TSTP Solution File: NUM501+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM501+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n004.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 10:44:30 EDT 2023
% Result : Theorem 73.14s 73.49s
% Output : Proof 73.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM501+1 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n004.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 16:27:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 73.14/73.49 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.kQEE1jjC2l/cvc5---1.0.5_14543.p...
% 73.14/73.49 ------- get file name : TPTP file name is NUM501+1
% 73.14/73.49 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_14543.smt2...
% 73.14/73.49 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 73.14/73.49 --- Run --no-e-matching --full-saturate-quant at 5...
% 73.14/73.49 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 73.14/73.49 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 73.14/73.49 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 73.14/73.49 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 73.14/73.49 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 73.14/73.49 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 73.14/73.49 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 73.14/73.49 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 73.14/73.49 --- Run --relevant-triggers --full-saturate-quant at 5...
% 73.14/73.49 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 73.14/73.49 --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 73.14/73.49 % SZS status Theorem for NUM501+1
% 73.14/73.49 % SZS output start Proof for NUM501+1
% 73.14/73.49 (
% 73.14/73.49 (let ((_let_1 (tptp.sdtasdt0 tptp.xn tptp.xm))) (let ((_let_2 (tptp.doDivides0 tptp.xr _let_1))) (let ((_let_3 (not _let_2))) (let ((_let_4 (tptp.aNaturalNumber0 tptp.xr))) (let ((_let_5 (and _let_4 (tptp.doDivides0 tptp.xr tptp.xk) (tptp.isPrime0 tptp.xr)))) (let ((_let_6 (= tptp.xk tptp.sz10))) (let ((_let_7 (= tptp.xk tptp.sz00))) (let ((_let_8 (tptp.sdtsldt0 _let_1 tptp.xp))) (let ((_let_9 (= tptp.xk _let_8))) (let ((_let_10 (tptp.doDivides0 tptp.xp _let_1))) (let ((_let_11 (tptp.isPrime0 tptp.xp))) (let ((_let_12 (and _let_11 _let_10))) (let ((_let_13 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_14 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_15 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_16 (and _let_15 _let_14 _let_13))) (let ((_let_17 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (= (tptp.isPrime0 W0) (and (not (= W0 tptp.sz00)) (not (= W0 tptp.sz10)) (forall ((W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0)) (or (= W1 tptp.sz10) (= W1 W0)))))))))) (let ((_let_18 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtsldt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2)))))))))) (let ((_let_19 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2))))))))) (let ((_let_20 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (= (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))))) (let ((_let_21 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_22 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_23 (tptp.sdtasdt0 tptp.xp _let_8))) (let ((_let_24 (= _let_1 _let_23))) (let ((_let_25 (tptp.sdtasdt0 tptp.xr SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_26 (= _let_8 _let_25))) (let ((_let_27 (= _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_28 (= _let_23 (tptp.sdtasdt0 _let_8 tptp.xp)))) (let ((_let_29 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.xp))) (let ((_let_30 (tptp.sdtasdt0 tptp.xr _let_29))) (let ((_let_31 (= (tptp.sdtasdt0 _let_25 tptp.xp) _let_30))) (let ((_let_32 (= _let_1 _let_30))) (let ((_let_33 (tptp.aNaturalNumber0 _let_8))) (let ((_let_34 (and _let_33 _let_24))) (let ((_let_35 (not _let_10))) (let ((_let_36 (= tptp.sz00 tptp.xp))) (let ((_let_37 (tptp.aNaturalNumber0 _let_1))) (let ((_let_38 (not _let_37))) (let ((_let_39 (not _let_13))) (let ((_let_40 (or _let_39 _let_38 _let_36 _let_35 _let_34))) (let ((_let_41 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1614 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= tptp.sz00 W0) (not (tptp.doDivides0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1614) (= W1 (tptp.sdtasdt0 W0 BOUND_VARIABLE_1614))) (= (tptp.sdtsldt0 W1 W0) BOUND_VARIABLE_1614)))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (_let_41))) (let ((_let_44 (not _let_14))) (let ((_let_45 (not _let_15))) (let ((_let_46 (or _let_45 _let_44 _let_37))) (let ((_let_47 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (_let_47))) (let ((_let_50 ((tptp.sdtasdt0 W0 W1)))) (let ((_let_51 (1))) (let ((_let_52 (ASSUME :args (_let_16)))) (let ((_let_53 (0))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_45 _let_44 _let_37 (not _let_46)))) (AND_ELIM _let_52 :args _let_53) (AND_ELIM _let_52 :args _let_51) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (tptp.xn tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_50)) :args _let_49)) _let_48 :args (_let_46 false _let_47)) :args (_let_37 false _let_15 false _let_14 false _let_46)))) (let ((_let_55 (not _let_36))) (let ((_let_56 (and _let_55 (not (= tptp.sz10 tptp.xp)) (forall ((W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (not (tptp.doDivides0 W1 tptp.xp)) (= tptp.sz10 W1) (= W1 tptp.xp)))))) (let ((_let_57 (= _let_11 _let_56))) (let ((_let_58 (or _let_39 _let_57))) (let ((_let_59 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (= (tptp.isPrime0 W0) (and (not (= tptp.sz00 W0)) (not (= tptp.sz10 W0)) (forall ((W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (not (tptp.doDivides0 W1 W0)) (= tptp.sz10 W1) (= W0 W1))))))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (AND_ELIM _let_52 :args (2)))) (let ((_let_62 (ASSUME :args (_let_12)))) (let ((_let_63 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_56 0)) :args ((or _let_55 (not _let_56)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_57)) :args ((or (not _let_11) _let_56 (not _let_57)))) (AND_ELIM _let_62 :args _let_53) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_39 _let_57 (not _let_58)))) _let_61 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_60 :args (tptp.xp QUANTIFIERS_INST_CBQI_PROP)) :args (_let_59)))) _let_60 :args (_let_58 false _let_59)) :args (_let_57 false _let_13 false _let_58)) :args (_let_56 false _let_11 false _let_57)) :args (_let_55 false _let_56)))) (let ((_let_64 (AND_ELIM _let_62 :args _let_51))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_39 _let_35 _let_36 _let_38 _let_34 (not _let_40)))) _let_61 _let_64 _let_63 _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_42 :args (tptp.xp _let_1 _let_8 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_43))) _let_42 :args (_let_40 false _let_41)) :args (_let_34 false _let_13 false _let_10 true _let_36 false _let_37 false _let_40)))) (let ((_let_66 (not _let_34))) (let ((_let_67 (not _let_26))) (let ((_let_68 (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_69 (not _let_68))) (let ((_let_70 (or _let_69 _let_67))) (let ((_let_71 (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtsldt0 (tptp.sdtasdt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtasdt0 tptp.xr W2))))))) (let ((_let_72 (not _let_70))) (let ((_let_73 (not _let_71))) (let ((_let_74 (tptp.doDivides0 tptp.xr _let_8))) (let ((_let_75 (= _let_74 _let_73))) (let ((_let_76 (not _let_33))) (let ((_let_77 (not _let_4))) (let ((_let_78 (or _let_77 _let_76 _let_75))) (let ((_let_79 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2))))))))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (_let_79))) (let ((_let_82 ((tptp.doDivides0 W0 W1)))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_34 0)) :args ((or _let_33 _let_66))) _let_65 :args (_let_33 false _let_34)))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO (ASSUME :args (_let_9)) :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (AND_ELIM _let_84 :args _let_53))) (let ((_let_86 (or))) (let ((_let_87 (_let_73))) (let ((_let_88 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_87)) :args _let_87)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_73) _let_71))) (REFL :args (_let_72)) :args _let_86)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_75)) :args ((or (not _let_74) _let_73 (not _let_75)))) (AND_ELIM _let_84 :args _let_51) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_78)) :args ((or _let_77 _let_76 _let_75 (not _let_78)))) _let_85 _let_83 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (tptp.xr _let_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_82)) :args _let_81)) _let_80 :args (_let_78 false _let_79)) :args (_let_75 false _let_4 false _let_33 false _let_78)) :args (_let_73 false _let_74 false _let_75)) :args (_let_72 true _let_71)))) (let ((_let_89 (REFL :args (_let_70)))) (let ((_let_90 (= _let_1 (tptp.sdtasdt0 tptp.xp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))) (let ((_let_91 (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_92 (and _let_91 _let_90))) (let ((_let_93 (= _let_92 _let_27))) (let ((_let_94 (or _let_39 _let_38 _let_36 _let_35 _let_93))) (let ((_let_95 (not _let_90))) (let ((_let_96 (not _let_91))) (let ((_let_97 (or _let_96 _let_95))) (let ((_let_98 (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xm) (tptp.sdtasdt0 tptp.xp W2))))))) (let ((_let_99 (not _let_97))) (let ((_let_100 (not _let_98))) (let ((_let_101 (= _let_10 _let_100))) (let ((_let_102 (or _let_39 _let_38 _let_101))) (let ((_let_103 (_let_100))) (let ((_let_104 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_103)) :args _let_103)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_100) _let_98))) (REFL :args (_let_99)) :args _let_86)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_101)) :args ((or _let_35 _let_100 (not _let_101)))) _let_64 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_102)) :args ((or _let_39 _let_38 _let_101 (not _let_102)))) _let_61 _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (tptp.xp _let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_82)) :args _let_81)) _let_80 :args (_let_102 false _let_79)) :args (_let_101 false _let_13 false _let_37 false _let_102)) :args (_let_100 false _let_10 false _let_101)) :args (_let_99 true _let_98)))) (let ((_let_105 (REFL :args (_let_97)))) (let ((_let_106 (or _let_39 _let_76 _let_28))) (let ((_let_107 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_108 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_109 (or _let_77 _let_69 _let_39 _let_31))) (let ((_let_110 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (= (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))))) (let ((_let_111 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_112 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_70 0)) (CONG _let_89 (MACRO_SR_PRED_INTRO :args ((= (not _let_69) _let_68))) :args _let_86)) :args ((or _let_68 _let_70))) _let_88 :args (_let_68 true _let_70)))) (let ((_let_113 (not _let_32))) (let ((_let_114 (tptp.aNaturalNumber0 _let_29))) (let ((_let_115 (not _let_114))) (let ((_let_116 (or _let_115 _let_113))) (let ((_let_117 (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xm) (tptp.sdtasdt0 tptp.xr W2))))))) (let ((_let_118 (not _let_117))) (let ((_let_119 (= _let_2 _let_118))) (let ((_let_120 (or _let_77 _let_38 _let_119))) (let ((_let_121 (not _let_119))) (let ((_let_122 (_let_117))) (let ((_let_123 (or _let_69 _let_39 _let_114))) (let ((_let_124 (ASSUME :args (_let_113)))) (let ((_let_125 (ASSUME :args (_let_31)))) (let ((_let_126 (APPLY_UF tptp.sdtasdt0))) (let ((_let_127 (REFL :args (tptp.xp)))) (let ((_let_128 (ASSUME :args (_let_26)))) (let ((_let_129 (ASSUME :args (_let_27)))) (let ((_let_130 (ASSUME :args (_let_28)))) (let ((_let_131 (ASSUME :args (_let_24)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO (MODUS_PONENS (AND_INTRO _let_125 _let_128 _let_129 _let_130 _let_131) (SCOPE (TRANS (SYMM (SYMM _let_131)) (SYMM (SYMM _let_130)) (CONG _let_129 _let_127 :args _let_126) (CONG (TRANS (SYMM _let_129) (SYMM (SYMM _let_128))) _let_127 :args _let_126) (SYMM (SYMM _let_125))) :args (_let_31 _let_26 _let_27 _let_28 _let_24))) _let_124) :args (_let_24 _let_26 _let_27 _let_28 _let_31 _let_113)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO (SYMM (SYMM (ASSUME :args (_let_32)))))) (FALSE_INTRO _let_124))) :args (_let_32 _let_113)) :args ((not (and _let_24 _let_26 _let_27 _let_28 _let_31 _let_113)) SB_LITERAL))) (CONG (REFL :args ((not _let_24))) (REFL :args (_let_67)) (REFL :args ((not _let_27))) (REFL :args ((not _let_28))) (REFL :args ((not _let_31))) (MACRO_SR_PRED_INTRO :args ((= (not _let_113) _let_32))) :args _let_86)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_116)) :args ((or _let_115 _let_113 (not _let_116)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_123)) :args ((or _let_39 _let_69 _let_114 (not _let_123)))) _let_61 _let_112 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.xp QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_50)) :args _let_49)) _let_48 :args (_let_123 false _let_47)) :args (_let_114 false _let_13 false _let_68 false _let_123)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_122) :args (_let_29 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtasdt0 tptp.xr W2)))) :args _let_122)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_119)) (CONG (REFL :args (_let_121)) (REFL :args (_let_2)) (MACRO_SR_PRED_INTRO :args ((= (not _let_118) _let_117))) :args _let_86)) :args ((or _let_2 _let_117 _let_121))) (ASSUME :args (_let_3)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_120)) :args ((or _let_77 _let_38 _let_119 (not _let_120)))) _let_85 _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (tptp.xr _let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_82)) :args _let_81)) _let_80 :args (_let_120 false _let_79)) :args (_let_119 false _let_4 false _let_37 false _let_120)) :args (_let_117 true _let_2 false _let_119)) :args (_let_116 false _let_117)) :args (_let_113 false _let_114 false _let_116)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_109)) :args ((or _let_39 _let_77 _let_69 _let_31 (not _let_109)))) _let_61 _let_85 _let_112 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_111 :args (tptp.xr SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.xp QUANTIFIERS_INST_E_MATCHING ((tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2)))) :args (_let_110))) _let_111 :args (_let_109 false _let_110)) :args (_let_31 false _let_13 false _let_4 false _let_68 false _let_109)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_106)) :args ((or _let_39 _let_76 _let_28 (not _let_106)))) _let_61 _let_83 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (tptp.xp _let_8 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_107))) _let_108 :args (_let_106 false _let_107)) :args (_let_28 false _let_13 false _let_33 false _let_106)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_93)) :args ((or _let_27 (not _let_92) (not _let_93)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_92)) :args ((or _let_96 _let_95 _let_92))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_97 0)) (CONG _let_105 (MACRO_SR_PRED_INTRO :args ((= (not _let_96) _let_91))) :args _let_86)) :args ((or _let_91 _let_97))) _let_104 :args (_let_91 true _let_97)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_97 1)) (CONG _let_105 (MACRO_SR_PRED_INTRO :args ((= (not _let_95) _let_90))) :args _let_86)) :args ((or _let_90 _let_97))) _let_104 :args (_let_90 true _let_97)) :args (_let_92 false _let_91 false _let_90)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_94)) :args ((or _let_39 _let_35 _let_36 _let_38 _let_93 (not _let_94)))) _let_61 _let_64 _let_63 _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (tptp.xp _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_CBQI_PROP)) :args _let_43)) _let_42 :args (_let_94 false _let_41)) :args (_let_93 false _let_13 false _let_10 true _let_36 false _let_37 false _let_94)) :args (_let_27 false _let_92 false _let_93)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_70 1)) (CONG _let_89 (MACRO_SR_PRED_INTRO :args ((= (not _let_67) _let_26))) :args _let_86)) :args ((or _let_26 _let_70))) _let_88 :args (_let_26 true _let_70)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_34 1)) :args ((or _let_24 _let_66))) _let_65 :args (_let_24 false _let_34)) :args (false true _let_32 false _let_31 false _let_28 false _let_27 false _let_26 false _let_24)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) (tptp.aNaturalNumber0 tptp.sz00) (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) _let_22 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (= (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))) _let_21 _let_20 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 W2))) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (and (= (tptp.sdtasdt0 W0 _let_1) (tptp.sdtpldt0 (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2))) (= (tptp.sdtasdt0 _let_1 W0) (tptp.sdtpldt0 (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W0 W2)) (= (tptp.sdtpldt0 W1 W0) (tptp.sdtpldt0 W2 W0))) (= W1 W2)))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (=> (not (= W0 tptp.sz00)) (forall ((W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2)) (= (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))) (= W1 W2))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtpldt0 W0 W1) tptp.sz00) (and (= W0 tptp.sz00) (= W1 tptp.sz00))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtasdt0 W0 W1) tptp.sz00) (or (= W0 tptp.sz00) (= W1 tptp.sz00))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtlseqdt0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.sdtlseqdt0 W0 W1) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1))))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (tptp.sdtlseqdt0 W0 W0))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (or (tptp.sdtlseqdt0 W0 W1) (and (not (= W1 W0)) (tptp.sdtlseqdt0 W1 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 W2))) (let ((_let_2 (tptp.sdtpldt0 W0 W2))) (let ((_let_3 (tptp.sdtpldt0 W2 W1))) (let ((_let_4 (tptp.sdtpldt0 W2 W0))) (=> (tptp.aNaturalNumber0 W2) (and (not (= _let_4 _let_3)) (tptp.sdtlseqdt0 _let_4 _let_3) (not (= _let_2 _let_1)) (tptp.sdtlseqdt0 _let_2 _let_1))))))))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W2 W0))) (let ((_let_2 (tptp.sdtasdt0 W1 W0))) (let ((_let_3 (tptp.sdtasdt0 W0 W2))) (let ((_let_4 (tptp.sdtasdt0 W0 W1))) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (not (= W0 tptp.sz00)) (not (= W1 W2)) (tptp.sdtlseqdt0 W1 W2)) (and (not (= _let_4 _let_3)) (tptp.sdtlseqdt0 _let_4 _let_3) (not (= _let_2 _let_1)) (tptp.sdtlseqdt0 _let_2 _let_1))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (or (= W0 tptp.sz00) (= W0 tptp.sz10) (and (not (= tptp.sz10 W0)) (tptp.sdtlseqdt0 tptp.sz10 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (not (= W0 tptp.sz00)) (tptp.sdtlseqdt0 W1 (tptp.sdtasdt0 W1 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.iLess0 W0 W1) true))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1)))) _let_19 _let_18 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.doDivides0 W0 W1) (tptp.doDivides0 W1 W2)) (tptp.doDivides0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.doDivides0 W0 W1) (tptp.doDivides0 W0 W2)) (tptp.doDivides0 W0 (tptp.sdtpldt0 W1 W2))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.doDivides0 W0 W1) (tptp.doDivides0 W0 (tptp.sdtpldt0 W1 W2))) (tptp.doDivides0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.doDivides0 W0 W1) (not (= W1 tptp.sz00))) (tptp.sdtlseqdt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (=> (tptp.aNaturalNumber0 W2) (= (tptp.sdtasdt0 W2 (tptp.sdtsldt0 W1 W0)) (tptp.sdtsldt0 (tptp.sdtasdt0 W2 W1) W0))))))) _let_17 (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (not (= W0 tptp.sz00)) (not (= W0 tptp.sz10))) (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0) (tptp.isPrime0 W1))))) _let_16 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.isPrime0 W2) (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (=> (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (or (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1)))))) _let_12 (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xm)) (and (not (= tptp.xn tptp.xp)) (tptp.sdtlseqdt0 tptp.xn tptp.xp) (not (= tptp.xm tptp.xp)) (tptp.sdtlseqdt0 tptp.xm tptp.xp)) _let_9 (not (or _let_7 _let_6)) (and (not _let_7) (not _let_6)) _let_5 _let_3 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 73.24/73.50 )
% 73.24/73.50 % SZS output end Proof for NUM501+1
% 73.24/73.50 % cvc5---1.0.5 exiting
% 73.24/73.50 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------