TSTP Solution File: GRP631+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : GRP631+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n020.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 0.50s 0.74s
% Output : Proof 0.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : GRP631+1 : TPTP v8.1.2. Released v3.4.0.
% 0.13/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n020.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 : Mon Aug 28 19:52:13 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 %----Proving TF0_NAR, FOF, or CNF
% 0.50/0.74 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.xGgB5PuYfT/cvc5---1.0.5_24817.p...
% 0.50/0.74 ------- get file name : TPTP file name is GRP631+1
% 0.50/0.74 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_24817.smt2...
% 0.50/0.74 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.50/0.74 % SZS status Theorem for GRP631+1
% 0.50/0.74 % SZS output start Proof for GRP631+1
% 0.50/0.74 (
% 0.50/0.74 (let ((_let_1 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v1_group_1 A) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (= (tptp.k6_autgroup A (tptp.k2_group_1 A)) (tptp.k6_partfun1 (tptp.u1_struct_0 A))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C A B) (and (= (tptp.k7_relset_1 A A A B (tptp.k6_partfun1 A) C) C) (= (tptp.k7_relset_1 A B B B C (tptp.k6_partfun1 B)) C)))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.m2_relset_1 C A B) (tptp.m1_relset_1 C A B))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (tptp.m1_relset_1 E A B) (tptp.m1_relset_1 F C D)) (= (tptp.k7_relset_1 A B C D E F) (tptp.k5_relat_1 E F)))))) (let ((_let_5 (forall ((A $$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_6 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A)) (not (tptp.v1_xboole_0 (tptp.u1_struct_0 A))))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_fraenkel C A B)) (forall ((D $$unsorted)) (=> (tptp.m2_fraenkel D A B C) (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)))))))) (let ((_let_8 (forall ((A $$unsorted)) (=> (tptp.l1_group_1 A) (tptp.l1_struct_0 A))))) (let ((_let_9 (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_10 (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v1_group_1 A) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (tptp.m1_fraenkel (tptp.k4_autgroup A) _let_1 _let_1)))))) (let ((_let_11 (forall ((A $$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)))))) (let ((_let_12 (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)) (let ((_let_1 (tptp.k6_autgroup A B))) (let ((_let_2 (tptp.k6_autgroup A (tptp.k2_group_1 A)))) (let ((_let_3 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 B _let_3) (and (= (tptp.k7_funct_2 _let_3 _let_3 _let_3 _let_2 _let_1) _let_1) (= (tptp.k7_funct_2 _let_3 _let_3 _let_3 _let_1 _let_2) _let_1)))))))))))) (let ((_let_13 (tptp.k2_group_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_14 (tptp.k6_autgroup SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_13))) (let ((_let_15 (tptp.k6_autgroup SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_16 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_17 (tptp.k7_funct_2 _let_16 _let_16 _let_16 _let_15 _let_14))) (let ((_let_18 (= _let_15 _let_17))) (let ((_let_19 (tptp.k7_funct_2 _let_16 _let_16 _let_16 _let_14 _let_15))) (let ((_let_20 (= _let_15 _let_19))) (let ((_let_21 (and _let_20 _let_18))) (let ((_let_22 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_16))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.l1_group_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.v4_group_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_27 (not _let_26))) (let ((_let_28 (tptp.v3_group_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_29 (not _let_28))) (let ((_let_30 (tptp.v1_group_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_31 (not _let_30))) (let ((_let_32 (tptp.v3_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_33 (or _let_32 _let_31 _let_29 _let_27 _let_25 _let_23 _let_21))) (let ((_let_34 (forall ((A $$unsorted) (BOUND_VARIABLE_1467 $$unsorted)) (let ((_let_1 (tptp.k6_autgroup A (tptp.k2_group_1 A)))) (let ((_let_2 (tptp.k6_autgroup A BOUND_VARIABLE_1467))) (let ((_let_3 (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 BOUND_VARIABLE_1467 _let_3)) (and (= _let_2 (tptp.k7_funct_2 _let_3 _let_3 _let_3 _let_1 _let_2)) (= _let_2 (tptp.k7_funct_2 _let_3 _let_3 _let_3 _let_2 _let_1)))))))))) (let ((_let_35 (not _let_33))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (or))) (let ((_let_38 (not _let_34))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_36) :args (_let_38))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_34))) (REFL :args (_let_35)) :args _let_37)) _let_36 :args (_let_35 true _let_34)))) (let ((_let_40 (tptp.k6_partfun1 _let_16))) (let ((_let_41 (tptp.k7_relset_1 _let_16 _let_16 _let_16 _let_16 _let_15 _let_40))) (let ((_let_42 (= _let_41 (tptp.k5_relat_1 _let_15 _let_40)))) (let ((_let_43 (= _let_15 _let_41))) (let ((_let_44 (= _let_14 _let_40))) (let ((_let_45 (= _let_17 (tptp.k5_relat_1 _let_15 _let_14)))) (let ((_let_46 (tptp.m1_relset_1 _let_40 _let_16 _let_16))) (let ((_let_47 (not _let_46))) (let ((_let_48 (tptp.m1_relset_1 _let_15 _let_16 _let_16))) (let ((_let_49 (not _let_48))) (let ((_let_50 (or _let_49 _let_47 _let_42))) (let ((_let_51 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (or (not (tptp.m1_relset_1 E A B)) (not (tptp.m1_relset_1 F C D)) (= (tptp.k7_relset_1 A B C D E F) (tptp.k5_relat_1 E F)))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (_let_51))) (let ((_let_54 ((tptp.k7_relset_1 A B C D E F)))) (let ((_let_55 (tptp.m1_relset_1 _let_14 _let_16 _let_16))) (let ((_let_56 (or _let_32 _let_31 _let_29 _let_27 _let_25 _let_44))) (let ((_let_57 (forall ((A $$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)) (= (tptp.k6_autgroup A (tptp.k2_group_1 A)) (tptp.k6_partfun1 (tptp.u1_struct_0 A))))))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (REFL :args (_let_33)))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 4)) (CONG _let_59 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_37)) :args ((or _let_24 _let_33))) _let_39 :args (_let_24 true _let_33)))) (let ((_let_61 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 3)) (CONG _let_59 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_37)) :args ((or _let_26 _let_33))) _let_39 :args (_let_26 true _let_33)))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 2)) (CONG _let_59 (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_28))) :args _let_37)) :args ((or _let_28 _let_33))) _let_39 :args (_let_28 true _let_33)))) (let ((_let_63 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 1)) (CONG _let_59 (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_30))) :args _let_37)) :args ((or _let_30 _let_33))) _let_39 :args (_let_30 true _let_33)))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_33 0)) _let_39 :args ((not _let_32) true _let_33)))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_32 _let_31 _let_29 _let_27 _let_25 _let_44 (not _let_56)))) _let_64 _let_63 _let_62 _let_61 _let_60 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v3_struct_0 A) true))))) :args (_let_57))) _let_58 :args (_let_56 false _let_57)) :args (_let_44 true _let_32 false _let_30 false _let_28 false _let_26 false _let_24 false _let_56)))) (let ((_let_66 (tptp.m2_relset_1 _let_14 _let_16 _let_16))) (let ((_let_67 (= _let_55 _let_66))) (let ((_let_68 (_let_3))) (let ((_let_69 (ASSUME :args _let_68))) (let ((_let_70 ((tptp.m1_relset_1 C A B)))) (let ((_let_71 (tptp.v1_funct_2 _let_14 _let_16 _let_16))) (let ((_let_72 (tptp.v1_funct_1 _let_14))) (let ((_let_73 (and _let_72 _let_71 _let_66))) (let ((_let_74 (tptp.k4_autgroup SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_75 (tptp.m2_fraenkel _let_14 _let_16 _let_16 _let_74))) (let ((_let_76 (not _let_75))) (let ((_let_77 (tptp.m1_fraenkel _let_74 _let_16 _let_16))) (let ((_let_78 (not _let_77))) (let ((_let_79 (tptp.v1_xboole_0 _let_16))) (let ((_let_80 (or _let_79 _let_78 _let_76 _let_73))) (let ((_let_81 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (BOUND_VARIABLE_1742 $$unsorted)) (or (tptp.v1_xboole_0 B) (not (tptp.m1_fraenkel C A B)) (not (tptp.m2_fraenkel BOUND_VARIABLE_1742 A B C)) (and (tptp.v1_funct_1 BOUND_VARIABLE_1742) (tptp.v1_funct_2 BOUND_VARIABLE_1742 A B) (tptp.m2_relset_1 BOUND_VARIABLE_1742 A B)))))) (let ((_let_82 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_83 (_let_81))) (let ((_let_84 ((not (= (tptp.m2_fraenkel BOUND_VARIABLE_1742 A B C) false))))) (let ((_let_85 (tptp.m1_subset_1 _let_13 _let_16))) (let ((_let_86 (not _let_85))) (let ((_let_87 (or _let_32 _let_31 _let_29 _let_27 _let_25 _let_86 _let_75))) (let ((_let_88 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (tptp.v3_struct_0 A) (not (tptp.v1_group_1 A)) (not (tptp.v3_group_1 A)) (not (tptp.v4_group_1 A)) (not (tptp.l1_group_1 A)) (not (tptp.m1_subset_1 B _let_1)) (tptp.m2_fraenkel (tptp.k6_autgroup A B) _let_1 _let_1 (tptp.k4_autgroup A))))))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (_let_88))) (let ((_let_91 (or _let_32 _let_25 _let_85))) (let ((_let_92 (forall ((A $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.l1_group_1 A)) (tptp.m1_subset_1 (tptp.k2_group_1 A) (tptp.u1_struct_0 A)))))) (let ((_let_93 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_94 (or _let_32 _let_31 _let_29 _let_27 _let_25 _let_77))) (let ((_let_95 (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (tptp.v3_struct_0 A) (not (tptp.v1_group_1 A)) (not (tptp.v3_group_1 A)) (not (tptp.v4_group_1 A)) (not (tptp.l1_group_1 A)) (tptp.m1_fraenkel (tptp.k4_autgroup A) _let_1 _let_1)))))) (let ((_let_96 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_97 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_94)) :args ((or _let_32 _let_31 _let_29 _let_27 _let_25 _let_77 (not _let_94)))) _let_64 _let_63 _let_62 _let_61 _let_60 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_96 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v3_struct_0 A) true))))) :args (_let_95))) _let_96 :args (_let_94 false _let_95)) :args (_let_77 true _let_32 false _let_30 false _let_28 false _let_26 false _let_24 false _let_94)))) (let ((_let_98 (not _let_79))) (let ((_let_99 (tptp.l1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_100 (not _let_99))) (let ((_let_101 (or _let_32 _let_100 _let_98))) (let ((_let_102 (forall ((A $$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_103 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_104 (or _let_25 _let_99))) (let ((_let_105 (forall ((A $$unsorted)) (or (not (tptp.l1_group_1 A)) (tptp.l1_struct_0 A))))) (let ((_let_106 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_107 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_101)) :args ((or _let_32 _let_100 _let_98 (not _let_101)))) _let_64 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_104)) :args ((or _let_25 _let_99 (not _let_104)))) _let_60 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_106 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.l1_group_1 A) false))))) :args (_let_105))) _let_106 :args (_let_104 false _let_105)) :args (_let_99 false _let_24 false _let_104)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_103 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v3_struct_0 A) true))))) :args (_let_102))) _let_103 :args (_let_101 false _let_102)) :args (_let_98 true _let_32 false _let_99 false _let_101)))) (let ((_let_108 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_80)) :args ((or _let_79 _let_78 _let_76 _let_73 (not _let_80)))) _let_107 _let_97 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_32 _let_31 _let_29 _let_27 _let_25 _let_86 _let_75 (not _let_87)))) _let_64 _let_63 _let_62 _let_61 _let_60 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_91)) :args ((or _let_32 _let_25 _let_85 (not _let_91)))) _let_64 _let_60 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_93 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v3_struct_0 A) true))))) :args (_let_92))) _let_93 :args (_let_91 false _let_92)) :args (_let_85 true _let_32 false _let_24 false _let_91)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_89 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.k6_autgroup A B)))) :args _let_90)) _let_89 :args (_let_87 false _let_88)) :args (_let_75 true _let_32 false _let_30 false _let_28 false _let_26 false _let_24 false _let_85 false _let_87)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args (_let_16 _let_16 _let_74 _let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_84)) :args _let_83)) _let_82 :args (_let_80 false _let_81)) :args (_let_73 true _let_79 false _let_77 false _let_75 false _let_80)))) (let ((_let_109 (not _let_73))) (let ((_let_110 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_67)) :args ((or _let_55 (not _let_66) (not _let_67)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_73 2)) :args ((or _let_66 _let_109))) _let_108 :args (_let_66 false _let_73)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_69 :args 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(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 $$unsorted)) (let ((_let_1 (tptp.v1_funct_2 C A B))) (let ((_let_2 (tptp.v1_funct_1 C))) (=> (tptp.m1_relset_1 C A B) (=> (and _let_2 _let_1) (and _let_2 (not (tptp.v1_xboole_0 C)) (tptp.v1_partfun1 C A B) _let_1)))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.g1_group_1 A B))) (let ((_let_2 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 A) (tptp.m1_relset_1 B _let_2 A)) (and (tptp.v1_group_1 _let_1) (tptp.l1_group_1 _let_1)))))) true true _let_11 true _let_10 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_relat_1 B)) (tptp.v1_relat_1 (tptp.k5_relat_1 A B)))) _let_9 (forall ((A $$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))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (tptp.m1_relset_1 E A B) (tptp.m1_relset_1 F C D)) (tptp.m2_relset_1 (tptp.k7_relset_1 A B C D E F) A D))) _let_8 true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_fraenkel C A B) (and (not (tptp.v1_xboole_0 C)) (tptp.v1_fraenkel C)))) true true _let_7 (forall ((A $$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)) (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_6 (tptp.v1_xboole_0 tptp.k1_xboole_0) (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))))))) (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)) (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 $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (not (tptp.v1_xboole_0 B)))))) (forall ((A $$unsorted)) (= (tptp.k6_partfun1 A) (tptp.k6_relat_1 A))) _let_5 _let_4 (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_3 (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (tptp.m1_subset_1 A B))) _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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.50/0.75 )
% 0.50/0.75 % SZS output end Proof for GRP631+1
% 0.50/0.75 % cvc5---1.0.5 exiting
% 0.50/0.75 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------