TSTP Solution File: NUM469+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM469+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n010.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 10:44:12 EDT 2023
% Result : Theorem 0.65s 0.88s
% Output : Proof 0.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM469+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n010.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 08:25:50 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.65/0.88 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.fMAKS5c0fU/cvc5---1.0.5_26166.p...
% 0.65/0.88 ------- get file name : TPTP file name is NUM469+1
% 0.65/0.88 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_26166.smt2...
% 0.65/0.88 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.65/0.88 % SZS status Theorem for NUM469+1
% 0.65/0.88 % SZS output start Proof for NUM469+1
% 0.65/0.88 (
% 0.65/0.88 (let ((_let_1 (tptp.sdtpldt0 tptp.xm tptp.xn))) (let ((_let_2 (tptp.doDivides0 tptp.xl _let_1))) (let ((_let_3 (not _let_2))) (let ((_let_4 (tptp.doDivides0 tptp.xl tptp.xn))) (let ((_let_5 (tptp.doDivides0 tptp.xl tptp.xm))) (let ((_let_6 (and _let_5 _let_4))) (let ((_let_7 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_8 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_9 (tptp.aNaturalNumber0 tptp.xl))) (let ((_let_10 (and _let_9 _let_8 _let_7))) (let ((_let_11 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2))))))))) (let ((_let_12 (forall ((W0 $$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 ((_let_13 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))))) (let ((_let_14 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_15 (= _let_1 (tptp.sdtpldt0 tptp.xn tptp.xm)))) (let ((_let_16 (tptp.sdtasdt0 tptp.xl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_17 (= tptp.xm _let_16))) (let ((_let_18 (tptp.sdtasdt0 tptp.xl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_19 (= tptp.xn _let_18))) (let ((_let_20 (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_21 (tptp.sdtasdt0 tptp.xl _let_20))) (let ((_let_22 (= _let_21 (tptp.sdtpldt0 _let_18 _let_16)))) (let ((_let_23 (= _let_1 _let_21))) (let ((_let_24 (not _let_7))) (let ((_let_25 (not _let_8))) (let ((_let_26 (or _let_25 _let_24 _let_15))) (let ((_let_27 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (ASSUME :args (_let_10)))) (let ((_let_30 (AND_ELIM _let_29 :args (2)))) (let ((_let_31 (1))) (let ((_let_32 (AND_ELIM _let_29 :args _let_31))) (let ((_let_33 (not _let_17))) (let ((_let_34 (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_35 _let_33))) (let ((_let_37 (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= tptp.xm (tptp.sdtasdt0 tptp.xl W2))))))) (let ((_let_38 (not _let_36))) (let ((_let_39 (not _let_37))) (let ((_let_40 (= _let_5 _let_39))) (let ((_let_41 (not _let_9))) (let ((_let_42 (or _let_41 _let_25 _let_40))) (let ((_let_43 (forall ((W0 $$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_44 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_45 (_let_43))) (let ((_let_46 ((tptp.doDivides0 W0 W1)))) (let ((_let_47 (0))) (let ((_let_48 (AND_ELIM _let_29 :args _let_47))) (let ((_let_49 (ASSUME :args (_let_6)))) (let ((_let_50 (or))) (let ((_let_51 (_let_39))) (let ((_let_52 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_51)) :args _let_51)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_37))) (REFL :args (_let_38)) :args _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_40)) :args ((or (not _let_5) _let_39 (not _let_40)))) (AND_ELIM _let_49 :args _let_47) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_41 _let_25 _let_40 (not _let_42)))) _let_48 _let_32 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (tptp.xl tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_46)) :args _let_45)) _let_44 :args (_let_42 false _let_43)) :args (_let_40 false _let_9 false _let_8 false _let_42)) :args (_let_39 false _let_5 false _let_40)) :args (_let_38 true _let_37)))) (let ((_let_53 (REFL :args (_let_36)))) (let ((_let_54 (not _let_19))) (let ((_let_55 (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_56 (not _let_55))) (let ((_let_57 (or _let_56 _let_54))) (let ((_let_58 (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= tptp.xn (tptp.sdtasdt0 tptp.xl W2))))))) (let ((_let_59 (not _let_57))) (let ((_let_60 (not _let_58))) (let ((_let_61 (= _let_4 _let_60))) (let ((_let_62 (or _let_41 _let_24 _let_61))) (let ((_let_63 (_let_60))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_63)) :args _let_63)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_60) _let_58))) (REFL :args (_let_59)) :args _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_61)) :args ((or (not _let_4) _let_60 (not _let_61)))) (AND_ELIM _let_49 :args _let_31) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_41 _let_24 _let_61 (not _let_62)))) _let_48 _let_30 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (tptp.xl tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_46)) :args _let_45)) _let_44 :args (_let_62 false _let_43)) :args (_let_61 false _let_9 false _let_7 false _let_62)) :args (_let_60 false _let_4 false _let_61)) :args (_let_59 true _let_58)))) (let ((_let_65 (REFL :args (_let_57)))) (let ((_let_66 (and _let_22 (= (tptp.sdtasdt0 _let_20 tptp.xl) (tptp.sdtpldt0 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.xl) (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.xl)))))) (let ((_let_67 (or _let_41 _let_56 _let_35 _let_66))) (let ((_let_68 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 W2))) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (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 ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_57 0)) (CONG _let_65 (MACRO_SR_PRED_INTRO :args ((= (not _let_56) _let_55))) :args _let_50)) :args ((or _let_55 _let_57))) _let_64 :args (_let_55 true _let_57)))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_36 0)) (CONG _let_53 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) :args _let_50)) :args ((or _let_34 _let_36))) _let_52 :args (_let_34 true _let_36)))) (let ((_let_72 (not _let_23))) (let ((_let_73 (tptp.aNaturalNumber0 _let_20))) (let ((_let_74 (not _let_73))) (let ((_let_75 (or _let_74 _let_72))) (let ((_let_76 (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtpldt0 tptp.xm tptp.xn) (tptp.sdtasdt0 tptp.xl W2))))))) (let ((_let_77 (not _let_76))) (let ((_let_78 (= _let_2 _let_77))) (let ((_let_79 (tptp.aNaturalNumber0 _let_1))) (let ((_let_80 (not _let_79))) (let ((_let_81 (or _let_41 _let_80 _let_78))) (let ((_let_82 (or _let_25 _let_24 _let_79))) (let ((_let_83 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (_let_83))) (let ((_let_86 ((tptp.sdtpldt0 W0 W1)))) (let ((_let_87 (not _let_78))) (let ((_let_88 (_let_76))) (let ((_let_89 (or _let_56 _let_35 _let_73))) (let ((_let_90 (ASSUME :args (_let_72)))) (let ((_let_91 (ASSUME :args (_let_22)))) (let ((_let_92 (ASSUME :args (_let_17)))) (let ((_let_93 (ASSUME :args (_let_19)))) (let ((_let_94 (ASSUME :args (_let_15)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO (MODUS_PONENS (AND_INTRO _let_91 _let_93 _let_92 _let_94) (SCOPE (TRANS (SYMM (SYMM _let_94)) (CONG (SYMM (SYMM _let_93)) (SYMM (SYMM _let_92)) :args (APPLY_UF tptp.sdtpldt0)) (SYMM _let_91)) :args (_let_22 _let_19 _let_17 _let_15))) _let_90) :args (_let_15 _let_17 _let_19 _let_22 _let_72)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO (SYMM (SYMM (ASSUME :args (_let_23)))))) (FALSE_INTRO _let_90))) :args (_let_23 _let_72)) :args ((not (and _let_15 _let_17 _let_19 _let_22 _let_72)) SB_LITERAL))) (CONG (REFL :args ((not _let_15))) (REFL :args (_let_33)) (REFL :args (_let_54)) (REFL :args ((not _let_22))) (MACRO_SR_PRED_INTRO :args ((= (not _let_72) _let_23))) :args _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_74 _let_72 (not _let_75)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_89)) :args ((or _let_35 _let_56 _let_73 (not _let_89)))) _let_71 _let_70 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_86)) :args _let_85)) _let_84 :args (_let_89 false _let_83)) :args (_let_73 false _let_34 false _let_55 false _let_89)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_88) :args (_let_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtasdt0 tptp.xl W2)))) :args _let_88)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_78)) (CONG (REFL :args (_let_87)) (REFL :args (_let_2)) (MACRO_SR_PRED_INTRO :args ((= (not _let_77) _let_76))) :args _let_50)) :args ((or _let_2 _let_76 _let_87))) (ASSUME :args (_let_3)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_81)) :args ((or _let_41 _let_80 _let_78 (not _let_81)))) _let_48 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_25 _let_24 _let_79 (not _let_82)))) _let_32 _let_30 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (tptp.xm tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_86)) :args _let_85)) _let_84 :args (_let_82 false _let_83)) :args (_let_79 false _let_8 false _let_7 false _let_82)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (tptp.xl _let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_46)) :args _let_45)) _let_44 :args (_let_81 false _let_43)) :args (_let_78 false _let_9 false _let_79 false _let_81)) :args (_let_76 true _let_2 false _let_78)) :args (_let_75 false _let_76)) :args (_let_72 false _let_73 false _let_75)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_66 0)) :args ((or _let_22 (not _let_66)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_67)) :args ((or _let_41 _let_35 _let_56 _let_66 (not _let_67)))) _let_48 _let_71 _let_70 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (tptp.xl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((tptp.sdtpldt0 (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2))))) :args (_let_68))) _let_69 :args (_let_67 false _let_68)) :args (_let_66 false _let_9 false _let_34 false _let_55 false _let_67)) :args (_let_22 false _let_66)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_57 1)) (CONG _let_65 (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_19))) :args _let_50)) :args ((or _let_19 _let_57))) _let_64 :args (_let_19 true _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_36 1)) (CONG _let_53 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_17))) :args _let_50)) :args ((or _let_17 _let_36))) _let_52 :args (_let_17 true _let_36)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_25 _let_24 _let_15 (not _let_26)))) _let_32 _let_30 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (tptp.xm tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtpldt0 W0 W1)))) :args (_let_27))) _let_28 :args (_let_26 false _let_27)) :args (_let_15 false _let_8 false _let_7 false _let_26)) :args (false true _let_23 false _let_22 false _let_19 false _let_17 false _let_15)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) (tptp.aNaturalNumber0 tptp.sz00) (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00))) _let_14 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))) _let_13 (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 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))) _let_12 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W0 W2)) (= (tptp.sdtpldt0 W1 W0) (tptp.sdtpldt0 W2 W0))) (= W1 W2)))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (=> (not (= W0 tptp.sz00)) (forall ((W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2)) (= (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))) (= W1 W2))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtpldt0 W0 W1) tptp.sz00) (and (= W0 tptp.sz00) (= W1 tptp.sz00))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtasdt0 W0 W1) tptp.sz00) (or (= W0 tptp.sz00) (= W1 tptp.sz00))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtlseqdt0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.sdtlseqdt0 W0 W1) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1))))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (tptp.sdtlseqdt0 W0 W0))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (or (tptp.sdtlseqdt0 W0 W1) (and (not (= W1 W0)) (tptp.sdtlseqdt0 W1 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 W2))) (let ((_let_2 (tptp.sdtpldt0 W0 W2))) (let ((_let_3 (tptp.sdtpldt0 W2 W1))) (let ((_let_4 (tptp.sdtpldt0 W2 W0))) (=> (tptp.aNaturalNumber0 W2) (and (not (= _let_4 _let_3)) (tptp.sdtlseqdt0 _let_4 _let_3) (not (= _let_2 _let_1)) (tptp.sdtlseqdt0 _let_2 _let_1))))))))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W2 W0))) (let ((_let_2 (tptp.sdtasdt0 W1 W0))) (let ((_let_3 (tptp.sdtasdt0 W0 W2))) (let ((_let_4 (tptp.sdtasdt0 W0 W1))) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (not (= W0 tptp.sz00)) (not (= W1 W2)) (tptp.sdtlseqdt0 W1 W2)) (and (not (= _let_4 _let_3)) (tptp.sdtlseqdt0 _let_4 _let_3) (not (= _let_2 _let_1)) (tptp.sdtlseqdt0 _let_2 _let_1))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (or (= W0 tptp.sz00) (= W0 tptp.sz10) (and (not (= tptp.sz10 W0)) (tptp.sdtlseqdt0 tptp.sz10 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (not (= W0 tptp.sz00)) (tptp.sdtlseqdt0 W1 (tptp.sdtasdt0 W1 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.iLess0 W0 W1) true))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1)))) _let_11 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtsldt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2)))))))) (forall ((W0 $$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)))) _let_10 _let_6 (=> (not (= tptp.xl tptp.sz00)) (= _let_1 (tptp.sdtasdt0 tptp.xl (tptp.sdtpldt0 (tptp.sdtsldt0 tptp.xm tptp.xl) (tptp.sdtsldt0 tptp.xn tptp.xl))))) _let_3 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.65/0.89 )
% 0.65/0.89 % SZS output end Proof for NUM469+1
% 0.65/0.89 % cvc5---1.0.5 exiting
% 0.65/0.89 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------