TSTP Solution File: SEU222+3 by cvc5---1.0.5

%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU222+3 : TPTP v8.1.2. Released v3.2.0.
% 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 16:30:10 EDT 2023

% Result   : Theorem 48.31s 48.57s
% Output   : Proof 48.31s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU222+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.34  % Computer : n016.cluster.edu
% 0.15/0.34  % Model    : x86_64 x86_64
% 0.15/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34  % Memory   : 8042.1875MB
% 0.15/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34  % CPULimit   : 300
% 0.15/0.34  % WCLimit    : 300
% 0.15/0.34  % DateTime   : Wed Aug 23 18:05:53 EDT 2023
% 0.18/0.34  % CPUTime    : 
% 0.18/0.45  %----Proving TF0_NAR, FOF, or CNF
% 48.31/48.57  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.UURXJASy33/cvc5---1.0.5_28297.p...
% 48.31/48.57  ------- get file name : TPTP file name is SEU222+3
% 48.31/48.57  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_28297.smt2...
% 48.31/48.57  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 48.31/48.57  --- Run --no-e-matching --full-saturate-quant at 5...
% 48.31/48.57  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 48.31/48.57  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 48.31/48.57  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 48.31/48.57  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 48.31/48.57  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 48.31/48.57  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 48.31/48.57  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 48.31/48.57  % SZS status Theorem for SEU222+3
% 48.31/48.57  % SZS output start Proof for SEU222+3
% 48.31/48.57  (
% 48.31/48.57  (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_dom (tptp.relation_dom_restriction B A)) (tptp.set_intersection2 (tptp.relation_dom B) A)))))) (let ((_let_2 (not (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (forall ((C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (= (= B (tptp.relation_dom_restriction C A)) (and (= (tptp.relation_dom B) (tptp.set_intersection2 (tptp.relation_dom C) A)) (forall ((D $$unsorted)) (=> (tptp.in D (tptp.relation_dom B)) (= (tptp.apply B D) (tptp.apply C D))))))))))))) (let ((_let_3 (tptp.relation tptp.empty_set))) (let ((_let_4 (tptp.empty tptp.empty_set))) (let ((_let_5 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (= B (tptp.relation_dom A)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (tptp.in (tptp.ordered_pair C D) A)))))))))) (let ((_let_6 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (forall ((B $$unsorted) (C $$unsorted)) (let ((_let_1 (= C (tptp.apply A B)))) (let ((_let_2 (tptp.in B (tptp.relation_dom A)))) (and (=> _let_2 (= _let_1 (tptp.in (tptp.ordered_pair B C) A))) (=> (not _let_2) (= _let_1 (= C tptp.empty_set))))))))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_intersection2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (tptp.in D B)))))))) (let ((_let_8 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (= (= C (tptp.relation_dom_restriction A B)) (forall ((D $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.ordered_pair D E))) (= (tptp.in _let_1 C) (and (tptp.in D B) (tptp.in _let_1 A)))))))))))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A B) (tptp.set_intersection2 B A))))) (let ((_let_10 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_214))) (let ((_let_11 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_215 _let_10))) (let ((_let_12 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_214))) (let ((_let_13 (= _let_10 _let_12))) (let ((_let_14 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_215 _let_12))) (let ((_let_15 (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_214 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_215))) (let ((_let_16 (tptp.in _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_17 (= _let_16 _let_11))) (let ((_let_18 (tptp.relation_dom SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_19 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_214 _let_18))) (let ((_let_20 (not _let_19))) (let ((_let_21 (or _let_20 _let_17))) (let ((_let_22 (forall ((BOUND_VARIABLE_1079 $$unsorted) (BOUND_VARIABLE_1081 $$unsorted)) (or (not (tptp.in BOUND_VARIABLE_1079 (tptp.relation_dom SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (= (= BOUND_VARIABLE_1081 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 BOUND_VARIABLE_1079)) (tptp.in (tptp.ordered_pair BOUND_VARIABLE_1079 BOUND_VARIABLE_1081) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))))) (let ((_let_23 (and _let_22 (forall ((BOUND_VARIABLE_1093 $$unsorted) (BOUND_VARIABLE_1095 $$unsorted)) (or (tptp.in BOUND_VARIABLE_1093 (tptp.relation_dom SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) (= (= tptp.empty_set BOUND_VARIABLE_1095) (= BOUND_VARIABLE_1095 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 BOUND_VARIABLE_1093)))))))) (let ((_let_24 (tptp.function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or _let_27 _let_25 _let_23))) (let ((_let_29 (forall ((A $$unsorted)) (or (not (tptp.relation A)) (not (tptp.function A)) (and (forall ((BOUND_VARIABLE_1079 $$unsorted) (BOUND_VARIABLE_1081 $$unsorted)) (or (not (tptp.in BOUND_VARIABLE_1079 (tptp.relation_dom A))) (= (= BOUND_VARIABLE_1081 (tptp.apply A BOUND_VARIABLE_1079)) (tptp.in (tptp.ordered_pair BOUND_VARIABLE_1079 BOUND_VARIABLE_1081) A)))) (forall ((BOUND_VARIABLE_1093 $$unsorted) (BOUND_VARIABLE_1095 $$unsorted)) (or (tptp.in BOUND_VARIABLE_1093 (tptp.relation_dom A)) (= (= BOUND_VARIABLE_1095 (tptp.apply A BOUND_VARIABLE_1093)) (= tptp.empty_set BOUND_VARIABLE_1095))))))))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (_let_29))) (let ((_let_32 ((not (= (tptp.relation A) false))))) (let ((_let_33 (forall ((D $$unsorted)) (or (not (tptp.in D (tptp.relation_dom SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 D) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 D)))))) (let ((_let_34 (tptp.set_intersection2 _let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_35 (tptp.relation_dom SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_36 (= _let_35 _let_34))) (let ((_let_37 (and _let_36 _let_33))) (let ((_let_38 (tptp.relation_dom_restriction SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_39 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 _let_38))) (let ((_let_40 (= _let_39 _let_37))) (let ((_let_41 (or _let_27 _let_25 _let_40))) (let ((_let_42 (forall ((C $$unsorted)) (or (not (tptp.relation C)) (not (tptp.function C)) (= (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 (tptp.relation_dom_restriction C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)) (and (= (tptp.relation_dom SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) (tptp.set_intersection2 (tptp.relation_dom C) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)) (forall ((D $$unsorted)) (or (not (tptp.in D (tptp.relation_dom SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (= (tptp.apply C D) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 D)))))))))) (let ((_let_43 (not _let_41))) (let ((_let_44 (tptp.function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_45 (not _let_44))) (let ((_let_46 (tptp.relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_47 (not _let_46))) (let ((_let_48 (or _let_47 _let_45 _let_42))) (let ((_let_49 (not _let_42))) (let ((_let_50 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.relation B)) (not (tptp.function B)) (forall ((C $$unsorted)) (or (not (tptp.relation C)) (not (tptp.function C)) (= (= B (tptp.relation_dom_restriction C A)) (and (= (tptp.relation_dom B) (tptp.set_intersection2 (tptp.relation_dom C) A)) (forall ((D $$unsorted)) (or (not (tptp.in D (tptp.relation_dom B))) (= (tptp.apply B D) (tptp.apply C D)))))))))))) (let ((_let_51 (not _let_48))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (or))) (let ((_let_54 (not _let_50))) (let ((_let_55 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_52) :args (_let_54)) (REWRITE :args ((=> _let_54 (not (or _let_47 _let_45 (forall ((C $$unsorted)) (or (not (tptp.relation C)) (not (tptp.function C)) (= (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 (tptp.relation_dom_restriction C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)) (and (= (tptp.relation_dom SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) (tptp.set_intersection2 (tptp.relation_dom C) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)) (forall ((D $$unsorted)) (or (not (tptp.in D (tptp.relation_dom SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 D) (tptp.apply C D))))))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_50))) (REFL :args (_let_51)) :args _let_53)) _let_52 :args (_let_51 true _let_50)))) (let ((_let_56 (_let_49))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_56)) :args _let_56) (REWRITE :args ((=> _let_49 (not (or _let_27 _let_25 (= _let_39 (and _let_36 (forall ((D $$unsorted)) (or (not (tptp.in D (tptp.relation_dom SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 D) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 D))))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_42))) (REFL :args (_let_43)) :args _let_53)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_48 2)) _let_55 :args (_let_49 true _let_48)) :args (_let_43 true _let_42)))) (let ((_let_58 (REFL :args (_let_41)))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_41 0)) (CONG _let_58 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_53)) :args ((or _let_26 _let_41))) _let_57 :args (_let_26 true _let_41)))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_23 0)) :args ((or _let_22 (not _let_23)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_28)) :args ((or _let_27 _let_25 _let_23 (not _let_28)))) _let_59 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_41 1)) (CONG _let_58 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_53)) :args ((or _let_24 _let_41))) _let_57 :args (_let_24 true _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_30 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_32)) :args _let_31))) _let_30 :args (_let_28 false _let_29)) :args (_let_23 false _let_26 false _let_24 false _let_28)) :args (_let_22 false _let_23)))) (let ((_let_61 (_let_22))) (let ((_let_62 ((tptp.ordered_pair BOUND_VARIABLE_1079 BOUND_VARIABLE_1081)))) (let ((_let_63 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_214 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_215 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_62))) (let ((_let_64 (ASSUME :args _let_61))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_64 :args _let_63) :args _let_61))) _let_60 :args (_let_21 false _let_22)))) (let ((_let_66 (forall ((D $$unsorted)) (not (tptp.in (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_214 D) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))))) (let ((_let_67 (not _let_66))) (let ((_let_68 (= _let_19 _let_67))) (let ((_let_69 (forall ((C $$unsorted)) (= (not (forall ((D $$unsorted)) (not (tptp.in (tptp.ordered_pair C D) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))) (tptp.in C (tptp.relation_dom SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))))) (let ((_let_70 (forall ((B $$unsorted)) (= (= B (tptp.relation_dom SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) (forall ((C $$unsorted)) (= (tptp.in C B) (not (forall ((D $$unsorted)) (not (tptp.in (tptp.ordered_pair C D) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))))))))) (let ((_let_71 (or _let_27 _let_70))) (let ((_let_72 (forall ((A $$unsorted)) (or (not (tptp.relation A)) (forall ((B $$unsorted)) (= (= B (tptp.relation_dom A)) (forall ((C $$unsorted)) (= (tptp.in C B) (not (forall ((D $$unsorted)) (not (tptp.in (tptp.ordered_pair C D) A)))))))))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (_let_72))) (let ((_let_75 ((not (= (tptp.relation A) false))))) (let ((_let_76 (_let_70))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_76) :args (_let_18 QUANTIFIERS_INST_CBQI_PROP)) :args _let_76))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_71)) :args ((or _let_27 _let_70 (not _let_71)))) _let_59 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_75)) :args _let_74)) _let_73 :args (_let_71 false _let_72)) :args (_let_70 false _let_26 false _let_71)) :args (_let_69 false _let_70)))) (let ((_let_78 (_let_69))) (let ((_let_79 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_214 QUANTIFIERS_INST_CBQI_PROP))) (let ((_let_80 (ASSUME :args _let_78))) (let ((_let_81 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_214 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_82 (and _let_81 _let_16))) (let ((_let_83 (tptp.in _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_84 (= _let_83 _let_82))) (let ((_let_85 (forall ((D $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.ordered_pair D E))) (= (tptp.in _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) (and (tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) (tptp.in _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))))))) (let ((_let_86 (not _let_84))) (let ((_let_87 (= _let_39 _let_85))) (let ((_let_88 (not _let_85))) (let ((_let_89 (or _let_47 _let_87))) (let ((_let_90 (forall ((B $$unsorted) (C $$unsorted)) (or (not (tptp.relation C)) (= (= C (tptp.relation_dom_restriction SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 B)) (forall ((D $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.ordered_pair D E))) (= (tptp.in _let_1 C) (and (tptp.in D B) (tptp.in _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))))))))) (let ((_let_91 (or _let_27 _let_90))) (let ((_let_92 (forall ((A $$unsorted)) (or (not (tptp.relation A)) (forall ((B $$unsorted) (C $$unsorted)) (or (not (tptp.relation C)) (= (= C (tptp.relation_dom_restriction A B)) (forall ((D $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.ordered_pair D E))) (= (tptp.in _let_1 C) (and (tptp.in D B) (tptp.in _let_1 A)))))))))))) (let ((_let_93 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_94 (_let_90))) (let ((_let_95 (REFL :args (_let_48)))) (let ((_let_96 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 0)) (CONG _let_95 (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_46))) :args _let_53)) :args ((or _let_46 _let_48))) _let_55 :args (_let_46 true _let_48)))) (let ((_let_97 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_89)) :args ((or _let_47 _let_87 (not _let_89)))) _let_96 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_94) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_CBQI_PROP)) :args _let_94)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_91)) :args ((or _let_27 _let_90 (not _let_91)))) _let_59 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_93 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.relation A) false))))) :args (_let_92))) _let_93 :args (_let_91 false _let_92)) :args (_let_90 false _let_26 false _let_91)) :args (_let_89 false _let_90)) :args (_let_87 false _let_46 false _let_89)))) (let ((_let_98 (= _let_34 (tptp.relation_dom _let_38)))) (let ((_let_99 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_100 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_101 (= _let_100 _let_99))) (let ((_let_102 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_35))) (let ((_let_103 (not _let_102))) (let ((_let_104 (or _let_103 _let_101))) (let ((_let_105 (= _let_100 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_114))) (let ((_let_106 (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_114))) (let ((_let_107 (tptp.in _let_106 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_108 (= _let_107 _let_105))) (let ((_let_109 (or _let_103 _let_108))) (let ((_let_110 (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_18))) (let ((_let_111 (= _let_34 _let_110))) (let ((_let_112 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_110))) (let ((_let_113 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_18))) (let ((_let_114 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_115 (and _let_114 _let_113))) (let ((_let_116 (= _let_112 _let_115))) (let ((_let_117 (forall ((D $$unsorted)) (not (tptp.in (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 D) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))))) (let ((_let_118 (not _let_117))) (let ((_let_119 (= _let_113 _let_118))) (let ((_let_120 (= _let_99 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_114))) (let ((_let_121 (tptp.in _let_106 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_122 (= _let_121 _let_120))) (let ((_let_123 (not _let_113))) (let ((_let_124 (or _let_123 _let_122))) (let ((_let_125 (and _let_114 _let_121))) (let ((_let_126 (= _let_107 _let_125))) (let ((_let_127 (not _let_39))) (let ((_let_128 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_41 2)) _let_57 :args ((not _let_40) true _let_41)))) (let ((_let_129 (_let_40))) (let ((_let_130 (or _let_27 _let_98))) (let ((_let_131 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.relation B)) (= (tptp.relation_dom (tptp.relation_dom_restriction B A)) (tptp.set_intersection2 (tptp.relation_dom B) A)))))) (let ((_let_132 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_133 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_130)) :args ((or _let_27 _let_98 (not _let_130)))) _let_59 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE 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(CNF_EQUIV_NEG2 :args _let_129) _let_128 :args (_let_127 true _let_126 true _let_107 true _let_105 false _let_125 false _let_120 false _let_121 false _let_122 false _let_124 true _let_117 false _let_119 false _let_113 false _let_114 false _let_115 false _let_116 false _let_112 false _let_111 false _let_98 false _let_108 false _let_109 true _let_101 false _let_102 true _let_104 true _let_33 false _let_85 false _let_87 false _let_36 false _let_98 true _let_37 true _let_40)))) (let ((_let_175 (_let_88))) (let ((_let_176 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_175)) :args _let_175)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_88) _let_85))) (REFL :args (_let_86)) :args _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_141) :args ((or _let_39 _let_88 _let_140))) _let_174 _let_97 :args (_let_88 true _let_39 false _let_87)) :args (_let_86 true _let_85)))) (let ((_let_177 (forall ((D $$unsorted)) (not (tptp.in 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(let ((_let_219 (ASSUME :args (_let_36)))) (let ((_let_220 (SYMM _let_219))) (let ((_let_221 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_214)))) (let ((_let_222 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_164 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_214 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)))) :args _let_163)) _let_162 :args (_let_187 false _let_159)))) (let ((_let_223 (not _let_187))) (let ((_let_224 (not _let_185))) (let ((_let_225 (_let_187))) (let ((_let_226 (not _let_186))) (let ((_let_227 (REORDERING (CNF_OR_POS :args (_let_21)) :args ((or _let_20 _let_17 (not _let_21)))))) (let ((_let_228 (not _let_17))) (let ((_let_229 (not _let_11))) (let ((_let_230 (_let_17))) (let ((_let_231 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_230) :args ((or _let_16 _let_229 _let_228))) _let_227 _let_65 (CNF_AND_NEG :args (_let_82)) (REORDERING (CNF_AND_POS :args (_let_186 1)) :args ((or _let_19 _let_226))) (REORDERING (CNF_AND_POS :args (_let_186 0)) :args ((or _let_81 _let_226))) (REORDERING (CNF_EQUIV_POS1 :args _let_225) :args ((or _let_186 _let_224 _let_223))) _let_222 (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_217)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_218 _let_219 _let_157) (SCOPE (TRUE_ELIM (TRANS (CONG _let_221 _let_158 :args _let_155) (CONG _let_221 _let_220 :args _let_155) (TRUE_INTRO _let_218))) :args (_let_179 _let_36 _let_111))) :args (_let_36 _let_111 _let_179))) :args (true _let_217)) :args ((or _let_216 _let_215 _let_185 _let_182))) _let_214 _let_152 (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_210)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_211 _let_213) (SCOPE (TRANS (SYMM (SYMM _let_213)) _let_212) :args (_let_13 _let_14))) :args (_let_14 _let_13))) :args (true _let_210)) :args ((or _let_11 _let_209 _let_208))) (REORDERING (CNF_EQUIV_POS1 :args _let_207) :args ((or _let_188 _let_14 _let_206))) _let_205 _let_204 _let_200 _let_199 (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_180)) (CONG (REFL :args (_let_197)) (REFL :args _let_198) (MACRO_SR_PRED_INTRO :args ((= (not _let_178) _let_177))) :args _let_53)) :args ((or _let_179 _let_177 _let_197))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_196) :args _let_79) :args _let_196))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_195) :args (_let_35 QUANTIFIERS_INST_CBQI_PROP)) :args _let_195))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_194)) :args ((or _let_47 _let_193 (not _let_194)))) _let_96 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_75)) :args _let_74)) _let_73 :args (_let_194 false _let_72)) :args (_let_193 false _let_46 false _let_194)) :args (_let_192 false _let_193)) :args (_let_180 false _let_192)) (REORDERING (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_190) :args _let_191) :args _let_190)) :args ((or _let_188 _let_178))) (CNF_EQUIV_NEG2 :args _let_189) _let_176 :args (_let_188 false _let_17 false _let_21 true _let_16 false _let_19 false _let_81 false _let_186 false _let_187 false _let_185 false _let_36 false _let_111 false _let_11 false _let_14 false _let_13 false _let_184 false _let_181 false _let_183 false _let_179 false _let_180 true _let_177 true _let_82 true _let_84)))) (let ((_let_232 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_189) :args ((or _let_83 _let_82 _let_84))) _let_231 _let_176 :args (_let_82 true _let_83 true _let_84)))) (let ((_let_233 (not _let_82))) (let ((_let_234 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_82 1)) :args ((or _let_16 _let_233))) _let_232 :args (_let_16 false _let_82)))) (let ((_let_235 (not _let_16))) (let ((_let_236 (_let_66))) (let ((_let_237 (not _let_68))) (let ((_let_238 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_68)) (CONG (REFL :args (_let_237)) (REFL :args (_let_19)) (MACRO_SR_PRED_INTRO :args ((= (not _let_67) _let_66))) :args _let_53)) :args ((or _let_19 _let_66 _let_237))) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_236) :args _let_191) :args _let_236)) :args ((or _let_235 _let_67))) _let_234 :args (_let_67 false _let_16)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_80 :args _let_79) :args _let_78))) _let_77 :args (_let_68 false _let_69)) :args (_let_19 true _let_66 false _let_68)))) (let ((_let_239 (and _let_36 _let_111 _let_185))) (let ((_let_240 (ASSUME :args (_let_185)))) (let ((_let_241 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_239)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_240 _let_157 _let_219) (SCOPE (TRUE_ELIM (TRANS (CONG _let_221 (SYMM _let_220) :args _let_155) (CONG _let_221 (SYMM _let_158) :args _let_155) (TRUE_INTRO _let_240))) :args (_let_185 _let_111 _let_36))) :args (_let_36 _let_111 _let_185))) :args (true _let_239)) :args ((or _let_216 _let_215 _let_179 _let_224))) _let_214 _let_152 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_225) :args ((or _let_185 _let_226 _let_223))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_186)) :args ((or (not _let_81) _let_20 _let_186))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_82 0)) :args ((or _let_81 _let_233))) _let_232 :args (_let_81 false _let_82)) _let_238 :args (_let_186 false _let_81 false _let_19)) _let_222 :args (_let_185 false _let_186 false _let_187)) :args (_let_179 false _let_36 false _let_111 false _let_185)))) (let ((_let_242 (and _let_11 _let_13))) (let ((_let_243 (ASSUME :args (_let_11)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_242)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_211 _let_243) (SCOPE (TRANS (SYMM (SYMM _let_243)) (SYMM _let_212)) :args (_let_13 _let_11))) :args (_let_11 _let_13))) :args (true _let_242)) :args ((or _let_14 _let_229 _let_208))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_207) :args ((or _let_83 _let_209 _let_206))) _let_231 (MACRO_RESOLUTION_TRUST _let_200 _let_241 _let_199 :args (_let_181 false _let_179 false _let_183)) :args (_let_209 true _let_83 false _let_181)) (MACRO_RESOLUTION_TRUST _let_205 _let_241 _let_204 :args (_let_13 false _let_179 false _let_184)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_230) :args ((or _let_235 _let_11 _let_228))) _let_234 (MACRO_RESOLUTION_TRUST _let_227 _let_238 _let_65 :args (_let_17 false _let_19 false _let_21)) :args (_let_11 false _let_16 false _let_17)) :args (false true _let_14 false _let_13 false _let_11)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.function A))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.relation A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.function A))) (let ((_let_2 (tptp.relation A))) (=> (and _let_2 (tptp.empty A) _let_1) (and _let_2 _let_1 (tptp.one_to_one A)))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.unordered_pair A B) (tptp.unordered_pair B A))) _let_9 _let_8 _let_7 _let_6 _let_5 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.ordered_pair A B) (tptp.unordered_pair (tptp.unordered_pair A B) (tptp.singleton A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation A) (tptp.relation (tptp.relation_dom_restriction A B)))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (and _let_4 _let_3 (tptp.relation_empty_yielding tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_dom_restriction A B))) (=> (and (tptp.relation A) (tptp.relation_empty_yielding A)) (and (tptp.relation _let_1) (tptp.relation_empty_yielding _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.set_intersection2 A B)))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) _let_4 (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.empty (tptp.ordered_pair A B)))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.singleton A)))) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.empty (tptp.unordered_pair A B)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_dom_restriction A B))) (=> (and (tptp.relation A) (tptp.function A)) (and (tptp.relation _let_1) (tptp.function _let_1))))) (and _let_4 _let_3) (forall ((A $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation A)) (not (tptp.empty (tptp.relation_dom A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation_dom A))) (=> (tptp.empty A) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A A) A)) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.empty A) (tptp.relation A))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (exists ((A $$unsorted)) (tptp.empty A)) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.empty A) (tptp.function A))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.relation A))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (exists ((A $$unsorted)) (not (tptp.empty A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) (forall ((A $$unsorted)) (= (tptp.set_intersection2 A tptp.empty_set) tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.in A B) (tptp.element B (tptp.powerset C))) (tptp.element A C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))) _let_2 (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_dom_restriction B A) B))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 48.31/48.57  )
% 48.31/48.57  % SZS output end Proof for SEU222+3
% 48.31/48.57  % cvc5---1.0.5 exiting
% 48.31/48.58  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------