TSTP Solution File: SCT022-1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SCT022-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n001.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 14:11:49 EDT 2023
% Result : Unsatisfiable 63.00s 63.54s
% Output : Proof 63.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.20 % Problem : SCT022-1 : TPTP v8.1.2. Released v4.1.0.
% 0.13/0.21 % Command : do_cvc5 %s %d
% 0.20/0.42 % Computer : n001.cluster.edu
% 0.20/0.42 % Model : x86_64 x86_64
% 0.20/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.42 % Memory : 8042.1875MB
% 0.20/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.42 % CPULimit : 300
% 0.20/0.42 % WCLimit : 300
% 0.20/0.42 % DateTime : Thu Aug 24 15:29:56 EDT 2023
% 0.20/0.43 % CPUTime :
% 0.28/0.63 %----Proving TF0_NAR, FOF, or CNF
% 0.28/0.64 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.nIdkW9AX8q/cvc5---1.0.5_13164.p...
% 0.28/0.78 ------- get file name : TPTP file name is SCT022-1
% 0.28/0.78 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_13164.smt2...
% 0.28/0.78 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.67/10.90 --- Run --no-e-matching --full-saturate-quant at 5...
% 15.75/15.97 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.75/21.06 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.83/26.14 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 30.83/31.25 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 36.03/36.39 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 41.13/41.45 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 46.08/46.58 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 51.25/51.70 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 56.28/56.87 --- Run --relevant-triggers --full-saturate-quant at 5...
% 61.48/61.98 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 63.00/63.54 % SZS status Unsatisfiable for SCT022-1
% 63.00/63.54 % SZS output start Proof for SCT022-1
% 63.05/63.58 (
% 63.05/63.58 (let ((_let_1 (forall ((V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.v_P tptp.v_xa))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (or (tptp.hBOOL (tptp.c_in _let_3 (tptp.v_F tptp.v_P) _let_2)) (not (tptp.hBOOL (tptp.c_in _let_3 (tptp.hAPP tptp.v_P tptp.v_i) _let_2))) (= V_a V_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) _let_1 tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl _let_1 tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans _let_1 tptp.tc_Arrow__Order__Mirabelle_Oalt))))))))) (let ((_let_2 (tptp.hAPP tptp.v_P tptp.v_x))) (let ((_let_3 (not (tptp.c_Relation_Otrans _let_2 tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (let ((_let_4 (not (tptp.c_Relation_Oirrefl _let_2 tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (let ((_let_5 (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool))) (let ((_let_6 (tptp.c_Orderings_Otop__class_Otop _let_5))) (let ((_let_7 (not (tptp.c_Relation_Ototal__on _let_6 _let_2 tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (let ((_let_8 (tptp.v_F tptp.v_P))) (let ((_let_9 (or (tptp.c_Relation_Oirrefl _let_8 tptp.tc_Arrow__Order__Mirabelle_Oalt) _let_7 _let_4 _let_3))) (let ((_let_10 (or (tptp.c_Relation_Otrans _let_8 tptp.tc_Arrow__Order__Mirabelle_Oalt) _let_7 _let_4 _let_3))) (let ((_let_11 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_12 (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_13 (not (tptp.hBOOL (tptp.c_in _let_12 (tptp.hAPP tptp.v_P tptp.v_i) _let_11))))) (let ((_let_14 (tptp.hBOOL (tptp.c_in _let_12 _let_8 _let_11)))) (let ((_let_15 (forall ((V_x $$unsorted)) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (let ((_let_16 (forall ((V_x $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (let ((_let_17 (forall ((V_x $$unsorted)) (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (let ((_let_18 (forall ((V_xa $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_xa V_x T_a T_a) V_r _let_1)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_xa T_a T_a) V_r _let_1)) (= V_x V_xa) (not (tptp.hBOOL (tptp.c_in V_xa V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Relation_Ototal__on V_A V_r T_a))))))) (let ((_let_19 (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (let ((_let_20 (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Oirrefl V_r T_a)))))) (let ((_let_21 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a tptp.tc_bool)))) (let ((_let_22 (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) _let_2 _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) V_r _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) _let_2 _let_1))))))))) (let ((_let_23 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Transitive__Closure_Otrancl V_r T_a) V_r) (not (tptp.c_Relation_Otrans V_r T_a)))))) (let ((_let_24 (forall ((b_V_xa it_3_$$unsorted) (b_V_x it_3_$$unsorted) (T_a $$unsorted) (b_V_r it_3_$$unsorted) (b_V_A it_3_$$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (io_tptp.hBOOL_11 (io_tptp.c_in_10 (io_tptp.c_Pair_14 b_V_xa b_V_x T_a T_a) b_V_r _let_1)) (io_tptp.hBOOL_11 (io_tptp.c_in_10 (io_tptp.c_Pair_14 b_V_x b_V_xa T_a T_a) b_V_r _let_1)) (= b_V_xa b_V_x) (not (io_tptp.hBOOL_11 (io_tptp.c_in_10 b_V_xa b_V_A T_a))) (not (io_tptp.hBOOL_11 (io_tptp.c_in_10 b_V_x b_V_A T_a))) (not (io_tptp.c_Relation_Ototal__on_58 b_V_A b_V_r T_a))))))) (let ((_let_25 (io_tptp.hAPP_4 i_tptp.v_P_100 i_tptp.v_i_104))) (let ((_let_26 (io_tptp.c_Orderings_Otop__class_Otop_38 _let_5))) (let ((_let_27 (io_tptp.c_Relation_Ototal__on_58 _let_26 _let_25 tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_28 (not _let_27))) (let ((_let_29 (io_tptp.hBOOL_11 (io_tptp.c_in_10 i_tptp.v_a_101 _let_26 tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (let ((_let_30 (not _let_29))) (let ((_let_31 (io_tptp.hBOOL_11 (io_tptp.c_in_10 i_tptp.v_b_102 _let_26 tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (let ((_let_32 (not _let_31))) (let ((_let_33 (= i_tptp.v_a_101 i_tptp.v_b_102))) (let ((_let_34 (io_tptp.c_Pair_14 i_tptp.v_a_101 i_tptp.v_b_102 tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_35 (io_tptp.hBOOL_11 (io_tptp.c_in_10 _let_34 _let_25 _let_11)))) (let ((_let_36 (io_tptp.c_Pair_14 i_tptp.v_b_102 i_tptp.v_a_101 tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_37 (io_tptp.hBOOL_11 (io_tptp.c_in_10 _let_36 _let_25 _let_11)))) (let ((_let_38 (or _let_37 _let_35 _let_33 _let_32 _let_30 _let_28))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_18)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((V_xa $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_xa V_x T_a T_a) V_r _let_1)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_xa T_a T_a) V_r _let_1)) (= V_xa V_x) (not (tptp.hBOOL (tptp.c_in V_xa V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Relation_Ototal__on V_A V_r T_a))))) _let_24))))))) (let ((_let_40 (not _let_38))) (let ((_let_41 (forall ((b_V_x it_3_$$unsorted)) (io_tptp.c_Relation_Ototal__on_58 (io_tptp.c_Orderings_Otop__class_Otop_38 (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (io_tptp.hAPP_4 i_tptp.v_P_100 b_V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_15)) (PREPROCESS :args ((= _let_15 _let_41)))))) (let ((_let_43 (_let_41))) (let ((_let_44 (forall ((b_V_x it_3_$$unsorted) (T_a $$unsorted)) (io_tptp.hBOOL_11 (io_tptp.c_in_10 b_V_x (io_tptp.c_Orderings_Otop__class_Otop_38 (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_19)) (PREPROCESS :args ((= _let_19 _let_44)))))) (let ((_let_46 (_let_44))) (let ((_let_47 (not _let_37))) (let ((_let_48 (io_tptp.v_F_103 i_tptp.v_P_100))) (let ((_let_49 (io_tptp.hBOOL_11 (io_tptp.c_in_10 _let_36 _let_48 _let_11)))) (let ((_let_50 (or _let_49 _let_47 _let_33))) (let ((_let_51 (forall ((b_V_a it_3_$$unsorted) (b_V_b it_3_$$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (io_tptp.c_Pair_14 b_V_a b_V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (or (io_tptp.hBOOL_11 (io_tptp.c_in_10 _let_2 (io_tptp.v_F_103 i_tptp.v_P_100) _let_1)) (not (io_tptp.hBOOL_11 (io_tptp.c_in_10 _let_2 (io_tptp.hAPP_4 i_tptp.v_P_100 i_tptp.v_i_104) _let_1))) (= b_V_a b_V_b))))))) (let ((_let_52 (io_tptp.hAPP_4 i_tptp.v_P_100 i_tptp.v_xa_105))) (let ((_let_53 (io_tptp.c_Relation_Otrans_57 _let_52 tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_54 (io_tptp.c_Relation_Oirrefl_41 _let_52 tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_55 (io_tptp.c_Relation_Ototal__on_58 _let_26 _let_52 tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_56 (forall ((b_V_x it_3_$$unsorted)) (io_tptp.c_Relation_Otrans_57 (io_tptp.hAPP_4 i_tptp.v_P_100 b_V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_17)) (PREPROCESS :args ((= _let_17 _let_56)))))) (let ((_let_58 (not _let_56))) (let ((_let_59 (_let_56))) (let ((_let_60 (i_tptp.v_xa_105 QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_61 (forall ((b_V_x it_3_$$unsorted)) (io_tptp.c_Relation_Oirrefl_41 (io_tptp.hAPP_4 i_tptp.v_P_100 b_V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_16)) (PREPROCESS :args ((= _let_16 _let_61)))))) (let ((_let_63 (not _let_61))) (let ((_let_64 (_let_61))) (let ((_let_65 (not _let_41))) (let ((_let_66 (tptp.hAPP tptp.v_P tptp.v_xa))) (let ((_let_67 (_let_51))) (let ((_let_68 (io_tptp.c_Transitive__Closure_Otrancl_33 _let_48 tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_69 (io_tptp.hBOOL_11 (io_tptp.c_in_10 _let_34 _let_68 _let_11)))) (let ((_let_70 (not _let_69))) (let ((_let_71 (not _let_49))) (let ((_let_72 (io_tptp.c_Pair_14 i_tptp.v_a_101 i_tptp.v_a_101 tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_73 (io_tptp.hBOOL_11 (io_tptp.c_in_10 _let_72 _let_68 _let_11)))) (let ((_let_74 (or _let_73 _let_71 _let_70))) (let ((_let_75 (forall ((b_V_a it_3_$$unsorted) (b_V_c it_3_$$unsorted) (T_a $$unsorted) (b_V_r it_3_$$unsorted) (b_V_b it_3_$$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (io_tptp.c_Transitive__Closure_Otrancl_33 b_V_r T_a))) (or (io_tptp.hBOOL_11 (io_tptp.c_in_10 (io_tptp.c_Pair_14 b_V_a b_V_c T_a T_a) _let_2 _let_1)) (not (io_tptp.hBOOL_11 (io_tptp.c_in_10 (io_tptp.c_Pair_14 b_V_b b_V_c T_a T_a) b_V_r _let_1))) (not (io_tptp.hBOOL_11 (io_tptp.c_in_10 (io_tptp.c_Pair_14 b_V_a b_V_b T_a T_a) _let_2 _let_1))))))))) (let ((_let_76 (EQ_RESOLVE (ASSUME :args (_let_22)) (PREPROCESS :args ((= _let_22 _let_75)))))) (let ((_let_77 (= _let_48 _let_68))) (let ((_let_78 (io_tptp.hBOOL_11 (io_tptp.c_in_10 _let_34 _let_48 _let_11)))) (let ((_let_79 (io_tptp.c_Relation_Otrans_57 _let_48 tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_80 (not _let_79))) (let ((_let_81 (or _let_77 _let_80))) (let ((_let_82 (forall ((b_V_r it_3_$$unsorted) (T_a $$unsorted)) (or (= b_V_r (io_tptp.c_Transitive__Closure_Otrancl_33 b_V_r T_a)) (not (io_tptp.c_Relation_Otrans_57 b_V_r T_a)))))) (let ((_let_83 (EQ_RESOLVE (ASSUME :args (_let_23)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (= V_r (tptp.c_Transitive__Closure_Otrancl V_r T_a)) (not (tptp.c_Relation_Otrans V_r T_a)))) _let_82))))))) (let ((_let_84 (io_tptp.hAPP_4 i_tptp.v_P_100 i_tptp.v_x_24))) (let ((_let_85 (io_tptp.c_Relation_Otrans_57 _let_84 tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_86 (io_tptp.c_Relation_Oirrefl_41 _let_84 tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_87 (io_tptp.c_Relation_Ototal__on_58 _let_26 _let_84 tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_88 (i_tptp.v_x_24 QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :args _let_88) :args _let_59)) :args ((or _let_85 _let_58))) _let_57 :args (_let_85 false _let_56)))) (let ((_let_90 (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args _let_88) :args _let_64)) :args ((or _let_86 _let_63))) _let_62 :args (_let_86 false _let_61)))) (let ((_let_91 (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args _let_88) :args _let_43)) :args ((or _let_87 _let_65))) _let_42 :args (_let_87 false _let_41)))) (let ((_let_92 (not _let_85))) (let ((_let_93 (not _let_86))) (let ((_let_94 (not _let_87))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_81)) :args ((or _let_80 _let_77 (not _let_81)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_10)) (PREPROCESS :args ((= _let_10 (or _let_79 _let_94 _let_93 _let_92))))) _let_91 _let_90 _let_89 :args (_let_79 false _let_87 false _let_86 false _let_85)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_83 :args (_let_48 tptp.tc_Arrow__Order__Mirabelle_Oalt QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (io_tptp.c_Relation_Otrans_57 b_V_r T_a) false))))) :args (_let_82))) _let_83 :args (_let_81 false _let_82)) :args (_let_77 false _let_79 false _let_81)))) (let ((_let_96 (EQ_RESOLVE (ASSUME :args (_let_14)) (PREPROCESS :args ((= _let_14 _let_78)))))) (let ((_let_97 (and _let_78 _let_77))) (let ((_let_98 (_let_78 _let_77))) (let ((_let_99 (TRUE_INTRO _let_96))) (let ((_let_100 (APPLY_UF io_tptp.hBOOL_11))) (let ((_let_101 (APPLY_UF io_tptp.c_in_10))) (let ((_let_102 (REFL :args (_let_11)))) (let ((_let_103 (ASSUME :args (_let_77)))) (let ((_let_104 (SYMM _let_103))) (let ((_let_105 (io_tptp.hBOOL_11 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(tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Transitive__Closure_Ortrancl V_R T_a) _let_1) (tptp.c_Transitive__Closure_Ortrancl V_S T_a)) (tptp.c_Transitive__Closure_Ortrancl (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R _let_1) V_S) T_a) _let_1))) (forall ((V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_c $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_3 (tptp.c_Relation_OImage V_r T_b T_a))) (tptp.c_lessequals (tptp.hAPP _let_3 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_c _let_2)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A (tptp.c_COMBB _let_3 V_B _let_2 _let_1 T_c) T_c _let_1) _let_1))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1))) (or (= (tptp.hAPP _let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_C V_B T_b _let_1)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_C (tptp.c_COMBB _let_2 V_B _let_1 _let_1 T_b) T_b _let_1)) (= V_C (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 V_P V_r T_a)))) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (forall ((V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Relation_ORange V_A T_b T_a) _let_1) (tptp.c_Relation_ORange V_B T_b T_a)) (tptp.c_Relation_ORange (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_bool)) V_B) T_b T_a) _let_1))) (forall ((V_A $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) V_B) _let_1) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_A) V_B _let_1))))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_A) _let_1) V_B) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A _let_1) V_B)) (not (tptp.hBOOL (tptp.c_in V_x V_B T_a)))))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_COMBK V_C (tptp.tc_fun T_a tptp.tc_bool) T_b))) (or (tptp.c_lessequals (tptp.c_Product__Type_OSigma V_A _let_1 T_b T_a) (tptp.c_Product__Type_OSigma V_B _let_1 T_b T_a) (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_x V_C T_a)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_COMBK V_C (tptp.tc_fun T_a tptp.tc_bool) T_b))) (or (tptp.c_lessequals V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals (tptp.c_Product__Type_OSigma V_A _let_1 T_b T_a) (tptp.c_Product__Type_OSigma V_B _let_1 T_b T_a) (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_x V_C T_a)))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Set_Oinsert V_x T_a))) (or (tptp.c_lessequals V_A (tptp.hAPP _let_2 V_B) _let_1) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A _let_1) (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) V_B _let_1)))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Set_Oinsert V_x T_a))) (or (tptp.c_lessequals V_A (tptp.hAPP _let_2 V_B) _let_1) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A _let_1) (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) V_B _let_1)))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Set_Oinsert V_x T_a))) (or (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A _let_1) (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) V_B _let_1) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_lessequals V_A (tptp.hAPP _let_2 V_B) _let_1)))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1) V_B) (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A _let_1) V_B) V_A)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_f (tptp.tc_fun tptp.t_a T_b)) V_g) tptp.v_x) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP V_f tptp.v_x) T_b) (tptp.hAPP V_g tptp.v_x))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Relation_ODomain V_A T_a T_b) _let_1) (tptp.c_Relation_ODomain V_B T_a T_b)) (tptp.c_Relation_ODomain (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)) V_B) T_a T_b) _let_1))) (forall ((V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B _let_1) V_C) _let_1) V_A) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B _let_1) V_A) _let_1) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C _let_1) V_A))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B _let_1) V_C)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP _let_2 V_B) _let_1) (tptp.hAPP _let_2 V_C)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a))) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y T_a) V_z)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP _let_1 V_y) T_a) (tptp.hAPP _let_1 V_z)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y T_a) V_z) T_a) V_x) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) V_x) T_a) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_z T_a) V_x))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals (tptp.c_Relation_OId__on V_A T_a) (tptp.c_Product__Type_OSigma V_A (tptp.c_COMBK V_A (tptp.tc_fun T_a tptp.tc_bool) T_a) T_a T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (forall ((V_r $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_lessequals V_r (tptp.c_Product__Type_OSigma V_A (tptp.c_COMBK V_A (tptp.tc_fun T_a tptp.tc_bool) T_a) T_a T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_A)) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_x) V_x))) (forall ((V_r_H $$unsorted) (V_s_H $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_r $$unsorted) (V_s $$unsorted)) (or (tptp.c_lessequals (tptp.c_Relation_Orel__comp V_r_H V_s_H T_a T_b T_c) (tptp.c_Relation_Orel__comp V_r V_s T_a T_b T_c) (tptp.tc_fun (tptp.tc_prod T_a T_c) tptp.tc_bool)) (not (tptp.c_lessequals V_s_H V_s (tptp.tc_fun (tptp.tc_prod T_b T_c) tptp.tc_bool))) (not (tptp.c_lessequals V_r_H V_r (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool))))) (forall ((V_R $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_S $$unsorted) (V_A $$unsorted)) (= (tptp.hAPP (tptp.c_Relation_OImage (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_bool)) V_S) T_b T_a) V_A) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Relation_OImage V_R T_b T_a) V_A) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Relation_OImage V_S T_b T_a) V_A)))) (forall ((V_R $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Relation_OImage V_R T_b T_a))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_b tptp.tc_bool)) V_B)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP _let_1 V_A) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP _let_1 V_B))))) (forall ((V_P $$unsorted) (V_Rb $$unsorted) (V_R $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_Rb)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Osko__Recdef__Xtfl__wf__induct__1__1 V_P V_R T_a)))) (not (tptp.c_Wellfounded_Owf V_R T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert V_x T_a))) (let ((_let_2 (tptp.c_Set_Oinsert V_y T_a))) (= (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_A)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_A)))))) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBB V_P V_Q T_b T_a T_c) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))) (forall ((V_P $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_Q $$unsorted)) (= (tptp.hAPP (tptp.c_COMBK V_P T_a T_b) V_Q) V_P)) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A _let_1) V_B))) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_2 _let_1) V_B) _let_2)))) (forall ((V_C $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1))) (or (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_C (tptp.c_COMBB _let_2 V_B _let_1 _let_1 T_b) T_b _let_1) (tptp.hAPP _let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_C V_B T_b _let_1))) (= V_C (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))))) (forall ((V_xa $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_Set_Oinsert V_xa T_a))) (let ((_let_3 (tptp.c_Set_Oinsert V_x T_a))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 _let_1)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 _let_1))))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_C $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (or (tptp.c_lessequals (tptp.hAPP (tptp.c_Relation_OImage V_r T_a T_b) V_C) V_B _let_1) (not (tptp.c_lessequals V_r (tptp.c_Product__Type_OSigma V_A (tptp.c_COMBK V_B _let_1 T_a) T_a T_b) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)))))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_xa T_a) V_y) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_x T_a) V_x))) (= V_xa V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_x T_a) V_x) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_x_H T_a) V_y_H))) (= V_x_H V_y_H))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oimage V_f V_A T_b T_a) _let_1) (tptp.c_Set_Oimage V_f V_B T_b T_a)) (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_b tptp.tc_bool)) V_B) T_b T_a) _let_1))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_1))) (let ((_let_3 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_C)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_C))))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_1))) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP _let_2 V_B) _let_1) V_C) (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B _let_1) V_C)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP _let_1 V_y) T_a) V_z) (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y T_a) V_z)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_z)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_z))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_z)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_z))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP _let_1 V_y) T_a) V_z) (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y T_a) V_z)))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1) V_B) V_A) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1) V_B) V_B) (not (tptp.c_lessequals V_B V_A _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y) V_x) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (not (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y) V_x)) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y) V_y) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_1) V_B) V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((V_B $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals V_B (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_1) V_B) _let_1))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_1) V_B) _let_1))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_1) V_B) V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a T_a) V_b) V_x T_a) (not (tptp.c_lessequals V_b V_x T_a)) (not (tptp.c_lessequals V_a V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_y (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y T_a) V_z) V_x T_a) (not (tptp.c_lessequals V_z V_x T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_z T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals V_y (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals V_x (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) T_a))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1) V_B) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B _let_1) V_A)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1 T_a) V_x) _let_1)))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_2 _let_1) V_B) _let_2)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1) _let_2) _let_2)))) (forall ((V_B $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_B (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_B) (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_b tptp.tc_bool)) V_B) T_b T_a) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oimage V_f V_A T_b T_a) _let_1) (tptp.c_Set_Oimage V_f V_B T_b T_a)) _let_1))) (forall ((V_R $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Relation_OImage V_R T_b T_a))) (tptp.c_lessequals (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_b tptp.tc_bool)) V_B)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP _let_2 V_A) _let_1) (tptp.hAPP _let_2 V_B)) _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1))) (or (not (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP _let_2 V_B) _let_1) V_C) (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B _let_1) V_C)))) (tptp.c_lessequals V_C V_A _let_1))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1))) (or (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP _let_2 V_B) _let_1) V_C) (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B _let_1) V_C))) (not (tptp.c_lessequals V_C V_A _let_1)))))) (forall ((V_I $$unsorted) (T_a $$unsorted) (V_J $$unsorted) (V_C $$unsorted) (T_b $$unsorted)) (= (tptp.c_Product__Type_OSigma (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_I (tptp.tc_fun T_a tptp.tc_bool)) V_J) V_C T_a T_b) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Product__Type_OSigma V_I V_C T_a T_b) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)) (tptp.c_Product__Type_OSigma V_J V_C T_a T_b)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)) V_A))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A _let_1) V_A) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_A $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_c tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Relation_Orel__comp V_r V_s T_a T_b T_c) (tptp.c_Product__Type_OSigma V_A (tptp.c_COMBK V_C _let_1 T_a) T_a T_c) (tptp.tc_fun (tptp.tc_prod T_a T_c) tptp.tc_bool)) (not (tptp.c_lessequals V_s (tptp.c_Product__Type_OSigma V_B (tptp.c_COMBK V_C _let_1 T_b) T_b T_c) (tptp.tc_fun (tptp.tc_prod T_b T_c) tptp.tc_bool))) (not (tptp.c_lessequals V_r (tptp.c_Product__Type_OSigma V_A (tptp.c_COMBK V_B (tptp.tc_fun T_b tptp.tc_bool) T_a) T_a T_b) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)))))) (forall ((V_R $$unsorted) (T_a $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (or (tptp.c_Wellfounded_Owf (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R _let_1) V_S) T_a) (not (tptp.c_lessequals (tptp.c_Relation_Orel__comp V_R V_S T_a T_a T_a) V_R _let_1)) (not (tptp.c_Wellfounded_Owf V_S T_a)) (not (tptp.c_Wellfounded_Owf V_R T_a))))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_x))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_r $$unsorted) (V_s $$unsorted)) (or (tptp.c_Relation_Orefl__on (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) V_s) T_a) (not (tptp.c_Relation_Orefl__on V_B V_s T_a)) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP _let_1 V_y) T_a) V_z) (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) V_z)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_z)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_z))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_z)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_z))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP _let_1 V_y) T_a) V_z) (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) V_z)))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1))) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP _let_2 V_B) _let_1) V_C) (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B _let_1) V_C)))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1))) (let ((_let_3 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_C)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_C))))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) (tptp.c_Orderings_Obot__class_Obot T_a)) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot T_a) T_a) V_x) V_x))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot _let_1) _let_1) V_B) V_B))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)) V_A))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_2 _let_1) V_A) _let_2)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_b $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_A))) (let ((_let_3 (tptp.tc_prod T_a T_b))) (let ((_let_4 (tptp.c_COMBK (tptp.hAPP (tptp.c_Set_Oinsert V_b T_b) V_B) _let_1 T_a))) (= (tptp.c_Product__Type_OSigma _let_2 _let_4 T_a T_b) (tptp.hAPP (tptp.c_Set_Oinsert (tptp.c_Pair V_a V_b T_a T_b) _let_3) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Product__Type_OSigma V_A _let_4 T_a T_b) (tptp.tc_fun _let_3 tptp.tc_bool)) (tptp.c_Product__Type_OSigma _let_2 (tptp.c_COMBK V_B _let_1 T_a) T_a T_b))))))))) (forall ((V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A _let_1) V_B)) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_2 V_A) _let_1) (tptp.hAPP _let_2 V_B)))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A _let_1) V_B) _let_1) V_C) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1) V_C) _let_1) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B _let_1) V_C))))) (forall ((V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_a T_b) V_A T_b T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_c T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A _let_1) V_B) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_C _let_1) V_D) _let_1) (not (tptp.c_lessequals V_D V_B _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) V_z)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP _let_1 V_y) T_a) (tptp.hAPP _let_1 V_z)) T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1) V_C) _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B _let_1) V_C)) (tptp.hAPP _let_2 V_B))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y)) V_x))) (forall ((V_P $$unsorted) (V_xb $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_xb)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 V_P V_r T_a)))) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Oacyclic V_r T_a) (not (tptp.c_Wellfounded_Oacyclic (tptp.c_Relation_Oconverse V_r T_a T_a) T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Oacyclic (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) (not (tptp.c_Wellfounded_Oacyclic V_r T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y)) V_x))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A _let_1) V_B) _let_1) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1) V_B)) V_A))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) V_x) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (not (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) V_y)) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) V_y) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_1) V_B) V_B) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_1) V_B) V_A) (not (tptp.c_lessequals V_B V_A _let_1))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_1) V_B) V_B)) (tptp.c_lessequals V_A V_B _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_1))) (= (tptp.hAPP _let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_C V_B T_b _let_1)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_C (tptp.c_COMBB _let_2 V_B _let_1 _let_1 T_b) T_b _let_1))))) (forall ((V_C $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_1))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_C (tptp.c_COMBB _let_2 V_B _let_1 _let_1 T_b) T_b _let_1) (tptp.hAPP _let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_C V_B T_b _let_1)))))) (forall ((V_B $$unsorted) (T_a $$unsorted) (V_I $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B _let_1))) (= (tptp.hAPP _let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_I V_A T_b _let_1)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_I (tptp.c_COMBB _let_2 V_A _let_1 _let_1 T_b) T_b _let_1))))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) _let_1)) (tptp.hAPP (tptp.c_Set_Oinsert V_c T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_d T_a) _let_1)))) (= V_a V_d) (= V_a V_c)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) _let_1)) (tptp.hAPP (tptp.c_Set_Oinsert V_c T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_d T_a) _let_1)))) (= V_b V_c) (= V_a V_c)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) _let_1)) (tptp.hAPP (tptp.c_Set_Oinsert V_c T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_d T_a) _let_1)))) (= V_a V_d) (= V_b V_d)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) _let_1)) (tptp.hAPP (tptp.c_Set_Oinsert V_c T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_d T_a) _let_1)))) (= V_b V_c) (= V_b V_d)))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (let ((_let_2 (tptp.c_Product__Type_OSigma V_A (tptp.c_COMBK V_A (tptp.tc_fun T_a tptp.tc_bool) T_a) T_a T_a))) (or (tptp.c_lessequals (tptp.c_Transitive__Closure_Otrancl V_r T_a) _let_2 _let_1) (not (tptp.c_lessequals V_r _let_2 _let_1)))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_s $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (let ((_let_2 (tptp.c_Transitive__Closure_Ortrancl V_s T_a))) (or (tptp.c_lessequals (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_2 _let_1) (not (tptp.c_lessequals V_r _let_2 _let_1)))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (= V_A _let_2) (not (tptp.c_lessequals V_A _let_2 _let_1)))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.c_lessequals _let_2 _let_2 _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_A)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Set_Oinsert V_a T_a))) (or (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP _let_2 V_B) _let_1) V_C) (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B _let_1) V_C))) (not (tptp.hBOOL (tptp.c_in V_a V_C T_a))))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_Set_Oinsert V_a T_a))) (or (= (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_B))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.c_Set_Oinsert V_a T_b) V_B) T_b T_a) (tptp.hAPP (tptp.c_Set_Oinsert (tptp.hAPP V_f V_a) T_a) (tptp.c_Set_Oimage V_f V_B T_b T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_1) V_B) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C _let_1) V_D) _let_1) (not (tptp.c_lessequals V_B V_D _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_s $$unsorted)) (= (tptp.c_Relation_Oconverse (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_bool)) V_s) T_b T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_Oconverse V_r T_b T_a) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)) (tptp.c_Relation_Oconverse V_s T_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y) V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y) V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) V_z) T_a) (not (tptp.c_lessequals V_x V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) V_z) T_a) (not (tptp.c_lessequals V_x V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a T_a) V_b) T_a) (not (tptp.c_lessequals V_x V_b T_a)) (not (tptp.c_lessequals V_x V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y) V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y) V_x T_a))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1) V_B) V_A _let_1))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1) V_B) V_B _let_1))) (forall ((V_C $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1) V_B) _let_1) (not (tptp.c_lessequals V_C V_B _let_1)) (not (tptp.c_lessequals V_C V_A _let_1))))) (forall ((V_C $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1) V_B) _let_1) (not (tptp.c_lessequals V_C V_B _let_1)) (not (tptp.c_lessequals V_C V_A _let_1))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_COMBK V_C (tptp.tc_fun T_b tptp.tc_bool) T_a))) (= (tptp.c_Product__Type_OSigma (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) _let_1 T_a T_b) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Product__Type_OSigma V_A _let_1 T_a T_b) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)) (tptp.c_Product__Type_OSigma V_B _let_1 T_a T_b))))) (forall ((V_C $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Set_Oinsert V_a T_a))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_C (tptp.c_COMBB _let_2 V_B _let_1 _let_1 T_b) T_b _let_1) (tptp.hAPP _let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_C V_B T_b _let_1)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) V_z) T_a) V_x) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y T_a) V_x) T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_z T_a) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a))) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) V_z)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP _let_1 V_y) T_a) (tptp.hAPP _let_1 V_z)))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B _let_1) V_C)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP _let_2 V_B) _let_1) (tptp.hAPP _let_2 V_C)))))) (forall ((V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B _let_1) V_C) _let_1) V_A) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B _let_1) V_A) _let_1) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C _let_1) V_A))))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_A) V_x))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_A) V_B _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.hBOOL (tptp.c_in V_x V_B T_a)))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (V_A $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Set_Oimage V_g V_A T_c T_b) T_b T_a) (tptp.c_Set_Oimage (tptp.c_COMBB V_f V_g T_b T_a T_c) V_A T_c T_a))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_COMBK V_C (tptp.tc_fun T_b tptp.tc_bool) T_a))) (= (tptp.c_Product__Type_OSigma (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) _let_1 T_a T_b) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Product__Type_OSigma V_A _let_1 T_a T_b) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)) (tptp.c_Product__Type_OSigma V_B _let_1 T_a T_b))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP _let_1 V_B))) (= (tptp.hAPP _let_1 _let_2) _let_2)))) (forall ((V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (= (tptp.c_Relation_ORange (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_bool)) V_B) T_b T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_ORange V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Relation_ORange V_B T_b T_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Set_Oinsert V_a T_a))) (or (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A _let_1) (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))) V_A) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_x) V_x))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_A)) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_y V_z T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a T_a) V_b) T_a) (not (tptp.c_lessequals V_x V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) V_x)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Oacyclic V_r T_a) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_1) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_B _let_1) V_A)) V_B) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP _let_1 V_y) T_a) (tptp.hAPP _let_1 V_z)) (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y T_a) V_z)) T_a)))) (forall ((V_S $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (let ((_let_2 (tptp.c_Transitive__Closure_Ortrancl V_R T_a))) (or (= (tptp.c_Transitive__Closure_Ortrancl V_S T_a) _let_2) (not (tptp.c_lessequals V_S _let_2 _let_1)) (not (tptp.c_lessequals V_R V_S _let_1)))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A _let_1) V_B) V_A _let_1))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert V_a T_a))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A _let_2) (tptp.hAPP _let_1 (tptp.c_Orderings_Obot__class_Obot _let_2)))) (tptp.hAPP _let_1 V_A))))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) _let_1) (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) _let_1))) (= V_a V_b)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1) V_B) _let_1) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B _let_1) V_C)) _let_1) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C _let_1) V_A)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_1) V_B) _let_1) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B _let_1) V_C)) _let_1) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C _let_1) V_A))))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_A) V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_I $$unsorted) (T_a $$unsorted) (V_J $$unsorted) (V_C $$unsorted) (T_b $$unsorted)) (= (tptp.c_Product__Type_OSigma (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_I (tptp.tc_fun T_a tptp.tc_bool)) V_J) V_C T_a T_b) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Product__Type_OSigma V_I V_C T_a T_b) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)) (tptp.c_Product__Type_OSigma V_J V_C T_a T_b)))) (forall ((V_y $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert V_y T_a) V_A) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_B) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_B) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_B) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_B) _let_1)) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)))) (or (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_B)) (tptp.hAPP _let_1 V_B)) (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_B) _let_1) V_C) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B _let_1) V_C)) (tptp.hBOOL (tptp.c_in V_a V_C T_a))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_1) V_B) _let_2)) (= V_B _let_2))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_1) V_B) _let_2)) (= V_A _let_2))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A T_a) V_B) _let_1)) (= V_A _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A T_a) V_B) _let_1)) (= V_B _let_1)))) (forall ((V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_B _let_1) V_A) _let_1) V_A) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B _let_1) V_A)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_B _let_1) V_A)) (tptp.hAPP _let_2 V_B))))) (forall ((V_S $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_T $$unsorted) (V_R $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_Orel__comp (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_S (tptp.tc_fun (tptp.tc_prod T_a T_c) tptp.tc_bool)) V_T) V_R T_a T_c T_b) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_Orel__comp V_S V_R T_a T_c T_b) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)) (tptp.c_Relation_Orel__comp V_T V_R T_a T_c T_b)))) (forall ((V_R $$unsorted) (V_S $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (V_T $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Orel__comp V_R (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_S (tptp.tc_fun (tptp.tc_prod T_c T_b) tptp.tc_bool)) V_T) T_a T_c T_b) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_Orel__comp V_R V_S T_a T_c T_b) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)) (tptp.c_Relation_Orel__comp V_R V_T T_a T_c T_b)))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (not (tptp.class_HOL_Ominus T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun tptp.t_a T_b)) V_B) tptp.v_x) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP V_A tptp.v_x) T_b) (tptp.hAPP V_B tptp.v_x))))) (forall ((V_C $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C V_B _let_1) (not (tptp.c_lessequals V_C (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1) V_B) _let_1))))) (forall ((V_C $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C V_A _let_1) (not (tptp.c_lessequals V_C (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1) V_B) _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_a T_a) (not (tptp.c_lessequals V_x (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a T_a) V_b) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_b T_a) (not (tptp.c_lessequals V_x (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a T_a) V_b) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a T_a) V_b) V_x T_a) (not (tptp.c_lessequals V_a V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a T_a) V_b) V_x T_a) (not (tptp.c_lessequals V_b V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_lessequals V_x (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) V_z) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_x (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) V_z) T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_1) V_B) _let_1) V_C) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A _let_1) V_C) _let_1) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_B _let_1) V_C))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_1) V_B) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B _let_1) V_A)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y T_a) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y T_a) V_x)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)) V_B) T_a T_b) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_ODomain V_A T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Relation_ODomain V_B T_a T_b)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Set_Oinsert V_a T_a))) (= (tptp.hAPP _let_2 V_A) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)) _let_1) V_A))))) (forall ((V_R2 $$unsorted) (T_a $$unsorted) (V_R1 $$unsorted)) (or (tptp.c_lessequals (tptp.c_Wellfounded_Oacc V_R2 T_a) (tptp.c_Wellfounded_Oacc V_R1 T_a) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_R1 V_R2 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP _let_1 V_B))) (= (tptp.hAPP _let_1 _let_2) _let_2)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_B _let_1) V_A)) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a T_a) V_b)))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 V_P V_r T_a)))) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (forall ((V_R $$unsorted) (T_a $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (= (tptp.c_Transitive__Closure_Ortrancl (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Transitive__Closure_Ortrancl V_R T_a) _let_1) (tptp.c_Transitive__Closure_Ortrancl V_S T_a)) T_a) (tptp.c_Transitive__Closure_Ortrancl (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R _let_1) V_S) T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Set_Oinsert V_x T_a))) (or (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_2 V_A) _let_1) V_B) (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A _let_1) V_B))) (tptp.hBOOL (tptp.c_in V_x V_B T_a)))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Set_Oinsert V_x T_a))) (or (tptp.c_lessequals V_A (tptp.hAPP _let_2 V_B) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A _let_1) (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) V_B _let_1)))))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_x))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_x))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Relation_ORange (tptp.hAPP (tptp.c_Set_Oinsert (tptp.c_Pair V_a V_b T_b T_a) (tptp.tc_prod T_b T_a)) V_r) T_b T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) (tptp.c_Relation_ORange V_r T_b T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Set_Oinsert V_x T_a))) (or (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_2 V_A) _let_1) (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) V_A) (tptp.hBOOL (tptp.c_in V_x V_A T_a)))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A _let_1) V_B) V_C _let_1) (not (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B _let_1) V_C) _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B _let_1) V_C) _let_1) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A _let_1) V_B) V_C _let_1))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_List_Osko__Recdef__Xcuts__eq__1__1 V_f V_g V_r V_x T_a T_b))) (or (not (= (tptp.hAPP V_f _let_1) (tptp.hAPP V_g _let_1))) (= (tptp.c_Recdef_Ocut V_f V_r V_x T_a T_b) (tptp.c_Recdef_Ocut V_g V_r V_x T_a T_b))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_Wellfounded_Oacyclic V_r T_a) (not (tptp.c_Wellfounded_Oacyclic (tptp.hAPP (tptp.c_Set_Oinsert (tptp.c_Pair V_y V_x T_a T_a) (tptp.tc_prod T_a T_a)) V_r) T_a)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_g $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_HOL_Oord T_b)) (tptp.c_lessequals (tptp.hAPP V_f V_x) (tptp.hAPP V_g V_x) T_b) (not (tptp.c_lessequals V_f V_g (tptp.tc_fun T_a T_b))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) V_A) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) V_B) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_B T_a))))) (forall ((V_t $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_t V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_t V_A T_a))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a V_A T_a)) (= V_a V_b) (not (tptp.hBOOL (tptp.c_in V_a (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) V_A) T_a))))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (tptp.hBOOL (tptp.c_in V_c V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) T_a))))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) T_a))))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_A) T_a))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (tptp.hBOOL (tptp.c_in V_a (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_B) T_a))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_B) T_a))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) T_a)) (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) T_a)) (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert V_x T_a))) (or (not (= (tptp.hAPP _let_1 V_A) (tptp.hAPP _let_1 V_B))) (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (= V_A V_B)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (= (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_A) V_A) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Otop T_a)) (tptp.c_lessequals V_x (tptp.c_Orderings_Otop__class_Otop T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Orderings_Otop__class_Otop T_a) T_a) V_x) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) (tptp.c_Orderings_Otop__class_Otop T_a)) V_x))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A T_a) V_B) _let_1)) (= V_A _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A T_a) V_B) _let_1)) (= V_B _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1 T_a) V_x) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) _let_1) _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals V_A (tptp.c_Orderings_Otop__class_Otop _let_1) _let_1))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1) (tptp.c_Orderings_Otop__class_Otop _let_1)) V_A))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Orderings_Otop__class_Otop _let_1) _let_1) V_B) V_B))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_1) _let_2) _let_2)))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2 _let_1) V_B) _let_2)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in V_a V_A T_a)) (= V_a V_b) (not (tptp.c_lessequals V_r (tptp.c_Product__Type_OSigma V_A (tptp.c_COMBK V_A (tptp.tc_fun T_a tptp.tc_bool) T_a) T_a T_a) (tptp.tc_fun _let_1 tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1)))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.c_Relation_OImage V_r T_a T_a))) (or (tptp.c_lessequals (tptp.hAPP _let_3 (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) _let_2)) (tptp.hAPP _let_3 (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) _let_2)) _let_1) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a))))))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)) T_a)) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 V_a V_b V_r T_a) V_b T_a T_a) V_r _let_1)) (= V_a V_b) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a T_a) V_b) T_a) (not (tptp.c_lessequals V_x V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_b V_x T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a T_a) V_b) V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_a V_x T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a T_a) V_b) V_x T_a)))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_C _let_1) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_1) V_B) V_C _let_1))))) (forall ((V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_B V_C _let_1) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_1) V_B) V_C _let_1))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_f (tptp.tc_fun tptp.t_a T_b)) V_g) tptp.v_x) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP V_f tptp.v_x) T_b) (tptp.hAPP V_g tptp.v_x))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_x V_x (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_A V_A (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_Q $$unsorted) (V_x $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.c_lessequals V_P V_Q (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_p $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.c_Wellfounded_Owf V_p T_a) (not (tptp.c_lessequals V_p V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (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 ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_s $$unsorted)) (or (tptp.c_Relation_Oantisym V_r T_a) (not (tptp.c_Relation_Oantisym V_s T_a)) (not (tptp.c_lessequals V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))))) (forall ((V_Q $$unsorted) (V_x $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.c_lessequals V_P V_Q (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_s $$unsorted)) (or (tptp.c_Wellfounded_Oacyclic V_r T_a) (not (tptp.c_lessequals V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (not (tptp.c_Wellfounded_Oacyclic V_s T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_s $$unsorted)) (or (tptp.c_Relation_Osingle__valued V_r T_a T_b) (not (tptp.c_Relation_Osingle__valued V_s T_a T_b)) (not (tptp.c_lessequals V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1) V_B) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C _let_1) V_D) _let_1) (not (tptp.c_lessequals V_B V_D _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus V_A _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B _let_1) V_C)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP _let_2 V_B) _let_1) (tptp.hAPP _let_2 V_C)))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1))) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_2 V_B) _let_1) V_C) (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_B _let_1) V_C)))))) (forall ((V_A $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (V_M $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_b tptp.tc_bool)) V_B) V_M T_b _let_1) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_M T_b _let_1) _let_1) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_B V_M T_b _let_1))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_s $$unsorted)) (or (tptp.c_lessequals (tptp.c_Relation_ODomain V_r T_a T_b) (tptp.c_Relation_ODomain V_s T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) _let_2))) (or (= V_A _let_3) (= V_A _let_2) (not (tptp.c_lessequals V_A _let_3 _let_1))))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus V_A _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B _let_1) V_C)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP _let_2 V_B) _let_1) (tptp.hAPP _let_2 V_C)))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_B _let_1) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_C _let_1) V_A)) V_A) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_x T_a) V_y) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_x_H T_a) V_y_H))) (tptp.c_lessequals V_y_H V_x_H T_a) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_x T_a) V_y) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_x_H T_a) V_y_H))) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_y_H V_x_H T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_lessequals V_x V_A (tptp.tc_fun T_b tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_x T_b T_a) (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Set_Oinsert V_a T_a))) (or (tptp.c_lessequals (tptp.hAPP _let_2 V_C) (tptp.hAPP _let_2 V_D) _let_1) (not (tptp.c_lessequals V_C V_D _let_1)))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2 _let_1) _let_2) _let_2)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_b tptp.tc_bool)) V_B) T_b T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_B T_b T_a)))) (forall ((V_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.hAPP (tptp.c_Set_Oinsert V_a T_b) V_A) V_B T_b _let_1) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP V_B V_a) _let_1) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_b _let_1))))) (forall ((V_r_H $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A_H $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (or (tptp.c_lessequals (tptp.hAPP (tptp.c_Relation_OImage V_r_H T_a T_b) V_A_H) (tptp.hAPP (tptp.c_Relation_OImage V_r T_a T_b) V_A) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_A_H V_A (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_r_H V_r (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool))))) (forall ((V_r $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_lessequals V_r (tptp.c_Product__Type_OSigma V_A (tptp.c_COMBK V_A (tptp.tc_fun T_a tptp.tc_bool) T_a) T_a T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((V_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (= (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_b T_a) V_A T_a T_b) (tptp.hAPP (tptp.c_Set_Oinsert V_c T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.c_Wellfounded_Oacyclic (tptp.hAPP (tptp.c_Set_Oinsert (tptp.c_Pair V_y V_x T_a T_a) _let_1) V_r) T_a) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1)) (not (tptp.c_Wellfounded_Oacyclic V_r T_a))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1))) (not (tptp.c_Wellfounded_Oacyclic (tptp.hAPP (tptp.c_Set_Oinsert (tptp.c_Pair V_y V_x T_a T_a) _let_1) V_r) T_a))))) (forall ((T_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_COMBB (tptp.c_HOL_Ominus__class_Ominus V_A _let_1) V_B _let_1 _let_1 T_b) T_b _let_1) (tptp.c_Orderings_Otop__class_Otop _let_1)))) (forall ((T_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_COMBB (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1) V_B _let_1 _let_1 T_b) T_b _let_1) (tptp.c_Orderings_Otop__class_Otop _let_1)))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_xa $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_xa) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hBOOL (tptp.c_in V_x V_xa T_a)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (= V_b V_a) (not (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) T_a))))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.hBOOL (tptp.c_in V_x V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1) V_B) (tptp.c_Orderings_Obot__class_Obot _let_1)))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) T_a))) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f V_A T_a T_b))) (or (= (tptp.hAPP (tptp.c_Set_Oinsert (tptp.hAPP V_f V_x) T_b) _let_1) _let_1) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a)))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))) (not (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_b T_a) V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (tptp.c_lessequals V_x (tptp.c_Complete__Lattice_OSup__class_OSup V_A T_a) T_a) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_M $$unsorted) (T_a $$unsorted) (V_i $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_b)) (tptp.c_lessequals (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_M T_a T_b) (tptp.hAPP V_M V_i) T_b) (not (tptp.hBOOL (tptp.c_in V_i V_A T_a))))) (forall ((V_Q $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_xa $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 V_Q V_r T_a) V_Q T_a)) (not (tptp.hBOOL (tptp.c_in V_xa V_Q T_a))) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (forall ((V_Q $$unsorted) (V_R $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 V_Q V_R T_a) V_Q T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_Q T_a))) (not (tptp.c_Wellfounded_Owf V_R T_a)))) (forall ((V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_B $$unsorted) (V_A $$unsorted) (V_i $$unsorted) (T_a $$unsorted) (V_I $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_B (tptp.hAPP V_A V_i) _let_1) (not (tptp.hBOOL (tptp.c_in V_i V_I T_b))) (not (tptp.c_lessequals V_B (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_I V_A T_b _let_1) _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_a _let_1) (tptp.hAPP V_B V_a) _let_1) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a)))))) (forall ((V_A $$unsorted) (V_k $$unsorted) (T_b $$unsorted) (V_I $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_I V_A T_a _let_1))) (or (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP V_A V_k) _let_1) _let_2) _let_2) (not (tptp.hBOOL (tptp.c_in V_k V_I T_a))))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A _let_1) (tptp.c_Orderings_Otop__class_Otop _let_1)) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_COMBK V_C (tptp.tc_fun T_a tptp.tc_bool) T_b))) (or (not (= (tptp.c_Product__Type_OSigma V_A _let_1 T_b T_a) (tptp.c_Product__Type_OSigma V_B _let_1 T_b T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_C T_a))) (= V_A V_B)))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_Wellfounded_Owf V_r T_a) (not (tptp.c_Wellfounded_Owf (tptp.hAPP (tptp.c_Set_Oinsert (tptp.c_Pair V_y V_x T_a T_a) (tptp.tc_prod T_a T_a)) V_r) T_a)))) (forall ((V_A $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Relation__XImageE__1__1 V_A V_b V_r T_b T_a) V_A T_b)) (not (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP (tptp.c_Relation_OImage V_r T_b T_a) V_A) T_a))))) (forall ((V_A $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 V_A V_b V_r T_b T_a) V_A T_b)) (not (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP (tptp.c_Relation_OImage V_r T_b T_a) V_A) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) T_a) V_a))) (forall ((V_x $$unsorted) (V_R $$unsorted) (T_a $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in V_x (tptp.c_Transitive__Closure_Ortrancl (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R (tptp.tc_fun _let_1 tptp.tc_bool)) V_S) T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Transitive__Closure_Ortrancl V_R T_a) _let_1)))))) (forall ((V_x $$unsorted) (V_R $$unsorted) (T_a $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in V_x (tptp.c_Transitive__Closure_Ortrancl (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R (tptp.tc_fun _let_1 tptp.tc_bool)) V_S) T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Transitive__Closure_Ortrancl V_S T_a) _let_1)))))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_M $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_b)) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A (tptp.c_COMBK V_M T_b T_a) T_a T_b) V_M) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_p $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in V_p (tptp.c_Transitive__Closure_Otrancl V_s T_a) _let_1)) (not (tptp.c_lessequals V_r V_s (tptp.tc_fun _let_1 tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_p (tptp.c_Transitive__Closure_Otrancl V_r T_a) _let_1)))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)))) (= (tptp.c_Set_Oimage (tptp.c_COMBB V_f V_g T_c T_a T_b) _let_1 T_b T_a) (tptp.c_Set_Oimage V_f (tptp.c_Set_Oimage V_g _let_1 T_b T_c) T_c T_a)))) (forall ((V_A $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A (tptp.c_COMBK V_c _let_1 T_b) T_b _let_1) V_c) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))))) (forall ((T_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_A T_b _let_1) _let_1) V_B) V_B))) (forall ((V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_1) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_B T_b _let_1)) V_A))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.c_Set_Oimage V_f V_A T_c T_b) V_B T_b _let_1) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A (tptp.c_COMBB V_B V_f T_b _let_1 T_c) T_c _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_f $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A (tptp.c_COMBB V_B V_f T_c _let_1 T_b) T_b _let_1) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.c_Set_Oimage V_f V_A T_b T_c) V_B T_c _let_1)))) (forall ((V_B $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (or (not (= (tptp.hAPP V_B (tptp.c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__1__1 V_A V_B T_b T_a)) _let_2)) (= _let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_b _let_1)))))) (forall ((V_B $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (or (not (= (tptp.hAPP V_B (tptp.c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__2__1 V_A V_B T_b T_a)) _let_2)) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_b _let_1) _let_2))))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 V_P V_r T_a)))) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Wellfounded_Oacc V_r T_a) T_a))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__Wellfounded__Xacc__Xinducts__1 V_P V_r)))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Wellfounded_Oacc V_r tptp.t_a) tptp.t_a))))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc V_r T_a))) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 V_P V_r T_a) _let_1 T_a)) (not (tptp.hBOOL (tptp.c_in V_a _let_1 T_a)))))) (forall ((V_R $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc V_R T_a))) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 V_R V_x T_a) _let_1 T_a))) (tptp.hBOOL (tptp.c_in V_x _let_1 T_a))))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 V_P V_r T_a)))) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Wellfounded_Oacc V_r T_a) T_a))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__Wellfounded__Xacc__Xinduct__1 V_P V_r)))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Wellfounded_Oacc V_r tptp.t_a) tptp.t_a))))) (forall ((V_x $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc V_r T_a))) (or (tptp.hBOOL (tptp.c_in V_x _let_1 T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 V_r V_x T_a) _let_1 T_a)))))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc V_r T_a))) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 V_P V_r T_a) _let_1 T_a)) (not (tptp.hBOOL (tptp.c_in V_a _let_1 T_a)))))) (forall ((V_R $$unsorted) (T_a $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (or (tptp.c_Wellfounded_Owf (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_Orel__comp V_R V_R T_a T_a T_a) _let_1) (tptp.c_Relation_Orel__comp V_S V_R T_a T_a T_a)) _let_1) V_S) T_a) (not (tptp.c_Wellfounded_Owf (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R _let_1) V_S) T_a))))) (forall ((V_R $$unsorted) (T_a $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (or (tptp.c_Wellfounded_Owf (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R _let_1) V_S) T_a) (not (tptp.c_Wellfounded_Owf (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_Orel__comp V_R V_R T_a T_a T_a) _let_1) (tptp.c_Relation_Orel__comp V_S V_R T_a T_a T_a)) _let_1) V_S) T_a))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_s $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Relation_ODomain V_r T_a T_a) _let_1) (tptp.c_Relation_ORange V_s T_a T_a)) (tptp.c_Orderings_Obot__class_Obot _let_1))) (not (tptp.c_Wellfounded_Owf V_s T_a)) (not (tptp.c_Wellfounded_Owf V_r T_a)) (tptp.c_Wellfounded_Owf (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) V_s) T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Otrancl V_r T_a))) (= _let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_Orel__comp _let_1 V_r T_a T_a T_a))))) (forall ((V_R $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl V_R T_a))) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)) _let_1))) (forall ((V_R $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)) T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)) T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Oantisym (tptp.c_Transitive__Closure_Ortrancl V_r T_a) T_a) (not (tptp.c_Wellfounded_Oacyclic V_r T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_lessequals (tptp.c_Relation_Orel__comp V_r V_r T_a T_a T_a) V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (not (tptp.c_Relation_Otrans V_r T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Osym (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_Oconverse V_r T_a T_a)) T_a)) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Otrans (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)) T_a) (not (tptp.c_Relation_Otrans V_r T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.c_Relation_OImage (tptp.c_Relation_OId__on V_A T_a) T_a T_a) V_B) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Oantisym V_r T_a) (not (tptp.c_Relation_Oantisym (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)) T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Oantisym (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)) T_a) (not (tptp.c_Relation_Oantisym V_r T_a)))) (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Ototal__on V_A V_r T_a) (not (tptp.c_Relation_Ototal__on V_A (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)) T_a)))) (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Ototal__on V_A (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)) T_a) (not (tptp.c_Relation_Ototal__on V_A V_r T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 V_a V_b V_r T_a) T_a T_a) _let_2 _let_1)) (= V_a V_b) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) _let_2 _let_1))))))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 V_P V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (forall ((V_P $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_xa)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 V_P V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (forall ((V_P $$unsorted) (V_Ra $$unsorted) (V_y $$unsorted) (V_R $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_Ra)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.c_List_Osko__Recdef__Xtfl__wf__induct__1__1 V_P V_R T_a) T_a T_a) V_R (tptp.tc_prod T_a T_a)))) (not (tptp.c_Wellfounded_Owf V_R T_a)))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 V_P V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 V_r T_a))) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) V_r _let_1))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair _let_2 _let_2 T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) _let_1)))))) (forall ((V_r $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a))) (let ((_let_3 (tptp.c_Pair V_x V_z T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 V_r V_x V_z T_a) V_z T_a T_a) _let_2 _let_1)) (tptp.hBOOL (tptp.c_in _let_3 V_r _let_1)) (not (tptp.hBOOL (tptp.c_in _let_3 _let_2 _let_1)))))))) (forall ((V_x $$unsorted) (V_R $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 V_R V_x V_y T_a) T_a T_a) V_R _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_R T_a) _let_1)))))) (forall ((V_a1 $$unsorted) (V_a2 $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.t_a tptp.t_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Otrancl V_r tptp.t_a))) (let ((_let_3 (tptp.c_Pair V_a1 V_a2 tptp.t_a tptp.t_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a1 (tptp.v_sko__Transitive__Closure__Xtrancl__Xcases__1 V_a1 V_a2 V_r) tptp.t_a tptp.t_a) _let_2 _let_1)) (tptp.hBOOL (tptp.c_in _let_3 V_r _let_1)) (not (tptp.hBOOL (tptp.c_in _let_3 _let_2 _let_1)))))))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_prod T_a T_a)))) (not (tptp.c_Wellfounded_Oacyclic V_r T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Pair V_a V_b T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 V_a V_b V_r T_a) V_b T_a T_a) V_r _let_1)) (tptp.hBOOL (tptp.c_in _let_2 V_r _let_1)) (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a) _let_1))))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a))) (let ((_let_3 (tptp.c_Pair V_a V_b T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 V_a V_b V_r T_a) T_a T_a) _let_2 _let_1)) (tptp.hBOOL (tptp.c_in _let_3 V_r _let_1)) (not (tptp.hBOOL (tptp.c_in _let_3 _let_2 _let_1)))))))) (forall ((V_R $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 V_R V_x V_y T_a) V_y T_a T_a) V_R _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_R T_a) _let_1)))))) (forall ((V_x $$unsorted) (V_r $$unsorted) (V_z $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Pair V_x V_z T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 V_r V_x V_z T_a) T_a T_a) V_r _let_1)) (tptp.hBOOL (tptp.c_in _let_2 V_r _let_1)) (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a) _let_1))))))) (forall ((V_a1 $$unsorted) (V_a2 $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.t_a tptp.t_a))) (let ((_let_2 (tptp.c_Pair V_a1 V_a2 tptp.t_a tptp.t_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.v_sko__Transitive__Closure__Xtrancl__Xcases__1 V_a1 V_a2 V_r) V_a2 tptp.t_a tptp.t_a) V_r _let_1)) (tptp.hBOOL (tptp.c_in _let_2 V_r _let_1)) (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Otrancl V_r tptp.t_a) _let_1))))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.c_Relation_OImage V_r T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in V_b V_A T_a))) (not (tptp.c_lessequals (tptp.hAPP _let_3 (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) _let_2)) (tptp.hAPP _let_3 (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) _let_2)) _let_1)) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a))))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.c_Relation_OImage V_r T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP _let_3 (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) _let_2)) _let_1) (tptp.hAPP _let_3 (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) _let_2))) T_a))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Orderings_Otop__class_Otop _let_1) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_b _let_1)) (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__1__1 V_A V_B T_b T_a) V_A T_b))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_b _let_1) (tptp.c_Orderings_Otop__class_Otop _let_1)) (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__2__1 V_A V_B T_b T_a) V_A T_b))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 V_a V_c V_r V_s T_a T_b T_c) V_c T_c T_b) V_s (tptp.tc_prod T_c T_b))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_b) (tptp.c_Relation_Orel__comp V_r V_s T_a T_c T_b) (tptp.tc_prod T_a T_b)))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a (tptp.c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 V_a V_c V_r V_s T_a T_b T_c) T_a T_c) V_r (tptp.tc_prod T_a T_c))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_b) (tptp.c_Relation_Orel__comp V_r V_s T_a T_c T_b) (tptp.tc_prod T_a T_b)))))) (forall ((T_b $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_COMBK V_c _let_1 T_b) T_b _let_1) (tptp.c_Orderings_Otop__class_Otop _let_1)))) (forall ((T_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_A T_b _let_1) _let_1) V_B) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Orderings_Otop__class_Otop _let_1) _let_1) V_B)))) (forall ((V_p $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_ATP__Linkup_Osko__Relation__XIdE__1__1 V_p T_a))) (or (= V_p (tptp.c_Pair _let_1 _let_1 T_a T_a)) (not (tptp.hBOOL (tptp.c_in V_p (tptp.c_Relation_OId T_a) (tptp.tc_prod T_a T_a))))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A (tptp.c_Orderings_Obot__class_Obot _let_1)) (not (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_Relation_OImage V_R T_a T_a) V_A) _let_1)) (not (tptp.c_Wellfounded_Owf V_R T_a))))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Owf V_r T_a) (not (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 V_r T_a) (tptp.c_Wellfounded_Oacc V_r T_a) T_a))))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Owf V_r T_a) (not (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 V_r T_a) (tptp.c_Wellfounded_Oacc V_r T_a) T_a))))) (forall ((V_A $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Relation__XId__onE__1__1 V_A V_c T_a) V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Relation_OId__on V_A T_a) (tptp.tc_prod T_a T_a)))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_ATP__Linkup_Osko__Relation__XId__onE__1__1 V_A V_c T_a))) (or (= V_c (tptp.c_Pair _let_1 _let_1 T_a T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Relation_OId__on V_A T_a) (tptp.tc_prod T_a T_a))))))) (forall ((V_f $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_g $$unsorted)) (or (= (tptp.c_Recdef_Ocut V_f V_r V_x T_a T_b) (tptp.c_Recdef_Ocut V_g V_r V_x T_a T_b)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_List_Osko__Recdef__Xcuts__eq__1__1 V_f V_g V_r V_x T_a T_b) V_x T_a T_a) V_r (tptp.tc_prod T_a T_a))))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)) T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (= _let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_OId T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_Orel__comp _let_1 V_r T_a T_a T_a))))) (forall ((T_a $$unsorted) (V_r $$unsorted)) (tptp.c_Relation_Orefl__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)) T_a)) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_lessequals V_r (tptp.c_Relation_Orel__comp (tptp.c_Relation_Oconverse V_r T_a T_a) V_r T_a T_a T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))) (= (tptp.c_Relation_ORange tptp.v_r tptp.t_a tptp.t_b) (tptp.c_Relation_ODomain (tptp.c_Relation_Oconverse tptp.v_r tptp.t_a tptp.t_b) tptp.t_b tptp.t_a)) (forall ((V_R $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Relation_OImage V_R T_b T_a))) (or (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_b tptp.tc_bool)) V_B)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP _let_1 V_A) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP _let_1 V_B))) (not (tptp.c_Relation_Osingle__valued (tptp.c_Relation_Oconverse V_R T_b T_a) T_a T_b))))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Otrans (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)) T_a) (not (tptp.c_Relation_Oantisym V_r T_a)) (not (tptp.c_Relation_Otrans V_r T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 V_r T_a))) (or (tptp.c_Nitpick_Orefl_H V_r T_a) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair _let_1 _let_1 T_a T_a) V_r (tptp.tc_prod T_a T_a))))))) (forall ((V_y $$unsorted) (V_Q $$unsorted) (T_a $$unsorted) (V_R $$unsorted) (V_x $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_y V_Q T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 V_Q V_R T_a) T_a T_a) V_R (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in V_x V_Q T_a))) (not (tptp.c_Wellfounded_Owf V_R T_a)))) (forall ((V_y $$unsorted) (V_Q $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_xa $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_y V_Q T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 V_Q V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in V_xa V_Q T_a))) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP (tptp.hAPP V_f V_a) V_b) (tptp.c_Set_Oimage (tptp.c_split V_f T_a T_b T_c) V_A _let_1 T_c) T_c)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) V_A _let_1)))))) (forall ((V_A $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XImageE__1__1 V_A V_b V_r T_b T_a) V_b T_b T_a) V_r (tptp.tc_prod T_b T_a))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP (tptp.c_Relation_OImage V_r T_b T_a) V_A) T_a))))) (forall ((V_A $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XImage__iff__1__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))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP (tptp.c_Relation_OImage V_r T_b T_a) V_A) T_a))))) (forall ((V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a (tptp.c_ATP__Linkup_Osko__Relation__XDomainE__1__1 V_a V_r T_a T_b) T_a T_b) V_r (tptp.tc_prod T_a T_b))) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Relation_ODomain V_r T_a T_b) T_a))))) (forall ((V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a (tptp.c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 V_a V_r T_a T_b) T_a T_b) V_r (tptp.tc_prod T_a T_b))) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Relation_ODomain V_r T_a T_b) T_a))))) (forall ((V_R $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 V_R V_x T_a) V_x T_a T_a) V_R (tptp.tc_prod T_a T_a))) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Wellfounded_Oacc V_R T_a) T_a)))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 V_P V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Wellfounded_Oacc V_r T_a) T_a))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.v_sko__Wellfounded__Xacc__Xinduct__1 V_P V_r) tptp.t_a tptp.t_a) V_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Wellfounded_Oacc V_r tptp.t_a) tptp.t_a))))) (forall ((V_x $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x (tptp.c_Wellfounded_Oacc V_r T_a) T_a)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 V_r V_x T_a) V_x T_a T_a) V_r (tptp.tc_prod T_a T_a))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_ya $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc V_r tptp.t_a))) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.c_in V_ya _let_1 tptp.t_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_ya (tptp.v_sko__Wellfounded__Xacc__Xinducts__1 V_P V_r) tptp.t_a tptp.t_a) V_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (tptp.hBOOL (tptp.c_in V_x _let_1 tptp.t_a)))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.v_sko__Wellfounded__Xacc__Xinducts__1 V_P V_r) tptp.t_a tptp.t_a) V_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Wellfounded_Oacc V_r tptp.t_a) tptp.t_a))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_ya $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc V_r tptp.t_a))) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.c_in V_ya _let_1 tptp.t_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_ya (tptp.v_sko__Wellfounded__Xacc__Xinduct__1 V_P V_r) tptp.t_a tptp.t_a) V_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (tptp.hBOOL (tptp.c_in V_x _let_1 tptp.t_a)))))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 V_P V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Wellfounded_Oacc V_r T_a) T_a))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (not (tptp.hBOOL (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))) (not (tptp.c_Wellfounded_Owf (tptp.hAPP (tptp.c_Set_Oinsert (tptp.c_Pair V_y V_x T_a T_a) _let_1) 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 (tptp.c_Wellfounded_Owf (tptp.hAPP (tptp.c_Set_Oinsert (tptp.c_Pair V_y V_x T_a T_a) _let_1) V_r) T_a) (tptp.hBOOL (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)) (not (tptp.c_Wellfounded_Owf V_r T_a))))) (forall ((V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XRangeE__1__1 V_b V_r T_a T_b) V_b T_b T_a) V_r (tptp.tc_prod T_b T_a))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.c_Relation_ORange V_r T_b T_a) T_a))))) (forall ((V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 V_a V_r T_a T_b) V_a T_b T_a) V_r (tptp.tc_prod T_b T_a))) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Relation_ORange V_r T_b T_a) T_a))))) (forall ((V_x $$unsorted) (V_R $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 V_R V_x V_y T_a) T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_R T_a) _let_1)))))) (forall ((V_R $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 V_R V_x V_y T_a) V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_R T_a) _let_1)))))) (forall ((V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.hAPP (tptp.c_Relation_OImage V_r T_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_lessequals (tptp.c_Relation_Orel__comp (tptp.c_Relation_Oconverse V_r T_a T_a) V_r T_a T_a T_a) V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (not (tptp.c_Relation_Otrans V_r T_a)) (not (tptp.c_Relation_Osym V_r T_a)))) (forall ((V_b $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP (tptp.c_Relation_OImage V_r T_b T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))) T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_b T_a) V_r (tptp.tc_prod T_b T_a)))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_b T_a) V_r (tptp.tc_prod T_b T_a))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP (tptp.c_Relation_OImage V_r T_b T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))) T_a))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_Relation_OImage V_r T_a T_a))) (or (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) _let_1)) (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_Set_Oinsert V_y T_a) _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_Relation_OImage V_r T_a T_a))) (or (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) _let_1)) (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Otrans V_r T_a) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XtransI__1__1 V_r T_a) (tptp.c_ATP__Linkup_Osko__Relation__XtransI__1__3 V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a)))))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Otrans V_r T_a) (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XtransI__1__2 V_r T_a) (tptp.c_ATP__Linkup_Osko__Relation__XtransI__1__3 V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a))))) (forall ((V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_c $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_3 (tptp.c_Relation_OImage V_r T_b T_a))) (or (= (tptp.hAPP _let_3 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_c _let_2)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A (tptp.c_COMBB _let_3 V_B _let_2 _let_1 T_c) T_c _let_1)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_c tptp.tc_bool))) (not (tptp.c_Relation_Osingle__valued (tptp.c_Relation_Oconverse V_r T_b T_a) T_a T_b))))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_Relation_OImage V_r T_a T_a))) (or (not (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) _let_1)) (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) _let_1)))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in V_b V_A T_a))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_Relation_OImage V_r T_a T_a))) (or (not (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) _let_1)) (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_Set_Oinsert V_y T_a) _let_1)))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in V_y V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_Relation_OImage V_r T_a T_a))) (or (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) _let_1)) (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_Set_Oinsert V_y T_a) _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in V_y V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_Relation_OImage V_r T_a T_a))) (or (not (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) _let_1)) (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_Set_Oinsert V_y T_a) _let_1)))) (not (tptp.hBOOL (tptp.c_in V_y V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a))))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Pair V_x V_y T_a T_a))) (or (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Otrancl V_R T_a) _let_1)) (= V_x V_y) (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Ortrancl V_R T_a) _let_1))))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Pair V_x V_y T_a T_a))) (or (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Ortrancl V_R T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Otrancl V_R T_a) _let_1))) (= V_x V_y))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) V_r _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1)))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r _let_1)))))) (forall ((V_p $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in V_p (tptp.c_Transitive__Closure_Otrancl V_r T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in V_p V_r _let_1)))))) (forall ((V_p $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in V_p (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in V_p V_r _let_1)))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (not (= (tptp.c_Orderings_Otop__class_Otop _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_Relation_Otrans V_r T_a) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_Relation_Otrans V_r T_a) (not (tptp.c_Order__Relation_Ostrict__linear__order__on V_A V_r T_a)))) (forall ((T_a $$unsorted)) (tptp.c_Relation_Otrans (tptp.c_Relation_OId T_a) T_a)) (forall ((V_r $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Relation_Otrans (tptp.c_Relation_Oinv__image V_r V_f T_a T_b) T_b) (not (tptp.c_Relation_Otrans V_r T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Otrans (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) (not (tptp.c_Relation_Otrans V_r T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Otrans V_r T_a) (not (tptp.c_Relation_Otrans (tptp.c_Relation_Oconverse V_r T_a T_a) T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Otrans (tptp.c_Transitive__Closure_Ortrancl V_r T_a) T_a)) (forall ((V_r $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Otrans (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a)) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Otrans (tptp.c_Relation_OId__on V_A T_a) T_a)) _let_23 (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Ototal__on V_A (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) (not (tptp.c_Relation_Ototal__on V_A V_r T_a)))) (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Ototal__on V_A V_r T_a) (not (tptp.c_Relation_Ototal__on V_A (tptp.c_Relation_Oconverse V_r T_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_r $$unsorted)) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_r T_a)) (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Ototal__on V_A V_r T_a) (not (tptp.c_Order__Relation_Ostrict__linear__order__on V_A V_r T_a)))) (forall ((V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc V_r T_a))) (or (tptp.hBOOL (tptp.c_in V_b _let_1 T_a)) (not (tptp.hBOOL (tptp.c_in V_a _let_1 T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_a T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a))))))) (forall ((V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc V_r T_a))) (or (tptp.hBOOL (tptp.c_in V_b _let_1 T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_a T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in V_a _let_1 T_a)))))) (forall ((V_x $$unsorted) (V_R $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x (tptp.c_Relation_ODomain V_R T_a T_a) T_a)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a) (tptp.tc_prod T_a T_a))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (or (= V_x V_y) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a) (tptp.tc_prod T_a T_a)))) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Relation_ODomain V_R T_a T_a) T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_Relation_Oirrefl V_r T_a) (not (tptp.c_Order__Relation_Ostrict__linear__order__on V_A V_r T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Pair V_a V_b T_a T_a))) (or (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Otrancl V_R T_a) _let_1)) (= V_a V_b) (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Ortrancl V_R T_a) _let_1))))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) _let_1)))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_z V_y T_a T_a) _let_2 _let_1)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_z T_a T_a) _let_2 _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_z T_a T_a) _let_2 _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) _let_2 _let_1))) (not (tptp.c_Relation_Osingle__valued V_r 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 (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a) _let_1))))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) _let_2 _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) _let_2 _let_1))))))) (forall ((V_x $$unsorted) (V_z $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_z T_a T_a) _let_2 _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_z T_a T_a) _let_2 _let_1))) (not (tptp.hBOOL (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) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Pair V_x V_y T_a T_a))) (or (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Relation_Oconverse (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Otrancl (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) _let_1))))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Pair V_x V_y T_a T_a))) (or (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Otrancl (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Relation_Oconverse (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a T_a) _let_1))))))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (= (tptp.hAPP (tptp.c_split V_f T_b T_c T_a) (tptp.c_Pair V_a V_b T_b T_c)) (tptp.hAPP (tptp.hAPP V_f V_a) V_b))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (= (tptp.hAPP (tptp.c_split V_f T_a T_b T_c) (tptp.c_Pair V_a V_b T_a T_b)) (tptp.hAPP (tptp.hAPP V_f V_a) V_b))) (forall ((V_R $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP V_R V_a) V_b) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_split V_R T_a T_b (tptp.tc_fun T_c tptp.tc_bool)) (tptp.c_Pair V_a V_b T_a T_b)) V_c))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_aa $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_x V_A T_aa))) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_aa T_a) T_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_b $$unsorted) (V_B $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP V_B V_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_b))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_b (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_a V_A T_b))) (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP V_B V_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_b (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_b (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_b $$unsorted) (V_B $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP V_B V_x) T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_b (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_c $$unsorted) (T_a $$unsorted)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_B $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_a) V_b)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)) V_b))))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_b $$unsorted) (T_b $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)) V_b))))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_x) V_b)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)) V_b))))) (forall ((V_x $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x (tptp.c_Wellfounded_Oacc V_r T_a) T_a)) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Osingle__valued (tptp.c_Relation_OId__on V_A T_a) T_a T_a)) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Osym (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a) (not (tptp.c_Relation_Osym V_r T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Osym V_r T_a) (not (tptp.c_Relation_Osym (tptp.c_Relation_Oconverse V_r T_a T_a) T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Osym (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) (not (tptp.c_Relation_Osym V_r T_a)))) (forall ((V_R $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.c_Transitive__Closure_Ortrancl V_R T_a) T_a T_a) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a T_a) (tptp.c_Relation_ODomain V_r T_a T_a))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a))) (forall ((T_a $$unsorted)) (tptp.c_Relation_Osym (tptp.c_Relation_OId T_a) T_a)) (forall ((V_P $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2 V_P T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((T_a $$unsorted) (V_R $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_Orel__comp (tptp.c_Relation_OId T_a) V_R T_a T_a T_b) V_R)) (forall ((V_R $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Orel__comp V_R (tptp.c_Relation_OId T_b) T_a T_b T_b) V_R)) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Oantisym (tptp.c_Relation_OId__on V_A T_a) T_a)) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Owf (tptp.c_Relation_Oconverse (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a T_a) T_a) (not (tptp.c_Wellfounded_Owf (tptp.c_Relation_Oconverse V_r T_a T_a) T_a)))) (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Orefl__on V_A V_r T_a) (not (tptp.c_Relation_Orefl__on V_A (tptp.c_Relation_Oconverse V_r T_a T_a) T_a)))) (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Orefl__on V_A (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Osym (tptp.c_Transitive__Closure_Ortrancl V_r T_a) T_a) (not (tptp.c_Relation_Osym V_r T_a)))) (forall ((V_R $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Owf (tptp.c_Relation_Orel__comp V_R V_R T_a T_a T_a) T_a) (not (tptp.c_Wellfounded_Owf V_R T_a)))) (forall ((V_R $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Owf V_R T_a) (not (tptp.c_Wellfounded_Owf (tptp.c_Relation_Orel__comp V_R V_R T_a T_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (= (tptp.hAPP (tptp.c_Relation_OImage (tptp.c_Relation_OId T_a) T_a T_a) V_A) V_A)) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.c_Relation_OId T_a) T_a T_a) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted)) (tptp.c_Relation_Osingle__valued (tptp.c_Relation_OId T_a) T_a T_a)) (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1 V_A V_r T_a) (tptp.c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2 V_A V_r T_a))) (tptp.c_Relation_Ototal__on V_A V_r T_a))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.c_Relation_OId__on V_A T_a) T_a T_a) V_A)) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Relation_Oconverse V_r T_a T_a) V_r) (not (tptp.c_Relation_Osym V_r T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Relation_Oconverse V_r T_a T_a) V_r)) (tptp.c_Relation_Osym V_r T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a T_a) (tptp.c_Relation_ORange V_r T_a T_a))) (forall ((V_r $$unsorted) (V_s $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oconverse (tptp.c_Relation_Orel__comp V_r V_s T_b T_c T_a) T_b T_a) (tptp.c_Relation_Orel__comp (tptp.c_Relation_Oconverse V_s T_c T_a) (tptp.c_Relation_Oconverse V_r T_b T_c) T_a T_c T_b))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Osym (tptp.c_Relation_OId__on V_A T_a) T_a)) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Orefl__on V_A (tptp.c_Relation_OId__on V_A T_a) T_a)) (forall ((V_r $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Wellfounded_Owf (tptp.c_Relation_Oinv__image V_r V_f T_a T_b) T_b) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (forall ((T_a $$unsorted)) (= (tptp.c_Relation_ORange (tptp.c_Relation_OId T_a) T_a T_a) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (= (tptp.c_Relation_Orel__comp V_r _let_1 T_a T_a T_a) (tptp.c_Relation_Orel__comp _let_1 V_r T_a T_a T_a)))) (forall ((T_b $$unsorted)) (or (not (tptp.class_Orderings_Obot T_b)) (= (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Orderings_Obot__class_Obot T_b)))) (forall ((V_r $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Relation_Osym (tptp.c_Relation_Oinv__image V_r V_f T_a T_b) T_b) (not (tptp.c_Relation_Osym V_r T_a)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_b T_a))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_R $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl V_R T_a))) (= (tptp.c_Transitive__Closure_Otrancl _let_1 T_a) _let_1))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Relation_OId T_a))) (= (tptp.c_Relation_Oconverse _let_1 T_a T_a) _let_1))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Owf (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (forall ((V_R $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Relation_OImage V_R T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_R $$unsorted) (V_S $$unsorted) (T_a $$unsorted) (T_d $$unsorted) (T_c $$unsorted) (V_T $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_Orel__comp (tptp.c_Relation_Orel__comp V_R V_S T_a T_d T_c) V_T T_a T_c T_b) (tptp.c_Relation_Orel__comp V_R (tptp.c_Relation_Orel__comp V_S V_T T_d T_c T_b) T_a T_d T_b))) (forall ((V_R $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oconverse (tptp.c_Relation_Oinv__image V_R V_f T_b T_a) T_a T_a) (tptp.c_Relation_Oinv__image (tptp.c_Relation_Oconverse V_R T_b T_b) V_f T_b T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) (tptp.c_Relation_Oconverse (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a T_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Relation_OId__on V_A T_a))) (= (tptp.c_Relation_Oconverse _let_1 T_a T_a) _let_1))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Relation_Orel__comp (tptp.c_Relation_Oconverse V_r T_a T_a) V_r T_a T_a T_a) V_r)) (tptp.c_Equiv__Relations_Oequiv (tptp.c_Relation_ODomain V_r T_a T_a) V_r T_a))) (forall ((T_a $$unsorted)) (tptp.c_Relation_Oantisym (tptp.c_Relation_OId T_a) T_a)) (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_ORange (tptp.c_Relation_Oconverse V_r T_a T_b) T_b T_a) (tptp.c_Relation_ODomain V_r T_a T_b))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange (tptp.c_Relation_OId__on V_A T_a) T_a T_a) V_A)) (forall ((V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (tptp.c_Relation_Osingle__valued (tptp.c_Relation_Orel__comp V_r V_s T_a T_b T_c) T_a T_c) (not (tptp.c_Relation_Osingle__valued V_s T_b T_c)) (not (tptp.c_Relation_Osingle__valued V_r T_a T_b)))) (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse V_r T_a T_b) T_b T_a) V_r)) (forall ((T_a $$unsorted) (V_r $$unsorted)) (tptp.c_Relation_Orefl__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) T_a)) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Relation_Orel__comp (tptp.c_Relation_Oconverse V_r T_a T_a) V_r T_a T_a T_a) V_r) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))) (forall ((V_R $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl V_R T_a))) (= (tptp.c_Relation_Orel__comp _let_1 _let_1 T_a T_a T_a) _let_1))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Oantisym V_r T_a) (not (tptp.c_Relation_Oantisym (tptp.c_Relation_Oconverse V_r T_a T_a) T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Oantisym (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) (not (tptp.c_Relation_Oantisym V_r T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_x)))) (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Orefl__on V_A V_r T_a) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))) (forall ((V_R $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange (tptp.c_Transitive__Closure_Ortrancl V_R T_a) T_a T_a) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) (tptp.c_Relation_Oconverse (tptp.c_Transitive__Closure_Ortrancl V_r T_a) T_a T_a))) (forall ((T_a $$unsorted)) (tptp.c_Relation_Orefl__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Relation_OId T_a) T_a)) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_Relation_Osym V_r T_a) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))) (forall ((T_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_B T_b _let_1) (tptp.c_Orderings_Otop__class_Otop _let_1)))) (forall ((V_r2 $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_r1 $$unsorted)) (or (tptp.c_Equiv__Relations_Ocongruent V_r2 (tptp.hAPP V_f V_a) T_b T_c) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Equiv__Relations_Ocongruent2 V_r1 V_r2 V_f T_a T_b T_c)) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r1 T_a)))) (forall ((V_P $$unsorted) (V_xb $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_xb)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Set__Xball__UNIV__1__1 V_P T_a)))))) (forall ((V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.c_Relation_Oconverse V_r T_b T_a) T_a T_b) (tptp.c_Relation_ORange V_r T_b T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.c_Relation_Orel__comp (tptp.c_Transitive__Closure_Ortrancl V_r T_a) V_r T_a T_a T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.c_Relation_Orel__comp V_r (tptp.c_Transitive__Closure_Ortrancl V_r T_a) T_a T_a T_a))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange V_r T_b T_a) (tptp.c_Relation_ODomain (tptp.c_Relation_Oconverse V_r T_b T_a) T_a T_b))) (forall ((V_R $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl (tptp.c_Transitive__Closure_Otrancl V_R T_a) T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (= (tptp.c_Transitive__Closure_Ortrancl _let_1 T_a) _let_1))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Otrans V_r T_a) (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1 V_r T_a) (tptp.c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2 V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a))))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Otrans V_r T_a) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1 V_r T_a) (tptp.c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3 V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a)))))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Otrans V_r T_a) (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XtransI__1__1 V_r T_a) (tptp.c_ATP__Linkup_Osko__Relation__XtransI__1__2 V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a))))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Otrans V_r T_a) (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2 V_r T_a) (tptp.c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3 V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a))))) (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Ototal__on V_A V_r T_a) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2 V_A V_r T_a) (tptp.c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1 V_A V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a)))))) (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Ototal__on V_A V_r T_a) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1 V_A V_r T_a) (tptp.c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2 V_A V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a)))))) (forall ((V_z $$unsorted) (V_c $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_z (tptp.hAPP (tptp.c_split V_c T_b T_c (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Pair V_a V_b T_b T_c)) T_a)) (not (tptp.hBOOL (tptp.c_in V_z (tptp.hAPP (tptp.hAPP V_c V_a) V_b) T_a))))) (forall ((V_f $$unsorted) (V_y1 $$unsorted) (V_y2 $$unsorted) (V_z1 $$unsorted) (V_z2 $$unsorted) (T_b $$unsorted) (V_r2 $$unsorted) (T_a $$unsorted) (V_r1 $$unsorted) (T_c $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_f V_y1) V_y2) (tptp.hAPP (tptp.hAPP V_f V_z1) V_z2)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y2 V_z2 T_b T_b) V_r2 (tptp.tc_prod T_b T_b)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y1 V_z1 T_a T_a) V_r1 (tptp.tc_prod T_a T_a)))) (not (tptp.c_Equiv__Relations_Ocongruent2 V_r1 V_r2 V_f T_a T_b T_c)))) (forall ((V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (or (= V_y V_z) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_z T_a T_b) V_r _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_b) V_r _let_1))) (not (tptp.c_Relation_Osingle__valued V_r T_a T_b))))) (forall ((V_f $$unsorted) (V_R $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (= (tptp.hAPP (tptp.c_Recdef_Ocut V_f V_R V_a T_a T_b) V_x) (tptp.hAPP V_f V_x)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_a T_a T_a) V_R (tptp.tc_prod T_a T_a)))))) (forall ((V_f $$unsorted) (V_r $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (= (tptp.hAPP (tptp.c_Recdef_Ocut V_f V_r V_a T_a T_b) V_x) (tptp.hAPP V_f V_x)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_a T_a T_a) V_r (tptp.tc_prod T_a T_a)))))) (forall ((V_R $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_FunDef_Oin__rel V_R V_x V_y T_a T_b) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_b) V_R (tptp.tc_prod T_a T_b)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_R $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_b) V_R (tptp.tc_prod T_a T_b))) (not (tptp.c_FunDef_Oin__rel V_R V_x V_y T_a T_b)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (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))) (not (tptp.hBOOL (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 $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_a T_b T_a) (tptp.c_Relation_Oconverse V_r T_a T_b) (tptp.tc_prod T_b T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) V_r (tptp.tc_prod T_a T_b)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_a T_b T_a) V_r (tptp.tc_prod T_b T_a))) (not (tptp.hBOOL (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)))))) _let_22 (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) _let_2 _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) _let_2 _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r _let_1))))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) _let_2 _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) V_r _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) _let_2 _let_1))))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) _let_2 _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) _let_2 _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r _let_1))))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Pair V_a V_b T_a T_a))) (or (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in _let_2 V_r _let_1))))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) _let_2 _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) _let_2 _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) _let_2 _let_1))))))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_a T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a) (tptp.tc_prod T_a T_a)))) (forall ((V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_a T_a T_a) V_r _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_x T_a T_a) V_r _let_1))) (not (tptp.c_Wellfounded_Owf V_r T_a))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (= V_x V_y) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) V_r _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r _let_1))) (not (tptp.c_Relation_Oantisym V_r 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))) (or (= V_a V_b) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_a T_a T_a) V_r _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r _let_1))) (not (tptp.c_Relation_Oantisym V_r T_a))))) (forall ((V_f $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (T_b $$unsorted)) (or (= (tptp.hAPP V_f V_y) (tptp.hAPP V_f V_z)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_z T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Equiv__Relations_Ocongruent V_r V_f T_a T_b)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (= V_x V_y) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Relation_OId__on V_A T_a) (tptp.tc_prod T_a T_a)))))) (forall ((V_f $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_g $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Recdef_Ocut V_f V_r V_x T_a T_b) (tptp.c_Recdef_Ocut V_g V_r V_x T_a T_b))) (= (tptp.hAPP V_f V_y) (tptp.hAPP V_g V_y)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (or (= V_a V_b) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Relation_OId T_a) (tptp.tc_prod T_a T_a)))))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.c_Nitpick_Orefl_H V_r T_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_a T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Relation_Oinv__image V_r V_f T_b T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y) T_b T_b) V_r (tptp.tc_prod T_b T_b)))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y) T_b T_b) V_r (tptp.tc_prod T_b T_b))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Relation_Oinv__image V_r V_f T_b T_a) (tptp.tc_prod T_a 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 (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) V_r _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r _let_1))) (not (tptp.c_Relation_Osym V_r T_a))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_a T_a T_a) V_r _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r _let_1))) (not (tptp.c_Relation_Osym V_r T_a))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_b $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_c) (tptp.c_Relation_Orel__comp V_r V_s T_a T_b T_c) (tptp.tc_prod T_a T_c))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_b T_c) V_s (tptp.tc_prod T_b T_c)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) V_r (tptp.tc_prod T_a T_b)))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_R $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_R T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) V_R _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_R _let_1)))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) _let_2 _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) _let_2 _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) _let_2 _let_1))))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) (tptp.c_Relation_OId T_a) (tptp.tc_prod T_a T_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_a T_a T_a) (tptp.c_Relation_OId T_a) (tptp.tc_prod T_a T_a)))) (forall ((T_a $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Set__XUNIV__witness__1__1 T_a) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((V_P $$unsorted) (T_a $$unsorted) (V_xa $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1 V_P T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_xa))) (not (tptp.hBOOL (tptp.c_in V_xa (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (or (not (= _let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_b _let_1))) (= (tptp.hAPP V_B V_x) _let_2) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))))) (forall ((V_P $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2 V_P T_a) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_A) (not (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1 V_A T_a) V_A T_a))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Set__Xball__UNIV__1__2 V_P T_a)))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) T_a))) (forall ((V_P $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_xa)) (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Set__Xball__UNIV__1__1 V_P T_a) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (or (not (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_b _let_1) _let_2)) (= (tptp.hAPP V_B V_x) _let_2) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))))) (= (tptp.hAPP _let_21 tptp.v_x) (tptp.c_in tptp.v_x _let_21 tptp.t_a)) (forall ((T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (or (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_z) _let_1)) (not (tptp.hBOOL (tptp.c_in _let_2 V_L _let_1))) (= V_x V_y) (= V_x V_z))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (or (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_z) _let_1)) (not (tptp.hBOOL (tptp.c_in _let_2 V_L _let_1))) (= V_y V_z) (= V_x V_z))))) (forall ((V_x $$unsorted) (V_L $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_x) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_x) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (or (tptp.hBOOL (tptp.c_in _let_2 V_L _let_1)) (= V_y V_z) (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_z) _let_1))))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted)) (or (= V_x V_y) (= V_y V_x) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_x) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))) (forall ((V_x $$unsorted) (V_L $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_x) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))) (forall ((V_xa $$unsorted) (V_x $$unsorted) (V_L $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_xa V_x tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_x) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (or (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_z) _let_1)) (not (tptp.hBOOL (tptp.c_in _let_2 V_L _let_1))) (= V_x V_y) (= V_y V_z))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (or (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_z) _let_1)) (not (tptp.hBOOL (tptp.c_in _let_2 V_L _let_1))) (= V_x V_z) (= V_y V_z))))) (forall ((V_xa $$unsorted) (V_x $$unsorted) (V_L $$unsorted)) (let ((_let_1 (= V_xa V_x))) (or _let_1 _let_1 (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_xa V_x tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_x) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (or (tptp.hBOOL (tptp.c_in _let_2 V_L _let_1)) (= V_x V_z) (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_z) _let_1))))))) (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Ototal__on V_A V_r T_a) (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1 V_A V_r T_a) V_A T_a)))) (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Ototal__on V_A V_r T_a) (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2 V_A V_r T_a) V_A T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Product__Type_OSigma V_A V_B T_a T_b) (tptp.tc_prod T_a T_b))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP V_B V_a) T_b))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Product__Type_OSigma V_A V_B T_a T_b) (tptp.tc_prod T_a T_b))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP V_B V_a) T_b))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc V_r T_a))) (or (tptp.hBOOL (tptp.c_in V_a _let_1 T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in V_b _let_1 T_a)))))) (forall ((V_y $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc V_r T_a))) (or (tptp.hBOOL (tptp.c_in V_y _let_1 T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_a T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in V_a _let_1 T_a)))))) (forall ((V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP (tptp.c_Relation_OImage V_r T_a T_b) V_A) T_b)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) V_r (tptp.tc_prod T_a T_b)))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_b $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP (tptp.c_Relation_OImage V_r T_b T_a) V_A) T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_b T_b T_a) V_r (tptp.tc_prod T_b T_a)))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Relation_OId__on V_A T_a) (tptp.tc_prod T_a T_a)))))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) (tptp.c_Relation_OId__on V_A T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_y V_A T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))) (forall ((V_a $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Relation_ORange V_r T_b T_a) T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_a T_b T_a) V_r (tptp.tc_prod T_b T_a)))))) (forall ((V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.c_Relation_ORange V_r T_a T_b) T_b)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) V_r (tptp.tc_prod T_a T_b)))))) (forall ((V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Relation_ODomain V_r T_a T_b) T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_x T_a T_b) V_r (tptp.tc_prod T_a T_b)))))) (forall ((V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Relation_ODomain V_r T_a T_b) T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) V_r (tptp.tc_prod T_a T_b)))))) (forall ((V_b $$unsorted) (V_B $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP V_B V_a) T_b)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Product__Type_OSigma V_A V_B T_a T_b) (tptp.tc_prod T_a T_b)))))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a V_A T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Product__Type_OSigma V_A V_B T_a T_b) (tptp.tc_prod T_a T_b)))))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))) (forall ((V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_y V_A T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_a T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 V_r T_a))) (or (tptp.c_Relation_Oirrefl V_r T_a) (tptp.hBOOL (tptp.c_in (tptp.c_Pair _let_1 _let_1 T_a T_a) V_r (tptp.tc_prod T_a T_a)))))) (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Order__Relation_Ostrict__linear__order__on V_A V_r T_a) (not (tptp.c_Relation_Ototal__on V_A V_r T_a)) (not (tptp.c_Relation_Oirrefl V_r T_a)) (not (tptp.c_Relation_Otrans V_r 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_b V_b_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_a V_a_H))) (forall ((V_x $$unsorted) (V_z $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_z T_a T_a) V_r _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_z T_a T_a) V_r _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r _let_1))) (not (tptp.c_Relation_Otrans V_r T_a))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) V_r _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) V_r _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r _let_1))) (not (tptp.c_Relation_Otrans V_r T_a))))) _let_20 (forall ((T_b $$unsorted)) (or (not (tptp.class_Orderings_Otop T_b)) (= (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Orderings_Otop__class_Otop T_b)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_x))) _let_19 _let_18 (forall ((V_x $$unsorted) (V_S $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_S T_a)) (not (tptp.hBOOL (tptp.hAPP V_S V_x))))) (forall ((V_S $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_S V_x)) (not (tptp.hBOOL (tptp.c_in V_x V_S T_a))))) _let_17 _let_16 _let_15 _let_14 _let_13 _let_10 _let_9 (or (tptp.c_Relation_Ototal__on _let_6 _let_8 tptp.tc_Arrow__Order__Mirabelle_Oalt) _let_7 _let_4 _let_3) _let_1 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Complete__Lattice_Ocomplete__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Oupper__semilattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Olower__semilattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Odistrib__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Odistrib__lattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Obounded__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Obounded__lattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Opreorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Olattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Oorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Otop (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Otop T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Obot (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Obot T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Ominus (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Ominus T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Oord (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Oord T_1)))) (tptp.class_Complete__Lattice_Ocomplete__lattice tptp.tc_bool) (tptp.class_Lattices_Oupper__semilattice tptp.tc_bool) (tptp.class_Lattices_Olower__semilattice tptp.tc_bool) (tptp.class_Lattices_Odistrib__lattice tptp.tc_bool) (tptp.class_Lattices_Obounded__lattice tptp.tc_bool) (tptp.class_Orderings_Opreorder tptp.tc_bool) (tptp.class_Lattices_Olattice tptp.tc_bool) (tptp.class_Orderings_Oorder tptp.tc_bool) (tptp.class_Orderings_Otop tptp.tc_bool) (tptp.class_Orderings_Obot tptp.tc_bool) (tptp.class_HOL_Ominus tptp.tc_bool) (tptp.class_HOL_Oord tptp.tc_bool) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_fequal V_x V_x T_a)) (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.c_fequal V_X V_Y T_a)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 63.05/63.58 )
% 63.05/63.59 % SZS output end Proof for SCT022-1
% 63.05/63.59 % cvc5---1.0.5 exiting
% 63.05/63.59 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------