%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET775+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n016.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 14:40:17 EDT 2023

% Result   : Theorem 0.21s 0.56s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET775+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n016.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   : Sat Aug 26 10:44:56 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.48  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.56  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.s2NcWNs685/cvc5---1.0.5_17672.p...
% 0.21/0.56  ------- get file name : TPTP file name is SET775+4
% 0.21/0.56  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_17672.smt2...
% 0.21/0.56  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.56  % SZS status Theorem for SET775+4
% 0.21/0.56  % SZS output start Proof for SET775+4
% 0.21/0.56  (
% 0.21/0.56  (let ((_let_1 (not (forall ((E $$unsorted) (P $$unsorted) (R $$unsorted)) (=> (and (tptp.pre_order P E) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.member A E) (tptp.member B E)) (= (tptp.apply R A B) (and (tptp.apply P A B) (tptp.apply P B A)))))) (tptp.equivalence R E)))))) (let ((_let_2 (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.pre_order R E) (and (forall ((X $$unsorted)) (=> (tptp.member X E) (tptp.apply R X X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.member X E) (tptp.member Y E) (tptp.member Z E)) (=> (and (tptp.apply R X Y) (tptp.apply R Y Z)) (tptp.apply R X Z))))))))) (let ((_let_3 (forall ((A $$unsorted) (R $$unsorted)) (= (tptp.equivalence R A) (and (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.apply R X X))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y A)) (=> (tptp.apply R X Y) (tptp.apply R Y X)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y A) (tptp.member Z A)) (=> (and (tptp.apply R X Y) (tptp.apply R Y Z)) (tptp.apply R X Z))))))))) (let ((_let_4 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_5 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_6 (and _let_5 _let_4))) (let ((_let_7 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_8 (= _let_7 _let_6))) (let ((_let_9 (not _let_6))) (let ((_let_10 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_11 (not _let_10))) (let ((_let_12 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_13 (not _let_12))) (let ((_let_14 (or _let_13 _let_11 _let_8))) (let ((_let_15 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.member A SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member B SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 A B) (and (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 A B) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 B A))))))) (let ((_let_16 (tptp.equivalence SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_17 (not _let_15))) (let ((_let_18 (tptp.pre_order SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_19 (not _let_18))) (let ((_let_20 (or _let_19 _let_17 _let_16))) (let ((_let_21 (forall ((E $$unsorted) (P $$unsorted) (R $$unsorted)) (or (not (tptp.pre_order P E)) (not (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.member A E)) (not (tptp.member B E)) (= (tptp.apply R A B) (and (tptp.apply P A B) (tptp.apply P B A)))))) (tptp.equivalence R E))))) (let ((_let_22 (not _let_20))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_24 (or))) (let ((_let_25 (not _let_21))) (let ((_let_26 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_23) :args (_let_25))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_21))) (REFL :args (_let_22)) :args _let_24)) _let_23 :args (_let_22 true _let_21)))) (let ((_let_27 (REFL :args (_let_20)))) (let ((_let_28 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_20 1)) (CONG _let_27 (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_15))) :args _let_24)) :args ((or _let_15 _let_20))) _let_26 :args (_let_15 true _let_20)))) (let ((_let_29 (_let_15))) (let ((_let_30 ((tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 A B)))) (let ((_let_31 (ASSUME :args _let_29))) (let ((_let_32 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_33 (not _let_32))) (let ((_let_34 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_35 (not _let_34))) (let ((_let_36 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_13 _let_37 _let_11 _let_35 _let_33 _let_7))) (let ((_let_39 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Y Z)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X Z))))) (let ((_let_40 (not _let_38))) (let ((_let_41 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X Y)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Y X))))) (let ((_let_42 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X X))))) (let ((_let_43 (and _let_42 _let_41 _let_39))) (let ((_let_44 (not _let_39))) (let ((_let_45 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_46 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_47 (not _let_46))) (let ((_let_48 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_49 (not _let_48))) (let ((_let_50 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_51 _let_49 _let_47 _let_45))) (let ((_let_53 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_54 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_55 (and _let_54 _let_53))) (let ((_let_56 (= _let_46 _let_55))) (let ((_let_57 (or _let_51 _let_49 _let_56))) (let ((_let_58 (and _let_53 _let_54))) (let ((_let_59 (= _let_45 _let_58))) (let ((_let_60 (or _let_49 _let_51 _let_59))) (let ((_let_61 (REFL :args (_let_52)))) (let ((_let_62 (not _let_55))) (let ((_let_63 (not _let_41))) (let ((_let_64 (_let_63))) (let ((_let_65 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_66 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_67 (not _let_66))) (let ((_let_68 (or _let_67 _let_65))) (let ((_let_69 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_70 (= _let_65 _let_69))) (let ((_let_71 (or _let_67 _let_67 _let_70))) (let ((_let_72 (or _let_67 _let_69))) (let ((_let_73 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X X))))) (let ((_let_74 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Y Z)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Z))))) (let ((_let_75 (and _let_73 _let_74))) (let ((_let_76 (= _let_18 _let_75))) (let ((_let_77 (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.pre_order R E) (and (forall ((X $$unsorted)) (or (not (tptp.member X E)) (tptp.apply R X X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member X E)) (not (tptp.member Y E)) (not (tptp.member Z E)) (not (tptp.apply R X Y)) (not (tptp.apply R Y Z)) (tptp.apply R X Z)))))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_76)) :args ((or _let_19 _let_75 (not _let_76)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_20 0)) (CONG _let_27 (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) :args _let_24)) :args ((or _let_18 _let_20))) _let_26 :args (_let_18 true _let_20)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.pre_order R E)))) :args (_let_77))) _let_78 :args (_let_76 false _let_77)) :args (_let_75 false _let_18 false _let_76)))) (let ((_let_80 (not _let_75))) (let ((_let_81 (_let_73))) (let ((_let_82 (not _let_42))) (let ((_let_83 (_let_82))) (let ((_let_84 (= _let_16 _let_43))) (let ((_let_85 (not _let_43))) (let ((_let_86 (forall ((A $$unsorted) (R $$unsorted)) (= (tptp.equivalence R A) (and (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.apply R X X))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Y A)) (not (tptp.apply R X Y)) (tptp.apply R Y X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Y A)) (not (tptp.member Z A)) (not (tptp.apply R X Y)) (not (tptp.apply R Y Z)) (tptp.apply R X Z)))))))) (let ((_let_87 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (_let_44))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_88)) :args _let_88)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_39))) (REFL :args (_let_40)) :args _let_24)) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_84)) :args ((or _let_16 _let_85 (not _let_84)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_20 2)) _let_26 :args ((not _let_16) true _let_20)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_87 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equivalence R A)))) :args (_let_86))) _let_87 :args (_let_84 false _let_86)) :args (_let_85 true _let_16 false _let_84)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_83)) :args _let_83)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_82) _let_42))) (REFL :args ((not _let_68))) :args _let_24)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_70)) :args ((or _let_65 (not _let_69) (not _let_70)))) (REORDERING (CNF_OR_POS :args (_let_72)) :args ((or _let_67 _let_69 (not _let_72)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_81) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) false))))) :args _let_81)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_75 0)) :args ((or _let_73 _let_80))) _let_79 :args (_let_73 false _let_75)) :args (_let_72 false _let_73)) (REORDERING (FACTORING (CNF_OR_POS :args (_let_71))) :args ((or _let_67 _let_70 (not _let_71)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_31 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_30)) :args _let_29))) _let_28 :args (_let_71 false _let_15)) (CNF_OR_NEG :args (_let_68 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_68 0)) (CONG (REFL :args (_let_68)) (MACRO_SR_PRED_INTRO :args ((= (not _let_67) _let_66))) :args _let_24)) :args ((or _let_66 _let_68))) :args (_let_68 false _let_69 false _let_72 false _let_70 false _let_71 true _let_65 false _let_66)) :args (_let_42 false _let_68)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_64)) :args _let_64)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_63) _let_41))) (REFL :args ((not _let_52))) :args _let_24)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_58)) :args ((or _let_58 (not _let_54) (not _let_53)))) (REORDERING (CNF_AND_POS :args (_let_55 1)) :args ((or _let_53 _let_62))) (REORDERING (CNF_AND_POS :args (_let_55 0)) :args ((or _let_54 _let_62))) (REORDERING (CNF_EQUIV_POS2 :args (_let_59)) :args ((or _let_45 (not _let_58) (not _let_59)))) (REORDERING (CNF_EQUIV_POS1 :args (_let_56)) :args ((or _let_47 _let_55 (not _let_56)))) (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_51 _let_49 _let_59 (not _let_60)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_30)) :args _let_29)) _let_28 :args (_let_60 false _let_15)) (REORDERING (CNF_OR_POS :args (_let_57)) :args ((or _let_51 _let_49 _let_56 (not _let_57)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_30)) :args _let_29)) _let_28 :args (_let_57 false _let_15)) (CNF_OR_NEG :args (_let_52 3)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_52 2)) (CONG _let_61 (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_46))) :args _let_24)) :args ((or _let_46 _let_52))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_52 1)) (CONG _let_61 (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_48))) :args _let_24)) :args ((or _let_48 _let_52))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_52 0)) (CONG _let_61 (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_50))) :args _let_24)) :args ((or _let_50 _let_52))) :args (_let_52 false _let_53 false _let_54 true _let_58 false _let_55 false _let_59 false _let_60 false _let_56 false _let_57 true _let_45 false _let_46 false _let_48 false _let_50)) :args (_let_41 false _let_52)) :args (_let_44 true _let_43 false _let_42 false _let_41)) :args (_let_40 true _let_39)))) (let ((_let_90 (REFL :args (_let_38)))) (let ((_let_91 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 2)) (CONG _let_90 (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_10))) :args _let_24)) :args ((or _let_10 _let_38))) _let_89 :args (_let_10 true _let_38)))) (let ((_let_92 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 0)) (CONG _let_90 (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_12))) :args _let_24)) :args ((or _let_12 _let_38))) _let_89 :args (_let_12 true _let_38)))) (let ((_let_93 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_94 (not _let_93))) (let ((_let_95 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_96 (not _let_95))) (let ((_let_97 (or _let_11 _let_37 _let_13 _let_96 _let_94 _let_4))) (let ((_let_98 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_75 1)) :args ((or _let_74 _let_80))) _let_79 :args (_let_74 false _let_75)))) (let ((_let_99 (_let_74))) (let ((_let_100 ((not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Z) true)) (not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y) false))))) (let ((_let_101 (ASSUME :args _let_99))) (let ((_let_102 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_103 (and _let_102 _let_95))) (let ((_let_104 (= _let_32 _let_103))) (let ((_let_105 (or _let_37 _let_11 _let_104))) (let ((_let_106 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 1)) (CONG _let_90 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_24)) :args ((or _let_36 _let_38))) _let_89 :args (_let_36 true _let_38)))) (let ((_let_107 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_104)) :args ((or _let_33 _let_103 (not _let_104)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 4)) (CONG _let_90 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_24)) :args ((or _let_32 _let_38))) _let_89 :args (_let_32 true _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_105)) :args ((or _let_37 _let_11 _let_104 (not _let_105)))) _let_106 _let_91 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_30)) :args _let_29)) _let_28 :args (_let_105 false _let_15)) :args (_let_104 false _let_36 false _let_10 false _let_105)) :args (_let_103 false _let_32 false _let_104)))) (let ((_let_108 (not _let_103))) (let ((_let_109 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_110 (and _let_109 _let_93))) (let ((_let_111 (= _let_34 _let_110))) (let ((_let_112 (or _let_13 _let_37 _let_111))) (let ((_let_113 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_111)) :args ((or _let_35 _let_110 (not _let_111)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 3)) (CONG _let_90 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) :args _let_24)) :args ((or _let_34 _let_38))) _let_89 :args (_let_34 true _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_112)) :args ((or _let_13 _let_37 _let_111 (not _let_112)))) _let_92 _let_106 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_30)) :args _let_29)) _let_28 :args (_let_112 false _let_15)) :args (_let_111 false _let_12 false _let_36 false _let_112)) :args (_let_110 false _let_34 false _let_111)))) (let ((_let_114 (not _let_110))) (let ((_let_115 (not _let_102))) (let ((_let_116 (not _let_109))) (let ((_let_117 (or _let_13 _let_37 _let_11 _let_116 _let_115 _let_5))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_6)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_117)) :args ((or _let_13 _let_37 _let_11 _let_5 _let_116 _let_115 (not _let_117)))) _let_92 _let_106 _let_91 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_110 0)) :args ((or _let_109 _let_114))) _let_113 :args (_let_109 false _let_110)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_103 0)) :args ((or _let_102 _let_108))) _let_107 :args (_let_102 false _let_103)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_101 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING _let_100)) :args _let_99)) _let_98 :args (_let_117 false _let_74)) :args (_let_5 false _let_12 false _let_36 false _let_10 false _let_109 false _let_102 false _let_117)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_97)) :args ((or _let_13 _let_37 _let_11 _let_4 _let_94 _let_96 (not _let_97)))) _let_92 _let_106 _let_91 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_110 1)) :args ((or _let_93 _let_114))) _let_113 :args (_let_93 false _let_110)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_103 1)) :args ((or _let_95 _let_108))) _let_107 :args (_let_95 false _let_103)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_101 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING _let_100)) :args _let_99)) _let_98 :args (_let_97 false _let_74)) :args (_let_4 false _let_12 false _let_36 false _let_10 false _let_93 false _let_95 false _let_97)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_8)) :args ((or _let_7 _let_9 (not _let_8)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_38 5)) _let_89 :args ((not _let_7) true _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_14)) :args ((or _let_13 _let_11 _let_8 (not _let_14)))) _let_92 _let_91 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_30)) :args _let_29)) _let_28 :args (_let_14 false _let_15)) :args (_let_8 false _let_12 false _let_10 false _let_14)) :args (_let_9 true _let_7 false _let_8)) :args (false false _let_5 false _let_4 true _let_6)) :args ((forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.power_set A)) (tptp.subset X A))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.intersection A B)) (and (tptp.member X A) (tptp.member X B)))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.union A B)) (or (tptp.member X A) (tptp.member X B)))) (forall ((X $$unsorted)) (not (tptp.member X tptp.empty_set))) (forall ((B $$unsorted) (A $$unsorted) (E $$unsorted)) (= (tptp.member B (tptp.difference E A)) (and (tptp.member B E) (not (tptp.member B A))))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.singleton A)) (= X A))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.unordered_pair A B)) (or (= X A) (= X B)))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.sum A)) (exists ((Y $$unsorted)) (and (tptp.member Y A) (tptp.member X Y))))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.product A)) (forall ((Y $$unsorted)) (=> (tptp.member Y A) (tptp.member X Y))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (not (exists ((X $$unsorted)) (and (tptp.member X A) (tptp.member X B)))))) (forall ((A $$unsorted) (E $$unsorted)) (= (tptp.partition A E) (and (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.subset X E))) (forall ((X $$unsorted)) (=> (tptp.member X E) (exists ((Y $$unsorted)) (and (tptp.member Y A) (tptp.member X Y))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y A)) (=> (exists ((Z $$unsorted)) (and (tptp.member Z X) (tptp.member Z Y))) (= X Y))))))) _let_3 (forall ((R $$unsorted) (E $$unsorted) (A $$unsorted) (X $$unsorted)) (= (tptp.member X (tptp.equivalence_class A E R)) (and (tptp.member X E) (tptp.apply R A X)))) _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.56  )
% 0.21/0.56  % SZS output end Proof for SET775+4
% 0.21/0.56  % cvc5---1.0.5 exiting
% 0.21/0.56  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------