TSTP Solution File: NUM481+3 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM481+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n008.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 10:44:19 EDT 2023
% Result : Theorem 3.01s 3.18s
% Output : Proof 3.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM481+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n008.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 07:59:02 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 3.01/3.18 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.9Q2EIzuoSF/cvc5---1.0.5_10566.p...
% 3.01/3.18 ------- get file name : TPTP file name is NUM481+3
% 3.01/3.18 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_10566.smt2...
% 3.01/3.18 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 3.01/3.18 % SZS status Theorem for NUM481+3
% 3.01/3.18 % SZS output start Proof for NUM481+3
% 3.01/3.18 (
% 3.01/3.18 (let ((_let_1 (not (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (not (= W0 tptp.sz00)) (not (= W0 tptp.sz10))) (=> (forall ((W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W1) (not (= W1 tptp.sz00)) (not (= W1 tptp.sz10))) (=> (tptp.iLess0 W1 W0) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (exists ((W3 $$unsorted)) (and (tptp.aNaturalNumber0 W3) (= W1 (tptp.sdtasdt0 W2 W3)))) (tptp.doDivides0 W2 W1) (not (= W2 tptp.sz00)) (not (= W2 tptp.sz10)) (forall ((W3 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W3) (or (exists ((W4 $$unsorted)) (and (tptp.aNaturalNumber0 W4) (= W2 (tptp.sdtasdt0 W3 W4)))) (tptp.doDivides0 W3 W2))) (or (= W3 tptp.sz10) (= W3 W2)))) (tptp.isPrime0 W2)))))) (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (or (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= W0 (tptp.sdtasdt0 W1 W2)))) (tptp.doDivides0 W1 W0)) (or (and (not (= W1 tptp.sz00)) (not (= W1 tptp.sz10)) (forall ((W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W2) (exists ((W3 $$unsorted)) (and (tptp.aNaturalNumber0 W3) (= W1 (tptp.sdtasdt0 W2 W3)))) (tptp.doDivides0 W2 W1)) (or (= W2 tptp.sz10) (= W2 W1))))) (tptp.isPrime0 W1)))))))))) (let ((_let_2 (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_3 (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 ((_let_4 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2))))))))) (let ((_let_5 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1)))))) (let ((_let_6 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))) (let ((_let_7 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))) (let ((_let_8 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (= (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))))) (let ((_let_9 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_10 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))) (let ((_let_11 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_12 (tptp.aNaturalNumber0 tptp.sz10))) (let ((_let_13 (and _let_12 (not (= tptp.sz10 tptp.sz00))))) (let ((_let_14 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_15 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14))) (let ((_let_16 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_17 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_16))) (let ((_let_18 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_19 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_18))) (let ((_let_20 (= (tptp.sdtasdt0 _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14) _let_19))) (let ((_let_21 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_19))) (let ((_let_22 (not _let_15))) (let ((_let_23 (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or _let_24 _let_22))) (let ((_let_26 (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 W2))))))) (let ((_let_27 (not _let_25))) (let ((_let_28 (not _let_26))) (let ((_let_29 (tptp.doDivides0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_30 (= _let_29 _let_28))) (let ((_let_31 (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_32 (not _let_31))) (let ((_let_33 (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_34 (not _let_33))) (let ((_let_35 (or _let_34 _let_32 _let_30))) (let ((_let_36 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2))))))))))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_39 (= tptp.sz10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_40 (not _let_29))) (let ((_let_41 (or _let_34 _let_40 _let_39 _let_38))) (let ((_let_42 (forall ((W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (not (tptp.doDivides0 W1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (= tptp.sz10 W1) (= W1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_43 (not _let_41))) (let ((_let_44 (= tptp.sz10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_45 (not _let_44))) (let ((_let_46 (= tptp.sz00 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_47 (not _let_46))) (let ((_let_48 (and _let_47 _let_45 _let_42))) (let ((_let_49 (not _let_42))) (let ((_let_50 (tptp.isPrime0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_51 (= _let_50 _let_48))) (let ((_let_52 (not _let_48))) (let ((_let_53 (or _let_32 _let_51))) (let ((_let_54 (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_55 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (forall ((W1 $$unsorted) (BOUND_VARIABLE_1919 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (and (or (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1919)) (not (= (tptp.sdtasdt0 W1 BOUND_VARIABLE_1919) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (not (tptp.doDivides0 W1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (and (or (= tptp.sz00 W1) (= tptp.sz10 W1) (not (forall ((W2 $$unsorted) (BOUND_VARIABLE_1887 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (tptp.doDivides0 W2 W1)) (= tptp.sz10 W2) (= W1 W2) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1887)) (not (= W1 (tptp.sdtasdt0 W2 BOUND_VARIABLE_1887))))))) (not (tptp.isPrime0 W1))))))) (let ((_let_57 (not _let_56))) (let ((_let_58 (forall ((W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (= tptp.sz00 W1) (= tptp.sz10 W1) (not (tptp.iLess0 W1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (forall ((W2 $$unsorted) (BOUND_VARIABLE_1830 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (tptp.doDivides0 W2 W1)) (= tptp.sz00 W2) (= tptp.sz10 W2) (not (forall ((W3 $$unsorted) (BOUND_VARIABLE_1807 $$unsorted)) (or (not (tptp.aNaturalNumber0 W3)) (and (or (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1807)) (not (= W2 (tptp.sdtasdt0 W3 BOUND_VARIABLE_1807)))) (not (tptp.doDivides0 W3 W2))) (= tptp.sz10 W3) (= W2 W3)))) (not (tptp.isPrime0 W2)) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1830)) (not (= W1 (tptp.sdtasdt0 W2 BOUND_VARIABLE_1830)))))))))) (let ((_let_59 (not _let_58))) (let ((_let_60 (or _let_32 _let_46 _let_44 _let_59 _let_57))) (let ((_let_61 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (= tptp.sz00 W0) (= tptp.sz10 W0) (not (forall ((W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (= tptp.sz00 W1) (= tptp.sz10 W1) (not (tptp.iLess0 W1 W0)) (not (forall ((W2 $$unsorted) (BOUND_VARIABLE_1830 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (tptp.doDivides0 W2 W1)) (= tptp.sz00 W2) (= tptp.sz10 W2) (not (forall ((W3 $$unsorted) (BOUND_VARIABLE_1807 $$unsorted)) (or (not (tptp.aNaturalNumber0 W3)) (and (or (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1807)) (not (= W2 (tptp.sdtasdt0 W3 BOUND_VARIABLE_1807)))) (not (tptp.doDivides0 W3 W2))) (= tptp.sz10 W3) (= W2 W3)))) (not (tptp.isPrime0 W2)) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1830)) (not (= W1 (tptp.sdtasdt0 W2 BOUND_VARIABLE_1830))))))))) (not (forall ((W1 $$unsorted) (BOUND_VARIABLE_1919 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (and (or (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1919)) (not (= W0 (tptp.sdtasdt0 W1 BOUND_VARIABLE_1919)))) (not (tptp.doDivides0 W1 W0))) (and (or (= tptp.sz00 W1) (= tptp.sz10 W1) (not (forall ((W2 $$unsorted) (BOUND_VARIABLE_1887 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (tptp.doDivides0 W2 W1)) (= tptp.sz10 W2) (= W1 W2) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1887)) (not (= W1 (tptp.sdtasdt0 W2 BOUND_VARIABLE_1887))))))) (not (tptp.isPrime0 W1)))))))))) (let ((_let_62 (not _let_60))) (let ((_let_63 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_64 (or))) (let ((_let_65 (not _let_61))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_63) :args (_let_65)) (REWRITE :args ((=> _let_65 (not (or _let_32 _let_46 _let_44 _let_59 (not (forall ((W1 $$unsorted) (BOUND_VARIABLE_1919 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (and (or (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1919)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.sdtasdt0 W1 BOUND_VARIABLE_1919)))) (not (tptp.doDivides0 W1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (and (or (= tptp.sz00 W1) (= tptp.sz10 W1) (not (forall ((W2 $$unsorted) (BOUND_VARIABLE_1887 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (tptp.doDivides0 W2 W1)) (= tptp.sz10 W2) (= W1 W2) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1887)) (not (= W1 (tptp.sdtasdt0 W2 BOUND_VARIABLE_1887))))))) (not (tptp.isPrime0 W1))))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_61))) (REFL :args (_let_62)) :args _let_64)) _let_63 :args (_let_62 true _let_61)))) (let ((_let_67 (REFL :args (_let_60)))) (let ((_let_68 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_60 0)) (CONG _let_67 (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_31))) :args _let_64)) :args ((or _let_31 _let_60))) _let_66 :args (_let_31 true _let_60)))) (let ((_let_69 (not _let_50))) (let ((_let_70 (and (or _let_46 _let_44 (not (forall ((W2 $$unsorted) (BOUND_VARIABLE_1887 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (tptp.doDivides0 W2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (= tptp.sz10 W2) (= W2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1887)) (not (= (tptp.sdtasdt0 W2 BOUND_VARIABLE_1887) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))))) _let_69))) (let ((_let_71 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.sz10)))) (let ((_let_72 (not _let_71))) (let ((_let_73 (not _let_12))) (let ((_let_74 (or _let_73 _let_72))) (let ((_let_75 (and _let_74 (not (tptp.doDivides0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_76 (or _let_32 _let_75 _let_70))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_60 4)) (CONG _let_67 (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_56))) :args _let_64)) :args ((or _let_56 _let_60))) _let_66 :args (_let_56 true _let_60)))) (let ((_let_78 (_let_56))) (let ((_let_79 ((tptp.sdtasdt0 W1 BOUND_VARIABLE_1919)))) (let ((_let_80 (ASSUME :args _let_78))) (let ((_let_81 (not _let_75))) (let ((_let_82 (not _let_74))) (let ((_let_83 (and _let_71 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.sdtasdt0 tptp.sz10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_84 (or _let_32 _let_83))) (let ((_let_85 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (and (= W0 (tptp.sdtasdt0 W0 tptp.sz10)) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_60 1)) _let_66 :args (_let_47 true _let_60)))) (let ((_let_88 (_let_49))) (let ((_let_89 (_let_48))) (let ((_let_90 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_88)) :args _let_88) (REWRITE :args ((=> _let_49 (not (or _let_34 _let_40 _let_39 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_42))) (REFL :args (_let_43)) :args _let_64)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_89) (CONG (REFL :args _let_89) (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_46))) (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_44))) (REFL :args _let_88) :args _let_64)) :args ((or _let_46 _let_44 _let_48 _let_49))) _let_87 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_60 2)) _let_66 :args (_let_45 true _let_60)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_51)) :args ((or _let_50 _let_52 (not _let_51)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_70 1)) :args ((or _let_69 (not _let_70)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_32 _let_75 _let_70 (not _let_76)))) _let_68 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_75 0)) :args ((or _let_74 _let_81))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_74)) :args ((or _let_73 _let_72 _let_82))) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))) :args (0)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_83 0)) :args ((or _let_71 (not _let_83)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_84)) :args ((or _let_32 _let_83 (not _let_84)))) _let_68 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_86 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aNaturalNumber0 W0) false))))) :args (_let_85))) _let_86 :args (_let_84 false _let_85)) :args (_let_83 false _let_31 false _let_84)) :args (_let_71 false _let_83)) :args (_let_82 false _let_12 false _let_71)) :args (_let_81 true _let_74)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_80 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.sz10 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_let_90 :args (_let_33 true _let_41)))) (let ((_let_93 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_41 1)) (CONG _let_91 (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_29))) :args _let_64)) :args ((or _let_29 _let_41))) _let_90 :args (_let_29 true _let_41)))) (let ((_let_94 (_let_28))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_94)) :args _let_94)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_26))) (REFL :args (_let_27)) :args _let_64)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_30)) :args ((or _let_40 _let_28 (not _let_30)))) _let_93 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_32 _let_34 _let_30 (not _let_35)))) _let_68 _let_92 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.doDivides0 W0 W1)))) 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(tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_107 (not _let_106))) (let ((_let_108 (or _let_107 _let_105 _let_104 _let_103 (not (forall ((W3 $$unsorted) (BOUND_VARIABLE_1807 $$unsorted)) (or (not (tptp.aNaturalNumber0 W3)) (and (or (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1807)) (not (= (tptp.sdtasdt0 W3 BOUND_VARIABLE_1807) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (not (tptp.doDivides0 W3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (= tptp.sz10 W3) (= W3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15)))) _let_102 _let_100 _let_98))) (let ((_let_109 (forall ((W2 $$unsorted) (BOUND_VARIABLE_1830 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (tptp.doDivides0 W2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (= tptp.sz00 W2) (= tptp.sz10 W2) (not (forall ((W3 $$unsorted) (BOUND_VARIABLE_1807 $$unsorted)) (or (not (tptp.aNaturalNumber0 W3)) (and (or (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1807)) (not (= W2 (tptp.sdtasdt0 W3 BOUND_VARIABLE_1807)))) (not (tptp.doDivides0 W3 W2))) 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_let_160))) (let ((_let_162 (or _let_161 _let_159))) (let ((_let_163 (and _let_162 (not (tptp.doDivides0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_164 (and (or _let_104 _let_103 (not (forall ((W2 $$unsorted) (BOUND_VARIABLE_1887 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (tptp.doDivides0 W2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15)) (= tptp.sz10 W2) (= W2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1887)) (not (= (tptp.sdtasdt0 W2 BOUND_VARIABLE_1887) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15)))))) _let_102))) (let ((_let_165 (or _let_107 _let_163 _let_164))) (let ((_let_166 (not _let_164))) (let ((_let_167 (or _let_100 _let_24 _let_160))) (let ((_let_168 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_169 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_170 (ASSUME :args (_let_159)))) (let ((_let_171 (ASSUME :args (_let_20)))) (let ((_let_172 (ASSUME :args (_let_17)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_170 (MODUS_PONENS (AND_INTRO _let_171 _let_172 _let_149) (SCOPE (TRANS _let_150 (CONG (SYMM (SYMM _let_172)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)) :args _let_146) (SYMM (SYMM _let_171))) :args (_let_20 _let_17 _let_15)))) :args (_let_15 _let_17 _let_20 _let_159)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO (SYMM (SYMM (ASSUME :args (_let_21)))))) (FALSE_INTRO _let_170))) :args (_let_159 _let_21)) :args ((not (and _let_15 _let_17 _let_20 _let_159)) SB_LITERAL))) (CONG (REFL :args (_let_22)) (REFL :args (_let_98)) (REFL :args ((not _let_20))) (MACRO_SR_PRED_INTRO :args ((= (not _let_159) _let_21))) :args _let_64)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_162)) :args ((or _let_161 _let_159 (not _let_162)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_167)) :args ((or _let_24 _let_100 _let_160 (not _let_167)))) _let_134 _let_157 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_169 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtasdt0 W0 W1)))) :args (_let_168))) _let_169 :args (_let_167 false _let_168)) :args (_let_160 false _let_23 false _let_99 false _let_167)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_163 0)) :args ((or _let_162 (not _let_163)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_165)) :args ((or _let_107 _let_164 _let_163 (not _let_165)))) _let_158 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_164 1)) :args ((or _let_102 _let_166))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_108 5)) (CONG _let_153 (MACRO_SR_PRED_INTRO :args ((= (not _let_102) _let_101))) :args _let_64)) :args ((or _let_101 _let_108))) _let_152 :args (_let_101 true _let_108)) :args (_let_166 false _let_101)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_80 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_79)) :args _let_78))) _let_77 :args (_let_165 false _let_56)) :args (_let_163 false _let_106 true _let_164 false _let_165)) :args (_let_162 false _let_163)) :args (_let_159 false _let_160 false _let_162)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_154)) :args ((or _let_24 _let_107 _let_100 _let_20 (not _let_154)))) _let_134 _let_158 _let_157 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_156 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING ((tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2)))) :args (_let_155))) _let_156 :args (_let_154 false _let_155)) :args (_let_20 false _let_23 false _let_106 false _let_99 false _let_154)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_108 7)) (CONG _let_153 (MACRO_SR_PRED_INTRO :args ((= (not _let_98) _let_17))) :args _let_64)) :args ((or _let_17 _let_108))) _let_152 :args (_let_17 true _let_108)) _let_97 :args (false true _let_21 false _let_20 false _let_17 false _let_15)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) (tptp.aNaturalNumber0 tptp.sz00) _let_13 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) _let_11 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (= (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))) _let_10 _let_9 _let_8 _let_7 _let_6 (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))) _let_5 _let_4 (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)))) (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)))) _let_3 (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_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 3.01/3.20 )
% 3.01/3.20 % SZS output end Proof for NUM481+3
% 3.01/3.20 % cvc5---1.0.5 exiting
% 3.01/3.20 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------