TSTP Solution File: TOP041+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : TOP041+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n011.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 : Fri Sep 1 05:54:47 EDT 2023
% Result : Theorem 3.93s 4.17s
% Output : Proof 3.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.15 % Problem : TOP041+1 : TPTP v8.1.2. Released v3.4.0.
% 0.13/0.17 % Command : do_cvc5 %s %d
% 0.17/0.39 % Computer : n011.cluster.edu
% 0.17/0.39 % Model : x86_64 x86_64
% 0.17/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39 % Memory : 8042.1875MB
% 0.17/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39 % CPULimit : 300
% 0.24/0.39 % WCLimit : 300
% 0.24/0.39 % DateTime : Sat Aug 26 23:29:54 EDT 2023
% 0.24/0.39 % CPUTime :
% 0.24/0.55 %----Proving TF0_NAR, FOF, or CNF
% 3.93/4.17 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.vSk3EuMHxW/cvc5---1.0.5_4116.p...
% 3.93/4.17 ------- get file name : TPTP file name is TOP041+1
% 3.93/4.17 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_4116.smt2...
% 3.93/4.17 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 3.93/4.17 % SZS status Theorem for TOP041+1
% 3.93/4.17 % SZS output start Proof for TOP041+1
% 3.93/4.17 (
% 3.93/4.17 (let ((_let_1 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (=> (tptp.v3_pre_topc B A) (= (tptp.k3_tex_4 A B) B)))))))) (let ((_let_2 (forall ((A $$unsorted)) (=> (tptp.l1_pre_topc A) (forall ((B $$unsorted)) (=> (tptp.m1_pre_topc B A) (tptp.m1_subset_1 (tptp.u1_struct_0 B) (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))))))))) (let ((_let_3 (forall ((A $$unsorted)) (=> (tptp.l1_pre_topc A) (forall ((B $$unsorted)) (= (tptp.m2_tsp_1 B A) (tptp.m1_pre_topc B A))))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.m2_relset_1 C A B) (tptp.m1_relset_1 C A B))))) (let ((_let_5 (forall ((A $$unsorted)) (=> (tptp.l1_pre_topc A) (forall ((B $$unsorted)) (= (tptp.m1_tsp_1 B A) (tptp.m1_pre_topc B A))))))) (let ((_let_6 (forall ((A $$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))))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v2_pre_topc A) (tptp.l1_pre_topc A) (not (tptp.v3_struct_0 B)) (tptp.v2_tsp_2 B A) (tptp.m1_pre_topc B A)) (= (tptp.k4_tsp_2 A B) (tptp.k1_tsp_2 A B)))))) (let ((_let_8 (forall ((A $$unsorted)) (=> (tptp.l1_pre_topc A) (forall ((B $$unsorted)) (=> (tptp.m2_tsp_1 B A) (tptp.l1_pre_topc B))))))) (let ((_let_9 (forall ((A $$unsorted)) (=> (tptp.l1_pre_topc A) (tptp.l1_struct_0 A))))) (let ((_let_10 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (let ((_let_2 (tptp.u1_struct_0 A))) (let ((_let_3 (tptp.k4_tsp_2 A B))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v2_pre_topc A) (tptp.l1_pre_topc A) (not (tptp.v3_struct_0 B)) (tptp.v2_tsp_2 B A) (tptp.m1_pre_topc B A)) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.v5_pre_topc _let_3 A B) (tptp.m2_relset_1 _let_3 _let_2 _let_1))))))))) (let ((_let_11 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (let ((_let_2 (tptp.u1_struct_0 A))) (=> (and (tptp.l1_struct_0 A) (tptp.l1_struct_0 B) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_2 _let_1) (tptp.m1_relset_1 C _let_2 _let_1)) (tptp.m1_subset_1 (tptp.k4_pre_topc A B C D) (tptp.k1_zfmisc_1 _let_1)))))))) (let ((_let_12 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (let ((_let_2 (tptp.u1_struct_0 A))) (let ((_let_3 (tptp.k1_tsp_2 A B))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v2_pre_topc A) (tptp.l1_pre_topc A) (not (tptp.v3_struct_0 B)) (tptp.v2_tsp_2 B A) (tptp.m1_pre_topc B A)) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.v5_pre_topc _let_3 A B) (tptp.m2_relset_1 _let_3 _let_2 _let_1))))))))) (let ((_let_13 (forall ((A $$unsorted)) (=> (tptp.l1_pre_topc A) (forall ((B $$unsorted)) (=> (tptp.l1_pre_topc B) (= (tptp.m1_tsp_1 B A) (and (tptp.r1_tarski (tptp.u1_struct_0 B) (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.u1_struct_0 B))) (= (tptp.v3_pre_topc C B) (exists ((D $$unsorted)) (and (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (tptp.v3_pre_topc D A) (= C (tptp.k3_xboole_0 D (tptp.u1_struct_0 B)))))))))))))))) (let ((_let_14 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v2_tsp_2 B A) (tptp.m2_tsp_1 B A)) (forall ((C $$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.v5_pre_topc C A B) (tptp.m2_relset_1 C _let_2 _let_1)) (= (= C (tptp.k4_tsp_2 A B)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (=> (= D (tptp.u1_struct_0 B)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 E (tptp.k1_zfmisc_1 _let_1)) (= (tptp.k5_subset_1 _let_1 D (tptp.k3_tex_4 A E)) (tptp.k4_pre_topc A B C E))))))))))))))))))) (let ((_let_15 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k3_xboole_0 A B) (tptp.k3_xboole_0 B A))))) (let ((_let_16 (not (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v2_tsp_2 B A) (tptp.m2_tsp_1 B A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (=> (tptp.v3_pre_topc C A) (tptp.v3_pre_topc (tptp.k4_pre_topc A B (tptp.k4_tsp_2 A B) C) B))))))))))) (let ((_let_17 (tptp.k3_tex_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_18 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_17))) (let ((_let_19 (tptp.k1_tsp_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_20 (tptp.k4_tsp_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_21 (= _let_20 _let_19))) (let ((_let_22 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_23 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_24 (tptp.k5_subset_1 _let_23 _let_22 _let_17))) (let ((_let_25 (= _let_24 (tptp.k4_pre_topc SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_26 (tptp.k3_xboole_0 _let_22 _let_17))) (let ((_let_27 (= _let_24 _let_26))) (let ((_let_28 (= _let_26 (tptp.k3_xboole_0 _let_17 _let_22)))) (let ((_let_29 (tptp.k4_pre_topc SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_30 (= _let_29 (tptp.k3_xboole_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_22)))) (let ((_let_31 (tptp.v3_pre_topc SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_32 (not _let_31))) (let ((_let_33 (tptp.k1_zfmisc_1 _let_23))) (let ((_let_34 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_33))) (let ((_let_35 (not _let_34))) (let ((_let_36 (tptp.l1_pre_topc SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_37 (not _let_36))) (let ((_let_38 (tptp.v2_pre_topc SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_39 (not _let_38))) (let ((_let_40 (tptp.v3_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_41 (or _let_40 _let_39 _let_37 _let_35 _let_32 _let_18))) (let ((_let_42 (forall ((A $$unsorted) (BOUND_VARIABLE_4026 $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v2_pre_topc A)) (not (tptp.l1_pre_topc A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_4026 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (not (tptp.v3_pre_topc BOUND_VARIABLE_4026 A)) (= BOUND_VARIABLE_4026 (tptp.k3_tex_4 A BOUND_VARIABLE_4026)))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (tptp.v3_pre_topc _let_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_45 (tptp.m2_tsp_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_46 (not _let_45))) (let ((_let_47 (tptp.v2_tsp_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_48 (not _let_47))) (let ((_let_49 (tptp.v3_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_50 (or _let_40 _let_39 _let_37 _let_49 _let_48 _let_46 _let_35 _let_32 _let_44))) (let ((_let_51 (forall ((A $$unsorted) (BOUND_VARIABLE_2309 $$unsorted) (BOUND_VARIABLE_2307 $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v2_pre_topc A)) (not (tptp.l1_pre_topc A)) (tptp.v3_struct_0 BOUND_VARIABLE_2307) (not (tptp.v2_tsp_2 BOUND_VARIABLE_2307 A)) (not (tptp.m2_tsp_1 BOUND_VARIABLE_2307 A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_2309 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (not (tptp.v3_pre_topc BOUND_VARIABLE_2309 A)) (tptp.v3_pre_topc (tptp.k4_pre_topc A BOUND_VARIABLE_2307 (tptp.k4_tsp_2 A BOUND_VARIABLE_2307) BOUND_VARIABLE_2309) BOUND_VARIABLE_2307))))) (let ((_let_52 (not _let_50))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (or))) (let ((_let_55 (not _let_51))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_53) :args (_let_55))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_51))) (REFL :args (_let_52)) :args _let_54)) _let_53 :args (_let_52 true _let_51)))) (let ((_let_57 (REFL :args (_let_50)))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_50 7)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_31))) :args _let_54)) :args ((or _let_31 _let_50))) _let_56 :args (_let_31 true _let_50)))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_50 6)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) :args _let_54)) :args ((or _let_34 _let_50))) _let_56 :args (_let_34 true _let_50)))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_50 2)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_54)) :args ((or _let_36 _let_50))) _let_56 :args (_let_36 true _let_50)))) (let ((_let_61 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_50 1)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_54)) :args ((or _let_38 _let_50))) _let_56 :args (_let_38 true _let_50)))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_50 0)) _let_56 :args ((not _let_40) true _let_50)))) (let ((_let_63 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_40 _let_39 _let_37 _let_35 _let_32 _let_18 (not _let_41)))) _let_62 _let_61 _let_60 _let_59 _let_58 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.m1_subset_1 BOUND_VARIABLE_4026 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) false))))) :args (_let_42))) _let_43 :args (_let_41 false _let_42)) :args (_let_18 true _let_40 false _let_38 false _let_36 false _let_34 false _let_31 false _let_41)))) (let ((_let_64 (tptp.m1_pre_topc SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_65 (not _let_64))) (let ((_let_66 (or _let_40 _let_39 _let_37 _let_49 _let_48 _let_65 _let_21))) (let ((_let_67 (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v2_pre_topc A)) (not (tptp.l1_pre_topc A)) (tptp.v3_struct_0 B) (not (tptp.v2_tsp_2 B A)) (not (tptp.m1_pre_topc B A)) (= (tptp.k4_tsp_2 A B) (tptp.k1_tsp_2 A B)))))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (= _let_45 _let_64))) (let ((_let_70 (or _let_37 _let_69))) (let ((_let_71 (forall ((A $$unsorted) (BOUND_VARIABLE_3958 $$unsorted)) (or (not (tptp.l1_pre_topc A)) (= (tptp.m2_tsp_1 BOUND_VARIABLE_3958 A) (tptp.m1_pre_topc BOUND_VARIABLE_3958 A)))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_50 5)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_45))) :args _let_54)) :args ((or _let_45 _let_50))) _let_56 :args (_let_45 true _let_50)))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_69)) :args ((or _let_46 _let_64 (not _let_69)))) _let_73 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_37 _let_69 (not _let_70)))) _let_60 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.m2_tsp_1 BOUND_VARIABLE_3958 A)))) :args (_let_71))) _let_72 :args (_let_70 false _let_71)) :args (_let_69 false _let_36 false _let_70)) :args (_let_64 false _let_45 false _let_69)))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_50 4)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_47))) :args _let_54)) :args ((or _let_47 _let_50))) _let_56 :args (_let_47 true _let_50)))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_50 3)) _let_56 :args ((not _let_49) true _let_50)))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_40 _let_39 _let_37 _let_49 _let_48 _let_65 _let_21 (not _let_66)))) _let_62 _let_61 _let_60 _let_76 _let_75 _let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v2_tsp_2 B A) false))))) :args (_let_67))) _let_68 :args (_let_66 false _let_67)) :args (_let_21 true _let_40 false _let_38 false _let_36 true _let_49 false _let_47 false _let_64 false _let_66)))) (let ((_let_78 (or _let_35 _let_25))) (let ((_let_79 (forall ((BOUND_VARIABLE_3318 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (or (not (tptp.m1_subset_1 BOUND_VARIABLE_3318 (tptp.k1_zfmisc_1 _let_1))) (= (tptp.k5_subset_1 _let_1 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (tptp.k3_tex_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 BOUND_VARIABLE_3318)) (tptp.k4_pre_topc SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.k1_tsp_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) BOUND_VARIABLE_3318))))))) (let ((_let_80 (tptp.m1_subset_1 _let_22 _let_33))) (let ((_let_81 (not _let_80))) (let ((_let_82 (or _let_81 _let_79))) (let ((_let_83 (= _let_21 _let_82))) (let ((_let_84 (tptp.m2_relset_1 _let_19 _let_23 _let_22))) (let ((_let_85 (not _let_84))) (let ((_let_86 (tptp.v5_pre_topc _let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_87 (not _let_86))) (let ((_let_88 (tptp.v1_funct_2 _let_19 _let_23 _let_22))) (let ((_let_89 (not _let_88))) (let ((_let_90 (tptp.v1_funct_1 _let_19))) (let ((_let_91 (not _let_90))) (let ((_let_92 (or _let_40 _let_39 _let_37 _let_49 _let_48 _let_46 _let_91 _let_89 _let_87 _let_85 _let_83))) (let ((_let_93 (forall ((A $$unsorted) (BOUND_VARIABLE_3407 $$unsorted) (BOUND_VARIABLE_3405 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.u1_struct_0 BOUND_VARIABLE_3405))) (or (tptp.v3_struct_0 A) (not (tptp.v2_pre_topc A)) (not (tptp.l1_pre_topc A)) (tptp.v3_struct_0 BOUND_VARIABLE_3405) (not (tptp.v2_tsp_2 BOUND_VARIABLE_3405 A)) (not (tptp.m2_tsp_1 BOUND_VARIABLE_3405 A)) (not (tptp.v1_funct_1 BOUND_VARIABLE_3407)) (not (tptp.v1_funct_2 BOUND_VARIABLE_3407 _let_1 _let_2)) (not (tptp.v5_pre_topc BOUND_VARIABLE_3407 A BOUND_VARIABLE_3405)) (not (tptp.m2_relset_1 BOUND_VARIABLE_3407 _let_1 _let_2)) (= (or (not (tptp.m1_subset_1 _let_2 (tptp.k1_zfmisc_1 _let_1))) (forall ((BOUND_VARIABLE_3318 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (not (tptp.m1_subset_1 BOUND_VARIABLE_3318 (tptp.k1_zfmisc_1 _let_1))) (= (tptp.k5_subset_1 _let_1 (tptp.u1_struct_0 BOUND_VARIABLE_3405) (tptp.k3_tex_4 A BOUND_VARIABLE_3318)) (tptp.k4_pre_topc A BOUND_VARIABLE_3405 BOUND_VARIABLE_3407 BOUND_VARIABLE_3318)))))) (= BOUND_VARIABLE_3407 (tptp.k4_tsp_2 A BOUND_VARIABLE_3405))))))))) (let ((_let_94 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_95 (and _let_90 _let_88 _let_86 _let_84))) (let ((_let_96 (or _let_40 _let_39 _let_37 _let_49 _let_48 _let_65 _let_95))) (let ((_let_97 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (let ((_let_2 (tptp.u1_struct_0 A))) (let ((_let_3 (tptp.k1_tsp_2 A B))) (or (tptp.v3_struct_0 A) (not (tptp.v2_pre_topc A)) (not (tptp.l1_pre_topc A)) (tptp.v3_struct_0 B) (not (tptp.v2_tsp_2 B A)) (not (tptp.m1_pre_topc B A)) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.v5_pre_topc _let_3 A B) (tptp.m2_relset_1 _let_3 _let_2 _let_1))))))))) (let ((_let_98 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_99 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_96)) :args ((or _let_40 _let_39 _let_37 _let_49 _let_48 _let_65 _let_95 (not _let_96)))) _let_62 _let_61 _let_60 _let_76 _let_75 _let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_98 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v2_tsp_2 B A) false))))) :args (_let_97))) _let_98 :args (_let_96 false _let_97)) :args (_let_95 true _let_40 false _let_38 false _let_36 true _let_49 false _let_47 false _let_64 false _let_96)))) (let ((_let_100 (not _let_95))) (let ((_let_101 (not _let_21))) (let ((_let_102 (or _let_37 _let_65 _let_80))) (let ((_let_103 (forall ((A $$unsorted) (BOUND_VARIABLE_3982 $$unsorted)) (or (not (tptp.l1_pre_topc A)) (not (tptp.m1_pre_topc BOUND_VARIABLE_3982 A)) (tptp.m1_subset_1 (tptp.u1_struct_0 BOUND_VARIABLE_3982) (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))))))) (let ((_let_104 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_105 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_102)) :args ((or _let_37 _let_65 _let_80 (not _let_102)))) _let_60 _let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_104 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.m1_pre_topc BOUND_VARIABLE_3982 A) false))))) :args (_let_103))) _let_104 :args (_let_102 false _let_103)) :args (_let_80 false _let_36 false _let_64 false _let_102)))) (let ((_let_106 (_let_79))) (let ((_let_107 (tptp.m1_subset_1 _let_17 _let_33))) (let ((_let_108 (not _let_107))) (let ((_let_109 (or _let_81 _let_108 _let_27))) (let ((_let_110 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (or (not (tptp.m1_subset_1 B _let_1)) (not (tptp.m1_subset_1 C _let_1)) (= (tptp.k5_subset_1 A B C) (tptp.k3_xboole_0 B C))))))) (let ((_let_111 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_112 (and _let_34 _let_18))) (let ((_let_113 (_let_34 _let_18))) (let ((_let_114 (ASSUME :args (_let_34)))) (let ((_let_115 (ASSUME :args (_let_18)))) (let ((_let_116 (SYMM _let_115))) (let ((_let_117 (_let_15))) (let ((_let_118 (ASSUME :args _let_117))) (let ((_let_119 (not _let_30))) (let ((_let_120 (or _let_35 _let_32 _let_119))) (let ((_let_121 (forall ((D $$unsorted)) (or (not (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 (tptp.u1_struct_0 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(tptp.v3_pre_topc D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (= C (tptp.k3_xboole_0 D (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))))))))) (let ((_let_129 (and (tptp.r1_tarski _let_22 _let_23) _let_128))) (let ((_let_130 (tptp.m1_tsp_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_131 (= _let_130 _let_129))) (let ((_let_132 (tptp.l1_pre_topc SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_133 (not _let_132))) (let ((_let_134 (or _let_37 _let_133 _let_131))) (let ((_let_135 (forall ((A $$unsorted) (BOUND_VARIABLE_3472 $$unsorted)) (or (not (tptp.l1_pre_topc A)) (not (tptp.l1_pre_topc BOUND_VARIABLE_3472)) (= (tptp.m1_tsp_1 BOUND_VARIABLE_3472 A) (and (tptp.r1_tarski (tptp.u1_struct_0 BOUND_VARIABLE_3472) (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (or (not (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.u1_struct_0 BOUND_VARIABLE_3472)))) (= (tptp.v3_pre_topc C BOUND_VARIABLE_3472) (not (forall ((D $$unsorted)) (or (not 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BOUND_VARIABLE_3599 A) false))))) :args (_let_138))) _let_139 :args (_let_137 false _let_138)) :args (_let_132 false _let_36 false _let_45 false _let_137)))) (let ((_let_141 (= _let_64 _let_130))) (let ((_let_142 (or _let_37 _let_141))) (let ((_let_143 (forall ((A $$unsorted) (BOUND_VARIABLE_3946 $$unsorted)) (or (not (tptp.l1_pre_topc A)) (= (tptp.m1_tsp_1 BOUND_VARIABLE_3946 A) (tptp.m1_pre_topc BOUND_VARIABLE_3946 A)))))) (let ((_let_144 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_145 (_let_128))) (let ((_let_146 (tptp.m1_relset_1 _let_20 _let_23 _let_22))) (let ((_let_147 (not _let_146))) (let ((_let_148 (tptp.v1_funct_2 _let_20 _let_23 _let_22))) (let ((_let_149 (not _let_148))) (let ((_let_150 (tptp.v1_funct_1 _let_20))) (let ((_let_151 (not _let_150))) (let ((_let_152 (tptp.l1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_153 (not _let_152))) (let ((_let_154 (tptp.l1_struct_0 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(or _let_40 _let_39 _let_37 _let_49 _let_48 _let_65 _let_163))) (let ((_let_165 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (let ((_let_2 (tptp.u1_struct_0 A))) (let ((_let_3 (tptp.k4_tsp_2 A B))) (or (tptp.v3_struct_0 A) (not (tptp.v2_pre_topc A)) (not (tptp.l1_pre_topc A)) (tptp.v3_struct_0 B) (not (tptp.v2_tsp_2 B A)) (not (tptp.m1_pre_topc B A)) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.v5_pre_topc _let_3 A B) (tptp.m2_relset_1 _let_3 _let_2 _let_1))))))))) (let ((_let_166 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_167 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_164)) :args ((or _let_40 _let_39 _let_37 _let_49 _let_48 _let_65 _let_163 (not _let_164)))) _let_62 _let_61 _let_60 _let_76 _let_75 _let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_166 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 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(SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_177)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_115 _let_178 _let_179 _let_180 _let_181) (SCOPE (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (SYMM (SYMM _let_181)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) :args (APPLY_UF tptp.k4_pre_topc)) (SYMM _let_180) (SYMM (SYMM _let_179)) (SYMM (SYMM _let_178)) (CONG _let_116 (REFL :args (_let_22)) :args (APPLY_UF tptp.k3_xboole_0))) :args (_let_18 _let_28 _let_27 _let_25 _let_21))) :args (_let_21 _let_18 _let_25 _let_27 _let_28))) :args (true _let_177)) :args ((or _let_101 (not _let_18) (not _let_25) (not _let_27) _let_30 (not _let_28)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_120)) :args ((or _let_35 _let_32 _let_119 (not _let_120)))) _let_59 _let_58 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_176) :args 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$$unsorted)) (=> (tptp.v2_membered A) (tptp.v1_membered A))) (forall ((A $$unsorted)) (=> (and (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (=> (tptp.v3_tops_1 B A) (tptp.v2_tops_1 B A)))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.v2_pre_topc A))) (let ((_let_2 (not (tptp.v3_struct_0 A)))) (=> (tptp.l1_pre_topc A) (=> (and _let_2 _let_1 (not (tptp.v2_t_0topsp A))) (and _let_2 (not (tptp.v3_realset2 A)) _let_1 (not (tptp.v1_tdlat_3 A)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (forall ((B $$unsorted)) (=> (tptp.m1_pre_topc B A) (=> (not (tptp.v1_tex_3 B A)) (and (tptp.v2_pre_topc B) (not (tptp.v2_tsp_2 B A)))))))) (forall ((A $$unsorted)) (=> (and (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.v2_tops_1 B A))) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v4_pre_topc B A) _let_1) (and _let_1 (tptp.v3_tops_1 B A)))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.v2_pre_topc A))) (let ((_let_2 (not (tptp.v3_realset2 A)))) (let ((_let_3 (not (tptp.v3_struct_0 A)))) (=> (tptp.l1_pre_topc A) (=> (and _let_3 _let_2 _let_1 (tptp.v2_tdlat_3 A)) (and _let_3 _let_2 _let_1 (not (tptp.v2_t_0topsp A))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (forall ((B $$unsorted)) (=> (tptp.m1_pre_topc B A) (=> (and (tptp.v1_tsep_1 B A) (tptp.v2_tsp_2 B A)) (and (tptp.v2_pre_topc B) (not (tptp.v2_tex_2 B A)))))))) (forall ((A $$unsorted)) (=> (and (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.v3_tops_1 B A))) (let ((_let_2 (tptp.v3_pre_topc B A))) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (=> (and _let_2 _let_1) (and (tptp.v1_xboole_0 B) _let_2 (tptp.v4_pre_topc B A) (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B) (tptp.v4_membered B) (tptp.v5_membered B) (tptp.v2_tops_1 B A) _let_1)))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.v2_t_0topsp A))) (let ((_let_2 (tptp.v2_tdlat_3 A))) (let ((_let_3 (tptp.v2_pre_topc A))) (let ((_let_4 (not (tptp.v3_struct_0 A)))) (=> (tptp.l1_pre_topc A) (=> (and _let_4 _let_3 _let_2 _let_1) (and _let_4 (tptp.v3_realset2 A) _let_3 (tptp.v1_tdlat_3 A) _let_2 (tptp.v3_tdlat_3 A) (tptp.v4_tdlat_3 A) (tptp.v5_tdlat_3 A) _let_1)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (forall ((B $$unsorted)) (=> (tptp.m1_pre_topc B A) (=> (and (tptp.v1_tsep_1 B A) (tptp.v2_tex_2 B A)) (and (tptp.v2_pre_topc B) (not (tptp.v2_tsp_2 B A)))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.v2_pre_topc A))) (let ((_let_2 (not (tptp.v3_realset2 A)))) (let ((_let_3 (not (tptp.v3_struct_0 A)))) (=> (tptp.l1_pre_topc A) (=> (and _let_3 _let_2 _let_1 (tptp.v2_t_0topsp A)) (and _let_3 _let_2 _let_1 (not (tptp.v2_tdlat_3 A))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (forall ((B $$unsorted)) (=> (tptp.m1_pre_topc B A) (=> (and (tptp.v2_tex_2 B A) (tptp.v2_tsp_2 B A)) (and (tptp.v2_pre_topc B) (not (tptp.v1_tsep_1 B A)))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.v2_t_0topsp A))) (let ((_let_2 (tptp.v3_tdlat_3 A))) (let ((_let_3 (tptp.v2_pre_topc A))) (let ((_let_4 (not (tptp.v3_struct_0 A)))) (=> (tptp.l1_pre_topc A) (=> (and _let_4 _let_3 _let_2 _let_1) (and _let_4 _let_3 (tptp.v1_tdlat_3 A) _let_2 (tptp.v4_tdlat_3 A) (tptp.v5_tdlat_3 A) _let_1)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (forall ((B $$unsorted)) (=> (tptp.m1_pre_topc B A) (=> (and (tptp.v1_borsuk_1 B A) (tptp.v2_tsp_2 B A)) (and (tptp.v2_pre_topc B) (not (tptp.v2_tex_2 B A)))))))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.v1_tdlat_3 A)))) (let ((_let_2 (tptp.v2_pre_topc A))) (let ((_let_3 (not (tptp.v3_struct_0 A)))) (=> (tptp.l1_pre_topc A) (=> (and _let_3 _let_2 _let_1 (tptp.v3_tdlat_3 A)) (and _let_3 (not (tptp.v3_realset2 A)) _let_2 _let_1 (not (tptp.v2_t_0topsp A))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (forall ((B $$unsorted)) (=> (tptp.m1_pre_topc B A) (=> (and (tptp.v2_tex_2 B A) (tptp.v1_borsuk_1 B A)) (and (tptp.v2_pre_topc B) (not (tptp.v2_tsp_2 B A)))))))) _let_15 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (and (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k5_subset_1 A B C) (tptp.k5_subset_1 A C B))))) _let_14 _let_13 _let_12 true true true (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_pre_topc A) (tptp.m1_subset_1 B _let_1)) (tptp.m1_subset_1 (tptp.k3_tex_4 A B) _let_1)))) true _let_11 _let_10 (forall ((A $$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)))) true _let_9 true (forall ((A $$unsorted)) (=> (tptp.l1_pre_topc A) (forall ((B $$unsorted)) (=> (tptp.m1_pre_topc B A) (tptp.l1_pre_topc B))))) true true (forall ((A $$unsorted)) (=> (tptp.l1_pre_topc A) (forall ((B $$unsorted)) (=> (tptp.m1_tsp_1 B A) (tptp.l1_pre_topc B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C A B) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B))))) _let_8 true (exists ((A $$unsorted)) (tptp.l1_pre_topc A)) (exists ((A $$unsorted)) (tptp.l1_struct_0 A)) (forall ((A $$unsorted)) (=> (tptp.l1_pre_topc A) (exists ((B $$unsorted)) (tptp.m1_pre_topc B A)))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.m1_relset_1 C A B))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.m1_subset_1 B A))) (forall ((A $$unsorted)) (=> (tptp.l1_pre_topc A) (exists ((B $$unsorted)) (tptp.m1_tsp_1 B A)))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.m2_relset_1 C A B))) (forall ((A $$unsorted)) (=> (tptp.l1_pre_topc A) (exists ((B $$unsorted)) (tptp.m2_tsp_1 B A)))) (forall ((A $$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 $$unsorted)) (not (tptp.v1_xboole_0 (tptp.k1_zfmisc_1 A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_membered A) (tptp.v1_membered (tptp.k3_xboole_0 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_membered A) (tptp.v1_membered (tptp.k3_xboole_0 B A)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k3_xboole_0 A B))) (=> (tptp.v2_membered A) (and (tptp.v1_membered _let_1) (tptp.v2_membered _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k3_xboole_0 B A))) (=> (tptp.v2_membered A) (and (tptp.v1_membered _let_1) (tptp.v2_membered _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k3_xboole_0 A B))) (=> (tptp.v3_membered A) (and (tptp.v1_membered _let_1) (tptp.v2_membered _let_1) (tptp.v3_membered _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k3_xboole_0 B A))) (=> (tptp.v3_membered A) (and (tptp.v1_membered _let_1) (tptp.v2_membered _let_1) (tptp.v3_membered _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k3_xboole_0 A B))) (=> (tptp.v4_membered A) (and (tptp.v1_membered _let_1) (tptp.v2_membered _let_1) (tptp.v3_membered _let_1) (tptp.v4_membered _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k3_xboole_0 B A))) (=> (tptp.v4_membered A) (and (tptp.v1_membered _let_1) (tptp.v2_membered _let_1) (tptp.v3_membered _let_1) (tptp.v4_membered _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k3_xboole_0 A B))) (=> (tptp.v5_membered A) (and (tptp.v1_membered _let_1) (tptp.v2_membered _let_1) (tptp.v3_membered _let_1) (tptp.v4_membered _let_1) (tptp.v5_membered _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k3_xboole_0 B A))) (=> (tptp.v5_membered A) (and (tptp.v1_membered _let_1) (tptp.v2_membered _let_1) (tptp.v3_membered _let_1) (tptp.v4_membered _let_1) (tptp.v5_membered _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B))) (not (tptp.v1_xboole_0 (tptp.k2_zfmisc_1 A B))))) (and (tptp.v1_xboole_0 tptp.k1_xboole_0) (tptp.v1_membered tptp.k1_xboole_0) (tptp.v2_membered tptp.k1_xboole_0) (tptp.v3_membered tptp.k1_xboole_0) (tptp.v4_membered tptp.k1_xboole_0) (tptp.v5_membered tptp.k1_xboole_0)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k3_xboole_0 A A) A)) (forall ((A $$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)))) (exists ((A $$unsorted)) (and (not (tptp.v1_xboole_0 A)) (tptp.v1_membered A) (tptp.v2_membered A) (tptp.v3_membered A) (tptp.v4_membered A) (tptp.v5_membered A))) (forall ((A $$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)) (=> (and (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (tptp.v3_pre_topc B A))))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (tptp.v1_xboole_0 B)))) (forall ((A $$unsorted)) (=> (and (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (tptp.v3_pre_topc B A) (tptp.v4_pre_topc B A))))) (exists ((A $$unsorted)) (and (tptp.l1_struct_0 A) (not (tptp.v3_struct_0 A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (not (tptp.v1_xboole_0 B)) (tptp.v3_pre_topc B A) (tptp.v4_pre_topc B A))))) (forall ((A $$unsorted)) (=> (tptp.l1_pre_topc A) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (tptp.v1_xboole_0 B) (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B) (tptp.v4_membered B) (tptp.v5_membered B) (tptp.v2_tops_1 B 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 $$unsorted)) (=> (and (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (tptp.v1_xboole_0 B) (tptp.v3_pre_topc B A) (tptp.v4_pre_topc B A) (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B) (tptp.v4_membered B) (tptp.v5_membered B) (tptp.v2_tops_1 B A) (tptp.v3_tops_1 B A))))) (forall ((A $$unsorted)) (=> (and (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (tptp.v4_pre_topc B A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (not (tptp.v1_xboole_0 B)) (tptp.v4_pre_topc B A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (let ((_let_2 (tptp.u1_struct_0 A))) (=> (and (tptp.l1_struct_0 A) (tptp.l1_struct_0 B) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_2 _let_1) (tptp.m1_relset_1 C _let_2 _let_1)) (= (tptp.k4_pre_topc A B C D) (tptp.k9_relat_1 C D)))))) _let_7 _let_6 _let_5 _let_4 _let_3 (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (tptp.m1_subset_1 A B))) _let_2 (forall ((A $$unsorted)) (= (tptp.k3_xboole_0 A tptp.k1_xboole_0) tptp.k1_xboole_0)) (forall ((A $$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))) _let_1 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.r2_hidden A B) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 C)) (tptp.v1_xboole_0 C)))) (forall ((A $$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)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.v1_xboole_0 A) (not (= A B)) (tptp.v1_xboole_0 B)))) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 3.93/4.20 )
% 3.93/4.20 % SZS output end Proof for TOP041+1
% 3.93/4.20 % cvc5---1.0.5 exiting
% 3.93/4.20 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------