TSTP Solution File: SET854-1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET854-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n004.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 14:40:43 EDT 2023
% Result : Unsatisfiable 179.30s 179.50s
% Output : Proof 179.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.23 % Problem : SET854-1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.23 % Command : do_cvc5 %s %d
% 0.24/0.45 % Computer : n004.cluster.edu
% 0.24/0.45 % Model : x86_64 x86_64
% 0.24/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.45 % Memory : 8042.1875MB
% 0.24/0.45 % OS : Linux 3.10.0-693.el7.x86_64
% 0.24/0.45 % CPULimit : 300
% 0.24/0.45 % WCLimit : 300
% 0.24/0.45 % DateTime : Sat Aug 26 10:56:08 EDT 2023
% 0.24/0.45 % CPUTime :
% 0.31/0.69 %----Proving TF0_NAR, FOF, or CNF
% 0.31/0.70 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.b5lEX95gkl/cvc5---1.0.5_19219.p...
% 0.54/0.82 ------- get file name : TPTP file name is SET854-1
% 0.54/0.83 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_19219.smt2...
% 0.54/0.83 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.78/10.98 --- Run --no-e-matching --full-saturate-quant at 5...
% 15.91/16.11 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.96/21.23 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 26.12/26.29 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 31.07/31.41 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 36.28/36.50 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 41.42/41.61 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 46.62/46.81 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 51.72/51.92 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 56.73/57.04 --- Run --relevant-triggers --full-saturate-quant at 5...
% 61.90/62.16 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 67.08/67.28 --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 77.18/77.40 --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 87.29/87.51 --- Run --no-cbqi --full-saturate-quant at 10...
% 97.42/97.62 --- Run --macros-quant --macros-quant-mode=all --full-saturate-quant...
% 179.30/179.50 % SZS status Unsatisfiable for SET854-1
% 179.30/179.50 % SZS output start Proof for SET854-1
% 179.30/179.52 (
% 179.30/179.52 (let ((_let_1 (forall ((V_V $$unsorted) (V_U $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_set tptp.t_a)))) (or (tptp.c_lessequals (tptp.c_Zorn_Osucc tptp.v_S V_V tptp.t_a) V_U _let_1) (= V_V V_U) (not (tptp.c_lessequals V_V V_U _let_1)) (not (tptp.c_in V_V (tptp.c_Zorn_OTFin tptp.v_S tptp.t_a) _let_1)) (not (tptp.c_in V_U tptp.v_Y _let_1))))))) (let ((_let_2 (tptp.tc_set tptp.t_a))) (let ((_let_3 (tptp.tc_set _let_2))) (let ((_let_4 (tptp.c_Union tptp.v_Y _let_2))) (let ((_let_5 (tptp.c_Zorn_Osucc tptp.v_S tptp.v_x tptp.t_a))) (let ((_let_6 (tptp.c_lessequals _let_5 _let_4 _let_3))) (let ((_let_7 (not _let_6))) (let ((_let_8 (= tptp.v_x _let_4))) (let ((_let_9 (not _let_8))) (let ((_let_10 (tptp.c_lessequals tptp.v_x _let_4 _let_3))) (let ((_let_11 (tptp.c_Zorn_OTFin tptp.v_S tptp.t_a))) (let ((_let_12 (tptp.c_in tptp.v_x _let_11 _let_3))) (let ((_let_13 (tptp.c_lessequals tptp.v_Y _let_11 (tptp.tc_set _let_3)))) (let ((_let_14 (forall ((V_B $$unsorted) (V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (let ((_let_2 (tptp.c_Union V_C T_a))) (or (not (tptp.c_lessequals V_B (tptp.c_Zorn_OUnion__lemma0__1 V_A V_B V_C T_a) _let_1)) (tptp.c_lessequals V_B _let_2 _let_1) (tptp.c_lessequals _let_2 V_A _let_1))))))) (let ((_let_15 (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (let ((_let_2 (tptp.c_Union V_C T_a))) (or (not (tptp.c_lessequals (tptp.c_Zorn_OUnion__lemma0__1 V_A V_B V_C T_a) V_A _let_1)) (tptp.c_lessequals V_B _let_2 _let_1) (tptp.c_lessequals _let_2 V_A _let_1))))))) (let ((_let_16 (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (let ((_let_2 (tptp.c_Union V_C T_a))) (or (tptp.c_in (tptp.c_Zorn_OUnion__lemma0__1 V_A V_B V_C T_a) V_C _let_1) (tptp.c_lessequals V_B _let_2 _let_1) (tptp.c_lessequals _let_2 V_A _let_1))))))) (let ((_let_17 (forall ((V_m $$unsorted) (V_S $$unsorted) (T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_set T_a)))) (let ((_let_2 (tptp.c_Zorn_OTFin V_S T_a))) (or (not (tptp.c_in V_m _let_2 _let_1)) (not (tptp.c_in V_n _let_2 _let_1)) (not (tptp.c_lessequals (tptp.c_Zorn_Osucc V_S (tptp.c_Zorn_OTFin__linear__lemma1__1 V_S V_m T_a) T_a) V_m _let_1)) (tptp.c_lessequals V_n V_m _let_1) (tptp.c_lessequals (tptp.c_Zorn_Osucc V_S V_m T_a) V_n _let_1))))))) (let ((_let_18 (forall ((V_m $$unsorted) (V_S $$unsorted) (T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_set T_a)))) (let ((_let_2 (tptp.c_Zorn_OTFin V_S T_a))) (or (not (tptp.c_in V_m _let_2 _let_1)) (not (tptp.c_in V_n _let_2 _let_1)) (not (= (tptp.c_Zorn_OTFin__linear__lemma1__1 V_S V_m T_a) V_m)) (tptp.c_lessequals V_n V_m _let_1) (tptp.c_lessequals (tptp.c_Zorn_Osucc V_S V_m T_a) V_n _let_1))))))) (let ((_let_19 (forall ((V_m $$unsorted) (V_S $$unsorted) (T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_set T_a)))) (let ((_let_2 (tptp.c_Zorn_OTFin V_S T_a))) (or (not (tptp.c_in V_m _let_2 _let_1)) (not (tptp.c_in V_n _let_2 _let_1)) (tptp.c_lessequals V_n V_m _let_1) (tptp.c_lessequals (tptp.c_Zorn_OTFin__linear__lemma1__1 V_S V_m T_a) V_m _let_1) (tptp.c_lessequals (tptp.c_Zorn_Osucc V_S V_m T_a) V_n _let_1))))))) (let ((_let_20 (forall ((V_m $$unsorted) (V_S $$unsorted) (T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_set T_a)))) (let ((_let_2 (tptp.c_Zorn_OTFin V_S T_a))) (or (not (tptp.c_in V_m _let_2 _let_1)) (not (tptp.c_in V_n _let_2 _let_1)) (tptp.c_in (tptp.c_Zorn_OTFin__linear__lemma1__1 V_S V_m T_a) _let_2 _let_1) (tptp.c_lessequals V_n V_m _let_1) (tptp.c_lessequals (tptp.c_Zorn_Osucc V_S V_m T_a) V_n _let_1))))))) (let ((_let_21 (forall ((V_x $$unsorted) (V_S $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_x (tptp.c_Zorn_Osucc V_S V_x T_a) (tptp.tc_set (tptp.tc_set T_a)))))) (let ((_let_22 (forall ((V_B $$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)))))) (let ((_let_23 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in (tptp.c_Main_OsubsetI__1 V_A V_B T_a) V_B T_a)) (tptp.c_lessequals V_A V_B (tptp.tc_set T_a)))))) (let ((_let_24 (forall ((V_A $$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)))))) (let ((_let_25 (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))))) (let ((_let_26 (tptp.c_Zorn_OUnion__lemma0__1 tptp.v_x _let_5 tptp.v_Y _let_2))) (let ((_let_27 (tptp.c_in _let_26 tptp.v_Y _let_3))) (let ((_let_28 (not _let_27))) (let ((_let_29 (tptp.c_Zorn_OTFin__linear__lemma1__1 tptp.v_S _let_26 tptp.t_a))) (let ((_let_30 (tptp.c_in _let_29 _let_11 _let_3))) (let ((_let_31 (not _let_30))) (let ((_let_32 (tptp.c_lessequals _let_29 _let_26 _let_3))) (let ((_let_33 (not _let_32))) (let ((_let_34 (= _let_26 _let_29))) (let ((_let_35 (tptp.c_lessequals (tptp.c_Zorn_Osucc tptp.v_S _let_29 tptp.t_a) _let_26 _let_3))) (let ((_let_36 (or _let_35 _let_34 _let_33 _let_31 _let_28))) (let ((_let_37 (tptp.c_lessequals _let_4 tptp.v_x _let_3))) (let ((_let_38 (or _let_27 _let_6 _let_37))) (let ((_let_39 (_let_16))) (let ((_let_40 (ASSUME :args _let_39))) (let ((_let_41 (tptp.tc_set T_a))) (let ((_let_42 (tptp.c_Union V_C T_a))) (let ((_let_43 (not _let_37))) (let ((_let_44 (not _let_10))) (let ((_let_45 (or _let_44 _let_43 _let_8))) (let ((_let_46 (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_B V_A)))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_45)) :args ((or _let_8 _let_44 _let_43 (not _let_45)))) (ASSUME :args (_let_9)) (ASSUME :args (_let_10)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (tptp.v_x _let_4 _let_2 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_lessequals V_B V_A (tptp.tc_set T_a)) false))))) :args (_let_46))) _let_47 :args (_let_45 false _let_46)) :args (_let_43 true _let_8 false _let_10 false _let_45)))) (let ((_let_49 (ASSUME :args (_let_7)))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_6 _let_37 _let_27 (not _let_38)))) _let_49 _let_48 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (tptp.v_x _let_5 tptp.v_Y _let_2 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_lessequals V_B _let_42 _let_41) true)) (not (= (tptp.c_lessequals _let_42 V_A _let_41) true))))) :args _let_39)) _let_40 :args (_let_38 false _let_16)) :args (_let_27 true _let_6 true _let_37 false _let_38)))) (let ((_let_51 (_let_1))) (let ((_let_52 (ASSUME :args _let_51))) (let ((_let_53 ((not (= (tptp.c_lessequals (tptp.c_Zorn_Osucc tptp.v_S V_V tptp.t_a) V_U _let_3) true))))) (let ((_let_54 (tptp.c_Zorn_Osucc tptp.v_S _let_26 tptp.t_a))) (let ((_let_55 (tptp.c_lessequals _let_54 tptp.v_x _let_3))) (let ((_let_56 (tptp.c_lessequals tptp.v_x _let_26 _let_3))) (let ((_let_57 (not _let_35))) (let ((_let_58 (not _let_12))) (let ((_let_59 (tptp.c_in _let_26 _let_11 _let_3))) (let ((_let_60 (not _let_59))) (let ((_let_61 (or _let_60 _let_58 _let_57 _let_56 _let_55))) (let ((_let_62 (_let_17))) (let ((_let_63 (ASSUME :args _let_62))) (let ((_let_64 (tptp.c_Main_OsubsetI__1 _let_26 tptp.v_x _let_2))) (let ((_let_65 (tptp.c_in _let_64 tptp.v_x _let_2))) (let ((_let_66 (not _let_55))) (let ((_let_67 (tptp.c_in _let_64 _let_54 _let_2))) (let ((_let_68 (not _let_67))) (let ((_let_69 (or _let_68 _let_66 _let_65))) (let ((_let_70 (_let_25))) (let ((_let_71 (ASSUME :args _let_70))) (let ((_let_72 (tptp.c_lessequals _let_26 _let_54 _let_3))) (let ((_let_73 (not _let_72))) (let ((_let_74 (tptp.c_in _let_64 _let_26 _let_2))) (let ((_let_75 (not _let_74))) (let ((_let_76 (or _let_75 _let_73 _let_67))) (let ((_let_77 (_let_21))) (let ((_let_78 (ASSUME :args _let_77))) (let ((_let_79 (tptp.c_lessequals _let_26 tptp.v_x _let_3))) (let ((_let_80 (or _let_74 _let_79))) (let ((_let_81 (_let_24))) (let ((_let_82 (ASSUME :args _let_81))) (let ((_let_83 (not _let_79))) (let ((_let_84 (or _let_83 _let_6 _let_37))) (let ((_let_85 (_let_15))) (let ((_let_86 (ASSUME :args _let_85))) (let ((_let_87 (tptp.tc_set T_a))) (let ((_let_88 (tptp.c_Union V_C T_a))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_84)) :args ((or _let_6 _let_37 _let_83 (not _let_84)))) _let_49 _let_48 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_86 :args (tptp.v_x _let_5 tptp.v_Y _let_2 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_lessequals V_B _let_88 _let_87) true)) (not (= (tptp.c_lessequals _let_88 V_A _let_87) true))))) :args _let_85)) _let_86 :args (_let_84 false _let_15)) :args (_let_83 true _let_6 true _let_37 false _let_84)))) (let ((_let_90 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_80)) :args ((or _let_79 _let_74 (not _let_80)))) _let_89 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args (_let_26 tptp.v_x _let_2 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_lessequals V_A V_B (tptp.tc_set T_a)) true))))) :args _let_81)) _let_82 :args (_let_80 false _let_24)) :args (_let_74 true _let_79 false _let_80)))) (let ((_let_91 (not _let_65))) (let ((_let_92 (or _let_91 _let_79))) (let ((_let_93 (_let_23))) (let ((_let_94 (ASSUME :args _let_93))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_92)) :args ((or _let_79 _let_91 (not _let_92)))) _let_89 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_94 :args (_let_26 tptp.v_x _let_2 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_lessequals V_A V_B (tptp.tc_set T_a)) true))))) :args _let_93)) _let_94 :args (_let_92 false _let_23)) :args (_let_91 true _let_79 false _let_92)))) (let ((_let_96 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_65 _let_68 _let_66 (not _let_69)))) _let_95 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_75 _let_73 _let_67 (not _let_76)))) _let_90 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (_let_26 tptp.v_S tptp.t_a QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_Zorn_Osucc V_S V_x T_a)))) :args _let_77)) _let_78 :args (_let_72 false _let_21)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (_let_64 _let_26 _let_2 _let_54 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_in V_c V_A T_a) false)) (not (= (tptp.c_lessequals V_A V_B (tptp.tc_set T_a)) false))))) :args _let_70)) _let_71 :args (_let_76 false _let_25)) :args (_let_67 false _let_74 false _let_72 false _let_76)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (_let_64 _let_54 _let_2 tptp.v_x QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_70)) _let_71 :args (_let_69 false _let_25)) :args (_let_66 true _let_65 false _let_67 false _let_69)))) (let ((_let_97 (not _let_56))) (let ((_let_98 (= tptp.v_x _let_26))) (let ((_let_99 (tptp.c_lessequals _let_5 _let_26 _let_3))) (let ((_let_100 (or _let_99 _let_98 _let_97 _let_58 _let_28))) (let ((_let_101 (not _let_98))) (let ((_let_102 (ASSUME :args (_let_74)))) (let ((_let_103 (ASSUME :args (_let_98)))) (let ((_let_104 (ASSUME :args (_let_91)))) (let ((_let_105 (not _let_99))) (let ((_let_106 (or _let_105 _let_6 _let_37))) (let ((_let_107 (_let_14))) (let ((_let_108 (ASSUME :args _let_107))) (let ((_let_109 (tptp.tc_set T_a))) (let ((_let_110 (tptp.c_Union V_C T_a))) (let ((_let_111 (ASSUME :args (_let_12)))) (let ((_let_112 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_100)) :args ((or _let_58 _let_99 _let_28 _let_98 _let_97 (not _let_100)))) _let_111 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_106)) :args ((or _let_6 _let_37 _let_105 (not _let_106)))) _let_49 _let_48 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (_let_5 tptp.v_x tptp.v_Y _let_2 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_lessequals _let_110 V_A _let_109) true)) (not (= (tptp.c_lessequals V_B _let_110 _let_109) true))))) :args _let_107)) _let_108 :args (_let_106 false _let_14)) :args (_let_105 true _let_6 true _let_37 false _let_106)) _let_50 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_102 _let_103 _let_104) :args (_let_74 _let_91 _let_98)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_104)) (CONG (REFL :args (_let_64)) (SYMM (SYMM _let_103)) (REFL :args (_let_2)) :args (APPLY_UF tptp.c_in)) (TRUE_INTRO 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$$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 (= 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$$unsorted) (V_X $$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 $$unsorted)) (let ((_let_1 (tptp.c_insert V_x tptp.c_emptyset T_a))) (or (not 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$$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)))) (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))) _let_25 _let_24 _let_23 _let_22 (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_A V_A (tptp.tc_set T_a))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (not (tptp.c_in V_a V_A T_a)) (tptp.c_in (tptp.c_Sum__Type_OInl V_a T_a T_b) (tptp.c_Sum__Type_OPlus V_A V_B T_a T_b) (tptp.tc_sum T_a T_b)))) (forall ((V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (not (tptp.c_in V_b V_B T_a)) (tptp.c_in (tptp.c_Sum__Type_OInr V_b T_a T_b) (tptp.c_Sum__Type_OPlus V_A V_B T_b T_a) (tptp.tc_sum T_b T_a)))) (forall ((V_u $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (tptp.c_in V_u (tptp.c_Sum__Type_OPlus V_A V_B T_a T_b) (tptp.tc_sum T_a T_b))) (= V_u (tptp.c_Sum__Type_OInl (tptp.c_Main_OPlusE__1 V_A V_u T_a T_b) T_a T_b)) (= V_u (tptp.c_Sum__Type_OInr (tptp.c_Main_OPlusE__2 V_B V_u T_b T_a) T_b T_a)))) (forall ((V_u $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (tptp.c_in V_u (tptp.c_Sum__Type_OPlus V_A V_B T_a T_b) (tptp.tc_sum T_a T_b))) (tptp.c_in (tptp.c_Main_OPlusE__2 V_B V_u T_b T_a) V_B T_b) (= V_u (tptp.c_Sum__Type_OInl (tptp.c_Main_OPlusE__1 V_A V_u T_a T_b) T_a T_b)))) (forall ((V_u $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (tptp.c_in V_u (tptp.c_Sum__Type_OPlus V_A V_B T_a T_b) (tptp.tc_sum T_a T_b))) (tptp.c_in (tptp.c_Main_OPlusE__1 V_A V_u T_a T_b) V_A T_a) (= V_u (tptp.c_Sum__Type_OInr (tptp.c_Main_OPlusE__2 V_B V_u T_b T_a) T_b T_a)))) (forall ((V_u $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (tptp.c_in V_u (tptp.c_Sum__Type_OPlus V_A V_B T_a T_b) (tptp.tc_sum T_a T_b))) (tptp.c_in (tptp.c_Main_OPlusE__1 V_A V_u T_a T_b) V_A T_a) (tptp.c_in (tptp.c_Main_OPlusE__2 V_B V_u T_b T_a) V_B T_b))) (forall ((V_p $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (not (tptp.c_in V_p V_r _let_1)) (tptp.c_in V_p (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (tptp.c_in (tptp.c_Pair V_a V_a T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Pair V_a V_b T_a T_a))) (or (not (tptp.c_in _let_2 V_r _let_1)) (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a) _let_1))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Pair V_a V_b T_a T_a))) (or (not (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a) _let_1)) (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1))))) (forall ((T_a $$unsorted)) (tptp.c_Wellfounded__Recursion_Owf tptp.c_emptyset T_a)) (tptp.c_Relation_Otrans tptp.c_Wellfounded__Relations_Oless__than tptp.tc_nat) (forall ((V_R2 $$unsorted) (T_b $$unsorted) (V_R1 $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Relation_Otrans V_R2 T_b)) (not (tptp.c_Relation_Otrans V_R1 T_a)) (tptp.c_Relation_Otrans (tptp.c_Wellfounded__Relations_Olex__prod V_R1 V_R2 T_a T_b) (tptp.tc_prod T_a T_b)))) (tptp.c_Wellfounded__Recursion_Owf tptp.c_Wellfounded__Relations_Oless__than tptp.tc_nat) (forall ((V_rb $$unsorted) (T_b $$unsorted) (V_ra $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Wellfounded__Recursion_Owf V_rb T_b)) (not (tptp.c_Wellfounded__Recursion_Owf V_ra T_a)) (tptp.c_Wellfounded__Recursion_Owf (tptp.c_Wellfounded__Relations_Olex__prod V_ra V_rb T_a T_b) (tptp.tc_prod T_a T_b)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Finite__Set_Ofinite (tptp.tc_Datatype_Ooption T_1)) (not (tptp.class_Finite__Set_Ofinite T_1)))) (tptp.class_HOL_Ominus tptp.tc_IntDef_Oint) (tptp.class_HOL_Oone tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Osemiring tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Ocomm__semiring tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Ocomm__semiring__0 tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Oab__group__add tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Osemiring__0__cancel tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Oring tptp.tc_IntDef_Oint) (tptp.class_HOL_Oplus tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Ocomm__semiring__0__cancel tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Ocomm__ring tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Oaxclass__0__neq__1 tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Ocomm__monoid__mult tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Osemiring__1 tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Osemiring__1__cancel tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Oring__1 tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Ocomm__semiring__1__cancel tptp.tc_IntDef_Oint) (tptp.class_HOL_Otimes tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Ocomm__ring__1 tptp.tc_IntDef_Oint) (tptp.class_Orderings_Oorder tptp.tc_IntDef_Oint) (tptp.class_LOrder_Omeet__semilorder tptp.tc_IntDef_Oint) (tptp.class_LOrder_Ojoin__semilorder tptp.tc_IntDef_Oint) (tptp.class_LOrder_Olorder tptp.tc_IntDef_Oint) (tptp.class_Orderings_Olinorder tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Oordered__cancel__ab__semigroup__add tptp.tc_IntDef_Oint) (tptp.class_HOL_Ozero tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Opordered__semiring tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Opordered__cancel__semiring tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Oordered__semiring__strict tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Opordered__comm__semiring tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Opordered__cancel__comm__semiring tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Oaxclass__abs__if tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Opordered__ab__group__add tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Olordered__ab__group tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Opordered__ring tptp.tc_IntDef_Oint) (tptp.class_Orderings_Oord tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Olordered__ab__group__abs tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Olordered__ab__group__meet tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Olordered__ab__group__join tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Olordered__ring tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Oaxclass__no__zero__divisors tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Oordered__ring__strict tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Oidom tptp.tc_IntDef_Oint) (tptp.class_Ring__and__Field_Oordered__idom tptp.tc_IntDef_Oint) (tptp.class_Numeral_Onumber tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Osemigroup__add tptp.tc_IntDef_Oint) (tptp.class_Numeral_Onumber__ring tptp.tc_IntDef_Oint) (tptp.class_Divides_Odiv tptp.tc_IntDef_Oint) (tptp.class_Nat_Opower tptp.tc_IntDef_Oint) (tptp.class_Power_Orecpower tptp.tc_IntDef_Oint) (tptp.class_Parity_Oeven__odd tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Osemigroup__mult tptp.tc_IntDef_Oint) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_IntDef_Oint) (tptp.class_Finite__Set_Ofinite tptp.tc_Product__Type_Ounit) (tptp.class_Finite__Set_Ofinite tptp.tc_bool) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Finite__Set_Ofinite (tptp.tc_fun T_2 T_1)) (not (tptp.class_Finite__Set_Ofinite T_1)) (not (tptp.class_Finite__Set_Ofinite T_2)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (tptp.class_Nat_Opower (tptp.tc_fun T_2 T_1))) (tptp.class_HOL_Oone tptp.tc_nat) (tptp.class_HOL_Ozero tptp.tc_nat) (tptp.class_HOL_Oplus tptp.tc_nat) (tptp.class_HOL_Otimes tptp.tc_nat) (tptp.class_Nat_Opower tptp.tc_nat) (tptp.class_Ring__and__Field_Oaxclass__0__neq__1 tptp.tc_nat) (tptp.class_OrderedGroup_Osemigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Osemigroup__mult tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring tptp.tc_nat) (tptp.class_Orderings_Oord tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring__0 tptp.tc_nat) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__mult tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__1 tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__0__cancel tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__1__cancel tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring__0__cancel tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring__1__cancel tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le tptp.tc_nat) (tptp.class_OrderedGroup_Oordered__cancel__ab__semigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_Opordered__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Opordered__cancel__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semiring__strict tptp.tc_nat) (tptp.class_LOrder_Omeet__semilorder tptp.tc_nat) (tptp.class_Ring__and__Field_Opordered__comm__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Opordered__cancel__comm__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict tptp.tc_nat) 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((T_1 $$unsorted)) (tptp.class_Nat_Opower (tptp.tc_set T_1))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Finite__Set_Ofinite (tptp.tc_sum T_2 T_1)) (not (tptp.class_Finite__Set_Ofinite T_1)) (not (tptp.class_Finite__Set_Ofinite T_2)))) (forall ((T $$unsorted)) (or (not (tptp.class_LOrder_Ojoin__semilorder T)) (tptp.class_Orderings_Oord T))) (forall ((T $$unsorted)) (or (not (tptp.class_LOrder_Ojoin__semilorder T)) (tptp.class_Orderings_Oorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_LOrder_Olorder T)) (tptp.class_LOrder_Omeet__semilorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_LOrder_Olorder T)) (tptp.class_Orderings_Oord T))) (forall ((T $$unsorted)) (or (not (tptp.class_LOrder_Olorder T)) (tptp.class_Orderings_Oorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_LOrder_Olorder T)) (tptp.class_LOrder_Ojoin__semilorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_LOrder_Omeet__semilorder T)) (tptp.class_Orderings_Oord T))) (forall ((T $$unsorted)) (or (not (tptp.class_LOrder_Omeet__semilorder T)) (tptp.class_Orderings_Oorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_HOL_Oplus T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_OrderedGroup_Osemigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_Ring__and__Field_Osemiring__0 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_Ring__and__Field_Ocomm__semiring__0 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_HOL_Ominus T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_OrderedGroup_Ocancel__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_OrderedGroup_Oab__group__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_Ring__and__Field_Osemiring__0__cancel T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_Ring__and__Field_Oring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_Ring__and__Field_Ocomm__semiring__0__cancel T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_Ring__and__Field_Ocomm__ring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_OrderedGroup_Oab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_HOL_Oone T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_Ring__and__Field_Oaxclass__0__neq__1 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_OrderedGroup_Omonoid__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_OrderedGroup_Ocomm__monoid__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_Ring__and__Field_Osemiring__1 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_Ring__and__Field_Ocomm__semiring__1 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_Ring__and__Field_Osemiring__1__cancel T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_Ring__and__Field_Oring__1 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_Ring__and__Field_Ocomm__semiring__1__cancel T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_Ring__and__Field_Ocomm__ring__1 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T)) (tptp.class_HOL_Otimes T))) (forall ((T $$unsorted)) (or (not 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T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T)) (tptp.class_HOL_Ozero T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T)) (tptp.class_OrderedGroup_Oab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T)) (tptp.class_OrderedGroup_Osemigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T)) (tptp.class_HOL_Oplus T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T)) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T)) (tptp.class_OrderedGroup_Ocancel__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__add T)) (tptp.class_OrderedGroup_Osemigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__add T)) (tptp.class_HOL_Oplus T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T)) (tptp.class_OrderedGroup_Osemigroup__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T)) (tptp.class_HOL_Otimes T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T)) (tptp.class_OrderedGroup_Oab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T)) (tptp.class_OrderedGroup_Osemigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T)) (tptp.class_HOL_Oplus T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T)) (tptp.class_OrderedGroup_Ocancel__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T)) (tptp.class_OrderedGroup_Osemigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T)) 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$$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T)) (tptp.class_OrderedGroup_Omonoid__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T)) (tptp.class_OrderedGroup_Opordered__ab__group__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T)) (tptp.class_OrderedGroup_Oab__group__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T)) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T)) (tptp.class_OrderedGroup_Oab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T)) (tptp.class_OrderedGroup_Ocancel__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T)) (tptp.class_OrderedGroup_Osemigroup__add T))) (forall ((T $$unsorted)) (or (not 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$$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T)) (tptp.class_OrderedGroup_Oab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T)) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T)) (tptp.class_OrderedGroup_Ocancel__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T)) (tptp.class_Ring__and__Field_Osemiring__0__cancel T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T)) (tptp.class_Ring__and__Field_Osemiring__0 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T)) (tptp.class_OrderedGroup_Osemigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T)) (tptp.class_HOL_Oplus T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T)) (tptp.class_OrderedGroup_Osemigroup__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T)) (tptp.class_HOL_Otimes T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T)) (tptp.class_OrderedGroup_Oab__group__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T)) (tptp.class_HOL_Ominus T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T)) (tptp.class_OrderedGroup_Ocomm__monoid__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T)) (tptp.class_HOL_Ozero T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T)) (tptp.class_Ring__and__Field_Oring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T)) (tptp.class_OrderedGroup_Oab__group__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T)) (tptp.class_OrderedGroup_Ocomm__monoid__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T)) (tptp.class_OrderedGroup_Oab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T)) (tptp.class_OrderedGroup_Osemigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T)) (tptp.class_HOL_Oplus T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T)) (tptp.class_HOL_Ozero T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T)) (tptp.class_Ring__and__Field_Osemiring__1 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T)) (tptp.class_Ring__and__Field_Oaxclass__0__neq__1 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T)) (tptp.class_OrderedGroup_Omonoid__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T)) (tptp.class_HOL_Oone T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T)) (tptp.class_Ring__and__Field_Osemiring__1__cancel T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T)) (tptp.class_HOL_Ominus T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T)) (tptp.class_Ring__and__Field_Osemiring__0__cancel T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T)) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T)) (tptp.class_OrderedGroup_Ocancel__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T)) (tptp.class_Ring__and__Field_Osemiring__0 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T)) (tptp.class_Ring__and__Field_Osemiring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T)) (tptp.class_OrderedGroup_Osemigroup__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T)) (tptp.class_HOL_Otimes T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring T)) (tptp.class_OrderedGroup_Oab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring T)) (tptp.class_OrderedGroup_Osemigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring T)) (tptp.class_HOL_Oplus T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring T)) (tptp.class_OrderedGroup_Osemigroup__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring T)) (tptp.class_HOL_Otimes T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T)) (tptp.class_Ring__and__Field_Osemiring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T)) (tptp.class_OrderedGroup_Oab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T)) (tptp.class_OrderedGroup_Osemigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T)) (tptp.class_HOL_Oplus T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T)) (tptp.class_OrderedGroup_Osemigroup__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T)) (tptp.class_HOL_Otimes T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T)) (tptp.class_OrderedGroup_Ocomm__monoid__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T)) (tptp.class_HOL_Ozero T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0__cancel T)) (tptp.class_Ring__and__Field_Osemiring__0 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0__cancel T)) (tptp.class_Ring__and__Field_Osemiring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0__cancel T)) (tptp.class_OrderedGroup_Ocancel__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0__cancel T)) (tptp.class_OrderedGroup_Osemigroup__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0__cancel T)) (tptp.class_HOL_Otimes T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0__cancel T)) (tptp.class_OrderedGroup_Ocomm__monoid__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0__cancel T)) (tptp.class_OrderedGroup_Oab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0__cancel T)) (tptp.class_OrderedGroup_Osemigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0__cancel T)) (tptp.class_HOL_Oplus T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0__cancel T)) (tptp.class_HOL_Ozero T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0__cancel T)) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T)) (tptp.class_Ring__and__Field_Oaxclass__0__neq__1 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T)) (tptp.class_HOL_Ozero T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T)) (tptp.class_HOL_Oplus T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T)) (tptp.class_OrderedGroup_Omonoid__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T)) (tptp.class_HOL_Oone T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T)) (tptp.class_Ring__and__Field_Osemiring__0 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T)) (tptp.class_Ring__and__Field_Osemiring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T)) (tptp.class_OrderedGroup_Osemigroup__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T)) (tptp.class_HOL_Otimes T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T)) (tptp.class_OrderedGroup_Ocomm__monoid__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T)) (tptp.class_OrderedGroup_Oab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T)) (tptp.class_OrderedGroup_Osemigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_Ring__and__Field_Osemiring__1 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_Ring__and__Field_Oaxclass__0__neq__1 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_HOL_Oone T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_OrderedGroup_Osemigroup__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_HOL_Otimes T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_OrderedGroup_Ocancel__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_Ring__and__Field_Osemiring__0__cancel T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_Ring__and__Field_Osemiring__0 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_Ring__and__Field_Osemiring T))) (forall ((T $$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 $$unsorted)) (or (not (tptp.class_Wellfounded__Recursion_Owellorder T)) (tptp.class_Orderings_Olinorder T))) _let_21 _let_20 _let_19 _let_18 _let_17 _let_16 _let_15 _let_14 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_set T_a)))) (or (not (tptp.c_lessequals V_x V_y _let_1)) (tptp.c_lessequals V_x (tptp.c_Zorn_Osucc V_S V_y T_a) _let_1)))) _let_13 _let_12 _let_10 _let_9 _let_7 _let_1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 179.30/179.52 )
% 179.30/179.55 % SZS output end Proof for SET854-1
% 179.30/179.55 % cvc5---1.0.5 exiting
% 179.30/179.55 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------