%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : ALG225+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 : Wed Aug 30 16:08:47 EDT 2023

% Result   : Theorem 25.74s 26.20s
% Output   : Proof 25.74s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : ALG225+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.14  % 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 03:28:29 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 25.74/26.20  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.uaTurD1O5E/cvc5---1.0.5_11289.p...
% 25.74/26.20  ------- get file name : TPTP file name is ALG225+1
% 25.74/26.20  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_11289.smt2...
% 25.74/26.20  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 25.74/26.20  --- Run --no-e-matching --full-saturate-quant at 5...
% 25.74/26.20  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 25.74/26.20  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.74/26.20  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 25.74/26.20  % SZS status Theorem for ALG225+1
% 25.74/26.20  % SZS output start Proof for ALG225+1
% 25.74/26.20  (
% 25.74/26.20  (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 B) (=> (tptp.r1_tarski (tptp.k1_relat_1 B) A) (= (tptp.k7_relat_1 B A) B)))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (tptp.m1_subset_1 A B))))) (let ((_let_3 (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (tptp.m1_pboole B A) (forall ((C $$unsorted)) (=> (tptp.m1_pboole C A) (= (tptp.k1_funct_4 B C) C))))))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_pboole C B)) (= (tptp.r2_hidden A (tptp.a_2_0_closure3 B C)) (exists ((D $$unsorted)) (and (tptp.m1_subset_1 D B) (= A D) (not (= (tptp.k1_funct_1 C D) tptp.k1_xboole_0))))))))) (let ((_let_5 (tptp.v1_xboole_0 tptp.k1_xboole_0))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_pboole B A) (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)))))) (let ((_let_7 (forall ((A $$unsorted)) (tptp.m1_pboole (tptp.k1_pboole A) A)))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.r1_tarski A B) (forall ((C $$unsorted)) (=> (tptp.r2_hidden C A) (tptp.r2_hidden C B))))))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (= (tptp.m1_pboole B A) (= (tptp.k1_relat_1 B) A)))))) (let ((_let_10 (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (tptp.m1_pboole B A) (forall ((C $$unsorted)) (= (= C (tptp.k1_closure3 A B)) (= C (tptp.a_2_0_closure3 A B)))))))))) (let ((_let_11 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_pboole B A) (= (tptp.v2_relat_1 B) (forall ((C $$unsorted)) (not (and (tptp.r2_hidden C A) (tptp.v1_xboole_0 (tptp.k1_funct_1 B C)))))))))) (let ((_let_12 (not (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (and (tptp.v2_relat_1 B) (tptp.m1_pboole B A)) (= B (tptp.k1_funct_4 (tptp.k1_pboole A) (tptp.k7_relat_1 B (tptp.k1_closure3 A B))))))))))) (let ((_let_13 (tptp.k1_closure3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_14 (tptp.k7_relat_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_13))) (let ((_let_15 (tptp.k1_pboole SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_16 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.k1_funct_4 _let_15 _let_14)))) (let ((_let_17 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.k1_funct_4 _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_18 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_14))) (let ((_let_19 (tptp.m1_pboole SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_20 (not _let_19))) (let ((_let_21 (tptp.v2_relat_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_22 (not _let_21))) (let ((_let_23 (tptp.v1_xboole_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_24 (or _let_23 _let_22 _let_20 _let_16))) (let ((_let_25 (forall ((A $$unsorted) (BOUND_VARIABLE_1208 $$unsorted)) (or (tptp.v1_xboole_0 A) (not (tptp.v2_relat_1 BOUND_VARIABLE_1208)) (not (tptp.m1_pboole BOUND_VARIABLE_1208 A)) (= BOUND_VARIABLE_1208 (tptp.k1_funct_4 (tptp.k1_pboole A) (tptp.k7_relat_1 BOUND_VARIABLE_1208 (tptp.k1_closure3 A BOUND_VARIABLE_1208)))))))) (let ((_let_26 (not _let_24))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (or))) (let ((_let_29 (not _let_25))) (let ((_let_30 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_27) :args (_let_29))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_25))) (REFL :args (_let_26)) :args _let_28)) _let_27 :args (_let_26 true _let_25)))) (let ((_let_31 (tptp.m1_pboole _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_32 (not _let_31))) (let ((_let_33 (or _let_23 _let_32 _let_20 _let_17))) (let ((_let_34 (forall ((A $$unsorted) (BOUND_VARIABLE_1760 $$unsorted) (BOUND_VARIABLE_1758 $$unsorted)) (or (tptp.v1_xboole_0 A) (not (tptp.m1_pboole BOUND_VARIABLE_1758 A)) (not (tptp.m1_pboole BOUND_VARIABLE_1760 A)) (= BOUND_VARIABLE_1760 (tptp.k1_funct_4 BOUND_VARIABLE_1758 BOUND_VARIABLE_1760)))))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (_let_7))) (let ((_let_37 (ASSUME :args _let_36))) (let ((_let_38 (REFL :args (_let_24)))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_24 2)) (CONG _let_38 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_28)) :args ((or _let_19 _let_24))) _let_30 :args (_let_19 true _let_24)))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_24 0)) _let_30 :args ((not _let_23) true _let_24)))) (let ((_let_41 (tptp.k1_relat_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_42 (tptp.r1_tarski _let_41 _let_13))) (let ((_let_43 (not _let_42))) (let ((_let_44 (tptp.v1_relat_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_45 (not _let_44))) (let ((_let_46 (or _let_45 _let_43 _let_18))) (let ((_let_47 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.v1_relat_1 B)) (not (tptp.r1_tarski (tptp.k1_relat_1 B) A)) (= B (tptp.k7_relat_1 B A)))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (forall ((C $$unsorted)) (or (not (tptp.r2_hidden C (tptp.k1_relat_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (tptp.r2_hidden C (tptp.k1_closure3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))))) (let ((_let_50 (= _let_42 _let_49))) (let ((_let_51 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.r1_tarski A B) (forall ((C $$unsorted)) (or (not (tptp.r2_hidden C A)) (tptp.r2_hidden C B))))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (tptp.r2_hidden SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_40 _let_13))) (let ((_let_54 (tptp.r2_hidden SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_40 _let_41))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_55 _let_53))) (let ((_let_57 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_40 _let_41))) (let ((_let_58 (or _let_55 _let_57))) (let ((_let_59 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_41))) (let ((_let_60 (tptp.r2_hidden SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_40 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_61 (tptp.a_2_0_closure3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_62 (= _let_13 _let_61))) (let ((_let_63 (tptp.r2_hidden SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_40 _let_61))) (let ((_let_64 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_40 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_65 (tptp.k1_funct_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_40))) (let ((_let_66 (tptp.v1_xboole_0 _let_65))) (let ((_let_67 (not _let_66))) (let ((_let_68 (not _let_60))) (let ((_let_69 (or _let_68 _let_67))) (let ((_let_70 (= tptp.k1_xboole_0 _let_65))) (let ((_let_71 (not _let_70))) (let ((_let_72 (and _let_64 _let_71))) (let ((_let_73 (= _let_63 _let_72))) (let ((_let_74 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.r2_hidden A B)) (tptp.m1_subset_1 A B))))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (= _let_19 _let_59))) (let ((_let_77 (tptp.v1_funct_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_78 (not _let_77))) (let ((_let_79 (or _let_45 _let_78 _let_76))) (let ((_let_80 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.v1_relat_1 B)) (not (tptp.v1_funct_1 B)) (= (tptp.m1_pboole B A) (= A (tptp.k1_relat_1 B))))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (and _let_44 _let_77))) (let ((_let_83 (or _let_20 _let_82))) (let ((_let_84 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.m1_pboole B A)) (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)))))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_83)) :args ((or _let_20 _let_82 (not _let_83)))) _let_39 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_85 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.m1_pboole B A) false))))) :args (_let_84))) _let_85 :args (_let_83 false _let_84)) :args (_let_82 false _let_19 false _let_83)))) (let ((_let_87 (not _let_82))) (let ((_let_88 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_82 0)) :args ((or _let_44 _let_87))) _let_86 :args (_let_44 false _let_82)))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_76)) :args ((or _let_20 _let_59 (not _let_76)))) _let_39 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_79)) :args ((or _let_45 _let_78 _let_76 (not _let_79)))) _let_88 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_82 1)) :args ((or _let_77 _let_87))) _let_86 :args (_let_77 false _let_82)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_81 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.m1_pboole B A)))) :args (_let_80))) _let_81 :args (_let_79 false _let_80)) :args (_let_76 false _let_44 false _let_77 false _let_79)) :args (_let_59 false _let_19 false _let_76)))) (let ((_let_90 (and _let_59 _let_54))) (let ((_let_91 (ASSUME :args (_let_54)))) (let ((_let_92 (APPLY_UF tptp.r2_hidden))) (let ((_let_93 (ASSUME :args (_let_59)))) (let ((_let_94 (SYMM (SYMM _let_93)))) (let ((_let_95 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_40)))) (let ((_let_96 (or _let_23 _let_20 _let_62))) (let ((_let_97 (forall ((A $$unsorted) (BOUND_VARIABLE_1357 $$unsorted) (BOUND_VARIABLE_1355 $$unsorted)) (or (tptp.v1_xboole_0 A) (not (tptp.m1_pboole BOUND_VARIABLE_1355 A)) (= (= BOUND_VARIABLE_1357 (tptp.k1_closure3 A BOUND_VARIABLE_1355)) (= BOUND_VARIABLE_1357 (tptp.a_2_0_closure3 A BOUND_VARIABLE_1355))))))) (let ((_let_98 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_99 (not _let_53))) (let ((_let_100 (and _let_99 _let_62))) (let ((_let_101 (_let_99 _let_62))) (let ((_let_102 (ASSUME :args (_let_99)))) (let ((_let_103 (ASSUME :args (_let_62)))) (let ((_let_104 (and _let_59 _let_57))) (let ((_let_105 (ASSUME :args (_let_57)))) (let ((_let_106 (forall ((C $$unsorted)) (or (not (tptp.r2_hidden C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.v1_xboole_0 (tptp.k1_funct_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 C))))))) (let ((_let_107 (= _let_21 _let_106))) (let ((_let_108 (or _let_20 _let_107))) (let ((_let_109 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.m1_pboole B A)) (= (tptp.v2_relat_1 B) (forall ((C $$unsorted)) (or (not (tptp.r2_hidden C A)) (not (tptp.v1_xboole_0 (tptp.k1_funct_1 B C)))))))))) (let ((_let_110 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_111 (_let_106))) (let ((_let_112 (or _let_23 _let_20 _let_73))) (let ((_let_113 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.v1_xboole_0 B) (not (tptp.m1_pboole C B)) (= (tptp.r2_hidden A (tptp.a_2_0_closure3 B C)) (and (tptp.m1_subset_1 A B) (not (= tptp.k1_xboole_0 (tptp.k1_funct_1 C A))))))))) (let ((_let_114 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_115 (not _let_64))) (let ((_let_116 (_let_72))) (let ((_let_117 (ASSUME :args (_let_5)))) (let ((_let_118 (ASSUME :args (_let_70)))) (let ((_let_119 (ASSUME :args (_let_67)))) (let ((_let_120 (not _let_49))) (let ((_let_121 (_let_120))) (let ((_let_122 (and _let_18 _let_17))) (let ((_let_123 (_let_18 _let_17))) (let ((_let_124 (ASSUME :args (_let_18)))) (let ((_let_125 (ASSUME :args (_let_17)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_122)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_124 _let_125) (SCOPE (TRANS (SYMM (SYMM _let_125)) (CONG (REFL :args (_let_15)) (SYMM (SYMM _let_124)) :args (APPLY_UF tptp.k1_funct_4))) :args _let_123)) :args _let_123)) :args (true _let_122)) :args ((or _let_16 (not _let_18) (not _let_17)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_45 _let_43 _let_18 (not _let_46)))) _let_88 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_50)) :args ((or _let_42 _let_120 (not _let_50)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_121)) :args _let_121)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_120) _let_49))) (REFL :args ((not _let_56))) :args _let_28)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_117 _let_118 _let_119) :args (_let_5 _let_67 _let_70)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_119)) (CONG (SYMM _let_118) :args (APPLY_UF tptp.v1_xboole_0)) (TRUE_INTRO _let_117))) :args (_let_5 _let_70 _let_67)) :args ((not (and _let_5 _let_67 _let_70)) SB_LITERAL))) (CONG (REFL :args ((not _let_5))) (MACRO_SR_PRED_INTRO :args ((= (not _let_67) _let_66))) (REFL :args (_let_71)) :args _let_28)) _let_117 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_116) (CONG (REFL :args _let_116) (REFL :args (_let_115)) (MACRO_SR_PRED_INTRO :args ((= (not _let_71) _let_70))) :args _let_28)) :args ((or _let_70 _let_72 _let_115))) (REORDERING (CNF_EQUIV_POS2 :args (_let_73)) :args ((or _let_63 (not _let_72) (not _let_73)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_112)) :args ((or _let_23 _let_20 _let_73 (not _let_112)))) _let_40 _let_39 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_114 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_40 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_113))) _let_114 :args (_let_112 false _let_113)) :args (_let_73 true _let_23 false _let_19 false _let_112)) (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_68 _let_67 (not _let_69)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_111) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_40 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.r2_hidden C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) false))))) :args _let_111)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_107)) :args ((or _let_22 _let_106 (not _let_107)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_24 1)) (CONG _let_38 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_28)) :args ((or _let_21 _let_24))) _let_30 :args (_let_21 true _let_24)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_108)) :args ((or _let_20 _let_107 (not _let_108)))) _let_39 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_110 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.m1_pboole B A) false))))) :args (_let_109))) _let_110 :args (_let_108 false _let_109)) :args (_let_107 false _let_19 false _let_108)) :args (_let_106 false _let_21 false _let_107)) :args (_let_69 false _let_106)) (RESOLUTION (CNF_AND_NEG :args (_let_104)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_105 _let_93) (SCOPE (TRUE_ELIM (TRANS (CONG _let_95 _let_94 :args (APPLY_UF tptp.m1_subset_1)) (TRUE_INTRO _let_105))) :args (_let_57 _let_59))) :args (_let_59 _let_57))) :args (true _let_104)) _let_89 (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_100)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_102 _let_103) (SCOPE (FALSE_ELIM (TRANS (CONG _let_95 (SYMM _let_103) :args _let_92) (FALSE_INTRO _let_102))) :args _let_101)) :args _let_101)) :args (true _let_100)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_99) _let_53))) (REFL :args ((not _let_62))) (REFL :args ((not _let_63))) :args _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_96)) :args ((or _let_23 _let_20 _let_62 (not _let_96)))) _let_40 _let_39 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_98 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_61 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_97)))) _let_98 :args (_let_96 false _let_97)) :args (_let_62 true _let_23 false _let_19 false _let_96)) (RESOLUTION (CNF_AND_NEG :args (_let_90)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_91 _let_93) (SCOPE (TRUE_ELIM (TRANS (CONG _let_95 _let_94 :args _let_92) (TRUE_INTRO _let_91))) :args (_let_54 _let_59))) :args (_let_59 _let_54))) :args (true _let_90)) _let_89 (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_55 _let_57 (not _let_58)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_75 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_40 _let_41 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.r2_hidden A B) false))))) :args (_let_74))) _let_75 :args (_let_58 false _let_74)) (CNF_OR_NEG :args (_let_56 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_56 0)) (CONG (REFL :args (_let_56)) (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_54))) :args _let_28)) :args ((or _let_54 _let_56))) :args (_let_56 false _let_5 false _let_70 true _let_72 false _let_73 true _let_66 false _let_69 false _let_64 false _let_59 true _let_63 false _let_62 false _let_60 false _let_59 false _let_57 false _let_58 true _let_53 false _let_54)) :args (_let_49 false _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (_let_41 _let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.r1_tarski A B)))) :args (_let_51))) _let_52 :args (_let_50 false _let_51)) :args (_let_42 false _let_49 false _let_50)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (_let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.k7_relat_1 B A)))) :args (_let_47))) _let_48 :args (_let_46 false _let_47)) :args (_let_18 false _let_44 false _let_42 false _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_33)) :args ((or _let_23 _let_20 _let_32 _let_17 (not _let_33)))) _let_40 _let_39 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.k1_pboole A)))) :args _let_36)) _let_37 :args (_let_31 false _let_7)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_15 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.m1_pboole BOUND_VARIABLE_1758 A) false)) (not (= (tptp.m1_pboole BOUND_VARIABLE_1760 A) false))))) :args (_let_34))) _let_35 :args (_let_33 false _let_34)) :args (_let_17 true _let_23 false _let_19 false _let_31 false _let_33)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_24 3)) _let_30 :args ((not _let_16) true _let_24)) :args (false false _let_18 false _let_17 true _let_16)) :args (_let_12 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (not (tptp.r2_hidden B A)))) (forall ((A $$unsorted)) (=> (tptp.v1_xboole_0 A) (tptp.v1_fraenkel A))) (forall ((A $$unsorted)) (=> (tptp.v1_xboole_0 A) (tptp.v1_finset_1 A))) (forall ((A $$unsorted)) (=> (tptp.v1_xboole_0 A) (tptp.v1_funct_1 A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_pboole B A) (=> (tptp.v3_relat_1 B) (tptp.v1_pre_circ B A)))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (tptp.m1_pboole B A) (=> (tptp.v2_relat_1 B) (not (tptp.v3_relat_1 B))))))) (forall ((A $$unsorted)) (=> (tptp.v1_finset_1 A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (tptp.v1_finset_1 B))))) (forall ((A $$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 $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (forall ((B $$unsorted)) (=> (tptp.m1_pboole B A) (=> (tptp.v3_relat_1 B) (not (tptp.v2_relat_1 B))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= A B) (and (tptp.r1_tarski A B) (tptp.r1_tarski B A)))) _let_11 _let_10 _let_9 _let_8 (forall ((A $$unsorted)) (= (tptp.k1_pboole A) (tptp.k2_funcop_1 A tptp.k1_xboole_0))) true true (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_funct_4 A B))) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (and (tptp.v1_relat_1 _let_1) (tptp.v1_funct_1 _let_1))))) _let_7 true true true true (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 A) (tptp.v1_relat_1 (tptp.k7_relat_1 A B)))) _let_6 true (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.m1_pboole B A))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.m1_subset_1 B A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_pboole A))) (and (tptp.v1_relat_1 _let_1) (tptp.v3_relat_1 _let_1) (tptp.v1_funct_1 _let_1) (tptp.v1_pre_circ _let_1 A)))) (forall ((A $$unsorted)) (not (tptp.v1_xboole_0 (tptp.k1_zfmisc_1 A)))) _let_5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v2_relat_1 B) (tptp.m1_pboole B A) (tptp.m1_subset_1 C A)) (not (tptp.v1_xboole_0 (tptp.k1_funct_1 B C))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_pboole A))) (and (tptp.v1_relat_1 _let_1) (tptp.v3_relat_1 _let_1) (tptp.v1_funct_1 _let_1)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k7_relat_1 A B))) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (and (tptp.v1_relat_1 _let_1) (tptp.v1_funct_1 _let_1))))) _let_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.v2_relat_1 C) (tptp.m1_pboole C B)) (= (tptp.r2_hidden A (tptp.a_2_1_closure3 B C)) (exists ((D $$unsorted)) (and (tptp.m1_subset_1 D B) (= A D) (not (= (tptp.k1_funct_1 C D) tptp.k1_xboole_0))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)) (= (tptp.k1_funct_4 A A) A))) (exists ((A $$unsorted)) (and (tptp.v1_xboole_0 A) (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v2_funct_1 A) (tptp.v1_finset_1 A) (tptp.v1_fraenkel A))) (exists ((A $$unsorted)) (and (not (tptp.v1_xboole_0 A)) (tptp.v1_finset_1 A))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v3_relat_1 A) (tptp.v1_funct_1 A))) (forall ((A $$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)) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_xboole_0 A) (tptp.v1_funct_1 A))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.m1_pboole B A) (tptp.v1_relat_1 B) (tptp.v3_relat_1 B) (tptp.v1_funct_1 B)))) (forall ((A $$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))) (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)) (tptp.v1_finset_1 B))))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v2_funct_1 A))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.m1_pboole B A) (tptp.v1_relat_1 B) (tptp.v2_relat_1 B) (tptp.v1_funct_1 B)))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (not (tptp.v1_xboole_0 B)) (tptp.v1_finset_1 B))))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v3_relat_1 A) (tptp.v1_funct_1 A))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v2_relat_1 A) (tptp.v1_funct_1 A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski A A)) _let_3 _let_2 (forall ((A $$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))) (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)))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 25.74/26.20  )
% 25.74/26.20  % SZS output end Proof for ALG225+1
% 25.74/26.20  % cvc5---1.0.5 exiting
% 25.74/26.20  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------