%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM564+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n018.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 10:45:07 EDT 2023

% Result   : Theorem 25.54s 25.99s
% Output   : Proof 25.54s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : NUM564+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11  % Command    : do_cvc5 %s %d
% 0.11/0.31  % Computer : n018.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit   : 300
% 0.11/0.31  % WCLimit    : 300
% 0.11/0.31  % DateTime   : Fri Aug 25 09:23:58 EDT 2023
% 0.11/0.31  % CPUTime    : 
% 0.15/0.44  %----Proving TF0_NAR, FOF, or CNF
% 25.54/25.99  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.g0pHpZy8S3/cvc5---1.0.5_11585.p...
% 25.54/25.99  ------- get file name : TPTP file name is NUM564+1
% 25.54/25.99  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_11585.smt2...
% 25.54/25.99  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 25.54/25.99  --- Run --no-e-matching --full-saturate-quant at 5...
% 25.54/25.99  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 25.54/25.99  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.54/25.99  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 25.54/25.99  % SZS status Theorem for NUM564+1
% 25.54/25.99  % SZS output start Proof for NUM564+1
% 25.54/25.99  (
% 25.54/25.99  (let ((_let_1 (not (tptp.aElementOf0 tptp.slcrc0 (tptp.slbdtsldtrb0 tptp.xS tptp.sz00))))) (let ((_let_2 (= tptp.xK tptp.sz00))) (let ((_let_3 (tptp.szDzozmdt0 tptp.xc))) (let ((_let_4 (tptp.slbdtsldtrb0 tptp.xS tptp.xK))) (let ((_let_5 (= _let_3 _let_4))) (let ((_let_6 (and (tptp.aFunction0 tptp.xc) _let_5 (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 tptp.xc _let_3) tptp.xT)))) (let ((_let_7 (tptp.aSubsetOf0 tptp.xS tptp.szNzAzT0))) (let ((_let_8 (and _let_7 (tptp.isCountable0 tptp.xS)))) (let ((_let_9 (tptp.aElementOf0 tptp.xK tptp.szNzAzT0))) (let ((_let_10 (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))))))))))) (let ((_let_11 (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0))) (let ((_let_12 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (= (= (tptp.sbrdtbr0 W0) tptp.sz00) (= W0 tptp.slcrc0)))))) (let ((_let_13 (tptp.aSet0 tptp.szNzAzT0))) (let ((_let_14 (and _let_13 (tptp.isCountable0 tptp.szNzAzT0)))) (let ((_let_15 (forall ((W0 $$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)))))))))) (let ((_let_16 (forall ((W0 $$unsorted)) (= (= W0 tptp.slcrc0) (and (tptp.aSet0 W0) (not (exists ((W1 $$unsorted)) (tptp.aElementOf0 W1 W0)))))))) (let ((_let_17 (forall ((W1 $$unsorted)) (not (tptp.aElementOf0 W1 (tptp.slbdtrb0 tptp.xK)))))) (let ((_let_18 (tptp.slbdtrb0 tptp.xK))) (let ((_let_19 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_18))) (let ((_let_20 (tptp.aSet0 _let_18))) (let ((_let_21 (and _let_20 _let_17))) (let ((_let_22 (forall ((W0 $$unsorted)) (= (and (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (not (tptp.aElementOf0 W1 W0)))) (= W0 (tptp.slbdtrb0 tptp.xK)))))) (let ((_let_23 (AND_INTRO (SYMM (ASSUME :args (_let_2))) (SYMM (ASSUME :args (_let_11)))))) (let ((_let_24 (EQ_RESOLVE (ASSUME :args (_let_16)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_23 :args ((forall ((W0 $$unsorted)) (= (= tptp.slcrc0 W0) (and (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (not (tptp.aElementOf0 W1 W0)))))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_25 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_24 :args (_let_18 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_22)))) _let_24 :args (_let_21 false _let_22)))) (let ((_let_26 (not _let_21))) (let ((_let_27 (not _let_19))) (let ((_let_28 (or _let_27 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 tptp.xS)))) (let ((_let_29 (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 (tptp.slbdtrb0 tptp.xK))) (tptp.aElementOf0 W2 tptp.xS))))) (let ((_let_30 (not _let_28))) (let ((_let_31 (and _let_20 _let_29))) (let ((_let_32 (not _let_29))) (let ((_let_33 (tptp.aSubsetOf0 _let_18 tptp.xS))) (let ((_let_34 (= _let_33 _let_31))) (let ((_let_35 (not _let_31))) (let ((_let_36 (tptp.aSet0 tptp.xS))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_37 _let_34))) (let ((_let_39 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1712 $$unsorted)) (or (not (tptp.aSet0 W0)) (= (tptp.aSubsetOf0 BOUND_VARIABLE_1712 W0) (and (tptp.aSet0 BOUND_VARIABLE_1712) (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 BOUND_VARIABLE_1712)) (tptp.aElementOf0 W2 W0))))))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (_let_39))) (let ((_let_42 (and _let_36 (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 tptp.xS)) (tptp.aElementOf0 W2 tptp.szNzAzT0)))))) (let ((_let_43 (= _let_7 _let_42))) (let ((_let_44 (not _let_13))) (let ((_let_45 (or _let_44 _let_43))) (let ((_let_46 (0))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_42 0)) :args ((or _let_36 (not _let_42)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_43)) :args ((or (not _let_7) _let_42 (not _let_43)))) (AND_ELIM (ASSUME :args (_let_8)) :args _let_46) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_45)) :args ((or _let_44 _let_43 (not _let_45)))) (AND_ELIM (ASSUME :args (_let_14)) :args _let_46) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (tptp.szNzAzT0 tptp.xS QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aSubsetOf0 BOUND_VARIABLE_1712 W0)))) :args _let_41)) _let_40 :args (_let_45 false _let_39)) :args (_let_43 false _let_13 false _let_45)) :args (_let_42 false _let_7 false _let_43)) :args (_let_36 false _let_42)))) (let ((_let_48 (= tptp.xK (tptp.sbrdtbr0 _let_18)))) (let ((_let_49 (and _let_33 _let_48))) (let ((_let_50 (not _let_33))) (let ((_let_51 (tptp.aElementOf0 _let_18 _let_3))) (let ((_let_52 (= _let_51 _let_49))) (let ((_let_53 (not _let_49))) (let ((_let_54 (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 (tptp.szDzozmdt0 tptp.xc)) (and (tptp.aSubsetOf0 W3 tptp.xS) (= (tptp.sbrdtbr0 W3) tptp.xK)))))) (let ((_let_55 (and (tptp.aSet0 _let_3) _let_54))) (let ((_let_56 (= _let_5 _let_55))) (let ((_let_57 (not _let_9))) (let ((_let_58 (or _let_37 _let_57 _let_56))) (let ((_let_59 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_2396 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 W1 tptp.szNzAzT0)) (= (= (tptp.slbdtsldtrb0 W0 W1) BOUND_VARIABLE_2396) (and (tptp.aSet0 BOUND_VARIABLE_2396) (forall ((W3 $$unsorted)) (= (and (tptp.aSubsetOf0 W3 W0) (= W1 (tptp.sbrdtbr0 W3))) (tptp.aElementOf0 W3 BOUND_VARIABLE_2396))))))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (AND_ELIM (ASSUME :args (_let_6)) :args (1)))) (let ((_let_62 (not _let_5))) (let ((_let_63 (_let_54))) (let ((_let_64 (tptp.aElementOf0 _let_18 _let_4))) (let ((_let_65 (not _let_51))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO _let_23 :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (or))) (let ((_let_68 (not _let_64))) (let ((_let_69 (and _let_5 _let_68))) (let ((_let_70 (ASSUME :args (_let_5)))) (let ((_let_71 (not _let_20))) (let ((_let_72 (or _let_71 _let_48))) (let ((_let_73 (forall ((W0 $$unsorted)) (or (not (tptp.aSet0 W0)) (= (= W0 (tptp.slbdtrb0 tptp.xK)) (= (tptp.sbrdtbr0 W0) tptp.xK)))))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_12)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_23 :args ((forall ((W0 $$unsorted)) (or (not (tptp.aSet0 W0)) (= (= tptp.sz00 (tptp.sbrdtbr0 W0)) (= tptp.slcrc0 W0)))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_21 0)) :args ((or _let_20 _let_26))) _let_25 :args (_let_20 false _let_21)))) (let ((_let_76 (_let_32))) (let ((_let_77 (_let_17))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_77) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_77)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 0)) (CONG (REFL :args (_let_28)) (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_19))) :args _let_67)) :args ((or _let_19 _let_28))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_76)) :args _let_76)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_29))) (REFL :args (_let_30)) :args _let_67)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_31)) :args ((or _let_71 _let_31 _let_32))) _let_75 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_34)) :args ((or _let_33 _let_35 (not _let_34)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_49)) :args ((or (not _let_48) _let_50 _let_49))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_72)) :args ((or _let_71 _let_48 (not _let_72)))) _let_75 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_74 :args (_let_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aSet0 W0) false))))) :args (_let_73)))) _let_74 :args (_let_72 false _let_73)) :args (_let_48 false _let_20 false _let_72)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_52)) :args ((or _let_51 _let_53 (not _let_52)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_69)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_66 _let_70) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (_let_18)) (SYMM (SYMM _let_70)) :args (APPLY_UF tptp.aElementOf0)) (FALSE_INTRO _let_66))) :args (_let_68 _let_5))) :args (_let_5 _let_68))) :args (true _let_69)) (CONG (REFL :args (_let_62)) (MACRO_SR_PRED_INTRO :args ((= (not _let_68) _let_64))) (REFL :args (_let_65)) :args _let_67)) :args ((or _let_64 _let_62 _let_65))) _let_66 _let_61 :args (_let_65 true _let_64 false _let_5)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_63) :args (_let_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aElementOf0 W3 _let_3)))) :args _let_63))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_55 1)) :args ((or _let_54 (not _let_55)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_56)) :args ((or _let_62 _let_55 (not _let_56)))) _let_61 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_57 _let_37 _let_56 (not _let_58)))) (ASSUME :args (_let_9)) _let_47 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_60 :args (tptp.xS tptp.xK _let_3 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_59)))) _let_60 :args (_let_58 false _let_59)) :args (_let_56 false _let_9 false _let_36 false _let_58)) :args (_let_55 false _let_5 false _let_56)) :args (_let_54 false _let_55)) :args (_let_52 false _let_54)) :args (_let_53 true _let_51 false _let_52)) :args (_let_50 false _let_48 true _let_49)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_37 _let_34 (not _let_38)))) _let_47 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (tptp.xS _let_18 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.aSet0 W0) false)) (tptp.aSet0 BOUND_VARIABLE_1712)))) :args _let_41)) _let_40 :args (_let_38 false _let_39)) :args (_let_34 false _let_36 false _let_38)) :args (_let_35 true _let_33 false _let_34)) :args (_let_32 false _let_20 true _let_31)) :args (_let_30 true _let_29)) :args (_let_19 true _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_21 1)) :args ((or _let_17 _let_26))) _let_25 :args (_let_17 false _let_21)) :args (false false _let_19 false _let_17)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (=> (tptp.isFinite0 W0) true))) _let_16 (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 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isCountable0 W0)) (not (= W0 tptp.slcrc0)))) _let_15 (forall ((W0 $$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 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.isFinite0 W1)) (tptp.isFinite0 (tptp.sdtpldt0 W1 W0)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.isFinite0 W1)) (tptp.isFinite0 (tptp.sdtmndt0 W1 W0)))))) _let_14 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0) (forall ((W0 $$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 $$unsorted)) (=> (tptp.aSet0 W0) (= (tptp.aElementOf0 (tptp.sbrdtbr0 W0) tptp.szNzAzT0) (tptp.isFinite0 W0)))) _let_12 (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isFinite0 W0)) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (=> (not (tptp.aElementOf0 W1 W0)) (= (tptp.sbrdtbr0 (tptp.sdtpldt0 W0 W1)) (tptp.szszuzczcdt0 (tptp.sbrdtbr0 W0)))))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.isFinite0 W0) (tptp.aElementOf0 W1 W0)) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 (tptp.sdtmndt0 W0 W1))) (tptp.sbrdtbr0 W0)))))) (forall ((W0 $$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)))) _let_11 (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 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (= (tptp.sbrdtbr0 (tptp.slbdtrb0 W0)) W0))) _let_10 (forall ((W0 $$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 $$unsorted)) (=> (and (tptp.aElementOf0 W1 tptp.szNzAzT0) (not (= W1 tptp.sz00))) (tptp.isCountable0 (tptp.slbdtsldtrb0 W0 W1)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.slbdtsldtrb0 W1 W0))) (=> (and (tptp.aSet0 W1) (tptp.aSet0 W2) (not (= W0 tptp.sz00))) (=> (and (tptp.aSubsetOf0 _let_1 (tptp.slbdtsldtrb0 W2 W0)) (not (= _let_1 tptp.slcrc0))) (tptp.aSubsetOf0 W1 W2))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (forall ((W2 $$unsorted)) (=> (and (tptp.aSubsetOf0 W2 (tptp.slbdtsldtrb0 W0 W1)) (tptp.isFinite0 W2)) (exists ((W3 $$unsorted)) (and (tptp.aSubsetOf0 W3 W0) (tptp.isFinite0 W3) (tptp.aSubsetOf0 W2 (tptp.slbdtsldtrb0 W3 W1)))))))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (tptp.aSet0 (tptp.szDzozmdt0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 (tptp.szDzozmdt0 W0)) (tptp.aElement0 (tptp.sdtlpdtrp0 W0 W1)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aFunction0 W0) (tptp.aElement0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtlbdtrb0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aElementOf0 W3 (tptp.szDzozmdt0 W0)) (= (tptp.sdtlpdtrp0 W0 W3) W1))))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aFunction0 W0) (tptp.aElement0 W1)) (tptp.aSubsetOf0 (tptp.sdtlbdtrb0 W0 W1) (tptp.szDzozmdt0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 (tptp.szDzozmdt0 W0)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtlcdtrc0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (exists ((W4 $$unsorted)) (and (tptp.aElementOf0 W4 W1) (= (tptp.sdtlpdtrp0 W0 W4) W3)))))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.szDzozmdt0 W0))) (=> (tptp.aElementOf0 W1 _let_1) (tptp.aElementOf0 (tptp.sdtlpdtrp0 W0 W1) (tptp.sdtlcdtrc0 W0 _let_1))))))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 (tptp.szDzozmdt0 W0)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtexdt0 W0 W1)) (and (tptp.aFunction0 W2) (= (tptp.szDzozmdt0 W2) W1) (forall ((W3 $$unsorted)) (=> (tptp.aElementOf0 W3 W1) (= (tptp.sdtlpdtrp0 W2 W3) (tptp.sdtlpdtrp0 W0 W3))))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSubsetOf0 W1 (tptp.szDzozmdt0 W0)) (tptp.isCountable0 W1)) (=> (forall ((W2 $$unsorted) (W3 $$unsorted)) (let ((_let_1 (tptp.szDzozmdt0 W0))) (=> (and (tptp.aElementOf0 W2 _let_1) (tptp.aElementOf0 W3 _let_1) (not (= W2 W3))) (not (= (tptp.sdtlpdtrp0 W0 W2) (tptp.sdtlpdtrp0 W0 W3)))))) (tptp.isCountable0 (tptp.sdtlcdtrc0 W0 W1))))))) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szDzizrdt0 W0))) (let ((_let_2 (tptp.szDzozmdt0 W0))) (=> (tptp.aFunction0 W0) (=> (and (tptp.isCountable0 _let_2) (tptp.isFinite0 (tptp.sdtlcdtrc0 W0 _let_2))) (and (tptp.aElement0 _let_1) (tptp.isCountable0 (tptp.sdtlbdtrb0 W0 _let_1)))))))) (and (tptp.aSet0 tptp.xT) (tptp.isFinite0 tptp.xT)) _let_9 _let_8 _let_6 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSubsetOf0 W1 tptp.szNzAzT0) (tptp.isCountable0 W1)) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.szDzozmdt0 W2))) (=> (and (tptp.aFunction0 W2) (= _let_1 (tptp.slbdtsldtrb0 W1 W0)) (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 W2 _let_1) tptp.xT)) (=> (tptp.iLess0 W0 tptp.xK) (exists ((W3 $$unsorted)) (and (tptp.aElementOf0 W3 tptp.xT) (exists ((W4 $$unsorted)) (and (tptp.aSubsetOf0 W4 W1) (tptp.isCountable0 W4) (forall ((W5 $$unsorted)) (=> (tptp.aElementOf0 W5 (tptp.slbdtsldtrb0 W4 W0)) (= (tptp.sdtlpdtrp0 W2 W5) W3))))))))))))))) _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 25.54/25.99  )
% 25.54/25.99  % SZS output end Proof for NUM564+1
% 25.54/25.99  % cvc5---1.0.5 exiting
% 25.54/25.99  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------