TSTP Solution File: NUM513+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM513+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n031.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 10:44:39 EDT 2023
% Result : Theorem 13.97s 14.18s
% Output : Proof 13.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM513+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n031.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 09:04:52 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.48 %----Proving TF0_NAR, FOF, or CNF
% 13.97/14.18 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.4qHS77cOVS/cvc5---1.0.5_1043.p...
% 13.97/14.18 ------- get file name : TPTP file name is NUM513+1
% 13.97/14.18 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_1043.smt2...
% 13.97/14.18 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 13.97/14.18 --- Run --no-e-matching --full-saturate-quant at 5...
% 13.97/14.18 % SZS status Theorem for NUM513+1
% 13.97/14.18 % SZS output start Proof for NUM513+1
% 13.97/14.18 (
% 13.97/14.18 (let ((_let_1 (tptp.sdtsldt0 tptp.xn tptp.xr))) (let ((_let_2 (tptp.sdtasdt0 _let_1 tptp.xm))) (let ((_let_3 (tptp.sdtasdt0 tptp.xp (tptp.sdtsldt0 tptp.xk tptp.xr)))) (let ((_let_4 (not (= _let_3 _let_2)))) (let ((_let_5 (tptp.sdtasdt0 tptp.xn tptp.xm))) (let ((_let_6 (= _let_5 (tptp.sdtasdt0 (tptp.sdtsldt0 (tptp.sdtasdt0 tptp.xp tptp.xk) tptp.xr) tptp.xr)))) (let ((_let_7 (tptp.sdtasdt0 _let_2 tptp.xr))) (let ((_let_8 (and (= _let_7 _let_5) _let_6))) (let ((_let_9 (tptp.doDivides0 tptp.xr tptp.xn))) (let ((_let_10 (tptp.doDivides0 tptp.xr _let_5))) (let ((_let_11 (and (tptp.sdtlseqdt0 tptp.xr tptp.xk) _let_10))) (let ((_let_12 (tptp.isPrime0 tptp.xr))) (let ((_let_13 (tptp.aNaturalNumber0 tptp.xr))) (let ((_let_14 (and _let_13 (tptp.doDivides0 tptp.xr tptp.xk) _let_12))) (let ((_let_15 (= tptp.xk tptp.sz10))) (let ((_let_16 (= tptp.xk tptp.sz00))) (let ((_let_17 (tptp.sdtsldt0 _let_5 tptp.xp))) (let ((_let_18 (= tptp.xk _let_17))) (let ((_let_19 (tptp.doDivides0 tptp.xp _let_5))) (let ((_let_20 (tptp.isPrime0 tptp.xp))) (let ((_let_21 (and _let_20 _let_19))) (let ((_let_22 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_23 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_24 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_25 (and _let_24 _let_23 _let_22))) (let ((_let_26 (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_27 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (=> (tptp.aNaturalNumber0 W2) (= (tptp.sdtasdt0 W2 (tptp.sdtsldt0 W1 W0)) (tptp.sdtsldt0 (tptp.sdtasdt0 W2 W1) W0))))))))) (let ((_let_28 (forall ((W0 $$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_29 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_30 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_31 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_32 (tptp.aNaturalNumber0 _let_2))) (let ((_let_33 (not _let_23))) (let ((_let_34 (tptp.aNaturalNumber0 _let_1))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_35 _let_33 _let_32))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (not _let_36))) (let ((_let_39 (and _let_34 (= tptp.xn (tptp.sdtasdt0 tptp.xr _let_1))))) (let ((_let_40 (not _let_9))) (let ((_let_41 (= tptp.sz00 tptp.xr))) (let ((_let_42 (not _let_24))) (let ((_let_43 (not _let_13))) (let ((_let_44 (or _let_43 _let_42 _let_41 _let_40 _let_39))) (let ((_let_45 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1639 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= tptp.sz00 W0) (not (tptp.doDivides0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1639) (= W1 (tptp.sdtasdt0 W0 BOUND_VARIABLE_1639))) (= (tptp.sdtsldt0 W1 W0) BOUND_VARIABLE_1639)))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (_let_45))) (let ((_let_48 (not _let_41))) (let ((_let_49 (and _let_48 (not (= tptp.sz10 tptp.xr)) (forall ((W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (not (tptp.doDivides0 W1 tptp.xr)) (= tptp.sz10 W1) (= W1 tptp.xr)))))) (let ((_let_50 (= _let_12 _let_49))) (let ((_let_51 (or _let_43 _let_50))) (let ((_let_52 (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_53 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (_let_52))) (let ((_let_55 (0))) (let ((_let_56 (ASSUME :args (_let_18)))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO _let_56 :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (AND_ELIM _let_57 :args _let_55))) (let ((_let_59 (2))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_49 0)) :args ((or _let_48 (not _let_49)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_50)) :args ((or (not _let_12) _let_49 (not _let_50)))) (AND_ELIM _let_57 :args _let_59) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_43 _let_50 (not _let_51)))) _let_58 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_53 :args (tptp.xr QUANTIFIERS_INST_CBQI_PROP)) :args _let_54))) _let_53 :args (_let_51 false _let_52)) :args (_let_50 false _let_13 false _let_51)) :args (_let_49 false _let_12 false _let_50)) :args (_let_48 false _let_49)))) (let ((_let_61 (ASSUME :args (_let_25)))) (let ((_let_62 (AND_ELIM _let_61 :args _let_55))) (let ((_let_63 (tptp.sdtasdt0 tptp.xr _let_2))) (let ((_let_64 (= _let_5 _let_63))) (let ((_let_65 (and _let_32 _let_64))) (let ((_let_66 (not _let_32))) (let ((_let_67 (= _let_2 (tptp.sdtsldt0 _let_5 tptp.xr)))) (let ((_let_68 (= _let_65 _let_67))) (let ((_let_69 (not _let_65))) (let ((_let_70 (not _let_10))) (let ((_let_71 (tptp.aNaturalNumber0 _let_5))) (let ((_let_72 (not _let_71))) (let ((_let_73 (or _let_43 _let_72 _let_41 _let_70 _let_68))) (let ((_let_74 (or _let_42 _let_33 _let_71))) (let ((_let_75 (_let_31))) (let ((_let_76 (1))) (let ((_let_77 (AND_ELIM _let_61 :args _let_76))) (let ((_let_78 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_74)) :args ((or _let_42 _let_33 _let_71 (not _let_74)))) _let_62 _let_77 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (tptp.xn tptp.xm QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_75)) _let_37 :args (_let_74 false _let_31)) :args (_let_71 false _let_24 false _let_23 false _let_74)))) (let ((_let_79 (tptp.sdtasdt0 tptp.xp (tptp.sdtsldt0 _let_17 tptp.xr)))) (let ((_let_80 (tptp.sdtasdt0 tptp.xp _let_17))) (let ((_let_81 (= (tptp.sdtsldt0 _let_80 tptp.xr) _let_79))) (let ((_let_82 (= _let_5 _let_80))) (let ((_let_83 (= _let_2 _let_79))) (let ((_let_84 (not _let_67))) (let ((_let_85 (not _let_22))) (let ((_let_86 (tptp.doDivides0 tptp.xr _let_17))) (let ((_let_87 (not _let_86))) (let ((_let_88 (tptp.aNaturalNumber0 _let_17))) (let ((_let_89 (not _let_88))) (let ((_let_90 (or _let_43 _let_89 _let_41 _let_87 _let_85 _let_81))) (let ((_let_91 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1731 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= tptp.sz00 W0) (not (tptp.doDivides0 W0 W1)) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1731)) (= (tptp.sdtasdt0 BOUND_VARIABLE_1731 (tptp.sdtsldt0 W1 W0)) (tptp.sdtsldt0 (tptp.sdtasdt0 BOUND_VARIABLE_1731 W1) W0)))))) (let ((_let_92 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_93 (and _let_88 _let_82))) (let ((_let_94 (not _let_19))) (let ((_let_95 (= tptp.sz00 tptp.xp))) (let ((_let_96 (or _let_85 _let_72 _let_95 _let_94 _let_93))) (let ((_let_97 (not _let_95))) (let ((_let_98 (and _let_97 (not (= tptp.sz10 tptp.xp)) (forall ((W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (not (tptp.doDivides0 W1 tptp.xp)) (= tptp.sz10 W1) (= W1 tptp.xp)))))) (let ((_let_99 (= _let_20 _let_98))) (let ((_let_100 (or _let_85 _let_99))) (let ((_let_101 (AND_ELIM _let_61 :args _let_59))) (let ((_let_102 (ASSUME :args (_let_21)))) (let ((_let_103 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_96)) :args ((or _let_85 _let_94 _let_95 _let_72 _let_93 (not _let_96)))) _let_101 (AND_ELIM _let_102 :args _let_76) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_98 0)) :args ((or _let_97 (not _let_98)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_99)) :args ((or (not _let_20) _let_98 (not _let_99)))) (AND_ELIM _let_102 :args _let_55) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_100)) :args ((or _let_85 _let_99 (not _let_100)))) _let_101 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_53 :args (tptp.xp QUANTIFIERS_INST_CBQI_PROP)) :args _let_54))) _let_53 :args (_let_100 false _let_52)) :args (_let_99 false _let_22 false _let_100)) :args (_let_98 false _let_20 false _let_99)) :args (_let_97 false _let_98)) _let_78 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_46 :args (tptp.xp _let_5 _let_17 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_47))) _let_46 :args (_let_96 false _let_45)) :args (_let_93 false _let_22 false _let_19 true _let_95 false _let_71 false _let_96)))) (let ((_let_104 (not _let_93))) (let ((_let_105 (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_56 :args ((not (= _let_2 _let_3)) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_106 (not _let_81))) (let ((_let_107 (not _let_82))) (let ((_let_108 (not _let_83))) (let ((_let_109 (and _let_108 _let_82 _let_81))) (let ((_let_110 (ASSUME :args (_let_81)))) (let ((_let_111 (ASSUME :args (_let_82)))) (let ((_let_112 (= _let_7 _let_63))) (let ((_let_113 (or _let_66 _let_43 _let_112))) (let ((_let_114 (= _let_5 _let_7))) (let ((_let_115 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_116 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_117 (and _let_114 _let_112))) (let ((_let_118 (ASSUME :args (_let_112)))) (let ((_let_119 (ASSUME :args (_let_114)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (_let_1 tptp.xm QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_75)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_36)) :args ((or _let_33 _let_32 _let_35 _let_38))) _let_77 (MACRO_RESOLUTION_TRUST (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_117)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_118 _let_119) (SCOPE (TRANS (SYMM (SYMM _let_119)) (SYMM (SYMM _let_118))) :args (_let_112 _let_114))) :args (_let_114 _let_112))) :args (true _let_117)) :args ((or (not _let_114) _let_64 (not _let_112)))) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_8)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_56 :args ((and _let_114 _let_6) SB_DEFAULT SBA_FIXPOINT)))) :args _let_55) (REORDERING (CNF_AND_NEG :args (_let_65)) :args ((or _let_66 _let_65 (not _let_64)))) (REORDERING (CNF_OR_POS :args (_let_113)) :args ((or _let_43 _let_66 _let_112 (not _let_113)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_116 :args (_let_2 tptp.xr QUANTIFIERS_INST_CBQI_PROP)) :args (_let_115))) _let_116 :args (_let_113 false _let_115)) _let_58 :args ((or _let_66 _let_65) false _let_114 true _let_64 false _let_112 false _let_113 false _let_13)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_68)) :args ((or _let_67 _let_69 (not _let_68)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_109)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_105 _let_110 _let_111) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (_let_2)) (TRANS (CONG (SYMM (SYMM _let_111)) (REFL :args (tptp.xr)) :args (APPLY_UF tptp.sdtsldt0)) (SYMM (SYMM _let_110))) :args (=)) (FALSE_INTRO _let_105))) :args (_let_108 _let_81 _let_82))) :args (_let_108 _let_82 _let_81))) :args (true _let_109)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_108) _let_83))) (REFL :args (_let_107)) (REFL :args (_let_106)) (REFL :args (_let_84)) :args (or))) :args ((or _let_83 _let_107 _let_84 _let_106))) _let_105 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_93 1)) :args ((or _let_82 _let_104))) _let_103 :args (_let_82 false _let_93)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_90)) :args ((or _let_85 _let_43 _let_87 _let_89 _let_41 _let_81 (not _let_90)))) _let_101 _let_58 (AND_ELIM _let_57 :args _let_76) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_93 0)) :args ((or _let_88 _let_104))) _let_103 :args (_let_88 false _let_93)) _let_60 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_92 :args (tptp.xr _let_17 tptp.xp QUANTIFIERS_INST_CBQI_PROP)) :args (_let_91)))) _let_92 :args (_let_90 false _let_91)) :args (_let_81 false _let_22 false _let_13 false _let_86 false _let_88 true _let_41 false _let_90)) :args (_let_84 true _let_83 false _let_82 false _let_81)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_43 _let_70 _let_72 _let_41 _let_68 (not _let_73)))) _let_58 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO _let_56 :args (_let_11 SB_DEFAULT SBA_FIXPOINT))) :args _let_76) _let_78 _let_60 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_46 :args (tptp.xr _let_5 _let_2 QUANTIFIERS_INST_CBQI_PROP)) :args _let_47))) _let_46 :args (_let_73 false _let_45)) :args (_let_68 false _let_13 false _let_10 false _let_71 true _let_41 false _let_73)) :args (_let_69 true _let_67 false _let_68)) :args (_let_66 true _let_65)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_39 0)) :args ((or _let_34 (not _let_39)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_44)) :args ((or _let_40 _let_42 _let_43 _let_41 _let_39 (not _let_44)))) (ASSUME :args (_let_9)) _let_62 _let_58 _let_60 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_46 :args (tptp.xr tptp.xn _let_1 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_47))) _let_46 :args (_let_44 false _let_45)) :args (_let_39 false _let_9 false _let_24 false _let_13 true _let_41 false _let_44)) :args (_let_34 false _let_39)) :args (_let_38 false _let_23 true _let_32 false _let_34)) _let_37 :args (false true _let_36 false _let_31)) :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 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) _let_30 (forall ((W0 $$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 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))) _let_29 (forall ((W0 $$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))))) (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)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2))))))) _let_28 (forall ((W0 $$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_27 _let_26 (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_25 (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_21 (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_18 (not (or _let_16 _let_15)) (and (not _let_16) (not _let_15)) _let_14 _let_11 (and (not (= tptp.xk tptp.xp)) (tptp.sdtlseqdt0 tptp.xk tptp.xp)) (or _let_9 (tptp.doDivides0 tptp.xr tptp.xm)) _let_9 (and (not (= _let_1 tptp.xn)) (tptp.sdtlseqdt0 _let_1 tptp.xn)) _let_8 _let_4 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 13.97/14.18 )
% 13.97/14.18 % SZS output end Proof for NUM513+1
% 13.97/14.18 % cvc5---1.0.5 exiting
% 13.97/14.19 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------