TSTP Solution File: LAT291+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : LAT291+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n029.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 06:03:40 EDT 2023
% Result : Theorem 0.22s 0.74s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LAT291+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n029.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 24 10:00:08 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.74 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.2HKPd1QgVK/cvc5---1.0.5_32052.p...
% 0.22/0.74 ------- get file name : TPTP file name is LAT291+1
% 0.22/0.74 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_32052.smt2...
% 0.22/0.74 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.74 % SZS status Theorem for LAT291+1
% 0.22/0.74 % SZS output start Proof for LAT291+1
% 0.22/0.74 (
% 0.22/0.74 (let ((_let_1 (forall ((A $$unsorted)) (= (tptp.k4_xboole_0 A tptp.k1_xboole_0) A)))) (let ((_let_2 (forall ((A $$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)))))) (let ((_let_3 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (not (tptp.v3_realset2 A)) (tptp.l3_lattices A)) (= (tptp.k8_funct_2 (tptp.u1_struct_0 A) (tptp.k1_zfmisc_1 (tptp.k7_lopclset A)) (tptp.k9_lopclset A) (tptp.k5_lattices A)) tptp.k1_xboole_0))))) (let ((_let_4 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (not (tptp.v3_realset2 A)) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k9_lopclset A))) (let ((_let_2 (tptp.k7_lopclset A))) (let ((_let_3 (tptp.k1_zfmisc_1 _let_2))) (let ((_let_4 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 B _let_4) (= (tptp.k4_xboole_0 _let_2 (tptp.k8_funct_2 _let_4 _let_3 _let_1 B)) (tptp.k8_funct_2 _let_4 _let_3 _let_1 (tptp.k7_lattices A B))))))))))))) (let ((_let_5 (forall ((A $$unsorted)) (=> (tptp.l3_lattices A) (and (tptp.l1_lattices A) (tptp.l2_lattices A)))))) (let ((_let_6 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_lattices A)) (tptp.m1_subset_1 (tptp.k5_lattices A) (tptp.u1_struct_0 A)))))) (let ((_let_7 (not (forall ((A $$unsorted)) (let ((_let_1 (tptp.k7_lopclset A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (not (tptp.v3_realset2 A)) (tptp.l3_lattices A)) (= (tptp.k8_funct_2 (tptp.u1_struct_0 A) (tptp.k1_zfmisc_1 _let_1) (tptp.k9_lopclset A) (tptp.k6_lattices A)) _let_1))))))) (let ((_let_8 (tptp.k6_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_9 (tptp.k9_lopclset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_10 (tptp.k7_lopclset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_11 (tptp.k1_zfmisc_1 _let_10))) (let ((_let_12 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_13 (= _let_10 (tptp.k8_funct_2 _let_12 _let_11 _let_9 _let_8)))) (let ((_let_14 (tptp.k5_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_15 (tptp.k8_funct_2 _let_12 _let_11 _let_9 _let_14))) (let ((_let_16 (= tptp.k1_xboole_0 _let_15))) (let ((_let_17 (tptp.k7_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14))) (let ((_let_18 (= _let_8 _let_17))) (let ((_let_19 (= (tptp.k4_xboole_0 _let_10 _let_15) (tptp.k8_funct_2 _let_12 _let_11 _let_9 _let_17)))) (let ((_let_20 (= _let_10 (tptp.k4_xboole_0 _let_10 tptp.k1_xboole_0)))) (let ((_let_21 (tptp.l3_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_22 (not _let_21))) (let ((_let_23 (tptp.v3_realset2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_24 (tptp.v17_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.v10_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_27 (not _let_26))) (let ((_let_28 (tptp.v3_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_29 (or _let_28 _let_27 _let_25 _let_23 _let_22 _let_13))) (let ((_let_30 (not _let_13))) (let ((_let_31 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k7_lopclset A))) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.v17_lattices A)) (tptp.v3_realset2 A) (not (tptp.l3_lattices A)) (= _let_1 (tptp.k8_funct_2 (tptp.u1_struct_0 A) (tptp.k1_zfmisc_1 _let_1) (tptp.k9_lopclset A) (tptp.k6_lattices A)))))))) (let ((_let_32 (not _let_29))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (or))) (let ((_let_35 (not _let_31))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_33) :args (_let_35))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_31))) (REFL :args (_let_32)) :args _let_34)) _let_33 :args (_let_32 true _let_31)))) (let ((_let_37 (or _let_28 _let_27 _let_25 _let_23 _let_22 _let_16))) (let ((_let_38 (forall ((A $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.v17_lattices A)) (tptp.v3_realset2 A) (not (tptp.l3_lattices A)) (= tptp.k1_xboole_0 (tptp.k8_funct_2 (tptp.u1_struct_0 A) (tptp.k1_zfmisc_1 (tptp.k7_lopclset A)) (tptp.k9_lopclset A) (tptp.k5_lattices A))))))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (REFL :args (_let_29)))) (let ((_let_41 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 4)) (CONG _let_40 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_34)) :args ((or _let_21 _let_29))) _let_36 :args (_let_21 true _let_29)))) (let ((_let_42 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_29 3)) _let_36 :args ((not _let_23) true _let_29)))) (let ((_let_43 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 2)) (CONG _let_40 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_34)) :args ((or _let_24 _let_29))) _let_36 :args (_let_24 true _let_29)))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 1)) (CONG _let_40 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_34)) :args ((or _let_26 _let_29))) _let_36 :args (_let_26 true _let_29)))) (let ((_let_45 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_29 0)) _let_36 :args ((not _let_28) true _let_29)))) (let ((_let_46 (or _let_28 _let_27 _let_25 _let_22 _let_18))) (let ((_let_47 (forall ((A $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.v17_lattices A)) (not (tptp.l3_lattices A)) (= (tptp.k7_lattices A (tptp.k5_lattices A)) (tptp.k6_lattices A)))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (tptp.m1_subset_1 _let_14 _let_12))) (let ((_let_50 (not _let_49))) (let ((_let_51 (or _let_28 _let_27 _let_25 _let_23 _let_22 _let_50 _let_19))) (let ((_let_52 (forall ((A $$unsorted) (BOUND_VARIABLE_2563 $$unsorted)) (let ((_let_1 (tptp.k9_lopclset A))) (let ((_let_2 (tptp.k7_lopclset A))) (let ((_let_3 (tptp.k1_zfmisc_1 _let_2))) (let ((_let_4 (tptp.u1_struct_0 A))) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.v17_lattices A)) (tptp.v3_realset2 A) (not (tptp.l3_lattices A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_2563 _let_4)) (= (tptp.k4_xboole_0 _let_2 (tptp.k8_funct_2 _let_4 _let_3 _let_1 BOUND_VARIABLE_2563)) (tptp.k8_funct_2 _let_4 _let_3 _let_1 (tptp.k7_lattices A BOUND_VARIABLE_2563))))))))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (tptp.l1_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_28 _let_55 _let_49))) (let ((_let_57 (forall ((A $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.l1_lattices A)) (tptp.m1_subset_1 (tptp.k5_lattices A) (tptp.u1_struct_0 A)))))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (and _let_54 (tptp.l2_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_60 (or _let_22 _let_59))) (let ((_let_61 (forall ((A $$unsorted)) (or (not (tptp.l3_lattices A)) (and (tptp.l1_lattices A) (tptp.l2_lattices A)))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (forall ((A $$unsorted)) (= A (tptp.k4_xboole_0 A tptp.k1_xboole_0))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (not _let_20))) (let ((_let_66 (_let_65))) (let ((_let_67 (ASSUME :args (_let_20)))) (let ((_let_68 (ASSUME :args (_let_30)))) (let ((_let_69 (ASSUME :args (_let_18)))) (let ((_let_70 (ASSUME :args (_let_19)))) (let ((_let_71 (ASSUME :args (_let_16)))) (let ((_let_72 (REFL :args (_let_10)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO (MODUS_PONENS (AND_INTRO _let_68 _let_69 _let_70 _let_71) (SCOPE (FALSE_ELIM (TRANS (CONG _let_72 (TRANS (CONG _let_72 (SYMM (SYMM _let_71)) :args (APPLY_UF tptp.k4_xboole_0)) (SYMM (SYMM _let_70)) (CONG (REFL :args (_let_12)) (REFL :args (_let_11)) (REFL :args (_let_9)) (SYMM _let_69) :args (APPLY_UF tptp.k8_funct_2))) :args (=)) (FALSE_INTRO _let_68))) :args (_let_30 _let_18 _let_19 _let_16))) _let_67) :args (_let_30 _let_16 _let_18 _let_19 _let_20)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args _let_66))) (TRUE_INTRO _let_67))) :args (_let_65 _let_20)) :args ((not (and _let_30 _let_16 _let_18 _let_19 _let_20)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_13))) (REFL :args ((not _let_16))) (REFL :args ((not _let_18))) (REFL :args ((not _let_19))) (REFL :args _let_66) :args _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (_let_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.k4_xboole_0 A tptp.k1_xboole_0)))) :args (_let_63))) _let_64 :args (_let_20 false _let_63)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_28 _let_27 _let_25 _let_23 _let_22 _let_50 _let_19 (not _let_51)))) _let_45 _let_44 _let_43 _let_42 _let_41 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_28 _let_55 _let_49 (not _let_56)))) _let_45 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_59 0)) :args ((or _let_54 (not _let_59)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_22 _let_59 (not _let_60)))) _let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.l3_lattices A) false))))) :args (_let_61))) _let_62 :args (_let_60 false _let_61)) :args (_let_59 false _let_21 false _let_60)) :args (_let_54 false _let_59)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v3_struct_0 A) true))))) :args (_let_57))) _let_58 :args (_let_56 false _let_57)) :args (_let_49 true _let_28 false _let_54 false _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.m1_subset_1 BOUND_VARIABLE_2563 (tptp.u1_struct_0 A)) false))))) :args (_let_52))) _let_53 :args (_let_51 false _let_52)) :args (_let_19 true _let_28 false _let_26 false _let_24 true _let_23 false _let_21 false _let_49 false _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_28 _let_27 _let_25 _let_22 _let_18 (not _let_46)))) _let_45 _let_44 _let_43 _let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_48 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v3_struct_0 A) true))))) :args (_let_47)))) _let_48 :args (_let_46 false _let_47)) :args (_let_18 true _let_28 false _let_26 false _let_24 false _let_21 false _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_37)) :args ((or _let_28 _let_27 _let_25 _let_23 _let_22 _let_16 (not _let_37)))) _let_45 _let_44 _let_43 _let_42 _let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v3_struct_0 A) true))))) :args (_let_38))) _let_39 :args (_let_37 false _let_38)) :args (_let_16 true _let_28 false _let_26 false _let_24 true _let_23 false _let_21 false _let_37)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_29 5)) _let_36 :args (_let_30 true _let_29)) :args (false false _let_20 false _let_19 false _let_18 false _let_16 true _let_13)) :args (_let_7 (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.v1_xboole_0 A) (tptp.v1_finset_1 A))) (forall ((A $$unsorted)) (=> (tptp.v4_finsub_1 A) (and (tptp.v1_finsub_1 A) (tptp.v3_finsub_1 A)))) (forall ((A $$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 $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v10_lattices A)) (and _let_1 (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A)))))) (forall ((A $$unsorted)) (=> (tptp.v5_membered A) (tptp.v4_membered A))) (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)) (=> (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.v1_finset_1 A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (tptp.v1_finset_1 B))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_finsub_1 A) (tptp.v3_finsub_1 A)) (tptp.v4_finsub_1 A))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A)) (and _let_1 (tptp.v10_lattices A)))))) (forall ((A $$unsorted)) (=> (tptp.v4_membered A) (tptp.v3_membered 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)) (=> (tptp.v3_membered A) (tptp.v2_membered A))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v15_lattices A)) (and _let_1 (tptp.v13_lattices A) (tptp.v14_lattices A)))))) (forall ((A $$unsorted)) (=> (tptp.v2_membered A) (tptp.v1_membered 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)) (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 $$unsorted) (B $$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)) (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)))))) (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.v10_lattices A) (tptp.v17_lattices A) (not (tptp.v3_realset2 A)) (tptp.l3_lattices A)) (= (tptp.k7_lopclset A) (tptp.a_1_1_lopclset A)))) true true true true true _let_6 (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)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (not (tptp.v3_realset2 A)) (tptp.l3_lattices A)) (tptp.m1_subset_1 (tptp.k7_lopclset A) (tptp.k1_zfmisc_1 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))))) (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 $$unsorted)) (let ((_let_1 (tptp.k8_lopclset A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (not (tptp.v3_realset2 A)) (tptp.l3_lattices A)) (and (tptp.v1_relat_1 _let_1) (tptp.v1_funct_1 _let_1))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 (tptp.k7_lopclset A)))) (let ((_let_2 (tptp.u1_struct_0 A))) (let ((_let_3 (tptp.k9_lopclset A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (not (tptp.v3_realset2 A)) (tptp.l3_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 $$unsorted)) (=> (tptp.l1_lattices A) (tptp.l1_struct_0 A))) true (forall ((A $$unsorted)) (=> (tptp.l2_lattices A) (tptp.l1_struct_0 A))) _let_5 (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)))))))) true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C A B) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B))))) true (exists ((A $$unsorted)) (tptp.l1_lattices A)) (exists ((A $$unsorted)) (tptp.l1_struct_0 A)) (exists ((A $$unsorted)) (tptp.l2_lattices A)) (exists ((A $$unsorted)) (tptp.l3_lattices A)) (forall ((A $$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) (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 $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.m2_relset_1 C A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_finset_1 A) (tptp.v1_finset_1 (tptp.k4_xboole_0 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_finset_1 A) (tptp.v1_finset_1 B)) (tptp.v1_finset_1 (tptp.k2_zfmisc_1 A B)))) (forall ((A $$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 $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A)) (not (tptp.v1_xboole_0 (tptp.u1_struct_0 A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (not (tptp.v3_realset2 A)) (tptp.l3_lattices A)) (not (tptp.v1_xboole_0 (tptp.k7_lopclset A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_membered A) (tptp.v1_membered (tptp.k4_xboole_0 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k4_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.k4_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.k4_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.k4_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))))) (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)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.v17_lattices B) (not (tptp.v3_realset2 B)) (tptp.l3_lattices B)) (= (tptp.r2_hidden A (tptp.a_1_1_lopclset B)) (exists ((C $$unsorted)) (and (tptp.m1_filter_0 C B) (= A C) (tptp.v1_filter_0 C B)))))) (exists ((A $$unsorted)) (and (not (tptp.v1_xboole_0 A)) (tptp.v1_finset_1 A))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (and (tptp.m1_relset_1 C A B) (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B)))) (exists ((A $$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.v11_lattices A) (tptp.v12_lattices A) (tptp.v13_lattices A) (tptp.v14_lattices A) (tptp.v15_lattices A) (tptp.v16_lattices A) (tptp.v17_lattices A) (not (tptp.v3_realset2 A)))) (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) (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 $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (not (tptp.v1_xboole_0 B)) (tptp.v1_finset_1 B))))) (exists ((A $$unsorted)) (and (tptp.l1_struct_0 A) (not (tptp.v3_struct_0 A)))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (not (tptp.v1_xboole_0 B)) (tptp.v1_finset_1 B))))) (forall ((A $$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) (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)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (not (tptp.v3_realset2 A)) (tptp.l3_lattices A)) (= (tptp.k9_lopclset A) (tptp.k8_lopclset A)))) (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 $$unsorted)) (tptp.r1_tarski A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (tptp.m1_subset_1 A B))) _let_4 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 A B) (or (tptp.v1_xboole_0 B) (tptp.r2_hidden A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted)) (= (tptp.r2_hidden C A) (tptp.r2_hidden C B))) (= A B))) _let_3 _let_2 _let_1 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.m1_subset_1 A (tptp.k1_zfmisc_1 B)) (tptp.r1_tarski A B))) (forall ((A $$unsorted)) (= (tptp.k4_xboole_0 tptp.k1_xboole_0 A) tptp.k1_xboole_0)) (forall ((A $$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)) (=> (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.75 )
% 0.22/0.75 % SZS output end Proof for LAT291+1
% 0.22/0.75 % cvc5---1.0.5 exiting
% 0.22/0.75 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------