TSTP Solution File: NUM558+3 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM558+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n001.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 10:45:05 EDT 2023
% Result : Theorem 0.44s 0.76s
% Output : Proof 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM558+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n001.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri Aug 25 18:26:59 EDT 2023
% 0.21/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.44/0.76 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.VYkcnIUPNM/cvc5---1.0.5_541.p...
% 0.44/0.76 ------- get file name : TPTP file name is NUM558+3
% 0.44/0.76 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_541.smt2...
% 0.44/0.76 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.44/0.76 % SZS status Theorem for NUM558+3
% 0.44/0.76 % SZS output start Proof for NUM558+3
% 0.44/0.76 (
% 0.44/0.76 (let ((_let_1 (tptp.aElementOf0 tptp.xx tptp.xT))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.slbdtsldtrb0 tptp.xS tptp.xk))) (let ((_let_4 (tptp.aElementOf0 tptp.xP _let_3))) (let ((_let_5 (tptp.sbrdtbr0 tptp.xP))) (let ((_let_6 (and (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xP) (tptp.aElementOf0 W0 tptp.xS))) (tptp.aSubsetOf0 tptp.xP tptp.xS) (= _let_5 tptp.xk) _let_4))) (let ((_let_7 (tptp.sdtmndt0 tptp.xQ tptp.xy))) (let ((_let_8 (tptp.aSet0 tptp.xP))) (let ((_let_9 (and (tptp.aSet0 _let_7) (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.sdtmndt0 tptp.xQ tptp.xy)) (and (tptp.aElement0 W0) (tptp.aElementOf0 W0 tptp.xQ) (not (= W0 tptp.xy))))) _let_8 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 tptp.xP) (and (tptp.aElement0 W0) (or (tptp.aElementOf0 W0 (tptp.sdtmndt0 tptp.xQ tptp.xy)) (= W0 tptp.xx))))) (= tptp.xP (tptp.sdtpldt0 _let_7 tptp.xx))))) (let ((_let_10 (not (tptp.aElementOf0 tptp.xx tptp.xQ)))) (let ((_let_11 (= (tptp.sbrdtbr0 tptp.xQ) tptp.xk))) (let ((_let_12 (tptp.aSet0 tptp.xQ))) (let ((_let_13 (tptp.aElementOf0 tptp.xx tptp.xS))) (let ((_let_14 (tptp.slbdtsldtrb0 tptp.xT tptp.xk))) (let ((_let_15 (and (tptp.aSet0 _let_3) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 tptp.xS tptp.xk)))) (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))))))) (tptp.aSet0 _let_14) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 tptp.xT tptp.xk)))) (let ((_let_2 (= (tptp.sbrdtbr0 W0) tptp.xk))) (let ((_let_3 (tptp.aSubsetOf0 W0 tptp.xT))) (let ((_let_4 (tptp.aSet0 W0))) (and (=> _let_1 (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xT))) _let_3 _let_2)) (=> (and (or (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xT)))) _let_3) _let_2) _let_1))))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 tptp.xS tptp.xk)) (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 tptp.xT tptp.xk)))) (tptp.aSubsetOf0 _let_3 _let_14) (not (=> (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 tptp.xS tptp.xk)))) (let ((_let_2 (= (tptp.sbrdtbr0 W0) tptp.xk))) (let ((_let_3 (tptp.aSubsetOf0 W0 tptp.xS))) (let ((_let_4 (tptp.aSet0 W0))) (and (=> _let_1 (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xS))) _let_3 _let_2)) (=> (and (or (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xS)))) _let_3) _let_2) _let_1))))))) (or (not (exists ((W0 $$unsorted)) (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 tptp.xS tptp.xk)))) (= _let_3 tptp.slcrc0))))))) (let ((_let_16 (tptp.aSet0 tptp.xT))) (let ((_let_17 (tptp.aSet0 tptp.xS))) (let ((_let_18 (and _let_17 _let_16 (not (= tptp.xk tptp.sz00))))) (let ((_let_19 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (= (tptp.aSubsetOf0 W1 W0) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 W0)))))))))) (let ((_let_20 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))))) (let ((_let_21 (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xP)) (tptp.aElementOf0 W1 tptp.xT))))) (let ((_let_22 (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 tptp.xP)) (tptp.aElementOf0 W2 tptp.xT))))) (let ((_let_23 (tptp.aElementOf0 tptp.xx tptp.xP))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or _let_24 _let_1))) (let ((_let_26 (not _let_25))) (let ((_let_27 (tptp.aElement0 tptp.xx))) (let ((_let_28 (= _let_27 _let_23))) (let ((_let_29 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 tptp.xP) (and (tptp.aElement0 W0) (or (tptp.aElementOf0 W0 (tptp.sdtmndt0 tptp.xQ tptp.xy)) (= tptp.xx W0))))))) (let ((_let_30 (3))) (let ((_let_31 (_let_29))) (let ((_let_32 (not _let_13))) (let ((_let_33 (not _let_17))) (let ((_let_34 (or _let_33 _let_32 _let_27))) (let ((_let_35 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1519 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1519 W0)) (tptp.aElement0 BOUND_VARIABLE_1519))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (_let_21))) (let ((_let_39 (and _let_8 _let_22))) (let ((_let_40 (tptp.aSubsetOf0 tptp.xP tptp.xT))) (let ((_let_41 (= _let_40 _let_39))) (let ((_let_42 (not _let_16))) (let ((_let_43 (or _let_42 _let_41))) (let ((_let_44 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1584 $$unsorted)) (or (not (tptp.aSet0 W0)) (= (tptp.aSubsetOf0 BOUND_VARIABLE_1584 W0) (and (tptp.aSet0 BOUND_VARIABLE_1584) (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 BOUND_VARIABLE_1584)) (tptp.aElementOf0 W2 W0))))))))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_46 (and _let_8 (or (not (tptp.aElementOf0 tptp.xy tptp.xP)) (tptp.aElementOf0 tptp.xy tptp.xT)) _let_40 (= tptp.xk _let_5)))) (let ((_let_47 (tptp.aElementOf0 tptp.xP _let_14))) (let ((_let_48 (not _let_47))) (let ((_let_49 (or _let_48 _let_46))) (let ((_let_50 (forall ((BOUND_VARIABLE_2484 $$unsorted) (BOUND_VARIABLE_2521 $$unsorted)) (or (not (tptp.aElementOf0 BOUND_VARIABLE_2484 (tptp.slbdtsldtrb0 tptp.xT tptp.xk))) (and (tptp.aSet0 BOUND_VARIABLE_2484) (or (not (tptp.aElementOf0 BOUND_VARIABLE_2521 BOUND_VARIABLE_2484)) (tptp.aElementOf0 BOUND_VARIABLE_2521 tptp.xT)) (tptp.aSubsetOf0 BOUND_VARIABLE_2484 tptp.xT) (= tptp.xk (tptp.sbrdtbr0 BOUND_VARIABLE_2484))))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (_let_50))) (let ((_let_53 (not _let_4))) (let ((_let_54 (or _let_53 _let_47))) (let ((_let_55 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 tptp.xS tptp.xk))) (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 tptp.xT tptp.xk)))))) (let ((_let_56 (_let_55))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (ALPHA_EQUIV :args (_let_21 (= W1 W2)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_39 1)) :args ((or _let_22 (not _let_39)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_41)) :args ((or (not _let_40) _let_39 (not _let_41)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_46 2)) :args ((or _let_40 (not _let_46)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_48 _let_46 (not _let_49)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_53 _let_47 (not _let_54)))) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) :args _let_30) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_56) :args (tptp.xP QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 W0 _let_3) false))))) :args _let_56)) (AND_ELIM _let_51 :args (2)) :args (_let_54 false _let_55)) :args (_let_47 false _let_4 false _let_54)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_52) :args (tptp.xP tptp.xy QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aElementOf0 BOUND_VARIABLE_2521 BOUND_VARIABLE_2484)))) :args _let_52)) (AND_ELIM _let_51 :args (7)) :args (_let_49 false _let_50)) :args (_let_46 false _let_47 false _let_49)) :args (_let_40 false _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_42 _let_41 (not _let_43)))) (AND_ELIM _let_37 :args (1)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_45 :args (tptp.xT tptp.xP QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aSubsetOf0 BOUND_VARIABLE_1584 W0)))) :args (_let_44))) _let_45 :args (_let_43 false _let_44)) :args (_let_41 false _let_16 false _let_43)) :args (_let_39 false _let_40 false _let_41)) :args (_let_22 false _let_39)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_38) :args (tptp.xx QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 W1 tptp.xT) true))))) :args _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_1 _let_24 _let_26))) (ASSUME :args (_let_2)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_28)) :args ((or (not _let_27) _let_23 (not _let_28)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_33 _let_32 _let_27 (not _let_34)))) (AND_ELIM _let_37 :args (0)) (ASSUME :args (_let_13)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (tptp.xS tptp.xx QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 BOUND_VARIABLE_1519 W0) false))))) :args (_let_35))) _let_36 :args (_let_34 false _let_35)) :args (_let_27 false _let_17 false _let_13 false _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_31) :args (tptp.xx QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aElement0 W0)))) :args _let_31))) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))) :args _let_30) :args (_let_28 false _let_29)) :args (_let_23 false _let_27 false _let_28)) :args (_let_26 true _let_1 false _let_23)) :args ((not _let_21) true _let_25)) :args (false false _let_22 true _let_21)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)) _let_20 (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)))))) (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 $$unsorted)) (=> (tptp.aSet0 W0) (tptp.aElement0 (tptp.sbrdtbr0 W0)))) (forall ((W0 $$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 $$unsorted)) (=> (and (tptp.aElementOf0 W1 tptp.szNzAzT0) (not (= W1 tptp.sz00))) (tptp.isCountable0 (tptp.slbdtsldtrb0 W0 W1)))))) (tptp.aElementOf0 tptp.xk tptp.szNzAzT0) _let_18 _let_15 _let_13 (and _let_12 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xQ) (tptp.aElementOf0 W0 tptp.xS))) (tptp.aSubsetOf0 tptp.xQ tptp.xS) _let_11 (tptp.aElementOf0 tptp.xQ _let_3)) (and _let_12 (tptp.isFinite0 tptp.xQ) _let_11) (and (tptp.aElement0 tptp.xy) (tptp.aElementOf0 tptp.xy tptp.xQ)) _let_10 _let_10 _let_9 _let_6 _let_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.44/0.77 )
% 0.44/0.77 % SZS output end Proof for NUM558+3
% 0.44/0.77 % cvc5---1.0.5 exiting
% 0.44/0.77 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------