TSTP Solution File: NUM541+2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM541+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n016.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 10:44:55 EDT 2023
% Result : Theorem 6.12s 6.33s
% Output : Proof 6.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM541+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n016.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 18:22:25 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.48 %----Proving TF0_NAR, FOF, or CNF
% 6.12/6.33 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.7WTX83icVI/cvc5---1.0.5_11052.p...
% 6.12/6.33 ------- get file name : TPTP file name is NUM541+2
% 6.12/6.33 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_11052.smt2...
% 6.12/6.33 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 6.12/6.33 % SZS status Theorem for NUM541+2
% 6.12/6.33 % SZS output start Proof for NUM541+2
% 6.12/6.33 (
% 6.12/6.33 (let ((_let_1 (tptp.szszuzczcdt0 tptp.xn))) (let ((_let_2 (tptp.aElementOf0 tptp.xm (tptp.slbdtrb0 _let_1)))) (let ((_let_3 (tptp.szszuzczcdt0 tptp.xm))) (let ((_let_4 (tptp.sdtlseqdt0 _let_3 _let_1))) (let ((_let_5 (or _let_4 _let_2))) (let ((_let_6 (= tptp.xm tptp.xn))) (let ((_let_7 (tptp.aElementOf0 tptp.xm (tptp.slbdtrb0 tptp.xn)))) (let ((_let_8 (tptp.sdtlseqdt0 _let_3 tptp.xn))) (let ((_let_9 (and _let_8 _let_7))) (let ((_let_10 (or _let_9 _let_6))) (let ((_let_11 (=> _let_10 _let_5))) (let ((_let_12 (or _let_8 _let_7 _let_6))) (let ((_let_13 (and _let_4 _let_2))) (let ((_let_14 (=> _let_13 _let_12))) (let ((_let_15 (not (and _let_14 _let_11)))) (let ((_let_16 (tptp.aElementOf0 tptp.xn tptp.szNzAzT0))) (let ((_let_17 (tptp.aElementOf0 tptp.xm tptp.szNzAzT0))) (let ((_let_18 (and _let_17 _let_16))) (let ((_let_19 (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)))))) (let ((_let_20 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0) (tptp.aElementOf0 W2 tptp.szNzAzT0)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))))) (let ((_let_21 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))))) (let ((_let_22 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 W0 (tptp.szszuzczcdt0 W0)))))) (let ((_let_23 (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_24 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (not (= W0 (tptp.szszuzczcdt0 W0))))))) (let ((_let_25 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (or (= W0 tptp.sz00) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.szNzAzT0) (= W0 (tptp.szszuzczcdt0 W1))))))))) (let ((_let_26 (forall ((W0 $$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_27 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (not (tptp.aElementOf0 W1 tptp.szNzAzT0)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W0)) (= W0 W1))))) (let ((_let_28 (tptp.sdtlseqdt0 tptp.xn tptp.xm))) (let ((_let_29 (not _let_28))) (let ((_let_30 (tptp.sdtlseqdt0 tptp.xm tptp.xn))) (let ((_let_31 (not _let_30))) (let ((_let_32 (not _let_16))) (let ((_let_33 (not _let_17))) (let ((_let_34 (or _let_33 _let_32 _let_31 _let_29 _let_6))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (not _let_34))) (let ((_let_37 (= _let_4 _let_30))) (let ((_let_38 (or _let_33 _let_32 _let_37))) (let ((_let_39 (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_40 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (_let_39))) (let ((_let_42 ((tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W0) (tptp.szszuzczcdt0 W1))))) (let ((_let_43 (ASSUME :args (_let_18)))) (let ((_let_44 (AND_ELIM _let_43 :args (1)))) (let ((_let_45 (AND_ELIM _let_43 :args (0)))) (let ((_let_46 (tptp.aElementOf0 _let_1 tptp.szNzAzT0))) (let ((_let_47 (tptp.sdtlseqdt0 _let_1 tptp.xm))) (let ((_let_48 (not _let_46))) (let ((_let_49 (or _let_48 _let_33 _let_47 _let_4))) (let ((_let_50 (tptp.sdtlseqdt0 tptp.xn _let_1))) (let ((_let_51 (tptp.aElementOf0 _let_3 tptp.szNzAzT0))) (let ((_let_52 (not _let_50))) (let ((_let_53 (not _let_8))) (let ((_let_54 (not _let_51))) (let ((_let_55 (or _let_54 _let_32 _let_48 _let_53 _let_52 _let_4))) (let ((_let_56 (tptp.szszuzczcdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_57 (= _let_1 _let_56))) (let ((_let_58 (tptp.sdtlseqdt0 _let_1 tptp.xn))) (let ((_let_59 (_let_11))) (let ((_let_60 (= tptp.sz00 _let_1))) (let ((_let_61 (not _let_60))) (let ((_let_62 (and _let_46 _let_61))) (let ((_let_63 (or _let_32 _let_62))) (let ((_let_64 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szszuzczcdt0 W0))) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (and (tptp.aElementOf0 _let_1 tptp.szNzAzT0) (not (= tptp.sz00 _let_1)))))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (_let_64))) (let ((_let_67 ((tptp.szszuzczcdt0 W0)))) (let ((_let_68 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_63)) :args ((or _let_32 _let_62 (not _let_63)))) _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_67)) :args _let_66)) _let_65 :args (_let_63 false _let_64)) :args (_let_62 false _let_16 false _let_63)))) (let ((_let_69 (not _let_62))) (let ((_let_70 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_62 0)) :args ((or _let_46 _let_69))) _let_68 :args (_let_46 false _let_62)))) (let ((_let_71 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (not (tptp.aElementOf0 W1 tptp.szNzAzT0)) (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W1) W0))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (_let_71))) (let ((_let_74 (or _let_32 _let_50))) (let ((_let_75 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (tptp.sdtlseqdt0 W0 (tptp.szszuzczcdt0 W0)))))) (let ((_let_76 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_74)) :args ((or _let_32 _let_50 (not _let_74)))) _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_76 :args (tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.szszuzczcdt0 W0)))) :args (_let_75))) _let_76 :args (_let_74 false _let_75)) :args (_let_50 false _let_16 false _let_74)))) (let ((_let_78 (and _let_51 (not (= tptp.sz00 _let_3))))) (let ((_let_79 (or _let_33 _let_78))) (let ((_let_80 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_78 0)) :args ((or _let_51 (not _let_78)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_79)) :args ((or _let_33 _let_78 (not _let_79)))) _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_67)) :args _let_66)) _let_65 :args (_let_79 false _let_64)) :args (_let_78 false _let_17 false _let_79)) :args (_let_51 false _let_78)))) (let ((_let_81 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (not (tptp.aElementOf0 W1 tptp.szNzAzT0)) (not (tptp.aElementOf0 W2 tptp.szNzAzT0)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2))))) (let ((_let_82 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_83 (not _let_57))) (let ((_let_84 (not (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 tptp.szNzAzT0)))) (let ((_let_85 (or _let_84 _let_83))) (let ((_let_86 (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.szNzAzT0)) (not (= (tptp.szszuzczcdt0 W1) (tptp.szszuzczcdt0 tptp.xn))))))) (let ((_let_87 (not _let_85))) (let ((_let_88 (not _let_86))) (let ((_let_89 (or _let_48 _let_60 _let_88))) (let ((_let_90 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (= tptp.sz00 W0) (not (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.szNzAzT0)) (not (= W0 (tptp.szszuzczcdt0 W1)))))))))) (let ((_let_91 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_92 (or))) (let ((_let_93 (_let_88))) (let ((_let_94 (= tptp.xn _let_1))) (let ((_let_95 (not _let_58))) (let ((_let_96 (or _let_32 _let_48 _let_52 _let_95 _let_94))) (let ((_let_97 (_let_27))) (let ((_let_98 ((not (= (tptp.sdtlseqdt0 W0 W1) false))))) (let ((_let_99 (not _let_94))) (let ((_let_100 (or _let_32 _let_99))) (let ((_let_101 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (not (= W0 (tptp.szszuzczcdt0 W0))))))) (let ((_let_102 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_103 (not _let_6))) (let ((_let_104 (ASSUME :args (_let_95)))) (let ((_let_105 (APPLY_UF tptp.sdtlseqdt0))) (let ((_let_106 (ASSUME :args (_let_6)))) (let ((_let_107 (ASSUME :args (_let_57)))) (let ((_let_108 (ASSUME :args (_let_47)))) (let ((_let_109 (MACRO_RESOLUTION_TRUST (NOT_AND (ASSUME :args (_let_15))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_104 _let_107 _let_106 _let_108) :args (_let_6 _let_95 _let_47 _let_57)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_108)) (CONG _let_107 (REFL :args (tptp.xm)) :args _let_105) (CONG (SYMM _let_107) (SYMM (SYMM _let_106)) :args _let_105) (FALSE_INTRO _let_104))) :args (_let_95 _let_57 _let_6 _let_47)) :args ((not (and _let_6 _let_95 _let_47 _let_57)) SB_LITERAL))) (CONG (REFL :args (_let_103)) (MACRO_SR_PRED_INTRO :args ((= (not _let_95) _let_58))) (REFL :args ((not _let_47))) (REFL :args (_let_83)) :args _let_92)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_96)) :args ((or _let_32 _let_94 _let_48 _let_52 _let_95 (not _let_96)))) _let_44 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_100)) :args ((or _let_32 _let_99 (not _let_100)))) _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_102 :args (tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.szszuzczcdt0 W0)))) :args (_let_101))) _let_102 :args (_let_100 false _let_101)) :args (_let_99 false _let_16 false _let_100)) _let_70 _let_77 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (tptp.xn _let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_98)) :args _let_97)) _let_35 :args (_let_96 false _let_27)) :args (_let_95 false _let_16 true _let_94 false _let_46 false _let_50 false _let_96)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_85 1)) (CONG (REFL :args (_let_85)) (MACRO_SR_PRED_INTRO :args ((= (not _let_83) _let_57))) :args _let_92)) :args ((or _let_57 _let_85))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_93)) :args _let_93) (REWRITE :args ((=> _let_88 (not (or _let_84 (not (= _let_56 _let_1))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_88) _let_86))) (REFL :args (_let_87)) :args _let_92)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_89)) :args ((or _let_60 _let_48 _let_88 (not _let_89)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_62 1)) :args ((or _let_61 _let_69))) _let_68 :args (_let_61 false _let_62)) _let_70 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_91 :args (_let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 W0 tptp.szNzAzT0) false))))) :args (_let_90)))) _let_91 :args (_let_89 false _let_90)) :args (_let_88 true _let_60 false _let_46 false _let_89)) :args (_let_87 true _let_86)) :args (_let_57 true _let_85)) (REORDERING (CNF_OR_POS :args (_let_10)) :args ((or _let_6 _let_9 (not _let_10)))) (REORDERING (CNF_AND_POS :args (_let_9 0)) :args ((or _let_8 (not _let_9)))) (REORDERING (CNF_OR_POS :args (_let_55)) :args ((or _let_4 _let_32 _let_53 _let_48 _let_54 _let_52 (not _let_55)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args (_let_3 tptp.xn _let_1 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.sdtlseqdt0 W1 W2) false)) (not (= (tptp.aElementOf0 W0 tptp.szNzAzT0) false))))) :args (_let_81))) _let_82 :args (_let_55 false _let_81)) _let_80 _let_70 _let_77 _let_44 (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_4 _let_33 _let_48 _let_47 (not _let_49)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (_let_1 tptp.xm QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W1) W0) true))))) :args _let_73)) _let_72 :args (_let_49 false _let_71)) _let_70 _let_45 (CNF_OR_NEG :args (_let_5 0)) (CNF_IMPLIES_NEG2 :args _let_59) (REORDERING (CNF_IMPLIES_NEG1 :args _let_59) :args ((or _let_10 _let_11))) :args (_let_11 true _let_58 false _let_57 false _let_6 true _let_9 true _let_8 false _let_55 false _let_51 false _let_46 false _let_50 false _let_16 false _let_47 false _let_49 false _let_46 false _let_17 true _let_4 true _let_5 false _let_10)) :args ((not _let_14) false _let_11)))) (let ((_let_110 (_let_14))) (let ((_let_111 (tptp.sdtlseqdt0 _let_1 _let_3))) (let ((_let_112 (= _let_111 _let_28))) (let ((_let_113 (or _let_32 _let_33 _let_112))) (let ((_let_114 (or _let_54 _let_32 _let_8 _let_111))) (let ((_let_115 (MACRO_RESOLUTION_TRUST (CNF_IMPLIES_NEG2 :args _let_110) _let_109 :args ((not _let_12) true _let_14)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (tptp.xm tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_98)) :args _let_97)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_6 _let_33 _let_32 _let_29 _let_31 _let_36))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_12 2)) _let_115 :args (_let_103 true _let_12)) _let_45 _let_44 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_112)) :args ((or (not _let_111) _let_28 (not _let_112)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_114)) :args ((or _let_8 _let_32 _let_54 _let_111 (not _let_114)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_12 0)) _let_115 :args (_let_53 true _let_12)) _let_44 _let_80 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (_let_3 tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.sdtlseqdt0 W0 W1) true))))) :args _let_73)) _let_72 :args (_let_114 false _let_71)) :args (_let_111 true _let_8 false _let_16 false _let_51 false _let_114)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_113)) :args ((or _let_33 _let_32 _let_112 (not _let_113)))) _let_45 _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_40 :args (tptp.xn tptp.xm QUANTIFIERS_INST_E_MATCHING _let_42)) :args _let_41))) _let_40 :args (_let_113 false _let_39)) :args (_let_112 false _let_17 false _let_16 false _let_113)) :args (_let_28 false _let_111 false _let_112)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_37)) :args ((or (not _let_4) _let_30 (not _let_37)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_13 0)) :args ((or _let_4 (not _let_13)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_IMPLIES_NEG1 :args _let_110) :args ((or _let_13 _let_14))) _let_109 :args (_let_13 true _let_14)) :args (_let_4 false _let_13)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_33 _let_32 _let_37 (not _let_38)))) _let_45 _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_40 :args (tptp.xm tptp.xn QUANTIFIERS_INST_E_MATCHING _let_42)) :args _let_41))) _let_40 :args (_let_38 false _let_39)) :args (_let_37 false _let_17 false _let_16 false _let_38)) :args (_let_30 false _let_4 false _let_37)) :args (_let_36 true _let_6 false _let_17 false _let_16 false _let_28 false _let_30)) _let_35 :args (false true _let_34 false _let_27)) :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))))) (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) _let_26 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (= (tptp.szszuzczcdt0 W0) (tptp.szszuzczcdt0 W1)) (= W0 W1)))) _let_25 _let_24 (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_23 _let_22 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 W0 W0))) _let_21 _let_20 _let_19 (forall ((W0 $$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) _let_18 _let_15 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 6.12/6.35 )
% 6.12/6.35 % SZS output end Proof for NUM541+2
% 6.12/6.36 % cvc5---1.0.5 exiting
% 6.12/6.36 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------