TSTP Solution File: RNG126+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : RNG126+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n028.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 13:50:12 EDT 2023
% Result : Theorem 26.17s 26.36s
% Output : Proof 26.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : RNG126+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n028.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 : Sun Aug 27 01:45:23 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 26.17/26.36 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.KjS5WsHqBD/cvc5---1.0.5_25301.p...
% 26.17/26.36 ------- get file name : TPTP file name is RNG126+1
% 26.17/26.36 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_25301.smt2...
% 26.17/26.36 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 26.17/26.36 --- Run --no-e-matching --full-saturate-quant at 5...
% 26.17/26.36 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 26.17/26.36 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 26.17/26.36 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 26.17/26.36 % SZS status Theorem for RNG126+1
% 26.17/26.36 % SZS output start Proof for RNG126+1
% 26.17/26.36 (
% 26.17/26.36 (let ((_let_1 (tptp.slsdtgt0 tptp.xb))) (let ((_let_2 (tptp.slsdtgt0 tptp.xa))) (let ((_let_3 (tptp.sdtpldt1 _let_2 _let_1))) (let ((_let_4 (tptp.aElementOf0 tptp.xc _let_3))) (let ((_let_5 (not _let_4))) (let ((_let_6 (tptp.doDivides0 tptp.xu tptp.xc))) (let ((_let_7 (tptp.aElementOf0 tptp.xu tptp.xI))) (let ((_let_8 (and _let_7 (not (= tptp.xu tptp.sz00)) (forall ((W0 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.xI) (not (= W0 tptp.sz00))) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu)))))))) (let ((_let_9 (and (tptp.aIdeal0 tptp.xI) (= tptp.xI _let_3)))) (let ((_let_10 (tptp.aGcdOfAnd0 tptp.xc tptp.xa tptp.xb))) (let ((_let_11 (tptp.aElement0 tptp.xb))) (let ((_let_12 (tptp.aElement0 tptp.xa))) (let ((_let_13 (and _let_12 _let_11))) (let ((_let_14 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (forall ((W2 $$unsorted)) (= (tptp.aGcdOfAnd0 W2 W0 W1) (and (tptp.aDivisorOf0 W2 W0) (tptp.aDivisorOf0 W2 W1) (forall ((W3 $$unsorted)) (=> (and (tptp.aDivisorOf0 W3 W0) (tptp.aDivisorOf0 W3 W1)) (tptp.doDivides0 W3 W2)))))))))) (let ((_let_15 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (= (tptp.aDivisorOf0 W1 W0) (and (tptp.aElement0 W1) (tptp.doDivides0 W1 W0)))))))) (let ((_let_16 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (= (tptp.doDivides0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aElement0 W2) (= (tptp.sdtasdt0 W0 W2) W1)))))))) (let ((_let_17 (forall ((W0 $$unsorted)) (= (tptp.aIdeal0 W0) (and (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (and (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W0) (tptp.aElementOf0 (tptp.sdtpldt0 W1 W2) W0))) (forall ((W2 $$unsorted)) (=> (tptp.aElement0 W2) (tptp.aElementOf0 (tptp.sdtasdt0 W2 W1) W0))))))))))) (let ((_let_18 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))))) (let ((_let_19 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_20 (tptp.sdtasdt0 tptp.xu SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_21 (= tptp.xc _let_20))) (let ((_let_22 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 tptp.xu))) (let ((_let_23 (= _let_20 _let_22))) (let ((_let_24 (tptp.aElementOf0 _let_22 _let_3))) (let ((_let_25 (ASSUME :args (_let_5)))) (let ((_let_26 (not _let_21))) (let ((_let_27 (tptp.aElement0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or _let_28 _let_26))) (let ((_let_30 (forall ((W2 $$unsorted)) (or (not (tptp.aElement0 W2)) (not (= tptp.xc (tptp.sdtasdt0 tptp.xu W2))))))) (let ((_let_31 (not _let_29))) (let ((_let_32 (not _let_30))) (let ((_let_33 (= _let_6 _let_32))) (let ((_let_34 (tptp.aElement0 tptp.xc))) (let ((_let_35 (not _let_34))) (let ((_let_36 (tptp.aElement0 tptp.xu))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_37 _let_35 _let_33))) (let ((_let_39 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aElement0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2))))))))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (and _let_34 (tptp.doDivides0 tptp.xc tptp.xa)))) (let ((_let_42 (tptp.aDivisorOf0 tptp.xc tptp.xa))) (let ((_let_43 (= _let_42 _let_41))) (let ((_let_44 (not _let_12))) (let ((_let_45 (or _let_44 _let_43))) (let ((_let_46 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1573 $$unsorted)) (or (not (tptp.aElement0 W0)) (= (tptp.aDivisorOf0 BOUND_VARIABLE_1573 W0) (and (tptp.aElement0 BOUND_VARIABLE_1573) (tptp.doDivides0 BOUND_VARIABLE_1573 W0))))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (0))) (let ((_let_49 (ASSUME :args (_let_13)))) (let ((_let_50 (AND_ELIM _let_49 :args _let_48))) (let ((_let_51 (and _let_42 (tptp.aDivisorOf0 tptp.xc tptp.xb) (forall ((W3 $$unsorted)) (or (not (tptp.aDivisorOf0 W3 tptp.xa)) (not (tptp.aDivisorOf0 W3 tptp.xb)) (tptp.doDivides0 W3 tptp.xc)))))) (let ((_let_52 (= _let_10 _let_51))) (let ((_let_53 (not _let_11))) (let ((_let_54 (or _let_44 _let_53 _let_52))) (let ((_let_55 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1601 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (= (tptp.aGcdOfAnd0 BOUND_VARIABLE_1601 W0 W1) (and (tptp.aDivisorOf0 BOUND_VARIABLE_1601 W0) (tptp.aDivisorOf0 BOUND_VARIABLE_1601 W1) (forall ((W3 $$unsorted)) (or (not (tptp.aDivisorOf0 W3 W0)) (not (tptp.aDivisorOf0 W3 W1)) (tptp.doDivides0 W3 BOUND_VARIABLE_1601))))))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (1))) (let ((_let_58 (tptp.aElementOf0 tptp.xu _let_3))) (let ((_let_59 (not _let_58))) (let ((_let_60 (tptp.aSet0 _let_3))) (let ((_let_61 (not _let_60))) (let ((_let_62 (or _let_61 _let_59 _let_36))) (let ((_let_63 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1290 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1290 W0)) (tptp.aElement0 BOUND_VARIABLE_1290))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (forall ((W1 $$unsorted) (BOUND_VARIABLE_1414 $$unsorted) (BOUND_VARIABLE_1407 $$unsorted)) (let ((_let_1 (tptp.sdtpldt1 (tptp.slsdtgt0 tptp.xa) (tptp.slsdtgt0 tptp.xb)))) (or (not (tptp.aElementOf0 W1 _let_1)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1407 _let_1)) (tptp.aElementOf0 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1407) _let_1)) (or (not (tptp.aElement0 BOUND_VARIABLE_1414)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1414 W1) _let_1)))))))) (let ((_let_66 (and _let_60 _let_65))) (let ((_let_67 (tptp.aIdeal0 _let_3))) (let ((_let_68 (= _let_67 _let_66))) (let ((_let_69 (forall ((W0 $$unsorted)) (= (tptp.aIdeal0 W0) (and (tptp.aSet0 W0) (forall ((W1 $$unsorted) (BOUND_VARIABLE_1414 $$unsorted) (BOUND_VARIABLE_1407 $$unsorted)) (or (not (tptp.aElementOf0 W1 W0)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1407 W0)) (tptp.aElementOf0 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1407) W0)) (or (not (tptp.aElement0 BOUND_VARIABLE_1414)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1414 W1) W0)))))))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (ASSUME :args (_let_9)))) (let ((_let_72 (AND_ELIM _let_71 :args _let_57))) (let ((_let_73 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_68)) :args ((or (not _let_67) _let_66 (not _let_68)))) (EQ_RESOLVE _let_71 (MACRO_SR_EQ_INTRO _let_72 :args (_let_9 SB_DEFAULT SBA_FIXPOINT))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_70 :args (_let_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aIdeal0 W0)))) :args (_let_69))) _let_70 :args (_let_68 false _let_69)) :args (_let_66 false _let_67 false _let_68)))) (let ((_let_74 (not _let_66))) (let ((_let_75 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_8)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_72 :args ((and _let_7 (not (= tptp.sz00 tptp.xu)) (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (= tptp.sz00 W0) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu)))))) SB_DEFAULT SBA_FIXPOINT)))) :args _let_48))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_59 _let_61 _let_36 (not _let_62)))) _let_75 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_66 0)) :args ((or _let_60 _let_74))) _let_73 :args (_let_60 false _let_66)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (_let_3 tptp.xu QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 BOUND_VARIABLE_1290 W0) false))))) :args (_let_63))) _let_64 :args (_let_62 false _let_63)) :args (_let_36 false _let_58 false _let_60 false _let_62)))) (let ((_let_77 (or))) (let ((_let_78 (_let_32))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_78)) :args _let_78)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_30))) (REFL :args (_let_31)) :args _let_77)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_33)) :args ((or (not _let_6) _let_32 (not _let_33)))) (ASSUME :args (_let_6)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_37 _let_35 _let_33 (not _let_38)))) _let_76 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_41 0)) :args ((or _let_34 (not _let_41)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_43)) :args ((or (not _let_42) _let_41 (not _let_43)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_51 0)) :args ((or _let_42 (not _let_51)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_52)) :args ((or (not _let_10) _let_51 (not _let_52)))) (ASSUME :args (_let_10)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_44 _let_53 _let_52 (not _let_54)))) _let_50 (AND_ELIM _let_49 :args _let_57) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (tptp.xa tptp.xb tptp.xc QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aGcdOfAnd0 BOUND_VARIABLE_1601 W0 W1)))) :args (_let_55))) _let_56 :args (_let_54 false _let_55)) :args (_let_52 false _let_12 false _let_11 false _let_54)) :args (_let_51 false _let_10 false _let_52)) :args (_let_42 false _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_45)) :args ((or _let_44 _let_43 (not _let_45)))) _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (tptp.xa tptp.xc QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_46))) _let_47 :args (_let_45 false _let_46)) :args (_let_43 false _let_12 false _let_45)) :args (_let_41 false _let_42 false _let_43)) :args (_let_34 false _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (tptp.xu tptp.xc QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.doDivides0 W0 W1)))) :args (_let_39))) _let_40 :args (_let_38 false _let_39)) :args (_let_33 false _let_36 false _let_34 false _let_38)) :args (_let_32 false _let_6 false _let_33)) :args (_let_31 true _let_30)))) (let ((_let_80 (REFL :args (_let_29)))) (let ((_let_81 (or _let_28 _let_37 _let_23))) (let ((_let_82 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_83 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 0)) (CONG _let_80 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) :args _let_77)) :args ((or _let_27 _let_29))) _let_79 :args (_let_27 true _let_29)))) (let ((_let_85 (or _let_28 _let_24))) (let ((_let_86 (and (or (not (tptp.aElementOf0 tptp.xa _let_3)) (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xu tptp.xa) _let_3)) _let_85))) (let ((_let_87 (or _let_59 _let_86))) (let ((_let_88 (_let_65))) (let ((_let_89 (ASSUME :args (_let_24)))) (let ((_let_90 (ASSUME :args (_let_23)))) (let ((_let_91 (ASSUME :args (_let_21)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_89 _let_90 _let_91 _let_25) :args (_let_5 _let_21 _let_23 _let_24)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_25)) (CONG (TRANS (SYMM (SYMM _let_91)) (SYMM (SYMM _let_90))) (REFL :args (_let_3)) :args (APPLY_UF tptp.aElementOf0)) (TRUE_INTRO _let_89))) :args (_let_24 _let_23 _let_21 _let_5)) :args ((not (and _let_5 _let_21 _let_23 _let_24)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_5) _let_4))) (REFL :args (_let_26)) (REFL :args ((not _let_23))) (REFL :args ((not _let_24))) :args _let_77)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_85)) :args ((or _let_28 _let_24 (not _let_85)))) _let_84 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_86 1)) :args ((or _let_85 (not _let_86)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_59 _let_86 (not _let_87)))) _let_75 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_88) :args (tptp.xu SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 tptp.xa QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_88)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_66 1)) :args ((or _let_65 _let_74))) _let_73 :args (_let_65 false _let_66)) :args (_let_87 false _let_65)) :args (_let_86 false _let_58 false _let_87)) :args (_let_85 false _let_86)) :args (_let_24 false _let_27 false _let_85)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_81)) :args ((or _let_37 _let_28 _let_23 (not _let_81)))) _let_76 _let_84 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_83 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 tptp.xu QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtasdt0 W1 W0)))) :args (_let_82)))) _let_83 :args (_let_81 false _let_82)) :args (_let_23 false _let_36 false _let_27 false _let_81)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 1)) (CONG _let_80 (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_21))) :args _let_77)) :args ((or _let_21 _let_29))) _let_79 :args (_let_21 true _let_29)) _let_25 :args (false false _let_24 false _let_23 false _let_21 true _let_4)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)) (tptp.aElement0 tptp.sz00) (tptp.aElement0 tptp.sz10) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (tptp.aElement0 (tptp.smndt0 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2)) (= (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.smndt0 W0))) (=> (tptp.aElement0 W0) (and (= (tptp.sdtpldt0 W0 _let_1) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 _let_1 W0)))))) _let_19 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2)) (= (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 W2))) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2)) (and (= (tptp.sdtasdt0 W0 _let_1) (tptp.sdtpldt0 (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2))) (= (tptp.sdtasdt0 _let_1 W0) (tptp.sdtpldt0 (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))))))) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.smndt0 tptp.sz10))) (let ((_let_2 (tptp.smndt0 W0))) (=> (tptp.aElement0 W0) (and (= (tptp.sdtasdt0 _let_1 W0) _let_2) (= _let_2 (tptp.sdtasdt0 W0 _let_1))))))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (=> (= (tptp.sdtasdt0 W0 W1) tptp.sz00) (or (= W0 tptp.sz00) (= W1 tptp.sz00))))) (not (= tptp.sz10 tptp.sz00)) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) true)) _let_18 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aSet0 W1)) (=> (and (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W0) (tptp.aElementOf0 W2 W1))) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 W0)))) (= W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aSet0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtpldt1 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (exists ((W4 $$unsorted) (W5 $$unsorted)) (and (tptp.aElementOf0 W4 W0) (tptp.aElementOf0 W5 W1) (= (tptp.sdtpldt0 W4 W5) W3)))))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aSet0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtasasdt0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aElementOf0 W3 W0) (tptp.aElementOf0 W3 W1))))))))) _let_17 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aIdeal0 W0) (tptp.aIdeal0 W1)) (tptp.aIdeal0 (tptp.sdtpldt1 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aIdeal0 W0) (tptp.aIdeal0 W1)) (tptp.aIdeal0 (tptp.sdtasasdt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aIdeal0 W2)) (= (tptp.sdteqdtlpzmzozddtrp0 W0 W1 W2) (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 W1)) W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aIdeal0 W0) (tptp.aIdeal0 W1)) (=> (forall ((W2 $$unsorted)) (=> (tptp.aElement0 W2) (tptp.aElementOf0 W2 (tptp.sdtpldt1 W0 W1)))) (forall ((W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aElement0 W2) (tptp.aElement0 W3)) (exists ((W4 $$unsorted)) (and (tptp.aElement0 W4) (tptp.sdteqdtlpzmzozddtrp0 W4 W2 W0) (tptp.sdteqdtlpzmzozddtrp0 W4 W3 W1)))))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) (forall ((W0 $$unsorted)) (=> (and (tptp.aElement0 W0) (not (= W0 tptp.sz00))) (tptp.aNaturalNumber0 (tptp.sbrdtbr0 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.iLess0 W0 W1) true))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (not (= W1 tptp.sz00))) (exists ((W2 $$unsorted) (W3 $$unsorted)) (and (tptp.aElement0 W2) (tptp.aElement0 W3) (= W0 (tptp.sdtpldt0 (tptp.sdtasdt0 W2 W1) W3)) (=> (not (= W3 tptp.sz00)) (tptp.iLess0 (tptp.sbrdtbr0 W3) (tptp.sbrdtbr0 W1))))))) _let_16 _let_15 _let_14 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (= (tptp.misRelativelyPrime0 W0 W1) (tptp.aGcdOfAnd0 tptp.sz10 W0 W1)))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (= (= W1 (tptp.slsdtgt0 W0)) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (= (tptp.aElementOf0 W2 W1) (exists ((W3 $$unsorted)) (and (tptp.aElement0 W3) (= (tptp.sdtasdt0 W0 W3) W2)))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (tptp.aIdeal0 (tptp.slsdtgt0 W0)))) _let_13 (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00))) _let_10 _let_9 (and (tptp.aElementOf0 tptp.sz00 _let_2) (tptp.aElementOf0 tptp.xa _let_2) (tptp.aElementOf0 tptp.sz00 _let_1) (tptp.aElementOf0 tptp.xb _let_1)) (exists ((W0 $$unsorted)) (and (tptp.aElementOf0 W0 (tptp.sdtpldt1 (tptp.slsdtgt0 tptp.xa) (tptp.slsdtgt0 tptp.xb))) (not (= W0 tptp.sz00)))) _let_8 (and (tptp.aDivisorOf0 tptp.xu tptp.xa) (tptp.aDivisorOf0 tptp.xu tptp.xb)) _let_6 _let_5 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 26.19/26.37 )
% 26.19/26.37 % SZS output end Proof for RNG126+1
% 26.19/26.37 % cvc5---1.0.5 exiting
% 26.19/26.37 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------