TSTP Solution File: SET811+4 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET811+4 : TPTP v8.1.2. Released v3.2.0.
% 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 14:40:25 EDT 2023
% Result : Theorem 0.21s 0.64s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET811+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 12:23:47 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.54 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.64 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.zxeSTjyOjX/cvc5---1.0.5_1375.p...
% 0.21/0.64 ------- get file name : TPTP file name is SET811+4
% 0.21/0.64 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_1375.smt2...
% 0.21/0.64 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.64 % SZS status Theorem for SET811+4
% 0.21/0.64 % SZS output start Proof for SET811+4
% 0.21/0.64 (
% 0.21/0.64 (let ((_let_1 (not (forall ((A $$unsorted)) (=> (tptp.member A tptp.on) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.equal_set X (tptp.initial_segment X tptp.member_predicate A))))))))) (let ((_let_2 (forall ((X $$unsorted) (R $$unsorted) (A $$unsorted) (Y $$unsorted)) (= (tptp.member Y (tptp.initial_segment X R A)) (and (tptp.member Y A) (tptp.apply R Y X)))))) (let ((_let_3 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.apply tptp.member_predicate X Y) (tptp.member X Y))))) (let ((_let_4 (forall ((A $$unsorted)) (= (tptp.member A tptp.on) (and (tptp.set A) (tptp.strict_well_order tptp.member_predicate A) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.subset X A)))))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_7 (tptp.apply tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_8 (and (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_7))) (let ((_let_9 (tptp.initial_segment SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_10 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_9))) (let ((_let_11 (= _let_10 _let_8))) (let ((_let_12 (_let_2))) (let ((_let_13 (ASSUME :args _let_12))) (let ((_let_14 ((tptp.member Y (tptp.initial_segment X R A))))) (let ((_let_15 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_16 (not _let_10))) (let ((_let_17 (or _let_16 _let_15))) (let ((_let_18 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.initial_segment SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))) (let ((_let_19 (not _let_17))) (let ((_let_20 (tptp.subset _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_21 (= _let_20 _let_18))) (let ((_let_22 (not _let_18))) (let ((_let_23 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_24 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_25 (_let_23))) (let ((_let_26 ((tptp.subset A B)))) (let ((_let_27 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_9))) (let ((_let_28 (and _let_27 _let_20))) (let ((_let_29 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (tptp.member X (tptp.initial_segment SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))))) (let ((_let_30 (= _let_27 _let_29))) (let ((_let_31 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_9))) (let ((_let_32 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_33 (not _let_32))) (let ((_let_34 (or _let_33 _let_31))) (let ((_let_35 (tptp.apply tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_36 (= _let_32 _let_35))) (let ((_let_37 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_38 (or _let_33 _let_37))) (let ((_let_39 (and _let_37 _let_35))) (let ((_let_40 (= _let_31 _let_39))) (let ((_let_41 (or))) (let ((_let_42 (_let_3))) (let ((_let_43 (ASSUME :args _let_42))) (let ((_let_44 ((tptp.member X Y)))) (let ((_let_45 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_46 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_47 (= _let_46 _let_45))) (let ((_let_48 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_49 (not _let_48))) (let ((_let_50 (or _let_49 _let_46))) (let ((_let_51 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.subset X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_52 (and (tptp.set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.strict_well_order tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_51))) (let ((_let_53 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.on))) (let ((_let_54 (= _let_53 _let_52))) (let ((_let_55 (forall ((A $$unsorted)) (= (tptp.member A tptp.on) (and (tptp.set A) (tptp.strict_well_order tptp.member_predicate A) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.subset X A)))))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (tptp.equal_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_9))) (let ((_let_58 (not _let_53))) (let ((_let_59 (or _let_58 _let_49 _let_57))) (let ((_let_60 (forall ((A $$unsorted) (BOUND_VARIABLE_968 $$unsorted)) (or (not (tptp.member A tptp.on)) (not (tptp.member BOUND_VARIABLE_968 A)) (tptp.equal_set BOUND_VARIABLE_968 (tptp.initial_segment BOUND_VARIABLE_968 tptp.member_predicate A)))))) (let ((_let_61 (not _let_59))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (not _let_60))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_62) :args (_let_63))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_63) _let_60))) (REFL :args (_let_61)) :args _let_41)) _let_62 :args (_let_61 true _let_60)))) (let ((_let_65 (REFL :args (_let_59)))) (let ((_let_66 (_let_51))) (let ((_let_67 (_let_45))) (let ((_let_68 (not _let_29))) (let ((_let_69 (_let_68))) (let ((_let_70 (= _let_57 _let_28))) (let ((_let_71 (not _let_28))) (let ((_let_72 (_let_5))) (let ((_let_73 (ASSUME :args _let_72))) (let ((_let_74 (_let_22))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_74)) :args _let_74)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_18))) (REFL :args (_let_19)) :args _let_41)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_21)) :args ((or _let_20 _let_22 (not _let_21)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_70)) :args ((or _let_57 _let_71 (not _let_70)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_59 2)) _let_64 :args ((not _let_57) true _let_59)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equal_set A B)))) :args _let_72)) _let_73 :args (_let_70 false _let_5)) :args (_let_71 true _let_57 false _let_70)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_30)) :args ((or _let_27 _let_68 (not _let_30)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_69)) :args _let_69)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_68) _let_29))) (REFL :args ((not _let_34))) :args _let_41)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_39)) :args ((or _let_39 (not _let_35) (not _let_37)))) (REORDERING (CNF_EQUIV_POS2 :args (_let_40)) :args ((or _let_31 (not _let_39) (not _let_40)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING _let_14)) :args _let_12)) _let_13 :args (_let_40 false _let_2)) (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_33 _let_37 (not _let_38)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_67) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) false))))) :args _let_67)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_47)) :args ((or (not _let_46) _let_45 (not _let_47)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_49 _let_46 (not _let_50)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_59 1)) (CONG _let_65 (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_48))) :args _let_41)) :args ((or _let_48 _let_59))) _let_64 :args (_let_48 true _let_59)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_66) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) false))))) :args _let_66)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_52 2)) :args ((or _let_51 (not _let_52)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_54)) :args ((or _let_58 _let_52 (not _let_54)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_59 0)) (CONG _let_65 (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_53))) :args _let_41)) :args ((or _let_53 _let_59))) _let_64 :args (_let_53 true _let_59)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.member A tptp.on)))) :args (_let_55))) _let_56 :args (_let_54 false _let_55)) :args (_let_52 false _let_53 false _let_54)) :args (_let_51 false _let_52)) :args (_let_50 false _let_51)) :args (_let_46 false _let_48 false _let_50)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_26)) :args _let_25)) _let_24 :args (_let_47 false _let_23)) :args (_let_45 false _let_46 false _let_47)) :args (_let_38 false _let_45)) (REORDERING (CNF_EQUIV_POS1 :args (_let_36)) :args ((or _let_33 _let_35 (not _let_36)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_43 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_44)) :args _let_42))) _let_43 :args (_let_36 false _let_3)) (CNF_OR_NEG :args (_let_34 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 0)) (CONG (REFL :args (_let_34)) (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_41)) :args ((or _let_32 _let_34))) :args (_let_34 true _let_39 false _let_40 false _let_37 false _let_38 false _let_35 false _let_36 true _let_31 false _let_32)) :args (_let_29 false _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_26)) :args _let_25)) _let_24 :args (_let_30 false _let_23)) :args (_let_27 false _let_29 false _let_30)) :args ((not _let_20) true _let_28 false _let_27)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (_let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_26)) :args _let_25)) _let_24 :args (_let_21 false _let_23)) :args (_let_22 true _let_20 false _let_21)) :args (_let_19 true _let_18)))) (let ((_let_76 (= _let_15 _let_7))) (let ((_let_77 (not _let_7))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_8 1)) :args ((or _let_7 (not _let_8)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_76)) :args ((or _let_15 _let_77 (not _let_76)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_17 1)) _let_75 :args ((not _let_15) true _let_17)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_43 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_44)) :args _let_42))) _let_43 :args (_let_76 false _let_3)) :args (_let_77 true _let_15 false _let_76)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_11)) :args ((or _let_16 _let_8 (not _let_11)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_17 0)) (CONG (REFL :args (_let_17)) (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_10))) :args _let_41)) :args ((or _let_10 _let_17))) _let_75 :args (_let_10 true _let_17)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING _let_14)) :args _let_12)) _let_13 :args (_let_11 false _let_2)) :args (_let_8 false _let_10 false _let_11)) :args (false true _let_7 false _let_8)) :args (_let_6 _let_5 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.power_set A)) (tptp.subset X A))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.intersection A B)) (and (tptp.member X A) (tptp.member X B)))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.union A B)) (or (tptp.member X A) (tptp.member X B)))) (forall ((X $$unsorted)) (not (tptp.member X tptp.empty_set))) (forall ((B $$unsorted) (A $$unsorted) (E $$unsorted)) (= (tptp.member B (tptp.difference E A)) (and (tptp.member B E) (not (tptp.member B A))))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.singleton A)) (= X A))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.unordered_pair A B)) (or (= X A) (= X B)))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.sum A)) (exists ((Y $$unsorted)) (and (tptp.member Y A) (tptp.member X Y))))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.product A)) (forall ((Y $$unsorted)) (=> (tptp.member Y A) (tptp.member X Y))))) _let_4 (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.strict_well_order R E) (and (tptp.strict_order R E) (forall ((A $$unsorted)) (=> (and (tptp.subset A E) (exists ((X $$unsorted)) (tptp.member X A))) (exists ((Y $$unsorted)) (tptp.least Y R A))))))) (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.least M R E) (and (tptp.member M E) (forall ((X $$unsorted)) (=> (tptp.member X E) (or (= M X) (tptp.apply R M X))))))) _let_3 (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.strict_order R E) (and (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X E) (tptp.member Y E)) (not (and (tptp.apply R X Y) (tptp.apply R Y X))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.member X E) (tptp.member Y E) (tptp.member Z E)) (=> (and (tptp.apply R X Y) (tptp.apply R Y Z)) (tptp.apply R X Z))))))) (forall ((X $$unsorted)) (=> (tptp.set X) (forall ((Y $$unsorted)) (=> (tptp.member Y X) (tptp.set Y))))) _let_2 (forall ((A $$unsorted) (X $$unsorted)) (= (tptp.member X (tptp.suc A)) (tptp.member X (tptp.union A (tptp.singleton A))))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.65 )
% 0.21/0.65 % SZS output end Proof for SET811+4
% 0.21/0.65 % cvc5---1.0.5 exiting
% 0.21/0.65 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------