V_n tptp.c_0 tptp.tc_nat))) (not (= tptp.c_Numeral_Obit_OB0 tptp.c_Numeral_Obit_OB1)) (not (= tptp.c_Numeral_Obit_OB1 tptp.c_Numeral_Obit_OB0)) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_less V_x V_x T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a_H $$unsorted) (V_b_H $$unsorted)) (or (not (= (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Pair V_a_H V_b_H T_a T_b))) (= V_a V_a_H))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a_H $$unsorted) (V_b_H $$unsorted)) (or (not (= (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Pair V_a_H V_b_H T_a T_b))) (= V_b V_b_H))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (tptp.c_in (tptp.c_Pair V_a V_a T_a T_a) tptp.c_Relation_OId (tptp.tc_prod T_a T_a))) (forall ((V_b $$unsorted) (V_r $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_b (tptp.c_Relation_OImage V_r (tptp.c_insert V_a tptp.c_emptyset T_b) T_b T_a) T_a)) (tptp.c_in (tptp.c_Pair V_a V_b T_b T_a) V_r (tptp.tc_prod T_b T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_a V_b T_b T_a) V_r (tptp.tc_prod T_b T_a))) (tptp.c_in V_b (tptp.c_Relation_OImage V_r (tptp.c_insert V_a tptp.c_emptyset T_b) T_b T_a) T_a))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_r $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Relation_Oconverse V_r T_b T_a) (tptp.tc_prod T_a T_b))) (tptp.c_in (tptp.c_Pair V_b V_a T_b T_a) V_r (tptp.tc_prod T_b T_a)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_b V_a T_b T_a) V_r (tptp.tc_prod T_b T_a))) (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Relation_Oconverse V_r T_b T_a) (tptp.tc_prod T_a T_b)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) tptp.c_Relation_OId (tptp.tc_prod T_a T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (= (tptp.c_SetInterval_OatLeast V_x T_a) (tptp.c_SetInterval_OatLeast V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_in V_i (tptp.c_SetInterval_OatLeast V_k T_a) T_a)) (tptp.c_lessequals V_k V_i T_a))) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_i $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_lessequals V_k V_i T_a)) (tptp.c_in V_i (tptp.c_SetInterval_OatLeast V_k T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_lessequals (tptp.c_SetInterval_OatLeast V_x T_a) (tptp.c_SetInterval_OatLeast V_y T_a) (tptp.tc_set T_a))) (tptp.c_lessequals V_y V_x T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_lessequals V_y V_x T_a)) (tptp.c_lessequals (tptp.c_SetInterval_OatLeast V_x T_a) (tptp.c_SetInterval_OatLeast V_y T_a) (tptp.tc_set T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (= (tptp.c_SetInterval_OatMost V_x T_a) (tptp.c_SetInterval_OatMost V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_in V_i (tptp.c_SetInterval_OatMost V_k T_a) T_a)) (tptp.c_lessequals V_i V_k T_a))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_lessequals V_i V_k T_a)) (tptp.c_in V_i (tptp.c_SetInterval_OatMost V_k T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_lessequals (tptp.c_SetInterval_OatMost V_x T_a) (tptp.c_SetInterval_OatMost V_y T_a) (tptp.tc_set T_a))) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_lessequals V_x V_y T_a)) (tptp.c_lessequals (tptp.c_SetInterval_OatMost V_x T_a) (tptp.c_SetInterval_OatMost V_y T_a) (tptp.tc_set T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (= (tptp.c_SetInterval_OgreaterThan V_x T_a) (tptp.c_SetInterval_OgreaterThan V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_in V_i (tptp.c_SetInterval_OgreaterThan V_k T_a) T_a)) (tptp.c_less V_k V_i T_a))) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_i $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_less V_k V_i T_a)) (tptp.c_in V_i (tptp.c_SetInterval_OgreaterThan V_k T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals (tptp.c_SetInterval_OgreaterThan V_x T_a) (tptp.c_SetInterval_OgreaterThan V_y T_a) (tptp.tc_set T_a))) (tptp.c_lessequals V_y V_x T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_y V_x T_a)) (tptp.c_lessequals (tptp.c_SetInterval_OgreaterThan V_x T_a) (tptp.c_SetInterval_OgreaterThan V_y T_a) (tptp.tc_set T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (= (tptp.c_SetInterval_OlessThan V_x T_a) (tptp.c_SetInterval_OlessThan V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_in V_i (tptp.c_SetInterval_OlessThan V_k T_a) T_a)) (tptp.c_less V_i V_k T_a))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_less V_i V_k T_a)) (tptp.c_in V_i (tptp.c_SetInterval_OlessThan V_k T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals (tptp.c_SetInterval_OlessThan V_x T_a) (tptp.c_SetInterval_OlessThan V_y T_a) (tptp.tc_set T_a))) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_x V_y T_a)) (tptp.c_lessequals (tptp.c_SetInterval_OlessThan V_x T_a) (tptp.c_SetInterval_OlessThan V_y T_a) (tptp.tc_set T_a)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_c V_A T_a)) (not (tptp.c_in V_c (tptp.c_uminus V_A (tptp.tc_set T_a)) T_a)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_c V_A T_a) (tptp.c_in V_c (tptp.c_uminus V_A (tptp.tc_set T_a)) T_a))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (= (tptp.c_uminus V_A _let_1) (tptp.c_uminus V_B _let_1))) (= V_A V_B)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_lessequals (tptp.c_uminus V_A _let_1) (tptp.c_uminus V_B _let_1) _let_1)) (tptp.c_lessequals V_B V_A _let_1)))) (forall ((V_B $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_lessequals V_B V_A _let_1)) (tptp.c_lessequals (tptp.c_uminus V_A _let_1) (tptp.c_uminus V_B _let_1) _let_1)))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.c_in V_c V_B T_a)) (not (tptp.c_in V_c (tptp.c_minus V_A V_B (tptp.tc_set T_a)) T_a)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_minus V_A V_B (tptp.tc_set T_a)) T_a)) (tptp.c_in V_c V_A T_a))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (tptp.c_in V_c V_A T_a)) (tptp.c_in V_c V_B T_a) (tptp.c_in V_c (tptp.c_minus V_A V_B (tptp.tc_set T_a)) T_a))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_inter V_A V_B T_a) T_a)) (tptp.c_in V_c V_B T_a))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_inter V_A V_B T_a) T_a)) (tptp.c_in V_c V_A T_a))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.c_in V_c V_B T_a)) (not (tptp.c_in V_c V_A T_a)) (tptp.c_in V_c (tptp.c_inter V_A V_B T_a) T_a))) (forall ((V_X $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.c_in V_X V_C (tptp.tc_set T_a))) (not (tptp.c_in V_A (tptp.c_Inter V_C T_a) T_a)) (tptp.c_in V_A V_X T_a))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in V_A (tptp.c_Pow V_B T_a) _let_1)) (tptp.c_lessequals V_A V_B _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.c_in V_A (tptp.c_Pow V_B T_a) _let_1)))) (not (= tptp.c_UNIV tptp.c_emptyset)) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.c_in V_c V_B T_a)) (tptp.c_in V_c (tptp.c_union V_A V_B T_a) T_a))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (tptp.c_in V_c V_A T_a)) (tptp.c_in V_c (tptp.c_union V_A V_B T_a) T_a))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_union V_A V_B T_a) T_a)) (tptp.c_in V_c V_B T_a) (tptp.c_in V_c V_A T_a))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_union V_A V_B T_a) tptp.c_emptyset)) (= V_A tptp.c_emptyset))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_union V_A V_B T_a) tptp.c_emptyset)) (= V_B tptp.c_emptyset))) (forall ((T_a $$unsorted)) (= (tptp.c_union tptp.c_emptyset tptp.c_emptyset T_a) tptp.c_emptyset)) (forall ((V_A $$unsorted) (V_X $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (or (not (tptp.c_in V_A V_X T_a)) (not (tptp.c_in V_X V_C (tptp.tc_set T_a))) (tptp.c_in V_A (tptp.c_Union V_C T_a) T_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (not (tptp.c_in V_a tptp.c_emptyset T_a))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.c_in V_a V_B T_a)) (tptp.c_in V_a (tptp.c_insert V_b V_B T_a) T_a))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (tptp.c_in V_x (tptp.c_insert V_x V_B T_a) T_a)) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_a (tptp.c_insert V_b V_A T_a) T_a)) (tptp.c_in V_a V_A T_a) (= V_a V_b))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (not (tptp.c_less V_A tptp.c_emptyset (tptp.tc_set T_a)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (not (= (tptp.c_insert V_a V_A T_a) (tptp.c_insert V_b tptp.c_emptyset T_a))) (= V_a V_b))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_insert V_b tptp.c_emptyset T_a))) (or (not (= (tptp.c_insert V_a V_A T_a) _let_1)) (tptp.c_lessequals V_A _let_1 (tptp.tc_set T_a))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_insert V_x tptp.c_emptyset T_a))) (or (not (tptp.c_lessequals V_A _let_1 (tptp.tc_set T_a))) (= (tptp.c_insert V_x V_A T_a) _let_1)))) (forall ((V_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (or (not (= (tptp.c_insert V_b tptp.c_emptyset T_a) (tptp.c_insert V_a V_A T_a))) (= V_a V_b))) (forall ((V_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_insert V_b tptp.c_emptyset T_a))) (or (not (= _let_1 (tptp.c_insert V_a V_A T_a))) (tptp.c_lessequals V_A _let_1 (tptp.tc_set T_a))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_insert V_x tptp.c_emptyset T_a))) (or (not (tptp.c_lessequals V_A _let_1 (tptp.tc_set T_a))) (= _let_1 (tptp.c_insert V_x V_A T_a))))) (forall ((V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Sum__Type_OInl V_x T_a T_b) (tptp.c_Sum__Type_OInl V_y T_a T_b))) (= V_x V_y))) (forall ((V_a $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_b $$unsorted)) (not (= (tptp.c_Sum__Type_OInl V_a T_a T_b) (tptp.c_Sum__Type_OInr V_b T_b T_a)))) (forall ((V_x $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Sum__Type_OInr V_x T_b T_a) (tptp.c_Sum__Type_OInr V_y T_b T_a))) (= V_x V_y))) (forall ((V_b $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (not (= (tptp.c_Sum__Type_OInr V_b T_b T_a) (tptp.c_Sum__Type_OInl V_a T_a T_b)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Wellfounded__Recursion_Oacyclic (tptp.c_Relation_Oconverse V_r T_a T_a) T_a)) (tptp.c_Wellfounded__Recursion_Oacyclic V_r T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Wellfounded__Recursion_Oacyclic V_r T_a)) (tptp.c_Wellfounded__Recursion_Oacyclic (tptp.c_Relation_Oconverse V_r T_a T_a) T_a))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.c_Wellfounded__Recursion_Oacyclic (tptp.c_insert (tptp.c_Pair V_y V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)) T_a)) (tptp.c_Wellfounded__Recursion_Oacyclic V_r T_a))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (not (tptp.c_Wellfounded__Recursion_Oacyclic (tptp.c_insert (tptp.c_Pair V_y V_x T_a T_a) V_r _let_1) T_a)) (not (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (not (tptp.c_Wellfounded__Recursion_Oacyclic V_r T_a)) (tptp.c_Wellfounded__Recursion_Oacyclic (tptp.c_insert (tptp.c_Pair V_y V_x T_a T_a) V_r _let_1) T_a) (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.c_Wellfounded__Recursion_Owf (tptp.c_insert (tptp.c_Pair V_y V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)) T_a)) (tptp.c_Wellfounded__Recursion_Owf V_r T_a))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (not (tptp.c_Wellfounded__Recursion_Owf (tptp.c_insert (tptp.c_Pair V_y V_x T_a T_a) V_r _let_1) T_a)) (not (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (not (tptp.c_Wellfounded__Recursion_Owf V_r T_a)) (tptp.c_Wellfounded__Recursion_Owf (tptp.c_insert (tptp.c_Pair V_y V_x T_a T_a) V_r _let_1) T_a) (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_x V_y tptp.tc_nat tptp.tc_nat) tptp.c_Wellfounded__Relations_Oless__than (tptp.tc_prod tptp.tc_nat tptp.tc_nat))) (tptp.c_less V_x V_y tptp.tc_nat))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_less V_x V_y tptp.tc_nat)) (tptp.c_in (tptp.c_Pair V_x V_y tptp.tc_nat tptp.tc_nat) tptp.c_Wellfounded__Relations_Oless__than (tptp.tc_prod tptp.tc_nat tptp.tc_nat)))) (not (tptp.c_in tptp.c_Message_Oagent_OServer tptp.c_Event_Obad tptp.tc_Message_Oagent)) (tptp.c_in tptp.c_Message_Oagent_OSpy tptp.c_Event_Obad tptp.tc_Message_Oagent) _let_61 (forall ((V_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg) (tptp.c_Event_Oevent_OGets V_agent_H V_msg_H)))) (forall ((V_agent_H $$unsorted) (V_msg_H $$unsorted) (V_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted)) (not (= (tptp.c_Event_Oevent_OGets V_agent_H V_msg_H) (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg)))) (forall ((V_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg) (tptp.c_Event_Oevent_ONotes V_agent_H V_msg_H)))) (forall ((V_agent_H $$unsorted) (V_msg_H $$unsorted) (V_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted)) (not (= (tptp.c_Event_Oevent_ONotes V_agent_H V_msg_H) (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg)))) (forall ((V_agent $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Event_Oevent_OGets V_agent V_msg) (tptp.c_Event_Oevent_ONotes V_agent_H V_msg_H)))) (forall ((V_agent_H $$unsorted) (V_msg_H $$unsorted) (V_agent $$unsorted) (V_msg $$unsorted)) (not (= (tptp.c_Event_Oevent_ONotes V_agent_H V_msg_H) (tptp.c_Event_Oevent_OGets V_agent V_msg)))) (forall ((V_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted) (V_agent1_H $$unsorted) (V_agent2_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg) (tptp.c_Event_Oevent_OSays V_agent1_H V_agent2_H V_msg_H))) (= V_agent1 V_agent1_H))) (forall ((V_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted) (V_agent1_H $$unsorted) (V_agent2_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg) (tptp.c_Event_Oevent_OSays V_agent1_H V_agent2_H V_msg_H))) (= V_agent2 V_agent2_H))) (forall ((V_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted) (V_agent1_H $$unsorted) (V_agent2_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg) (tptp.c_Event_Oevent_OSays V_agent1_H V_agent2_H V_msg_H))) (= V_msg V_msg_H))) (forall ((V_agent $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_OGets V_agent V_msg) (tptp.c_Event_Oevent_OGets V_agent_H V_msg_H))) (= V_agent V_agent_H))) (forall ((V_agent $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_OGets V_agent V_msg) (tptp.c_Event_Oevent_OGets V_agent_H V_msg_H))) (= V_msg V_msg_H))) (forall ((V_agent $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_ONotes V_agent V_msg) (tptp.c_Event_Oevent_ONotes V_agent_H V_msg_H))) (= V_agent V_agent_H))) (forall ((V_agent $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_ONotes V_agent V_msg) (tptp.c_Event_Oevent_ONotes V_agent_H V_msg_H))) (= V_msg V_msg_H))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (not (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)) (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_OKey V_K) V_H tptp.tc_Message_Omsg)))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (let ((_let_2 (tptp.c_Message_Osynth V_H))) (or (not (tptp.c_in _let_1 _let_2 tptp.tc_Message_Omsg)) (tptp.c_in V_X _let_2 tptp.tc_Message_Omsg) (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_X_H $$unsorted) (V_Y_H $$unsorted)) (or (not (= (tptp.c_Message_OHPair V_X V_Y) (tptp.c_Message_Omsg_OMPair V_X_H V_Y_H))) (= V_X_H (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_Y))))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_X_H $$unsorted) (V_Y_H $$unsorted)) (or (not (= (tptp.c_Message_OHPair V_X V_Y) (tptp.c_Message_Omsg_OMPair V_X_H V_Y_H))) (= V_Y_H V_Y))) (forall ((V_X $$unsorted) (V_x $$unsorted)) (= (tptp.c_Message_OHPair V_X V_x) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_x)) V_x))) (forall ((V_X_H $$unsorted) (V_Y_H $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (or (not (= (tptp.c_Message_OHPair V_X_H V_Y_H) (tptp.c_Message_OHPair V_X V_Y))) (= V_X_H V_X))) (forall ((V_X_H $$unsorted) (V_Y_H $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (or (not (= (tptp.c_Message_OHPair V_X_H V_Y_H) (tptp.c_Message_OHPair V_X V_Y))) (= V_Y_H V_Y))) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (not (= (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_OHPair V_X V_Y)))) (forall ((V_N $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (not (= (tptp.c_Message_Omsg_ONonce V_N) (tptp.c_Message_OHPair V_X V_Y)))) (forall ((V_N $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (not (= (tptp.c_Message_Omsg_ONumber V_N) (tptp.c_Message_OHPair V_X V_Y)))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (not (= (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_OHPair V_X V_Y)))) (forall ((V_Z $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (not (= (tptp.c_Message_Omsg_OHash V_Z) (tptp.c_Message_OHPair V_X V_Y)))) (forall ((V_K $$unsorted) (V_X_H $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (not (= (tptp.c_Message_Omsg_OCrypt V_K V_X_H) (tptp.c_Message_OHPair V_X V_Y)))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_A $$unsorted)) (not (= (tptp.c_Message_OHPair V_X V_Y) (tptp.c_Message_Omsg_OAgent V_A)))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_K $$unsorted) (V_X_H $$unsorted)) (not (= (tptp.c_Message_OHPair V_X V_Y) (tptp.c_Message_Omsg_OCrypt V_K V_X_H)))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_Z $$unsorted)) (not (= (tptp.c_Message_OHPair V_X V_Y) (tptp.c_Message_Omsg_OHash V_Z)))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_K $$unsorted)) (not (= (tptp.c_Message_OHPair V_X V_Y) (tptp.c_Message_Omsg_OKey V_K)))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_N $$unsorted)) (not (= (tptp.c_Message_OHPair V_X V_Y) (tptp.c_Message_Omsg_ONonce V_N)))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_N $$unsorted)) (not (= (tptp.c_Message_OHPair V_X V_Y) (tptp.c_Message_Omsg_ONumber V_N)))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OHash V_X))) (let ((_let_2 (tptp.c_Message_Osynth V_H))) (or (not (tptp.c_in _let_1 _let_2 tptp.tc_Message_Omsg)) (tptp.c_in V_X _let_2 tptp.tc_Message_Omsg) (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey V_K))) (or (not (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)) (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg)))) _let_60 (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)) (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))) (forall ((V_X_H $$unsorted) (V_Y_H $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OMPair V_X_H V_Y_H) (tptp.c_Message_OHPair V_X V_Y))) (= V_X_H (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_Y))))) (forall ((V_X_H $$unsorted) (V_Y_H $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OMPair V_X_H V_Y_H) (tptp.c_Message_OHPair V_X V_Y))) (= V_Y_H V_Y))) (forall ((V_X $$unsorted) (V_x $$unsorted)) (= (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_x)) V_x) (tptp.c_Message_OHPair V_X V_x))) _let_59 _let_58 (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OMPair V_X V_Y))) (let ((_let_2 (tptp.c_Message_Osynth V_H))) (or (not (tptp.c_in _let_1 _let_2 tptp.tc_Message_Omsg)) (tptp.c_in V_Y _let_2 tptp.tc_Message_Omsg) (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OMPair V_X V_Y))) (let ((_let_2 (tptp.c_Message_Osynth V_H))) (or (not (tptp.c_in _let_1 _let_2 tptp.tc_Message_Omsg)) (tptp.c_in V_X _let_2 tptp.tc_Message_Omsg) (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)) (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)) (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (not (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)))) (forall ((V_n $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce V_n))) (or (not (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)) (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg)))) (forall ((V_nat_H $$unsorted)) (not (= tptp.c_Message_Oagent_OServer (tptp.c_Message_Oagent_OFriend V_nat_H)))) (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_Message_Oagent_OFriend V_nat_H) tptp.c_Message_Oagent_OServer))) (not (= tptp.c_Message_Oagent_OServer tptp.c_Message_Oagent_OSpy)) (not (= tptp.c_Message_Oagent_OSpy tptp.c_Message_Oagent_OServer)) (forall ((V_nat $$unsorted)) (not (= (tptp.c_Message_Oagent_OFriend V_nat) tptp.c_Message_Oagent_OSpy))) (forall ((V_nat $$unsorted)) (not (= tptp.c_Message_Oagent_OSpy (tptp.c_Message_Oagent_OFriend V_nat)))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.c_Message_Oagent_OFriend V_nat) (tptp.c_Message_Oagent_OFriend V_nat_H))) (= V_nat V_nat_H))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in V_X V_H tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (not (tptp.c_in V_X (tptp.c_Message_Oanalz _let_1) tptp.tc_Message_Omsg)) (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))) (forall ((V_c $$unsorted) (V_G $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Message_Oparts (tptp.c_union V_G V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg) (tptp.c_in V_c (tptp.c_Message_Oparts V_G) tptp.tc_Message_Omsg))) (forall ((V_agent $$unsorted) (V_agent_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OAgent V_agent) (tptp.c_Message_Omsg_OAgent V_agent_H))) (= V_agent V_agent_H))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_ONumber V_nat) (tptp.c_Message_Omsg_ONumber V_nat_H))) (= V_nat V_nat_H))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_ONonce V_nat) (tptp.c_Message_Omsg_ONonce V_nat_H))) (= V_nat V_nat_H))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OKey V_nat) (tptp.c_Message_Omsg_OKey V_nat_H))) (= V_nat V_nat_H))) (forall ((V_msg $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OHash V_msg) (tptp.c_Message_Omsg_OHash V_msg_H))) (= V_msg V_msg_H))) (forall ((V_msg1 $$unsorted) (V_msg2 $$unsorted) (V_msg1_H $$unsorted) (V_msg2_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OMPair V_msg1 V_msg2) (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H))) (= V_msg1 V_msg1_H))) (forall ((V_msg1 $$unsorted) (V_msg2 $$unsorted) (V_msg1_H $$unsorted) (V_msg2_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OMPair V_msg1 V_msg2) (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H))) (= V_msg2 V_msg2_H))) (forall ((V_nat $$unsorted) (V_msg $$unsorted) (V_nat_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OCrypt V_nat V_msg) (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H))) (= V_nat V_nat_H))) (forall ((V_nat $$unsorted) (V_msg $$unsorted) (V_nat_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OCrypt V_nat V_msg) (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H))) (= V_msg V_msg_H))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in V_X V_H tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg))) (forall ((V_X $$unsorted)) (not (tptp.c_in V_X (tptp.c_Message_Oparts tptp.c_emptyset) tptp.tc_Message_Omsg))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (not (tptp.c_in V_X (tptp.c_Message_Oparts _let_1) tptp.tc_Message_Omsg)) (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))) (forall ((V_agt $$unsorted) (V_H $$unsorted)) (tptp.c_in (tptp.c_Message_Omsg_OAgent V_agt) (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (or (not (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_in (tptp.c_Message_Omsg_OKey V_K) V_H tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) _let_1 tptp.tc_Message_Omsg)))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (or (not (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OHash V_X) _let_1 tptp.tc_Message_Omsg)))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in V_X V_H tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (or (not (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)))) (forall ((V_n $$unsorted) (V_H $$unsorted)) (tptp.c_in (tptp.c_Message_Omsg_ONumber V_n) (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (or (not (tptp.c_in V_X (tptp.c_Message_Osynth _let_1) tptp.tc_Message_Omsg)) (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))) _let_57 (forall ((V_Z $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (not (tptp.c_in V_Z (tptp.c_Message_Oparts (tptp.c_insert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (tptp.c_in V_Z (tptp.c_union _let_1 (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg) tptp.tc_Message_Omsg)))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_in (tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey V_K)) _let_1 tptp.tc_Message_Omsg)) (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))) _let_56 _let_55 _let_54 (forall ((V_evs $$unsorted) (V_A $$unsorted)) (or (not (tptp.c_in V_evs tptp.c_OtwayRees_Ootway (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OKey (tptp.c_Public_OshrK V_A)) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent))) _let_53 (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Event_Oused V_H))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)) (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Event_Oused V_H))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)) (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))) (forall ((V_N $$unsorted) (V_B $$unsorted)) (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_N) (tptp.c_Message_Oparts (tptp.c_Event_OinitState V_B)) tptp.tc_Message_Omsg))) (forall ((V_A $$unsorted) (V_b $$unsorted) (V_evs $$unsorted)) (or (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (tptp.c_in (tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey (tptp.c_Public_OpublicKey V_b V_A))) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (or (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (tptp.c_in (tptp.c_Message_Omsg_OKey (tptp.c_Public_OshrK V_A)) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (tptp.c_in (tptp.c_Message_Omsg_OKey (tptp.c_Public_OpublicKey V_b V_A)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (not (= tptp.c_Public_Okeymode_OSignature tptp.c_Public_Okeymode_OEncryption)) (not (= tptp.c_Public_Okeymode_OEncryption tptp.c_Public_Okeymode_OSignature)) (forall ((V_b $$unsorted) (V_A $$unsorted)) (not (tptp.c_in (tptp.c_Message_OinvKey (tptp.c_Public_OpublicKey V_b V_A)) tptp.c_Message_OsymKeys tptp.tc_nat))) (forall ((V_b $$unsorted) (V_A $$unsorted)) (not (tptp.c_in (tptp.c_Public_OpublicKey V_b V_A) tptp.c_Message_OsymKeys tptp.tc_nat))) (forall ((V_b $$unsorted) (V_A $$unsorted)) (tptp.c_in (tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey (tptp.c_Public_OpublicKey V_b V_A))) (tptp.c_Event_OinitState V_A) tptp.tc_Message_Omsg)) (forall ((V_A $$unsorted) (V_b $$unsorted) (V_C $$unsorted)) (not (= (tptp.c_Public_OshrK V_A) (tptp.c_Message_OinvKey (tptp.c_Public_OpublicKey V_b V_C))))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_c $$unsorted) (V_A_H $$unsorted)) (not (= (tptp.c_Message_OinvKey (tptp.c_Public_OpublicKey V_b V_A)) (tptp.c_Public_OpublicKey V_c V_A_H)))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (tptp.c_in (tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey (tptp.c_Public_OpublicKey V_b V_A))) (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg)) (forall ((V_A $$unsorted) (V_b $$unsorted) (V_C $$unsorted)) (not (= (tptp.c_Public_OshrK V_A) (tptp.c_Public_OpublicKey V_b V_C)))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (tptp.c_in (tptp.c_Message_Omsg_OKey (tptp.c_Public_OpublicKey V_b V_A)) (tptp.c_Event_OinitState V_B) tptp.tc_Message_Omsg)) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_c $$unsorted) (V_A_H $$unsorted)) (or (not (= (tptp.c_Public_OpublicKey V_b V_A) (tptp.c_Public_OpublicKey V_c V_A_H))) (= V_b V_c))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_c $$unsorted) (V_A_H $$unsorted)) (or (not (= (tptp.c_Public_OpublicKey V_b V_A) (tptp.c_Public_OpublicKey V_c V_A_H))) (= V_A V_A_H))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (tptp.c_in (tptp.c_Message_Omsg_OKey (tptp.c_Public_OpublicKey V_b V_A)) (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg)) (forall ((V_c $$unsorted) (V_A_H $$unsorted) (V_b $$unsorted) (V_A $$unsorted)) (not (= (tptp.c_Public_OpublicKey V_c V_A_H) (tptp.c_Message_OinvKey (tptp.c_Public_OpublicKey V_b V_A))))) (forall ((V_X $$unsorted)) (tptp.c_in (tptp.c_Public_OshrK V_X) tptp.c_Message_OsymKeys tptp.tc_nat)) (forall ((V_A $$unsorted)) (tptp.c_in (tptp.c_Message_Omsg_OKey (tptp.c_Public_OshrK V_A)) (tptp.c_Event_OinitState V_A) tptp.tc_Message_Omsg)) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (tptp.c_in (tptp.c_Message_Omsg_OKey (tptp.c_Public_OshrK V_A)) (tptp.c_Event_Oknows V_A V_evs) tptp.tc_Message_Omsg)) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (tptp.c_in (tptp.c_Message_Omsg_OKey (tptp.c_Public_OshrK V_A)) (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg)) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Public_OshrK V_x) (tptp.c_Public_OshrK V_y))) (= V_x V_y))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (tptp.c_in (tptp.c_Message_Omsg_OKey (tptp.c_Public_OpublicKey V_b V_A)) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg)) (forall ((V_K $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_OinvKey V_K) tptp.c_Message_OsymKeys tptp.tc_nat)) (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat))) (forall ((V_K $$unsorted)) (or (not (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat)) (tptp.c_in (tptp.c_Message_OinvKey V_K) tptp.c_Message_OsymKeys tptp.tc_nat))) (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_NA $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OAgent V_B))) (let ((_let_2 (tptp.c_Message_Omsg_OAgent V_A))) (let ((_let_3 (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair _let_2 _let_1))))) (or (not (tptp.c_in V_evs tptp.c_OtwayRees_Ootway (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in _let_3 (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays V_A V_B (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OMPair _let_1 _let_3)))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))))) _let_52 _let_51 _let_49 (forall ((V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey tptp.v_K))) (or (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_1)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_X _let_1))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (= tptp.v_A tptp.v_Aa)))) (or _let_10 _let_15 _let_1) (forall ((V_Y $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey tptp.v_K))) (or (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_1)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_Y _let_1))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= tptp.v_K tptp.v_KAB) (= tptp.v_A tptp.v_Aa)))) (forall ((V_V $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (or (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OKey tptp.v_K))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs3)) tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Ba) (tptp.c_Message_Omsg_OMPair _let_2 _let_1)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_V _let_1))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= tptp.v_A tptp.v_Aa))))) (forall ((V_BA $$unsorted) (V_V $$unsorted)) (let ((_let_1 (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (let ((_let_3 (tptp.c_Public_OshrK tptp.v_B))) (let ((_let_4 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (let ((_let_5 (tptp.c_Message_Omsg_OKey tptp.v_K))) (or (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_5)) (tptp.c_Message_Omsg_OCrypt _let_3 (tptp.c_Message_Omsg_OMPair V_BA _let_5))))) _let_1 tptp.tc_Event_Oevent)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_4 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Ba) (tptp.c_Message_Omsg_OMPair _let_4 _let_2)) (tptp.c_Message_Omsg_OCrypt _let_3 (tptp.c_Message_Omsg_OMPair V_V _let_2))))) _let_1 tptp.tc_Event_Oevent)) (= tptp.v_A tptp.v_Aa)))))))) _let_48 (forall ((V_BC $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey tptp.v_K))) (or (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_1)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_BC _let_1))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= tptp.v_A tptp.v_Ba) (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NAa))))) _let_47 (forall ((V_BD $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey tptp.v_K))) (or (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_1)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_BD _let_1))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NAa))))) (or _let_10 _let_15 _let_46) _let_45 (forall ((V_BE $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey tptp.v_K))) (or (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_1)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_BE _let_1))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= tptp.v_K tptp.v_KAB) (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NAa))))) (forall ((V_BB $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (or (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OKey tptp.v_K))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs3)) tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Ba) (tptp.c_Message_Omsg_OMPair _let_2 _let_1)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_BB _let_1))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NAa)))))) (forall ((V_BG $$unsorted) (V_BB $$unsorted)) (let ((_let_1 (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (let ((_let_3 (tptp.c_Public_OshrK tptp.v_B))) (let ((_let_4 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (let ((_let_5 (tptp.c_Message_Omsg_OKey tptp.v_K))) (or (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_5)) (tptp.c_Message_Omsg_OCrypt _let_3 (tptp.c_Message_Omsg_OMPair V_BG _let_5))))) _let_1 tptp.tc_Event_Oevent)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_4 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Ba) (tptp.c_Message_Omsg_OMPair _let_4 _let_2)) (tptp.c_Message_Omsg_OCrypt _let_3 (tptp.c_Message_Omsg_OMPair V_BB _let_2))))) _let_1 tptp.tc_Event_Oevent)) (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NAa))))))))) (or _let_10 _let_12 _let_15) (forall ((V_BI $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey tptp.v_K))) (or (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_1)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_BI _let_1))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= tptp.v_A tptp.v_Ba) (= tptp.v_K tptp.v_KAB)))) (or _let_10 _let_3 _let_15) (forall ((V_BJ $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey tptp.v_K))) (or (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_1)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_BJ _let_1))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (= tptp.v_K tptp.v_KAB)))) (forall ((V_BH $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (or (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OKey tptp.v_K))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs3)) tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Ba) (tptp.c_Message_Omsg_OMPair _let_2 _let_1)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_BH _let_1))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= tptp.v_K tptp.v_KAB))))) (forall ((V_BM $$unsorted) (V_BH $$unsorted)) (let ((_let_1 (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (let ((_let_3 (tptp.c_Public_OshrK tptp.v_B))) (let ((_let_4 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (let ((_let_5 (tptp.c_Message_Omsg_OKey tptp.v_K))) (or (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_5)) (tptp.c_Message_Omsg_OCrypt _let_3 (tptp.c_Message_Omsg_OMPair V_BM _let_5))))) _let_1 tptp.tc_Event_Oevent)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_4 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Ba) (tptp.c_Message_Omsg_OMPair _let_4 _let_2)) (tptp.c_Message_Omsg_OCrypt _let_3 (tptp.c_Message_Omsg_OMPair V_BH _let_2))))) _let_1 tptp.tc_Event_Oevent)) (= tptp.v_K tptp.v_KAB)))))))) (forall ((V_U $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (or (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OKey tptp.v_K))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs3)) tptp.tc_Message_Omsg) (= tptp.v_A tptp.v_Ba) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair _let_2 _let_1)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_U _let_1))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))))) _let_42 (forall ((V_BU $$unsorted) (V_U $$unsorted)) (let ((_let_1 (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (let ((_let_3 (tptp.c_Public_OshrK tptp.v_B))) (let ((_let_4 (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (let ((_let_5 (tptp.c_Message_Omsg_OKey tptp.v_K))) (or (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_5)) (tptp.c_Message_Omsg_OCrypt _let_3 (tptp.c_Message_Omsg_OMPair V_BU _let_5))))) _let_1 tptp.tc_Event_Oevent)) (= tptp.v_A tptp.v_Ba) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_4 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair _let_4 _let_2)) (tptp.c_Message_Omsg_OCrypt _let_3 (tptp.c_Message_Omsg_OMPair V_U _let_2))))) _let_1 tptp.tc_Event_Oevent))))))))) (forall ((V_U $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (or (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OKey tptp.v_K))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs3)) tptp.tc_Message_Omsg) (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair _let_2 _let_1)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_U _let_1))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))))) (forall ((V_BV $$unsorted) (V_U $$unsorted)) (let ((_let_1 (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (let ((_let_3 (tptp.c_Public_OshrK tptp.v_B))) (let ((_let_4 (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (let ((_let_5 (tptp.c_Message_Omsg_OKey tptp.v_K))) (or (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_5)) (tptp.c_Message_Omsg_OCrypt _let_3 (tptp.c_Message_Omsg_OMPair V_BV _let_5))))) _let_1 tptp.tc_Event_Oevent)) (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_4 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair _let_4 _let_2)) (tptp.c_Message_Omsg_OCrypt _let_3 (tptp.c_Message_Omsg_OMPair V_U _let_2))))) _let_1 tptp.tc_Event_Oevent))))))))) (forall ((V_U $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (or (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OKey tptp.v_K))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs3)) tptp.tc_Message_Omsg) (= tptp.v_K tptp.v_KAB) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair _let_2 _let_1)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_U _let_1))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))))) (forall ((V_BW $$unsorted) (V_U $$unsorted)) (let ((_let_1 (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (let ((_let_3 (tptp.c_Public_OshrK tptp.v_B))) (let ((_let_4 (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (let ((_let_5 (tptp.c_Message_Omsg_OKey tptp.v_K))) (or (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_5)) (tptp.c_Message_Omsg_OCrypt _let_3 (tptp.c_Message_Omsg_OMPair V_BW _let_5))))) _let_1 tptp.tc_Event_Oevent)) (= tptp.v_K tptp.v_KAB) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_4 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair _let_4 _let_2)) (tptp.c_Message_Omsg_OCrypt _let_3 (tptp.c_Message_Omsg_OMPair V_U _let_2))))) _let_1 tptp.tc_Event_Oevent))))))))) (forall ((V_BT $$unsorted) (V_U $$unsorted)) (let ((_let_1 (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (let ((_let_3 (tptp.c_Public_OshrK tptp.v_B))) (let ((_let_4 (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (let ((_let_5 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (or (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OKey tptp.v_K))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs3)) tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_5 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Ba) (tptp.c_Message_Omsg_OMPair _let_5 _let_2)) (tptp.c_Message_Omsg_OCrypt _let_3 (tptp.c_Message_Omsg_OMPair V_BT _let_2))))) _let_1 tptp.tc_Event_Oevent)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_4 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair _let_4 _let_2)) (tptp.c_Message_Omsg_OCrypt _let_3 (tptp.c_Message_Omsg_OMPair V_U _let_2))))) _let_1 tptp.tc_Event_Oevent))))))))) (forall ((V_BY $$unsorted) (V_BT $$unsorted) (V_U $$unsorted)) (let ((_let_1 (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (let ((_let_3 (tptp.c_Public_OshrK tptp.v_B))) (let ((_let_4 (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (let ((_let_5 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (let ((_let_6 (tptp.c_Message_Omsg_OKey tptp.v_K))) (or (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_6)) (tptp.c_Message_Omsg_OCrypt _let_3 (tptp.c_Message_Omsg_OMPair V_BY _let_6))))) _let_1 tptp.tc_Event_Oevent)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_5 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Ba) (tptp.c_Message_Omsg_OMPair _let_5 _let_2)) (tptp.c_Message_Omsg_OCrypt _let_3 (tptp.c_Message_Omsg_OMPair V_BT _let_2))))) _let_1 tptp.tc_Event_Oevent)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_4 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair _let_4 _let_2)) (tptp.c_Message_Omsg_OCrypt _let_3 (tptp.c_Message_Omsg_OMPair V_U _let_2))))) _let_1 tptp.tc_Event_Oevent)))))))))) _let_30 _let_26 (forall ((V_BO $$unsorted) (V_U $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey tptp.v_K))) (or (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_1)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_BO _let_1))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= tptp.v_A tptp.v_Ba) (not (= V_U (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (not (= tptp.v_B tptp.v_Ba))))) _let_25 _let_16 (forall ((V_BP $$unsorted) (V_U $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (let ((_let_2 (tptp.c_Message_Omsg_OKey tptp.v_K))) (or (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_2)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_BP _let_2))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= tptp.v_NA _let_1) (not (= V_U _let_1)) (not (= tptp.v_B tptp.v_Ba)))))) (forall ((V_U $$unsorted)) (or (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OKey tptp.v_K))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs3)) tptp.tc_Message_Omsg) (= tptp.v_K tptp.v_KAB) (not (= V_U (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (not (= tptp.v_B tptp.v_Ba)))) (forall ((V_BQ $$unsorted) (V_U $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey tptp.v_K))) (or (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_1)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_BQ _let_1))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= tptp.v_K tptp.v_KAB) (not (= V_U (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (not (= tptp.v_B tptp.v_Ba))))) (forall ((V_BN $$unsorted) (V_U $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (let ((_let_2 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (or (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OKey tptp.v_K))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs3)) tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_1 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Ba) (tptp.c_Message_Omsg_OMPair _let_1 _let_2)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_BN _let_2))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (= V_U _let_1)) (not (= tptp.v_B tptp.v_Ba)))))) (forall ((V_BS $$unsorted) (V_BN $$unsorted) (V_U $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (let ((_let_2 (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent))) (let ((_let_3 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (let ((_let_4 (tptp.c_Public_OshrK tptp.v_B))) (let ((_let_5 (tptp.c_Message_Omsg_OKey tptp.v_K))) (or (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_5)) (tptp.c_Message_Omsg_OCrypt _let_4 (tptp.c_Message_Omsg_OMPair V_BS _let_5))))) _let_2 tptp.tc_Event_Oevent)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_1 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Ba) (tptp.c_Message_Omsg_OMPair _let_1 _let_3)) (tptp.c_Message_Omsg_OCrypt _let_4 (tptp.c_Message_Omsg_OMPair V_BN _let_3))))) _let_2 tptp.tc_Event_Oevent)) (not (= V_U _let_1)) (not (= tptp.v_B tptp.v_Ba))))))))) (forall ((V_V $$unsorted)) (or (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OKey tptp.v_K))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs3)) tptp.tc_Message_Omsg) (not (= V_V (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (not (= tptp.v_Ba tptp.v_Aa)) (not (= tptp.v_NB tptp.v_NAa)) (not (= tptp.v_B tptp.v_Ba)) (= tptp.v_A tptp.v_Aa))) (forall ((V_Z $$unsorted) (V_V $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey tptp.v_K))) (or (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_1)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_Z _let_1))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (= V_V (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (not (= tptp.v_Ba tptp.v_Aa)) (not (= tptp.v_NB tptp.v_NAa)) (not (= tptp.v_B tptp.v_Ba)) (= tptp.v_A tptp.v_Aa)))) (forall ((V_BB $$unsorted)) (or (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OKey tptp.v_K))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs3)) tptp.tc_Message_Omsg) (not (= V_BB (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (not (= tptp.v_Ba tptp.v_Aa)) (not (= tptp.v_NB tptp.v_NAa)) (not (= tptp.v_B tptp.v_Ba)) (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NAa)))) (forall ((V_BF $$unsorted) (V_BB $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey tptp.v_K))) (or (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_1)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_BF _let_1))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (= V_BB (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (not (= tptp.v_Ba tptp.v_Aa)) (not (= tptp.v_NB tptp.v_NAa)) (not (= tptp.v_B tptp.v_Ba)) (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NAa))))) (or _let_10 _let_15) (forall ((V_BK $$unsorted)) (let ((_let_1 (= tptp.v_K tptp.v_KAB))) (or (not (= V_BK (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (not _let_1) (not (= tptp.v_A tptp.v_Aa)) (not (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (not (= tptp.v_B tptp.v_Ba)) _let_1))) (forall ((V_BH $$unsorted)) (or (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OKey tptp.v_K))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs3)) tptp.tc_Message_Omsg) (not (= V_BH (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (not (= tptp.v_Ba tptp.v_Aa)) (not (= tptp.v_NB tptp.v_NAa)) (not (= tptp.v_B tptp.v_Ba)) (= tptp.v_K tptp.v_KAB))) (forall ((V_BL $$unsorted) (V_BH $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey tptp.v_K))) (or (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_1)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_BL _let_1))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (= V_BH (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (not (= tptp.v_Ba tptp.v_Aa)) (not (= tptp.v_NB tptp.v_NAa)) (not (= tptp.v_B tptp.v_Ba)) (= tptp.v_K tptp.v_KAB)))) (forall ((V_BN $$unsorted) (V_U $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (or (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OKey tptp.v_K))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs3)) tptp.tc_Message_Omsg) (not (= V_BN _let_1)) (not (= tptp.v_Ba tptp.v_Aa)) (not (= tptp.v_NB tptp.v_NAa)) (not (= V_U _let_1)) (not (= tptp.v_B tptp.v_Ba))))) (forall ((V_BR $$unsorted) (V_BN $$unsorted) (V_U $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (let ((_let_2 (tptp.c_Message_Omsg_OKey tptp.v_K))) (or (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_2)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_BR _let_2))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (= V_BN _let_1)) (not (= tptp.v_Ba tptp.v_Aa)) (not (= tptp.v_NB tptp.v_NAa)) (not (= V_U _let_1)) (not (= tptp.v_B tptp.v_Ba)))))) (forall ((V_BT $$unsorted) (V_U $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (or (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OKey tptp.v_K))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs3)) tptp.tc_Message_Omsg) (not (= V_BT (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (not (= tptp.v_Ba tptp.v_Aa)) (not (= tptp.v_NB tptp.v_NAa)) (not (= tptp.v_B tptp.v_Ba)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair _let_2 _let_1)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_U _let_1))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))))) (forall ((V_BX $$unsorted) (V_BT $$unsorted) (V_U $$unsorted)) (let ((_let_1 (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (let ((_let_3 (tptp.c_Public_OshrK tptp.v_B))) (let ((_let_4 (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (let ((_let_5 (tptp.c_Message_Omsg_OKey tptp.v_K))) (or (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_5)) (tptp.c_Message_Omsg_OCrypt _let_3 (tptp.c_Message_Omsg_OMPair V_BX _let_5))))) _let_1 tptp.tc_Event_Oevent)) (not (= V_BT (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (not (= tptp.v_Ba tptp.v_Aa)) (not (= tptp.v_NB tptp.v_NAa)) (not (= tptp.v_B tptp.v_Ba)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_4 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair _let_4 _let_2)) (tptp.c_Message_Omsg_OCrypt _let_3 (tptp.c_Message_Omsg_OMPair V_U _let_2))))) _let_1 tptp.tc_Event_Oevent))))))))) (forall ((V_W $$unsorted)) (let ((_let_1 (= tptp.v_A tptp.v_Aa))) (or (not (= V_W (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (not (= tptp.v_K tptp.v_KAB)) (not _let_1) (not (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (not (= tptp.v_B tptp.v_Ba)) (= tptp.v_A tptp.v_Ba) _let_1))) (forall ((V_X $$unsorted)) (let ((_let_1 (= tptp.v_A tptp.v_Aa))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (or (not (= V_X _let_2)) (not (= tptp.v_K tptp.v_KAB)) (not _let_1) (not (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (not (= tptp.v_B tptp.v_Ba)) (= tptp.v_NA _let_2) _let_1)))) (forall ((V_Y $$unsorted)) (let ((_let_1 (= tptp.v_A tptp.v_Aa))) (let ((_let_2 (= tptp.v_K tptp.v_KAB))) (or (not (= V_Y (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (not _let_2) (not _let_1) (not (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (not (= tptp.v_B tptp.v_Ba)) _let_2 _let_1)))) _let_14 (forall ((V_BA $$unsorted) (V_V $$unsorted)) (let ((_let_1 (= tptp.v_A tptp.v_Aa))) (let ((_let_2 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (let ((_let_3 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (or (not (= V_BA _let_3)) (not (= tptp.v_K tptp.v_KAB)) (not _let_1) (not (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (not (= tptp.v_B tptp.v_Ba)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_3 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Ba) (tptp.c_Message_Omsg_OMPair _let_3 _let_2)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_V _let_2))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) _let_1))))) (forall ((V_BC $$unsorted)) (let ((_let_1 (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NAa)))) (or (not (= V_BC (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (not (= tptp.v_K tptp.v_KAB)) (not (= tptp.v_A tptp.v_Aa)) (not _let_1) (not (= tptp.v_B tptp.v_Ba)) (= tptp.v_A tptp.v_Ba) _let_1))) (forall ((V_BD $$unsorted)) (let ((_let_1 (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NAa)))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (or (not (= V_BD _let_2)) (not (= tptp.v_K tptp.v_KAB)) (not (= tptp.v_A tptp.v_Aa)) (not _let_1) (not (= tptp.v_B tptp.v_Ba)) (= tptp.v_NA _let_2) _let_1)))) (forall ((V_BE $$unsorted)) (let ((_let_1 (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NAa)))) (let ((_let_2 (= tptp.v_K tptp.v_KAB))) (or (not (= V_BE (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (not _let_2) (not (= tptp.v_A tptp.v_Aa)) (not _let_1) (not (= tptp.v_B tptp.v_Ba)) _let_2 _let_1)))) (forall ((V_BG $$unsorted) (V_BB $$unsorted)) (let ((_let_1 (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NAa)))) (let ((_let_2 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (let ((_let_3 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (or (not (= V_BG _let_3)) (not (= tptp.v_K tptp.v_KAB)) (not (= tptp.v_A tptp.v_Aa)) (not _let_1) (not (= tptp.v_B tptp.v_Ba)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_3 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Ba) (tptp.c_Message_Omsg_OMPair _let_3 _let_2)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_BB _let_2))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) _let_1))))) (forall ((V_BI $$unsorted)) (let ((_let_1 (= tptp.v_K tptp.v_KAB))) (or (not (= V_BI (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (not _let_1) (not (= tptp.v_A tptp.v_Aa)) (not (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (not (= tptp.v_B tptp.v_Ba)) (= tptp.v_A tptp.v_Ba) _let_1))) (forall ((V_BJ $$unsorted)) (let ((_let_1 (= tptp.v_K tptp.v_KAB))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (or (not (= V_BJ _let_2)) (not _let_1) (not (= tptp.v_A tptp.v_Aa)) (not (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (not (= tptp.v_B tptp.v_Ba)) (= tptp.v_NA _let_2) _let_1)))) (forall ((V_BM $$unsorted) (V_BH $$unsorted)) (let ((_let_1 (= tptp.v_K tptp.v_KAB))) (let ((_let_2 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (let ((_let_3 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (or (not (= V_BM _let_3)) (not _let_1) (not (= tptp.v_A tptp.v_Aa)) (not (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (not (= tptp.v_B tptp.v_Ba)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_3 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Ba) (tptp.c_Message_Omsg_OMPair _let_3 _let_2)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_BH _let_2))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) _let_1))))) (forall ((V_BO $$unsorted) (V_U $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (or (not (= V_BO _let_1)) (not (= tptp.v_K tptp.v_KAB)) (not (= tptp.v_A tptp.v_Aa)) (not (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (= tptp.v_A tptp.v_Ba) (not (= V_U _let_1)) (not (= tptp.v_B tptp.v_Ba))))) (forall ((V_BP $$unsorted) (V_U $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (or (not (= V_BP _let_1)) (not (= tptp.v_K tptp.v_KAB)) (not (= tptp.v_A tptp.v_Aa)) (not (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (= tptp.v_NA _let_1) (not (= V_U _let_1)) (not (= tptp.v_B tptp.v_Ba))))) _let_13 (forall ((V_BQ $$unsorted) (V_U $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (let ((_let_2 (= tptp.v_K tptp.v_KAB))) (or (not (= V_BQ _let_1)) (not _let_2) (not (= tptp.v_A tptp.v_Aa)) (not (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) _let_2 (not (= V_U _let_1)) (not (= tptp.v_B tptp.v_Ba)))))) (forall ((V_BS $$unsorted) (V_BN $$unsorted) (V_U $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (let ((_let_2 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (or (not (= V_BS _let_1)) (not (= tptp.v_K tptp.v_KAB)) (not (= tptp.v_A tptp.v_Aa)) (not (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_1 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Ba) (tptp.c_Message_Omsg_OMPair _let_1 _let_2)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_BN _let_2))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (= V_U _let_1)) (not (= tptp.v_B tptp.v_Ba)))))) (forall ((V_BU $$unsorted) (V_U $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (or (not (= V_BU (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (not (= tptp.v_K tptp.v_KAB)) (not (= tptp.v_A tptp.v_Aa)) (not (= tptp.v_NA _let_2)) (not (= tptp.v_B tptp.v_Ba)) (= tptp.v_A tptp.v_Ba) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair _let_2 _let_1)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_U _let_1))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))))) (forall ((V_BV $$unsorted) (V_U $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (let ((_let_3 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (or (not (= V_BV _let_3)) (not (= tptp.v_K tptp.v_KAB)) (not (= tptp.v_A tptp.v_Aa)) (not (= tptp.v_NA _let_2)) (not (= tptp.v_B tptp.v_Ba)) (= tptp.v_NA _let_3) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair _let_2 _let_1)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_U _let_1))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))))) (forall ((V_BW $$unsorted) (V_U $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (let ((_let_3 (= tptp.v_K tptp.v_KAB))) (or (not (= V_BW (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (not _let_3) (not (= tptp.v_A tptp.v_Aa)) (not (= tptp.v_NA _let_2)) (not (= tptp.v_B tptp.v_Ba)) _let_3 (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair _let_2 _let_1)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_U _let_1))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))))) (forall ((V_BY $$unsorted) (V_BT $$unsorted) (V_U $$unsorted)) (let ((_let_1 (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (let ((_let_3 (tptp.c_Public_OshrK tptp.v_B))) (let ((_let_4 (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (let ((_let_5 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (or (not (= V_BY _let_5)) (not (= tptp.v_K tptp.v_KAB)) (not (= tptp.v_A tptp.v_Aa)) (not (= tptp.v_NA _let_4)) (not (= tptp.v_B tptp.v_Ba)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_5 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Ba) (tptp.c_Message_Omsg_OMPair _let_5 _let_2)) (tptp.c_Message_Omsg_OCrypt _let_3 (tptp.c_Message_Omsg_OMPair V_BT _let_2))))) _let_1 tptp.tc_Event_Oevent)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_4 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair _let_4 _let_2)) (tptp.c_Message_Omsg_OCrypt _let_3 (tptp.c_Message_Omsg_OMPair V_U _let_2))))) _let_1 tptp.tc_Event_Oevent))))))))) (forall ((V_Z $$unsorted) (V_V $$unsorted)) (let ((_let_1 (= tptp.v_A tptp.v_Aa))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (or (not (= V_Z _let_2)) (not (= tptp.v_K tptp.v_KAB)) (not _let_1) (not (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (not (= V_V _let_2)) (not (= tptp.v_Ba tptp.v_Aa)) (not (= tptp.v_NB tptp.v_NAa)) (not (= tptp.v_B tptp.v_Ba)) _let_1)))) (forall ((V_BF $$unsorted) (V_BB $$unsorted)) (let ((_let_1 (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NAa)))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (or (not (= V_BF _let_2)) (not (= tptp.v_K tptp.v_KAB)) (not (= tptp.v_A tptp.v_Aa)) (not _let_1) (not (= V_BB _let_2)) (not (= tptp.v_Ba tptp.v_Aa)) (not (= tptp.v_NB tptp.v_NAa)) (not (= tptp.v_B tptp.v_Ba)) _let_1)))) (forall ((V_BL $$unsorted) (V_BH $$unsorted)) (let ((_let_1 (= tptp.v_K tptp.v_KAB))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (or (not (= V_BL _let_2)) (not _let_1) (not (= tptp.v_A tptp.v_Aa)) (not (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (not (= V_BH _let_2)) (not (= tptp.v_Ba tptp.v_Aa)) (not (= tptp.v_NB tptp.v_NAa)) (not (= tptp.v_B tptp.v_Ba)) _let_1)))) (forall ((V_BR $$unsorted) (V_BN $$unsorted) (V_U $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (or (not (= V_BR _let_1)) (not (= tptp.v_K tptp.v_KAB)) (not (= tptp.v_A tptp.v_Aa)) (not (= tptp.v_NA (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (not (= V_BN _let_1)) (not (= tptp.v_Ba tptp.v_Aa)) (not (= tptp.v_NB tptp.v_NAa)) (not (= V_U _let_1)) (not (= tptp.v_B tptp.v_Ba))))) (forall ((V_W $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey tptp.v_K))) (or (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_1)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_W _let_1))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= tptp.v_A tptp.v_Ba) (= tptp.v_A tptp.v_Aa)))) (forall ((V_BX $$unsorted) (V_BT $$unsorted) (V_U $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey tptp.v_KAB))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (let ((_let_3 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (or (not (= V_BX _let_3)) (not (= tptp.v_K tptp.v_KAB)) (not (= tptp.v_A tptp.v_Aa)) (not (= tptp.v_NA _let_2)) (not (= V_BT _let_3)) (not (= tptp.v_Ba tptp.v_Aa)) (not (= tptp.v_NB tptp.v_NAa)) (not (= tptp.v_B tptp.v_Ba)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair _let_2 _let_1)) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair V_U _let_1))))) (tptp.c_List_Oset tptp.v_evs3 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))))) _let_11)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 27.56/27.80  )
% 27.56/27.81  % SZS output end Proof for SWV296-1
% 27.56/27.81  % cvc5---1.0.5 exiting
% 27.56/27.82  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------