TSTP Solution File: NUM586+1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM586+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 10:45:21 EDT 2023
% Result : Theorem 26.03s 26.25s
% Output : Proof 26.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM586+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : do_cvc5 %s %d
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri Aug 25 16:12:58 EDT 2023
% 0.11/0.31 % CPUTime :
% 0.16/0.41 %----Proving TF0_NAR, FOF, or CNF
% 26.03/26.25 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.7HWGM20H9j/cvc5---1.0.5_20062.p...
% 26.03/26.25 ------- get file name : TPTP file name is NUM586+1
% 26.03/26.25 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_20062.smt2...
% 26.03/26.25 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 26.03/26.25 --- Run --no-e-matching --full-saturate-quant at 5...
% 26.03/26.25 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 26.03/26.25 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 26.03/26.25 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 26.03/26.25 % SZS status Theorem for NUM586+1
% 26.03/26.25 % SZS output start Proof for NUM586+1
% 26.03/26.25 (
% 26.03/26.25 (let ((_let_1 (not (exists ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN tptp.xi))) (and (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1)) tptp.xk)) (= (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC tptp.xi) W0) tptp.xx))))))) (let ((_let_2 (tptp.sdtlpdtrp0 tptp.xC tptp.xi))) (let ((_let_3 (tptp.szDzozmdt0 _let_2))) (let ((_let_4 (tptp.sdtlcdtrc0 _let_2 _let_3))) (let ((_let_5 (tptp.aElementOf0 tptp.xx _let_4))) (let ((_let_6 (tptp.aElementOf0 tptp.xi tptp.szNzAzT0))) (let ((_let_7 (tptp.szDzozmdt0 tptp.xC))) (let ((_let_8 (tptp.aFunction0 tptp.xC))) (let ((_let_9 (and _let_8 (= _let_7 tptp.szNzAzT0) (forall ((W0 $$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 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (=> (and (tptp.aSet0 W1) (tptp.aElementOf0 W1 (tptp.slbdtsldtrb0 (tptp.sdtmndt0 _let_1 _let_2) tptp.xk))) (= (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC W0) W1) (tptp.sdtlpdtrp0 tptp.xc (tptp.sdtpldt0 W1 _let_2))))))))))))))) (let ((_let_10 (tptp.szDzozmdt0 tptp.xN))) (let ((_let_11 (and (tptp.aFunction0 tptp.xN) (= _let_10 tptp.szNzAzT0) (= (tptp.sdtlpdtrp0 tptp.xN tptp.sz00) tptp.xS) (forall ((W0 $$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)))))))))) (let ((_let_12 (and (tptp.aElementOf0 tptp.xk tptp.szNzAzT0) (= (tptp.szszuzczcdt0 tptp.xk) tptp.xK)))) (let ((_let_13 (not (= tptp.xK tptp.sz00)))) (let ((_let_14 (tptp.szDzozmdt0 tptp.xc))) (let ((_let_15 (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 $$unsorted)) (and (tptp.aElementOf0 W4 W1) (= (tptp.sdtlpdtrp0 W0 W4) W3)))))))))))))) (let ((_let_16 (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (tptp.aSet0 (tptp.szDzozmdt0 W0)))))) (let ((_let_17 (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0))) (let ((_let_18 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (tptp.aSubsetOf0 W0 W0))))) (let ((_let_19 (tptp.sdtlpdtrp0 tptp.xN tptp.xi))) (let ((_let_20 (tptp.szmzizndt0 _let_19))) (let ((_let_21 (tptp.slbdtsldtrb0 (tptp.sdtmndt0 _let_19 _let_20) tptp.xk))) (let ((_let_22 (= _let_3 _let_21))) (let ((_let_23 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 _let_3))) (let ((_let_24 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 _let_21))) (let ((_let_25 (tptp.aFunction0 _let_2))) (let ((_let_26 (and _let_25 _let_22 (or (not (tptp.aSet0 tptp.sz00)) (not (tptp.aElementOf0 tptp.sz00 _let_21)) (= (tptp.sdtlpdtrp0 _let_2 tptp.sz00) (tptp.sdtlpdtrp0 tptp.xc (tptp.sdtpldt0 tptp.sz00 _let_20))))))) (let ((_let_27 (tptp.aElementOf0 tptp.xi _let_10))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or _let_28 _let_26))) (let ((_let_30 (forall ((W0 $$unsorted) (BOUND_VARIABLE_3221 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (let ((_let_3 (tptp.sdtlpdtrp0 tptp.xC W0))) (let ((_let_4 (tptp.slbdtsldtrb0 (tptp.sdtmndt0 _let_1 _let_2) tptp.xk))) (or (not (tptp.aElementOf0 W0 (tptp.szDzozmdt0 tptp.xN))) (and (tptp.aFunction0 _let_3) (= (tptp.szDzozmdt0 _let_3) _let_4) (or (not (tptp.aSet0 BOUND_VARIABLE_3221)) (not (tptp.aElementOf0 BOUND_VARIABLE_3221 _let_4)) (= (tptp.sdtlpdtrp0 _let_3 BOUND_VARIABLE_3221) (tptp.sdtlpdtrp0 tptp.xc (tptp.sdtpldt0 BOUND_VARIABLE_3221 _let_2))))))))))))) (let ((_let_31 (2))) (let ((_let_32 (1))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (AND_INTRO (AND_ELIM _let_33 :args _let_31) (AND_ELIM _let_33 :args _let_32) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))) :args _let_32) (SYMM (ASSUME :args (_let_17)))))) (let ((_let_35 (_let_30))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_28 _let_26 (not _let_29)))) (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO _let_34 :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_35) :args (tptp.xi tptp.sz00 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_35)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_9)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_34 :args ((and _let_8 (= tptp.szNzAzT0 _let_7) (forall ((W0 $$unsorted) (BOUND_VARIABLE_3221 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (let ((_let_3 (tptp.sdtlpdtrp0 tptp.xC W0))) (let ((_let_4 (tptp.slbdtsldtrb0 (tptp.sdtmndt0 _let_1 _let_2) tptp.xk))) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (and (tptp.aFunction0 _let_3) (= (tptp.szDzozmdt0 _let_3) _let_4) (or (not (tptp.aSet0 BOUND_VARIABLE_3221)) (not (tptp.aElementOf0 BOUND_VARIABLE_3221 _let_4)) (= (tptp.sdtlpdtrp0 _let_3 BOUND_VARIABLE_3221) (tptp.sdtlpdtrp0 tptp.xc (tptp.sdtpldt0 BOUND_VARIABLE_3221 _let_2)))))))))))) SB_DEFAULT SBA_FIXPOINT)))) :args _let_31) :args (_let_29 false _let_30)) :args (_let_26 false _let_27 false _let_29)))) (let ((_let_37 (not _let_26))) (let ((_let_38 (= tptp.xx (tptp.sdtlpdtrp0 _let_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20)))) (let ((_let_39 (not _let_38))) (let ((_let_40 (not _let_23))) (let ((_let_41 (or _let_40 _let_39))) (let ((_let_42 (forall ((W4 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xC tptp.xi))) (or (not (tptp.aElementOf0 W4 (tptp.szDzozmdt0 _let_1))) (not (= tptp.xx (tptp.sdtlpdtrp0 _let_1 W4)))))))) (let ((_let_43 (not _let_41))) (let ((_let_44 (not _let_42))) (let ((_let_45 (= _let_5 _let_44))) (let ((_let_46 (forall ((W3 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xC tptp.xi))) (= (not (forall ((W4 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xC tptp.xi))) (or (not (tptp.aElementOf0 W4 (tptp.szDzozmdt0 _let_1))) (not (= W3 (tptp.sdtlpdtrp0 _let_1 W4))))))) (tptp.aElementOf0 W3 (tptp.sdtlcdtrc0 _let_1 (tptp.szDzozmdt0 _let_1)))))))) (let ((_let_47 (and (tptp.aSet0 _let_4) _let_46))) (let ((_let_48 (tptp.aSubsetOf0 _let_3 _let_3))) (let ((_let_49 (not _let_48))) (let ((_let_50 (not _let_25))) (let ((_let_51 (or _let_50 _let_49 _let_47))) (let ((_let_52 (forall ((W0 $$unsorted) (BOUND_VARIABLE_2839 $$unsorted) (BOUND_VARIABLE_2837 $$unsorted)) (or (not (tptp.aFunction0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_2837 (tptp.szDzozmdt0 W0))) (= (and (tptp.aSet0 BOUND_VARIABLE_2839) (forall ((W3 $$unsorted)) (= (not (forall ((W4 $$unsorted)) (or (not (tptp.aElementOf0 W4 BOUND_VARIABLE_2837)) (not (= W3 (tptp.sdtlpdtrp0 W0 W4)))))) (tptp.aElementOf0 W3 BOUND_VARIABLE_2839)))) (= BOUND_VARIABLE_2839 (tptp.sdtlcdtrc0 W0 BOUND_VARIABLE_2837))))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (tptp.aSet0 _let_3))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_55 _let_48))) (let ((_let_57 (forall ((W0 $$unsorted)) (or (not (tptp.aSet0 W0)) (tptp.aSubsetOf0 W0 W0))))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (or _let_50 _let_54))) (let ((_let_60 (forall ((W0 $$unsorted)) (or (not (tptp.aFunction0 W0)) (tptp.aSet0 (tptp.szDzozmdt0 W0)))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_26 0)) :args ((or _let_25 _let_37))) _let_36 :args (_let_25 false _let_26)))) (let ((_let_63 (_let_46))) (let ((_let_64 (or))) (let ((_let_65 (_let_44))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_65)) :args _let_65)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_42))) (REFL :args (_let_43)) :args _let_64)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_45)) :args ((or (not _let_5) _let_44 (not _let_45)))) (ASSUME :args (_let_5)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_63) :args (tptp.xx QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aElementOf0 W3 _let_4)))) :args _let_63))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_47 1)) :args ((or _let_46 (not _let_47)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_50 _let_49 _let_47 (not _let_51)))) _let_62 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_48 _let_55 (not _let_56)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_50 _let_54 (not _let_59)))) _let_62 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (_let_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.szDzozmdt0 W0)))) :args (_let_60))) _let_61 :args (_let_59 false _let_60)) :args (_let_54 false _let_25 false _let_59)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (_let_3 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_57))) _let_58 :args (_let_56 false _let_57)) :args (_let_48 false _let_54 false _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_53 :args (_let_2 _let_4 _let_3 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_52)))) _let_53 :args (_let_51 false _let_52)) :args (_let_47 false _let_25 false _let_48 false _let_51)) :args (_let_46 false _let_47)) :args (_let_45 false _let_46)) :args (_let_44 false _let_5 false _let_45)) :args (_let_43 true _let_42)))) (let ((_let_67 (REFL :args (_let_41)))) (let ((_let_68 (not _let_24))) (let ((_let_69 (or _let_68 _let_39))) (let ((_let_70 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN tptp.xi))) (or (not (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1)) tptp.xk))) (not (= tptp.xx (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC tptp.xi) W0)))))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (ASSUME :args (_let_68)))) (let ((_let_73 (ASSUME :args (_let_22)))) (let ((_let_74 (ASSUME :args (_let_23)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_72 _let_73 _let_74) :args (_let_22 _let_23 _let_68)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_74)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20)) (SYMM (SYMM _let_73)) :args (APPLY_UF tptp.aElementOf0)) (FALSE_INTRO _let_72))) :args (_let_68 _let_22 _let_23)) :args ((not (and _let_22 _let_23 _let_68)) SB_LITERAL))) (CONG (REFL :args ((not _let_22))) (REFL :args (_let_40)) (MACRO_SR_PRED_INTRO :args ((= (not _let_68) _let_24))) :args _let_64)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_39 _let_68 (not _let_69)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_41 1)) (CONG _let_67 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_64)) :args ((or _let_38 _let_41))) _let_66 :args (_let_38 true _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_70))) _let_71 :args (_let_69 false _let_70)) :args (_let_68 false _let_38 false _let_69)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_41 0)) (CONG _let_67 (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_23))) :args _let_64)) :args ((or _let_23 _let_41))) _let_66 :args (_let_23 true _let_41)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_26 1)) :args ((or _let_22 _let_37))) _let_36 :args (_let_22 false _let_26)) :args (false true _let_24 false _let_23 false _let_22)) :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 $$unsorted)) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 W0)))))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isFinite0 W0)) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (tptp.isFinite0 W1))))) _let_18 (forall ((W0 $$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_17 (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 $$unsorted)) (=> (tptp.aFunction0 W0) true)) _let_16 (forall ((W0 $$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 $$unsorted)) (=> (and (tptp.aFunction0 W0) (tptp.aElement0 W1)) (tptp.aSubsetOf0 (tptp.sdtlbdtrb0 W0 W1) (tptp.szDzozmdt0 W0)))) _let_15 (forall ((W0 $$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_14 (tptp.slbdtsldtrb0 tptp.xS tptp.xK)) (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 tptp.xc _let_14) 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_13 _let_13 _let_12 _let_11 (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)))))))) _let_9 _let_6 _let_5 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 26.03/26.26 )
% 26.03/26.26 % SZS output end Proof for NUM586+1
% 26.03/26.26 % cvc5---1.0.5 exiting
% 26.03/26.26 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------