TSTP Solution File: GRP646+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : GRP646+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n015.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 00:26:53 EDT 2023
% Result : Theorem 26.29s 26.53s
% Output : Proof 26.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP646+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n015.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 : Mon Aug 28 23:46:25 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 26.29/26.53 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.fULNwQBRpW/cvc5---1.0.5_1960.p...
% 26.29/26.53 ------- get file name : TPTP file name is GRP646+1
% 26.29/26.53 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_1960.smt2...
% 26.29/26.53 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 26.29/26.53 --- Run --no-e-matching --full-saturate-quant at 5...
% 26.29/26.53 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 26.29/26.53 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 26.29/26.53 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 26.29/26.53 % SZS status Theorem for GRP646+1
% 26.29/26.53 % SZS output start Proof for GRP646+1
% 26.29/26.53 (
% 26.29/26.53 (let ((_let_1 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (forall ((B $$unsorted)) (=> (tptp.m1_group_2 B A) (tptp.m1_group_2 (tptp.k5_group_2 A) B))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.r2_hidden A B) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 C))) (tptp.m1_subset_1 A C))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (tptp.r1_tarski (tptp.k1_setfam_1 B) A))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D A B) (tptp.m2_relset_1 D A B)) (=> (not (= B tptp.k1_xboole_0)) (forall ((E $$unsorted)) (=> (exists ((F $$unsorted)) (and (tptp.r2_hidden F A) (tptp.r2_hidden F C) (= E (tptp.k1_funct_1 D F)))) (tptp.r2_hidden E (tptp.k9_relat_1 D C))))))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 A B) (or (tptp.v1_xboole_0 B) (tptp.r2_hidden A B)))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A) (tptp.v1_group_1 B) (tptp.m1_group_2 B A) (tptp.v1_group_1 C) (tptp.m1_group_2 C A)) (= (tptp.r1_group_2 A B C) (= B C)))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.m2_relset_1 C A B) (tptp.m1_relset_1 C A B))))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.k1_zfmisc_1 A))) (= (tptp.k6_setfam_1 A B) (tptp.k1_setfam_1 B)))))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m1_relset_1 C A B)) (= (tptp.k2_funct_2 A B C D) (tptp.k9_relat_1 C D)))))) (let ((_let_10 (tptp.v1_xboole_0 tptp.k1_xboole_0))) (let ((_let_11 (forall ((A $$unsorted)) (not (tptp.v1_xboole_0 (tptp.k1_zfmisc_1 A)))))) (let ((_let_12 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (not (tptp.v1_xboole_0 (tptp.k1_group_3 A))))))) (let ((_let_13 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.l1_group_1 A)) (forall ((B $$unsorted)) (=> (tptp.m1_group_2 B A) (and (not (tptp.v3_struct_0 B)) (tptp.v3_group_1 B) (tptp.l1_group_1 B)))))))) (let ((_let_14 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k5_group_2 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (and (tptp.v1_group_1 _let_1) (tptp.m1_group_2 _let_1 A))))))) (let ((_let_15 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_latsubgr A B))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.k1_group_3 A)))) (and (tptp.v1_group_1 _let_1) (tptp.m1_group_2 _let_1 A))))))) (let ((_let_16 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m1_relset_1 C A B)) (tptp.m1_subset_1 (tptp.k2_funct_2 A B C D) (tptp.k1_zfmisc_1 B)))))) (let ((_let_17 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (let ((_let_2 (tptp.k1_group_3 A))) (let ((_let_3 (tptp.k1_latsubgr A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.m2_relset_1 _let_3 _let_2 _let_1))))))))) (let ((_let_18 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v1_group_1 B) (tptp.m1_group_2 B A)) (= (= B (tptp.k5_group_2 A)) (= (tptp.u1_struct_0 B) (tptp.k6_domain_1 (tptp.u1_struct_0 A) (tptp.k2_group_1 A)))))))))) (let ((_let_19 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.l1_group_1 A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v3_group_1 B) (tptp.l1_group_1 B)) (= (tptp.m1_group_2 B A) (and (tptp.r1_tarski _let_1 (tptp.u1_struct_0 A)) (= (tptp.u1_group_1 B) (tptp.k1_realset1 (tptp.u1_group_1 A) _let_1))))))))))) (let ((_let_20 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.k1_group_3 A)))) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (tptp.v1_group_1 C) (tptp.m1_group_2 C A)) (= (= C (tptp.k2_latsubgr A B)) (= (tptp.u1_struct_0 C) (tptp.k6_setfam_1 _let_1 (tptp.k2_funct_2 (tptp.k1_group_3 A) (tptp.k1_zfmisc_1 _let_1) (tptp.k1_latsubgr A) B))))))))))))) (let ((_let_21 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (let ((_let_2 (tptp.k1_group_3 A))) (=> (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.k1_latsubgr A)) (forall ((C $$unsorted)) (=> (and (tptp.v1_group_1 C) (tptp.m1_group_2 C A)) (= (tptp.k1_funct_1 B C) (tptp.u1_struct_0 C))))))))))))) (let ((_let_22 (forall ((A $$unsorted) (B $$unsorted)) (= (= A B) (and (tptp.r1_tarski A B) (tptp.r1_tarski B A)))))) (let ((_let_23 (not (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k5_group_2 A))) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.k1_group_3 A)))) (=> (tptp.r2_hidden _let_1 B) (tptp.r1_group_2 A (tptp.k2_latsubgr A B) _let_1)))))))))) (let ((_let_24 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_25 (tptp.k1_zfmisc_1 _let_24))) (let ((_let_26 (tptp.v1_xboole_0 _let_25))) (let ((_let_27 (= tptp.k1_xboole_0 _let_25))) (let ((_let_28 (ASSUME :args (_let_10)))) (let ((_let_29 (not _let_26))) (let ((_let_30 (_let_11))) (let ((_let_31 (ASSUME :args _let_30))) (let ((_let_32 (tptp.k5_group_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_33 (tptp.r2_hidden _let_32 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_34 (not _let_33))) (let ((_let_35 (tptp.k1_group_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_36 (tptp.r2_hidden _let_32 _let_35))) (let ((_let_37 (not _let_36))) (let ((_let_38 (tptp.k1_latsubgr SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_39 (tptp.k9_relat_1 _let_38 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_40 (tptp.k1_funct_1 _let_38 _let_32))) (let ((_let_41 (tptp.r2_hidden _let_40 _let_39))) (let ((_let_42 (tptp.m2_relset_1 _let_38 _let_35 _let_25))) (let ((_let_43 (not _let_42))) (let ((_let_44 (tptp.v1_funct_2 _let_38 _let_35 _let_25))) (let ((_let_45 (not _let_44))) (let ((_let_46 (tptp.v1_funct_1 _let_38))) (let ((_let_47 (not _let_46))) (let ((_let_48 (or _let_47 _let_45 _let_43 _let_27 _let_41 _let_37 _let_34))) (let ((_let_49 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (BOUND_VARIABLE_2378 $$unsorted)) (or (not (tptp.v1_funct_1 D)) (not (tptp.v1_funct_2 D A B)) (not (tptp.m2_relset_1 D A B)) (= tptp.k1_xboole_0 B) (tptp.r2_hidden (tptp.k1_funct_1 D BOUND_VARIABLE_2378) (tptp.k9_relat_1 D C)) (not (tptp.r2_hidden BOUND_VARIABLE_2378 A)) (not (tptp.r2_hidden BOUND_VARIABLE_2378 C)))))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (tptp.k2_funct_2 _let_35 _let_25 _let_38 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_52 (tptp.u1_struct_0 _let_32))) (let ((_let_53 (tptp.r2_hidden _let_52 _let_51))) (let ((_let_54 (= _let_51 _let_39))) (let ((_let_55 (= _let_52 _let_40))) (let ((_let_56 (not _let_41))) (let ((_let_57 (tptp.k1_setfam_1 _let_51))) (let ((_let_58 (tptp.r1_tarski _let_57 _let_52))) (let ((_let_59 (not _let_53))) (let ((_let_60 (or _let_59 _let_58))) (let ((_let_61 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.r2_hidden A B)) (tptp.r1_tarski (tptp.k1_setfam_1 B) A))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (tptp.k6_setfam_1 _let_24 _let_51))) (let ((_let_64 (= _let_63 _let_57))) (let ((_let_65 (tptp.k2_latsubgr SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_66 (tptp.u1_struct_0 _let_65))) (let ((_let_67 (tptp.r1_tarski _let_66 _let_52))) (let ((_let_68 (= _let_66 _let_63))) (let ((_let_69 (not _let_58))) (let ((_let_70 (tptp.m1_subset_1 _let_51 (tptp.k1_zfmisc_1 _let_25)))) (let ((_let_71 (not _let_70))) (let ((_let_72 (or _let_71 _let_64))) (let ((_let_73 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.k1_zfmisc_1 A)))) (= (tptp.k6_setfam_1 A B) (tptp.k1_setfam_1 B)))))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (tptp.m1_relset_1 _let_38 _let_35 _let_25))) (let ((_let_76 (not _let_75))) (let ((_let_77 (or _let_47 _let_45 _let_76 _let_70))) (let ((_let_78 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (or (not (tptp.v1_funct_1 C)) (not (tptp.v1_funct_2 C A B)) (not (tptp.m1_relset_1 C A B)) (tptp.m1_subset_1 (tptp.k2_funct_2 A B C D) (tptp.k1_zfmisc_1 B)))))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (= _let_42 _let_75))) (let ((_let_81 (_let_7))) (let ((_let_82 (ASSUME :args _let_81))) (let ((_let_83 (and _let_46 _let_44 _let_42))) (let ((_let_84 (tptp.l1_group_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_85 (not _let_84))) (let ((_let_86 (tptp.v4_group_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_87 (not _let_86))) (let ((_let_88 (tptp.v3_group_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_89 (not _let_88))) (let ((_let_90 (tptp.v3_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_91 (or _let_90 _let_89 _let_87 _let_85 _let_83))) (let ((_let_92 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (let ((_let_2 (tptp.k1_group_3 A))) (let ((_let_3 (tptp.k1_latsubgr A))) (or (tptp.v3_struct_0 A) (not (tptp.v3_group_1 A)) (not (tptp.v4_group_1 A)) (not (tptp.l1_group_1 A)) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.m2_relset_1 _let_3 _let_2 _let_1))))))))) (let ((_let_93 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_94 (tptp.r1_group_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_65 _let_32))) (let ((_let_95 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.k1_zfmisc_1 _let_35)))) (let ((_let_96 (not _let_95))) (let ((_let_97 (tptp.v1_xboole_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_98 (or _let_90 _let_89 _let_87 _let_85 _let_97 _let_96 _let_34 _let_94))) (let ((_let_99 (forall ((A $$unsorted) (BOUND_VARIABLE_1600 $$unsorted)) (let ((_let_1 (tptp.k5_group_2 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)) (tptp.v1_xboole_0 BOUND_VARIABLE_1600) (not (tptp.m1_subset_1 BOUND_VARIABLE_1600 (tptp.k1_zfmisc_1 (tptp.k1_group_3 A)))) (not (tptp.r2_hidden _let_1 BOUND_VARIABLE_1600)) (tptp.r1_group_2 A (tptp.k2_latsubgr A BOUND_VARIABLE_1600) _let_1)))))) (let ((_let_100 (not _let_98))) (let ((_let_101 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_102 (or))) (let ((_let_103 (not _let_99))) (let ((_let_104 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_101) :args (_let_103))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_103) _let_99))) (REFL :args (_let_100)) :args _let_102)) _let_101 :args (_let_100 true _let_99)))) (let ((_let_105 (REFL :args (_let_98)))) (let ((_let_106 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_98 3)) (CONG _let_105 (MACRO_SR_PRED_INTRO :args ((= (not _let_85) _let_84))) :args _let_102)) :args ((or _let_84 _let_98))) _let_104 :args (_let_84 true _let_98)))) (let ((_let_107 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_98 2)) (CONG _let_105 (MACRO_SR_PRED_INTRO :args ((= (not _let_87) _let_86))) :args _let_102)) :args ((or _let_86 _let_98))) _let_104 :args (_let_86 true _let_98)))) (let ((_let_108 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_98 1)) (CONG _let_105 (MACRO_SR_PRED_INTRO :args ((= (not _let_89) _let_88))) :args _let_102)) :args ((or _let_88 _let_98))) _let_104 :args (_let_88 true _let_98)))) (let ((_let_109 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_98 0)) _let_104 :args ((not _let_90) true _let_98)))) (let ((_let_110 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_91)) :args ((or _let_90 _let_89 _let_87 _let_85 _let_83 (not _let_91)))) _let_109 _let_108 _let_107 _let_106 (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_83 true _let_90 false _let_88 false _let_86 false _let_84 false _let_91)))) (let ((_let_111 (not _let_83))) (let ((_let_112 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_83 2)) :args ((or _let_42 _let_111))) _let_110 :args (_let_42 false _let_83)))) (let ((_let_113 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_80)) :args ((or _let_43 _let_75 (not _let_80)))) _let_112 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args (_let_35 _let_25 _let_38 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(tptp.v1_xboole_0 C)) (tptp.v1_partfun1 C A B) _let_1)))))))) _let_22 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (forall ((B $$unsorted)) (= (= B (tptp.k1_group_3 A)) (forall ((C $$unsorted)) (= (tptp.r2_hidden C B) (and (tptp.v1_group_1 C) (tptp.m1_group_2 C A)))))))) _let_21 _let_20 _let_19 _let_18 (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)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B A)) (tptp.m1_subset_1 (tptp.k18_group_2 A B) (tptp.k5_finsub_1 A)))) true true _let_17 true true true true true _let_16 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_group_1 A)) (tptp.m1_subset_1 (tptp.k2_group_1 A) (tptp.u1_struct_0 A)))) _let_15 true (forall ((A $$unsorted)) (tptp.v4_finsub_1 (tptp.k5_finsub_1 A))) _let_14 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B A)) (tptp.m1_subset_1 (tptp.k6_domain_1 A B) (tptp.k1_zfmisc_1 A)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 _let_1)) (tptp.m1_subset_1 (tptp.k6_setfam_1 A B) _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m1_relset_1 C A B) (tptp.m1_subset_1 D A)) (tptp.m1_subset_1 (tptp.k8_funct_2 A B C D) B))) true (forall ((A $$unsorted)) (=> (tptp.l1_group_1 A) (tptp.l1_struct_0 A))) true _let_13 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A) (tptp.m1_group_2 B A)) (forall ((C $$unsorted)) (=> (tptp.m1_group_6 C A B) (tptp.m1_group_2 C A))))) true true (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 $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.l1_group_1 A)) (exists ((B $$unsorted)) (tptp.m1_group_2 B 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) (tptp.m1_group_2 B A)) (exists ((C $$unsorted)) (tptp.m1_group_6 C A B)))) (forall ((A $$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)) (exists ((C $$unsorted)) (tptp.m2_relset_1 C A B))) _let_12 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A)) (not (tptp.v1_xboole_0 (tptp.u1_struct_0 A))))) _let_11 _let_10 (forall ((A $$unsorted)) (not (tptp.v1_xboole_0 (tptp.k1_tarski A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B))) (not (tptp.v1_xboole_0 (tptp.k2_zfmisc_1 A B))))) (forall ((A $$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 $$unsorted)) (=> (= (tptp.g1_group_1 A B) (tptp.g1_group_1 C D)) (and (= A C) (= B D))))))) (forall ((A $$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)))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (not (tptp.v1_xboole_0 B)))))) (exists ((A $$unsorted)) (tptp.v1_xboole_0 A)) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (and (tptp.m1_relset_1 C A B) (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (tptp.v1_xboole_0 B)))) (exists ((A $$unsorted)) (not (tptp.v1_xboole_0 A))) (exists ((A $$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 $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B A)) (= (tptp.k18_group_2 A B) (tptp.k1_tarski B)))) _let_9 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B A)) (= (tptp.k6_domain_1 A B) (tptp.k1_tarski B)))) _let_8 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B) (tptp.m1_relset_1 C A B) (tptp.m1_subset_1 D A)) (= (tptp.k8_funct_2 A B C D) (tptp.k1_funct_1 C D)))) (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) (tptp.m1_group_2 B A)) (forall ((C $$unsorted)) (= (tptp.m1_group_6 C A B) (tptp.m1_group_2 C B))))) _let_7 _let_6 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A) (tptp.v1_group_1 B) (tptp.m1_group_2 B A) (tptp.v1_group_1 C) (tptp.m1_group_2 C A)) (tptp.r1_group_2 A B B))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski A A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A) (tptp.v1_group_1 B) (tptp.m1_group_2 B A) (tptp.v1_group_1 C) (tptp.m1_group_2 C A)) (=> (tptp.r1_group_2 A B C) (tptp.r1_group_2 A C B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (tptp.m1_subset_1 A B))) _let_5 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.m1_subset_1 A (tptp.k1_zfmisc_1 B)) (tptp.r1_tarski A B))) _let_4 _let_3 _let_2 (forall ((A $$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 $$unsorted)) (=> (tptp.v1_xboole_0 A) (= A tptp.k1_xboole_0))) _let_1 (forall ((A $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 26.29/26.54 )
% 26.29/26.54 % SZS output end Proof for GRP646+1
% 26.29/26.54 % cvc5---1.0.5 exiting
% 26.29/26.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------