TSTP Solution File: NUM390+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM390+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n010.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 10:43:38 EDT 2023
% Result : Theorem 0.21s 0.59s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : NUM390+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.15 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n010.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Aug 25 11:39:20 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.51 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.59 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.t0qwiFY00K/cvc5---1.0.5_2431.p...
% 0.21/0.59 ------- get file name : TPTP file name is NUM390+1
% 0.21/0.59 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_2431.smt2...
% 0.21/0.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.59 % SZS status Theorem for NUM390+1
% 0.21/0.59 % SZS output start Proof for NUM390+1
% 0.21/0.59 (
% 0.21/0.59 (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.subset B A)))))) (let ((_let_2 (not (forall ((A $$unsorted)) (=> (tptp.epsilon_transitive A) (forall ((B $$unsorted)) (=> (tptp.ordinal B) (forall ((C $$unsorted)) (=> (tptp.ordinal C) (=> (and (tptp.subset A B) (tptp.in B C)) (tptp.in A C))))))))))) (let ((_let_3 (forall ((A $$unsorted)) (=> (tptp.epsilon_transitive A) (forall ((B $$unsorted)) (=> (tptp.ordinal B) (=> (tptp.proper_subset A B) (tptp.in A B)))))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset B C)) (tptp.subset A C))))) (let ((_let_5 (tptp.relation tptp.empty_set))) (let ((_let_6 (tptp.empty tptp.empty_set))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.proper_subset A B) (and (tptp.subset A B) (not (= A B))))))) (let ((_let_8 (forall ((A $$unsorted)) (= (tptp.epsilon_transitive A) (forall ((B $$unsorted)) (=> (tptp.in B A) (tptp.subset B A))))))) (let ((_let_9 (forall ((A $$unsorted)) (=> (tptp.ordinal A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)))))) (let ((_let_10 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_11 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_12 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_13 (not _let_10))) (let ((_let_14 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_15 (not _let_14))) (let ((_let_16 (or _let_15 _let_13))) (let ((_let_17 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.in A B)) (not (tptp.subset B A)))))) (let ((_let_18 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_19 (tptp.proper_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_20 (not _let_19))) (let ((_let_21 (tptp.ordinal SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_22 (not _let_21))) (let ((_let_23 (tptp.epsilon_transitive SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or _let_24 _let_22 _let_20 _let_14))) (let ((_let_26 (forall ((A $$unsorted) (BOUND_VARIABLE_1045 $$unsorted)) (or (not (tptp.epsilon_transitive A)) (not (tptp.ordinal BOUND_VARIABLE_1045)) (not (tptp.proper_subset A BOUND_VARIABLE_1045)) (tptp.in A BOUND_VARIABLE_1045))))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (_let_26))) (let ((_let_29 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_30 (not _let_29))) (let ((_let_31 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_32 (and _let_31 _let_30))) (let ((_let_33 (= _let_19 _let_32))) (let ((_let_34 (_let_7))) (let ((_let_35 (ASSUME :args _let_34))) (let ((_let_36 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_37 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_38 (not _let_36))) (let ((_let_39 (tptp.ordinal SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_40 (not _let_39))) (let ((_let_41 (not _let_31))) (let ((_let_42 (or _let_24 _let_22 _let_41 _let_40 _let_38 _let_37))) (let ((_let_43 (forall ((A $$unsorted) (BOUND_VARIABLE_1095 $$unsorted) (BOUND_VARIABLE_1093 $$unsorted)) (or (not (tptp.epsilon_transitive A)) (not (tptp.ordinal BOUND_VARIABLE_1093)) (not (tptp.subset A BOUND_VARIABLE_1093)) (not (tptp.ordinal BOUND_VARIABLE_1095)) (not (tptp.in BOUND_VARIABLE_1093 BOUND_VARIABLE_1095)) (tptp.in A BOUND_VARIABLE_1095))))) (let ((_let_44 (not _let_42))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_46 (or))) (let ((_let_47 (not _let_43))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_45) :args (_let_47))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_43))) (REFL :args (_let_44)) :args _let_46)) _let_45 :args (_let_44 true _let_43)))) (let ((_let_49 (REFL :args (_let_42)))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 4)) (CONG _let_49 (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_36))) :args _let_46)) :args ((or _let_36 _let_42))) _let_48 :args (_let_36 true _let_42)))) (let ((_let_51 (not _let_37))) (let ((_let_52 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_42 5)) _let_48 :args (_let_51 true _let_42)))) (let ((_let_53 (ASSUME :args (_let_36)))) (let ((_let_54 (ASSUME :args (_let_29)))) (let ((_let_55 (ASSUME :args (_let_51)))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 2)) (CONG _let_49 (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_31))) :args _let_46)) :args ((or _let_31 _let_42))) _let_48 :args (_let_31 true _let_42)))) (let ((_let_57 (_let_32))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 0)) (CONG _let_49 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_46)) :args ((or _let_23 _let_42))) _let_48 :args (_let_23 true _let_42)))) (let ((_let_59 (or _let_38 _let_11))) (let ((_let_60 (forall ((B $$unsorted)) (or (not (tptp.in B SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)) (tptp.subset B SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))))) (let ((_let_61 (tptp.epsilon_transitive SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_62 (= _let_61 _let_60))) (let ((_let_63 (forall ((A $$unsorted)) (= (tptp.epsilon_transitive A) (forall ((B $$unsorted)) (or (not (tptp.in B A)) (tptp.subset B A))))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (and _let_61 (tptp.epsilon_connected SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)))) (let ((_let_66 (or _let_40 _let_65))) (let ((_let_67 (forall ((A $$unsorted)) (or (not (tptp.ordinal A)) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)))))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 3)) (CONG _let_49 (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_39))) :args _let_46)) :args ((or _let_39 _let_42))) _let_48 :args (_let_39 true _let_42)))) (let ((_let_70 (_let_60))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_38 _let_11 (not _let_59)))) _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_70) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.in B SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14) false))))) :args _let_70)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_62)) :args ((or (not _let_61) _let_60 (not _let_62)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_65 0)) :args ((or _let_61 (not _let_65)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_40 _let_65 (not _let_66)))) _let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ordinal A) false))))) :args (_let_67))) _let_68 :args (_let_66 false _let_67)) :args (_let_65 false _let_39 false _let_66)) :args (_let_61 false _let_65)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.epsilon_transitive A)))) :args (_let_63))) _let_64 :args (_let_62 false _let_63)) :args (_let_60 false _let_61 false _let_62)) :args (_let_59 false _let_60)) :args (_let_11 false _let_36 false _let_59)))) (let ((_let_72 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_73 (not _let_12))) (let ((_let_74 (and _let_72 _let_73))) (let ((_let_75 (not _let_11))) (let ((_let_76 (or _let_41 _let_75 _let_72))) (let ((_let_77 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subset A B)) (not (tptp.subset B C)) (tptp.subset A C))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (tptp.proper_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_80 (= _let_79 _let_74))) (let ((_let_81 (not _let_74))) (let ((_let_82 (not _let_79))) (let ((_let_83 (or _let_24 _let_40 _let_82 _let_37))) (let ((_let_84 (not _let_72))) (let ((_let_85 (_let_74))) (let ((_let_86 (ASSUME :args (_let_13)))) (let ((_let_87 (ASSUME :args (_let_12)))) (let ((_let_88 (ASSUME :args (_let_11)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_86 _let_87 _let_88) :args (_let_12 _let_13 _let_11)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_88)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15)) (SYMM _let_87) :args (APPLY_UF tptp.subset)) (FALSE_INTRO _let_86))) :args (_let_13 _let_12 _let_11)) :args ((not (and _let_12 _let_13 _let_11)) SB_LITERAL))) (CONG (REFL :args (_let_73)) (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_10))) (REFL :args (_let_75)) :args _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_85) (CONG (REFL :args _let_85) (REFL :args (_let_84)) (MACRO_SR_PRED_INTRO :args ((= (not _let_73) _let_12))) :args _let_46)) :args ((or _let_12 _let_74 _let_84))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_80)) :args ((or _let_79 _let_81 (not _let_80)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_83)) :args ((or _let_24 _let_40 _let_37 _let_82 (not _let_83)))) _let_58 _let_69 _let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.in A BOUND_VARIABLE_1045) true))))) :args _let_28)) _let_27 :args (_let_83 false _let_26)) :args (_let_82 false _let_23 false _let_39 true _let_37 false _let_83)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.proper_subset A B)))) :args _let_34)) _let_35 :args (_let_80 false _let_7)) :args (_let_81 true _let_79 false _let_80)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_41 _let_72 _let_75 (not _let_76)))) _let_56 _let_71 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.subset A B) false)) (not (= (tptp.subset B C) false))))) :args (_let_77))) _let_78 :args (_let_76 false _let_77)) :args (_let_72 false _let_31 false _let_11 false _let_76)) :args (_let_12 true _let_74 false _let_72)) _let_71 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_16)) :args ((or _let_15 _let_13 (not _let_16)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_24 _let_22 _let_20 _let_14 (not _let_25)))) _let_58 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 1)) (CONG _let_49 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_46)) :args ((or _let_21 _let_42))) _let_48 :args (_let_21 true _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_33)) :args ((or _let_19 (not _let_32) (not _let_33)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_57) (CONG (REFL :args _let_57) (REFL :args (_let_41)) (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_46)) :args ((or _let_41 _let_29 _let_32))) _let_56 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_53 _let_54 _let_55) :args (_let_36 _let_51 _let_29)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_55)) (CONG (SYMM (SYMM _let_54)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)) :args (APPLY_UF tptp.in)) (TRUE_INTRO _let_53))) :args (_let_36 _let_29 _let_51)) :args ((not (and _let_36 _let_51 _let_29)) SB_LITERAL))) (CONG (REFL :args (_let_38)) (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_37))) (REFL :args (_let_30)) :args _let_46)) _let_52 _let_50 :args (_let_30 true _let_37 false _let_36)) :args (_let_32 false _let_31 true _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset A B)))) :args _let_34)) _let_35 :args (_let_33 false _let_7)) :args (_let_19 false _let_32 false _let_33)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.proper_subset A BOUND_VARIABLE_1045) false))))) :args _let_28)) _let_27 :args (_let_25 false _let_26)) :args (_let_14 false _let_23 false _let_21 false _let_19 false _let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.in A B) false))))) :args (_let_17))) _let_18 :args (_let_16 false _let_17)) :args (_let_13 false _let_14 false _let_16)) :args (false false _let_12 false _let_11 true _let_10)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.proper_subset A B) (not (tptp.proper_subset B A)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.function A))) _let_9 (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.relation A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.function A))) (let ((_let_2 (tptp.relation A))) (=> (and _let_2 (tptp.empty A) _let_1) (and _let_2 _let_1 (tptp.one_to_one A)))))) (forall ((A $$unsorted)) (=> (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)) (tptp.ordinal A))) _let_8 _let_7 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (and _let_6 _let_5 (tptp.relation_empty_yielding tptp.empty_set)) _let_6 (and _let_6 _let_5) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.proper_subset A A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A))) (exists ((A $$unsorted)) (and (tptp.empty A) (tptp.relation A))) (exists ((A $$unsorted)) (tptp.empty A)) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.empty A) (tptp.function A))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.relation A))) (exists ((A $$unsorted)) (not (tptp.empty A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_non_empty A) (tptp.function A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) _let_4 _let_3 _let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.in A B) (tptp.element B (tptp.powerset C))) (tptp.element A C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))) _let_1 (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.60 )
% 0.21/0.60 % SZS output end Proof for NUM390+1
% 0.21/0.60 % cvc5---1.0.5 exiting
% 0.21/0.60 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------