TSTP Solution File: NUM404+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM404+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n001.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 10:43:42 EDT 2023
% Result : Theorem 21.36s 21.73s
% Output : Proof 21.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUM404+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.11 % Command : do_cvc5 %s %d
% 0.12/0.30 % Computer : n001.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Fri Aug 25 12:32:58 EDT 2023
% 0.12/0.31 % CPUTime :
% 0.15/0.41 %----Proving TF0_NAR, FOF, or CNF
% 21.36/21.73 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.Rzs3WR7qLb/cvc5---1.0.5_30171.p...
% 21.36/21.73 ------- get file name : TPTP file name is NUM404+1
% 21.36/21.73 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_30171.smt2...
% 21.36/21.73 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 21.36/21.73 --- Run --no-e-matching --full-saturate-quant at 5...
% 21.36/21.73 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 21.36/21.73 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 21.36/21.73 % SZS status Theorem for NUM404+1
% 21.36/21.73 % SZS output start Proof for NUM404+1
% 21.36/21.73 (
% 21.36/21.73 (let ((_let_1 (forall ((A $$unsorted)) (not (forall ((B $$unsorted)) (= (tptp.in B A) (tptp.ordinal B))))))) (let ((_let_2 (not _let_1))) (let ((_let_3 (forall ((A $$unsorted)) (=> (tptp.ordinal A) (forall ((B $$unsorted)) (=> (tptp.ordinal B) (not (and (not (tptp.in A B)) (not (= A B)) (not (tptp.in B A)))))))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.ordinal B) (=> (tptp.in A B) (tptp.ordinal A)))))) (let ((_let_5 (tptp.relation tptp.empty_set))) (let ((_let_6 (tptp.empty tptp.empty_set))) (let ((_let_7 (tptp.relation_empty_yielding tptp.empty_set))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((C $$unsorted)) (=> (tptp.in C A) (tptp.in C B))))))) (let ((_let_9 (forall ((A $$unsorted)) (= (tptp.epsilon_connected A) (forall ((B $$unsorted) (C $$unsorted)) (not (and (tptp.in B A) (tptp.in C A) (not (tptp.in B C)) (not (= B C)) (not (tptp.in C B))))))))) (let ((_let_10 (forall ((A $$unsorted)) (= (tptp.epsilon_transitive A) (forall ((B $$unsorted)) (=> (tptp.in B A) (tptp.subset B A))))))) (let ((_let_11 (forall ((A $$unsorted)) (=> (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)) (tptp.ordinal A))))) (let ((_let_12 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))))) (let ((_let_13 (forall ((B $$unsorted)) (= (tptp.ordinal B) (tptp.in B SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))))) (let ((_let_14 (tptp.ordinal SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_72))) (let ((_let_15 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_72 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_16 (= _let_15 _let_14))) (let ((_let_17 (_let_2))) (let ((_let_18 (ASSUME :args _let_17))) (let ((_let_19 (or))) (let ((_let_20 (_let_13))) (let ((_let_21 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_18) :args _let_17) (REWRITE :args ((=> _let_2 (not (not (forall ((B $$unsorted)) (= (tptp.in B SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15) (tptp.ordinal B)))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args _let_20) :args _let_19)) _let_18 :args (_let_13 true _let_1)))) (let ((_let_22 (not _let_16))) (let ((_let_23 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_72 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_57))) (let ((_let_24 (not _let_23))) (let ((_let_25 (tptp.ordinal SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_57))) (let ((_let_26 (not _let_25))) (let ((_let_27 (or _let_26 _let_24 _let_14))) (let ((_let_28 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ordinal B)) (not (tptp.in A B)) (tptp.ordinal A))))) (let ((_let_29 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_30 (or _let_24 _let_15))) (let ((_let_31 (forall ((C $$unsorted)) (or (not (tptp.in C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_57)) (tptp.in C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))))) (let ((_let_32 (not _let_30))) (let ((_let_33 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_57 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_34 (= _let_33 _let_31))) (let ((_let_35 (not _let_31))) (let ((_let_36 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((C $$unsorted)) (or (not (tptp.in C A)) (tptp.in C B))))))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_57 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_39 (not _let_38))) (let ((_let_40 (or _let_39 _let_33))) (let ((_let_41 (forall ((B $$unsorted)) (or (not (tptp.in B SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15)) (tptp.subset B SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))))) (let ((_let_42 (not _let_40))) (let ((_let_43 (tptp.epsilon_transitive SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_44 (= _let_43 _let_41))) (let ((_let_45 (not _let_41))) (let ((_let_46 (forall ((A $$unsorted)) (= (tptp.epsilon_transitive A) (forall ((B $$unsorted)) (or (not (tptp.in B A)) (tptp.subset B A))))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_FMF_FMC_EXH))) (let ((_let_49 (tptp.ordinal SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_50 (tptp.epsilon_connected SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_51 (not _let_50))) (let ((_let_52 (not _let_43))) (let ((_let_53 (or _let_52 _let_51 _let_49))) (let ((_let_54 (forall ((A $$unsorted)) (or (not (tptp.epsilon_transitive A)) (not (tptp.epsilon_connected A)) (tptp.ordinal A))))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (forall ((B $$unsorted) (C $$unsorted)) (or (not (tptp.in B SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15)) (not (tptp.in C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15)) (tptp.in B C) (= B C) (tptp.in C B))))) (let ((_let_57 (= _let_50 _let_56))) (let ((_let_58 (forall ((A $$unsorted)) (= (tptp.epsilon_connected A) (forall ((B $$unsorted) (C $$unsorted)) (or (not (tptp.in B A)) (not (tptp.in C A)) (tptp.in B C) (= B C) (tptp.in C B))))))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_93))) (let ((_let_61 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_93 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94))) (let ((_let_62 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_93 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94))) (let ((_let_63 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_64 (not _let_63))) (let ((_let_65 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_93 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_66 (not _let_65))) (let ((_let_67 (or _let_66 _let_64 _let_62 _let_61 _let_60))) (let ((_let_68 (tptp.ordinal SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_93))) (let ((_let_69 (= _let_65 _let_68))) (let ((_let_70 (tptp.ordinal SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94))) (let ((_let_71 (= _let_63 _let_70))) (let ((_let_72 (not _let_68))) (let ((_let_73 (not _let_70))) (let ((_let_74 (or _let_73 _let_72 _let_60 _let_61 _let_62))) (let ((_let_75 (REFL :args (_let_67)))) (let ((_let_76 (ASSUME :args _let_20))) (let ((_let_77 (forall ((A $$unsorted) (BOUND_VARIABLE_1112 $$unsorted)) (or (not (tptp.ordinal A)) (not (tptp.ordinal BOUND_VARIABLE_1112)) (tptp.in A BOUND_VARIABLE_1112) (= A BOUND_VARIABLE_1112) (tptp.in BOUND_VARIABLE_1112 A))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (not _let_56))) (let ((_let_80 (_let_79))) (let ((_let_81 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_82 (= _let_49 _let_81))) (let ((_let_83 (not _let_49))) (let ((_let_84 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.in A B)) (not (tptp.in B A)))))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (_let_45))) (let ((_let_87 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_86)) :args _let_86)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_41))) (REFL :args (_let_42)) :args _let_19)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_44)) :args ((or _let_43 _let_45 (not _let_44)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_53)) :args ((or _let_49 _let_51 _let_52 (not _let_53)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_82)) :args ((or _let_81 _let_83 (not _let_82)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_85 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_84)))) _let_85 :args ((not _let_81) false _let_84)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_76 :args _let_48) :args _let_20)) _let_21 :args (_let_82 false _let_13)) :args (_let_83 true _let_81 false _let_82)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_57)) :args ((or _let_50 _let_79 (not _let_57)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_80)) :args _let_80)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_79) _let_56))) (REFL :args ((not _let_67))) :args _let_19)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_74)) :args ((or _let_62 _let_61 _let_60 _let_72 _let_73 (not _let_74)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_78 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_93 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_77)))) _let_78 :args (_let_74 false _let_77)) (REORDERING (CNF_EQUIV_POS1 :args (_let_71)) :args ((or _let_64 _let_70 (not _let_71)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_76 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94 QUANTIFIERS_INST_FMF_FMC_EXH)) :args _let_20))) _let_21 :args (_let_71 false _let_13)) (REORDERING (CNF_EQUIV_POS1 :args (_let_69)) :args ((or _let_66 _let_68 (not _let_69)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_76 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_93 QUANTIFIERS_INST_FMF_FMC_EXH)) :args _let_20))) _let_21 :args (_let_69 false _let_13)) (CNF_OR_NEG :args (_let_67 4)) (CNF_OR_NEG :args (_let_67 3)) (CNF_OR_NEG :args (_let_67 2)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_67 1)) (CONG _let_75 (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_63))) :args _let_19)) :args ((or _let_63 _let_67))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_67 0)) (CONG _let_75 (MACRO_SR_PRED_INTRO :args ((= (not _let_66) _let_65))) :args _let_19)) :args ((or _let_65 _let_67))) :args (_let_67 false _let_74 false _let_70 false _let_71 false _let_68 false _let_69 true _let_60 true _let_61 true _let_62 false _let_63 false _let_65)) :args (_let_56 false _let_67)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args _let_48) :args (_let_58))) _let_59 :args (_let_57 false _let_58)) :args (_let_50 false _let_56 false _let_57)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_54))) _let_55 :args (_let_53 false _let_54)) :args (_let_52 true _let_49 false _let_50 false _let_53)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args _let_48) :args (_let_46))) _let_47 :args (_let_44 false _let_46)) :args (_let_45 true _let_43 false _let_44)) :args (_let_42 true _let_41)))) (let ((_let_88 (_let_35))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_88)) :args _let_88)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_31))) (REFL :args (_let_32)) :args _let_19)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_34)) :args ((or _let_33 _let_35 (not _let_34)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_40 1)) _let_87 :args ((not _let_33) true _let_40)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_57 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_FMF_FMC_EXH)) :args (_let_36))) _let_37 :args (_let_34 false _let_36)) :args (_let_35 true _let_33 false _let_34)) :args (_let_32 true _let_31)))) (let ((_let_90 (= _let_38 _let_25))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_76 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_72 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_20))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_16)) :args ((or _let_15 (not _let_14) _let_22))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_30 1)) _let_89 :args ((not _let_15) true _let_30)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_27)) :args ((or _let_26 _let_24 _let_14 (not _let_27)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_90)) :args ((or _let_39 _let_25 (not _let_90)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 0)) (CONG (REFL :args (_let_40)) (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_19)) :args ((or _let_38 _let_40))) _let_87 :args (_let_38 true _let_40)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_76 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_57 QUANTIFIERS_INST_FMF_FMC_EXH)) :args _let_20))) _let_21 :args (_let_90 false _let_13)) :args (_let_25 false _let_38 false _let_90)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_30 0)) (CONG (REFL :args (_let_30)) (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_19)) :args ((or _let_23 _let_30))) _let_89 :args (_let_23 true _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_29 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_72 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_57 QUANTIFIERS_INST_FMF_FMC_EXH)) :args (_let_28))) _let_29 :args (_let_27 false _let_28)) :args (_let_14 false _let_25 false _let_23 false _let_27)) :args (_let_22 true _let_15 false _let_14)) _let_21 :args (false true _let_16 false _let_13)) :args (_let_12 (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.function A))) (forall ((A $$unsorted)) (=> (tptp.ordinal A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)))) (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)))))) _let_11 (forall ((A $$unsorted)) (=> (tptp.empty A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A)))) _let_10 _let_9 _let_8 (forall ((A $$unsorted)) (= (tptp.ordinal A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (and _let_6 _let_5 _let_7) _let_6 (and _let_5 _let_7 (tptp.function tptp.empty_set) (tptp.one_to_one tptp.empty_set) _let_6 (tptp.epsilon_transitive tptp.empty_set) (tptp.epsilon_connected tptp.empty_set) (tptp.ordinal tptp.empty_set)) (and _let_6 _let_5) (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 (tptp.relation A) (tptp.function A) (tptp.one_to_one A) (tptp.empty A) (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal 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 (not (tptp.empty A)) (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal 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 $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) _let_4 _let_3 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) _let_2 (forall ((A $$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)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 21.36/21.73 )
% 21.36/21.73 % SZS output end Proof for NUM404+1
% 21.36/21.73 % cvc5---1.0.5 exiting
% 21.36/21.73 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------