%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : RNG122+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n002.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 13:50:11 EDT 2023

% Result   : Theorem 25.99s 26.28s
% Output   : Proof 25.99s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : RNG122+4 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.15  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n002.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Sun Aug 27 02:41:03 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.21/0.51  %----Proving TF0_NAR, FOF, or CNF
% 25.99/26.28  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.gCSlYFprxx/cvc5---1.0.5_6992.p...
% 25.99/26.28  ------- get file name : TPTP file name is RNG122+4
% 25.99/26.28  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_6992.smt2...
% 25.99/26.28  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 25.99/26.28  --- Run --no-e-matching --full-saturate-quant at 5...
% 25.99/26.28  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 25.99/26.28  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.99/26.28  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 25.99/26.28  % SZS status Theorem for RNG122+4
% 25.99/26.28  % SZS output start Proof for RNG122+4
% 25.99/26.28  (
% 25.99/26.28  (let ((_let_1 (tptp.sdtasdt0 tptp.xq tptp.xu))) (let ((_let_2 (tptp.smndt0 _let_1))) (let ((_let_3 (not (= tptp.xr (tptp.sdtpldt0 _let_2 tptp.xb))))) (let ((_let_4 (tptp.aElementOf0 _let_2 tptp.xI))) (let ((_let_5 (and (exists ((W0 $$unsorted) (W1 $$unsorted)) (and (tptp.aElementOf0 W0 (tptp.slsdtgt0 tptp.xa)) (tptp.aElementOf0 W1 (tptp.slsdtgt0 tptp.xb)) (= (tptp.sdtpldt0 W0 W1) (tptp.smndt0 (tptp.sdtasdt0 tptp.xq tptp.xu))))) _let_4))) (let ((_let_6 (= tptp.xr tptp.sz00))) (let ((_let_7 (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu)))) (let ((_let_8 (tptp.sdtpldt0 _let_1 tptp.xr))) (let ((_let_9 (= tptp.xb _let_8))) (let ((_let_10 (tptp.aElement0 tptp.xr))) (let ((_let_11 (tptp.aElement0 tptp.xq))) (let ((_let_12 (and _let_11 _let_10 _let_9 (or _let_6 _let_7)))) (let ((_let_13 (tptp.doDivides0 tptp.xu tptp.xb))) (let ((_let_14 (tptp.doDivides0 tptp.xu tptp.xa))) (let ((_let_15 (tptp.aElementOf0 tptp.xu tptp.xI))) (let ((_let_16 (and (exists ((W0 $$unsorted) (W1 $$unsorted)) (and (tptp.aElementOf0 W0 (tptp.slsdtgt0 tptp.xa)) (tptp.aElementOf0 W1 (tptp.slsdtgt0 tptp.xb)) (= (tptp.sdtpldt0 W0 W1) tptp.xu))) _let_15 (not (= tptp.xu tptp.sz00)) (forall ((W0 $$unsorted)) (=> (and (or (exists ((W1 $$unsorted) (W2 $$unsorted)) (and (tptp.aElementOf0 W1 (tptp.slsdtgt0 tptp.xa)) (tptp.aElementOf0 W2 (tptp.slsdtgt0 tptp.xb)) (= (tptp.sdtpldt0 W1 W2) W0))) (tptp.aElementOf0 W0 tptp.xI)) (not (= W0 tptp.sz00))) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu)))))))) (let ((_let_17 (tptp.slsdtgt0 tptp.xb))) (let ((_let_18 (tptp.slsdtgt0 tptp.xa))) (let ((_let_19 (= tptp.xI (tptp.sdtpldt1 _let_18 _let_17)))) (let ((_let_20 (tptp.aIdeal0 tptp.xI))) (let ((_let_21 (tptp.aSet0 tptp.xI))) (let ((_let_22 (and _let_21 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xI) (and (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xI) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xI))) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xI)))))) _let_20 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.slsdtgt0 tptp.xa)) (exists ((W1 $$unsorted)) (and (tptp.aElement0 W1) (= (tptp.sdtasdt0 tptp.xa W1) W0))))) (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.slsdtgt0 tptp.xb)) (exists ((W1 $$unsorted)) (and (tptp.aElement0 W1) (= (tptp.sdtasdt0 tptp.xb W1) W0))))) (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 tptp.xI) (exists ((W1 $$unsorted) (W2 $$unsorted)) (and (tptp.aElementOf0 W1 (tptp.slsdtgt0 tptp.xa)) (tptp.aElementOf0 W2 (tptp.slsdtgt0 tptp.xb)) (= (tptp.sdtpldt0 W1 W2) W0))))) _let_19))) (let ((_let_23 (tptp.aElement0 tptp.xc))) (let ((_let_24 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))))) (let ((_let_25 (forall ((W0 $$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 ((_let_26 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))) (let ((_let_27 (forall ((W0 $$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 ((_let_28 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_29 (tptp.sdtpldt0 _let_2 _let_8))) (let ((_let_30 (= tptp.xr _let_29))) (let ((_let_31 (= tptp.xr (tptp.sdtpldt0 tptp.sz00 tptp.xr)))) (let ((_let_32 (tptp.sdtpldt0 _let_2 _let_1))) (let ((_let_33 (= _let_29 (tptp.sdtpldt0 _let_32 tptp.xr)))) (let ((_let_34 (= tptp.sz00 _let_32))) (let ((_let_35 (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT)))) (let ((_let_36 (ASSUME :args (_let_22)))) (let ((_let_37 (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT)))) (let ((_let_38 (ASSUME :args (_let_12)))) (let ((_let_39 (AND_INTRO (AND_ELIM (EQ_RESOLVE _let_38 _let_37) :args (2)) (AND_ELIM (EQ_RESOLVE _let_36 _let_35) :args (6))))) (let ((_let_40 (and (= tptp.xr (tptp.sdtpldt0 tptp.xr tptp.sz00)) _let_31))) (let ((_let_41 (not _let_10))) (let ((_let_42 (or _let_41 _let_40))) (let ((_let_43 (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (= W0 (tptp.sdtpldt0 W0 tptp.sz00)) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_45 (1))) (let ((_let_46 (EQ_RESOLVE _let_38 (TRANS _let_37 (MACRO_SR_EQ_INTRO _let_39 :args ((and _let_11 _let_10 _let_9 (or (= tptp.sz00 tptp.xr) _let_7)) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_47 (AND_ELIM _let_46 :args _let_45))) (let ((_let_48 (tptp.aElement0 _let_1))) (let ((_let_49 (not _let_48))) (let ((_let_50 (tptp.aElement0 _let_2))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_51 _let_49 _let_41 _let_33))) (let ((_let_53 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (= (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (tptp.sdtpldt1 _let_18 (tptp.slsdtgt0 _let_8)))) (let ((_let_56 (tptp.aElementOf0 _let_2 _let_55))) (let ((_let_57 (not _let_56))) (let ((_let_58 (tptp.aSet0 _let_55))) (let ((_let_59 (not _let_58))) (let ((_let_60 (or _let_59 _let_57 _let_50))) (let ((_let_61 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1580 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1580 W0)) (tptp.aElement0 BOUND_VARIABLE_1580))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (_let_61))) (let ((_let_64 ((not (= (tptp.aElementOf0 BOUND_VARIABLE_1580 W0) false))))) (let ((_let_65 (0))) (let ((_let_66 (AND_ELIM (EQ_RESOLVE _let_36 (TRANS _let_35 (MACRO_SR_EQ_INTRO _let_39 :args ((and _let_21 (forall ((W0 $$unsorted) (BOUND_VARIABLE_2087 $$unsorted) (BOUND_VARIABLE_2080 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_2080 tptp.xI)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 BOUND_VARIABLE_2080) tptp.xI)) (or (not (tptp.aElement0 BOUND_VARIABLE_2087)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_2087 W0) tptp.xI))))) _let_20 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.slsdtgt0 tptp.xa)) (not (forall ((W1 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (= W0 (tptp.sdtasdt0 tptp.xa W1)))))))) (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.slsdtgt0 tptp.xb)) (not (forall ((W1 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (= W0 (tptp.sdtasdt0 tptp.xb W1)))))))) (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 tptp.xI) (not (forall ((W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aElementOf0 W1 (tptp.slsdtgt0 tptp.xa))) (not (tptp.aElementOf0 W2 (tptp.slsdtgt0 tptp.xb))) (not (= W0 (tptp.sdtpldt0 W1 W2)))))))) _let_19) SB_DEFAULT SBA_FIXPOINT)))) :args _let_65))) (let ((_let_67 (tptp.aElement0 tptp.xu))) (let ((_let_68 (not _let_67))) (let ((_let_69 (not _let_11))) (let ((_let_70 (or _let_69 _let_68 _let_48))) (let ((_let_71 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (tptp.aElementOf0 tptp.xu _let_55))) (let ((_let_74 (not _let_73))) (let ((_let_75 (or _let_59 _let_74 _let_67))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_69 _let_68 _let_48 (not _let_70)))) (AND_ELIM _let_46 :args _let_65) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_59 _let_74 _let_67 (not _let_75)))) _let_66 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_16)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_39 :args ((and (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElementOf0 W0 (tptp.slsdtgt0 tptp.xa))) (not (tptp.aElementOf0 W1 (tptp.slsdtgt0 tptp.xb))) (not (= tptp.xu (tptp.sdtpldt0 W0 W1)))))) _let_15 (not (= tptp.sz00 tptp.xu)) (forall ((W0 $$unsorted) (BOUND_VARIABLE_2311 $$unsorted) (BOUND_VARIABLE_2309 $$unsorted)) (or (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_2309 (tptp.slsdtgt0 tptp.xa))) (not (tptp.aElementOf0 BOUND_VARIABLE_2311 (tptp.slsdtgt0 tptp.xb))) (not (= W0 (tptp.sdtpldt0 BOUND_VARIABLE_2309 BOUND_VARIABLE_2311)))) (not (tptp.aElementOf0 W0 tptp.xI))) (= tptp.sz00 W0) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu)))))) SB_DEFAULT SBA_FIXPOINT)))) :args _let_45) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (_let_55 tptp.xu QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_64)) :args _let_63)) _let_62 :args (_let_75 false _let_61)) :args (_let_67 false _let_58 false _let_73 false _let_75)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (tptp.xq tptp.xu QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtasdt0 W0 W1)))) :args (_let_71))) _let_72 :args (_let_70 false _let_71)) :args (_let_48 false _let_11 false _let_67 false _let_70)))) (let ((_let_77 (and (= tptp.sz00 (tptp.sdtpldt0 _let_1 _let_2)) _let_34))) (let ((_let_78 (or _let_49 _let_77))) (let ((_let_79 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.smndt0 W0))) (or (not (tptp.aElement0 W0)) (and (= tptp.sz00 (tptp.sdtpldt0 W0 _let_1)) (= tptp.sz00 (tptp.sdtpldt0 _let_1 W0)))))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (and _let_33 _let_31 _let_34))) (let ((_let_82 (ASSUME :args (_let_33)))) (let ((_let_83 (ASSUME :args (_let_34)))) (let ((_let_84 (ASSUME :args (_let_31)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_81)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_82 _let_83 _let_84) (SCOPE (TRANS (SYMM (SYMM _let_84)) (CONG (SYMM (SYMM _let_83)) (REFL :args (tptp.xr)) :args (APPLY_UF tptp.sdtpldt0)) (SYMM _let_82)) :args (_let_33 _let_34 _let_31))) :args (_let_33 _let_31 _let_34))) :args (true _let_81)) :args ((or _let_30 (not _let_33) (not _let_31) (not _let_34)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_77 1)) :args ((or _let_34 (not _let_77)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_78)) :args ((or _let_49 _let_77 (not _let_78)))) _let_76 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (_let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.smndt0 W0)))) :args (_let_79))) _let_80 :args (_let_78 false _let_79)) :args (_let_77 false _let_48 false _let_78)) :args (_let_34 false _let_77)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_41 _let_49 _let_51 _let_33 (not _let_52)))) _let_47 _let_76 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_59 _let_57 _let_50 (not _let_60)))) _let_66 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_5)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_39 :args ((and (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElementOf0 W0 (tptp.slsdtgt0 tptp.xa))) (not (tptp.aElementOf0 W1 (tptp.slsdtgt0 tptp.xb))) (not (= (tptp.sdtpldt0 W0 W1) (tptp.smndt0 (tptp.sdtasdt0 tptp.xq tptp.xu))))))) _let_4) SB_DEFAULT SBA_FIXPOINT)))) :args _let_45) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (_let_55 _let_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_64)) :args _let_63)) _let_62 :args (_let_60 false _let_61)) :args (_let_50 false _let_58 false _let_56 false _let_60)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_54 :args (_let_2 _let_1 tptp.xr QUANTIFIERS_INST_E_MATCHING ((tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))) :args (_let_53)))) _let_54 :args (_let_52 false _let_53)) :args (_let_33 false _let_10 false _let_48 false _let_50 false _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_40 1)) :args ((or _let_31 (not _let_40)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_41 _let_40 (not _let_42)))) _let_47 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (tptp.xr QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElement0 W0) false))))) :args (_let_43))) _let_44 :args (_let_42 false _let_43)) :args (_let_40 false _let_10 false _let_42)) :args (_let_31 false _let_40)) (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO _let_39 :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) :args (false false _let_34 false _let_33 false _let_31 true _let_30)) :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_28 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))) _let_27 _let_26 _let_25 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))) (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_24 (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))))))))) (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))))))))) (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 $$unsorted)) (and (tptp.aElement0 W2) (tptp.aElement0 W3) (= W0 (tptp.sdtpldt0 (tptp.sdtasdt0 W2 W1) W3)) (=> (not (= W3 tptp.sz00)) (tptp.iLess0 (tptp.sbrdtbr0 W3) (tptp.sbrdtbr0 W1))))))) (forall ((W0 $$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)))))) (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 $$unsorted)) (=> (tptp.aElement0 W0) (tptp.aIdeal0 (tptp.slsdtgt0 W0)))) (and (tptp.aElement0 tptp.xa) (tptp.aElement0 tptp.xb)) (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00))) (and _let_23 (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xc W0) tptp.xa))) (tptp.doDivides0 tptp.xc tptp.xa) (tptp.aDivisorOf0 tptp.xc tptp.xa) _let_23 (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xc W0) tptp.xb))) (tptp.doDivides0 tptp.xc tptp.xb) (tptp.aDivisorOf0 tptp.xc tptp.xb) (forall ((W0 $$unsorted)) (=> (and (or (and (tptp.aElement0 W0) (or (exists ((W1 $$unsorted)) (and (tptp.aElement0 W1) (= (tptp.sdtasdt0 W0 W1) tptp.xa))) (tptp.doDivides0 W0 tptp.xa))) (tptp.aDivisorOf0 W0 tptp.xa)) (or (exists ((W1 $$unsorted)) (and (tptp.aElement0 W1) (= (tptp.sdtasdt0 W0 W1) tptp.xb))) (tptp.doDivides0 W0 tptp.xb) (tptp.aDivisorOf0 W0 tptp.xb))) (and (exists ((W1 $$unsorted)) (and (tptp.aElement0 W1) (= (tptp.sdtasdt0 W0 W1) tptp.xc))) (tptp.doDivides0 W0 tptp.xc)))) (tptp.aGcdOfAnd0 tptp.xc tptp.xa tptp.xb)) _let_22 (and (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xa W0) tptp.sz00))) (tptp.aElementOf0 tptp.sz00 _let_18) (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xa W0) tptp.xa))) (tptp.aElementOf0 tptp.xa _let_18) (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xb W0) tptp.sz00))) (tptp.aElementOf0 tptp.sz00 _let_17) (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xb W0) tptp.xb))) (tptp.aElementOf0 tptp.xb _let_17)) (exists ((W0 $$unsorted)) (and (forall ((W1 $$unsorted)) (= (tptp.aElementOf0 W1 (tptp.slsdtgt0 tptp.xa)) (exists ((W2 $$unsorted)) (and (tptp.aElement0 W2) (= (tptp.sdtasdt0 tptp.xa W2) W1))))) (forall ((W1 $$unsorted)) (= (tptp.aElementOf0 W1 (tptp.slsdtgt0 tptp.xb)) (exists ((W2 $$unsorted)) (and (tptp.aElement0 W2) (= (tptp.sdtasdt0 tptp.xb W2) W1))))) (exists ((W1 $$unsorted) (W2 $$unsorted)) (and (tptp.aElementOf0 W1 (tptp.slsdtgt0 tptp.xa)) (tptp.aElementOf0 W2 (tptp.slsdtgt0 tptp.xb)) (= (tptp.sdtpldt0 W1 W2) W0))) (tptp.aElementOf0 W0 (tptp.sdtpldt1 (tptp.slsdtgt0 tptp.xa) (tptp.slsdtgt0 tptp.xb))) (not (= W0 tptp.sz00)))) _let_16 (not (and (or (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xu W0) tptp.xa))) _let_14 (tptp.aDivisorOf0 tptp.xu tptp.xa)) (or (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xu W0) tptp.xb))) _let_13 (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 (and (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xu W0) tptp.xa))) _let_14))) (not (or (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xu W0) tptp.xb))) _let_13)) _let_12 (not _let_6) _let_5 (and (exists ((W0 $$unsorted) (W1 $$unsorted)) (and (tptp.aElementOf0 W0 (tptp.slsdtgt0 tptp.xa)) (tptp.aElementOf0 W1 (tptp.slsdtgt0 tptp.xb)) (= (tptp.sdtpldt0 W0 W1) tptp.xb))) (exists ((W0 $$unsorted) (W1 $$unsorted)) (and (tptp.aElementOf0 W0 (tptp.slsdtgt0 tptp.xa)) (tptp.aElementOf0 W1 (tptp.slsdtgt0 tptp.xb)) (= (tptp.sdtpldt0 W0 W1) tptp.xb))) (tptp.aElementOf0 tptp.xb tptp.xI)) _let_3 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 25.99/26.29  )
% 25.99/26.29  % SZS output end Proof for RNG122+4
% 25.99/26.29  % cvc5---1.0.5 exiting
% 25.99/26.29  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------