TSTP Solution File: NUM924_1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM924_1 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n015.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 10:48:53 EDT 2023
% Result : Theorem 0.21s 0.67s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM924_1 : TPTP v8.1.2. Released v5.3.0.
% 0.12/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n015.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri Aug 25 13:58:22 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.67 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.G7N7rT971j/cvc5---1.0.5_6572.p...
% 0.21/0.67 ------- get file name : TPTP file name is NUM924_1
% 0.21/0.67 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_6572.smt2...
% 0.21/0.67 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.67 % SZS status Theorem for NUM924_1
% 0.21/0.67 % SZS output start Proof for NUM924_1
% 0.21/0.67 (
% 0.21/0.67 (let ((_let_1 (tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.bit0 _let_1))) (let ((_let_3 (tptp.number_number_of_nat _let_2))) (let ((_let_4 (tptp.power_power_int tptp.s _let_3))) (let ((_let_5 (tptp.plus_plus_int _let_4 tptp.one_one_int))) (let ((_let_6 (tptp.ord_less_int _let_5 tptp.zero_zero_int))) (let ((_let_7 (not _let_6))) (let ((_let_8 (tptp.number_number_of_int tptp.pls))) (let ((_let_9 (= tptp.zero_zero_int _let_8))) (let ((_let_10 (tptp.number_number_of_nat _let_1))) (let ((_let_11 (forall ((K tptp.int)) (= (tptp.ord_less_eq_int (tptp.bit1 K) tptp.pls) (tptp.ord_less_int K tptp.pls))))) (let ((_let_12 (forall ((W tptp.int)) (= (tptp.times_times_int tptp.pls W) tptp.pls)))) (let ((_let_13 (tptp.plus_plus_nat tptp.one_one_nat tptp.one_one_nat))) (let ((_let_14 (= _let_13 _let_3))) (let ((_let_15 (forall ((Y_1 tptp.int)) (= (tptp.ord_less_eq_int tptp.one_one_int (tptp.number_number_of_int Y_1)) (tptp.ord_less_eq_int (tptp.bit1 tptp.pls) Y_1))))) (let ((_let_16 (tptp.number_number_of_nat tptp.pls))) (let ((_let_17 (forall ((Z_1 tptp.int) (W_1 tptp.int)) (= (tptp.ord_less_int Z_1 W_1) (and (tptp.ord_less_eq_int Z_1 W_1) (not (= Z_1 W_1))))))) (let ((_let_18 (tptp.ord_less_eq_int tptp.pls tptp.pls))) (let ((_let_19 (forall ((X tptp.int) (Y tptp.nat) (Z tptp.nat)) (= (tptp.power_power_int X (tptp.plus_plus_nat Y Z)) (tptp.times_times_int (tptp.power_power_int X Y) (tptp.power_power_int X Z)))))) (let ((_let_20 (forall ((Z tptp.int) (W tptp.int)) (= (tptp.times_times_int Z W) (tptp.times_times_int W Z))))) (let ((_let_21 (forall ((K_1 tptp.int)) (= (tptp.number_number_of_int K_1) K_1)))) (let ((_let_22 (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_2)) tptp.m) tptp.one_one_int))) (let ((_let_23 (tptp.times_times_int _let_22 tptp.t))) (let ((_let_24 (tptp.power_power_int tptp.one_one_int _let_3))) (let ((_let_25 (= _let_24 tptp.one_one_int))) (let ((_let_26 (forall ((X_1 tptp.int) (Y_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (= (tptp.plus_plus_int (tptp.power_power_int X_1 _let_1) (tptp.power_power_int Y_1 _let_1)) tptp.zero_zero_int) (and (= X_1 tptp.zero_zero_int) (= Y_1 tptp.zero_zero_int))))))) (let ((_let_27 (= _let_5 _let_23))) (let ((_let_28 (tptp.times_times_int _let_22 tptp.zero_zero_int))) (let ((_let_29 (tptp.ord_less_int _let_23 _let_28))) (let ((_let_30 (= _let_23 _let_5))) (let ((_let_31 (= tptp.one_one_int _let_24))) (let ((_let_32 (= _let_3 _let_13))) (let ((_let_33 (= tptp.pls _let_8))) (let ((_let_34 (= _let_28 (tptp.times_times_int tptp.zero_zero_int _let_22)))) (let ((_let_35 (tptp.power_power_int tptp.s tptp.one_one_nat))) (let ((_let_36 (= (tptp.power_power_int tptp.s _let_13) (tptp.times_times_int _let_35 _let_35)))) (let ((_let_37 (tptp.power_power_int tptp.one_one_int tptp.one_one_nat))) (let ((_let_38 (= (tptp.power_power_int tptp.one_one_int _let_13) (tptp.times_times_int _let_37 _let_37)))) (let ((_let_39 (tptp.ord_less_eq_int _let_23 _let_28))) (let ((_let_40 (tptp.ord_less_eq_int _let_5 tptp.zero_zero_int))) (let ((_let_41 (= tptp.pls (tptp.times_times_int tptp.pls _let_22)))) (let ((_let_42 (SYMM (ASSUME :args (_let_27))))) (let ((_let_43 (SYMM (ASSUME :args (_let_25))))) (let ((_let_44 (SYMM (ASSUME :args (_let_14))))) (let ((_let_45 (ASSUME :args (_let_9)))) (let ((_let_46 (forall ((K_1 tptp.int)) (= K_1 (tptp.number_number_of_int K_1))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (tptp.pls QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.number_number_of_int K_1)))) :args (_let_46))) _let_47 :args (_let_33 false _let_46)))) (let ((_let_49 (_let_20))) (let ((_let_50 (ASSUME :args _let_49))) (let ((_let_51 (_let_19))) (let ((_let_52 (ASSUME :args _let_51))) (let ((_let_53 ((tptp.power_power_int X (tptp.plus_plus_nat Y Z))))) (let ((_let_54 (and _let_39 (not (= _let_23 _let_28))))) (let ((_let_55 (= _let_29 _let_54))) (let ((_let_56 (_let_17))) (let ((_let_57 (ASSUME :args _let_56))) (let ((_let_58 ((tptp.ord_less_int Z_1 W_1)))) (let ((_let_59 (= tptp.zero_zero_int _let_5))) (let ((_let_60 (not _let_59))) (let ((_let_61 (and _let_40 _let_60))) (let ((_let_62 (not _let_40))) (let ((_let_63 (= _let_6 _let_61))) (let ((_let_64 (not _let_61))) (let ((_let_65 (= tptp.zero_zero_int (tptp.plus_plus_int _let_4 _let_24)))) (let ((_let_66 (= tptp.one_one_int tptp.zero_zero_int))) (let ((_let_67 (and (= tptp.zero_zero_int tptp.s) _let_66))) (let ((_let_68 (= _let_65 _let_67))) (let ((_let_69 (not _let_65))) (let ((_let_70 (forall ((X_1 tptp.int) (Y_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (= tptp.zero_zero_int (tptp.plus_plus_int (tptp.power_power_int X_1 _let_1) (tptp.power_power_int Y_1 _let_1))) (and (= tptp.zero_zero_int X_1) (= tptp.zero_zero_int Y_1))))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (not _let_67))) (let ((_let_73 (tptp.ord_less_eq_int tptp.one_one_int _let_8))) (let ((_let_74 (not _let_66))) (let ((_let_75 (tptp.ord_less_eq_int _let_1 tptp.pls))) (let ((_let_76 (= _let_75 _let_73))) (let ((_let_77 (not _let_73))) (let ((_let_78 (_let_15))) (let ((_let_79 (ASSUME :args _let_78))) (let ((_let_80 (tptp.ord_less_int tptp.pls tptp.pls))) (let ((_let_81 (= _let_80 _let_75))) (let ((_let_82 (not _let_75))) (let ((_let_83 (_let_11))) (let ((_let_84 (ASSUME :args _let_83))) (let ((_let_85 (ASSUME :args (_let_18)))) (let ((_let_86 (not _let_33))) (let ((_let_87 (not _let_9))) (let ((_let_88 (not _let_18))) (let ((_let_89 (or))) (let ((_let_90 (REFL :args (_let_86)))) (let ((_let_91 (REFL :args (_let_87)))) (let ((_let_92 (APPLY_UF tptp.ord_less_eq_int))) (let ((_let_93 (ASSUME :args (_let_33)))) (let ((_let_94 (SYMM _let_93))) (let ((_let_95 (SYMM _let_45))) (let ((_let_96 (TRANS (SYMM _let_95) _let_94))) (let ((_let_97 (ASSUME :args (_let_66)))) (let ((_let_98 (ASSUME :args (_let_77)))) (let ((_let_99 (not _let_31))) (let ((_let_100 (REFL :args (_let_99)))) (let ((_let_101 (and _let_31 _let_69))) (let ((_let_102 (ASSUME :args (_let_69)))) (let ((_let_103 (APPLY_UF tptp.plus_plus_int))) (let ((_let_104 (SYMM _let_43))) (let ((_let_105 (REFL :args (_let_4)))) (let ((_let_106 (REFL :args (tptp.zero_zero_int)))) (let ((_let_107 (_let_62))) (let ((_let_108 (_let_61))) (let ((_let_109 (forall ((W tptp.int)) (= tptp.pls (tptp.times_times_int tptp.pls W))))) (let ((_let_110 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_111 (not _let_41))) (let ((_let_112 (not _let_39))) (let ((_let_113 (not _let_38))) (let ((_let_114 (not _let_36))) (let ((_let_115 (not _let_34))) (let ((_let_116 (not _let_32))) (let ((_let_117 (not _let_30))) (let ((_let_118 (ASSUME :args (_let_39)))) (let ((_let_119 (ASSUME :args (_let_34)))) (let ((_let_120 (ASSUME :args (_let_41)))) (let ((_let_121 (SYMM _let_42))) (let ((_let_122 (APPLY_UF tptp.power_power_int))) (let ((_let_123 (SYMM _let_44))) (let ((_let_124 (ASSUME :args (_let_38)))) (let ((_let_125 (ASSUME :args (_let_36)))) (let ((_let_126 (TRANS (CONG (TRANS (SYMM _let_125) (CONG (REFL :args (tptp.s)) _let_123 :args _let_122)) (TRANS (SYMM _let_124) (CONG (REFL :args (tptp.one_one_int)) _let_123 :args _let_122)) :args _let_103) (CONG _let_105 _let_104 :args _let_103) _let_121))) (let ((_let_127 (ASSUME :args _let_107))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_118 _let_42 _let_43 _let_44 _let_125 _let_124 _let_119 _let_45 _let_93 _let_120 _let_127) :args (_let_9 _let_30 _let_31 _let_32 _let_33 _let_34 _let_36 _let_38 _let_39 _let_62 _let_41)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_127)) (CONG (TRANS _let_121 (SYMM _let_126)) _let_106 :args _let_92) (CONG _let_126 (TRANS _let_45 _let_94 (SYMM (SYMM _let_120)) (CONG (TRANS (SYMM _let_94) _let_95) (REFL :args (_let_22)) :args (APPLY_UF tptp.times_times_int)) (SYMM _let_119)) :args _let_92) (TRUE_INTRO _let_118))) :args (_let_39 _let_30 _let_31 _let_32 _let_36 _let_38 _let_34 _let_9 _let_33 _let_41 _let_62)) :args ((not (and _let_9 _let_30 _let_31 _let_32 _let_33 _let_34 _let_36 _let_38 _let_39 _let_62 _let_41)) SB_LITERAL))) (CONG _let_91 (REFL :args (_let_117)) _let_100 (REFL :args (_let_116)) _let_90 (REFL :args (_let_115)) (REFL :args (_let_114)) (REFL :args (_let_113)) (REFL :args (_let_112)) (MACRO_SR_PRED_INTRO :args ((= (not _let_62) _let_40))) (REFL :args (_let_111)) :args _let_89)) :args ((or _let_117 _let_99 _let_116 _let_87 _let_40 _let_86 _let_115 _let_114 _let_113 _let_112 _let_111))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_110 :args (_let_22 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.times_times_int tptp.pls W) tptp.pls))))) :args (_let_109))) _let_110 :args (_let_41 false _let_109)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_108) (CONG (REFL :args _let_108) (REFL :args _let_107) (MACRO_SR_PRED_INTRO :args ((= (not _let_60) _let_59))) :args _let_89)) :args ((or _let_59 _let_61 _let_62))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_101)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_102 _let_43) (SCOPE (FALSE_ELIM (TRANS (CONG _let_106 (CONG _let_105 (SYMM _let_104) :args _let_103) :args (=)) (FALSE_INTRO _let_102))) :args (_let_69 _let_31))) :args (_let_31 _let_69))) :args (true _let_101)) (CONG _let_100 (MACRO_SR_PRED_INTRO :args ((= (not _let_69) _let_65))) (REFL :args (_let_60)) :args _let_89)) :args ((or _let_60 _let_99 _let_65))) _let_43 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_68)) :args ((or _let_67 _let_69 (not _let_68)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_67 1)) :args ((or _let_66 _let_72))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_85 _let_93 _let_45 _let_97 _let_98) :args (_let_18 _let_9 _let_66 _let_33 _let_77)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_98)) (CONG (TRANS (SYMM (SYMM _let_97)) _let_96) _let_95 :args _let_92) (CONG (REFL :args (tptp.pls)) _let_96 :args _let_92) (TRUE_INTRO _let_85))) :args (_let_18 _let_33 _let_9 _let_66 _let_77)) :args ((not (and _let_18 _let_9 _let_66 _let_33 _let_77)) SB_LITERAL))) (CONG (REFL :args (_let_88)) _let_91 (REFL :args (_let_74)) _let_90 (MACRO_SR_PRED_INTRO :args ((= (not _let_77) _let_73))) :args _let_89)) :args ((or _let_88 _let_87 _let_74 _let_73 _let_86))) _let_85 _let_45 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_76)) :args ((or _let_75 _let_77 (not _let_76)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_81)) :args ((or _let_80 _let_82 (not _let_81)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_57 :args (tptp.pls tptp.pls QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.ord_less_eq_int Z_1 W_1)))) :args _let_56))) _let_57 :args ((not _let_80) false _let_17)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_84 :args (tptp.pls QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.bit1 K)))) :args _let_83))) _let_84 :args (_let_81 false _let_11)) :args (_let_82 true _let_80 false _let_81)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_79 :args (tptp.pls QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.number_number_of_int Y_1)))) :args _let_78))) _let_79 :args (_let_76 false _let_15)) :args (_let_77 true _let_75 false _let_76)) _let_48 :args (_let_74 false _let_18 false _let_9 true _let_73 false _let_33)) :args (_let_72 true _let_66)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_71 :args (tptp.s tptp.one_one_int QUANTIFIERS_INST_E_MATCHING ((tptp.plus_plus_int (tptp.power_power_int X_1 _let_3) (tptp.power_power_int Y_1 _let_3))))) :args (_let_70)))) _let_71 :args (_let_68 false _let_70)) :args (_let_69 true _let_67 false _let_68)) :args (_let_60 false _let_31 true _let_65)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_63)) :args ((or _let_6 _let_64 (not _let_63)))) (ASSUME :args (_let_7)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_57 :args (_let_5 tptp.zero_zero_int QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_58)) :args _let_56))) _let_57 :args (_let_63 false _let_17)) :args (_let_64 true _let_6 false _let_63)) :args (_let_62 true _let_59 true _let_61)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_54 0)) :args ((or _let_39 (not _let_54)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_55)) :args ((or (not _let_29) _let_54 (not _let_55)))) (ASSUME :args (_let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :args (_let_23 _let_28 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_58)) :args _let_56)) _let_57 :args (_let_55 false _let_17)) :args (_let_54 false _let_29 false _let_55)) :args (_let_39 false _let_54)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (tptp.one_one_int tptp.one_one_nat tptp.one_one_nat QUANTIFIERS_INST_E_MATCHING _let_53)) :args _let_51)) _let_52 :args (_let_38 false _let_19)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (tptp.s tptp.one_one_nat tptp.one_one_nat QUANTIFIERS_INST_E_MATCHING _let_53)) :args _let_51)) _let_52 :args (_let_36 false _let_19)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (_let_22 tptp.zero_zero_int QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.times_times_int Z W)))) :args _let_49)) _let_50 :args (_let_34 false _let_20)) _let_48 _let_45 _let_44 _let_43 _let_42 :args (false false _let_41 true _let_40 false _let_39 false _let_38 false _let_36 false _let_34 false _let_33 false _let_9 false _let_32 false _let_31 false _let_30)) :args ((tptp.ord_less_int tptp.t tptp.zero_zero_int) (tptp.ord_less_int tptp.t tptp.one_one_int) _let_29 _let_27 (=> (= tptp.t tptp.zero_zero_int) (= _let_5 tptp.zero_zero_int)) (not (tptp.ord_less_eq_int tptp.one_one_int tptp.t)) (tptp.ord_less_int tptp.zero_zero_int _let_22) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (not (tptp.ord_less_int (tptp.plus_plus_int (tptp.power_power_int X _let_1) (tptp.power_power_int Y _let_1)) tptp.zero_zero_int)))) (forall ((X_1 tptp.int) (Y_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.ord_less_int tptp.zero_zero_int (tptp.plus_plus_int (tptp.power_power_int X_1 _let_1) (tptp.power_power_int Y_1 _let_1))) (or (not (= X_1 tptp.zero_zero_int)) (not (= Y_1 tptp.zero_zero_int)))))) _let_26 (forall ((A_2 tptp.int)) (not (tptp.ord_less_int (tptp.power_power_int A_2 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) tptp.zero_zero_int))) (forall ((A_1 tptp.int)) (= (tptp.ord_less_int tptp.zero_zero_int (tptp.power_power_int A_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (not (= A_1 tptp.zero_zero_int)))) (= (tptp.power_power_nat tptp.one_one_nat _let_3) tptp.one_one_nat) _let_25 (= (tptp.power_power_nat tptp.zero_zero_nat _let_3) tptp.zero_zero_nat) (= (tptp.power_power_int tptp.zero_zero_int _let_3) tptp.zero_zero_int) (forall ((A_1 tptp.int)) (= (= (tptp.power_power_int A_1 (tptp.number_number_of_nat (tptp.bit0 (tptp.bit1 tptp.pls)))) tptp.zero_zero_int) (= A_1 tptp.zero_zero_int))) (forall ((W_6 tptp.int)) (= (tptp.plus_plus_int tptp.one_one_int (tptp.number_number_of_int W_6)) (tptp.number_number_of_int (tptp.plus_plus_int (tptp.bit1 tptp.pls) W_6)))) (forall ((V_13 tptp.int)) (= (tptp.plus_plus_int (tptp.number_number_of_int V_13) tptp.one_one_int) (tptp.number_number_of_int (tptp.plus_plus_int V_13 (tptp.bit1 tptp.pls))))) (tptp.ord_less_int tptp.t _let_22) (not (forall ((T tptp.int)) (let ((_let_1 (tptp.bit0 (tptp.bit1 tptp.pls)))) (not (= (tptp.plus_plus_int (tptp.power_power_int tptp.s (tptp.number_number_of_nat _let_1)) tptp.one_one_int) (tptp.times_times_int (tptp.plus_plus_int (tptp.times_times_int (tptp.number_number_of_int (tptp.bit0 _let_1)) tptp.m) tptp.one_one_int) T)))))) (tptp.zprime _let_22) (tptp.twoSqu1431725154sum2sq _let_23) (forall ((W tptp.int)) (tptp.ord_less_eq_int W W)) _let_21 _let_20 (forall ((Z tptp.int) (W tptp.int)) (or (tptp.ord_less_eq_int Z W) (tptp.ord_less_eq_int W Z))) (forall ((V_2 tptp.int) (W tptp.int)) (= (tptp.times_times_int (tptp.number_number_of_int V_2) (tptp.number_number_of_int W)) (tptp.number_number_of_int (tptp.times_times_int V_2 W)))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.ord_less_eq_int (tptp.number_number_of_int K) (tptp.number_number_of_int L)) (tptp.ord_less_eq_int K L))) (forall ((X_1 tptp.int) (Y_1 tptp.int)) (= (tptp.ord_less_eq_int (tptp.number_number_of_int X_1) (tptp.number_number_of_int Y_1)) (tptp.ord_less_eq_int X_1 Y_1))) (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (= (tptp.times_times_int (tptp.times_times_int Z1 Z2) Z3) (tptp.times_times_int Z1 (tptp.times_times_int Z2 Z3)))) (forall ((K_1 tptp.int) (I tptp.int) (J tptp.int)) (=> (tptp.ord_less_eq_int I J) (=> (tptp.ord_less_eq_int J K_1) (tptp.ord_less_eq_int I K_1)))) (forall ((Z tptp.int) (W tptp.int)) (=> (tptp.ord_less_eq_int Z W) (=> (tptp.ord_less_eq_int W Z) (= Z W)))) _let_19 (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.ord_less_eq_int (tptp.bit1 K1) (tptp.bit1 K2)) (tptp.ord_less_eq_int K1 K2))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.ord_less_eq_int (tptp.bit1 K) (tptp.bit1 L)) (tptp.ord_less_eq_int K L))) _let_18 (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.ord_less_eq_int (tptp.bit0 K1) (tptp.bit0 K2)) (tptp.ord_less_eq_int K1 K2))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.ord_less_eq_int (tptp.bit0 K) (tptp.bit0 L)) (tptp.ord_less_eq_int K L))) _let_17 (forall ((K_1 tptp.int) (I tptp.int) (J tptp.int)) (=> (tptp.ord_less_eq_int I J) (tptp.ord_less_eq_int (tptp.plus_plus_int K_1 I) (tptp.plus_plus_int K_1 J)))) (forall ((V_7 tptp.int)) (= (= (tptp.number_number_of_nat V_7) tptp.zero_zero_nat) (tptp.ord_less_eq_int V_7 tptp.pls))) (forall ((V_7 tptp.int)) (= (= tptp.zero_zero_nat (tptp.number_number_of_nat V_7)) (tptp.ord_less_eq_int V_7 tptp.pls))) (forall ((V_12 tptp.int) (V_11 tptp.int)) (=> (tptp.ord_less_eq_int tptp.pls V_11) (=> (tptp.ord_less_eq_int tptp.pls V_12) (= (tptp.times_times_nat (tptp.number_number_of_nat V_11) (tptp.number_number_of_nat V_12)) (tptp.number_number_of_nat (tptp.times_times_int V_11 V_12)))))) (forall ((V_12 tptp.int) (V_11 tptp.int)) (=> (tptp.ord_less_eq_int tptp.pls V_11) (=> (tptp.ord_less_eq_int tptp.pls V_12) (= (tptp.times_times_int (tptp.number_number_of_int V_11) (tptp.number_number_of_int V_12)) (tptp.number_number_of_int (tptp.times_times_int V_11 V_12)))))) (forall ((V_10 tptp.int) (W_5 tptp.int) (Z_3 tptp.int)) (= (tptp.times_times_int (tptp.number_number_of_int V_10) (tptp.times_times_int (tptp.number_number_of_int W_5) Z_3)) (tptp.times_times_int (tptp.number_number_of_int (tptp.times_times_int V_10 W_5)) Z_3))) (forall ((V_9 tptp.int) (W_4 tptp.int)) (= (tptp.times_times_int (tptp.number_number_of_int V_9) (tptp.number_number_of_int W_4)) (tptp.number_number_of_int (tptp.times_times_int V_9 W_4)))) (forall ((V_8 tptp.int) (W_3 tptp.int)) (= (tptp.number_number_of_int (tptp.times_times_int V_8 W_3)) (tptp.times_times_int (tptp.number_number_of_int V_8) (tptp.number_number_of_int W_3)))) (forall ((X_1 tptp.int) (Y_1 tptp.int)) (= (tptp.ord_less_eq_int (tptp.plus_plus_int (tptp.times_times_int X_1 X_1) (tptp.times_times_int Y_1 Y_1)) tptp.zero_zero_int) (and (= X_1 tptp.zero_zero_int) (= Y_1 tptp.zero_zero_int)))) (forall ((X_2 tptp.int) (Y_2 tptp.int)) (tptp.ord_less_eq_int tptp.zero_zero_int (tptp.plus_plus_int (tptp.times_times_int X_2 X_2) (tptp.times_times_int Y_2 Y_2)))) (forall ((X_1 tptp.int)) (= (tptp.ord_less_eq_int (tptp.number_number_of_int X_1) tptp.zero_zero_int) (tptp.ord_less_eq_int X_1 tptp.pls))) (forall ((Y_1 tptp.int)) (= (tptp.ord_less_eq_int tptp.zero_zero_int (tptp.number_number_of_int Y_1)) (tptp.ord_less_eq_int tptp.pls Y_1))) (forall ((V_7 tptp.int)) (= (tptp.ord_less_nat tptp.zero_zero_nat (tptp.number_number_of_nat V_7)) (tptp.ord_less_int tptp.pls V_7))) (forall ((V_7 tptp.int) (W_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_int V_7))) (let ((_let_2 (tptp.number_number_of_int W_1))) (= (tptp.ord_less_eq_int _let_1 _let_2) (not (tptp.ord_less_int _let_2 _let_1)))))) (forall ((V_7 tptp.int) (W_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat V_7))) (let ((_let_2 (tptp.number_number_of_nat W_1))) (= (tptp.ord_less_eq_nat _let_1 _let_2) (not (tptp.ord_less_nat _let_2 _let_1)))))) (forall ((K tptp.int)) (= (tptp.ord_less_eq_int tptp.pls (tptp.bit1 K)) (tptp.ord_less_eq_int tptp.pls K))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.ord_less_eq_int (tptp.bit0 K1) (tptp.bit1 K2)) (tptp.ord_less_eq_int K1 K2))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.ord_less_eq_int (tptp.bit0 K) (tptp.bit1 L)) (tptp.ord_less_eq_int K L))) (forall ((K tptp.int)) (= (tptp.ord_less_eq_int (tptp.bit0 K) tptp.pls) (tptp.ord_less_eq_int K tptp.pls))) (forall ((K tptp.int)) (= (tptp.ord_less_eq_int tptp.pls (tptp.bit0 K)) (tptp.ord_less_eq_int tptp.pls K))) (forall ((Z_2 tptp.int) (Z tptp.int) (W_2 tptp.int) (W tptp.int)) (=> (tptp.ord_less_int W_2 W) (=> (tptp.ord_less_eq_int Z_2 Z) (tptp.ord_less_int (tptp.plus_plus_int W_2 Z_2) (tptp.plus_plus_int W Z))))) (= _let_16 tptp.zero_zero_nat) (= tptp.zero_zero_nat _let_16) (forall ((X_1 tptp.int)) (= (tptp.ord_less_eq_int (tptp.number_number_of_int X_1) tptp.one_one_int) (tptp.ord_less_eq_int X_1 (tptp.bit1 tptp.pls)))) _let_15 _let_14 _let_12 (forall ((K_1 tptp.int) (L_1 tptp.int)) (= (tptp.times_times_int (tptp.bit0 K_1) L_1) (tptp.bit0 (tptp.times_times_int K_1 L_1)))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.ord_less_int (tptp.number_number_of_int K) (tptp.number_number_of_int L)) (tptp.ord_less_int K L))) (forall ((Z tptp.int)) (= (tptp.times_times_int Z tptp.one_one_int) Z)) (forall ((Z tptp.int)) (= (tptp.times_times_int tptp.one_one_int Z) Z)) (forall ((V_2 tptp.int) (W tptp.int)) (= (tptp.plus_plus_int (tptp.number_number_of_int V_2) (tptp.number_number_of_int W)) (tptp.number_number_of_int (tptp.plus_plus_int V_2 W)))) (forall ((Z1 tptp.int) (Z2 tptp.int) (W tptp.int)) (= (tptp.times_times_int (tptp.plus_plus_int Z1 Z2) W) (tptp.plus_plus_int (tptp.times_times_int Z1 W) (tptp.times_times_int Z2 W)))) (forall ((W tptp.int) (Z1 tptp.int) (Z2 tptp.int)) (= (tptp.times_times_int W (tptp.plus_plus_int Z1 Z2)) (tptp.plus_plus_int (tptp.times_times_int W Z1) (tptp.times_times_int W Z2)))) _let_11 (forall ((K tptp.int)) (= (tptp.ord_less_int tptp.pls (tptp.bit1 K)) (tptp.ord_less_eq_int tptp.pls K))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.ord_less_eq_int (tptp.bit1 K1) (tptp.bit0 K2)) (tptp.ord_less_int K1 K2))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.ord_less_eq_int (tptp.bit1 K) (tptp.bit0 L)) (tptp.ord_less_int K L))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.ord_less_int (tptp.bit0 K1) (tptp.bit1 K2)) (tptp.ord_less_eq_int K1 K2))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.ord_less_int (tptp.bit0 K) (tptp.bit1 L)) (tptp.ord_less_eq_int K L))) (forall ((V_7 tptp.int) (V_6 tptp.int)) (let ((_let_1 (tptp.ord_less_int V_7 V_6))) (= (tptp.ord_less_nat (tptp.number_number_of_nat V_7) (tptp.number_number_of_nat V_6)) (and (=> _let_1 (tptp.ord_less_int tptp.pls V_6)) _let_1)))) (forall ((Z_1 tptp.int)) (= (tptp.ord_less_eq_int tptp.one_one_int Z_1) (tptp.ord_less_int tptp.zero_zero_int Z_1))) (= _let_10 tptp.one_one_nat) (= tptp.one_one_nat _let_10) (forall ((W tptp.int) (Z tptp.int)) (=> (tptp.ord_less_int W Z) (tptp.ord_less_eq_int (tptp.plus_plus_int W tptp.one_one_int) Z))) (forall ((W_1 tptp.int) (Z_1 tptp.int)) (= (tptp.ord_less_eq_int (tptp.plus_plus_int W_1 tptp.one_one_int) Z_1) (tptp.ord_less_int W_1 Z_1))) (forall ((W_1 tptp.int) (Z_1 tptp.int)) (= (tptp.ord_less_int W_1 (tptp.plus_plus_int Z_1 tptp.one_one_int)) (tptp.ord_less_eq_int W_1 Z_1))) (forall ((V_5 tptp.int) (V_4 tptp.int)) (=> (tptp.ord_less_eq_int tptp.pls V_4) (=> (tptp.ord_less_eq_int tptp.pls V_5) (= (tptp.plus_plus_int (tptp.number_number_of_int V_4) (tptp.number_number_of_int V_5)) (tptp.number_number_of_int (tptp.plus_plus_int V_4 V_5)))))) (forall ((V_5 tptp.int) (V_4 tptp.int)) (=> (tptp.ord_less_eq_int tptp.pls V_4) (=> (tptp.ord_less_eq_int tptp.pls V_5) (= (tptp.plus_plus_nat (tptp.number_number_of_nat V_4) (tptp.number_number_of_nat V_5)) (tptp.number_number_of_nat (tptp.plus_plus_int V_4 V_5)))))) (forall ((V_3 tptp.int) (V_2 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat V_3))) (let ((_let_2 (tptp.number_number_of_nat V_2))) (let ((_let_3 (tptp.plus_plus_nat _let_2 _let_1))) (let ((_let_4 (tptp.ord_less_int V_3 tptp.pls))) (let ((_let_5 (tptp.ord_less_int V_2 tptp.pls))) (and (=> _let_5 (= _let_3 _let_1)) (=> (not _let_5) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (tptp.number_number_of_nat (tptp.plus_plus_int V_2 V_3))))))))))))) (forall ((Z tptp.int)) (=> (tptp.ord_less_eq_int tptp.zero_zero_int Z) (tptp.ord_less_int tptp.zero_zero_int (tptp.plus_plus_int tptp.one_one_int Z)))) (forall ((X_1 tptp.int) (Y_1 tptp.int)) (= (= (tptp.number_number_of_int X_1) (tptp.number_number_of_int Y_1)) (= X_1 Y_1))) (forall ((W_1 tptp.int) (X_1 tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat W_1))) (= (= _let_1 X_1) (= X_1 _let_1)))) (forall ((W_1 tptp.int) (X_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_int W_1))) (= (= _let_1 X_1) (= X_1 _let_1)))) (forall ((K tptp.int) (L tptp.int)) (= (= (tptp.bit1 K) (tptp.bit1 L)) (= K L))) (forall ((K tptp.int) (L tptp.int)) (= (= (tptp.bit0 K) (tptp.bit0 L)) (= K L))) (forall ((X tptp.int) (Y tptp.int)) (or (tptp.ord_less_int X Y) (= X Y) (tptp.ord_less_int Y X))) (forall ((X_1 tptp.int) (Y_1 tptp.int)) (= (= (tptp.plus_plus_int (tptp.times_times_int X_1 X_1) (tptp.times_times_int Y_1 Y_1)) tptp.zero_zero_int) (and (= X_1 tptp.zero_zero_int) (= Y_1 tptp.zero_zero_int)))) (forall ((A tptp.int) (B_1 tptp.int) (V_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_int V_1))) (= (tptp.times_times_int (tptp.plus_plus_int A B_1) _let_1) (tptp.plus_plus_int (tptp.times_times_int A _let_1) (tptp.times_times_int B_1 _let_1))))) (forall ((A tptp.nat) (B_1 tptp.nat) (V_1 tptp.int)) (let ((_let_1 (tptp.number_number_of_nat V_1))) (= (tptp.times_times_nat (tptp.plus_plus_nat A B_1) _let_1) (tptp.plus_plus_nat (tptp.times_times_nat A _let_1) (tptp.times_times_nat B_1 _let_1))))) (forall ((V tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.number_number_of_int V))) (= (tptp.times_times_int _let_1 (tptp.plus_plus_int B C)) (tptp.plus_plus_int (tptp.times_times_int _let_1 B) (tptp.times_times_int _let_1 C))))) (forall ((V tptp.int) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.number_number_of_nat V))) (= (tptp.times_times_nat _let_1 (tptp.plus_plus_nat B C)) (tptp.plus_plus_nat (tptp.times_times_nat _let_1 B) (tptp.times_times_nat _let_1 C))))) (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (= (tptp.plus_plus_int (tptp.plus_plus_int Z1 Z2) Z3) (tptp.plus_plus_int Z1 (tptp.plus_plus_int Z2 Z3)))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (tptp.plus_plus_int X (tptp.plus_plus_int Y Z)) (tptp.plus_plus_int Y (tptp.plus_plus_int X Z)))) (forall ((Z tptp.int) (W tptp.int)) (= (tptp.plus_plus_int Z W) (tptp.plus_plus_int W Z))) _let_9 _let_7 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.67 )
% 0.21/0.67 % SZS output end Proof for NUM924_1
% 0.21/0.67 % cvc5---1.0.5 exiting
% 0.21/0.67 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------