%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : RNG121+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n021.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 75.40s 75.64s
% Output   : Proof 75.40s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : RNG121+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n021.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 02:18:12 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 75.40/75.64  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.bz1JOfylzj/cvc5---1.0.5_5174.p...
% 75.40/75.64  ------- get file name : TPTP file name is RNG121+1
% 75.40/75.64  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_5174.smt2...
% 75.40/75.64  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 75.40/75.64  --- Run --no-e-matching --full-saturate-quant at 5...
% 75.40/75.64  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 75.40/75.64  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 75.40/75.64  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 75.40/75.64  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 75.40/75.64  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 75.40/75.64  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 75.40/75.64  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 75.40/75.64  --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 75.40/75.64  --- Run --relevant-triggers --full-saturate-quant at 5...
% 75.40/75.64  --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 75.40/75.64  --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 75.40/75.64  % SZS status Theorem for RNG121+1
% 75.40/75.64  % SZS output start Proof for RNG121+1
% 75.40/75.64  (
% 75.40/75.64  (let ((_let_1 (not (tptp.aElementOf0 tptp.xb tptp.xI)))) (let ((_let_2 (tptp.sdtasdt0 tptp.xq tptp.xu))) (let ((_let_3 (= tptp.xr tptp.sz00))) (let ((_let_4 (tptp.sdtpldt0 _let_2 tptp.xr))) (let ((_let_5 (and (tptp.aElement0 tptp.xq) (tptp.aElement0 tptp.xr) (= tptp.xb _let_4) (or _let_3 (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu)))))) (let ((_let_6 (tptp.slsdtgt0 tptp.xb))) (let ((_let_7 (tptp.slsdtgt0 tptp.xa))) (let ((_let_8 (tptp.aElementOf0 tptp.sz00 _let_7))) (let ((_let_9 (and _let_8 (tptp.aElementOf0 tptp.xa _let_7) (tptp.aElementOf0 tptp.sz00 _let_6) (tptp.aElementOf0 tptp.xb _let_6)))) (let ((_let_10 (and (tptp.aIdeal0 tptp.xI) (= tptp.xI (tptp.sdtpldt1 _let_7 _let_6))))) (let ((_let_11 (tptp.aElement0 tptp.xa))) (let ((_let_12 (and _let_11 (tptp.aElement0 tptp.xb)))) (let ((_let_13 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (tptp.aIdeal0 (tptp.slsdtgt0 W0)))))) (let ((_let_14 (forall ((W0 $$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 $$unsorted)) (=> (tptp.aElement0 W2) (tptp.aElementOf0 (tptp.sdtasdt0 W2 W1) W0))))))))))) (let ((_let_15 (forall ((W0 $$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 $$unsorted)) (and (tptp.aElementOf0 W4 W0) (tptp.aElementOf0 W5 W1) (= (tptp.sdtpldt0 W4 W5) W3)))))))))))) (let ((_let_16 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))) (let ((_let_17 (forall ((W4 $$unsorted) (W5 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xq tptp.xu) tptp.xr))) (or (not (tptp.aElementOf0 W4 (tptp.slsdtgt0 tptp.xa))) (not (tptp.aElementOf0 W5 (tptp.slsdtgt0 _let_1))) (not (= (tptp.sdtpldt0 W4 W5) _let_1))))))) (let ((_let_18 (= _let_4 (tptp.sdtpldt0 tptp.sz00 _let_4)))) (let ((_let_19 (not _let_18))) (let ((_let_20 (tptp.slsdtgt0 _let_4))) (let ((_let_21 (tptp.aElementOf0 _let_4 _let_20))) (let ((_let_22 (not _let_21))) (let ((_let_23 (not _let_8))) (let ((_let_24 (or _let_23 _let_22 _let_19))) (let ((_let_25 (not _let_17))) (let ((_let_26 (tptp.sdtpldt1 _let_7 _let_20))) (let ((_let_27 (tptp.aElementOf0 _let_4 _let_26))) (let ((_let_28 (= _let_27 _let_25))) (let ((_let_29 (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 (tptp.sdtpldt1 (tptp.slsdtgt0 tptp.xa) (tptp.slsdtgt0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xq tptp.xu) tptp.xr)))) (not (forall ((W4 $$unsorted) (W5 $$unsorted)) (or (not (tptp.aElementOf0 W4 (tptp.slsdtgt0 tptp.xa))) (not (tptp.aElementOf0 W5 (tptp.slsdtgt0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xq tptp.xu) tptp.xr)))) (not (= W3 (tptp.sdtpldt0 W4 W5)))))))))) (let ((_let_30 (and (tptp.aSet0 _let_26) _let_29))) (let ((_let_31 (tptp.aSet0 _let_20))) (let ((_let_32 (not _let_31))) (let ((_let_33 (tptp.aSet0 _let_7))) (let ((_let_34 (not _let_33))) (let ((_let_35 (or _let_34 _let_32 _let_30))) (let ((_let_36 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1380 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSet0 W1)) (= (= (tptp.sdtpldt1 W0 W1) BOUND_VARIABLE_1380) (and (tptp.aSet0 BOUND_VARIABLE_1380) (forall ((W3 $$unsorted)) (= (not (forall ((W4 $$unsorted) (W5 $$unsorted)) (or (not (tptp.aElementOf0 W4 W0)) (not (tptp.aElementOf0 W5 W1)) (not (= W3 (tptp.sdtpldt0 W4 W5)))))) (tptp.aElementOf0 W3 BOUND_VARIABLE_1380))))))))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (and _let_31 (forall ((W1 $$unsorted) (BOUND_VARIABLE_1445 $$unsorted) (BOUND_VARIABLE_1438 $$unsorted)) (let ((_let_1 (tptp.slsdtgt0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xq tptp.xu) tptp.xr)))) (or (not (tptp.aElementOf0 W1 _let_1)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1438 _let_1)) (tptp.aElementOf0 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1438) _let_1)) (or (not (tptp.aElement0 BOUND_VARIABLE_1445)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1445 W1) _let_1))))))))) (let ((_let_39 (tptp.aIdeal0 _let_20))) (let ((_let_40 (= _let_39 _let_38))) (let ((_let_41 (forall ((W0 $$unsorted)) (= (tptp.aIdeal0 W0) (and (tptp.aSet0 W0) (forall ((W1 $$unsorted) (BOUND_VARIABLE_1445 $$unsorted) (BOUND_VARIABLE_1438 $$unsorted)) (or (not (tptp.aElementOf0 W1 W0)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1438 W0)) (tptp.aElementOf0 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1438) W0)) (or (not (tptp.aElement0 BOUND_VARIABLE_1445)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1445 W1) W0)))))))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (_let_41))) (let ((_let_44 ((tptp.aIdeal0 W0)))) (let ((_let_45 (tptp.aElement0 _let_4))) (let ((_let_46 (not _let_45))) (let ((_let_47 (or _let_46 _let_39))) (let ((_let_48 (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (tptp.aIdeal0 (tptp.slsdtgt0 W0)))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (_let_48))) (let ((_let_51 ((not (= (tptp.aElement0 W0) false))))) (let ((_let_52 (1))) (let ((_let_53 (AND_INTRO (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) :args (2)) (AND_ELIM (ASSUME :args (_let_10)) :args _let_52)))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO _let_53 :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (AND_ELIM _let_54 :args _let_52))) (let ((_let_56 (and _let_33 (forall ((W1 $$unsorted) (BOUND_VARIABLE_1445 $$unsorted) (BOUND_VARIABLE_1438 $$unsorted)) (let ((_let_1 (tptp.slsdtgt0 tptp.xa))) (or (not (tptp.aElementOf0 W1 _let_1)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1438 _let_1)) (tptp.aElementOf0 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1438) _let_1)) (or (not (tptp.aElement0 BOUND_VARIABLE_1445)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1445 W1) _let_1))))))))) (let ((_let_57 (tptp.aIdeal0 _let_7))) (let ((_let_58 (= _let_57 _let_56))) (let ((_let_59 (not _let_11))) (let ((_let_60 (or _let_59 _let_57))) (let ((_let_61 (0))) (let ((_let_62 (_let_29))) (let ((_let_63 (not _let_28))) (let ((_let_64 (not _let_24))) (let ((_let_65 (and (= _let_4 (tptp.sdtpldt0 _let_4 tptp.sz00)) _let_18))) (let ((_let_66 (or _let_46 _let_65))) (let ((_let_67 (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (= W0 (tptp.sdtpldt0 W0 tptp.sz00)) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO _let_53 :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (_let_17))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_70) :args (tptp.sz00 _let_4 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_70))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_24)) :args ((or _let_23 _let_22 _let_19 _let_64))) (AND_ELIM _let_69 :args _let_61) (AND_ELIM _let_69 :args (3)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_65 1)) :args ((or _let_18 (not _let_65)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_46 _let_65 (not _let_66)))) _let_55 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args (_let_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElement0 W0) false))))) :args (_let_67))) _let_68 :args (_let_66 false _let_67)) :args (_let_65 false _let_45 false _let_66)) :args (_let_18 false _let_65)) :args (_let_64 false _let_8 false _let_21 false _let_18)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_28)) (CONG (REFL :args (_let_63)) (REFL :args (_let_27)) (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_17))) :args (or))) :args ((or _let_27 _let_17 _let_63))) (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO _let_53 :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_62) :args (_let_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aElementOf0 W3 _let_26)))) :args _let_62))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_30 1)) :args ((or _let_29 (not _let_30)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_34 _let_32 _let_30 (not _let_35)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_56 0)) :args ((or _let_33 (not _let_56)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_58)) :args ((or (not _let_57) _let_56 (not _let_58)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_59 _let_57 (not _let_60)))) (AND_ELIM _let_54 :args _let_61) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (tptp.xa QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_51)) :args _let_50)) _let_49 :args (_let_60 false _let_48)) :args (_let_57 false _let_11 false _let_60)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (_let_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_44)) :args _let_43)) _let_42 :args (_let_58 false _let_41)) :args (_let_56 false _let_57 false _let_58)) :args (_let_33 false _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_38 0)) :args ((or _let_31 (not _let_38)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_40)) :args ((or (not _let_39) _let_38 (not _let_40)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_46 _let_39 (not _let_47)))) _let_55 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (_let_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_51)) :args _let_50)) _let_49 :args (_let_47 false _let_48)) :args (_let_39 false _let_45 false _let_47)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (_let_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_44)) :args _let_43)) _let_42 :args (_let_40 false _let_41)) :args (_let_38 false _let_39 false _let_40)) :args (_let_31 false _let_38)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_37 :args (_let_7 _let_20 _let_26 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_36)))) _let_37 :args (_let_35 false _let_36)) :args (_let_30 false _let_33 false _let_31 false _let_35)) :args (_let_29 false _let_30)) :args (_let_28 false _let_29)) :args (_let_17 true _let_27 false _let_28)) :args (false true _let_24 false _let_17)) :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 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1)))) (forall ((W0 $$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))))) _let_16 (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 $$unsorted)) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 W0)))) (= W0 W1)))) _let_15 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aSet0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtasasdt0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aElementOf0 W3 W0) (tptp.aElementOf0 W3 W1))))))))) _let_14 (forall ((W0 $$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 $$unsorted)) (and (tptp.aElement0 W3) (= (tptp.sdtasdt0 W0 W3) W2)))))))))) _let_13 _let_12 (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00))) (tptp.aGcdOfAnd0 tptp.xc tptp.xa tptp.xb) _let_10 _let_9 (exists ((W0 $$unsorted)) (and (tptp.aElementOf0 W0 (tptp.sdtpldt1 (tptp.slsdtgt0 tptp.xa) (tptp.slsdtgt0 tptp.xb))) (not (= W0 tptp.sz00)))) (and (tptp.aElementOf0 tptp.xu tptp.xI) (not (= tptp.xu tptp.sz00)) (forall ((W0 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.xI) (not (= W0 tptp.sz00))) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu)))))) (not (and (tptp.aDivisorOf0 tptp.xu tptp.xa) (tptp.aDivisorOf0 tptp.xu tptp.xb))) (exists ((W0 $$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))) (not (tptp.doDivides0 tptp.xu tptp.xb)) _let_5 (not _let_3) (tptp.aElementOf0 (tptp.smndt0 _let_2) tptp.xI) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 75.40/75.65  )
% 75.40/75.65  % SZS output end Proof for RNG121+1
% 75.40/75.65  % cvc5---1.0.5 exiting
% 75.40/75.65  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------