TSTP Solution File: ALG215+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ALG215+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n024.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 : Wed Aug 30 16:08:41 EDT 2023
% Result : Theorem 0.21s 0.68s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ALG215+1 : TPTP v8.1.2. Released v3.4.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n024.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 06:05:53 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.68 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.hy9uXVmJh4/cvc5---1.0.5_29582.p...
% 0.21/0.68 ------- get file name : TPTP file name is ALG215+1
% 0.21/0.68 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_29582.smt2...
% 0.21/0.68 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.68 % SZS status Theorem for ALG215+1
% 0.21/0.68 % SZS output start Proof for ALG215+1
% 0.21/0.68 (
% 0.21/0.68 (let ((_let_1 (forall ((A $$unsorted)) (=> (tptp.v1_xboole_0 A) (= A tptp.k1_xboole_0))))) (let ((_let_2 (forall ((A $$unsorted)) (=> (tptp.r1_tarski A tptp.k1_xboole_0) (= A tptp.k1_xboole_0))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_rlvect_1 A) (tptp.v4_rlvect_1 A) (tptp.v5_rlvect_1 A) (tptp.v6_rlvect_1 A) (tptp.v4_group_1 A) (tptp.v6_vectsp_1 A) (tptp.v7_vectsp_1 A) (tptp.v8_vectsp_1 A) (tptp.l3_vectsp_1 A) (not (tptp.v3_struct_0 B)) (tptp.v3_rlvect_1 B) (tptp.v4_rlvect_1 B) (tptp.v5_rlvect_1 B) (tptp.v6_rlvect_1 B) (tptp.v5_vectsp_2 B A) (tptp.l1_vectsp_2 B A) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.u1_struct_0 B)))) (forall ((D $$unsorted)) (=> (tptp.m2_rmod_4 D A B C) (tptp.m1_rmod_4 D A B))))))) (let ((_let_4 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_subset_1 A))) (and (tptp.v1_xboole_0 _let_1) (tptp.m1_subset_1 _let_1 (tptp.k1_zfmisc_1 A))))))) (let ((_let_5 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_rlvect_1 A) (tptp.v4_rlvect_1 A) (tptp.v5_rlvect_1 A) (tptp.v6_rlvect_1 A) (tptp.v4_group_1 A) (tptp.v6_vectsp_1 A) (tptp.v7_vectsp_1 A) (tptp.v8_vectsp_1 A) (tptp.l3_vectsp_1 A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v3_rlvect_1 B) (tptp.v4_rlvect_1 B) (tptp.v5_rlvect_1 B) (tptp.v6_rlvect_1 B) (tptp.v5_vectsp_2 B A) (tptp.l1_vectsp_2 B A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.u1_struct_0 B))) (forall ((D $$unsorted)) (=> (tptp.m1_rmod_4 D A B) (= (tptp.m2_rmod_4 D A B C) (tptp.r1_tarski (tptp.k2_rmod_4 A B D) C)))))))))))) (let ((_let_6 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_rlvect_1 A) (tptp.v4_rlvect_1 A) (tptp.v5_rlvect_1 A) (tptp.v6_rlvect_1 A) (tptp.v4_group_1 A) (tptp.v6_vectsp_1 A) (tptp.v7_vectsp_1 A) (tptp.v8_vectsp_1 A) (tptp.l3_vectsp_1 A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v3_rlvect_1 B) (tptp.v4_rlvect_1 B) (tptp.v5_rlvect_1 B) (tptp.v6_rlvect_1 B) (tptp.v5_vectsp_2 B A) (tptp.l1_vectsp_2 B A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.u1_struct_0 B))) (= (tptp.v1_rmod_5 C A B) (forall ((D $$unsorted)) (=> (tptp.m2_rmod_4 D A B C) (=> (= (tptp.k5_rmod_4 A B D) (tptp.k1_rlvect_1 B)) (= (tptp.k2_rmod_4 A B D) tptp.k1_xboole_0))))))))))))) (let ((_let_7 (not (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_rlvect_1 A) (tptp.v4_rlvect_1 A) (tptp.v5_rlvect_1 A) (tptp.v6_rlvect_1 A) (tptp.v4_group_1 A) (tptp.v6_vectsp_1 A) (tptp.v7_vectsp_1 A) (tptp.v8_vectsp_1 A) (tptp.l3_vectsp_1 A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v3_rlvect_1 B) (tptp.v4_rlvect_1 B) (tptp.v5_rlvect_1 B) (tptp.v6_rlvect_1 B) (tptp.v5_vectsp_2 B A) (tptp.l1_vectsp_2 B A)) (tptp.v1_rmod_5 (tptp.k1_subset_1 (tptp.u1_struct_0 B)) A B)))))))) (let ((_let_8 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_9 (tptp.k1_subset_1 _let_8))) (let ((_let_10 (= tptp.k1_xboole_0 _let_9))) (let ((_let_11 (tptp.k2_rmod_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25))) (let ((_let_12 (tptp.r1_tarski _let_11 _let_9))) (let ((_let_13 (tptp.r1_tarski _let_11 tptp.k1_xboole_0))) (let ((_let_14 (tptp.v1_xboole_0 _let_9))) (let ((_let_15 (not _let_14))) (let ((_let_16 (or _let_15 _let_10))) (let ((_let_17 (forall ((A $$unsorted)) (or (not (tptp.v1_xboole_0 A)) (= tptp.k1_xboole_0 A))))) (let ((_let_18 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_19 (forall ((BOUND_VARIABLE_1869 $$unsorted)) (tptp.v1_xboole_0 (tptp.k1_subset_1 BOUND_VARIABLE_1869))))) (let ((_let_20 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_21 (_let_19))) (let ((_let_22 (tptp.m2_rmod_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_9))) (let ((_let_23 (= _let_22 _let_12))) (let ((_let_24 (tptp.m1_rmod_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.m1_subset_1 _let_9 (tptp.k1_zfmisc_1 _let_8)))) (let ((_let_27 (not _let_26))) (let ((_let_28 (tptp.l1_vectsp_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_29 (not _let_28))) (let ((_let_30 (tptp.v5_vectsp_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_31 (not _let_30))) (let ((_let_32 (tptp.v6_rlvect_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_33 (not _let_32))) (let ((_let_34 (tptp.v5_rlvect_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_35 (not _let_34))) (let ((_let_36 (tptp.v4_rlvect_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_37 (not _let_36))) (let ((_let_38 (tptp.v3_rlvect_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_39 (not _let_38))) (let ((_let_40 (tptp.v3_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_41 (tptp.l3_vectsp_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_42 (not _let_41))) (let ((_let_43 (tptp.v8_vectsp_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_44 (not _let_43))) (let ((_let_45 (tptp.v7_vectsp_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_46 (not _let_45))) (let ((_let_47 (tptp.v6_vectsp_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_48 (not _let_47))) (let ((_let_49 (tptp.v4_group_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_50 (not _let_49))) (let ((_let_51 (tptp.v6_rlvect_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_52 (not _let_51))) (let ((_let_53 (tptp.v5_rlvect_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_54 (not _let_53))) (let ((_let_55 (tptp.v4_rlvect_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_56 (not _let_55))) (let ((_let_57 (tptp.v3_rlvect_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_58 (not _let_57))) (let ((_let_59 (tptp.v3_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_60 (or _let_59 _let_58 _let_56 _let_54 _let_52 _let_50 _let_48 _let_46 _let_44 _let_42 _let_40 _let_39 _let_37 _let_35 _let_33 _let_31 _let_29 _let_27 _let_25 _let_23))) (let ((_let_61 (forall ((A $$unsorted) (BOUND_VARIABLE_1830 $$unsorted) (BOUND_VARIABLE_1828 $$unsorted) (BOUND_VARIABLE_1826 $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v3_rlvect_1 A)) (not (tptp.v4_rlvect_1 A)) (not (tptp.v5_rlvect_1 A)) (not (tptp.v6_rlvect_1 A)) (not (tptp.v4_group_1 A)) (not (tptp.v6_vectsp_1 A)) (not (tptp.v7_vectsp_1 A)) (not (tptp.v8_vectsp_1 A)) (not (tptp.l3_vectsp_1 A)) (tptp.v3_struct_0 BOUND_VARIABLE_1826) (not (tptp.v3_rlvect_1 BOUND_VARIABLE_1826)) (not (tptp.v4_rlvect_1 BOUND_VARIABLE_1826)) (not (tptp.v5_rlvect_1 BOUND_VARIABLE_1826)) (not (tptp.v6_rlvect_1 BOUND_VARIABLE_1826)) (not (tptp.v5_vectsp_2 BOUND_VARIABLE_1826 A)) (not (tptp.l1_vectsp_2 BOUND_VARIABLE_1826 A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_1830 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 BOUND_VARIABLE_1826)))) (not (tptp.m1_rmod_4 BOUND_VARIABLE_1828 A BOUND_VARIABLE_1826)) (= (tptp.m2_rmod_4 BOUND_VARIABLE_1828 A BOUND_VARIABLE_1826 BOUND_VARIABLE_1830) (tptp.r1_tarski (tptp.k2_rmod_4 A BOUND_VARIABLE_1826 BOUND_VARIABLE_1828) BOUND_VARIABLE_1830)))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (not _let_22))) (let ((_let_64 (or _let_59 _let_58 _let_56 _let_54 _let_52 _let_50 _let_48 _let_46 _let_44 _let_42 _let_40 _let_39 _let_37 _let_35 _let_33 _let_31 _let_29 _let_27 _let_63 _let_24))) (let ((_let_65 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (BOUND_VARIABLE_2073 $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v3_rlvect_1 A)) (not (tptp.v4_rlvect_1 A)) (not (tptp.v5_rlvect_1 A)) (not (tptp.v6_rlvect_1 A)) (not (tptp.v4_group_1 A)) (not (tptp.v6_vectsp_1 A)) (not (tptp.v7_vectsp_1 A)) (not (tptp.v8_vectsp_1 A)) (not (tptp.l3_vectsp_1 A)) (tptp.v3_struct_0 B) (not (tptp.v3_rlvect_1 B)) (not (tptp.v4_rlvect_1 B)) (not (tptp.v5_rlvect_1 B)) (not (tptp.v6_rlvect_1 B)) (not (tptp.v5_vectsp_2 B A)) (not (tptp.l1_vectsp_2 B A)) (not (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.u1_struct_0 B)))) (not (tptp.m2_rmod_4 BOUND_VARIABLE_2073 A B C)) (tptp.m1_rmod_4 BOUND_VARIABLE_2073 A B))))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (= tptp.k1_xboole_0 _let_11))) (let ((_let_68 (tptp.k5_rmod_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25))) (let ((_let_69 (tptp.k1_rlvect_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_70 (or _let_63 (not (= _let_69 _let_68)) _let_67))) (let ((_let_71 (forall ((D $$unsorted)) (or (not (tptp.m2_rmod_4 D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.k1_subset_1 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (not (= (tptp.k5_rmod_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 D) (tptp.k1_rlvect_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (= tptp.k1_xboole_0 (tptp.k2_rmod_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 D)))))) (let ((_let_72 (not _let_70))) (let ((_let_73 (tptp.v1_rmod_5 _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_74 (= _let_73 _let_71))) (let ((_let_75 (not _let_71))) (let ((_let_76 (or _let_59 _let_58 _let_56 _let_54 _let_52 _let_50 _let_48 _let_46 _let_44 _let_42 _let_40 _let_39 _let_37 _let_35 _let_33 _let_31 _let_29 _let_27 _let_74))) (let ((_let_77 (forall ((A $$unsorted) (BOUND_VARIABLE_1649 $$unsorted) (BOUND_VARIABLE_1647 $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v3_rlvect_1 A)) (not (tptp.v4_rlvect_1 A)) (not (tptp.v5_rlvect_1 A)) (not (tptp.v6_rlvect_1 A)) (not (tptp.v4_group_1 A)) (not (tptp.v6_vectsp_1 A)) (not (tptp.v7_vectsp_1 A)) (not (tptp.v8_vectsp_1 A)) (not (tptp.l3_vectsp_1 A)) (tptp.v3_struct_0 BOUND_VARIABLE_1647) (not (tptp.v3_rlvect_1 BOUND_VARIABLE_1647)) (not (tptp.v4_rlvect_1 BOUND_VARIABLE_1647)) (not (tptp.v5_rlvect_1 BOUND_VARIABLE_1647)) (not (tptp.v6_rlvect_1 BOUND_VARIABLE_1647)) (not (tptp.v5_vectsp_2 BOUND_VARIABLE_1647 A)) (not (tptp.l1_vectsp_2 BOUND_VARIABLE_1647 A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_1649 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 BOUND_VARIABLE_1647)))) (= (tptp.v1_rmod_5 BOUND_VARIABLE_1649 A BOUND_VARIABLE_1647) (forall ((D $$unsorted)) (or (not (tptp.m2_rmod_4 D A BOUND_VARIABLE_1647 BOUND_VARIABLE_1649)) (not (= (tptp.k5_rmod_4 A BOUND_VARIABLE_1647 D) (tptp.k1_rlvect_1 BOUND_VARIABLE_1647))) (= tptp.k1_xboole_0 (tptp.k2_rmod_4 A BOUND_VARIABLE_1647 D))))))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (forall ((BOUND_VARIABLE_1875 $$unsorted)) (tptp.m1_subset_1 (tptp.k1_subset_1 BOUND_VARIABLE_1875) (tptp.k1_zfmisc_1 BOUND_VARIABLE_1875))))) (let ((_let_80 (_let_79))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_80) :args (_let_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.k1_subset_1 BOUND_VARIABLE_1875)))) :args _let_80)) (AND_ELIM _let_20 :args (1)) :args (_let_26 false _let_79)))) (let ((_let_82 (or _let_59 _let_58 _let_56 _let_54 _let_52 _let_50 _let_48 _let_46 _let_44 _let_42 _let_40 _let_39 _let_37 _let_35 _let_33 _let_31 _let_29 _let_73))) (let ((_let_83 (forall ((A $$unsorted) (BOUND_VARIABLE_1555 $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v3_rlvect_1 A)) (not (tptp.v4_rlvect_1 A)) (not (tptp.v5_rlvect_1 A)) (not (tptp.v6_rlvect_1 A)) (not (tptp.v4_group_1 A)) (not (tptp.v6_vectsp_1 A)) (not (tptp.v7_vectsp_1 A)) (not (tptp.v8_vectsp_1 A)) (not (tptp.l3_vectsp_1 A)) (tptp.v3_struct_0 BOUND_VARIABLE_1555) (not (tptp.v3_rlvect_1 BOUND_VARIABLE_1555)) (not (tptp.v4_rlvect_1 BOUND_VARIABLE_1555)) (not (tptp.v5_rlvect_1 BOUND_VARIABLE_1555)) (not (tptp.v6_rlvect_1 BOUND_VARIABLE_1555)) (not (tptp.v5_vectsp_2 BOUND_VARIABLE_1555 A)) (not (tptp.l1_vectsp_2 BOUND_VARIABLE_1555 A)) (tptp.v1_rmod_5 (tptp.k1_subset_1 (tptp.u1_struct_0 BOUND_VARIABLE_1555)) A BOUND_VARIABLE_1555))))) (let ((_let_84 (not _let_82))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (or))) (let ((_let_87 (not _let_83))) (let ((_let_88 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_85) :args (_let_87))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_87) _let_83))) (REFL :args (_let_84)) :args _let_86)) _let_85 :args (_let_84 true _let_83)))) (let ((_let_89 (REFL :args (_let_82)))) (let ((_let_90 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_82 16)) (CONG _let_89 (MACRO_SR_PRED_INTRO :args ((= 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_let_33 _let_31 _let_29 _let_27 _let_63 _let_24 (not _let_64)))) _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_81 _let_109 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.m2_rmod_4 BOUND_VARIABLE_2073 A B C) false))))) :args (_let_65))) _let_66 :args (_let_64 false _let_65)) :args (_let_24 true _let_59 false _let_57 false _let_55 false _let_53 false _let_51 false _let_49 false _let_47 false _let_45 false _let_43 false _let_41 true _let_40 false _let_38 false _let_36 false _let_34 false _let_32 false _let_30 false _let_28 false _let_26 false _let_22 false _let_64)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9 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(tptp.m1_rmod_4 C A B) (= (tptp.k2_rmod_4 A B C) (tptp.a_3_0_rmod_4 A B C)))))))) _let_5 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (tptp.m1_fraenkel (tptp.k1_fraenkel A B) A B))) true true (forall ((A $$unsorted)) (=> (tptp.l2_struct_0 A) (tptp.m1_subset_1 (tptp.k1_rlvect_1 A) (tptp.u1_struct_0 A)))) _let_4 true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k2_rmod_4 A B C))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_rlvect_1 A) (tptp.v4_rlvect_1 A) (tptp.v5_rlvect_1 A) (tptp.v6_rlvect_1 A) (tptp.v4_group_1 A) (tptp.v6_vectsp_1 A) (tptp.v7_vectsp_1 A) (tptp.v8_vectsp_1 A) (tptp.l3_vectsp_1 A) (not (tptp.v3_struct_0 B)) (tptp.v3_rlvect_1 B) (tptp.v4_rlvect_1 B) (tptp.v5_rlvect_1 B) (tptp.v6_rlvect_1 B) (tptp.v5_vectsp_2 B A) (tptp.l1_vectsp_2 B A) (tptp.m1_rmod_4 C A B)) (and (tptp.v1_finset_1 _let_1) (tptp.m1_subset_1 _let_1 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 B))))))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_rlvect_1 A) (tptp.v4_rlvect_1 A) (tptp.v5_rlvect_1 A) (tptp.v6_rlvect_1 A) (tptp.v4_group_1 A) (tptp.v6_vectsp_1 A) (tptp.v7_vectsp_1 A) (tptp.v8_vectsp_1 A) (tptp.l3_vectsp_1 A) (not (tptp.v3_struct_0 B)) (tptp.v3_rlvect_1 B) (tptp.v4_rlvect_1 B) (tptp.v5_rlvect_1 B) (tptp.v6_rlvect_1 B) (tptp.v5_vectsp_2 B A) (tptp.l1_vectsp_2 B A) (tptp.m1_rmod_4 C A B)) (tptp.m1_subset_1 (tptp.k5_rmod_4 A B C) (tptp.u1_struct_0 B)))) (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))) (forall ((A $$unsorted)) (=> (tptp.l1_group_1 A) (tptp.l1_struct_0 A))) (forall ((A $$unsorted)) (=> (tptp.l1_rlvect_1 A) (tptp.l2_struct_0 A))) true (forall ((A $$unsorted)) (=> (tptp.l1_vectsp_1 A) (tptp.l1_group_1 A))) (forall ((A $$unsorted)) (=> (tptp.l1_struct_0 A) (forall ((B $$unsorted)) (=> (tptp.l1_vectsp_2 B A) (tptp.l1_rlvect_1 B))))) (forall ((A $$unsorted)) (=> (tptp.l2_struct_0 A) (tptp.l1_struct_0 A))) (forall ((A $$unsorted)) (=> (tptp.l2_vectsp_1 A) (and (tptp.l1_vectsp_1 A) (tptp.l2_struct_0 A)))) (forall ((A $$unsorted)) (=> (tptp.l3_vectsp_1 A) (and (tptp.l1_rlvect_1 A) (tptp.l2_vectsp_1 A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_fraenkel C A B) (and (not (tptp.v1_xboole_0 C)) (tptp.v1_fraenkel C)))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_rlvect_1 A) (tptp.v4_rlvect_1 A) (tptp.v5_rlvect_1 A) (tptp.v6_rlvect_1 A) (tptp.v4_group_1 A) (tptp.v6_vectsp_1 A) (tptp.v7_vectsp_1 A) (tptp.v8_vectsp_1 A) (tptp.l3_vectsp_1 A) (not (tptp.v3_struct_0 B)) (tptp.v3_rlvect_1 B) (tptp.v4_rlvect_1 B) (tptp.v5_rlvect_1 B) (tptp.v6_rlvect_1 B) (tptp.v5_vectsp_2 B A) (tptp.l1_vectsp_2 B A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.u1_struct_0 B))) (=> (tptp.m1_rmod_4 C A B) (tptp.m2_fraenkel C _let_2 _let_1 (tptp.k1_fraenkel _let_2 _let_1)))))))) 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 $$unsorted)) (=> (tptp.m2_relset_1 C A B) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B))))) _let_3 true (exists ((A $$unsorted)) (tptp.l1_group_1 A)) (exists ((A $$unsorted)) (tptp.l1_rlvect_1 A)) (exists ((A $$unsorted)) (tptp.l1_struct_0 A)) (exists ((A $$unsorted)) (tptp.l1_vectsp_1 A)) (forall ((A $$unsorted)) (=> (tptp.l1_struct_0 A) (exists ((B $$unsorted)) (tptp.l1_vectsp_2 B A)))) (exists ((A $$unsorted)) (tptp.l2_struct_0 A)) (exists ((A $$unsorted)) (tptp.l2_vectsp_1 A)) (exists ((A $$unsorted)) (tptp.l3_vectsp_1 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 $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_rlvect_1 A) (tptp.v4_rlvect_1 A) (tptp.v5_rlvect_1 A) (tptp.v6_rlvect_1 A) (tptp.v4_group_1 A) (tptp.v6_vectsp_1 A) (tptp.v7_vectsp_1 A) (tptp.v8_vectsp_1 A) (tptp.l3_vectsp_1 A) (not (tptp.v3_struct_0 B)) (tptp.v3_rlvect_1 B) (tptp.v4_rlvect_1 B) (tptp.v5_rlvect_1 B) (tptp.v6_rlvect_1 B) (tptp.v5_vectsp_2 B A) (tptp.l1_vectsp_2 B A)) (exists ((C $$unsorted)) (tptp.m1_rmod_4 C A B)))) (forall ((A $$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) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_rlvect_1 A) (tptp.v4_rlvect_1 A) (tptp.v5_rlvect_1 A) (tptp.v6_rlvect_1 A) (tptp.v4_group_1 A) (tptp.v6_vectsp_1 A) (tptp.v7_vectsp_1 A) (tptp.v8_vectsp_1 A) (tptp.l3_vectsp_1 A) (not (tptp.v3_struct_0 B)) (tptp.v3_rlvect_1 B) (tptp.v4_rlvect_1 B) (tptp.v5_rlvect_1 B) (tptp.v6_rlvect_1 B) (tptp.v5_vectsp_2 B A) (tptp.l1_vectsp_2 B A) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.u1_struct_0 B)))) (exists ((D $$unsorted)) (tptp.m2_rmod_4 D A B C)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A)) (not (tptp.v1_xboole_0 (tptp.u1_struct_0 A))))) (forall ((A $$unsorted)) (not (tptp.v1_xboole_0 (tptp.k1_zfmisc_1 A)))) (tptp.v1_xboole_0 tptp.k1_xboole_0) (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) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v3_rlvect_1 B) (tptp.v4_rlvect_1 B) (tptp.v5_rlvect_1 B) (tptp.v6_rlvect_1 B) (tptp.v4_group_1 B) (tptp.v6_vectsp_1 B) (tptp.v7_vectsp_1 B) (tptp.v8_vectsp_1 B) (tptp.l3_vectsp_1 B) (not (tptp.v3_struct_0 C)) (tptp.v3_rlvect_1 C) (tptp.v4_rlvect_1 C) (tptp.v5_rlvect_1 C) (tptp.v6_rlvect_1 C) (tptp.v5_vectsp_2 C B) (tptp.l1_vectsp_2 C B) (tptp.m1_rmod_4 D B C)) (= (tptp.r2_hidden A (tptp.a_3_0_rmod_4 B C D)) (exists ((E $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 C))) (and (tptp.m1_subset_1 E _let_1) (= A E) (not (= (tptp.k8_funct_2 _let_1 (tptp.u1_struct_0 B) D E) (tptp.k1_rlvect_1 B))))))))) (forall ((A $$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 $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (not (tptp.v1_xboole_0 B)) (tptp.v1_finset_1 B))))) (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)))) (exists ((A $$unsorted)) (and (tptp.l2_struct_0 A) (not (tptp.v3_struct_0 A)))) (forall ((A $$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.l1_struct_0 A) (exists ((B $$unsorted)) (and (tptp.l1_vectsp_2 B A) (not (tptp.v3_struct_0 B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (= (tptp.k1_fraenkel A B) (tptp.k1_funct_2 A B)))) (forall ((A $$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 $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_fraenkel C A B)) (forall ((D $$unsorted)) (= (tptp.m2_fraenkel D A B C) (tptp.m1_subset_1 D C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.m2_relset_1 C A B) (tptp.m1_relset_1 C A B))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski A A)) (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)) (=> (forall ((C $$unsorted)) (= (tptp.r2_hidden C A) (tptp.r2_hidden C B))) (= A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.m1_subset_1 A (tptp.k1_zfmisc_1 B)) (tptp.r1_tarski A B))) _let_2 (forall ((A $$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))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.r2_hidden A B) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 C)) (tptp.v1_xboole_0 C)))) _let_1 (forall ((A $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.68 )
% 0.21/0.68 % SZS output end Proof for ALG215+1
% 0.21/0.68 % cvc5---1.0.5 exiting
% 0.21/0.69 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------