TSTP Solution File: NUM612+3 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM612+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n019.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 10:45:38 EDT 2023
% Result : Theorem 0.21s 0.73s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : NUM612+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n019.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Aug 25 10:38:43 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.51 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.73 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.OQTNuCv86d/cvc5---1.0.5_17477.p...
% 0.21/0.73 ------- get file name : TPTP file name is NUM612+3
% 0.21/0.73 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_17477.smt2...
% 0.21/0.73 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.73 % SZS status Theorem for NUM612+3
% 0.21/0.73 % SZS output start Proof for NUM612+3
% 0.21/0.73 (
% 0.21/0.73 (let ((_let_1 (tptp.sbrdtbr0 tptp.xP))) (let ((_let_2 (tptp.aElementOf0 _let_1 tptp.szNzAzT0))) (let ((_let_3 (tptp.sbrdtbr0 tptp.xQ))) (let ((_let_4 (tptp.szszuzczcdt0 _let_1))) (let ((_let_5 (not (and (= _let_4 _let_3) _let_2)))) (let ((_let_6 (tptp.aSubsetOf0 tptp.xP tptp.xQ))) (let ((_let_7 (and (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xP) (tptp.aElementOf0 W0 tptp.xQ))) _let_6))) (let ((_let_8 (tptp.aElementOf0 tptp.xp tptp.xQ))) (let ((_let_9 (tptp.szmzizndt0 tptp.xQ))) (let ((_let_10 (= tptp.xP (tptp.sdtmndt0 tptp.xQ _let_9)))) (let ((_let_11 (tptp.aSet0 tptp.xP))) (let ((_let_12 (and _let_11 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xQ) (tptp.sdtlseqdt0 (tptp.szmzizndt0 tptp.xQ) W0))) (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 tptp.xP) (and (tptp.aElement0 W0) (tptp.aElementOf0 W0 tptp.xQ) (not (= W0 (tptp.szmzizndt0 tptp.xQ)))))) _let_10))) (let ((_let_13 (= tptp.xp _let_9))) (let ((_let_14 (and _let_8 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xQ) (tptp.sdtlseqdt0 tptp.xp W0))) _let_13))) (let ((_let_15 (tptp.szDzozmdt0 tptp.xc))) (let ((_let_16 (tptp.aSubsetOf0 tptp.xQ tptp.xS))) (let ((_let_17 (tptp.aSet0 tptp.xQ))) (let ((_let_18 (and _let_17 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xQ) (tptp.aElementOf0 W0 tptp.xO))) (tptp.aSubsetOf0 tptp.xQ tptp.xO) (= _let_3 tptp.xK) (tptp.aElementOf0 tptp.xQ (tptp.slbdtsldtrb0 tptp.xO tptp.xK))))) (let ((_let_19 (tptp.aSet0 tptp.xO))) (let ((_let_20 (tptp.szDzizrdt0 tptp.xd))) (let ((_let_21 (tptp.sdtlbdtrb0 tptp.xd _let_20))) (let ((_let_22 (tptp.aSet0 _let_21))) (let ((_let_23 (tptp.szDzozmdt0 tptp.xd))) (let ((_let_24 (tptp.sdtlcdtrc0 tptp.xd _let_23))) (let ((_let_25 (not (= tptp.xK tptp.sz00)))) (let ((_let_26 (tptp.sdtlcdtrc0 tptp.xc _let_15))) (let ((_let_27 (tptp.aElementOf0 tptp.xK tptp.szNzAzT0))) (let ((_let_28 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.isFinite0 W0) (tptp.aElementOf0 W1 W0)) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 (tptp.sdtmndt0 W0 W1))) (tptp.sbrdtbr0 W0)))))))) (let ((_let_29 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (= (tptp.aElementOf0 (tptp.sbrdtbr0 W0) tptp.szNzAzT0) (tptp.isFinite0 W0)))))) (let ((_let_30 (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isFinite0 W0)) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (tptp.isFinite0 W1))))))) (let ((_let_31 (= _let_3 (tptp.szszuzczcdt0 (tptp.sbrdtbr0 (tptp.sdtmndt0 tptp.xQ tptp.xp)))))) (let ((_let_32 (= _let_3 _let_4))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (3))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (not _let_8))) (let ((_let_37 (tptp.isFinite0 tptp.xQ))) (let ((_let_38 (not _let_37))) (let ((_let_39 (not _let_17))) (let ((_let_40 (or _let_39 _let_38 _let_36 _let_31))) (let ((_let_41 (forall ((W0 $$unsorted) (BOUND_VARIABLE_3110 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.isFinite0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_3110 W0)) (= (tptp.sbrdtbr0 W0) (tptp.szszuzczcdt0 (tptp.sbrdtbr0 (tptp.sdtmndt0 W0 BOUND_VARIABLE_3110)))))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (tptp.aElementOf0 _let_3 tptp.szNzAzT0))) (let ((_let_44 (= _let_37 _let_43))) (let ((_let_45 (or _let_39 _let_44))) (let ((_let_46 (forall ((W0 $$unsorted)) (or (not (tptp.aSet0 W0)) (= (tptp.aElementOf0 (tptp.sbrdtbr0 W0) tptp.szNzAzT0) (tptp.isFinite0 W0)))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (_let_46))) (let ((_let_49 ((not (= (tptp.aSet0 W0) false))))) (let ((_let_50 (0))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (AND_ELIM _let_51 :args _let_50))) (let ((_let_53 (= tptp.xK _let_3))) (let ((_let_54 (ASSUME :args (_let_27)))) (let ((_let_55 (and _let_27 _let_53))) (let ((_let_56 (_let_27 _let_53))) (let ((_let_57 (ASSUME :args (_let_53)))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_44)) :args ((or _let_37 (not _let_43) (not _let_44)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_55)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_54 _let_57) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM _let_57) (REFL :args (tptp.szNzAzT0)) :args (APPLY_UF tptp.aElementOf0)) (TRUE_INTRO _let_54))) :args _let_56)) :args _let_56)) :args (true _let_55)) _let_54 (AND_ELIM _let_51 :args _let_34) :args (_let_43 false _let_27 false _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_45)) :args ((or _let_39 _let_44 (not _let_45)))) _let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_47 :args (tptp.xQ QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_49)) :args _let_48))) _let_47 :args (_let_45 false _let_46)) :args (_let_44 false _let_17 false _let_45)) :args (_let_37 false _let_43 false _let_44)))) (let ((_let_59 (tptp.isFinite0 tptp.xP))) (let ((_let_60 (= _let_2 _let_59))) (let ((_let_61 (not _let_11))) (let ((_let_62 (or _let_61 _let_60))) (let ((_let_63 (not _let_6))) (let ((_let_64 (or _let_39 _let_38 _let_63 _let_59))) (let ((_let_65 (forall ((W0 $$unsorted) (BOUND_VARIABLE_2693 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.isFinite0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_2693 W0)) (tptp.isFinite0 BOUND_VARIABLE_2693))))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (and _let_13 _let_10 _let_31))) (let ((_let_68 (ASSUME :args (_let_10)))) (let ((_let_69 (ASSUME :args (_let_13)))) (let ((_let_70 (ASSUME :args (_let_31)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_67)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_68 _let_69 _let_70) (SCOPE (TRANS (SYMM (SYMM _let_70)) (CONG (CONG (TRANS (CONG (REFL :args (tptp.xQ)) (SYMM (SYMM _let_69)) :args (APPLY_UF tptp.sdtmndt0)) (SYMM _let_68)) :args (APPLY_UF tptp.sbrdtbr0)) :args (APPLY_UF tptp.szszuzczcdt0))) :args (_let_10 _let_13 _let_31))) :args (_let_13 _let_10 _let_31))) :args (true _let_67)) :args ((or _let_32 (not _let_13) (not _let_10) (not _let_31)))) (MACRO_RESOLUTION_TRUST (NOT_AND (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_60)) :args ((or _let_2 (not _let_59) (not _let_60)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_64)) :args ((or _let_39 _let_63 _let_38 _let_59 (not _let_64)))) _let_52 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))) :args (1)) _let_58 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (tptp.xQ tptp.xP QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aSubsetOf0 BOUND_VARIABLE_2693 W0) false))))) :args (_let_65))) _let_66 :args (_let_64 false _let_65)) :args (_let_59 false _let_17 false _let_6 false _let_37 false _let_64)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_61 _let_60 (not _let_62)))) (AND_ELIM _let_35 :args _let_50) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (tptp.xP QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_49)) :args _let_48)) _let_47 :args (_let_62 false _let_46)) :args (_let_60 false _let_11 false _let_62)) :args (_let_2 false _let_59 false _let_60)) :args ((not _let_32) false _let_2)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_39 _let_36 _let_38 _let_31 (not _let_40)))) _let_52 (AND_ELIM _let_33 :args _let_50) _let_58 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (tptp.xQ tptp.xp QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 BOUND_VARIABLE_3110 W0) false))))) :args (_let_41))) _let_42 :args (_let_40 false _let_41)) :args (_let_31 false _let_17 false _let_8 false _let_37 false _let_40)) (AND_ELIM _let_35 :args _let_34) (AND_ELIM _let_33 :args (2)) :args (false true _let_32 false _let_31 false _let_10 false _let_13)) :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)))))))) _let_30 (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)) (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 $$unsorted)) (=> (tptp.aSet0 W0) (tptp.aElement0 (tptp.sbrdtbr0 W0)))) _let_29 (forall ((W0 $$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)))))))) _let_28 (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)))))) (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 $$unsorted)) (let ((_let_1 (tptp.szDzizrdt0 W0))) (let ((_let_2 (tptp.szDzozmdt0 W0))) (=> (tptp.aFunction0 W0) (=> (and (tptp.isCountable0 _let_2) (tptp.isFinite0 (tptp.sdtlcdtrc0 W0 _let_2))) (and (tptp.aElement0 _let_1) (tptp.isCountable0 (tptp.sdtlbdtrb0 W0 _let_1)))))))) (and (tptp.aSet0 tptp.xT) (tptp.isFinite0 tptp.xT)) _let_27 (and (tptp.aSet0 tptp.xS) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xS) (tptp.aElementOf0 W0 tptp.szNzAzT0))) (tptp.aSubsetOf0 tptp.xS tptp.szNzAzT0) (tptp.isCountable0 tptp.xS)) (and (tptp.aFunction0 tptp.xc) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 (tptp.szDzozmdt0 tptp.xc)))) (let ((_let_2 (= (tptp.sbrdtbr0 W0) tptp.xK))) (let ((_let_3 (tptp.aSubsetOf0 W0 tptp.xS))) (let ((_let_4 (tptp.aSet0 W0))) (and (=> _let_1 (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xS))) _let_3 _let_2)) (=> (and (or (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xS)))) _let_3) _let_2) _let_1))))))) (= _let_15 (tptp.slbdtsldtrb0 tptp.xS tptp.xK)) (tptp.aSet0 _let_26) (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.sdtlcdtrc0 tptp.xc (tptp.szDzozmdt0 tptp.xc))) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 (tptp.szDzozmdt0 tptp.xc)) (= (tptp.sdtlpdtrp0 tptp.xc W1) W0))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.sdtlcdtrc0 tptp.xc (tptp.szDzozmdt0 tptp.xc))) (tptp.aElementOf0 W0 tptp.xT))) (tptp.aSubsetOf0 _let_26 tptp.xT)) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (=> (and (or (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 tptp.szNzAzT0)))) (tptp.aSubsetOf0 W1 tptp.szNzAzT0)) (tptp.isCountable0 W1)) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.szDzozmdt0 W2))) (let ((_let_2 (tptp.sdtlcdtrc0 W2 _let_1))) (=> (and (tptp.aFunction0 W2) (or (forall ((W3 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W3 (tptp.szDzozmdt0 W2)))) (let ((_let_2 (= (tptp.sbrdtbr0 W3) W0))) (let ((_let_3 (tptp.aSubsetOf0 W3 W1))) (let ((_let_4 (tptp.aSet0 W3))) (and (=> _let_1 (and (or (and _let_4 (forall ((W4 $$unsorted)) (=> (tptp.aElementOf0 W4 W3) (tptp.aElementOf0 W4 W1)))) _let_3) _let_2)) (=> (and _let_4 (forall ((W4 $$unsorted)) (=> (tptp.aElementOf0 W4 W3) (tptp.aElementOf0 W4 W1))) _let_3 _let_2) _let_1))))))) (= _let_1 (tptp.slbdtsldtrb0 W1 W0))) (=> (and (tptp.aSet0 _let_2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 (tptp.sdtlcdtrc0 W2 (tptp.szDzozmdt0 W2))) (exists ((W4 $$unsorted)) (and (tptp.aElementOf0 W4 (tptp.szDzozmdt0 W2)) (= (tptp.sdtlpdtrp0 W2 W4) W3)))))) (or (forall ((W3 $$unsorted)) (=> (tptp.aElementOf0 W3 (tptp.sdtlcdtrc0 W2 (tptp.szDzozmdt0 W2))) (tptp.aElementOf0 W3 tptp.xT))) (tptp.aSubsetOf0 _let_2 tptp.xT)))) (=> (tptp.iLess0 W0 tptp.xK) (exists ((W3 $$unsorted)) (and (tptp.aElementOf0 W3 tptp.xT) (exists ((W4 $$unsorted)) (and (tptp.aSet0 W4) (forall ((W5 $$unsorted)) (=> (tptp.aElementOf0 W5 W4) (tptp.aElementOf0 W5 W1))) (tptp.aSubsetOf0 W4 W1) (tptp.isCountable0 W4) (forall ((W5 $$unsorted)) (=> (or (and (or (and (tptp.aSet0 W5) (forall ((W6 $$unsorted)) (=> (tptp.aElementOf0 W6 W5) (tptp.aElementOf0 W6 W4)))) (tptp.aSubsetOf0 W5 W4)) (= (tptp.sbrdtbr0 W5) W0)) (tptp.aElementOf0 W5 (tptp.slbdtsldtrb0 W4 W0))) (= (tptp.sdtlpdtrp0 W2 W5) W3)))))))))))))))) _let_25 _let_25 (and (tptp.aElementOf0 tptp.xk tptp.szNzAzT0) (= (tptp.szszuzczcdt0 tptp.xk) tptp.xK)) (and (tptp.aFunction0 tptp.xN) (= (tptp.szDzozmdt0 tptp.xN) tptp.szNzAzT0) (= (tptp.sdtlpdtrp0 tptp.xN tptp.sz00) tptp.xS) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)))) (let ((_let_2 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_3 (tptp.szmzizndt0 _let_2))) (let ((_let_4 (tptp.sdtmndt0 _let_2 _let_3))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (=> (and (or (and (tptp.aSet0 _let_2) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 (tptp.sdtlpdtrp0 tptp.xN W0)) (tptp.aElementOf0 W1 tptp.szNzAzT0)))) (tptp.aSubsetOf0 _let_2 tptp.szNzAzT0)) (tptp.isCountable0 _let_2)) (and (tptp.aElementOf0 _let_3 _let_2) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W1 _let_1) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W1)))) (tptp.aSet0 _let_4) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (= (tptp.aElementOf0 W1 (tptp.sdtmndt0 _let_1 _let_2)) (and (tptp.aElement0 W1) (tptp.aElementOf0 W1 _let_1) (not (= W1 _let_2))))))) (tptp.aSet0 _let_1) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0))) (tptp.aElementOf0 W1 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1)))))) (tptp.aSubsetOf0 _let_1 _let_4) (tptp.isCountable0 _let_1)))))))))) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (and (tptp.aSet0 _let_1) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 (tptp.sdtlpdtrp0 tptp.xN W0)) (tptp.aElementOf0 W1 tptp.szNzAzT0))) (tptp.aSubsetOf0 _let_1 tptp.szNzAzT0) (tptp.isCountable0 _let_1))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (tptp.sdtlseqdt0 W1 W0) (and (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN W0)) (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN W1)))) (tptp.aSubsetOf0 (tptp.sdtlpdtrp0 tptp.xN W0) (tptp.sdtlpdtrp0 tptp.xN W1)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W1))) (let ((_let_2 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_3 (tptp.szmzizndt0 _let_2))) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0) (not (= W0 W1))) (not (=> (and (tptp.aElementOf0 _let_3 _let_2) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W2 _let_1) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W2))))) (or (and (tptp.aElementOf0 _let_3 _let_1) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN W1)) (tptp.sdtlseqdt0 (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN W0)) W2)))) (= _let_3 (tptp.szmzizndt0 _let_1)))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (let ((_let_3 (tptp.sdtpldt0 W1 _let_2))) (let ((_let_4 (tptp.aElementOf0 _let_2 _let_1))) (let ((_let_5 (tptp.sdtmndt0 _let_1 _let_2))) (=> (and (tptp.aSet0 W1) (=> (and _let_4 (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W2 _let_1) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W2))))) (=> (and (tptp.aSet0 _let_5) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (= (tptp.aElementOf0 W2 (tptp.sdtmndt0 _let_1 _let_2)) (and (tptp.aElement0 W2) (tptp.aElementOf0 W2 _let_1) (not (= W2 _let_2)))))))) (or (and (or (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1)))))) (tptp.aSubsetOf0 W1 _let_5)) (= (tptp.sbrdtbr0 W1) tptp.xk)) (tptp.aElementOf0 W1 (tptp.slbdtsldtrb0 _let_5 tptp.xk)))))) (and _let_4 (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W2 _let_1) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W2)))) (tptp.aSet0 _let_3) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN W0)))) (= (tptp.aElementOf0 W2 (tptp.sdtpldt0 W1 _let_1)) (and (tptp.aElement0 W2) (or (tptp.aElementOf0 W2 W1) (= W2 _let_1)))))) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 (tptp.sdtpldt0 W1 (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN W0)))) (tptp.aElementOf0 W2 tptp.xS))) (tptp.aSubsetOf0 _let_3 tptp.xS) (= (tptp.sbrdtbr0 _let_3) tptp.xK) (tptp.aElementOf0 _let_3 (tptp.slbdtsldtrb0 tptp.xS tptp.xK)))))))))))) (and (tptp.aFunction0 tptp.xC) (= (tptp.szDzozmdt0 tptp.xC) tptp.szNzAzT0) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (let ((_let_3 (tptp.sdtmndt0 _let_1 _let_2))) (let ((_let_4 (tptp.sdtlpdtrp0 tptp.xC W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (and (tptp.aFunction0 _let_4) (tptp.aElementOf0 _let_2 _let_1) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W1 _let_1) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W1)))) (tptp.aSet0 _let_3) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (= (tptp.aElementOf0 W1 (tptp.sdtmndt0 _let_1 _let_2)) (and (tptp.aElement0 W1) (tptp.aElementOf0 W1 _let_1) (not (= W1 _let_2))))))) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W1 (tptp.szDzozmdt0 (tptp.sdtlpdtrp0 tptp.xC W0))))) (let ((_let_2 (= (tptp.sbrdtbr0 W1) tptp.xk))) (let ((_let_3 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_4 (tptp.aSubsetOf0 W1 (tptp.sdtmndt0 _let_3 (tptp.szmzizndt0 _let_3))))) (let ((_let_5 (tptp.aSet0 W1))) (and (=> _let_1 (and _let_5 (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1)))))) _let_4 _let_2)) (=> (and (or (and _let_5 (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1))))))) _let_4) _let_2) _let_1)))))))) (= (tptp.szDzozmdt0 _let_4) (tptp.slbdtsldtrb0 _let_3 tptp.xk)) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (let ((_let_3 (tptp.aElementOf0 _let_2 _let_1))) (let ((_let_4 (tptp.sdtmndt0 _let_1 _let_2))) (=> (and (tptp.aSet0 W1) (=> (and _let_3 (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W2 _let_1) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W2))))) (=> (and (tptp.aSet0 _let_4) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (= (tptp.aElementOf0 W2 (tptp.sdtmndt0 _let_1 _let_2)) (and (tptp.aElement0 W2) (tptp.aElementOf0 W2 _let_1) (not (= W2 _let_2)))))))) (or (and (or (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1)))))) (tptp.aSubsetOf0 W1 _let_4)) (= (tptp.sbrdtbr0 W1) tptp.xk)) (tptp.aElementOf0 W1 (tptp.slbdtsldtrb0 _let_4 tptp.xk)))))) (and _let_3 (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W2 _let_1) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W2)))) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN W0)))) (= (tptp.aElementOf0 W2 (tptp.sdtpldt0 W1 _let_1)) (and (tptp.aElement0 W2) (or (tptp.aElementOf0 W2 W1) (= W2 _let_1)))))) (= (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC W0) W1) (tptp.sdtlpdtrp0 tptp.xc (tptp.sdtpldt0 W1 _let_2)))))))))))))))))) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xC W0))) (let ((_let_2 (tptp.sdtlcdtrc0 _let_1 (tptp.szDzozmdt0 _let_1)))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (and (tptp.aSet0 _let_2) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xC W0))) (= (tptp.aElementOf0 W1 (tptp.sdtlcdtrc0 _let_1 (tptp.szDzozmdt0 _let_1))) (exists ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xC W0))) (and (tptp.aElementOf0 W2 (tptp.szDzozmdt0 _let_1)) (= (tptp.sdtlpdtrp0 _let_1 W2) W1))))))) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xC W0))) (=> (tptp.aElementOf0 W1 (tptp.sdtlcdtrc0 _let_1 (tptp.szDzozmdt0 _let_1))) (tptp.aElementOf0 W1 tptp.xT)))) (tptp.aSubsetOf0 _let_2 tptp.xT)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (let ((_let_3 (tptp.sdtmndt0 _let_1 _let_2))) (=> (and (=> (and (tptp.aElementOf0 _let_2 _let_1) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W2 _let_1) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W2))))) (=> (and (tptp.aSet0 _let_3) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (= (tptp.aElementOf0 W2 (tptp.sdtmndt0 _let_1 _let_2)) (and (tptp.aElement0 W2) (tptp.aElementOf0 W2 _let_1) (not (= W2 _let_2)))))))) (or (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1))))))) (tptp.aSubsetOf0 W1 _let_3)))) (tptp.isCountable0 W1)) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (let ((_let_3 (tptp.sdtmndt0 _let_1 _let_2))) (=> (and (tptp.aSet0 W2) (or (and (or (forall ((W3 $$unsorted)) (=> (tptp.aElementOf0 W3 W2) (tptp.aElementOf0 W3 W1))) (tptp.aSubsetOf0 W2 W1)) (= (tptp.sbrdtbr0 W2) tptp.xk)) (tptp.aElementOf0 W2 (tptp.slbdtsldtrb0 W1 tptp.xk)))) (and (tptp.aElementOf0 _let_2 _let_1) (forall ((W3 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W3 _let_1) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W3)))) (tptp.aSet0 _let_3) (forall ((W3 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (= (tptp.aElementOf0 W3 (tptp.sdtmndt0 _let_1 _let_2)) (and (tptp.aElement0 W3) (tptp.aElementOf0 W3 _let_1) (not (= W3 _let_2))))))) (forall ((W3 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W3 W2) (tptp.aElementOf0 W3 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1)))))) (tptp.aSubsetOf0 W2 _let_3) (tptp.aElementOf0 W2 (tptp.slbdtsldtrb0 _let_3 tptp.xk))))))))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.xT) (exists ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (let ((_let_3 (tptp.sdtmndt0 _let_1 _let_2))) (and (tptp.aElementOf0 _let_2 _let_1) (forall ((W3 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W3 _let_1) (tptp.sdtlseqdt0 (tptp.szmzizndt0 _let_1) W3)))) (tptp.aSet0 _let_3) (forall ((W3 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (= (tptp.aElementOf0 W3 (tptp.sdtmndt0 _let_1 _let_2)) (and (tptp.aElement0 W3) (tptp.aElementOf0 W3 _let_1) (not (= W3 _let_2))))))) (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W3 W2) (tptp.aElementOf0 W3 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1)))))) (tptp.aSubsetOf0 W2 _let_3) (tptp.isCountable0 W2) (forall ((W3 $$unsorted)) (=> (and (tptp.aSet0 W3) (or (and (or (forall ((W4 $$unsorted)) (=> (tptp.aElementOf0 W4 W3) (tptp.aElementOf0 W4 W2))) (tptp.aSubsetOf0 W3 W2)) (= (tptp.sbrdtbr0 W3) tptp.xk)) (tptp.aElementOf0 W3 (tptp.slbdtsldtrb0 W2 tptp.xk)))) (= (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC W0) W3) W1)))))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.xT) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)))) (=> (and (tptp.aSet0 W2) (or (and (or (forall ((W3 $$unsorted)) (=> (tptp.aElementOf0 W3 W2) (tptp.aElementOf0 W3 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0))))) (tptp.aSubsetOf0 W2 _let_1)) (= (tptp.sbrdtbr0 W2) tptp.xk)) (tptp.aElementOf0 W2 (tptp.slbdtsldtrb0 _let_1 tptp.xk)))) (= (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC W0) W2) W1)))))))) (and (tptp.aFunction0 tptp.xe) (= (tptp.szDzozmdt0 tptp.xe) tptp.szNzAzT0) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.sdtlpdtrp0 tptp.xe W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (and (tptp.aElementOf0 _let_2 _let_1) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 (tptp.sdtlpdtrp0 tptp.xN W0)) (tptp.sdtlseqdt0 (tptp.sdtlpdtrp0 tptp.xe W0) W1))) (= _let_2 (tptp.szmzizndt0 _let_1)))))))) (and (tptp.aFunction0 tptp.xd) (= _let_23 tptp.szNzAzT0) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)))) (=> (and (tptp.aSet0 W1) (or (and (or (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0))))) (tptp.aSubsetOf0 W1 _let_1)) (= (tptp.sbrdtbr0 W1) tptp.xk)) (tptp.aElementOf0 W1 (tptp.slbdtsldtrb0 _let_1 tptp.xk)))) (= (tptp.sdtlpdtrp0 tptp.xd W0) (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC W0) W1)))))))) (and (tptp.aSet0 _let_24) (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.sdtlcdtrc0 tptp.xd (tptp.szDzozmdt0 tptp.xd))) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 (tptp.szDzozmdt0 tptp.xd)) (= (tptp.sdtlpdtrp0 tptp.xd W1) W0))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.sdtlcdtrc0 tptp.xd (tptp.szDzozmdt0 tptp.xd))) (tptp.aElementOf0 W0 tptp.xT))) (tptp.aSubsetOf0 _let_24 tptp.xT)) (and (tptp.aElementOf0 _let_20 tptp.xT) _let_22 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szDzizrdt0 tptp.xd))) (= (tptp.aElementOf0 W0 (tptp.sdtlbdtrb0 tptp.xd _let_1)) (and (tptp.aElementOf0 W0 (tptp.szDzozmdt0 tptp.xd)) (= (tptp.sdtlpdtrp0 tptp.xd W0) _let_1)))))) (and _let_19 _let_22 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szDzizrdt0 tptp.xd))) (= (tptp.aElementOf0 W0 (tptp.sdtlbdtrb0 tptp.xd _let_1)) (and (tptp.aElementOf0 W0 (tptp.szDzozmdt0 tptp.xd)) (= (tptp.sdtlpdtrp0 tptp.xd W0) _let_1))))) (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 tptp.xO) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 (tptp.sdtlbdtrb0 tptp.xd (tptp.szDzizrdt0 tptp.xd))) (= (tptp.sdtlpdtrp0 tptp.xe W1) W0))))) (= tptp.xO (tptp.sdtlcdtrc0 tptp.xe _let_21))) (and _let_19 (tptp.isCountable0 tptp.xO)) (forall ((W0 $$unsorted)) (=> (or (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 (tptp.sdtlbdtrb0 tptp.xd (tptp.szDzizrdt0 tptp.xd))) (= (tptp.sdtlpdtrp0 tptp.xe W1) W0))) (tptp.aElementOf0 W0 tptp.xO)) (exists ((W1 $$unsorted)) (let ((_let_1 (tptp.szDzizrdt0 tptp.xd))) (and (tptp.aElementOf0 W1 tptp.szNzAzT0) (= (tptp.sdtlpdtrp0 tptp.xd W1) _let_1) (tptp.aElementOf0 W1 (tptp.sdtlbdtrb0 tptp.xd _let_1)) (= (tptp.sdtlpdtrp0 tptp.xe W1) W0)))))) (and (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xO) (tptp.aElementOf0 W0 tptp.xS))) (tptp.aSubsetOf0 tptp.xO tptp.xS)) _let_18 (and (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xQ) (tptp.aElementOf0 W0 tptp.xO))) (not (or (not (exists ((W0 $$unsorted)) (tptp.aElementOf0 W0 tptp.xQ))) (= tptp.xQ tptp.slcrc0)))) (and (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xQ) (tptp.aElementOf0 W0 tptp.szNzAzT0))) (tptp.aSubsetOf0 tptp.xQ tptp.szNzAzT0)) (and (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xQ) (tptp.aElementOf0 W0 tptp.xS))) _let_16 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xQ) (tptp.aElementOf0 W0 tptp.xS))) _let_16 (tptp.aElementOf0 tptp.xQ _let_15)) _let_14 _let_12 _let_8 (exists ((W0 $$unsorted)) (and (tptp.aElementOf0 W0 (tptp.sdtlbdtrb0 tptp.xd (tptp.szDzizrdt0 tptp.xd))) (= (tptp.sdtlpdtrp0 tptp.xe W0) tptp.xp))) _let_7 (and (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xP) (tptp.aElementOf0 W0 tptp.xO))) (tptp.aSubsetOf0 tptp.xP tptp.xO)) _let_5 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.73 )
% 0.21/0.73 % SZS output end Proof for NUM612+3
% 0.21/0.73 % cvc5---1.0.5 exiting
% 0.21/0.73 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------