TSTP Solution File: NUM552+1 by cvc5---1.0.5

%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM552+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n013.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 10:45:01 EDT 2023

% Result   : Theorem 47.98s 48.22s
% Output   : Proof 47.98s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUM552+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n013.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Fri Aug 25 15:51:47 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.20/0.48  %----Proving TF0_NAR, FOF, or CNF
% 47.98/48.22  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.FvHwCvK0HY/cvc5---1.0.5_27049.p...
% 47.98/48.22  ------- get file name : TPTP file name is NUM552+1
% 47.98/48.22  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_27049.smt2...
% 47.98/48.22  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 47.98/48.22  --- Run --no-e-matching --full-saturate-quant at 5...
% 47.98/48.22  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 47.98/48.22  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 47.98/48.22  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 47.98/48.22  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 47.98/48.22  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 47.98/48.22  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 47.98/48.22  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 47.98/48.22  % SZS status Theorem for NUM552+1
% 47.98/48.22  % SZS output start Proof for NUM552+1
% 47.98/48.22  (
% 47.98/48.22  (let ((_let_1 (tptp.aElementOf0 tptp.xx tptp.xT))) (let ((_let_2 (tptp.aElementOf0 tptp.xx tptp.xQ))) (let ((_let_3 (not (=> _let_2 _let_1)))) (let ((_let_4 (tptp.sbrdtbr0 tptp.xQ))) (let ((_let_5 (tptp.aSet0 tptp.xQ))) (let ((_let_6 (and _let_5 (tptp.isFinite0 tptp.xQ) (= _let_4 tptp.xk)))) (let ((_let_7 (tptp.slbdtsldtrb0 tptp.xS tptp.xk))) (let ((_let_8 (tptp.aElementOf0 tptp.xQ _let_7))) (let ((_let_9 (tptp.aSubsetOf0 _let_7 (tptp.slbdtsldtrb0 tptp.xT tptp.xk)))) (let ((_let_10 (and _let_9 (not (= _let_7 tptp.slcrc0))))) (let ((_let_11 (tptp.aSet0 tptp.xT))) (let ((_let_12 (tptp.aSet0 tptp.xS))) (let ((_let_13 (and _let_12 _let_11 (not (= tptp.xk tptp.sz00))))) (let ((_let_14 (tptp.aElementOf0 tptp.xk tptp.szNzAzT0))) (let ((_let_15 (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))))))))))) (let ((_let_16 (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0))) (let ((_let_17 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (= (tptp.aSubsetOf0 W1 W0) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 W0)))))))))) (let ((_let_18 (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sbrdtbr0 tptp.xQ))) (or (not (tptp.aElementOf0 W2 (tptp.slbdtsldtrb0 tptp.xS _let_1))) (tptp.aElementOf0 W2 (tptp.slbdtsldtrb0 tptp.xT _let_1))))))) (let ((_let_19 (tptp.slbdtsldtrb0 tptp.xT _let_4))) (let ((_let_20 (tptp.aElementOf0 tptp.xQ _let_19))) (let ((_let_21 (tptp.slbdtsldtrb0 tptp.xS _let_4))) (let ((_let_22 (tptp.aElementOf0 tptp.xQ _let_21))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_23 _let_20))) (let ((_let_25 (and (tptp.aSet0 _let_21) _let_18))) (let ((_let_26 (tptp.aSubsetOf0 _let_21 _let_19))) (let ((_let_27 (= _let_26 _let_25))) (let ((_let_28 (forall ((W1 $$unsorted)) (= (tptp.aSubsetOf0 W1 (tptp.slbdtsldtrb0 tptp.xT (tptp.sbrdtbr0 tptp.xQ))) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 W1)) (tptp.aElementOf0 W2 (tptp.slbdtsldtrb0 tptp.xT (tptp.sbrdtbr0 tptp.xQ)))))))))) (let ((_let_29 (tptp.aSet0 _let_19))) (let ((_let_30 (not _let_29))) (let ((_let_31 (or _let_30 _let_28))) (let ((_let_32 (forall ((W0 $$unsorted)) (or (not (tptp.aSet0 W0)) (forall ((W1 $$unsorted)) (= (tptp.aSubsetOf0 W1 W0) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 W1)) (tptp.aElementOf0 W2 W0)))))))))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (_let_32))) (let ((_let_35 ((not (= (tptp.aSet0 W0) false))))) (let ((_let_36 (forall ((W3 $$unsorted)) (let ((_let_1 (tptp.sbrdtbr0 tptp.xQ))) (= (and (tptp.aSubsetOf0 W3 tptp.xT) (= (tptp.sbrdtbr0 W3) _let_1)) (tptp.aElementOf0 W3 (tptp.slbdtsldtrb0 tptp.xT _let_1))))))) (let ((_let_37 (and _let_29 _let_36))) (let ((_let_38 (forall ((W2 $$unsorted)) (= (= W2 (tptp.slbdtsldtrb0 tptp.xT (tptp.sbrdtbr0 tptp.xQ))) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aSubsetOf0 W3 tptp.xT) (= (tptp.sbrdtbr0 W3) (tptp.sbrdtbr0 tptp.xQ)))))))))) (let ((_let_39 (tptp.aElementOf0 _let_4 tptp.szNzAzT0))) (let ((_let_40 (not _let_39))) (let ((_let_41 (not _let_11))) (let ((_let_42 (or _let_41 _let_40 _let_38))) (let ((_let_43 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (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) (= W1 (tptp.sbrdtbr0 W3)))))))))))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_45 (AND_INTRO (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) :args (2)) (SYMM (ASSUME :args (_let_16)))))) (let ((_let_46 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_13)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_45 :args ((and _let_12 _let_11 (not (= tptp.sz00 tptp.xk))) SB_DEFAULT SBA_FIXPOINT)))) :args (1)))) (let ((_let_47 (_let_38))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_47) :args (_let_19 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_47))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_40 _let_41 _let_38 (not _let_42)))) (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO _let_45 :args (_let_14 SB_DEFAULT SBA_FIXPOINT))) _let_46 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_44 :args (tptp.xT _let_4 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_43)))) _let_44 :args (_let_42 false _let_43)) :args (_let_38 false _let_39 false _let_11 false _let_42)) :args (_let_37 false _let_38)))) (let ((_let_49 (not _let_37))) (let ((_let_50 (_let_28))) (let ((_let_51 (not _let_24))) (let ((_let_52 (tptp.aSubsetOf0 tptp.xQ tptp.xT))) (let ((_let_53 (= _let_52 _let_20))) (let ((_let_54 (not _let_20))) (let ((_let_55 (_let_36))) (let ((_let_56 (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 tptp.xQ)) (tptp.aElementOf0 W2 tptp.xT))))) (let ((_let_57 (and _let_5 _let_56))) (let ((_let_58 (= _let_52 _let_57))) (let ((_let_59 (not _let_52))) (let ((_let_60 (forall ((W1 $$unsorted)) (= (tptp.aSubsetOf0 W1 tptp.xT) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 W1)) (tptp.aElementOf0 W2 tptp.xT)))))))) (let ((_let_61 (or _let_41 _let_60))) (let ((_let_62 (_let_60))) (let ((_let_63 (not _let_57))) (let ((_let_64 (not _let_2))) (let ((_let_65 (or _let_64 _let_1))) (let ((_let_66 (not _let_65))) (let ((_let_67 (ASSUME :args (_let_3)))) (let ((_let_68 (_let_56))) (let ((_let_69 (_let_18))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_69) :args (tptp.xQ QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_69)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_24)) :args ((or _let_23 _let_20 _let_51))) (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO _let_45 :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_53)) :args ((or _let_52 _let_54 (not _let_53)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_58)) :args ((or _let_57 _let_59 (not _let_58)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_57 1)) :args ((or _let_56 _let_63))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_68) :args (tptp.xx QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_68)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_65)) :args ((or _let_1 _let_64 _let_66))) (NOT_IMPLIES_ELIM2 _let_67) (NOT_IMPLIES_ELIM1 _let_67) :args (_let_66 true _let_1 false _let_2)) :args ((not _let_56) true _let_65)) :args (_let_63 true _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_62) :args (tptp.xQ QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aSet0 W1)))) :args _let_62)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_61)) :args ((or _let_41 _let_60 (not _let_61)))) _let_46 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (tptp.xT QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_35)) :args _let_34)) _let_33 :args (_let_61 false _let_32)) :args (_let_60 false _let_11 false _let_61)) :args (_let_58 false _let_60)) :args (_let_59 true _let_57 false _let_58)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_55) :args (tptp.xQ QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sbrdtbr0 W3)))) :args _let_55))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_37 1)) :args ((or _let_36 _let_49))) _let_48 :args (_let_36 false _let_37)) :args (_let_53 false _let_36)) :args (_let_54 true _let_52 false _let_53)) :args (_let_51 false _let_22 true _let_20)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_25 1)) :args ((or _let_18 (not _let_25)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_27)) :args ((or (not _let_26) _let_25 (not _let_27)))) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_10)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_45 :args ((and _let_9 (not (= tptp.slcrc0 _let_7))) SB_DEFAULT SBA_FIXPOINT)))) :args (0)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_50) :args (_let_21 QUANTIFIERS_INST_CBQI_PROP)) :args _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_31)) :args ((or _let_30 _let_28 (not _let_31)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_37 0)) :args ((or _let_29 _let_49))) _let_48 :args (_let_29 false _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (_let_19 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_35)) :args _let_34)) _let_33 :args (_let_31 false _let_32)) :args (_let_28 false _let_29 false _let_31)) :args (_let_27 false _let_28)) :args (_let_25 false _let_26 false _let_27)) :args (_let_18 false _let_25)) :args (false true _let_24 false _let_18)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (=> (tptp.isFinite0 W0) true))) (forall ((W0 $$unsorted)) (= (= W0 tptp.slcrc0) (and (tptp.aSet0 W0) (not (exists ((W1 $$unsorted)) (tptp.aElementOf0 W1 W0)))))) (tptp.isFinite0 tptp.slcrc0) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (=> (tptp.isCountable0 W0) true))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isCountable0 W0)) (not (tptp.isFinite0 W0)))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isCountable0 W0)) (not (= W0 tptp.slcrc0)))) _let_17 (forall ((W0 $$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 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.isFinite0 (tptp.slbdtrb0 W0)))) _let_16 (forall ((W0 $$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))) _let_15 (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)))))) _let_14 _let_13 _let_10 (tptp.aElementOf0 tptp.xx tptp.xS) _let_8 _let_6 (and (tptp.aElement0 tptp.xy) (tptp.aElementOf0 tptp.xy tptp.xQ)) _let_3 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 47.98/48.23  )
% 47.98/48.23  % SZS output end Proof for NUM552+1
% 47.98/48.23  % cvc5---1.0.5 exiting
% 47.98/48.23  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------