TSTP Solution File: SWV304-1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV304-1 : 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 21:50:21 EDT 2023
% Result : Unsatisfiable 27.57s 27.85s
% Output : Proof 27.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.23 % Problem : SWV304-1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.24 % Command : do_cvc5 %s %d
% 0.25/0.46 % Computer : n022.cluster.edu
% 0.25/0.46 % Model : x86_64 x86_64
% 0.25/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.46 % Memory : 8042.1875MB
% 0.25/0.46 % OS : Linux 3.10.0-693.el7.x86_64
% 0.25/0.46 % CPULimit : 300
% 0.25/0.46 % WCLimit : 300
% 0.25/0.46 % DateTime : Tue Aug 29 09:54:24 EDT 2023
% 0.25/0.46 % CPUTime :
% 0.46/0.73 %----Proving TF0_NAR, FOF, or CNF
% 0.46/0.73 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.5Ny54rNlMr/cvc5---1.0.5_23113.p...
% 0.57/0.88 ------- get file name : TPTP file name is SWV304-1
% 0.57/0.88 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_23113.smt2...
% 0.57/0.88 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.86/11.05 --- Run --no-e-matching --full-saturate-quant at 5...
% 15.97/16.21 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 21.03/21.35 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 26.22/26.43 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 27.57/27.85 % SZS status Unsatisfiable for SWV304-1
% 27.57/27.85 % SZS output start Proof for SWV304-1
% 27.57/27.87 (
% 27.57/27.87 (let ((_let_1 (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (let ((_let_2 (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent))) (let ((_let_3 (tptp.c_Message_Omsg_OAgent tptp.v_B))) (let ((_let_4 (tptp.c_Message_Omsg_OAgent tptp.v_A))) (let ((_let_5 (tptp.c_Public_OshrK tptp.v_B))) (let ((_let_6 (tptp.c_Message_Omsg_OCrypt _let_5 (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair tptp.v_NB (tptp.c_Message_Omsg_OMPair _let_4 _let_3)))))) (let ((_let_7 (tptp.c_Message_Omsg_OMPair tptp.v_x _let_6))) (let ((_let_8 (tptp.c_Message_Omsg_OMPair _let_3 _let_7))) (let ((_let_9 (tptp.c_Message_Omsg_OMPair _let_4 _let_8))) (let ((_let_10 (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.v_B tptp.c_Message_Oagent_OServer (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_9)) _let_2 tptp.tc_Event_Oevent))) (let ((_let_11 (tptp.c_Message_Omsg_OKey tptp.v_K))) (let ((_let_12 (tptp.c_Message_Omsg_OMPair tptp.v_NB _let_11))) (let ((_let_13 (tptp.c_Message_Omsg_OCrypt _let_5 _let_12))) (let ((_let_14 (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_11)) _let_13))) _let_2 tptp.tc_Event_Oevent))) (let ((_let_15 (not _let_14))) (let ((_let_16 (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4))) (let ((_let_17 (tptp.c_in _let_13 (tptp.c_Message_Oparts (tptp.c_insert tptp.v_X _let_16 tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))) (let ((_let_18 (tptp.c_Message_Omsg_ONonce tptp.v_NBa))) (let ((_let_19 (tptp.c_Public_OshrK tptp.v_Ba))) (let ((_let_20 (tptp.c_Message_Omsg_OCrypt _let_19 (tptp.c_Message_Omsg_OMPair _let_18 (tptp.c_Message_Omsg_OKey tptp.v_Ka))))) (let ((_let_21 (tptp.c_Message_Omsg_OMPair tptp.v_X _let_20))) (let ((_let_22 (tptp.c_Message_Omsg_OMPair _let_1 _let_21))) (let ((_let_23 (tptp.c_in (tptp.c_Event_Oevent_OGets tptp.v_Ba _let_22) _let_2 tptp.tc_Event_Oevent))) (let ((_let_24 (tptp.c_Message_Omsg_OAgent tptp.v_Ba))) (let ((_let_25 (tptp.c_Message_Omsg_OAgent tptp.v_Aa))) (let ((_let_26 (forall ((V_U $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey tptp.v_K))) (let ((_let_2 (tptp.c_Public_OshrK tptp.v_B))) (let ((_let_3 (tptp.c_Message_Omsg_OCrypt _let_2 (tptp.c_Message_Omsg_OMPair tptp.v_NB _let_1)))) (let ((_let_4 (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent))) (let ((_let_5 (tptp.c_Message_Omsg_OAgent tptp.v_B))) (let ((_let_6 (tptp.c_Message_Omsg_OAgent tptp.v_A))) (or (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_B (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA _let_1)) _let_3))) _let_4 tptp.tc_Event_Oevent) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.v_B tptp.c_Message_Oagent_OServer (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair _let_6 (tptp.c_Message_Omsg_OMPair _let_5 (tptp.c_Message_Omsg_OMPair V_U (tptp.c_Message_Omsg_OCrypt _let_2 (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair tptp.v_NB (tptp.c_Message_Omsg_OMPair _let_6 _let_5))))))))) _let_4 tptp.tc_Event_Oevent)) (not (tptp.c_in _let_3 (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))))))))))) (let ((_let_27 (or _let_10 (= _let_9 tptp.v_X)))) (let ((_let_28 (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (let ((_let_29 (tptp.c_in tptp.v_evs4 tptp.c_OtwayRees_Ootway _let_28))) (let ((_let_30 (tptp.c_in tptp.v_B tptp.c_Event_Obad tptp.tc_Message_Oagent))) (let ((_let_31 (not _let_30))) (let ((_let_32 (forall ((V_evs $$unsorted) (V_B $$unsorted) (V_NA $$unsorted) (V_NB $$unsorted) (V_A $$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_B) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair V_NB (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_B tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays V_B tptp.c_Message_Oagent_OServer (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OMPair _let_1 (tptp.c_Message_Omsg_OMPair (tptp.v_sko__u__1 V_A V_B V_NA V_NB V_evs) _let_3))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))))))) (let ((_let_33 (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 ((_let_34 (forall ((V_evs $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (or (not (tptp.c_in V_evs tptp.c_OtwayRees_Ootway (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets V_B V_X) _let_1 tptp.tc_Event_Oevent)) (tptp.c_in (tptp.c_Event_Oevent_OSays (tptp.v_sko__usf V_B V_X V_evs) V_B V_X) _let_1 tptp.tc_Event_Oevent)))))) (let ((_let_35 (forall ((V_c $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg))))) (let ((_let_36 (forall ((V_Z $$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)))))) (let ((_let_37 (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_38 (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))))) (let ((_let_39 (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)) (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)))))) (let ((_let_40 (forall ((V_X $$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)))))) (let ((_let_41 (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)) (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)))))) (let ((_let_42 (forall ((V_K $$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)))))) (let ((_let_43 (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))))) (let ((_let_44 (forall ((V_U $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OAgent tptp.v_B))) (let ((_let_2 (tptp.c_Message_Omsg_OAgent tptp.v_A))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.v_B tptp.c_Message_Oagent_OServer (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OMPair _let_1 (tptp.c_Message_Omsg_OMPair V_U (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair tptp.v_NB (tptp.c_Message_Omsg_OMPair _let_2 _let_1))))))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))))) (let ((_let_45 (tptp.v_sko__u__1 tptp.v_A tptp.v_B tptp.v_NA tptp.v_NB tptp.v_evs4))) (let ((_let_46 (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.v_B tptp.c_Message_Oagent_OServer (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair _let_4 (tptp.c_Message_Omsg_OMPair _let_3 (tptp.c_Message_Omsg_OMPair _let_45 _let_6))))) _let_2 tptp.tc_Event_Oevent))) (let ((_let_47 (tptp.c_Message_Oparts _let_16))) (let ((_let_48 (tptp.c_in _let_13 _let_47 tptp.tc_Message_Omsg))) (let ((_let_49 (tptp.c_Message_Oanalz _let_16))) (let ((_let_50 (tptp.c_in _let_13 _let_49 tptp.tc_Message_Omsg))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_51 _let_48))) (let ((_let_53 (tptp.c_Message_Osynth _let_49))) (let ((_let_54 (tptp.c_in _let_13 (tptp.c_union _let_53 _let_47 tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))) (let ((_let_55 (tptp.c_in _let_13 _let_53 tptp.tc_Message_Omsg))) (let ((_let_56 (not _let_54))) (let ((_let_57 (or _let_56 _let_48 _let_55))) (let ((_let_58 (tptp.c_Message_Omsg_OKey _let_5))) (let ((_let_59 (tptp.c_in _let_58 _let_49 tptp.tc_Message_Omsg))) (let ((_let_60 (not _let_55))) (let ((_let_61 (or _let_60 _let_50 _let_59))) (let ((_let_62 (_let_35))) (let ((_let_63 (ASSUME :args _let_62))) (let ((_let_64 ((not (= (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg) true))))) (let ((_let_65 (tptp.c_in tptp.v_X _let_53 tptp.tc_Message_Omsg))) (let ((_let_66 (not _let_65))) (let ((_let_67 (not _let_17))) (let ((_let_68 (or _let_67 _let_66 _let_54))) (let ((_let_69 (_let_36))) (let ((_let_70 (ASSUME :args _let_69))) (let ((_let_71 (tptp.c_in tptp.v_X _let_49 tptp.tc_Message_Omsg))) (let ((_let_72 (not _let_71))) (let ((_let_73 (or _let_72 _let_65))) (let ((_let_74 (_let_38))) (let ((_let_75 (ASSUME :args _let_74))) (let ((_let_76 (tptp.c_in _let_21 _let_49 tptp.tc_Message_Omsg))) (let ((_let_77 (not _let_76))) (let ((_let_78 (or _let_77 _let_71))) (let ((_let_79 (_let_40))) (let ((_let_80 (ASSUME :args _let_79))) (let ((_let_81 (tptp.c_in _let_22 _let_49 tptp.tc_Message_Omsg))) (let ((_let_82 (not _let_81))) (let ((_let_83 (or _let_82 _let_76))) (let ((_let_84 (_let_41))) (let ((_let_85 (ASSUME :args _let_84))) (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.v_sko__usf tptp.v_Ba _let_22 tptp.v_evs4))) (let ((_let_88 (tptp.c_in (tptp.c_Event_Oevent_OSays _let_87 tptp.v_Ba _let_22) _let_2 tptp.tc_Event_Oevent))) (let ((_let_89 (not _let_88))) (let ((_let_90 (or _let_89 _let_81))) (let ((_let_91 (_let_37))) (let ((_let_92 (ASSUME :args _let_91))) (let ((_let_93 (not _let_23))) (let ((_let_94 (not _let_29))) (let ((_let_95 (or _let_94 _let_93 _let_88))) (let ((_let_96 (_let_34))) (let ((_let_97 (ASSUME :args _let_96))) (let ((_let_98 (ASSUME :args (_let_29)))) (let ((_let_99 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_78)) :args ((or _let_71 _let_77 (not _let_78)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_83)) :args ((or _let_82 _let_76 (not _let_83)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_90)) :args ((or _let_89 _let_81 (not _let_90)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_95)) :args ((or _let_94 _let_93 _let_88 (not _let_95)))) _let_98 (ASSUME :args (_let_23)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_97 :args (tptp.v_evs4 tptp.v_Ba _let_22 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_96)) _let_97 :args (_let_95 false _let_34)) :args (_let_88 false _let_29 false _let_23 false _let_95)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_92 :args (_let_87 tptp.v_Ba _let_22 tptp.v_evs4 QUANTIFIERS_INST_E_MATCHING ((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))))) :args _let_91)) _let_92 :args (_let_90 false _let_37)) :args (_let_81 false _let_88 false _let_90)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_85 :args (_let_1 _let_21 _let_16 QUANTIFIERS_INST_E_MATCHING _let_86)) :args _let_84)) _let_85 :args (_let_83 false _let_41)) :args (_let_76 false _let_81 false _let_83)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (tptp.v_X _let_20 _let_16 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_79)) _let_80 :args (_let_78 false _let_40)) :args (_let_71 false _let_76 false _let_78)))) (let ((_let_100 (_let_43))) (let ((_let_101 (ASSUME :args _let_100))) (let ((_let_102 (tptp.c_in _let_58 _let_47 tptp.tc_Message_Omsg))) (let ((_let_103 (not _let_59))) (let ((_let_104 (or _let_103 _let_102))) (let ((_let_105 (not _let_102))) (let ((_let_106 (or _let_94 _let_105 _let_30))) (let ((_let_107 (_let_33))) (let ((_let_108 (ASSUME :args _let_107))) (let ((_let_109 (ASSUME :args (_let_31)))) (let ((_let_110 (_let_42))) (let ((_let_111 (ASSUME :args _let_110))) (let ((_let_112 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_15)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_61)) :args ((or _let_50 _let_60 _let_59 (not _let_61)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM 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(_let_57)) :args ((or _let_48 _let_56 _let_55 (not _let_57)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_101 :args (_let_13 _let_53 _let_47 tptp.tc_Message_Omsg QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_in V_c (tptp.c_union V_A V_B T_a) T_a) false))))) :args _let_100)) _let_101 :args (_let_57 false _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_67 _let_66 _let_54 (not _let_68)))) (ASSUME :args (_let_17)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_65 _let_72 (not _let_73)))) _let_99 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_75 :args (tptp.v_X _let_49 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_in V_X (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg) true))))) :args _let_74)) _let_75 :args (_let_73 false _let_38)) :args (_let_65 false _let_71 false _let_73)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_70 :args (_let_13 tptp.v_X _let_16 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(not _let_118))) (let ((_let_120 (or _let_119 _let_113))) (let ((_let_121 (_let_39))) (let ((_let_122 (ASSUME :args _let_121))) (let ((_let_123 ((tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oparts V_H)))) (let ((_let_124 (tptp.c_in _let_8 _let_47 tptp.tc_Message_Omsg))) (let ((_let_125 (not _let_124))) (let ((_let_126 (or _let_125 _let_118))) (let ((_let_127 (tptp.c_in _let_8 _let_49 tptp.tc_Message_Omsg))) (let ((_let_128 (not _let_127))) (let ((_let_129 (or _let_128 _let_124))) (let ((_let_130 (tptp.c_in _let_9 _let_49 tptp.tc_Message_Omsg))) (let ((_let_131 (not _let_130))) (let ((_let_132 (or _let_131 _let_127))) (let ((_let_133 (= tptp.v_X _let_9))) (let ((_let_134 (not _let_10))) (let ((_let_135 (_let_44))) (let ((_let_136 (ASSUME :args _let_135))) (let ((_let_137 (and _let_133 _let_71))) (let ((_let_138 (ASSUME :args (_let_71)))) (let ((_let_139 (ASSUME :args (_let_133)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_136 :args (_let_45 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_135)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_115)) :args ((or _let_30 _let_94 _let_114 _let_46 (not _let_115)))) _let_109 _let_98 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_120)) :args ((or _let_113 _let_119 (not _let_120)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_126)) :args ((or _let_118 _let_125 (not _let_126)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_129)) :args ((or _let_128 _let_124 (not _let_129)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_132)) :args ((or _let_131 _let_127 (not _let_132)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_137)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_138 _let_139) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM _let_139) (REFL :args (_let_49)) (REFL :args (tptp.tc_Message_Omsg)) :args (APPLY_UF tptp.c_in)) (TRUE_INTRO _let_138))) :args (_let_71 _let_133))) :args (_let_133 _let_71))) :args (true _let_137)) :args ((or (not _let_133) _let_130 _let_72))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_136 :args (tptp.v_x QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_135)) :args ((or _let_134 (not _let_44)))) _let_112 :args (_let_134 false _let_44)) :args (_let_133 true _let_10)) _let_99 :args (_let_130 false _let_133 false _let_71)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_85 :args (_let_4 _let_8 _let_16 QUANTIFIERS_INST_E_MATCHING _let_86)) :args _let_84)) _let_85 :args (_let_132 false _let_41)) :args (_let_127 false _let_130 false _let_132)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_63 :args (_let_8 _let_16 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_in V_c (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg) false))))) :args _let_62)) _let_63 :args (_let_129 false _let_35)) :args (_let_124 false _let_127 false _let_129)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_122 :args (_let_3 _let_7 _let_16 QUANTIFIERS_INST_E_MATCHING _let_123)) :args _let_121)) _let_122 :args (_let_126 false _let_39)) :args (_let_118 false _let_124 false _let_126)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_122 :args (tptp.v_x _let_6 _let_16 QUANTIFIERS_INST_E_MATCHING _let_123)) :args _let_121)) _let_122 :args (_let_120 false _let_39)) :args (_let_113 false _let_118 false _let_120)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_117 :args (tptp.v_evs4 tptp.v_B tptp.v_NA tptp.v_NB tptp.v_A QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_in V_evs tptp.c_OtwayRees_Ootway _let_28) false)) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair V_NB (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OAgent V_B))))))) :args _let_116)) _let_117 :args (_let_115 false _let_32)) :args (_let_46 true _let_30 false _let_29 false _let_113 false _let_115)) _let_112 :args (false false _let_46 false _let_44)) :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 $$unsorted)) (or (not 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T_1))) (tptp.class_HOL_Oone tptp.tc_nat) (tptp.class_HOL_Ozero tptp.tc_nat) (tptp.class_HOL_Oplus tptp.tc_nat) (tptp.class_HOL_Otimes tptp.tc_nat) (tptp.class_Nat_Opower tptp.tc_nat) (tptp.class_Ring__and__Field_Oaxclass__0__neq__1 tptp.tc_nat) (tptp.class_OrderedGroup_Osemigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Osemigroup__mult tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring tptp.tc_nat) (tptp.class_Orderings_Oord tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring__0 tptp.tc_nat) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__mult tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__1 tptp.tc_nat) 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(tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_Ring__and__Field_Osemiring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_OrderedGroup_Ocomm__monoid__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_HOL_Ozero T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_OrderedGroup_Oab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_OrderedGroup_Osemigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_HOL_Oplus T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_OrderedGroup_Omonoid__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_Wellfounded__Recursion_Owellorder T)) (tptp.class_Orderings_Oord T))) (forall ((T $$unsorted)) (or (not (tptp.class_Wellfounded__Recursion_Owellorder T)) (tptp.class_Orderings_Oorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Wellfounded__Recursion_Owellorder T)) (tptp.class_LOrder_Omeet__semilorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Wellfounded__Recursion_Owellorder T)) (tptp.class_LOrder_Ojoin__semilorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Wellfounded__Recursion_Owellorder T)) (tptp.class_LOrder_Olorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Wellfounded__Recursion_Owellorder T)) (tptp.class_Orderings_Olinorder T))) (forall ((V_x $$unsorted) (V_xo $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_x (tptp.c_Datatype_Oo2s V_xo T_a) T_a)) (= V_xo (tptp.c_Datatype_Ooption_OSome V_x T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_in V_x (tptp.c_Datatype_Oo2s (tptp.c_Datatype_Ooption_OSome V_x T_a) T_a) T_a)) (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (= V_x tptp.c_Datatype_Ooption_ONone) (= V_x (tptp.c_Datatype_Ooption_OSome (tptp.c_Main_Onot__None__eq__iff1__1 V_x T_a) T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (= V_x tptp.c_Datatype_Ooption_ONone) (= V_x (tptp.c_Datatype_Ooption_OSome (tptp.c_Main_Onot__Some__eq__iff1__1 V_x T_a) T_a)))) (forall ((V_a_H $$unsorted) (T_a $$unsorted)) (not (= tptp.c_Datatype_Ooption_ONone (tptp.c_Datatype_Ooption_OSome V_a_H T_a)))) (forall ((V_a_H $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Datatype_Ooption_OSome V_a_H T_a) tptp.c_Datatype_Ooption_ONone))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_a_H $$unsorted)) (or (not (= (tptp.c_Datatype_Ooption_OSome V_a T_a) (tptp.c_Datatype_Ooption_OSome V_a_H T_a))) (= V_a V_a_H))) (forall ((V_a $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_b $$unsorted)) (or (not (= (tptp.c_Datatype__Universe_OAtom V_a T_a T_b) (tptp.c_Datatype__Universe_OAtom V_b T_a T_b))) (= V_a V_b))) (forall ((V_a $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_M $$unsorted) (V_N $$unsorted)) (not (= (tptp.c_Datatype__Universe_OAtom V_a T_a T_b) (tptp.c_Datatype__Universe_OScons V_M V_N T_a T_b)))) (forall ((V_M $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_N $$unsorted)) (or (not (= (tptp.c_Datatype__Universe_OIn0 V_M T_a T_b) (tptp.c_Datatype__Universe_OIn0 V_N T_a T_b))) (= V_M V_N))) (forall ((V_M $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_N $$unsorted)) (not (= (tptp.c_Datatype__Universe_OIn0 V_M T_a T_b) (tptp.c_Datatype__Universe_OIn1 V_N T_a T_b)))) (forall ((V_M $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_N $$unsorted)) (or (not (= (tptp.c_Datatype__Universe_OIn1 V_M T_a T_b) (tptp.c_Datatype__Universe_OIn1 V_N T_a T_b))) (= V_M V_N))) (forall ((V_N $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_M $$unsorted)) (not (= (tptp.c_Datatype__Universe_OIn1 V_N T_a T_b) (tptp.c_Datatype__Universe_OIn0 V_M T_a T_b)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_k $$unsorted)) (not (= (tptp.c_Datatype__Universe_OLeaf V_a T_a T_b) (tptp.c_Datatype__Universe_ONumb V_k T_a T_b)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_M $$unsorted) (V_N $$unsorted)) (not (= (tptp.c_Datatype__Universe_OLeaf V_a T_a T_b) (tptp.c_Datatype__Universe_OScons V_M V_N T_a T_b)))) (forall ((V_k $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted)) (not (= (tptp.c_Datatype__Universe_ONumb V_k T_a T_b) (tptp.c_Datatype__Universe_OLeaf V_a T_a T_b)))) (forall ((V_k $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_M $$unsorted) (V_N $$unsorted)) (not (= (tptp.c_Datatype__Universe_ONumb V_k T_a T_b) (tptp.c_Datatype__Universe_OScons V_M V_N T_a T_b)))) (forall ((V_M $$unsorted) (V_N $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_M_H $$unsorted) (V_N_H $$unsorted)) (or (not (= (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))) (= V_M V_M_H))) (forall ((V_M $$unsorted) (V_N $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_M_H $$unsorted) (V_N_H $$unsorted)) (or (not (= (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))) (= V_N V_N_H))) (forall ((V_M $$unsorted) (V_N $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted)) (not (= (tptp.c_Datatype__Universe_OScons V_M V_N T_a T_b) (tptp.c_Datatype__Universe_OAtom V_a T_a T_b)))) (forall ((V_M $$unsorted) (V_N $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted)) (not (= (tptp.c_Datatype__Universe_OScons V_M V_N T_a T_b) (tptp.c_Datatype__Universe_OLeaf V_a T_a T_b)))) (forall ((V_M $$unsorted) (V_N $$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))) _let_43 (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) (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))) (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))) _let_42 (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 $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OKey V_K))) (or (not (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)) (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg)))) _let_41 _let_40 (forall ((V_X_H $$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 $$unsorted)) (= (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_x)) V_x) (tptp.c_Message_OHPair V_X V_x))) _let_39 (forall ((V_X $$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)))) (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)))) _let_38 (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 $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (or (not (tptp.c_in V_X (tptp.c_Message_Osynth _let_1) tptp.tc_Message_Omsg)) (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))) _let_37 _let_36 (forall ((V_K $$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_35 (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) _let_1 tptp.tc_Message_Omsg)) (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))) _let_34 _let_33 (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_NA_H $$unsorted) (V_NA $$unsorted) (V_A_H $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)))) (let ((_let_2 (tptp.c_Message_Omsg_OAgent V_A))) (let ((_let_3 (tptp.c_Public_OshrK V_A))) (or (not (tptp.c_in V_evs tptp.c_OtwayRees_Ootway (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt _let_3 (tptp.c_Message_Omsg_OMPair V_NA_H (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A_H) _let_2)))) _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt _let_3 (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OAgent V_B)))) _let_1 tptp.tc_Message_Omsg)) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)))))) (forall ((V_X $$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 $$unsorted)) (or (not (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat)) (tptp.c_in (tptp.c_Message_OinvKey V_K) tptp.c_Message_OsymKeys tptp.tc_nat))) _let_32 (forall ((V_evs $$unsorted) (V_B $$unsorted) (V_NC $$unsorted) (V_NB $$unsorted) (V_C $$unsorted) (V_NA $$unsorted) (V_A $$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_B))) (let ((_let_3 (tptp.c_Public_OshrK V_B))) (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_NC (tptp.c_Message_Omsg_OMPair V_NB (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_C) _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 V_NB (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) _let_2)))) _let_1 tptp.tc_Message_Omsg)) (tptp.c_in V_B tptp.c_Event_Obad tptp.tc_Message_Oagent) (= V_NC V_NA)))))) (forall ((V_evs $$unsorted) (V_B $$unsorted) (V_NC $$unsorted) (V_NB $$unsorted) (V_C $$unsorted) (V_NA $$unsorted) (V_A $$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_B))) (let ((_let_3 (tptp.c_Public_OshrK V_B))) (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_NC (tptp.c_Message_Omsg_OMPair V_NB (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_C) _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 V_NB (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) _let_2)))) _let_1 tptp.tc_Message_Omsg)) (tptp.c_in V_B tptp.c_Event_Obad tptp.tc_Message_Oagent) (= V_C V_A)))))) _let_31 _let_29 _let_27 _let_26 (not (= tptp.v_Ba tptp.c_Message_Oagent_OServer)) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.v_Ba tptp.c_Message_Oagent_OServer (tptp.c_Message_Omsg_OMPair _let_1 (tptp.c_Message_Omsg_OMPair _let_25 (tptp.c_Message_Omsg_OMPair _let_24 (tptp.c_Message_Omsg_OMPair tptp.v_X_H (tptp.c_Message_Omsg_OCrypt _let_19 (tptp.c_Message_Omsg_OMPair _let_1 (tptp.c_Message_Omsg_OMPair _let_18 (tptp.c_Message_Omsg_OMPair _let_25 _let_24))))))))) _let_2 tptp.tc_Event_Oevent) _let_23 _let_17 _let_15 (or _let_10 (= tptp.v_B tptp.v_Ba)) (or _let_10 (= tptp.c_Message_Oagent_OServer tptp.v_Aa)) (or _let_10 (= tptp.v_NA _let_1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 27.57/27.87 )
% 27.66/27.88 % SZS output end Proof for SWV304-1
% 27.66/27.88 % cvc5---1.0.5 exiting
% 27.66/27.88 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------