%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : ITP004_2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n008.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 03:13:57 EDT 2023

% Result   : Theorem 2.33s 2.56s
% Output   : Proof 2.36s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : ITP004_2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.00/0.11  % Command    : do_cvc5 %s %d
% 0.10/0.32  % Computer : n008.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit   : 300
% 0.10/0.32  % WCLimit    : 300
% 0.10/0.32  % DateTime   : Sun Aug 27 12:20:02 EDT 2023
% 0.10/0.32  % CPUTime    : 
% 0.16/0.43  %----Proving TF0_NAR, FOF, or CNF
% 2.33/2.56  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.XwDUFXRDLg/cvc5---1.0.5_19490.p...
% 2.33/2.56  ------- get file name : TPTP file name is ITP004_2
% 2.33/2.56  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_19490.smt2...
% 2.33/2.56  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 2.33/2.56  % SZS status Theorem for ITP004_2
% 2.33/2.56  % SZS output start Proof for ITP004_2
% 2.33/2.56  (
% 2.33/2.56  (let ((_let_1 (not (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (tptp.mem V0s (tptp.arr A_27a tptp.bool)) (tptp.p (tptp.ap (tptp.ap (tptp.c_2Epred__set_2ESUBSET A_27a) (tptp.ap (tptp.c_2Epred__set_2EREST A_27a) V0s)) V0s))))))) (let ((_let_2 (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (tptp.mem V0s (tptp.arr A_27a tptp.bool)) (= (tptp.ap (tptp.c_2Epred__set_2EREST A_27a) V0s) (tptp.ap (tptp.ap (tptp.c_2Epred__set_2EDELETE A_27a) V0s) (tptp.ap (tptp.c_2Epred__set_2ECHOICE A_27a) V0s))))))) (let ((_let_3 (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (tptp.mem V0s (tptp.arr A_27a tptp.bool)) (forall ((V1x $$unsorted)) (=> (tptp.mem V1x A_27a) (forall ((V2y $$unsorted)) (let ((_let_1 (tptp.ap (tptp.c_2Ebool_2EIN A_27a) V1x))) (=> (tptp.mem V2y A_27a) (= (tptp.p (tptp.ap _let_1 (tptp.ap (tptp.ap (tptp.c_2Epred__set_2EDELETE A_27a) V0s) V2y))) (and (tptp.p (tptp.ap _let_1 V0s)) (not (= V1x V2y))))))))))))) (let ((_let_4 (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (tptp.mem V0s (tptp.arr A_27a tptp.bool)) (forall ((V1t $$unsorted)) (=> (tptp.mem V1t (tptp.arr A_27a tptp.bool)) (= (tptp.p (tptp.ap (tptp.ap (tptp.c_2Epred__set_2ESUBSET A_27a) V0s) V1t)) (forall ((V2x $$unsorted)) (let ((_let_1 (tptp.ap (tptp.c_2Ebool_2EIN A_27a) V2x))) (=> (tptp.mem V2x A_27a) (=> (tptp.p (tptp.ap _let_1 V0s)) (tptp.p (tptp.ap _let_1 V1t))))))))))))) (let ((_let_5 (forall ((A_27a tptp.del)) (let ((_let_1 (tptp.arr A_27a tptp.bool))) (tptp.mem (tptp.c_2Epred__set_2EREST A_27a) (tptp.arr _let_1 _let_1)))))) (let ((_let_6 (forall ((A_27a tptp.del)) (tptp.mem (tptp.c_2Epred__set_2ECHOICE A_27a) (tptp.arr (tptp.arr A_27a tptp.bool) A_27a))))) (let ((_let_7 (tptp.arr tptp.bool tptp.bool))) (let ((_let_8 (tptp.arr tptp.bool _let_7))) (let ((_let_9 (forall ((A tptp.del) (B tptp.del) (F $$unsorted)) (=> (tptp.mem F (tptp.arr A B)) (forall ((X $$unsorted)) (=> (tptp.mem X A) (tptp.mem (tptp.ap F X) B))))))) (let ((_let_10 (tptp.c_2Epred__set_2ECHOICE SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_11 (tptp.ap _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_12 (tptp.ap (tptp.ap (tptp.c_2Epred__set_2EDELETE SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) _let_11))) (let ((_let_13 (tptp.c_2Epred__set_2EREST SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_14 (tptp.ap _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_15 (= _let_14 _let_12))) (let ((_let_16 (tptp.ap (tptp.c_2Ebool_2EIN SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_45))) (let ((_let_17 (tptp.p (tptp.ap _let_16 _let_14)))) (let ((_let_18 (tptp.p (tptp.ap _let_16 _let_12)))) (let ((_let_19 (tptp.arr SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.bool))) (let ((_let_20 (tptp.mem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_19))) (let ((_let_21 (not _let_20))) (let ((_let_22 (or _let_21 _let_15))) (let ((_let_23 (forall ((A_27a tptp.del) (V0s $$unsorted)) (or (not (tptp.mem V0s (tptp.arr A_27a tptp.bool))) (= (tptp.ap (tptp.c_2Epred__set_2EREST A_27a) V0s) (tptp.ap (tptp.ap (tptp.c_2Epred__set_2EDELETE A_27a) V0s) (tptp.ap (tptp.c_2Epred__set_2ECHOICE A_27a) V0s))))))) (let ((_let_24 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_25 (tptp.p (tptp.ap (tptp.ap (tptp.c_2Epred__set_2ESUBSET SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_14) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_26 (or _let_21 _let_25))) (let ((_let_27 (forall ((A_27a tptp.del) (V0s $$unsorted)) (or (not (tptp.mem V0s (tptp.arr A_27a tptp.bool))) (tptp.p (tptp.ap (tptp.ap (tptp.c_2Epred__set_2ESUBSET A_27a) (tptp.ap (tptp.c_2Epred__set_2EREST A_27a) V0s)) V0s)))))) (let ((_let_28 (not _let_26))) (let ((_let_29 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_30 (or))) (let ((_let_31 (not _let_27))) (let ((_let_32 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_29) :args (_let_31))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_27))) (REFL :args (_let_28)) :args _let_30)) _let_29 :args (_let_28 true _let_27)))) (let ((_let_33 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 0)) (CONG (REFL :args (_let_26)) (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_30)) :args ((or _let_20 _let_26))) _let_32 :args (_let_20 true _let_26)))) (let ((_let_34 (tptp.p (tptp.ap _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_35 (not _let_17))) (let ((_let_36 (tptp.mem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_45 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_37 _let_35 _let_34))) (let ((_let_39 (forall ((V2x $$unsorted)) (let ((_let_1 (tptp.ap (tptp.c_2Ebool_2EIN SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) V2x))) (or (not (tptp.mem V2x SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.p (tptp.ap _let_1 (tptp.ap (tptp.c_2Epred__set_2EREST SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (tptp.p (tptp.ap _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))))) (let ((_let_40 (not _let_38))) (let ((_let_41 (= _let_25 _let_39))) (let ((_let_42 (not _let_39))) (let ((_let_43 (tptp.mem _let_14 _let_19))) (let ((_let_44 (not _let_43))) (let ((_let_45 (or _let_44 _let_21 _let_41))) (let ((_let_46 (forall ((A_27a tptp.del) (V0s $$unsorted) (BOUND_VARIABLE_1163 $$unsorted)) (let ((_let_1 (tptp.arr A_27a tptp.bool))) (or (not (tptp.mem V0s _let_1)) (not (tptp.mem BOUND_VARIABLE_1163 _let_1)) (= (tptp.p (tptp.ap (tptp.ap (tptp.c_2Epred__set_2ESUBSET A_27a) V0s) BOUND_VARIABLE_1163)) (forall ((V2x $$unsorted)) (let ((_let_1 (tptp.ap (tptp.c_2Ebool_2EIN A_27a) V2x))) (or (not (tptp.mem V2x A_27a)) (not (tptp.p (tptp.ap _let_1 V0s))) (tptp.p (tptp.ap _let_1 BOUND_VARIABLE_1163))))))))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (tptp.mem _let_13 (tptp.arr _let_19 _let_19)))) (let ((_let_49 (not _let_48))) (let ((_let_50 (or _let_49 _let_21 _let_43))) (let ((_let_51 (forall ((A tptp.del) (B tptp.del) (F $$unsorted) (BOUND_VARIABLE_961 $$unsorted)) (or (not (tptp.mem F (tptp.arr A B))) (not (tptp.mem BOUND_VARIABLE_961 A)) (tptp.mem (tptp.ap F BOUND_VARIABLE_961) B))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (_let_51))) (let ((_let_54 (tptp.arr A B))) (let ((_let_55 (_let_5))) (let ((_let_56 (ASSUME :args _let_55))) (let ((_let_57 (_let_42))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_57)) :args _let_57)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_39))) (REFL :args (_let_40)) :args _let_30)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_41)) :args ((or _let_25 _let_42 (not _let_41)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_26 1)) _let_32 :args ((not _let_25) true _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_45)) :args ((or _let_21 _let_44 _let_41 (not _let_45)))) _let_33 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_21 _let_43 _let_49 (not _let_50)))) _let_33 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_2Epred__set_2EREST A_27a)))) :args _let_55)) _let_56 :args (_let_48 false _let_5)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (_let_19 _let_19 _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING (_let_54 (not (= (tptp.mem (tptp.ap F BOUND_VARIABLE_961) B) true))))) :args _let_53)) _let_52 :args (_let_50 false _let_51)) :args (_let_43 false _let_20 false _let_48 false _let_50)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((tptp.ap (tptp.ap (tptp.c_2Epred__set_2ESUBSET A_27a) V0s) BOUND_VARIABLE_1163)))) :args (_let_46))) _let_47 :args (_let_45 false _let_46)) :args (_let_41 false _let_20 false _let_43 false _let_45)) :args (_let_42 true _let_25 false _let_41)) :args (_let_40 true _let_39)))) (let ((_let_59 (REFL :args (_let_38)))) (let ((_let_60 (and _let_34 (not (= _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_45))))) (let ((_let_61 (= _let_18 _let_60))) (let ((_let_62 (not _let_18))) (let ((_let_63 (tptp.mem _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_64 (not _let_63))) (let ((_let_65 (or _let_21 _let_37 _let_64 _let_61))) (let ((_let_66 (forall ((A_27a tptp.del) (V0s $$unsorted) (BOUND_VARIABLE_1213 $$unsorted) (BOUND_VARIABLE_1211 $$unsorted)) (let ((_let_1 (tptp.ap (tptp.c_2Ebool_2EIN A_27a) BOUND_VARIABLE_1211))) (or (not (tptp.mem V0s (tptp.arr A_27a tptp.bool))) (not (tptp.mem BOUND_VARIABLE_1211 A_27a)) (not (tptp.mem BOUND_VARIABLE_1213 A_27a)) (= (tptp.p (tptp.ap _let_1 (tptp.ap (tptp.ap (tptp.c_2Epred__set_2EDELETE A_27a) V0s) BOUND_VARIABLE_1213))) (and (tptp.p (tptp.ap _let_1 V0s)) (not (= BOUND_VARIABLE_1211 BOUND_VARIABLE_1213))))))))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (tptp.mem _let_10 (tptp.arr _let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_69 (not _let_68))) (let ((_let_70 (or _let_69 _let_21 _let_63))) (let ((_let_71 (_let_6))) (let ((_let_72 (ASSUME :args _let_71))) (let ((_let_73 (not _let_60))) (let ((_let_74 (and _let_15 _let_17))) (let ((_let_75 (ASSUME :args (_let_17)))) (let ((_let_76 (ASSUME :args (_let_15)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_74)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_75 _let_76) (SCOPE (TRUE_ELIM (TRANS (CONG (CONG (REFL :args (_let_16)) (SYMM _let_76) :args (APPLY_UF tptp.ap)) :args (APPLY_UF tptp.p)) (TRUE_INTRO _let_75))) :args (_let_17 _let_15))) :args (_let_15 _let_17))) :args (true _let_74)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_61)) :args ((or _let_60 _let_62 (not _let_61)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_60 0)) :args ((or _let_34 _let_73))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_38 2)) _let_58 :args ((not _let_34) true _let_38)) :args (_let_73 true _let_34)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_65)) :args ((or _let_21 _let_64 _let_37 _let_61 (not _let_65)))) _let_33 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_21 _let_69 _let_63 (not _let_70)))) _let_33 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.arr A_27a tptp.bool)))) :args _let_71)) _let_72 :args (_let_68 false _let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (_let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.mem F _let_54) false)) (not (= (tptp.mem BOUND_VARIABLE_961 A) false))))) :args _let_53)) _let_52 :args (_let_70 false _let_51)) :args (_let_63 false _let_20 false _let_68 false _let_70)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 0)) (CONG _let_59 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_30)) :args ((or _let_36 _let_38))) _let_58 :args (_let_36 true _let_38)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_67 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_45 QUANTIFIERS_INST_E_MATCHING ((tptp.ap (tptp.ap (tptp.c_2Ebool_2EIN A_27a) BOUND_VARIABLE_1211) (tptp.ap (tptp.ap (tptp.c_2Epred__set_2EDELETE A_27a) V0s) BOUND_VARIABLE_1213))))) :args (_let_66)))) _let_67 :args (_let_65 false _let_66)) :args (_let_61 false _let_20 false _let_63 false _let_36 false _let_65)) :args (_let_62 true _let_60 false _let_61)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 1)) (CONG _let_59 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_17))) :args _let_30)) :args ((or _let_17 _let_38))) _let_58 :args (_let_17 true _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_22)) :args ((or _let_21 _let_15 (not _let_22)))) _let_33 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.mem V0s (tptp.arr A_27a tptp.bool)) false))))) :args (_let_23))) _let_24 :args (_let_22 false _let_23)) :args (_let_15 false _let_20 false _let_22)) :args (false true _let_18 false _let_17 false _let_15)) :args (_let_9 (forall ((Q $$unsorted)) (=> (tptp.mem Q tptp.bool) (forall ((R $$unsorted)) (=> (tptp.mem R tptp.bool) (=> (= (tptp.p Q) (tptp.p R)) (= Q R)))))) (forall ((A tptp.del) (B tptp.del) (F $$unsorted)) (=> (tptp.mem F (tptp.arr A B)) (forall ((G $$unsorted)) (=> (tptp.mem G (tptp.arr A B)) (=> (forall ((X $$unsorted)) (=> (tptp.mem X A) (= (tptp.ap F X) (tptp.ap G X)))) (= F G)))))) (forall ((A tptp.del) (Y $$unsorted) (X $$unsorted)) (=> (tptp.mem X A) (= (tptp.ap (tptp.k A Y) X) Y))) (forall ((A tptp.del) (X $$unsorted)) (=> (tptp.mem X A) (= (tptp.ap (tptp.i A) X) X))) (forall ((X tptp.tp__o)) (= (tptp.surj__o (tptp.inj__o X)) X)) (forall ((X tptp.tp__o)) (tptp.mem (tptp.inj__o X) tptp.bool)) (forall ((X $$unsorted)) (=> (tptp.mem X tptp.bool) (= X (tptp.inj__o (tptp.surj__o X))))) (tptp.mem tptp.c_2Emin_2E_3D_3D_3E _let_8) (forall ((X0 tptp.tp__o) (X1 tptp.tp__o)) (= (tptp.inj__o (tptp.fo__c_2Emin_2E_3D_3D_3E X0 X1)) (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E (tptp.inj__o X0)) (tptp.inj__o X1)))) (forall ((Q $$unsorted)) (=> (tptp.mem Q tptp.bool) (forall ((R $$unsorted)) (=> (tptp.mem R tptp.bool) (= (tptp.p (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E Q) R)) (=> (tptp.p Q) (tptp.p R))))))) (forall ((A_27a tptp.del)) (let ((_let_1 (tptp.arr A_27a tptp.bool))) (tptp.mem (tptp.c_2Epred__set_2ESUBSET A_27a) (tptp.arr _let_1 (tptp.arr _let_1 tptp.bool))))) (tptp.mem tptp.c_2Ebool_2E_7E _let_7) (forall ((X0 tptp.tp__o)) (= (tptp.inj__o (tptp.fo__c_2Ebool_2E_7E X0)) (tptp.ap tptp.c_2Ebool_2E_7E (tptp.inj__o X0)))) (forall ((Q $$unsorted)) (=> (tptp.mem Q tptp.bool) (= (tptp.p (tptp.ap tptp.c_2Ebool_2E_7E Q)) (not (tptp.p Q))))) (tptp.mem tptp.c_2Ebool_2E_2F_5C _let_8) (forall ((X0 tptp.tp__o) (X1 tptp.tp__o)) (= (tptp.inj__o (tptp.fo__c_2Ebool_2E_2F_5C X0 X1)) (tptp.ap (tptp.ap tptp.c_2Ebool_2E_2F_5C (tptp.inj__o X0)) (tptp.inj__o X1)))) (forall ((Q $$unsorted)) (=> (tptp.mem Q tptp.bool) (forall ((R $$unsorted)) (=> (tptp.mem R tptp.bool) (= (tptp.p (tptp.ap (tptp.ap tptp.c_2Ebool_2E_2F_5C Q) R)) (and (tptp.p Q) (tptp.p R))))))) (forall ((A_27a tptp.del)) (tptp.mem (tptp.c_2Ebool_2EIN A_27a) (tptp.arr A_27a (tptp.arr (tptp.arr A_27a tptp.bool) tptp.bool)))) _let_6 (forall ((A_27a tptp.del)) (let ((_let_1 (tptp.arr A_27a tptp.bool))) (tptp.mem (tptp.c_2Epred__set_2EDELETE A_27a) (tptp.arr _let_1 (tptp.arr A_27a _let_1))))) _let_5 (forall ((A_27a tptp.del)) (tptp.mem (tptp.c_2Emin_2E_3D A_27a) (tptp.arr A_27a (tptp.arr A_27a tptp.bool)))) (forall ((A tptp.del) (X $$unsorted)) (=> (tptp.mem X A) (forall ((Y $$unsorted)) (=> (tptp.mem Y A) (= (tptp.p (tptp.ap (tptp.ap (tptp.c_2Emin_2E_3D A) X) Y)) (= X Y)))))) (forall ((A_27a tptp.del)) (tptp.mem (tptp.c_2Ebool_2E_21 A_27a) (tptp.arr (tptp.arr A_27a tptp.bool) tptp.bool))) (forall ((A tptp.del) (Q $$unsorted)) (=> (tptp.mem Q (tptp.arr A tptp.bool)) (= (tptp.p (tptp.ap (tptp.c_2Ebool_2E_21 A) Q)) (forall ((X $$unsorted)) (=> (tptp.mem X A) (tptp.p (tptp.ap Q X))))))) _let_4 _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 2.36/2.57  )
% 2.36/2.57  % SZS output end Proof for ITP004_2
% 2.36/2.57  % cvc5---1.0.5 exiting
% 2.36/2.57  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------