TSTP Solution File: GRP624+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : GRP624+1 : TPTP v8.1.2. Released v3.4.0.
% 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 00:26:40 EDT 2023
% Result : Theorem 0.21s 0.76s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP624+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.17/0.36 % Computer : n008.cluster.edu
% 0.17/0.36 % Model : x86_64 x86_64
% 0.17/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.36 % Memory : 8042.1875MB
% 0.17/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.36 % CPULimit : 300
% 0.17/0.36 % WCLimit : 300
% 0.17/0.36 % DateTime : Mon Aug 28 23:45:47 EDT 2023
% 0.17/0.36 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.76 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.Divz85C093/cvc5---1.0.5_31548.p...
% 0.21/0.76 ------- get file name : TPTP file name is GRP624+1
% 0.21/0.76 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_31548.smt2...
% 0.21/0.76 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.76 % SZS status Theorem for GRP624+1
% 0.21/0.76 % SZS output start Proof for GRP624+1
% 0.21/0.76 (
% 0.21/0.76 (let ((_let_1 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v1_group_1 A) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (forall ((B $$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_2 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.m2_relset_1 C A B) (tptp.m1_relset_1 C A B))))) (let ((_let_3 (forall ((A $$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 $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A B))) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (tptp.v1_funct_1 D) (tptp.v1_funct_2 D _let_1 C) (tptp.m1_relset_1 D _let_1 C) (tptp.m1_subset_1 E A) (tptp.m1_subset_1 F B)) (= (tptp.k2_binop_1 A B C D E F) (tptp.k1_binop_1 D E F))))))) (let ((_let_5 (forall ((A $$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 $$unsorted)) (=> (tptp.m1_fraenkel C A B) (and (not (tptp.v1_xboole_0 C)) (tptp.v1_fraenkel C)))))) (let ((_let_7 (forall ((A $$unsorted)) (=> (tptp.l1_group_1 A) (tptp.l1_struct_0 A))))) (let ((_let_8 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_autgroup A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.k2_autgroup A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v1_group_1 A) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.m2_relset_1 _let_3 _let_2 _let_1))))))))) (let ((_let_9 (forall ((A $$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.k1_autgroup A) _let_1 _let_1)))))) (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.k1_autgroup A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 _let_1) (tptp.m2_relset_1 B _let_2 _let_1)) (= (= B (tptp.k2_autgroup A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m2_fraenkel C _let_1 _let_1 (tptp.k1_autgroup A)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k1_autgroup A))) (=> (tptp.m2_fraenkel D _let_1 _let_1 _let_2) (= (tptp.k2_binop_1 _let_2 _let_2 _let_2 B C D) (tptp.k7_funct_2 _let_1 _let_1 _let_1 D C)))))))))))))))))) (let ((_let_11 (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.u1_struct_0 A))) (=> (tptp.m2_fraenkel B _let_1 _let_1 (tptp.k4_autgroup A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m2_fraenkel C _let_1 _let_1 (tptp.k4_autgroup A)) (= (tptp.k1_binop_1 (tptp.k2_autgroup A) B C) (tptp.k7_funct_2 _let_1 _let_1 _let_1 C B))))))))))))) (let ((_let_12 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_13 (tptp.k7_funct_2 _let_12 _let_12 _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_14 (tptp.k2_autgroup SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_15 (tptp.k1_binop_1 _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_16 (= _let_15 _let_13))) (let ((_let_17 (tptp.k1_autgroup SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_18 (tptp.k2_binop_1 _let_17 _let_17 _let_17 _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_19 (= _let_13 _let_18))) (let ((_let_20 (= _let_15 _let_18))) (let ((_let_21 (tptp.k4_autgroup SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_22 (tptp.m2_fraenkel SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_12 _let_12 _let_21))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.m2_fraenkel SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_12 _let_12 _let_21))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.l1_group_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_27 (not _let_26))) (let ((_let_28 (tptp.v4_group_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_29 (not _let_28))) (let ((_let_30 (tptp.v3_group_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_31 (not _let_30))) (let ((_let_32 (tptp.v1_group_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_33 (not _let_32))) (let ((_let_34 (tptp.v3_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_35 (or _let_34 _let_33 _let_31 _let_29 _let_27 _let_25 _let_23 _let_16))) (let ((_let_36 (not _let_16))) (let ((_let_37 (forall ((A $$unsorted) (BOUND_VARIABLE_1441 $$unsorted) (BOUND_VARIABLE_1439 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k4_autgroup 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_1439 _let_1 _let_1 _let_2)) (not (tptp.m2_fraenkel BOUND_VARIABLE_1441 _let_1 _let_1 _let_2)) (= (tptp.k1_binop_1 (tptp.k2_autgroup A) BOUND_VARIABLE_1439 BOUND_VARIABLE_1441) (tptp.k7_funct_2 _let_1 _let_1 _let_1 BOUND_VARIABLE_1441 BOUND_VARIABLE_1439)))))))) (let ((_let_38 (not _let_35))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (or))) (let ((_let_41 (not _let_37))) (let ((_let_42 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_39) :args (_let_41))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_37))) (REFL :args (_let_38)) :args _let_40)) _let_39 :args (_let_38 true _let_37)))) (let ((_let_43 (tptp.m2_fraenkel SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_12 _let_12 _let_17))) (let ((_let_44 (not _let_43))) (let ((_let_45 (tptp.m2_fraenkel SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_12 _let_12 _let_17))) (let ((_let_46 (not _let_45))) (let ((_let_47 (or _let_46 _let_44 _let_19))) (let ((_let_48 (forall ((C $$unsorted) (BOUND_VARIABLE_1611 $$unsorted)) (let ((_let_1 (tptp.k1_autgroup SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_2 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (or (not (tptp.m2_fraenkel C _let_2 _let_2 _let_1)) (not (tptp.m2_fraenkel BOUND_VARIABLE_1611 _let_2 _let_2 _let_1)) (= (tptp.k7_funct_2 _let_2 _let_2 _let_2 BOUND_VARIABLE_1611 C) (tptp.k2_binop_1 _let_1 _let_1 _let_1 (tptp.k2_autgroup SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) C BOUND_VARIABLE_1611)))))))) (let ((_let_49 (tptp.k2_zfmisc_1 _let_17 _let_17))) (let ((_let_50 (tptp.m2_relset_1 _let_14 _let_49 _let_17))) (let ((_let_51 (not _let_50))) (let ((_let_52 (tptp.v1_funct_2 _let_14 _let_49 _let_17))) (let ((_let_53 (not _let_52))) (let ((_let_54 (tptp.v1_funct_1 _let_14))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_34 _let_33 _let_31 _let_29 _let_27 _let_55 _let_53 _let_51 _let_48))) (let ((_let_57 (forall ((A $$unsorted) (BOUND_VARIABLE_1644 $$unsorted)) (let ((_let_1 (tptp.k1_autgroup A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (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.v1_funct_1 BOUND_VARIABLE_1644)) (not (tptp.v1_funct_2 BOUND_VARIABLE_1644 _let_2 _let_1)) (not (tptp.m2_relset_1 BOUND_VARIABLE_1644 _let_2 _let_1)) (= (= (tptp.k2_autgroup A) BOUND_VARIABLE_1644) (forall ((C $$unsorted) (BOUND_VARIABLE_1611 $$unsorted)) (let ((_let_1 (tptp.k1_autgroup A))) (let ((_let_2 (tptp.u1_struct_0 A))) (or (not (tptp.m2_fraenkel C _let_2 _let_2 _let_1)) (not (tptp.m2_fraenkel BOUND_VARIABLE_1611 _let_2 _let_2 _let_1)) (= (tptp.k7_funct_2 _let_2 _let_2 _let_2 BOUND_VARIABLE_1611 C) (tptp.k2_binop_1 _let_1 _let_1 _let_1 BOUND_VARIABLE_1644 C BOUND_VARIABLE_1611))))))))))))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (tptp.k1_autgroup A))) (let ((_let_60 (and _let_54 _let_52 _let_50))) (let ((_let_61 (or _let_34 _let_33 _let_31 _let_29 _let_27 _let_60))) (let ((_let_62 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_autgroup A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.k2_autgroup 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)) (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))))))))) (let ((_let_63 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_64 (REFL :args (_let_35)))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_35 4)) (CONG _let_64 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_40)) :args ((or _let_26 _let_35))) _let_42 :args (_let_26 true _let_35)))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_35 3)) (CONG _let_64 (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_28))) :args _let_40)) :args ((or _let_28 _let_35))) _let_42 :args (_let_28 true _let_35)))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_35 2)) (CONG _let_64 (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_30))) :args _let_40)) :args ((or _let_30 _let_35))) _let_42 :args (_let_30 true _let_35)))) (let ((_let_68 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_35 1)) (CONG _let_64 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_40)) :args ((or _let_32 _let_35))) _let_42 :args (_let_32 true _let_35)))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_35 0)) _let_42 :args ((not _let_34) true _let_35)))) (let ((_let_70 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_61)) :args ((or _let_34 _let_33 _let_31 _let_29 _let_27 _let_60 (not _let_61)))) _let_69 _let_68 _let_67 _let_66 _let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_63 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v3_struct_0 A) true))))) :args (_let_62))) _let_63 :args (_let_61 false _let_62)) :args (_let_60 true _let_34 false _let_32 false _let_30 false _let_28 false _let_26 false _let_61)))) (let ((_let_71 (not _let_60))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_60 2)) :args ((or _let_50 _let_71))) _let_70 :args (_let_50 false _let_60)))) (let ((_let_73 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_60 1)) :args ((or _let_52 _let_71))) _let_70 :args (_let_52 false _let_60)))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_60 0)) :args ((or _let_54 _let_71))) _let_70 :args (_let_54 false _let_60)))) (let ((_let_75 (_let_48))) (let ((_let_76 (or _let_34 _let_33 _let_31 _let_29 _let_27 _let_23 _let_43))) (let ((_let_77 (forall ((A $$unsorted) (BOUND_VARIABLE_2048 $$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_2048 _let_1 _let_1 (tptp.k4_autgroup A))) (tptp.m2_fraenkel BOUND_VARIABLE_2048 _let_1 _let_1 (tptp.k1_autgroup A))))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (_let_77))) (let ((_let_80 (tptp.u1_struct_0 A))) (let ((_let_81 ((not (= (tptp.m2_fraenkel BOUND_VARIABLE_2048 _let_80 _let_80 (tptp.k4_autgroup A)) false))))) (let ((_let_82 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_34 _let_33 _let_31 _let_29 _let_27 _let_23 _let_43 (not _let_76)))) _let_69 _let_68 _let_67 _let_66 _let_65 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_35 6)) (CONG _let_64 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_40)) :args ((or _let_22 _let_35))) _let_42 :args (_let_22 true _let_35)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_81)) :args _let_79)) _let_78 :args (_let_76 false _let_77)) :args (_let_43 true _let_34 false _let_32 false _let_30 false _let_28 false _let_26 false _let_22 false _let_76)))) (let ((_let_83 (or _let_34 _let_33 _let_31 _let_29 _let_27 _let_25 _let_45))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_83)) :args ((or _let_34 _let_33 _let_31 _let_29 _let_27 _let_25 _let_45 (not _let_83)))) _let_69 _let_68 _let_67 _let_66 _let_65 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_35 5)) (CONG _let_64 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_40)) :args ((or _let_24 _let_35))) _let_42 :args (_let_24 true _let_35)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_81)) :args _let_79)) _let_78 :args (_let_83 false _let_77)) :args (_let_45 true _let_34 false _let_32 false _let_30 false _let_28 false _let_26 false _let_24 false _let_83)))) (let ((_let_85 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_17))) (let ((_let_86 (not _let_85))) (let ((_let_87 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_17))) (let ((_let_88 (not _let_87))) (let ((_let_89 (tptp.m1_relset_1 _let_14 _let_49 _let_17))) (let 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(_let_47)) :args ((or _let_46 _let_44 _let_19 (not _let_47)))) _let_84 _let_82 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_75) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.k7_funct_2 _let_12 _let_12 _let_12 BOUND_VARIABLE_1611 C)))) :args _let_75)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_34 _let_33 _let_31 _let_29 _let_27 _let_55 _let_53 _let_51 _let_48 (not _let_56)))) _let_69 _let_68 _let_67 _let_66 _let_65 _let_74 _let_73 _let_72 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_58 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.v1_funct_2 BOUND_VARIABLE_1644 (tptp.k2_zfmisc_1 _let_59 _let_59) _let_59) false))))) :args (_let_57)))) _let_58 :args (_let_56 false _let_57)) :args (_let_48 true _let_34 false _let_32 false _let_30 false _let_28 false _let_26 false _let_54 false _let_52 false _let_50 false _let_56)) :args (_let_47 false _let_48)) :args (_let_19 false _let_45 false _let_43 false _let_47)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_35 7)) _let_42 :args (_let_36 true _let_35)) :args (false false _let_20 false _let_19 true _let_16)) :args (_let_11 (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) (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 $$unsorted)) (let ((_let_1 (tptp.v1_funct_2 C A B))) (let ((_let_2 (tptp.v1_funct_1 C))) (=> (tptp.m1_relset_1 C A B) (=> (and _let_2 _let_1) (and _let_2 (not (tptp.v1_xboole_0 C)) (tptp.v1_partfun1 C A B) _let_1)))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k2_tarski A B) (tptp.k2_tarski B A))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.k1_binop_1 A B C) (tptp.k1_funct_1 A (tptp.k4_tarski B C)))))) _let_10 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k4_tarski A B) (tptp.k2_tarski (tptp.k2_tarski A B) (tptp.k1_tarski A)))) (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_9 true true true true true _let_8 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A B))) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (tptp.v1_funct_1 D) (tptp.v1_funct_2 D _let_1 C) (tptp.m1_relset_1 D _let_1 C) (tptp.m1_subset_1 E A) (tptp.m1_subset_1 F B)) (tptp.m1_subset_1 (tptp.k2_binop_1 A B C D E F) C)))) true true (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v1_group_1 A) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (tptp.m1_fraenkel (tptp.k4_autgroup A) _let_1 _let_1)))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_relat_1 B)) (tptp.v1_relat_1 (tptp.k5_relat_1 A B)))) (forall ((A $$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_7 true _let_6 true true (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)))))) (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 $$unsorted)) (let ((_let_1 (tptp.g1_group_1 A B))) (let ((_let_2 (tptp.k2_zfmisc_1 A A))) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 A) (tptp.m1_relset_1 B _let_2 A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v1_group_1 _let_1)))))) _let_5 (tptp.v1_xboole_0 tptp.k1_xboole_0) (forall ((A $$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 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m1_relset_1 D A B) (tptp.v1_funct_1 E) (tptp.v1_funct_2 E B C) (tptp.m1_relset_1 E B C)) (= (tptp.k7_funct_2 A B C D E) (tptp.k5_relat_1 D E)))) _let_3 _let_2 (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski A A)) _let_1 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (tptp.m1_subset_1 A B))) (forall ((A $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.77 )
% 0.21/0.77 % SZS output end Proof for GRP624+1
% 0.21/0.77 % cvc5---1.0.5 exiting
% 0.21/0.77 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------