TSTP Solution File: NUM526+3 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM526+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n026.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 10:44:47 EDT 2023
% Result : Theorem 83.40s 83.60s
% Output : Proof 83.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM526+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n026.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 11:34:17 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.50 %----Proving TF0_NAR, FOF, or CNF
% 83.40/83.60 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.9q8iiYBfpK/cvc5---1.0.5_9587.p...
% 83.40/83.60 ------- get file name : TPTP file name is NUM526+3
% 83.40/83.60 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_9587.smt2...
% 83.40/83.60 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 83.40/83.60 --- Run --no-e-matching --full-saturate-quant at 5...
% 83.40/83.60 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 83.40/83.60 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 83.40/83.60 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 83.40/83.60 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 83.40/83.60 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 83.40/83.60 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 83.40/83.60 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 83.40/83.60 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 83.40/83.60 --- Run --relevant-triggers --full-saturate-quant at 5...
% 83.40/83.60 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 83.40/83.60 --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 83.40/83.60 --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 83.40/83.60 % SZS status Theorem for NUM526+3
% 83.40/83.60 % SZS output start Proof for NUM526+3
% 83.40/83.60 (
% 83.40/83.60 (let ((_let_1 (tptp.sdtasdt0 tptp.xq tptp.xq))) (let ((_let_2 (tptp.sdtasdt0 tptp.xp _let_1))) (let ((_let_3 (tptp.sdtasdt0 tptp.xm tptp.xm))) (let ((_let_4 (= _let_3 _let_2))) (let ((_let_5 (tptp.sdtasdt0 tptp.xp tptp.xq))) (let ((_let_6 (tptp.aNaturalNumber0 tptp.xq))) (let ((_let_7 (and _let_6 (= tptp.xn _let_5) (= tptp.xq (tptp.sdtsldt0 tptp.xn tptp.xp))))) (let ((_let_8 (tptp.doDivides0 tptp.xp tptp.xn))) (let ((_let_9 (tptp.sdtasdt0 tptp.xn tptp.xn))) (let ((_let_10 (tptp.doDivides0 tptp.xp _let_9))) (let ((_let_11 (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W0)))) _let_10 (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xn (tptp.sdtasdt0 tptp.xp W0)))) _let_8))) (let ((_let_12 (tptp.isPrime0 tptp.xp))) (let ((_let_13 (and (not (= tptp.xp tptp.sz10)) (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (or (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (= tptp.xp (tptp.sdtasdt0 W0 W1)))) (tptp.doDivides0 W0 tptp.xp))) (or (= W0 tptp.sz10) (= W0 tptp.xp)))) _let_12))) (let ((_let_14 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2) (not (= W0 tptp.sz00)) (not (= W1 tptp.sz00)) (not (= W2 tptp.sz00))) (=> (= (tptp.sdtasdt0 W2 (tptp.sdtasdt0 W1 W1)) (tptp.sdtasdt0 W0 W0)) (=> (tptp.iLess0 W0 tptp.xn) (not (or (and (not (= W2 tptp.sz10)) (forall ((W3 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W3) (exists ((W4 $$unsorted)) (and (tptp.aNaturalNumber0 W4) (= W2 (tptp.sdtasdt0 W3 W4)))) (tptp.doDivides0 W3 W2)) (or (= W3 tptp.sz10) (= W3 W2))))) (tptp.isPrime0 W2))))))))) (let ((_let_15 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_16 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_17 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_18 (and _let_17 _let_16 _let_15 (not (= tptp.xn tptp.sz00)) (not (= tptp.xm tptp.sz00)) (not (= tptp.xp tptp.sz00))))) (let ((_let_19 (forall ((W0 $$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))) (or (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))))))) (let ((_let_20 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (=> (tptp.aNaturalNumber0 W2) (= (tptp.sdtasdt0 W2 (tptp.sdtsldt0 W1 W0)) (tptp.sdtsldt0 (tptp.sdtasdt0 W2 W1) W0))))))))) (let ((_let_21 (forall ((W0 $$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_22 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2))))))))) (let ((_let_23 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1)))))) (let ((_let_24 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (not (= W0 tptp.sz00)) (tptp.sdtlseqdt0 W1 (tptp.sdtasdt0 W1 W0))))))) (let ((_let_25 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (or (= W0 tptp.sz00) (= W0 tptp.sz10) (and (not (= tptp.sz10 W0)) (tptp.sdtlseqdt0 tptp.sz10 W0))))))) (let ((_let_26 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtlseqdt0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1)))))))) (let ((_let_27 (forall ((W0 $$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))))))))) (let ((_let_28 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))) (let ((_let_29 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))) (let ((_let_30 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (= (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))))) (let ((_let_31 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_32 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))) (let ((_let_33 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_34 (tptp.aNaturalNumber0 tptp.sz10))) (let ((_let_35 (and _let_34 (not (= tptp.sz10 tptp.sz00))))) (let ((_let_36 (tptp.sdtsldt0 _let_5 tptp.xp))) (let ((_let_37 (= tptp.xq _let_36))) (let ((_let_38 (tptp.sdtasdt0 _let_5 tptp.xq))) (let ((_let_39 (= _let_2 _let_38))) (let ((_let_40 (tptp.sdtasdt0 tptp.xq _let_5))) (let ((_let_41 (= (tptp.sdtasdt0 tptp.xq _let_36) (tptp.sdtsldt0 _let_40 tptp.xp)))) (let ((_let_42 (= _let_40 _let_38))) (let ((_let_43 (= _let_2 (tptp.sdtasdt0 tptp.xp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26)))) (let ((_let_44 (tptp.sdtsldt0 tptp.xm tptp.xp))) (let ((_let_45 (= (tptp.sdtasdt0 tptp.xm _let_44) (tptp.sdtsldt0 _let_3 tptp.xp)))) (let ((_let_46 (= tptp.xm (tptp.sdtpldt0 tptp.sz00 tptp.xm)))) (let ((_let_47 (tptp.sdtasdt0 tptp.xp _let_44))) (let ((_let_48 (= tptp.xm _let_47))) (let ((_let_49 (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 _let_44 _let_44)))) (let ((_let_50 (= (tptp.sdtasdt0 _let_47 _let_44) _let_49))) (let ((_let_51 (= _let_1 _let_49))) (let ((_let_52 (1))) (let ((_let_53 (ASSUME :args (_let_7)))) (let ((_let_54 (AND_ELIM _let_53 :args _let_52))) (let ((_let_55 (EQ_RESOLVE _let_53 (MACRO_SR_EQ_INTRO _let_54 :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (AND_ELIM _let_55 :args _let_52))) (let ((_let_57 (ASSUME :args (_let_4)))) (let ((_let_58 (not _let_6))) (let ((_let_59 (not _let_15))) (let ((_let_60 (or _let_59 _let_58 _let_58 _let_39))) (let ((_let_61 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (= (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (_let_61))) (let ((_let_64 (0))) (let ((_let_65 (AND_ELIM _let_55 :args _let_64))) (let ((_let_66 (2))) (let ((_let_67 (= tptp.sz00 tptp.xp))) (let ((_let_68 (= tptp.sz00 tptp.xm))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_18)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_54 :args ((and _let_17 _let_16 _let_15 (not (= tptp.sz00 tptp.xn)) (not _let_68) (not _let_67)) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_70 (AND_ELIM _let_69 :args _let_66))) (let ((_let_71 (tptp.doDivides0 tptp.xp _let_5))) (let ((_let_72 (not _let_71))) (let ((_let_73 (tptp.aNaturalNumber0 _let_5))) (let ((_let_74 (not _let_73))) (let ((_let_75 (or _let_59 _let_74 _let_67 _let_72 _let_58 _let_41))) (let ((_let_76 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1786 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= tptp.sz00 W0) (not (tptp.doDivides0 W0 W1)) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1786)) (= (tptp.sdtasdt0 BOUND_VARIABLE_1786 (tptp.sdtsldt0 W1 W0)) (tptp.sdtsldt0 (tptp.sdtasdt0 BOUND_VARIABLE_1786 W1) W0)))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (_let_76))) (let ((_let_79 (3))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_11)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_54 :args ((and (not (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W0)))))) _let_10 (not (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= tptp.xn (tptp.sdtasdt0 tptp.xp W0)))))) _let_8) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_81 (AND_ELIM _let_80 :args _let_79))) (let ((_let_82 (AND_ELIM _let_69 :args _let_64))) (let ((_let_83 (AND_ELIM _let_69 :args (5)))) (let ((_let_84 (or _let_74 _let_58 _let_42))) (let ((_let_85 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_31)) (MACRO_SR_EQ_INTRO :args (_let_31 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (_let_85))) (let ((_let_88 (not _let_43))) (let ((_let_89 (or (not (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26)) _let_88))) (let ((_let_90 (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xq tptp.xq)) (tptp.sdtasdt0 tptp.xp W2))))))) (let ((_let_91 (not _let_89))) (let ((_let_92 (tptp.aNaturalNumber0 _let_1))) (let ((_let_93 (not _let_90))) (let ((_let_94 (or _let_58 _let_58 _let_92))) (let ((_let_95 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_96 (EQ_RESOLVE (ASSUME :args (_let_33)) (MACRO_SR_EQ_INTRO :args (_let_33 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_97 (_let_95))) (let ((_let_98 ((tptp.sdtasdt0 W0 W1)))) (let ((_let_99 (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_94))) :args ((or _let_58 _let_92 (not _let_94)))) _let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_96 :args (tptp.xq tptp.xq QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_98)) :args _let_97)) _let_96 :args (_let_94 false _let_95)) :args (_let_92 false _let_6 false _let_94)))) (let ((_let_100 (not _let_92))) (let ((_let_101 (_let_90))) (let ((_let_102 (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_101) :args (_let_1 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_101))) :args ((or _let_100 _let_93))) _let_99 :args (_let_93 false _let_92)))) (let ((_let_103 (or))) (let ((_let_104 (MACRO_SR_PRED_INTRO :args ((= (not _let_93) _let_90))))) (let ((_let_105 (_let_93))) (let ((_let_106 (not _let_16))) (let ((_let_107 (tptp.doDivides0 tptp.xp tptp.xm))) (let ((_let_108 (not _let_107))) (let ((_let_109 (or _let_59 _let_106 _let_67 _let_108 _let_106 _let_45))) (let ((_let_110 (tptp.doDivides0 tptp.xp _let_3))) (let ((_let_111 (not _let_110))) (let ((_let_112 (not _let_12))) (let ((_let_113 (or _let_106 _let_106 _let_59 _let_112 _let_111 _let_107 _let_107))) (let ((_let_114 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))))) (let ((_let_115 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_116 (tptp.doDivides0 tptp.xp _let_2))) (let ((_let_117 (= _let_116 _let_93))) (let ((_let_118 (tptp.aNaturalNumber0 _let_2))) (let ((_let_119 (not _let_118))) (let ((_let_120 (or _let_59 _let_119 _let_117))) (let ((_let_121 (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_122 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_123 (or _let_59 _let_100 _let_118))) (let ((_let_124 (not _let_117))) (let ((_let_125 (_let_116))) (let ((_let_126 (and _let_4 _let_116))) (let ((_let_127 (ASSUME :args _let_125))) (let ((_let_128 (SYMM _let_57))) (let ((_let_129 (REFL :args (tptp.xp)))) (let ((_let_130 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_131 (AND_ELIM _let_130 :args _let_66))) (let ((_let_132 (AND_ELIM _let_69 :args _let_52))) (let ((_let_133 (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_113))) :args ((or _let_106 _let_59 _let_112 _let_111 _let_107 (not _let_113)))) _let_132 _let_70 _let_131 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_126)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_127 _let_57) (SCOPE (TRUE_ELIM (TRANS (CONG _let_129 (SYMM _let_128) :args (APPLY_UF tptp.doDivides0)) (TRUE_INTRO _let_127))) :args (_let_116 _let_4))) :args (_let_4 _let_116))) :args (true _let_126)) _let_57 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_117)) (CONG (REFL :args (_let_124)) (REFL :args _let_125) _let_104 :args _let_103)) :args ((or _let_116 _let_90 _let_124))) _let_102 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_120)) :args ((or _let_59 _let_119 _let_117 (not _let_120)))) _let_70 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_123)) :args ((or _let_59 _let_100 _let_118 (not _let_123)))) _let_70 _let_99 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE 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_let_109)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_89 1)) (CONG (REFL :args (_let_89)) (MACRO_SR_PRED_INTRO :args ((= (not _let_88) _let_43))) :args _let_103)) :args ((or _let_43 _let_89))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_105)) :args _let_105)) (CONG _let_104 (REFL :args (_let_91)) :args _let_103)) _let_102 :args (_let_91 true _let_90)) :args (_let_43 true _let_89)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_84)) :args ((or _let_74 _let_58 _let_42 (not _let_84)))) _let_82 _let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_86 :args (_let_5 tptp.xq QUANTIFIERS_INST_CBQI_PROP)) :args _let_87))) _let_86 :args (_let_84 false _let_85)) :args (_let_42 false _let_73 false _let_6 false _let_84)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_67 _let_74 _let_59 _let_72 _let_58 _let_41 (not _let_75)))) _let_83 _let_82 _let_70 _let_81 _let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_77 :args (tptp.xp _let_5 tptp.xq QUANTIFIERS_INST_E_MATCHING ((tptp.sdtasdt0 BOUND_VARIABLE_1786 (tptp.sdtsldt0 W1 W0))))) :args _let_78)) _let_77 :args (_let_75 false _let_76)) :args (_let_41 true _let_67 false _let_73 false _let_15 false _let_71 false _let_6 false _let_75)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_60))) :args ((or _let_59 _let_58 _let_39 (not _let_60)))) _let_70 _let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_62 :args (tptp.xp tptp.xq tptp.xq QUANTIFIERS_INST_E_MATCHING ((tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))) :args _let_63))) _let_62 :args (_let_60 false _let_61)) :args (_let_39 false _let_15 false _let_6 false _let_60)) _let_57 _let_56 :args (false true _let_51 false _let_50 false _let_48 false _let_46 false _let_45 false _let_43 false _let_42 false _let_41 false _let_39 false _let_4 false _let_37)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) (tptp.aNaturalNumber0 tptp.sz00) _let_35 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) _let_33 (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 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (= (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))) _let_32 _let_31 _let_30 _let_29 _let_28 (forall ((W0 $$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 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W0 W2)) (= (tptp.sdtpldt0 W1 W0) (tptp.sdtpldt0 W2 W0))) (= W1 W2)))) _let_27 (forall ((W0 $$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 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtasdt0 W0 W1) tptp.sz00) (or (= W0 tptp.sz00) (= W1 tptp.sz00))))) _let_26 (forall ((W0 $$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))))))))) _let_25 _let_24 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.iLess0 W0 W1) true))) _let_23 _let_22 _let_21 (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 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.doDivides0 W0 W1) (not (= W1 tptp.sz00))) (tptp.sdtlseqdt0 W0 W1)))) _let_20 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (= (tptp.isPrime0 W0) (and (not (= W0 tptp.sz00)) (not (= W0 tptp.sz10)) (forall ((W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0)) (or (= W1 tptp.sz10) (= W1 W0)))))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (not (= W0 tptp.sz00)) (not (= W0 tptp.sz10))) (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0) (tptp.isPrime0 W1))))) _let_19 _let_18 _let_14 (= (tptp.sdtasdt0 tptp.xp _let_3) _let_9) _let_13 _let_11 _let_7 _let_4 (not (and (not (= tptp.xm tptp.xn)) (or (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xm W0) tptp.xn))) (tptp.sdtlseqdt0 tptp.xm tptp.xn)))) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 83.40/83.60 )
% 83.40/83.60 % SZS output end Proof for NUM526+3
% 83.40/83.61 % cvc5---1.0.5 exiting
% 83.40/83.61 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------