TSTP Solution File: NUM545+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM545+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n032.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 10:44:56 EDT 2023
% Result : Theorem 0.14s 0.79s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUM545+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11 % Command : do_cvc5 %s %d
% 0.12/0.30 % Computer : n032.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 14:14:43 EDT 2023
% 0.12/0.30 % CPUTime :
% 0.14/0.39 %----Proving TF0_NAR, FOF, or CNF
% 0.14/0.79 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.4PRqVTFQQT/cvc5---1.0.5_27137.p...
% 0.14/0.79 ------- get file name : TPTP file name is NUM545+1
% 0.14/0.79 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_27137.smt2...
% 0.14/0.79 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.14/0.79 % SZS status Theorem for NUM545+1
% 0.14/0.79 % SZS output start Proof for NUM545+1
% 0.14/0.79 (
% 0.14/0.79 (let ((_let_1 (not (exists ((W0 $$unsorted)) (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aSubsetOf0 tptp.xS (tptp.slbdtrb0 W0))))))) (let ((_let_2 (tptp.szmzazxdt0 tptp.xS))) (let ((_let_3 (tptp.szszuzczcdt0 _let_2))) (let ((_let_4 (tptp.aSubsetOf0 tptp.xS (tptp.slbdtrb0 _let_3)))) (let ((_let_5 (=> (not (= tptp.xS tptp.slcrc0)) _let_4))) (let ((_let_6 (tptp.isFinite0 tptp.xS))) (let ((_let_7 (tptp.aSubsetOf0 tptp.xS tptp.szNzAzT0))) (let ((_let_8 (and _let_7 _let_6))) (let ((_let_9 (tptp.slbdtrb0 tptp.sz00))) (let ((_let_10 (= _let_9 tptp.slcrc0))) (let ((_let_11 (forall ((W0 $$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_12 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szszuzczcdt0 W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (and (tptp.aElementOf0 _let_1 tptp.szNzAzT0) (not (= _let_1 tptp.sz00)))))))) (let ((_let_13 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0))) (let ((_let_14 (tptp.aSet0 tptp.szNzAzT0))) (let ((_let_15 (and _let_14 (tptp.isCountable0 tptp.szNzAzT0)))) (let ((_let_16 (forall ((W0 $$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_17 (forall ((W0 $$unsorted)) (= (= W0 tptp.slcrc0) (and (tptp.aSet0 W0) (not (exists ((W1 $$unsorted)) (tptp.aElementOf0 W1 W0)))))))) (let ((_let_18 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (not (tptp.aSubsetOf0 tptp.xS (tptp.slbdtrb0 W0))))))) (let ((_let_19 (not _let_4))) (let ((_let_20 (tptp.aElementOf0 _let_3 tptp.szNzAzT0))) (let ((_let_21 (not _let_20))) (let ((_let_22 (or _let_21 _let_19))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_24 (not _let_22))) (let ((_let_25 (and _let_20 (not (= tptp.sz00 _let_3))))) (let ((_let_26 (tptp.aElementOf0 _let_2 tptp.szNzAzT0))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or _let_27 _let_25))) (let ((_let_29 (forall ((W0 $$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_30 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (tptp.aElementOf0 _let_2 tptp.xS))) (let ((_let_32 (not _let_31))) (let ((_let_33 (or _let_32 _let_26))) (let ((_let_34 (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 tptp.xS)) (tptp.aElementOf0 W2 tptp.szNzAzT0))))) (let ((_let_35 (tptp.aSet0 tptp.xS))) (let ((_let_36 (and _let_35 _let_34))) (let ((_let_37 (= _let_7 _let_36))) (let ((_let_38 (not _let_14))) (let ((_let_39 (or _let_38 _let_37))) (let ((_let_40 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1334 $$unsorted)) (or (not (tptp.aSet0 W0)) (= (tptp.aSubsetOf0 BOUND_VARIABLE_1334 W0) (and (tptp.aSet0 BOUND_VARIABLE_1334) (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 BOUND_VARIABLE_1334)) (tptp.aElementOf0 W2 W0))))))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (_let_40))) (let ((_let_43 ((tptp.aSubsetOf0 BOUND_VARIABLE_1334 W0)))) (let ((_let_44 (0))) (let ((_let_45 (ASSUME :args (_let_8)))) (let ((_let_46 (AND_ELIM _let_45 :args _let_44))) (let ((_let_47 (not _let_7))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_37)) :args ((or _let_47 _let_36 (not _let_37)))) _let_46 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_38 _let_37 (not _let_39)))) (AND_ELIM (ASSUME :args (_let_15)) :args _let_44) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (tptp.szNzAzT0 tptp.xS QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_43)) :args _let_42)) _let_41 :args (_let_39 false _let_40)) :args (_let_37 false _let_14 false _let_39)) :args (_let_36 false _let_7 false _let_37)))) (let ((_let_49 (not _let_36))) (let ((_let_50 (_let_34))) (let ((_let_51 (and _let_31 (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 tptp.xS)) (tptp.sdtlseqdt0 W2 (tptp.szmzazxdt0 tptp.xS))))))) (let ((_let_52 (= tptp.slcrc0 tptp.xS))) (let ((_let_53 (not _let_6))) (let ((_let_54 (or _let_47 _let_53 _let_52 _let_51))) (let ((_let_55 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1897 $$unsorted)) (or (not (tptp.aSubsetOf0 W0 tptp.szNzAzT0)) (not (tptp.isFinite0 W0)) (= tptp.slcrc0 W0) (= (and (tptp.aElementOf0 BOUND_VARIABLE_1897 W0) (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 W0)) (tptp.sdtlseqdt0 W2 BOUND_VARIABLE_1897)))) (= (tptp.szmzazxdt0 W0) BOUND_VARIABLE_1897)))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (= tptp.slcrc0 _let_9))) (let ((_let_58 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.xS))) (let ((_let_59 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_9))) (let ((_let_60 (not _let_52))) (let ((_let_61 (SYMM (ASSUME :args (_let_10))))) (let ((_let_62 (not _let_58))) (let ((_let_63 (or _let_62 _let_59))) (let ((_let_64 (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 tptp.xS)) (tptp.aElementOf0 W2 (tptp.slbdtrb0 tptp.sz00)))))) (let ((_let_65 (not _let_63))) (let ((_let_66 (and _let_35 _let_64))) (let ((_let_67 (not _let_64))) (let ((_let_68 (tptp.aSubsetOf0 tptp.xS _let_9))) (let ((_let_69 (= _let_68 _let_66))) (let ((_let_70 (not _let_66))) (let ((_let_71 (tptp.aSet0 _let_9))) (let ((_let_72 (not _let_71))) (let ((_let_73 (or _let_72 _let_69))) (let ((_let_74 (tptp.aSet0 tptp.slcrc0))) (let ((_let_75 (and _let_74 (forall ((W1 $$unsorted)) (not (tptp.aElementOf0 W1 tptp.slcrc0)))))) (let ((_let_76 (forall ((W0 $$unsorted)) (= (= tptp.slcrc0 W0) (and (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (not (tptp.aElementOf0 W1 W0)))))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (and _let_74 _let_57))) (let ((_let_79 (_let_74 _let_57))) (let ((_let_80 (ASSUME :args (_let_74)))) (let ((_let_81 (SYMM _let_61))) (let ((_let_82 (not _let_68))) (let ((_let_83 (not _let_13))) (let ((_let_84 (or _let_83 _let_82))) (let ((_let_85 (_let_18))) (let ((_let_86 ((not (= (tptp.aElementOf0 W0 tptp.szNzAzT0) false))))) (let ((_let_87 (or))) (let ((_let_88 (_let_67))) (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_67) _let_64))) (REFL :args (_let_65)) :args _let_87)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_66)) :args ((or (not _let_35) _let_66 _let_67))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_36 0)) :args ((or _let_35 _let_49))) _let_48 :args (_let_35 false _let_36)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_69)) :args ((or _let_68 _let_70 (not _let_69)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_84)) :args ((or _let_83 _let_82 (not _let_84)))) (ASSUME :args (_let_13)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (tptp.sz00 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_86)) :args _let_85)) _let_23 :args (_let_84 false _let_18)) :args (_let_82 false _let_13 false _let_84)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_72 _let_69 (not _let_73)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_78)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_80 _let_61) (SCOPE (TRUE_ELIM (TRANS (CONG _let_81 :args (APPLY_UF tptp.aSet0)) (TRUE_INTRO _let_80))) :args _let_79)) :args _let_79)) :args (true _let_78)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_75 0)) :args ((or _let_74 (not _let_75)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_77 :args (tptp.slcrc0 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aSet0 W0)))) :args (_let_76)))) _let_77 :args (_let_75 false _let_76)) :args (_let_74 false _let_75)) _let_61 :args (_let_71 false _let_74 false _let_57)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (_let_9 tptp.xS QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_43)) :args _let_42)) _let_41 :args (_let_73 false _let_40)) :args (_let_69 false _let_71 false _let_73)) :args (_let_70 true _let_68 false _let_69)) :args (_let_67 false _let_35 true _let_66)) :args (_let_65 true _let_64)))) (let ((_let_90 (not _let_59))) (let ((_let_91 (not _let_57))) (let ((_let_92 (ASSUME :args (_let_90)))) (let ((_let_93 (ASSUME :args (_let_52)))) (let ((_let_94 (ASSUME :args (_let_58)))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_92 _let_61 _let_93 _let_94) :args (_let_57 _let_52 _let_58 _let_90)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_94)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (TRANS (SYMM _let_93) (SYMM _let_81)) :args (APPLY_UF tptp.aElementOf0)) (FALSE_INTRO _let_92))) :args (_let_90 _let_57 _let_52 _let_58)) :args ((not (and _let_57 _let_52 _let_58 _let_90)) SB_LITERAL))) (CONG (REFL :args (_let_91)) (REFL :args (_let_60)) (REFL :args (_let_62)) (MACRO_SR_PRED_INTRO :args ((= (not _let_90) _let_59))) :args _let_87)) :args ((or _let_60 _let_91 _let_62 _let_59))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_63 1)) _let_89 :args (_let_90 true _let_63)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_63 0)) (CONG (REFL :args (_let_63)) (MACRO_SR_PRED_INTRO :args ((= (not _let_62) _let_58))) :args _let_87)) :args ((or _let_58 _let_63))) _let_89 :args (_let_58 true _let_63)) _let_61 :args (_let_60 true _let_59 false _let_58 false _let_57)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (_let_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_86)) :args _let_85)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_22)) :args ((or _let_19 _let_21 _let_24))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_60) _let_52))) (REFL :args (_let_4)) :args _let_87)) :args ((or _let_4 _let_52))) _let_95 :args (_let_4 true _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_25 0)) :args ((or _let_20 (not _let_25)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_28)) :args ((or _let_27 _let_25 (not _let_28)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_33)) :args ((or _let_26 _let_32 (not _let_33)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_51 0)) :args ((or _let_31 (not _let_51)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_52 _let_47 _let_53 _let_51 (not _let_54)))) _let_95 _let_46 (AND_ELIM _let_45 :args (1)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_56 :args (tptp.xS _let_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aElementOf0 BOUND_VARIABLE_1897 W0)))) :args (_let_55)))) _let_56 :args (_let_54 false _let_55)) :args (_let_51 true _let_52 false _let_7 false _let_6 false _let_54)) :args (_let_31 false _let_51)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_50) :args (_let_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 W2 tptp.szNzAzT0) true))))) :args _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_36 1)) :args ((or _let_34 _let_49))) _let_48 :args (_let_34 false _let_36)) :args (_let_33 false _let_34)) :args (_let_26 false _let_31 false _let_33)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (_let_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.szszuzczcdt0 W0)))) :args (_let_29))) _let_30 :args (_let_28 false _let_29)) :args (_let_25 false _let_26 false _let_28)) :args (_let_20 false _let_25)) :args (_let_24 false _let_4 false _let_20)) _let_23 :args (false true _let_22 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 $$unsorted)) (=> (tptp.aSet0 W0) (=> (tptp.isFinite0 W0) true))) _let_17 (tptp.isFinite0 tptp.slcrc0) (forall ((W0 $$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_16 (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_15 _let_13 _let_12 (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_11 (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_10 (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_8 _let_5 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.14/0.80 )
% 0.14/0.80 % SZS output end Proof for NUM545+1
% 0.14/0.80 % cvc5---1.0.5 exiting
% 0.14/0.80 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------