%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : RNG119+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n020.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 13:50:09 EDT 2023

% Result   : Theorem 0.22s 0.69s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : RNG119+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n020.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Sun Aug 27 01:30:59 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.22/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.69  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.vCBzY3w9cR/cvc5---1.0.5_19919.p...
% 0.22/0.69  ------- get file name : TPTP file name is RNG119+1
% 0.22/0.69  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_19919.smt2...
% 0.22/0.69  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.69  % SZS status Theorem for RNG119+1
% 0.22/0.69  % SZS output start Proof for RNG119+1
% 0.22/0.69  (
% 0.22/0.69  (let ((_let_1 (= tptp.xr tptp.sz00))) (let ((_let_2 (not (not _let_1)))) (let ((_let_3 (tptp.sdtasdt0 tptp.xq tptp.xu))) (let ((_let_4 (= tptp.xb (tptp.sdtpldt0 _let_3 tptp.xr)))) (let ((_let_5 (tptp.aElement0 tptp.xq))) (let ((_let_6 (and _let_5 (tptp.aElement0 tptp.xr) _let_4 (or _let_1 (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu)))))) (let ((_let_7 (tptp.doDivides0 tptp.xu tptp.xb))) (let ((_let_8 (not _let_7))) (let ((_let_9 (tptp.aElementOf0 tptp.xu tptp.xI))) (let ((_let_10 (and _let_9 (not (= tptp.xu tptp.sz00)) (forall ((W0 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.xI) (not (= W0 tptp.sz00))) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu)))))))) (let ((_let_11 (tptp.slsdtgt0 tptp.xb))) (let ((_let_12 (tptp.slsdtgt0 tptp.xa))) (let ((_let_13 (tptp.aIdeal0 tptp.xI))) (let ((_let_14 (and _let_13 (= tptp.xI (tptp.sdtpldt1 _let_12 _let_11))))) (let ((_let_15 (tptp.aElement0 tptp.xb))) (let ((_let_16 (and (tptp.aElement0 tptp.xa) _let_15))) (let ((_let_17 (forall ((W0 $$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_18 (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_19 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))))) (let ((_let_20 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_21 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))) (let ((_let_22 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_23 (= tptp.sz00 tptp.xr))) (let ((_let_24 (tptp.sdtasdt0 tptp.xu tptp.xq))) (let ((_let_25 (= _let_3 _let_24))) (let ((_let_26 (= _let_3 (tptp.sdtpldt0 _let_3 tptp.sz00)))) (let ((_let_27 (= tptp.xb _let_24))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_30 (tptp.aElement0 tptp.xu))) (let ((_let_31 (not _let_30))) (let ((_let_32 (not _let_5))) (let ((_let_33 (or _let_32 _let_31 _let_25))) (let ((_let_34 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (not _let_9))) (let ((_let_37 (tptp.aSet0 tptp.xI))) (let ((_let_38 (not _let_37))) (let ((_let_39 (or _let_38 _let_36 _let_30))) (let ((_let_40 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1318 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1318 W0)) (tptp.aElement0 BOUND_VARIABLE_1318))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (and _let_37 (forall ((W1 $$unsorted) (BOUND_VARIABLE_1442 $$unsorted) (BOUND_VARIABLE_1435 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xI)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1435 tptp.xI)) (tptp.aElementOf0 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1435) tptp.xI)) (or (not (tptp.aElement0 BOUND_VARIABLE_1442)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1442 W1) tptp.xI)))))))) (let ((_let_43 (= _let_13 _let_42))) (let ((_let_44 (forall ((W0 $$unsorted)) (= (tptp.aIdeal0 W0) (and (tptp.aSet0 W0) (forall ((W1 $$unsorted) (BOUND_VARIABLE_1442 $$unsorted) (BOUND_VARIABLE_1435 $$unsorted)) (or (not (tptp.aElementOf0 W1 W0)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1435 W0)) (tptp.aElementOf0 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1435) W0)) (or (not (tptp.aElement0 BOUND_VARIABLE_1442)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1442 W1) W0)))))))))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_46 (0))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_36 _let_30 _let_38 (not _let_39)))) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))) :args _let_46) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_42 0)) :args ((or _let_37 (not _let_42)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_43)) :args ((or (not _let_13) _let_42 (not _let_43)))) (AND_ELIM (ASSUME :args (_let_14)) :args _let_46) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_45 :args (tptp.xI QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aIdeal0 W0)))) :args (_let_44))) _let_45 :args (_let_43 false _let_44)) :args (_let_42 false _let_13 false _let_43)) :args (_let_37 false _let_42)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (tptp.xI tptp.xu QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 BOUND_VARIABLE_1318 W0) false))))) :args (_let_40))) _let_41 :args (_let_39 false _let_40)) :args (_let_30 false _let_9 false _let_37 false _let_39)))) (let ((_let_48 (AND_ELIM _let_28 :args _let_46))) (let ((_let_49 (and _let_26 (= _let_3 (tptp.sdtpldt0 tptp.sz00 _let_3))))) (let ((_let_50 (tptp.aElement0 _let_3))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_51 _let_49))) (let ((_let_53 (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (= W0 (tptp.sdtpldt0 W0 tptp.sz00)) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (or _let_32 _let_31 _let_50))) (let ((_let_56 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (not _let_27))) (let ((_let_59 (or _let_32 _let_58))) (let ((_let_60 (forall ((W2 $$unsorted)) (or (not (tptp.aElement0 W2)) (not (= tptp.xb (tptp.sdtasdt0 tptp.xu W2))))))) (let ((_let_61 (not _let_60))) (let ((_let_62 (= _let_7 _let_61))) (let ((_let_63 (not _let_15))) (let ((_let_64 (or _let_31 _let_63 _let_62))) (let ((_let_65 (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_66 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (not _let_62))) (let ((_let_68 (or))) (let ((_let_69 (_let_60))) (let ((_let_70 (ASSUME :args (_let_58)))) (let ((_let_71 (ASSUME :args (_let_25)))) (let ((_let_72 (ASSUME :args (_let_26)))) (let ((_let_73 (ASSUME :args (_let_4)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO (MODUS_PONENS (AND_INTRO _let_71 _let_72 _let_29 _let_73) (SCOPE (TRANS (SYMM (SYMM _let_73)) (CONG (REFL :args (_let_3)) (SYMM _let_29) :args (APPLY_UF tptp.sdtpldt0)) (SYMM _let_72) (SYMM (SYMM _let_71))) :args (_let_25 _let_26 _let_23 _let_4))) _let_70) :args (_let_4 _let_23 _let_26 _let_25 _let_58)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO (SYMM (SYMM (ASSUME :args (_let_27)))))) (FALSE_INTRO _let_70))) :args (_let_27 _let_58)) :args ((not (and _let_4 _let_23 _let_26 _let_25 _let_58)) SB_LITERAL))) (CONG (REFL :args ((not _let_4))) (REFL :args ((not _let_23))) (REFL :args ((not _let_26))) (REFL :args ((not _let_25))) (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_27))) :args _let_68)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_32 _let_58 (not _let_59)))) _let_48 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_69) :args (tptp.xq QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtasdt0 tptp.xu W2)))) :args _let_69)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_62)) (CONG (REFL :args (_let_67)) (REFL :args (_let_7)) (MACRO_SR_PRED_INTRO :args ((= (not _let_61) _let_60))) :args _let_68)) :args ((or _let_7 _let_60 _let_67))) (ASSUME :args (_let_8)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_64)) :args ((or _let_63 _let_31 _let_62 (not _let_64)))) (AND_ELIM (ASSUME :args (_let_16)) :args (1)) _let_47 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (tptp.xu tptp.xb QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.doDivides0 W0 W1)))) :args (_let_65))) _let_66 :args (_let_64 false _let_65)) :args (_let_62 false _let_15 false _let_30 false _let_64)) :args (_let_60 true _let_7 false _let_62)) :args (_let_59 false _let_60)) :args (_let_58 false _let_5 false _let_59)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_49 0)) :args ((or _let_26 (not _let_49)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_51 _let_49 (not _let_52)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_55)) :args ((or _let_32 _let_31 _let_50 (not _let_55)))) _let_48 _let_47 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :args (tptp.xq tptp.xu QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtasdt0 W0 W1)))) :args (_let_56))) _let_57 :args (_let_55 false _let_56)) :args (_let_50 false _let_5 false _let_30 false _let_55)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (_let_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtpldt0 W0 tptp.sz00)))) :args (_let_53))) _let_54 :args (_let_52 false _let_53)) :args (_let_49 false _let_50 false _let_52)) :args (_let_26 false _let_49)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_33)) :args ((or _let_32 _let_31 _let_25 (not _let_33)))) _let_48 _let_47 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (tptp.xq tptp.xu QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtasdt0 W0 W1)))) :args (_let_34))) _let_35 :args (_let_33 false _let_34)) :args (_let_25 false _let_5 false _let_30 false _let_33)) _let_29 (AND_ELIM _let_28 :args (2)) :args (false true _let_27 false _let_26 false _let_25 false _let_23 false _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 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1)))) _let_22 (forall ((W0 $$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))))) _let_21 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.smndt0 W0))) (=> (tptp.aElement0 W0) (and (= (tptp.sdtpldt0 W0 _let_1) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 _let_1 W0)))))) _let_20 (forall ((W0 $$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 $$unsorted)) (=> (tptp.aSet0 W0) true)) _let_19 (forall ((W0 $$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 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aElementOf0 W3 W0) (tptp.aElementOf0 W3 W1))))))))) _let_18 (forall ((W0 $$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_17 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (= (tptp.aDivisorOf0 W1 W0) (and (tptp.aElement0 W1) (tptp.doDivides0 W1 W0)))))) (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)))))))) (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 $$unsorted)) (=> (tptp.aElement0 W0) (tptp.aIdeal0 (tptp.slsdtgt0 W0)))) _let_16 (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00))) (tptp.aGcdOfAnd0 tptp.xc tptp.xa tptp.xb) _let_14 (and (tptp.aElementOf0 tptp.sz00 _let_12) (tptp.aElementOf0 tptp.xa _let_12) (tptp.aElementOf0 tptp.sz00 _let_11) (tptp.aElementOf0 tptp.xb _let_11)) (exists ((W0 $$unsorted)) (and (tptp.aElementOf0 W0 (tptp.sdtpldt1 (tptp.slsdtgt0 tptp.xa) (tptp.slsdtgt0 tptp.xb))) (not (= W0 tptp.sz00)))) _let_10 (not (and (tptp.aDivisorOf0 tptp.xu tptp.xa) (tptp.aDivisorOf0 tptp.xu tptp.xb))) (exists ((W0 $$unsorted) (W1 $$unsorted)) (and (tptp.aElement0 W0) (tptp.aElement0 W1) (= tptp.xu (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xa W0) (tptp.sdtasdt0 tptp.xb W1))))) (not (not (tptp.doDivides0 tptp.xu tptp.xa))) _let_8 _let_6 _let_2 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.70  )
% 0.22/0.70  % SZS output end Proof for RNG119+1
% 0.22/0.70  % cvc5---1.0.5 exiting
% 0.22/0.70  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------