%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : TOP025+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n009.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 05:54:36 EDT 2023

% Result   : Theorem 0.44s 0.63s
% Output   : Proof 0.44s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : TOP025+1 : TPTP v8.1.2. Released v3.4.0.
% 0.06/0.14  % Command    : do_cvc5 %s %d
% 0.13/0.34  % Computer : n009.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sat Aug 26 22:54:05 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 0.19/0.48  %----Proving TF0_NAR, FOF, or CNF
% 0.44/0.63  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.VLsj5mnQNC/cvc5---1.0.5_553.p...
% 0.44/0.63  ------- get file name : TPTP file name is TOP025+1
% 0.44/0.63  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_553.smt2...
% 0.44/0.63  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.44/0.63  % SZS status Theorem for TOP025+1
% 0.44/0.63  % SZS output start Proof for TOP025+1
% 0.44/0.63  (
% 0.44/0.63  (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.v4_pre_topc B A) (= (tptp.k3_tex_4 A B) B)))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (tptp.m1_subset_1 B _let_1) (= (tptp.v1_tex_2 B _let_1) (not (= B A)))))))) (let ((_let_3 (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_4 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 _let_1)) (= (tptp.v1_tsp_2 B A) (and (tptp.v1_tsp_1 B A) (= (tptp.k3_tex_4 A B) _let_1)))))))))) (let ((_let_5 (not (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (=> (tptp.m1_subset_1 B _let_1) (not (and (or (tptp.v3_pre_topc B A) (tptp.v4_pre_topc B A)) (tptp.v1_tsp_2 B A) (tptp.v1_tex_2 B _let_1))))))))))) (let ((_let_6 (forall ((A $$unsorted) (BOUND_VARIABLE_2084 $$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_2084 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (not (tptp.v3_pre_topc BOUND_VARIABLE_2084 A)) (= BOUND_VARIABLE_2084 (tptp.k3_tex_4 A BOUND_VARIABLE_2084)))))) (let ((_let_7 (tptp.k3_tex_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_8 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_7))) (let ((_let_9 (tptp.v3_pre_topc SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_10 (not _let_9))) (let ((_let_11 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_12 (tptp.k1_zfmisc_1 _let_11))) (let ((_let_13 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_12))) (let ((_let_14 (not _let_13))) (let ((_let_15 (tptp.l1_pre_topc SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_16 (not _let_15))) (let ((_let_17 (tptp.v2_pre_topc SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_18 (not _let_17))) (let ((_let_19 (tptp.v3_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_20 (or _let_19 _let_18 _let_16 _let_14 _let_10 _let_8))) (let ((_let_21 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_22 (not _let_20))) (let ((_let_23 (= _let_11 _let_7))) (let ((_let_24 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_11))) (let ((_let_25 (not _let_8))) (let ((_let_26 (and (tptp.v1_tsp_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_23))) (let ((_let_27 (tptp.v1_tsp_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_28 (= _let_27 _let_26))) (let ((_let_29 (or _let_19 _let_18 _let_16 _let_14 _let_28))) (let ((_let_30 (forall ((A $$unsorted) (BOUND_VARIABLE_1812 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (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_1812 (tptp.k1_zfmisc_1 _let_1))) (= (tptp.v1_tsp_2 BOUND_VARIABLE_1812 A) (and (tptp.v1_tsp_1 BOUND_VARIABLE_1812 A) (= _let_1 (tptp.k3_tex_4 A BOUND_VARIABLE_1812))))))))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (tptp.v1_tex_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_12))) (let ((_let_33 (not _let_32))) (let ((_let_34 (not _let_27))) (let ((_let_35 (tptp.v4_pre_topc SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_36 (not _let_35))) (let ((_let_37 (and _let_10 _let_36))) (let ((_let_38 (or _let_19 _let_18 _let_16 _let_14 _let_37 _let_34 _let_33))) (let ((_let_39 (forall ((A $$unsorted) (BOUND_VARIABLE_1343 $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (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_1343 _let_1)) (and (not (tptp.v3_pre_topc BOUND_VARIABLE_1343 A)) (not (tptp.v4_pre_topc BOUND_VARIABLE_1343 A))) (not (tptp.v1_tsp_2 BOUND_VARIABLE_1343 A)) (not (tptp.v1_tex_2 BOUND_VARIABLE_1343 _let_1))))))) (let ((_let_40 (not _let_38))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (or))) (let ((_let_43 (not _let_39))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_41) :args (_let_43))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_39))) (REFL :args (_let_40)) :args _let_42)) _let_41 :args (_let_40 true _let_39)))) (let ((_let_45 (REFL :args (_let_38)))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 3)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) :args _let_42)) :args ((or _let_13 _let_38))) _let_44 :args (_let_13 true _let_38)))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 2)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_42)) :args ((or _let_15 _let_38))) _let_44 :args (_let_15 true _let_38)))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 1)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_42)) :args ((or _let_17 _let_38))) _let_44 :args (_let_17 true _let_38)))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_38 0)) _let_44 :args ((not _let_19) true _let_38)))) (let ((_let_50 (not _let_24))) (let ((_let_51 (= _let_32 _let_50))) (let ((_let_52 (or _let_14 _let_51))) (let ((_let_53 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (or (not (tptp.m1_subset_1 B _let_1)) (= (tptp.v1_tex_2 B _let_1) (not (= A B)))))))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (not _let_23))) (let ((_let_56 (and _let_23 _let_50))) (let ((_let_57 (ASSUME :args (_let_50)))) (let ((_let_58 (ASSUME :args (_let_23)))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_56)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_57 _let_58) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (SYMM _let_58) :args (=)) (FALSE_INTRO _let_57))) :args (_let_50 _let_23))) :args (_let_23 _let_50))) :args (true _let_56)) (CONG (REFL :args (_let_55)) (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_24))) (REFL :args (_let_25)) :args _let_42)) :args ((or _let_24 _let_55 _let_25))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_51)) :args ((or _let_33 _let_50 (not _let_51)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 6)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_42)) :args ((or _let_32 _let_38))) _let_44 :args (_let_32 true _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_14 _let_51 (not _let_52)))) _let_46 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_54 :args (_let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) false))))) :args (_let_53)))) _let_54 :args (_let_52 false _let_53)) :args (_let_51 false _let_13 false _let_52)) :args (_let_50 false _let_32 false _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_26 1)) :args ((or _let_23 (not _let_26)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_28)) :args ((or _let_34 _let_26 (not _let_28)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 5)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_27))) :args _let_42)) :args ((or _let_27 _let_38))) _let_44 :args (_let_27 true _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_19 _let_18 _let_16 _let_14 _let_28 (not _let_29)))) _let_49 _let_48 _let_47 _let_46 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.m1_subset_1 BOUND_VARIABLE_1812 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) false))))) :args (_let_30))) _let_31 :args (_let_29 false _let_30)) :args (_let_28 true _let_19 false _let_17 false _let_15 false _let_13 false _let_29)) :args (_let_26 false _let_27 false _let_28)) :args (_let_23 false _let_26)) :args (_let_25 true _let_24 false _let_23)))) (let ((_let_60 (or _let_19 _let_18 _let_16 _let_14 _let_36 _let_8))) (let ((_let_61 (forall ((A $$unsorted) (BOUND_VARIABLE_2131 $$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_2131 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (not (tptp.v4_pre_topc BOUND_VARIABLE_2131 A)) (= BOUND_VARIABLE_2131 (tptp.k3_tex_4 A BOUND_VARIABLE_2131)))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (_let_37))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.m1_subset_1 BOUND_VARIABLE_2084 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) false))))) :args (_let_6))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_20)) :args ((or _let_19 _let_18 _let_16 _let_14 _let_10 _let_8 _let_22))) _let_49 _let_48 _let_47 _let_46 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_63) (CONG (REFL :args _let_63) (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_9))) (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_35))) :args _let_42)) :args ((or _let_9 _let_35 _let_37))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_19 _let_18 _let_16 _let_14 _let_36 _let_8 (not _let_60)))) _let_49 _let_48 _let_47 _let_46 _let_59 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.m1_subset_1 BOUND_VARIABLE_2131 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) false))))) :args (_let_61))) _let_62 :args (_let_60 false _let_61)) :args (_let_36 true _let_19 false _let_17 false _let_15 false _let_13 true _let_8 false _let_60)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_38 4)) _let_44 :args ((not _let_37) true _let_38)) :args (_let_9 true _let_35 true _let_37)) _let_59 :args (_let_22 true _let_19 false _let_17 false _let_15 false _let_13 false _let_9 true _let_8)) _let_21 :args (false true _let_20 false _let_6)) :args (_let_5 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (not (tptp.r2_hidden B A)))) (forall ((A $$unsorted)) (=> (tptp.v1_membered A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B A) (tptp.v1_xcmplx_0 B))))) (forall ((A $$unsorted)) (=> (tptp.v2_membered A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B A) (and (tptp.v1_xcmplx_0 B) (tptp.v1_xreal_0 B)))))) (forall ((A $$unsorted)) (=> (tptp.v3_membered A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B A) (and (tptp.v1_xcmplx_0 B) (tptp.v1_xreal_0 B) (tptp.v1_rat_1 B)))))) (forall ((A $$unsorted)) (=> (tptp.v4_membered A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B A) (and (tptp.v1_xcmplx_0 B) (tptp.v1_xreal_0 B) (tptp.v1_int_1 B) (tptp.v1_rat_1 B)))))) (forall ((A $$unsorted)) (=> (tptp.v5_membered A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B A) (and (tptp.v1_xcmplx_0 B) (tptp.v4_ordinal2 B) (tptp.v1_xreal_0 B) (tptp.v1_int_1 B) (tptp.v1_rat_1 B)))))) (forall ((A $$unsorted)) (=> (tptp.v1_xboole_0 A) (and (tptp.v1_membered A) (tptp.v2_membered A) (tptp.v3_membered A) (tptp.v4_membered A) (tptp.v5_membered A)))) (forall ((A $$unsorted)) (=> (tptp.v1_membered A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (tptp.v1_membered B))))) (forall ((A $$unsorted)) (=> (tptp.v2_membered A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (and (tptp.v1_membered B) (tptp.v2_membered B)))))) (forall ((A $$unsorted)) (=> (tptp.v3_membered A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (and (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B)))))) (forall ((A $$unsorted)) (=> (tptp.v4_membered A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (and (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B) (tptp.v4_membered B)))))) (forall ((A $$unsorted)) (=> (tptp.v5_membered A) (tptp.v4_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.v1_xboole_0 B) (and (tptp.v3_pre_topc B A) (tptp.v4_pre_topc B A))))))) (forall ((A $$unsorted)) (=> (tptp.v5_membered A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (and (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B) (tptp.v4_membered B) (tptp.v5_membered B)))))) (forall ((A $$unsorted)) (=> (tptp.v4_membered A) (tptp.v3_membered A))) (forall ((A $$unsorted)) (=> (tptp.l1_pre_topc A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (=> (tptp.v1_xboole_0 B) (tptp.v2_tops_1 B A)))))) (forall ((A $$unsorted)) (=> (tptp.v3_membered A) (tptp.v2_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.v1_xboole_0 B) (tptp.v3_tops_1 B A)))))) (forall ((A $$unsorted)) (=> (tptp.v2_membered A) (tptp.v1_membered A))) (forall ((A $$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)) (=> (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)) (=> (and (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.v3_tops_1 B A))) (let ((_let_2 (tptp.v3_pre_topc B A))) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (=> (and _let_2 _let_1) (and (tptp.v1_xboole_0 B) _let_2 (tptp.v4_pre_topc B A) (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B) (tptp.v4_membered B) (tptp.v5_membered B) (tptp.v2_tops_1 B A) _let_1)))))))) _let_4 true true (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_pre_topc A) (tptp.m1_subset_1 B _let_1)) (tptp.m1_subset_1 (tptp.k3_tex_4 A B) _let_1)))) (forall ((A $$unsorted)) (=> (tptp.l1_pre_topc A) (tptp.l1_struct_0 A))) true true true (exists ((A $$unsorted)) (tptp.l1_pre_topc A)) (exists ((A $$unsorted)) (tptp.l1_struct_0 A)) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.m1_subset_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)))) (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)) (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)) (tptp.r1_tarski 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 $$unsorted)) (=> (and (tptp.r2_hidden A B) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 C))) (tptp.m1_subset_1 A C))) _let_3 (forall ((A $$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)))) _let_2 _let_1 (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.44/0.63  )
% 0.44/0.63  % SZS output end Proof for TOP025+1
% 0.44/0.63  % cvc5---1.0.5 exiting
% 0.44/0.64  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------