%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GRP622+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n032.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 00:26:39 EDT 2023

% Result   : Theorem 0.14s 0.60s
% Output   : Proof 0.14s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem    : GRP622+1 : TPTP v8.1.2. Released v3.4.0.
% 0.09/0.10  % Command    : do_cvc5 %s %d
% 0.09/0.29  % Computer : n032.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit   : 300
% 0.09/0.29  % WCLimit    : 300
% 0.09/0.29  % DateTime   : Tue Aug 29 00:46:46 EDT 2023
% 0.09/0.29  % CPUTime    : 
% 0.14/0.39  %----Proving TF0_NAR, FOF, or CNF
% 0.14/0.60  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.eUVi54uVLV/cvc5---1.0.5_5965.p...
% 0.14/0.60  ------- get file name : TPTP file name is GRP622+1
% 0.14/0.60  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_5965.smt2...
% 0.14/0.60  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.14/0.60  % SZS status Theorem for GRP622+1
% 0.14/0.60  % SZS output start Proof for GRP622+1
% 0.14/0.60  (
% 0.14/0.60  (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (tptp.m1_subset_1 A B))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B A A) (tptp.m2_relset_1 B A A)) (tptp.r2_hidden B (tptp.k1_funct_2 A A)))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_fraenkel C A B)) (forall ((D $$unsorted)) (= (tptp.m2_fraenkel D A B C) (tptp.m1_subset_1 D C))))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (= (tptp.k1_fraenkel A B) (tptp.k1_funct_2 A B)))))) (let ((_let_5 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A)) (not (tptp.v1_xboole_0 (tptp.u1_struct_0 A))))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_fraenkel C A B)) (forall ((D $$unsorted)) (=> (tptp.m2_fraenkel D A B C) (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)))))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_fraenkel C A B) (and (not (tptp.v1_xboole_0 C)) (tptp.v1_fraenkel C)))))) (let ((_let_8 (forall ((A $$unsorted)) (=> (tptp.l1_group_1 A) (tptp.l1_struct_0 A))))) (let ((_let_9 (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v1_group_1 A) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (tptp.m1_fraenkel (tptp.k4_autgroup A) _let_1 _let_1)))))) (let ((_let_10 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.r1_tarski A B) (forall ((C $$unsorted)) (=> (tptp.r2_hidden C A) (tptp.r2_hidden C B))))))) (let ((_let_11 (forall ((A $$unsorted)) (=> (tptp.v1_fraenkel A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B A) (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)))))))) (let ((_let_12 (not (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v1_group_1 A) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (tptp.r1_tarski (tptp.k4_autgroup A) (tptp.k1_fraenkel _let_1 _let_1)))))))) (let ((_let_13 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_14 (tptp.k1_funct_2 _let_13 _let_13))) (let ((_let_15 (tptp.r2_hidden SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 _let_14))) (let ((_let_16 (tptp.m2_relset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 _let_13 _let_13))) (let ((_let_17 (not _let_16))) (let ((_let_18 (tptp.v1_funct_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 _let_13 _let_13))) (let ((_let_19 (not _let_18))) (let ((_let_20 (tptp.v1_funct_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_21 (not _let_20))) (let ((_let_22 (or _let_21 _let_19 _let_17 _let_15))) (let ((_let_23 (tptp.k1_fraenkel _let_13 _let_13))) (let ((_let_24 (tptp.r2_hidden SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 _let_23))) (let ((_let_25 (= _let_23 _let_14))) (let ((_let_26 (not _let_15))) (let ((_let_27 (tptp.k4_autgroup SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_28 (tptp.r2_hidden SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 _let_27))) (let ((_let_29 (not _let_28))) (let ((_let_30 (or _let_29 _let_24))) (let ((_let_31 (not _let_24))) (let ((_let_32 (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (or (not (tptp.r2_hidden C (tptp.k4_autgroup SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (tptp.r2_hidden C (tptp.k1_fraenkel _let_1 _let_1))))))) (let ((_let_33 (not _let_30))) (let ((_let_34 (tptp.r1_tarski _let_27 _let_23))) (let ((_let_35 (= _let_34 _let_32))) (let ((_let_36 (not _let_32))) (let ((_let_37 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.r1_tarski A B) (forall ((C $$unsorted)) (or (not (tptp.r2_hidden C A)) (tptp.r2_hidden C B))))))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_39 (tptp.l1_group_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_40 (not _let_39))) (let ((_let_41 (tptp.v4_group_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_42 (not _let_41))) (let ((_let_43 (tptp.v3_group_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_44 (not _let_43))) (let ((_let_45 (tptp.v1_group_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_46 (not _let_45))) (let ((_let_47 (tptp.v3_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_48 (or _let_47 _let_46 _let_44 _let_42 _let_40 _let_34))) (let ((_let_49 (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (tptp.v3_struct_0 A) (not (tptp.v1_group_1 A)) (not (tptp.v3_group_1 A)) (not (tptp.v4_group_1 A)) (not (tptp.l1_group_1 A)) (tptp.r1_tarski (tptp.k4_autgroup A) (tptp.k1_fraenkel _let_1 _let_1))))))) (let ((_let_50 (not _let_48))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (or))) (let ((_let_53 (not _let_49))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_51) :args (_let_53))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_49))) (REFL :args (_let_50)) :args _let_52)) _let_51 :args (_let_50 true _let_49)))) (let ((_let_55 (_let_36))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_55)) :args _let_55)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_32))) (REFL :args (_let_33)) :args _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_35)) :args ((or _let_34 _let_36 (not _let_35)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_48 5)) _let_54 :args ((not _let_34) true _let_48)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (_let_27 _let_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.r1_tarski A B)))) :args (_let_37))) _let_38 :args (_let_35 false _let_37)) :args (_let_36 true _let_34 false _let_35)) :args (_let_33 true _let_32)))) (let ((_let_57 (tptp.v1_xboole_0 _let_13))) (let ((_let_58 (or _let_57 _let_25))) (let ((_let_59 (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.v1_xboole_0 B) (= (tptp.k1_fraenkel A B) (tptp.k1_funct_2 A B)))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (not _let_57))) (let ((_let_62 (tptp.l1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_63 (not _let_62))) (let ((_let_64 (or _let_47 _let_63 _let_61))) (let ((_let_65 (forall ((A $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.l1_struct_0 A)) (not (tptp.v1_xboole_0 (tptp.u1_struct_0 A))))))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (or _let_40 _let_62))) (let ((_let_68 (forall ((A $$unsorted)) (or (not (tptp.l1_group_1 A)) (tptp.l1_struct_0 A))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (REFL :args (_let_48)))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 4)) (CONG _let_70 (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_39))) :args _let_52)) :args ((or _let_39 _let_48))) _let_54 :args (_let_39 true _let_48)))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_48 0)) _let_54 :args ((not _let_47) true _let_48)))) (let ((_let_73 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_64)) :args ((or _let_47 _let_63 _let_61 (not _let_64)))) _let_72 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_67)) :args ((or _let_40 _let_62 (not _let_67)))) _let_71 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.l1_group_1 A) false))))) :args (_let_68))) _let_69 :args (_let_67 false _let_68)) :args (_let_62 false _let_39 false _let_67)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v3_struct_0 A) true))))) :args (_let_65))) _let_66 :args (_let_64 false _let_65)) :args (_let_61 true _let_47 false _let_62 false _let_64)))) (let ((_let_74 (and _let_25 _let_31))) (let ((_let_75 (ASSUME :args (_let_31)))) (let ((_let_76 (ASSUME :args (_let_25)))) (let ((_let_77 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.v1_funct_1 B)) (not (tptp.v1_funct_2 B A A)) (not (tptp.m2_relset_1 B A A)) (tptp.r2_hidden B (tptp.k1_funct_2 A A)))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (and (tptp.v1_relat_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18) _let_20))) (let ((_let_80 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 _let_27))) (let ((_let_81 (not _let_80))) (let ((_let_82 (tptp.v1_fraenkel _let_27))) (let ((_let_83 (not _let_82))) (let ((_let_84 (or _let_83 _let_81 _let_79))) (let ((_let_85 (forall ((A $$unsorted) (BOUND_VARIABLE_1245 $$unsorted)) (or (not (tptp.v1_fraenkel A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_1245 A)) (and (tptp.v1_relat_1 BOUND_VARIABLE_1245) (tptp.v1_funct_1 BOUND_VARIABLE_1245)))))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (or _let_29 _let_80))) (let ((_let_88 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.r2_hidden A B)) (tptp.m1_subset_1 A B))))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_29 _let_80 (not _let_87)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_30 0)) (CONG (REFL :args (_let_30)) (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_28))) :args _let_52)) :args ((or _let_28 _let_30))) _let_56 :args (_let_28 true _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_89 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 _let_27 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.r2_hidden A B) false))))) :args (_let_88))) _let_89 :args (_let_87 false _let_88)) :args (_let_80 false _let_28 false _let_87)))) (let ((_let_91 (and (not (tptp.v1_xboole_0 _let_27)) _let_82))) (let ((_let_92 (tptp.m1_fraenkel _let_27 _let_13 _let_13))) (let ((_let_93 (not _let_92))) (let ((_let_94 (or _let_93 _let_91))) (let ((_let_95 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.m1_fraenkel C A B)) (and (not (tptp.v1_xboole_0 C)) (tptp.v1_fraenkel C)))))) (let ((_let_96 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_97 (or _let_47 _let_46 _let_44 _let_42 _let_40 _let_92))) (let ((_let_98 (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (tptp.v3_struct_0 A) (not (tptp.v1_group_1 A)) (not (tptp.v3_group_1 A)) (not (tptp.v4_group_1 A)) (not (tptp.l1_group_1 A)) (tptp.m1_fraenkel (tptp.k4_autgroup A) _let_1 _let_1)))))) (let ((_let_99 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_100 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_97)) :args ((or _let_47 _let_46 _let_44 _let_42 _let_40 _let_92 (not _let_97)))) _let_72 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 1)) (CONG _let_70 (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_45))) :args _let_52)) :args ((or _let_45 _let_48))) _let_54 :args (_let_45 true _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 2)) (CONG _let_70 (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) :args _let_52)) :args ((or _let_43 _let_48))) _let_54 :args (_let_43 true _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 3)) (CONG _let_70 (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_41))) :args _let_52)) :args ((or _let_41 _let_48))) _let_54 :args (_let_41 true _let_48)) _let_71 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_99 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v3_struct_0 A) true))))) :args (_let_98))) _let_99 :args (_let_97 false _let_98)) :args (_let_92 true _let_47 false _let_45 false _let_43 false _let_41 false _let_39 false _let_97)))) (let ((_let_101 (and _let_20 _let_18 _let_16))) (let ((_let_102 (tptp.m2_fraenkel SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 _let_13 _let_13 _let_27))) (let ((_let_103 (not _let_102))) (let ((_let_104 (or _let_57 _let_93 _let_103 _let_101))) (let ((_let_105 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (BOUND_VARIABLE_1398 $$unsorted)) (or (tptp.v1_xboole_0 B) (not (tptp.m1_fraenkel C A B)) (not (tptp.m2_fraenkel BOUND_VARIABLE_1398 A B C)) (and (tptp.v1_funct_1 BOUND_VARIABLE_1398) (tptp.v1_funct_2 BOUND_VARIABLE_1398 A B) (tptp.m2_relset_1 BOUND_VARIABLE_1398 A B)))))) (let ((_let_106 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_107 (= _let_80 _let_102))) (let ((_let_108 (or _let_57 _let_93 _let_107))) (let ((_let_109 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (BOUND_VARIABLE_1645 $$unsorted)) (or (tptp.v1_xboole_0 B) (not (tptp.m1_fraenkel C A B)) (= (tptp.m2_fraenkel BOUND_VARIABLE_1645 A B C) (tptp.m1_subset_1 BOUND_VARIABLE_1645 C)))))) (let ((_let_110 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_111 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_104)) :args ((or _let_57 _let_93 _let_101 _let_103 (not _let_104)))) _let_73 _let_100 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_107)) :args ((or _let_81 _let_102 (not _let_107)))) _let_90 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_108)) :args ((or _let_57 _let_93 _let_107 (not _let_108)))) _let_73 _let_100 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_110 :args (_let_13 _let_13 _let_27 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.m1_fraenkel C A B) false)) (tptp.m1_subset_1 BOUND_VARIABLE_1645 C)))) :args (_let_109)))) _let_110 :args (_let_108 false _let_109)) :args (_let_107 true _let_57 false _let_92 false _let_108)) :args (_let_102 false _let_80 false _let_107)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_106 :args (_let_13 _let_13 _let_27 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.m2_fraenkel BOUND_VARIABLE_1398 A B C) false))))) :args (_let_105))) _let_106 :args (_let_104 false _let_105)) :args (_let_101 true _let_57 false _let_92 false _let_102 false _let_104)))) (let ((_let_112 (not _let_101))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_22)) :args ((or _let_21 _let_19 _let_17 _let_15 (not _let_22)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_101 2)) :args ((or _let_16 _let_112))) _let_111 :args (_let_16 false _let_101)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_101 1)) :args ((or _let_18 _let_112))) _let_111 :args (_let_18 false _let_101)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_79 1)) :args ((or _let_20 (not _let_79)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_84)) :args ((or _let_83 _let_81 _let_79 (not _let_84)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_91 1)) :args ((or _let_82 (not _let_91)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_94)) :args ((or _let_93 _let_91 (not _let_94)))) _let_100 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_96 :args (_let_13 _let_13 _let_27 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.m1_fraenkel C A B) false))))) :args (_let_95))) _let_96 :args (_let_94 false _let_95)) :args (_let_91 false _let_92 false _let_94)) :args (_let_82 false _let_91)) _let_90 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_86 :args (_let_27 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.m1_subset_1 BOUND_VARIABLE_1245 A) false))))) :args (_let_85))) _let_86 :args (_let_84 false _let_85)) :args (_let_79 false _let_82 false _let_80 false _let_84)) :args (_let_20 false _let_79)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (_let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.r2_hidden B (tptp.k1_funct_2 A A)) true))))) :args (_let_77))) _let_78 :args (_let_22 false _let_77)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_74)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_75 _let_76) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18)) (SYMM _let_76) :args (APPLY_UF tptp.r2_hidden)) (FALSE_INTRO _let_75))) :args (_let_31 _let_25))) :args (_let_25 _let_31))) :args (true _let_74)) (CONG (REFL :args ((not _let_25))) (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_24))) (REFL :args (_let_26)) :args _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_57 _let_25 (not _let_58)))) _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (_let_13 _let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.k1_fraenkel A B)))) :args (_let_59))) _let_60 :args (_let_58 false _let_59)) :args (_let_25 true _let_57 false _let_58)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_30 1)) _let_56 :args (_let_31 true _let_30)) :args (_let_26 false _let_25 true _let_24)) :args (false false _let_16 false _let_18 false _let_20 false _let_22 true _let_15)) :args (_let_12 (forall ((A $$unsorted)) (=> (tptp.l1_group_1 A) (=> (tptp.v1_group_1 A) (= A (tptp.g1_group_1 (tptp.u1_struct_0 A) (tptp.u1_group_1 A)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (not (tptp.r2_hidden B A)))) _let_11 (forall ((A $$unsorted)) (=> (tptp.v1_xboole_0 A) (tptp.v1_funct_1 A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.v1_funct_1 C))) (=> (tptp.m1_relset_1 C A B) (=> (and _let_1 (tptp.v1_partfun1 C A B)) (and _let_1 (tptp.v1_funct_2 C A B)))))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l1_group_1 A) (=> (and _let_1 (tptp.v3_group_1 A)) (and _let_1 (tptp.v2_group_1 A)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B))) (tptp.v1_relat_1 C))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.v1_funct_1 A))) (let ((_let_2 (tptp.v1_relat_1 A))) (=> (and _let_2 (tptp.v1_xboole_0 A) _let_1) (and _let_2 _let_1 (tptp.v2_funct_1 A)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.v1_funct_2 C A B))) (let ((_let_2 (tptp.v1_funct_1 C))) (=> (tptp.m1_relset_1 C A B) (=> (and _let_2 _let_1) (and _let_2 (tptp.v1_partfun1 C A B) _let_1)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B))) (forall ((C $$unsorted)) (let ((_let_1 (tptp.v1_funct_2 C A B))) (let ((_let_2 (tptp.v1_funct_1 C))) (=> (tptp.m1_relset_1 C A B) (=> (and _let_2 _let_1) (and _let_2 (not (tptp.v1_xboole_0 C)) (tptp.v1_partfun1 C A B) _let_1)))))))) _let_10 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.g1_group_1 A B))) (let ((_let_2 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 A) (tptp.m1_relset_1 B _let_2 A)) (and (tptp.v1_group_1 _let_1) (tptp.l1_group_1 _let_1)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (tptp.m1_fraenkel (tptp.k1_fraenkel A B) A B))) true true true true _let_9 _let_8 true _let_7 true true _let_6 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C A B) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u1_group_1 A))) (=> (tptp.l1_group_1 A) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.m2_relset_1 _let_3 _let_2 _let_1))))))) true (exists ((A $$unsorted)) (tptp.l1_group_1 A)) (exists ((A $$unsorted)) (tptp.l1_struct_0 A)) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.m1_fraenkel C A B))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.m1_relset_1 C A B))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.m1_subset_1 B A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_fraenkel C A B)) (exists ((D $$unsorted)) (tptp.m2_fraenkel D A B C)))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.m2_relset_1 C A B))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.v1_fraenkel (tptp.k1_funct_2 A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (not (tptp.v1_xboole_0 (tptp.k1_funct_2 A B))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.g1_group_1 A B))) (let ((_let_2 (tptp.k2_zfmisc_1 A A))) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 A) (tptp.m1_relset_1 B _let_2 A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v1_group_1 _let_1)))))) _let_5 (tptp.v1_xboole_0 tptp.k1_xboole_0) (forall ((A $$unsorted)) (not (tptp.v1_xboole_0 (tptp.k1_funct_2 A A)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m1_relset_1 B _let_1 A)) (forall ((C $$unsorted) (D $$unsorted)) (=> (= (tptp.g1_group_1 A B) (tptp.g1_group_1 C D)) (and (= A C) (= B D))))))) (exists ((A $$unsorted)) (and (not (tptp.v1_xboole_0 A)) (tptp.v1_fraenkel A))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (and (tptp.m1_relset_1 C A B) (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B)))) (exists ((A $$unsorted)) (and (tptp.l1_group_1 A) (tptp.v1_group_1 A))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v2_funct_1 A) (tptp.v1_xboole_0 A))) (exists ((A $$unsorted)) (tptp.v1_xboole_0 A)) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_xboole_0 A) (tptp.v1_funct_1 A))) (exists ((A $$unsorted)) (and (tptp.l1_group_1 A) (not (tptp.v3_struct_0 A)) (tptp.v1_group_1 A))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (and (tptp.m1_relset_1 C A B) (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)))) (exists ((A $$unsorted)) (not (tptp.v1_xboole_0 A))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v2_funct_1 A))) (exists ((A $$unsorted)) (and (tptp.l1_group_1 A) (not (tptp.v3_struct_0 A)) (tptp.v1_group_1 A) (tptp.v2_group_1 A) (tptp.v3_group_1 A) (tptp.v4_group_1 A))) (exists ((A $$unsorted)) (and (tptp.l1_struct_0 A) (not (tptp.v3_struct_0 A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (not (tptp.v1_xboole_0 B)))))) _let_4 _let_3 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.m2_relset_1 C A B) (tptp.m1_relset_1 C A B))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski A A)) _let_2 _let_1 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 A B) (or (tptp.v1_xboole_0 B) (tptp.r2_hidden A B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.m1_subset_1 A (tptp.k1_zfmisc_1 B)) (tptp.r1_tarski A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.r2_hidden A B) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 C))) (tptp.m1_subset_1 A C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.r2_hidden A B) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 C)) (tptp.v1_xboole_0 C)))) (forall ((A $$unsorted)) (=> (tptp.v1_xboole_0 A) (= A tptp.k1_xboole_0))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.r2_hidden A B) (tptp.v1_xboole_0 B)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.v1_xboole_0 A) (not (= A B)) (tptp.v1_xboole_0 B)))) true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.14/0.61  )
% 0.14/0.61  % SZS output end Proof for GRP622+1
% 0.14/0.61  % cvc5---1.0.5 exiting
% 0.14/0.61  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------