TSTP Solution File: NUM544+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM544+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n011.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 10:44:56 EDT 2023
% Result : Theorem 26.76s 26.98s
% Output : Proof 26.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM544+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 10:03:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 26.76/26.98 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.wdN3HfsLqp/cvc5---1.0.5_21194.p...
% 26.76/26.98 ------- get file name : TPTP file name is NUM544+1
% 26.76/26.98 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_21194.smt2...
% 26.76/26.98 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 26.76/26.98 --- Run --no-e-matching --full-saturate-quant at 5...
% 26.76/26.98 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 26.76/26.98 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 26.76/26.98 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 26.76/26.98 % SZS status Theorem for NUM544+1
% 26.76/26.98 % SZS output start Proof for NUM544+1
% 26.76/26.98 (
% 26.76/26.98 (let ((_let_1 (tptp.szmzazxdt0 tptp.xS))) (let ((_let_2 (tptp.szszuzczcdt0 _let_1))) (let ((_let_3 (tptp.slbdtrb0 _let_2))) (let ((_let_4 (tptp.aSubsetOf0 tptp.xS _let_3))) (let ((_let_5 (not (=> (not (= tptp.xS tptp.slcrc0)) _let_4)))) (let ((_let_6 (tptp.isFinite0 tptp.xS))) (let ((_let_7 (tptp.aSubsetOf0 tptp.xS tptp.szNzAzT0))) (let ((_let_8 (and _let_7 _let_6))) (let ((_let_9 (tptp.slbdtrb0 tptp.sz00))) (let ((_let_10 (= _let_9 tptp.slcrc0))) (let ((_let_11 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (= (= W1 (tptp.slbdtrb0 W0)) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (= (tptp.aElementOf0 W2 W1) (and (tptp.aElementOf0 W2 tptp.szNzAzT0) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W2) W0))))))))))) (let ((_let_12 (forall ((W0 $$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)))))))))) (let ((_let_13 (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))))))) (let ((_let_14 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szszuzczcdt0 W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (and (tptp.aElementOf0 _let_1 tptp.szNzAzT0) (not (= _let_1 tptp.sz00)))))))) (let ((_let_15 (tptp.aSet0 tptp.szNzAzT0))) (let ((_let_16 (and _let_15 (tptp.isCountable0 tptp.szNzAzT0)))) (let ((_let_17 (forall ((W0 $$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 (tptp.aElementOf0 _let_1 tptp.szNzAzT0))) (let ((_let_19 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 tptp.szNzAzT0))) (let ((_let_20 (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24) _let_2))) (let ((_let_21 (tptp.sdtlseqdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 _let_1))) (let ((_let_22 (= _let_21 _let_20))) (let ((_let_23 (not _let_18))) (let ((_let_24 (not _let_19))) (let ((_let_25 (or _let_24 _let_23 _let_22))) (let ((_let_26 (tptp.aElementOf0 _let_1 tptp.xS))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or _let_27 _let_18))) (let ((_let_29 (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 tptp.xS)) (tptp.aElementOf0 W2 tptp.szNzAzT0))))) (let ((_let_30 (tptp.aSet0 tptp.xS))) (let ((_let_31 (and _let_30 _let_29))) (let ((_let_32 (= _let_7 _let_31))) (let ((_let_33 (not _let_15))) (let ((_let_34 (or _let_33 _let_32))) (let ((_let_35 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1327 $$unsorted)) (or (not (tptp.aSet0 W0)) (= (tptp.aSubsetOf0 BOUND_VARIABLE_1327 W0) (and (tptp.aSet0 BOUND_VARIABLE_1327) (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 BOUND_VARIABLE_1327)) (tptp.aElementOf0 W2 W0))))))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (_let_35))) (let ((_let_38 ((tptp.aSubsetOf0 BOUND_VARIABLE_1327 W0)))) (let ((_let_39 (0))) (let ((_let_40 (ASSUME :args (_let_8)))) (let ((_let_41 (AND_ELIM _let_40 :args _let_39))) (let ((_let_42 (not _let_7))) (let ((_let_43 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_32)) :args ((or _let_42 _let_31 (not _let_32)))) _let_41 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_33 _let_32 (not _let_34)))) (AND_ELIM (ASSUME :args (_let_16)) :args _let_39) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (tptp.szNzAzT0 tptp.xS QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_38)) :args _let_37)) _let_36 :args (_let_34 false _let_35)) :args (_let_32 false _let_15 false _let_34)) :args (_let_31 false _let_7 false _let_32)))) (let ((_let_44 (not _let_31))) (let ((_let_45 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_31 1)) :args ((or _let_29 _let_44))) _let_43 :args (_let_29 false _let_31)))) (let ((_let_46 (_let_29))) (let ((_let_47 (ASSUME :args _let_46))) (let ((_let_48 (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 tptp.xS)) (tptp.sdtlseqdt0 W2 (tptp.szmzazxdt0 tptp.xS)))))) (let ((_let_49 (and _let_26 _let_48))) (let ((_let_50 (= _let_9 tptp.xS))) (let ((_let_51 (not _let_6))) (let ((_let_52 (or _let_42 _let_51 _let_50 _let_49))) (let ((_let_53 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1890 $$unsorted)) (or (not (tptp.aSubsetOf0 W0 tptp.szNzAzT0)) (not (tptp.isFinite0 W0)) (= W0 (tptp.slbdtrb0 tptp.sz00)) (= (and (tptp.aElementOf0 BOUND_VARIABLE_1890 W0) (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 W0)) (tptp.sdtlseqdt0 W2 BOUND_VARIABLE_1890)))) (= (tptp.szmzazxdt0 W0) BOUND_VARIABLE_1890)))))) (let ((_let_54 (SYMM (ASSUME :args (_let_10))))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_12)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_54 :args ((forall ((W0 $$unsorted) (BOUND_VARIABLE_1890 $$unsorted)) (or (not (tptp.aSubsetOf0 W0 tptp.szNzAzT0)) (not (tptp.isFinite0 W0)) (= tptp.slcrc0 W0) (= (and (tptp.aElementOf0 BOUND_VARIABLE_1890 W0) (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 W0)) (tptp.sdtlseqdt0 W2 BOUND_VARIABLE_1890)))) (= (tptp.szmzazxdt0 W0) BOUND_VARIABLE_1890)))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_5)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_54 :args ((not (=> (not (= tptp.slcrc0 tptp.xS)) _let_4)) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_50 _let_42 _let_51 _let_49 (not _let_52)))) (NOT_IMPLIES_ELIM1 _let_56) _let_41 (AND_ELIM _let_40 :args (1)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_55 :args (tptp.xS _let_1 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_53)))) _let_55 :args (_let_52 false _let_53)) :args (_let_49 true _let_50 false _let_7 false _let_6 false _let_52)))) (let ((_let_58 (not _let_49))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_28)) :args ((or _let_18 _let_27 (not _let_28)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_49 0)) :args ((or _let_26 _let_58))) _let_57 :args (_let_26 false _let_49)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (_let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 W2 tptp.szNzAzT0) true))))) :args _let_46)) _let_45 :args (_let_28 false _let_29)) :args (_let_18 false _let_26 false _let_28)))) (let ((_let_60 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 tptp.xS))) (let ((_let_61 (not _let_60))) (let ((_let_62 (or _let_61 _let_19))) (let ((_let_63 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 _let_3))) (let ((_let_64 (or _let_61 _let_63))) (let ((_let_65 (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 tptp.xS)) (tptp.aElementOf0 W2 (tptp.slbdtrb0 (tptp.szszuzczcdt0 (tptp.szmzazxdt0 tptp.xS)))))))) (let ((_let_66 (not _let_64))) (let ((_let_67 (and _let_30 _let_65))) (let ((_let_68 (not _let_65))) (let ((_let_69 (= _let_4 _let_67))) (let ((_let_70 (not _let_67))) (let ((_let_71 (tptp.aSet0 _let_3))) (let ((_let_72 (not _let_71))) (let ((_let_73 (or _let_72 _let_69))) (let ((_let_74 (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.szszuzczcdt0 (tptp.szmzazxdt0 tptp.xS)))) (= (and (tptp.aElementOf0 W2 tptp.szNzAzT0) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W2) _let_1)) (tptp.aElementOf0 W2 (tptp.slbdtrb0 _let_1))))))) (let ((_let_75 (and _let_71 _let_74))) (let ((_let_76 (tptp.aElementOf0 _let_2 tptp.szNzAzT0))) (let ((_let_77 (not _let_76))) (let ((_let_78 (or _let_77 _let_75))) (let ((_let_79 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1932 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (= (= (tptp.slbdtrb0 W0) BOUND_VARIABLE_1932) (and (tptp.aSet0 BOUND_VARIABLE_1932) (forall ((W2 $$unsorted)) (= (and (tptp.aElementOf0 W2 tptp.szNzAzT0) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W2) W0)) (tptp.aElementOf0 W2 BOUND_VARIABLE_1932))))))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (and _let_76 (not (= tptp.sz00 _let_2))))) (let ((_let_82 (or _let_23 _let_81))) (let ((_let_83 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szszuzczcdt0 W0))) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (and (tptp.aElementOf0 _let_1 tptp.szNzAzT0) (not (= tptp.sz00 _let_1)))))))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_78)) :args ((or _let_77 _let_75 (not _let_78)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_81 0)) :args ((or _let_76 (not _let_81)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_23 _let_81 (not _let_82)))) _let_59 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (_let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.szszuzczcdt0 W0)))) :args (_let_83))) _let_84 :args (_let_82 false _let_83)) :args (_let_81 false _let_18 false _let_82)) :args (_let_76 false _let_81)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_80 :args (_let_2 _let_3 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_79)))) _let_80 :args (_let_78 false _let_79)) :args (_let_75 false _let_76 false _let_78)))) (let ((_let_86 (not _let_75))) (let ((_let_87 (or))) (let ((_let_88 (_let_68))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_88)) :args _let_88)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_68) _let_65))) (REFL :args (_let_66)) :args _let_87)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_67)) :args ((or (not _let_30) _let_67 _let_68))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_31 0)) :args ((or _let_30 _let_44))) _let_43 :args (_let_30 false _let_31)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_69)) :args ((or _let_4 _let_70 (not _let_69)))) (NOT_IMPLIES_ELIM2 _let_56) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_72 _let_69 (not _let_73)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_75 0)) :args ((or _let_71 _let_86))) _let_85 :args (_let_71 false _let_75)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (_let_3 tptp.xS QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_38)) :args _let_37)) _let_36 :args (_let_73 false _let_35)) :args (_let_69 false _let_71 false _let_73)) :args (_let_70 true _let_4 false _let_69)) :args (_let_68 false _let_30 true _let_67)) :args (_let_66 true _let_65)))) (let ((_let_90 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_64 0)) (CONG (REFL :args (_let_64)) (MACRO_SR_PRED_INTRO :args ((= (not _let_61) _let_60))) :args _let_87)) :args ((or _let_60 _let_64))) _let_89 :args (_let_60 true _let_64)))) (let ((_let_91 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_61 _let_19 (not _let_62)))) _let_90 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 W2 tptp.xS) false))))) :args _let_46)) _let_45 :args (_let_62 false _let_29)) :args (_let_19 false _let_60 false _let_62)))) (let ((_let_92 (not _let_22))) (let ((_let_93 (or _let_61 _let_21))) (let ((_let_94 (_let_48))) (let ((_let_95 (and _let_19 _let_20))) (let ((_let_96 (not _let_20))) (let ((_let_97 (= _let_63 _let_95))) (let ((_let_98 (not _let_95))) (let ((_let_99 (_let_74))) (let ((_let_100 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (not (tptp.aElementOf0 W1 tptp.szNzAzT0)) (= (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W0) (tptp.szszuzczcdt0 W1))))))) (let ((_let_101 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_23 _let_24 _let_22 (not _let_25)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_101 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 _let_1 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_100))) _let_101 :args (_let_25 false _let_100)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_22)) :args ((or _let_20 (not _let_21) _let_92))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_95)) :args ((or _let_24 _let_95 _let_96))) _let_91 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_97)) :args ((or _let_63 _let_98 (not _let_97)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_64 1)) _let_89 :args ((not _let_63) true _let_64)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_99) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aElementOf0 W2 _let_3)))) :args _let_99))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_75 1)) :args ((or _let_74 _let_86))) _let_85 :args (_let_74 false _let_75)) :args (_let_97 false _let_74)) :args (_let_98 true _let_63 false _let_97)) :args (_let_96 false _let_19 true _let_95)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_93)) :args ((or _let_61 _let_21 (not _let_93)))) _let_90 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_94) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 W2 tptp.xS) false))))) :args _let_94)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_49 1)) :args ((or _let_48 _let_58))) _let_57 :args (_let_48 false _let_49)) :args (_let_93 false _let_48)) :args (_let_21 false _let_60 false _let_93)) :args (_let_92 true _let_20 false _let_21)) _let_91 _let_59 :args (false false _let_25 true _let_22 false _let_19 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 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.isFinite0 W1)) (tptp.isFinite0 (tptp.sdtmndt0 W1 W0)))))) _let_16 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0) _let_14 (forall ((W0 $$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)))) _let_13 (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 $$unsorted)) (=> (tptp.aElementOf0 W2 W0) (tptp.sdtlseqdt0 W1 W2)))))))) _let_12 (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.szmzizndt0 W1))) (let ((_let_2 (tptp.szmzizndt0 W0))) (=> (and (tptp.aSubsetOf0 W0 tptp.szNzAzT0) (tptp.aSubsetOf0 W1 tptp.szNzAzT0) (not (= W0 tptp.slcrc0)) (not (= W1 tptp.slcrc0))) (=> (and (tptp.aElementOf0 _let_2 W1) (tptp.aElementOf0 _let_1 W0)) (= _let_2 _let_1)))))) _let_11 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.isFinite0 (tptp.slbdtrb0 W0)))) _let_10 (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))))) _let_8 _let_5 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 26.79/26.98 )
% 26.79/26.98 % SZS output end Proof for NUM544+1
% 26.79/26.98 % cvc5---1.0.5 exiting
% 26.79/26.98 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------