%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : RNG109+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n013.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 11.77s 12.02s
% Output   : Proof 11.77s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15  % Problem    : RNG109+4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.16  % Command    : do_cvc5 %s %d
% 0.16/0.38  % Computer : n013.cluster.edu
% 0.16/0.38  % Model    : x86_64 x86_64
% 0.16/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38  % Memory   : 8042.1875MB
% 0.16/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38  % CPULimit   : 300
% 0.16/0.38  % WCLimit    : 300
% 0.16/0.38  % DateTime   : Sun Aug 27 02:35:32 EDT 2023
% 0.16/0.38  % CPUTime    : 
% 0.23/0.53  %----Proving TF0_NAR, FOF, or CNF
% 11.77/12.02  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.MDSTZB2L2Z/cvc5---1.0.5_2120.p...
% 11.77/12.02  ------- get file name : TPTP file name is RNG109+4
% 11.77/12.02  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_2120.smt2...
% 11.77/12.02  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 11.77/12.02  --- Run --no-e-matching --full-saturate-quant at 5...
% 11.77/12.02  % SZS status Theorem for RNG109+4
% 11.77/12.02  % SZS output start Proof for RNG109+4
% 11.77/12.02  (
% 11.77/12.02  (let ((_let_1 (not (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 $$unsorted)) (and (tptp.aElement0 W2) (= (tptp.sdtasdt0 tptp.xb W2) W1))))) (or (exists ((W1 $$unsorted) (W2 $$unsorted)) (and (tptp.aElementOf0 W1 (tptp.slsdtgt0 tptp.xa)) (tptp.aElementOf0 W2 (tptp.slsdtgt0 tptp.xb)) (= (tptp.sdtpldt0 W1 W2) W0))) (tptp.aElementOf0 W0 (tptp.sdtpldt1 (tptp.slsdtgt0 tptp.xa) (tptp.slsdtgt0 tptp.xb)))))) (not (= W0 tptp.sz00))))))) (let ((_let_2 (tptp.slsdtgt0 tptp.xb))) (let ((_let_3 (tptp.aElementOf0 tptp.xb _let_2))) (let ((_let_4 (tptp.aElementOf0 tptp.sz00 _let_2))) (let ((_let_5 (tptp.slsdtgt0 tptp.xa))) (let ((_let_6 (tptp.aElementOf0 tptp.xa _let_5))) (let ((_let_7 (tptp.aElementOf0 tptp.sz00 _let_5))) (let ((_let_8 (and (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xa W0) tptp.sz00))) _let_7 (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xa W0) tptp.xa))) _let_6 (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xb W0) tptp.sz00))) _let_4 (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xb W0) tptp.xb))) _let_3))) (let ((_let_9 (tptp.sdtpldt1 _let_5 _let_2))) (let ((_let_10 (tptp.aElement0 tptp.xc))) (let ((_let_11 (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00))))) (let ((_let_12 (tptp.aElement0 tptp.xb))) (let ((_let_13 (tptp.aElement0 tptp.xa))) (let ((_let_14 (and _let_13 _let_12))) (let ((_let_15 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))) (let ((_let_16 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))))) (let ((_let_17 (tptp.aElement0 tptp.sz00))) (let ((_let_18 (tptp.sdtpldt0 tptp.sz00 tptp.xb))) (let ((_let_19 (= tptp.sz00 _let_18))) (let ((_let_20 (not _let_3))) (let ((_let_21 (not _let_7))) (let ((_let_22 (or _let_21 _let_20))) (let ((_let_23 (= _let_4 (not (forall ((W2 $$unsorted)) (or (not (tptp.aElement0 W2)) (not (= tptp.sz00 (tptp.sdtasdt0 tptp.xb W2))))))))) (let ((_let_24 (= _let_7 (not (forall ((W2 $$unsorted)) (or (not (tptp.aElement0 W2)) (not (= tptp.sz00 (tptp.sdtasdt0 tptp.xa W2))))))))) (let ((_let_25 (and _let_24 _let_23 _let_22 (not (tptp.aElementOf0 _let_18 _let_9))))) (let ((_let_26 (or _let_25 _let_19))) (let ((_let_27 (tptp.sdtpldt0 tptp.xb tptp.sz00))) (let ((_let_28 (= _let_18 _let_27))) (let ((_let_29 (= tptp.xb _let_27))) (let ((_let_30 (= tptp.sz00 tptp.xb))) (let ((_let_31 (not _let_19))) (let ((_let_32 (not _let_12))) (let ((_let_33 (not _let_17))) (let ((_let_34 (or _let_33 _let_32 _let_28))) (let ((_let_35 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (1))) (let ((_let_38 (ASSUME :args (_let_14)))) (let ((_let_39 (AND_ELIM _let_38 :args _let_37))) (let ((_let_40 (and _let_29 (= tptp.xb _let_18)))) (let ((_let_41 (or _let_32 _let_40))) (let ((_let_42 (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (= W0 (tptp.sdtpldt0 W0 tptp.sz00)) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (_let_42))) (let ((_let_45 (= tptp.sz00 tptp.xa))) (let ((_let_46 (not _let_30))) (let ((_let_47 (tptp.sdtpldt0 tptp.xa tptp.sz00))) (let ((_let_48 (= tptp.sz00 _let_47))) (let ((_let_49 (= tptp.xa _let_47))) (let ((_let_50 (not _let_4))) (let ((_let_51 (not _let_6))) (let ((_let_52 (or _let_51 _let_50))) (let ((_let_53 (and _let_24 _let_23 _let_52 (not (tptp.aElementOf0 _let_47 _let_9))))) (let ((_let_54 (or _let_53 _let_48))) (let ((_let_55 (forall ((W0 $$unsorted) (BOUND_VARIABLE_2131 $$unsorted) (BOUND_VARIABLE_2129 $$unsorted) (BOUND_VARIABLE_2120 $$unsorted) (BOUND_VARIABLE_2111 $$unsorted)) (let ((_let_1 (tptp.slsdtgt0 tptp.xb))) (let ((_let_2 (tptp.slsdtgt0 tptp.xa))) (or (and (= (tptp.aElementOf0 BOUND_VARIABLE_2111 _let_2) (not (forall ((W2 $$unsorted)) (or (not (tptp.aElement0 W2)) (not (= (tptp.sdtasdt0 tptp.xa W2) BOUND_VARIABLE_2111)))))) (= (tptp.aElementOf0 BOUND_VARIABLE_2120 _let_1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aElement0 W2)) (not (= (tptp.sdtasdt0 tptp.xb W2) BOUND_VARIABLE_2120)))))) (or (not (tptp.aElementOf0 BOUND_VARIABLE_2129 _let_2)) (not (tptp.aElementOf0 BOUND_VARIABLE_2131 _let_1)) (not (= W0 (tptp.sdtpldt0 BOUND_VARIABLE_2129 BOUND_VARIABLE_2131)))) (not (tptp.aElementOf0 W0 (tptp.sdtpldt1 _let_2 _let_1)))) (= tptp.sz00 W0))))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (_let_55))) (let ((_let_58 (not _let_53))) (let ((_let_59 (not _let_52))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (and _let_49 (= tptp.xa (tptp.sdtpldt0 tptp.sz00 tptp.xa))))) (let ((_let_62 (not _let_13))) (let ((_let_63 (or _let_62 _let_61))) (let ((_let_64 (and _let_49 _let_48))) (let ((_let_65 (_let_49 _let_48))) (let ((_let_66 (ASSUME :args (_let_49)))) (let ((_let_67 (ASSUME :args (_let_48)))) (let ((_let_68 (and _let_46 _let_29 _let_28))) (let ((_let_69 (_let_46 _let_29 _let_28))) (let ((_let_70 (ASSUME :args (_let_46)))) (let ((_let_71 (ASSUME :args (_let_29)))) (let ((_let_72 (ASSUME :args (_let_28)))) (let ((_let_73 (not _let_25))) (let ((_let_74 (not _let_22))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_19 _let_25 (not _let_26)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_25 2)) :args ((or _let_22 _let_73))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_22)) :args ((or _let_21 _let_20 _let_74))) (AND_ELIM _let_60 :args _let_37) (AND_ELIM _let_60 :args (7)) :args (_let_74 false _let_7 false _let_3)) :args (_let_73 true _let_22)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_56 :args (_let_18 tptp.xb tptp.sz00 tptp.sz00 tptp.sz00 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_57))) _let_56 :args (_let_26 false _let_55)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_68)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_70 _let_71 _let_72) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (tptp.sz00)) (TRANS (SYMM (SYMM _let_72)) (SYMM _let_71)) :args (=)) (FALSE_INTRO _let_70))) :args _let_69)) :args _let_69)) :args (true _let_68)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_30))) (REFL :args ((not _let_29))) (REFL :args ((not _let_28))) (REFL :args (_let_31)) :args (or))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_64)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_66 _let_67) (SCOPE (TRANS (SYMM (SYMM _let_67)) (SYMM _let_66)) :args _let_65)) :args _let_65)) :args (true _let_64)) :args ((or _let_45 (not _let_49) (not _let_48)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_61 0)) :args ((or _let_49 (not _let_61)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_63)) :args ((or _let_62 _let_61 (not _let_63)))) (AND_ELIM _let_38 :args (0)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (tptp.xa QUANTIFIERS_INST_ENUM)) :args _let_44)) _let_43 :args (_let_63 false _let_42)) :args (_let_61 false _let_13 false _let_63)) :args (_let_49 false _let_61)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_48 _let_53 (not _let_54)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_53 2)) :args ((or _let_52 _let_58))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_51 _let_50 _let_59))) (AND_ELIM _let_60 :args (3)) (AND_ELIM _let_60 :args (5)) :args (_let_59 false _let_6 false _let_4)) :args (_let_58 true _let_52)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_56 :args (_let_47 tptp.sz00 tptp.xa tptp.sz00 tptp.sz00 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_57))) _let_56 :args (_let_54 false _let_55)) :args (_let_48 true _let_53 false _let_54)) :args (_let_45 false _let_49 false _let_48)) :args (_let_46 false _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_40 0)) :args ((or _let_29 (not _let_40)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_32 _let_40 (not _let_41)))) _let_39 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (tptp.xb QUANTIFIERS_INST_ENUM)) :args _let_44)) _let_43 :args (_let_41 false _let_42)) :args (_let_40 false _let_12 false _let_41)) :args (_let_29 false _let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_33 _let_32 _let_28 (not _let_34)))) (ASSUME :args (_let_17)) _let_39 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (tptp.sz00 tptp.xb QUANTIFIERS_INST_ENUM)) :args (_let_35))) _let_36 :args (_let_34 false _let_35)) :args (_let_28 false _let_17 false _let_12 false _let_34)) :args (_let_31 true _let_30 false _let_29 false _let_28)) :args (false true _let_25 false _let_26 true _let_19)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)) _let_17 (tptp.aElement0 tptp.sz10) (forall ((W0 $$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)))) _let_16 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2)) (= (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))) _let_15 (forall ((W0 $$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 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2)) (= (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))) (forall ((W0 $$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)) (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 $$unsorted)) (=> (tptp.aElement0 W0) (tptp.aIdeal0 (tptp.slsdtgt0 W0)))) _let_14 _let_11 (and _let_10 (exists ((W0 $$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_10 (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 _let_9)) _let_8 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 11.77/12.03  )
% 11.77/12.03  % SZS output end Proof for RNG109+4
% 11.77/12.03  % cvc5---1.0.5 exiting
% 11.77/12.03  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------