TSTP Solution File: TOP026+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : TOP026+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 05:54:37 EDT 2023
% Result : Theorem 0.24s 0.65s
% Output : Proof 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.15 % Problem : TOP026+1 : TPTP v8.1.2. Released v3.4.0.
% 0.08/0.16 % Command : do_cvc5 %s %d
% 0.15/0.38 % Computer : n011.cluster.edu
% 0.15/0.38 % Model : x86_64 x86_64
% 0.15/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38 % Memory : 8042.1875MB
% 0.15/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38 % CPULimit : 300
% 0.15/0.38 % WCLimit : 300
% 0.15/0.38 % DateTime : Sat Aug 26 23:30:24 EDT 2023
% 0.15/0.38 % CPUTime :
% 0.24/0.54 %----Proving TF0_NAR, FOF, or CNF
% 0.24/0.65 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.YezWcwSlHx/cvc5---1.0.5_9783.p...
% 0.24/0.65 ------- get file name : TPTP file name is TOP026+1
% 0.24/0.65 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_9783.smt2...
% 0.24/0.65 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.24/0.65 % SZS status Theorem for TOP026+1
% 0.24/0.65 % SZS output start Proof for TOP026+1
% 0.24/0.65 (
% 0.24/0.65 (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.v1_tsp_2 B A) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 _let_1)) (=> (tptp.v4_pre_topc C A) (= C (tptp.k3_tex_4 A (tptp.k5_subset_1 _let_1 B C)))))))))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v2_pre_topc A) (tptp.l1_pre_topc A) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (tptp.v4_pre_topc (tptp.k6_pre_topc A B) A))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (=> (and (tptp.l1_pre_topc A) (tptp.m1_subset_1 B _let_1)) (tptp.m1_subset_1 (tptp.k6_pre_topc A B) _let_1)))))) (let ((_let_4 (not (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (=> (tptp.v1_tsp_2 B A) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k6_pre_topc A C))) (let ((_let_2 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 _let_2)) (= _let_1 (tptp.k3_tex_4 A (tptp.k5_subset_1 _let_2 B _let_1))))))))))))))) (let ((_let_5 (tptp.v3_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_6 (tptp.v2_pre_topc SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_7 (tptp.l1_pre_topc SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_8 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_9 (tptp.k1_zfmisc_1 _let_8))) (let ((_let_10 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_9))) (let ((_let_11 (tptp.v1_tsp_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_12 (tptp.k6_pre_topc SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_13 (= _let_12 (tptp.k3_tex_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.k5_subset_1 _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_12))))) (let ((_let_14 (tptp.v4_pre_topc _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_15 (not _let_14))) (let ((_let_16 (tptp.m1_subset_1 _let_12 _let_9))) (let ((_let_17 (not _let_16))) (let ((_let_18 (not _let_11))) (let ((_let_19 (not _let_10))) (let ((_let_20 (not _let_7))) (let ((_let_21 (not _let_6))) (let ((_let_22 (or _let_5 _let_21 _let_20 _let_19 _let_18 _let_17 _let_15 _let_13))) (let ((_let_23 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_9))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or _let_5 _let_21 _let_20 _let_19 _let_18 _let_24 _let_13))) (let ((_let_26 (forall ((A $$unsorted) (BOUND_VARIABLE_1522 $$unsorted) (BOUND_VARIABLE_1520 $$unsorted)) (let ((_let_1 (tptp.k6_pre_topc A BOUND_VARIABLE_1522))) (let ((_let_2 (tptp.u1_struct_0 A))) (let ((_let_3 (tptp.k1_zfmisc_1 _let_2))) (or (tptp.v3_struct_0 A) (not (tptp.v2_pre_topc A)) (not (tptp.l1_pre_topc A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_1520 _let_3)) (not (tptp.v1_tsp_2 BOUND_VARIABLE_1520 A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_1522 _let_3)) (= _let_1 (tptp.k3_tex_4 A (tptp.k5_subset_1 _let_2 BOUND_VARIABLE_1520 _let_1)))))))))) (let ((_let_27 (not _let_25))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (or))) (let ((_let_30 (not _let_26))) (let ((_let_31 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_28) :args (_let_30))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_26))) (REFL :args (_let_27)) :args _let_29)) _let_28 :args (_let_27 true _let_26)))) (let ((_let_32 (REFL :args (_let_25)))) (let ((_let_33 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 1)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_6))) :args _let_29)) :args ((or _let_6 _let_25))) _let_31 :args (_let_6 true _let_25)))) (let ((_let_34 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 2)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_7))) :args _let_29)) :args ((or _let_7 _let_25))) _let_31 :args (_let_7 true _let_25)))) (let ((_let_35 (forall ((A $$unsorted) (BOUND_VARIABLE_2367 $$unsorted) (BOUND_VARIABLE_2365 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k1_zfmisc_1 _let_1))) (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_2365 _let_2)) (not (tptp.v1_tsp_2 BOUND_VARIABLE_2365 A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_2367 _let_2)) (not (tptp.v4_pre_topc BOUND_VARIABLE_2367 A)) (= BOUND_VARIABLE_2367 (tptp.k3_tex_4 A (tptp.k5_subset_1 _let_1 BOUND_VARIABLE_2365 BOUND_VARIABLE_2367))))))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (or _let_20 _let_24 _let_16))) (let ((_let_38 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (or (not (tptp.l1_pre_topc A)) (not (tptp.m1_subset_1 B _let_1)) (tptp.m1_subset_1 (tptp.k6_pre_topc A B) _let_1)))))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 5)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_29)) :args ((or _let_23 _let_25))) _let_31 :args (_let_23 true _let_25)))) (let ((_let_41 (or _let_21 _let_20 _let_24 _let_14))) (let ((_let_42 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.v2_pre_topc A)) (not (tptp.l1_pre_topc A)) (not (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (tptp.v4_pre_topc (tptp.k6_pre_topc A B) A))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_22)) :args ((or _let_5 _let_21 _let_20 _let_19 _let_18 _let_13 _let_17 _let_15 (not _let_22)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_21 _let_20 _let_24 _let_14 (not _let_41)))) _let_33 _let_34 _let_40 (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 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) false))))) :args (_let_42))) _let_43 :args (_let_41 false _let_42)) :args (_let_14 false _let_6 false _let_7 false _let_23 false _let_41)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_37)) :args ((or _let_20 _let_24 _let_16 (not _let_37)))) _let_34 _let_40 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.k6_pre_topc A B)))) :args (_let_38))) _let_39 :args (_let_37 false _let_38)) :args (_let_16 false _let_7 false _let_23 false _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((tptp.k5_subset_1 (tptp.u1_struct_0 A) BOUND_VARIABLE_2365 BOUND_VARIABLE_2367)))) :args (_let_35))) _let_36 :args (_let_22 false _let_35)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_25 6)) _let_31 :args ((not _let_13) true _let_25)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 4)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_11))) :args _let_29)) :args ((or _let_11 _let_25))) _let_31 :args (_let_11 true _let_25)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 3)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_10))) :args _let_29)) :args ((or _let_10 _let_25))) _let_31 :args (_let_10 true _let_25)) _let_34 _let_33 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_25 0)) _let_31 :args ((not _let_5) true _let_25)) :args (false false _let_14 false _let_16 false _let_22 true _let_13 false _let_11 false _let_10 false _let_7 false _let_6 true _let_5)) :args (_let_4 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (not (tptp.r2_hidden B A)))) true (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 $$unsorted)) (=> (tptp.v1_membered A) (forall ((B $$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)) (=> (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 $$unsorted)) (=> (tptp.v3_membered A) (tptp.v2_membered A))) (forall ((A $$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)))))))) (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))))) (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)) (=> (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)) (=> (and (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (tptp.v3_pre_topc B A) (tptp.v4_pre_topc B A))))) (forall ((A $$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 (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) (B $$unsorted)) (=> (tptp.r2_hidden A B) (tptp.m1_subset_1 A B))) (forall ((A $$unsorted)) (= (tptp.k3_xboole_0 A tptp.k1_xboole_0) tptp.k1_xboole_0)) (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)))) (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)) (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski A A)) (exists ((A $$unsorted)) (tptp.l1_struct_0 A)) true true (forall ((A $$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 $$unsorted)) (=> (and (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (forall ((B $$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 $$unsorted)) (=> (tptp.l1_pre_topc A) (forall ((B $$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 $$unsorted)) (=> (and (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (forall ((B $$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 $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A)) (not (tptp.v1_xboole_0 (tptp.u1_struct_0 A))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (not (tptp.v1_xboole_0 B)))))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (tptp.v1_xboole_0 B)))) (exists ((A $$unsorted)) (and (tptp.l1_struct_0 A) (not (tptp.v3_struct_0 A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (not (tptp.v1_xboole_0 B)))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (exists ((B $$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.m1_subset_1 A B) (or (tptp.v1_xboole_0 B) (tptp.r2_hidden A B)))) (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 $$unsorted)) (not (and (tptp.v1_xboole_0 A) (not (= A B)) (tptp.v1_xboole_0 B)))) (forall ((A $$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 $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (and (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k5_subset_1 A B B) B)))) (exists ((A $$unsorted)) (tptp.l1_pre_topc A)) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.m1_subset_1 B A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (and (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k5_subset_1 A B C) (tptp.k3_xboole_0 B C))))) true (forall ((A $$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) (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)))) _let_3 (forall ((A $$unsorted)) (=> (tptp.l1_pre_topc A) (tptp.l1_struct_0 A))) true true (forall ((A $$unsorted)) (not (tptp.v1_xboole_0 (tptp.k1_zfmisc_1 A)))) _let_2 (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 $$unsorted) (B $$unsorted)) (= (tptp.m1_subset_1 A (tptp.k1_zfmisc_1 B)) (tptp.r1_tarski A B))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))
% 0.24/0.65 )
% 0.24/0.65 % SZS output end Proof for TOP026+1
% 0.24/0.65 % cvc5---1.0.5 exiting
% 0.24/0.65 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------