%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM545+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n026.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 10:44:57 EDT 2023

% Result   : Theorem 0.21s 0.74s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUM545+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n026.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 18:04:03 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.21/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.74  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.xLZ2urfwi9/cvc5---1.0.5_20423.p...
% 0.21/0.74  ------- get file name : TPTP file name is NUM545+2
% 0.21/0.74  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_20423.smt2...
% 0.21/0.74  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.74  % SZS status Theorem for NUM545+2
% 0.21/0.74  % SZS output start Proof for NUM545+2
% 0.21/0.74  (
% 0.21/0.74  (let ((_let_1 (not (exists ((W0 $$unsorted)) (let ((_let_1 (tptp.slbdtrb0 W0))) (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (=> (and (tptp.aSet0 _let_1) (forall ((W1 $$unsorted)) (= (tptp.aElementOf0 W1 (tptp.slbdtrb0 W0)) (and (tptp.aElementOf0 W1 tptp.szNzAzT0) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W1) W0))))) (or (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xS) (tptp.aElementOf0 W1 (tptp.slbdtrb0 W0)))) (tptp.aSubsetOf0 tptp.xS _let_1))))))))) (let ((_let_2 (tptp.szmzazxdt0 tptp.xS))) (let ((_let_3 (tptp.szszuzczcdt0 _let_2))) (let ((_let_4 (tptp.slbdtrb0 _let_3))) (let ((_let_5 (tptp.aSubsetOf0 tptp.xS _let_4))) (let ((_let_6 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szszuzczcdt0 (tptp.szmzazxdt0 tptp.xS)))) (= (tptp.aElementOf0 W0 (tptp.slbdtrb0 _let_1)) (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W0) _let_1))))))) (let ((_let_7 (tptp.aSet0 _let_4))) (let ((_let_8 (tptp.aElementOf0 _let_2 tptp.xS))) (let ((_let_9 (=> (not (and (not (exists ((W0 $$unsorted)) (tptp.aElementOf0 W0 tptp.xS))) (= tptp.xS tptp.slcrc0))) (and _let_8 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xS) (tptp.sdtlseqdt0 W0 (tptp.szmzazxdt0 tptp.xS)))) _let_7 _let_6 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xS) (tptp.aElementOf0 W0 (tptp.slbdtrb0 (tptp.szszuzczcdt0 (tptp.szmzazxdt0 tptp.xS)))))) _let_5)))) (let ((_let_10 (tptp.isFinite0 tptp.xS))) (let ((_let_11 (tptp.aSubsetOf0 tptp.xS tptp.szNzAzT0))) (let ((_let_12 (and (tptp.aSet0 tptp.xS) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xS) (tptp.aElementOf0 W0 tptp.szNzAzT0))) _let_11 _let_10))) (let ((_let_13 (tptp.slbdtrb0 tptp.sz00))) (let ((_let_14 (= _let_13 tptp.slcrc0))) (let ((_let_15 (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 $$unsorted)) (=> (tptp.aElementOf0 W2 W0) (tptp.sdtlseqdt0 W2 W1)))))))))) (let ((_let_16 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szszuzczcdt0 W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (and (tptp.aElementOf0 _let_1 tptp.szNzAzT0) (not (= _let_1 tptp.sz00)))))))) (let ((_let_17 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0))) (let ((_let_18 (tptp.aElementOf0 _let_3 tptp.szNzAzT0))) (let ((_let_19 (not _let_5))) (let ((_let_20 (tptp.aElementOf0 _let_2 tptp.szNzAzT0))) (let ((_let_21 (and _let_7 (= (tptp.aElementOf0 _let_2 _let_4) (and _let_20 (tptp.sdtlseqdt0 _let_3 _let_3))) (not (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xS)) (tptp.aElementOf0 W1 (tptp.slbdtrb0 (tptp.szszuzczcdt0 (tptp.szmzazxdt0 tptp.xS))))))) _let_19))) (let ((_let_22 (not _let_18))) (let ((_let_23 (or _let_22 _let_21))) (let ((_let_24 (and _let_18 (not (= tptp.sz00 _let_3))))) (let ((_let_25 (not _let_20))) (let ((_let_26 (or _let_25 _let_24))) (let ((_let_27 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szszuzczcdt0 W0))) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (and (tptp.aElementOf0 _let_1 tptp.szNzAzT0) (not (= tptp.sz00 _let_1)))))))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (not _let_8))) (let ((_let_30 (or _let_29 _let_20))) (let ((_let_31 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xS)) (tptp.aElementOf0 W0 tptp.szNzAzT0))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (_let_31))) (let ((_let_34 (and _let_8 (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 tptp.xS)) (tptp.sdtlseqdt0 W2 (tptp.szmzazxdt0 tptp.xS))))))) (let ((_let_35 (= tptp.slcrc0 tptp.xS))) (let ((_let_36 (not _let_10))) (let ((_let_37 (not _let_11))) (let ((_let_38 (or _let_37 _let_36 _let_35 _let_34))) (let ((_let_39 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1953 $$unsorted)) (or (not (tptp.aSubsetOf0 W0 tptp.szNzAzT0)) (not (tptp.isFinite0 W0)) (= tptp.slcrc0 W0) (= (and (tptp.aElementOf0 BOUND_VARIABLE_1953 W0) (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 W0)) (tptp.sdtlseqdt0 W2 BOUND_VARIABLE_1953)))) (= (tptp.szmzazxdt0 W0) BOUND_VARIABLE_1953)))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_13))) (let ((_let_42 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 tptp.xS))) (let ((_let_43 (= tptp.slcrc0 _let_13))) (let ((_let_44 (not _let_35))) (let ((_let_45 (not _let_42))) (let ((_let_46 (or _let_45 _let_41))) (let ((_let_47 (not _let_41))) (let ((_let_48 (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xS)) (tptp.aElementOf0 W1 (tptp.slbdtrb0 tptp.sz00)))))) (let ((_let_49 (not _let_46))) (let ((_let_50 (not _let_48))) (let ((_let_51 (and (tptp.aSet0 _let_13) (= (tptp.aElementOf0 _let_2 _let_13) (and _let_20 (tptp.sdtlseqdt0 _let_3 tptp.sz00))) _let_50 (not (tptp.aSubsetOf0 tptp.xS _let_13))))) (let ((_let_52 (not _let_17))) (let ((_let_53 (or _let_52 _let_51))) (let ((_let_54 (forall ((W0 $$unsorted) (BOUND_VARIABLE_2075 $$unsorted)) (let ((_let_1 (tptp.slbdtrb0 W0))) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (and (tptp.aSet0 _let_1) (= (tptp.aElementOf0 BOUND_VARIABLE_2075 _let_1) (and (tptp.aElementOf0 BOUND_VARIABLE_2075 tptp.szNzAzT0) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 BOUND_VARIABLE_2075) W0))) (not (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xS)) (tptp.aElementOf0 W1 (tptp.slbdtrb0 W0))))) (not (tptp.aSubsetOf0 tptp.xS _let_1)))))))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (_let_54))) (let ((_let_57 ((tptp.aElementOf0 BOUND_VARIABLE_2075 (tptp.slbdtrb0 W0))))) (let ((_let_58 (or))) (let ((_let_59 (_let_50))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_59)) :args _let_59)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_48))) (REFL :args (_let_49)) :args _let_58)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_51 2)) :args ((or _let_50 (not _let_51)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_53)) :args ((or _let_52 _let_51 (not _let_53)))) (ASSUME :args (_let_17)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (tptp.sz00 _let_2 QUANTIFIERS_INST_E_MATCHING _let_57)) :args _let_56)) _let_55 :args (_let_53 false _let_54)) :args (_let_51 false _let_17 false _let_53)) :args (_let_50 false _let_51)) :args (_let_49 true _let_48)))) (let ((_let_61 (SYMM (ASSUME :args (_let_14))))) (let ((_let_62 (ASSUME :args (_let_47)))) (let ((_let_63 (ASSUME :args (_let_35)))) (let ((_let_64 (ASSUME :args (_let_42)))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_62 _let_61 _let_63 _let_64) :args (_let_43 _let_35 _let_42 _let_47)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_64)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)) (TRANS (SYMM _let_63) (SYMM (SYMM _let_61))) :args (APPLY_UF tptp.aElementOf0)) (FALSE_INTRO _let_62))) :args (_let_47 _let_43 _let_35 _let_42)) :args ((not (and _let_43 _let_35 _let_42 _let_47)) SB_LITERAL))) (CONG (REFL :args ((not _let_43))) (REFL :args (_let_44)) (REFL :args (_let_45)) (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_41))) :args _let_58)) _let_61 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 0)) (CONG (REFL :args (_let_46)) (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_42))) :args _let_58)) :args ((or _let_42 _let_46))) _let_60 :args (_let_42 true _let_46)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_46 1)) _let_60 :args (_let_47 true _let_46)) :args (_let_44 false _let_43 false _let_42 true _let_41)))) (let ((_let_66 (not _let_21))) (let ((_let_67 (and _let_8 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xS)) (tptp.sdtlseqdt0 W0 (tptp.szmzazxdt0 tptp.xS)))) _let_7 _let_6 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xS)) (tptp.aElementOf0 W0 (tptp.slbdtrb0 (tptp.szszuzczcdt0 (tptp.szmzazxdt0 tptp.xS)))))) _let_5))) (let ((_let_68 (and (forall ((W0 $$unsorted)) (not (tptp.aElementOf0 W0 tptp.xS))) _let_35))) (let ((_let_69 (not _let_68))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_23)) :args ((or _let_22 _let_21 (not _let_23)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (_let_3 _let_2 QUANTIFIERS_INST_E_MATCHING _let_57)) :args _let_56)) _let_55 :args (_let_23 false _let_54)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_21 3)) :args ((or _let_19 _let_66))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_67 5)) :args ((or _let_5 (not _let_67)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT)))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_69) _let_68))) (REFL :args (_let_67)) :args _let_58)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_68 1)) :args ((or _let_35 _let_69))) _let_65 :args (_let_69 true _let_35)) :args (_let_67 true _let_68)) :args (_let_5 false _let_67)) :args (_let_66 false _let_5)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_24 0)) :args ((or _let_18 (not _let_24)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_25 _let_24 (not _let_26)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_30)) :args ((or _let_29 _let_20 (not _let_30)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_34 0)) :args ((or _let_8 (not _let_34)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_35 _let_37 _let_36 _let_34 (not _let_38)))) _let_65 (AND_ELIM _let_32 :args (2)) (AND_ELIM _let_32 :args (3)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_40 :args (tptp.xS _let_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aElementOf0 BOUND_VARIABLE_1953 W0)))) :args (_let_39)))) _let_40 :args (_let_38 false _let_39)) :args (_let_34 true _let_35 false _let_11 false _let_10 false _let_38)) :args (_let_8 false _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_33) :args (_let_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 W0 tptp.xS) false))))) :args _let_33)) (AND_ELIM _let_32 :args (1)) :args (_let_30 false _let_31)) :args (_let_20 false _let_8 false _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (_let_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.szszuzczcdt0 W0)))) :args (_let_27))) _let_28 :args (_let_26 false _let_27)) :args (_let_24 false _let_20 false _let_26)) :args (_let_18 false _let_24)) :args (false false _let_23 true _let_21 false _let_18)) :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 $$unsorted)) (=> (tptp.aSet0 W0) (=> (tptp.isFinite0 W0) true))) (forall ((W0 $$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 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.isFinite0 W1)) (tptp.isFinite0 (tptp.sdtpldt0 W1 W0)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.isFinite0 W1)) (tptp.isFinite0 (tptp.sdtmndt0 W1 W0)))))) (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0)) _let_17 _let_16 (forall ((W0 $$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 $$unsorted)) (=> (tptp.aSet0 W0) (= (= (tptp.sbrdtbr0 W0) tptp.sz00) (= W0 tptp.slcrc0)))) (forall ((W0 $$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 $$unsorted)) (=> (tptp.aElementOf0 W2 W0) (tptp.sdtlseqdt0 W1 W2)))))))) _let_15 (forall ((W0 $$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 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.isFinite0 (tptp.slbdtrb0 W0)))) _let_14 (forall ((W0 $$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))))) _let_12 _let_9 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.75  )
% 0.21/0.75  % SZS output end Proof for NUM545+2
% 0.21/0.75  % cvc5---1.0.5 exiting
% 0.21/0.75  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------