%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : LAT297+2 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n005.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 06:03:46 EDT 2023

% Result   : Theorem 88.67s 88.94s
% Output   : Proof 88.77s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.30  % Problem    : LAT297+2 : TPTP v8.1.2. Released v3.4.0.
% 0.30/0.31  % Command    : do_cvc5 %s %d
% 0.30/0.52  % Computer : n005.cluster.edu
% 0.30/0.52  % Model    : x86_64 x86_64
% 0.30/0.52  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.30/0.52  % Memory   : 8042.1875MB
% 0.30/0.52  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.30/0.52  % CPULimit   : 300
% 0.30/0.52  % WCLimit    : 300
% 0.30/0.52  % DateTime   : Thu Aug 24 04:38:09 EDT 2023
% 0.37/0.52  % CPUTime    : 
% 0.76/0.92  %----Proving TF0_NAR, FOF, or CNF
% 88.67/88.94  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.R4S0TNZC6l/cvc5---1.0.5_26436.p...
% 88.67/88.94  ------- get file name : TPTP file name is LAT297+2
% 88.67/88.94  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_26436.smt2...
% 88.67/88.94  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 88.67/88.94  --- Run --no-e-matching --full-saturate-quant at 5...
% 88.67/88.94  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 88.67/88.94  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 88.67/88.94  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 88.67/88.94  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 88.67/88.94  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 88.67/88.94  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 88.67/88.94  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 88.67/88.94  --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 88.67/88.94  --- Run --relevant-triggers --full-saturate-quant at 5...
% 88.67/88.94  --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 88.67/88.94  --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 88.67/88.94  --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 88.67/88.94  % SZS status Theorem for LAT297+2
% 88.67/88.94  % SZS output start Proof for LAT297+2
% 88.67/88.94  (
% 88.67/88.94  (let ((_let_1 (not (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (=> (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (= (and (tptp.r2_hidden C B) (tptp.r2_hidden D B)) (tptp.r2_hidden (tptp.k4_lattices A C D) B)))))) (tptp.m2_lattice4 B A))))))))) (let ((_let_2 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (tptp.m2_lattice4 B A))))))) (let ((_let_3 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (= (tptp.m2_lattice4 B A) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (=> (and (tptp.r2_hidden C B) (tptp.r2_hidden D B)) (and (tptp.r2_hidden (tptp.k4_lattices A C D) B) (tptp.r2_hidden (tptp.k3_lattices A C D) B)))))))))))))) (let ((_let_4 (tptp.v10_lattices tptp.k13_nat_lat))) (let ((_let_5 (not (tptp.v3_struct_0 tptp.k13_nat_lat)))) (let ((_let_6 (tptp.k2_zfmisc_1 tptp.k7_nat_lat tptp.k7_nat_lat))) (let ((_let_7 (tptp.l3_lattices tptp.k6_nat_lat))) (let ((_let_8 (tptp.v10_lattices tptp.k6_nat_lat))) (let ((_let_9 (not (tptp.v3_struct_0 tptp.k6_nat_lat)))) (let ((_let_10 (tptp.g3_lattices tptp.k5_numbers tptp.k2_nat_lat tptp.k1_nat_lat))) (let ((_let_11 (tptp.u1_struct_0 _let_10))) (let ((_let_12 (tptp.k2_zfmisc_1 tptp.k5_numbers tptp.k5_numbers))) (let ((_let_13 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (= (tptp.m1_filter_0 B A) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (= (and (tptp.r2_hidden C B) (tptp.r2_hidden D B)) (tptp.r2_hidden (tptp.k4_lattices A C D) B))))))))))))) (let ((_let_14 (tptp.k1_tarski (tptp.k4_tarski tptp.np__0 tptp.np__0)))) (let ((_let_15 (tptp.k1_tarski tptp.np__0))) (let ((_let_16 (tptp.k1_tarski tptp.k1_xboole_0))) (let ((_let_17 (tptp.r2_hidden tptp.k1_xboole_0 tptp.f1_s4_ordinal2))) (let ((_let_18 (= (tptp.k2_relat_1 tptp.k1_xboole_0) tptp.k1_xboole_0))) (let ((_let_19 (tptp.v3_ordinal1 tptp.k1_xboole_0))) (let ((_let_20 (tptp.v1_xboole_0 tptp.k1_xboole_0))) (let ((_let_21 (tptp.v3_relat_1 tptp.k1_xboole_0))) (let ((_let_22 (tptp.v1_relat_1 tptp.k1_xboole_0))) (let ((_let_23 (and _let_20 _let_22))) (let ((_let_24 (forall ((A $$unsorted)) (let ((_let_1 (tptp.r1_xboole_0 A A))) (let ((_let_2 (= A tptp.k1_xboole_0))) (and (not (and (not _let_1) _let_2)) (not (and (not _let_2) _let_1)))))))) (let ((_let_25 (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.v1_xboole_0 A) (not (= A B)) (tptp.v1_xboole_0 B)))))) (let ((_let_26 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.r1_xboole_0 A B))) (and (not (and (not _let_1) (forall ((C $$unsorted)) (not (and (tptp.r2_hidden C A) (tptp.r2_hidden C B)))))) (not (and (exists ((C $$unsorted)) (and (tptp.r2_hidden C A) (tptp.r2_hidden C B))) _let_1))))))) (let ((_let_27 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.v1_xboole_0 A)) (= A B) (not (tptp.v1_xboole_0 B)))))) (let ((_let_28 (tptp.v1_xboole_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69))) (let ((_let_29 (not _let_28))) (let ((_let_30 (= tptp.k1_xboole_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69))) (let ((_let_31 (not _let_20))) (let ((_let_32 (or _let_31 _let_30 _let_29))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (not _let_32))) (let ((_let_35 (forall ((C $$unsorted) (BOUND_VARIABLE_80646 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68))) (or (not (tptp.m1_subset_1 C _let_1)) (not (tptp.m1_subset_1 BOUND_VARIABLE_80646 _let_1)) (= (and (tptp.r2_hidden C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69) (tptp.r2_hidden BOUND_VARIABLE_80646 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69)) (tptp.r2_hidden (tptp.k4_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68 C BOUND_VARIABLE_80646) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69))))))) (let ((_let_36 (tptp.m1_filter_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68))) (let ((_let_37 (= _let_36 _let_35))) (let ((_let_38 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68))) (let ((_let_39 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69 (tptp.k1_zfmisc_1 _let_38)))) (let ((_let_40 (not _let_39))) (let ((_let_41 (tptp.l3_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68))) (let ((_let_42 (not _let_41))) (let ((_let_43 (tptp.v10_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68))) (let ((_let_44 (not _let_43))) (let ((_let_45 (tptp.v3_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68))) (let ((_let_46 (or _let_45 _let_44 _let_42 _let_28 _let_40 _let_37))) (let ((_let_47 (forall ((A $$unsorted) (BOUND_VARIABLE_80677 $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.l3_lattices A)) (tptp.v1_xboole_0 BOUND_VARIABLE_80677) (not (tptp.m1_subset_1 BOUND_VARIABLE_80677 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (= (tptp.m1_filter_0 BOUND_VARIABLE_80677 A) (forall ((C $$unsorted) (BOUND_VARIABLE_80646 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (not (tptp.m1_subset_1 C _let_1)) (not (tptp.m1_subset_1 BOUND_VARIABLE_80646 _let_1)) (= (and (tptp.r2_hidden C BOUND_VARIABLE_80677) (tptp.r2_hidden BOUND_VARIABLE_80646 BOUND_VARIABLE_80677)) (tptp.r2_hidden (tptp.k4_lattices A C BOUND_VARIABLE_80646) BOUND_VARIABLE_80677)))))))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (not _let_37))) (let ((_let_50 (forall ((C $$unsorted) (BOUND_VARIABLE_99351 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68))) (or (not (tptp.m1_subset_1 C _let_1)) (not (tptp.m1_subset_1 BOUND_VARIABLE_99351 _let_1)) (= (and (tptp.r2_hidden C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69) (tptp.r2_hidden BOUND_VARIABLE_99351 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69)) (tptp.r2_hidden (tptp.k4_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68 C BOUND_VARIABLE_99351) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69))))))) (let ((_let_51 (tptp.m2_lattice4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68))) (let ((_let_52 (not _let_50))) (let ((_let_53 (or _let_45 _let_44 _let_42 _let_40 _let_52 _let_51))) (let ((_let_54 (forall ((A $$unsorted) (BOUND_VARIABLE_99382 $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.l3_lattices A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_99382 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (not (forall ((C $$unsorted) (BOUND_VARIABLE_99351 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (not (tptp.m1_subset_1 C _let_1)) (not (tptp.m1_subset_1 BOUND_VARIABLE_99351 _let_1)) (= (and (tptp.r2_hidden C BOUND_VARIABLE_99382) (tptp.r2_hidden BOUND_VARIABLE_99351 BOUND_VARIABLE_99382)) (tptp.r2_hidden (tptp.k4_lattices A C BOUND_VARIABLE_99351) BOUND_VARIABLE_99382)))))) (tptp.m2_lattice4 BOUND_VARIABLE_99382 A))))) (let ((_let_55 (not _let_53))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (or))) (let ((_let_58 (not _let_54))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_56) :args (_let_58))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_54))) (REFL :args (_let_55)) :args _let_57)) _let_56 :args (_let_55 true _let_54)))) (let ((_let_60 (REFL :args (_let_53)))) (let ((_let_61 (not _let_36))) (let ((_let_62 (or _let_45 _let_44 _let_42 _let_61 _let_51))) (let ((_let_63 (forall ((A $$unsorted) (BOUND_VARIABLE_94698 $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.l3_lattices A)) (not (tptp.m1_filter_0 BOUND_VARIABLE_94698 A)) (tptp.m2_lattice4 BOUND_VARIABLE_94698 A))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_53 5)) _let_59 :args ((not _let_51) true _let_53)))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_53 2)) (CONG _let_60 (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_41))) :args _let_57)) :args ((or _let_41 _let_53))) _let_59 :args (_let_41 true _let_53)))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_53 1)) (CONG _let_60 (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) :args _let_57)) :args ((or _let_43 _let_53))) _let_59 :args (_let_43 true _let_53)))) (let ((_let_68 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_53 0)) _let_59 :args ((not _let_45) true _let_53)))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_53 3)) (CONG _let_60 (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_39))) :args _let_57)) :args ((or _let_39 _let_53))) _let_59 :args (_let_39 true _let_53)))) (let ((_let_70 (tptp.r2_hidden SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_377 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69))) (let ((_let_71 (tptp.r2_hidden SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_377 tptp.k1_xboole_0))) (let ((_let_72 (not _let_30))) (let ((_let_73 (not _let_70))) (let ((_let_74 (or (not (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_377 _let_38)) _let_73 (not (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_378 _let_38)) (not (tptp.r2_hidden SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_378 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69)) (and (tptp.r2_hidden (tptp.k4_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_377 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_378) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69) (tptp.r2_hidden (tptp.k3_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_377 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_378) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69))))) (let ((_let_75 (forall ((C $$unsorted) (BOUND_VARIABLE_94627 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68))) (or (not (tptp.m1_subset_1 C _let_1)) (not (tptp.r2_hidden C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69)) (not (tptp.m1_subset_1 BOUND_VARIABLE_94627 _let_1)) (not (tptp.r2_hidden BOUND_VARIABLE_94627 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69)) (and (tptp.r2_hidden (tptp.k4_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68 C BOUND_VARIABLE_94627) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69) (tptp.r2_hidden (tptp.k3_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68 C BOUND_VARIABLE_94627) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69))))))) (let ((_let_76 (not _let_74))) (let ((_let_77 (= _let_51 _let_75))) (let ((_let_78 (not _let_75))) (let ((_let_79 (or _let_45 _let_44 _let_42 _let_40 _let_77))) (let ((_let_80 (forall ((A $$unsorted) (BOUND_VARIABLE_94658 $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.l3_lattices A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_94658 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (= (tptp.m2_lattice4 BOUND_VARIABLE_94658 A) (forall ((C $$unsorted) (BOUND_VARIABLE_94627 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (not (tptp.m1_subset_1 C _let_1)) (not (tptp.r2_hidden C BOUND_VARIABLE_94658)) (not (tptp.m1_subset_1 BOUND_VARIABLE_94627 _let_1)) (not (tptp.r2_hidden BOUND_VARIABLE_94627 BOUND_VARIABLE_94658)) (and (tptp.r2_hidden (tptp.k4_lattices A C BOUND_VARIABLE_94627) BOUND_VARIABLE_94658) (tptp.r2_hidden (tptp.k3_lattices A C BOUND_VARIABLE_94627) BOUND_VARIABLE_94658)))))))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (_let_78))) (let ((_let_83 (not _let_71))) (let ((_let_84 (tptp.r1_xboole_0 tptp.k1_xboole_0 tptp.k1_xboole_0))) (let ((_let_85 (not _let_84))) (let ((_let_86 (or _let_85 _let_83 _let_83))) (let ((_let_87 (forall ((BOUND_VARIABLE_42581 $$unsorted) (BOUND_VARIABLE_42583 $$unsorted) (BOUND_VARIABLE_42597 $$unsorted)) (or (not (tptp.r1_xboole_0 BOUND_VARIABLE_42581 BOUND_VARIABLE_42583)) (not (tptp.r2_hidden BOUND_VARIABLE_42597 BOUND_VARIABLE_42581)) (not (tptp.r2_hidden BOUND_VARIABLE_42597 BOUND_VARIABLE_42583)))))) (let ((_let_88 (_let_87))) (let ((_let_89 (0))) (let ((_let_90 (ASSUME :args (_let_83)))) (let ((_let_91 (ASSUME :args (_let_30)))) (let ((_let_92 (ASSUME :args (_let_70)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (tptp.k1_xboole_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_27))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_31 _let_30 _let_29 _let_34))) (AND_ELIM (ASSUME :args (_let_23)) :args _let_89) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_90 _let_91 _let_92) :args (_let_30 _let_70 _let_83)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_92)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_377)) (SYMM _let_91) :args (APPLY_UF tptp.r2_hidden)) (FALSE_INTRO _let_90))) :args (_let_83 _let_30 _let_70)) :args ((not (and _let_30 _let_70 _let_83)) SB_LITERAL))) (CONG (REFL :args (_let_72)) (REFL :args (_let_73)) (MACRO_SR_PRED_INTRO :args ((= (not _let_83) _let_71))) :args _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_86))) :args ((or _let_85 _let_83 (not _let_86)))) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))) :args _let_89) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_88) :args (tptp.k1_xboole_0 tptp.k1_xboole_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_377 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_88)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))) :args (1)) :args (_let_86 false _let_87)) :args (_let_83 false _let_84 false _let_86)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_74 1)) (CONG (REFL :args (_let_74)) (MACRO_SR_PRED_INTRO :args ((= (not _let_73) _let_70))) :args _let_57)) :args ((or _let_70 _let_74))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_82)) :args _let_82)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_78) _let_75))) (REFL :args (_let_76)) :args _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_77)) :args ((or _let_51 _let_78 (not _let_77)))) _let_65 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_79)) :args ((or _let_45 _let_44 _let_42 _let_40 _let_77 (not _let_79)))) _let_68 _let_67 _let_66 _let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_81 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.m1_subset_1 BOUND_VARIABLE_94658 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) false))))) :args (_let_80))) _let_81 :args (_let_79 false _let_80)) :args (_let_77 true _let_45 false _let_43 false _let_41 false _let_39 false _let_79)) :args (_let_78 true _let_51 false _let_77)) :args (_let_76 true _let_75)) :args (_let_70 true _let_74)) :args (_let_72 true _let_71 false _let_70)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_45 _let_44 _let_42 _let_40 _let_28 _let_37 (not _let_46)))) _let_68 _let_67 _let_66 _let_69 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_37)) :args ((or _let_36 (not _let_35) _let_49))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_45 _let_44 _let_42 _let_51 _let_61 (not _let_62)))) _let_68 _let_67 _let_66 _let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.m2_lattice4 BOUND_VARIABLE_94698 A) true))))) :args (_let_63))) _let_64 :args (_let_62 false _let_63)) :args (_let_61 true _let_45 false _let_43 false _let_41 true _let_51 false _let_62)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_50 (= C C) (= BOUND_VARIABLE_99351 BOUND_VARIABLE_80646)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_53 4)) (CONG _let_60 (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_50))) :args _let_57)) :args ((or _let_50 _let_53))) _let_59 :args (_let_50 true _let_53)) :args (_let_35 false _let_50)) :args (_let_49 true _let_36 false _let_35)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.m1_subset_1 BOUND_VARIABLE_80677 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) false))))) :args (_let_47))) _let_48 :args (_let_46 false _let_47)) :args (_let_28 true _let_45 false _let_43 false _let_41 false _let_39 true _let_37 false _let_46)) :args (_let_34 false _let_20 true _let_30 false _let_28)) _let_33 :args (false true _let_32 false _let_27)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (not (tptp.r2_hidden B A)))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted)) (= (tptp.r2_hidden C A) (tptp.r2_hidden C B))) (= A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.k1_tarski A)) (forall ((C $$unsorted)) (= (tptp.r2_hidden C B) (= C A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.k2_tarski A B)) (forall ((D $$unsorted)) (= (tptp.r2_hidden D C) (or (= D A) (= D B)))))) true true (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.r1_tarski A B) (forall ((C $$unsorted)) (=> (tptp.r2_hidden C A) (tptp.r2_hidden C B))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.k3_tarski A)) (forall ((C $$unsorted)) (= (tptp.r2_hidden C B) (exists ((D $$unsorted)) (and (tptp.r2_hidden C D) (tptp.r2_hidden D A))))))) true true (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.r2_hidden A B) (forall ((C $$unsorted)) (not (and (tptp.r2_hidden C B) (forall ((D $$unsorted)) (not (and (tptp.r2_hidden D B) (tptp.r2_hidden D C)))))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k4_tarski A B) (tptp.k2_tarski (tptp.k2_tarski A B) (tptp.k1_tarski A)))) true (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.r2_tarski A B) (exists ((C $$unsorted)) (and (forall ((D $$unsorted)) (not (and (tptp.r2_hidden D A) (forall ((E $$unsorted)) (not (and (tptp.r2_hidden E B) (tptp.r2_hidden (tptp.k4_tarski D E) C))))))) (forall ((D $$unsorted)) (not (and (tptp.r2_hidden D B) (forall ((E $$unsorted)) (not (and (tptp.r2_hidden E A) (tptp.r2_hidden (tptp.k4_tarski E D) C))))))) (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted)) (=> (and (tptp.r2_hidden (tptp.k4_tarski D E) C) (tptp.r2_hidden (tptp.k4_tarski F G) C)) (= (= D F) (= E G)))))))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.r2_hidden A B) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.r2_hidden C B) (tptp.r1_tarski D C)) (tptp.r2_hidden D B))) (forall ((C $$unsorted)) (not (and (tptp.r2_hidden C B) (forall ((D $$unsorted)) (not (and (tptp.r2_hidden D B) (forall ((E $$unsorted)) (=> (tptp.r1_tarski E C) (tptp.r2_hidden E D))))))))) (forall ((C $$unsorted)) (not (and (tptp.r1_tarski C B) (not (tptp.r2_tarski C B)) (not (tptp.r2_hidden C B)))))))) (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.p1_s1_tarski A B) (tptp.p1_s1_tarski A C)) (= B C))) (exists ((A $$unsorted)) (forall ((B $$unsorted)) (= (tptp.r2_hidden B A) (exists ((C $$unsorted)) (and (tptp.r2_hidden C tptp.f1_s1_tarski) (tptp.p1_s1_tarski C B))))))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski A A)) true true (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k2_tarski A B) (tptp.k2_tarski B A))) true true _let_20 (exists ((A $$unsorted)) (tptp.v1_xboole_0 A)) (exists ((A $$unsorted)) (not (tptp.v1_xboole_0 A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 (tptp.k2_xboole_0 A B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 (tptp.k2_xboole_0 B A))))) (forall ((A $$unsorted)) (= (= A tptp.k1_xboole_0) (forall ((B $$unsorted)) (not (tptp.r2_hidden B A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.k2_xboole_0 A B)) (forall ((D $$unsorted)) (= (tptp.r2_hidden D C) (or (tptp.r2_hidden D A) (tptp.r2_hidden D B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.k3_xboole_0 A B)) (forall ((D $$unsorted)) (= (tptp.r2_hidden D C) (and (tptp.r2_hidden D A) (tptp.r2_hidden D B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.k4_xboole_0 A B)) (forall ((D $$unsorted)) (= (tptp.r2_hidden D C) (and (tptp.r2_hidden D A) (not (tptp.r2_hidden D B))))))) (forall ((A $$unsorted)) (= (tptp.v1_xboole_0 A) (= A tptp.k1_xboole_0))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k5_xboole_0 A B) (tptp.k2_xboole_0 (tptp.k4_xboole_0 A B) (tptp.k4_xboole_0 B A)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.r1_xboole_0 A B) (= (tptp.k3_xboole_0 A B) tptp.k1_xboole_0))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.r2_xboole_0 A B) (and (tptp.r1_tarski A B) (not (= A B))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.r3_xboole_0 A B) (or (tptp.r1_tarski A B) (tptp.r1_tarski B A)))) (forall ((A $$unsorted) (B $$unsorted)) (= (= A B) (and (tptp.r1_tarski A B) (tptp.r1_tarski B A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.r2_hidden A (tptp.k5_xboole_0 B C)) (not (= (tptp.r2_hidden A B) (tptp.r2_hidden A C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (forall ((D $$unsorted)) (= (not (tptp.r2_hidden D A)) (= (tptp.r2_hidden D B) (tptp.r2_hidden D C)))) (= A (tptp.k5_xboole_0 B C)))) _let_26 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.r1_xboole_0 A B))) (and (not (and (not _let_1) (forall ((C $$unsorted)) (not (tptp.r2_hidden C (tptp.k3_xboole_0 A B)))))) (not (and (exists ((C $$unsorted)) (tptp.r2_hidden C (tptp.k3_xboole_0 A B))) _let_1))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.r2_hidden C A))) (let ((_let_2 (tptp.r2_hidden C B))) (not (and (tptp.r1_xboole_0 A B) (tptp.r2_hidden C (tptp.k2_xboole_0 A B)) (not (and _let_1 (not _let_2))) (not (and _let_2 (not _let_1)))))))) (exists ((A $$unsorted)) (forall ((B $$unsorted)) (= (tptp.r2_hidden B A) (and (tptp.r2_hidden B tptp.f1_s1_xboole_0) (tptp.p1_s1_xboole_0 B))))) (=> (and (forall ((A $$unsorted)) (= (tptp.r2_hidden A tptp.f1_s2_xboole_0) (tptp.p1_s2_xboole_0 A))) (forall ((A $$unsorted)) (= (tptp.r2_hidden A tptp.f2_s2_xboole_0) (tptp.p1_s2_xboole_0 A)))) (= tptp.f1_s2_xboole_0 tptp.f2_s2_xboole_0)) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (forall ((C $$unsorted)) (= (tptp.r2_hidden C A) (tptp.p1_s3_xboole_0 C))) (forall ((C $$unsorted)) (= (tptp.r2_hidden C B) (tptp.p1_s3_xboole_0 C)))) (= A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r1_xboole_0 A B) (tptp.r1_xboole_0 B A))) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.r2_xboole_0 A A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_xboole_0 A B) (not (tptp.r2_xboole_0 B A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r3_xboole_0 A B) (tptp.r3_xboole_0 B A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.r3_xboole_0 A A)) true true (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k2_xboole_0 A B) (tptp.k2_xboole_0 B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k2_xboole_0 A A) A)) true (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k3_xboole_0 A B) (tptp.k3_xboole_0 B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k3_xboole_0 A A) A)) true true (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k5_xboole_0 A B) (tptp.k5_xboole_0 B A))) (forall ((A $$unsorted)) (= (tptp.k2_xboole_0 A tptp.k1_xboole_0) A)) (forall ((A $$unsorted)) (= (tptp.k3_xboole_0 A tptp.k1_xboole_0) tptp.k1_xboole_0)) (forall ((A $$unsorted)) (= (tptp.k4_xboole_0 A tptp.k1_xboole_0) A)) (forall ((A $$unsorted)) (= (tptp.k4_xboole_0 tptp.k1_xboole_0 A) tptp.k1_xboole_0)) (forall ((A $$unsorted)) (= (tptp.k5_xboole_0 A tptp.k1_xboole_0) A)) (forall ((A $$unsorted)) (=> (tptp.v1_xboole_0 A) (= A tptp.k1_xboole_0))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.r2_hidden A B) (tptp.v1_xboole_0 B)))) _let_25 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.r1_tarski A B) (tptp.r1_tarski B C)) (tptp.r1_tarski A C))) (forall ((A $$unsorted)) (tptp.r1_tarski tptp.k1_xboole_0 A)) (forall ((A $$unsorted)) (=> (tptp.r1_tarski A tptp.k1_xboole_0) (= A tptp.k1_xboole_0))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k2_xboole_0 (tptp.k2_xboole_0 A B) C) (tptp.k2_xboole_0 A (tptp.k2_xboole_0 B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k2_xboole_0 (tptp.k2_xboole_0 A B) C) (tptp.k2_xboole_0 (tptp.k2_xboole_0 A C) (tptp.k2_xboole_0 B C)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_xboole_0 A B))) (= (tptp.k2_xboole_0 A _let_1) _let_1))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski A (tptp.k2_xboole_0 A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.r1_tarski A B) (tptp.r1_tarski C B)) (tptp.r1_tarski (tptp.k2_xboole_0 A C) B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r1_tarski A B) (tptp.r1_tarski (tptp.k2_xboole_0 A C) (tptp.k2_xboole_0 B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r1_tarski A B) (tptp.r1_tarski A (tptp.k2_xboole_0 C B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r1_tarski (tptp.k2_xboole_0 A B) C) (tptp.r1_tarski A C))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r1_tarski A B) (= (tptp.k2_xboole_0 A B) B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.r1_tarski A B) (tptp.r1_tarski C D)) (tptp.r1_tarski (tptp.k2_xboole_0 A C) (tptp.k2_xboole_0 B D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.r1_tarski A B) (tptp.r1_tarski C B) (forall ((D $$unsorted)) (=> (and (tptp.r1_tarski A D) (tptp.r1_tarski C D)) (tptp.r1_tarski B D)))) (= B (tptp.k2_xboole_0 A C)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (= (tptp.k2_xboole_0 A B) tptp.k1_xboole_0) (= A tptp.k1_xboole_0))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k3_xboole_0 (tptp.k3_xboole_0 A B) C) (tptp.k3_xboole_0 A (tptp.k3_xboole_0 B C)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski (tptp.k3_xboole_0 A B) A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r1_tarski A (tptp.k3_xboole_0 B C)) (tptp.r1_tarski A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.r1_tarski A B) (tptp.r1_tarski A C)) (tptp.r1_tarski A (tptp.k3_xboole_0 B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.r1_tarski A B) (tptp.r1_tarski A C) (forall ((D $$unsorted)) (=> (and (tptp.r1_tarski D B) (tptp.r1_tarski D C)) (tptp.r1_tarski D A)))) (= A (tptp.k3_xboole_0 B C)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k3_xboole_0 A (tptp.k2_xboole_0 A B)) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k2_xboole_0 A (tptp.k3_xboole_0 A B)) A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k3_xboole_0 A (tptp.k2_xboole_0 B C)) (tptp.k2_xboole_0 (tptp.k3_xboole_0 A B) (tptp.k3_xboole_0 A C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k2_xboole_0 A (tptp.k3_xboole_0 B C)) (tptp.k3_xboole_0 (tptp.k2_xboole_0 A B) (tptp.k2_xboole_0 A C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k2_xboole_0 (tptp.k2_xboole_0 (tptp.k3_xboole_0 A B) (tptp.k3_xboole_0 B C)) (tptp.k3_xboole_0 C A)) (tptp.k3_xboole_0 (tptp.k3_xboole_0 (tptp.k2_xboole_0 A B) (tptp.k2_xboole_0 B C)) (tptp.k2_xboole_0 C A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r1_tarski A B) (tptp.r1_tarski (tptp.k3_xboole_0 A C) (tptp.k3_xboole_0 B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.r1_tarski A B) (tptp.r1_tarski C D)) (tptp.r1_tarski (tptp.k3_xboole_0 A C) (tptp.k3_xboole_0 B D)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r1_tarski A B) (= (tptp.k3_xboole_0 A B) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.r1_tarski (tptp.k3_xboole_0 A B) (tptp.k2_xboole_0 A C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r1_tarski A B) (= (tptp.k2_xboole_0 A (tptp.k3_xboole_0 C B)) (tptp.k3_xboole_0 (tptp.k2_xboole_0 A C) B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.r1_tarski (tptp.k2_xboole_0 (tptp.k3_xboole_0 A B) (tptp.k3_xboole_0 A C)) (tptp.k2_xboole_0 B C))) (forall ((A $$unsorted) (B $$unsorted)) (=> (= (tptp.k4_xboole_0 A B) (tptp.k4_xboole_0 B A)) (= A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r1_tarski A B) (tptp.r1_tarski (tptp.k4_xboole_0 A C) (tptp.k4_xboole_0 B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r1_tarski A B) (tptp.r1_tarski (tptp.k4_xboole_0 C B) (tptp.k4_xboole_0 C A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.r1_tarski A B) (tptp.r1_tarski C D)) (tptp.r1_tarski (tptp.k4_xboole_0 A D) (tptp.k4_xboole_0 B C)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski (tptp.k4_xboole_0 A B) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.k4_xboole_0 A B) tptp.k1_xboole_0) (tptp.r1_tarski A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r1_tarski A (tptp.k4_xboole_0 B A)) (= A tptp.k1_xboole_0))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k2_xboole_0 A (tptp.k4_xboole_0 B A)) (tptp.k2_xboole_0 A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k4_xboole_0 (tptp.k2_xboole_0 A B) B) (tptp.k4_xboole_0 A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k4_xboole_0 (tptp.k4_xboole_0 A B) C) (tptp.k4_xboole_0 A (tptp.k2_xboole_0 B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k4_xboole_0 (tptp.k2_xboole_0 A B) C) (tptp.k2_xboole_0 (tptp.k4_xboole_0 A C) (tptp.k4_xboole_0 B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r1_tarski A (tptp.k2_xboole_0 B C)) (tptp.r1_tarski (tptp.k4_xboole_0 A B) C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r1_tarski (tptp.k4_xboole_0 A B) C) (tptp.r1_tarski A (tptp.k2_xboole_0 B C)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r1_tarski A B) (= B (tptp.k2_xboole_0 A (tptp.k4_xboole_0 B A))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k4_xboole_0 A (tptp.k2_xboole_0 A B)) tptp.k1_xboole_0)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k4_xboole_0 A (tptp.k3_xboole_0 A B)) (tptp.k4_xboole_0 A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k4_xboole_0 A (tptp.k4_xboole_0 A B)) (tptp.k3_xboole_0 A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k3_xboole_0 A (tptp.k4_xboole_0 B C)) (tptp.k4_xboole_0 (tptp.k3_xboole_0 A B) C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k3_xboole_0 A (tptp.k4_xboole_0 B C)) (tptp.k4_xboole_0 (tptp.k3_xboole_0 A B) (tptp.k3_xboole_0 A C)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k2_xboole_0 (tptp.k3_xboole_0 A B) (tptp.k4_xboole_0 A B)) A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k4_xboole_0 A (tptp.k4_xboole_0 B C)) (tptp.k2_xboole_0 (tptp.k4_xboole_0 A B) (tptp.k3_xboole_0 A C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k4_xboole_0 A (tptp.k2_xboole_0 B C)) (tptp.k3_xboole_0 (tptp.k4_xboole_0 A B) (tptp.k4_xboole_0 A C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k4_xboole_0 A (tptp.k3_xboole_0 B C)) (tptp.k2_xboole_0 (tptp.k4_xboole_0 A B) (tptp.k4_xboole_0 A C)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k4_xboole_0 (tptp.k2_xboole_0 A B) (tptp.k3_xboole_0 A B)) (tptp.k2_xboole_0 (tptp.k4_xboole_0 A B) (tptp.k4_xboole_0 B A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.r2_xboole_0 A B) (tptp.r2_xboole_0 B C)) (tptp.r2_xboole_0 A C))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.r2_xboole_0 A B) (tptp.r2_xboole_0 B A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.r2_xboole_0 A B) (tptp.r1_tarski B C)) (tptp.r2_xboole_0 A C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.r1_tarski A B) (tptp.r2_xboole_0 B C)) (tptp.r2_xboole_0 A C))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.r1_tarski A B) (tptp.r2_xboole_0 B A)))) (forall ((A $$unsorted)) (=> (not (= A tptp.k1_xboole_0)) (tptp.r2_xboole_0 tptp.k1_xboole_0 A))) (forall ((A $$unsorted)) (not (tptp.r2_xboole_0 A tptp.k1_xboole_0))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.r1_tarski A B) (tptp.r1_xboole_0 B C)) (tptp.r1_xboole_0 A C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.r1_tarski A B) (tptp.r1_tarski C D) (tptp.r1_xboole_0 B D)) (tptp.r1_xboole_0 A C))) (forall ((A $$unsorted)) (tptp.r1_xboole_0 A tptp.k1_xboole_0)) _let_24 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.r1_tarski A B) (tptp.r1_tarski A C) (tptp.r1_xboole_0 B C)) (= A tptp.k1_xboole_0))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (not (and (tptp.r1_tarski C A) (tptp.r1_tarski C B) (tptp.r1_xboole_0 A B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (not (and (tptp.r1_tarski B A) (tptp.r1_xboole_0 B A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.r1_xboole_0 A (tptp.k2_xboole_0 B C)))) (let ((_let_2 (tptp.r1_xboole_0 A C))) (let ((_let_3 (tptp.r1_xboole_0 A B))) (and (not (and (not _let_1) _let_3 _let_2)) (not (and (not (and _let_3 _let_2)) _let_1))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (= (tptp.k2_xboole_0 A B) (tptp.k2_xboole_0 C B)) (tptp.r1_xboole_0 A B) (tptp.r1_xboole_0 C B)) (= A C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (= (tptp.k2_xboole_0 A B) (tptp.k2_xboole_0 C D)) (tptp.r1_xboole_0 C A) (tptp.r1_xboole_0 D B)) (= C B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.r1_tarski A (tptp.k2_xboole_0 B C)) (tptp.r1_xboole_0 A C)) (tptp.r1_tarski A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (not (tptp.r1_xboole_0 A (tptp.k3_xboole_0 B C))) (tptp.r1_xboole_0 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (not (tptp.r1_xboole_0 A B)) (tptp.r1_xboole_0 (tptp.k3_xboole_0 A B) B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r1_xboole_0 A B) (tptp.r1_xboole_0 (tptp.k3_xboole_0 C A) (tptp.k3_xboole_0 C B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (not (tptp.r1_xboole_0 A B)) (tptp.r1_tarski A C) (tptp.r1_xboole_0 A (tptp.k3_xboole_0 B C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r1_xboole_0 A B) (= (tptp.k3_xboole_0 A (tptp.k2_xboole_0 B C)) (tptp.k3_xboole_0 A C)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_xboole_0 (tptp.k4_xboole_0 A B) B)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r1_xboole_0 A B) (tptp.r1_xboole_0 A (tptp.k4_xboole_0 B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r1_xboole_0 A (tptp.k4_xboole_0 B C)) (tptp.r1_xboole_0 B (tptp.k4_xboole_0 A C)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_xboole_0 (tptp.k4_xboole_0 A B) (tptp.k4_xboole_0 B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.r1_xboole_0 A B) (= (tptp.k4_xboole_0 A B) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (not (tptp.r1_xboole_0 A B)) (tptp.r1_xboole_0 A C) (tptp.r1_xboole_0 A (tptp.k4_xboole_0 B C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r1_tarski A B) (tptp.r1_xboole_0 A (tptp.k4_xboole_0 C B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.r1_tarski A B) (tptp.r1_xboole_0 A C)) (tptp.r1_tarski A (tptp.k4_xboole_0 B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r1_xboole_0 A B) (= (tptp.k2_xboole_0 (tptp.k4_xboole_0 C A) B) (tptp.k4_xboole_0 (tptp.k2_xboole_0 C B) A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r1_xboole_0 A B) (= (tptp.k4_xboole_0 (tptp.k2_xboole_0 A B) B) A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_xboole_0 (tptp.k3_xboole_0 A B) (tptp.k4_xboole_0 A B))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_xboole_0 (tptp.k4_xboole_0 A (tptp.k3_xboole_0 A B)) B)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k5_xboole_0 (tptp.k5_xboole_0 A B) C) (tptp.k5_xboole_0 A (tptp.k5_xboole_0 B C)))) (forall ((A $$unsorted)) (= (tptp.k5_xboole_0 A A) tptp.k1_xboole_0)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k2_xboole_0 A B) (tptp.k2_xboole_0 (tptp.k5_xboole_0 A B) (tptp.k3_xboole_0 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k2_xboole_0 A B) (tptp.k5_xboole_0 (tptp.k5_xboole_0 A B) (tptp.k3_xboole_0 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k3_xboole_0 A B) (tptp.k5_xboole_0 (tptp.k5_xboole_0 A B) (tptp.k2_xboole_0 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski (tptp.k4_xboole_0 A B) (tptp.k5_xboole_0 A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.r1_tarski (tptp.k4_xboole_0 A B) C) (tptp.r1_tarski (tptp.k4_xboole_0 B A) C)) (tptp.r1_tarski (tptp.k5_xboole_0 A B) C))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k2_xboole_0 A B) (tptp.k5_xboole_0 A (tptp.k4_xboole_0 B A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k4_xboole_0 (tptp.k5_xboole_0 A B) C) (tptp.k2_xboole_0 (tptp.k4_xboole_0 A (tptp.k2_xboole_0 B C)) (tptp.k4_xboole_0 B (tptp.k2_xboole_0 A C))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k4_xboole_0 A B) (tptp.k5_xboole_0 A (tptp.k3_xboole_0 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k5_xboole_0 A B) (tptp.k4_xboole_0 (tptp.k2_xboole_0 A B) (tptp.k3_xboole_0 A B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k4_xboole_0 A (tptp.k5_xboole_0 B C)) (tptp.k2_xboole_0 (tptp.k4_xboole_0 A (tptp.k2_xboole_0 B C)) (tptp.k3_xboole_0 (tptp.k3_xboole_0 A B) C)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_xboole_0 (tptp.k3_xboole_0 A B) (tptp.k5_xboole_0 A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (not (and (not (tptp.r2_xboole_0 A B)) (not (= A B)) (not (tptp.r2_xboole_0 B A)))) (tptp.r3_xboole_0 A B))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.r2_xboole_0 A B) (= (tptp.k4_xboole_0 B A) tptp.k1_xboole_0)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r1_tarski A (tptp.k4_xboole_0 B C)) (and (tptp.r1_tarski A B) (tptp.r1_xboole_0 A C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.r1_tarski A (tptp.k5_xboole_0 B C)) (and (tptp.r1_tarski A (tptp.k2_xboole_0 B C)) (tptp.r1_xboole_0 A (tptp.k3_xboole_0 B C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r1_tarski A B) (tptp.r1_tarski (tptp.k3_xboole_0 A C) B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r1_tarski A B) (tptp.r1_tarski (tptp.k4_xboole_0 A C) B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.r1_tarski A B) (tptp.r1_tarski C B)) (tptp.r1_tarski (tptp.k5_xboole_0 A C) B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k4_xboole_0 (tptp.k3_xboole_0 A B) (tptp.k3_xboole_0 C B)) (tptp.k3_xboole_0 (tptp.k4_xboole_0 A C) B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k5_xboole_0 (tptp.k3_xboole_0 A B) (tptp.k3_xboole_0 C B)) (tptp.k3_xboole_0 (tptp.k5_xboole_0 A C) B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k2_xboole_0 (tptp.k2_xboole_0 (tptp.k2_xboole_0 A B) C) D) (tptp.k2_xboole_0 A (tptp.k2_xboole_0 (tptp.k2_xboole_0 B C) D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.r1_xboole_0 A D) (tptp.r1_xboole_0 B D) (tptp.r1_xboole_0 C D)) (tptp.r1_xboole_0 (tptp.k2_xboole_0 (tptp.k2_xboole_0 A B) C) D))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (= D (tptp.k1_enumset1 A B C)) (forall ((E $$unsorted)) (= (tptp.r2_hidden E D) (not (and (not (= E A)) (not (= E B)) (not (= E C)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (= (= E (tptp.k2_enumset1 A B C D)) (forall ((F $$unsorted)) (= (tptp.r2_hidden F E) (not (and (not (= F A)) (not (= F B)) (not (= F C)) (not (= F D)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (= (= F (tptp.k3_enumset1 A B C D E)) (forall ((G $$unsorted)) (= (tptp.r2_hidden G F) (not (and (not (= G A)) (not (= G B)) (not (= G C)) (not (= G D)) (not (= G E)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted)) (= (= G (tptp.k4_enumset1 A B C D E F)) (forall ((H $$unsorted)) (= (tptp.r2_hidden H G) (not (and (not (= H A)) (not (= H B)) (not (= H C)) (not (= H D)) (not (= H E)) (not (= H F)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted)) (= (= H (tptp.k5_enumset1 A B C D E F G)) (forall ((I $$unsorted)) (= (tptp.r2_hidden I H) (not (and (not (= I A)) (not (= I B)) (not (= I C)) (not (= I D)) (not (= I E)) (not (= I F)) (not (= I G)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted) (I $$unsorted)) (= (= I (tptp.k6_enumset1 A B C D E F G H)) (forall ((J $$unsorted)) (= (tptp.r2_hidden J I) (not (and (not (= J A)) (not (= J B)) (not (= J C)) (not (= J D)) (not (= J E)) (not (= J F)) (not (= J G)) (not (= J H)))))))) true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k2_tarski A B) (tptp.k2_xboole_0 (tptp.k1_tarski A) (tptp.k1_tarski B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k1_enumset1 A B C) (tptp.k2_xboole_0 (tptp.k1_tarski A) (tptp.k2_tarski B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k1_enumset1 A B C) (tptp.k2_xboole_0 (tptp.k2_tarski A B) (tptp.k1_tarski C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k2_enumset1 A B C D) (tptp.k2_xboole_0 (tptp.k1_tarski A) (tptp.k1_enumset1 B C D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k2_enumset1 A B C D) (tptp.k2_xboole_0 (tptp.k2_tarski A B) (tptp.k2_tarski C D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k2_enumset1 A B C D) (tptp.k2_xboole_0 (tptp.k1_enumset1 A B C) (tptp.k1_tarski D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (= (tptp.k3_enumset1 A B C D E) (tptp.k2_xboole_0 (tptp.k1_tarski A) (tptp.k2_enumset1 B C D E)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (= (tptp.k3_enumset1 A B C D E) (tptp.k2_xboole_0 (tptp.k2_tarski A B) (tptp.k1_enumset1 C D E)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (= (tptp.k3_enumset1 A B C D E) (tptp.k2_xboole_0 (tptp.k1_enumset1 A B C) (tptp.k2_tarski D E)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (= (tptp.k3_enumset1 A B C D E) (tptp.k2_xboole_0 (tptp.k2_enumset1 A B C D) (tptp.k1_tarski E)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (= (tptp.k4_enumset1 A B C D E F) (tptp.k2_xboole_0 (tptp.k1_tarski A) (tptp.k3_enumset1 B C D E F)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (= (tptp.k4_enumset1 A B C D E F) (tptp.k2_xboole_0 (tptp.k2_tarski A B) (tptp.k2_enumset1 C D E F)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (= (tptp.k4_enumset1 A B C D E F) (tptp.k2_xboole_0 (tptp.k1_enumset1 A B C) (tptp.k1_enumset1 D E F)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (= (tptp.k4_enumset1 A B C D E F) (tptp.k2_xboole_0 (tptp.k2_enumset1 A B C D) (tptp.k2_tarski E F)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (= (tptp.k4_enumset1 A B C D E F) (tptp.k2_xboole_0 (tptp.k3_enumset1 A B C D E) (tptp.k1_tarski F)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted)) (= (tptp.k5_enumset1 A B C D E F G) (tptp.k2_xboole_0 (tptp.k1_tarski A) (tptp.k4_enumset1 B C D E F G)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted)) (= (tptp.k5_enumset1 A B C D E F G) (tptp.k2_xboole_0 (tptp.k2_tarski A B) (tptp.k3_enumset1 C D E F G)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted)) (= (tptp.k5_enumset1 A B C D E F G) (tptp.k2_xboole_0 (tptp.k1_enumset1 A B C) (tptp.k2_enumset1 D E F G)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted)) (= (tptp.k5_enumset1 A B C D E F G) (tptp.k2_xboole_0 (tptp.k2_enumset1 A B C D) (tptp.k1_enumset1 E F G)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted)) (= (tptp.k5_enumset1 A B C D E F G) (tptp.k2_xboole_0 (tptp.k3_enumset1 A B C D E) (tptp.k2_tarski F G)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted)) (= (tptp.k5_enumset1 A B C D E F G) (tptp.k2_xboole_0 (tptp.k4_enumset1 A B C D E F) (tptp.k1_tarski G)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted)) (= (tptp.k6_enumset1 A B C D E F G H) (tptp.k2_xboole_0 (tptp.k1_tarski A) (tptp.k5_enumset1 B C D E F G H)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted)) (= (tptp.k6_enumset1 A B C D E F G H) (tptp.k2_xboole_0 (tptp.k2_tarski A B) (tptp.k4_enumset1 C D E F G H)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted)) (= (tptp.k6_enumset1 A B C D E F G H) (tptp.k2_xboole_0 (tptp.k1_enumset1 A B C) (tptp.k3_enumset1 D E F G H)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted)) (= (tptp.k6_enumset1 A B C D E F G H) (tptp.k2_xboole_0 (tptp.k2_enumset1 A B C D) (tptp.k2_enumset1 E F G H)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted)) (= (tptp.k6_enumset1 A B C D E F G H) (tptp.k2_xboole_0 (tptp.k3_enumset1 A B C D E) (tptp.k1_enumset1 F G H)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted)) (= (tptp.k6_enumset1 A B C D E F G H) (tptp.k2_xboole_0 (tptp.k4_enumset1 A B C D E F) (tptp.k2_tarski G H)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted)) (= (tptp.k6_enumset1 A B C D E F G H) (tptp.k2_xboole_0 (tptp.k5_enumset1 A B C D E F G) (tptp.k1_tarski H)))) (forall ((A $$unsorted)) (= (tptp.k2_tarski A A) (tptp.k1_tarski A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k1_enumset1 A A B) (tptp.k2_tarski A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k2_enumset1 A A B C) (tptp.k1_enumset1 A B C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k3_enumset1 A A B C D) (tptp.k2_enumset1 A B C D))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (= (tptp.k4_enumset1 A A B C D E) (tptp.k3_enumset1 A B C D E))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (= (tptp.k5_enumset1 A A B C D E F) (tptp.k4_enumset1 A B C D E F))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted)) (= (tptp.k6_enumset1 A A B C D E F G) (tptp.k5_enumset1 A B C D E F G))) (forall ((A $$unsorted)) (= (tptp.k1_enumset1 A A A) (tptp.k1_tarski A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k2_enumset1 A A A B) (tptp.k2_tarski A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k3_enumset1 A A A B C) (tptp.k1_enumset1 A B C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k4_enumset1 A A A B C D) (tptp.k2_enumset1 A B C D))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (= (tptp.k5_enumset1 A A A B C D E) (tptp.k3_enumset1 A B C D E))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (= (tptp.k6_enumset1 A A A B C D E F) (tptp.k4_enumset1 A B C D E F))) (forall ((A $$unsorted)) (= (tptp.k2_enumset1 A A A A) (tptp.k1_tarski A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k3_enumset1 A A A A B) (tptp.k2_tarski A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k4_enumset1 A A A A B C) (tptp.k1_enumset1 A B C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k5_enumset1 A A A A B C D) (tptp.k2_enumset1 A B C D))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (= (tptp.k6_enumset1 A A A A B C D E) (tptp.k3_enumset1 A B C D E))) (forall ((A $$unsorted)) (= (tptp.k3_enumset1 A A A A A) (tptp.k1_tarski A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k4_enumset1 A A A A A B) (tptp.k2_tarski A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k5_enumset1 A A A A A B C) (tptp.k1_enumset1 A B C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k6_enumset1 A A A A A B C D) (tptp.k2_enumset1 A B C D))) (forall ((A $$unsorted)) (= (tptp.k4_enumset1 A A A A A A) (tptp.k1_tarski A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k5_enumset1 A A A A A A B) (tptp.k2_tarski A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k6_enumset1 A A A A A A B C) (tptp.k1_enumset1 A B C))) (forall ((A $$unsorted)) (= (tptp.k5_enumset1 A A A A A A A) (tptp.k1_tarski A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k6_enumset1 A A A A A A A B) (tptp.k2_tarski A B))) (forall ((A $$unsorted)) (= (tptp.k6_enumset1 A A A A A A A A) (tptp.k1_tarski A))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k1_enumset1 A B C) (tptp.k1_enumset1 A C B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k1_enumset1 A B C) (tptp.k1_enumset1 B A C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k1_enumset1 A B C) (tptp.k1_enumset1 B C A))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k1_enumset1 A B C) (tptp.k1_enumset1 C B A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k2_enumset1 A B C D) (tptp.k2_enumset1 A B D C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k2_enumset1 A B C D) (tptp.k2_enumset1 A C B D))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k2_enumset1 A B C D) (tptp.k2_enumset1 A C D B))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k2_enumset1 A B C D) (tptp.k2_enumset1 A D C B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k2_enumset1 A B C D) (tptp.k2_enumset1 B A C D))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k2_enumset1 A B C D) (tptp.k2_enumset1 B A D C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k2_enumset1 A B C D) (tptp.k2_enumset1 B C A D))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k2_enumset1 A B C D) (tptp.k2_enumset1 B C D A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k2_enumset1 A B C D) (tptp.k2_enumset1 B D A C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k2_enumset1 A B C D) (tptp.k2_enumset1 B D C A))) true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k2_enumset1 A B C D) (tptp.k2_enumset1 C B A D))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k2_enumset1 A B C D) (tptp.k2_enumset1 C B D A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k2_enumset1 A B C D) (tptp.k2_enumset1 C D A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k2_enumset1 A B C D) (tptp.k2_enumset1 C D B A))) true true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k2_enumset1 A B C D) (tptp.k2_enumset1 D B C A))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k2_enumset1 A B C D) (tptp.k2_enumset1 D C B A))) true true true true true true (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.v1_xboole_0 (tptp.k4_tarski A B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (= (tptp.r2_hidden C B) (tptp.r1_tarski C A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.k2_zfmisc_1 A B)) (forall ((D $$unsorted)) (= (tptp.r2_hidden D C) (exists ((E $$unsorted) (F $$unsorted)) (and (tptp.r2_hidden E A) (tptp.r2_hidden F B) (= D (tptp.k4_tarski E F)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k3_zfmisc_1 A B C) (tptp.k2_zfmisc_1 (tptp.k2_zfmisc_1 A B) C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k4_zfmisc_1 A B C D) (tptp.k2_zfmisc_1 (tptp.k3_zfmisc_1 A B C) D))) (= (tptp.k1_zfmisc_1 tptp.k1_xboole_0) _let_16) (= (tptp.k3_tarski tptp.k1_xboole_0) tptp.k1_xboole_0) true true true (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r1_tarski (tptp.k1_tarski A) (tptp.k1_tarski B)) (= A B))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (= (tptp.k1_tarski A) (tptp.k2_tarski B C)) (= A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (= (tptp.k1_tarski A) (tptp.k2_tarski B C)) (= B C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (not (and (= (tptp.k2_tarski A B) (tptp.k2_tarski C D)) (not (= A C)) (not (= A D))))) true (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski (tptp.k1_tarski A) (tptp.k2_tarski A B))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_tarski A))) (=> (= (tptp.k2_xboole_0 _let_1 (tptp.k1_tarski B)) _let_1) (= A B)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_tarski A B))) (= (tptp.k2_xboole_0 (tptp.k1_tarski A) _let_1) _let_1))) true (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.r1_xboole_0 (tptp.k1_tarski A) (tptp.k1_tarski B)) (= A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (= A B)) (tptp.r1_xboole_0 (tptp.k1_tarski A) (tptp.k1_tarski B)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_tarski A))) (=> (= (tptp.k3_xboole_0 _let_1 (tptp.k1_tarski B)) _let_1) (= A B)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_tarski A))) (= (tptp.k3_xboole_0 _let_1 (tptp.k2_tarski A B)) _let_1))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_tarski A))) (= (= (tptp.k4_xboole_0 _let_1 (tptp.k1_tarski B)) _let_1) (not (= A B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (= (tptp.k4_xboole_0 (tptp.k1_tarski A) (tptp.k1_tarski B)) tptp.k1_xboole_0) (= A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k4_xboole_0 (tptp.k1_tarski A) (tptp.k2_tarski A B)) tptp.k1_xboole_0)) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (= A B)) (= (tptp.k4_xboole_0 (tptp.k2_tarski A B) (tptp.k1_tarski B)) (tptp.k1_tarski A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r1_tarski (tptp.k1_tarski A) (tptp.k1_tarski B)) (= A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.r1_tarski (tptp.k1_tarski A) (tptp.k2_tarski B C)) (not (= A B)) (not (= A C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r1_tarski (tptp.k2_tarski A B) (tptp.k1_tarski C)) (= A C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_tarski C))) (let ((_let_2 (tptp.k2_tarski A B))) (=> (tptp.r1_tarski _let_2 _let_1) (= _let_2 _let_1))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (not (and (tptp.r1_tarski (tptp.k2_tarski A B) (tptp.k2_tarski C D)) (not (= A C)) (not (= A D))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (= A B)) (= (tptp.k5_xboole_0 (tptp.k1_tarski A) (tptp.k1_tarski B)) (tptp.k2_tarski A B)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_tarski A))) (= (tptp.k1_zfmisc_1 _let_1) (tptp.k2_tarski tptp.k1_xboole_0 _let_1)))) (forall ((A $$unsorted)) (= (tptp.k3_tarski (tptp.k1_tarski A)) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k3_tarski (tptp.k2_tarski (tptp.k1_tarski A) (tptp.k1_tarski B))) (tptp.k2_tarski A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (= (tptp.k4_tarski A B) (tptp.k4_tarski C D)) (and (= A C) (= B D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.r2_hidden (tptp.k4_tarski A B) (tptp.k2_zfmisc_1 (tptp.k1_tarski C) (tptp.k1_tarski D))) (and (= A C) (= B D)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k2_zfmisc_1 (tptp.k1_tarski A) (tptp.k1_tarski B)) (tptp.k1_tarski (tptp.k4_tarski A B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k4_tarski A C))) (and (= (tptp.k2_zfmisc_1 (tptp.k1_tarski A) (tptp.k2_tarski B C)) (tptp.k2_tarski (tptp.k4_tarski A B) _let_1)) (= (tptp.k2_zfmisc_1 (tptp.k2_tarski A B) (tptp.k1_tarski C)) (tptp.k2_tarski _let_1 (tptp.k4_tarski B C)))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.r1_tarski (tptp.k1_tarski A) B) (tptp.r2_hidden A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.r1_tarski (tptp.k2_tarski A B) C) (and (tptp.r2_hidden A C) (tptp.r2_hidden B C)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_tarski B))) (= (tptp.r1_tarski A _let_1) (or (= A tptp.k1_xboole_0) (= A _let_1))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r1_tarski A B) (or (tptp.r2_hidden C A) (tptp.r1_tarski A (tptp.k4_xboole_0 B (tptp.k1_tarski C)))))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (not (= A (tptp.k1_tarski B))) (not (= A tptp.k1_xboole_0)) (forall ((C $$unsorted)) (not (and (tptp.r2_hidden C A) (not (= C B)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k2_tarski B C))) (= (tptp.r1_tarski A _let_1) (not (and (not (= A tptp.k1_xboole_0)) (not (= A (tptp.k1_tarski B))) (not (= A (tptp.k1_tarski C))) (not (= A _let_1))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_tarski A))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= C _let_1))) (not (and (= _let_1 (tptp.k2_xboole_0 B C)) (not (and _let_2 _let_3)) (not (and (= B tptp.k1_xboole_0) _let_3)) (not (and _let_2 (= C tptp.k1_xboole_0))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (= (tptp.k1_tarski A) (tptp.k2_xboole_0 B C)) (not (= B C)) (not (= B tptp.k1_xboole_0)) (not (= C tptp.k1_xboole_0))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r1_tarski (tptp.k2_xboole_0 (tptp.k1_tarski A) B) B) (tptp.r2_hidden A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (= (tptp.k2_xboole_0 (tptp.k1_tarski A) B) B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r1_tarski (tptp.k2_xboole_0 (tptp.k2_tarski A B) C) C) (tptp.r2_hidden A C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.r2_hidden A B) (tptp.r2_hidden C B)) (= (tptp.k2_xboole_0 (tptp.k2_tarski A C) B) B))) (forall ((A $$unsorted) (B $$unsorted)) (not (= (tptp.k2_xboole_0 (tptp.k1_tarski A) B) tptp.k1_xboole_0))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (= (tptp.k2_xboole_0 (tptp.k2_tarski A B) C) tptp.k1_xboole_0))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_tarski B))) (=> (= (tptp.k3_xboole_0 A _let_1) _let_1) (tptp.r2_hidden B A)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_tarski A))) (=> (tptp.r2_hidden A B) (= (tptp.k3_xboole_0 B _let_1) _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k2_tarski A C))) (=> (and (tptp.r2_hidden A B) (tptp.r2_hidden C B)) (= (tptp.k3_xboole_0 _let_1 B) _let_1)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.r1_xboole_0 (tptp.k1_tarski A) B) (tptp.r2_hidden A B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.r1_xboole_0 (tptp.k2_tarski A B) C) (tptp.r2_hidden A C)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.r2_hidden A B)) (tptp.r1_xboole_0 (tptp.k1_tarski A) B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (not (tptp.r2_hidden A B)) (not (tptp.r2_hidden C B)) (not (tptp.r1_xboole_0 (tptp.k2_tarski A C) B))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_tarski A))) (or (tptp.r1_xboole_0 _let_1 B) (= (tptp.k3_xboole_0 _let_1 B) _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (= (tptp.k3_xboole_0 (tptp.k2_tarski A B) C) (tptp.k1_tarski A)) (tptp.r2_hidden B C) (not (= A B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r2_hidden A B) (or (and (tptp.r2_hidden C B) (not (= A C))) (= (tptp.k3_xboole_0 (tptp.k2_tarski A C) B) (tptp.k1_tarski A))))) true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k2_tarski A B))) (=> (= (tptp.k3_xboole_0 _let_1 C) _let_1) (tptp.r2_hidden A C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.r2_hidden A (tptp.k4_xboole_0 B (tptp.k1_tarski C))) (and (tptp.r2_hidden A B) (not (= A C))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.k4_xboole_0 A (tptp.k1_tarski B)) A) (not (tptp.r2_hidden B A)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_tarski B))) (not (and (= (tptp.k4_xboole_0 A _let_1) tptp.k1_xboole_0) (not (= A tptp.k1_xboole_0)) (not (= A _let_1)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_tarski A))) (= (= (tptp.k4_xboole_0 _let_1 B) _let_1) (not (tptp.r2_hidden A B))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.k4_xboole_0 (tptp.k1_tarski A) B) tptp.k1_xboole_0) (tptp.r2_hidden A B))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_tarski A))) (let ((_let_2 (tptp.k4_xboole_0 _let_1 B))) (or (= _let_2 tptp.k1_xboole_0) (= _let_2 _let_1))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= (tptp.k4_xboole_0 (tptp.k2_tarski A B) C) (tptp.k1_tarski A)) (and (not (tptp.r2_hidden A C)) (or (tptp.r2_hidden B C) (= A B))))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k2_tarski A B))) (= (= (tptp.k4_xboole_0 _let_1 C) _let_1) (and (not (tptp.r2_hidden A C)) (not (tptp.r2_hidden B C)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= (tptp.k4_xboole_0 (tptp.k2_tarski A B) C) tptp.k1_xboole_0) (and (tptp.r2_hidden A C) (tptp.r2_hidden B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k2_tarski A B))) (let ((_let_2 (tptp.k4_xboole_0 _let_1 C))) (not (and (not (= _let_2 tptp.k1_xboole_0)) (not (= _let_2 (tptp.k1_tarski A))) (not (= _let_2 (tptp.k1_tarski B))) (not (= _let_2 _let_1))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k2_tarski B C))) (= (= (tptp.k4_xboole_0 A _let_1) tptp.k1_xboole_0) (not (and (not (= A tptp.k1_xboole_0)) (not (= A (tptp.k1_tarski B))) (not (= A (tptp.k1_tarski C))) (not (= A _let_1))))))) true true true (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r1_tarski A B) (tptp.r1_tarski (tptp.k1_zfmisc_1 A) (tptp.k1_zfmisc_1 B)))) (forall ((A $$unsorted)) (tptp.r1_tarski (tptp.k1_tarski A) (tptp.k1_zfmisc_1 A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski (tptp.k2_xboole_0 (tptp.k1_zfmisc_1 A) (tptp.k1_zfmisc_1 B)) (tptp.k1_zfmisc_1 (tptp.k2_xboole_0 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (= (tptp.k2_xboole_0 (tptp.k1_zfmisc_1 A) (tptp.k1_zfmisc_1 B)) (tptp.k1_zfmisc_1 (tptp.k2_xboole_0 A B))) (tptp.r3_xboole_0 A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k1_zfmisc_1 (tptp.k3_xboole_0 A B)) (tptp.k3_xboole_0 (tptp.k1_zfmisc_1 A) (tptp.k1_zfmisc_1 B)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski (tptp.k1_zfmisc_1 (tptp.k4_xboole_0 A B)) (tptp.k2_xboole_0 (tptp.k1_tarski tptp.k1_xboole_0) (tptp.k4_xboole_0 (tptp.k1_zfmisc_1 A) (tptp.k1_zfmisc_1 B))))) true (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski (tptp.k2_xboole_0 (tptp.k1_zfmisc_1 (tptp.k4_xboole_0 A B)) (tptp.k1_zfmisc_1 (tptp.k4_xboole_0 B A))) (tptp.k1_zfmisc_1 (tptp.k5_xboole_0 A B)))) true true true true true (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (tptp.r1_tarski A (tptp.k3_tarski B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k3_tarski (tptp.k2_tarski A B)) (tptp.k2_xboole_0 A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted)) (=> (tptp.r2_hidden C A) (tptp.r1_tarski C B))) (tptp.r1_tarski (tptp.k3_tarski A) B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r1_tarski A B) (tptp.r1_tarski (tptp.k3_tarski A) (tptp.k3_tarski B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k3_tarski (tptp.k2_xboole_0 A B)) (tptp.k2_xboole_0 (tptp.k3_tarski A) (tptp.k3_tarski B)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski (tptp.k3_tarski (tptp.k3_xboole_0 A B)) (tptp.k3_xboole_0 (tptp.k3_tarski A) (tptp.k3_tarski B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted)) (=> (tptp.r2_hidden C A) (tptp.r1_xboole_0 C B))) (tptp.r1_xboole_0 (tptp.k3_tarski A) B))) (forall ((A $$unsorted)) (= (tptp.k3_tarski (tptp.k1_zfmisc_1 A)) A)) (forall ((A $$unsorted)) (tptp.r1_tarski A (tptp.k1_zfmisc_1 (tptp.k3_tarski A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k2_xboole_0 A B))) (=> (and (tptp.r2_hidden C _let_1) (tptp.r2_hidden D _let_1)) (or (= C D) (tptp.r1_xboole_0 C D))))) (= (tptp.k3_tarski (tptp.k3_xboole_0 A B)) (tptp.k3_xboole_0 (tptp.k3_tarski A) (tptp.k3_tarski B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.r2_hidden A (tptp.k2_zfmisc_1 B C)) (forall ((D $$unsorted) (E $$unsorted)) (not (= (tptp.k4_tarski D E) A)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (not (and (tptp.r1_tarski A (tptp.k2_zfmisc_1 B C)) (tptp.r2_hidden D A) (forall ((E $$unsorted) (F $$unsorted)) (not (and (tptp.r2_hidden E B) (tptp.r2_hidden F C) (= D (tptp.k4_tarski E F)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (not (and (tptp.r2_hidden A (tptp.k3_xboole_0 (tptp.k2_zfmisc_1 B C) (tptp.k2_zfmisc_1 D E))) (forall ((F $$unsorted) (G $$unsorted)) (not (and (= A (tptp.k4_tarski F G)) (tptp.r2_hidden F (tptp.k3_xboole_0 B D)) (tptp.r2_hidden G (tptp.k3_xboole_0 C E)))))))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski (tptp.k2_zfmisc_1 A B) (tptp.k1_zfmisc_1 (tptp.k1_zfmisc_1 (tptp.k2_xboole_0 A B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.r2_hidden (tptp.k4_tarski A B) (tptp.k2_zfmisc_1 C D)) (and (tptp.r2_hidden A C) (tptp.r2_hidden B D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.r2_hidden (tptp.k4_tarski A B) (tptp.k2_zfmisc_1 C D)) (tptp.r2_hidden (tptp.k4_tarski B A) (tptp.k2_zfmisc_1 D C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (forall ((E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.k4_tarski E F))) (= (tptp.r2_hidden _let_1 (tptp.k2_zfmisc_1 A B)) (tptp.r2_hidden _let_1 (tptp.k2_zfmisc_1 C D))))) (= (tptp.k2_zfmisc_1 A B) (tptp.k2_zfmisc_1 C D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.r1_tarski A (tptp.k2_zfmisc_1 B C)) (forall ((E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.k4_tarski E F))) (=> (tptp.r2_hidden _let_1 A) (tptp.r2_hidden _let_1 D))))) (tptp.r1_tarski A D))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (tptp.r1_tarski A (tptp.k2_zfmisc_1 B C)) (tptp.r1_tarski D (tptp.k2_zfmisc_1 E F)) (forall ((G $$unsorted) (H $$unsorted)) (let ((_let_1 (tptp.k4_tarski G H))) (= (tptp.r2_hidden _let_1 A) (tptp.r2_hidden _let_1 D))))) (= A D))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (forall ((C $$unsorted)) (not (and (tptp.r2_hidden C A) (forall ((D $$unsorted) (E $$unsorted)) (not (= C (tptp.k4_tarski D E))))))) (forall ((C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k4_tarski C D))) (=> (tptp.r2_hidden _let_1 A) (tptp.r2_hidden _let_1 B))))) (tptp.r1_tarski A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (forall ((C $$unsorted)) (not (and (tptp.r2_hidden C A) (forall ((D $$unsorted) (E $$unsorted)) (not (= C (tptp.k4_tarski D E))))))) (forall ((C $$unsorted)) (not (and (tptp.r2_hidden C B) (forall ((D $$unsorted) (E $$unsorted)) (not (= C (tptp.k4_tarski D E))))))) (forall ((C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k4_tarski C D))) (= (tptp.r2_hidden _let_1 A) (tptp.r2_hidden _let_1 B))))) (= A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.k2_zfmisc_1 A B) tptp.k1_xboole_0) (or (= A tptp.k1_xboole_0) (= B tptp.k1_xboole_0)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (= (tptp.k2_zfmisc_1 A B) (tptp.k2_zfmisc_1 B A)) (or (= A tptp.k1_xboole_0) (= B tptp.k1_xboole_0) (= A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (= (tptp.k2_zfmisc_1 A A) (tptp.k2_zfmisc_1 B B)) (= A B))) (forall ((A $$unsorted)) (=> (tptp.r1_tarski A (tptp.k2_zfmisc_1 A A)) (= A tptp.k1_xboole_0))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (or (tptp.r1_tarski (tptp.k2_zfmisc_1 B A) (tptp.k2_zfmisc_1 C A)) (tptp.r1_tarski (tptp.k2_zfmisc_1 A B) (tptp.k2_zfmisc_1 A C))) (not (tptp.r1_tarski B C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r1_tarski A B) (and (tptp.r1_tarski (tptp.k2_zfmisc_1 A C) (tptp.k2_zfmisc_1 B C)) (tptp.r1_tarski (tptp.k2_zfmisc_1 C A) (tptp.k2_zfmisc_1 C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.r1_tarski A B) (tptp.r1_tarski C D)) (tptp.r1_tarski (tptp.k2_zfmisc_1 A C) (tptp.k2_zfmisc_1 B D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k2_xboole_0 A B))) (and (= (tptp.k2_zfmisc_1 _let_1 C) (tptp.k2_xboole_0 (tptp.k2_zfmisc_1 A C) (tptp.k2_zfmisc_1 B C))) (= (tptp.k2_zfmisc_1 C _let_1) (tptp.k2_xboole_0 (tptp.k2_zfmisc_1 C A) (tptp.k2_zfmisc_1 C B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k2_zfmisc_1 (tptp.k2_xboole_0 A B) (tptp.k2_xboole_0 C D)) (tptp.k2_xboole_0 (tptp.k2_xboole_0 (tptp.k2_xboole_0 (tptp.k2_zfmisc_1 A C) (tptp.k2_zfmisc_1 A D)) (tptp.k2_zfmisc_1 B C)) (tptp.k2_zfmisc_1 B D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k3_xboole_0 A B))) (and (= (tptp.k2_zfmisc_1 _let_1 C) (tptp.k3_xboole_0 (tptp.k2_zfmisc_1 A C) (tptp.k2_zfmisc_1 B C))) (= (tptp.k2_zfmisc_1 C _let_1) (tptp.k3_xboole_0 (tptp.k2_zfmisc_1 C A) (tptp.k2_zfmisc_1 C B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k2_zfmisc_1 (tptp.k3_xboole_0 A B) (tptp.k3_xboole_0 C D)) (tptp.k3_xboole_0 (tptp.k2_zfmisc_1 A C) (tptp.k2_zfmisc_1 B D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.r1_tarski A B) (tptp.r1_tarski C D)) (= (tptp.k3_xboole_0 (tptp.k2_zfmisc_1 A D) (tptp.k2_zfmisc_1 B C)) (tptp.k2_zfmisc_1 A C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k4_xboole_0 A B))) (and (= (tptp.k2_zfmisc_1 _let_1 C) (tptp.k4_xboole_0 (tptp.k2_zfmisc_1 A C) (tptp.k2_zfmisc_1 B C))) (= (tptp.k2_zfmisc_1 C _let_1) (tptp.k4_xboole_0 (tptp.k2_zfmisc_1 C A) (tptp.k2_zfmisc_1 C B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k4_xboole_0 (tptp.k2_zfmisc_1 A B) (tptp.k2_zfmisc_1 C D)) (tptp.k2_xboole_0 (tptp.k2_zfmisc_1 (tptp.k4_xboole_0 A C) B) (tptp.k2_zfmisc_1 A (tptp.k4_xboole_0 B D))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (or (tptp.r1_xboole_0 A B) (tptp.r1_xboole_0 C D)) (tptp.r1_xboole_0 (tptp.k2_zfmisc_1 A C) (tptp.k2_zfmisc_1 B D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.r2_hidden (tptp.k4_tarski A B) (tptp.k2_zfmisc_1 (tptp.k1_tarski C) D)) (and (= A C) (tptp.r2_hidden B D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.r2_hidden (tptp.k4_tarski A B) (tptp.k2_zfmisc_1 C (tptp.k1_tarski D))) (and (tptp.r2_hidden A C) (= B D)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_tarski B))) (=> (not (= A tptp.k1_xboole_0)) (and (not (= (tptp.k2_zfmisc_1 _let_1 A) tptp.k1_xboole_0)) (not (= (tptp.k2_zfmisc_1 A _let_1) tptp.k1_xboole_0)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k1_tarski B))) (let ((_let_2 (tptp.k1_tarski A))) (=> (not (= A B)) (and (tptp.r1_xboole_0 (tptp.k2_zfmisc_1 _let_2 C) (tptp.k2_zfmisc_1 _let_1 D)) (tptp.r1_xboole_0 (tptp.k2_zfmisc_1 C _let_2) (tptp.k2_zfmisc_1 D _let_1))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_tarski B))) (let ((_let_2 (tptp.k1_tarski A))) (let ((_let_3 (tptp.k2_tarski A B))) (and (= (tptp.k2_zfmisc_1 _let_3 C) (tptp.k2_xboole_0 (tptp.k2_zfmisc_1 _let_2 C) (tptp.k2_zfmisc_1 _let_1 C))) (= (tptp.k2_zfmisc_1 C _let_3) (tptp.k2_xboole_0 (tptp.k2_zfmisc_1 C _let_2) (tptp.k2_zfmisc_1 C _let_1)))))))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (= (tptp.k2_zfmisc_1 A B) (tptp.k2_zfmisc_1 C D)) (or (= A tptp.k1_xboole_0) (= B tptp.k1_xboole_0) (and (= A C) (= B D))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (or (tptp.r1_tarski A (tptp.k2_zfmisc_1 A B)) (tptp.r1_tarski A (tptp.k2_zfmisc_1 B A))) (= A tptp.k1_xboole_0))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.r2_hidden A B) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.r2_hidden C B) (tptp.r1_tarski D C)) (tptp.r2_hidden D B))) (forall ((C $$unsorted)) (=> (tptp.r2_hidden C B) (tptp.r2_hidden (tptp.k1_zfmisc_1 C) B))) (forall ((C $$unsorted)) (not (and (tptp.r1_tarski C B) (not (tptp.r2_tarski C B)) (not (tptp.r2_hidden C B)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (tptp.r2_hidden A (tptp.k2_zfmisc_1 B C)) (tptp.r2_hidden A (tptp.k2_zfmisc_1 D E))) (tptp.r2_hidden A (tptp.k2_zfmisc_1 (tptp.k3_xboole_0 B D) (tptp.k3_xboole_0 C E))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A B))) (=> (tptp.r1_tarski _let_1 (tptp.k2_zfmisc_1 C D)) (or (= _let_1 tptp.k1_xboole_0) (and (tptp.r1_tarski A C) (tptp.r1_tarski B D)))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (or (tptp.r1_tarski (tptp.k2_zfmisc_1 A B) (tptp.k2_zfmisc_1 C D)) (tptp.r1_tarski (tptp.k2_zfmisc_1 B A) (tptp.k2_zfmisc_1 D C))) (tptp.r1_tarski B D))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_tarski A))) (=> (tptp.r2_hidden A B) (= (tptp.k2_xboole_0 (tptp.k4_xboole_0 B _let_1) _let_1) B)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_tarski A))) (=> (not (tptp.r2_hidden A B)) (= (tptp.k4_xboole_0 (tptp.k2_xboole_0 B _let_1) _let_1) B)))) true true true true (forall ((A $$unsorted)) (not (tptp.v1_xboole_0 (tptp.k1_zfmisc_1 A)))) (forall ((A $$unsorted)) (not (tptp.v1_xboole_0 (tptp.k1_tarski A)))) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.v1_xboole_0 (tptp.k2_tarski A B)))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (not (tptp.v1_xboole_0 B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B))) (not (tptp.v1_xboole_0 (tptp.k2_zfmisc_1 A B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (not (tptp.v1_xboole_0 C))) (not (tptp.v1_xboole_0 (tptp.k3_zfmisc_1 A B C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (not (tptp.v1_xboole_0 C)) (not (tptp.v1_xboole_0 D))) (not (tptp.v1_xboole_0 (tptp.k4_zfmisc_1 A B C D))))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (tptp.v1_xboole_0 B)))) true (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.m1_subset_1 B A))) (let ((_let_2 (tptp.v1_xboole_0 A))) (and (=> (not _let_2) (= _let_1 (tptp.r2_hidden B A))) (=> _let_2 (= _let_1 (tptp.v1_xboole_0 B))))))) (forall ((A $$unsorted)) (= (tptp.k1_subset_1 A) tptp.k1_xboole_0)) (forall ((A $$unsorted)) (= (tptp.k2_subset_1 A) A)) true true true (forall ((A $$unsorted)) (tptp.m1_subset_1 tptp.k1_xboole_0 (tptp.k1_zfmisc_1 A))) true true (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (=> (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (=> (tptp.r2_hidden D B) (tptp.r2_hidden D C)))) (tptp.r1_tarski B C)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (=> (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (= (tptp.r2_hidden D B) (tptp.r2_hidden D C)))) (= B C)))))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (not (and (not (= B tptp.k1_xboole_0)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (not (tptp.r2_hidden C B)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (= (tptp.k3_subset_1 A B) (tptp.k4_xboole_0 A B)))) true true true true (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 A)) (=> (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (= (tptp.r2_hidden E B) (or (tptp.r2_hidden E C) (tptp.r2_hidden E D))))) (= B (tptp.k4_subset_1 A C D))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 A)) (=> (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (= (tptp.r2_hidden E B) (and (tptp.r2_hidden E C) (tptp.r2_hidden E D))))) (= B (tptp.k5_subset_1 A C D))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 A)) (=> (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (= (tptp.r2_hidden E B) (and (tptp.r2_hidden E C) (not (tptp.r2_hidden E D)))))) (= B (tptp.k6_subset_1 A C D))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 A)) (=> (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (= (tptp.r2_hidden E B) (not (= (tptp.r2_hidden E C) (tptp.r2_hidden E D)))))) (= B (tptp.k7_subset_1 A C D))))))))) true true (forall ((A $$unsorted)) (= (tptp.k1_subset_1 A) (tptp.k3_subset_1 A (tptp.k2_subset_1 A)))) (forall ((A $$unsorted)) (= (tptp.k2_subset_1 A) (tptp.k3_subset_1 A (tptp.k1_subset_1 A)))) true true (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (= (tptp.k4_subset_1 A B (tptp.k3_subset_1 A B)) (tptp.k2_subset_1 A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (tptp.r1_xboole_0 B (tptp.k3_subset_1 A B)))) true (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_subset_1 A))) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (= (tptp.k4_subset_1 A B _let_1) _let_1)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (= (tptp.k3_subset_1 A (tptp.k4_subset_1 A B C)) (tptp.k5_subset_1 A (tptp.k3_subset_1 A B) (tptp.k3_subset_1 A C))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (= (tptp.k3_subset_1 A (tptp.k5_subset_1 A B C)) (tptp.k4_subset_1 A (tptp.k3_subset_1 A B) (tptp.k3_subset_1 A C))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (= (tptp.r1_tarski B C) (tptp.r1_tarski (tptp.k3_subset_1 A C) (tptp.k3_subset_1 A B))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (= (tptp.k6_subset_1 A B C) (tptp.k5_subset_1 A B (tptp.k3_subset_1 A C))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (= (tptp.k3_subset_1 A (tptp.k6_subset_1 A B C)) (tptp.k4_subset_1 A (tptp.k3_subset_1 A B) C)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (= (tptp.k3_subset_1 A (tptp.k7_subset_1 A B C)) (tptp.k4_subset_1 A (tptp.k5_subset_1 A B C) (tptp.k5_subset_1 A (tptp.k3_subset_1 A B) (tptp.k3_subset_1 A C)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (=> (tptp.r1_tarski B (tptp.k3_subset_1 A C)) (tptp.r1_tarski C (tptp.k3_subset_1 A B))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (=> (tptp.r1_tarski (tptp.k3_subset_1 A B) C) (tptp.r1_tarski (tptp.k3_subset_1 A C) B)))))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (= (tptp.r1_tarski B (tptp.k3_subset_1 A B)) (= B (tptp.k1_subset_1 A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (= (tptp.r1_tarski (tptp.k3_subset_1 A B) B) (= B (tptp.k2_subset_1 A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (=> (and (tptp.r1_tarski B C) (tptp.r1_tarski B (tptp.k3_subset_1 A C))) (= B tptp.k1_xboole_0)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (tptp.r1_tarski (tptp.k3_subset_1 A (tptp.k4_subset_1 A B C)) (tptp.k3_subset_1 A B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (tptp.r1_tarski (tptp.k3_subset_1 A B) (tptp.k3_subset_1 A (tptp.k5_subset_1 A B C))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (= (tptp.r1_xboole_0 B C) (tptp.r1_tarski B (tptp.k3_subset_1 A C))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (= (tptp.r1_xboole_0 B (tptp.k3_subset_1 A C)) (tptp.r1_tarski B C)))))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k3_subset_1 A C))) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (=> (and (tptp.r1_xboole_0 B C) (tptp.r1_xboole_0 (tptp.k3_subset_1 A B) _let_1)) (= B _let_1))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 A)) (=> (and (tptp.r1_tarski B C) (tptp.r1_xboole_0 D C)) (tptp.r1_tarski B (tptp.k3_subset_1 A D))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (=> (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D B) (tptp.r2_hidden D C))) (tptp.r1_tarski B C)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (=> (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (tptp.r2_hidden C B))) (= A B)))) (forall ((A $$unsorted)) (=> (not (= A tptp.k1_xboole_0)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (=> (not (tptp.r2_hidden C B)) (tptp.r2_hidden C (tptp.k3_subset_1 A B))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (=> (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (= (tptp.r2_hidden D B) (not (tptp.r2_hidden D C))))) (= B (tptp.k3_subset_1 A C))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (=> (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (= (not (tptp.r2_hidden D B)) (tptp.r2_hidden D C)))) (= B (tptp.k3_subset_1 A C))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (=> (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (not (= (tptp.r2_hidden D B) (tptp.r2_hidden D C))))) (= B (tptp.k3_subset_1 A C))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (not (and (tptp.r2_hidden B (tptp.k3_subset_1 A C)) (tptp.r2_hidden B C))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B A) (=> (not (= A tptp.k1_xboole_0)) (tptp.m1_subset_1 (tptp.k1_tarski B) (tptp.k1_zfmisc_1 A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B A) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (=> (not (= A tptp.k1_xboole_0)) (tptp.m1_subset_1 (tptp.k2_tarski B C) (tptp.k1_zfmisc_1 A))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B A) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (=> (not (= A tptp.k1_xboole_0)) (tptp.m1_subset_1 (tptp.k1_enumset1 B C D) (tptp.k1_zfmisc_1 A))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B A) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (=> (not (= A tptp.k1_xboole_0)) (tptp.m1_subset_1 (tptp.k2_enumset1 B C D E) (tptp.k1_zfmisc_1 A))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B A) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F A) (=> (not (= A tptp.k1_xboole_0)) (tptp.m1_subset_1 (tptp.k3_enumset1 B C D E F) (tptp.k1_zfmisc_1 A))))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B A) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F A) (forall ((G $$unsorted)) (=> (tptp.m1_subset_1 G A) (=> (not (= A tptp.k1_xboole_0)) (tptp.m1_subset_1 (tptp.k4_enumset1 B C D E F G) (tptp.k1_zfmisc_1 A))))))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B A) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F A) (forall ((G $$unsorted)) (=> (tptp.m1_subset_1 G A) (forall ((H $$unsorted)) (=> (tptp.m1_subset_1 H A) (=> (not (= A tptp.k1_xboole_0)) (tptp.m1_subset_1 (tptp.k5_enumset1 B C D E F G H) (tptp.k1_zfmisc_1 A))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B A) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F A) (forall ((G $$unsorted)) (=> (tptp.m1_subset_1 G A) (forall ((H $$unsorted)) (=> (tptp.m1_subset_1 H A) (forall ((I $$unsorted)) (=> (tptp.m1_subset_1 I A) (=> (not (= A tptp.k1_xboole_0)) (tptp.m1_subset_1 (tptp.k6_enumset1 B C D E F G H I) (tptp.k1_zfmisc_1 A))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (tptp.m1_subset_1 (tptp.k1_tarski A) (tptp.k1_zfmisc_1 B)))) (forall ((A $$unsorted)) (=> (not true) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B A) (= B (tptp.k8_subset_1 A)))))) (exists ((A $$unsorted)) (and (tptp.m1_subset_1 A (tptp.k1_zfmisc_1 tptp.f1_s1_subset_1)) (forall ((B $$unsorted)) (= (tptp.r2_hidden B A) (and (tptp.r2_hidden B tptp.f1_s1_subset_1) (tptp.p1_s1_subset_1 B)))))) (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A (tptp.k1_zfmisc_1 tptp.f1_s2_subset_1)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 tptp.f1_s2_subset_1)) (=> (and (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C tptp.f1_s2_subset_1) (= (tptp.r2_hidden C A) (tptp.p1_s2_subset_1 C)))) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C tptp.f1_s2_subset_1) (= (tptp.r2_hidden C B) (tptp.p1_s2_subset_1 C))))) (= A B)))))) (exists ((A $$unsorted)) (and (tptp.m1_subset_1 A (tptp.k1_zfmisc_1 tptp.f1_s3_subset_1)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B tptp.f1_s3_subset_1) (= (tptp.r2_hidden B A) (tptp.p1_s3_subset_1 B)))))) (=> (and (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A tptp.f1_s4_subset_1) (= (tptp.r2_hidden A tptp.f2_s4_subset_1) (tptp.p1_s4_subset_1 A)))) (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A tptp.f1_s4_subset_1) (= (tptp.r2_hidden A tptp.f3_s4_subset_1) (tptp.p1_s4_subset_1 A))))) (= tptp.f2_s4_subset_1 tptp.f3_s4_subset_1)) true (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.m1_subset_1 B A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A))) (forall ((C $$unsorted)) (=> (tptp.m2_subset_1 C A B) (tptp.m1_subset_1 C A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A))) (exists ((C $$unsorted)) (tptp.m2_subset_1 C A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A))) (forall ((C $$unsorted)) (= (tptp.m2_subset_1 C A B) (tptp.m1_subset_1 C B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B))) (=> (tptp.r1_subset_1 A B) (tptp.r1_subset_1 B A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B))) (not (tptp.r1_subset_1 A A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B))) (= (tptp.r1_subset_1 A B) (tptp.r1_xboole_0 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B))) (=> (tptp.r2_subset_1 A B) (tptp.r2_subset_1 B A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B))) (not (tptp.r2_subset_1 A A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B))) (= (tptp.r2_subset_1 A B) (tptp.r1_xboole_0 A B)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_subset_1 A))) (and (tptp.v1_xboole_0 _let_1) (tptp.m1_subset_1 _let_1 (tptp.k1_zfmisc_1 A))))) (forall ((A $$unsorted)) (tptp.m1_subset_1 (tptp.k2_subset_1 A) (tptp.k1_zfmisc_1 A))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 (tptp.k3_subset_1 A B) _let_1)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (= (tptp.k3_subset_1 A (tptp.k3_subset_1 A B)) B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (and (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (tptp.m1_subset_1 (tptp.k4_subset_1 A B C) _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (and (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k4_subset_1 A B C) (tptp.k4_subset_1 A C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (and (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k4_subset_1 A B B) B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (and (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k4_subset_1 A B C) (tptp.k2_xboole_0 B C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (and (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (tptp.m1_subset_1 (tptp.k5_subset_1 A B C) _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (and (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k5_subset_1 A B C) (tptp.k5_subset_1 A C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (and (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k5_subset_1 A B B) B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (and (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k5_subset_1 A B C) (tptp.k3_xboole_0 B C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (and (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (tptp.m1_subset_1 (tptp.k6_subset_1 A B C) _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (and (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k6_subset_1 A B C) (tptp.k4_xboole_0 B C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (and (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (tptp.m1_subset_1 (tptp.k7_subset_1 A B C) _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (and (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k7_subset_1 A B C) (tptp.k7_subset_1 A C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (and (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k7_subset_1 A B C) (tptp.k5_xboole_0 B C))))) (forall ((A $$unsorted)) (tptp.m1_subset_1 (tptp.k8_subset_1 A) A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (tptp.m1_subset_1 A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 A B) (or (tptp.v1_xboole_0 B) (tptp.r2_hidden A B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.m1_subset_1 A (tptp.k1_zfmisc_1 B)) (tptp.r1_tarski A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.r2_hidden A B) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 C))) (tptp.m1_subset_1 A C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.r2_hidden A B) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 C)) (tptp.v1_xboole_0 C)))) (exists ((A $$unsorted)) (and (tptp.v1_xboole_0 A) (tptp.v1_relat_1 A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_relat_1 B)) (tptp.v1_relat_1 (tptp.k3_xboole_0 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_relat_1 B)) (tptp.v1_relat_1 (tptp.k2_xboole_0 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_relat_1 B)) (tptp.v1_relat_1 (tptp.k4_xboole_0 A B)))) (forall ((A $$unsorted)) (=> (tptp.v1_xboole_0 A) (tptp.v1_relat_1 A))) _let_23 (exists ((A $$unsorted)) (and (not (tptp.v1_xboole_0 A)) (tptp.v1_relat_1 A))) (forall ((A $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v1_relat_1 A)) (not (tptp.v1_xboole_0 (tptp.k1_relat_1 A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v1_relat_1 A)) (not (tptp.v1_xboole_0 (tptp.k2_relat_1 A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_relat_1 A))) (=> (tptp.v1_xboole_0 A) (and (tptp.v1_xboole_0 _let_1) (tptp.v1_relat_1 _let_1))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k2_relat_1 A))) (=> (tptp.v1_xboole_0 A) (and (tptp.v1_xboole_0 _let_1) (tptp.v1_relat_1 _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k5_relat_1 A B))) (=> (and (tptp.v1_xboole_0 A) (tptp.v1_relat_1 B)) (and (tptp.v1_xboole_0 _let_1) (tptp.v1_relat_1 _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k5_relat_1 B A))) (=> (and (tptp.v1_xboole_0 A) (tptp.v1_relat_1 B)) (and (tptp.v1_xboole_0 _let_1) (tptp.v1_relat_1 _let_1))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k4_relat_1 A))) (=> (tptp.v1_xboole_0 A) (and (tptp.v1_xboole_0 _let_1) (tptp.v1_relat_1 _let_1))))) (and _let_20 _let_22 _let_21) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v3_relat_1 A))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k7_relat_1 A B))) (=> (and (tptp.v1_relat_1 A) (tptp.v3_relat_1 A)) (and (tptp.v1_relat_1 _let_1) (tptp.v3_relat_1 _let_1))))) (forall ((A $$unsorted)) (= (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (not (and (tptp.r2_hidden B A) (forall ((C $$unsorted) (D $$unsorted)) (not (= B (tptp.k4_tarski C D))))))))) true true (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (=> (tptp.r1_tarski A B) (tptp.v1_relat_1 A)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.v1_relat_1 (tptp.k1_tarski (tptp.k4_tarski A B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (tptp.v1_relat_1 (tptp.k2_tarski (tptp.k4_tarski A B) (tptp.k4_tarski C D)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.v1_relat_1 (tptp.k2_zfmisc_1 A B))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (= A B) (forall ((C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k4_tarski C D))) (= (tptp.r2_hidden _let_1 A) (tptp.r2_hidden _let_1 B))))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (tptp.r1_tarski A B) (forall ((C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k4_tarski C D))) (=> (tptp.r2_hidden _let_1 A) (tptp.r2_hidden _let_1 B))))))))) true true (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (tptp.v1_relat_1 (tptp.k3_xboole_0 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (tptp.v1_relat_1 (tptp.k4_xboole_0 B A)))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (= (= B (tptp.k1_relat_1 A)) (forall ((C $$unsorted)) (= (tptp.r2_hidden C B) (exists ((D $$unsorted)) (tptp.r2_hidden (tptp.k4_tarski C D) A)))))))) true true (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (tptp.k1_relat_1 (tptp.k2_xboole_0 A B)) (tptp.k2_xboole_0 (tptp.k1_relat_1 A) (tptp.k1_relat_1 B))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (tptp.r1_tarski (tptp.k1_relat_1 (tptp.k3_xboole_0 A B)) (tptp.k3_xboole_0 (tptp.k1_relat_1 A) (tptp.k1_relat_1 B))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (tptp.r1_tarski (tptp.k4_xboole_0 (tptp.k1_relat_1 A) (tptp.k1_relat_1 B)) (tptp.k1_relat_1 (tptp.k4_xboole_0 A B))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (= (= B (tptp.k2_relat_1 A)) (forall ((C $$unsorted)) (= (tptp.r2_hidden C B) (exists ((D $$unsorted)) (tptp.r2_hidden (tptp.k4_tarski D C) A)))))))) true true (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (not (and (tptp.r2_hidden A (tptp.k1_relat_1 B)) (forall ((C $$unsorted)) (not (tptp.r2_hidden C (tptp.k2_relat_1 B)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (not (and (tptp.r2_hidden A (tptp.k2_relat_1 B)) (forall ((C $$unsorted)) (not (tptp.r2_hidden C (tptp.k1_relat_1 B)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (=> (tptp.r2_hidden (tptp.k4_tarski A B) C) (and (tptp.r2_hidden A (tptp.k1_relat_1 C)) (tptp.r2_hidden B (tptp.k2_relat_1 C)))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (tptp.r1_tarski A (tptp.k2_zfmisc_1 (tptp.k1_relat_1 A) (tptp.k2_relat_1 A))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.k3_xboole_0 A (tptp.k2_zfmisc_1 (tptp.k1_relat_1 A) (tptp.k2_relat_1 A))) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (=> (= C (tptp.k1_tarski (tptp.k4_tarski A B))) (and (= (tptp.k1_relat_1 C) (tptp.k1_tarski A)) (= (tptp.k2_relat_1 C) (tptp.k1_tarski B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (tptp.v1_relat_1 E) (=> (= E (tptp.k2_tarski (tptp.k4_tarski A B) (tptp.k4_tarski C D))) (and (= (tptp.k1_relat_1 E) (tptp.k2_tarski A C)) (= (tptp.k2_relat_1 E) (tptp.k2_tarski B D)))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (=> (tptp.r1_tarski A B) (and (tptp.r1_tarski (tptp.k1_relat_1 A) (tptp.k1_relat_1 B)) (tptp.r1_tarski (tptp.k2_relat_1 A) (tptp.k2_relat_1 B)))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (tptp.k2_relat_1 (tptp.k2_xboole_0 A B)) (tptp.k2_xboole_0 (tptp.k2_relat_1 A) (tptp.k2_relat_1 B))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (tptp.r1_tarski (tptp.k2_relat_1 (tptp.k3_xboole_0 A B)) (tptp.k3_xboole_0 (tptp.k2_relat_1 A) (tptp.k2_relat_1 B))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (tptp.r1_tarski (tptp.k4_xboole_0 (tptp.k2_relat_1 A) (tptp.k2_relat_1 B)) (tptp.k2_relat_1 (tptp.k4_xboole_0 A B))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.k3_relat_1 A) (tptp.k2_xboole_0 (tptp.k1_relat_1 A) (tptp.k2_relat_1 A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k3_relat_1 A))) (=> (tptp.v1_relat_1 A) (and (tptp.r1_tarski (tptp.k1_relat_1 A) _let_1) (tptp.r1_tarski (tptp.k2_relat_1 A) _let_1))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k3_relat_1 C))) (=> (tptp.v1_relat_1 C) (=> (tptp.r2_hidden (tptp.k4_tarski A B) C) (and (tptp.r2_hidden A _let_1) (tptp.r2_hidden B _let_1)))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (=> (tptp.r1_tarski A B) (tptp.r1_tarski (tptp.k3_relat_1 A) (tptp.k3_relat_1 B))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (=> (= C (tptp.k1_tarski (tptp.k4_tarski A B))) (= (tptp.k3_relat_1 C) (tptp.k2_tarski A B))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (tptp.k3_relat_1 (tptp.k2_xboole_0 A B)) (tptp.k2_xboole_0 (tptp.k3_relat_1 A) (tptp.k3_relat_1 B))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (tptp.r1_tarski (tptp.k3_relat_1 (tptp.k3_xboole_0 A B)) (tptp.k3_xboole_0 (tptp.k3_relat_1 A) (tptp.k3_relat_1 B))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (= B (tptp.k4_relat_1 A)) (forall ((C $$unsorted) (D $$unsorted)) (= (tptp.r2_hidden (tptp.k4_tarski C D) B) (tptp.r2_hidden (tptp.k4_tarski D C) A)))))))) true true (forall ((A $$unsorted)) (let ((_let_1 (tptp.k4_relat_1 A))) (=> (tptp.v1_relat_1 A) (and (= (tptp.k2_relat_1 A) (tptp.k1_relat_1 _let_1)) (= (tptp.k1_relat_1 A) (tptp.k2_relat_1 _let_1)))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.k3_relat_1 A) (tptp.k3_relat_1 (tptp.k4_relat_1 A))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (tptp.k4_relat_1 (tptp.k3_xboole_0 A B)) (tptp.k3_xboole_0 (tptp.k4_relat_1 A) (tptp.k4_relat_1 B))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (tptp.k4_relat_1 (tptp.k2_xboole_0 A B)) (tptp.k2_xboole_0 (tptp.k4_relat_1 A) (tptp.k4_relat_1 B))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (tptp.k4_relat_1 (tptp.k4_xboole_0 A B)) (tptp.k4_xboole_0 (tptp.k4_relat_1 A) (tptp.k4_relat_1 B))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (forall ((C $$unsorted)) (=> (tptp.v1_relat_1 C) (= (= C (tptp.k5_relat_1 A B)) (forall ((D $$unsorted) (E $$unsorted)) (= (tptp.r2_hidden (tptp.k4_tarski D E) C) (exists ((F $$unsorted)) (and (tptp.r2_hidden (tptp.k4_tarski D F) A) (tptp.r2_hidden (tptp.k4_tarski F E) B)))))))))))) true true (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (tptp.r1_tarski (tptp.k1_relat_1 (tptp.k5_relat_1 A B)) (tptp.k1_relat_1 A)))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (tptp.r1_tarski (tptp.k2_relat_1 (tptp.k5_relat_1 A B)) (tptp.k2_relat_1 B)))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (=> (tptp.r1_tarski (tptp.k2_relat_1 A) (tptp.k1_relat_1 B)) (= (tptp.k1_relat_1 (tptp.k5_relat_1 A B)) (tptp.k1_relat_1 A))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (=> (tptp.r1_tarski (tptp.k1_relat_1 A) (tptp.k2_relat_1 B)) (= (tptp.k2_relat_1 (tptp.k5_relat_1 B A)) (tptp.k2_relat_1 A))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (forall ((C $$unsorted)) (=> (tptp.v1_relat_1 C) (=> (tptp.r1_tarski A B) (tptp.r1_tarski (tptp.k5_relat_1 C A) (tptp.k5_relat_1 C B))))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (forall ((C $$unsorted)) (=> (tptp.v1_relat_1 C) (=> (tptp.r1_tarski A B) (tptp.r1_tarski (tptp.k5_relat_1 A C) (tptp.k5_relat_1 B C))))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (forall ((C $$unsorted)) (=> (tptp.v1_relat_1 C) (forall ((D $$unsorted)) (=> (tptp.v1_relat_1 D) (=> (and (tptp.r1_tarski A B) (tptp.r1_tarski C D)) (tptp.r1_tarski (tptp.k5_relat_1 A C) (tptp.k5_relat_1 B D))))))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (forall ((C $$unsorted)) (=> (tptp.v1_relat_1 C) (= (tptp.k5_relat_1 A (tptp.k2_xboole_0 B C)) (tptp.k2_xboole_0 (tptp.k5_relat_1 A B) (tptp.k5_relat_1 A C))))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (forall ((C $$unsorted)) (=> (tptp.v1_relat_1 C) (tptp.r1_tarski (tptp.k5_relat_1 A (tptp.k3_xboole_0 B C)) (tptp.k3_xboole_0 (tptp.k5_relat_1 A B) (tptp.k5_relat_1 A C))))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (forall ((C $$unsorted)) (=> (tptp.v1_relat_1 C) (tptp.r1_tarski (tptp.k4_xboole_0 (tptp.k5_relat_1 A B) (tptp.k5_relat_1 A C)) (tptp.k5_relat_1 A (tptp.k4_xboole_0 B C))))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (tptp.k4_relat_1 (tptp.k5_relat_1 A B)) (tptp.k5_relat_1 (tptp.k4_relat_1 B) (tptp.k4_relat_1 A))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (forall ((C $$unsorted)) (=> (tptp.v1_relat_1 C) (= (tptp.k5_relat_1 (tptp.k5_relat_1 A B) C) (tptp.k5_relat_1 A (tptp.k5_relat_1 B C))))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (=> (forall ((B $$unsorted) (C $$unsorted)) (not (tptp.r2_hidden (tptp.k4_tarski B C) A))) (= A tptp.k1_xboole_0)))) true true true (and (= (tptp.k1_relat_1 tptp.k1_xboole_0) tptp.k1_xboole_0) _let_18) true (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (and (= (tptp.k5_relat_1 tptp.k1_xboole_0 A) tptp.k1_xboole_0) (= (tptp.k5_relat_1 A tptp.k1_xboole_0) tptp.k1_xboole_0)))) true (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (=> (or (= (tptp.k1_relat_1 A) tptp.k1_xboole_0) (= (tptp.k2_relat_1 A) tptp.k1_xboole_0)) (= A tptp.k1_xboole_0)))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (= (tptp.k1_relat_1 A) tptp.k1_xboole_0) (= (tptp.k2_relat_1 A) tptp.k1_xboole_0)))) (= (tptp.k4_relat_1 tptp.k1_xboole_0) tptp.k1_xboole_0) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (=> (tptp.r1_xboole_0 (tptp.k2_relat_1 A) (tptp.k1_relat_1 B)) (= (tptp.k5_relat_1 A B) tptp.k1_xboole_0)))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.v2_relat_1 A) (not (tptp.r2_hidden tptp.k1_xboole_0 (tptp.k2_relat_1 A)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (= B (tptp.k6_relat_1 A)) (forall ((C $$unsorted) (D $$unsorted)) (= (tptp.r2_hidden (tptp.k4_tarski C D) B) (and (tptp.r2_hidden C A) (= C D))))))) true true true (forall ((A $$unsorted)) (let ((_let_1 (tptp.k6_relat_1 A))) (and (= (tptp.k1_relat_1 _let_1) A) (= (tptp.k2_relat_1 _let_1) A)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k6_relat_1 A))) (= (tptp.k4_relat_1 _let_1) _let_1))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (=> (forall ((C $$unsorted)) (=> (tptp.r2_hidden C A) (tptp.r2_hidden (tptp.k4_tarski C C) B))) (tptp.r1_tarski (tptp.k6_relat_1 A) B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k4_tarski A B))) (=> (tptp.v1_relat_1 D) (= (tptp.r2_hidden _let_1 (tptp.k5_relat_1 (tptp.k6_relat_1 C) D)) (and (tptp.r2_hidden A C) (tptp.r2_hidden _let_1 D)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k4_tarski A B))) (=> (tptp.v1_relat_1 D) (= (tptp.r2_hidden _let_1 (tptp.k5_relat_1 D (tptp.k6_relat_1 C))) (and (tptp.r2_hidden B C) (tptp.r2_hidden _let_1 D)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k6_relat_1 A))) (=> (tptp.v1_relat_1 B) (and (tptp.r1_tarski (tptp.k5_relat_1 B _let_1) B) (tptp.r1_tarski (tptp.k5_relat_1 _let_1 B) B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (=> (tptp.r1_tarski (tptp.k1_relat_1 B) A) (= (tptp.k5_relat_1 (tptp.k6_relat_1 A) B) B)))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.k5_relat_1 (tptp.k6_relat_1 (tptp.k1_relat_1 A)) A) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (=> (tptp.r1_tarski (tptp.k2_relat_1 B) A) (= (tptp.k5_relat_1 B (tptp.k6_relat_1 A)) B)))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.k5_relat_1 A (tptp.k6_relat_1 (tptp.k2_relat_1 A))) A))) (= (tptp.k6_relat_1 tptp.k1_xboole_0) tptp.k1_xboole_0) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (forall ((C $$unsorted)) (=> (tptp.v1_relat_1 C) (forall ((D $$unsorted)) (=> (tptp.v1_relat_1 D) (=> (and (= (tptp.k1_relat_1 B) A) (tptp.r1_tarski (tptp.k2_relat_1 C) A) (= (tptp.k5_relat_1 C B) (tptp.k6_relat_1 (tptp.k1_relat_1 D))) (= (tptp.k5_relat_1 B D) (tptp.k6_relat_1 A))) (= D C)))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (= (= C (tptp.k7_relat_1 A B)) (forall ((D $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.k4_tarski D E))) (= (tptp.r2_hidden _let_1 C) (and (tptp.r2_hidden D B) (tptp.r2_hidden _let_1 A)))))))))) true true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (= (tptp.r2_hidden A (tptp.k1_relat_1 (tptp.k7_relat_1 C B))) (and (tptp.r2_hidden A B) (tptp.r2_hidden A (tptp.k1_relat_1 C)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (tptp.r1_tarski (tptp.k1_relat_1 (tptp.k7_relat_1 B A)) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (tptp.r1_tarski (tptp.k7_relat_1 B A) B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (tptp.r1_tarski (tptp.k1_relat_1 (tptp.k7_relat_1 B A)) (tptp.k1_relat_1 B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (tptp.k1_relat_1 (tptp.k7_relat_1 B A)) (tptp.k3_xboole_0 (tptp.k1_relat_1 B) A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (=> (tptp.r1_tarski A (tptp.k1_relat_1 B)) (= (tptp.k1_relat_1 (tptp.k7_relat_1 B A)) A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (forall ((C $$unsorted)) (=> (tptp.v1_relat_1 C) (tptp.r1_tarski (tptp.k5_relat_1 (tptp.k7_relat_1 B A) C) (tptp.k5_relat_1 B C)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (forall ((C $$unsorted)) (=> (tptp.v1_relat_1 C) (tptp.r1_tarski (tptp.k5_relat_1 B (tptp.k7_relat_1 C A)) (tptp.k5_relat_1 B C)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (tptp.k7_relat_1 B A) (tptp.k5_relat_1 (tptp.k6_relat_1 A) B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (= (tptp.k7_relat_1 B A) tptp.k1_xboole_0) (tptp.r1_xboole_0 (tptp.k1_relat_1 B) A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (tptp.k7_relat_1 B A) (tptp.k3_xboole_0 B (tptp.k2_zfmisc_1 A (tptp.k2_relat_1 B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (=> (tptp.r1_tarski (tptp.k1_relat_1 B) A) (= (tptp.k7_relat_1 B A) B)))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.k7_relat_1 A (tptp.k1_relat_1 A)) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (tptp.r1_tarski (tptp.k2_relat_1 (tptp.k7_relat_1 B A)) (tptp.k2_relat_1 B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (= (tptp.k7_relat_1 (tptp.k7_relat_1 C A) B) (tptp.k7_relat_1 C (tptp.k3_xboole_0 A B))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k7_relat_1 B A))) (=> (tptp.v1_relat_1 B) (= (tptp.k7_relat_1 _let_1 A) _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k7_relat_1 C A))) (=> (tptp.v1_relat_1 C) (=> (tptp.r1_tarski A B) (= (tptp.k7_relat_1 _let_1 B) _let_1))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (=> (tptp.r1_tarski A B) (= (tptp.k7_relat_1 (tptp.k7_relat_1 C B) A) (tptp.k7_relat_1 C A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (=> (tptp.r1_tarski A B) (tptp.r1_tarski (tptp.k7_relat_1 C A) (tptp.k7_relat_1 C B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (forall ((C $$unsorted)) (=> (tptp.v1_relat_1 C) (=> (tptp.r1_tarski B C) (tptp.r1_tarski (tptp.k7_relat_1 B A) (tptp.k7_relat_1 C A))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (forall ((D $$unsorted)) (=> (tptp.v1_relat_1 D) (=> (and (tptp.r1_tarski C D) (tptp.r1_tarski A B)) (tptp.r1_tarski (tptp.k7_relat_1 C A) (tptp.k7_relat_1 D B))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (= (tptp.k7_relat_1 C (tptp.k2_xboole_0 A B)) (tptp.k2_xboole_0 (tptp.k7_relat_1 C A) (tptp.k7_relat_1 C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (= (tptp.k7_relat_1 C (tptp.k3_xboole_0 A B)) (tptp.k3_xboole_0 (tptp.k7_relat_1 C A) (tptp.k7_relat_1 C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (= (tptp.k7_relat_1 C (tptp.k4_xboole_0 A B)) (tptp.k4_xboole_0 (tptp.k7_relat_1 C A) (tptp.k7_relat_1 C B))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.k7_relat_1 A tptp.k1_xboole_0) tptp.k1_xboole_0))) (forall ((A $$unsorted)) (= (tptp.k7_relat_1 tptp.k1_xboole_0 A) tptp.k1_xboole_0)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (forall ((C $$unsorted)) (=> (tptp.v1_relat_1 C) (= (tptp.k7_relat_1 (tptp.k5_relat_1 B C) A) (tptp.k5_relat_1 (tptp.k7_relat_1 B A) C)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (forall ((C $$unsorted)) (=> (tptp.v1_relat_1 C) (= (= C (tptp.k8_relat_1 A B)) (forall ((D $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.k4_tarski D E))) (= (tptp.r2_hidden _let_1 C) (and (tptp.r2_hidden E A) (tptp.r2_hidden _let_1 B)))))))))) true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (= (tptp.r2_hidden A (tptp.k2_relat_1 (tptp.k8_relat_1 B C))) (and (tptp.r2_hidden A B) (tptp.r2_hidden A (tptp.k2_relat_1 C)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (tptp.r1_tarski (tptp.k2_relat_1 (tptp.k8_relat_1 A B)) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (tptp.r1_tarski (tptp.k8_relat_1 A B) B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (tptp.r1_tarski (tptp.k2_relat_1 (tptp.k8_relat_1 A B)) (tptp.k2_relat_1 B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (tptp.k2_relat_1 (tptp.k8_relat_1 A B)) (tptp.k3_xboole_0 (tptp.k2_relat_1 B) A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (=> (tptp.r1_tarski A (tptp.k2_relat_1 B)) (= (tptp.k2_relat_1 (tptp.k8_relat_1 A B)) A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (forall ((C $$unsorted)) (=> (tptp.v1_relat_1 C) (tptp.r1_tarski (tptp.k5_relat_1 (tptp.k8_relat_1 A B) C) (tptp.k5_relat_1 B C)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (forall ((C $$unsorted)) (=> (tptp.v1_relat_1 C) (tptp.r1_tarski (tptp.k5_relat_1 B (tptp.k8_relat_1 A C)) (tptp.k5_relat_1 B C)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (tptp.k8_relat_1 A B) (tptp.k5_relat_1 B (tptp.k6_relat_1 A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (tptp.k8_relat_1 A B) (tptp.k3_xboole_0 B (tptp.k2_zfmisc_1 (tptp.k1_relat_1 B) A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (=> (tptp.r1_tarski (tptp.k2_relat_1 B) A) (= (tptp.k8_relat_1 A B) B)))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.k8_relat_1 (tptp.k2_relat_1 A) A) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (= (tptp.k8_relat_1 A (tptp.k8_relat_1 B C)) (tptp.k8_relat_1 (tptp.k3_xboole_0 A B) C)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k8_relat_1 A B))) (=> (tptp.v1_relat_1 B) (= (tptp.k8_relat_1 A _let_1) _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k8_relat_1 A C))) (=> (tptp.v1_relat_1 C) (=> (tptp.r1_tarski A B) (= (tptp.k8_relat_1 B _let_1) _let_1))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (=> (tptp.r1_tarski A B) (= (tptp.k8_relat_1 A (tptp.k8_relat_1 B C)) (tptp.k8_relat_1 A C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (=> (tptp.r1_tarski A B) (tptp.r1_tarski (tptp.k8_relat_1 A C) (tptp.k8_relat_1 B C))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (forall ((C $$unsorted)) (=> (tptp.v1_relat_1 C) (=> (tptp.r1_tarski B C) (tptp.r1_tarski (tptp.k8_relat_1 A B) (tptp.k8_relat_1 A C))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (forall ((D $$unsorted)) (=> (tptp.v1_relat_1 D) (=> (and (tptp.r1_tarski C D) (tptp.r1_tarski A B)) (tptp.r1_tarski (tptp.k8_relat_1 A C) (tptp.k8_relat_1 B D))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (= (tptp.k8_relat_1 (tptp.k2_xboole_0 A B) C) (tptp.k2_xboole_0 (tptp.k8_relat_1 A C) (tptp.k8_relat_1 B C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (= (tptp.k8_relat_1 (tptp.k3_xboole_0 A B) C) (tptp.k3_xboole_0 (tptp.k8_relat_1 A C) (tptp.k8_relat_1 B C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (= (tptp.k8_relat_1 (tptp.k4_xboole_0 A B) C) (tptp.k4_xboole_0 (tptp.k8_relat_1 A C) (tptp.k8_relat_1 B C))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.k8_relat_1 tptp.k1_xboole_0 A) tptp.k1_xboole_0))) (forall ((A $$unsorted)) (= (tptp.k8_relat_1 A tptp.k1_xboole_0) tptp.k1_xboole_0)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (forall ((C $$unsorted)) (=> (tptp.v1_relat_1 C) (= (tptp.k8_relat_1 A (tptp.k5_relat_1 B C)) (tptp.k5_relat_1 B (tptp.k8_relat_1 A C))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (= (tptp.k7_relat_1 (tptp.k8_relat_1 A C) B) (tptp.k8_relat_1 A (tptp.k7_relat_1 C B))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted) (C $$unsorted)) (= (= C (tptp.k9_relat_1 A B)) (forall ((D $$unsorted)) (= (tptp.r2_hidden D C) (exists ((E $$unsorted)) (and (tptp.r2_hidden (tptp.k4_tarski E D) A) (tptp.r2_hidden E B))))))))) true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (= (tptp.r2_hidden A (tptp.k9_relat_1 C B)) (exists ((D $$unsorted)) (and (tptp.r2_hidden D (tptp.k1_relat_1 C)) (tptp.r2_hidden (tptp.k4_tarski D A) C) (tptp.r2_hidden D B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (tptp.r1_tarski (tptp.k9_relat_1 B A) (tptp.k2_relat_1 B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (tptp.k9_relat_1 B A) (tptp.k9_relat_1 B (tptp.k3_xboole_0 (tptp.k1_relat_1 B) A))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.k9_relat_1 A (tptp.k1_relat_1 A)) (tptp.k2_relat_1 A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (tptp.r1_tarski (tptp.k9_relat_1 B A) (tptp.k9_relat_1 B (tptp.k1_relat_1 B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (tptp.k2_relat_1 (tptp.k7_relat_1 B A)) (tptp.k9_relat_1 B A)))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.k9_relat_1 A tptp.k1_xboole_0) tptp.k1_xboole_0))) (forall ((A $$unsorted)) (= (tptp.k9_relat_1 tptp.k1_xboole_0 A) tptp.k1_xboole_0)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (= (tptp.k9_relat_1 B A) tptp.k1_xboole_0) (tptp.r1_xboole_0 (tptp.k1_relat_1 B) A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (not (and (not (= A tptp.k1_xboole_0)) (tptp.r1_tarski A (tptp.k1_relat_1 B)) (= (tptp.k9_relat_1 B A) tptp.k1_xboole_0))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (= (tptp.k9_relat_1 C (tptp.k2_xboole_0 A B)) (tptp.k2_xboole_0 (tptp.k9_relat_1 C A) (tptp.k9_relat_1 C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (tptp.r1_tarski (tptp.k9_relat_1 C (tptp.k3_xboole_0 A B)) (tptp.k3_xboole_0 (tptp.k9_relat_1 C A) (tptp.k9_relat_1 C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (tptp.r1_tarski (tptp.k4_xboole_0 (tptp.k9_relat_1 C A) (tptp.k9_relat_1 C B)) (tptp.k9_relat_1 C (tptp.k4_xboole_0 A B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (=> (tptp.r1_tarski A B) (tptp.r1_tarski (tptp.k9_relat_1 C A) (tptp.k9_relat_1 C B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (forall ((C $$unsorted)) (=> (tptp.v1_relat_1 C) (=> (tptp.r1_tarski B C) (tptp.r1_tarski (tptp.k9_relat_1 B A) (tptp.k9_relat_1 C A))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (forall ((D $$unsorted)) (=> (tptp.v1_relat_1 D) (=> (and (tptp.r1_tarski C D) (tptp.r1_tarski A B)) (tptp.r1_tarski (tptp.k9_relat_1 C A) (tptp.k9_relat_1 D B))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (forall ((C $$unsorted)) (=> (tptp.v1_relat_1 C) (= (tptp.k9_relat_1 (tptp.k5_relat_1 B C) A) (tptp.k9_relat_1 C (tptp.k9_relat_1 B A))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (tptp.k2_relat_1 (tptp.k5_relat_1 A B)) (tptp.k9_relat_1 B (tptp.k2_relat_1 A))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (tptp.r1_tarski (tptp.k9_relat_1 (tptp.k7_relat_1 C A) B) (tptp.k9_relat_1 C B)))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (tptp.r1_tarski (tptp.k3_xboole_0 (tptp.k1_relat_1 B) A) (tptp.k9_relat_1 (tptp.k4_relat_1 B) (tptp.k9_relat_1 B A))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted) (C $$unsorted)) (= (= C (tptp.k10_relat_1 A B)) (forall ((D $$unsorted)) (= (tptp.r2_hidden D C) (exists ((E $$unsorted)) (and (tptp.r2_hidden (tptp.k4_tarski D E) A) (tptp.r2_hidden E B))))))))) true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (= (tptp.r2_hidden A (tptp.k10_relat_1 C B)) (exists ((D $$unsorted)) (and (tptp.r2_hidden D (tptp.k2_relat_1 C)) (tptp.r2_hidden (tptp.k4_tarski A D) C) (tptp.r2_hidden D B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (tptp.r1_tarski (tptp.k10_relat_1 B A) (tptp.k1_relat_1 B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (tptp.k10_relat_1 B A) (tptp.k10_relat_1 B (tptp.k3_xboole_0 (tptp.k2_relat_1 B) A))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.k10_relat_1 A (tptp.k2_relat_1 A)) (tptp.k1_relat_1 A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (tptp.r1_tarski (tptp.k10_relat_1 B A) (tptp.k10_relat_1 B (tptp.k2_relat_1 B))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.k10_relat_1 A tptp.k1_xboole_0) tptp.k1_xboole_0))) (forall ((A $$unsorted)) (= (tptp.k10_relat_1 tptp.k1_xboole_0 A) tptp.k1_xboole_0)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (= (tptp.k10_relat_1 B A) tptp.k1_xboole_0) (tptp.r1_xboole_0 (tptp.k2_relat_1 B) A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (not (and (not (= A tptp.k1_xboole_0)) (tptp.r1_tarski A (tptp.k2_relat_1 B)) (= (tptp.k10_relat_1 B A) tptp.k1_xboole_0))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (= (tptp.k10_relat_1 C (tptp.k2_xboole_0 A B)) (tptp.k2_xboole_0 (tptp.k10_relat_1 C A) (tptp.k10_relat_1 C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (tptp.r1_tarski (tptp.k10_relat_1 C (tptp.k3_xboole_0 A B)) (tptp.k3_xboole_0 (tptp.k10_relat_1 C A) (tptp.k10_relat_1 C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (tptp.r1_tarski (tptp.k4_xboole_0 (tptp.k10_relat_1 C A) (tptp.k10_relat_1 C B)) (tptp.k10_relat_1 C (tptp.k4_xboole_0 A B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (=> (tptp.r1_tarski A B) (tptp.r1_tarski (tptp.k10_relat_1 C A) (tptp.k10_relat_1 C B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (forall ((C $$unsorted)) (=> (tptp.v1_relat_1 C) (=> (tptp.r1_tarski B C) (tptp.r1_tarski (tptp.k10_relat_1 B A) (tptp.k10_relat_1 C A))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (forall ((D $$unsorted)) (=> (tptp.v1_relat_1 D) (=> (and (tptp.r1_tarski C D) (tptp.r1_tarski A B)) (tptp.r1_tarski (tptp.k10_relat_1 C A) (tptp.k10_relat_1 D B))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (forall ((C $$unsorted)) (=> (tptp.v1_relat_1 C) (= (tptp.k10_relat_1 (tptp.k5_relat_1 B C) A) (tptp.k10_relat_1 B (tptp.k10_relat_1 C A))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (tptp.k1_relat_1 (tptp.k5_relat_1 A B)) (tptp.k10_relat_1 A (tptp.k1_relat_1 B))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (tptp.r1_tarski (tptp.k3_xboole_0 (tptp.k2_relat_1 B) A) (tptp.k10_relat_1 (tptp.k4_relat_1 B) (tptp.k10_relat_1 B A))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.v3_relat_1 A) (tptp.r1_tarski (tptp.k2_relat_1 A) (tptp.k1_tarski tptp.k1_xboole_0))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.v3_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.r2_hidden B (tptp.k2_relat_1 A)) (= B tptp.k1_xboole_0)))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (forall ((C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k2_xboole_0 C D))) (=> (and (= (tptp.k7_relat_1 A C) (tptp.k7_relat_1 B C)) (= (tptp.k7_relat_1 A D) (tptp.k7_relat_1 B D))) (= (tptp.k7_relat_1 A _let_1) (tptp.k7_relat_1 B _let_1))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (forall ((C $$unsorted)) (=> (tptp.v1_relat_1 C) (=> (and (tptp.r1_tarski (tptp.k1_relat_1 C) A) (tptp.r1_tarski C B)) (tptp.r1_tarski C (tptp.k7_relat_1 B A))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.r1_xboole_0 B (tptp.k1_relat_1 A)) (= (tptp.k7_relat_1 A B) tptp.k1_xboole_0))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.r1_tarski C D) (= (tptp.k7_relat_1 A D) (tptp.k7_relat_1 B D))) (= (tptp.k7_relat_1 A C) (tptp.k7_relat_1 B C)))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (tptp.k7_relat_1 A (tptp.k1_relat_1 B)) (tptp.k7_relat_1 A (tptp.k1_relat_1 (tptp.k7_relat_1 B (tptp.k1_relat_1 A))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (not (and (not (tptp.v3_relat_1 (tptp.k7_relat_1 B A))) (tptp.v3_relat_1 B))))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.r2_hidden (tptp.k4_tarski B C) A) (and (tptp.r2_hidden B tptp.f1_s1_relat_1) (tptp.r2_hidden C tptp.f2_s1_relat_1) (tptp.p1_s1_relat_1 B C)))))) true true true (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (tptp.v1_relat_1 (tptp.k4_relat_1 A)))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.k4_relat_1 (tptp.k4_relat_1 A)) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_relat_1 B)) (tptp.v1_relat_1 (tptp.k5_relat_1 A B)))) (forall ((A $$unsorted)) (tptp.v1_relat_1 (tptp.k6_relat_1 A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 A) (tptp.v1_relat_1 (tptp.k7_relat_1 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (tptp.v1_relat_1 (tptp.k8_relat_1 A B)))) true true (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A))) (forall ((A $$unsorted)) (=> (tptp.v1_xboole_0 A) (tptp.v1_funct_1 A))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k5_relat_1 A B))) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (and (tptp.v1_relat_1 _let_1) (tptp.v1_funct_1 _let_1))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k6_relat_1 A))) (and (tptp.v1_relat_1 _let_1) (tptp.v1_funct_1 _let_1)))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_xboole_0 A) (tptp.v1_funct_1 A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.v1_funct_1 A))) (let ((_let_2 (tptp.v1_relat_1 A))) (=> (and _let_2 (tptp.v1_xboole_0 A) _let_1) (and _let_2 _let_1 (tptp.v2_funct_1 A)))))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v2_funct_1 A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k4_relat_1 A))) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v2_funct_1 A)) (and (tptp.v1_relat_1 _let_1) (tptp.v1_funct_1 _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k7_relat_1 A B))) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (and (tptp.v1_relat_1 _let_1) (tptp.v1_funct_1 _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k8_relat_1 A B))) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (and (tptp.v1_relat_1 _let_1) (tptp.v1_funct_1 _let_1))))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v3_relat_1 A) (tptp.v1_funct_1 A))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v2_relat_1 A) (tptp.v1_funct_1 A))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v2_relat_1 A) (tptp.v1_funct_1 A)) (tptp.v1_setfam_1 (tptp.k2_relat_1 A)))) (forall ((A $$unsorted)) (= (tptp.v1_funct_1 A) (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.r2_hidden (tptp.k4_tarski B C) A) (tptp.r2_hidden (tptp.k4_tarski B D) A)) (= C D))))) true (forall ((A $$unsorted)) (=> (and (forall ((B $$unsorted)) (not (and (tptp.r2_hidden B A) (forall ((C $$unsorted) (D $$unsorted)) (not (= (tptp.k4_tarski C D) B)))))) (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.r2_hidden (tptp.k4_tarski B C) A) (tptp.r2_hidden (tptp.k4_tarski B D) A)) (= C D)))) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)))) true true (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted) (C $$unsorted)) (let ((_let_1 (= C (tptp.k1_funct_1 A B)))) (let ((_let_2 (tptp.r2_hidden B (tptp.k1_relat_1 A)))) (and (=> _let_2 (= _let_1 (tptp.r2_hidden (tptp.k4_tarski B C) A))) (=> (not _let_2) (= _let_1 (= C tptp.k1_xboole_0))))))))) true true true true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (= (tptp.r2_hidden (tptp.k4_tarski A B) C) (and (tptp.r2_hidden A (tptp.k1_relat_1 C)) (= B (tptp.k1_funct_1 C A)))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (and (= (tptp.k1_relat_1 A) (tptp.k1_relat_1 B)) (forall ((C $$unsorted)) (=> (tptp.r2_hidden C (tptp.k1_relat_1 A)) (= (tptp.k1_funct_1 A C) (tptp.k1_funct_1 B C))))) (= A B)))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted)) (= (= B (tptp.k2_relat_1 A)) (forall ((C $$unsorted)) (= (tptp.r2_hidden C B) (exists ((D $$unsorted)) (and (tptp.r2_hidden D (tptp.k1_relat_1 A)) (= C (tptp.k1_funct_1 A D)))))))))) true true (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (tptp.r2_hidden A (tptp.k1_relat_1 B)) (tptp.r2_hidden (tptp.k1_funct_1 B A) (tptp.k2_relat_1 B))))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (= (tptp.k1_relat_1 B) (tptp.k1_tarski A)) (= (tptp.k2_relat_1 B) (tptp.k1_tarski (tptp.k1_funct_1 B A)))))) (forall ((A $$unsorted)) (=> (not (= A tptp.k1_xboole_0)) (forall ((B $$unsorted)) (exists ((C $$unsorted)) (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (= (tptp.k1_relat_1 C) A) (= (tptp.k2_relat_1 C) (tptp.k1_tarski B))))))) (forall ((A $$unsorted)) (=> (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (forall ((C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (and (= (tptp.k1_relat_1 B) A) (= (tptp.k1_relat_1 C) A)) (= B C)))))) (= A tptp.k1_xboole_0))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k1_tarski A))) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (and (= (tptp.k1_relat_1 B) (tptp.k1_relat_1 C)) (= (tptp.k2_relat_1 B) _let_1) (= (tptp.k2_relat_1 C) _let_1)) (= B C))))))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (not (and (= A tptp.k1_xboole_0) (not (= B tptp.k1_xboole_0)))) (forall ((C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (not (and (= B (tptp.k1_relat_1 C)) (tptp.r1_tarski (tptp.k2_relat_1 C) A)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (forall ((C $$unsorted)) (not (and (tptp.r2_hidden C A) (forall ((D $$unsorted)) (not (and (tptp.r2_hidden D (tptp.k1_relat_1 B)) (= C (tptp.k1_funct_1 B D)))))))) (tptp.r1_tarski A (tptp.k2_relat_1 B))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (forall ((C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (and (forall ((D $$unsorted)) (= (tptp.r2_hidden D (tptp.k1_relat_1 C)) (and (tptp.r2_hidden D (tptp.k1_relat_1 A)) (tptp.r2_hidden (tptp.k1_funct_1 A D) (tptp.k1_relat_1 B))))) (forall ((D $$unsorted)) (=> (tptp.r2_hidden D (tptp.k1_relat_1 C)) (= (tptp.k1_funct_1 C D) (tptp.k1_funct_1 B (tptp.k1_funct_1 A D)))))) (= C (tptp.k5_relat_1 A B))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (forall ((C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (= (tptp.r2_hidden A (tptp.k1_relat_1 (tptp.k5_relat_1 C B))) (and (tptp.r2_hidden A (tptp.k1_relat_1 C)) (tptp.r2_hidden (tptp.k1_funct_1 C A) (tptp.k1_relat_1 B)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k5_relat_1 C B))) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (tptp.r2_hidden A (tptp.k1_relat_1 _let_1)) (= (tptp.k1_funct_1 _let_1 A) (tptp.k1_funct_1 B (tptp.k1_funct_1 C A))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (forall ((C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (tptp.r2_hidden A (tptp.k1_relat_1 B)) (= (tptp.k1_funct_1 (tptp.k5_relat_1 B C) A) (tptp.k1_funct_1 C (tptp.k1_funct_1 B A)))))))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (forall ((C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (tptp.r2_hidden A (tptp.k2_relat_1 (tptp.k5_relat_1 C B))) (tptp.r2_hidden A (tptp.k2_relat_1 B))))))) true (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (= (tptp.k1_relat_1 (tptp.k5_relat_1 B A)) (tptp.k1_relat_1 B)) (tptp.r1_tarski (tptp.k2_relat_1 B) (tptp.k1_relat_1 A))))))) true true true true true (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_relat_1 B))) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (and (tptp.r1_tarski _let_1 A) (forall ((C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (forall ((D $$unsorted)) (=> (and (tptp.v1_relat_1 D) (tptp.v1_funct_1 D)) (=> (and (= (tptp.k1_relat_1 C) A) (= (tptp.k1_relat_1 D) A) (= (tptp.k5_relat_1 B C) (tptp.k5_relat_1 B D))) (= C D))))))) (= A _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (= (= B (tptp.k6_relat_1 A)) (and (= (tptp.k1_relat_1 B) A) (forall ((C $$unsorted)) (=> (tptp.r2_hidden C A) (= (tptp.k1_funct_1 B C) C))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden B A) (= (tptp.k1_funct_1 (tptp.k6_relat_1 A) B) B))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (= (tptp.k1_relat_1 (tptp.k5_relat_1 (tptp.k6_relat_1 A) B)) (tptp.k3_xboole_0 (tptp.k1_relat_1 B) A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (tptp.r2_hidden B (tptp.k3_xboole_0 (tptp.k1_relat_1 C) A)) (= (tptp.k1_funct_1 C B) (tptp.k1_funct_1 (tptp.k5_relat_1 (tptp.k6_relat_1 A) C) B))))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (= (tptp.r2_hidden B (tptp.k1_relat_1 (tptp.k5_relat_1 C (tptp.k6_relat_1 A)))) (and (tptp.r2_hidden B (tptp.k1_relat_1 C)) (tptp.r2_hidden (tptp.k1_funct_1 C B) A))))) true (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (and (= (tptp.k5_relat_1 (tptp.k6_relat_1 (tptp.k1_relat_1 A)) A) A) (= (tptp.k5_relat_1 A (tptp.k6_relat_1 (tptp.k2_relat_1 A))) A)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k5_relat_1 (tptp.k6_relat_1 B) (tptp.k6_relat_1 A)) (tptp.k6_relat_1 (tptp.k3_xboole_0 A B)))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k1_relat_1 B))) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (and (= (tptp.k2_relat_1 A) _let_1) (= (tptp.k5_relat_1 A B) A)) (= B (tptp.k6_relat_1 _let_1)))))))) true true (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (= (tptp.v2_funct_1 A) (forall ((B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_relat_1 A))) (=> (and (tptp.r2_hidden B _let_1) (tptp.r2_hidden C _let_1) (= (tptp.k1_funct_1 A B) (tptp.k1_funct_1 A C))) (= B C))))))) true (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (and (tptp.v2_funct_1 A) (tptp.v2_funct_1 B)) (tptp.v2_funct_1 (tptp.k5_relat_1 A B))))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (and (tptp.v2_funct_1 (tptp.k5_relat_1 B A)) (tptp.r1_tarski (tptp.k2_relat_1 B) (tptp.k1_relat_1 A))) (tptp.v2_funct_1 B)))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (and (tptp.v2_funct_1 (tptp.k5_relat_1 B A)) (= (tptp.k2_relat_1 B) (tptp.k1_relat_1 A))) (and (tptp.v2_funct_1 B) (tptp.v2_funct_1 A))))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (= (tptp.v2_funct_1 A) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k1_relat_1 A))) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (and (tptp.r1_tarski (tptp.k2_relat_1 B) _let_1) (tptp.r1_tarski (tptp.k2_relat_1 C) _let_1) (= (tptp.k1_relat_1 B) (tptp.k1_relat_1 C)) (= (tptp.k5_relat_1 B A) (tptp.k5_relat_1 C A))) (= B C)))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (forall ((C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (and (= (tptp.k1_relat_1 B) A) (= (tptp.k1_relat_1 C) A) (tptp.r1_tarski (tptp.k2_relat_1 C) A) (tptp.v2_funct_1 B) (= (tptp.k5_relat_1 C B) B)) (= C (tptp.k6_relat_1 A))))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (and (= (tptp.k2_relat_1 (tptp.k5_relat_1 B A)) (tptp.k2_relat_1 A)) (tptp.v2_funct_1 A)) (tptp.r1_tarski (tptp.k1_relat_1 A) (tptp.k2_relat_1 B))))))) (forall ((A $$unsorted)) (tptp.v2_funct_1 (tptp.k6_relat_1 A))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (=> (exists ((B $$unsorted)) (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B) (= (tptp.k5_relat_1 A B) (tptp.k6_relat_1 (tptp.k1_relat_1 A))))) (tptp.v2_funct_1 A)))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (=> (tptp.v2_funct_1 A) (= (tptp.k2_funct_1 A) (tptp.k4_relat_1 A))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (=> (tptp.v2_funct_1 A) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (= (= B (tptp.k2_funct_1 A)) (and (= (tptp.k1_relat_1 B) (tptp.k2_relat_1 A)) (forall ((C $$unsorted) (D $$unsorted)) (let ((_let_1 (and (tptp.r2_hidden C (tptp.k2_relat_1 A)) (= D (tptp.k1_funct_1 B C))))) (let ((_let_2 (and (tptp.r2_hidden D (tptp.k1_relat_1 A)) (= C (tptp.k1_funct_1 A D))))) (and (=> _let_1 _let_2) (=> _let_2 _let_1)))))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k2_funct_1 A))) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (=> (tptp.v2_funct_1 A) (and (= (tptp.k2_relat_1 A) (tptp.k1_relat_1 _let_1)) (= (tptp.k1_relat_1 A) (tptp.k2_relat_1 _let_1))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_funct_1 B))) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (and (tptp.v2_funct_1 B) (tptp.r2_hidden A (tptp.k1_relat_1 B))) (and (= A (tptp.k1_funct_1 _let_1 (tptp.k1_funct_1 B A))) (= A (tptp.k1_funct_1 (tptp.k5_relat_1 B _let_1) A))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_funct_1 B))) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (and (tptp.v2_funct_1 B) (tptp.r2_hidden A (tptp.k2_relat_1 B))) (and (= A (tptp.k1_funct_1 B (tptp.k1_funct_1 _let_1 A))) (= A (tptp.k1_funct_1 (tptp.k5_relat_1 _let_1 B) A))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_relat_1 A))) (let ((_let_2 (tptp.k5_relat_1 A (tptp.k2_funct_1 A)))) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (=> (tptp.v2_funct_1 A) (and (= (tptp.k1_relat_1 _let_2) _let_1) (= (tptp.k2_relat_1 _let_2) _let_1))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k2_relat_1 A))) (let ((_let_2 (tptp.k5_relat_1 (tptp.k2_funct_1 A) A))) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (=> (tptp.v2_funct_1 A) (and (= (tptp.k1_relat_1 _let_2) _let_1) (= (tptp.k2_relat_1 _let_2) _let_1))))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (and (tptp.v2_funct_1 A) (= (tptp.k1_relat_1 A) (tptp.k2_relat_1 B)) (= (tptp.k2_relat_1 A) (tptp.k1_relat_1 B)) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.r2_hidden C (tptp.k1_relat_1 A)) (tptp.r2_hidden D (tptp.k1_relat_1 B))) (= (= (tptp.k1_funct_1 A C) D) (= (tptp.k1_funct_1 B D) C))))) (= B (tptp.k2_funct_1 A))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k2_funct_1 A))) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (=> (tptp.v2_funct_1 A) (and (= (tptp.k5_relat_1 A _let_1) (tptp.k6_relat_1 (tptp.k1_relat_1 A))) (= (tptp.k5_relat_1 _let_1 A) (tptp.k6_relat_1 (tptp.k2_relat_1 A)))))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (=> (tptp.v2_funct_1 A) (tptp.v2_funct_1 (tptp.k2_funct_1 A))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (and (tptp.v2_funct_1 A) (= (tptp.k2_relat_1 A) (tptp.k1_relat_1 B)) (= (tptp.k5_relat_1 A B) (tptp.k6_relat_1 (tptp.k1_relat_1 A)))) (= B (tptp.k2_funct_1 A))))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (and (tptp.v2_funct_1 A) (= (tptp.k2_relat_1 B) (tptp.k1_relat_1 A)) (= (tptp.k5_relat_1 B A) (tptp.k6_relat_1 (tptp.k2_relat_1 A)))) (= B (tptp.k2_funct_1 A))))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (=> (tptp.v2_funct_1 A) (= (tptp.k2_funct_1 (tptp.k2_funct_1 A)) A)))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (and (tptp.v2_funct_1 A) (tptp.v2_funct_1 B)) (= (tptp.k2_funct_1 (tptp.k5_relat_1 A B)) (tptp.k5_relat_1 (tptp.k2_funct_1 B) (tptp.k2_funct_1 A)))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k6_relat_1 A))) (= (tptp.k2_funct_1 _let_1) _let_1))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (forall ((C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (= (= B (tptp.k7_relat_1 C A)) (and (= (tptp.k1_relat_1 B) (tptp.k3_xboole_0 (tptp.k1_relat_1 C) A)) (forall ((D $$unsorted)) (=> (tptp.r2_hidden D (tptp.k1_relat_1 B)) (= (tptp.k1_funct_1 B D) (tptp.k1_funct_1 C D)))))))))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k7_relat_1 C A))) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (tptp.r2_hidden B (tptp.k1_relat_1 _let_1)) (= (tptp.k1_funct_1 _let_1 B) (tptp.k1_funct_1 C B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (tptp.r2_hidden B (tptp.k3_xboole_0 (tptp.k1_relat_1 C) A)) (= (tptp.k1_funct_1 (tptp.k7_relat_1 C A) B) (tptp.k1_funct_1 C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (tptp.r2_hidden B A) (= (tptp.k1_funct_1 (tptp.k7_relat_1 C A) B) (tptp.k1_funct_1 C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (and (tptp.r2_hidden B (tptp.k1_relat_1 C)) (tptp.r2_hidden B A)) (tptp.r2_hidden (tptp.k1_funct_1 C B) (tptp.k2_relat_1 (tptp.k7_relat_1 C A)))))) true true (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k7_relat_1 B A))) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (and (tptp.r1_tarski (tptp.k1_relat_1 _let_1) (tptp.k1_relat_1 B)) (tptp.r1_tarski (tptp.k2_relat_1 _let_1) (tptp.k2_relat_1 B)))))) true true true true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k7_relat_1 C A))) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (tptp.r1_tarski A B) (and (= (tptp.k7_relat_1 _let_1 B) _let_1) (= (tptp.k7_relat_1 (tptp.k7_relat_1 C B) A) _let_1)))))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (tptp.v2_funct_1 B) (tptp.v2_funct_1 (tptp.k7_relat_1 B A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (forall ((C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (= (= B (tptp.k8_relat_1 A C)) (and (forall ((D $$unsorted)) (= (tptp.r2_hidden D (tptp.k1_relat_1 B)) (and (tptp.r2_hidden D (tptp.k1_relat_1 C)) (tptp.r2_hidden (tptp.k1_funct_1 C D) A)))) (forall ((D $$unsorted)) (=> (tptp.r2_hidden D (tptp.k1_relat_1 B)) (= (tptp.k1_funct_1 B D) (tptp.k1_funct_1 C D)))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (= (tptp.r2_hidden B (tptp.k1_relat_1 (tptp.k8_relat_1 A C))) (and (tptp.r2_hidden B (tptp.k1_relat_1 C)) (tptp.r2_hidden (tptp.k1_funct_1 C B) A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k8_relat_1 A C))) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (tptp.r2_hidden B (tptp.k1_relat_1 _let_1)) (= (tptp.k1_funct_1 _let_1 B) (tptp.k1_funct_1 C B)))))) true (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k8_relat_1 A B))) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (and (tptp.r1_tarski (tptp.k1_relat_1 _let_1) (tptp.k1_relat_1 B)) (tptp.r1_tarski (tptp.k2_relat_1 _let_1) (tptp.k2_relat_1 B)))))) true true true true true true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k8_relat_1 A C))) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (tptp.r1_tarski A B) (and (= (tptp.k8_relat_1 B _let_1) _let_1) (= (tptp.k8_relat_1 A (tptp.k8_relat_1 B C)) _let_1)))))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (tptp.v2_funct_1 B) (tptp.v2_funct_1 (tptp.k8_relat_1 A B))))) true true (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted) (C $$unsorted)) (= (= C (tptp.k9_relat_1 A B)) (forall ((D $$unsorted)) (= (tptp.r2_hidden D C) (exists ((E $$unsorted)) (and (tptp.r2_hidden E (tptp.k1_relat_1 A)) (tptp.r2_hidden E B) (= D (tptp.k1_funct_1 A E)))))))))) true true true true true true true true true true true true true true true true true (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (tptp.r2_hidden A (tptp.k1_relat_1 B)) (= (tptp.k9_relat_1 B (tptp.k1_tarski A)) (tptp.k1_tarski (tptp.k1_funct_1 B A)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_relat_1 C))) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (and (tptp.r2_hidden A _let_1) (tptp.r2_hidden B _let_1)) (= (tptp.k9_relat_1 C (tptp.k2_tarski A B)) (tptp.k2_tarski (tptp.k1_funct_1 C A) (tptp.k1_funct_1 C B))))))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (tptp.r1_tarski (tptp.k9_relat_1 (tptp.k8_relat_1 A C) B) (tptp.k9_relat_1 C B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (tptp.v2_funct_1 C) (= (tptp.k9_relat_1 C (tptp.k3_xboole_0 A B)) (tptp.k3_xboole_0 (tptp.k9_relat_1 C A) (tptp.k9_relat_1 C B)))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (=> (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.k9_relat_1 A (tptp.k3_xboole_0 B C)) (tptp.k3_xboole_0 (tptp.k9_relat_1 A B) (tptp.k9_relat_1 A C)))) (tptp.v2_funct_1 A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (tptp.v2_funct_1 C) (= (tptp.k9_relat_1 C (tptp.k4_xboole_0 A B)) (tptp.k4_xboole_0 (tptp.k9_relat_1 C A) (tptp.k9_relat_1 C B)))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (=> (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.k9_relat_1 A (tptp.k4_xboole_0 B C)) (tptp.k4_xboole_0 (tptp.k9_relat_1 A B) (tptp.k9_relat_1 A C)))) (tptp.v2_funct_1 A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (and (tptp.r1_xboole_0 A B) (tptp.v2_funct_1 C)) (tptp.r1_xboole_0 (tptp.k9_relat_1 C A) (tptp.k9_relat_1 C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (= (tptp.k9_relat_1 (tptp.k8_relat_1 A C) B) (tptp.k3_xboole_0 A (tptp.k9_relat_1 C B))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted) (C $$unsorted)) (= (= C (tptp.k10_relat_1 A B)) (forall ((D $$unsorted)) (= (tptp.r2_hidden D C) (and (tptp.r2_hidden D (tptp.k1_relat_1 A)) (tptp.r2_hidden (tptp.k1_funct_1 A D) B)))))))) true true true true true true true true true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (= (tptp.k10_relat_1 C (tptp.k3_xboole_0 A B)) (tptp.k3_xboole_0 (tptp.k10_relat_1 C A) (tptp.k10_relat_1 C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (= (tptp.k10_relat_1 C (tptp.k4_xboole_0 A B)) (tptp.k4_xboole_0 (tptp.k10_relat_1 C A) (tptp.k10_relat_1 C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (= (tptp.k10_relat_1 (tptp.k7_relat_1 C A) B) (tptp.k3_xboole_0 A (tptp.k10_relat_1 C B))))) true true (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (tptp.r2_hidden A (tptp.k2_relat_1 B)) (not (= (tptp.k10_relat_1 B (tptp.k1_tarski A)) tptp.k1_xboole_0))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (=> (forall ((C $$unsorted)) (not (and (tptp.r2_hidden C A) (= (tptp.k10_relat_1 B (tptp.k1_tarski C)) tptp.k1_xboole_0)))) (tptp.r1_tarski A (tptp.k2_relat_1 B))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (= (forall ((B $$unsorted)) (not (and (tptp.r2_hidden B (tptp.k2_relat_1 A)) (forall ((C $$unsorted)) (not (= (tptp.k10_relat_1 A (tptp.k1_tarski B)) (tptp.k1_tarski C))))))) (tptp.v2_funct_1 A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (tptp.r1_tarski (tptp.k9_relat_1 B (tptp.k10_relat_1 B A)) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (=> (tptp.r1_tarski A (tptp.k1_relat_1 B)) (tptp.r1_tarski A (tptp.k10_relat_1 B (tptp.k9_relat_1 B A)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (tptp.r1_tarski A (tptp.k2_relat_1 B)) (= (tptp.k9_relat_1 B (tptp.k10_relat_1 B A)) A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (= (tptp.k9_relat_1 B (tptp.k10_relat_1 B A)) (tptp.k3_xboole_0 A (tptp.k9_relat_1 B (tptp.k1_relat_1 B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (tptp.r1_tarski (tptp.k9_relat_1 C (tptp.k3_xboole_0 A (tptp.k10_relat_1 C B))) (tptp.k3_xboole_0 (tptp.k9_relat_1 C A) B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (= (tptp.k9_relat_1 C (tptp.k3_xboole_0 A (tptp.k10_relat_1 C B))) (tptp.k3_xboole_0 (tptp.k9_relat_1 C A) B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (tptp.r1_tarski (tptp.k3_xboole_0 A (tptp.k10_relat_1 C B)) (tptp.k10_relat_1 C (tptp.k3_xboole_0 (tptp.k9_relat_1 C A) B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (tptp.v2_funct_1 B) (tptp.r1_tarski (tptp.k10_relat_1 B (tptp.k9_relat_1 B A)) A)))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (=> (forall ((B $$unsorted)) (tptp.r1_tarski (tptp.k10_relat_1 A (tptp.k9_relat_1 A B)) B)) (tptp.v2_funct_1 A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (tptp.v2_funct_1 B) (= (tptp.k9_relat_1 B A) (tptp.k10_relat_1 (tptp.k2_funct_1 B) A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (tptp.v2_funct_1 B) (= (tptp.k10_relat_1 B A) (tptp.k9_relat_1 (tptp.k2_funct_1 B) A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (forall ((C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (forall ((D $$unsorted)) (=> (and (tptp.v1_relat_1 D) (tptp.v1_funct_1 D)) (=> (and (= A (tptp.k2_relat_1 B)) (= (tptp.k1_relat_1 C) A) (= (tptp.k1_relat_1 D) A) (= (tptp.k5_relat_1 B C) (tptp.k5_relat_1 B D))) (= C D)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (and (tptp.r1_tarski (tptp.k9_relat_1 C A) (tptp.k9_relat_1 C B)) (tptp.r1_tarski A (tptp.k1_relat_1 C)) (tptp.v2_funct_1 C)) (tptp.r1_tarski A B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (and (tptp.r1_tarski (tptp.k10_relat_1 C A) (tptp.k10_relat_1 C B)) (tptp.r1_tarski A (tptp.k2_relat_1 C))) (tptp.r1_tarski A B)))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (= (tptp.v2_funct_1 A) (forall ((B $$unsorted)) (exists ((C $$unsorted)) (tptp.r1_tarski (tptp.k10_relat_1 A (tptp.k1_tarski B)) (tptp.k1_tarski C))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (forall ((C $$unsorted)) (=> (tptp.v1_relat_1 C) (=> (tptp.r1_tarski (tptp.k2_relat_1 B) (tptp.k1_relat_1 C)) (tptp.r1_tarski (tptp.k10_relat_1 B A) (tptp.k10_relat_1 (tptp.k5_relat_1 B C) (tptp.k9_relat_1 C A)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k2_relat_1 C))) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (and (= (tptp.k10_relat_1 C A) (tptp.k10_relat_1 C B)) (tptp.r1_tarski A _let_1) (tptp.r1_tarski B _let_1)) (= A B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (= (tptp.k9_relat_1 (tptp.k6_relat_1 A) B) B))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (= (tptp.v3_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.r2_hidden B (tptp.k1_relat_1 A)) (tptp.v1_xboole_0 (tptp.k1_funct_1 A B))))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (= (tptp.v2_relat_1 A) (forall ((B $$unsorted)) (not (and (tptp.r2_hidden B (tptp.k1_relat_1 A)) (tptp.v1_xboole_0 (tptp.k1_funct_1 A B)))))))) (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.p1_s1_funct_1 A B) (tptp.p1_s1_funct_1 A C)) (= B C))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.r2_hidden (tptp.k4_tarski B C) A) (and (tptp.r2_hidden B tptp.f1_s1_funct_1) (tptp.p1_s1_funct_1 B C))))))) (=> (and (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.r2_hidden A tptp.f1_s2_funct_1) (tptp.p1_s2_funct_1 A B) (tptp.p1_s2_funct_1 A C)) (= B C))) (forall ((A $$unsorted)) (not (and (tptp.r2_hidden A tptp.f1_s2_funct_1) (forall ((B $$unsorted)) (not (tptp.p1_s2_funct_1 A B))))))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (= (tptp.k1_relat_1 A) tptp.f1_s2_funct_1) (forall ((B $$unsorted)) (=> (tptp.r2_hidden B tptp.f1_s2_funct_1) (tptp.p1_s2_funct_1 B (tptp.k1_funct_1 A B))))))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (= (tptp.k1_relat_1 A) tptp.f1_s3_funct_1) (forall ((B $$unsorted)) (=> (tptp.r2_hidden B tptp.f1_s3_funct_1) (= (tptp.k1_funct_1 A B) (tptp.f2_s3_funct_1 B)))))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (= (tptp.k1_relat_1 A) tptp.f1_s4_funct_1) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B tptp.f1_s4_funct_1) (= (tptp.k1_funct_1 A B) (tptp.f2_s4_funct_1 B)))))) true (forall ((A $$unsorted)) (let ((_let_1 (tptp.k2_funct_1 A))) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (and (tptp.v1_relat_1 _let_1) (tptp.v1_funct_1 _let_1))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (= (tptp.r1_relat_2 A B) (forall ((C $$unsorted)) (=> (tptp.r2_hidden C B) (tptp.r2_hidden (tptp.k4_tarski C C) A))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (= (tptp.r2_relat_2 A B) (forall ((C $$unsorted)) (not (and (tptp.r2_hidden C B) (tptp.r2_hidden (tptp.k4_tarski C C) A)))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (= (tptp.r3_relat_2 A B) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.r2_hidden C B) (tptp.r2_hidden D B) (tptp.r2_hidden (tptp.k4_tarski C D) A)) (tptp.r2_hidden (tptp.k4_tarski D C) A))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (= (tptp.r4_relat_2 A B) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.r2_hidden C B) (tptp.r2_hidden D B) (tptp.r2_hidden (tptp.k4_tarski C D) A) (tptp.r2_hidden (tptp.k4_tarski D C) A)) (= C D))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (= (tptp.r5_relat_2 A B) (forall ((C $$unsorted) (D $$unsorted)) (not (and (tptp.r2_hidden C B) (tptp.r2_hidden D B) (tptp.r2_hidden (tptp.k4_tarski C D) A) (tptp.r2_hidden (tptp.k4_tarski D C) A)))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (= (tptp.r6_relat_2 A B) (forall ((C $$unsorted) (D $$unsorted)) (not (and (tptp.r2_hidden C B) (tptp.r2_hidden D B) (not (= C D)) (not (tptp.r2_hidden (tptp.k4_tarski C D) A)) (not (tptp.r2_hidden (tptp.k4_tarski D C) A))))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (= (tptp.r7_relat_2 A B) (forall ((C $$unsorted) (D $$unsorted)) (not (and (tptp.r2_hidden C B) (tptp.r2_hidden D B) (not (tptp.r2_hidden (tptp.k4_tarski C D) A)) (not (tptp.r2_hidden (tptp.k4_tarski D C) A))))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (= (tptp.r8_relat_2 A B) (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (tptp.r2_hidden C B) (tptp.r2_hidden D B) (tptp.r2_hidden E B) (tptp.r2_hidden (tptp.k4_tarski C D) A) (tptp.r2_hidden (tptp.k4_tarski D E) A)) (tptp.r2_hidden (tptp.k4_tarski C E) A))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.v1_relat_2 A) (tptp.r1_relat_2 A (tptp.k3_relat_1 A))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.v2_relat_2 A) (tptp.r2_relat_2 A (tptp.k3_relat_1 A))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.v3_relat_2 A) (tptp.r3_relat_2 A (tptp.k3_relat_1 A))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.v4_relat_2 A) (tptp.r4_relat_2 A (tptp.k3_relat_1 A))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.v5_relat_2 A) (tptp.r5_relat_2 A (tptp.k3_relat_1 A))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.v6_relat_2 A) (tptp.r6_relat_2 A (tptp.k3_relat_1 A))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.v7_relat_2 A) (tptp.r7_relat_2 A (tptp.k3_relat_1 A))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.v8_relat_2 A) (tptp.r8_relat_2 A (tptp.k3_relat_1 A))))) true true true true true true true true true true true true true true true true (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.v1_relat_2 A) (tptp.r1_tarski (tptp.k6_relat_1 (tptp.k3_relat_1 A)) A)))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.v2_relat_2 A) (tptp.r1_xboole_0 (tptp.k6_relat_1 (tptp.k3_relat_1 A)) A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (= (tptp.r4_relat_2 B A) (tptp.r5_relat_2 (tptp.k4_xboole_0 B (tptp.k6_relat_1 A)) A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (=> (tptp.r5_relat_2 B A) (tptp.r4_relat_2 (tptp.k2_xboole_0 B (tptp.k6_relat_1 A)) A)))) true (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (=> (and (tptp.v3_relat_2 A) (tptp.v8_relat_2 A)) (tptp.v1_relat_2 A)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k6_relat_1 A))) (and (tptp.v3_relat_2 _let_1) (tptp.v8_relat_2 _let_1)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k6_relat_1 A))) (and (tptp.v4_relat_2 _let_1) (tptp.v1_relat_2 _let_1)))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (=> (and (tptp.v2_relat_2 A) (tptp.v8_relat_2 A)) (tptp.v5_relat_2 A)))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (=> (tptp.v5_relat_2 A) (and (tptp.v2_relat_2 A) (tptp.v4_relat_2 A))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (=> (tptp.v1_relat_2 A) (tptp.v1_relat_2 (tptp.k4_relat_1 A))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (=> (tptp.v2_relat_2 A) (tptp.v2_relat_2 (tptp.k4_relat_1 A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k4_relat_1 A))) (=> (tptp.v1_relat_1 A) (=> (tptp.v1_relat_2 A) (and (= (tptp.k1_relat_1 A) (tptp.k1_relat_1 _let_1)) (= (tptp.k2_relat_1 A) (tptp.k2_relat_1 _let_1))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.v3_relat_2 A) (= A (tptp.k4_relat_1 A))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (=> (and (tptp.v1_relat_2 A) (tptp.v1_relat_2 B)) (and (tptp.v1_relat_2 (tptp.k2_xboole_0 A B)) (tptp.v1_relat_2 (tptp.k3_xboole_0 A B)))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (=> (and (tptp.v2_relat_2 A) (tptp.v2_relat_2 B)) (and (tptp.v2_relat_2 (tptp.k2_xboole_0 A B)) (tptp.v2_relat_2 (tptp.k3_xboole_0 A B)))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (=> (tptp.v2_relat_2 A) (tptp.v2_relat_2 (tptp.k4_xboole_0 A B))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (=> (tptp.v3_relat_2 A) (tptp.v3_relat_2 (tptp.k4_relat_1 A))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (=> (and (tptp.v3_relat_2 A) (tptp.v3_relat_2 B)) (and (tptp.v3_relat_2 (tptp.k2_xboole_0 A B)) (tptp.v3_relat_2 (tptp.k3_xboole_0 A B)) (tptp.v3_relat_2 (tptp.k4_xboole_0 A B)))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (=> (tptp.v5_relat_2 A) (tptp.v5_relat_2 (tptp.k4_relat_1 A))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (=> (and (tptp.v5_relat_2 A) (tptp.v5_relat_2 B)) (tptp.v5_relat_2 (tptp.k3_xboole_0 A B))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (=> (tptp.v5_relat_2 A) (tptp.v5_relat_2 (tptp.k4_xboole_0 A B))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.v4_relat_2 A) (tptp.r1_tarski (tptp.k3_xboole_0 A (tptp.k4_relat_1 A)) (tptp.k6_relat_1 (tptp.k1_relat_1 A)))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (=> (tptp.v4_relat_2 A) (tptp.v4_relat_2 (tptp.k4_relat_1 A))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (=> (tptp.v4_relat_2 A) (and (tptp.v4_relat_2 (tptp.k3_xboole_0 A B)) (tptp.v4_relat_2 (tptp.k4_xboole_0 A B)))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (=> (tptp.v8_relat_2 A) (tptp.v8_relat_2 (tptp.k4_relat_1 A))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (=> (tptp.v1_relat_1 B) (=> (and (tptp.v8_relat_2 A) (tptp.v8_relat_2 B)) (tptp.v8_relat_2 (tptp.k3_xboole_0 A B))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.v8_relat_2 A) (tptp.r1_tarski (tptp.k5_relat_1 A A) A)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k3_relat_1 A))) (=> (tptp.v1_relat_1 A) (= (tptp.v6_relat_2 A) (tptp.r1_tarski (tptp.k4_xboole_0 (tptp.k2_zfmisc_1 _let_1 _let_1) (tptp.k6_relat_1 _let_1)) (tptp.k2_xboole_0 A (tptp.k4_relat_1 A))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (=> (tptp.v7_relat_2 A) (and (tptp.v6_relat_2 A) (tptp.v1_relat_2 A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k3_relat_1 A))) (=> (tptp.v1_relat_1 A) (= (tptp.v7_relat_2 A) (= (tptp.k2_zfmisc_1 _let_1 _let_1) (tptp.k2_xboole_0 A (tptp.k4_relat_1 A))))))) (forall ((A $$unsorted)) (not (tptp.v1_xboole_0 (tptp.k1_ordinal1 A)))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (and (tptp.v1_ordinal1 A) (tptp.v2_ordinal1 A)))) (forall ((A $$unsorted)) (=> (and (tptp.v1_ordinal1 A) (tptp.v2_ordinal1 A)) (tptp.v3_ordinal1 A))) (exists ((A $$unsorted)) (and (tptp.v1_ordinal1 A) (tptp.v2_ordinal1 A) (tptp.v3_ordinal1 A))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v2_funct_1 A) (tptp.v1_xboole_0 A) (tptp.v1_ordinal1 A) (tptp.v2_ordinal1 A) (tptp.v3_ordinal1 A))) (forall ((A $$unsorted)) (=> (tptp.v1_xboole_0 A) (and (tptp.v1_ordinal1 A) (tptp.v2_ordinal1 A) (tptp.v3_ordinal1 A)))) (and _let_22 _let_21 (tptp.v1_funct_1 tptp.k1_xboole_0) (tptp.v2_funct_1 tptp.k1_xboole_0) _let_20 (tptp.v1_ordinal1 tptp.k1_xboole_0) (tptp.v2_ordinal1 tptp.k1_xboole_0) _let_19) (exists ((A $$unsorted)) (and (not (tptp.v1_xboole_0 A)) (tptp.v1_ordinal1 A) (tptp.v2_ordinal1 A) (tptp.v3_ordinal1 A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_ordinal1 A))) (=> (tptp.v3_ordinal1 A) (and (not (tptp.v1_xboole_0 _let_1)) (tptp.v1_ordinal1 _let_1) (tptp.v2_ordinal1 _let_1) (tptp.v3_ordinal1 _let_1))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k3_tarski A))) (=> (tptp.v3_ordinal1 A) (and (tptp.v1_ordinal1 _let_1) (tptp.v2_ordinal1 _let_1) (tptp.v3_ordinal1 _let_1))))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v5_ordinal1 A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_relat_1 A))) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v5_ordinal1 A)) (and (tptp.v1_ordinal1 _let_1) (tptp.v2_ordinal1 _let_1) (tptp.v3_ordinal1 _let_1))))) true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.r2_hidden A B) (tptp.r2_hidden B C) (tptp.r2_hidden C A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (not (and (tptp.r2_hidden A B) (tptp.r2_hidden B C) (tptp.r2_hidden C D) (tptp.r2_hidden D A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (not (and (tptp.r2_hidden A B) (tptp.r2_hidden B C) (tptp.r2_hidden C D) (tptp.r2_hidden D E) (tptp.r2_hidden E A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (not (and (tptp.r2_hidden A B) (tptp.r2_hidden B C) (tptp.r2_hidden C D) (tptp.r2_hidden D E) (tptp.r2_hidden E F) (tptp.r2_hidden F A)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.r2_hidden A B) (tptp.r1_tarski B A)))) (forall ((A $$unsorted)) (= (tptp.k1_ordinal1 A) (tptp.k2_xboole_0 A (tptp.k1_tarski A)))) true true (forall ((A $$unsorted)) (tptp.r2_hidden A (tptp.k1_ordinal1 A))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (= (tptp.k1_ordinal1 A) (tptp.k1_ordinal1 B)) (= A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.r2_hidden A (tptp.k1_ordinal1 B)) (or (tptp.r2_hidden A B) (= A B)))) (forall ((A $$unsorted)) (not (= A (tptp.k1_ordinal1 A)))) (forall ((A $$unsorted)) (= (tptp.v1_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.r2_hidden B A) (tptp.r1_tarski B A))))) (forall ((A $$unsorted)) (= (tptp.v2_ordinal1 A) (forall ((B $$unsorted) (C $$unsorted)) (not (and (tptp.r2_hidden B A) (tptp.r2_hidden C A) (not (tptp.r2_hidden B C)) (not (= B C)) (not (tptp.r2_hidden C B))))))) (forall ((A $$unsorted)) (= (tptp.v3_ordinal1 A) (and (tptp.v1_ordinal1 A) (tptp.v2_ordinal1 A)))) true true true true (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (forall ((C $$unsorted)) (=> (tptp.v1_ordinal1 C) (=> (and (tptp.r2_hidden C A) (tptp.r2_hidden A B)) (tptp.r2_hidden C B)))))))) true (forall ((A $$unsorted)) (=> (tptp.v1_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (=> (tptp.r2_xboole_0 A B) (tptp.r2_hidden A B)))))) (forall ((A $$unsorted)) (=> (tptp.v1_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (forall ((C $$unsorted)) (=> (tptp.v3_ordinal1 C) (=> (and (tptp.r1_tarski A B) (tptp.r2_hidden B C)) (tptp.r2_hidden A C)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v3_ordinal1 B) (=> (tptp.r2_hidden A B) (tptp.v3_ordinal1 A)))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (not (and (not (tptp.r2_hidden A B)) (not (= A B)) (not (tptp.r2_hidden B A)))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (tptp.r3_xboole_0 A B))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (or (tptp.r1_ordinal1 A B) (tptp.r2_hidden B A)))))) _let_19 true (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (tptp.v3_ordinal1 (tptp.k1_ordinal1 A)))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (tptp.v3_ordinal1 (tptp.k3_tarski A)))) (forall ((A $$unsorted)) (=> (forall ((B $$unsorted)) (=> (tptp.r2_hidden B A) (and (tptp.v3_ordinal1 B) (tptp.r1_tarski B A)))) (tptp.v3_ordinal1 A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v3_ordinal1 B) (not (and (tptp.r1_tarski A B) (not (= A tptp.k1_xboole_0)) (forall ((C $$unsorted)) (=> (tptp.v3_ordinal1 C) (not (and (tptp.r2_hidden C A) (forall ((D $$unsorted)) (=> (tptp.v3_ordinal1 D) (=> (tptp.r2_hidden D A) (tptp.r1_ordinal1 C D)))))))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (= (tptp.r2_hidden A B) (tptp.r1_ordinal1 (tptp.k1_ordinal1 A) B)))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (= (tptp.r2_hidden A (tptp.k1_ordinal1 B)) (tptp.r1_ordinal1 A B)))))) (forall ((A $$unsorted)) (=> (forall ((B $$unsorted)) (=> (tptp.r2_hidden B A) (tptp.v3_ordinal1 B))) (tptp.v3_ordinal1 (tptp.k3_tarski A)))) (forall ((A $$unsorted)) (not (and (forall ((B $$unsorted)) (=> (tptp.r2_hidden B A) (tptp.v3_ordinal1 B))) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (not (tptp.r1_tarski A B))))))) (forall ((A $$unsorted)) (not (forall ((B $$unsorted)) (= (tptp.r2_hidden B A) (tptp.v3_ordinal1 B))))) (forall ((A $$unsorted)) (not (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (tptp.r2_hidden B A))))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.v3_ordinal1 B) (not (tptp.r2_hidden B A)) (forall ((C $$unsorted)) (=> (tptp.v3_ordinal1 C) (=> (not (tptp.r2_hidden C A)) (tptp.r1_ordinal1 B C))))))) true (forall ((A $$unsorted)) (= (tptp.v4_ordinal1 A) (= A (tptp.k3_tarski A)))) true (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (= (tptp.v4_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (=> (tptp.r2_hidden B A) (tptp.r2_hidden (tptp.k1_ordinal1 B) A))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.v4_ordinal1 A))) (=> (tptp.v3_ordinal1 A) (and (not (and (not _let_1) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (not (= A (tptp.k1_ordinal1 B))))))) (not (and (exists ((B $$unsorted)) (and (tptp.v3_ordinal1 B) (= A (tptp.k1_ordinal1 B)))) _let_1)))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (= (tptp.v5_ordinal1 A) (tptp.v3_ordinal1 (tptp.k1_relat_1 A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B) (tptp.v5_ordinal1 B)) (= (tptp.m1_ordinal1 B A) (tptp.r1_tarski (tptp.k2_relat_1 B) A)))) true true (forall ((A $$unsorted)) (tptp.m1_ordinal1 tptp.k1_xboole_0 A)) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (=> (tptp.v3_ordinal1 (tptp.k1_relat_1 A)) (tptp.m1_ordinal1 A (tptp.k2_relat_1 A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r1_tarski A B) (forall ((C $$unsorted)) (=> (tptp.m1_ordinal1 C A) (tptp.m1_ordinal1 C B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_ordinal1 B A) (forall ((C $$unsorted)) (=> (tptp.v3_ordinal1 C) (tptp.m1_ordinal1 (tptp.k2_ordinal1 B C) A))))) (forall ((A $$unsorted)) (= (tptp.v6_ordinal1 A) (forall ((B $$unsorted) (C $$unsorted)) (=> (and (tptp.r2_hidden B A) (tptp.r2_hidden C A)) (tptp.r3_xboole_0 B C))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k3_tarski A))) (=> (and (forall ((B $$unsorted)) (=> (tptp.r2_hidden B A) (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B) (tptp.v5_ordinal1 B)))) (tptp.v6_ordinal1 A)) (and (tptp.v1_relat_1 _let_1) (tptp.v1_funct_1 _let_1) (tptp.v5_ordinal1 _let_1))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (not (and (not (tptp.r2_xboole_0 A B)) (not (= A B)) (not (tptp.r2_xboole_0 B A)))))))) (=> (exists ((A $$unsorted)) (and (tptp.v3_ordinal1 A) (tptp.p1_s1_ordinal1 A))) (exists ((A $$unsorted)) (and (tptp.v3_ordinal1 A) (tptp.p1_s1_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (=> (tptp.p1_s1_ordinal1 B) (tptp.r1_ordinal1 A B))))))) (=> (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (=> (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (=> (tptp.r2_hidden B A) (tptp.p1_s2_ordinal1 B)))) (tptp.p1_s2_ordinal1 A)))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (tptp.p1_s2_ordinal1 A)))) (=> (and (= (tptp.k1_relat_1 tptp.f3_s3_ordinal1) tptp.f1_s3_ordinal1) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B) (tptp.v5_ordinal1 B)) (=> (and (tptp.r2_hidden A tptp.f1_s3_ordinal1) (= B (tptp.k2_ordinal1 tptp.f3_s3_ordinal1 A))) (= (tptp.k1_funct_1 tptp.f3_s3_ordinal1 A) (tptp.f2_s3_ordinal1 B))))))) (= (tptp.k1_relat_1 tptp.f4_s3_ordinal1) tptp.f1_s3_ordinal1) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B) (tptp.v5_ordinal1 B)) (=> (and (tptp.r2_hidden A tptp.f1_s3_ordinal1) (= B (tptp.k2_ordinal1 tptp.f4_s3_ordinal1 A))) (= (tptp.k1_funct_1 tptp.f4_s3_ordinal1 A) (tptp.f2_s3_ordinal1 B)))))))) (= tptp.f3_s3_ordinal1 tptp.f4_s3_ordinal1)) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v5_ordinal1 A) (= (tptp.k1_relat_1 A) tptp.f1_s4_ordinal1) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (forall ((C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (tptp.v5_ordinal1 C)) (=> (and (tptp.r2_hidden B tptp.f1_s4_ordinal1) (= C (tptp.k2_ordinal1 A B))) (= (tptp.k1_funct_1 A B) (tptp.f2_s4_ordinal1 C))))))))) (=> (and (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (= (= B (tptp.f2_s5_ordinal1 A)) (exists ((C $$unsorted)) (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (tptp.v5_ordinal1 C) (= B (tptp.f3_s5_ordinal1 C)) (= (tptp.k1_relat_1 C) A) (forall ((D $$unsorted)) (=> (tptp.v3_ordinal1 D) (=> (tptp.r2_hidden D A) (= (tptp.k1_funct_1 C D) (tptp.f3_s5_ordinal1 (tptp.k2_ordinal1 C D)))))))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (=> (tptp.r2_hidden A (tptp.k1_relat_1 tptp.f1_s5_ordinal1)) (= (tptp.k1_funct_1 tptp.f1_s5_ordinal1 A) (tptp.f2_s5_ordinal1 A)))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (=> (tptp.r2_hidden A (tptp.k1_relat_1 tptp.f1_s5_ordinal1)) (= (tptp.k1_funct_1 tptp.f1_s5_ordinal1 A) (tptp.f3_s5_ordinal1 (tptp.k2_ordinal1 tptp.f1_s5_ordinal1 A))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_ordinal1 B A) (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B) (tptp.v5_ordinal1 B)))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.m1_ordinal1 B A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v3_ordinal1 A) (tptp.v3_ordinal1 B)) (tptp.r1_ordinal1 A A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v3_ordinal1 A) (tptp.v3_ordinal1 B)) (or (tptp.r1_ordinal1 A B) (tptp.r1_ordinal1 B A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v3_ordinal1 A) (tptp.v3_ordinal1 B)) (= (tptp.r1_ordinal1 A B) (tptp.r1_tarski A B)))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v5_ordinal1 A) (tptp.v3_ordinal1 B)) (tptp.m1_ordinal1 (tptp.k2_ordinal1 A B) (tptp.k2_relat_1 A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v5_ordinal1 A) (tptp.v3_ordinal1 B)) (= (tptp.k2_ordinal1 A B) (tptp.k7_relat_1 A B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B))) (tptp.v1_relat_1 C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.m1_relset_1 C A B) (tptp.r1_tarski C (tptp.k2_zfmisc_1 A B)))) true true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.m2_relset_1 D B C) (=> (tptp.r1_tarski A D) (tptp.m2_relset_1 A B C)))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.m2_relset_1 D A B) (not (and (tptp.r2_hidden C D) (forall ((E $$unsorted) (F $$unsorted)) (not (and (= C (tptp.k4_tarski E F)) (tptp.r2_hidden E A) (tptp.r2_hidden F B)))))))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.r2_hidden C A) (tptp.r2_hidden D B)) (tptp.m2_relset_1 (tptp.k1_tarski (tptp.k4_tarski C D)) A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (=> (tptp.r1_tarski (tptp.k1_relat_1 B) A) (tptp.m2_relset_1 B A (tptp.k2_relat_1 B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (=> (tptp.r1_tarski (tptp.k2_relat_1 B) A) (tptp.m2_relset_1 B (tptp.k1_relat_1 B) A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.v1_relat_1 C) (=> (and (tptp.r1_tarski (tptp.k1_relat_1 C) A) (tptp.r1_tarski (tptp.k2_relat_1 C) B)) (tptp.m2_relset_1 C A B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C A B) (and (tptp.r1_tarski (tptp.k1_relat_1 C) A) (tptp.r1_tarski (tptp.k2_relat_1 C) B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.m2_relset_1 D A C) (=> (tptp.r1_tarski (tptp.k1_relat_1 D) B) (tptp.m2_relset_1 D B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.m2_relset_1 D C A) (=> (tptp.r1_tarski (tptp.k2_relat_1 D) B) (tptp.m2_relset_1 D C B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.m2_relset_1 D A C) (=> (tptp.r1_tarski A B) (tptp.m2_relset_1 D B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.m2_relset_1 D C A) (=> (tptp.r1_tarski A B) (tptp.m2_relset_1 D C B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (tptp.m2_relset_1 E A C) (=> (and (tptp.r1_tarski A B) (tptp.r1_tarski C D)) (tptp.m2_relset_1 E B D)))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C A B) (tptp.r1_tarski (tptp.k3_relat_1 C) (tptp.k2_xboole_0 A B)))) true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C B A) (= (forall ((D $$unsorted)) (not (and (tptp.r2_hidden D B) (forall ((E $$unsorted)) (not (tptp.r2_hidden (tptp.k4_tarski D E) C)))))) (= (tptp.k4_relset_1 B A C) B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C A B) (= (forall ((D $$unsorted)) (not (and (tptp.r2_hidden D B) (forall ((E $$unsorted)) (not (tptp.r2_hidden (tptp.k4_tarski E D) C)))))) (= (tptp.k5_relset_1 A B C) B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k6_relset_1 A B C))) (=> (tptp.m2_relset_1 C A B) (and (= (tptp.k4_relset_1 B A _let_1) (tptp.k5_relset_1 A B C)) (= (tptp.k5_relset_1 B A _let_1) (tptp.k4_relset_1 A B C)))))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.m2_relset_1 tptp.k1_xboole_0 A B)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C A B) (=> (tptp.m2_relset_1 C tptp.k1_xboole_0 B) (= C tptp.k1_xboole_0)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C B A) (=> (tptp.m2_relset_1 C B tptp.k1_xboole_0) (= C tptp.k1_xboole_0)))) (forall ((A $$unsorted)) (tptp.r1_tarski (tptp.k6_relat_1 A) (tptp.k2_zfmisc_1 A A))) (forall ((A $$unsorted)) (tptp.m2_relset_1 (tptp.k6_relat_1 A) A A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.m2_relset_1 D A B) (=> (tptp.r1_tarski (tptp.k6_relat_1 C) D) (and (tptp.r1_tarski C (tptp.k4_relset_1 A B D)) (tptp.r1_tarski C (tptp.k5_relset_1 A B D)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C B A) (=> (tptp.r1_tarski (tptp.k6_relat_1 B) C) (and (= B (tptp.k4_relset_1 B A C)) (tptp.r1_tarski B (tptp.k5_relset_1 B A C)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C A B) (=> (tptp.r1_tarski (tptp.k6_relat_1 B) C) (and (tptp.r1_tarski B (tptp.k4_relset_1 A B C)) (= B (tptp.k5_relset_1 A B C)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.m2_relset_1 D A C) (tptp.m2_relset_1 (tptp.k8_relset_1 A C D B) B C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.m2_relset_1 D B A) (=> (tptp.r1_tarski B C) (= (tptp.k8_relset_1 B A D C) D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.m2_relset_1 D C A) (tptp.m2_relset_1 (tptp.k9_relset_1 C A B D) C B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.m2_relset_1 D A B) (=> (tptp.r1_tarski B C) (= (tptp.k9_relset_1 A B C D) D)))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C A B) (and (= (tptp.k10_relset_1 A B C A) (tptp.k5_relset_1 A B C)) (= (tptp.k11_relset_1 A B C B) (tptp.k4_relset_1 A B C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C B A) (and (= (tptp.k10_relset_1 B A C (tptp.k11_relset_1 B A C A)) (tptp.k5_relset_1 B A C)) (= (tptp.k11_relset_1 B A C (tptp.k10_relset_1 B A C B)) (tptp.k4_relset_1 B A C))))) true true true true true (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k6_relat_1 A))) (=> (tptp.m2_relset_1 B A A) (and (= (tptp.k5_relat_1 B _let_1) B) (= (tptp.k5_relat_1 _let_1 B) B))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (not (= (tptp.k6_relat_1 A) tptp.k1_xboole_0)))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (tptp.m2_relset_1 C A B) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (= (tptp.r2_hidden D (tptp.k4_relset_1 A B C)) (exists ((E $$unsorted)) (and (tptp.m1_subset_1 E B) (tptp.r2_hidden (tptp.k4_tarski D E) C)))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (tptp.m2_relset_1 C B A) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (= (tptp.r2_hidden D (tptp.k5_relset_1 B A C)) (exists ((E $$unsorted)) (and (tptp.m1_subset_1 E B) (tptp.r2_hidden (tptp.k4_tarski E D) C)))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (tptp.m2_relset_1 C A B) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (not (and (tptp.r2_hidden D (tptp.k4_relset_1 A B C)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E B) (not (tptp.r2_hidden E (tptp.k5_relset_1 A B C))))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (tptp.m2_relset_1 C B A) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (not (and (tptp.r2_hidden D (tptp.k5_relset_1 B A C)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E B) (not (tptp.r2_hidden E (tptp.k4_relset_1 B A C))))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (tptp.m2_relset_1 D A B) (forall ((E $$unsorted)) (=> (tptp.m2_relset_1 E B C) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F A) (forall ((G $$unsorted)) (=> (tptp.m1_subset_1 G C) (= (tptp.r2_hidden (tptp.k4_tarski F G) (tptp.k7_relset_1 A B B C D E)) (exists ((H $$unsorted)) (and (tptp.m1_subset_1 H B) (tptp.r2_hidden (tptp.k4_tarski F H) D) (tptp.r2_hidden (tptp.k4_tarski H G) E)))))))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (tptp.m2_relset_1 D C A) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (= (tptp.r2_hidden E (tptp.k10_relset_1 C A D B)) (exists ((F $$unsorted)) (and (tptp.m1_subset_1 F C) (tptp.r2_hidden (tptp.k4_tarski F E) D) (tptp.r2_hidden F B)))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (tptp.m2_relset_1 D A C) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (= (tptp.r2_hidden E (tptp.k11_relset_1 A C D B)) (exists ((F $$unsorted)) (and (tptp.m1_subset_1 F C) (tptp.r2_hidden (tptp.k4_tarski E F) D) (tptp.r2_hidden F B)))))))))))))) (exists ((A $$unsorted)) (and (tptp.m2_relset_1 A tptp.f1_s1_relset_1 tptp.f2_s1_relset_1) (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.r2_hidden (tptp.k4_tarski B C) A) (and (tptp.r2_hidden B tptp.f1_s1_relset_1) (tptp.r2_hidden C tptp.f2_s1_relset_1) (tptp.p1_s1_relset_1 B C)))))) (exists ((A $$unsorted)) (and (tptp.m2_relset_1 A tptp.f1_s2_relset_1 tptp.f2_s2_relset_1) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B tptp.f1_s2_relset_1) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C tptp.f2_s2_relset_1) (= (tptp.r2_hidden (tptp.k4_tarski B C) A) (tptp.p1_s2_relset_1 B C)))))))) true (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.m1_relset_1 C A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C A B) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B))))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.m2_relset_1 C A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.m2_relset_1 C A B) (tptp.m1_relset_1 C A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.m1_relset_1 C A B) (tptp.m1_relset_1 D A B)) (tptp.m2_relset_1 (tptp.k1_relset_1 A B C D) A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.m1_relset_1 C A B) (tptp.m1_relset_1 D A B)) (= (tptp.k1_relset_1 A B C D) (tptp.k1_relset_1 A B D C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.m1_relset_1 C A B) (tptp.m1_relset_1 D A B)) (= (tptp.k1_relset_1 A B C C) C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.m1_relset_1 C A B) (tptp.m1_relset_1 D A B)) (= (tptp.k1_relset_1 A B C D) (tptp.k2_xboole_0 C D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.m1_relset_1 C A B) (tptp.m1_relset_1 D A B)) (tptp.m2_relset_1 (tptp.k2_relset_1 A B C D) A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.m1_relset_1 C A B) (tptp.m1_relset_1 D A B)) (= (tptp.k2_relset_1 A B C D) (tptp.k2_relset_1 A B D C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.m1_relset_1 C A B) (tptp.m1_relset_1 D A B)) (= (tptp.k2_relset_1 A B C C) C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.m1_relset_1 C A B) (tptp.m1_relset_1 D A B)) (= (tptp.k2_relset_1 A B C D) (tptp.k3_xboole_0 C D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.m1_relset_1 C A B) (tptp.m1_relset_1 D A B)) (tptp.m2_relset_1 (tptp.k3_relset_1 A B C D) A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.m1_relset_1 C A B) (tptp.m1_relset_1 D A B)) (= (tptp.k3_relset_1 A B C D) (tptp.k4_xboole_0 C D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_relset_1 C A B) (tptp.m1_subset_1 (tptp.k4_relset_1 A B C) (tptp.k1_zfmisc_1 A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_relset_1 C A B) (= (tptp.k4_relset_1 A B C) (tptp.k1_relat_1 C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_relset_1 C A B) (tptp.m1_subset_1 (tptp.k5_relset_1 A B C) (tptp.k1_zfmisc_1 B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_relset_1 C A B) (= (tptp.k5_relset_1 A B C) (tptp.k2_relat_1 C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_relset_1 C A B) (tptp.m2_relset_1 (tptp.k6_relset_1 A B C) B A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_relset_1 C A B) (= (tptp.k6_relset_1 A B (tptp.k6_relset_1 A B C)) C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_relset_1 C A B) (= (tptp.k6_relset_1 A B C) (tptp.k4_relat_1 C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (tptp.m1_relset_1 E A B) (tptp.m1_relset_1 F C D)) (tptp.m2_relset_1 (tptp.k7_relset_1 A B C D E F) A D))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (tptp.m1_relset_1 E A B) (tptp.m1_relset_1 F C D)) (= (tptp.k7_relset_1 A B C D E F) (tptp.k5_relat_1 E F)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.m1_relset_1 C A B) (tptp.m2_relset_1 (tptp.k8_relset_1 A B C D) A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.m1_relset_1 C A B) (= (tptp.k8_relset_1 A B C D) (tptp.k7_relat_1 C D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.m1_relset_1 D A B) (tptp.m2_relset_1 (tptp.k9_relset_1 A B C D) A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.m1_relset_1 D A B) (= (tptp.k9_relset_1 A B C D) (tptp.k8_relat_1 C D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.m1_relset_1 C A B) (tptp.m1_subset_1 (tptp.k10_relset_1 A B C D) (tptp.k1_zfmisc_1 B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.m1_relset_1 C A B) (= (tptp.k10_relset_1 A B C D) (tptp.k9_relat_1 C D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.m1_relset_1 C A B) (tptp.m1_subset_1 (tptp.k11_relset_1 A B C D) (tptp.k1_zfmisc_1 A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.m1_relset_1 C A B) (= (tptp.k11_relset_1 A B C D) (tptp.k10_relat_1 C D)))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v2_funct_1 A) (tptp.v1_xboole_0 A))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (and (tptp.m1_relset_1 C A B) (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)))) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.v1_xboole_0 (tptp.k4_partfun1 A B)))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.m1_relset_1 B A A) (tptp.v1_relat_1 B) (tptp.v1_relat_2 B) (tptp.v3_relat_2 B) (tptp.v4_relat_2 B) (tptp.v8_relat_2 B) (tptp.v1_partfun1 B A A)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.v1_relat_1 A))) (=> (and _let_1 (tptp.v3_relat_2 A) (tptp.v8_relat_2 A)) (and _let_1 (tptp.v1_relat_2 A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k6_relat_1 A))) (and (tptp.v1_relat_1 _let_1) (tptp.v1_funct_1 _let_1) (tptp.v1_relat_2 _let_1) (tptp.v3_relat_2 _let_1) (tptp.v4_relat_2 _let_1) (tptp.v8_relat_2 _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (tptp.r1_tarski A (tptp.k2_zfmisc_1 B C)) (tptp.r1_tarski D (tptp.k2_zfmisc_1 E F))) (tptp.r1_tarski (tptp.k2_xboole_0 A D) (tptp.k2_zfmisc_1 (tptp.k2_xboole_0 B E) (tptp.k2_xboole_0 C F))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (not (and (forall ((C $$unsorted)) (=> (tptp.r2_hidden C (tptp.k3_xboole_0 (tptp.k1_relat_1 A) (tptp.k1_relat_1 B))) (= (tptp.k1_funct_1 A C) (tptp.k1_funct_1 B C)))) (forall ((C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (not (= (tptp.k2_xboole_0 A B) C)))))))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (forall ((C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (= (tptp.k2_xboole_0 A B) C) (forall ((D $$unsorted)) (=> (tptp.r2_hidden D (tptp.k3_xboole_0 (tptp.k1_relat_1 A) (tptp.k1_relat_1 B))) (= (tptp.k1_funct_1 A D) (tptp.k1_funct_1 B D))))))))))) true true true true true true _let_18 true true true true true true true true true true true true true (forall ((A $$unsorted)) (let ((_let_1 (tptp.v1_funct_1 A))) (=> (and (tptp.v1_relat_1 A) _let_1) (and _let_1 (tptp.m2_relset_1 A (tptp.k1_relat_1 A) (tptp.k2_relat_1 A)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.v1_funct_1 B))) (=> (and (tptp.v1_relat_1 B) _let_1) (=> (tptp.r1_tarski (tptp.k2_relat_1 B) A) (and _let_1 (tptp.m2_relset_1 B (tptp.k1_relat_1 B) A)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D A B)) (not (and (tptp.r2_hidden C (tptp.k2_relat_1 D)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (not (and (tptp.r2_hidden E (tptp.k4_relset_1 A B D)) (= C (tptp.k1_funct_1 D E)))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D A B)) (=> (tptp.r2_hidden C (tptp.k4_relset_1 A B D)) (tptp.r2_hidden (tptp.k1_funct_1 D C) B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.v1_funct_1 D))) (=> (and _let_1 (tptp.m2_relset_1 D A B)) (=> (tptp.r1_tarski (tptp.k4_relset_1 A B D) C) (and _let_1 (tptp.m2_relset_1 D C B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.v1_funct_1 D))) (=> (and _let_1 (tptp.m2_relset_1 D A B)) (=> (tptp.r1_tarski (tptp.k2_relat_1 D) C) (and _let_1 (tptp.m2_relset_1 D A C)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.v1_funct_1 D))) (=> (and _let_1 (tptp.m2_relset_1 D A B)) (=> (tptp.r1_tarski A C) (and _let_1 (tptp.m2_relset_1 D C B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.v1_funct_1 D))) (=> (and _let_1 (tptp.m2_relset_1 D A B)) (=> (tptp.r1_tarski B C) (and _let_1 (tptp.m2_relset_1 D A C)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.v1_funct_1 E))) (=> (and _let_1 (tptp.m2_relset_1 E A B)) (=> (and (tptp.r1_tarski A C) (tptp.r1_tarski B D)) (and _let_1 (tptp.m2_relset_1 E C D)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D A B)) (=> (tptp.r1_tarski C D) (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D A B)) (=> (and (= (tptp.k4_relset_1 A B C) (tptp.k4_relset_1 A B D)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (=> (tptp.r2_hidden E (tptp.k4_relset_1 A B C)) (= (tptp.k1_funct_1 C E) (tptp.k1_funct_1 D E)))))) (= C D)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D (tptp.k2_zfmisc_1 A B) C)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A B))) (=> (and (tptp.v1_funct_1 E) (tptp.m2_relset_1 E _let_1 C)) (=> (and (= (tptp.k4_relset_1 _let_1 C D) (tptp.k4_relset_1 _let_1 C E)) (forall ((F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.k4_tarski F G))) (=> (tptp.r2_hidden _let_1 (tptp.k4_relset_1 (tptp.k2_zfmisc_1 A B) C D)) (= (tptp.k1_funct_1 D _let_1) (tptp.k1_funct_1 E _let_1)))))) (= D E))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C A B) (= (tptp.k5_relat_1 (tptp.k6_relat_1 A) C) C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C A B) (= (tptp.k5_relat_1 C (tptp.k6_relat_1 B)) C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (=> (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (forall ((E $$unsorted)) (let ((_let_1 (tptp.k4_relset_1 A B C))) (=> (tptp.m1_subset_1 E A) (=> (and (tptp.r2_hidden D _let_1) (tptp.r2_hidden E _let_1) (= (tptp.k1_funct_1 C D) (tptp.k1_funct_1 C E))) (= D E))))))) (tptp.v2_funct_1 C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k2_funct_1 C))) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (=> (tptp.v2_funct_1 C) (and (tptp.v1_funct_1 _let_1) (tptp.m2_relset_1 _let_1 B A)))))) true true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k8_relset_1 A B D C))) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D A B)) (and (tptp.v1_funct_1 _let_1) (tptp.m2_relset_1 _let_1 C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k8_relset_1 A B D C))) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D A B)) (and (tptp.v1_funct_1 _let_1) (tptp.m2_relset_1 _let_1 A B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k9_relset_1 A B C D))) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D A B)) (and (tptp.v1_funct_1 _let_1) (tptp.m2_relset_1 _let_1 A C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k9_relset_1 A B C D))) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D A B)) (and (tptp.v1_funct_1 _let_1) (tptp.m2_relset_1 _let_1 A B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k7_relat_1 (tptp.k8_relat_1 A C) B))) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (and (tptp.v1_funct_1 _let_1) (tptp.m2_relset_1 _let_1 B A))))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D A B)) (not (and (tptp.r2_hidden C (tptp.k9_relat_1 D A)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (not (and (tptp.r2_hidden E (tptp.k4_relset_1 A B D)) (= C (tptp.k1_funct_1 D E)))))))))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (= (tptp.k9_relat_1 C A) (tptp.k2_relat_1 C)))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (= (tptp.k10_relat_1 C B) (tptp.k4_relset_1 A B C)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.m2_relset_1 B tptp.k1_xboole_0 A)) (and (= (tptp.k4_relset_1 tptp.k1_xboole_0 A B) tptp.k1_xboole_0) (= (tptp.k2_relat_1 B) tptp.k1_xboole_0)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.v1_funct_1 C))) (=> (and (tptp.v1_relat_1 C) _let_1) (=> (= (tptp.k1_relat_1 C) tptp.k1_xboole_0) (and _let_1 (tptp.m2_relset_1 C A B)))))) (forall ((A $$unsorted) (B $$unsorted)) (and (tptp.v1_funct_1 tptp.k1_xboole_0) (tptp.m2_relset_1 tptp.k1_xboole_0 A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.m2_relset_1 B tptp.k1_xboole_0 A)) (= B tptp.k1_xboole_0))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C tptp.k1_xboole_0 A)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D tptp.k1_xboole_0 B)) (= C D))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.m2_relset_1 B tptp.k1_xboole_0 A)) (tptp.v2_funct_1 B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C tptp.k1_xboole_0 A)) (= (tptp.k9_relat_1 C B) tptp.k1_xboole_0))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C tptp.k1_xboole_0 A)) (= (tptp.k10_relat_1 C B) tptp.k1_xboole_0))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.m2_relset_1 B A tptp.k1_xboole_0)) (and (= (tptp.k4_relset_1 A tptp.k1_xboole_0 B) tptp.k1_xboole_0) (= (tptp.k2_relat_1 B) tptp.k1_xboole_0)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.v1_funct_1 C))) (=> (and (tptp.v1_relat_1 C) _let_1) (=> (= (tptp.k2_relat_1 C) tptp.k1_xboole_0) (and _let_1 (tptp.m2_relset_1 C A B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.m2_relset_1 B A tptp.k1_xboole_0)) (= B tptp.k1_xboole_0))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A tptp.k1_xboole_0)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D B tptp.k1_xboole_0)) (= C D))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.m2_relset_1 B A tptp.k1_xboole_0)) (tptp.v2_funct_1 B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A tptp.k1_xboole_0)) (= (tptp.k9_relat_1 C B) tptp.k1_xboole_0))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A tptp.k1_xboole_0)) (= (tptp.k10_relat_1 C B) tptp.k1_xboole_0))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C (tptp.k1_tarski A) B)) (tptp.r1_tarski (tptp.k2_relat_1 C) (tptp.k1_tarski (tptp.k1_funct_1 C A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C (tptp.k1_tarski A) B)) (tptp.v2_funct_1 C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D (tptp.k1_tarski A) B)) (tptp.r1_tarski (tptp.k9_relat_1 D C) (tptp.k1_tarski (tptp.k1_funct_1 D A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.v1_funct_1 D))) (=> (and (tptp.v1_relat_1 D) _let_1) (=> (and (= (tptp.k1_relat_1 D) (tptp.k1_tarski A)) (tptp.r2_hidden A B) (tptp.r2_hidden (tptp.k1_funct_1 D A) C)) (and _let_1 (tptp.m2_relset_1 D B C)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k1_tarski B))) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D A _let_1)) (=> (tptp.r2_hidden C (tptp.k4_relset_1 A _let_1 D)) (= (tptp.k1_funct_1 D C) B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A (tptp.k1_tarski B))) (forall ((D $$unsorted)) (let ((_let_1 (tptp.k1_tarski B))) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D A _let_1)) (=> (= (tptp.k4_relset_1 A _let_1 C) (tptp.k4_relset_1 A _let_1 D)) (= C D))))))) true true (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.k3_partfun1 A B C) (tptp.k7_relat_1 (tptp.k8_relat_1 C A) B))))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (tptp.r1_tarski (tptp.k3_partfun1 C A B) C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k3_partfun1 C A B))) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (and (tptp.r1_tarski (tptp.k4_relset_1 A B _let_1) (tptp.k1_relat_1 C)) (tptp.r1_tarski (tptp.k2_relat_1 _let_1) (tptp.k2_relat_1 C)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_relat_1 D) (tptp.v1_funct_1 D)) (= (tptp.r2_hidden A (tptp.k4_relset_1 B C (tptp.k3_partfun1 D B C))) (and (tptp.r2_hidden A (tptp.k1_relat_1 D)) (tptp.r2_hidden A B) (tptp.r2_hidden (tptp.k1_funct_1 D A) C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k1_funct_1 D A))) (=> (and (tptp.v1_relat_1 D) (tptp.v1_funct_1 D)) (=> (and (tptp.r2_hidden A (tptp.k1_relat_1 D)) (tptp.r2_hidden A B) (tptp.r2_hidden _let_1 C)) (= (tptp.k1_funct_1 (tptp.k3_partfun1 D B C) A) _let_1))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k3_partfun1 D B C))) (=> (and (tptp.v1_relat_1 D) (tptp.v1_funct_1 D)) (=> (tptp.r2_hidden A (tptp.k4_relset_1 B C _let_1)) (= (tptp.k1_funct_1 _let_1 A) (tptp.k1_funct_1 D A)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (forall ((D $$unsorted)) (=> (and (tptp.v1_relat_1 D) (tptp.v1_funct_1 D)) (=> (tptp.r1_tarski C D) (tptp.r1_tarski (tptp.k3_partfun1 C A B) (tptp.k3_partfun1 D A B))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_relat_1 D) (tptp.v1_funct_1 D)) (=> (tptp.r1_tarski A B) (tptp.r1_tarski (tptp.k3_partfun1 D A C) (tptp.k3_partfun1 D B C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_relat_1 D) (tptp.v1_funct_1 D)) (=> (tptp.r1_tarski A B) (tptp.r1_tarski (tptp.k3_partfun1 D C A) (tptp.k3_partfun1 D C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (tptp.v1_relat_1 E) (tptp.v1_funct_1 E)) (=> (and (tptp.r1_tarski A B) (tptp.r1_tarski C D)) (tptp.r1_tarski (tptp.k3_partfun1 E A C) (tptp.k3_partfun1 E B D))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (and (tptp.r1_tarski (tptp.k1_relat_1 C) A) (tptp.r1_tarski (tptp.k2_relat_1 C) B)) (= C (tptp.k3_partfun1 C A B))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (= A (tptp.k3_partfun1 A (tptp.k1_relat_1 A) (tptp.k2_relat_1 A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (= (tptp.k3_partfun1 C A B) C))) true true true (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k3_partfun1 tptp.k1_xboole_0 A B) tptp.k1_xboole_0)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_relat_1 D) (tptp.v1_funct_1 D)) (forall ((E $$unsorted)) (=> (and (tptp.v1_relat_1 E) (tptp.v1_funct_1 E)) (tptp.r1_tarski (tptp.k1_partfun1 C A A B (tptp.k3_partfun1 D C A) (tptp.k3_partfun1 E A B)) (tptp.k3_partfun1 (tptp.k5_relat_1 D E) C B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_relat_1 D) (tptp.v1_funct_1 D)) (forall ((E $$unsorted)) (=> (and (tptp.v1_relat_1 E) (tptp.v1_funct_1 E)) (=> (tptp.r1_tarski (tptp.k3_xboole_0 (tptp.k2_relat_1 D) (tptp.k1_relat_1 E)) A) (= (tptp.k1_partfun1 C A A B (tptp.k3_partfun1 D C A) (tptp.k3_partfun1 E A B)) (tptp.k3_partfun1 (tptp.k5_relat_1 D E) C B))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (tptp.v2_funct_1 C) (tptp.v2_funct_1 (tptp.k3_partfun1 C A B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (tptp.v2_funct_1 C) (= (tptp.k2_funct_1 (tptp.k3_partfun1 C A B)) (tptp.k3_partfun1 (tptp.k2_funct_1 C) B A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_relat_1 D) (tptp.v1_funct_1 D)) (= (tptp.k2_partfun1 A B (tptp.k3_partfun1 D A B) C) (tptp.k3_partfun1 D (tptp.k3_xboole_0 A C) B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_relat_1 D) (tptp.v1_funct_1 D)) (= (tptp.k9_relset_1 B C A (tptp.k3_partfun1 D B C)) (tptp.k3_partfun1 D B (tptp.k3_xboole_0 A C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C A B) (= (tptp.v1_partfun1 C A B) (= (tptp.k4_relset_1 A B C) A)))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (=> (and (tptp.v1_partfun1 C A B) (= B tptp.k1_xboole_0)) (= A tptp.k1_xboole_0)))) true true true true true true true true true true true true (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.m2_relset_1 B tptp.k1_xboole_0 A)) (tptp.v1_partfun1 B tptp.k1_xboole_0 A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (tptp.v1_partfun1 (tptp.k3_partfun1 C A B) A B) (tptp.r1_tarski A (tptp.k1_relat_1 C))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_partfun1 (tptp.k3_partfun1 tptp.k1_xboole_0 A B) A B) (= A tptp.k1_xboole_0))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (and (tptp.r1_tarski A (tptp.k1_relat_1 C)) (tptp.r1_tarski (tptp.k2_relat_1 C) B)) (tptp.v1_partfun1 (tptp.k3_partfun1 C A B) A B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (tptp.v1_partfun1 (tptp.k3_partfun1 C A B) A B) (tptp.r1_tarski (tptp.k9_relat_1 C A) B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (and (tptp.r1_tarski A (tptp.k1_relat_1 C)) (tptp.r1_tarski (tptp.k9_relat_1 C A) B)) (tptp.v1_partfun1 (tptp.k3_partfun1 C A B) A B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.k4_partfun1 A B)) (forall ((D $$unsorted)) (= (tptp.r2_hidden D C) (exists ((E $$unsorted)) (and (tptp.v1_relat_1 E) (tptp.v1_funct_1 E) (= D E) (tptp.r1_tarski (tptp.k1_relat_1 E) A) (tptp.r1_tarski (tptp.k2_relat_1 E) B))))))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (tptp.r2_hidden C (tptp.k4_partfun1 A B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r2_hidden C (tptp.k4_partfun1 A B)) (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k4_partfun1 A B)) (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)))) (forall ((A $$unsorted)) (= (tptp.k4_partfun1 tptp.k1_xboole_0 A) (tptp.k1_tarski tptp.k1_xboole_0))) (forall ((A $$unsorted)) (= (tptp.k4_partfun1 A tptp.k1_xboole_0) (tptp.k1_tarski tptp.k1_xboole_0))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r1_tarski A B) (tptp.r1_tarski (tptp.k4_partfun1 A C) (tptp.k4_partfun1 B C)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski (tptp.k4_partfun1 tptp.k1_xboole_0 A) (tptp.k4_partfun1 B A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r1_tarski A B) (tptp.r1_tarski (tptp.k4_partfun1 C A) (tptp.k4_partfun1 C B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.r1_tarski A B) (tptp.r1_tarski C D)) (tptp.r1_tarski (tptp.k4_partfun1 A C) (tptp.k4_partfun1 B D)))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (= (tptp.r1_partfun1 A B) (forall ((C $$unsorted)) (=> (tptp.r2_hidden C (tptp.k3_xboole_0 (tptp.k1_relat_1 A) (tptp.k1_relat_1 B))) (= (tptp.k1_funct_1 A C) (tptp.k1_funct_1 B C))))))))) true (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (= (tptp.r1_partfun1 A B) (exists ((C $$unsorted)) (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (= (tptp.k2_xboole_0 A B) C)))))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (= (tptp.r1_partfun1 A B) (exists ((C $$unsorted)) (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (tptp.r1_tarski A C) (tptp.r1_tarski B C)))))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (tptp.r1_tarski (tptp.k1_relat_1 A) (tptp.k1_relat_1 B)) (= (tptp.r1_partfun1 A B) (forall ((C $$unsorted)) (=> (tptp.r2_hidden C (tptp.k1_relat_1 A)) (= (tptp.k1_funct_1 A C) (tptp.k1_funct_1 B C)))))))))) true true (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (tptp.r1_tarski A B) (tptp.r1_partfun1 A B)))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (and (= (tptp.k1_relat_1 A) (tptp.k1_relat_1 B)) (tptp.r1_partfun1 A B)) (= A B)))))) true (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (tptp.r1_xboole_0 (tptp.k1_relat_1 A) (tptp.k1_relat_1 B)) (tptp.r1_partfun1 A B)))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (forall ((C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (and (tptp.r1_tarski A C) (tptp.r1_tarski B C)) (tptp.r1_partfun1 A B)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D A B)) (forall ((E $$unsorted)) (=> (and (tptp.v1_relat_1 E) (tptp.v1_funct_1 E)) (=> (and (tptp.r1_partfun1 C E) (tptp.r1_tarski D C)) (tptp.r1_partfun1 D E)))))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (tptp.r1_partfun1 tptp.k1_xboole_0 A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (tptp.r1_partfun1 (tptp.k3_partfun1 tptp.k1_xboole_0 A B) C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A (tptp.k1_tarski B))) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D A (tptp.k1_tarski B))) (tptp.r1_partfun1 C D))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (tptp.r1_partfun1 (tptp.k7_relat_1 B A) B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (tptp.r1_partfun1 (tptp.k8_relat_1 A B) B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (tptp.r1_partfun1 (tptp.k7_relat_1 (tptp.k8_relat_1 A C) B) C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (tptp.r1_partfun1 (tptp.k3_partfun1 C A B) C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D A B)) (=> (and (tptp.v1_partfun1 C A B) (tptp.v1_partfun1 D A B) (tptp.r1_partfun1 C D)) (= C D)))))) true true true true true true true true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D A B)) (forall ((E $$unsorted)) (=> (and (tptp.v1_funct_1 E) (tptp.m2_relset_1 E A B)) (=> (and (tptp.r1_partfun1 C E) (tptp.r1_partfun1 D E) (tptp.v1_partfun1 E A B)) (tptp.r1_partfun1 C D)))))))) true true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D A B)) (not (and (=> (= B tptp.k1_xboole_0) (= A tptp.k1_xboole_0)) (tptp.r1_partfun1 C D) (forall ((E $$unsorted)) (=> (and (tptp.v1_funct_1 E) (tptp.m2_relset_1 E A B)) (not (and (tptp.v1_partfun1 E A B) (tptp.r1_partfun1 C E) (tptp.r1_partfun1 D E))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (= (= D (tptp.k5_partfun1 A B C)) (forall ((E $$unsorted)) (= (tptp.r2_hidden E D) (exists ((F $$unsorted)) (and (tptp.v1_funct_1 F) (tptp.m2_relset_1 F A B) (= F E) (tptp.v1_partfun1 F A B) (tptp.r1_partfun1 C F))))))))) true true true true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (tptp.r2_hidden D (tptp.k5_partfun1 A B C)) (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D A B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D A B)) (=> (tptp.r2_hidden D (tptp.k5_partfun1 A B C)) (tptp.v1_partfun1 D A B)))))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_relat_1 D) (tptp.v1_funct_1 D)) (=> (tptp.r2_hidden D (tptp.k5_partfun1 A B C)) (tptp.r1_partfun1 C D)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.m2_relset_1 B A tptp.k1_xboole_0)) (=> (not (= A tptp.k1_xboole_0)) (= (tptp.k5_partfun1 A tptp.k1_xboole_0 B) tptp.k1_xboole_0)))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (= (tptp.v1_partfun1 C A B) (= (tptp.k5_partfun1 A B C) (tptp.k1_tarski C))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.m2_relset_1 B tptp.k1_xboole_0 A)) (= (tptp.k5_partfun1 tptp.k1_xboole_0 A B) (tptp.k1_tarski B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.m2_relset_1 B tptp.k1_xboole_0 A)) (= (tptp.k5_partfun1 tptp.k1_xboole_0 A B) (tptp.k1_tarski tptp.k1_xboole_0)))) true true true true true true true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D A B)) (=> (not (tptp.r1_xboole_0 (tptp.k5_partfun1 A B C) (tptp.k5_partfun1 A B D))) (tptp.r1_partfun1 C D)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D A B)) (not (and (=> (= B tptp.k1_xboole_0) (= A tptp.k1_xboole_0)) (tptp.r1_partfun1 C D) (tptp.r1_xboole_0 (tptp.k5_partfun1 A B C) (tptp.k5_partfun1 A B D)))))))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (= (tptp.k1_relat_1 A) tptp.f1_s1_partfun1) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k1_funct_1 A B))) (let ((_let_2 (tptp.p1_s1_partfun1 B))) (=> (tptp.r2_hidden B tptp.f1_s1_partfun1) (and (=> _let_2 (= _let_1 (tptp.f2_s1_partfun1 B))) (=> (not _let_2) (= _let_1 (tptp.f3_s1_partfun1 B)))))))))) (=> (and (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.r2_hidden A tptp.f1_s2_partfun1) (tptp.p1_s2_partfun1 A B)) (tptp.r2_hidden B tptp.f2_s2_partfun1))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.r2_hidden A tptp.f1_s2_partfun1) (tptp.p1_s2_partfun1 A B) (tptp.p1_s2_partfun1 A C)) (= B C)))) (exists ((A $$unsorted)) (and (tptp.v1_funct_1 A) (tptp.m2_relset_1 A tptp.f1_s2_partfun1 tptp.f2_s2_partfun1) (forall ((B $$unsorted)) (= (tptp.r2_hidden B (tptp.k4_relset_1 tptp.f1_s2_partfun1 tptp.f2_s2_partfun1 A)) (and (tptp.r2_hidden B tptp.f1_s2_partfun1) (exists ((C $$unsorted)) (tptp.p1_s2_partfun1 B C))))) (forall ((B $$unsorted)) (=> (tptp.r2_hidden B (tptp.k4_relset_1 tptp.f1_s2_partfun1 tptp.f2_s2_partfun1 A)) (tptp.p1_s2_partfun1 B (tptp.k1_funct_1 A B))))))) (=> (forall ((A $$unsorted)) (=> (tptp.p1_s3_partfun1 A) (tptp.r2_hidden (tptp.f3_s3_partfun1 A) tptp.f2_s3_partfun1))) (exists ((A $$unsorted)) (and (tptp.v1_funct_1 A) (tptp.m2_relset_1 A tptp.f1_s3_partfun1 tptp.f2_s3_partfun1) (forall ((B $$unsorted)) (= (tptp.r2_hidden B (tptp.k4_relset_1 tptp.f1_s3_partfun1 tptp.f2_s3_partfun1 A)) (and (tptp.r2_hidden B tptp.f1_s3_partfun1) (tptp.p1_s3_partfun1 B)))) (forall ((B $$unsorted)) (=> (tptp.r2_hidden B (tptp.k4_relset_1 tptp.f1_s3_partfun1 tptp.f2_s3_partfun1 A)) (= (tptp.k1_funct_1 A B) (tptp.f3_s3_partfun1 B))))))) (=> (and (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.r2_hidden A tptp.f1_s4_partfun1) (tptp.r2_hidden B tptp.f2_s4_partfun1) (tptp.p1_s4_partfun1 A B C)) (tptp.r2_hidden C tptp.f3_s4_partfun1))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.r2_hidden A tptp.f1_s4_partfun1) (tptp.r2_hidden B tptp.f2_s4_partfun1) (tptp.p1_s4_partfun1 A B C) (tptp.p1_s4_partfun1 A B D)) (= C D)))) (exists ((A $$unsorted)) (and (tptp.v1_funct_1 A) (tptp.m2_relset_1 A (tptp.k2_zfmisc_1 tptp.f1_s4_partfun1 tptp.f2_s4_partfun1) tptp.f3_s4_partfun1) (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.r2_hidden (tptp.k4_tarski B C) (tptp.k4_relset_1 (tptp.k2_zfmisc_1 tptp.f1_s4_partfun1 tptp.f2_s4_partfun1) tptp.f3_s4_partfun1 A)) (and (tptp.r2_hidden B tptp.f1_s4_partfun1) (tptp.r2_hidden C tptp.f2_s4_partfun1) (exists ((D $$unsorted)) (tptp.p1_s4_partfun1 B C D))))) (forall ((B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k4_tarski B C))) (=> (tptp.r2_hidden _let_1 (tptp.k4_relset_1 (tptp.k2_zfmisc_1 tptp.f1_s4_partfun1 tptp.f2_s4_partfun1) tptp.f3_s4_partfun1 A)) (tptp.p1_s4_partfun1 B C (tptp.k1_funct_1 A _let_1)))))))) (=> (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.p1_s5_partfun1 A B) (tptp.r2_hidden (tptp.f4_s5_partfun1 A B) tptp.f3_s5_partfun1))) (exists ((A $$unsorted)) (and (tptp.v1_funct_1 A) (tptp.m2_relset_1 A (tptp.k2_zfmisc_1 tptp.f1_s5_partfun1 tptp.f2_s5_partfun1) tptp.f3_s5_partfun1) (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.r2_hidden (tptp.k4_tarski B C) (tptp.k4_relset_1 (tptp.k2_zfmisc_1 tptp.f1_s5_partfun1 tptp.f2_s5_partfun1) tptp.f3_s5_partfun1 A)) (and (tptp.r2_hidden B tptp.f1_s5_partfun1) (tptp.r2_hidden C tptp.f2_s5_partfun1) (tptp.p1_s5_partfun1 B C)))) (forall ((B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k4_tarski B C))) (=> (tptp.r2_hidden _let_1 (tptp.k4_relset_1 (tptp.k2_zfmisc_1 tptp.f1_s5_partfun1 tptp.f2_s5_partfun1) tptp.f3_s5_partfun1 A)) (= (tptp.k1_funct_1 A _let_1) (tptp.f4_s5_partfun1 B C)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (tptp.r1_partfun1 A B) (tptp.r1_partfun1 B A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (tptp.r1_partfun1 A A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.k1_partfun1 A B C D E F))) (=> (and (tptp.v1_funct_1 E) (tptp.m1_relset_1 E A B) (tptp.v1_funct_1 F) (tptp.m1_relset_1 F C D)) (and (tptp.v1_funct_1 _let_1) (tptp.m2_relset_1 _let_1 A D))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (tptp.v1_funct_1 E) (tptp.m1_relset_1 E A B) (tptp.v1_funct_1 F) (tptp.m1_relset_1 F C D)) (= (tptp.k1_partfun1 A B C D E F) (tptp.k5_relat_1 E F)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k2_partfun1 A B C D))) (=> (and (tptp.v1_funct_1 C) (tptp.m1_relset_1 C A B)) (and (tptp.v1_funct_1 _let_1) (tptp.m2_relset_1 _let_1 A B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m1_relset_1 C A B)) (= (tptp.k2_partfun1 A B C D) (tptp.k7_relat_1 C D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k3_partfun1 A B C))) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (and (tptp.v1_funct_1 _let_1) (tptp.m2_relset_1 _let_1 B C))))) true true (forall ((A $$unsorted)) (let ((_let_1 (tptp.k6_partfun1 A))) (and (tptp.v1_partfun1 _let_1 A A) (tptp.m2_relset_1 _let_1 A A)))) (forall ((A $$unsorted)) (= (tptp.k6_partfun1 A) (tptp.k6_relat_1 A))) (forall ((A $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (forall ((B $$unsorted)) (not (and (tptp.r2_hidden B A) (tptp.r1_xboole_0 B A))))))) (forall ((A $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (forall ((B $$unsorted)) (not (and (tptp.r2_hidden B A) (forall ((C $$unsorted)) (=> (tptp.r2_hidden C B) (tptp.r1_xboole_0 C A))))))))) (forall ((A $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (forall ((B $$unsorted)) (not (and (tptp.r2_hidden B A) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.r2_hidden C D) (tptp.r2_hidden D B)) (tptp.r1_xboole_0 C A))))))))) (forall ((A $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (forall ((B $$unsorted)) (not (and (tptp.r2_hidden B A) (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (tptp.r2_hidden C D) (tptp.r2_hidden D E) (tptp.r2_hidden E B)) (tptp.r1_xboole_0 C A))))))))) (forall ((A $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (forall ((B $$unsorted)) (not (and (tptp.r2_hidden B A) (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (tptp.r2_hidden C D) (tptp.r2_hidden D E) (tptp.r2_hidden E F) (tptp.r2_hidden F B)) (tptp.r1_xboole_0 C A))))))))) (forall ((A $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (forall ((B $$unsorted)) (not (and (tptp.r2_hidden B A) (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted)) (=> (and (tptp.r2_hidden C D) (tptp.r2_hidden D E) (tptp.r2_hidden E F) (tptp.r2_hidden F G) (tptp.r2_hidden G B)) (tptp.r1_xboole_0 C A))))))))) (forall ((A $$unsorted)) (=> (exists ((B $$unsorted) (C $$unsorted)) (= A (tptp.k4_tarski B C))) (forall ((B $$unsorted)) (= (= B (tptp.k1_mcart_1 A)) (forall ((C $$unsorted) (D $$unsorted)) (=> (= A (tptp.k4_tarski C D)) (= B C))))))) (forall ((A $$unsorted)) (=> (exists ((B $$unsorted) (C $$unsorted)) (= A (tptp.k4_tarski B C))) (forall ((B $$unsorted)) (= (= B (tptp.k2_mcart_1 A)) (forall ((C $$unsorted) (D $$unsorted)) (=> (= A (tptp.k4_tarski C D)) (= B D))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k4_tarski A B))) (and (= (tptp.k1_mcart_1 _let_1) A) (= (tptp.k2_mcart_1 _let_1) B)))) (forall ((A $$unsorted)) (=> (exists ((B $$unsorted) (C $$unsorted)) (= A (tptp.k4_tarski B C))) (= (tptp.k4_tarski (tptp.k1_mcart_1 A) (tptp.k2_mcart_1 A)) A))) (forall ((A $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (forall ((B $$unsorted)) (not (and (tptp.r2_hidden B A) (forall ((C $$unsorted) (D $$unsorted)) (not (and (or (tptp.r2_hidden C A) (tptp.r2_hidden D A)) (= B (tptp.k4_tarski C D))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r2_hidden A (tptp.k2_zfmisc_1 B C)) (and (tptp.r2_hidden (tptp.k1_mcart_1 A) B) (tptp.r2_hidden (tptp.k2_mcart_1 A) C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.r2_hidden (tptp.k1_mcart_1 A) B) (tptp.r2_hidden (tptp.k2_mcart_1 A) C)) (or (forall ((D $$unsorted) (E $$unsorted)) (not (= A (tptp.k4_tarski D E)))) (tptp.r2_hidden A (tptp.k2_zfmisc_1 B C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r2_hidden A (tptp.k2_zfmisc_1 (tptp.k1_tarski B) C)) (and (= (tptp.k1_mcart_1 A) B) (tptp.r2_hidden (tptp.k2_mcart_1 A) C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r2_hidden A (tptp.k2_zfmisc_1 B (tptp.k1_tarski C))) (and (tptp.r2_hidden (tptp.k1_mcart_1 A) B) (= (tptp.k2_mcart_1 A) C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r2_hidden A (tptp.k2_zfmisc_1 (tptp.k1_tarski B) (tptp.k1_tarski C))) (and (= (tptp.k1_mcart_1 A) B) (= (tptp.k2_mcart_1 A) C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k1_mcart_1 A))) (=> (tptp.r2_hidden A (tptp.k2_zfmisc_1 (tptp.k2_tarski B C) D)) (and (or (= _let_1 B) (= _let_1 C)) (tptp.r2_hidden (tptp.k2_mcart_1 A) D))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k2_mcart_1 A))) (=> (tptp.r2_hidden A (tptp.k2_zfmisc_1 B (tptp.k2_tarski C D))) (and (tptp.r2_hidden (tptp.k1_mcart_1 A) B) (or (= _let_1 C) (= _let_1 D)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k1_mcart_1 A))) (=> (tptp.r2_hidden A (tptp.k2_zfmisc_1 (tptp.k2_tarski B C) (tptp.k1_tarski D))) (and (or (= _let_1 B) (= _let_1 C)) (= (tptp.k2_mcart_1 A) D))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k2_mcart_1 A))) (=> (tptp.r2_hidden A (tptp.k2_zfmisc_1 (tptp.k1_tarski B) (tptp.k2_tarski C D))) (and (= (tptp.k1_mcart_1 A) B) (or (= _let_1 C) (= _let_1 D)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.k2_mcart_1 A))) (let ((_let_2 (tptp.k1_mcart_1 A))) (=> (tptp.r2_hidden A (tptp.k2_zfmisc_1 (tptp.k2_tarski B C) (tptp.k2_tarski D E))) (and (or (= _let_2 B) (= _let_2 C)) (or (= _let_1 D) (= _let_1 E))))))) (forall ((A $$unsorted)) (=> (exists ((B $$unsorted) (C $$unsorted)) (= A (tptp.k4_tarski B C))) (and (not (= A (tptp.k1_mcart_1 A))) (not (= A (tptp.k2_mcart_1 A)))))) true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r2_hidden A (tptp.k2_zfmisc_1 B C)) (= A (tptp.k4_tarski (tptp.k1_mcart_1 A) (tptp.k2_mcart_1 A))))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (not (= B tptp.k1_xboole_0)) (not (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k2_zfmisc_1 A B)) (= C (tptp.k4_tarski (tptp.k1_mcart_1 C) (tptp.k2_mcart_1 C))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k2_zfmisc_1 (tptp.k2_tarski A B) (tptp.k2_tarski C D)) (tptp.k2_enumset1 (tptp.k4_tarski A C) (tptp.k4_tarski A D) (tptp.k4_tarski B C) (tptp.k4_tarski B D)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (not (= B tptp.k1_xboole_0)) (not (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k2_zfmisc_1 A B)) (and (not (= C (tptp.k1_mcart_1 C))) (not (= C (tptp.k2_mcart_1 C)))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k3_mcart_1 A B C) (tptp.k4_tarski (tptp.k4_tarski A B) C))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (= (tptp.k3_mcart_1 A B C) (tptp.k3_mcart_1 D E F)) (and (= A D) (= B E) (= C F)))) (forall ((A $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (forall ((B $$unsorted)) (not (and (tptp.r2_hidden B A) (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (not (and (or (tptp.r2_hidden C A) (tptp.r2_hidden D A)) (= B (tptp.k3_mcart_1 C D E))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k4_mcart_1 A B C D) (tptp.k4_tarski (tptp.k3_mcart_1 A B C) D))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k4_mcart_1 A B C D) (tptp.k4_tarski (tptp.k4_tarski (tptp.k4_tarski A B) C) D))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k4_mcart_1 A B C D) (tptp.k3_mcart_1 (tptp.k4_tarski A B) C D))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted)) (=> (= (tptp.k4_mcart_1 A B C D) (tptp.k4_mcart_1 E F G H)) (and (= A E) (= B F) (= C G) (= D H)))) (forall ((A $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (forall ((B $$unsorted)) (not (and (tptp.r2_hidden B A) (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (not (and (or (tptp.r2_hidden C A) (tptp.r2_hidden D A)) (= B (tptp.k4_mcart_1 C D E F))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (and (not (= A tptp.k1_xboole_0)) (not (= B tptp.k1_xboole_0)) (not (= C tptp.k1_xboole_0))) (not (= (tptp.k3_zfmisc_1 A B C) tptp.k1_xboole_0)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (= (tptp.k3_zfmisc_1 A B C) (tptp.k3_zfmisc_1 D E F)) (or (= A tptp.k1_xboole_0) (= B tptp.k1_xboole_0) (= C tptp.k1_xboole_0) (and (= A D) (= B E) (= C F))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.k3_zfmisc_1 A B C))) (=> (= _let_1 (tptp.k3_zfmisc_1 D E F)) (or (= _let_1 tptp.k1_xboole_0) (and (= A D) (= B E) (= C F)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (= (tptp.k3_zfmisc_1 A A A) (tptp.k3_zfmisc_1 B B B)) (= A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.k3_zfmisc_1 (tptp.k1_tarski A) (tptp.k1_tarski B) (tptp.k1_tarski C)) (tptp.k1_tarski (tptp.k3_mcart_1 A B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k3_zfmisc_1 (tptp.k2_tarski A B) (tptp.k1_tarski C) (tptp.k1_tarski D)) (tptp.k2_tarski (tptp.k3_mcart_1 A C D) (tptp.k3_mcart_1 B C D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k3_zfmisc_1 (tptp.k1_tarski A) (tptp.k2_tarski B C) (tptp.k1_tarski D)) (tptp.k2_tarski (tptp.k3_mcart_1 A B D) (tptp.k3_mcart_1 A C D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k3_zfmisc_1 (tptp.k1_tarski A) (tptp.k1_tarski B) (tptp.k2_tarski C D)) (tptp.k2_tarski (tptp.k3_mcart_1 A B C) (tptp.k3_mcart_1 A B D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (= (tptp.k3_zfmisc_1 (tptp.k2_tarski A B) (tptp.k2_tarski C D) (tptp.k1_tarski E)) (tptp.k2_enumset1 (tptp.k3_mcart_1 A C E) (tptp.k3_mcart_1 B C E) (tptp.k3_mcart_1 A D E) (tptp.k3_mcart_1 B D E)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (= (tptp.k3_zfmisc_1 (tptp.k2_tarski A B) (tptp.k1_tarski C) (tptp.k2_tarski D E)) (tptp.k2_enumset1 (tptp.k3_mcart_1 A C D) (tptp.k3_mcart_1 B C D) (tptp.k3_mcart_1 A C E) (tptp.k3_mcart_1 B C E)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (= (tptp.k3_zfmisc_1 (tptp.k1_tarski A) (tptp.k2_tarski B C) (tptp.k2_tarski D E)) (tptp.k2_enumset1 (tptp.k3_mcart_1 A B D) (tptp.k3_mcart_1 A C D) (tptp.k3_mcart_1 A B E) (tptp.k3_mcart_1 A C E)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (= (tptp.k3_zfmisc_1 (tptp.k2_tarski A B) (tptp.k2_tarski C D) (tptp.k2_tarski E F)) (tptp.k6_enumset1 (tptp.k3_mcart_1 A C E) (tptp.k3_mcart_1 A D E) (tptp.k3_mcart_1 A C F) (tptp.k3_mcart_1 A D F) (tptp.k3_mcart_1 B C E) (tptp.k3_mcart_1 B D E) (tptp.k3_mcart_1 B C F) (tptp.k3_mcart_1 B D F)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (not (= B tptp.k1_xboole_0)) (not (= C tptp.k1_xboole_0)) (not (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k3_zfmisc_1 A B C)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (= (= E (tptp.k5_mcart_1 A B C D)) (forall ((F $$unsorted) (G $$unsorted) (H $$unsorted)) (=> (= D (tptp.k3_mcart_1 F G H)) (= E F)))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (not (= B tptp.k1_xboole_0)) (not (= C tptp.k1_xboole_0)) (not (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k3_zfmisc_1 A B C)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E B) (= (= E (tptp.k6_mcart_1 A B C D)) (forall ((F $$unsorted) (G $$unsorted) (H $$unsorted)) (=> (= D (tptp.k3_mcart_1 F G H)) (= E G)))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (not (= B tptp.k1_xboole_0)) (not (= C tptp.k1_xboole_0)) (not (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k3_zfmisc_1 A B C)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E C) (= (= E (tptp.k7_mcart_1 A B C D)) (forall ((F $$unsorted) (G $$unsorted) (H $$unsorted)) (=> (= D (tptp.k3_mcart_1 F G H)) (= E H)))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (not (= B tptp.k1_xboole_0)) (not (= C tptp.k1_xboole_0)) (exists ((D $$unsorted)) (and (tptp.m1_subset_1 D (tptp.k3_zfmisc_1 A B C)) (exists ((E $$unsorted) (F $$unsorted) (G $$unsorted)) (and (= D (tptp.k3_mcart_1 E F G)) (not (and (= (tptp.k5_mcart_1 A B C D) E) (= (tptp.k6_mcart_1 A B C D) F) (= (tptp.k7_mcart_1 A B C D) G)))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (not (= B tptp.k1_xboole_0)) (not (= C tptp.k1_xboole_0)) (not (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k3_zfmisc_1 A B C)) (= D (tptp.k3_mcart_1 (tptp.k5_mcart_1 A B C D) (tptp.k6_mcart_1 A B C D) (tptp.k7_mcart_1 A B C D))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (not (and (not (tptp.r1_tarski A (tptp.k3_zfmisc_1 A B C))) (not (tptp.r1_tarski A (tptp.k3_zfmisc_1 B C A))) (not (tptp.r1_tarski A (tptp.k3_zfmisc_1 C A B))))) (= A tptp.k1_xboole_0))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (not (= B tptp.k1_xboole_0)) (not (= C tptp.k1_xboole_0)) (not (forall ((D $$unsorted)) (let ((_let_1 (tptp.k1_mcart_1 D))) (=> (tptp.m1_subset_1 D (tptp.k3_zfmisc_1 A B C)) (and (= (tptp.k5_mcart_1 A B C D) (tptp.k1_mcart_1 _let_1)) (= (tptp.k6_mcart_1 A B C D) (tptp.k2_mcart_1 _let_1)) (= (tptp.k7_mcart_1 A B C D) (tptp.k2_mcart_1 D)))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (not (= B tptp.k1_xboole_0)) (not (= C tptp.k1_xboole_0)) (not (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k3_zfmisc_1 A B C)) (and (not (= D (tptp.k5_mcart_1 A B C D))) (not (= D (tptp.k6_mcart_1 A B C D))) (not (= D (tptp.k7_mcart_1 A B C D)))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (not (tptp.r1_xboole_0 (tptp.k3_zfmisc_1 A B C) (tptp.k3_zfmisc_1 D E F))) (and (not (tptp.r1_xboole_0 A D)) (not (tptp.r1_xboole_0 B E)) (not (tptp.r1_xboole_0 C F))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k4_zfmisc_1 A B C D) (tptp.k2_zfmisc_1 (tptp.k2_zfmisc_1 (tptp.k2_zfmisc_1 A B) C) D))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k3_zfmisc_1 (tptp.k2_zfmisc_1 A B) C D) (tptp.k4_zfmisc_1 A B C D))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (and (not (= A tptp.k1_xboole_0)) (not (= B tptp.k1_xboole_0)) (not (= C tptp.k1_xboole_0)) (not (= D tptp.k1_xboole_0))) (not (= (tptp.k4_zfmisc_1 A B C D) tptp.k1_xboole_0)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted)) (=> (= (tptp.k4_zfmisc_1 A B C D) (tptp.k4_zfmisc_1 E F G H)) (or (= A tptp.k1_xboole_0) (= B tptp.k1_xboole_0) (= C tptp.k1_xboole_0) (= D tptp.k1_xboole_0) (and (= A E) (= B F) (= C G) (= D H))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted)) (let ((_let_1 (tptp.k4_zfmisc_1 A B C D))) (=> (= _let_1 (tptp.k4_zfmisc_1 E F G H)) (or (= _let_1 tptp.k1_xboole_0) (and (= A E) (= B F) (= C G) (= D H)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (= (tptp.k4_zfmisc_1 A A A A) (tptp.k4_zfmisc_1 B B B B)) (= A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (not (= B tptp.k1_xboole_0)) (not (= C tptp.k1_xboole_0)) (not (= D tptp.k1_xboole_0)) (not (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k4_zfmisc_1 A B C D)) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F A) (= (= F (tptp.k8_mcart_1 A B C D E)) (forall ((G $$unsorted) (H $$unsorted) (I $$unsorted) (J $$unsorted)) (=> (= E (tptp.k4_mcart_1 G H I J)) (= F G)))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (not (= B tptp.k1_xboole_0)) (not (= C tptp.k1_xboole_0)) (not (= D tptp.k1_xboole_0)) (not (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k4_zfmisc_1 A B C D)) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F B) (= (= F (tptp.k9_mcart_1 A B C D E)) (forall ((G $$unsorted) (H $$unsorted) (I $$unsorted) (J $$unsorted)) (=> (= E (tptp.k4_mcart_1 G H I J)) (= F H)))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (not (= B tptp.k1_xboole_0)) (not (= C tptp.k1_xboole_0)) (not (= D tptp.k1_xboole_0)) (not (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k4_zfmisc_1 A B C D)) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F C) (= (= F (tptp.k10_mcart_1 A B C D E)) (forall ((G $$unsorted) (H $$unsorted) (I $$unsorted) (J $$unsorted)) (=> (= E (tptp.k4_mcart_1 G H I J)) (= F I)))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (not (= B tptp.k1_xboole_0)) (not (= C tptp.k1_xboole_0)) (not (= D tptp.k1_xboole_0)) (not (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k4_zfmisc_1 A B C D)) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F D) (= (= F (tptp.k11_mcart_1 A B C D E)) (forall ((G $$unsorted) (H $$unsorted) (I $$unsorted) (J $$unsorted)) (=> (= E (tptp.k4_mcart_1 G H I J)) (= F J)))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (not (= B tptp.k1_xboole_0)) (not (= C tptp.k1_xboole_0)) (not (= D tptp.k1_xboole_0)) (exists ((E $$unsorted)) (and (tptp.m1_subset_1 E (tptp.k4_zfmisc_1 A B C D)) (exists ((F $$unsorted) (G $$unsorted) (H $$unsorted) (I $$unsorted)) (and (= E (tptp.k4_mcart_1 F G H I)) (not (and (= (tptp.k8_mcart_1 A B C D E) F) (= (tptp.k9_mcart_1 A B C D E) G) (= (tptp.k10_mcart_1 A B C D E) H) (= (tptp.k11_mcart_1 A B C D E) I)))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (not (= B tptp.k1_xboole_0)) (not (= C tptp.k1_xboole_0)) (not (= D tptp.k1_xboole_0)) (not (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k4_zfmisc_1 A B C D)) (= E (tptp.k4_mcart_1 (tptp.k8_mcart_1 A B C D E) (tptp.k9_mcart_1 A B C D E) (tptp.k10_mcart_1 A B C D E) (tptp.k11_mcart_1 A B C D E))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (not (= B tptp.k1_xboole_0)) (not (= C tptp.k1_xboole_0)) (not (= D tptp.k1_xboole_0)) (not (forall ((E $$unsorted)) (let ((_let_1 (tptp.k1_mcart_1 E))) (let ((_let_2 (tptp.k1_mcart_1 _let_1))) (=> (tptp.m1_subset_1 E (tptp.k4_zfmisc_1 A B C D)) (and (= (tptp.k8_mcart_1 A B C D E) (tptp.k1_mcart_1 _let_2)) (= (tptp.k9_mcart_1 A B C D E) (tptp.k2_mcart_1 _let_2)) (= (tptp.k10_mcart_1 A B C D E) (tptp.k2_mcart_1 _let_1)) (= (tptp.k11_mcart_1 A B C D E) (tptp.k2_mcart_1 E))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (not (= B tptp.k1_xboole_0)) (not (= C tptp.k1_xboole_0)) (not (= D tptp.k1_xboole_0)) (not (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k4_zfmisc_1 A B C D)) (and (not (= E (tptp.k8_mcart_1 A B C D E))) (not (= E (tptp.k9_mcart_1 A B C D E))) (not (= E (tptp.k10_mcart_1 A B C D E))) (not (= E (tptp.k11_mcart_1 A B C D E)))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (not (and (not (tptp.r1_tarski A (tptp.k4_zfmisc_1 A B C D))) (not (tptp.r1_tarski A (tptp.k4_zfmisc_1 B C D A))) (not (tptp.r1_tarski A (tptp.k4_zfmisc_1 C D A B))) (not (tptp.r1_tarski A (tptp.k4_zfmisc_1 D A B C))))) (= A tptp.k1_xboole_0))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted)) (=> (not (tptp.r1_xboole_0 (tptp.k4_zfmisc_1 A B C D) (tptp.k4_zfmisc_1 E F G H))) (and (not (tptp.r1_xboole_0 A E)) (not (tptp.r1_xboole_0 B F)) (not (tptp.r1_xboole_0 C G)) (not (tptp.r1_xboole_0 D H))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.k4_zfmisc_1 (tptp.k1_tarski A) (tptp.k1_tarski B) (tptp.k1_tarski C) (tptp.k1_tarski D)) (tptp.k1_tarski (tptp.k4_mcart_1 A B C D)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (= (tptp.k2_zfmisc_1 A B) tptp.k1_xboole_0)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k2_zfmisc_1 A B)) (and (not (= C (tptp.k1_mcart_1 C))) (not (= C (tptp.k2_mcart_1 C)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r2_hidden A (tptp.k2_zfmisc_1 B C)) (and (not (= A (tptp.k1_mcart_1 A))) (not (= A (tptp.k2_mcart_1 A)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k3_zfmisc_1 A B C)) (not (and (not (= A tptp.k1_xboole_0)) (not (= B tptp.k1_xboole_0)) (not (= C tptp.k1_xboole_0)) (exists ((E $$unsorted) (F $$unsorted) (G $$unsorted)) (and (= D (tptp.k3_mcart_1 E F G)) (not (and (= (tptp.k5_mcart_1 A B C D) E) (= (tptp.k6_mcart_1 A B C D) F) (= (tptp.k7_mcart_1 A B C D) G))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k3_zfmisc_1 A B C)) (=> (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F A) (forall ((G $$unsorted)) (=> (tptp.m1_subset_1 G B) (forall ((H $$unsorted)) (=> (tptp.m1_subset_1 H C) (=> (= E (tptp.k3_mcart_1 F G H)) (= D F)))))))) (or (= A tptp.k1_xboole_0) (= B tptp.k1_xboole_0) (= C tptp.k1_xboole_0) (= D (tptp.k5_mcart_1 A B C E)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k3_zfmisc_1 A B C)) (=> (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F A) (forall ((G $$unsorted)) (=> (tptp.m1_subset_1 G B) (forall ((H $$unsorted)) (=> (tptp.m1_subset_1 H C) (=> (= E (tptp.k3_mcart_1 F G H)) (= D G)))))))) (or (= A tptp.k1_xboole_0) (= B tptp.k1_xboole_0) (= C tptp.k1_xboole_0) (= D (tptp.k6_mcart_1 A B C E)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k3_zfmisc_1 A B C)) (=> (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F A) (forall ((G $$unsorted)) (=> (tptp.m1_subset_1 G B) (forall ((H $$unsorted)) (=> (tptp.m1_subset_1 H C) (=> (= E (tptp.k3_mcart_1 F G H)) (= D H)))))))) (or (= A tptp.k1_xboole_0) (= B tptp.k1_xboole_0) (= C tptp.k1_xboole_0) (= D (tptp.k7_mcart_1 A B C E)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (not (and (tptp.r2_hidden A (tptp.k3_zfmisc_1 B C D)) (forall ((E $$unsorted) (F $$unsorted) (G $$unsorted)) (not (and (tptp.r2_hidden E B) (tptp.r2_hidden F C) (tptp.r2_hidden G D) (= A (tptp.k3_mcart_1 E F G)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (= (tptp.r2_hidden (tptp.k3_mcart_1 A B C) (tptp.k3_zfmisc_1 D E F)) (and (tptp.r2_hidden A D) (tptp.r2_hidden B E) (tptp.r2_hidden C F)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (forall ((E $$unsorted)) (= (tptp.r2_hidden E A) (exists ((F $$unsorted) (G $$unsorted) (H $$unsorted)) (and (tptp.r2_hidden F B) (tptp.r2_hidden G C) (tptp.r2_hidden H D) (= E (tptp.k3_mcart_1 F G H)))))) (= A (tptp.k3_zfmisc_1 B C D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (not (= B tptp.k1_xboole_0)) (not (= C tptp.k1_xboole_0)) (not (= D tptp.k1_xboole_0)) (not (= E tptp.k1_xboole_0)) (not (= F tptp.k1_xboole_0)) (exists ((G $$unsorted)) (and (tptp.m1_subset_1 G (tptp.k3_zfmisc_1 A B C)) (exists ((H $$unsorted)) (and (tptp.m1_subset_1 H (tptp.k3_zfmisc_1 D E F)) (= G H) (not (and (= (tptp.k5_mcart_1 A B C G) (tptp.k5_mcart_1 D E F H)) (= (tptp.k6_mcart_1 A B C G) (tptp.k6_mcart_1 D E F H)) (= (tptp.k7_mcart_1 A B C G) (tptp.k7_mcart_1 D E F H))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 A)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k1_zfmisc_1 B)) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F (tptp.k1_zfmisc_1 C)) (forall ((G $$unsorted)) (=> (tptp.m1_subset_1 G (tptp.k3_zfmisc_1 A B C)) (=> (tptp.r2_hidden G (tptp.k3_zfmisc_1 D E F)) (and (tptp.r2_hidden (tptp.k5_mcart_1 A B C G) D) (tptp.r2_hidden (tptp.k6_mcart_1 A B C G) E) (tptp.r2_hidden (tptp.k7_mcart_1 A B C G) F))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (tptp.r1_tarski A B) (tptp.r1_tarski C D) (tptp.r1_tarski E F)) (tptp.r1_tarski (tptp.k3_zfmisc_1 A C E) (tptp.k3_zfmisc_1 B D F)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k4_zfmisc_1 A B C D)) (not (and (not (= A tptp.k1_xboole_0)) (not (= B tptp.k1_xboole_0)) (not (= C tptp.k1_xboole_0)) (not (= D tptp.k1_xboole_0)) (exists ((F $$unsorted) (G $$unsorted) (H $$unsorted) (I $$unsorted)) (and (= E (tptp.k4_mcart_1 F G H I)) (not (and (= (tptp.k8_mcart_1 A B C D E) F) (= (tptp.k9_mcart_1 A B C D E) G) (= (tptp.k10_mcart_1 A B C D E) H) (= (tptp.k11_mcart_1 A B C D E) I))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (tptp.m1_subset_1 F (tptp.k4_zfmisc_1 A B C D)) (=> (forall ((G $$unsorted)) (=> (tptp.m1_subset_1 G A) (forall ((H $$unsorted)) (=> (tptp.m1_subset_1 H B) (forall ((I $$unsorted)) (=> (tptp.m1_subset_1 I C) (forall ((J $$unsorted)) (=> (tptp.m1_subset_1 J D) (=> (= F (tptp.k4_mcart_1 G H I J)) (= E G)))))))))) (or (= A tptp.k1_xboole_0) (= B tptp.k1_xboole_0) (= C tptp.k1_xboole_0) (= D tptp.k1_xboole_0) (= E (tptp.k8_mcart_1 A B C D F)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (tptp.m1_subset_1 F (tptp.k4_zfmisc_1 A B C D)) (=> (forall ((G $$unsorted)) (=> (tptp.m1_subset_1 G A) (forall ((H $$unsorted)) (=> (tptp.m1_subset_1 H B) (forall ((I $$unsorted)) (=> (tptp.m1_subset_1 I C) (forall ((J $$unsorted)) (=> (tptp.m1_subset_1 J D) (=> (= F (tptp.k4_mcart_1 G H I J)) (= E H)))))))))) (or (= A tptp.k1_xboole_0) (= B tptp.k1_xboole_0) (= C tptp.k1_xboole_0) (= D tptp.k1_xboole_0) (= E (tptp.k9_mcart_1 A B C D F)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (tptp.m1_subset_1 F (tptp.k4_zfmisc_1 A B C D)) (=> (forall ((G $$unsorted)) (=> (tptp.m1_subset_1 G A) (forall ((H $$unsorted)) (=> (tptp.m1_subset_1 H B) (forall ((I $$unsorted)) (=> (tptp.m1_subset_1 I C) (forall ((J $$unsorted)) (=> (tptp.m1_subset_1 J D) (=> (= F (tptp.k4_mcart_1 G H I J)) (= E I)))))))))) (or (= A tptp.k1_xboole_0) (= B tptp.k1_xboole_0) (= C tptp.k1_xboole_0) (= D tptp.k1_xboole_0) (= E (tptp.k10_mcart_1 A B C D F)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (tptp.m1_subset_1 F (tptp.k4_zfmisc_1 A B C D)) (=> (forall ((G $$unsorted)) (=> (tptp.m1_subset_1 G A) (forall ((H $$unsorted)) (=> (tptp.m1_subset_1 H B) (forall ((I $$unsorted)) (=> (tptp.m1_subset_1 I C) (forall ((J $$unsorted)) (=> (tptp.m1_subset_1 J D) (=> (= F (tptp.k4_mcart_1 G H I J)) (= E J)))))))))) (or (= A tptp.k1_xboole_0) (= B tptp.k1_xboole_0) (= C tptp.k1_xboole_0) (= D tptp.k1_xboole_0) (= E (tptp.k11_mcart_1 A B C D F)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (not (and (tptp.r2_hidden A (tptp.k4_zfmisc_1 B C D E)) (forall ((F $$unsorted) (G $$unsorted) (H $$unsorted) (I $$unsorted)) (not (and (tptp.r2_hidden F B) (tptp.r2_hidden G C) (tptp.r2_hidden H D) (tptp.r2_hidden I E) (= A (tptp.k4_mcart_1 F G H I)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted)) (= (tptp.r2_hidden (tptp.k4_mcart_1 A B C D) (tptp.k4_zfmisc_1 E F G H)) (and (tptp.r2_hidden A E) (tptp.r2_hidden B F) (tptp.r2_hidden C G) (tptp.r2_hidden D H)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (forall ((F $$unsorted)) (= (tptp.r2_hidden F A) (exists ((G $$unsorted) (H $$unsorted) (I $$unsorted) (J $$unsorted)) (and (tptp.r2_hidden G B) (tptp.r2_hidden H C) (tptp.r2_hidden I D) (tptp.r2_hidden J E) (= F (tptp.k4_mcart_1 G H I J)))))) (= A (tptp.k4_zfmisc_1 B C D E)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (not (= B tptp.k1_xboole_0)) (not (= C tptp.k1_xboole_0)) (not (= D tptp.k1_xboole_0)) (not (= E tptp.k1_xboole_0)) (not (= F tptp.k1_xboole_0)) (not (= G tptp.k1_xboole_0)) (not (= H tptp.k1_xboole_0)) (exists ((I $$unsorted)) (and (tptp.m1_subset_1 I (tptp.k4_zfmisc_1 A B C D)) (exists ((J $$unsorted)) (and (tptp.m1_subset_1 J (tptp.k4_zfmisc_1 E F G H)) (= I J) (not (and (= (tptp.k8_mcart_1 A B C D I) (tptp.k8_mcart_1 E F G H J)) (= (tptp.k9_mcart_1 A B C D I) (tptp.k9_mcart_1 E F G H J)) (= (tptp.k10_mcart_1 A B C D I) (tptp.k10_mcart_1 E F G H J)) (= (tptp.k11_mcart_1 A B C D I) (tptp.k11_mcart_1 E F G H J))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k1_zfmisc_1 A)) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F (tptp.k1_zfmisc_1 B)) (forall ((G $$unsorted)) (=> (tptp.m1_subset_1 G (tptp.k1_zfmisc_1 C)) (forall ((H $$unsorted)) (=> (tptp.m1_subset_1 H (tptp.k1_zfmisc_1 D)) (forall ((I $$unsorted)) (=> (tptp.m1_subset_1 I (tptp.k4_zfmisc_1 A B C D)) (=> (tptp.r2_hidden I (tptp.k4_zfmisc_1 E F G H)) (and (tptp.r2_hidden (tptp.k8_mcart_1 A B C D I) E) (tptp.r2_hidden (tptp.k9_mcart_1 A B C D I) F) (tptp.r2_hidden (tptp.k10_mcart_1 A B C D I) G) (tptp.r2_hidden (tptp.k11_mcart_1 A B C D I) H))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted)) (=> (and (tptp.r1_tarski A B) (tptp.r1_tarski C D) (tptp.r1_tarski E F) (tptp.r1_tarski G H)) (tptp.r1_tarski (tptp.k4_zfmisc_1 A C E G) (tptp.k4_zfmisc_1 B D F H)))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (= (= B (tptp.k15_mcart_1 A)) (and (= (tptp.k1_relat_1 B) (tptp.k1_relat_1 A)) (forall ((C $$unsorted)) (=> (tptp.r2_hidden C (tptp.k1_relat_1 A)) (= (tptp.k1_funct_1 B C) (tptp.k1_mcart_1 (tptp.k1_funct_1 A C))))))))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (= (= B (tptp.k16_mcart_1 A)) (and (= (tptp.k1_relat_1 B) (tptp.k1_relat_1 A)) (forall ((C $$unsorted)) (=> (tptp.r2_hidden C (tptp.k1_relat_1 A)) (= (tptp.k1_funct_1 B C) (tptp.k2_mcart_1 (tptp.k1_funct_1 A C))))))))))) (forall ((A $$unsorted)) (= (tptp.k17_mcart_1 A) (tptp.k1_mcart_1 (tptp.k1_mcart_1 A)))) (forall ((A $$unsorted)) (= (tptp.k18_mcart_1 A) (tptp.k2_mcart_1 (tptp.k1_mcart_1 A)))) (forall ((A $$unsorted)) (= (tptp.k19_mcart_1 A) (tptp.k1_mcart_1 (tptp.k2_mcart_1 A)))) (forall ((A $$unsorted)) (= (tptp.k20_mcart_1 A) (tptp.k2_mcart_1 (tptp.k2_mcart_1 A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.k4_tarski F (tptp.k4_tarski D E)))) (let ((_let_2 (tptp.k4_tarski (tptp.k4_tarski A B) C))) (and (= (tptp.k17_mcart_1 _let_2) A) (= (tptp.k18_mcart_1 _let_2) B) (= (tptp.k19_mcart_1 _let_1) D) (= (tptp.k20_mcart_1 _let_1) E))))) true true true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k3_zfmisc_1 A B C)) (tptp.m1_subset_1 (tptp.k5_mcart_1 A B C D) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k3_zfmisc_1 A B C)) (tptp.m1_subset_1 (tptp.k6_mcart_1 A B C D) B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k3_zfmisc_1 A B C)) (tptp.m1_subset_1 (tptp.k7_mcart_1 A B C D) C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k4_zfmisc_1 A B C D)) (tptp.m1_subset_1 (tptp.k8_mcart_1 A B C D E) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k4_zfmisc_1 A B C D)) (tptp.m1_subset_1 (tptp.k9_mcart_1 A B C D E) B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k4_zfmisc_1 A B C D)) (tptp.m1_subset_1 (tptp.k10_mcart_1 A B C D E) C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k4_zfmisc_1 A B C D)) (tptp.m1_subset_1 (tptp.k11_mcart_1 A B C D E) D))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 B))) (tptp.m1_subset_1 (tptp.k12_mcart_1 A B C D) (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 B))) (= (tptp.k12_mcart_1 A B C D) (tptp.k2_zfmisc_1 C D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 A)) (tptp.m1_subset_1 E (tptp.k1_zfmisc_1 B)) (tptp.m1_subset_1 F (tptp.k1_zfmisc_1 C))) (tptp.m1_subset_1 (tptp.k13_mcart_1 A B C D E F) (tptp.k1_zfmisc_1 (tptp.k3_zfmisc_1 A B C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 A)) (tptp.m1_subset_1 E (tptp.k1_zfmisc_1 B)) (tptp.m1_subset_1 F (tptp.k1_zfmisc_1 C))) (= (tptp.k13_mcart_1 A B C D E F) (tptp.k3_zfmisc_1 D E F)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted)) (=> (and (tptp.m1_subset_1 E (tptp.k1_zfmisc_1 A)) (tptp.m1_subset_1 F (tptp.k1_zfmisc_1 B)) (tptp.m1_subset_1 G (tptp.k1_zfmisc_1 C)) (tptp.m1_subset_1 H (tptp.k1_zfmisc_1 D))) (tptp.m1_subset_1 (tptp.k14_mcart_1 A B C D E F G H) (tptp.k1_zfmisc_1 (tptp.k4_zfmisc_1 A B C D))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted)) (=> (and (tptp.m1_subset_1 E (tptp.k1_zfmisc_1 A)) (tptp.m1_subset_1 F (tptp.k1_zfmisc_1 B)) (tptp.m1_subset_1 G (tptp.k1_zfmisc_1 C)) (tptp.m1_subset_1 H (tptp.k1_zfmisc_1 D))) (= (tptp.k14_mcart_1 A B C D E F G H) (tptp.k4_zfmisc_1 E F G H)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k15_mcart_1 A))) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (and (tptp.v1_relat_1 _let_1) (tptp.v1_funct_1 _let_1))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k16_mcart_1 A))) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (and (tptp.v1_relat_1 _let_1) (tptp.v1_funct_1 _let_1))))) true true true true (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (and (tptp.m1_relset_1 C A B) (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.v1_funct_1 C))) (=> (tptp.m1_relset_1 C A B) (=> (and _let_1 (tptp.v1_partfun1 C A B)) (and _let_1 (tptp.v1_funct_2 C A B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (not (tptp.v1_xboole_0 (tptp.k1_funct_2 A B))))) (forall ((A $$unsorted)) (not (tptp.v1_xboole_0 (tptp.k1_funct_2 A A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.v1_funct_2 C A B))) (let ((_let_2 (tptp.v1_funct_1 C))) (=> (tptp.m1_relset_1 C A B) (=> (and _let_2 _let_1 (tptp.v3_funct_2 C A B)) (and _let_2 (tptp.v2_funct_1 C) _let_1 (tptp.v2_funct_2 C A B))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.v1_funct_2 C A B))) (let ((_let_2 (tptp.v1_funct_1 C))) (=> (tptp.m1_relset_1 C A B) (=> (and _let_2 (tptp.v2_funct_1 C) _let_1 (tptp.v2_funct_2 C A B)) (and _let_2 _let_1 (tptp.v3_funct_2 C A B))))))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.m1_relset_1 B A A) (tptp.v1_relat_1 B) (tptp.v1_funct_1 B) (tptp.v2_funct_1 B) (tptp.v1_funct_2 B A A) (tptp.v2_funct_2 B A A) (tptp.v3_funct_2 B A A)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.v1_funct_2 B A A))) (let ((_let_2 (tptp.v1_funct_1 B))) (=> (tptp.m1_relset_1 B A A) (=> (and _let_2 (tptp.v1_partfun1 B A A) (tptp.v1_relat_2 B) _let_1) (and _let_2 (tptp.v2_funct_1 B) _let_1 (tptp.v2_funct_2 B A A) (tptp.v3_funct_2 B A A))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.v1_funct_2 C A B))) (let ((_let_2 (tptp.v1_funct_1 C))) (=> (tptp.m1_relset_1 C A B) (=> (and _let_2 _let_1) (and _let_2 (tptp.v1_partfun1 C A B) _let_1)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B))) (forall ((C $$unsorted)) (let ((_let_1 (tptp.v1_funct_2 C A B))) (let ((_let_2 (tptp.v1_funct_1 C))) (=> (tptp.m1_relset_1 C A B) (=> (and _let_2 _let_1) (and _let_2 (not (tptp.v1_xboole_0 C)) (tptp.v1_partfun1 C A B) _let_1)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.v1_funct_2 C A B))) (let ((_let_2 (= A tptp.k1_xboole_0))) (let ((_let_3 (= B tptp.k1_xboole_0))) (=> (tptp.m2_relset_1 C A B) (and (=> (=> _let_3 _let_2) (= _let_1 (= A (tptp.k4_relset_1 A B C)))) (=> _let_3 (or _let_2 (= _let_1 (= C tptp.k1_xboole_0)))))))))) true true (forall ((A $$unsorted)) (let ((_let_1 (tptp.k2_relat_1 A))) (let ((_let_2 (tptp.k1_relat_1 A))) (let ((_let_3 (tptp.v1_funct_1 A))) (=> (and (tptp.v1_relat_1 A) _let_3) (and _let_3 (tptp.v1_funct_2 A _let_2 _let_1) (tptp.m2_relset_1 A _let_2 _let_1))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_relat_1 B))) (let ((_let_2 (tptp.v1_funct_1 B))) (=> (and (tptp.v1_relat_1 B) _let_2) (=> (tptp.r1_tarski (tptp.k2_relat_1 B) A) (and _let_2 (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.v1_funct_1 C))) (=> (and (tptp.v1_relat_1 C) _let_1) (=> (and (= (tptp.k1_relat_1 C) A) (forall ((D $$unsorted)) (=> (tptp.r2_hidden D A) (tptp.r2_hidden (tptp.k1_funct_1 C D) B)))) (and _let_1 (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (=> (tptp.r2_hidden C A) (or (= B tptp.k1_xboole_0) (tptp.r2_hidden (tptp.k1_funct_1 D C) (tptp.k2_relat_1 D)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (=> (tptp.r2_hidden C A) (or (= B tptp.k1_xboole_0) (tptp.r2_hidden (tptp.k1_funct_1 D C) B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.v1_funct_1 D))) (=> (and _let_1 (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (=> (tptp.r1_tarski (tptp.k2_relat_1 D) C) (or (and (= B tptp.k1_xboole_0) (not (= A tptp.k1_xboole_0))) (and _let_1 (tptp.v1_funct_2 D A C) (tptp.m2_relset_1 D A C))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.v1_funct_1 D))) (=> (and _let_1 (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (=> (tptp.r1_tarski B C) (or (and (= B tptp.k1_xboole_0) (not (= A tptp.k1_xboole_0))) (and _let_1 (tptp.v1_funct_2 D A C) (tptp.m2_relset_1 D A C))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.k1_funct_2 A B)) (forall ((D $$unsorted)) (= (tptp.r2_hidden D C) (exists ((E $$unsorted)) (and (tptp.v1_relat_1 E) (tptp.v1_funct_1 E) (= D E) (= (tptp.k1_relat_1 E) A) (tptp.r1_tarski (tptp.k2_relat_1 E) B))))))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (=> (=> (= B tptp.k1_xboole_0) (= A tptp.k1_xboole_0)) (tptp.r2_hidden C (tptp.k1_funct_2 A B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B A A) (tptp.m2_relset_1 B A A)) (tptp.r2_hidden B (tptp.k1_funct_2 A A)))) true (forall ((A $$unsorted)) (=> (not (= A tptp.k1_xboole_0)) (= (tptp.k1_funct_2 A tptp.k1_xboole_0) tptp.k1_xboole_0))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (=> (forall ((D $$unsorted)) (not (and (tptp.r2_hidden D B) (forall ((E $$unsorted)) (not (and (tptp.r2_hidden E A) (= D (tptp.k1_funct_1 C E)))))))) (or (= B tptp.k1_xboole_0) (= (tptp.k2_relat_1 C) B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (not (and (tptp.r2_hidden C B) (= (tptp.k2_relat_1 D) B) (forall ((E $$unsorted)) (not (and (tptp.r2_hidden E A) (= (tptp.k1_funct_1 D E) C)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (=> (forall ((E $$unsorted)) (=> (tptp.r2_hidden E A) (= (tptp.k1_funct_1 C E) (tptp.k1_funct_1 D E)))) (= C D)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.k1_partfun1 A B B C D E))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E B C) (tptp.m2_relset_1 E B C)) (=> (not (and (= B tptp.k1_xboole_0) (not (= C tptp.k1_xboole_0)) (not (= A tptp.k1_xboole_0)))) (and (tptp.v1_funct_1 _let_1) (tptp.v1_funct_2 _let_1 A C) (tptp.m2_relset_1 _let_1 A C)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (forall ((E $$unsorted)) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E B C) (tptp.m2_relset_1 E B C)) (=> (and (= (tptp.k2_relat_1 D) B) (= (tptp.k2_relat_1 E) C)) (or (= B tptp.k1_xboole_0) (= C tptp.k1_xboole_0) (= (tptp.k2_relat_1 (tptp.k1_partfun1 A B B C D E)) C))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (forall ((E $$unsorted)) (=> (and (tptp.v1_relat_1 E) (tptp.v1_funct_1 E)) (=> (tptp.r2_hidden C A) (or (= B tptp.k1_xboole_0) (= (tptp.k1_funct_1 (tptp.k5_relat_1 D E) C) (tptp.k1_funct_1 E (tptp.k1_funct_1 D C))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (=> (not (= B tptp.k1_xboole_0)) (= (= (tptp.k2_relat_1 C) B) (forall ((D $$unsorted)) (=> (not (= D tptp.k1_xboole_0)) (forall ((E $$unsorted)) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E B D) (tptp.m2_relset_1 E B D)) (forall ((F $$unsorted)) (=> (and (tptp.v1_funct_1 F) (tptp.v1_funct_2 F B D) (tptp.m2_relset_1 F B D)) (=> (= (tptp.k1_partfun1 A B B D C E) (tptp.k1_partfun1 A B B D C F)) (= E F)))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C A B) (and (= (tptp.k7_relset_1 A A A B (tptp.k6_partfun1 A) C) C) (= (tptp.k7_relset_1 A B B B C (tptp.k6_partfun1 B)) C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D B A) (tptp.m2_relset_1 D B A)) (=> (= (tptp.k1_partfun1 B A A B D C) (tptp.k6_partfun1 B)) (= (tptp.k2_relat_1 C) B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (=> (=> (= B tptp.k1_xboole_0) (= A tptp.k1_xboole_0)) (= (tptp.v2_funct_1 C) (forall ((D $$unsorted) (E $$unsorted)) (=> (and (tptp.r2_hidden D A) (tptp.r2_hidden E A) (= (tptp.k1_funct_1 C D) (tptp.k1_funct_1 C E))) (= D E))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (forall ((E $$unsorted)) (let ((_let_1 (= B tptp.k1_xboole_0))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E B C) (tptp.m2_relset_1 E B C)) (=> (tptp.v2_funct_1 (tptp.k1_partfun1 A B B C D E)) (or (and (= C tptp.k1_xboole_0) (not _let_1)) (and _let_1 (not (= A tptp.k1_xboole_0))) (tptp.v2_funct_1 D)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (not (and (not (= A tptp.k1_xboole_0)) (not (= B tptp.k1_xboole_0)) (not (= (tptp.v2_funct_1 C) (forall ((D $$unsorted) (E $$unsorted)) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E D A) (tptp.m2_relset_1 E D A)) (forall ((F $$unsorted)) (=> (and (tptp.v1_funct_1 F) (tptp.v1_funct_2 F D A) (tptp.m2_relset_1 F D A)) (=> (= (tptp.k1_partfun1 D A A B E C) (tptp.k1_partfun1 D A A B F C)) (= E F)))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (forall ((E $$unsorted)) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E B C) (tptp.m2_relset_1 E B C)) (=> (and (= (tptp.k2_relat_1 (tptp.k1_partfun1 A B B C D E)) C) (tptp.v2_funct_1 E)) (or (= C tptp.k1_xboole_0) (= (tptp.k2_relat_1 D) B))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D B A) (tptp.m2_relset_1 D B A)) (=> (= (tptp.k1_partfun1 A B B A C D) (tptp.k6_partfun1 A)) (or (= B tptp.k1_xboole_0) (and (tptp.v2_funct_1 C) (= (tptp.k2_relat_1 D) A)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (forall ((E $$unsorted)) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E B C) (tptp.m2_relset_1 E B C)) (=> (and (tptp.v2_funct_1 (tptp.k1_partfun1 A B B C D E)) (= (tptp.k2_relat_1 D) B)) (or (and (= C tptp.k1_xboole_0) (not (= B tptp.k1_xboole_0))) (and (tptp.v2_funct_1 D) (tptp.v2_funct_1 E)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k2_funct_1 C))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (=> (and (tptp.v2_funct_1 C) (= (tptp.k2_relat_1 C) B)) (and (tptp.v1_funct_1 _let_1) (tptp.v1_funct_2 _let_1 B A) (tptp.m2_relset_1 _let_1 B A)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (=> (and (tptp.v2_funct_1 D) (tptp.r2_hidden C A)) (or (= B tptp.k1_xboole_0) (= (tptp.k1_funct_1 (tptp.k2_funct_1 D) (tptp.k1_funct_1 D C)) C))))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D B A) (tptp.m2_relset_1 D B A)) (=> (and (= (tptp.k2_relat_1 C) B) (tptp.v2_funct_1 C) (forall ((E $$unsorted) (F $$unsorted)) (let ((_let_1 (and (tptp.r2_hidden E B) (= (tptp.k1_funct_1 D E) F)))) (let ((_let_2 (and (tptp.r2_hidden F A) (= (tptp.k1_funct_1 C F) E)))) (and (=> _let_1 _let_2) (=> _let_2 _let_1)))))) (or (= A tptp.k1_xboole_0) (= B tptp.k1_xboole_0) (= D (tptp.k2_funct_1 C)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k2_funct_1 C))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (=> (and (= (tptp.k2_relat_1 C) B) (tptp.v2_funct_1 C)) (or (= B tptp.k1_xboole_0) (and (= (tptp.k5_relat_1 C _let_1) (tptp.k6_partfun1 A)) (= (tptp.k5_relat_1 _let_1 C) (tptp.k6_partfun1 B)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D B A) (tptp.m2_relset_1 D B A)) (=> (and (= (tptp.k2_relat_1 C) B) (= (tptp.k1_partfun1 A B B A C D) (tptp.k6_partfun1 A)) (tptp.v2_funct_1 C)) (or (= A tptp.k1_xboole_0) (= B tptp.k1_xboole_0) (= D (tptp.k2_funct_1 C)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (not (and (not (= B tptp.k1_xboole_0)) (exists ((D $$unsorted)) (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D B A) (tptp.m2_relset_1 D B A) (= (tptp.k1_partfun1 A B B A C D) (tptp.k6_partfun1 A)))) (not (tptp.v2_funct_1 C)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k2_partfun1 A B D C))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (=> (tptp.r1_tarski C A) (or (and (= B tptp.k1_xboole_0) (not (= A tptp.k1_xboole_0))) (and (tptp.v1_funct_1 _let_1) (tptp.v1_funct_2 _let_1 C B) (tptp.m2_relset_1 _let_1 C B))))))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (=> (tptp.r1_tarski A C) (= (tptp.k2_partfun1 A B D C) D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.k1_funct_1 E C))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E A B) (tptp.m2_relset_1 E A B)) (=> (and (tptp.r2_hidden C A) (tptp.r2_hidden _let_1 D)) (or (= B tptp.k1_xboole_0) (= (tptp.k1_funct_1 (tptp.k9_relset_1 A B D E) C) _let_1)))))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (=> (not (= B tptp.k1_xboole_0)) (forall ((E $$unsorted)) (=> (exists ((F $$unsorted)) (and (tptp.r2_hidden F A) (tptp.r2_hidden F C) (= E (tptp.k1_funct_1 D F)))) (tptp.r2_hidden E (tptp.k9_relat_1 D C))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (tptp.r1_tarski (tptp.k9_relat_1 D C) B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (=> (=> (= B tptp.k1_xboole_0) (= A tptp.k1_xboole_0)) (= (tptp.k2_funct_2 A B C A) (tptp.k2_relat_1 C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (=> (not (= B tptp.k1_xboole_0)) (forall ((E $$unsorted)) (= (tptp.r2_hidden E (tptp.k10_relat_1 D C)) (and (tptp.r2_hidden E A) (tptp.r2_hidden (tptp.k1_funct_1 D E) C))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D A B)) (tptp.r1_tarski (tptp.k10_relat_1 D C) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (=> (=> (= B tptp.k1_xboole_0) (= A tptp.k1_xboole_0)) (= (tptp.k3_funct_2 A B C B) A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (= (forall ((D $$unsorted)) (not (and (tptp.r2_hidden D B) (= (tptp.k3_funct_2 A B C (tptp.k1_tarski D)) tptp.k1_xboole_0)))) (= (tptp.k2_relat_1 C) B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (=> (tptp.r1_tarski C A) (or (and (= B tptp.k1_xboole_0) (not (= A tptp.k1_xboole_0))) (tptp.r1_tarski C (tptp.k3_funct_2 A B D (tptp.k2_funct_2 A B D C))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (=> (=> (= B tptp.k1_xboole_0) (= A tptp.k1_xboole_0)) (= (tptp.k3_funct_2 A B C (tptp.k2_funct_2 A B C A)) A)))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E A B) (tptp.m2_relset_1 E A B)) (forall ((F $$unsorted)) (let ((_let_1 (= B tptp.k1_xboole_0))) (=> (and (tptp.v1_funct_1 F) (tptp.v1_funct_2 F B C) (tptp.m2_relset_1 F B C)) (not (and (=> (= C tptp.k1_xboole_0) _let_1) (=> _let_1 (= A tptp.k1_xboole_0)) (not (tptp.r1_tarski (tptp.k3_funct_2 A B E D) (tptp.k3_funct_2 A C (tptp.k1_partfun1 A B B C E F) (tptp.k2_funct_2 B C F D))))))))))) true (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.v1_funct_1 B))) (=> (and (tptp.v1_relat_1 B) _let_1) (=> (= (tptp.k1_relat_1 B) tptp.k1_xboole_0) (and _let_1 (tptp.v1_funct_2 B tptp.k1_xboole_0 A) (tptp.m2_relset_1 B tptp.k1_xboole_0 A)))))) true true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C tptp.k1_xboole_0 A) (tptp.m2_relset_1 C tptp.k1_xboole_0 A)) (= (tptp.k2_funct_2 tptp.k1_xboole_0 A C B) tptp.k1_xboole_0))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C tptp.k1_xboole_0 A) (tptp.m2_relset_1 C tptp.k1_xboole_0 A)) (= (tptp.k3_funct_2 tptp.k1_xboole_0 A C B) tptp.k1_xboole_0))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_tarski A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 B) (tptp.m2_relset_1 C _let_1 B)) (=> (not (= B tptp.k1_xboole_0)) (tptp.r2_hidden (tptp.k1_funct_1 C A) B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_tarski A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 B) (tptp.m2_relset_1 C _let_1 B)) (=> (not (= B tptp.k1_xboole_0)) (= (tptp.k2_relat_1 C) (tptp.k1_tarski (tptp.k1_funct_1 C A))))))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k1_tarski A))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D _let_1 B) (tptp.m2_relset_1 D _let_1 B)) (=> (not (= B tptp.k1_xboole_0)) (tptp.r1_tarski (tptp.k2_funct_2 _let_1 B D C) (tptp.k1_tarski (tptp.k1_funct_1 D A))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k1_tarski B))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A _let_1) (tptp.m2_relset_1 D A _let_1)) (=> (tptp.r2_hidden C A) (= (tptp.k1_funct_1 D C) B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_tarski B))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A _let_1) (tptp.m2_relset_1 C A _let_1)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.k1_tarski B))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A _let_1) (tptp.m2_relset_1 D A _let_1)) (= C D))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B A A) (tptp.m2_relset_1 B A A)) (and (= (tptp.k4_relset_1 A A B) A) (tptp.r1_tarski (tptp.k2_relat_1 B) A)))) true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A A) (tptp.m2_relset_1 C A A)) (forall ((D $$unsorted)) (=> (and (tptp.v1_relat_1 D) (tptp.v1_funct_1 D)) (=> (tptp.r2_hidden B A) (= (tptp.k1_funct_1 (tptp.k5_relat_1 C D) B) (tptp.k1_funct_1 D (tptp.k1_funct_1 C B)))))))) true true (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B A A) (tptp.m2_relset_1 B A A)) (forall ((C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A A) (tptp.m2_relset_1 C A A)) (=> (and (= (tptp.k2_relat_1 B) A) (= (tptp.k2_relat_1 C) A)) (= (tptp.k2_relat_1 (tptp.k4_funct_2 A B C)) A)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k6_partfun1 A))) (=> (tptp.m2_relset_1 B A A) (and (= (tptp.k7_relset_1 A A A A B _let_1) B) (= (tptp.k7_relset_1 A A A A _let_1 B) B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B A A) (tptp.m2_relset_1 B A A)) (forall ((C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A A) (tptp.m2_relset_1 C A A)) (=> (and (= (tptp.k4_funct_2 A B C) B) (= (tptp.k2_relat_1 B) A)) (= C (tptp.k6_partfun1 A))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B A A) (tptp.m2_relset_1 B A A)) (forall ((C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A A) (tptp.m2_relset_1 C A A)) (=> (and (= (tptp.k4_funct_2 A C B) B) (tptp.v2_funct_1 B)) (= C (tptp.k6_partfun1 A))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B A A) (tptp.m2_relset_1 B A A)) (= (tptp.v2_funct_1 B) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.r2_hidden C A) (tptp.r2_hidden D A) (= (tptp.k1_funct_1 B C) (tptp.k1_funct_1 B D))) (= C D)))))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B A A) (tptp.m2_relset_1 B A A)) (= (tptp.k2_funct_2 A A B A) (tptp.k2_relat_1 B)))) true true (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B A A) (tptp.m2_relset_1 B A A)) (= (tptp.k3_funct_2 A A B (tptp.k2_funct_2 A A B A)) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (= (tptp.v2_funct_2 C A B) (= (tptp.k2_relat_1 C) B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (= (tptp.v3_funct_2 C A B) (and (tptp.v2_funct_1 C) (tptp.v2_funct_2 C A B))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.m2_relset_1 B A A))) (let ((_let_2 (tptp.v1_funct_2 B A A))) (let ((_let_3 (tptp.v1_funct_1 B))) (=> (and _let_3 _let_2 _let_1) (=> (and (tptp.v2_funct_1 B) (= (tptp.k2_relat_1 B) A)) (and _let_3 _let_2 (tptp.v3_funct_2 B A A) _let_1))))))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B A A) (tptp.m2_relset_1 B A A)) (=> (tptp.v2_funct_1 B) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.r2_hidden C A) (tptp.r2_hidden D A) (= (tptp.k1_funct_1 B C) (tptp.k1_funct_1 B D))) (= C D)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B A A) (tptp.v3_funct_2 B A A) (tptp.m2_relset_1 B A A)) (forall ((C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A A) (tptp.v3_funct_2 C A A) (tptp.m2_relset_1 C A A)) (=> (= (tptp.k5_funct_2 A B C) C) (= B (tptp.k6_partfun1 A))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B A A) (tptp.v3_funct_2 B A A) (tptp.m2_relset_1 B A A)) (forall ((C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A A) (tptp.v3_funct_2 C A A) (tptp.m2_relset_1 C A A)) (=> (= (tptp.k5_funct_2 A B C) (tptp.k6_partfun1 A)) (= C (tptp.k6_funct_2 A B))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k6_partfun1 A))) (let ((_let_2 (tptp.k6_funct_2 A B))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B A A) (tptp.v3_funct_2 B A A) (tptp.m2_relset_1 B A A)) (and (= (tptp.k5_funct_2 A B _let_2) _let_1) (= (tptp.k5_funct_2 A _let_2 B) _let_1)))))) true true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A A) (tptp.v3_funct_2 C A A) (tptp.m2_relset_1 C A A)) (=> (tptp.r1_tarski B A) (and (= (tptp.k2_funct_2 A A C (tptp.k3_funct_2 A A C B)) B) (= (tptp.k3_funct_2 A A C (tptp.k2_funct_2 A A C B)) B))))) true true true true true true true true true true true true true true true true true true true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (=> (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (= (tptp.k1_funct_1 C E) (tptp.k1_funct_1 D E)))) (= C D)))))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (forall ((E $$unsorted)) (not (and (tptp.r2_hidden E (tptp.k2_funct_2 A B D C)) (forall ((F $$unsorted)) (not (and (tptp.r2_hidden F A) (tptp.r2_hidden F C) (= E (tptp.k1_funct_1 D F)))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (forall ((E $$unsorted)) (not (and (tptp.r2_hidden E (tptp.k2_funct_2 A B D C)) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F A) (not (and (tptp.r2_hidden F C) (= E (tptp.k1_funct_1 D F))))))))))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A B))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D _let_1 C) (tptp.m2_relset_1 D _let_1 C)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A B))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E _let_1 C) (tptp.m2_relset_1 E _let_1 C)) (=> (forall ((F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.k4_tarski F G))) (=> (and (tptp.r2_hidden F A) (tptp.r2_hidden G B)) (= (tptp.k1_funct_1 D _let_1) (tptp.k1_funct_1 E _let_1))))) (= D E)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A B))) (=> (and (tptp.v1_funct_1 F) (tptp.v1_funct_2 F _let_1 C) (tptp.m2_relset_1 F _let_1 C)) (=> (and (tptp.r2_hidden D A) (tptp.r2_hidden E B)) (or (= C tptp.k1_xboole_0) (tptp.r2_hidden (tptp.k1_funct_1 F (tptp.k4_tarski D E)) C)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A B))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D _let_1 C) (tptp.m2_relset_1 D _let_1 C)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A B))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E _let_1 C) (tptp.m2_relset_1 E _let_1 C)) (=> (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F A) (forall ((G $$unsorted)) (let ((_let_1 (tptp.k4_tarski F G))) (=> (tptp.m1_subset_1 G B) (= (tptp.k1_funct_1 D _let_1) (tptp.k1_funct_1 E _let_1))))))) (= D E)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.r2_hidden C (tptp.k1_funct_2 A B)) (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)))) true true true true true true true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.m2_relset_1 C A B))) (let ((_let_2 (tptp.v1_funct_1 C))) (=> (and _let_2 _let_1) (=> (= (tptp.k4_relset_1 A B C) A) (and _let_2 (tptp.v1_funct_2 C A B) _let_1)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.m2_relset_1 C A B))) (let ((_let_2 (tptp.v1_funct_1 C))) (=> (and _let_2 _let_1) (=> (tptp.v1_partfun1 C A B) (and _let_2 (tptp.v1_funct_2 C A B) _let_1)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.m2_relset_1 C A B))) (let ((_let_2 (tptp.v1_funct_1 C))) (=> (and _let_2 _let_1) (=> (and _let_2 (tptp.v1_funct_2 C A B) _let_1) (or (and (= B tptp.k1_xboole_0) (not (= A tptp.k1_xboole_0))) (tptp.v1_partfun1 C A B))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (=> (=> (= B tptp.k1_xboole_0) (= A tptp.k1_xboole_0)) (tptp.v1_partfun1 (tptp.k3_partfun1 C A B) A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B A A) (tptp.m2_relset_1 B A A)) (tptp.v1_partfun1 (tptp.k3_partfun1 B A A) A A))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (not (and (=> (= B tptp.k1_xboole_0) (= A tptp.k1_xboole_0)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (exists ((E $$unsorted)) (and (tptp.r2_hidden E (tptp.k4_relset_1 A B C)) (not (= (tptp.k1_funct_1 D E) (tptp.k1_funct_1 C E))))))))))) true true true true (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski (tptp.k1_funct_2 A B) (tptp.k4_partfun1 A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (=> (tptp.r1_partfun1 C D) (or (and (= B tptp.k1_xboole_0) (not (= A tptp.k1_xboole_0))) (= C D))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B A A) (tptp.m2_relset_1 B A A)) (forall ((C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A A) (tptp.m2_relset_1 C A A)) (=> (tptp.r1_partfun1 B C) (= B C)))))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (=> (=> (= B tptp.k1_xboole_0) (= A tptp.k1_xboole_0)) (= (tptp.r1_partfun1 C D) (forall ((E $$unsorted)) (=> (tptp.r2_hidden E (tptp.k4_relset_1 A B C)) (= (tptp.k1_funct_1 C E) (tptp.k1_funct_1 D E)))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.m2_relset_1 B A A)) (forall ((C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A A) (tptp.m2_relset_1 C A A)) (= (tptp.r1_partfun1 B C) (forall ((D $$unsorted)) (=> (tptp.r2_hidden D (tptp.k4_relset_1 A A B)) (= (tptp.k1_funct_1 B D) (tptp.k1_funct_1 C D))))))))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (not (and (=> (= B tptp.k1_xboole_0) (= A tptp.k1_xboole_0)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (not (tptp.r1_partfun1 C D)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.m2_relset_1 B A A)) (exists ((C $$unsorted)) (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A A) (tptp.m2_relset_1 C A A) (tptp.r1_partfun1 B C))))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D A B)) (forall ((E $$unsorted)) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E A B) (tptp.m2_relset_1 E A B)) (=> (and (tptp.r1_partfun1 C E) (tptp.r1_partfun1 D E)) (or (and (= B tptp.k1_xboole_0) (not (= A tptp.k1_xboole_0))) (tptp.r1_partfun1 C D))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.m2_relset_1 B A A)) (forall ((C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A A)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A A) (tptp.m2_relset_1 D A A)) (=> (and (tptp.r1_partfun1 B D) (tptp.r1_partfun1 C D)) (tptp.r1_partfun1 B C)))))))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D A B)) (not (and (=> (= B tptp.k1_xboole_0) (= A tptp.k1_xboole_0)) (tptp.r1_partfun1 C D) (forall ((E $$unsorted)) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E A B) (tptp.m2_relset_1 E A B)) (not (and (tptp.r1_partfun1 C E) (tptp.r1_partfun1 D E))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (=> (tptp.r1_partfun1 C D) (or (and (= B tptp.k1_xboole_0) (not (= A tptp.k1_xboole_0))) (tptp.r2_hidden D (tptp.k5_partfun1 A B C)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.m2_relset_1 B A A)) (forall ((C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A A) (tptp.m2_relset_1 C A A)) (=> (tptp.r1_partfun1 B C) (tptp.r2_hidden C (tptp.k5_partfun1 A A B))))))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (tptp.r2_hidden D (tptp.k5_partfun1 A B C)) (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (tptp.r1_tarski (tptp.k5_partfun1 A B C) (tptp.k1_funct_2 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k5_partfun1 A B (tptp.k3_partfun1 tptp.k1_xboole_0 A B)) (tptp.k1_funct_2 A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (=> (=> (= B tptp.k1_xboole_0) (= A tptp.k1_xboole_0)) (= (tptp.k5_partfun1 A B (tptp.k3_partfun1 C A B)) (tptp.k1_tarski C))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B A A) (tptp.m2_relset_1 B A A)) (= (tptp.k5_partfun1 A A (tptp.k3_partfun1 B A A)) (tptp.k1_tarski B)))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A (tptp.k1_tarski B))) (forall ((D $$unsorted)) (let ((_let_1 (tptp.k1_tarski B))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A _let_1) (tptp.m2_relset_1 D A _let_1)) (= (tptp.k5_partfun1 A _let_1 C) (tptp.k1_tarski D))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D A B)) (=> (tptp.r1_tarski D C) (tptp.r1_tarski (tptp.k5_partfun1 A B C) (tptp.k5_partfun1 A B D))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D A B)) (=> (and (tptp.r1_tarski (tptp.k4_relset_1 A B D) (tptp.k4_relset_1 A B C)) (tptp.r1_tarski (tptp.k5_partfun1 A B C) (tptp.k5_partfun1 A B D))) (tptp.r1_tarski D C)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D A B)) (=> (and (tptp.r1_tarski (tptp.k5_partfun1 A B C) (tptp.k5_partfun1 A B D)) (forall ((E $$unsorted)) (not (= B (tptp.k1_tarski E))))) (tptp.r1_tarski D C)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.m2_relset_1 D A B)) (=> (and (forall ((E $$unsorted)) (not (= B (tptp.k1_tarski E)))) (= (tptp.k5_partfun1 A B C) (tptp.k5_partfun1 A B D))) (= C D)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k1_tarski C))) (let ((_let_2 (tptp.k2_zfmisc_1 (tptp.k1_tarski A) (tptp.k1_tarski B)))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D _let_2 _let_1) (tptp.m2_relset_1 D _let_2 _let_1)) (= D (tptp.k9_funct_2 A B C)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)) (=> (tptp.r2_hidden C (tptp.k1_funct_2 A B)) (and (= (tptp.k1_relat_1 C) A) (tptp.r1_tarski (tptp.k2_relat_1 C) B))))) (=> (forall ((A $$unsorted)) (not (and (tptp.r2_hidden A tptp.f1_s1_funct_2) (forall ((B $$unsorted)) (not (and (tptp.r2_hidden B tptp.f2_s1_funct_2) (tptp.p1_s1_funct_2 A B))))))) (exists ((A $$unsorted)) (and (tptp.v1_funct_1 A) (tptp.v1_funct_2 A tptp.f1_s1_funct_2 tptp.f2_s1_funct_2) (tptp.m2_relset_1 A tptp.f1_s1_funct_2 tptp.f2_s1_funct_2) (forall ((B $$unsorted)) (=> (tptp.r2_hidden B tptp.f1_s1_funct_2) (tptp.p1_s1_funct_2 B (tptp.k1_funct_1 A B))))))) (=> (forall ((A $$unsorted)) (=> (tptp.r2_hidden A tptp.f1_s2_funct_2) (tptp.r2_hidden (tptp.f3_s2_funct_2 A) tptp.f2_s2_funct_2))) (exists ((A $$unsorted)) (and (tptp.v1_funct_1 A) (tptp.v1_funct_2 A tptp.f1_s2_funct_2 tptp.f2_s2_funct_2) (tptp.m2_relset_1 A tptp.f1_s2_funct_2 tptp.f2_s2_funct_2) (forall ((B $$unsorted)) (=> (tptp.r2_hidden B tptp.f1_s2_funct_2) (= (tptp.k1_funct_1 A B) (tptp.f3_s2_funct_2 B))))))) (=> (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A tptp.f1_s3_funct_2) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B tptp.f2_s3_funct_2) (tptp.p1_s3_funct_2 A B))))) (exists ((A $$unsorted)) (and (tptp.v1_funct_1 A) (tptp.v1_funct_2 A tptp.f1_s3_funct_2 tptp.f2_s3_funct_2) (tptp.m2_relset_1 A tptp.f1_s3_funct_2 tptp.f2_s3_funct_2) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B tptp.f1_s3_funct_2) (tptp.p1_s3_funct_2 B (tptp.k8_funct_2 tptp.f1_s3_funct_2 tptp.f2_s3_funct_2 A B))))))) (exists ((A $$unsorted)) (and (tptp.v1_funct_1 A) (tptp.v1_funct_2 A tptp.f1_s4_funct_2 tptp.f2_s4_funct_2) (tptp.m2_relset_1 A tptp.f1_s4_funct_2 tptp.f2_s4_funct_2) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B tptp.f1_s4_funct_2) (= (tptp.k8_funct_2 tptp.f1_s4_funct_2 tptp.f2_s4_funct_2 A B) (tptp.f3_s4_funct_2 B)))))) (=> (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.r2_hidden A tptp.f1_s5_funct_2) (tptp.r2_hidden B tptp.f2_s5_funct_2) (forall ((C $$unsorted)) (not (and (tptp.r2_hidden C tptp.f3_s5_funct_2) (tptp.p1_s5_funct_2 A B C))))))) (exists ((A $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 tptp.f1_s5_funct_2 tptp.f2_s5_funct_2))) (and (tptp.v1_funct_1 A) (tptp.v1_funct_2 A _let_1 tptp.f3_s5_funct_2) (tptp.m2_relset_1 A _let_1 tptp.f3_s5_funct_2) (forall ((B $$unsorted) (C $$unsorted)) (=> (and (tptp.r2_hidden B tptp.f1_s5_funct_2) (tptp.r2_hidden C tptp.f2_s5_funct_2)) (tptp.p1_s5_funct_2 B C (tptp.k1_funct_1 A (tptp.k4_tarski B C))))))))) (=> (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.r2_hidden A tptp.f1_s6_funct_2) (tptp.r2_hidden B tptp.f2_s6_funct_2)) (tptp.r2_hidden (tptp.f4_s6_funct_2 A B) tptp.f3_s6_funct_2))) (exists ((A $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 tptp.f1_s6_funct_2 tptp.f2_s6_funct_2))) (and (tptp.v1_funct_1 A) (tptp.v1_funct_2 A _let_1 tptp.f3_s6_funct_2) (tptp.m2_relset_1 A _let_1 tptp.f3_s6_funct_2) (forall ((B $$unsorted) (C $$unsorted)) (=> (and (tptp.r2_hidden B tptp.f1_s6_funct_2) (tptp.r2_hidden C tptp.f2_s6_funct_2)) (= (tptp.k1_funct_1 A (tptp.k4_tarski B C)) (tptp.f4_s6_funct_2 B C)))))))) (=> (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A tptp.f1_s7_funct_2) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B tptp.f2_s7_funct_2) (exists ((C $$unsorted)) (and (tptp.m1_subset_1 C tptp.f3_s7_funct_2) (tptp.p1_s7_funct_2 A B C))))))) (exists ((A $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 tptp.f1_s7_funct_2 tptp.f2_s7_funct_2))) (and (tptp.v1_funct_1 A) (tptp.v1_funct_2 A _let_1 tptp.f3_s7_funct_2) (tptp.m2_relset_1 A _let_1 tptp.f3_s7_funct_2) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B tptp.f1_s7_funct_2) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C tptp.f2_s7_funct_2) (tptp.p1_s7_funct_2 B C (tptp.k1_funct_1 A (tptp.k4_tarski B C))))))))))) (exists ((A $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 tptp.f1_s8_funct_2 tptp.f2_s8_funct_2))) (and (tptp.v1_funct_1 A) (tptp.v1_funct_2 A _let_1 tptp.f3_s8_funct_2) (tptp.m2_relset_1 A _let_1 tptp.f3_s8_funct_2) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B tptp.f1_s8_funct_2) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C tptp.f2_s8_funct_2) (= (tptp.k1_funct_1 A (tptp.k4_tarski B C)) (tptp.f4_s8_funct_2 B C))))))))) (=> (forall ((A $$unsorted)) (let ((_let_1 (tptp.p1_s9_funct_2 A))) (=> (tptp.r2_hidden A tptp.f1_s9_funct_2) (and (=> _let_1 (tptp.r2_hidden (tptp.f3_s9_funct_2 A) tptp.f2_s9_funct_2)) (=> (not _let_1) (tptp.r2_hidden (tptp.f4_s9_funct_2 A) tptp.f2_s9_funct_2)))))) (exists ((A $$unsorted)) (and (tptp.v1_funct_1 A) (tptp.v1_funct_2 A tptp.f1_s9_funct_2 tptp.f2_s9_funct_2) (tptp.m2_relset_1 A tptp.f1_s9_funct_2 tptp.f2_s9_funct_2) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k1_funct_1 A B))) (let ((_let_2 (tptp.p1_s9_funct_2 B))) (=> (tptp.r2_hidden B tptp.f1_s9_funct_2) (and (=> _let_2 (= _let_1 (tptp.f3_s9_funct_2 B))) (=> (not _let_2) (= _let_1 (tptp.f4_s9_funct_2 B))))))))))) (exists ((A $$unsorted)) (and (tptp.v1_funct_1 A) (tptp.v1_funct_2 A tptp.f1_s10_funct_2 tptp.f2_s10_funct_2) (tptp.m2_relset_1 A tptp.f1_s10_funct_2 tptp.f2_s10_funct_2) (= (tptp.k8_funct_2 tptp.f1_s10_funct_2 tptp.f2_s10_funct_2 A tptp.f3_s10_funct_2) tptp.f4_s10_funct_2) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B tptp.f1_s10_funct_2) (=> (not (= B tptp.f3_s10_funct_2)) (= (tptp.k8_funct_2 tptp.f1_s10_funct_2 tptp.f2_s10_funct_2 A B) (tptp.f5_s10_funct_2 B))))))) (=> (not (= tptp.f3_s11_funct_2 tptp.f4_s11_funct_2)) (exists ((A $$unsorted)) (and (tptp.v1_funct_1 A) (tptp.v1_funct_2 A tptp.f1_s11_funct_2 tptp.f2_s11_funct_2) (tptp.m2_relset_1 A tptp.f1_s11_funct_2 tptp.f2_s11_funct_2) (= (tptp.k8_funct_2 tptp.f1_s11_funct_2 tptp.f2_s11_funct_2 A tptp.f3_s11_funct_2) tptp.f5_s11_funct_2) (= (tptp.k8_funct_2 tptp.f1_s11_funct_2 tptp.f2_s11_funct_2 A tptp.f4_s11_funct_2) tptp.f6_s11_funct_2) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B tptp.f1_s11_funct_2) (not (and (not (= B tptp.f3_s11_funct_2)) (not (= B tptp.f4_s11_funct_2)) (not (= (tptp.k8_funct_2 tptp.f1_s11_funct_2 tptp.f2_s11_funct_2 A B) (tptp.f7_s11_funct_2 B)))))))))) (=> (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A tptp.f1_s12_funct_2) (tptp.r2_hidden (tptp.f3_s12_funct_2 A) tptp.f2_s12_funct_2))) (exists ((A $$unsorted)) (and (tptp.v1_funct_1 A) (tptp.v1_funct_2 A tptp.f1_s12_funct_2 tptp.f2_s12_funct_2) (tptp.m2_relset_1 A tptp.f1_s12_funct_2 tptp.f2_s12_funct_2) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B tptp.f1_s12_funct_2) (= (tptp.k8_funct_2 tptp.f1_s12_funct_2 tptp.f2_s12_funct_2 A B) (tptp.f3_s12_funct_2 B))))))) (=> (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A tptp.f1_s13_funct_2) (tptp.m1_subset_1 (tptp.f3_s13_funct_2 A) tptp.f2_s13_funct_2))) (exists ((A $$unsorted)) (and (tptp.v1_funct_1 A) (tptp.v1_funct_2 A tptp.f1_s13_funct_2 tptp.f2_s13_funct_2) (tptp.m2_relset_1 A tptp.f1_s13_funct_2 tptp.f2_s13_funct_2) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B tptp.f1_s13_funct_2) (= (tptp.k8_funct_2 tptp.f1_s13_funct_2 tptp.f2_s13_funct_2 A B) (tptp.f3_s13_funct_2 B))))))) (=> (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A tptp.f1_s14_funct_2) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B tptp.f2_s14_funct_2) (tptp.p1_s14_funct_2 A B))))) (exists ((A $$unsorted)) (and (tptp.v1_funct_1 A) (tptp.v1_funct_2 A tptp.f1_s14_funct_2 tptp.f2_s14_funct_2) (tptp.m2_relset_1 A tptp.f1_s14_funct_2 tptp.f2_s14_funct_2) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B tptp.f1_s14_funct_2) (tptp.p1_s14_funct_2 B (tptp.k8_funct_2 tptp.f1_s14_funct_2 tptp.f2_s14_funct_2 A B))))))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m1_relset_1 C A B)) (tptp.m1_subset_1 (tptp.k2_funct_2 A B C D) (tptp.k1_zfmisc_1 B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m1_relset_1 C A B)) (= (tptp.k2_funct_2 A B C D) (tptp.k9_relat_1 C D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m1_relset_1 C A B)) (tptp.m1_subset_1 (tptp.k3_funct_2 A B C D) (tptp.k1_zfmisc_1 A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.m1_relset_1 C A B)) (= (tptp.k3_funct_2 A B C D) (tptp.k10_relat_1 C D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k4_funct_2 A B C))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B A A) (tptp.m1_relset_1 B A A) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A A) (tptp.m1_relset_1 C A A)) (and (tptp.v1_funct_1 _let_1) (tptp.v1_funct_2 _let_1 A A) (tptp.m2_relset_1 _let_1 A A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B A A) (tptp.m1_relset_1 B A A) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A A) (tptp.m1_relset_1 C A A)) (= (tptp.k4_funct_2 A B C) (tptp.k5_relat_1 B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k5_funct_2 A B C))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B A A) (tptp.v3_funct_2 B A A) (tptp.m1_relset_1 B A A) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A A) (tptp.v3_funct_2 C A A) (tptp.m1_relset_1 C A A)) (and (tptp.v1_funct_1 _let_1) (tptp.v1_funct_2 _let_1 A A) (tptp.v3_funct_2 _let_1 A A) (tptp.m2_relset_1 _let_1 A A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B A A) (tptp.v3_funct_2 B A A) (tptp.m1_relset_1 B A A) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A A) (tptp.v3_funct_2 C A A) (tptp.m1_relset_1 C A A)) (= (tptp.k5_funct_2 A B C) (tptp.k5_relat_1 B C)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k6_funct_2 A B))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B A A) (tptp.v3_funct_2 B A A) (tptp.m1_relset_1 B A A)) (and (tptp.v1_funct_1 _let_1) (tptp.v1_funct_2 _let_1 A A) (tptp.v3_funct_2 _let_1 A A) (tptp.m2_relset_1 _let_1 A A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B A A) (tptp.v3_funct_2 B A A) (tptp.m1_relset_1 B A A)) (= (tptp.k6_funct_2 A B) (tptp.k2_funct_1 B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.k7_funct_2 A B C D E))) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m1_relset_1 D A B) (tptp.v1_funct_1 E) (tptp.v1_funct_2 E B C) (tptp.m1_relset_1 E B C)) (and (tptp.v1_funct_1 _let_1) (tptp.v1_funct_2 _let_1 A C) (tptp.m2_relset_1 _let_1 A C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m1_relset_1 D A B) (tptp.v1_funct_1 E) (tptp.v1_funct_2 E B C) (tptp.m1_relset_1 E B C)) (= (tptp.k7_funct_2 A B C D E) (tptp.k5_relat_1 D E)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m1_relset_1 C A B) (tptp.m1_subset_1 D A)) (tptp.m1_subset_1 (tptp.k8_funct_2 A B C D) B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m1_relset_1 C A B) (tptp.m1_subset_1 D A)) (= (tptp.k8_funct_2 A B C D) (tptp.k1_funct_1 C D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_tarski C))) (let ((_let_2 (tptp.k2_zfmisc_1 (tptp.k1_tarski A) (tptp.k1_tarski B)))) (let ((_let_3 (tptp.k9_funct_2 A B C))) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.m2_relset_1 _let_3 _let_2 _let_1)))))) true true true true true true true true (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (not (and (tptp.r2_hidden A (tptp.k2_zfmisc_1 B C)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D B) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E C) (not (= A (tptp.k4_tarski D E))))))))))))) true true (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k2_zfmisc_1 A B)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k2_zfmisc_1 A B)) (=> (and (= (tptp.k1_mcart_1 C) (tptp.k1_mcart_1 D)) (= (tptp.k2_mcart_1 C) (tptp.k2_mcart_1 D))) (= C D)))))))))) true true (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (not (tptp.v1_xboole_0 D)) (= (tptp.r2_hidden A (tptp.k3_zfmisc_1 B C D)) (exists ((E $$unsorted)) (and (tptp.m1_subset_1 E B) (exists ((F $$unsorted)) (and (tptp.m1_subset_1 F C) (exists ((G $$unsorted)) (and (tptp.m1_subset_1 G D) (= A (tptp.k3_mcart_1 E F G))))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (not (tptp.v1_xboole_0 D)) (=> (forall ((E $$unsorted)) (= (tptp.r2_hidden E A) (exists ((F $$unsorted)) (and (tptp.m1_subset_1 F B) (exists ((G $$unsorted)) (and (tptp.m1_subset_1 G C) (exists ((H $$unsorted)) (and (tptp.m1_subset_1 H D) (= E (tptp.k3_mcart_1 F G H)))))))))) (= A (tptp.k3_zfmisc_1 B C D))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (not (tptp.v1_xboole_0 D)) (= (= A (tptp.k3_zfmisc_1 B C D)) (forall ((E $$unsorted)) (= (tptp.r2_hidden E A) (exists ((F $$unsorted)) (and (tptp.m1_subset_1 F B) (exists ((G $$unsorted)) (and (tptp.m1_subset_1 G C) (exists ((H $$unsorted)) (and (tptp.m1_subset_1 H D) (= E (tptp.k3_mcart_1 F G H))))))))))))))))))) true true true true true true (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (not (tptp.v1_xboole_0 D)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k3_zfmisc_1 B C D)) (= (= A (tptp.k5_mcart_1 B C D E)) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F B) (forall ((G $$unsorted)) (=> (tptp.m1_subset_1 G C) (forall ((H $$unsorted)) (=> (tptp.m1_subset_1 H D) (=> (= E (tptp.k4_domain_1 B C D F G H)) (= A F))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (not (tptp.v1_xboole_0 D)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k3_zfmisc_1 B C D)) (= (= A (tptp.k6_mcart_1 B C D E)) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F B) (forall ((G $$unsorted)) (=> (tptp.m1_subset_1 G C) (forall ((H $$unsorted)) (=> (tptp.m1_subset_1 H D) (=> (= E (tptp.k4_domain_1 B C D F G H)) (= A G))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (not (tptp.v1_xboole_0 D)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k3_zfmisc_1 B C D)) (= (= A (tptp.k7_mcart_1 B C D E)) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F B) (forall ((G $$unsorted)) (=> (tptp.m1_subset_1 G C) (forall ((H $$unsorted)) (=> (tptp.m1_subset_1 H D) (=> (= E (tptp.k4_domain_1 B C D F G H)) (= A H))))))))))))))))) true (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k3_zfmisc_1 A B C)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k3_zfmisc_1 A B C)) (=> (and (= (tptp.k5_mcart_1 A B C D) (tptp.k5_mcart_1 A B C E)) (= (tptp.k6_mcart_1 A B C D) (tptp.k6_mcart_1 A B C E)) (= (tptp.k7_mcart_1 A B C D) (tptp.k7_mcart_1 A B C E))) (= D E)))))))))))) true true (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (not (tptp.v1_xboole_0 D)) (forall ((E $$unsorted)) (=> (not (tptp.v1_xboole_0 E)) (= (tptp.r2_hidden A (tptp.k4_zfmisc_1 B C D E)) (exists ((F $$unsorted)) (and (tptp.m1_subset_1 F B) (exists ((G $$unsorted)) (and (tptp.m1_subset_1 G C) (exists ((H $$unsorted)) (and (tptp.m1_subset_1 H D) (exists ((I $$unsorted)) (and (tptp.m1_subset_1 I E) (= A (tptp.k4_mcart_1 F G H I))))))))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (not (tptp.v1_xboole_0 D)) (forall ((E $$unsorted)) (=> (not (tptp.v1_xboole_0 E)) (=> (forall ((F $$unsorted)) (= (tptp.r2_hidden F A) (exists ((G $$unsorted)) (and (tptp.m1_subset_1 G B) (exists ((H $$unsorted)) (and (tptp.m1_subset_1 H C) (exists ((I $$unsorted)) (and (tptp.m1_subset_1 I D) (exists ((J $$unsorted)) (and (tptp.m1_subset_1 J E) (= F (tptp.k4_mcart_1 G H I J)))))))))))) (= A (tptp.k4_zfmisc_1 B C D E))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (not (tptp.v1_xboole_0 D)) (forall ((E $$unsorted)) (=> (not (tptp.v1_xboole_0 E)) (= (= A (tptp.k4_zfmisc_1 B C D E)) (forall ((F $$unsorted)) (= (tptp.r2_hidden F A) (exists ((G $$unsorted)) (and (tptp.m1_subset_1 G B) (exists ((H $$unsorted)) (and (tptp.m1_subset_1 H C) (exists ((I $$unsorted)) (and (tptp.m1_subset_1 I D) (exists ((J $$unsorted)) (and (tptp.m1_subset_1 J E) (= F (tptp.k4_mcart_1 G H I J))))))))))))))))))))))) true true true true true true (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (not (tptp.v1_xboole_0 D)) (forall ((E $$unsorted)) (=> (not (tptp.v1_xboole_0 E)) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F (tptp.k4_zfmisc_1 B C D E)) (= (= A (tptp.k8_mcart_1 B C D E F)) (forall ((G $$unsorted)) (=> (tptp.m1_subset_1 G B) (forall ((H $$unsorted)) (=> (tptp.m1_subset_1 H C) (forall ((I $$unsorted)) (=> (tptp.m1_subset_1 I D) (forall ((J $$unsorted)) (=> (tptp.m1_subset_1 J E) (=> (= F (tptp.k5_domain_1 B C D E G H I J)) (= A G))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (not (tptp.v1_xboole_0 D)) (forall ((E $$unsorted)) (=> (not (tptp.v1_xboole_0 E)) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F (tptp.k4_zfmisc_1 B C D E)) (= (= A (tptp.k9_mcart_1 B C D E F)) (forall ((G $$unsorted)) (=> (tptp.m1_subset_1 G B) (forall ((H $$unsorted)) (=> (tptp.m1_subset_1 H C) (forall ((I $$unsorted)) (=> (tptp.m1_subset_1 I D) (forall ((J $$unsorted)) (=> (tptp.m1_subset_1 J E) (=> (= F (tptp.k5_domain_1 B C D E G H I J)) (= A H))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (not (tptp.v1_xboole_0 D)) (forall ((E $$unsorted)) (=> (not (tptp.v1_xboole_0 E)) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F (tptp.k4_zfmisc_1 B C D E)) (= (= A (tptp.k10_mcart_1 B C D E F)) (forall ((G $$unsorted)) (=> (tptp.m1_subset_1 G B) (forall ((H $$unsorted)) (=> (tptp.m1_subset_1 H C) (forall ((I $$unsorted)) (=> (tptp.m1_subset_1 I D) (forall ((J $$unsorted)) (=> (tptp.m1_subset_1 J E) (=> (= F (tptp.k5_domain_1 B C D E G H I J)) (= A I))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (not (tptp.v1_xboole_0 D)) (forall ((E $$unsorted)) (=> (not (tptp.v1_xboole_0 E)) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F (tptp.k4_zfmisc_1 B C D E)) (= (= A (tptp.k11_mcart_1 B C D E F)) (forall ((G $$unsorted)) (=> (tptp.m1_subset_1 G B) (forall ((H $$unsorted)) (=> (tptp.m1_subset_1 H C) (forall ((I $$unsorted)) (=> (tptp.m1_subset_1 I D) (forall ((J $$unsorted)) (=> (tptp.m1_subset_1 J E) (=> (= F (tptp.k5_domain_1 B C D E G H I J)) (= A J))))))))))))))))))))) true (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (not (tptp.v1_xboole_0 D)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k4_zfmisc_1 A B C D)) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F (tptp.k4_zfmisc_1 A B C D)) (=> (and (= (tptp.k8_mcart_1 A B C D E) (tptp.k8_mcart_1 A B C D F)) (= (tptp.k9_mcart_1 A B C D E) (tptp.k9_mcart_1 A B C D F)) (= (tptp.k10_mcart_1 A B C D E) (tptp.k10_mcart_1 A B C D F)) (= (tptp.k11_mcart_1 A B C D E) (tptp.k11_mcart_1 A B C D F))) (= E F)))))))))))))) true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 C A) (tptp.m1_subset_1 D B)) (tptp.m1_subset_1 (tptp.k1_domain_1 A B C D) (tptp.k2_zfmisc_1 A B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 C A) (tptp.m1_subset_1 D B)) (= (tptp.k1_domain_1 A B C D) (tptp.k4_tarski C D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 C (tptp.k2_zfmisc_1 A B))) (tptp.m1_subset_1 (tptp.k2_domain_1 A B C) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 C (tptp.k2_zfmisc_1 A B))) (= (tptp.k2_domain_1 A B C) (tptp.k1_mcart_1 C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 C (tptp.k2_zfmisc_1 A B))) (tptp.m1_subset_1 (tptp.k3_domain_1 A B C) B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 C (tptp.k2_zfmisc_1 A B))) (= (tptp.k3_domain_1 A B C) (tptp.k2_mcart_1 C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 D A) (tptp.m1_subset_1 E B) (tptp.m1_subset_1 F C)) (tptp.m1_subset_1 (tptp.k4_domain_1 A B C D E F) (tptp.k3_zfmisc_1 A B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 D A) (tptp.m1_subset_1 E B) (tptp.m1_subset_1 F C)) (= (tptp.k4_domain_1 A B C D E F) (tptp.k3_mcart_1 D E F)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (not (tptp.v1_xboole_0 C)) (not (tptp.v1_xboole_0 D)) (tptp.m1_subset_1 E A) (tptp.m1_subset_1 F B) (tptp.m1_subset_1 G C) (tptp.m1_subset_1 H D)) (tptp.m1_subset_1 (tptp.k5_domain_1 A B C D E F G H) (tptp.k4_zfmisc_1 A B C D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (not (tptp.v1_xboole_0 C)) (not (tptp.v1_xboole_0 D)) (tptp.m1_subset_1 E A) (tptp.m1_subset_1 F B) (tptp.m1_subset_1 G C) (tptp.m1_subset_1 H D)) (= (tptp.k5_domain_1 A B C D E F G H) (tptp.k4_mcart_1 E F G H)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B A)) (tptp.m1_subset_1 (tptp.k6_domain_1 A B) (tptp.k1_zfmisc_1 A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B A)) (= (tptp.k6_domain_1 A B) (tptp.k1_tarski B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A)) (tptp.m1_subset_1 (tptp.k7_domain_1 A B C) (tptp.k1_zfmisc_1 A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A)) (= (tptp.k7_domain_1 A B C) (tptp.k7_domain_1 A C B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A)) (= (tptp.k7_domain_1 A B C) (tptp.k2_tarski B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A) (tptp.m1_subset_1 D A)) (tptp.m1_subset_1 (tptp.k8_domain_1 A B C D) (tptp.k1_zfmisc_1 A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A) (tptp.m1_subset_1 D A)) (= (tptp.k8_domain_1 A B C D) (tptp.k1_enumset1 B C D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A) (tptp.m1_subset_1 D A) (tptp.m1_subset_1 E A)) (tptp.m1_subset_1 (tptp.k9_domain_1 A B C D E) (tptp.k1_zfmisc_1 A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A) (tptp.m1_subset_1 D A) (tptp.m1_subset_1 E A)) (= (tptp.k9_domain_1 A B C D E) (tptp.k2_enumset1 B C D E)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A) (tptp.m1_subset_1 D A) (tptp.m1_subset_1 E A) (tptp.m1_subset_1 F A)) (tptp.m1_subset_1 (tptp.k10_domain_1 A B C D E F) (tptp.k1_zfmisc_1 A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A) (tptp.m1_subset_1 D A) (tptp.m1_subset_1 E A) (tptp.m1_subset_1 F A)) (= (tptp.k10_domain_1 A B C D E F) (tptp.k3_enumset1 B C D E F)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A) (tptp.m1_subset_1 D A) (tptp.m1_subset_1 E A) (tptp.m1_subset_1 F A) (tptp.m1_subset_1 G A)) (tptp.m1_subset_1 (tptp.k11_domain_1 A B C D E F G) (tptp.k1_zfmisc_1 A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A) (tptp.m1_subset_1 D A) (tptp.m1_subset_1 E A) (tptp.m1_subset_1 F A) (tptp.m1_subset_1 G A)) (= (tptp.k11_domain_1 A B C D E F G) (tptp.k4_enumset1 B C D E F G)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A) (tptp.m1_subset_1 D A) (tptp.m1_subset_1 E A) (tptp.m1_subset_1 F A) (tptp.m1_subset_1 G A) (tptp.m1_subset_1 H A)) (tptp.m1_subset_1 (tptp.k12_domain_1 A B C D E F G H) (tptp.k1_zfmisc_1 A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A) (tptp.m1_subset_1 D A) (tptp.m1_subset_1 E A) (tptp.m1_subset_1 F A) (tptp.m1_subset_1 G A) (tptp.m1_subset_1 H A)) (= (tptp.k12_domain_1 A B C D E F G H) (tptp.k5_enumset1 B C D E F G H)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted) (I $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A) (tptp.m1_subset_1 D A) (tptp.m1_subset_1 E A) (tptp.m1_subset_1 F A) (tptp.m1_subset_1 G A) (tptp.m1_subset_1 H A) (tptp.m1_subset_1 I A)) (tptp.m1_subset_1 (tptp.k13_domain_1 A B C D E F G H I) (tptp.k1_zfmisc_1 A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted) (I $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A) (tptp.m1_subset_1 D A) (tptp.m1_subset_1 E A) (tptp.m1_subset_1 F A) (tptp.m1_subset_1 G A) (tptp.m1_subset_1 H A) (tptp.m1_subset_1 I A)) (= (tptp.k13_domain_1 A B C D E F G H I) (tptp.k6_enumset1 B C D E F G H I)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 D (tptp.k2_zfmisc_1 (tptp.k2_zfmisc_1 A B) C))) (tptp.m1_subset_1 (tptp.k14_domain_1 A B C D) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 D (tptp.k2_zfmisc_1 (tptp.k2_zfmisc_1 A B) C))) (= (tptp.k14_domain_1 A B C D) (tptp.k17_mcart_1 D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 D (tptp.k2_zfmisc_1 (tptp.k2_zfmisc_1 A B) C))) (tptp.m1_subset_1 (tptp.k15_domain_1 A B C D) B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 D (tptp.k2_zfmisc_1 (tptp.k2_zfmisc_1 A B) C))) (= (tptp.k15_domain_1 A B C D) (tptp.k18_mcart_1 D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 D (tptp.k2_zfmisc_1 A (tptp.k2_zfmisc_1 B C)))) (tptp.m1_subset_1 (tptp.k16_domain_1 A B C D) B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 D (tptp.k2_zfmisc_1 A (tptp.k2_zfmisc_1 B C)))) (= (tptp.k16_domain_1 A B C D) (tptp.k19_mcart_1 D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 D (tptp.k2_zfmisc_1 A (tptp.k2_zfmisc_1 B C)))) (tptp.m1_subset_1 (tptp.k17_domain_1 A B C D) C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 D (tptp.k2_zfmisc_1 A (tptp.k2_zfmisc_1 B C)))) (= (tptp.k17_domain_1 A B C D) (tptp.k20_mcart_1 D)))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (= A (tptp.a_1_0_domain_1 A)))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (= (tptp.k2_zfmisc_1 A B) (tptp.a_2_0_domain_1 A B)))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (= (tptp.k3_zfmisc_1 A B C) (tptp.a_3_0_domain_1 A B C)))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (not (tptp.v1_xboole_0 D)) (= (tptp.k4_zfmisc_1 A B C D) (tptp.a_4_0_domain_1 A B C D)))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (= B (tptp.a_2_1_domain_1 A B)))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 B)) (= (tptp.k12_mcart_1 A B C D) (tptp.a_4_1_domain_1 A B C D)))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 A)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k1_zfmisc_1 B)) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F (tptp.k1_zfmisc_1 C)) (= (tptp.k13_mcart_1 A B C D E F) (tptp.a_6_0_domain_1 A B C D E F)))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (not (tptp.v1_xboole_0 D)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k1_zfmisc_1 A)) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F (tptp.k1_zfmisc_1 B)) (forall ((G $$unsorted)) (=> (tptp.m1_subset_1 G (tptp.k1_zfmisc_1 C)) (forall ((H $$unsorted)) (=> (tptp.m1_subset_1 H (tptp.k1_zfmisc_1 D)) (= (tptp.k14_mcart_1 A B C D E F G H) (tptp.a_8_0_domain_1 A B C D E F G H)))))))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (= (tptp.k1_subset_1 A) (tptp.a_1_1_domain_1 A)))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (= (tptp.k3_subset_1 A B) (tptp.a_2_2_domain_1 A B)))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (= (tptp.k5_subset_1 A B C) (tptp.a_3_1_domain_1 A B C)))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (= (tptp.k4_subset_1 A B C) (tptp.a_3_2_domain_1 A B C)))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (= (tptp.k6_subset_1 A B C) (tptp.a_3_3_domain_1 A B C)))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (= (tptp.k7_subset_1 A B C) (tptp.a_3_4_domain_1 A B C)))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (= (tptp.k7_subset_1 A B C) (tptp.a_3_5_domain_1 A B C)))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (= (tptp.k7_subset_1 A B C) (tptp.a_3_6_domain_1 A B C)))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (= (tptp.k7_subset_1 A B C) (tptp.a_3_7_domain_1 A B C)))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 (tptp.a_1_2_domain_1 A) (tptp.k1_zfmisc_1 A)))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 (tptp.a_2_3_domain_1 A B) (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 (tptp.a_3_8_domain_1 A B C) (tptp.k1_zfmisc_1 (tptp.k3_zfmisc_1 A B C))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (not (tptp.v1_xboole_0 D)) (tptp.m1_subset_1 (tptp.a_4_2_domain_1 A B C D) (tptp.k1_zfmisc_1 (tptp.k4_zfmisc_1 A B C D))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (=> (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B A) (=> (tptp.p1_s5_domain_1 B) (tptp.p2_s5_domain_1 B)))) (tptp.r1_tarski (tptp.a_1_3_domain_1 A) (tptp.a_1_4_domain_1 A))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (=> (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B A) (= (tptp.p1_s6_domain_1 B) (tptp.p2_s6_domain_1 B)))) (= (tptp.a_1_5_domain_1 A) (tptp.a_1_6_domain_1 A))))) (tptp.m1_subset_1 tptp.a_0_0_domain_1 (tptp.k1_zfmisc_1 tptp.f1_s7_domain_1)) (tptp.m1_subset_1 tptp.a_0_1_domain_1 (tptp.k1_zfmisc_1 tptp.f2_s8_domain_1)) (tptp.m1_subset_1 tptp.a_0_2_domain_1 (tptp.k1_zfmisc_1 tptp.f3_s9_domain_1)) (= tptp.a_0_3_domain_1 (tptp.k3_xboole_0 tptp.a_0_4_domain_1 tptp.a_0_5_domain_1)) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (= (tptp.r2_hidden A (tptp.a_1_0_domain_1 B)) (exists ((C $$unsorted)) (and (tptp.m1_subset_1 C B) (= A C)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (not (tptp.v1_xboole_0 C))) (= (tptp.r2_hidden A (tptp.a_2_0_domain_1 B C)) (exists ((D $$unsorted) (E $$unsorted)) (and (tptp.m1_subset_1 D B) (tptp.m1_subset_1 E C) (= A (tptp.k1_domain_1 B C D E))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (not (tptp.v1_xboole_0 C)) (not (tptp.v1_xboole_0 D))) (= (tptp.r2_hidden A (tptp.a_3_0_domain_1 B C D)) (exists ((E $$unsorted) (F $$unsorted) (G $$unsorted)) (and (tptp.m1_subset_1 E B) (tptp.m1_subset_1 F C) (tptp.m1_subset_1 G D) (= A (tptp.k4_domain_1 B C D E F G))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (not (tptp.v1_xboole_0 C)) (not (tptp.v1_xboole_0 D)) (not (tptp.v1_xboole_0 E))) (= (tptp.r2_hidden A (tptp.a_4_0_domain_1 B C D E)) (exists ((F $$unsorted) (G $$unsorted) (H $$unsorted) (I $$unsorted)) (and (tptp.m1_subset_1 F B) (tptp.m1_subset_1 G C) (tptp.m1_subset_1 H D) (tptp.m1_subset_1 I E) (= A (tptp.k5_domain_1 B C D E F G H I))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 B))) (= (tptp.r2_hidden A (tptp.a_2_1_domain_1 B C)) (exists ((D $$unsorted)) (and (tptp.m1_subset_1 D B) (= A D) (tptp.r2_hidden D C)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 B)) (tptp.m1_subset_1 E (tptp.k1_zfmisc_1 C))) (= (tptp.r2_hidden A (tptp.a_4_1_domain_1 B C D E)) (exists ((F $$unsorted) (G $$unsorted)) (and (tptp.m1_subset_1 F B) (tptp.m1_subset_1 G C) (= A (tptp.k1_domain_1 B C F G)) (tptp.r2_hidden F D) (tptp.r2_hidden G E)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (not (tptp.v1_xboole_0 C)) (not (tptp.v1_xboole_0 D)) (tptp.m1_subset_1 E (tptp.k1_zfmisc_1 B)) (tptp.m1_subset_1 F (tptp.k1_zfmisc_1 C)) (tptp.m1_subset_1 G (tptp.k1_zfmisc_1 D))) (= (tptp.r2_hidden A (tptp.a_6_0_domain_1 B C D E F G)) (exists ((H $$unsorted) (I $$unsorted) (J $$unsorted)) (and (tptp.m1_subset_1 H B) (tptp.m1_subset_1 I C) (tptp.m1_subset_1 J D) (= A (tptp.k4_domain_1 B C D H I J)) (tptp.r2_hidden H E) (tptp.r2_hidden I F) (tptp.r2_hidden J G)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted) (I $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (not (tptp.v1_xboole_0 C)) (not (tptp.v1_xboole_0 D)) (not (tptp.v1_xboole_0 E)) (tptp.m1_subset_1 F (tptp.k1_zfmisc_1 B)) (tptp.m1_subset_1 G (tptp.k1_zfmisc_1 C)) (tptp.m1_subset_1 H (tptp.k1_zfmisc_1 D)) (tptp.m1_subset_1 I (tptp.k1_zfmisc_1 E))) (= (tptp.r2_hidden A (tptp.a_8_0_domain_1 B C D E F G H I)) (exists ((J $$unsorted) (K $$unsorted) (L $$unsorted) (M $$unsorted)) (and (tptp.m1_subset_1 J B) (tptp.m1_subset_1 K C) (tptp.m1_subset_1 L D) (tptp.m1_subset_1 M E) (= A (tptp.k5_domain_1 B C D E J K L M)) (tptp.r2_hidden J F) (tptp.r2_hidden K G) (tptp.r2_hidden L H) (tptp.r2_hidden M I)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (= (tptp.r2_hidden A (tptp.a_1_1_domain_1 B)) (exists ((C $$unsorted)) (and (tptp.m1_subset_1 C B) (= A C) (not true)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 B))) (= (tptp.r2_hidden A (tptp.a_2_2_domain_1 B C)) (exists ((D $$unsorted)) (and (tptp.m1_subset_1 D B) (= A D) (not (tptp.r2_hidden D C))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 B))) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 C _let_1) (tptp.m1_subset_1 D _let_1)) (= (tptp.r2_hidden A (tptp.a_3_1_domain_1 B C D)) (exists ((E $$unsorted)) (and (tptp.m1_subset_1 E B) (= A E) (tptp.r2_hidden E C) (tptp.r2_hidden E D))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 B))) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 C _let_1) (tptp.m1_subset_1 D _let_1)) (= (tptp.r2_hidden A (tptp.a_3_2_domain_1 B C D)) (exists ((E $$unsorted)) (and (tptp.m1_subset_1 E B) (= A E) (or (tptp.r2_hidden E C) (tptp.r2_hidden E D)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 B))) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 C _let_1) (tptp.m1_subset_1 D _let_1)) (= (tptp.r2_hidden A (tptp.a_3_3_domain_1 B C D)) (exists ((E $$unsorted)) (and (tptp.m1_subset_1 E B) (= A E) (tptp.r2_hidden E C) (not (tptp.r2_hidden E D)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 B))) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 C _let_1) (tptp.m1_subset_1 D _let_1)) (= (tptp.r2_hidden A (tptp.a_3_4_domain_1 B C D)) (exists ((E $$unsorted)) (let ((_let_1 (tptp.r2_hidden E D))) (let ((_let_2 (tptp.r2_hidden E C))) (and (tptp.m1_subset_1 E B) (= A E) (or (and _let_2 (not _let_1)) (and (not _let_2) _let_1)))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 B))) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 C _let_1) (tptp.m1_subset_1 D _let_1)) (= (tptp.r2_hidden A (tptp.a_3_5_domain_1 B C D)) (exists ((E $$unsorted)) (and (tptp.m1_subset_1 E B) (= A E) (= (not (tptp.r2_hidden E C)) (tptp.r2_hidden E D)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 B))) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 C _let_1) (tptp.m1_subset_1 D _let_1)) (= (tptp.r2_hidden A (tptp.a_3_6_domain_1 B C D)) (exists ((E $$unsorted)) (and (tptp.m1_subset_1 E B) (= A E) (= (tptp.r2_hidden E C) (not (tptp.r2_hidden E D))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 B))) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 C _let_1) (tptp.m1_subset_1 D _let_1)) (= (tptp.r2_hidden A (tptp.a_3_7_domain_1 B C D)) (exists ((E $$unsorted)) (and (tptp.m1_subset_1 E B) (= A E) (not (= (tptp.r2_hidden E C) (tptp.r2_hidden E D))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (= (tptp.r2_hidden A (tptp.a_1_2_domain_1 B)) (exists ((C $$unsorted)) (and (tptp.m1_subset_1 C B) (= A C) (tptp.p1_s1_domain_1 C)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (not (tptp.v1_xboole_0 C))) (= (tptp.r2_hidden A (tptp.a_2_3_domain_1 B C)) (exists ((D $$unsorted) (E $$unsorted)) (and (tptp.m1_subset_1 D B) (tptp.m1_subset_1 E C) (= A (tptp.k1_domain_1 B C D E)) (tptp.p1_s2_domain_1 D E)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (not (tptp.v1_xboole_0 C)) (not (tptp.v1_xboole_0 D))) (= (tptp.r2_hidden A (tptp.a_3_8_domain_1 B C D)) (exists ((E $$unsorted) (F $$unsorted) (G $$unsorted)) (and (tptp.m1_subset_1 E B) (tptp.m1_subset_1 F C) (tptp.m1_subset_1 G D) (= A (tptp.k4_domain_1 B C D E F G)) (tptp.p1_s3_domain_1 E F G)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (not (tptp.v1_xboole_0 C)) (not (tptp.v1_xboole_0 D)) (not (tptp.v1_xboole_0 E))) (= (tptp.r2_hidden A (tptp.a_4_2_domain_1 B C D E)) (exists ((F $$unsorted) (G $$unsorted) (H $$unsorted) (I $$unsorted)) (and (tptp.m1_subset_1 F B) (tptp.m1_subset_1 G C) (tptp.m1_subset_1 H D) (tptp.m1_subset_1 I E) (= A (tptp.k5_domain_1 B C D E F G H I)) (tptp.p1_s4_domain_1 F G H I)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (= (tptp.r2_hidden A (tptp.a_1_3_domain_1 B)) (exists ((C $$unsorted)) (and (tptp.m1_subset_1 C B) (= A C) (tptp.p1_s5_domain_1 C)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (= (tptp.r2_hidden A (tptp.a_1_4_domain_1 B)) (exists ((C $$unsorted)) (and (tptp.m1_subset_1 C B) (= A C) (tptp.p2_s5_domain_1 C)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (= (tptp.r2_hidden A (tptp.a_1_5_domain_1 B)) (exists ((C $$unsorted)) (and (tptp.m1_subset_1 C B) (= A C) (tptp.p1_s6_domain_1 C)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (= (tptp.r2_hidden A (tptp.a_1_6_domain_1 B)) (exists ((C $$unsorted)) (and (tptp.m1_subset_1 C B) (= A C) (tptp.p2_s6_domain_1 C)))))) (forall ((A $$unsorted)) (= (tptp.r2_hidden A tptp.a_0_0_domain_1) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B tptp.f1_s7_domain_1) (= A B) (tptp.p1_s7_domain_1 B))))) (forall ((A $$unsorted)) (= (tptp.r2_hidden A tptp.a_0_1_domain_1) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B tptp.f1_s8_domain_1) (= A (tptp.f3_s8_domain_1 B)) (tptp.p1_s8_domain_1 B))))) (forall ((A $$unsorted)) (= (tptp.r2_hidden A tptp.a_0_2_domain_1) (exists ((B $$unsorted) (C $$unsorted)) (and (tptp.m1_subset_1 B tptp.f1_s9_domain_1) (tptp.m1_subset_1 C tptp.f2_s9_domain_1) (= A (tptp.f4_s9_domain_1 B C)) (tptp.p1_s9_domain_1 B C))))) (forall ((A $$unsorted)) (= (tptp.r2_hidden A tptp.a_0_3_domain_1) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B tptp.f1_s10_domain_1) (= A B) (tptp.p1_s10_domain_1 B) (tptp.p2_s10_domain_1 B))))) (forall ((A $$unsorted)) (= (tptp.r2_hidden A tptp.a_0_4_domain_1) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B tptp.f1_s10_domain_1) (= A B) (tptp.p1_s10_domain_1 B))))) (forall ((A $$unsorted)) (= (tptp.r2_hidden A tptp.a_0_5_domain_1) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B tptp.f1_s10_domain_1) (= A B) (tptp.p2_s10_domain_1 B))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 tptp.k1_xboole_0 tptp.k1_xboole_0))) (let ((_let_2 (tptp.v1_funct_2 A _let_1 tptp.k1_xboole_0))) (let ((_let_3 (tptp.v1_funct_1 A))) (=> (tptp.m1_relset_1 A _let_1 tptp.k1_xboole_0) (=> (and _let_3 _let_2) (and _let_3 (tptp.v1_xboole_0 A) _let_2 (tptp.v1_binop_1 A tptp.k1_xboole_0) (tptp.v2_binop_1 A tptp.k1_xboole_0)))))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.k1_binop_1 A B C) (tptp.k1_funct_1 A (tptp.k4_tarski B C)))))) true (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A B))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D _let_1 C) (tptp.m2_relset_1 D _let_1 C)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A B))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E _let_1 C) (tptp.m2_relset_1 E _let_1 C)) (=> (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F A) (forall ((G $$unsorted)) (=> (tptp.m1_subset_1 G B) (= (tptp.k2_binop_1 A B C D F G) (tptp.k2_binop_1 A B C E F G)))))) (= D E)))))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (= (tptp.v1_binop_1 B A) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (= (tptp.k1_binop_1 B C D) (tptp.k1_binop_1 B D C)))))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (= (tptp.v2_binop_1 B A) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (= (tptp.k1_binop_1 B C (tptp.k1_binop_1 B D E)) (tptp.k1_binop_1 B (tptp.k1_binop_1 B C D) E)))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (= (tptp.v3_binop_1 B A) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (= (tptp.k1_binop_1 B C C) C))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B A) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A)) (= (tptp.r1_binop_1 A B C) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (= (tptp.k1_binop_1 C B D) D))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B A) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A)) (= (tptp.r2_binop_1 A B C) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (= (tptp.k1_binop_1 C D B) D))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B A) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A)) (= (tptp.r3_binop_1 A B C) (and (tptp.r1_binop_1 A B C) (tptp.r2_binop_1 A B C)))))))) true true true true true true true true (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (= (tptp.r3_binop_1 A C B) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (and (= (tptp.k1_binop_1 B C D) D) (= (tptp.k1_binop_1 B D C) D)))))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (=> (tptp.v1_binop_1 B A) (= (tptp.r3_binop_1 A C B) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (= (tptp.k1_binop_1 B C D) D)))))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (=> (tptp.v1_binop_1 B A) (= (tptp.r3_binop_1 A C B) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (= (tptp.k1_binop_1 B D C) D)))))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (=> (tptp.v1_binop_1 B A) (= (tptp.r3_binop_1 A C B) (tptp.r1_binop_1 A C B)))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (=> (tptp.v1_binop_1 B A) (= (tptp.r3_binop_1 A C B) (tptp.r2_binop_1 A C B)))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (=> (tptp.v1_binop_1 B A) (= (tptp.r1_binop_1 A C B) (tptp.r2_binop_1 A C B)))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (=> (and (tptp.r1_binop_1 A C B) (tptp.r2_binop_1 A D B)) (= C D))))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (=> (and (tptp.r3_binop_1 A C B) (tptp.r3_binop_1 A D B)) (= C D))))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (=> (exists ((C $$unsorted)) (and (tptp.m1_subset_1 C A) (tptp.r3_binop_1 A C B))) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (= (= C (tptp.k3_binop_1 A B)) (tptp.r3_binop_1 A C B)))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A)) (= (tptp.r4_binop_1 A B C) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F A) (= (tptp.k1_binop_1 B D (tptp.k1_binop_1 C E F)) (tptp.k1_binop_1 C (tptp.k1_binop_1 B D E) (tptp.k1_binop_1 B D F)))))))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A)) (= (tptp.r5_binop_1 A B C) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F A) (= (tptp.k1_binop_1 B (tptp.k1_binop_1 C D E) F) (tptp.k1_binop_1 C (tptp.k1_binop_1 B D F) (tptp.k1_binop_1 B E F)))))))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A)) (= (tptp.r6_binop_1 A B C) (and (tptp.r4_binop_1 A B C) (tptp.r5_binop_1 A B C))))))))) true true true true (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A)) (= (tptp.r6_binop_1 A B C) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (forall ((F $$unsorted)) (let ((_let_1 (tptp.k1_binop_1 B D F))) (=> (tptp.m1_subset_1 F A) (and (= (tptp.k1_binop_1 B D (tptp.k1_binop_1 C E F)) (tptp.k1_binop_1 C (tptp.k1_binop_1 B D E) _let_1)) (= (tptp.k1_binop_1 B (tptp.k1_binop_1 C D E) F) (tptp.k1_binop_1 C _let_1 (tptp.k1_binop_1 B E F)))))))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A)) (=> (tptp.v1_binop_1 C A) (= (tptp.r6_binop_1 A C B) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F A) (= (tptp.k2_binop_1 A A A C D (tptp.k2_binop_1 A A A B E F)) (tptp.k2_binop_1 A A A B (tptp.k2_binop_1 A A A C D E) (tptp.k2_binop_1 A A A C D F))))))))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A)) (=> (tptp.v1_binop_1 C A) (= (tptp.r6_binop_1 A C B) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F A) (= (tptp.k2_binop_1 A A A C (tptp.k2_binop_1 A A A B D E) F) (tptp.k2_binop_1 A A A B (tptp.k2_binop_1 A A A C D F) (tptp.k2_binop_1 A A A C E F))))))))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A)) (=> (tptp.v1_binop_1 C A) (= (tptp.r6_binop_1 A C B) (tptp.r4_binop_1 A C B))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A)) (=> (tptp.v1_binop_1 C A) (= (tptp.r6_binop_1 A C B) (tptp.r5_binop_1 A C B))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A)) (=> (tptp.v1_binop_1 C A) (= (tptp.r5_binop_1 A C B) (tptp.r4_binop_1 A C B))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B A A) (tptp.m2_relset_1 B A A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A)) (= (tptp.r7_binop_1 A B C) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (= (tptp.k1_funct_1 B (tptp.k1_binop_1 C D E)) (tptp.k1_binop_1 C (tptp.k1_funct_1 B D) (tptp.k1_funct_1 B E))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (= (tptp.v1_binop_1 B A) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (= (tptp.k2_binop_1 A A A B C D) (tptp.k2_binop_1 A A A B D C)))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (= (tptp.v2_binop_1 B A) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (= (tptp.k2_binop_1 A A A B C (tptp.k2_binop_1 A A A B D E)) (tptp.k2_binop_1 A A A B (tptp.k2_binop_1 A A A B C D) E)))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (= (tptp.v3_binop_1 B A) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (= (tptp.k2_binop_1 A A A B C C) C))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B A) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A)) (= (tptp.r1_binop_1 A B C) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (= (tptp.k2_binop_1 A A A C B D) D))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B A) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A)) (= (tptp.r2_binop_1 A B C) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (= (tptp.k2_binop_1 A A A C D B) D))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A)) (= (tptp.r4_binop_1 A B C) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F A) (= (tptp.k2_binop_1 A A A B D (tptp.k2_binop_1 A A A C E F)) (tptp.k2_binop_1 A A A C (tptp.k2_binop_1 A A A B D E) (tptp.k2_binop_1 A A A B D F)))))))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A)) (= (tptp.r5_binop_1 A B C) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F A) (= (tptp.k2_binop_1 A A A B (tptp.k2_binop_1 A A A C D E) F) (tptp.k2_binop_1 A A A C (tptp.k2_binop_1 A A A B D F) (tptp.k2_binop_1 A A A B E F)))))))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B A A) (tptp.m2_relset_1 B A A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A)) (= (tptp.r7_binop_1 A B C) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (= (tptp.k8_funct_2 A A B (tptp.k2_binop_1 A A A C D E)) (tptp.k2_binop_1 A A A C (tptp.k8_funct_2 A A B D) (tptp.k8_funct_2 A A B E))))))))))))))) (=> (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A tptp.f1_s1_binop_1) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B tptp.f1_s1_binop_1) (exists ((C $$unsorted)) (and (tptp.m1_subset_1 C tptp.f1_s1_binop_1) (tptp.p1_s1_binop_1 A B C))))))) (exists ((A $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 tptp.f1_s1_binop_1 tptp.f1_s1_binop_1))) (and (tptp.v1_funct_1 A) (tptp.v1_funct_2 A _let_1 tptp.f1_s1_binop_1) (tptp.m2_relset_1 A _let_1 tptp.f1_s1_binop_1) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B tptp.f1_s1_binop_1) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C tptp.f1_s1_binop_1) (tptp.p1_s1_binop_1 B C (tptp.k2_binop_1 tptp.f1_s1_binop_1 tptp.f1_s1_binop_1 tptp.f1_s1_binop_1 A B C)))))))))) (exists ((A $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 tptp.f1_s2_binop_1 tptp.f1_s2_binop_1))) (and (tptp.v1_funct_1 A) (tptp.v1_funct_2 A _let_1 tptp.f1_s2_binop_1) (tptp.m2_relset_1 A _let_1 tptp.f1_s2_binop_1) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B tptp.f1_s2_binop_1) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C tptp.f1_s2_binop_1) (= (tptp.k2_binop_1 tptp.f1_s2_binop_1 tptp.f1_s2_binop_1 tptp.f1_s2_binop_1 A B C) (tptp.f2_s2_binop_1 B C))))))))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A B))) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (tptp.v1_funct_1 D) (tptp.v1_funct_2 D _let_1 C) (tptp.m1_relset_1 D _let_1 C) (tptp.m1_subset_1 E A) (tptp.m1_subset_1 F B)) (tptp.m1_subset_1 (tptp.k2_binop_1 A B C D E F) C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A B))) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (tptp.v1_funct_1 D) (tptp.v1_funct_2 D _let_1 C) (tptp.m1_relset_1 D _let_1 C) (tptp.m1_subset_1 E A) (tptp.m1_subset_1 F B)) (= (tptp.k2_binop_1 A B C D E F) (tptp.k1_binop_1 D E F))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m1_relset_1 B _let_1 A)) (tptp.m1_subset_1 (tptp.k3_binop_1 A B) A)))) (and (tptp.v1_ordinal1 tptp.k5_ordinal2) (tptp.v2_ordinal1 tptp.k5_ordinal2) (tptp.v3_ordinal1 tptp.k5_ordinal2) (not (tptp.v1_xboole_0 tptp.k5_ordinal2))) (exists ((A $$unsorted)) (and (tptp.v1_ordinal1 A) (tptp.v2_ordinal1 A) (tptp.v3_ordinal1 A) (tptp.v4_ordinal1 A))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v5_ordinal1 A) (tptp.v1_ordinal2 A))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.m1_ordinal1 B A) (tptp.v1_ordinal2 B))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k7_relat_1 A B))) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v5_ordinal1 A) (tptp.v1_ordinal2 A) (tptp.v3_ordinal1 B)) (and (tptp.v1_relat_1 _let_1) (tptp.v1_funct_1 _let_1) (tptp.v1_ordinal2 _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_funct_1 A B))) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v5_ordinal1 A) (tptp.v1_ordinal2 A) (tptp.v3_ordinal1 B)) (and (tptp.v1_ordinal1 _let_1) (tptp.v2_ordinal1 _let_1) (tptp.v3_ordinal1 _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_funcop_1 A B))) (=> (tptp.v3_ordinal1 B) (and (tptp.v1_relat_1 _let_1) (tptp.v1_funct_1 _let_1) (tptp.v1_ordinal2 _let_1))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (= (tptp.r1_ordinal1 A B) (tptp.r1_ordinal1 (tptp.k1_ordinal1 A) (tptp.k1_ordinal1 B))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (= (tptp.k3_tarski (tptp.k1_ordinal1 A)) A))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (tptp.r1_tarski (tptp.k1_ordinal1 A) (tptp.k1_zfmisc_1 A)))) (tptp.v4_ordinal1 tptp.k1_xboole_0) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (tptp.r1_ordinal1 (tptp.k3_tarski A) A))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v5_ordinal1 A)) (= (tptp.k1_ordinal2 A) (tptp.k1_funct_1 A (tptp.k3_tarski (tptp.k1_relat_1 A)))))) true (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B) (tptp.v5_ordinal1 B)) (=> (= (tptp.k1_relat_1 B) (tptp.k1_ordinal1 A)) (= (tptp.k1_ordinal2 B) (tptp.k1_funct_1 B A))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.k2_ordinal2 A)) (forall ((C $$unsorted)) (= (tptp.r2_hidden C B) (and (tptp.r2_hidden C A) (tptp.v3_ordinal1 C)))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.k3_ordinal2 A)) (forall ((C $$unsorted)) (= (tptp.r2_hidden C B) (and (tptp.r2_hidden C A) (exists ((D $$unsorted)) (and (tptp.v3_ordinal1 D) (= C D) (tptp.v4_ordinal1 D)))))))) true (forall ((A $$unsorted)) (tptp.r1_tarski (tptp.k2_ordinal2 A) A)) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (= (tptp.k2_ordinal2 A) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r1_tarski A B) (tptp.r1_tarski (tptp.k2_ordinal2 A) (tptp.k2_ordinal2 B)))) true (forall ((A $$unsorted)) (tptp.r1_tarski (tptp.k3_ordinal2 A) A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r1_tarski A B) (tptp.r1_tarski (tptp.k3_ordinal2 A) (tptp.k3_ordinal2 B)))) (forall ((A $$unsorted)) (tptp.r1_tarski (tptp.k3_ordinal2 A) (tptp.k2_ordinal2 A))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (exists ((B $$unsorted)) (and (tptp.v3_ordinal1 B) (tptp.r2_hidden A B) (tptp.v4_ordinal1 B))))) (forall ((A $$unsorted)) (=> (forall ((B $$unsorted)) (=> (tptp.r2_hidden B A) (tptp.v3_ordinal1 B))) (tptp.v3_ordinal1 (tptp.k1_setfam_1 A)))) (= tptp.k4_ordinal2 (tptp.k1_ordinal1 tptp.k1_xboole_0)) (forall ((A $$unsorted)) (= (= A tptp.k5_ordinal2) (and (tptp.r2_hidden tptp.k1_xboole_0 A) (tptp.v4_ordinal1 A) (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (=> (and (tptp.r2_hidden tptp.k1_xboole_0 B) (tptp.v4_ordinal1 B)) (tptp.r1_tarski A B))))))) (forall ((A $$unsorted)) (= (tptp.k6_ordinal2 A) (tptp.k1_setfam_1 (tptp.k2_ordinal2 A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v3_ordinal1 B) (= (= B (tptp.k7_ordinal2 A)) (and (tptp.r1_tarski (tptp.k2_ordinal2 A) B) (forall ((C $$unsorted)) (=> (tptp.v3_ordinal1 C) (=> (tptp.r1_tarski (tptp.k2_ordinal2 A) C) (tptp.r1_ordinal1 B C)))))))) true (and (tptp.r2_hidden tptp.k1_xboole_0 tptp.k5_ordinal2) (tptp.v4_ordinal1 tptp.k5_ordinal2) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (=> (and (tptp.r2_hidden tptp.k1_xboole_0 A) (tptp.v4_ordinal1 A)) (tptp.r1_ordinal1 tptp.k5_ordinal2 A))))) true true (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.r2_hidden A B) (tptp.r1_ordinal1 (tptp.k6_ordinal2 B) A))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (forall ((C $$unsorted)) (=> (tptp.v3_ordinal1 C) (=> (tptp.r2_hidden C B) (tptp.r1_ordinal1 A C)))) (or (= (tptp.k2_ordinal2 B) tptp.k1_xboole_0) (tptp.r1_ordinal1 A (tptp.k6_ordinal2 B))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted) (C $$unsorted)) (=> (and (tptp.r2_hidden A B) (tptp.r1_tarski B C)) (tptp.r1_ordinal1 (tptp.k6_ordinal2 C) (tptp.k6_ordinal2 B)))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.r2_hidden A B) (tptp.r2_hidden (tptp.k6_ordinal2 B) B))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (= (tptp.k7_ordinal2 A) A))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.r2_hidden A B) (tptp.r2_hidden A (tptp.k7_ordinal2 B)))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (forall ((C $$unsorted)) (=> (tptp.v3_ordinal1 C) (=> (tptp.r2_hidden C B) (tptp.r2_hidden C A)))) (tptp.r1_ordinal1 (tptp.k7_ordinal2 B) A))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (not (and (tptp.r2_hidden A (tptp.k7_ordinal2 B)) (forall ((C $$unsorted)) (=> (tptp.v3_ordinal1 C) (not (and (tptp.r2_hidden C B) (tptp.r1_ordinal1 A C)))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r1_tarski A B) (tptp.r1_ordinal1 (tptp.k7_ordinal2 A) (tptp.k7_ordinal2 B)))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (= (tptp.k7_ordinal2 (tptp.k1_tarski A)) (tptp.k1_ordinal1 A)))) (forall ((A $$unsorted)) (tptp.r1_ordinal1 (tptp.k6_ordinal2 A) (tptp.k7_ordinal2 A))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (= (tptp.v1_ordinal2 A) (exists ((B $$unsorted)) (and (tptp.v3_ordinal1 B) (tptp.r1_tarski (tptp.k2_relat_1 A) B)))))) true (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B) (tptp.v5_ordinal1 B) (tptp.v1_ordinal2 B)) (=> (tptp.r2_hidden A (tptp.k1_relat_1 B)) (tptp.v3_ordinal1 (tptp.k1_funct_1 B A))))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v5_ordinal1 A)) (= (tptp.k8_ordinal2 A) (tptp.k7_ordinal2 (tptp.k2_relat_1 A))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v5_ordinal1 A)) (= (tptp.k9_ordinal2 A) (tptp.k6_ordinal2 (tptp.k2_relat_1 A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k2_relat_1 A))) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v5_ordinal1 A)) (and (= (tptp.k8_ordinal2 A) (tptp.k7_ordinal2 _let_1)) (= (tptp.k9_ordinal2 A) (tptp.k6_ordinal2 _let_1)))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v5_ordinal1 A)) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (= (= B (tptp.k10_ordinal2 A)) (exists ((C $$unsorted)) (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (tptp.v5_ordinal1 C) (tptp.v1_ordinal2 C) (= B (tptp.k9_ordinal2 C)) (= (tptp.k1_relat_1 C) (tptp.k1_relat_1 A)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.k1_relat_1 A))) (=> (tptp.v3_ordinal1 D) (=> (tptp.r2_hidden D _let_1) (= (tptp.k1_funct_1 C D) (tptp.k7_ordinal2 (tptp.k2_relat_1 (tptp.k7_relat_1 A (tptp.k4_xboole_0 _let_1 D)))))))))))))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v5_ordinal1 A)) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (= (= B (tptp.k11_ordinal2 A)) (exists ((C $$unsorted)) (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (tptp.v5_ordinal1 C) (tptp.v1_ordinal2 C) (= B (tptp.k8_ordinal2 C)) (= (tptp.k1_relat_1 C) (tptp.k1_relat_1 A)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.k1_relat_1 A))) (=> (tptp.v3_ordinal1 D) (=> (tptp.r2_hidden D _let_1) (= (tptp.k1_funct_1 C D) (tptp.k6_ordinal2 (tptp.k2_relat_1 (tptp.k7_relat_1 A (tptp.k4_xboole_0 _let_1 D)))))))))))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (let ((_let_1 (tptp.r1_ordinal2 A B))) (let ((_let_2 (= A tptp.k1_xboole_0))) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B) (tptp.v5_ordinal1 B) (tptp.v1_ordinal2 B)) (and (=> _let_2 (= _let_1 (exists ((C $$unsorted)) (and (tptp.v3_ordinal1 C) (tptp.r2_hidden C (tptp.k1_relat_1 B)) (forall ((D $$unsorted)) (=> (tptp.v3_ordinal1 D) (=> (and (tptp.r1_ordinal1 C D) (tptp.r2_hidden D (tptp.k1_relat_1 B))) (= (tptp.k1_funct_1 B D) tptp.k1_xboole_0)))))))) (=> (not _let_2) (= _let_1 (forall ((C $$unsorted)) (=> (tptp.v3_ordinal1 C) (forall ((D $$unsorted)) (=> (tptp.v3_ordinal1 D) (not (and (tptp.r2_hidden C A) (tptp.r2_hidden A D) (forall ((E $$unsorted)) (=> (tptp.v3_ordinal1 E) (not (and (tptp.r2_hidden E (tptp.k1_relat_1 B)) (forall ((F $$unsorted)) (let ((_let_1 (tptp.k1_funct_1 B F))) (=> (tptp.v3_ordinal1 F) (=> (and (tptp.r1_ordinal1 E F) (tptp.r2_hidden F (tptp.k1_relat_1 B))) (and (tptp.r2_hidden C _let_1) (tptp.r2_hidden _let_1 D))))))))))))))))))))))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v5_ordinal1 A) (tptp.v1_ordinal2 A)) (=> (exists ((B $$unsorted)) (and (tptp.v3_ordinal1 B) (tptp.r1_ordinal2 B A))) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (= (= B (tptp.k12_ordinal2 A)) (tptp.r1_ordinal2 B A))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B) (tptp.v5_ordinal1 B) (tptp.v1_ordinal2 B)) (= (tptp.k13_ordinal2 A B) (tptp.k12_ordinal2 (tptp.k2_ordinal1 B A))))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v5_ordinal1 A) (tptp.v1_ordinal2 A)) (= (tptp.v2_ordinal2 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (forall ((C $$unsorted)) (=> (tptp.v3_ordinal1 C) (=> (and (tptp.r2_hidden B C) (tptp.r2_hidden C (tptp.k1_relat_1 A))) (tptp.r2_hidden (tptp.k1_funct_1 A B) (tptp.k1_funct_1 A C)))))))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v5_ordinal1 A) (tptp.v1_ordinal2 A)) (= (tptp.v3_ordinal2 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (forall ((C $$unsorted)) (=> (tptp.v3_ordinal1 C) (=> (and (tptp.r2_hidden B (tptp.k1_relat_1 A)) (tptp.v4_ordinal1 B) (= C (tptp.k1_funct_1 A B))) (or (= B tptp.k1_xboole_0) (tptp.r1_ordinal2 C (tptp.k2_ordinal1 A B))))))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (forall ((C $$unsorted)) (=> (tptp.v3_ordinal1 C) (= (= C (tptp.k14_ordinal2 A B)) (exists ((D $$unsorted)) (and (tptp.v1_relat_1 D) (tptp.v1_funct_1 D) (tptp.v5_ordinal1 D) (tptp.v1_ordinal2 D) (= C (tptp.k1_ordinal2 D)) (= (tptp.k1_relat_1 D) (tptp.k1_ordinal1 B)) (= (tptp.k1_funct_1 D tptp.k1_xboole_0) A) (forall ((E $$unsorted)) (let ((_let_1 (tptp.k1_ordinal1 E))) (=> (tptp.v3_ordinal1 E) (=> (tptp.r2_hidden _let_1 (tptp.k1_ordinal1 B)) (= (tptp.k1_funct_1 D _let_1) (tptp.k1_ordinal1 (tptp.k1_funct_1 D E))))))) (forall ((E $$unsorted)) (=> (tptp.v3_ordinal1 E) (=> (and (tptp.r2_hidden E (tptp.k1_ordinal1 B)) (tptp.v4_ordinal1 E)) (or (= E tptp.k1_xboole_0) (= (tptp.k1_funct_1 D E) (tptp.k8_ordinal2 (tptp.k2_ordinal1 D E)))))))))))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (forall ((C $$unsorted)) (=> (tptp.v3_ordinal1 C) (= (= C (tptp.k15_ordinal2 A B)) (exists ((D $$unsorted)) (and (tptp.v1_relat_1 D) (tptp.v1_funct_1 D) (tptp.v5_ordinal1 D) (tptp.v1_ordinal2 D) (= C (tptp.k1_ordinal2 D)) (= (tptp.k1_relat_1 D) (tptp.k1_ordinal1 A)) (= (tptp.k1_funct_1 D tptp.k1_xboole_0) tptp.k1_xboole_0) (forall ((E $$unsorted)) (let ((_let_1 (tptp.k1_ordinal1 E))) (=> (tptp.v3_ordinal1 E) (=> (tptp.r2_hidden _let_1 (tptp.k1_ordinal1 A)) (= (tptp.k1_funct_1 D _let_1) (tptp.k14_ordinal2 (tptp.k1_funct_1 D E) B)))))) (forall ((E $$unsorted)) (=> (tptp.v3_ordinal1 E) (=> (and (tptp.r2_hidden E (tptp.k1_ordinal1 A)) (tptp.v4_ordinal1 E)) (or (= E tptp.k1_xboole_0) (= (tptp.k1_funct_1 D E) (tptp.k3_tarski (tptp.k8_ordinal2 (tptp.k2_ordinal1 D E))))))))))))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (forall ((C $$unsorted)) (=> (tptp.v3_ordinal1 C) (= (= C (tptp.k16_ordinal2 A B)) (exists ((D $$unsorted)) (and (tptp.v1_relat_1 D) (tptp.v1_funct_1 D) (tptp.v5_ordinal1 D) (tptp.v1_ordinal2 D) (= C (tptp.k1_ordinal2 D)) (= (tptp.k1_relat_1 D) (tptp.k1_ordinal1 B)) (= (tptp.k1_funct_1 D tptp.k1_xboole_0) tptp.k4_ordinal2) (forall ((E $$unsorted)) (let ((_let_1 (tptp.k1_ordinal1 E))) (=> (tptp.v3_ordinal1 E) (=> (tptp.r2_hidden _let_1 (tptp.k1_ordinal1 B)) (= (tptp.k1_funct_1 D _let_1) (tptp.k15_ordinal2 A (tptp.k1_funct_1 D E))))))) (forall ((E $$unsorted)) (=> (tptp.v3_ordinal1 E) (=> (and (tptp.r2_hidden E (tptp.k1_ordinal1 B)) (tptp.v4_ordinal1 E)) (or (= E tptp.k1_xboole_0) (= (tptp.k1_funct_1 D E) (tptp.k12_ordinal2 (tptp.k2_ordinal1 D E)))))))))))))))) true true true true true true true true (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (= (tptp.k14_ordinal2 A tptp.k1_xboole_0) A))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (= (tptp.k14_ordinal2 A (tptp.k1_ordinal1 B)) (tptp.k1_ordinal1 (tptp.k14_ordinal2 A B))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (=> (tptp.v4_ordinal1 A) (or (= A tptp.k1_xboole_0) (forall ((C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (tptp.v5_ordinal1 C) (tptp.v1_ordinal2 C)) (=> (and (= (tptp.k1_relat_1 C) A) (forall ((D $$unsorted)) (=> (tptp.v3_ordinal1 D) (=> (tptp.r2_hidden D A) (= (tptp.k1_funct_1 C D) (tptp.k14_ordinal2 B D)))))) (= (tptp.k14_ordinal2 B A) (tptp.k8_ordinal2 C))))))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (= (tptp.k14_ordinal2 tptp.k1_xboole_0 A) A))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (= (tptp.k14_ordinal2 A tptp.k4_ordinal2) (tptp.k1_ordinal1 A)))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (forall ((C $$unsorted)) (=> (tptp.v3_ordinal1 C) (=> (tptp.r2_hidden A B) (tptp.r2_hidden (tptp.k14_ordinal2 C A) (tptp.k14_ordinal2 C B))))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (forall ((C $$unsorted)) (=> (tptp.v3_ordinal1 C) (=> (tptp.r1_ordinal1 A B) (tptp.r1_ordinal1 (tptp.k14_ordinal2 C A) (tptp.k14_ordinal2 C B))))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (forall ((C $$unsorted)) (=> (tptp.v3_ordinal1 C) (=> (tptp.r1_ordinal1 A B) (tptp.r1_ordinal1 (tptp.k14_ordinal2 A C) (tptp.k14_ordinal2 B C))))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (= (tptp.k15_ordinal2 tptp.k1_xboole_0 A) tptp.k1_xboole_0))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (= (tptp.k15_ordinal2 (tptp.k1_ordinal1 A) B) (tptp.k14_ordinal2 (tptp.k15_ordinal2 A B) B)))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (=> (tptp.v4_ordinal1 A) (or (= A tptp.k1_xboole_0) (forall ((C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (tptp.v5_ordinal1 C) (tptp.v1_ordinal2 C)) (=> (and (= (tptp.k1_relat_1 C) A) (forall ((D $$unsorted)) (=> (tptp.v3_ordinal1 D) (=> (tptp.r2_hidden D A) (= (tptp.k1_funct_1 C D) (tptp.k15_ordinal2 D B)))))) (= (tptp.k15_ordinal2 A B) (tptp.k3_tarski (tptp.k8_ordinal2 C)))))))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (= (tptp.k15_ordinal2 A tptp.k1_xboole_0) tptp.k1_xboole_0))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (and (= (tptp.k15_ordinal2 tptp.k4_ordinal2 A) A) (= (tptp.k15_ordinal2 A tptp.k4_ordinal2) A)))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (forall ((C $$unsorted)) (=> (tptp.v3_ordinal1 C) (=> (tptp.r2_hidden B C) (or (= A tptp.k1_xboole_0) (tptp.r2_hidden (tptp.k15_ordinal2 B A) (tptp.k15_ordinal2 C A)))))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (forall ((C $$unsorted)) (=> (tptp.v3_ordinal1 C) (=> (tptp.r1_ordinal1 A B) (tptp.r1_ordinal1 (tptp.k15_ordinal2 A C) (tptp.k15_ordinal2 B C))))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (forall ((C $$unsorted)) (=> (tptp.v3_ordinal1 C) (=> (tptp.r1_ordinal1 A B) (tptp.r1_ordinal1 (tptp.k15_ordinal2 C A) (tptp.k15_ordinal2 C B))))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (= (tptp.k16_ordinal2 A tptp.k1_xboole_0) tptp.k4_ordinal2))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (= (tptp.k16_ordinal2 A (tptp.k1_ordinal1 B)) (tptp.k15_ordinal2 A (tptp.k16_ordinal2 A B))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (=> (tptp.v4_ordinal1 A) (or (= A tptp.k1_xboole_0) (forall ((C $$unsorted)) (=> (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (tptp.v5_ordinal1 C) (tptp.v1_ordinal2 C)) (=> (and (= (tptp.k1_relat_1 C) A) (forall ((D $$unsorted)) (=> (tptp.v3_ordinal1 D) (=> (tptp.r2_hidden D A) (= (tptp.k1_funct_1 C D) (tptp.k16_ordinal2 B D)))))) (= (tptp.k16_ordinal2 B A) (tptp.k12_ordinal2 C))))))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (and (= (tptp.k16_ordinal2 A tptp.k4_ordinal2) A) (= (tptp.k16_ordinal2 tptp.k4_ordinal2 A) tptp.k4_ordinal2)))) (forall ((A $$unsorted)) (= (tptp.v4_ordinal2 A) (tptp.r2_hidden A tptp.k5_ordinal2))) true (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (exists ((B $$unsorted)) (and (tptp.v3_ordinal1 B) (exists ((C $$unsorted)) (and (tptp.v3_ordinal1 C) (tptp.v4_ordinal1 B) (tptp.v4_ordinal2 C) (= A (tptp.k14_ordinal2 B C)))))))) (=> (and (tptp.p1_s1_ordinal2 tptp.k1_xboole_0) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (=> (tptp.p1_s1_ordinal2 A) (tptp.p1_s1_ordinal2 (tptp.k1_ordinal1 A))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (=> (and (tptp.v4_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (=> (tptp.r2_hidden B A) (tptp.p1_s1_ordinal2 B))))) (or (= A tptp.k1_xboole_0) (tptp.p1_s1_ordinal2 A)))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (tptp.p1_s1_ordinal2 A)))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v5_ordinal1 A) (= (tptp.k1_relat_1 A) tptp.f1_s2_ordinal2) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (=> (tptp.r2_hidden B tptp.f1_s2_ordinal2) (= (tptp.k1_funct_1 A B) (tptp.f2_s2_ordinal2 B))))))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v5_ordinal1 A) (tptp.v1_ordinal2 A) (= (tptp.k1_relat_1 A) tptp.f1_s3_ordinal2) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (=> (tptp.r2_hidden B tptp.f1_s3_ordinal2) (= (tptp.k1_funct_1 A B) (tptp.f2_s3_ordinal2 B))))))) (=> (and (= (tptp.k1_relat_1 tptp.f5_s4_ordinal2) tptp.f1_s4_ordinal2) (=> _let_17 (= (tptp.k1_funct_1 tptp.f5_s4_ordinal2 tptp.k1_xboole_0) tptp.f2_s4_ordinal2)) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_ordinal1 A))) (=> (tptp.v3_ordinal1 A) (=> (tptp.r2_hidden _let_1 tptp.f1_s4_ordinal2) (= (tptp.k1_funct_1 tptp.f5_s4_ordinal2 _let_1) (tptp.f3_s4_ordinal2 A (tptp.k1_funct_1 tptp.f5_s4_ordinal2 A))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (=> (and (tptp.r2_hidden A tptp.f1_s4_ordinal2) (tptp.v4_ordinal1 A)) (or (= A tptp.k1_xboole_0) (= (tptp.k1_funct_1 tptp.f5_s4_ordinal2 A) (tptp.f4_s4_ordinal2 A (tptp.k2_ordinal1 tptp.f5_s4_ordinal2 A))))))) (= (tptp.k1_relat_1 tptp.f6_s4_ordinal2) tptp.f1_s4_ordinal2) (=> _let_17 (= (tptp.k1_funct_1 tptp.f6_s4_ordinal2 tptp.k1_xboole_0) tptp.f2_s4_ordinal2)) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_ordinal1 A))) (=> (tptp.v3_ordinal1 A) (=> (tptp.r2_hidden _let_1 tptp.f1_s4_ordinal2) (= (tptp.k1_funct_1 tptp.f6_s4_ordinal2 _let_1) (tptp.f3_s4_ordinal2 A (tptp.k1_funct_1 tptp.f6_s4_ordinal2 A))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (=> (and (tptp.r2_hidden A tptp.f1_s4_ordinal2) (tptp.v4_ordinal1 A)) (or (= A tptp.k1_xboole_0) (= (tptp.k1_funct_1 tptp.f6_s4_ordinal2 A) (tptp.f4_s4_ordinal2 A (tptp.k2_ordinal1 tptp.f6_s4_ordinal2 A)))))))) (= tptp.f5_s4_ordinal2 tptp.f6_s4_ordinal2)) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v5_ordinal1 A) (= (tptp.k1_relat_1 A) tptp.f1_s5_ordinal2) (=> (tptp.r2_hidden tptp.k1_xboole_0 tptp.f1_s5_ordinal2) (= (tptp.k1_funct_1 A tptp.k1_xboole_0) tptp.f2_s5_ordinal2)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k1_ordinal1 B))) (=> (tptp.v3_ordinal1 B) (=> (tptp.r2_hidden _let_1 tptp.f1_s5_ordinal2) (= (tptp.k1_funct_1 A _let_1) (tptp.f3_s5_ordinal2 B (tptp.k1_funct_1 A B))))))) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (=> (and (tptp.r2_hidden B tptp.f1_s5_ordinal2) (tptp.v4_ordinal1 B)) (or (= B tptp.k1_xboole_0) (= (tptp.k1_funct_1 A B) (tptp.f4_s5_ordinal2 B (tptp.k2_ordinal1 A B))))))))) (=> (and (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (= (= B (tptp.f2_s6_ordinal2 A)) (exists ((C $$unsorted)) (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (tptp.v5_ordinal1 C) (= B (tptp.k1_ordinal2 C)) (= (tptp.k1_relat_1 C) (tptp.k1_ordinal1 A)) (= (tptp.k1_funct_1 C tptp.k1_xboole_0) tptp.f4_s6_ordinal2) (forall ((D $$unsorted)) (let ((_let_1 (tptp.k1_ordinal1 D))) (=> (tptp.v3_ordinal1 D) (=> (tptp.r2_hidden _let_1 (tptp.k1_ordinal1 A)) (= (tptp.k1_funct_1 C _let_1) (tptp.f5_s6_ordinal2 D (tptp.k1_funct_1 C D))))))) (forall ((D $$unsorted)) (=> (tptp.v3_ordinal1 D) (=> (and (tptp.r2_hidden D (tptp.k1_ordinal1 A)) (tptp.v4_ordinal1 D)) (or (= D tptp.k1_xboole_0) (= (tptp.k1_funct_1 C D) (tptp.f6_s6_ordinal2 D (tptp.k2_ordinal1 C D))))))))))))) (= (tptp.k1_relat_1 tptp.f1_s6_ordinal2) tptp.f3_s6_ordinal2) (=> (tptp.r2_hidden tptp.k1_xboole_0 tptp.f3_s6_ordinal2) (= (tptp.k1_funct_1 tptp.f1_s6_ordinal2 tptp.k1_xboole_0) tptp.f4_s6_ordinal2)) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_ordinal1 A))) (=> (tptp.v3_ordinal1 A) (=> (tptp.r2_hidden _let_1 tptp.f3_s6_ordinal2) (= (tptp.k1_funct_1 tptp.f1_s6_ordinal2 _let_1) (tptp.f5_s6_ordinal2 A (tptp.k1_funct_1 tptp.f1_s6_ordinal2 A))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (=> (and (tptp.r2_hidden A tptp.f3_s6_ordinal2) (tptp.v4_ordinal1 A)) (or (= A tptp.k1_xboole_0) (= (tptp.k1_funct_1 tptp.f1_s6_ordinal2 A) (tptp.f6_s6_ordinal2 A (tptp.k2_ordinal1 tptp.f1_s6_ordinal2 A)))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (=> (tptp.r2_hidden A (tptp.k1_relat_1 tptp.f1_s6_ordinal2)) (= (tptp.k1_funct_1 tptp.f1_s6_ordinal2 A) (tptp.f2_s6_ordinal2 A)))))) (and (exists ((A $$unsorted) (B $$unsorted)) (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B) (tptp.v5_ordinal1 B) (= A (tptp.k1_ordinal2 B)) (= (tptp.k1_relat_1 B) (tptp.k1_ordinal1 tptp.f1_s7_ordinal2)) (= (tptp.k1_funct_1 B tptp.k1_xboole_0) tptp.f2_s7_ordinal2) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k1_ordinal1 C))) (=> (tptp.v3_ordinal1 C) (=> (tptp.r2_hidden _let_1 (tptp.k1_ordinal1 tptp.f1_s7_ordinal2)) (= (tptp.k1_funct_1 B _let_1) (tptp.f3_s7_ordinal2 C (tptp.k1_funct_1 B C))))))) (forall ((C $$unsorted)) (=> (tptp.v3_ordinal1 C) (=> (and (tptp.r2_hidden C (tptp.k1_ordinal1 tptp.f1_s7_ordinal2)) (tptp.v4_ordinal1 C)) (or (= C tptp.k1_xboole_0) (= (tptp.k1_funct_1 B C) (tptp.f4_s7_ordinal2 C (tptp.k2_ordinal1 B C))))))))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (exists ((C $$unsorted)) (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (tptp.v5_ordinal1 C) (= A (tptp.k1_ordinal2 C)) (= (tptp.k1_relat_1 C) (tptp.k1_ordinal1 tptp.f1_s7_ordinal2)) (= (tptp.k1_funct_1 C tptp.k1_xboole_0) tptp.f2_s7_ordinal2) (forall ((D $$unsorted)) (let ((_let_1 (tptp.k1_ordinal1 D))) (=> (tptp.v3_ordinal1 D) (=> (tptp.r2_hidden _let_1 (tptp.k1_ordinal1 tptp.f1_s7_ordinal2)) (= (tptp.k1_funct_1 C _let_1) (tptp.f3_s7_ordinal2 D (tptp.k1_funct_1 C D))))))) (forall ((D $$unsorted)) (=> (tptp.v3_ordinal1 D) (=> (and (tptp.r2_hidden D (tptp.k1_ordinal1 tptp.f1_s7_ordinal2)) (tptp.v4_ordinal1 D)) (or (= D tptp.k1_xboole_0) (= (tptp.k1_funct_1 C D) (tptp.f4_s7_ordinal2 D (tptp.k2_ordinal1 C D))))))))) (exists ((C $$unsorted)) (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (tptp.v5_ordinal1 C) (= B (tptp.k1_ordinal2 C)) (= (tptp.k1_relat_1 C) (tptp.k1_ordinal1 tptp.f1_s7_ordinal2)) (= (tptp.k1_funct_1 C tptp.k1_xboole_0) tptp.f2_s7_ordinal2) (forall ((D $$unsorted)) (let ((_let_1 (tptp.k1_ordinal1 D))) (=> (tptp.v3_ordinal1 D) (=> (tptp.r2_hidden _let_1 (tptp.k1_ordinal1 tptp.f1_s7_ordinal2)) (= (tptp.k1_funct_1 C _let_1) (tptp.f3_s7_ordinal2 D (tptp.k1_funct_1 C D))))))) (forall ((D $$unsorted)) (=> (tptp.v3_ordinal1 D) (=> (and (tptp.r2_hidden D (tptp.k1_ordinal1 tptp.f1_s7_ordinal2)) (tptp.v4_ordinal1 D)) (or (= D tptp.k1_xboole_0) (= (tptp.k1_funct_1 C D) (tptp.f4_s7_ordinal2 D (tptp.k2_ordinal1 C D))))))))) (not (= A B)))))) (=> (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (= (= B (tptp.f1_s8_ordinal2 A)) (exists ((C $$unsorted)) (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (tptp.v5_ordinal1 C) (= B (tptp.k1_ordinal2 C)) (= (tptp.k1_relat_1 C) (tptp.k1_ordinal1 A)) (= (tptp.k1_funct_1 C tptp.k1_xboole_0) tptp.f2_s8_ordinal2) (forall ((D $$unsorted)) (let ((_let_1 (tptp.k1_ordinal1 D))) (=> (tptp.v3_ordinal1 D) (=> (tptp.r2_hidden _let_1 (tptp.k1_ordinal1 A)) (= (tptp.k1_funct_1 C _let_1) (tptp.f3_s8_ordinal2 D (tptp.k1_funct_1 C D))))))) (forall ((D $$unsorted)) (=> (tptp.v3_ordinal1 D) (=> (and (tptp.r2_hidden D (tptp.k1_ordinal1 A)) (tptp.v4_ordinal1 D)) (or (= D tptp.k1_xboole_0) (= (tptp.k1_funct_1 C D) (tptp.f4_s8_ordinal2 D (tptp.k2_ordinal1 C D))))))))))))) (= (tptp.f1_s8_ordinal2 tptp.k1_xboole_0) tptp.f2_s8_ordinal2)) (=> (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (= (= B (tptp.f4_s9_ordinal2 A)) (exists ((C $$unsorted)) (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (tptp.v5_ordinal1 C) (= B (tptp.k1_ordinal2 C)) (= (tptp.k1_relat_1 C) (tptp.k1_ordinal1 A)) (= (tptp.k1_funct_1 C tptp.k1_xboole_0) tptp.f1_s9_ordinal2) (forall ((D $$unsorted)) (let ((_let_1 (tptp.k1_ordinal1 D))) (=> (tptp.v3_ordinal1 D) (=> (tptp.r2_hidden _let_1 (tptp.k1_ordinal1 A)) (= (tptp.k1_funct_1 C _let_1) (tptp.f2_s9_ordinal2 D (tptp.k1_funct_1 C D))))))) (forall ((D $$unsorted)) (=> (tptp.v3_ordinal1 D) (=> (and (tptp.r2_hidden D (tptp.k1_ordinal1 A)) (tptp.v4_ordinal1 D)) (or (= D tptp.k1_xboole_0) (= (tptp.k1_funct_1 C D) (tptp.f3_s9_ordinal2 D (tptp.k2_ordinal1 C D))))))))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (= (tptp.f4_s9_ordinal2 (tptp.k1_ordinal1 A)) (tptp.f2_s9_ordinal2 A (tptp.f4_s9_ordinal2 A)))))) (=> (and (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (= (= B (tptp.f3_s10_ordinal2 A)) (exists ((C $$unsorted)) (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (tptp.v5_ordinal1 C) (= B (tptp.k1_ordinal2 C)) (= (tptp.k1_relat_1 C) (tptp.k1_ordinal1 A)) (= (tptp.k1_funct_1 C tptp.k1_xboole_0) tptp.f4_s10_ordinal2) (forall ((D $$unsorted)) (let ((_let_1 (tptp.k1_ordinal1 D))) (=> (tptp.v3_ordinal1 D) (=> (tptp.r2_hidden _let_1 (tptp.k1_ordinal1 A)) (= (tptp.k1_funct_1 C _let_1) (tptp.f5_s10_ordinal2 D (tptp.k1_funct_1 C D))))))) (forall ((D $$unsorted)) (=> (tptp.v3_ordinal1 D) (=> (and (tptp.r2_hidden D (tptp.k1_ordinal1 A)) (tptp.v4_ordinal1 D)) (or (= D tptp.k1_xboole_0) (= (tptp.k1_funct_1 C D) (tptp.f6_s10_ordinal2 D (tptp.k2_ordinal1 C D))))))))))))) (not (= tptp.f2_s10_ordinal2 tptp.k1_xboole_0)) (tptp.v4_ordinal1 tptp.f2_s10_ordinal2) (= (tptp.k1_relat_1 tptp.f1_s10_ordinal2) tptp.f2_s10_ordinal2) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (=> (tptp.r2_hidden A tptp.f2_s10_ordinal2) (= (tptp.k1_funct_1 tptp.f1_s10_ordinal2 A) (tptp.f3_s10_ordinal2 A)))))) (= (tptp.f3_s10_ordinal2 tptp.f2_s10_ordinal2) (tptp.f6_s10_ordinal2 tptp.f2_s10_ordinal2 tptp.f1_s10_ordinal2))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v5_ordinal1 A) (tptp.v1_ordinal2 A) (= (tptp.k1_relat_1 A) tptp.f1_s11_ordinal2) (=> (tptp.r2_hidden tptp.k1_xboole_0 tptp.f1_s11_ordinal2) (= (tptp.k1_funct_1 A tptp.k1_xboole_0) tptp.f2_s11_ordinal2)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k1_ordinal1 B))) (=> (tptp.v3_ordinal1 B) (=> (tptp.r2_hidden _let_1 tptp.f1_s11_ordinal2) (= (tptp.k1_funct_1 A _let_1) (tptp.f3_s11_ordinal2 B (tptp.k1_funct_1 A B))))))) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (=> (and (tptp.r2_hidden B tptp.f1_s11_ordinal2) (tptp.v4_ordinal1 B)) (or (= B tptp.k1_xboole_0) (= (tptp.k1_funct_1 A B) (tptp.f4_s11_ordinal2 B (tptp.k2_ordinal1 A B))))))))) (=> (and (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (= (= B (tptp.f2_s12_ordinal2 A)) (exists ((C $$unsorted)) (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (tptp.v5_ordinal1 C) (tptp.v1_ordinal2 C) (= B (tptp.k1_ordinal2 C)) (= (tptp.k1_relat_1 C) (tptp.k1_ordinal1 A)) (= (tptp.k1_funct_1 C tptp.k1_xboole_0) tptp.f4_s12_ordinal2) (forall ((D $$unsorted)) (let ((_let_1 (tptp.k1_ordinal1 D))) (=> (tptp.v3_ordinal1 D) (=> (tptp.r2_hidden _let_1 (tptp.k1_ordinal1 A)) (= (tptp.k1_funct_1 C _let_1) (tptp.f5_s12_ordinal2 D (tptp.k1_funct_1 C D))))))) (forall ((D $$unsorted)) (=> (tptp.v3_ordinal1 D) (=> (and (tptp.r2_hidden D (tptp.k1_ordinal1 A)) (tptp.v4_ordinal1 D)) (or (= D tptp.k1_xboole_0) (= (tptp.k1_funct_1 C D) (tptp.f6_s12_ordinal2 D (tptp.k2_ordinal1 C D)))))))))))))) (= (tptp.k1_relat_1 tptp.f1_s12_ordinal2) tptp.f3_s12_ordinal2) (=> (tptp.r2_hidden tptp.k1_xboole_0 tptp.f3_s12_ordinal2) (= (tptp.k1_funct_1 tptp.f1_s12_ordinal2 tptp.k1_xboole_0) tptp.f4_s12_ordinal2)) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_ordinal1 A))) (=> (tptp.v3_ordinal1 A) (=> (tptp.r2_hidden _let_1 tptp.f3_s12_ordinal2) (= (tptp.k1_funct_1 tptp.f1_s12_ordinal2 _let_1) (tptp.f5_s12_ordinal2 A (tptp.k1_funct_1 tptp.f1_s12_ordinal2 A))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (=> (and (tptp.r2_hidden A tptp.f3_s12_ordinal2) (tptp.v4_ordinal1 A)) (or (= A tptp.k1_xboole_0) (= (tptp.k1_funct_1 tptp.f1_s12_ordinal2 A) (tptp.f6_s12_ordinal2 A (tptp.k2_ordinal1 tptp.f1_s12_ordinal2 A)))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (=> (tptp.r2_hidden A (tptp.k1_relat_1 tptp.f1_s12_ordinal2)) (= (tptp.k1_funct_1 tptp.f1_s12_ordinal2 A) (tptp.f2_s12_ordinal2 A)))))) (and (exists ((A $$unsorted)) (and (tptp.v3_ordinal1 A) (exists ((B $$unsorted)) (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B) (tptp.v5_ordinal1 B) (tptp.v1_ordinal2 B) (= A (tptp.k1_ordinal2 B)) (= (tptp.k1_relat_1 B) (tptp.k1_ordinal1 tptp.f1_s13_ordinal2)) (= (tptp.k1_funct_1 B tptp.k1_xboole_0) tptp.f2_s13_ordinal2) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k1_ordinal1 C))) (=> (tptp.v3_ordinal1 C) (=> (tptp.r2_hidden _let_1 (tptp.k1_ordinal1 tptp.f1_s13_ordinal2)) (= (tptp.k1_funct_1 B _let_1) (tptp.f3_s13_ordinal2 C (tptp.k1_funct_1 B C))))))) (forall ((C $$unsorted)) (=> (tptp.v3_ordinal1 C) (=> (and (tptp.r2_hidden C (tptp.k1_ordinal1 tptp.f1_s13_ordinal2)) (tptp.v4_ordinal1 C)) (or (= C tptp.k1_xboole_0) (= (tptp.k1_funct_1 B C) (tptp.f4_s13_ordinal2 C (tptp.k2_ordinal1 B C))))))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (not (and (exists ((C $$unsorted)) (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (tptp.v5_ordinal1 C) (tptp.v1_ordinal2 C) (= A (tptp.k1_ordinal2 C)) (= (tptp.k1_relat_1 C) (tptp.k1_ordinal1 tptp.f1_s13_ordinal2)) (= (tptp.k1_funct_1 C tptp.k1_xboole_0) tptp.f2_s13_ordinal2) (forall ((D $$unsorted)) (let ((_let_1 (tptp.k1_ordinal1 D))) (=> (tptp.v3_ordinal1 D) (=> (tptp.r2_hidden _let_1 (tptp.k1_ordinal1 tptp.f1_s13_ordinal2)) (= (tptp.k1_funct_1 C _let_1) (tptp.f3_s13_ordinal2 D (tptp.k1_funct_1 C D))))))) (forall ((D $$unsorted)) (=> (tptp.v3_ordinal1 D) (=> (and (tptp.r2_hidden D (tptp.k1_ordinal1 tptp.f1_s13_ordinal2)) (tptp.v4_ordinal1 D)) (or (= D tptp.k1_xboole_0) (= (tptp.k1_funct_1 C D) (tptp.f4_s13_ordinal2 D (tptp.k2_ordinal1 C D))))))))) (exists ((C $$unsorted)) (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (tptp.v5_ordinal1 C) (tptp.v1_ordinal2 C) (= B (tptp.k1_ordinal2 C)) (= (tptp.k1_relat_1 C) (tptp.k1_ordinal1 tptp.f1_s13_ordinal2)) (= (tptp.k1_funct_1 C tptp.k1_xboole_0) tptp.f2_s13_ordinal2) (forall ((D $$unsorted)) (let ((_let_1 (tptp.k1_ordinal1 D))) (=> (tptp.v3_ordinal1 D) (=> (tptp.r2_hidden _let_1 (tptp.k1_ordinal1 tptp.f1_s13_ordinal2)) (= (tptp.k1_funct_1 C _let_1) (tptp.f3_s13_ordinal2 D (tptp.k1_funct_1 C D))))))) (forall ((D $$unsorted)) (=> (tptp.v3_ordinal1 D) (=> (and (tptp.r2_hidden D (tptp.k1_ordinal1 tptp.f1_s13_ordinal2)) (tptp.v4_ordinal1 D)) (or (= D tptp.k1_xboole_0) (= (tptp.k1_funct_1 C D) (tptp.f4_s13_ordinal2 D (tptp.k2_ordinal1 C D))))))))) (not (= A B))))))))) (=> (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (= (= B (tptp.f1_s14_ordinal2 A)) (exists ((C $$unsorted)) (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (tptp.v5_ordinal1 C) (tptp.v1_ordinal2 C) (= B (tptp.k1_ordinal2 C)) (= (tptp.k1_relat_1 C) (tptp.k1_ordinal1 A)) (= (tptp.k1_funct_1 C tptp.k1_xboole_0) tptp.f2_s14_ordinal2) (forall ((D $$unsorted)) (let ((_let_1 (tptp.k1_ordinal1 D))) (=> (tptp.v3_ordinal1 D) (=> (tptp.r2_hidden _let_1 (tptp.k1_ordinal1 A)) (= (tptp.k1_funct_1 C _let_1) (tptp.f3_s14_ordinal2 D (tptp.k1_funct_1 C D))))))) (forall ((D $$unsorted)) (=> (tptp.v3_ordinal1 D) (=> (and (tptp.r2_hidden D (tptp.k1_ordinal1 A)) (tptp.v4_ordinal1 D)) (or (= D tptp.k1_xboole_0) (= (tptp.k1_funct_1 C D) (tptp.f4_s14_ordinal2 D (tptp.k2_ordinal1 C D)))))))))))))) (= (tptp.f1_s14_ordinal2 tptp.k1_xboole_0) tptp.f2_s14_ordinal2)) (=> (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (= (= B (tptp.f4_s15_ordinal2 A)) (exists ((C $$unsorted)) (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (tptp.v5_ordinal1 C) (tptp.v1_ordinal2 C) (= B (tptp.k1_ordinal2 C)) (= (tptp.k1_relat_1 C) (tptp.k1_ordinal1 A)) (= (tptp.k1_funct_1 C tptp.k1_xboole_0) tptp.f1_s15_ordinal2) (forall ((D $$unsorted)) (let ((_let_1 (tptp.k1_ordinal1 D))) (=> (tptp.v3_ordinal1 D) (=> (tptp.r2_hidden _let_1 (tptp.k1_ordinal1 A)) (= (tptp.k1_funct_1 C _let_1) (tptp.f2_s15_ordinal2 D (tptp.k1_funct_1 C D))))))) (forall ((D $$unsorted)) (=> (tptp.v3_ordinal1 D) (=> (and (tptp.r2_hidden D (tptp.k1_ordinal1 A)) (tptp.v4_ordinal1 D)) (or (= D tptp.k1_xboole_0) (= (tptp.k1_funct_1 C D) (tptp.f3_s15_ordinal2 D (tptp.k2_ordinal1 C D)))))))))))))) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (= (tptp.f4_s15_ordinal2 (tptp.k1_ordinal1 A)) (tptp.f2_s15_ordinal2 A (tptp.f4_s15_ordinal2 A)))))) (=> (and (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (forall ((B $$unsorted)) (=> (tptp.v3_ordinal1 B) (= (= B (tptp.f3_s16_ordinal2 A)) (exists ((C $$unsorted)) (and (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (tptp.v5_ordinal1 C) (tptp.v1_ordinal2 C) (= B (tptp.k1_ordinal2 C)) (= (tptp.k1_relat_1 C) (tptp.k1_ordinal1 A)) (= (tptp.k1_funct_1 C tptp.k1_xboole_0) tptp.f4_s16_ordinal2) (forall ((D $$unsorted)) (let ((_let_1 (tptp.k1_ordinal1 D))) (=> (tptp.v3_ordinal1 D) (=> (tptp.r2_hidden _let_1 (tptp.k1_ordinal1 A)) (= (tptp.k1_funct_1 C _let_1) (tptp.f5_s16_ordinal2 D (tptp.k1_funct_1 C D))))))) (forall ((D $$unsorted)) (=> (tptp.v3_ordinal1 D) (=> (and (tptp.r2_hidden D (tptp.k1_ordinal1 A)) (tptp.v4_ordinal1 D)) (or (= D tptp.k1_xboole_0) (= (tptp.k1_funct_1 C D) (tptp.f6_s16_ordinal2 D (tptp.k2_ordinal1 C D)))))))))))))) (not (= tptp.f2_s16_ordinal2 tptp.k1_xboole_0)) (tptp.v4_ordinal1 tptp.f2_s16_ordinal2) (= (tptp.k1_relat_1 tptp.f1_s16_ordinal2) tptp.f2_s16_ordinal2) (forall ((A $$unsorted)) (=> (tptp.v3_ordinal1 A) (=> (tptp.r2_hidden A tptp.f2_s16_ordinal2) (= (tptp.k1_funct_1 tptp.f1_s16_ordinal2 A) (tptp.f3_s16_ordinal2 A)))))) (= (tptp.f3_s16_ordinal2 tptp.f2_s16_ordinal2) (tptp.f6_s16_ordinal2 tptp.f2_s16_ordinal2 tptp.f1_s16_ordinal2))) true true true (and (tptp.v3_ordinal1 tptp.k4_ordinal2) (not (tptp.v1_xboole_0 tptp.k4_ordinal2))) true (forall ((A $$unsorted)) (tptp.v3_ordinal1 (tptp.k6_ordinal2 A))) (forall ((A $$unsorted)) (tptp.v3_ordinal1 (tptp.k7_ordinal2 A))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v5_ordinal1 A)) (tptp.v3_ordinal1 (tptp.k8_ordinal2 A)))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v5_ordinal1 A)) (tptp.v3_ordinal1 (tptp.k9_ordinal2 A)))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v5_ordinal1 A)) (tptp.v3_ordinal1 (tptp.k10_ordinal2 A)))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v5_ordinal1 A)) (tptp.v3_ordinal1 (tptp.k11_ordinal2 A)))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v5_ordinal1 A) (tptp.v1_ordinal2 A)) (tptp.v3_ordinal1 (tptp.k12_ordinal2 A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v3_ordinal1 A) (tptp.v1_relat_1 B) (tptp.v1_funct_1 B) (tptp.v5_ordinal1 B) (tptp.v1_ordinal2 B)) (tptp.v3_ordinal1 (tptp.k13_ordinal2 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v3_ordinal1 A) (tptp.v3_ordinal1 B)) (tptp.v3_ordinal1 (tptp.k14_ordinal2 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v3_ordinal1 A) (tptp.v3_ordinal1 B)) (tptp.v3_ordinal1 (tptp.k15_ordinal2 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v3_ordinal1 A) (tptp.v3_ordinal1 B)) (tptp.v3_ordinal1 (tptp.k16_ordinal2 A B)))) (forall ((A $$unsorted)) (=> (tptp.v4_finsub_1 A) (and (tptp.v1_finsub_1 A) (tptp.v3_finsub_1 A)))) (forall ((A $$unsorted)) (=> (and (tptp.v1_finsub_1 A) (tptp.v3_finsub_1 A)) (tptp.v4_finsub_1 A))) (exists ((A $$unsorted)) (and (not (tptp.v1_xboole_0 A)) (tptp.v1_finsub_1 A) (tptp.v2_finsub_1 A) (tptp.v3_finsub_1 A) (tptp.v4_finsub_1 A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (and (not (tptp.v1_xboole_0 _let_1)) (tptp.v1_finsub_1 _let_1) (tptp.v3_finsub_1 _let_1) (tptp.v4_finsub_1 _let_1)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k5_finsub_1 A))) (and (not (tptp.v1_xboole_0 _let_1)) (tptp.v1_finsub_1 _let_1) (tptp.v3_finsub_1 _let_1) (tptp.v4_finsub_1 _let_1)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k5_finsub_1 A)) (tptp.v1_finset_1 B))) (forall ((A $$unsorted)) (= (tptp.v1_finsub_1 A) (forall ((B $$unsorted) (C $$unsorted)) (=> (and (tptp.r2_hidden B A) (tptp.r2_hidden C A)) (tptp.r2_hidden (tptp.k2_xboole_0 B C) A))))) (forall ((A $$unsorted)) (= (tptp.v2_finsub_1 A) (forall ((B $$unsorted) (C $$unsorted)) (=> (and (tptp.r2_hidden B A) (tptp.r2_hidden C A)) (tptp.r2_hidden (tptp.k3_xboole_0 B C) A))))) (forall ((A $$unsorted)) (= (tptp.v3_finsub_1 A) (forall ((B $$unsorted) (C $$unsorted)) (=> (and (tptp.r2_hidden B A) (tptp.r2_hidden C A)) (tptp.r2_hidden (tptp.k4_xboole_0 B C) A))))) (forall ((A $$unsorted)) (= (tptp.v4_finsub_1 A) (and (tptp.v1_finsub_1 A) (tptp.v3_finsub_1 A)))) true true true true true true true true true (forall ((A $$unsorted)) (= (tptp.v4_finsub_1 A) (forall ((B $$unsorted) (C $$unsorted)) (=> (and (tptp.r2_hidden B A) (tptp.r2_hidden C A)) (and (tptp.r2_hidden (tptp.k2_xboole_0 B C) A) (tptp.r2_hidden (tptp.k4_xboole_0 B C) A)))))) true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 C)) (tptp.v4_finsub_1 C)) (=> (and (tptp.m1_subset_1 A C) (tptp.m1_subset_1 B C)) (tptp.m1_subset_1 (tptp.k3_xboole_0 A B) C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 C)) (tptp.v4_finsub_1 C)) (=> (and (tptp.m1_subset_1 A C) (tptp.m1_subset_1 B C)) (tptp.m1_subset_1 (tptp.k5_xboole_0 A B) C)))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (=> (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B A) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (and (tptp.r2_hidden (tptp.k5_xboole_0 B C) A) (tptp.r2_hidden (tptp.k4_xboole_0 B C) A)))))) (tptp.v4_finsub_1 A)))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (=> (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B A) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (and (tptp.r2_hidden (tptp.k5_xboole_0 B C) A) (tptp.r2_hidden (tptp.k3_xboole_0 B C) A)))))) (tptp.v4_finsub_1 A)))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (=> (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B A) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (and (tptp.r2_hidden (tptp.k5_xboole_0 B C) A) (tptp.r2_hidden (tptp.k2_xboole_0 B C) A)))))) (tptp.v4_finsub_1 A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v4_finsub_1 A)) (tptp.r2_hidden tptp.k1_xboole_0 A))) true (forall ((A $$unsorted)) (tptp.v4_finsub_1 (tptp.k1_zfmisc_1 A))) (forall ((A $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v4_finsub_1 A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k3_xboole_0 A B))) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.v4_finsub_1 B)) (and (not (tptp.v1_xboole_0 _let_1)) (tptp.v4_finsub_1 _let_1))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v4_finsub_1 B) (= (= B (tptp.k5_finsub_1 A)) (forall ((C $$unsorted)) (= (tptp.r2_hidden C B) (and (tptp.r1_tarski C A) (tptp.v1_finset_1 C))))))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r1_tarski A B) (tptp.r1_tarski (tptp.k5_finsub_1 A) (tptp.k5_finsub_1 B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k5_finsub_1 (tptp.k3_xboole_0 A B)) (tptp.k3_xboole_0 (tptp.k5_finsub_1 A) (tptp.k5_finsub_1 B)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski (tptp.k2_xboole_0 (tptp.k5_finsub_1 A) (tptp.k5_finsub_1 B)) (tptp.k5_finsub_1 (tptp.k2_xboole_0 A B)))) (forall ((A $$unsorted)) (tptp.r1_tarski (tptp.k5_finsub_1 A) (tptp.k1_zfmisc_1 A))) (forall ((A $$unsorted)) (=> (tptp.v1_finset_1 A) (= (tptp.k5_finsub_1 A) (tptp.k1_zfmisc_1 A)))) (= (tptp.k5_finsub_1 tptp.k1_xboole_0) _let_16) true (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k5_finsub_1 A)) (tptp.v1_finset_1 B))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k5_finsub_1 A)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (=> (tptp.v1_finset_1 A) (tptp.m1_subset_1 B (tptp.k5_finsub_1 A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v4_finsub_1 A) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A)) (tptp.m1_subset_1 (tptp.k1_finsub_1 A B C) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v4_finsub_1 A) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A)) (= (tptp.k1_finsub_1 A B C) (tptp.k1_finsub_1 A C B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v4_finsub_1 A) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A)) (= (tptp.k1_finsub_1 A B B) B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v4_finsub_1 A) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A)) (= (tptp.k1_finsub_1 A B C) (tptp.k2_xboole_0 B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v4_finsub_1 A) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A)) (tptp.m1_subset_1 (tptp.k2_finsub_1 A B C) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v4_finsub_1 A) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A)) (= (tptp.k2_finsub_1 A B C) (tptp.k4_xboole_0 B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v4_finsub_1 A) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A)) (tptp.m1_subset_1 (tptp.k3_finsub_1 A B C) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v4_finsub_1 A) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A)) (= (tptp.k3_finsub_1 A B C) (tptp.k3_finsub_1 A C B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v4_finsub_1 A) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A)) (= (tptp.k3_finsub_1 A B B) B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v4_finsub_1 A) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A)) (= (tptp.k3_finsub_1 A B C) (tptp.k3_xboole_0 B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v4_finsub_1 A) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A)) (tptp.m1_subset_1 (tptp.k4_finsub_1 A B C) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v4_finsub_1 A) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A)) (= (tptp.k4_finsub_1 A B C) (tptp.k4_finsub_1 A C B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v4_finsub_1 A) (tptp.m1_subset_1 B A) (tptp.m1_subset_1 C A)) (= (tptp.k4_finsub_1 A B C) (tptp.k5_xboole_0 B C)))) (forall ((A $$unsorted)) (tptp.v4_finsub_1 (tptp.k5_finsub_1 A))) (not (tptp.v1_xboole_0 tptp.k1_numbers)) (not (tptp.v1_xboole_0 tptp.k2_numbers)) (not (tptp.v1_xboole_0 tptp.k3_numbers)) (not (tptp.v1_xboole_0 tptp.k4_numbers)) (= tptp.k1_numbers (tptp.k4_xboole_0 (tptp.k2_xboole_0 tptp.k2_arytm_2 (tptp.k2_zfmisc_1 _let_15 tptp.k2_arytm_2)) _let_14)) (= tptp.k3_numbers (tptp.k4_xboole_0 (tptp.k2_xboole_0 tptp.k6_arytm_3 (tptp.k2_zfmisc_1 _let_15 tptp.k6_arytm_3)) _let_14)) (= tptp.k4_numbers (tptp.k4_xboole_0 (tptp.k2_xboole_0 tptp.k5_ordinal2 (tptp.k2_zfmisc_1 _let_15 tptp.k5_ordinal2)) _let_14)) (tptp.r2_xboole_0 tptp.k1_numbers tptp.k2_numbers) (tptp.r2_xboole_0 tptp.k3_numbers tptp.k1_numbers) (tptp.r2_xboole_0 tptp.k3_numbers tptp.k2_numbers) (tptp.r2_xboole_0 tptp.k4_numbers tptp.k3_numbers) (tptp.r2_xboole_0 tptp.k4_numbers tptp.k1_numbers) (tptp.r2_xboole_0 tptp.k4_numbers tptp.k2_numbers) (tptp.r2_xboole_0 tptp.k5_numbers tptp.k4_numbers) (tptp.r2_xboole_0 tptp.k5_numbers tptp.k3_numbers) (tptp.r2_xboole_0 tptp.k5_numbers tptp.k1_numbers) (tptp.r2_xboole_0 tptp.k5_numbers tptp.k2_numbers) (tptp.r1_tarski tptp.k1_numbers tptp.k2_numbers) (tptp.r1_tarski tptp.k3_numbers tptp.k1_numbers) (tptp.r1_tarski tptp.k3_numbers tptp.k2_numbers) (tptp.r1_tarski tptp.k4_numbers tptp.k3_numbers) (tptp.r1_tarski tptp.k4_numbers tptp.k1_numbers) (tptp.r1_tarski tptp.k4_numbers tptp.k2_numbers) (tptp.r1_tarski tptp.k5_numbers tptp.k4_numbers) (tptp.r1_tarski tptp.k5_numbers tptp.k3_numbers) (tptp.r1_tarski tptp.k5_numbers tptp.k1_numbers) (tptp.r1_tarski tptp.k5_numbers tptp.k2_numbers) (not (= tptp.k1_numbers tptp.k2_numbers)) (not (= tptp.k3_numbers tptp.k1_numbers)) (not (= tptp.k3_numbers tptp.k2_numbers)) (not (= tptp.k4_numbers tptp.k3_numbers)) (not (= tptp.k4_numbers tptp.k1_numbers)) (not (= tptp.k4_numbers tptp.k2_numbers)) (not (= tptp.k5_numbers tptp.k4_numbers)) (not (= tptp.k5_numbers tptp.k3_numbers)) (not (= tptp.k5_numbers tptp.k1_numbers)) (not (= tptp.k5_numbers tptp.k2_numbers)) true true true true (tptp.m1_subset_1 tptp.k5_numbers (tptp.k1_zfmisc_1 tptp.k1_numbers)) (= tptp.k5_numbers tptp.k5_ordinal2) (= tptp.k2_numbers (tptp.k2_xboole_0 (tptp.k4_xboole_0 (tptp.k1_funct_2 (tptp.k2_tarski tptp.np__0 tptp.k13_arytm_3) tptp.k1_numbers) tptp.a_0_0_numbers) tptp.k1_numbers)) (forall ((A $$unsorted)) (= (tptp.r2_hidden A tptp.a_0_0_numbers) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_funct_2 (tptp.k2_tarski tptp.np__0 tptp.k13_arytm_3) tptp.k1_numbers)) (= A B) (= (tptp.k1_funct_1 B tptp.k13_arytm_3) tptp.np__0))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 A) (tptp.v1_relat_1 (tptp.k1_realset1 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_realset1 A B))) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (and (tptp.v1_relat_1 _let_1) (tptp.v1_funct_1 _let_1))))) (exists ((A $$unsorted)) (and (not (tptp.v1_xboole_0 A)) (tptp.v1_realset1 A))) (exists ((A $$unsorted)) (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_realset1 A)))) (forall ((A $$unsorted)) (=> (not (tptp.v1_realset1 A)) (not (tptp.v1_xboole_0 A)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_tarski A))) (and (not (tptp.v1_xboole_0 _let_1)) (tptp.v1_finset_1 _let_1) (tptp.v1_realset1 _let_1)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_realset1 A)) (tptp.m4_realset1 B A)) (not (tptp.v1_xboole_0 (tptp.k4_xboole_0 A B))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_realset1 A)) (exists ((B $$unsorted)) (and (tptp.m4_realset1 B A) (not (tptp.v1_xboole_0 B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A)) (=> (tptp.r2_hidden B _let_1) (tptp.r2_hidden (tptp.k1_funct_1 C B) A))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (exists ((C $$unsorted)) (and (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (forall ((D $$unsorted)) (=> (tptp.r2_hidden D (tptp.k2_zfmisc_1 C C)) (tptp.r2_hidden (tptp.k1_funct_1 B D) C)))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (= (tptp.r1_realset1 A B C) (forall ((D $$unsorted)) (=> (tptp.r2_hidden D (tptp.k2_zfmisc_1 C C)) (tptp.r2_hidden (tptp.k1_funct_1 B D) C))))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (= (tptp.m1_realset1 C A B) (forall ((D $$unsorted)) (=> (tptp.r2_hidden D (tptp.k2_zfmisc_1 C C)) (tptp.r2_hidden (tptp.k1_funct_1 B D) C))))))))) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (= (tptp.k1_realset1 A B) (tptp.k7_relat_1 A (tptp.k2_zfmisc_1 B B)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 C C))) (let ((_let_2 (tptp.k1_realset1 B C))) (=> (tptp.m1_realset1 C A B) (and (tptp.v1_funct_1 _let_2) (tptp.v1_funct_2 _let_2 _let_1 C) (tptp.m2_relset_1 _let_2 _let_1 C))))))))) (forall ((A $$unsorted)) (= (tptp.v1_realset1 A) (not (and (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (not (= A (tptp.k1_tarski B)))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (= (not (tptp.v1_realset1 A)) (forall ((B $$unsorted)) (not (tptp.v1_xboole_0 (tptp.k4_xboole_0 A (tptp.k1_tarski B)))))))) (exists ((A $$unsorted)) (and (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B A) (not (tptp.v1_xboole_0 (tptp.k4_xboole_0 A (tptp.k1_tarski B)))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (not (and (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B A) (not (tptp.v1_xboole_0 (tptp.k4_xboole_0 A (tptp.k1_tarski B)))))) (tptp.v1_realset1 A))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (=> (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B A) (not (tptp.v1_xboole_0 (tptp.k4_xboole_0 A (tptp.k1_tarski B)))))) (not (tptp.v1_realset1 A))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_realset1 A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k1_tarski C))) (let ((_let_2 (tptp.k4_xboole_0 A _let_1))) (let ((_let_3 (tptp.k2_zfmisc_1 _let_2 _let_2))) (let ((_let_4 (tptp.k4_xboole_0 (tptp.k1_realset1 B A) _let_1))) (=> (tptp.m1_subset_1 C A) (= (tptp.r2_realset1 A B C) (and (tptp.m1_realset1 _let_2 A B) (tptp.v1_funct_1 _let_4) (tptp.v1_funct_2 _let_4 _let_3 _let_2) (tptp.m2_relset_1 _let_4 _let_3 _let_2)))))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (exists ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A) (forall ((D $$unsorted)) (=> (tptp.r2_hidden D (tptp.k2_zfmisc_1 B B)) (tptp.r2_hidden (tptp.k1_funct_1 C D) B)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A)) (= (tptp.m2_realset1 C A B) (forall ((D $$unsorted)) (=> (tptp.r2_hidden D (tptp.k2_zfmisc_1 B B)) (tptp.r2_hidden (tptp.k1_funct_1 C D) B))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 B B))) (let ((_let_2 (tptp.k1_realset1 C B))) (=> (tptp.m2_realset1 C A B) (and (tptp.v1_funct_1 _let_2) (tptp.v1_funct_2 _let_2 _let_1 B) (tptp.m2_relset_1 _let_2 _let_1 B)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m2_realset1 C A B) (= (tptp.k3_realset1 A B C) (tptp.k1_realset1 C B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B A) (exists ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A) (forall ((D $$unsorted)) (let ((_let_1 (tptp.k4_xboole_0 A (tptp.k1_tarski B)))) (=> (tptp.r2_hidden D (tptp.k2_zfmisc_1 _let_1 _let_1)) (tptp.r2_hidden (tptp.k1_funct_1 C D) _let_1))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B A) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A)) (= (tptp.m3_realset1 C A B) (forall ((D $$unsorted)) (let ((_let_1 (tptp.k4_xboole_0 A (tptp.k1_tarski B)))) (=> (tptp.r2_hidden D (tptp.k2_zfmisc_1 _let_1 _let_1)) (tptp.r2_hidden (tptp.k1_funct_1 C D) _let_1)))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_realset1 A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B A) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k4_xboole_0 A (tptp.k1_tarski B)))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.k1_realset1 C _let_1))) (=> (tptp.m3_realset1 C A B) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.m2_relset_1 _let_3 _let_2 _let_1))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_realset1 A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B A) (forall ((C $$unsorted)) (=> (tptp.m3_realset1 C A B) (= (tptp.k4_realset1 A B C) (tptp.k1_realset1 C (tptp.k4_xboole_0 A (tptp.k1_tarski B)))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_realset1 A)) (forall ((B $$unsorted)) (= (tptp.m4_realset1 B A) (exists ((C $$unsorted)) (and (tptp.m1_subset_1 C A) (= B (tptp.k1_tarski C)))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_realset1 A)) (forall ((B $$unsorted)) (=> (tptp.m4_realset1 B A) (not (tptp.v1_xboole_0 (tptp.k4_xboole_0 A B))))))) (forall ((A $$unsorted)) (=> (tptp.v1_finset_1 A) (= (tptp.v1_realset1 A) (not (tptp.r1_xreal_0 tptp.np__2 (tptp.k4_card_1 A)))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.v1_realset1 A))) (and (not (and (not _let_1) (forall ((B $$unsorted) (C $$unsorted)) (not (and (tptp.r2_hidden B A) (tptp.r2_hidden C A) (not (= B C))))))) (not (and (exists ((B $$unsorted) (C $$unsorted)) (and (tptp.r2_hidden B A) (tptp.r2_hidden C A) (not (= B C)))) _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.v1_realset1 B))) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (and (not (and (not _let_1) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C A) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (not (and (tptp.r2_hidden C B) (tptp.r2_hidden D B) (not (= C D)))))))))) (not (and (exists ((C $$unsorted)) (and (tptp.m1_subset_1 C A) (exists ((D $$unsorted)) (and (tptp.m1_subset_1 D A) (tptp.r2_hidden C B) (tptp.r2_hidden D B) (not (= C D)))))) _let_1)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m1_relset_1 B _let_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_realset1 C A B) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m1_relset_1 B _let_1 A)) (exists ((C $$unsorted)) (tptp.m1_realset1 C A B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (tptp.m2_realset1 C A B) (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (exists ((C $$unsorted)) (tptp.m2_realset1 C A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B A) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (tptp.m3_realset1 C A B) (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B A) (exists ((C $$unsorted)) (tptp.m3_realset1 C A B)))) true (forall ((A $$unsorted)) (=> (not (tptp.v1_realset1 A)) (exists ((B $$unsorted)) (tptp.m4_realset1 B A)))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 C C))) (let ((_let_2 (tptp.k2_realset1 A B C))) (let ((_let_3 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_3 A) (tptp.m1_relset_1 B _let_3 A) (tptp.m1_realset1 C A B)) (and (tptp.v1_funct_1 _let_2) (tptp.v1_funct_2 _let_2 _let_1 C) (tptp.m2_relset_1 _let_2 _let_1 C))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m1_relset_1 B _let_1 A) (tptp.m1_realset1 C A B)) (= (tptp.k2_realset1 A B C) (tptp.k1_realset1 B C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 B B))) (let ((_let_2 (tptp.k3_realset1 A B C))) (=> (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (tptp.m2_realset1 C A B)) (and (tptp.v1_funct_1 _let_2) (tptp.v1_funct_2 _let_2 _let_1 B) (tptp.m2_relset_1 _let_2 _let_1 B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k4_xboole_0 A (tptp.k1_tarski B)))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.k4_realset1 A B C))) (=> (and (not (tptp.v1_realset1 A)) (tptp.m1_subset_1 B A) (tptp.m3_realset1 C A B)) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.m2_relset_1 _let_3 _let_2 _let_1))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_realset1 A)) (tptp.m1_subset_1 B A)) (tptp.m4_realset1 (tptp.k5_realset1 A B) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_realset1 A)) (tptp.m1_subset_1 B A)) (= (tptp.k5_realset1 A B) (tptp.k1_tarski B)))) (exists ((A $$unsorted)) (and (tptp.l1_struct_0 A) (tptp.v1_struct_0 A))) (exists ((A $$unsorted)) (and (tptp.l2_struct_0 A) (tptp.v2_struct_0 A))) (exists ((A $$unsorted)) (and (tptp.l1_struct_0 A) (not (tptp.v3_struct_0 A)))) (exists ((A $$unsorted)) (and (tptp.l2_struct_0 A) (not (tptp.v3_struct_0 A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A)) (not (tptp.v1_xboole_0 (tptp.u1_struct_0 A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (not (tptp.v1_xboole_0 B)))))) (forall ((A $$unsorted)) (=> (tptp.l1_struct_0 A) (= (tptp.v3_struct_0 A) (tptp.v1_xboole_0 (tptp.u1_struct_0 A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (forall ((C $$unsorted)) (=> (tptp.m1_struct_0 C A B) (tptp.m1_subset_1 C (tptp.u1_struct_0 A)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (exists ((C $$unsorted)) (tptp.m1_struct_0 C A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (forall ((C $$unsorted)) (= (tptp.m1_struct_0 C A B) (tptp.m1_subset_1 C B))))) true (exists ((A $$unsorted)) (tptp.l1_struct_0 A)) (forall ((A $$unsorted)) (=> (tptp.l2_struct_0 A) (tptp.l1_struct_0 A))) (exists ((A $$unsorted)) (tptp.l2_struct_0 A)) (forall ((A $$unsorted)) (=> (tptp.l1_struct_0 A) (=> (tptp.v1_struct_0 A) (= A (tptp.g1_struct_0 (tptp.u1_struct_0 A)))))) (forall ((A $$unsorted)) (=> (tptp.l2_struct_0 A) (=> (tptp.v2_struct_0 A) (= A (tptp.g2_struct_0 (tptp.u1_struct_0 A) (tptp.u2_struct_0 A)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A) (tptp.m1_subset_1 B _let_1)) (tptp.m1_subset_1 (tptp.k1_struct_0 A B) (tptp.k1_zfmisc_1 _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A) (tptp.m1_subset_1 B (tptp.u1_struct_0 A))) (= (tptp.k1_struct_0 A B) (tptp.k1_tarski B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (tptp.m1_subset_1 (tptp.k2_struct_0 A B C) (tptp.k1_zfmisc_1 _let_1))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k2_struct_0 A B C) (tptp.k2_struct_0 A C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k2_struct_0 A B C) (tptp.k2_tarski B C))))) true (forall ((A $$unsorted)) (=> (tptp.l2_struct_0 A) (tptp.m1_subset_1 (tptp.u2_struct_0 A) (tptp.u1_struct_0 A)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.g1_struct_0 A))) (and (tptp.v1_struct_0 _let_1) (tptp.l1_struct_0 _let_1)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (= (tptp.g1_struct_0 A) (tptp.g1_struct_0 B)) (= A B))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.g2_struct_0 A B))) (=> (tptp.m1_subset_1 B A) (and (tptp.v2_struct_0 _let_1) (tptp.l2_struct_0 _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B A) (forall ((C $$unsorted) (D $$unsorted)) (=> (= (tptp.g2_struct_0 A B) (tptp.g2_struct_0 C D)) (and (= A C) (= B D)))))) (exists ((A $$unsorted)) (and (tptp.l1_lattices A) (tptp.v1_lattices A))) (exists ((A $$unsorted)) (and (tptp.l2_lattices A) (tptp.v2_lattices A))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (tptp.v3_lattices A))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.g2_lattices A B))) (let ((_let_2 (tptp.k2_zfmisc_1 A A))) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 A) (tptp.m1_relset_1 B _let_2 A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v2_lattices _let_1)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.g1_lattices A B))) (let ((_let_2 (tptp.k2_zfmisc_1 A A))) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 A) (tptp.m1_relset_1 B _let_2 A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v1_lattices _let_1)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.g3_lattices A B C))) (let ((_let_2 (tptp.k2_zfmisc_1 A A))) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 A) (tptp.m1_relset_1 B _let_2 A) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_2 A) (tptp.m1_relset_1 C _let_2 A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1)))))) (exists ((A $$unsorted)) (and (tptp.l2_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v2_lattices A))) (exists ((A $$unsorted)) (and (tptp.l1_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v1_lattices A))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v10_lattices A)) (and _let_1 (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A)))))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A)) (and _let_1 (tptp.v10_lattices A)))))) (exists ((A $$unsorted)) (and (tptp.l2_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v2_lattices A) (tptp.v4_lattices A) (tptp.v5_lattices A))) (exists ((A $$unsorted)) (and (tptp.l1_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v1_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A) (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.v10_lattices A))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A) (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.v10_lattices A) (tptp.v11_lattices A) (tptp.v12_lattices A) (tptp.v13_lattices A) (tptp.v14_lattices A))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v13_lattices A) (tptp.v14_lattices A)) (and _let_1 (tptp.v15_lattices A)))))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v15_lattices A)) (and _let_1 (tptp.v13_lattices A) (tptp.v14_lattices A)))))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A) (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.v10_lattices A) (tptp.v13_lattices A) (tptp.v14_lattices A) (tptp.v15_lattices A))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A) (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.v10_lattices A) (tptp.v13_lattices A) (tptp.v14_lattices A) (tptp.v15_lattices A) (tptp.v16_lattices A))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v17_lattices A)) (and _let_1 (tptp.v11_lattices A) (tptp.v13_lattices A) (tptp.v14_lattices A) (tptp.v15_lattices A) (tptp.v16_lattices A)))))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v11_lattices A) (tptp.v15_lattices A) (tptp.v16_lattices A)) (and _let_1 (tptp.v17_lattices A)))))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A) (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.v10_lattices A) (tptp.v11_lattices A) (tptp.v13_lattices A) (tptp.v14_lattices A) (tptp.v15_lattices A) (tptp.v16_lattices A) (tptp.v17_lattices A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.v10_lattices A))) (let ((_let_2 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_2 _let_1 (tptp.v11_lattices A)) (and _let_2 (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) _let_1 (tptp.v12_lattices A))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l2_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 C _let_1) (= (tptp.k1_lattices A B C) (tptp.k2_binop_1 _let_1 _let_1 _let_1 (tptp.u2_lattices A) B C))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 C _let_1) (= (tptp.k2_lattices A B C) (tptp.k2_binop_1 _let_1 _let_1 _let_1 (tptp.u1_lattices A) B C))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l2_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (= (tptp.r1_lattices A B C) (= (tptp.k1_lattices A B C) C)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l2_lattices A)) (= (tptp.v4_lattices A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (= (tptp.k1_lattices A B C) (tptp.k1_lattices A C B))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l2_lattices A)) (= (tptp.v5_lattices A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (= (tptp.k1_lattices A B (tptp.k1_lattices A C D)) (tptp.k1_lattices A (tptp.k1_lattices A B C) D))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_lattices A)) (= (tptp.v6_lattices A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (= (tptp.k2_lattices A B C) (tptp.k2_lattices A C B))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_lattices A)) (= (tptp.v7_lattices A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (= (tptp.k2_lattices A B (tptp.k2_lattices A C D)) (tptp.k2_lattices A (tptp.k2_lattices A B C) D))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l3_lattices A)) (= (tptp.v8_lattices A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (= (tptp.k1_lattices A (tptp.k2_lattices A B C) C) C)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l3_lattices A)) (= (tptp.v9_lattices A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (= (tptp.k2_lattices A B (tptp.k1_lattices A B C)) B)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l3_lattices A)) (= (tptp.v10_lattices A) (and (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v8_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v9_lattices A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l3_lattices A)) (= (tptp.v11_lattices A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (= (tptp.k2_lattices A B (tptp.k1_lattices A C D)) (tptp.k1_lattices A (tptp.k2_lattices A B C) (tptp.k2_lattices A B D)))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l3_lattices A)) (= (tptp.v12_lattices A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (=> (tptp.r1_lattices A B D) (= (tptp.k1_lattices A B (tptp.k2_lattices A C D)) (tptp.k2_lattices A (tptp.k1_lattices A B C) D)))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_lattices A)) (= (tptp.v13_lattices A) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (and (= (tptp.k2_lattices A B C) B) (= (tptp.k2_lattices A C B) B))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l2_lattices A)) (= (tptp.v14_lattices A) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (and (= (tptp.k1_lattices A B C) B) (= (tptp.k1_lattices A C B) B))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l3_lattices A)) (= (tptp.v15_lattices A) (and (tptp.v13_lattices A) (tptp.v14_lattices A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_lattices A)) (=> (tptp.v13_lattices A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (= (= B (tptp.k5_lattices A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (and (= (tptp.k2_lattices A B C) B) (= (tptp.k2_lattices A C B) B)))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l2_lattices A)) (=> (tptp.v14_lattices A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (= (= B (tptp.k6_lattices A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (and (= (tptp.k1_lattices A B C) B) (= (tptp.k1_lattices A C B) B)))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k5_lattices A))) (let ((_let_2 (tptp.k6_lattices A))) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (= (tptp.r2_lattices A B C) (and (= (tptp.k1_lattices A B C) _let_2) (= (tptp.k1_lattices A C B) _let_2) (= (tptp.k2_lattices A B C) _let_1) (= (tptp.k2_lattices A C B) _let_1))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l3_lattices A)) (= (tptp.v16_lattices A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (exists ((C $$unsorted)) (and (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (tptp.r2_lattices A C B)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l3_lattices A)) (= (tptp.v17_lattices A) (and (tptp.v15_lattices A) (tptp.v16_lattices A) (tptp.v11_lattices A))))) true true true true true true true true true true true true true true true true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v6_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (= (tptp.k1_lattices A B B) B))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v6_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (= (tptp.k4_lattices A B B) B))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (= (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (= (tptp.k4_lattices A B (tptp.k3_lattices A C D)) (tptp.k3_lattices A (tptp.k4_lattices A B C) (tptp.k4_lattices A B D))))))))) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (= (tptp.k3_lattices A B (tptp.k4_lattices A C D)) (tptp.k4_lattices A (tptp.k3_lattices A B C) (tptp.k3_lattices A B D)))))))))))) true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (= (tptp.r1_lattices A B C) (= (tptp.k2_lattices A B C) B)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (tptp.r1_lattices A B (tptp.k1_lattices A B C)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v6_lattices A) (tptp.v8_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (tptp.r1_lattices A (tptp.k4_lattices A B C) B))))))) true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v5_lattices A) (tptp.l2_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (=> (and (tptp.r1_lattices A B C) (tptp.r1_lattices A C D)) (tptp.r1_lattices A B D)))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v4_lattices A) (tptp.l2_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (=> (and (tptp.r1_lattices A B C) (tptp.r1_lattices A C B)) (= B C)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (=> (tptp.r1_lattices A B C) (tptp.r1_lattices A (tptp.k2_lattices A B D) (tptp.k2_lattices A C D))))))))))) true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (=> (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (= (tptp.k3_lattices A (tptp.k3_lattices A (tptp.k4_lattices A B C) (tptp.k4_lattices A C D)) (tptp.k4_lattices A D B)) (tptp.k4_lattices A (tptp.k4_lattices A (tptp.k3_lattices A B C) (tptp.k3_lattices A C D)) (tptp.k3_lattices A D B))))))))) (tptp.v11_lattices A)))) true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v11_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (= (tptp.k3_lattices A B (tptp.k4_lattices A C D)) (tptp.k4_lattices A (tptp.k3_lattices A B C) (tptp.k3_lattices A B D))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v11_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (=> (and (= (tptp.k4_lattices A B C) (tptp.k4_lattices A B D)) (= (tptp.k3_lattices A B C) (tptp.k3_lattices A B D))) (= C D)))))))))) true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v11_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (= (tptp.k4_lattices A (tptp.k4_lattices A (tptp.k3_lattices A B C) (tptp.k3_lattices A C D)) (tptp.k3_lattices A D B)) (tptp.k3_lattices A (tptp.k3_lattices A (tptp.k4_lattices A B C) (tptp.k4_lattices A C D)) (tptp.k4_lattices A D B))))))))))) true true true true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v13_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (= (tptp.k3_lattices A (tptp.k5_lattices A) B) B))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v13_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k5_lattices A))) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (= (tptp.k4_lattices A _let_1 B) _let_1)))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v13_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (tptp.r3_lattices A (tptp.k5_lattices A) B))))) true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v14_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (= (tptp.k4_lattices A (tptp.k6_lattices A) B) B))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v14_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k6_lattices A))) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (= (tptp.k3_lattices A _let_1 B) _let_1)))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v14_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (tptp.r3_lattices A B (tptp.k6_lattices A)))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v11_lattices A) (tptp.v16_lattices A) (tptp.l3_lattices A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (= (= C (tptp.k7_lattices A B)) (tptp.r2_lattices A C B))))))))) true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (= (tptp.k4_lattices A (tptp.k7_lattices A B) B) (tptp.k5_lattices A)))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (= (tptp.k3_lattices A (tptp.k7_lattices A B) B) (tptp.k6_lattices A)))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (= (tptp.k7_lattices A (tptp.k7_lattices A B)) B))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (= (tptp.k7_lattices A (tptp.k4_lattices A B C)) (tptp.k3_lattices A (tptp.k7_lattices A B) (tptp.k7_lattices A C))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (= (tptp.k7_lattices A (tptp.k3_lattices A B C)) (tptp.k4_lattices A (tptp.k7_lattices A B) (tptp.k7_lattices A C))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (= (= (tptp.k4_lattices A B C) (tptp.k5_lattices A)) (tptp.r3_lattices A B (tptp.k7_lattices A C))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (=> (tptp.r3_lattices A B C) (tptp.r3_lattices A (tptp.k7_lattices A C) (tptp.k7_lattices A B))))))))) (forall ((A $$unsorted)) (=> (tptp.l1_lattices A) (tptp.l1_struct_0 A))) (exists ((A $$unsorted)) (tptp.l1_lattices A)) (forall ((A $$unsorted)) (=> (tptp.l2_lattices A) (tptp.l1_struct_0 A))) (exists ((A $$unsorted)) (tptp.l2_lattices A)) (forall ((A $$unsorted)) (=> (tptp.l3_lattices A) (and (tptp.l1_lattices A) (tptp.l2_lattices A)))) (exists ((A $$unsorted)) (tptp.l3_lattices A)) (forall ((A $$unsorted)) (=> (tptp.l1_lattices A) (=> (tptp.v1_lattices A) (= A (tptp.g1_lattices (tptp.u1_struct_0 A) (tptp.u1_lattices A)))))) (forall ((A $$unsorted)) (=> (tptp.l2_lattices A) (=> (tptp.v2_lattices A) (= A (tptp.g2_lattices (tptp.u1_struct_0 A) (tptp.u2_lattices A)))))) (forall ((A $$unsorted)) (=> (tptp.l3_lattices A) (=> (tptp.v3_lattices A) (= A (tptp.g3_lattices (tptp.u1_struct_0 A) (tptp.u2_lattices A) (tptp.u1_lattices A)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v6_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.l3_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (tptp.r3_lattices A B B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v6_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.l3_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.r3_lattices A B C) (tptp.r1_lattices A B C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l2_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (tptp.m1_subset_1 (tptp.k1_lattices A B C) _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (tptp.m1_subset_1 (tptp.k2_lattices A B C) _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v4_lattices A) (tptp.l2_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (tptp.m1_subset_1 (tptp.k3_lattices A B C) _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v4_lattices A) (tptp.l2_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k3_lattices A B C) (tptp.k3_lattices A C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v4_lattices A) (tptp.l2_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k3_lattices A B C) (tptp.k1_lattices A B C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v6_lattices A) (tptp.l1_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (tptp.m1_subset_1 (tptp.k4_lattices A B C) _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v6_lattices A) (tptp.l1_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k4_lattices A B C) (tptp.k4_lattices A C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v6_lattices A) (tptp.l1_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k4_lattices A B C) (tptp.k2_lattices A B C))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_lattices A)) (tptp.m1_subset_1 (tptp.k5_lattices A) (tptp.u1_struct_0 A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l2_lattices A)) (tptp.m1_subset_1 (tptp.k6_lattices A) (tptp.u1_struct_0 A)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l3_lattices A) (tptp.m1_subset_1 B _let_1)) (tptp.m1_subset_1 (tptp.k7_lattices A B) _let_1)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u1_lattices A))) (=> (tptp.l1_lattices A) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.m2_relset_1 _let_3 _let_2 _let_1))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u2_lattices A))) (=> (tptp.l2_lattices A) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.m2_relset_1 _let_3 _let_2 _let_1))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.g1_lattices A B))) (let ((_let_2 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 A) (tptp.m1_relset_1 B _let_2 A)) (and (tptp.v1_lattices _let_1) (tptp.l1_lattices _let_1)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m1_relset_1 B _let_1 A)) (forall ((C $$unsorted) (D $$unsorted)) (=> (= (tptp.g1_lattices A B) (tptp.g1_lattices C D)) (and (= A C) (= B D))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.g2_lattices A B))) (let ((_let_2 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 A) (tptp.m1_relset_1 B _let_2 A)) (and (tptp.v2_lattices _let_1) (tptp.l2_lattices _let_1)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m1_relset_1 B _let_1 A)) (forall ((C $$unsorted) (D $$unsorted)) (=> (= (tptp.g2_lattices A B) (tptp.g2_lattices C D)) (and (= A C) (= B D))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.g3_lattices A B C))) (let ((_let_2 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 A) (tptp.m1_relset_1 B _let_2 A) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_2 A) (tptp.m1_relset_1 C _let_2 A)) (and (tptp.v3_lattices _let_1) (tptp.l3_lattices _let_1)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m1_relset_1 B _let_1 A) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m1_relset_1 C _let_1 A)) (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (= (tptp.g3_lattices A B C) (tptp.g3_lattices D E F)) (and (= A D) (= B E) (= C F))))))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A) (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.v10_lattices A) (tptp.v3_filter_0 A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.v10_lattices A))) (let ((_let_2 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_2 _let_1 (tptp.v3_filter_0 A)) (and _let_2 (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) _let_1 (tptp.v11_lattices A) (tptp.v12_lattices A))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B _let_1) (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 C _let_1)) (not (tptp.v1_xboole_0 (tptp.k5_filter_0 A B C)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k8_filter_0 A B))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_filter_0 B A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1) (tptp.v4_lattices _let_1) (tptp.v5_lattices _let_1) (tptp.v6_lattices _let_1) (tptp.v7_lattices _let_1) (tptp.v8_lattices _let_1) (tptp.v9_lattices _let_1) (tptp.v10_lattices _let_1))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.k3_lattices A C D))) (let ((_let_2 (tptp.k3_lattices A D B))) (let ((_let_3 (tptp.k3_lattices A D C))) (let ((_let_4 (tptp.k3_lattices A B D))) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (=> (tptp.r3_lattices A B C) (and (tptp.r3_lattices A _let_2 _let_3) (tptp.r3_lattices A _let_4 _let_1) (tptp.r3_lattices A _let_4 _let_3) (tptp.r3_lattices A _let_2 _let_1))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (=> (tptp.r3_lattices A B C) (and (tptp.r3_lattices A (tptp.k4_lattices A B D) C) (tptp.r3_lattices A (tptp.k4_lattices A D B) C))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (=> (tptp.r3_lattices A B C) (and (tptp.r3_lattices A B (tptp.k3_lattices A D C)) (tptp.r3_lattices A B (tptp.k3_lattices A C D)))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.k3_lattices A B D))) (=> (tptp.m1_subset_1 E (tptp.u1_struct_0 A)) (=> (and (tptp.r3_lattices A B C) (tptp.r3_lattices A D E)) (and (tptp.r3_lattices A _let_1 (tptp.k3_lattices A C E)) (tptp.r3_lattices A _let_1 (tptp.k3_lattices A E C))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.k4_lattices A B D))) (=> (tptp.m1_subset_1 E (tptp.u1_struct_0 A)) (=> (and (tptp.r3_lattices A B C) (tptp.r3_lattices A D E)) (and (tptp.r3_lattices A _let_1 (tptp.k4_lattices A C E)) (tptp.r3_lattices A _let_1 (tptp.k4_lattices A E C))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (=> (and (tptp.r3_lattices A B C) (tptp.r3_lattices A D C)) (tptp.r3_lattices A (tptp.k3_lattices A B D) C)))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (=> (and (tptp.r3_lattices A B C) (tptp.r3_lattices A B D)) (tptp.r3_lattices A B (tptp.k4_lattices A C D))))))))))) _let_13 true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (= (tptp.m1_filter_0 B A) (and (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (=> (and (tptp.r2_hidden C B) (tptp.r2_hidden D B)) (tptp.r2_hidden (tptp.k4_lattices A C D) B)))))) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (=> (and (tptp.r2_hidden C B) (tptp.r3_lattices A C D)) (tptp.r2_hidden D B)))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_filter_0 D A) (=> (tptp.r2_hidden B D) (and (tptp.r2_hidden (tptp.k3_lattices A B C) D) (tptp.r2_hidden (tptp.k3_lattices A C B) D))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (exists ((C $$unsorted)) (and (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (tptp.r2_hidden C B))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v14_lattices A) (tptp.l3_lattices A)) (tptp.r2_hidden (tptp.k6_lattices A) B)))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.l3_lattices A))) (let ((_let_2 (tptp.v10_lattices A))) (let ((_let_3 (not (tptp.v3_struct_0 A)))) (=> (and _let_3 _let_2 _let_1) (=> (and _let_3 _let_2 (tptp.v14_lattices A) _let_1) (tptp.m1_filter_0 (tptp.k6_domain_1 (tptp.u1_struct_0 A) (tptp.k6_lattices A)) A))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 B _let_1) (=> (tptp.m1_filter_0 (tptp.k6_domain_1 _let_1 B) A) (tptp.v14_lattices A))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (tptp.m1_filter_0 (tptp.u1_struct_0 A) A))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (= (tptp.k1_filter_0 A) (tptp.u1_struct_0 A)))) true true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (= (tptp.r2_hidden B (tptp.k2_filter_0 A C)) (tptp.r3_lattices A C B)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_filter_0 A B))) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (and (tptp.r2_hidden B _let_1) (tptp.r2_hidden (tptp.k3_lattices A B C) _let_1) (tptp.r2_hidden (tptp.k3_lattices A C B) _let_1))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.l3_lattices A))) (let ((_let_2 (tptp.v10_lattices A))) (let ((_let_3 (not (tptp.v3_struct_0 A)))) (=> (and _let_3 _let_2 _let_1) (=> (and _let_3 _let_2 (tptp.v13_lattices A) _let_1) (= (tptp.k1_filter_0 A) (tptp.k2_filter_0 A (tptp.k5_lattices A))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (= (tptp.v1_filter_0 B A) (and (not (= B (tptp.u1_struct_0 A))) (forall ((C $$unsorted)) (=> (tptp.m1_filter_0 C A) (=> (tptp.r1_tarski B C) (or (= C (tptp.u1_struct_0 A)) (= B C))))))))))) true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (=> (tptp.v13_lattices A) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (not (and (not (= B (tptp.u1_struct_0 A))) (forall ((C $$unsorted)) (=> (tptp.m1_filter_0 C A) (not (and (tptp.r1_tarski B C) (tptp.v1_filter_0 C A)))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 B _let_1) (not (and (not (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (= (tptp.k4_lattices A B C) B)))) (= (tptp.k2_filter_0 A B) _let_1)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (not (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v13_lattices A) (tptp.l3_lattices A) (not (= B (tptp.k5_lattices A))) (forall ((C $$unsorted)) (=> (tptp.m1_filter_0 C A) (not (and (tptp.r2_hidden B C) (tptp.v1_filter_0 C A))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (forall ((C $$unsorted)) (=> (tptp.m1_filter_0 C A) (= (= C (tptp.k3_filter_0 A B)) (and (tptp.r1_tarski B C) (forall ((D $$unsorted)) (=> (tptp.m1_filter_0 D A) (=> (tptp.r1_tarski B D) (tptp.r1_tarski C D)))))))))))) true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (= (tptp.k3_filter_0 A B) B))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (forall ((C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (=> (tptp.r1_tarski B C) (tptp.r1_tarski (tptp.k3_filter_0 A B) (tptp.k3_filter_0 A C))))))))) true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (=> (tptp.r2_hidden B C) (tptp.r1_tarski (tptp.k2_filter_0 A B) (tptp.k3_filter_0 A C))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 _let_1))) (=> (= C (tptp.k6_domain_1 _let_1 B)) (= (tptp.k3_filter_0 A C) (tptp.k2_filter_0 A B)))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k3_filter_0 A B))) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 _let_1))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v13_lattices A) (tptp.l3_lattices A) (tptp.r2_hidden (tptp.k5_lattices A) B)) (and (= _let_2 (tptp.k1_filter_0 A)) (= _let_2 _let_1))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v13_lattices A) (tptp.l3_lattices A) (tptp.r2_hidden (tptp.k5_lattices A) B)) (and (= B (tptp.k1_filter_0 A)) (= B (tptp.u1_struct_0 A)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (= (tptp.v2_filter_0 B A) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (= (tptp.r2_hidden (tptp.k3_lattices A C D) B) (or (tptp.r2_hidden C B) (tptp.r2_hidden D B)))))))))))) true (forall ((A $$unsorted)) (let ((_let_1 (tptp.l3_lattices A))) (let ((_let_2 (tptp.v10_lattices A))) (let ((_let_3 (not (tptp.v3_struct_0 A)))) (=> (and _let_3 _let_2 _let_1) (=> (and _let_3 _let_2 (tptp.v17_lattices A) _let_1) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (and (tptp.r3_lattices A (tptp.k4_lattices A B (tptp.k3_lattices A (tptp.k7_lattices A B) C)) C) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (=> (tptp.r3_lattices A (tptp.k4_lattices A B D) C) (tptp.r3_lattices A D (tptp.k3_lattices A (tptp.k7_lattices A B) C)))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l3_lattices A)) (= (tptp.v3_filter_0 A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (exists ((D $$unsorted)) (and (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (tptp.r1_lattices A (tptp.k2_lattices A B D) C) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.u1_struct_0 A)) (=> (tptp.r1_lattices A (tptp.k2_lattices A B E) C) (tptp.r1_lattices A E D))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v3_filter_0 A) (tptp.l3_lattices A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (= (= D (tptp.k4_filter_0 A B C)) (and (tptp.r3_lattices A (tptp.k4_lattices A B D) C) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.u1_struct_0 A)) (=> (tptp.r3_lattices A (tptp.k4_lattices A B E) C) (tptp.r3_lattices A E D))))))))))))))) true true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v3_filter_0 A) (tptp.l3_lattices A)) (tptp.v14_lattices A))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v3_filter_0 A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (= (tptp.k4_filter_0 A B B) (tptp.k6_lattices A)))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v3_filter_0 A) (tptp.l3_lattices A)) (tptp.v11_lattices A))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (tptp.v3_filter_0 A))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v3_filter_0 A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_filter_0 D A) (=> (and (tptp.r2_hidden B D) (tptp.r2_hidden (tptp.k4_filter_0 A B C) D)) (tptp.r2_hidden C D)))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v3_filter_0 A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_filter_0 D A) (=> (tptp.r2_hidden B D) (tptp.r2_hidden (tptp.k4_filter_0 A C B) D)))))))))) true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (and (not (tptp.v1_xboole_0 D)) (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (forall ((E $$unsorted)) (let ((_let_1 (tptp.k5_filter_0 A D E))) (=> (and (not (tptp.v1_xboole_0 E)) (tptp.m1_subset_1 E (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (=> (and (tptp.r2_hidden B D) (tptp.r2_hidden C E)) (and (tptp.r2_hidden (tptp.k4_lattices A B C) _let_1) (tptp.r2_hidden (tptp.k4_lattices A C B) _let_1)))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (forall ((D $$unsorted)) (=> (and (not (tptp.v1_xboole_0 D)) (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (not (and (tptp.r2_hidden B (tptp.k5_filter_0 A C D)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.u1_struct_0 A)) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F (tptp.u1_struct_0 A)) (not (and (= B (tptp.k4_lattices A E F)) (tptp.r2_hidden E C) (tptp.r2_hidden F D))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (forall ((C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (= (tptp.k5_filter_0 A B C) (tptp.k5_filter_0 A C B)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k3_filter_0 A (tptp.k4_subset_1 _let_1 B C)))) (=> (and (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 _let_1))) (and (= _let_2 (tptp.k3_filter_0 A (tptp.k4_subset_1 _let_1 (tptp.k3_filter_0 A B) C))) (= _let_2 (tptp.k3_filter_0 A (tptp.k4_subset_1 _let_1 B (tptp.k3_filter_0 A C))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k5_filter_0 A B C))) (=> (tptp.m1_filter_0 C A) (and (tptp.r1_tarski B _let_1) (tptp.r1_tarski C _let_1))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (forall ((C $$unsorted)) (=> (tptp.m1_filter_0 C A) (= (tptp.k3_filter_0 A (tptp.k4_subset_1 (tptp.u1_struct_0 A) B C)) (tptp.k3_filter_0 A (tptp.k5_filter_0 A B C))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v3_filter_0 A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (forall ((C $$unsorted)) (=> (tptp.m1_filter_0 C A) (= (tptp.k3_filter_0 A (tptp.k4_subset_1 (tptp.u1_struct_0 A) B C)) (tptp.k6_filter_0 A B C)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (forall ((C $$unsorted)) (=> (tptp.m1_filter_0 C A) (= (tptp.k3_filter_0 A (tptp.k4_subset_1 (tptp.u1_struct_0 A) B C)) (tptp.k7_filter_0 A B C)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v3_filter_0 A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v1_xboole_0 D)) (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 _let_1))) (=> (tptp.r2_hidden B (tptp.k3_filter_0 A (tptp.k4_subset_1 _let_1 D (tptp.k6_domain_1 _let_1 C)))) (tptp.r2_hidden (tptp.k4_filter_0 A C B) (tptp.k3_filter_0 A D)))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v3_filter_0 A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (forall ((E $$unsorted)) (=> (tptp.m1_filter_0 E A) (=> (and (tptp.r2_hidden (tptp.k4_filter_0 A B C) E) (tptp.r2_hidden (tptp.k4_filter_0 A C D) E)) (tptp.r2_hidden (tptp.k4_filter_0 A B D) E)))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (= (tptp.k4_filter_0 A B C) (tptp.k3_lattices A (tptp.k7_lattices A B) C)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (= (tptp.r3_lattices A B C) (= (tptp.k4_lattices A B (tptp.k7_lattices A C)) (tptp.k5_lattices A))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (= (tptp.v1_filter_0 B A) (and (not (= B (tptp.u1_struct_0 A))) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (or (tptp.r2_hidden C B) (tptp.r2_hidden (tptp.k7_lattices A C) B)))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (= (and (not (= B (tptp.k1_filter_0 A))) (tptp.v2_filter_0 B A)) (tptp.v1_filter_0 B A)))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (=> (tptp.v1_filter_0 B A) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (= (tptp.r2_hidden C B) (not (tptp.r2_hidden (tptp.k7_lattices A C) B)))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (not (and (not (= B C)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.r2_hidden C D))) (let ((_let_2 (tptp.r2_hidden B D))) (=> (tptp.m1_filter_0 D A) (not (and (tptp.v1_filter_0 D A) (or (and _let_2 (not _let_1)) (and (not _let_2) _let_1)))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (forall ((C $$unsorted)) (=> (and (not (tptp.v3_struct_0 C)) (tptp.v10_lattices C) (tptp.l3_lattices C)) (= (= C (tptp.k8_filter_0 A B)) (exists ((D $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 B B))) (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D _let_1 B) (tptp.m2_relset_1 D _let_1 B) (exists ((E $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 B B))) (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E _let_1 B) (tptp.m2_relset_1 E _let_1 B) (= D (tptp.k1_realset1 (tptp.u2_lattices A) B)) (= E (tptp.k1_realset1 (tptp.u1_lattices A) B)) (= C (tptp.g3_lattices B D E))))))))))))))) true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A) (tptp.v10_lattices A) (tptp.l3_lattices A)) (= (tptp.k8_filter_0 A (tptp.k1_filter_0 A)) A))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k8_filter_0 A B))) (=> (tptp.m1_filter_0 B A) (and (= (tptp.u1_struct_0 _let_1) B) (= (tptp.u2_lattices _let_1) (tptp.k1_realset1 (tptp.u2_lattices A) B)) (= (tptp.u1_lattices _let_1) (tptp.k1_realset1 (tptp.u1_lattices A) B)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_filter_0 D A) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.u1_struct_0 (tptp.k8_filter_0 A D))) (forall ((F $$unsorted)) (let ((_let_1 (tptp.k8_filter_0 A D))) (=> (tptp.m1_subset_1 F (tptp.u1_struct_0 _let_1)) (=> (and (= B E) (= C F)) (and (= (tptp.k3_lattices A B C) (tptp.k3_lattices _let_1 E F)) (= (tptp.k4_lattices A B C) (tptp.k4_lattices _let_1 E F))))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_filter_0 D A) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.u1_struct_0 (tptp.k8_filter_0 A D))) (forall ((F $$unsorted)) (let ((_let_1 (tptp.k8_filter_0 A D))) (=> (tptp.m1_subset_1 F (tptp.u1_struct_0 _let_1)) (=> (and (= B E) (= C F)) (= (tptp.r3_lattices A B C) (tptp.r3_lattices _let_1 E F)))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (=> (tptp.v14_lattices A) (tptp.v14_lattices (tptp.k8_filter_0 A B))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (=> (tptp.v12_lattices A) (tptp.v12_lattices (tptp.k8_filter_0 A B))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (=> (tptp.v11_lattices A) (tptp.v11_lattices (tptp.k8_filter_0 A B))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v3_filter_0 A) (tptp.l3_lattices A)) (tptp.v3_filter_0 (tptp.k8_filter_0 A B))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (tptp.v13_lattices (tptp.k8_filter_0 A (tptp.k2_filter_0 A B))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (= (tptp.k5_lattices (tptp.k8_filter_0 A (tptp.k2_filter_0 A B))) B))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (=> (tptp.v14_lattices A) (= (tptp.k6_lattices (tptp.k8_filter_0 A (tptp.k2_filter_0 A B))) (tptp.k6_lattices A))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v14_lattices A) (tptp.l3_lattices A)) (tptp.v15_lattices (tptp.k8_filter_0 A (tptp.k2_filter_0 A B)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k8_filter_0 A (tptp.k2_filter_0 A B)))) (let ((_let_2 (tptp.l3_lattices A))) (let ((_let_3 (tptp.v10_lattices A))) (let ((_let_4 (not (tptp.v3_struct_0 A)))) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (=> (and _let_4 _let_3 (tptp.v15_lattices A) (tptp.v16_lattices A) _let_2 _let_4 _let_3 (tptp.v12_lattices A) _let_2) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v10_lattices _let_1) (tptp.v15_lattices _let_1) (tptp.v16_lattices _let_1) (tptp.l3_lattices _let_1))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k8_filter_0 A (tptp.k2_filter_0 A B)))) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v10_lattices _let_1) (tptp.v17_lattices _let_1) (tptp.l3_lattices _let_1)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (= (tptp.k9_filter_0 A B C) (tptp.k4_lattices A (tptp.k4_filter_0 A B C) (tptp.k4_filter_0 A C B))))))))) true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (= (tptp.k9_filter_0 A B C) (tptp.k9_filter_0 A C B)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v3_filter_0 A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (forall ((E $$unsorted)) (=> (tptp.m1_filter_0 E A) (=> (and (tptp.r2_hidden (tptp.k9_filter_0 A B C) E) (tptp.r2_hidden (tptp.k9_filter_0 A C D) E)) (tptp.r2_hidden (tptp.k9_filter_0 A B D) E)))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (forall ((C $$unsorted)) (=> (tptp.v1_relat_1 C) (= (= C (tptp.k10_filter_0 A B)) (and (tptp.r1_tarski (tptp.k3_relat_1 C) (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 E _let_1) (= (tptp.r2_hidden (tptp.k1_domain_1 _let_1 _let_1 D E) C) (tptp.r2_hidden (tptp.k9_filter_0 A D E) B))))))))))))))) true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_filter_0 B A) (tptp.m2_relset_1 (tptp.k10_filter_0 A B) _let_1 _let_1)))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v3_filter_0 A) (tptp.l3_lattices A)) (tptp.r1_relat_2 (tptp.k10_filter_0 A B) (tptp.u1_struct_0 A))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (tptp.r3_relat_2 (tptp.k10_filter_0 A B) (tptp.u1_struct_0 A)))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v3_filter_0 A) (tptp.l3_lattices A)) (tptp.r8_relat_2 (tptp.k10_filter_0 A B) (tptp.u1_struct_0 A))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k10_filter_0 A B))) (=> (tptp.m1_filter_0 B A) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v3_filter_0 A) (tptp.l3_lattices A)) (and (tptp.v3_relat_2 _let_2) (tptp.v8_relat_2 _let_2) (tptp.v1_partfun1 _let_2 _let_1 _let_1) (tptp.m2_relset_1 _let_2 _let_1 _let_1))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v3_filter_0 A) (tptp.l3_lattices A)) (= (tptp.k3_relat_1 (tptp.k10_filter_0 A B)) (tptp.u1_struct_0 A))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (= (tptp.r1_filter_0 A B C D) (tptp.r2_hidden (tptp.k9_filter_0 A C D) B)))))))))) true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_filter_0 D A) (= (tptp.r1_filter_0 A D B C) (tptp.r2_hidden (tptp.k1_domain_1 _let_1 _let_1 B C) (tptp.k10_filter_0 A D)))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (forall ((C $$unsorted)) (=> (and (not (tptp.v3_struct_0 C)) (tptp.v10_lattices C) (tptp.v3_filter_0 C) (tptp.l3_lattices C)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 C)) (forall ((E $$unsorted)) (=> (tptp.m1_filter_0 E C) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F (tptp.u1_struct_0 A)) (and (tptp.r1_filter_0 C E D D) (tptp.r1_filter_0 A B F F)))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_filter_0 D A) (=> (tptp.r1_filter_0 A D B C) (tptp.r1_filter_0 A D C B)))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (forall ((C $$unsorted)) (=> (and (not (tptp.v3_struct_0 C)) (tptp.v10_lattices C) (tptp.v3_filter_0 C) (tptp.l3_lattices C)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 C)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.u1_struct_0 C)) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F (tptp.u1_struct_0 C)) (forall ((G $$unsorted)) (=> (tptp.m1_filter_0 G C) (forall ((H $$unsorted)) (=> (tptp.m1_subset_1 H (tptp.u1_struct_0 A)) (forall ((I $$unsorted)) (=> (tptp.m1_subset_1 I (tptp.u1_struct_0 A)) (forall ((J $$unsorted)) (=> (tptp.m1_subset_1 J (tptp.u1_struct_0 A)) (and (=> (and (tptp.r1_filter_0 C G D E) (tptp.r1_filter_0 C G E F)) (tptp.r1_filter_0 C G D F)) (=> (and (tptp.r1_filter_0 A B H I) (tptp.r1_filter_0 A B I J)) (tptp.r1_filter_0 A B H J))))))))))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (exists ((B $$unsorted)) (tptp.m1_filter_0 B A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (tptp.m1_filter_0 (tptp.k1_filter_0 A) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_subset_1 B (tptp.u1_struct_0 A))) (tptp.m1_filter_0 (tptp.k2_filter_0 A B) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (tptp.m1_filter_0 (tptp.k3_filter_0 A B) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (tptp.m1_subset_1 (tptp.k4_filter_0 A B C) _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B _let_1) (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 C _let_1)) (tptp.m1_subset_1 (tptp.k5_filter_0 A B C) _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v11_lattices A) (tptp.l3_lattices A) (tptp.m1_filter_0 B A) (tptp.m1_filter_0 C A)) (tptp.m1_filter_0 (tptp.k6_filter_0 A B C) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v11_lattices A) (tptp.l3_lattices A) (tptp.m1_filter_0 B A) (tptp.m1_filter_0 C A)) (= (tptp.k6_filter_0 A B C) (tptp.k5_filter_0 A B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A) (tptp.m1_filter_0 B A) (tptp.m1_filter_0 C A)) (tptp.m1_filter_0 (tptp.k7_filter_0 A B C) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A) (tptp.m1_filter_0 B A) (tptp.m1_filter_0 C A)) (= (tptp.k7_filter_0 A B C) (tptp.k5_filter_0 A B C)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k8_filter_0 A B))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_filter_0 B A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v10_lattices _let_1) (tptp.l3_lattices _let_1))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (tptp.m1_subset_1 (tptp.k9_filter_0 A B C) _let_1)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_filter_0 B A)) (tptp.v1_relat_1 (tptp.k10_filter_0 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k11_filter_0 A B))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v3_filter_0 A) (tptp.l3_lattices A) (tptp.m1_filter_0 B A)) (and (tptp.v3_relat_2 _let_2) (tptp.v8_relat_2 _let_2) (tptp.v1_partfun1 _let_2 _let_1 _let_1) (tptp.m2_relset_1 _let_2 _let_1 _let_1)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v3_filter_0 A) (tptp.l3_lattices A) (tptp.m1_filter_0 B A)) (= (tptp.k11_filter_0 A B) (tptp.k10_filter_0 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k12_filter_0 A B))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A) (tptp.m1_filter_0 B A)) (and (tptp.v3_relat_2 _let_2) (tptp.v8_relat_2 _let_2) (tptp.v1_partfun1 _let_2 _let_1 _let_1) (tptp.m2_relset_1 _let_2 _let_1 _let_1)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A) (tptp.m1_filter_0 B A)) (= (tptp.k12_filter_0 A B) (tptp.k10_filter_0 A B)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (= (tptp.k2_filter_0 A B) (tptp.a_2_0_filter_0 A B)))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (forall ((C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (= (tptp.k5_filter_0 A B C) (tptp.a_3_0_filter_0 A B C)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (forall ((C $$unsorted)) (=> (tptp.m1_filter_0 C A) (= (tptp.k3_filter_0 A (tptp.k4_subset_1 (tptp.u1_struct_0 A) B C)) (tptp.a_3_1_filter_0 A B C)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B) (tptp.m1_subset_1 C (tptp.u1_struct_0 B))) (= (tptp.r2_hidden A (tptp.a_2_0_filter_0 B C)) (exists ((D $$unsorted)) (and (tptp.m1_subset_1 D (tptp.u1_struct_0 B)) (= A D) (tptp.r3_lattices B C D)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 B)))) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B) (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 C _let_1) (not (tptp.v1_xboole_0 D)) (tptp.m1_subset_1 D _let_1)) (= (tptp.r2_hidden A (tptp.a_3_0_filter_0 B C D)) (exists ((E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (and (tptp.m1_subset_1 E _let_1) (tptp.m1_subset_1 F _let_1) (= A (tptp.k4_lattices B E F)) (tptp.r2_hidden E C) (tptp.r2_hidden F D)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B) (tptp.m1_filter_0 C B) (tptp.m1_filter_0 D B)) (= (tptp.r2_hidden A (tptp.a_3_1_filter_0 B C D)) (exists ((E $$unsorted)) (and (tptp.m1_subset_1 E (tptp.u1_struct_0 B)) (= A E) (exists ((F $$unsorted)) (and (tptp.m1_subset_1 F (tptp.u1_struct_0 B)) (exists ((G $$unsorted)) (and (tptp.m1_subset_1 G (tptp.u1_struct_0 B)) (tptp.r3_lattices B (tptp.k4_lattices B F G) E) (tptp.r2_hidden F C) (tptp.r2_hidden G D)))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l3_lattices A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u2_lattices A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v4_lattices A) (tptp.l2_lattices A)) (and (tptp.v1_relat_1 _let_3) (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.v1_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u2_lattices A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v5_lattices A) (tptp.l2_lattices A)) (and (tptp.v1_relat_1 _let_3) (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.v2_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u1_lattices A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v6_lattices A) (tptp.l1_lattices A)) (and (tptp.v1_relat_1 _let_3) (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.v1_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u1_lattices A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v7_lattices A) (tptp.l1_lattices A)) (and (tptp.v1_relat_1 _let_3) (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.v2_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1) (tptp.v4_lattices _let_1) (tptp.v5_lattices _let_1) (tptp.v6_lattices _let_1) (tptp.v7_lattices _let_1) (tptp.v8_lattices _let_1) (tptp.v9_lattices _let_1) (tptp.v10_lattices _let_1))))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.v10_lattices A) (tptp.v1_lattice2 A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.v10_lattices A))) (let ((_let_2 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_2 _let_1 (tptp.v1_lattice2 A)) (and _let_2 (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) _let_1 (tptp.v13_lattices A) (tptp.v3_filter_0 A))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.v10_lattices A))) (let ((_let_2 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_2 _let_1 (tptp.v13_lattices A) (tptp.v3_filter_0 A)) (and _let_2 (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) _let_1 (tptp.v1_lattice2 A))))))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A) (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.v10_lattices A) (tptp.v13_lattices A) (tptp.v3_filter_0 A) (tptp.v1_lattice2 A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.v10_lattices A))) (let ((_let_2 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_2 (tptp.v6_group_1 A) _let_1) (and _let_2 (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) _let_1 (tptp.v13_lattices A))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.v10_lattices A))) (let ((_let_2 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_2 (tptp.v6_group_1 A) _let_1) (and _let_2 (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) _let_1 (tptp.v14_lattices A))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.v10_lattices A))) (let ((_let_2 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_2 (tptp.v6_group_1 A) _let_1) (and _let_2 (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) _let_1 (tptp.v13_lattices A) (tptp.v14_lattices A) (tptp.v15_lattices A))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.v10_lattices A))) (let ((_let_2 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_2 (tptp.v6_group_1 A) _let_1 (tptp.v11_lattices A)) (and _let_2 (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) _let_1 (tptp.v13_lattices A) (tptp.v3_filter_0 A) (tptp.v1_lattice2 A))))))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (= (tptp.k1_relat_1 (tptp.k2_partfun1 A B D C)) C))))))) true true (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (forall ((E $$unsorted)) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E A B) (tptp.m2_relset_1 E A B)) (= (= (tptp.k2_partfun1 A B D C) (tptp.k2_partfun1 A B E C)) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F A) (=> (tptp.r2_hidden F C) (= (tptp.k1_funct_1 E F) (tptp.k1_funct_1 D F)))))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.k1_funct_4 C (tptp.k2_partfun1 A B D E)))) (and (tptp.v1_funct_1 _let_1) (tptp.v1_funct_2 _let_1 A B) (tptp.m2_relset_1 _let_1 A B)))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (forall ((E $$unsorted)) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E A B) (tptp.m2_relset_1 E A B)) (= (tptp.k1_funct_4 (tptp.k2_partfun1 A B D C) E) E))))))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (=> (tptp.r1_tarski B A) (= (tptp.k1_funct_4 A B) A)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (= (tptp.k1_funct_4 D (tptp.k2_partfun1 A B D C)) D))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (forall ((E $$unsorted)) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E A B) (tptp.m2_relset_1 E A B)) (=> (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F A) (=> (tptp.r2_hidden F C) (= (tptp.k1_funct_1 D F) (tptp.k1_funct_1 E F))))) (= (tptp.k1_funct_4 E (tptp.k2_partfun1 A B D C)) E)))))))))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k5_finsub_1 A)) (= (tptp.k1_funct_4 (tptp.k2_partfun1 A B C E) D) D))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k5_finsub_1 A)) (= (tptp.k1_relat_1 (tptp.k2_partfun1 A B C D)) D))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k5_finsub_1 A)) (=> (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F A) (=> (tptp.r2_hidden F E) (= (tptp.k1_funct_1 C F) (tptp.k1_funct_1 D F))))) (= (tptp.k1_funct_4 D (tptp.k2_partfun1 A B C E)) D)))))))))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k5_finsub_1 A)) (=> (= (tptp.k2_partfun1 A B C E) (tptp.k2_partfun1 A B D E)) (= (tptp.k2_funct_2 A B C E) (tptp.k2_funct_2 A B D E))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m2_relset_1 B _let_1 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A)) (= (tptp.r1_lattice2 A B C) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (= (tptp.k2_binop_1 A A A B D (tptp.k2_binop_1 A A A C D E)) D)))))))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u2_lattices A))) (let ((_let_2 (tptp.u1_lattices A))) (let ((_let_3 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l3_lattices A)) (=> (and (tptp.v1_binop_1 _let_1 _let_3) (tptp.v2_binop_1 _let_1 _let_3) (tptp.v1_binop_1 _let_2 _let_3) (tptp.v2_binop_1 _let_2 _let_3) (tptp.r1_lattice2 _let_3 _let_1 _let_2) (tptp.r1_lattice2 _let_3 _let_2 _let_1)) (tptp.v10_lattices A))))))) (forall ((A $$unsorted)) (=> (tptp.l3_lattices A) (= (tptp.k1_lattice2 A) (tptp.g3_lattices (tptp.u1_struct_0 A) (tptp.u1_lattices A) (tptp.u2_lattices A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l3_lattices A)) (and (= (tptp.u1_struct_0 A) (tptp.u1_struct_0 _let_1)) (= (tptp.u2_lattices A) (tptp.u1_lattices _let_1)) (= (tptp.u1_lattices A) (tptp.u2_lattices _let_1)))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A) (tptp.l3_lattices A)) (= (tptp.k1_lattice2 (tptp.k1_lattice2 A)) A))) true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (=> (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (= (tptp.k3_lattices A B C) C))) (= B (tptp.k5_lattices A))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (=> (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 C _let_1) (= (tptp.k2_binop_1 _let_1 _let_1 _let_1 (tptp.u2_lattices A) B C) C)))) (= B (tptp.k5_lattices A))))))) true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (=> (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (= (tptp.k4_lattices A B C) C))) (= B (tptp.k6_lattices A))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (=> (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 C _let_1) (= (tptp.k2_binop_1 _let_1 _let_1 _let_1 (tptp.u1_lattices A) B C) C)))) (= B (tptp.k6_lattices A))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (tptp.v3_binop_1 (tptp.u2_lattices A) (tptp.u1_struct_0 A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v4_lattices A) (tptp.l2_lattices A)) (tptp.v1_binop_1 (tptp.u2_lattices A) (tptp.u1_struct_0 A)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u2_lattices A))) (let ((_let_2 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (=> (tptp.v1_setwiseo _let_1 _let_2) (= (tptp.k5_lattices A) (tptp.k3_binop_1 _let_2 _let_1))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v5_lattices A) (tptp.l2_lattices A)) (tptp.v2_binop_1 (tptp.u2_lattices A) (tptp.u1_struct_0 A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (tptp.v3_binop_1 (tptp.u1_lattices A) (tptp.u1_struct_0 A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v6_lattices A) (tptp.l1_lattices A)) (tptp.v1_binop_1 (tptp.u1_lattices A) (tptp.u1_struct_0 A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v7_lattices A) (tptp.l1_lattices A)) (tptp.v2_binop_1 (tptp.u1_lattices A) (tptp.u1_struct_0 A)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_lattices A))) (let ((_let_2 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (=> (tptp.v1_setwiseo _let_1 _let_2) (= (tptp.k6_lattices A) (tptp.k3_binop_1 _let_2 _let_1))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u2_lattices A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (tptp.r6_binop_1 (tptp.u1_struct_0 A) _let_1 _let_1)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.l3_lattices A))) (let ((_let_2 (tptp.v10_lattices A))) (let ((_let_3 (not (tptp.v3_struct_0 A)))) (=> (and _let_3 _let_2 _let_1) (=> (and _let_3 _let_2 (tptp.v11_lattices A) _let_1) (tptp.r6_binop_1 (tptp.u1_struct_0 A) (tptp.u2_lattices A) (tptp.u1_lattices A)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (=> (tptp.r6_binop_1 (tptp.u1_struct_0 A) (tptp.u2_lattices A) (tptp.u1_lattices A)) (tptp.v11_lattices A)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.l3_lattices A))) (let ((_let_2 (tptp.v10_lattices A))) (let ((_let_3 (not (tptp.v3_struct_0 A)))) (=> (and _let_3 _let_2 _let_1) (=> (and _let_3 _let_2 (tptp.v11_lattices A) _let_1) (tptp.r6_binop_1 (tptp.u1_struct_0 A) (tptp.u1_lattices A) (tptp.u2_lattices A)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (=> (tptp.r6_binop_1 (tptp.u1_struct_0 A) (tptp.u1_lattices A) (tptp.u2_lattices A)) (tptp.v11_lattices A)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_lattices A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (tptp.r6_binop_1 (tptp.u1_struct_0 A) _let_1 _let_1)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (tptp.r1_lattice2 (tptp.u1_struct_0 A) (tptp.u2_lattices A) (tptp.u1_lattices A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (tptp.r1_lattice2 (tptp.u1_struct_0 A) (tptp.u1_lattices A) (tptp.u2_lattices A)))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k5_finsub_1 A)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A _let_1) (tptp.m2_relset_1 D A _let_1)) (= (tptp.k2_lattice2 A B C D) (tptp.k7_setwiseo A _let_1 (tptp.u2_lattices B) C D))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k5_finsub_1 A)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A _let_1) (tptp.m2_relset_1 D A _let_1)) (= (tptp.k3_lattice2 A B C D) (tptp.k7_setwiseo A _let_1 (tptp.u1_lattices B) C D))))))))))) true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C B) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k5_finsub_1 B)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E B _let_1) (tptp.m2_relset_1 E B _let_1)) (=> (tptp.r2_hidden C D) (tptp.r3_lattices A (tptp.k8_funct_2 B _let_1 E C) (tptp.k2_lattice2 B A D E)))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k5_finsub_1 C)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E C _let_1) (tptp.m2_relset_1 E C _let_1)) (=> (exists ((F $$unsorted)) (and (tptp.m1_subset_1 F C) (tptp.r2_hidden F D) (tptp.r3_lattices A B (tptp.k8_funct_2 C (tptp.u1_struct_0 A) E F)))) (tptp.r3_lattices A B (tptp.k2_lattice2 C A D E)))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k5_finsub_1 C)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E C _let_1) (tptp.m2_relset_1 E C _let_1)) (=> (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F C) (=> (tptp.r2_hidden F D) (= (tptp.k8_funct_2 C (tptp.u1_struct_0 A) E F) B)))) (or (= D tptp.k1_xboole_0) (= (tptp.k2_lattice2 C A D E) B)))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k5_finsub_1 C)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E C _let_1) (tptp.m2_relset_1 E C _let_1)) (=> (tptp.r3_lattices A (tptp.k2_lattice2 C A D E) B) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F C) (=> (tptp.r2_hidden F D) (tptp.r3_lattices A (tptp.k8_funct_2 C (tptp.u1_struct_0 A) E F) B)))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k5_finsub_1 C)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E C _let_1) (tptp.m2_relset_1 E C _let_1)) (=> (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F C) (=> (tptp.r2_hidden F D) (tptp.r3_lattices A (tptp.k8_funct_2 C (tptp.u1_struct_0 A) E F) B)))) (or (= D tptp.k1_xboole_0) (tptp.r3_lattices A (tptp.k2_lattice2 C A D E) B)))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k5_finsub_1 B)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D B _let_1) (tptp.m2_relset_1 D B _let_1)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E B _let_1) (tptp.m2_relset_1 E B _let_1)) (=> (forall ((F $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 F B) (=> (tptp.r2_hidden F C) (tptp.r3_lattices A (tptp.k8_funct_2 B _let_1 D F) (tptp.k8_funct_2 B _let_1 E F)))))) (or (= C tptp.k1_xboole_0) (tptp.r3_lattices A (tptp.k2_lattice2 B A C D) (tptp.k2_lattice2 B A C E)))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k5_finsub_1 B)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D B _let_1) (tptp.m2_relset_1 D B _let_1)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E B _let_1) (tptp.m2_relset_1 E B _let_1)) (=> (= (tptp.k2_partfun1 B _let_1 D C) (tptp.k2_partfun1 B _let_1 E C)) (or (= C tptp.k1_xboole_0) (= (tptp.k2_lattice2 B A C D) (tptp.k2_lattice2 B A C E)))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k5_finsub_1 C)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E C _let_1) (tptp.m2_relset_1 E C _let_1)) (=> (not (= D tptp.k1_xboole_0)) (= (tptp.k3_lattices A B (tptp.k2_lattice2 C A D E)) (tptp.k2_lattice2 C A D (tptp.k8_funcop_1 _let_1 C (tptp.u2_lattices A) B E))))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k5_finsub_1 A)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A _let_1) (tptp.m2_relset_1 D A _let_1)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 B))) (let ((_let_2 (tptp.u1_struct_0 _let_1))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E A _let_2) (tptp.m2_relset_1 E A _let_2)) (=> (= D E) (and (= (tptp.k2_lattice2 A B C D) (tptp.k3_lattice2 A _let_1 C E)) (= (tptp.k3_lattice2 A B C D) (tptp.k2_lattice2 A _let_1 C E))))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 (tptp.k1_lattice2 A))) (forall ((E $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (=> (tptp.m1_subset_1 E (tptp.u1_struct_0 _let_1)) (=> (and (= B D) (= C E)) (and (= (tptp.k4_lattices A B C) (tptp.k3_lattices _let_1 D E)) (= (tptp.k3_lattices A B C) (tptp.k4_lattices _let_1 D E))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (=> (tptp.r3_lattices A B C) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 (tptp.k1_lattice2 A))) (forall ((E $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (=> (tptp.m1_subset_1 E (tptp.u1_struct_0 _let_1)) (=> (and (= B D) (= C E)) (tptp.r3_lattices _let_1 E D)))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 (tptp.k1_lattice2 A))) (forall ((E $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (=> (tptp.m1_subset_1 E (tptp.u1_struct_0 _let_1)) (=> (and (tptp.r3_lattices _let_1 D E) (= B D) (= C E)) (tptp.r3_lattices A C B))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C B) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k5_finsub_1 B)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E B _let_1) (tptp.m2_relset_1 E B _let_1)) (=> (tptp.r2_hidden C D) (tptp.r3_lattices A (tptp.k3_lattice2 B A D E) (tptp.k8_funct_2 B _let_1 E C)))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k5_finsub_1 C)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E C _let_1) (tptp.m2_relset_1 E C _let_1)) (=> (exists ((F $$unsorted)) (and (tptp.m1_subset_1 F C) (tptp.r2_hidden F D) (tptp.r3_lattices A (tptp.k8_funct_2 C (tptp.u1_struct_0 A) E F) B))) (tptp.r3_lattices A (tptp.k3_lattice2 C A D E) B))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k5_finsub_1 C)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E C _let_1) (tptp.m2_relset_1 E C _let_1)) (=> (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F C) (=> (tptp.r2_hidden F D) (= (tptp.k8_funct_2 C (tptp.u1_struct_0 A) E F) B)))) (or (= D tptp.k1_xboole_0) (= (tptp.k3_lattice2 C A D E) B)))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k5_finsub_1 C)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E C _let_1) (tptp.m2_relset_1 E C _let_1)) (=> (not (= D tptp.k1_xboole_0)) (= (tptp.k4_lattices A B (tptp.k3_lattice2 C A D E)) (tptp.k3_lattice2 C A D (tptp.k8_funcop_1 _let_1 C (tptp.u1_lattices A) B E))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k5_finsub_1 C)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E C _let_1) (tptp.m2_relset_1 E C _let_1)) (=> (tptp.r3_lattices A B (tptp.k3_lattice2 C A D E)) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F C) (=> (tptp.r2_hidden F D) (tptp.r3_lattices A B (tptp.k8_funct_2 C (tptp.u1_struct_0 A) E F))))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k5_finsub_1 B)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D B _let_1) (tptp.m2_relset_1 D B _let_1)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E B _let_1) (tptp.m2_relset_1 E B _let_1)) (=> (= (tptp.k2_partfun1 B _let_1 D C) (tptp.k2_partfun1 B _let_1 E C)) (or (= C tptp.k1_xboole_0) (= (tptp.k3_lattice2 B A C D) (tptp.k3_lattice2 B A C E)))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (not (tptp.v1_xboole_0 C)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k5_finsub_1 C)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E C _let_1) (tptp.m2_relset_1 E C _let_1)) (=> (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F C) (=> (tptp.r2_hidden F D) (tptp.r3_lattices A B (tptp.k8_funct_2 C (tptp.u1_struct_0 A) E F))))) (or (= D tptp.k1_xboole_0) (tptp.r3_lattices A B (tptp.k3_lattice2 C A D E))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k5_finsub_1 B)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D B _let_1) (tptp.m2_relset_1 D B _let_1)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E B _let_1) (tptp.m2_relset_1 E B _let_1)) (=> (forall ((F $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 F B) (=> (tptp.r2_hidden F C) (tptp.r3_lattices A (tptp.k8_funct_2 B _let_1 D F) (tptp.k8_funct_2 B _let_1 E F)))))) (or (= C tptp.k1_xboole_0) (tptp.r3_lattices A (tptp.k3_lattice2 B A C D) (tptp.k3_lattice2 B A C E)))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (= (tptp.v13_lattices A) (tptp.v14_lattices (tptp.k1_lattice2 A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (= (tptp.v14_lattices A) (tptp.v13_lattices (tptp.k1_lattice2 A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (let ((_let_2 (tptp.l3_lattices A))) (let ((_let_3 (tptp.v10_lattices A))) (let ((_let_4 (not (tptp.v3_struct_0 A)))) (=> (and _let_4 _let_3 _let_2) (= (and _let_4 _let_3 (tptp.v11_lattices A) _let_2) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v10_lattices _let_1) (tptp.v11_lattices _let_1) (tptp.l3_lattices _let_1))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v13_lattices A) (tptp.l3_lattices A)) (tptp.r3_binop_1 (tptp.u1_struct_0 A) (tptp.k5_lattices A) (tptp.u2_lattices A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v13_lattices A) (tptp.l3_lattices A)) (tptp.v1_setwiseo (tptp.u2_lattices A) (tptp.u1_struct_0 A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v13_lattices A) (tptp.l3_lattices A)) (= (tptp.k5_lattices A) (tptp.k3_binop_1 (tptp.u1_struct_0 A) (tptp.u2_lattices A))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k5_finsub_1 A)) (forall ((C $$unsorted)) (=> (and (not (tptp.v3_struct_0 C)) (tptp.v10_lattices C) (tptp.v13_lattices C) (tptp.l3_lattices C)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 C))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A _let_1) (tptp.m2_relset_1 D A _let_1)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 C))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E A _let_1) (tptp.m2_relset_1 E A _let_1)) (=> (= (tptp.k2_partfun1 A _let_1 D B) (tptp.k2_partfun1 A _let_1 E B)) (= (tptp.k2_lattice2 A C B D) (tptp.k2_lattice2 A C B E))))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k5_finsub_1 A)) (forall ((C $$unsorted)) (=> (and (not (tptp.v3_struct_0 C)) (tptp.v10_lattices C) (tptp.v13_lattices C) (tptp.l3_lattices C)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 C))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A _let_1) (tptp.m2_relset_1 D A _let_1)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.u1_struct_0 C)) (=> (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F A) (=> (tptp.r2_hidden F B) (tptp.r3_lattices C (tptp.k8_funct_2 A (tptp.u1_struct_0 C) D F) E)))) (tptp.r3_lattices C (tptp.k2_lattice2 A C B D) E))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k5_finsub_1 A)) (forall ((C $$unsorted)) (=> (and (not (tptp.v3_struct_0 C)) (tptp.v10_lattices C) (tptp.v13_lattices C) (tptp.l3_lattices C)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 C))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A _let_1) (tptp.m2_relset_1 D A _let_1)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 C))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E A _let_1) (tptp.m2_relset_1 E A _let_1)) (=> (forall ((F $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 C))) (=> (tptp.m1_subset_1 F A) (=> (tptp.r2_hidden F B) (tptp.r3_lattices C (tptp.k8_funct_2 A _let_1 D F) (tptp.k8_funct_2 A _let_1 E F)))))) (tptp.r3_lattices C (tptp.k2_lattice2 A C B D) (tptp.k2_lattice2 A C B E))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v14_lattices A) (tptp.l3_lattices A)) (tptp.r3_binop_1 (tptp.u1_struct_0 A) (tptp.k6_lattices A) (tptp.u1_lattices A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v14_lattices A) (tptp.l3_lattices A)) (tptp.v1_setwiseo (tptp.u1_lattices A) (tptp.u1_struct_0 A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v14_lattices A) (tptp.l3_lattices A)) (= (tptp.k6_lattices A) (tptp.k3_binop_1 (tptp.u1_struct_0 A) (tptp.u1_lattices A))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k5_finsub_1 A)) (forall ((C $$unsorted)) (=> (and (not (tptp.v3_struct_0 C)) (tptp.v10_lattices C) (tptp.v14_lattices C) (tptp.l3_lattices C)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 C))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A _let_1) (tptp.m2_relset_1 D A _let_1)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 C))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E A _let_1) (tptp.m2_relset_1 E A _let_1)) (=> (= (tptp.k2_partfun1 A _let_1 D B) (tptp.k2_partfun1 A _let_1 E B)) (= (tptp.k3_lattice2 A C B D) (tptp.k3_lattice2 A C B E))))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k5_finsub_1 A)) (forall ((C $$unsorted)) (=> (and (not (tptp.v3_struct_0 C)) (tptp.v10_lattices C) (tptp.v14_lattices C) (tptp.l3_lattices C)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 C))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A _let_1) (tptp.m2_relset_1 D A _let_1)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.u1_struct_0 C)) (=> (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F A) (=> (tptp.r2_hidden F B) (tptp.r3_lattices C E (tptp.k8_funct_2 A (tptp.u1_struct_0 C) D F))))) (tptp.r3_lattices C E (tptp.k3_lattice2 A C B D)))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k5_finsub_1 A)) (forall ((C $$unsorted)) (=> (and (not (tptp.v3_struct_0 C)) (tptp.v10_lattices C) (tptp.v14_lattices C) (tptp.l3_lattices C)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 C))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A _let_1) (tptp.m2_relset_1 D A _let_1)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 C))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E A _let_1) (tptp.m2_relset_1 E A _let_1)) (=> (forall ((F $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 C))) (=> (tptp.m1_subset_1 F A) (=> (tptp.r2_hidden F B) (tptp.r3_lattices C (tptp.k8_funct_2 A _let_1 D F) (tptp.k8_funct_2 A _let_1 E F)))))) (tptp.r3_lattices C (tptp.k3_lattice2 A C B D) (tptp.k3_lattice2 A C B E))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v13_lattices A) (tptp.l3_lattices A)) (= (tptp.k5_lattices A) (tptp.k6_lattices (tptp.k1_lattice2 A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v14_lattices A) (tptp.l3_lattices A)) (= (tptp.k6_lattices A) (tptp.k5_lattices (tptp.k1_lattice2 A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v11_lattices A) (tptp.v13_lattices A) (tptp.l3_lattices A)) (tptp.r6_binop_1 (tptp.u1_struct_0 A) (tptp.u1_lattices A) (tptp.u2_lattices A)))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k5_finsub_1 A)) (forall ((C $$unsorted)) (=> (and (not (tptp.v3_struct_0 C)) (tptp.v10_lattices C) (tptp.v11_lattices C) (tptp.v13_lattices C) (tptp.l3_lattices C)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 C))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A _let_1) (tptp.m2_relset_1 D A _let_1)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_lattices C))) (let ((_let_2 (tptp.u1_struct_0 C))) (=> (tptp.m1_subset_1 E _let_2) (= (tptp.k2_binop_1 _let_2 _let_2 _let_2 _let_1 E (tptp.k2_lattice2 A C B D)) (tptp.k2_lattice2 A C B (tptp.k8_funcop_1 _let_2 A _let_1 E D)))))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k5_finsub_1 A)) (forall ((C $$unsorted)) (=> (and (not (tptp.v3_struct_0 C)) (tptp.v10_lattices C) (tptp.v11_lattices C) (tptp.v13_lattices C) (tptp.l3_lattices C)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 C))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A _let_1) (tptp.m2_relset_1 D A _let_1)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 C))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E A _let_1) (tptp.m2_relset_1 E A _let_1)) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F (tptp.u1_struct_0 C)) (=> (forall ((G $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 C))) (=> (tptp.m1_subset_1 G A) (=> (tptp.r2_hidden G B) (= (tptp.k8_funct_2 A _let_1 D G) (tptp.k4_lattices C F (tptp.k8_funct_2 A _let_1 E G))))))) (= (tptp.k4_lattices C F (tptp.k2_lattice2 A C B E)) (tptp.k2_lattice2 A C B D))))))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k5_finsub_1 A)) (forall ((C $$unsorted)) (=> (and (not (tptp.v3_struct_0 C)) (tptp.v10_lattices C) (tptp.v11_lattices C) (tptp.v13_lattices C) (tptp.l3_lattices C)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 C))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A _let_1) (tptp.m2_relset_1 D A _let_1)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 C))) (=> (tptp.m1_subset_1 E _let_1) (= (tptp.k4_lattices C E (tptp.k2_lattice2 A C B D)) (tptp.k2_lattice2 A C B (tptp.k8_funcop_1 _let_1 A (tptp.u1_lattices C) E D))))))))))))))) true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (= (tptp.v1_lattice2 A) (and (tptp.v3_filter_0 A) (tptp.v13_lattices A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.l3_lattices A))) (let ((_let_2 (tptp.v10_lattices A))) (let ((_let_3 (not (tptp.v3_struct_0 A)))) (=> (and _let_3 _let_2 (tptp.v13_lattices A) _let_1) (= (and _let_3 _let_2 (tptp.v1_lattice2 A) _let_1) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (exists ((D $$unsorted)) (and (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (tptp.r3_lattices A (tptp.k4_lattices A B D) C) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.u1_struct_0 A)) (=> (tptp.r3_lattices A (tptp.k4_lattices A B E) C) (tptp.r3_lattices A E D)))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (= (tptp.v6_group_1 A) (tptp.v6_group_1 (tptp.k1_lattice2 A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (=> (tptp.l3_lattices A) (and (tptp.v3_lattices _let_1) (tptp.l3_lattices _let_1))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B) (tptp.m1_subset_1 C (tptp.k5_finsub_1 A)) (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A _let_1) (tptp.m1_relset_1 D A _let_1)) (tptp.m1_subset_1 (tptp.k2_lattice2 A B C D) _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B) (tptp.m1_subset_1 C (tptp.k5_finsub_1 A)) (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A _let_1) (tptp.m1_relset_1 D A _let_1)) (tptp.m1_subset_1 (tptp.k3_lattice2 A B C D) _let_1)))) (and _let_9 (tptp.v3_lattices tptp.k6_nat_lat) (tptp.v4_lattices tptp.k6_nat_lat) (tptp.v5_lattices tptp.k6_nat_lat) (tptp.v6_lattices tptp.k6_nat_lat) (tptp.v7_lattices tptp.k6_nat_lat) (tptp.v8_lattices tptp.k6_nat_lat) (tptp.v9_lattices tptp.k6_nat_lat) _let_8) (and (not (tptp.v1_xboole_0 tptp.k7_nat_lat)) (tptp.v1_membered tptp.k7_nat_lat) (tptp.v2_membered tptp.k7_nat_lat) (tptp.v3_membered tptp.k7_nat_lat) (tptp.v4_membered tptp.k7_nat_lat) (tptp.v5_membered tptp.k7_nat_lat)) (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A (tptp.k1_zfmisc_1 tptp.k1_numbers)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B A) (and (tptp.v1_xcmplx_0 B) (tptp.v1_xreal_0 B)))))) (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A (tptp.k1_zfmisc_1 tptp.k5_numbers)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B A) (and (tptp.v1_xcmplx_0 B) (tptp.v1_xreal_0 B)))))) (and _let_5 (tptp.v3_lattices tptp.k13_nat_lat) (tptp.v4_lattices tptp.k13_nat_lat) (tptp.v5_lattices tptp.k13_nat_lat) (tptp.v6_lattices tptp.k13_nat_lat) (tptp.v7_lattices tptp.k13_nat_lat) (tptp.v8_lattices tptp.k13_nat_lat) (tptp.v9_lattices tptp.k13_nat_lat) _let_4) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (exists ((B $$unsorted)) (and (tptp.m2_nat_lat B A) (not (tptp.v3_struct_0 B)) (tptp.v3_lattices B) (tptp.v4_lattices B) (tptp.v5_lattices B) (tptp.v6_lattices B) (tptp.v7_lattices B) (tptp.v8_lattices B) (tptp.v9_lattices B) (tptp.v10_lattices B))))) true true (forall ((A $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 tptp.k5_numbers tptp.k5_numbers))) (=> (and (tptp.v1_funct_1 A) (tptp.v1_funct_2 A _let_1 tptp.k5_numbers) (tptp.m2_relset_1 A _let_1 tptp.k5_numbers)) (= (= A tptp.k1_nat_lat) (forall ((B $$unsorted)) (=> (tptp.m2_subset_1 B tptp.k1_numbers tptp.k5_numbers) (forall ((C $$unsorted)) (=> (tptp.m2_subset_1 C tptp.k1_numbers tptp.k5_numbers) (= (tptp.k2_binop_1 tptp.k5_numbers tptp.k5_numbers tptp.k5_numbers A B C) (tptp.k6_nat_1 B C)))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 tptp.k5_numbers tptp.k5_numbers))) (=> (and (tptp.v1_funct_1 A) (tptp.v1_funct_2 A _let_1 tptp.k5_numbers) (tptp.m2_relset_1 A _let_1 tptp.k5_numbers)) (= (= A tptp.k2_nat_lat) (forall ((B $$unsorted)) (=> (tptp.m2_subset_1 B tptp.k1_numbers tptp.k5_numbers) (forall ((C $$unsorted)) (=> (tptp.m2_subset_1 C tptp.k1_numbers tptp.k5_numbers) (= (tptp.k2_binop_1 tptp.k5_numbers tptp.k5_numbers tptp.k5_numbers A B C) (tptp.k5_nat_1 B C)))))))))) (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A (tptp.u1_struct_0 (tptp.g3_lattices tptp.k5_numbers tptp.k2_nat_lat tptp.k1_nat_lat))) (= (tptp.k3_nat_lat A) A))) true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true true (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A (tptp.u1_struct_0 (tptp.g3_lattices tptp.k5_numbers tptp.k2_nat_lat tptp.k1_nat_lat))) (forall ((B $$unsorted)) (let ((_let_1 (tptp.g3_lattices tptp.k5_numbers tptp.k2_nat_lat tptp.k1_nat_lat))) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 _let_1)) (= (tptp.k1_lattices _let_1 A B) (tptp.k5_nat_1 (tptp.k3_nat_lat A) (tptp.k3_nat_lat B)))))))) (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A (tptp.u1_struct_0 (tptp.g3_lattices tptp.k5_numbers tptp.k2_nat_lat tptp.k1_nat_lat))) (forall ((B $$unsorted)) (let ((_let_1 (tptp.g3_lattices tptp.k5_numbers tptp.k2_nat_lat tptp.k1_nat_lat))) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 _let_1)) (= (tptp.k2_lattices _let_1 A B) (tptp.k6_nat_1 (tptp.k3_nat_lat A) (tptp.k3_nat_lat B)))))))) true true (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A (tptp.u1_struct_0 (tptp.g3_lattices tptp.k5_numbers tptp.k2_nat_lat tptp.k1_nat_lat))) (forall ((B $$unsorted)) (let ((_let_1 (tptp.g3_lattices tptp.k5_numbers tptp.k2_nat_lat tptp.k1_nat_lat))) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 _let_1)) (=> (tptp.r1_lattices _let_1 A B) (tptp.r1_nat_1 (tptp.k3_nat_lat A) (tptp.k3_nat_lat B)))))))) (= tptp.k4_nat_lat tptp.np__1) (= tptp.k5_nat_lat tptp.np__0) true true (= (tptp.k3_nat_lat tptp.k4_nat_lat) tptp.np__1) (forall ((A $$unsorted)) (let ((_let_1 (tptp.g3_lattices tptp.k5_numbers tptp.k2_nat_lat tptp.k1_nat_lat))) (=> (tptp.m1_subset_1 A (tptp.u1_struct_0 _let_1)) (and (= (tptp.k2_lattices _let_1 tptp.k4_nat_lat A) tptp.k4_nat_lat) (= (tptp.k2_lattices _let_1 A tptp.k4_nat_lat) tptp.k4_nat_lat))))) (= tptp.k6_nat_lat _let_10) true true true (and _let_9 _let_8 (tptp.v13_lattices tptp.k6_nat_lat) _let_7) (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A (tptp.u1_struct_0 tptp.k6_nat_lat)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 tptp.k6_nat_lat)) (= (tptp.k1_binop_1 tptp.k2_nat_lat A B) (tptp.k1_binop_1 tptp.k2_nat_lat B A)))))) (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A (tptp.u1_struct_0 tptp.k6_nat_lat)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 tptp.k6_nat_lat)) (= (tptp.k1_binop_1 tptp.k1_nat_lat A B) (tptp.k1_binop_1 tptp.k1_nat_lat B A)))))) (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A (tptp.u1_struct_0 tptp.k6_nat_lat)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 tptp.k6_nat_lat)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 tptp.k6_nat_lat)) (= (tptp.k1_binop_1 tptp.k2_nat_lat A (tptp.k1_binop_1 tptp.k2_nat_lat B C)) (tptp.k1_binop_1 tptp.k2_nat_lat (tptp.k1_binop_1 tptp.k2_nat_lat A B) C)))))))) (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A (tptp.u1_struct_0 tptp.k6_nat_lat)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 tptp.k6_nat_lat)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k1_binop_1 tptp.k2_nat_lat A (tptp.k1_binop_1 tptp.k2_nat_lat B C)))) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 tptp.k6_nat_lat)) (and (= _let_1 (tptp.k1_binop_1 tptp.k2_nat_lat (tptp.k1_binop_1 tptp.k2_nat_lat B A) C)) (= _let_1 (tptp.k1_binop_1 tptp.k2_nat_lat (tptp.k1_binop_1 tptp.k2_nat_lat A C) B)) (= _let_1 (tptp.k1_binop_1 tptp.k2_nat_lat (tptp.k1_binop_1 tptp.k2_nat_lat C B) A)) (= _let_1 (tptp.k1_binop_1 tptp.k2_nat_lat (tptp.k1_binop_1 tptp.k2_nat_lat C A) B)))))))))) (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A (tptp.u1_struct_0 tptp.k6_nat_lat)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 tptp.k6_nat_lat)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 tptp.k6_nat_lat)) (= (tptp.k1_binop_1 tptp.k1_nat_lat A (tptp.k1_binop_1 tptp.k1_nat_lat B C)) (tptp.k1_binop_1 tptp.k1_nat_lat (tptp.k1_binop_1 tptp.k1_nat_lat A B) C)))))))) (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A (tptp.u1_struct_0 tptp.k6_nat_lat)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 tptp.k6_nat_lat)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k1_binop_1 tptp.k1_nat_lat A (tptp.k1_binop_1 tptp.k1_nat_lat B C)))) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 tptp.k6_nat_lat)) (and (= _let_1 (tptp.k1_binop_1 tptp.k1_nat_lat (tptp.k1_binop_1 tptp.k1_nat_lat B A) C)) (= _let_1 (tptp.k1_binop_1 tptp.k1_nat_lat (tptp.k1_binop_1 tptp.k1_nat_lat A C) B)) (= _let_1 (tptp.k1_binop_1 tptp.k1_nat_lat (tptp.k1_binop_1 tptp.k1_nat_lat C B) A)) (= _let_1 (tptp.k1_binop_1 tptp.k1_nat_lat (tptp.k1_binop_1 tptp.k1_nat_lat C A) B)))))))))) (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A (tptp.u1_struct_0 tptp.k6_nat_lat)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k1_binop_1 tptp.k2_nat_lat A B))) (let ((_let_2 (tptp.k1_binop_1 tptp.k2_nat_lat B A))) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 tptp.k6_nat_lat)) (and (= (tptp.k1_binop_1 tptp.k1_nat_lat A _let_1) A) (= (tptp.k1_binop_1 tptp.k1_nat_lat _let_2 A) A) (= (tptp.k1_binop_1 tptp.k1_nat_lat A _let_2) A) (= (tptp.k1_binop_1 tptp.k1_nat_lat _let_1 A) A)))))))) (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A (tptp.u1_struct_0 tptp.k6_nat_lat)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k1_binop_1 tptp.k1_nat_lat A B))) (let ((_let_2 (tptp.k1_binop_1 tptp.k1_nat_lat B A))) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 tptp.k6_nat_lat)) (and (= (tptp.k1_binop_1 tptp.k2_nat_lat A _let_1) A) (= (tptp.k1_binop_1 tptp.k2_nat_lat _let_2 A) A) (= (tptp.k1_binop_1 tptp.k2_nat_lat A _let_2) A) (= (tptp.k1_binop_1 tptp.k2_nat_lat _let_1 A) A)))))))) (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A (tptp.k1_zfmisc_1 tptp.k5_numbers)) (= (= A tptp.k7_nat_lat) (forall ((B $$unsorted)) (=> (tptp.m2_subset_1 B tptp.k1_numbers tptp.k5_numbers) (= (tptp.r2_hidden B A) (not (tptp.r1_xreal_0 B tptp.np__0)))))))) (forall ((A $$unsorted)) (=> (tptp.m2_subset_1 A tptp.k1_numbers tptp.k5_numbers) (=> (not (tptp.r1_xreal_0 A tptp.np__0)) (= (tptp.k8_nat_lat A) A)))) (forall ((A $$unsorted)) (=> (tptp.m1_nat_lat A tptp.k1_numbers tptp.k5_numbers tptp.k7_nat_lat) (= (tptp.k9_nat_lat A) A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 tptp.k7_nat_lat tptp.k7_nat_lat))) (=> (and (tptp.v1_funct_1 A) (tptp.v1_funct_2 A _let_1 tptp.k7_nat_lat) (tptp.m2_relset_1 A _let_1 tptp.k7_nat_lat)) (= (= A tptp.k10_nat_lat) (forall ((B $$unsorted)) (=> (tptp.m1_nat_lat B tptp.k1_numbers tptp.k5_numbers tptp.k7_nat_lat) (forall ((C $$unsorted)) (=> (tptp.m1_nat_lat C tptp.k1_numbers tptp.k5_numbers tptp.k7_nat_lat) (= (tptp.k2_binop_1 tptp.k7_nat_lat tptp.k7_nat_lat tptp.k7_nat_lat A B C) (tptp.k6_nat_1 B C)))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 tptp.k7_nat_lat tptp.k7_nat_lat))) (=> (and (tptp.v1_funct_1 A) (tptp.v1_funct_2 A _let_1 tptp.k7_nat_lat) (tptp.m2_relset_1 A _let_1 tptp.k7_nat_lat)) (= (= A tptp.k11_nat_lat) (forall ((B $$unsorted)) (=> (tptp.m1_nat_lat B tptp.k1_numbers tptp.k5_numbers tptp.k7_nat_lat) (forall ((C $$unsorted)) (=> (tptp.m1_nat_lat C tptp.k1_numbers tptp.k5_numbers tptp.k7_nat_lat) (= (tptp.k2_binop_1 tptp.k7_nat_lat tptp.k7_nat_lat tptp.k7_nat_lat A B C) (tptp.k5_nat_1 B C)))))))))) (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A (tptp.u1_struct_0 (tptp.g3_lattices tptp.k7_nat_lat tptp.k11_nat_lat tptp.k10_nat_lat))) (= (tptp.k12_nat_lat A) A))) (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A (tptp.u1_struct_0 (tptp.g3_lattices tptp.k7_nat_lat tptp.k11_nat_lat tptp.k10_nat_lat))) (forall ((B $$unsorted)) (let ((_let_1 (tptp.g3_lattices tptp.k7_nat_lat tptp.k11_nat_lat tptp.k10_nat_lat))) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 _let_1)) (= (tptp.k1_lattices _let_1 A B) (tptp.k5_nat_1 (tptp.k12_nat_lat A) (tptp.k12_nat_lat B)))))))) (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A (tptp.u1_struct_0 (tptp.g3_lattices tptp.k7_nat_lat tptp.k11_nat_lat tptp.k10_nat_lat))) (forall ((B $$unsorted)) (let ((_let_1 (tptp.g3_lattices tptp.k7_nat_lat tptp.k11_nat_lat tptp.k10_nat_lat))) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 _let_1)) (= (tptp.k2_lattices _let_1 A B) (tptp.k6_nat_1 (tptp.k12_nat_lat A) (tptp.k12_nat_lat B)))))))) (= tptp.k13_nat_lat (tptp.g3_lattices tptp.k7_nat_lat tptp.k11_nat_lat tptp.k10_nat_lat)) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B)) (= (tptp.m2_nat_lat B A) (and (tptp.r1_tarski _let_1 (tptp.u1_struct_0 A)) (= (tptp.u2_lattices B) (tptp.k1_realset1 (tptp.u2_lattices A) _let_1)) (= (tptp.u1_lattices B) (tptp.k1_realset1 (tptp.u1_lattices A) _let_1))))))))) true true true true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (tptp.m2_nat_lat A A))) (tptp.m2_nat_lat tptp.k13_nat_lat tptp.k6_nat_lat) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 B))) (forall ((D $$unsorted)) (=> (tptp.m1_nat_lat D A B C) (tptp.m2_subset_1 D A B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 B))) (exists ((D $$unsorted)) (tptp.m1_nat_lat D A B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 B))) (forall ((D $$unsorted)) (= (tptp.m1_nat_lat D A B C) (tptp.m1_subset_1 D C))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m2_nat_lat B A) (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B)))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (exists ((B $$unsorted)) (tptp.m2_nat_lat B A)))) (and (tptp.v1_funct_1 tptp.k1_nat_lat) (tptp.v1_funct_2 tptp.k1_nat_lat _let_12 tptp.k5_numbers) (tptp.m2_relset_1 tptp.k1_nat_lat _let_12 tptp.k5_numbers)) (and (tptp.v1_funct_1 tptp.k2_nat_lat) (tptp.v1_funct_2 tptp.k2_nat_lat _let_12 tptp.k5_numbers) (tptp.m2_relset_1 tptp.k2_nat_lat _let_12 tptp.k5_numbers)) (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A (tptp.u1_struct_0 (tptp.g3_lattices tptp.k5_numbers tptp.k2_nat_lat tptp.k1_nat_lat))) (tptp.m2_subset_1 (tptp.k3_nat_lat A) tptp.k1_numbers tptp.k5_numbers))) (tptp.m1_subset_1 tptp.k4_nat_lat _let_11) (tptp.m1_subset_1 tptp.k5_nat_lat _let_11) (and _let_9 _let_8 _let_7) (tptp.m1_subset_1 tptp.k7_nat_lat (tptp.k1_zfmisc_1 tptp.k5_numbers)) (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A tptp.k5_numbers) (tptp.m1_nat_lat (tptp.k8_nat_lat A) tptp.k1_numbers tptp.k5_numbers tptp.k7_nat_lat))) (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A tptp.k7_nat_lat) (tptp.m1_nat_lat (tptp.k9_nat_lat A) tptp.k1_numbers tptp.k5_numbers tptp.k7_nat_lat))) (and (tptp.v1_funct_1 tptp.k10_nat_lat) (tptp.v1_funct_2 tptp.k10_nat_lat _let_6 tptp.k7_nat_lat) (tptp.m2_relset_1 tptp.k10_nat_lat _let_6 tptp.k7_nat_lat)) (and (tptp.v1_funct_1 tptp.k11_nat_lat) (tptp.v1_funct_2 tptp.k11_nat_lat _let_6 tptp.k7_nat_lat) (tptp.m2_relset_1 tptp.k11_nat_lat _let_6 tptp.k7_nat_lat)) (forall ((A $$unsorted)) (=> (tptp.m1_subset_1 A (tptp.u1_struct_0 (tptp.g3_lattices tptp.k7_nat_lat tptp.k11_nat_lat tptp.k10_nat_lat))) (tptp.m1_nat_lat (tptp.k12_nat_lat A) tptp.k1_numbers tptp.k5_numbers tptp.k7_nat_lat))) (and _let_5 _let_4 (tptp.l3_lattices tptp.k13_nat_lat)) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (exists ((B $$unsorted)) (and (tptp.m2_lattice4 B A) (not (tptp.v1_xboole_0 B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (not (tptp.v1_xboole_0 (tptp.k4_lattice4 A B))))) true true (forall ((A $$unsorted)) (not (and (not (= A tptp.k1_xboole_0)) (forall ((B $$unsorted)) (not (and (not (= B tptp.k1_xboole_0)) (tptp.r1_tarski B A) (tptp.v6_ordinal1 B) (forall ((C $$unsorted)) (not (and (tptp.r2_hidden C A) (forall ((D $$unsorted)) (=> (tptp.r2_hidden D B) (tptp.r1_tarski D C))))))))) (forall ((B $$unsorted)) (not (and (tptp.r2_hidden B A) (forall ((C $$unsorted)) (not (and (tptp.r2_hidden C A) (not (= C B)) (tptp.r1_tarski B C)))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (tptp.v2_filter_0 (tptp.k1_filter_0 A) A))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k3_filter_0 A (tptp.k1_finsub_1 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)) B C)))) (=> (tptp.m1_filter_0 C A) (and (tptp.r1_tarski B _let_1) (tptp.r1_tarski C _let_1))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 D _let_1) (not (and (tptp.r2_hidden C (tptp.k3_filter_0 A (tptp.k1_finsub_1 (tptp.k1_zfmisc_1 _let_1) (tptp.k2_filter_0 A D) B))) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.u1_struct_0 A)) (not (and (tptp.r2_hidden E B) (tptp.r3_lattices A (tptp.k4_lattices A D E) C)))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (let ((_let_2 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_2 _let_1) (tptp.m2_relset_1 C _let_2 _let_1)) (= (tptp.m1_lattice4 C A B) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (let ((_let_2 (tptp.u1_struct_0 A))) (let ((_let_3 (tptp.k8_funct_2 _let_2 _let_1 C E))) (let ((_let_4 (tptp.k8_funct_2 _let_2 _let_1 C D))) (=> (tptp.m1_subset_1 E _let_2) (and (= (tptp.k8_funct_2 _let_2 _let_1 C (tptp.k3_lattices A D E)) (tptp.k3_lattices B _let_4 _let_3)) (= (tptp.k8_funct_2 _let_2 _let_1 C (tptp.k4_lattices A D E)) (tptp.k4_lattices B _let_4 _let_3)))))))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (let ((_let_2 (tptp.u1_struct_0 A))) (=> (tptp.m1_lattice4 E A B) (=> (tptp.r3_lattices A C D) (tptp.r3_lattices B (tptp.k8_funct_2 _let_2 _let_1 E C) (tptp.k8_funct_2 _let_2 _let_1 E D))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (let ((_let_2 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_2 _let_1) (tptp.m2_relset_1 C _let_2 _let_1)) (= (tptp.v1_lattice4 C A B) (tptp.v2_funct_1 C)))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (let ((_let_2 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_2 _let_1) (tptp.m2_relset_1 C _let_2 _let_1)) (= (tptp.v2_lattice4 C A B) (= (tptp.k2_relat_1 C) _let_1)))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (let ((_let_2 (tptp.u1_struct_0 A))) (=> (tptp.m1_lattice4 E A B) (=> (tptp.v1_lattice4 E A B) (= (tptp.r3_lattices A C D) (tptp.r3_lattices B (tptp.k8_funct_2 _let_2 _let_1 E C) (tptp.k8_funct_2 _let_2 _let_1 E D)))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (let ((_let_2 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_2 _let_1) (tptp.m2_relset_1 C _let_2 _let_1)) (=> (tptp.v2_lattice4 C A B) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 B)) (exists ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (and (tptp.m1_subset_1 E _let_1) (= D (tptp.k8_funct_2 _let_1 (tptp.u1_struct_0 B) C E)))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B)) (forall ((C $$unsorted)) (=> (tptp.m1_lattice4 C A B) (= (tptp.v3_lattice4 C A B) (and (tptp.v1_lattice4 C A B) (tptp.v2_lattice4 C A B))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B)) (= (tptp.r1_filter_1 A B) (exists ((C $$unsorted)) (and (tptp.m1_lattice4 C A B) (tptp.v3_lattice4 C A B)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B)) (forall ((C $$unsorted)) (=> (tptp.m1_lattice4 C A B) (= (tptp.r1_lattice4 A B C) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (let ((_let_2 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 E _let_2) (= (tptp.k8_funct_2 _let_2 _let_1 C (tptp.k4_filter_0 A D E)) (tptp.k4_filter_0 B (tptp.k8_funct_2 _let_2 _let_1 C D) (tptp.k8_funct_2 _let_2 _let_1 C E)))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B)) (forall ((C $$unsorted)) (=> (tptp.m1_lattice4 C A B) (= (tptp.r2_lattice4 A B C) (= (tptp.k8_funct_2 (tptp.u1_struct_0 A) (tptp.u1_struct_0 B) C (tptp.k6_lattices A)) (tptp.k6_lattices B))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B)) (forall ((C $$unsorted)) (=> (tptp.m1_lattice4 C A B) (= (tptp.r3_lattice4 A B C) (= (tptp.k8_funct_2 (tptp.u1_struct_0 A) (tptp.u1_struct_0 B) C (tptp.k5_lattices A)) (tptp.k5_lattices B))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B)) (forall ((C $$unsorted)) (=> (tptp.m1_lattice4 C A B) (= (tptp.r4_lattice4 A B C) (forall ((D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (let ((_let_2 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 D _let_2) (= (tptp.k8_funct_2 _let_2 _let_1 C (tptp.k7_lattices A D)) (tptp.k7_lattices B (tptp.k8_funct_2 _let_2 _let_1 C D)))))))))))))) _let_3 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (tptp.m2_lattice4 (tptp.u1_struct_0 A) A))) _let_2 true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 B (tptp.k5_finsub_1 _let_1)) (= (tptp.k1_lattice4 A B) (tptp.k2_lattice2 _let_1 A B (tptp.k7_grcat_1 A)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 B (tptp.k5_finsub_1 _let_1)) (= (tptp.k2_lattice4 A B) (tptp.k3_lattice2 _let_1 A B (tptp.k7_grcat_1 A)))))))) true true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 B (tptp.k5_finsub_1 _let_1)) (= (tptp.k2_lattice4 A B) (tptp.k7_setwiseo _let_1 _let_1 (tptp.u1_lattices A) B (tptp.k7_grcat_1 A)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 B (tptp.k5_finsub_1 _let_1)) (= (tptp.k1_lattice4 A B) (tptp.k7_setwiseo _let_1 _let_1 (tptp.u2_lattices A) B (tptp.k7_grcat_1 A)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 B _let_1) (= (tptp.k1_lattice4 A (tptp.k2_setwiseo _let_1 B)) B)))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 B _let_1) (= (tptp.k2_lattice4 A (tptp.k2_setwiseo _let_1 B)) B)))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.v11_lattices B) (tptp.l3_lattices B)) (forall ((C $$unsorted)) (=> (tptp.m1_lattice4 C B A) (=> (tptp.v2_lattice4 C B A) (tptp.v11_lattices A)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.v13_lattices B) (tptp.l3_lattices B)) (forall ((C $$unsorted)) (=> (tptp.m1_lattice4 C B A) (=> (tptp.v2_lattice4 C B A) (and (tptp.v13_lattices A) (tptp.r3_lattice4 B A C))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v13_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k5_finsub_1 (tptp.u1_struct_0 A))) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D _let_1 _let_1) (tptp.m2_relset_1 D _let_1 _let_1)) (= (tptp.k2_lattice2 _let_1 A (tptp.k5_setwiseo _let_1 B (tptp.k2_setwiseo _let_1 C)) D) (tptp.k3_lattices A (tptp.k2_lattice2 _let_1 A B D) (tptp.k8_funct_2 _let_1 _let_1 D C)))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v13_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k5_finsub_1 (tptp.u1_struct_0 A))) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 C _let_1) (= (tptp.k1_lattice4 A (tptp.k5_setwiseo _let_1 B (tptp.k2_setwiseo _let_1 C))) (tptp.k3_lattices A (tptp.k1_lattice4 A B) C))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v13_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k5_finsub_1 (tptp.u1_struct_0 A))) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 C (tptp.k5_finsub_1 _let_1)) (= (tptp.k3_lattices A (tptp.k1_lattice4 A B) (tptp.k1_lattice4 A C)) (tptp.k1_lattice4 A (tptp.k5_setwiseo _let_1 B C)))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v13_lattices A) (tptp.l3_lattices A)) (= (tptp.k1_lattice4 A (tptp.k1_setwiseo (tptp.u1_struct_0 A))) (tptp.k5_lattices A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v13_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m2_lattice4 B A) (=> (tptp.r2_hidden (tptp.k5_lattices A) B) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k5_finsub_1 (tptp.u1_struct_0 A))) (=> (tptp.r1_tarski C B) (tptp.r2_hidden (tptp.k1_lattice4 A C) B))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.v14_lattices B) (tptp.l3_lattices B)) (forall ((C $$unsorted)) (=> (tptp.m1_lattice4 C B A) (=> (tptp.v2_lattice4 C B A) (and (tptp.v14_lattices A) (tptp.r2_lattice4 B A C))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v14_lattices A) (tptp.l3_lattices A)) (= (tptp.k2_lattice4 A (tptp.k1_setwiseo (tptp.u1_struct_0 A))) (tptp.k6_lattices A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v14_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k5_finsub_1 (tptp.u1_struct_0 A))) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D _let_1 _let_1) (tptp.m2_relset_1 D _let_1 _let_1)) (= (tptp.k3_lattice2 _let_1 A (tptp.k5_setwiseo _let_1 B (tptp.k2_setwiseo _let_1 C)) D) (tptp.k4_lattices A (tptp.k3_lattice2 _let_1 A B D) (tptp.k8_funct_2 _let_1 _let_1 D C)))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v14_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k5_finsub_1 (tptp.u1_struct_0 A))) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 C _let_1) (= (tptp.k2_lattice4 A (tptp.k5_setwiseo _let_1 B (tptp.k2_setwiseo _let_1 C))) (tptp.k4_lattices A (tptp.k2_lattice4 A B) C))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v14_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k5_finsub_1 (tptp.u1_struct_0 A))) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 _let_1) (tptp.m2_relset_1 C _let_1 _let_1)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D _let_1 _let_1) (tptp.m2_relset_1 D _let_1 _let_1)) (= (tptp.k3_lattice2 _let_1 A (tptp.k8_setwiseo _let_1 _let_1 C B) D) (tptp.k3_lattice2 _let_1 A B (tptp.k7_funct_2 _let_1 _let_1 _let_1 C D))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v14_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k5_finsub_1 (tptp.u1_struct_0 A))) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 C (tptp.k5_finsub_1 _let_1)) (= (tptp.k4_lattices A (tptp.k2_lattice4 A B) (tptp.k2_lattice4 A C)) (tptp.k2_lattice4 A (tptp.k5_setwiseo _let_1 B C)))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v14_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m2_lattice4 B A) (=> (tptp.r2_hidden (tptp.k6_lattices A) B) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k5_finsub_1 (tptp.u1_struct_0 A))) (=> (tptp.r1_tarski C B) (tptp.r2_hidden (tptp.k2_lattice4 A C) B))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v11_lattices A) (tptp.v14_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k5_finsub_1 (tptp.u1_struct_0 A))) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 C _let_1) (= (tptp.k3_lattices A (tptp.k2_lattice4 A B) C) (tptp.k2_lattice4 A (tptp.k8_setwiseo _let_1 _let_1 (tptp.k7_funcop_1 _let_1 _let_1 (tptp.u2_lattices A) (tptp.k7_grcat_1 A) C) B)))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v15_lattices A) (tptp.v16_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.v3_filter_0 B) (tptp.l3_lattices B)) (forall ((C $$unsorted)) (=> (tptp.m1_lattice4 C B A) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 B)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.u1_struct_0 B))) (=> (tptp.m1_subset_1 E _let_2) (tptp.r3_lattices A (tptp.k4_lattices A (tptp.k8_funct_2 _let_2 _let_1 C D) (tptp.k8_funct_2 _let_2 _let_1 C (tptp.k4_filter_0 B D E))) (tptp.k8_funct_2 _let_2 _let_1 C E)))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v15_lattices A) (tptp.v16_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.v3_filter_0 B) (tptp.l3_lattices B)) (forall ((C $$unsorted)) (=> (tptp.m1_lattice4 C B A) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 B)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.u1_struct_0 B)) (forall ((F $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.u1_struct_0 B))) (let ((_let_3 (tptp.k8_funct_2 _let_2 _let_1 C E))) (=> (tptp.m1_subset_1 F _let_2) (=> (and (tptp.v1_lattice4 C B A) (tptp.r3_lattices A (tptp.k4_lattices A (tptp.k8_funct_2 _let_2 _let_1 C D) _let_3) (tptp.k8_funct_2 _let_2 _let_1 C F))) (tptp.r3_lattices A _let_3 (tptp.k8_funct_2 _let_2 _let_1 C (tptp.k4_filter_0 B D F))))))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v15_lattices A) (tptp.v16_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.v3_filter_0 B) (tptp.l3_lattices B)) (forall ((C $$unsorted)) (=> (tptp.m1_lattice4 C B A) (=> (tptp.v3_lattice4 C B A) (and (tptp.v3_filter_0 A) (tptp.r1_lattice4 B A C))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (= (tptp.k7_lattices A (tptp.k6_lattices A)) (tptp.k5_lattices A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (= (tptp.k7_lattices A (tptp.k5_lattices A)) (tptp.k6_lattices A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v15_lattices A) (tptp.v16_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.v17_lattices B) (tptp.l3_lattices B)) (forall ((C $$unsorted)) (=> (tptp.m1_lattice4 C B A) (=> (tptp.v2_lattice4 C B A) (and (tptp.v17_lattices A) (tptp.r4_lattice4 B A C))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (= (tptp.m3_lattice4 B A) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (=> (and (tptp.r2_hidden C B) (tptp.r2_hidden D B)) (and (tptp.r2_hidden (tptp.k4_lattices A C D) B) (tptp.r2_hidden (tptp.k7_lattices A C) B)))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m3_lattice4 D A) (=> (and (tptp.r2_hidden B D) (tptp.r2_hidden C D)) (tptp.r2_hidden (tptp.k3_lattices A B C) D)))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m3_lattice4 D A) (=> (and (tptp.r2_hidden B D) (tptp.r2_hidden C D)) (tptp.r2_hidden (tptp.k4_filter_0 A B C) D)))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (tptp.m3_lattice4 (tptp.u1_struct_0 A) A))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m3_lattice4 B A) (tptp.m2_lattice4 B A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (forall ((C $$unsorted)) (=> (tptp.m3_lattice4 C A) (= (= C (tptp.k3_lattice4 A B)) (and (tptp.r1_tarski B C) (forall ((D $$unsorted)) (=> (tptp.m3_lattice4 D A) (=> (tptp.r1_tarski B D) (tptp.r1_tarski C D)))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.v17_lattices B) (tptp.l3_lattices B)) (forall ((C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.u1_struct_0 B)))) (= (tptp.r2_hidden A (tptp.k4_lattice4 B C)) (exists ((D $$unsorted)) (and (tptp.m1_subset_1 D (tptp.u1_struct_0 B)) (exists ((E $$unsorted)) (and (tptp.m1_subset_1 E (tptp.u1_struct_0 B)) (= A (tptp.k4_filter_0 B D E)) (tptp.r2_hidden D C) (tptp.r2_hidden E C)))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (= (tptp.r2_hidden C (tptp.k4_lattice4 A B)) (exists ((D $$unsorted)) (and (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (exists ((E $$unsorted)) (and (tptp.m1_subset_1 E (tptp.u1_struct_0 A)) (= C (tptp.k3_lattices A (tptp.k7_lattices A D) E)) (tptp.r2_hidden D B) (tptp.r2_hidden E B)))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 _let_1) (tptp.m2_relset_1 B _let_1 _let_1)) (= (= B (tptp.k5_lattice4 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 C _let_1) (= (tptp.k8_funct_2 _let_1 _let_1 B C) (tptp.k7_lattices A C))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k5_lattice4 A))) (let ((_let_2 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 C (tptp.k5_finsub_1 _let_2)) (= (tptp.k2_lattice2 _let_2 A (tptp.k5_setwiseo _let_2 C (tptp.k2_setwiseo _let_2 B)) _let_1) (tptp.k3_lattices A (tptp.k2_lattice2 _let_2 A C _let_1) (tptp.k7_lattices A B))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 B (tptp.k5_finsub_1 _let_1)) (= (tptp.k7_lattices A (tptp.k1_lattice4 A B)) (tptp.k3_lattice2 _let_1 A B (tptp.k5_lattice4 A)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k5_lattice4 A))) (let ((_let_2 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 C (tptp.k5_finsub_1 _let_2)) (= (tptp.k3_lattice2 _let_2 A (tptp.k5_setwiseo _let_2 C (tptp.k2_setwiseo _let_2 B)) _let_1) (tptp.k4_lattices A (tptp.k3_lattice2 _let_2 A C _let_1) (tptp.k7_lattices A B))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 B (tptp.k5_finsub_1 _let_1)) (= (tptp.k7_lattices A (tptp.k2_lattice4 A B)) (tptp.k2_lattice2 _let_1 A B (tptp.k5_lattice4 A)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m2_lattice4 B A)) (=> (and (tptp.r2_hidden (tptp.k5_lattices A) B) (tptp.r2_hidden (tptp.k6_lattices A) B)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k5_finsub_1 (tptp.u1_struct_0 A))) (not (and (tptp.r1_tarski C (tptp.k4_lattice4 A B)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 D (tptp.k5_finsub_1 _let_1)) (not (and (tptp.r1_tarski D (tptp.k4_lattice4 A B)) (= (tptp.k2_lattice2 _let_1 A C (tptp.k5_lattice4 A)) (tptp.k2_lattice4 A D)))))))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (let ((_let_2 (tptp.u1_struct_0 A))) (=> (tptp.m1_lattice4 C A B) (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_2 _let_1) (tptp.m2_relset_1 C _let_2 _let_1)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B)) (exists ((C $$unsorted)) (tptp.m1_lattice4 C A B)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m2_lattice4 B A) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (exists ((B $$unsorted)) (tptp.m2_lattice4 B A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m3_lattice4 B A) (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (exists ((B $$unsorted)) (tptp.m3_lattice4 B A)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_subset_1 B (tptp.k5_finsub_1 _let_1))) (tptp.m1_subset_1 (tptp.k1_lattice4 A B) _let_1)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_subset_1 B (tptp.k5_finsub_1 _let_1))) (tptp.m1_subset_1 (tptp.k2_lattice4 A B) _let_1)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (tptp.m3_lattice4 (tptp.k3_lattice4 A B) A))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B _let_1)) (tptp.m1_subset_1 (tptp.k4_lattice4 A B) _let_1)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k5_lattice4 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (and (tptp.v1_funct_1 _let_2) (tptp.v1_funct_2 _let_2 _let_1 _let_1) (tptp.m2_relset_1 _let_2 _let_1 _let_1)))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (= (tptp.k4_lattice4 A B) (tptp.a_2_0_lattice4 A B)))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m2_lattice4 B A)) (=> (and (tptp.r2_hidden (tptp.k5_lattices A) B) (tptp.r2_hidden (tptp.k6_lattices A) B)) (= (tptp.a_2_1_lattice4 A B) (tptp.k3_lattice4 A B))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.v17_lattices B) (tptp.l3_lattices B) (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.u1_struct_0 B)))) (= (tptp.r2_hidden A (tptp.a_2_0_lattice4 B C)) (exists ((D $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (and (tptp.m1_subset_1 D _let_1) (tptp.m1_subset_1 E _let_1) (= A (tptp.k4_filter_0 B D E)) (tptp.r2_hidden D C) (tptp.r2_hidden E C))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.v17_lattices B) (tptp.l3_lattices B) (not (tptp.v1_xboole_0 C)) (tptp.m2_lattice4 C B)) (= (tptp.r2_hidden A (tptp.a_2_1_lattice4 B C)) (exists ((D $$unsorted)) (and (tptp.m1_subset_1 D (tptp.k5_finsub_1 (tptp.u1_struct_0 B))) (= A (tptp.k2_lattice4 B D)) (tptp.r1_tarski D (tptp.k4_lattice4 B C))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_2 B A) (and (not (tptp.v1_xboole_0 B)) (tptp.m2_lattice4 B A)))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (exists ((B $$unsorted)) (tptp.m1_filter_2 B A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (= (tptp.m1_filter_2 B A) (tptp.m1_filter_0 B A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m2_filter_2 B A) (and (not (tptp.v1_xboole_0 B)) (tptp.m2_lattice4 B A)))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (exists ((B $$unsorted)) (tptp.m2_filter_2 B A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (=> (tptp.r1_filter_2 A B C) (tptp.r1_filter_2 A C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (tptp.r1_filter_2 A B B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.r1_filter_2 A B C) (= B C))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (tptp.m1_filter_2 (tptp.k1_filter_2 A) A))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (= (tptp.k1_filter_2 A) (tptp.k1_filter_0 A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_subset_1 B (tptp.u1_struct_0 A))) (tptp.m1_filter_2 (tptp.k2_filter_2 A B) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_subset_1 B (tptp.u1_struct_0 A))) (= (tptp.k2_filter_2 A B) (tptp.k2_filter_0 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (tptp.m1_filter_2 (tptp.k3_filter_2 A B) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (= (tptp.k3_filter_2 A B) (tptp.k3_filter_0 A B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v11_lattices A) (tptp.l3_lattices A) (tptp.m1_filter_0 B A) (tptp.m1_filter_0 C A)) (tptp.m1_filter_2 (tptp.k4_filter_2 A B C) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v11_lattices A) (tptp.l3_lattices A) (tptp.m1_filter_0 B A) (tptp.m1_filter_0 C A)) (= (tptp.k4_filter_2 A B C) (tptp.k5_filter_0 A B C)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_subset_1 B (tptp.u1_struct_0 A))) (tptp.m1_subset_1 (tptp.k5_filter_2 A B) (tptp.u1_struct_0 (tptp.k1_lattice2 A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_subset_1 B (tptp.u1_struct_0 (tptp.k1_lattice2 A)))) (tptp.m1_subset_1 (tptp.k6_filter_2 A B) (tptp.u1_struct_0 A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (tptp.m1_subset_1 (tptp.k7_filter_2 A B) (tptp.k1_zfmisc_1 (tptp.u1_struct_0 (tptp.k1_lattice2 A)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 (tptp.k1_lattice2 A))))) (tptp.m1_subset_1 (tptp.k8_filter_2 A B) (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m2_lattice4 B A)) (tptp.m2_lattice4 (tptp.k9_filter_2 A B) (tptp.k1_lattice2 A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m2_lattice4 B A)) (= (tptp.k9_filter_2 A B) (tptp.k7_filter_2 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k10_filter_2 A B))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m2_lattice4 B A)) (and (not (tptp.v1_xboole_0 _let_1)) (tptp.m2_lattice4 _let_1 (tptp.k1_lattice2 A)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m2_lattice4 B A)) (= (tptp.k10_filter_2 A B) (tptp.k7_filter_2 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m2_lattice4 B (tptp.k1_lattice2 A))) (tptp.m2_lattice4 (tptp.k11_filter_2 A B) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m2_lattice4 B (tptp.k1_lattice2 A))) (= (tptp.k11_filter_2 A B) (tptp.k8_filter_2 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k12_filter_2 A B))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m2_lattice4 B (tptp.k1_lattice2 A))) (and (not (tptp.v1_xboole_0 _let_1)) (tptp.m2_lattice4 _let_1 A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m2_lattice4 B (tptp.k1_lattice2 A))) (= (tptp.k12_filter_2 A B) (tptp.k8_filter_2 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_filter_0 B A)) (tptp.m2_filter_2 (tptp.k13_filter_2 A B) (tptp.k1_lattice2 A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_filter_0 B A)) (= (tptp.k13_filter_2 A B) (tptp.k7_filter_2 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_filter_0 B (tptp.k1_lattice2 A))) (tptp.m2_filter_2 (tptp.k14_filter_2 A B) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_filter_0 B (tptp.k1_lattice2 A))) (= (tptp.k14_filter_2 A B) (tptp.k8_filter_2 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m2_filter_2 B A)) (tptp.m1_filter_2 (tptp.k15_filter_2 A B) (tptp.k1_lattice2 A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m2_filter_2 B A)) (= (tptp.k15_filter_2 A B) (tptp.k7_filter_2 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m2_filter_2 B (tptp.k1_lattice2 A))) (tptp.m1_filter_2 (tptp.k16_filter_2 A B) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m2_filter_2 B (tptp.k1_lattice2 A))) (= (tptp.k16_filter_2 A B) (tptp.k8_filter_2 A B)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (tptp.m2_filter_2 (tptp.k17_filter_2 A) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_subset_1 B (tptp.u1_struct_0 A))) (tptp.m2_filter_2 (tptp.k18_filter_2 A B) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (tptp.m2_filter_2 (tptp.k19_filter_2 A B) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B _let_1) (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 C _let_1)) (tptp.m1_subset_1 (tptp.k20_filter_2 A B C) _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v11_lattices A) (tptp.l3_lattices A) (tptp.m2_filter_2 B A) (tptp.m2_filter_2 C A)) (tptp.m2_filter_2 (tptp.k21_filter_2 A B C) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v11_lattices A) (tptp.l3_lattices A) (tptp.m2_filter_2 B A) (tptp.m2_filter_2 C A)) (= (tptp.k21_filter_2 A B C) (tptp.k20_filter_2 A B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k22_filter_2 A B C))) (let ((_let_2 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_subset_1 B _let_2) (tptp.m1_subset_1 C _let_2)) (and (not (tptp.v1_xboole_0 _let_1)) (tptp.m2_lattice4 _let_1 A)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m2_lattice4 B A)) (tptp.m2_nat_lat (tptp.k23_filter_2 A B) A))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k24_filter_2 A B))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m2_nat_lat B A)) (and (tptp.v3_lattices _let_1) (tptp.m2_nat_lat _let_1 (tptp.k1_lattice2 A)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m2_nat_lat B A)) (= (tptp.k24_filter_2 A B) (tptp.k1_lattice2 B)))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A))) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 B B))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D _let_1 B) (tptp.m2_relset_1 D _let_1 B)) (=> (= D (tptp.k1_realset1 C B)) (and (=> (tptp.v1_binop_1 C A) (tptp.v1_binop_1 D B)) (=> (tptp.v3_binop_1 C A) (tptp.v3_binop_1 D B)) (=> (tptp.v2_binop_1 C A) (tptp.v2_binop_1 D B)))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A))) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 B B))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D _let_1 B) (tptp.m2_relset_1 D _let_1 B)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E A) (forall ((F $$unsorted)) (=> (tptp.m2_subset_1 F A B) (=> (and (= D (tptp.k1_realset1 C B)) (= F E)) (and (=> (tptp.r1_binop_1 A E C) (tptp.r1_binop_1 B F D)) (=> (tptp.r2_binop_1 A E C) (tptp.r2_binop_1 B F D)) (=> (tptp.r3_binop_1 A E C) (tptp.r3_binop_1 B F D)))))))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A))) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D _let_1 A) (tptp.m2_relset_1 D _let_1 A)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 B B))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E _let_1 B) (tptp.m2_relset_1 E _let_1 B)) (forall ((F $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 B B))) (=> (and (tptp.v1_funct_1 F) (tptp.v1_funct_2 F _let_1 B) (tptp.m2_relset_1 F _let_1 B)) (=> (and (= E (tptp.k1_realset1 C B)) (= F (tptp.k1_realset1 D B))) (and (=> (tptp.r4_binop_1 A C D) (tptp.r4_binop_1 B E F)) (=> (tptp.r5_binop_1 A C D) (tptp.r5_binop_1 B E F)))))))))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A))) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D _let_1 A) (tptp.m2_relset_1 D _let_1 A)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 B B))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E _let_1 B) (tptp.m2_relset_1 E _let_1 B)) (forall ((F $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 B B))) (=> (and (tptp.v1_funct_1 F) (tptp.v1_funct_2 F _let_1 B) (tptp.m2_relset_1 F _let_1 B)) (=> (and (= E (tptp.k1_realset1 C B)) (= F (tptp.k1_realset1 D B)) (tptp.r6_binop_1 A C D)) (tptp.r6_binop_1 B E F)))))))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A))) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m2_relset_1 C _let_1 A)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D _let_1 A) (tptp.m2_relset_1 D _let_1 A)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 B B))) (=> (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E _let_1 B) (tptp.m2_relset_1 E _let_1 B)) (forall ((F $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 B B))) (=> (and (tptp.v1_funct_1 F) (tptp.v1_funct_2 F _let_1 B) (tptp.m2_relset_1 F _let_1 B)) (=> (and (= E (tptp.k1_realset1 C B)) (= F (tptp.k1_realset1 D B)) (tptp.r1_lattice2 A C D)) (tptp.r1_lattice2 B E F)))))))))))))))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (= (tptp.r1_filter_2 A B C) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D A) (= (tptp.r2_hidden D B) (tptp.r2_hidden D C))))))))))) (forall ((A $$unsorted)) (=> (tptp.l3_lattices A) (forall ((B $$unsorted)) (=> (tptp.l3_lattices B) (=> (= (tptp.g3_lattices (tptp.u1_struct_0 A) (tptp.u2_lattices A) (tptp.u1_lattices A)) (tptp.g3_lattices (tptp.u1_struct_0 B) (tptp.u2_lattices B) (tptp.u1_lattices B))) (= (tptp.k1_lattice2 A) (tptp.k1_lattice2 B))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (= (tptp.k1_lattice2 (tptp.k1_lattice2 A)) (tptp.g3_lattices (tptp.u1_struct_0 A) (tptp.u2_lattices A) (tptp.u1_lattices A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.l3_lattices B)) (=> (= (tptp.g3_lattices (tptp.u1_struct_0 A) (tptp.u2_lattices A) (tptp.u1_lattices A)) (tptp.g3_lattices (tptp.u1_struct_0 B) (tptp.u2_lattices B) (tptp.u1_lattices B))) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.u1_struct_0 B)) (forall ((F $$unsorted)) (let ((_let_1 (tptp.r1_lattices A C D))) (let ((_let_2 (tptp.r1_lattices B E F))) (=> (tptp.m1_subset_1 F (tptp.u1_struct_0 B)) (=> (and (= C E) (= D F)) (and (= (tptp.k1_lattices A C D) (tptp.k1_lattices B E F)) (= (tptp.k2_lattices A C D) (tptp.k2_lattices B E F)) (=> _let_1 _let_2) (=> _let_2 _let_1)))))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v13_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.v13_lattices B) (tptp.l3_lattices B)) (=> (= (tptp.g3_lattices (tptp.u1_struct_0 A) (tptp.u2_lattices A) (tptp.u1_lattices A)) (tptp.g3_lattices (tptp.u1_struct_0 B) (tptp.u2_lattices B) (tptp.u1_lattices B))) (= (tptp.k5_lattices A) (tptp.k5_lattices B))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v14_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.v14_lattices B) (tptp.l3_lattices B)) (=> (= (tptp.g3_lattices (tptp.u1_struct_0 A) (tptp.u2_lattices A) (tptp.u1_lattices A)) (tptp.g3_lattices (tptp.u1_struct_0 B) (tptp.u2_lattices B) (tptp.u1_lattices B))) (= (tptp.k6_lattices A) (tptp.k6_lattices B))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v15_lattices A) (tptp.v16_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.v15_lattices B) (tptp.v16_lattices B) (tptp.l3_lattices B)) (=> (= (tptp.g3_lattices (tptp.u1_struct_0 A) (tptp.u2_lattices A) (tptp.u1_lattices A)) (tptp.g3_lattices (tptp.u1_struct_0 B) (tptp.u2_lattices B) (tptp.u1_lattices B))) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.u1_struct_0 B)) (forall ((F $$unsorted)) (=> (tptp.m1_subset_1 F (tptp.u1_struct_0 B)) (=> (and (= C E) (= D F) (tptp.r2_lattices A C D)) (tptp.r2_lattices B E F))))))))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.v17_lattices B) (tptp.l3_lattices B)) (=> (= (tptp.g3_lattices (tptp.u1_struct_0 A) (tptp.u2_lattices A) (tptp.u1_lattices A)) (tptp.g3_lattices (tptp.u1_struct_0 B) (tptp.u2_lattices B) (tptp.u1_lattices B))) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 B)) (=> (= C D) (= (tptp.k7_lattices A C) (tptp.k7_lattices B D)))))))))))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 88.77/88.97  )
% 88.77/88.97  % SZS output end Proof for LAT297+2
% 88.77/88.97  % cvc5---1.0.5 exiting
% 88.77/88.97  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------