%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM554+3 : TPTP v8.1.2. Released v4.0.0.
% 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 : Thu Aug 31 10:45:02 EDT 2023

% Result   : Theorem 0.50s 0.77s
% Output   : Proof 0.50s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : NUM554+3 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13  % 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   : Fri Aug 25 15:17:51 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.20/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.50/0.77  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.zunU6XeRff/cvc5---1.0.5_32473.p...
% 0.50/0.77  ------- get file name : TPTP file name is NUM554+3
% 0.50/0.77  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_32473.smt2...
% 0.50/0.77  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.50/0.77  % SZS status Theorem for NUM554+3
% 0.50/0.77  % SZS output start Proof for NUM554+3
% 0.50/0.77  (
% 0.50/0.77  (let ((_let_1 (tptp.slbdtsldtrb0 tptp.xS tptp.xk))) (let ((_let_2 (tptp.sbrdtbr0 tptp.xP))) (let ((_let_3 (tptp.aSubsetOf0 tptp.xP tptp.xS))) (let ((_let_4 (not (or (and (or (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xP) (tptp.aElementOf0 W0 tptp.xS))) _let_3) (= _let_2 tptp.xk)) (tptp.aElementOf0 tptp.xP _let_1))))) (let ((_let_5 (tptp.sdtmndt0 tptp.xQ tptp.xy))) (let ((_let_6 (tptp.sdtpldt0 _let_5 tptp.xx))) (let ((_let_7 (= tptp.xP _let_6))) (let ((_let_8 (tptp.aSet0 _let_5))) (let ((_let_9 (and _let_8 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.sdtmndt0 tptp.xQ tptp.xy)) (and (tptp.aElement0 W0) (tptp.aElementOf0 W0 tptp.xQ) (not (= W0 tptp.xy))))) (tptp.aSet0 tptp.xP) (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 tptp.xP) (and (tptp.aElement0 W0) (or (tptp.aElementOf0 W0 (tptp.sdtmndt0 tptp.xQ tptp.xy)) (= W0 tptp.xx))))) _let_7))) (let ((_let_10 (tptp.aElementOf0 tptp.xx tptp.xQ))) (let ((_let_11 (not _let_10))) (let ((_let_12 (tptp.aElementOf0 tptp.xy tptp.xQ))) (let ((_let_13 (tptp.aElement0 tptp.xy))) (let ((_let_14 (and _let_13 _let_12))) (let ((_let_15 (tptp.sbrdtbr0 tptp.xQ))) (let ((_let_16 (= _let_15 tptp.xk))) (let ((_let_17 (tptp.isFinite0 tptp.xQ))) (let ((_let_18 (tptp.aSet0 tptp.xQ))) (let ((_let_19 (and _let_18 _let_17 _let_16))) (let ((_let_20 (and _let_18 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xQ) (tptp.aElementOf0 W0 tptp.xS))) (tptp.aSubsetOf0 tptp.xQ tptp.xS) _let_16 (tptp.aElementOf0 tptp.xQ _let_1)))) (let ((_let_21 (tptp.aElementOf0 tptp.xx tptp.xS))) (let ((_let_22 (tptp.slbdtsldtrb0 tptp.xT tptp.xk))) (let ((_let_23 (tptp.aSet0 tptp.xS))) (let ((_let_24 (and _let_23 (tptp.aSet0 tptp.xT) (not (= tptp.xk tptp.sz00))))) (let ((_let_25 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.isFinite0 W0) (tptp.aElementOf0 W1 W0)) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 (tptp.sdtmndt0 W0 W1))) (tptp.sbrdtbr0 W0)))))))) (let ((_let_26 (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isFinite0 W0)) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (=> (not (tptp.aElementOf0 W1 W0)) (= (tptp.sbrdtbr0 (tptp.sdtpldt0 W0 W1)) (tptp.szszuzczcdt0 (tptp.sbrdtbr0 W0)))))))))) (let ((_let_27 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.isFinite0 W1)) (tptp.isFinite0 (tptp.sdtmndt0 W1 W0)))))))) (let ((_let_28 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))))) (let ((_let_29 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xS))) (let ((_let_30 (= tptp.xx SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_31 (ASSUME :args (_let_21)))) (let ((_let_32 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xP))) (let ((_let_33 (not _let_32))) (let ((_let_34 (or _let_33 _let_29))) (let ((_let_35 (not _let_29))) (let ((_let_36 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xP)) (tptp.aElementOf0 W0 tptp.xS))))) (let ((_let_37 (not _let_34))) (let ((_let_38 (or _let_36 _let_3))) (let ((_let_39 (not _let_36))) (let ((_let_40 (= tptp.xk _let_2))) (let ((_let_41 (tptp.szszuzczcdt0 (tptp.sbrdtbr0 _let_5)))) (let ((_let_42 (= _let_15 _let_41))) (let ((_let_43 (= _let_41 (tptp.sbrdtbr0 _let_6)))) (let ((_let_44 (= tptp.xk _let_15))) (let ((_let_45 (not _let_12))) (let ((_let_46 (not _let_17))) (let ((_let_47 (not _let_18))) (let ((_let_48 (or _let_47 _let_46 _let_45 _let_42))) (let ((_let_49 (forall ((W0 $$unsorted) (BOUND_VARIABLE_2027 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.isFinite0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_2027 W0)) (= (tptp.sbrdtbr0 W0) (tptp.szszuzczcdt0 (tptp.sbrdtbr0 (tptp.sdtmndt0 W0 BOUND_VARIABLE_2027)))))))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (1))) (let ((_let_52 (ASSUME :args (_let_14)))) (let ((_let_53 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))) :args _let_51))) (let ((_let_54 (0))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (AND_ELIM _let_55 :args _let_54))) (let ((_let_57 (tptp.aElementOf0 tptp.xx _let_5))) (let ((_let_58 (tptp.aElement0 tptp.xx))) (let ((_let_59 (not _let_58))) (let ((_let_60 (tptp.isFinite0 _let_5))) (let ((_let_61 (not _let_60))) (let ((_let_62 (not _let_8))) (let ((_let_63 (or _let_62 _let_61 _let_59 _let_57 _let_43))) (let ((_let_64 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1996 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.isFinite0 W0)) (not (tptp.aElement0 BOUND_VARIABLE_1996)) (tptp.aElementOf0 BOUND_VARIABLE_1996 W0) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 W0)) (tptp.sbrdtbr0 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1996))))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (and _let_58 _let_10 (not (= tptp.xx tptp.xy))))) (let ((_let_67 (= _let_57 _let_66))) (let ((_let_68 (not _let_57))) (let ((_let_69 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.sdtmndt0 tptp.xQ tptp.xy)) (and (tptp.aElement0 W0) (tptp.aElementOf0 W0 tptp.xQ) (not (= tptp.xy W0))))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (AND_ELIM _let_70 :args _let_51))) (let ((_let_72 (_let_69))) (let ((_let_73 (ASSUME :args _let_72))) (let ((_let_74 (not _let_66))) (let ((_let_75 (not _let_21))) (let ((_let_76 (not _let_23))) (let ((_let_77 (or _let_76 _let_75 _let_58))) (let ((_let_78 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1520 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1520 W0)) (tptp.aElement0 BOUND_VARIABLE_1520))))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (not _let_13))) (let ((_let_81 (or _let_80 _let_47 _let_46 _let_60))) (let ((_let_82 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1849 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aSet0 BOUND_VARIABLE_1849)) (not (tptp.isFinite0 BOUND_VARIABLE_1849)) (tptp.isFinite0 (tptp.sdtmndt0 BOUND_VARIABLE_1849 W0)))))) (let ((_let_83 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_84 (3))) (let ((_let_85 (and _let_7 _let_44 _let_43 _let_42))) (let ((_let_86 (ASSUME :args (_let_7)))) (let ((_let_87 (ASSUME :args (_let_43)))) (let ((_let_88 (ASSUME :args (_let_42)))) (let ((_let_89 (ASSUME :args (_let_44)))) (let ((_let_90 (or))) (let ((_let_91 (_let_39))) (let ((_let_92 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_91)) :args _let_91)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_36))) (REFL :args (_let_37)) :args _let_90)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_38 0)) (MACRO_RESOLUTION_TRUST (NOT_AND (NOT_OR_ELIM (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) :args _let_54)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_85)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_86 _let_87 _let_88 _let_89) (SCOPE (TRANS (SYMM (SYMM _let_89)) (SYMM (SYMM _let_88)) (SYMM (SYMM _let_87)) (CONG (SYMM _let_86) :args (APPLY_UF tptp.sbrdtbr0))) :args (_let_7 _let_43 _let_42 _let_44))) :args (_let_7 _let_44 _let_43 _let_42))) :args (true _let_85)) :args ((or _let_40 (not _let_44) (not _let_7) (not _let_43) (not _let_42)))) (AND_ELIM _let_55 :args _let_84) (AND_ELIM _let_70 :args (4)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_63)) :args ((or _let_62 _let_61 _let_59 _let_57 _let_43 (not _let_63)))) (AND_ELIM _let_70 :args _let_54) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_81)) :args ((or _let_47 _let_46 _let_80 _let_60 (not _let_81)))) _let_56 _let_53 (AND_ELIM _let_52 :args _let_54) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_83 :args (tptp.xy tptp.xQ QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtmndt0 BOUND_VARIABLE_1849 W0)))) :args (_let_82))) _let_83 :args (_let_81 false _let_82)) :args (_let_60 false _let_18 false _let_17 false _let_13 false _let_81)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_77)) :args ((or _let_76 _let_75 _let_58 (not _let_77)))) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))) :args _let_54) _let_31 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_79 :args (tptp.xS tptp.xx QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 BOUND_VARIABLE_1520 W0) false))))) :args (_let_78))) _let_79 :args (_let_77 false _let_78)) :args (_let_58 false _let_23 false _let_21 false _let_77)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_67)) :args ((or _let_66 _let_68 (not _let_67)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_66 1)) :args ((or _let_10 _let_74))) (ASSUME :args (_let_11)) :args (_let_74 true _let_10)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_73 :args (tptp.xx QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aElementOf0 W0 tptp.xQ)))) :args _let_72))) _let_71 :args (_let_67 false _let_69)) :args (_let_68 true _let_66 false _let_67)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (_let_5 tptp.xx QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtpldt0 W0 BOUND_VARIABLE_1996)))) :args (_let_64))) _let_65 :args (_let_63 false _let_64)) :args (_let_43 false _let_8 false _let_60 false _let_58 true _let_57 false _let_63)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_48)) :args ((or _let_47 _let_46 _let_45 _let_42 (not _let_48)))) _let_56 _let_53 (AND_ELIM _let_52 :args _let_51) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (tptp.xQ tptp.xy QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 BOUND_VARIABLE_2027 W0) false))))) :args (_let_49))) _let_50 :args (_let_48 false _let_49)) :args (_let_42 false _let_18 false _let_17 false _let_12 false _let_48)) :args (_let_40 false _let_44 false _let_7 false _let_43 false _let_42)) :args ((not _let_38) false _let_40)) :args (_let_39 true _let_38)) :args (_let_37 true _let_36)))) (let ((_let_93 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_34 1)) _let_92 :args (_let_35 true _let_34)))) (let ((_let_94 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_5))) (let ((_let_95 (or _let_94 _let_30))) (let ((_let_96 (tptp.aElement0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_97 (and _let_96 _let_95))) (let ((_let_98 (= _let_32 _let_97))) (let ((_let_99 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 tptp.xP) (and (tptp.aElement0 W0) (or (tptp.aElementOf0 W0 (tptp.sdtmndt0 tptp.xQ tptp.xy)) (= tptp.xx W0))))))) (let ((_let_100 (_let_99))) (let ((_let_101 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xQ))) (let ((_let_102 (and _let_96 _let_101 (not (= tptp.xy SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))) (let ((_let_103 (= _let_94 _let_102))) (let ((_let_104 (not _let_94))) (let ((_let_105 (not _let_102))) (let ((_let_106 (not _let_101))) (let ((_let_107 (or _let_106 _let_29))) (let ((_let_108 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xQ)) (tptp.aElementOf0 W0 tptp.xS))))) (let ((_let_109 (_let_108))) (let ((_let_110 (ASSUME :args (_let_35)))) (let ((_let_111 (ASSUME :args (_let_30)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_110 _let_111 _let_31) :args (_let_21 _let_35 _let_30)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_31)) (CONG (SYMM (SYMM _let_111)) (REFL :args (tptp.xS)) :args (APPLY_UF tptp.aElementOf0)) (FALSE_INTRO _let_110))) :args (_let_35 _let_30 _let_21)) :args ((not (and _let_21 _let_35 _let_30)) SB_LITERAL))) (CONG (REFL :args (_let_75)) (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_29))) (REFL :args ((not _let_30))) :args _let_90)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_95)) :args ((or _let_94 _let_30 (not _let_95)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_103)) :args ((or _let_104 _let_102 (not _let_103)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_102 1)) :args ((or _let_101 _let_105))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_107)) :args ((or _let_29 _let_106 (not _let_107)))) _let_93 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_109) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 W0 tptp.xS) true))))) :args _let_109)) (AND_ELIM _let_55 :args _let_51) :args (_let_107 false _let_108)) :args (_let_106 true _let_29 false _let_107)) :args (_let_105 true _let_101)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aElementOf0 W0 _let_5)))) :args _let_72)) _let_71 :args (_let_103 false _let_69)) :args (_let_104 true _let_102 false _let_103)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_97 1)) :args ((or _let_95 (not _let_97)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_98)) :args ((or _let_33 _let_97 (not _let_98)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 0)) (CONG (REFL :args (_let_34)) (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_90)) :args ((or _let_32 _let_34))) _let_92 :args (_let_32 true _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_100) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aElementOf0 W0 tptp.xP)))) :args _let_100)) (AND_ELIM _let_70 :args _let_84) :args (_let_98 false _let_99)) :args (_let_97 false _let_32 false _let_98)) :args (_let_95 false _let_97)) :args (_let_30 true _let_94 false _let_95)) _let_93 _let_31 :args (false false _let_30 true _let_29 false _let_21)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)) _let_28 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (=> (tptp.isFinite0 W0) true))) (forall ((W0 $$unsorted)) (= (= W0 tptp.slcrc0) (and (tptp.aSet0 W0) (not (exists ((W1 $$unsorted)) (tptp.aElementOf0 W1 W0)))))) (tptp.isFinite0 tptp.slcrc0) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (=> (tptp.isCountable0 W0) true))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isCountable0 W0)) (not (tptp.isFinite0 W0)))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isCountable0 W0)) (not (= W0 tptp.slcrc0)))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (= (tptp.aSubsetOf0 W1 W0) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 W0)))))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isFinite0 W0)) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (tptp.isFinite0 W1))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (tptp.aSubsetOf0 W0 W0))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aSet0 W1)) (=> (and (tptp.aSubsetOf0 W0 W1) (tptp.aSubsetOf0 W1 W0)) (= W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aSet0 W1) (tptp.aSet0 W2)) (=> (and (tptp.aSubsetOf0 W0 W1) (tptp.aSubsetOf0 W1 W2)) (tptp.aSubsetOf0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aElement0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtpldt0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aElement0 W3) (or (tptp.aElementOf0 W3 W0) (= W3 W1)))))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aElement0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aElement0 W3) (tptp.aElementOf0 W3 W0) (not (= W3 W1)))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (= (tptp.sdtpldt0 (tptp.sdtmndt0 W0 W1) W1) W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aSet0 W1)) (=> (not (tptp.aElementOf0 W0 W1)) (= (tptp.sdtmndt0 (tptp.sdtpldt0 W1 W0) W0) W1)))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.isCountable0 W1)) (tptp.isCountable0 (tptp.sdtpldt0 W1 W0)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.isCountable0 W1)) (tptp.isCountable0 (tptp.sdtmndt0 W1 W0)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.isFinite0 W1)) (tptp.isFinite0 (tptp.sdtpldt0 W1 W0)))))) _let_27 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0)) (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szszuzczcdt0 W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (and (tptp.aElementOf0 _let_1 tptp.szNzAzT0) (not (= _let_1 tptp.sz00)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (= (tptp.szszuzczcdt0 W0) (tptp.szszuzczcdt0 W1)) (= W0 W1)))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (or (= W0 tptp.sz00) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.szNzAzT0) (= W0 (tptp.szszuzczcdt0 W1))))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (not (= W0 (tptp.szszuzczcdt0 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (tptp.sdtlseqdt0 W0 W1) true))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 tptp.sz00 W0))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (not (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W0) tptp.sz00)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (= (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W0) (tptp.szszuzczcdt0 W1))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 W0 (tptp.szszuzczcdt0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 W0 W0))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0) (tptp.aElementOf0 W2 tptp.szNzAzT0)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (or (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W1) W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (tptp.iLess0 W0 W1) true))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.iLess0 W0 (tptp.szszuzczcdt0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (tptp.aElement0 (tptp.sbrdtbr0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (= (tptp.aElementOf0 (tptp.sbrdtbr0 W0) tptp.szNzAzT0) (tptp.isFinite0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (= (= (tptp.sbrdtbr0 W0) tptp.sz00) (= W0 tptp.slcrc0)))) _let_26 _let_25 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.isFinite0 W0) (tptp.aSubsetOf0 W1 W0)) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 W1) (tptp.sbrdtbr0 W0)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (and (tptp.isFinite0 W0) (tptp.sdtlseqdt0 W1 (tptp.sbrdtbr0 W0))) (exists ((W2 $$unsorted)) (and (tptp.aSubsetOf0 W2 W0) (= (tptp.sbrdtbr0 W2) W1)))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSubsetOf0 W0 tptp.szNzAzT0) (not (= W0 tptp.slcrc0))) (forall ((W1 $$unsorted)) (= (= W1 (tptp.szmzizndt0 W0)) (and (tptp.aElementOf0 W1 W0) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W0) (tptp.sdtlseqdt0 W1 W2)))))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSubsetOf0 W0 tptp.szNzAzT0) (tptp.isFinite0 W0) (not (= W0 tptp.slcrc0))) (forall ((W1 $$unsorted)) (= (= W1 (tptp.szmzazxdt0 W0)) (and (tptp.aElementOf0 W1 W0) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W0) (tptp.sdtlseqdt0 W2 W1)))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.szmzizndt0 W1))) (let ((_let_2 (tptp.szmzizndt0 W0))) (=> (and (tptp.aSubsetOf0 W0 tptp.szNzAzT0) (tptp.aSubsetOf0 W1 tptp.szNzAzT0) (not (= W0 tptp.slcrc0)) (not (= W1 tptp.slcrc0))) (=> (and (tptp.aElementOf0 _let_2 W1) (tptp.aElementOf0 _let_1 W0)) (= _let_2 _let_1)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (= (= W1 (tptp.slbdtrb0 W0)) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (= (tptp.aElementOf0 W2 W1) (and (tptp.aElementOf0 W2 tptp.szNzAzT0) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W2) W0))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.isFinite0 (tptp.slbdtrb0 W0)))) (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (= (tptp.aElementOf0 W0 (tptp.slbdtrb0 (tptp.szszuzczcdt0 W1))) (or (tptp.aElementOf0 W0 (tptp.slbdtrb0 W1)) (= W0 W1))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (= (tptp.sdtlseqdt0 W0 W1) (tptp.aSubsetOf0 (tptp.slbdtrb0 W0) (tptp.slbdtrb0 W1))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSubsetOf0 W0 tptp.szNzAzT0) (tptp.isFinite0 W0)) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.szNzAzT0) (tptp.aSubsetOf0 W0 (tptp.slbdtrb0 W1)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (= (tptp.sbrdtbr0 (tptp.slbdtrb0 W0)) W0))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.slbdtsldtrb0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aSubsetOf0 W3 W0) (= (tptp.sbrdtbr0 W3) W1))))))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isFinite0 W0)) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.szNzAzT0) (tptp.isFinite0 (tptp.slbdtsldtrb0 W0 W1)))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (not (tptp.isFinite0 W0))) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.szNzAzT0) (not (= (tptp.slbdtsldtrb0 W0 W1) tptp.slcrc0)))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isCountable0 W0)) (forall ((W1 $$unsorted)) (=> (and (tptp.aElementOf0 W1 tptp.szNzAzT0) (not (= W1 tptp.sz00))) (tptp.isCountable0 (tptp.slbdtsldtrb0 W0 W1)))))) (tptp.aElementOf0 tptp.xk tptp.szNzAzT0) _let_24 (and (tptp.aSet0 _let_1) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 tptp.xS tptp.xk)))) (let ((_let_2 (= (tptp.sbrdtbr0 W0) tptp.xk))) (let ((_let_3 (tptp.aSubsetOf0 W0 tptp.xS))) (let ((_let_4 (tptp.aSet0 W0))) (and (=> _let_1 (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xS))) _let_3 _let_2)) (=> (and (or (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xS)))) _let_3) _let_2) _let_1))))))) (tptp.aSet0 _let_22) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 tptp.xT tptp.xk)))) (let ((_let_2 (= (tptp.sbrdtbr0 W0) tptp.xk))) (let ((_let_3 (tptp.aSubsetOf0 W0 tptp.xT))) (let ((_let_4 (tptp.aSet0 W0))) (and (=> _let_1 (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xT))) _let_3 _let_2)) (=> (and (or (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xT)))) _let_3) _let_2) _let_1))))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 tptp.xS tptp.xk)) (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 tptp.xT tptp.xk)))) (tptp.aSubsetOf0 _let_1 _let_22) (not (=> (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 tptp.xS tptp.xk)))) (let ((_let_2 (= (tptp.sbrdtbr0 W0) tptp.xk))) (let ((_let_3 (tptp.aSubsetOf0 W0 tptp.xS))) (let ((_let_4 (tptp.aSet0 W0))) (and (=> _let_1 (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xS))) _let_3 _let_2)) (=> (and (or (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xS)))) _let_3) _let_2) _let_1))))))) (or (not (exists ((W0 $$unsorted)) (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 tptp.xS tptp.xk)))) (= _let_1 tptp.slcrc0))))) _let_21 _let_20 _let_19 _let_14 _let_11 _let_11 _let_9 _let_4 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.50/0.78  )
% 0.50/0.78  % SZS output end Proof for NUM554+3
% 0.50/0.78  % cvc5---1.0.5 exiting
% 0.64/0.78  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------