TSTP Solution File: NUM610+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM610+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n022.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 10:45:36 EDT 2023
% Result : Theorem 0.70s 0.91s
% Output : Proof 0.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : NUM610+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n022.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
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri Aug 25 13:09:11 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.23/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.70/0.91 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.HHPUKZXjdp/cvc5---1.0.5_25467.p...
% 0.70/0.91 ------- get file name : TPTP file name is NUM610+1
% 0.70/0.91 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_25467.smt2...
% 0.70/0.91 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.70/0.91 % SZS status Theorem for NUM610+1
% 0.70/0.91 % SZS output start Proof for NUM610+1
% 0.70/0.91 (
% 0.70/0.91 (let ((_let_1 (tptp.aSubsetOf0 tptp.xP tptp.xO))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.aSubsetOf0 tptp.xP tptp.xQ))) (let ((_let_4 (tptp.szmzizndt0 tptp.xQ))) (let ((_let_5 (tptp.aSet0 tptp.xP))) (let ((_let_6 (and _let_5 (= tptp.xP (tptp.sdtmndt0 tptp.xQ _let_4))))) (let ((_let_7 (tptp.szDzozmdt0 tptp.xc))) (let ((_let_8 (tptp.aSubsetOf0 tptp.xQ tptp.szNzAzT0))) (let ((_let_9 (tptp.aSubsetOf0 tptp.xQ tptp.xO))) (let ((_let_10 (and _let_9 (not (= tptp.xQ tptp.slcrc0))))) (let ((_let_11 (tptp.aSet0 tptp.xO))) (let ((_let_12 (tptp.szDzizrdt0 tptp.xd))) (let ((_let_13 (tptp.sdtlbdtrb0 tptp.xd _let_12))) (let ((_let_14 (and _let_11 (= tptp.xO (tptp.sdtlcdtrc0 tptp.xe _let_13))))) (let ((_let_15 (tptp.szDzozmdt0 tptp.xd))) (let ((_let_16 (not (= tptp.xK tptp.sz00)))) (let ((_let_17 (tptp.aSet0 tptp.szNzAzT0))) (let ((_let_18 (and _let_17 (tptp.isCountable0 tptp.szNzAzT0)))) (let ((_let_19 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (= (tptp.aSubsetOf0 W1 W0) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 W0)))))))))) (let ((_let_20 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 tptp.xP))) (let ((_let_21 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 tptp.xQ))) (let ((_let_22 (not _let_20))) (let ((_let_23 (or _let_22 _let_21))) (let ((_let_24 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 tptp.xO))) (let ((_let_25 (or _let_22 _let_24))) (let ((_let_26 (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 tptp.xP)) (tptp.aElementOf0 W2 tptp.xO))))) (let ((_let_27 (not _let_25))) (let ((_let_28 (and _let_5 _let_26))) (let ((_let_29 (not _let_26))) (let ((_let_30 (= _let_1 _let_28))) (let ((_let_31 (not _let_28))) (let ((_let_32 (not _let_11))) (let ((_let_33 (or _let_32 _let_30))) (let ((_let_34 (forall ((W0 $$unsorted) (BOUND_VARIABLE_2000 $$unsorted)) (or (not (tptp.aSet0 W0)) (= (tptp.aSubsetOf0 BOUND_VARIABLE_2000 W0) (and (tptp.aSet0 BOUND_VARIABLE_2000) (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 BOUND_VARIABLE_2000)) (tptp.aElementOf0 W2 W0))))))))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (_let_34))) (let ((_let_37 ((tptp.aSubsetOf0 BOUND_VARIABLE_2000 W0)))) (let ((_let_38 (0))) (let ((_let_39 (AND_ELIM (ASSUME :args (_let_14)) :args _let_38))) (let ((_let_40 (or))) (let ((_let_41 (_let_29))) (let ((_let_42 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_41)) :args _let_41)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_26))) (REFL :args (_let_27)) :args _let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_28)) :args ((or (not _let_5) _let_28 _let_29))) (AND_ELIM (ASSUME :args (_let_6)) :args _let_38) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_30)) :args ((or _let_1 _let_31 (not _let_30)))) (ASSUME :args (_let_2)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_33)) :args ((or _let_32 _let_30 (not _let_33)))) _let_39 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (tptp.xO tptp.xP QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_37)) :args _let_36)) _let_35 :args (_let_33 false _let_34)) :args (_let_30 false _let_11 false _let_33)) :args (_let_31 true _let_1 false _let_30)) :args (_let_29 false _let_5 true _let_28)) :args (_let_27 true _let_26)))) (let ((_let_43 (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 tptp.xP)) (tptp.aElementOf0 W2 tptp.xQ))))) (let ((_let_44 (and _let_5 _let_43))) (let ((_let_45 (= _let_3 _let_44))) (let ((_let_46 (tptp.aSet0 tptp.xQ))) (let ((_let_47 (not _let_46))) (let ((_let_48 (or _let_47 _let_45))) (let ((_let_49 (and _let_46 (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 tptp.xQ)) (tptp.aElementOf0 W2 tptp.szNzAzT0)))))) (let ((_let_50 (= _let_8 _let_49))) (let ((_let_51 (not _let_17))) (let ((_let_52 (or _let_51 _let_50))) (let ((_let_53 (_let_43))) (let ((_let_54 (not _let_21))) (let ((_let_55 (or _let_54 _let_24))) (let ((_let_56 (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 tptp.xQ)) (tptp.aElementOf0 W2 tptp.xO))))) (let ((_let_57 (and _let_46 _let_56))) (let ((_let_58 (= _let_9 _let_57))) (let ((_let_59 (or _let_32 _let_58))) (let ((_let_60 (_let_56))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_23)) :args ((or _let_22 _let_21 (not _let_23)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_55)) :args ((or _let_24 _let_54 (not _let_55)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_25 1)) _let_42 :args ((not _let_24) true _let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_60) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 W2 tptp.xO) true))))) :args _let_60)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_57 1)) :args ((or _let_56 (not _let_57)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_58)) :args ((or (not _let_9) _let_57 (not _let_58)))) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))) :args _let_38) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_32 _let_58 (not _let_59)))) _let_39 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (tptp.xO tptp.xQ QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_37)) :args _let_36)) _let_35 :args (_let_59 false _let_34)) :args (_let_58 false _let_11 false _let_59)) :args (_let_57 false _let_9 false _let_58)) :args (_let_56 false _let_57)) :args (_let_55 false _let_56)) :args (_let_54 true _let_24 false _let_55)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_53) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 W2 tptp.xP) false))))) :args _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_44 1)) :args ((or _let_43 (not _let_44)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_45)) :args ((or (not _let_3) _let_44 (not _let_45)))) (ASSUME :args (_let_3)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_48)) :args ((or _let_47 _let_45 (not _let_48)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_49 0)) :args ((or _let_46 (not _let_49)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_50)) :args ((or (not _let_8) _let_49 (not _let_50)))) (ASSUME :args (_let_8)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_51 _let_50 (not _let_52)))) (AND_ELIM (ASSUME :args (_let_18)) :args _let_38) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (tptp.szNzAzT0 tptp.xQ QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_37)) :args _let_36)) _let_35 :args (_let_52 false _let_34)) :args (_let_50 false _let_17 false _let_52)) :args (_let_49 false _let_8 false _let_50)) :args (_let_46 false _let_49)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (tptp.xQ tptp.xP QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_37)) :args _let_36)) _let_35 :args (_let_48 false _let_34)) :args (_let_45 false _let_46 false _let_48)) :args (_let_44 false _let_3 false _let_45)) :args (_let_43 false _let_44)) :args (_let_23 false _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 0)) (CONG (REFL :args (_let_25)) (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_20))) :args _let_40)) :args ((or _let_20 _let_25))) _let_42 :args (_let_20 true _let_25)) :args (false true _let_21 false _let_23 false _let_20)) :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)))) _let_19 (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_18 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szszuzczcdt0 W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (and (tptp.aElementOf0 _let_1 tptp.szNzAzT0) (not (= _let_1 tptp.sz00)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (= (tptp.szszuzczcdt0 W0) (tptp.szszuzczcdt0 W1)) (= W0 W1)))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (or (= W0 tptp.sz00) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.szNzAzT0) (= W0 (tptp.szszuzczcdt0 W1))))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (not (= W0 (tptp.szszuzczcdt0 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (tptp.sdtlseqdt0 W0 W1) true))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 tptp.sz00 W0))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (not (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W0) tptp.sz00)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (= (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W0) (tptp.szszuzczcdt0 W1))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 W0 (tptp.szszuzczcdt0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 W0 W0))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0) (tptp.aElementOf0 W2 tptp.szNzAzT0)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (or (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W1) W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (tptp.iLess0 W0 W1) true))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.iLess0 W0 (tptp.szszuzczcdt0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (tptp.aElement0 (tptp.sbrdtbr0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (= (tptp.aElementOf0 (tptp.sbrdtbr0 W0) tptp.szNzAzT0) (tptp.isFinite0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (= (= (tptp.sbrdtbr0 W0) tptp.sz00) (= W0 tptp.slcrc0)))) (forall ((W0 $$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)))) (= (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)) (tptp.aElementOf0 tptp.xK tptp.szNzAzT0) (and (tptp.aSubsetOf0 tptp.xS tptp.szNzAzT0) (tptp.isCountable0 tptp.xS)) (and (tptp.aFunction0 tptp.xc) (= _let_7 (tptp.slbdtsldtrb0 tptp.xS tptp.xK)) (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 tptp.xc _let_7) tptp.xT)) (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_16 _let_16 (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 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)))) (let ((_let_2 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (=> (and (tptp.aSubsetOf0 _let_2 tptp.szNzAzT0) (tptp.isCountable0 _let_2)) (and (tptp.aSubsetOf0 _let_1 (tptp.sdtmndt0 _let_2 (tptp.szmzizndt0 _let_2))) (tptp.isCountable0 _let_1)))))))) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (and (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) (tptp.aSubsetOf0 (tptp.sdtlpdtrp0 tptp.xN W0) (tptp.sdtlpdtrp0 tptp.xN W1))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0) (not (= W0 W1))) (not (= (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN W0)) (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN W1)))))) (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))) (=> (and (tptp.aSet0 W1) (tptp.aElementOf0 W1 (tptp.slbdtsldtrb0 (tptp.sdtmndt0 _let_1 _let_2) tptp.xk))) (tptp.aElementOf0 (tptp.sdtpldt0 W1 _let_2) (tptp.slbdtsldtrb0 tptp.xS tptp.xK)))))))) (and (tptp.aFunction0 tptp.xC) (= (tptp.szDzozmdt0 tptp.xC) tptp.szNzAzT0) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.sdtlpdtrp0 tptp.xC W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (and (tptp.aFunction0 _let_2) (= (tptp.szDzozmdt0 _let_2) (tptp.slbdtsldtrb0 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1)) tptp.xk)) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (=> (and (tptp.aSet0 W1) (tptp.aElementOf0 W1 (tptp.slbdtsldtrb0 (tptp.sdtmndt0 _let_1 _let_2) tptp.xk))) (= (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC W0) W1) (tptp.sdtlpdtrp0 tptp.xc (tptp.sdtpldt0 W1 _let_2))))))))))))) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xC W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 _let_1 (tptp.szDzozmdt0 _let_1)) tptp.xT)))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (and (tptp.aSubsetOf0 W1 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1))) (tptp.isCountable0 W1)) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (and (tptp.aSet0 W2) (tptp.aElementOf0 W2 (tptp.slbdtsldtrb0 W1 tptp.xk))) (tptp.aElementOf0 W2 (tptp.slbdtsldtrb0 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1)) tptp.xk)))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.xT) (exists ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (and (tptp.aSubsetOf0 W2 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1))) (tptp.isCountable0 W2) (forall ((W3 $$unsorted)) (=> (and (tptp.aSet0 W3) (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 $$unsorted)) (=> (and (tptp.aSet0 W2) (tptp.aElementOf0 W2 (tptp.slbdtsldtrb0 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)) tptp.xk))) (= (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC W0) W2) W1))))))) (and (tptp.aFunction0 tptp.xe) (= (tptp.szDzozmdt0 tptp.xe) tptp.szNzAzT0) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (= (tptp.sdtlpdtrp0 tptp.xe W0) (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN W0)))))) (and (tptp.aFunction0 tptp.xd) (= _let_15 tptp.szNzAzT0) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.aElementOf0 W1 (tptp.slbdtsldtrb0 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)) tptp.xk))) (= (tptp.sdtlpdtrp0 tptp.xd W0) (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC W0) W1))))))) (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 tptp.xd _let_15) tptp.xT) (and (tptp.aElementOf0 _let_12 tptp.xT) (tptp.isCountable0 _let_13)) _let_14 (and _let_11 (tptp.isCountable0 tptp.xO)) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xO) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.szNzAzT0) (tptp.aElementOf0 W1 (tptp.sdtlbdtrb0 tptp.xd (tptp.szDzizrdt0 tptp.xd))) (= (tptp.sdtlpdtrp0 tptp.xe W1) W0))))) (tptp.aSubsetOf0 tptp.xO tptp.xS) (tptp.aElementOf0 tptp.xQ (tptp.slbdtsldtrb0 tptp.xO tptp.xK)) _let_10 _let_8 (tptp.aElementOf0 tptp.xQ _let_7) (= tptp.xp _let_4) _let_6 (tptp.aElementOf0 tptp.xp tptp.xQ) (tptp.aElementOf0 tptp.xp tptp.xO) _let_3 _let_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.70/0.91 )
% 0.70/0.91 % SZS output end Proof for NUM610+1
% 0.70/0.91 % cvc5---1.0.5 exiting
% 0.70/0.91 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------