TSTP Solution File: GRP630+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : GRP630+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n018.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 00:26:44 EDT 2023
% Result : Theorem 2.33s 2.62s
% Output : Proof 2.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : GRP630+1 : TPTP v8.1.2. Released v3.4.0.
% 0.06/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n018.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 : Tue Aug 29 01:33:02 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 2.33/2.62 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.OBQOUHpODQ/cvc5---1.0.5_9234.p...
% 2.33/2.62 ------- get file name : TPTP file name is GRP630+1
% 2.33/2.62 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_9234.smt2...
% 2.33/2.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 2.33/2.62 % SZS status Theorem for GRP630+1
% 2.33/2.62 % SZS output start Proof for GRP630+1
% 2.33/2.62 (
% 2.33/2.62 (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m2_relset_1 C A B)) (forall ((D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D B A) (tptp.m2_relset_1 D B A)) (=> (and (= (tptp.k2_relat_1 C) B) (= (tptp.k1_partfun1 A B B A C D) (tptp.k6_partfun1 A)) (tptp.v2_funct_1 C)) (or (= A tptp.k1_xboole_0) (= B tptp.k1_xboole_0) (= D (tptp.k2_funct_1 C)))))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 A B) (or (tptp.v1_xboole_0 B) (tptp.r2_hidden A B)))))) (let ((_let_3 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v1_group_1 A) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 B _let_1) (= (tptp.k7_funct_2 _let_1 _let_1 _let_1 (tptp.k6_autgroup A B) (tptp.k6_autgroup A (tptp.k3_group_1 A B))) (tptp.k6_autgroup A (tptp.k2_group_1 A)))))))))) (let ((_let_4 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v1_group_1 A) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (= (tptp.k6_autgroup A (tptp.k2_group_1 A)) (tptp.k6_partfun1 (tptp.u1_struct_0 A))))))) (let ((_let_5 (forall ((A $$unsorted)) (=> (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)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m2_fraenkel B _let_1 _let_1 (tptp.k4_autgroup A)) (tptp.m2_fraenkel B _let_1 _let_1 (tptp.k1_autgroup A))))))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.m2_relset_1 C A B) (tptp.m1_relset_1 C A B))))) (let ((_let_7 (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_8 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m1_relset_1 D A B) (tptp.v1_funct_1 E) (tptp.v1_funct_2 E B C) (tptp.m1_relset_1 E B C)) (= (tptp.k7_funct_2 A B C D E) (tptp.k5_relat_1 D E)))))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (tptp.v1_funct_1 E) (tptp.m1_relset_1 E A B) (tptp.v1_funct_1 F) (tptp.m1_relset_1 F C D)) (= (tptp.k1_partfun1 A B C D E F) (tptp.k5_relat_1 E F)))))) (let ((_let_10 (forall ((A $$unsorted)) (=> (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)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k1_relat_1 B))) (=> (tptp.m2_fraenkel B _let_1 _let_1 (tptp.k1_autgroup A)) (and (= _let_2 (tptp.k2_relat_1 B)) (= _let_2 _let_1)))))))))) (let ((_let_11 (tptp.v1_xboole_0 tptp.k1_xboole_0))) (let ((_let_12 (forall ((A $$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_13 (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)))))) (let ((_let_14 (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_15 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_fraenkel C A B) (and (not (tptp.v1_xboole_0 C)) (tptp.v1_fraenkel C)))))) (let ((_let_16 (forall ((A $$unsorted)) (=> (tptp.l1_group_1 A) (tptp.l1_struct_0 A))))) (let ((_let_17 (forall ((A $$unsorted) (B $$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_subset_1 B _let_1)) (tptp.m2_fraenkel (tptp.k6_autgroup A B) _let_1 _let_1 (tptp.k4_autgroup A))))))) (let ((_let_18 (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v1_group_1 A) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (tptp.m1_fraenkel (tptp.k4_autgroup A) _let_1 _let_1)))))) (let ((_let_19 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A) (tptp.m1_subset_1 B _let_1)) (tptp.m1_subset_1 (tptp.k3_group_1 A B) _let_1)))))) (let ((_let_20 (forall ((A $$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.k1_autgroup A) _let_1 _let_1)))))) (let ((_let_21 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v1_group_1 A) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_fraenkel B _let_1 _let_1) (= (= B (tptp.k1_autgroup A)) (and (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m2_fraenkel C _let_1 _let_1 B) (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 _let_1) (tptp.v1_group_6 C A A) (tptp.m2_relset_1 C _let_1 _let_1))))) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 _let_1) (tptp.v1_group_6 C A A) (tptp.m2_relset_1 C _let_1 _let_1)) (= (tptp.r2_hidden C B) (and (tptp.v2_funct_1 C) (tptp.v3_group_6 C A A))))))))))))))) (let ((_let_22 (not (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v1_group_1 A) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (= (tptp.k6_autgroup A (tptp.k3_group_1 A B)) (tptp.k2_funct_1 (tptp.k6_autgroup A B)))))))))) (let ((_let_23 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.m1_subset_1 A B)) (tptp.v1_xboole_0 B) (tptp.r2_hidden A B))))) (let ((_let_24 (tptp.k1_autgroup SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_25 (tptp.k6_autgroup SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_26 (tptp.r2_hidden _let_25 _let_24))) (let ((_let_27 (tptp.v1_xboole_0 _let_24))) (let ((_let_28 (tptp.m1_subset_1 _let_25 _let_24))) (let ((_let_29 (not _let_28))) (let ((_let_30 (or _let_29 _let_27 _let_26))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (not _let_30))) (let ((_let_33 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_34 (tptp.m2_fraenkel _let_25 _let_33 _let_33 _let_24))) (let ((_let_35 (= _let_34 _let_28))) (let ((_let_36 (tptp.m1_fraenkel _let_24 _let_33 _let_33))) (let ((_let_37 (not _let_36))) (let ((_let_38 (tptp.v1_xboole_0 _let_33))) (let ((_let_39 (or _let_38 _let_37 _let_35))) (let ((_let_40 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (BOUND_VARIABLE_2442 $$unsorted)) (or (tptp.v1_xboole_0 B) (not (tptp.m1_fraenkel C A B)) (= (tptp.m2_fraenkel BOUND_VARIABLE_2442 A B C) (tptp.m1_subset_1 BOUND_VARIABLE_2442 C)))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (tptp.l1_group_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_43 (not _let_42))) (let ((_let_44 (tptp.v4_group_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_45 (not _let_44))) (let ((_let_46 (tptp.v3_group_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_47 (not _let_46))) (let ((_let_48 (tptp.v1_group_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_49 (not _let_48))) (let ((_let_50 (tptp.v3_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_51 (or _let_50 _let_49 _let_47 _let_45 _let_43 _let_36))) (let ((_let_52 (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (tptp.v3_struct_0 A) (not (tptp.v1_group_1 A)) (not (tptp.v3_group_1 A)) (not (tptp.v4_group_1 A)) (not (tptp.l1_group_1 A)) (tptp.m1_fraenkel (tptp.k1_autgroup A) _let_1 _let_1)))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (tptp.k3_group_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_55 (tptp.k6_autgroup SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_54))) (let ((_let_56 (= _let_55 (tptp.k2_funct_1 _let_25)))) (let ((_let_57 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_33))) (let ((_let_58 (not _let_57))) (let ((_let_59 (or _let_50 _let_49 _let_47 _let_45 _let_43 _let_58 _let_56))) (let ((_let_60 (forall ((A $$unsorted) (BOUND_VARIABLE_1671 $$unsorted)) (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)) (not (tptp.m1_subset_1 BOUND_VARIABLE_1671 (tptp.u1_struct_0 A))) (= (tptp.k6_autgroup A (tptp.k3_group_1 A BOUND_VARIABLE_1671)) (tptp.k2_funct_1 (tptp.k6_autgroup A BOUND_VARIABLE_1671))))))) (let ((_let_61 (not _let_59))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (or))) (let ((_let_64 (not _let_60))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_62) :args (_let_64))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_60))) (REFL :args (_let_61)) :args _let_63)) _let_62 :args (_let_61 true _let_60)))) (let ((_let_66 (REFL :args (_let_59)))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_59 4)) (CONG _let_66 (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_42))) :args _let_63)) :args ((or _let_42 _let_59))) _let_65 :args (_let_42 true _let_59)))) (let ((_let_68 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_59 3)) (CONG _let_66 (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_44))) :args _let_63)) :args ((or _let_44 _let_59))) _let_65 :args (_let_44 true _let_59)))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_59 2)) (CONG _let_66 (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_46))) :args _let_63)) :args ((or _let_46 _let_59))) _let_65 :args (_let_46 true _let_59)))) (let ((_let_70 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_59 1)) (CONG _let_66 (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_48))) :args _let_63)) :args ((or _let_48 _let_59))) _let_65 :args (_let_48 true _let_59)))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_59 0)) _let_65 :args ((not _let_50) true _let_59)))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_50 _let_49 _let_47 _let_45 _let_43 _let_36 (not _let_51)))) _let_71 _let_70 _let_69 _let_68 _let_67 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v3_struct_0 A) true))))) :args (_let_52))) _let_53 :args (_let_51 false _let_52)) :args (_let_36 true _let_50 false _let_48 false _let_46 false _let_44 false _let_42 false _let_51)))) (let ((_let_73 (not _let_38))) (let ((_let_74 (tptp.l1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_75 (not _let_74))) (let ((_let_76 (or _let_50 _let_75 _let_73))) (let ((_let_77 (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_78 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (or _let_43 _let_74))) (let ((_let_80 (forall ((A $$unsorted)) (or (not (tptp.l1_group_1 A)) (tptp.l1_struct_0 A))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_50 _let_75 _let_73 (not _let_76)))) _let_71 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_79)) :args ((or _let_43 _let_74 (not _let_79)))) _let_67 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_81 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.l1_group_1 A) false))))) :args (_let_80))) _let_81 :args (_let_79 false _let_80)) :args (_let_74 false _let_42 false _let_79)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v3_struct_0 A) true))))) :args (_let_77))) _let_78 :args (_let_76 false _let_77)) :args (_let_73 true _let_50 false _let_74 false _let_76)))) (let ((_let_83 (tptp.k4_autgroup SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_84 (tptp.m2_fraenkel _let_25 _let_33 _let_33 _let_83))) (let ((_let_85 (not _let_84))) (let ((_let_86 (or _let_50 _let_49 _let_47 _let_45 _let_43 _let_85 _let_34))) (let ((_let_87 (forall ((A $$unsorted) (BOUND_VARIABLE_2467 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (tptp.v3_struct_0 A) (not (tptp.v1_group_1 A)) (not (tptp.v3_group_1 A)) (not (tptp.v4_group_1 A)) (not (tptp.l1_group_1 A)) (not (tptp.m2_fraenkel BOUND_VARIABLE_2467 _let_1 _let_1 (tptp.k4_autgroup A))) (tptp.m2_fraenkel BOUND_VARIABLE_2467 _let_1 _let_1 (tptp.k1_autgroup A))))))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (_let_87))) (let ((_let_90 (tptp.u1_struct_0 A))) (let ((_let_91 ((not (= (tptp.m2_fraenkel BOUND_VARIABLE_2467 _let_90 _let_90 (tptp.k4_autgroup A)) false))))) (let ((_let_92 (or _let_50 _let_49 _let_47 _let_45 _let_43 _let_58 _let_84))) (let ((_let_93 (forall ((A $$unsorted) (B $$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)) (not (tptp.m1_subset_1 B _let_1)) (tptp.m2_fraenkel (tptp.k6_autgroup A B) _let_1 _let_1 (tptp.k4_autgroup A))))))) (let ((_let_94 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_95 (_let_93))) (let ((_let_96 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_59 5)) (CONG _let_66 (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_57))) :args _let_63)) :args ((or _let_57 _let_59))) _let_65 :args (_let_57 true _let_59)))) (let ((_let_97 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_92)) :args ((or _let_50 _let_49 _let_47 _let_45 _let_43 _let_58 _let_84 (not _let_92)))) _let_71 _let_70 _let_69 _let_68 _let_67 _let_96 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_94 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) false))))) :args _let_95)) _let_94 :args (_let_92 false _let_93)) :args (_let_84 true _let_50 false _let_48 false _let_46 false _let_44 false _let_42 false _let_57 false _let_92)))) (let ((_let_98 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_86)) :args ((or _let_50 _let_49 _let_47 _let_45 _let_43 _let_85 _let_34 (not _let_86)))) _let_71 _let_70 _let_69 _let_68 _let_67 _let_97 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_25 QUANTIFIERS_INST_E_MATCHING _let_91)) :args _let_89)) _let_88 :args (_let_86 false _let_87)) :args (_let_34 true _let_50 false _let_48 false _let_46 false _let_44 false _let_42 false _let_84 false _let_86)))) (let ((_let_99 (not _let_34))) (let ((_let_100 (tptp.v2_funct_1 _let_25))) (let ((_let_101 (and _let_100 (tptp.v3_group_6 _let_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_102 (= _let_101 _let_26))) (let ((_let_103 (not _let_26))) (let ((_let_104 (tptp.m2_relset_1 _let_25 _let_33 _let_33))) (let ((_let_105 (not _let_104))) (let ((_let_106 (tptp.v1_group_6 _let_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_107 (not _let_106))) (let ((_let_108 (tptp.v1_funct_2 _let_25 _let_33 _let_33))) (let ((_let_109 (not _let_108))) (let ((_let_110 (tptp.v1_funct_1 _let_25))) (let ((_let_111 (not _let_110))) (let ((_let_112 (or _let_111 _let_109 _let_107 _let_105 _let_102))) (let ((_let_113 (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (or (not (tptp.v1_funct_1 C)) (not (tptp.v1_funct_2 C _let_1 _let_1)) (not (tptp.v1_group_6 C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.m2_relset_1 C _let_1 _let_1)) (= (and (tptp.v2_funct_1 C) (tptp.v3_group_6 C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.r2_hidden C (tptp.k1_autgroup SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))))))) (let ((_let_114 (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (or (not (tptp.m2_fraenkel C _let_1 _let_1 (tptp.k1_autgroup SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 _let_1) (tptp.v1_group_6 C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.m2_relset_1 C _let_1 _let_1))))))) (let ((_let_115 (and _let_114 _let_113))) (let ((_let_116 (or _let_50 _let_49 _let_47 _let_45 _let_43 _let_37 _let_115))) (let ((_let_117 (forall ((A $$unsorted) (BOUND_VARIABLE_1883 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (tptp.v3_struct_0 A) (not (tptp.v1_group_1 A)) (not (tptp.v3_group_1 A)) (not (tptp.v4_group_1 A)) (not (tptp.l1_group_1 A)) (not (tptp.m1_fraenkel BOUND_VARIABLE_1883 _let_1 _let_1)) (= (= (tptp.k1_autgroup A) BOUND_VARIABLE_1883) (and (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (not (tptp.m2_fraenkel C _let_1 _let_1 BOUND_VARIABLE_1883)) (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 _let_1) (tptp.v1_group_6 C A A) (tptp.m2_relset_1 C _let_1 _let_1))))) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (not (tptp.v1_funct_1 C)) (not (tptp.v1_funct_2 C _let_1 _let_1)) (not (tptp.v1_group_6 C A A)) (not (tptp.m2_relset_1 C _let_1 _let_1)) (= (and (tptp.v2_funct_1 C) (tptp.v3_group_6 C A A)) (tptp.r2_hidden C BOUND_VARIABLE_1883)))))))))))) (let ((_let_118 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_119 (tptp.u1_struct_0 A))) (let ((_let_120 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_116)) :args ((or _let_50 _let_49 _let_47 _let_45 _let_43 _let_37 _let_115 (not _let_116)))) _let_71 _let_70 _let_69 _let_68 _let_67 _let_72 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_118 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_24 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.m1_fraenkel BOUND_VARIABLE_1883 _let_119 _let_119) false))))) :args (_let_117)))) _let_118 :args (_let_116 false _let_117)) :args (_let_115 true _let_50 false _let_48 false _let_46 false _let_44 false _let_42 false _let_36 false _let_116)))) (let ((_let_121 (not _let_115))) (let ((_let_122 (_let_113))) (let ((_let_123 (and _let_110 _let_108 _let_106 _let_104))) (let ((_let_124 (or _let_99 _let_123))) (let ((_let_125 (_let_114))) (let ((_let_126 (and _let_110 _let_108 _let_104))) (let ((_let_127 (tptp.m1_fraenkel _let_83 _let_33 _let_33))) (let ((_let_128 (not _let_127))) (let ((_let_129 (or _let_38 _let_128 _let_85 _let_126))) (let ((_let_130 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (BOUND_VARIABLE_2029 $$unsorted)) (or (tptp.v1_xboole_0 B) (not (tptp.m1_fraenkel C A B)) (not (tptp.m2_fraenkel BOUND_VARIABLE_2029 A B C)) (and (tptp.v1_funct_1 BOUND_VARIABLE_2029) (tptp.v1_funct_2 BOUND_VARIABLE_2029 A B) (tptp.m2_relset_1 BOUND_VARIABLE_2029 A B)))))) (let ((_let_131 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_132 (_let_130))) (let ((_let_133 ((not (= (tptp.m2_fraenkel BOUND_VARIABLE_2029 A B C) false))))) (let ((_let_134 (or _let_50 _let_49 _let_47 _let_45 _let_43 _let_127))) (let ((_let_135 (forall ((A $$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_136 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_137 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_134)) :args ((or _let_50 _let_49 _let_47 _let_45 _let_43 _let_127 (not _let_134)))) _let_71 _let_70 _let_69 _let_68 _let_67 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_136 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v3_struct_0 A) true))))) :args (_let_135))) _let_136 :args (_let_134 false _let_135)) :args (_let_127 true _let_50 false _let_48 false _let_46 false _let_44 false _let_42 false _let_134)))) (let ((_let_138 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_129)) :args ((or _let_38 _let_128 _let_85 _let_126 (not _let_129)))) _let_82 _let_137 _let_97 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_131 :args (_let_33 _let_33 _let_83 _let_25 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_133)) :args _let_132)) _let_131 :args (_let_129 false _let_130)) :args (_let_126 true _let_38 false _let_127 false _let_84 false _let_129)))) (let ((_let_139 (not _let_126))) (let ((_let_140 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_126 2)) :args ((or _let_104 _let_139))) _let_138 :args (_let_104 false _let_126)))) (let ((_let_141 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args 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_let_45 _let_43 _let_194 _let_190))) (let ((_let_196 (or _let_50 _let_47 _let_45 _let_43 _let_58 _let_193))) (let ((_let_197 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (tptp.v3_struct_0 A) (not (tptp.v3_group_1 A)) (not (tptp.v4_group_1 A)) (not (tptp.l1_group_1 A)) (not (tptp.m1_subset_1 B _let_1)) (tptp.m1_subset_1 (tptp.k3_group_1 A B) _let_1)))))) (let ((_let_198 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_199 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_195)) :args ((or _let_50 _let_49 _let_47 _let_45 _let_43 _let_194 _let_190 (not _let_195)))) _let_71 _let_70 _let_69 _let_68 _let_67 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_196)) :args ((or _let_50 _let_47 _let_45 _let_43 _let_58 _let_193 (not _let_196)))) _let_71 _let_69 _let_68 _let_67 _let_96 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_198 :args 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(MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_260)) :args ((or _let_111 _let_38 _let_182 _let_258 _let_109 _let_257 _let_259 _let_206 (not _let_260)))) _let_142 _let_82 _let_202 _let_263 _let_141 _let_240 _let_253 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_262 :args (_let_33 _let_33 _let_33 _let_25 _let_55 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.k7_funct_2 A B C D E)))) :args (_let_261))) _let_262 :args (_let_260 false _let_261)) :args (_let_206 false _let_110 true _let_38 false _let_171 false _let_188 false _let_108 false _let_220 false _let_251 false _let_260)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_214)) :args ((or _let_111 _let_182 _let_213 _let_211 _let_204 (not _let_214)))) _let_142 _let_202 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_254)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_255 _let_245 _let_246 _let_166 _let_168) (SCOPE (TRUE_ELIM (TRANS (CONG _let_256 _let_249 _let_250 :args _let_243) 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(INSTANTIATE (ASSUME :args _let_125) :args (_let_25 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.v1_funct_1 C)))) :args _let_125)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_115 0)) :args ((or _let_114 _let_121))) _let_120 :args (_let_114 false _let_115)) :args (_let_124 false _let_114)) :args (_let_123 false _let_34 false _let_124)) :args (_let_106 false _let_123)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_122) :args (_let_25 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v1_funct_1 C) false))))) :args _let_122)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_115 1)) :args ((or _let_113 _let_121))) _let_120 :args (_let_113 false _let_115)) :args (_let_112 false _let_113)) :args (_let_102 false _let_110 false _let_108 false _let_104 false _let_106 false _let_112)) :args (_let_103 true _let_101 false _let_102)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_35)) :args ((or _let_99 _let_28 (not _let_35)))) _let_98 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_38 _let_37 _let_35 (not _let_39)))) _let_82 _let_72 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (_let_33 _let_33 _let_24 _let_25 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.m2_fraenkel BOUND_VARIABLE_2442 A B C)))) :args (_let_40))) _let_41 :args (_let_39 false _let_40)) :args (_let_35 true _let_38 false _let_36 false _let_39)) :args (_let_28 false _let_34 false _let_35)) :args (_let_32 true _let_27 true _let_26 false _let_28)) _let_31 :args (false true _let_30 false _let_23)) :args (_let_22 (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 $$unsorted)) (=> (tptp.r2_hidden A B) (not (tptp.r2_hidden B A)))) (forall ((A $$unsorted)) (=> (tptp.v1_fraenkel A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B A) (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)))))) (forall ((A $$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 $$unsorted)) (let ((_let_1 (tptp.v1_relat_1 A))) (=> (and _let_1 (tptp.v3_relat_2 A) (tptp.v8_relat_2 A)) (and _let_1 (tptp.v1_relat_2 A))))) (forall ((A $$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 $$unsorted) (C $$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 (tptp.v3_funct_2 C A B)) (and _let_2 (tptp.v2_funct_1 C) _let_1 (tptp.v2_funct_2 C A B))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.v1_funct_2 C A B))) (let ((_let_2 (tptp.v1_funct_1 C))) (=> (tptp.m1_relset_1 C A B) (=> (and _let_2 (tptp.v2_funct_1 C) _let_1 (tptp.v2_funct_2 C A B)) (and _let_2 _let_1 (tptp.v3_funct_2 C A B))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.v1_funct_2 B A A))) (let ((_let_2 (tptp.v1_funct_1 B))) (=> (tptp.m1_relset_1 B A A) (=> (and _let_2 (tptp.v1_partfun1 B A A) (tptp.v1_relat_2 B) _let_1) (and _let_2 (tptp.v2_funct_1 B) _let_1 (tptp.v2_funct_2 B A A) (tptp.v3_funct_2 B A A))))))) (forall ((A $$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 $$unsorted)) (let ((_let_1 (tptp.v1_funct_2 C A B))) (let ((_let_2 (tptp.v1_funct_1 C))) (=> (tptp.m1_relset_1 C A B) (=> (and _let_2 _let_1) (and _let_2 (not (tptp.v1_xboole_0 C)) (tptp.v1_partfun1 C A B) _let_1)))))))) _let_21 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.g1_group_1 A B))) (let ((_let_2 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 A) (tptp.m1_relset_1 B _let_2 A)) (and (tptp.v1_group_1 _let_1) (tptp.l1_group_1 _let_1)))))) _let_20 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.k1_partfun1 A B C D E F))) (=> (and (tptp.v1_funct_1 E) (tptp.m1_relset_1 E A B) (tptp.v1_funct_1 F) (tptp.m1_relset_1 F C D)) (and (tptp.v1_funct_1 _let_1) (tptp.m2_relset_1 _let_1 A D))))) true true true (forall ((A $$unsorted)) (let ((_let_1 (tptp.k2_funct_1 A))) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (and (tptp.v1_relat_1 _let_1) (tptp.v1_funct_1 _let_1))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_group_1 A)) (tptp.m1_subset_1 (tptp.k2_group_1 A) (tptp.u1_struct_0 A)))) true true _let_19 _let_18 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_relat_1 B)) (tptp.v1_relat_1 (tptp.k5_relat_1 A B)))) _let_17 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k6_partfun1 A))) (and (tptp.v1_partfun1 _let_1 A A) (tptp.m2_relset_1 _let_1 A A)))) (forall ((A $$unsorted)) (tptp.v1_relat_1 (tptp.k6_relat_1 A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.k7_funct_2 A B C D E))) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m1_relset_1 D A B) (tptp.v1_funct_1 E) (tptp.v1_funct_2 E B C) (tptp.m1_relset_1 E B C)) (and (tptp.v1_funct_1 _let_1) (tptp.v1_funct_2 _let_1 A C) (tptp.m2_relset_1 _let_1 A C))))) _let_16 true _let_15 true true _let_14 (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))) _let_13 (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.m2_relset_1 C A B))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k5_relat_1 A B))) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (and (tptp.v1_relat_1 _let_1) (tptp.v1_funct_1 _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.g1_group_1 A B))) (let ((_let_2 (tptp.k2_zfmisc_1 A A))) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 A) (tptp.m1_relset_1 B _let_2 A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v1_group_1 _let_1)))))) _let_12 _let_11 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k6_relat_1 A))) (and (tptp.v1_relat_1 _let_1) (tptp.v1_funct_1 _let_1)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k6_relat_1 A))) (and (tptp.v1_relat_1 _let_1) (tptp.v1_funct_1 _let_1) (tptp.v1_relat_2 _let_1) (tptp.v3_relat_2 _let_1) (tptp.v4_relat_2 _let_1) (tptp.v8_relat_2 _let_1)))) (forall ((A $$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 $$unsorted)) (=> (= (tptp.g1_group_1 A B) (tptp.g1_group_1 C D)) (and (= A C) (= B D))))))) _let_10 (exists ((A $$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))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.m1_relset_1 B A A) (tptp.v1_relat_1 B) (tptp.v1_funct_1 B) (tptp.v2_funct_1 B) (tptp.v1_funct_2 B A A) (tptp.v2_funct_2 B A A) (tptp.v3_funct_2 B A 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 $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A) (not (tptp.v3_struct_0 B)) (tptp.v3_group_1 B) (tptp.v4_group_1 B) (tptp.l1_group_1 B)) (exists ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (let ((_let_2 (tptp.u1_struct_0 A))) (and (tptp.m1_relset_1 C _let_2 _let_1) (not (tptp.v1_xboole_0 C)) (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_2 _let_1) (tptp.v1_partfun1 C _let_2 _let_1) (tptp.v1_group_6 C A B))))))) (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))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.m1_relset_1 B A A) (tptp.v1_relat_1 B) (tptp.v1_relat_2 B) (tptp.v3_relat_2 B) (tptp.v4_relat_2 B) (tptp.v8_relat_2 B) (tptp.v1_partfun1 B A 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 $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (not (tptp.v1_xboole_0 B)))))) _let_9 (forall ((A $$unsorted)) (= (tptp.k6_partfun1 A) (tptp.k6_relat_1 A))) _let_8 _let_7 _let_6 (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski A A)) _let_5 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (tptp.m1_subset_1 A B))) _let_4 _let_3 _let_2 _let_1 (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 2.33/2.64 )
% 2.33/2.64 % SZS output end Proof for GRP630+1
% 2.33/2.64 % cvc5---1.0.5 exiting
% 2.33/2.64 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------