%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : ALG223+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n029.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 16:08:46 EDT 2023

% Result   : Theorem 0.21s 0.70s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : ALG223+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.35  % Computer : n029.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Mon Aug 28 03:01:56 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.21/0.51  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.70  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.LOpAxX2KIY/cvc5---1.0.5_17099.p...
% 0.21/0.70  ------- get file name : TPTP file name is ALG223+1
% 0.21/0.70  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_17099.smt2...
% 0.21/0.70  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.70  % SZS status Theorem for ALG223+1
% 0.21/0.70  % SZS output start Proof for ALG223+1
% 0.21/0.70  (
% 0.21/0.70  (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.r1_tarski A B) (tptp.r1_tarski B C)) (tptp.r1_tarski A C))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_pboole B A) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k1_closure2 A B))) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 (tptp.k1_closure2 A B))) (= (tptp.r1_closure3 A B C D) (forall ((E $$unsorted)) (not (and (tptp.r2_hidden E D) (forall ((F $$unsorted)) (not (and (tptp.r2_hidden F C) (tptp.r1_tarski E F)))))))))))))))) (let ((_let_3 (not (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_pboole B A) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k1_closure2 A B))) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 (tptp.k1_closure2 A B))) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k1_zfmisc_1 (tptp.k1_closure2 A B))) (=> (and (tptp.r1_closure3 A B D C) (tptp.r1_closure3 A B E D)) (tptp.r1_closure3 A B E C))))))))))))) (let ((_let_4 (tptp.r2_hidden SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_74 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_5 (tptp.r1_tarski SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_74))) (let ((_let_6 (not _let_5))) (let ((_let_7 (not _let_4))) (let ((_let_8 (or _let_7 _let_6))) (let ((_let_9 (tptp.r1_tarski SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_74))) (let ((_let_10 (not _let_9))) (let ((_let_11 (or _let_7 _let_10))) (let ((_let_12 (forall ((F $$unsorted)) (or (not (tptp.r2_hidden F SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.r1_tarski SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37 F)))))) (let ((_let_13 (not _let_11))) (let ((_let_14 (not _let_12))) (let ((_let_15 (tptp.r2_hidden SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_16 (not _let_15))) (let ((_let_17 (or _let_16 _let_14))) (let ((_let_18 (forall ((E $$unsorted)) (or (not (tptp.r2_hidden E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (forall ((F $$unsorted)) (or (not (tptp.r2_hidden F SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.r1_tarski E F))))))))) (let ((_let_19 (tptp.r1_closure3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_20 (= _let_19 _let_18))) (let ((_let_21 (tptp.k1_zfmisc_1 (tptp.k1_closure2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_22 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_21))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_21))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.m1_pboole SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or _let_27 _let_25 _let_23 _let_20))) (let ((_let_29 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_1152 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 (tptp.k1_closure2 A B)))) (or (not (tptp.m1_pboole B A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_1150 _let_1)) (not (tptp.m1_subset_1 BOUND_VARIABLE_1152 _let_1)) (= (tptp.r1_closure3 A B BOUND_VARIABLE_1150 BOUND_VARIABLE_1152) (forall ((E $$unsorted)) (or (not (tptp.r2_hidden E BOUND_VARIABLE_1152)) (not (forall ((F $$unsorted)) (or (not (tptp.r2_hidden F BOUND_VARIABLE_1150)) (not (tptp.r1_tarski E F))))))))))))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (_let_29))) (let ((_let_32 ((tptp.r1_closure3 A B BOUND_VARIABLE_1150 BOUND_VARIABLE_1152)))) (let ((_let_33 (tptp.r1_closure3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_34 (not _let_19))) (let ((_let_35 (tptp.r1_closure3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_36 (not _let_35))) (let ((_let_37 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_21))) (let ((_let_38 (not _let_37))) (let ((_let_39 (or _let_27 _let_38 _let_23 _let_36 _let_25 _let_34 _let_33))) (let ((_let_40 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_1042 $$unsorted) (BOUND_VARIABLE_1040 $$unsorted) (BOUND_VARIABLE_1038 $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 (tptp.k1_closure2 A B)))) (or (not (tptp.m1_pboole B A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_1038 _let_1)) (not (tptp.m1_subset_1 BOUND_VARIABLE_1042 _let_1)) (not (tptp.r1_closure3 A B BOUND_VARIABLE_1042 BOUND_VARIABLE_1038)) (not (tptp.m1_subset_1 BOUND_VARIABLE_1040 _let_1)) (not (tptp.r1_closure3 A B BOUND_VARIABLE_1040 BOUND_VARIABLE_1042)) (tptp.r1_closure3 A B BOUND_VARIABLE_1040 BOUND_VARIABLE_1038)))))) (let ((_let_41 (not _let_39))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (or))) (let ((_let_44 (not _let_40))) (let ((_let_45 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_42) :args (_let_44))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_40))) (REFL :args (_let_41)) :args _let_43)) _let_42 :args (_let_41 true _let_40)))) (let ((_let_46 (REFL :args (_let_39)))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 4)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_43)) :args ((or _let_24 _let_39))) _let_45 :args (_let_24 true _let_39)))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 2)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_43)) :args ((or _let_22 _let_39))) _let_45 :args (_let_22 true _let_39)))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 0)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_43)) :args ((or _let_26 _let_39))) _let_45 :args (_let_26 true _let_39)))) (let ((_let_50 (_let_18))) (let ((_let_51 (tptp.r1_tarski SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37))) (let ((_let_52 (not _let_51))) (let ((_let_53 (or _let_16 _let_52))) (let ((_let_54 (forall ((F $$unsorted)) (or (not (tptp.r2_hidden F SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.r1_tarski SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 F)))))) (let ((_let_55 (not _let_53))) (let ((_let_56 (not _let_54))) (let ((_let_57 (tptp.r2_hidden SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_58 (not _let_57))) (let ((_let_59 (or _let_58 _let_56))) (let ((_let_60 (forall ((E $$unsorted)) (or (not (tptp.r2_hidden E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (forall ((F $$unsorted)) (or (not (tptp.r2_hidden F SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.r1_tarski E F))))))))) (let ((_let_61 (= _let_35 _let_60))) (let ((_let_62 (or _let_27 _let_23 _let_38 _let_61))) (let ((_let_63 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 1)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_37))) :args _let_43)) :args ((or _let_37 _let_39))) _let_45 :args (_let_37 true _let_39)))) (let ((_let_64 (_let_60))) (let ((_let_65 (forall ((F $$unsorted)) (or (not (tptp.r2_hidden F SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.r1_tarski SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 F)))))) (let ((_let_66 (not _let_65))) (let ((_let_67 (or _let_58 _let_66))) (let ((_let_68 (forall ((E $$unsorted)) (or (not (tptp.r2_hidden E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (forall ((F $$unsorted)) (or (not (tptp.r2_hidden F SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.r1_tarski E F))))))))) (let ((_let_69 (not _let_67))) (let ((_let_70 (= _let_33 _let_68))) (let ((_let_71 (not _let_68))) (let ((_let_72 (or _let_27 _let_25 _let_38 _let_70))) (let ((_let_73 (_let_71))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_73)) :args _let_73)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_71) _let_68))) (REFL :args (_let_69)) :args _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_70)) :args ((or _let_33 _let_71 (not _let_70)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_39 6)) _let_45 :args ((not _let_33) true _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_72)) :args ((or _let_27 _let_38 _let_25 _let_70 (not _let_72)))) _let_49 _let_63 _let_47 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_32)) :args _let_31)) _let_30 :args (_let_72 false _let_29)) :args (_let_70 false _let_26 false _let_37 false _let_24 false _let_72)) :args (_let_71 true _let_33 false _let_70)) :args (_let_69 true _let_68)))) (let ((_let_75 (REFL :args (_let_67)))) (let ((_let_76 (_let_56))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_76)) :args _let_76)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_56) _let_54))) (REFL :args (_let_55)) :args _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_58 _let_56 (not _let_59)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_67 0)) (CONG _let_75 (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_57))) :args _let_43)) :args ((or _let_57 _let_67))) _let_74 :args (_let_57 true _let_67)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_64) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.r2_hidden E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) false))))) :args _let_64)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_61)) :args ((or _let_36 _let_60 (not _let_61)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 3)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_35))) :args _let_43)) :args ((or _let_35 _let_39))) _let_45 :args (_let_35 true _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_27 _let_38 _let_23 _let_61 (not _let_62)))) _let_49 _let_63 _let_48 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_32)) :args _let_31)) _let_30 :args (_let_62 false _let_29)) :args (_let_61 false _let_26 false _let_37 false _let_22 false _let_62)) :args (_let_60 false _let_35 false _let_61)) :args (_let_59 false _let_60)) :args (_let_56 false _let_57 false _let_59)) :args (_let_55 true _let_54)))) (let ((_let_78 (REFL :args (_let_53)))) (let ((_let_79 (_let_14))) (let ((_let_80 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_79)) :args _let_79)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_12))) (REFL :args (_let_13)) :args _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_17)) :args ((or _let_16 _let_14 (not _let_17)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_53 0)) (CONG _let_78 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_43)) :args ((or _let_15 _let_53))) _let_77 :args (_let_15 true _let_53)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_50) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.r2_hidden E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) false))))) :args _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_20)) :args ((or _let_34 _let_18 (not _let_20)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 5)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_19))) :args _let_43)) :args ((or _let_19 _let_39))) _let_45 :args (_let_19 true _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_28)) :args ((or _let_27 _let_23 _let_25 _let_20 (not _let_28)))) _let_49 _let_48 _let_47 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_32)) :args _let_31)) _let_30 :args (_let_28 false _let_29)) :args (_let_20 false _let_26 false _let_22 false _let_24 false _let_28)) :args (_let_18 false _let_19 false _let_20)) :args (_let_17 false _let_18)) :args (_let_14 false _let_15 false _let_17)) :args (_let_13 true _let_12)))) (let ((_let_81 (REFL :args (_let_11)))) (let ((_let_82 (_let_65))) (let ((_let_83 (or _let_52 _let_10 _let_5))) (let ((_let_84 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.r1_tarski A B)) (not (tptp.r1_tarski B C)) (tptp.r1_tarski A C))))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_8)) :args ((or _let_7 _let_6 (not _let_8)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_83)) :args ((or _let_52 _let_10 _let_5 (not _let_83)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_53 1)) (CONG _let_78 (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_51))) :args _let_43)) :args ((or _let_51 _let_53))) _let_77 :args (_let_51 true _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_11 1)) (CONG _let_81 (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_9))) :args _let_43)) :args ((or _let_9 _let_11))) _let_80 :args (_let_9 true _let_11)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_85 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_74 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.r1_tarski A B) false)) (not (= (tptp.r1_tarski B C) false))))) :args (_let_84))) _let_85 :args (_let_83 false _let_84)) :args (_let_5 false _let_51 false _let_9 false _let_83)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_82) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_74 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.r2_hidden F SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) false))))) :args _let_82)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_67 1)) (CONG _let_75 (MACRO_SR_PRED_INTRO :args ((= (not _let_66) _let_65))) :args _let_43)) :args ((or _let_65 _let_67))) _let_74 :args (_let_65 true _let_67)) :args (_let_8 false _let_65)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_11 0)) (CONG _let_81 (MACRO_SR_PRED_INTRO :args ((= (not _let_7) _let_4))) :args _let_43)) :args ((or _let_4 _let_11))) _let_80 :args (_let_4 true _let_11)) :args (false false _let_5 false _let_8 false _let_4)) :args (_let_3 (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 $$unsorted)) (=> (tptp.v1_finset_1 A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (tptp.v1_finset_1 B))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.v1_funct_1 A))) (let ((_let_2 (tptp.v1_relat_1 A))) (=> (and _let_2 (tptp.v1_xboole_0 A) _let_1) (and _let_2 _let_1 (tptp.v2_funct_1 A)))))) _let_2 true true true (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_pboole B A) (and (tptp.v1_relat_1 B) (tptp.v1_funct_1 B)))) true (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.m1_pboole B A))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.m1_subset_1 B A))) (forall ((A $$unsorted)) (not (tptp.v1_xboole_0 (tptp.k1_zfmisc_1 A)))) (tptp.v1_xboole_0 tptp.k1_xboole_0) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_closure2 A B))) (=> (tptp.m1_pboole B A) (and (not (tptp.v1_xboole_0 _let_1)) (tptp.v1_fraenkel _let_1) (tptp.v1_pralg_2 _let_1))))) (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 $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A))) (forall ((A $$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)) (=> (tptp.m1_pboole B A) (exists ((C $$unsorted)) (and (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k1_closure2 A B))) (not (tptp.v1_xboole_0 C)) (tptp.v1_fraenkel C) (tptp.v1_pralg_2 C))))) (exists ((A $$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_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) (B $$unsorted)) (=> (tptp.m1_pboole B A) (exists ((C $$unsorted)) (and (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k1_closure2 A B))) (tptp.v1_xboole_0 C) (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (tptp.v2_funct_1 C) (tptp.v1_finset_1 C) (tptp.v1_fraenkel C))))) (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)) (=> (not (tptp.v1_xboole_0 A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (not (tptp.v1_xboole_0 B)) (tptp.v1_finset_1 B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 (tptp.k1_closure2 A B)))) (=> (and (tptp.m1_pboole B A) (tptp.m1_subset_1 C _let_1) (tptp.m1_subset_1 D _let_1)) (tptp.r1_closure3 A B D D)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (tptp.m1_subset_1 A B))) _let_1 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 A B) (or (tptp.v1_xboole_0 B) (tptp.r2_hidden A B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.m1_subset_1 A (tptp.k1_zfmisc_1 B)) (tptp.r1_tarski A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.r2_hidden A B) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 C))) (tptp.m1_subset_1 A C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.r2_hidden A B) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 C)) (tptp.v1_xboole_0 C)))) (forall ((A $$unsorted)) (=> (tptp.v1_xboole_0 A) (= A tptp.k1_xboole_0))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.r2_hidden A B) (tptp.v1_xboole_0 B)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.v1_xboole_0 A) (not (= A B)) (tptp.v1_xboole_0 B)))) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.70  )
% 0.21/0.70  % SZS output end Proof for ALG223+1
% 0.21/0.71  % cvc5---1.0.5 exiting
% 0.21/0.71  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------