TSTP Solution File: RNG099+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : RNG099+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n010.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 13:50:02 EDT 2023
% Result : Theorem 0.20s 0.62s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : RNG099+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n010.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 01:37:35 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.48 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.62 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.ddkvxAvcLN/cvc5---1.0.5_29316.p...
% 0.20/0.62 ------- get file name : TPTP file name is RNG099+1
% 0.20/0.62 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_29316.smt2...
% 0.20/0.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.62 % SZS status Theorem for RNG099+1
% 0.20/0.62 % SZS output start Proof for RNG099+1
% 0.20/0.62 (
% 0.20/0.62 (let ((_let_1 (not (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI) (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ)))))) (let ((_let_2 (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xy)) tptp.xJ))) (let ((_let_3 (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xx)) tptp.xI))) (let ((_let_4 (tptp.sdtasdt0 tptp.xx tptp.xb))) (let ((_let_5 (tptp.sdtasdt0 tptp.xy tptp.xa))) (let ((_let_6 (tptp.sdtpldt0 _let_5 _let_4))) (let ((_let_7 (= tptp.xw _let_6))) (let ((_let_8 (tptp.aElementOf0 tptp.xb tptp.xJ))) (let ((_let_9 (tptp.aElementOf0 tptp.xa tptp.xI))) (let ((_let_10 (and _let_9 _let_8 (= (tptp.sdtpldt0 tptp.xa tptp.xb) tptp.sz10)))) (let ((_let_11 (tptp.aElement0 tptp.xy))) (let ((_let_12 (tptp.aElement0 tptp.xx))) (let ((_let_13 (and _let_12 _let_11))) (let ((_let_14 (tptp.aIdeal0 tptp.xJ))) (let ((_let_15 (tptp.aIdeal0 tptp.xI))) (let ((_let_16 (and _let_15 _let_14))) (let ((_let_17 (forall ((W0 $$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)))))) (let ((_let_18 (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_19 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))))) (let ((_let_20 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_21 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_22 (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ)))))) (let ((_let_23 (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xy tptp.xJ))) (let ((_let_24 (not _let_23))) (let ((_let_25 (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xx tptp.xI))) (let ((_let_26 (not _let_25))) (let ((_let_27 (tptp.aElement0 tptp.xw))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or _let_28 _let_26 _let_24))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (not _let_29))) (let ((_let_32 (= _let_2 _let_23))) (let ((_let_33 (not _let_14))) (let ((_let_34 (not _let_11))) (let ((_let_35 (or _let_28 _let_34 _let_33 _let_32))) (let ((_let_36 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.aIdeal0 W2)) (= (tptp.sdteqdtlpzmzozddtrp0 W0 W1 W2) (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 W1)) W2)))))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (_let_36))) (let ((_let_39 ((tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 W1)) W2)))) (let ((_let_40 (tptp.aElement0 _let_6))) (let ((_let_41 (tptp.aElement0 _let_4))) (let ((_let_42 (not _let_41))) (let ((_let_43 (tptp.aElement0 _let_5))) (let ((_let_44 (not _let_43))) (let ((_let_45 (or _let_44 _let_42 _let_40))) (let ((_let_46 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (tptp.aElement0 tptp.xb))) (let ((_let_49 (not _let_48))) (let ((_let_50 (not _let_12))) (let ((_let_51 (or _let_50 _let_49 _let_41))) (let ((_let_52 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (_let_52))) (let ((_let_55 ((tptp.sdtasdt0 W0 W1)))) (let ((_let_56 (not _let_8))) (let ((_let_57 (tptp.aSet0 tptp.xJ))) (let ((_let_58 (not _let_57))) (let ((_let_59 (or _let_58 _let_56 _let_48))) (let ((_let_60 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1092 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1092 W0)) (tptp.aElement0 BOUND_VARIABLE_1092))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (_let_60))) (let ((_let_63 ((not (= (tptp.aElementOf0 BOUND_VARIABLE_1092 W0) false))))) (let ((_let_64 (and _let_57 (forall ((W1 $$unsorted) (BOUND_VARIABLE_1216 $$unsorted) (BOUND_VARIABLE_1209 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xJ)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1209 tptp.xJ)) (tptp.aElementOf0 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1209) tptp.xJ)) (or (not (tptp.aElement0 BOUND_VARIABLE_1216)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1216 W1) tptp.xJ)))))))) (let ((_let_65 (= _let_14 _let_64))) (let ((_let_66 (forall ((W0 $$unsorted)) (= (tptp.aIdeal0 W0) (and (tptp.aSet0 W0) (forall ((W1 $$unsorted) (BOUND_VARIABLE_1216 $$unsorted) (BOUND_VARIABLE_1209 $$unsorted)) (or (not (tptp.aElementOf0 W1 W0)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1209 W0)) (tptp.aElementOf0 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1209) W0)) (or (not (tptp.aElement0 BOUND_VARIABLE_1216)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1216 W1) W0)))))))))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (_let_66))) (let ((_let_69 ((tptp.aIdeal0 W0)))) (let ((_let_70 (1))) (let ((_let_71 (ASSUME :args (_let_16)))) (let ((_let_72 (AND_ELIM _let_71 :args _let_70))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (0))) (let ((_let_75 (ASSUME :args (_let_13)))) (let ((_let_76 (AND_ELIM _let_75 :args _let_74))) (let ((_let_77 (tptp.aElement0 tptp.xa))) (let ((_let_78 (not _let_77))) (let ((_let_79 (or _let_34 _let_78 _let_43))) (let ((_let_80 (not _let_9))) (let ((_let_81 (tptp.aSet0 tptp.xI))) (let ((_let_82 (not _let_81))) (let ((_let_83 (or _let_82 _let_80 _let_77))) (let ((_let_84 (and _let_81 (forall ((W1 $$unsorted) (BOUND_VARIABLE_1216 $$unsorted) (BOUND_VARIABLE_1209 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xI)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1209 tptp.xI)) (tptp.aElementOf0 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1209) tptp.xI)) (or (not (tptp.aElement0 BOUND_VARIABLE_1216)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1216 W1) tptp.xI)))))))) (let ((_let_85 (= _let_15 _let_84))) (let ((_let_86 (AND_ELIM _let_71 :args _let_74))) (let ((_let_87 (not _let_15))) (let ((_let_88 (AND_ELIM _let_75 :args _let_70))) (let ((_let_89 (ASSUME :args (_let_7)))) (let ((_let_90 (and _let_7 _let_40))) (let ((_let_91 (ASSUME :args (_let_40)))) (let ((_let_92 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_90)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_91 _let_89) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM (SYMM _let_89)) :args (APPLY_UF tptp.aElement0)) (TRUE_INTRO _let_91))) :args (_let_40 _let_7))) :args (_let_7 _let_40))) :args (true _let_90)) :args ((or (not _let_7) _let_27 (not _let_40)))) _let_89 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_45)) :args ((or _let_44 _let_42 _let_40 (not _let_45)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_79)) :args ((or _let_34 _let_43 _let_78 (not _let_79)))) _let_88 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_83)) :args ((or _let_80 _let_77 _let_82 (not _let_83)))) (AND_ELIM _let_73 :args _let_74) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_84 0)) :args ((or _let_81 (not _let_84)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_85)) :args ((or _let_87 _let_84 (not _let_85)))) _let_86 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_67 :args (tptp.xI QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_69)) :args _let_68)) _let_67 :args (_let_85 false _let_66)) :args (_let_84 false _let_15 false _let_85)) :args (_let_81 false _let_84)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (tptp.xI tptp.xa QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_63)) :args _let_62)) _let_61 :args (_let_83 false _let_60)) :args (_let_77 false _let_9 false _let_81 false _let_83)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (tptp.xy tptp.xa QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_55)) :args _let_54)) _let_53 :args (_let_79 false _let_52)) :args (_let_43 false _let_11 false _let_77 false _let_79)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_50 _let_41 _let_49 (not _let_51)))) _let_76 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_56 _let_48 _let_58 (not _let_59)))) (AND_ELIM _let_73 :args _let_70) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_64 0)) :args ((or _let_57 (not _let_64)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_65)) :args ((or _let_33 _let_64 (not _let_65)))) _let_72 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_67 :args (tptp.xJ QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_69)) :args _let_68)) _let_67 :args (_let_65 false _let_66)) :args (_let_64 false _let_14 false _let_65)) :args (_let_57 false _let_64)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (tptp.xJ tptp.xb QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_63)) :args _let_62)) _let_61 :args (_let_59 false _let_60)) :args (_let_48 false _let_8 false _let_57 false _let_59)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (tptp.xx tptp.xb QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_55)) :args _let_54)) _let_53 :args (_let_51 false _let_52)) :args (_let_41 false _let_12 false _let_48 false _let_51)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (_let_5 _let_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtpldt0 W0 W1)))) :args (_let_46))) _let_47 :args (_let_45 false _let_46)) :args (_let_40 false _let_43 false _let_41 false _let_45)) :args (_let_27 false _let_7 false _let_40)))) (let ((_let_93 (= _let_3 _let_25))) (let ((_let_94 (or _let_28 _let_50 _let_87 _let_93))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (tptp.xw QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElement0 W0) false))))) :args (_let_22))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_28 _let_26 _let_24 _let_31))) _let_92 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_93)) :args ((or (not _let_3) _let_25 (not _let_93)))) (ASSUME :args (_let_3)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_94)) :args ((or _let_87 _let_50 _let_28 _let_93 (not _let_94)))) _let_86 _let_76 _let_92 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_37 :args (tptp.xw tptp.xx tptp.xI QUANTIFIERS_INST_E_MATCHING _let_39)) :args _let_38))) _let_37 :args (_let_94 false _let_36)) :args (_let_93 false _let_15 false _let_12 false _let_27 false _let_94)) :args (_let_25 false _let_3 false _let_93)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_32)) :args ((or (not _let_2) _let_23 (not _let_32)))) (ASSUME :args (_let_2)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_33 _let_34 _let_28 _let_32 (not _let_35)))) _let_72 _let_88 _let_92 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_37 :args (tptp.xw tptp.xy tptp.xJ QUANTIFIERS_INST_E_MATCHING _let_39)) :args _let_38))) _let_37 :args (_let_35 false _let_36)) :args (_let_32 false _let_14 false _let_11 false _let_27 false _let_35)) :args (_let_23 false _let_2 false _let_32)) :args (_let_31 false _let_27 false _let_25 false _let_23)) _let_30 :args (false true _let_29 false _let_22)) :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)))) _let_21 _let_20 (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))))) (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 $$unsorted)) (=> (tptp.aSet0 W0) true)) _let_19 (forall ((W0 $$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 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aElementOf0 W3 W0) (tptp.aElementOf0 W3 W1))))))))) _let_18 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aIdeal0 W0) (tptp.aIdeal0 W1)) (tptp.aIdeal0 (tptp.sdtpldt1 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aIdeal0 W0) (tptp.aIdeal0 W1)) (tptp.aIdeal0 (tptp.sdtasasdt0 W0 W1)))) _let_17 _let_16 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (tptp.aElementOf0 W0 (tptp.sdtpldt1 tptp.xI tptp.xJ)))) _let_13 _let_10 _let_7 _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.63 )
% 0.20/0.63 % SZS output end Proof for RNG099+1
% 0.20/0.63 % cvc5---1.0.5 exiting
% 0.20/0.63 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------