%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : RNG120+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n009.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 13:50:10 EDT 2023

% Result   : Theorem 35.39s 35.64s
% Output   : Proof 35.46s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13  % Problem    : RNG120+4 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n009.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 02:33:05 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 35.39/35.64  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.0PXCOuTxZm/cvc5---1.0.5_12793.p...
% 35.39/35.64  ------- get file name : TPTP file name is RNG120+4
% 35.39/35.64  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_12793.smt2...
% 35.39/35.64  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 35.39/35.64  --- Run --no-e-matching --full-saturate-quant at 5...
% 35.39/35.64  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 35.39/35.64  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 35.39/35.64  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 35.39/35.64  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 35.39/35.64  % SZS status Theorem for RNG120+4
% 35.39/35.64  % SZS output start Proof for RNG120+4
% 35.39/35.64  (
% 35.39/35.64  (let ((_let_1 (tptp.sdtasdt0 tptp.xq tptp.xu))) (let ((_let_2 (tptp.smndt0 _let_1))) (let ((_let_3 (tptp.aElementOf0 _let_2 tptp.xI))) (let ((_let_4 (not (or (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_3)))) (let ((_let_5 (= tptp.xr tptp.sz00))) (let ((_let_6 (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu)))) (let ((_let_7 (tptp.sdtpldt0 _let_1 tptp.xr))) (let ((_let_8 (= tptp.xb _let_7))) (let ((_let_9 (tptp.aElement0 tptp.xr))) (let ((_let_10 (tptp.aElement0 tptp.xq))) (let ((_let_11 (and _let_10 _let_9 _let_8 (or _let_5 _let_6)))) (let ((_let_12 (tptp.doDivides0 tptp.xu tptp.xb))) (let ((_let_13 (tptp.doDivides0 tptp.xu tptp.xa))) (let ((_let_14 (tptp.aElementOf0 tptp.xu tptp.xI))) (let ((_let_15 (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_14 (not (= tptp.xu tptp.sz00)) (forall ((W0 $$unsorted)) (=> (and (or (exists ((W1 $$unsorted) (W2 $$unsorted)) (and (tptp.aElementOf0 W1 (tptp.slsdtgt0 tptp.xa)) (tptp.aElementOf0 W2 (tptp.slsdtgt0 tptp.xb)) (= (tptp.sdtpldt0 W1 W2) W0))) (tptp.aElementOf0 W0 tptp.xI)) (not (= W0 tptp.sz00))) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu)))))))) (let ((_let_16 (tptp.slsdtgt0 tptp.xb))) (let ((_let_17 (tptp.slsdtgt0 tptp.xa))) (let ((_let_18 (= tptp.xI (tptp.sdtpldt1 _let_17 _let_16)))) (let ((_let_19 (tptp.aIdeal0 tptp.xI))) (let ((_let_20 (tptp.aSet0 tptp.xI))) (let ((_let_21 (and _let_20 (forall ((W0 $$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_19 (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 $$unsorted)) (and (tptp.aElementOf0 W1 (tptp.slsdtgt0 tptp.xa)) (tptp.aElementOf0 W2 (tptp.slsdtgt0 tptp.xb)) (= (tptp.sdtpldt0 W1 W2) W0))))) _let_18))) (let ((_let_22 (tptp.aElement0 tptp.xc))) (let ((_let_23 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))))) (let ((_let_24 (forall ((W0 $$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))))))))) (let ((_let_25 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_26 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_27 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (tptp.aElement0 (tptp.smndt0 W0)))))) (let ((_let_28 (tptp.aElement0 tptp.sz10))) (let ((_let_29 (tptp.sdtpldt1 _let_17 (tptp.slsdtgt0 _let_7)))) (let ((_let_30 (tptp.aElementOf0 _let_2 _let_29))) (let ((_let_31 (tptp.smndt0 tptp.sz10))) (let ((_let_32 (tptp.sdtasdt0 _let_31 _let_1))) (let ((_let_33 (= _let_2 _let_32))) (let ((_let_34 (tptp.aElementOf0 _let_32 _let_29))) (let ((_let_35 (1))) (let ((_let_36 (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT)))) (let ((_let_37 (ASSUME :args (_let_21)))) (let ((_let_38 (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT)))) (let ((_let_39 (ASSUME :args (_let_11)))) (let ((_let_40 (AND_INTRO (AND_ELIM (EQ_RESOLVE _let_39 _let_38) :args (2)) (AND_ELIM (EQ_RESOLVE _let_37 _let_36) :args (6))))) (let ((_let_41 (and _let_33 (= _let_2 (tptp.sdtasdt0 _let_1 _let_31))))) (let ((_let_42 (tptp.aElement0 _let_1))) (let ((_let_43 (not _let_42))) (let ((_let_44 (or _let_43 _let_41))) (let ((_let_45 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.smndt0 tptp.sz10))) (let ((_let_2 (tptp.smndt0 W0))) (or (not (tptp.aElement0 W0)) (and (= _let_2 (tptp.sdtasdt0 _let_1 W0)) (= _let_2 (tptp.sdtasdt0 W0 _let_1))))))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (tptp.sdtasdt0 tptp.xu tptp.xq))) (let ((_let_48 (tptp.aElement0 _let_47))) (let ((_let_49 (= _let_1 _let_47))) (let ((_let_50 (not _let_10))) (let ((_let_51 (tptp.aElement0 tptp.xu))) (let ((_let_52 (not _let_51))) (let ((_let_53 (or _let_52 _let_50 _let_48))) (let ((_let_54 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (tptp.aElementOf0 tptp.xu _let_29))) (let ((_let_57 (not _let_56))) (let ((_let_58 (tptp.aSet0 _let_29))) (let ((_let_59 (not _let_58))) (let ((_let_60 (or _let_59 _let_57 _let_51))) (let ((_let_61 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1558 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1558 W0)) (tptp.aElement0 BOUND_VARIABLE_1558))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_15)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_40 :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_14 (not (= tptp.sz00 tptp.xu)) (forall ((W0 $$unsorted) (BOUND_VARIABLE_2289 $$unsorted) (BOUND_VARIABLE_2287 $$unsorted)) (or (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_2287 (tptp.slsdtgt0 tptp.xa))) (not (tptp.aElementOf0 BOUND_VARIABLE_2289 (tptp.slsdtgt0 tptp.xb))) (not (= W0 (tptp.sdtpldt0 BOUND_VARIABLE_2287 BOUND_VARIABLE_2289)))) (not (tptp.aElementOf0 W0 tptp.xI))) (= tptp.sz00 W0) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu)))))) SB_DEFAULT SBA_FIXPOINT)))) :args _let_35))) (let ((_let_64 (0))) (let ((_let_65 (EQ_RESOLVE _let_37 (TRANS _let_36 (MACRO_SR_EQ_INTRO _let_40 :args ((and _let_20 (forall ((W0 $$unsorted) (BOUND_VARIABLE_2065 $$unsorted) (BOUND_VARIABLE_2058 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_2058 tptp.xI)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 BOUND_VARIABLE_2058) tptp.xI)) (or (not (tptp.aElement0 BOUND_VARIABLE_2065)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_2065 W0) tptp.xI))))) _let_19 (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 $$unsorted)) (or (not (tptp.aElementOf0 W1 (tptp.slsdtgt0 tptp.xa))) (not (tptp.aElementOf0 W2 (tptp.slsdtgt0 tptp.xb))) (not (= W0 (tptp.sdtpldt0 W1 W2)))))))) _let_18) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_59 _let_57 _let_51 (not _let_60)))) (AND_ELIM _let_65 :args _let_64) _let_63 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (_let_29 tptp.xu QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 BOUND_VARIABLE_1558 W0) false))))) :args (_let_61))) _let_62 :args (_let_60 false _let_61)) :args (_let_51 false _let_58 false _let_56 false _let_60)))) (let ((_let_67 (AND_ELIM (EQ_RESOLVE _let_39 (TRANS _let_38 (MACRO_SR_EQ_INTRO _let_40 :args ((and _let_10 _let_9 _let_8 (or (= tptp.sz00 tptp.xr) _let_6)) SB_DEFAULT SBA_FIXPOINT)))) :args _let_64))) (let ((_let_68 (or _let_52 _let_50 _let_49))) (let ((_let_69 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (and _let_49 _let_48))) (let ((_let_72 (ASSUME :args (_let_48)))) (let ((_let_73 (ASSUME :args (_let_49)))) (let ((_let_74 (tptp.aElement0 _let_31))) (let ((_let_75 (not _let_74))) (let ((_let_76 (or _let_75 _let_34))) (let ((_let_77 (not (tptp.aElementOf0 tptp.sz00 _let_29)))) (let ((_let_78 (and (or _let_77 (tptp.aElementOf0 (tptp.sdtpldt0 _let_1 tptp.sz00) _let_29)) _let_76))) (let ((_let_79 (tptp.aElementOf0 _let_1 _let_29))) (let ((_let_80 (not _let_79))) (let ((_let_81 (or _let_80 _let_78))) (let ((_let_82 (forall ((W0 $$unsorted) (BOUND_VARIABLE_2065 $$unsorted) (BOUND_VARIABLE_2058 $$unsorted)) (let ((_let_1 (tptp.sdtpldt1 (tptp.slsdtgt0 tptp.xa) (tptp.slsdtgt0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xq tptp.xu) tptp.xr))))) (or (not (tptp.aElementOf0 W0 _let_1)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_2058 _let_1)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 BOUND_VARIABLE_2058) _let_1)) (or (not (tptp.aElement0 BOUND_VARIABLE_2065)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_2065 W0) _let_1)))))))) (let ((_let_83 (AND_ELIM _let_65 :args _let_35))) (let ((_let_84 (_let_82))) (let ((_let_85 (ASSUME :args _let_84))) (let ((_let_86 (or _let_50 _let_79))) (let ((_let_87 (and (or _let_77 (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xu tptp.sz00) _let_29)) _let_86))) (let ((_let_88 (or _let_57 _let_87))) (let ((_let_89 (not _let_28))) (let ((_let_90 (or _let_89 _let_74))) (let ((_let_91 (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (tptp.aElement0 (tptp.smndt0 W0)))))) (let ((_let_92 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_93 (not _let_30))) (let ((_let_94 (ASSUME :args (_let_34)))) (let ((_let_95 (ASSUME :args (_let_33)))) (let ((_let_96 (ASSUME :args (_let_93)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_94 _let_95 _let_96) :args (_let_93 _let_33 _let_34)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_96)) (CONG (SYMM (SYMM _let_95)) (REFL :args (_let_29)) :args (APPLY_UF tptp.aElementOf0)) (TRUE_INTRO _let_94))) :args (_let_34 _let_33 _let_93)) :args ((not (and _let_93 _let_33 _let_34)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_93) _let_30))) (REFL :args ((not _let_33))) (REFL :args ((not _let_34))) :args (or))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_75 _let_34 (not _let_76)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_90)) :args ((or _let_89 _let_74 (not _let_90)))) (ASSUME :args (_let_28)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_92 :args (tptp.sz10 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_91))) _let_92 :args (_let_90 false _let_91)) :args (_let_74 false _let_28 false _let_90)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_78 1)) :args ((or _let_76 (not _let_78)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_81)) :args ((or _let_80 _let_78 (not _let_81)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_86)) :args ((or _let_50 _let_79 (not _let_86)))) _let_67 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_87 1)) :args ((or _let_86 (not _let_87)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_88)) :args ((or _let_57 _let_87 (not _let_88)))) _let_63 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_85 :args (tptp.xu tptp.xq tptp.sz00 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_84)) _let_83 :args (_let_88 false _let_82)) :args (_let_87 false _let_56 false _let_88)) :args (_let_86 false _let_87)) :args (_let_79 false _let_10 false _let_86)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_85 :args (_let_1 _let_31 tptp.sz00 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_84)) _let_83 :args (_let_81 false _let_82)) :args (_let_78 false _let_79 false _let_81)) :args (_let_76 false _let_78)) :args (_let_34 false _let_74 false _let_76)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_41 0)) :args ((or _let_33 (not _let_41)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_44)) :args ((or _let_43 _let_41 (not _let_44)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_71)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_72 _let_73) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM (SYMM _let_73)) :args (APPLY_UF tptp.aElement0)) (TRUE_INTRO _let_72))) :args (_let_48 _let_49))) :args (_let_49 _let_48))) :args (true _let_71)) :args ((or _let_42 (not _let_49) (not _let_48)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_50 _let_52 _let_49 (not _let_68)))) _let_67 _let_66 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_70 :args (tptp.xu tptp.xq QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtasdt0 W1 W0)))) :args (_let_69)))) _let_70 :args (_let_68 false _let_69)) :args (_let_49 false _let_10 false _let_51 false _let_68)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_53)) :args ((or _let_50 _let_52 _let_48 (not _let_53)))) _let_67 _let_66 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (tptp.xu tptp.xq QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_54))) _let_55 :args (_let_53 false _let_54)) :args (_let_48 false _let_10 false _let_51 false _let_53)) :args (_let_42 false _let_49 false _let_48)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (_let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.smndt0 W0)))) :args (_let_45))) _let_46 :args (_let_44 false _let_45)) :args (_let_41 false _let_42 false _let_44)) :args (_let_33 false _let_41)) (NOT_OR_ELIM (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_40 :args ((not (or (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElementOf0 W0 (tptp.slsdtgt0 tptp.xa))) (not (tptp.aElementOf0 W1 (tptp.slsdtgt0 tptp.xb))) (not (= (tptp.sdtpldt0 W0 W1) (tptp.smndt0 (tptp.sdtasdt0 tptp.xq tptp.xu))))))) _let_3)) SB_DEFAULT SBA_FIXPOINT)))) :args _let_35) :args (false false _let_34 false _let_33 true _let_30)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)) (tptp.aElement0 tptp.sz00) _let_28 _let_27 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1)))) _let_26 (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 $$unsorted)) (let ((_let_1 (tptp.smndt0 W0))) (=> (tptp.aElement0 W0) (and (= (tptp.sdtpldt0 W0 _let_1) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 _let_1 W0)))))) _let_25 (forall ((W0 $$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))))))) _let_24 (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_23 (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 $$unsorted)) (=> (tptp.aElement0 W0) (tptp.aIdeal0 (tptp.slsdtgt0 W0)))) (and (tptp.aElement0 tptp.xa) (tptp.aElement0 tptp.xb)) (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00))) (and _let_22 (exists ((W0 $$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_22 (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 $$unsorted)) (and (tptp.aElement0 W1) (= (tptp.sdtasdt0 W0 W1) tptp.xc))) (tptp.doDivides0 W0 tptp.xc)))) (tptp.aGcdOfAnd0 tptp.xc tptp.xa tptp.xb)) _let_21 (and (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xa W0) tptp.sz00))) (tptp.aElementOf0 tptp.sz00 _let_17) (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xa W0) tptp.xa))) (tptp.aElementOf0 tptp.xa _let_17) (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xb W0) tptp.sz00))) (tptp.aElementOf0 tptp.sz00 _let_16) (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xb W0) tptp.xb))) (tptp.aElementOf0 tptp.xb _let_16)) (exists ((W0 $$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_15 (not (and (or (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xu W0) tptp.xa))) _let_13 (tptp.aDivisorOf0 tptp.xu tptp.xa)) (or (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xu W0) tptp.xb))) _let_12 (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 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xu W0) tptp.xa))) _let_13))) (not (or (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xu W0) tptp.xb))) _let_12)) _let_11 (not _let_5) _let_4 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 35.46/35.64  )
% 35.46/35.64  % SZS output end Proof for RNG120+4
% 35.46/35.64  % cvc5---1.0.5 exiting
% 35.46/35.65  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------