TSTP Solution File: NUM507+1 by cvc5---1.0.5

%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM507+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n032.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 10:44:32 EDT 2023

% Result   : Theorem 11.83s 12.10s
% Output   : Proof 11.83s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM507+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command    : do_cvc5 %s %d
% 0.09/0.34  % Computer : n032.cluster.edu
% 0.09/0.34  % Model    : x86_64 x86_64
% 0.09/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34  % Memory   : 8042.1875MB
% 0.09/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.34  % CPULimit   : 300
% 0.09/0.34  % WCLimit    : 300
% 0.09/0.34  % DateTime   : Fri Aug 25 10:32:28 EDT 2023
% 0.09/0.34  % CPUTime    : 
% 0.16/0.49  %----Proving TF0_NAR, FOF, or CNF
% 11.83/12.10  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.Tl8ImWjn6V/cvc5---1.0.5_10801.p...
% 11.83/12.10  ------- get file name : TPTP file name is NUM507+1
% 11.83/12.10  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_10801.smt2...
% 11.83/12.10  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 11.83/12.10  --- Run --no-e-matching --full-saturate-quant at 5...
% 11.83/12.10  % SZS status Theorem for NUM507+1
% 11.83/12.10  % SZS output start Proof for NUM507+1
% 11.83/12.10  (
% 11.83/12.10  (let ((_let_1 (tptp.sdtpldt0 tptp.xn tptp.xm))) (let ((_let_2 (tptp.sdtpldt0 _let_1 tptp.xp))) (let ((_let_3 (tptp.sdtpldt0 _let_1 tptp.xr))) (let ((_let_4 (tptp.sdtlseqdt0 _let_3 _let_2))) (let ((_let_5 (not (and (not (= _let_3 _let_2)) _let_4)))) (let ((_let_6 (tptp.sdtlseqdt0 tptp.xk tptp.xp))) (let ((_let_7 (and (not (= tptp.xk tptp.xp)) _let_6))) (let ((_let_8 (tptp.sdtasdt0 tptp.xn tptp.xm))) (let ((_let_9 (and (tptp.sdtlseqdt0 tptp.xr tptp.xk) (tptp.doDivides0 tptp.xr _let_8)))) (let ((_let_10 (tptp.aNaturalNumber0 tptp.xr))) (let ((_let_11 (and _let_10 (tptp.doDivides0 tptp.xr tptp.xk) (tptp.isPrime0 tptp.xr)))) (let ((_let_12 (= tptp.xk tptp.sz10))) (let ((_let_13 (= tptp.xk tptp.sz00))) (let ((_let_14 (tptp.sdtsldt0 _let_8 tptp.xp))) (let ((_let_15 (= tptp.xk _let_14))) (let ((_let_16 (tptp.doDivides0 tptp.xp _let_8))) (let ((_let_17 (tptp.isPrime0 tptp.xp))) (let ((_let_18 (and _let_17 _let_16))) (let ((_let_19 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_20 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_21 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_22 (and _let_21 _let_20 _let_19))) (let ((_let_23 (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_24 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtsldt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2)))))))))) (let ((_let_25 (forall ((W0 $$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))))))))))))) (let ((_let_26 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))))) (let ((_let_27 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))))) (let ((_let_28 (forall ((W0 $$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 ((_let_29 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_30 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_31 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2))))) (let ((_let_32 (tptp.sdtlseqdt0 tptp.xr tptp.xp))) (let ((_let_33 (tptp.sdtlseqdt0 _let_14 tptp.xp))) (let ((_let_34 (not _let_33))) (let ((_let_35 (tptp.sdtlseqdt0 tptp.xr _let_14))) (let ((_let_36 (not _let_35))) (let ((_let_37 (not _let_19))) (let ((_let_38 (tptp.aNaturalNumber0 _let_14))) (let ((_let_39 (not _let_38))) (let ((_let_40 (not _let_10))) (let ((_let_41 (or _let_40 _let_39 _let_37 _let_36 _let_34 _let_32))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (not _let_41))) (let ((_let_44 (tptp.sdtpldt0 tptp.xp _let_1))) (let ((_let_45 (tptp.sdtpldt0 tptp.xr _let_1))) (let ((_let_46 (not (= _let_44 _let_45)))) (let ((_let_47 (= _let_2 _let_3))) (let ((_let_48 (not _let_47))) (let ((_let_49 (and _let_48 _let_4 _let_46 (tptp.sdtlseqdt0 _let_45 _let_44)))) (let ((_let_50 (tptp.aNaturalNumber0 _let_1))) (let ((_let_51 (not _let_50))) (let ((_let_52 (not _let_32))) (let ((_let_53 (= tptp.xp tptp.xr))) (let ((_let_54 (or _let_40 _let_37 _let_53 _let_52 _let_51 _let_49))) (let ((_let_55 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1511 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1511))) (let ((_let_2 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1511))) (let ((_let_3 (tptp.sdtpldt0 BOUND_VARIABLE_1511 W1))) (let ((_let_4 (tptp.sdtpldt0 BOUND_VARIABLE_1511 W0))) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1511)) (and (not (= _let_3 _let_4)) (tptp.sdtlseqdt0 _let_4 _let_3) (not (= _let_1 _let_2)) (tptp.sdtlseqdt0 _let_2 _let_1)))))))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (not _let_49))) (let ((_let_58 (not _let_4))) (let ((_let_59 (and _let_48 _let_46))) (let ((_let_60 (or _let_51 _let_37 _let_40 _let_59 _let_53))) (let ((_let_61 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (and (not (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W0 W2))) (not (= (tptp.sdtpldt0 W1 W0) (tptp.sdtpldt0 W2 W0)))) (= W1 W2))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (tptp.sdtlseqdt0 tptp.xp _let_14))) (let ((_let_64 (not _let_53))) (let ((_let_65 (0))) (let ((_let_66 (ASSUME :args (_let_15)))) (let ((_let_67 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO _let_66 :args (_let_9 SB_DEFAULT SBA_FIXPOINT))) :args _let_65))) (let ((_let_68 (= tptp.xp _let_14))) (let ((_let_69 (not _let_63))) (let ((_let_70 (or _let_39 _let_37 _let_34 _let_69 _let_68))) (let ((_let_71 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W0)) (= W0 W1))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (and _let_38 (= _let_8 (tptp.sdtasdt0 tptp.xp _let_14))))) (let ((_let_74 (not _let_16))) (let ((_let_75 (= tptp.sz00 tptp.xp))) (let ((_let_76 (tptp.aNaturalNumber0 _let_8))) (let ((_let_77 (not _let_76))) (let ((_let_78 (or _let_37 _let_77 _let_75 _let_74 _let_73))) (let ((_let_79 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1625 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= tptp.sz00 W0) (not (tptp.doDivides0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1625) (= W1 (tptp.sdtasdt0 W0 BOUND_VARIABLE_1625))) (= (tptp.sdtsldt0 W1 W0) BOUND_VARIABLE_1625)))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (not _let_20))) (let ((_let_82 (not _let_21))) (let ((_let_83 (or _let_82 _let_81 _let_76))) (let ((_let_84 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (tptp.xn tptp.xm QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_87 (1))) (let ((_let_88 (ASSUME :args (_let_22)))) (let ((_let_89 (AND_ELIM _let_88 :args _let_87))) (let ((_let_90 (AND_ELIM _let_88 :args _let_65))) (let ((_let_91 (not _let_75))) (let ((_let_92 (and _let_91 (not (= tptp.sz10 tptp.xp)) (forall ((W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (not (tptp.doDivides0 W1 tptp.xp)) (= tptp.sz10 W1) (= W1 tptp.xp)))))) (let ((_let_93 (= _let_17 _let_92))) (let ((_let_94 (or _let_37 _let_93))) (let ((_let_95 (forall ((W0 $$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_96 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_97 (AND_ELIM _let_88 :args (2)))) (let ((_let_98 (ASSUME :args (_let_18)))) (let ((_let_99 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_73 0)) :args ((or _let_38 (not _let_73)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_78)) :args ((or _let_37 _let_74 _let_75 _let_77 _let_73 (not _let_78)))) _let_97 (AND_ELIM _let_98 :args _let_87) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_92 0)) :args ((or _let_91 (not _let_92)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_93)) :args ((or (not _let_17) _let_92 (not _let_93)))) (AND_ELIM _let_98 :args _let_65) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_94)) :args ((or _let_37 _let_93 (not _let_94)))) _let_97 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_96 :args (tptp.xp QUANTIFIERS_INST_CBQI_PROP)) :args (_let_95)))) _let_96 :args (_let_94 false _let_95)) :args (_let_93 false _let_19 false _let_94)) :args (_let_92 false _let_17 false _let_93)) :args (_let_91 false _let_92)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_83)) :args ((or _let_82 _let_81 _let_76 (not _let_83)))) _let_90 _let_89 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_85 :args _let_86) :args (_let_84))) _let_85 :args (_let_83 false _let_84)) :args (_let_76 false _let_21 false _let_20 false _let_83)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_80 :args (tptp.xp _let_8 _let_14 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_79)))) _let_80 :args (_let_78 false _let_79)) :args (_let_73 false _let_19 false _let_16 true _let_75 false _let_76 false _let_78)) :args (_let_38 false _let_73)))) (let ((_let_100 (EQ_RESOLVE (ASSUME :args (_let_7)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_66 :args ((and (not (= tptp.xp tptp.xk)) _let_6) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_101 (AND_ELIM _let_100 :args _let_87))) (let ((_let_102 (or))) (let ((_let_103 (ASSUME :args (_let_69)))) (let ((_let_104 (ASSUME :args (_let_53)))) (let ((_let_105 (ASSUME :args (_let_35)))) (let ((_let_106 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_103 _let_104 _let_105) :args (_let_35 _let_53 _let_69)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_105)) (CONG (SYMM _let_104) (REFL :args (_let_14)) :args (APPLY_UF tptp.sdtlseqdt0)) (FALSE_INTRO _let_103))) :args (_let_69 _let_53 _let_35)) :args ((not (and _let_35 _let_53 _let_69)) SB_LITERAL))) (CONG (REFL :args (_let_36)) (REFL :args (_let_64)) (MACRO_SR_PRED_INTRO :args ((= (not _let_69) _let_63))) :args _let_102)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_68 _let_37 _let_34 _let_39 _let_69 (not _let_70)))) (AND_ELIM _let_100 :args _let_65) _let_97 _let_101 _let_99 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_72 :args (_let_14 tptp.xp QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_71)))) _let_72 :args (_let_70 false _let_71)) :args (_let_69 true _let_68 false _let_19 false _let_33 false _let_38 false _let_70)) _let_67 :args (_let_64 true _let_63 false _let_35)))) (let ((_let_107 (or _let_82 _let_81 _let_50))) (let ((_let_108 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_109 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_110 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_107)) :args ((or _let_82 _let_81 _let_50 (not _let_107)))) _let_90 _let_89 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_109 :args _let_86) :args (_let_108))) _let_109 :args (_let_107 false _let_108)) :args (_let_50 false _let_21 false _let_20 false _let_107)))) (let ((_let_111 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO _let_66 :args (_let_11 SB_DEFAULT SBA_FIXPOINT))) :args _let_65))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (tptp.xr _let_14 tptp.xp QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_31))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_37 _let_40 _let_36 _let_34 _let_39 _let_32 _let_43))) _let_97 _let_111 _let_67 _let_101 _let_99 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_37 _let_40 _let_51 _let_53 _let_52 _let_49 (not _let_54)))) _let_97 _let_111 _let_110 _let_106 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_49 1)) :args ((or _let_4 _let_57))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_47))) (REFL :args (_let_58)) :args _let_102)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_59 0)) :args ((or _let_48 (not _let_59)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_37 _let_40 _let_51 _let_59 _let_53 (not _let_60)))) _let_97 _let_111 _let_110 _let_106 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (_let_1 tptp.xp tptp.xr QUANTIFIERS_INST_CBQI_PROP)) :args (_let_61))) _let_62 :args (_let_60 false _let_61)) :args (_let_59 false _let_19 false _let_10 false _let_50 true _let_53 false _let_60)) :args (_let_48 false _let_59)) :args (_let_58 true _let_47)) :args (_let_57 true _let_4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_56 :args (tptp.xr tptp.xp _let_1 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_55)))) _let_56 :args (_let_54 false _let_55)) :args (_let_52 false _let_19 false _let_10 false _let_50 true _let_53 true _let_49 false _let_54)) :args (_let_43 false _let_19 false _let_10 false _let_35 false _let_33 false _let_38 true _let_32)) _let_42 :args (false true _let_41 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))) _let_30 _let_29 (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))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))) (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))))))) _let_28 (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))) _let_27 _let_26 (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))))) _let_25 (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 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2))))))) _let_24 (forall ((W0 $$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 $$unsorted)) (=> (tptp.aNaturalNumber0 W2) (= (tptp.sdtasdt0 W2 (tptp.sdtsldt0 W1 W0)) (tptp.sdtsldt0 (tptp.sdtasdt0 W2 W1) W0))))))) _let_23 (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (not (= W0 tptp.sz00)) (not (= W0 tptp.sz10))) (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0) (tptp.isPrime0 W1))))) _let_22 (forall ((W0 $$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_18 (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_15 (not (or _let_13 _let_12)) (and (not _let_13) (not _let_12)) _let_11 _let_9 _let_7 _let_5 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 11.83/12.11  )
% 11.83/12.11  % SZS output end Proof for NUM507+1
% 11.83/12.11  % cvc5---1.0.5 exiting
% 11.83/12.11  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------