%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : RNG108+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n023.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 13:50:06 EDT 2023

% Result   : Theorem 0.36s 0.61s
% Output   : Proof 0.36s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : RNG108+4 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n023.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 02:01:42 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.21/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.36/0.61  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.0GQ0MKev7k/cvc5---1.0.5_3001.p...
% 0.36/0.61  ------- get file name : TPTP file name is RNG108+4
% 0.36/0.61  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_3001.smt2...
% 0.36/0.61  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.36/0.61  % SZS status Theorem for RNG108+4
% 0.36/0.61  % SZS output start Proof for RNG108+4
% 0.36/0.61  (
% 0.36/0.61  (let ((_let_1 (tptp.slsdtgt0 tptp.xb))) (let ((_let_2 (tptp.aElementOf0 tptp.xb _let_1))) (let ((_let_3 (tptp.aElementOf0 tptp.sz00 _let_1))) (let ((_let_4 (tptp.slsdtgt0 tptp.xa))) (let ((_let_5 (tptp.aElementOf0 tptp.xa _let_4))) (let ((_let_6 (tptp.aElementOf0 tptp.sz00 _let_4))) (let ((_let_7 (not (and (or (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xa W0) tptp.sz00))) _let_6) (or (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xa W0) tptp.xa))) _let_5) (or (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xb W0) tptp.sz00))) _let_3) (or (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xb W0) tptp.xb))) _let_2))))) (let ((_let_8 (tptp.aElement0 tptp.xc))) (let ((_let_9 (tptp.aElement0 tptp.xb))) (let ((_let_10 (tptp.aElement0 tptp.xa))) (let ((_let_11 (and _let_10 _let_9))) (let ((_let_12 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))) (let ((_let_13 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))) (let ((_let_14 (tptp.aElement0 tptp.sz10))) (let ((_let_15 (tptp.aElement0 tptp.sz00))) (let ((_let_16 (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (= tptp.xb (tptp.sdtasdt0 tptp.xb W0))))))) (let ((_let_17 (not _let_16))) (let ((_let_18 (or _let_17 _let_2))) (let ((_let_19 (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (= tptp.sz00 (tptp.sdtasdt0 tptp.xb W0))))))) (let ((_let_20 (not _let_19))) (let ((_let_21 (or _let_20 _let_3))) (let ((_let_22 (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (= tptp.xa (tptp.sdtasdt0 tptp.xa W0))))))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_23 _let_5))) (let ((_let_25 (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (= tptp.sz00 (tptp.sdtasdt0 tptp.xa W0))))))) (let ((_let_26 (not _let_25))) (let ((_let_27 (or _let_26 _let_6))) (let ((_let_28 (= tptp.xb (tptp.sdtasdt0 tptp.xb tptp.sz10)))) (let ((_let_29 (not _let_28))) (let ((_let_30 (not _let_14))) (let ((_let_31 (or _let_30 _let_29))) (let ((_let_32 (not _let_31))) (let ((_let_33 (and _let_28 (= tptp.xb (tptp.sdtasdt0 tptp.sz10 tptp.xb))))) (let ((_let_34 (not _let_9))) (let ((_let_35 (or _let_34 _let_33))) (let ((_let_36 (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (= W0 (tptp.sdtasdt0 W0 tptp.sz10)) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (_let_36))) (let ((_let_39 ((not (= (tptp.aElement0 W0) false))))) (let ((_let_40 (ASSUME :args (_let_11)))) (let ((_let_41 (AND_ELIM _let_40 :args (1)))) (let ((_let_42 (ASSUME :args (_let_14)))) (let ((_let_43 (_let_16))) (let ((_let_44 (or))) (let ((_let_45 (= tptp.sz00 (tptp.sdtasdt0 tptp.xb tptp.sz00)))) (let ((_let_46 (not _let_45))) (let ((_let_47 (not _let_15))) (let ((_let_48 (or _let_47 _let_46))) (let ((_let_49 (not _let_48))) (let ((_let_50 (and _let_45 (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 tptp.xb))))) (let ((_let_51 (or _let_34 _let_50))) (let ((_let_52 (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (= tptp.sz00 (tptp.sdtasdt0 W0 tptp.sz00)) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (_let_52))) (let ((_let_55 ((not (= (tptp.aElement0 W0) false))))) (let ((_let_56 (ASSUME :args (_let_15)))) (let ((_let_57 (_let_19))) (let ((_let_58 (= tptp.xa (tptp.sdtasdt0 tptp.xa tptp.sz10)))) (let ((_let_59 (not _let_58))) (let ((_let_60 (or _let_30 _let_59))) (let ((_let_61 (not _let_60))) (let ((_let_62 (and _let_58 (= tptp.xa (tptp.sdtasdt0 tptp.sz10 tptp.xa))))) (let ((_let_63 (not _let_10))) (let ((_let_64 (or _let_63 _let_62))) (let ((_let_65 (AND_ELIM _let_40 :args (0)))) (let ((_let_66 (_let_22))) (let ((_let_67 (= tptp.sz00 (tptp.sdtasdt0 tptp.xa tptp.sz00)))) (let ((_let_68 (not _let_67))) (let ((_let_69 (or _let_47 _let_68))) (let ((_let_70 (not _let_69))) (let ((_let_71 (and _let_67 (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 tptp.xa))))) (let ((_let_72 (or _let_63 _let_71))) (let ((_let_73 (_let_25))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (NOT_AND (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 0)) (CONG (REFL :args (_let_27)) (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))) :args _let_44)) :args ((or _let_25 _let_27))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_73) :args (tptp.sz00 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElement0 W0) false))))) :args _let_73)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_47 _let_68 _let_70))) _let_56 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_71 0)) :args ((or _let_67 (not _let_71)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_72)) :args ((or _let_63 _let_71 (not _let_72)))) _let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (tptp.xa QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_55)) :args _let_54)) _let_53 :args (_let_72 false _let_52)) :args (_let_71 false _let_10 false _let_72)) :args (_let_67 false _let_71)) :args (_let_70 false _let_15 false _let_67)) :args (_let_26 true _let_69)) :args (_let_27 true _let_25)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_24 0)) (CONG (REFL :args (_let_24)) (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_44)) :args ((or _let_22 _let_24))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_66) :args (tptp.sz10 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElement0 W0) false))))) :args _let_66)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_30 _let_59 _let_61))) _let_42 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_62 0)) :args ((or _let_58 (not _let_62)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_64)) :args ((or _let_63 _let_62 (not _let_64)))) _let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (tptp.xa QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_39)) :args _let_38)) _let_37 :args (_let_64 false _let_36)) :args (_let_62 false _let_10 false _let_64)) :args (_let_58 false _let_62)) :args (_let_61 false _let_14 false _let_58)) :args (_let_23 true _let_60)) :args (_let_24 true _let_22)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_21 0)) (CONG (REFL :args (_let_21)) (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_44)) :args ((or _let_19 _let_21))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_57) :args (tptp.sz00 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElement0 W0) false))))) :args _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_48)) :args ((or _let_47 _let_46 _let_49))) _let_56 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_50 0)) :args ((or _let_45 (not _let_50)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_34 _let_50 (not _let_51)))) _let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (tptp.xb QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_55)) :args _let_54)) _let_53 :args (_let_51 false _let_52)) :args (_let_50 false _let_9 false _let_51)) :args (_let_45 false _let_50)) :args (_let_49 false _let_15 false _let_45)) :args (_let_20 true _let_48)) :args (_let_21 true _let_19)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_18 0)) (CONG (REFL :args (_let_18)) (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_16))) :args _let_44)) :args ((or _let_16 _let_18))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_43) :args (tptp.sz10 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElement0 W0) false))))) :args _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_31)) :args ((or _let_30 _let_29 _let_32))) _let_42 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_33 0)) :args ((or _let_28 (not _let_33)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_34 _let_33 (not _let_35)))) _let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (tptp.xb QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_39)) :args _let_38)) _let_37 :args (_let_35 false _let_36)) :args (_let_33 false _let_9 false _let_35)) :args (_let_28 false _let_33)) :args (_let_32 false _let_14 false _let_28)) :args (_let_17 true _let_31)) :args (_let_18 true _let_16)) :args (false false _let_27 false _let_24 false _let_21 false _let_18)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)) _let_15 _let_14 (forall ((W0 $$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 $$unsorted)) (let ((_let_1 (tptp.smndt0 W0))) (=> (tptp.aElement0 W0) (and (= (tptp.sdtpldt0 W0 _let_1) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 _let_1 W0)))))) (forall ((W0 $$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))))) _let_13 (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))))))) _let_12 (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 $$unsorted)) (=> (tptp.aSet0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))) (forall ((W0 $$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)))) _let_11 (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00))) (and _let_8 (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xc W0) tptp.xa))) (tptp.doDivides0 tptp.xc tptp.xa) (tptp.aDivisorOf0 tptp.xc tptp.xa) _let_8 (exists ((W0 $$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)) (and (tptp.aSet0 tptp.xI) (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 $$unsorted)) (=> (tptp.aElement0 W1) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xI)))))) (tptp.aIdeal0 tptp.xI) (forall ((W0 $$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))))) (= tptp.xI (tptp.sdtpldt1 _let_4 _let_1))) _let_7 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.36/0.61  )
% 0.36/0.61  % SZS output end Proof for RNG108+4
% 0.36/0.61  % cvc5---1.0.5 exiting
% 0.36/0.61  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------