%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU180+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n026.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 16:29:51 EDT 2023

% Result   : Theorem 4.12s 4.34s
% Output   : Proof 4.12s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU180+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n026.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   : Wed Aug 23 17:13:31 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.20/0.49  %----Proving TF0_NAR, FOF, or CNF
% 4.12/4.34  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.aqTgOtQrcE/cvc5---1.0.5_12842.p...
% 4.12/4.34  ------- get file name : TPTP file name is SEU180+2
% 4.12/4.34  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_12842.smt2...
% 4.12/4.34  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 4.12/4.34  % SZS status Theorem for SEU180+2
% 4.12/4.34  % SZS output start Proof for SEU180+2
% 4.12/4.34  (
% 4.12/4.34  (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A (tptp.set_union2 A B))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))))) (let ((_let_3 (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.relation_field C))) (=> (tptp.relation C) (=> (tptp.in (tptp.ordered_pair A B) C) (and (tptp.in A _let_1) (tptp.in B _let_1))))))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (=> (tptp.in (tptp.ordered_pair A B) C) (and (tptp.in A (tptp.relation_dom C)) (tptp.in B (tptp.relation_rng C)))))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset B C)) (tptp.subset A C))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (forall ((C $$unsorted)) (=> (tptp.in C B) (tptp.in C A))))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset (tptp.singleton A) B) (tptp.in A B))))) (let ((_let_8 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.relation_field A) (tptp.set_union2 (tptp.relation_dom A) (tptp.relation_rng A))))))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A B) (tptp.set_union2 B A))))) (let ((_let_10 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_2446 $$unsorted)) (or (not (tptp.element B (tptp.powerset A))) (not (tptp.in BOUND_VARIABLE_2446 B)) (tptp.in BOUND_VARIABLE_2446 A))))) (let ((_let_11 (tptp.relation_field SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_12 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_11))) (let ((_let_13 (tptp.relation_rng SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_14 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_13))) (let ((_let_15 (not _let_14))) (let ((_let_16 (tptp.element _let_13 (tptp.powerset _let_11)))) (let ((_let_17 (not _let_16))) (let ((_let_18 (or _let_17 _let_15 _let_12))) (let ((_let_19 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_20 (not _let_18))) (let ((_let_21 (tptp.relation_dom SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_22 (tptp.set_union2 _let_13 _let_21))) (let ((_let_23 (tptp.element _let_13 (tptp.powerset _let_22)))) (let ((_let_24 (tptp.set_union2 _let_21 _let_13))) (let ((_let_25 (= _let_24 _let_22))) (let ((_let_26 (= _let_11 _let_24))) (let ((_let_27 (tptp.subset _let_13 _let_22))) (let ((_let_28 (= _let_27 _let_23))) (let ((_let_29 (_let_2))) (let ((_let_30 (ASSUME :args _let_29))) (let ((_let_31 (_let_1))) (let ((_let_32 (ASSUME :args _let_31))) (let ((_let_33 ((tptp.set_union2 A B)))) (let ((_let_34 (_let_9))) (let ((_let_35 (ASSUME :args _let_34))) (let ((_let_36 (tptp.relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_37 _let_26))) (let ((_let_39 (forall ((A $$unsorted)) (or (not (tptp.relation A)) (= (tptp.relation_field A) (tptp.set_union2 (tptp.relation_dom A) (tptp.relation_rng A))))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_11))) (let ((_let_42 (and _let_41 _let_12))) (let ((_let_43 (tptp.in (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_44 (not _let_43))) (let ((_let_45 (or _let_37 _let_44 _let_42))) (let ((_let_46 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.relation_field C))) (or (not (tptp.relation C)) (not (tptp.in (tptp.ordered_pair A B) C)) (and (tptp.in A _let_1) (tptp.in B _let_1))))))) (let ((_let_47 (not _let_45))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (or))) (let ((_let_50 (not _let_46))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_48) :args (_let_50))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_46))) (REFL :args (_let_47)) :args _let_49)) _let_48 :args (_let_47 true _let_46)))) (let ((_let_52 (REFL :args (_let_45)))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 0)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_49)) :args ((or _let_36 _let_45))) _let_51 :args (_let_36 true _let_45)))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_37 _let_26 (not _let_38)))) _let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.relation A) false))))) :args (_let_39))) _let_40 :args (_let_38 false _let_39)) :args (_let_26 false _let_36 false _let_38)))) (let ((_let_55 (not _let_26))) (let ((_let_56 (and _let_26 _let_25 _let_23))) (let ((_let_57 (ASSUME :args (_let_23)))) (let ((_let_58 (APPLY_UF tptp.element))) (let ((_let_59 (APPLY_UF tptp.powerset))) (let ((_let_60 (ASSUME :args (_let_25)))) (let ((_let_61 (ASSUME :args (_let_26)))) (let ((_let_62 (SYMM _let_61))) (let ((_let_63 (SYMM _let_62))) (let ((_let_64 (CONG _let_62 :args _let_59))) (let ((_let_65 (REFL :args (_let_13)))) (let ((_let_66 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_21))) (let ((_let_67 (and _let_66 _let_14))) (let ((_let_68 (or _let_37 _let_44 _let_67))) (let ((_let_69 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.relation C)) (not (tptp.in (tptp.ordered_pair A B) C)) (and (tptp.in A (tptp.relation_dom C)) (tptp.in B (tptp.relation_rng C))))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_37 _let_44 _let_67 (not _let_68)))) _let_53 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 1)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) :args _let_49)) :args ((or _let_43 _let_45))) _let_51 :args (_let_43 true _let_45)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_70 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.in (tptp.ordered_pair A B) C) false))))) :args (_let_69))) _let_70 :args (_let_68 false _let_69)) :args (_let_67 false _let_36 false _let_43 false _let_68)))) (let ((_let_72 (not _let_67))) (let ((_let_73 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_74 (tptp.subset _let_73 _let_11))) (let ((_let_75 (= _let_41 _let_74))) (let ((_let_76 (_let_7))) (let ((_let_77 (ASSUME :args _let_76))) (let ((_let_78 ((tptp.in A B)))) (let ((_let_79 (tptp.subset _let_73 _let_24))) (let ((_let_80 (tptp.subset _let_21 _let_24))) (let ((_let_81 (not _let_80))) (let ((_let_82 (tptp.subset _let_73 _let_21))) (let ((_let_83 (not _let_82))) (let ((_let_84 (or _let_83 _let_81 _let_79))) (let ((_let_85 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subset A B)) (not (tptp.subset B C)) (tptp.subset A C))))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (= _let_66 _let_82))) (let ((_let_88 (and _let_26 _let_79))) (let ((_let_89 (ASSUME :args (_let_79)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_19 :args (_let_11 _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.in BOUND_VARIABLE_2446 A) true)) (not (= (tptp.element B (tptp.powerset A)) false))))) :args (_let_10))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_18)) :args ((or _let_12 _let_15 _let_17 _let_20))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_42)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_45 2)) _let_51 :args ((not _let_42) true _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_75)) :args ((or _let_41 (not _let_74) (not _let_75)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_88)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_89 _let_61) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (_let_73)) _let_63 :args (APPLY_UF tptp.subset)) (TRUE_INTRO _let_89))) :args (_let_79 _let_26))) :args (_let_26 _let_79))) :args (true _let_88)) :args ((or _let_74 _let_55 (not _let_79)))) _let_54 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_84)) :args ((or _let_83 _let_81 _let_79 (not _let_84)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_87)) :args ((or (not _let_66) _let_82 (not _let_87)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_67 0)) :args ((or _let_66 _let_72))) _let_71 :args (_let_66 false _let_67)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_77 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_21 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_78)) :args _let_76))) _let_77 :args (_let_87 false _let_7)) :args (_let_82 false _let_66 false _let_87)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (_let_21 _let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_33)) :args _let_31)) _let_32 :args (_let_80 false _let_1)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_86 :args (_let_73 _let_21 _let_24 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.subset A B) false)) (not (= (tptp.subset B C) false))))) :args (_let_85))) _let_86 :args (_let_84 false _let_85)) :args (_let_79 false _let_82 false _let_80 false _let_84)) :args (_let_74 false _let_26 false _let_79)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_77 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_78)) :args _let_76))) _let_77 :args (_let_75 false _let_7)) :args (_let_41 false _let_74 false _let_75)) :args ((not _let_12) true _let_42 false _let_41)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_67 1)) :args ((or _let_14 _let_72))) _let_71 :args (_let_14 false _let_67)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_56)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_57 _let_60 _let_61) (SCOPE (TRUE_ELIM (TRANS (CONG _let_65 (SYMM _let_64) :args _let_58) (CONG _let_65 (TRANS _let_64 (CONG (TRANS _let_63 (SYMM (SYMM _let_60))) :args _let_59)) :args _let_58) (TRUE_INTRO _let_57))) :args (_let_23 _let_25 _let_26))) :args (_let_26 _let_25 _let_23))) :args (true _let_56)) :args ((or _let_55 (not _let_25) _let_16 (not _let_23)))) _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (_let_21 _let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_union2 A B)))) :args _let_34)) _let_35 :args (_let_25 false _let_9)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_28)) :args ((or (not _let_27) _let_23 (not _let_28)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (_let_13 _let_21 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_33)) :args _let_31)) _let_32 :args (_let_27 false _let_1)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_30 :args (_let_13 _let_22 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset A B)))) :args _let_29))) _let_30 :args (_let_28 false _let_2)) :args (_let_23 false _let_27 false _let_28)) :args (_let_16 false _let_26 false _let_25 false _let_23)) :args (_let_20 true _let_12 false _let_14 false _let_16)) _let_19 :args (false true _let_18 false _let_10)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.proper_subset A B) (not (tptp.proper_subset B A)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.unordered_pair A B) (tptp.unordered_pair B A))) _let_9 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A B) (tptp.set_intersection2 B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (= A B) (and (tptp.subset A B) (tptp.subset B A)))) (forall ((A $$unsorted)) (= (tptp.relation A) (forall ((B $$unsorted)) (not (and (tptp.in B A) (forall ((C $$unsorted) (D $$unsorted)) (not (= B (tptp.ordered_pair C D))))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (= B (tptp.set_meet A)))) (let ((_let_2 (= A tptp.empty_set))) (and (=> (not _let_2) (= _let_1 (forall ((C $$unsorted)) (= (tptp.in C B) (forall ((D $$unsorted)) (=> (tptp.in D A) (tptp.in C D))))))) (=> _let_2 (= _let_1 (= B tptp.empty_set))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.singleton A)) (forall ((C $$unsorted)) (= (tptp.in C B) (= C A))))) (forall ((A $$unsorted)) (= (= A tptp.empty_set) (forall ((B $$unsorted)) (not (tptp.in B A))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.powerset A)) (forall ((C $$unsorted)) (= (tptp.in C B) (tptp.subset C A))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.element B A))) (let ((_let_2 (tptp.empty A))) (and (=> (not _let_2) (= _let_1 (tptp.in B A))) (=> _let_2 (= _let_1 (tptp.empty B))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.unordered_pair A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (or (= D A) (= D B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_union2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (or (tptp.in D A) (tptp.in D B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.cartesian_product2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted) (F $$unsorted)) (and (tptp.in E A) (tptp.in F B) (= D (tptp.ordered_pair E F)))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((C $$unsorted)) (=> (tptp.in C A) (tptp.in C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_intersection2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (tptp.in D B)))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (= B (tptp.relation_dom A)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (tptp.in (tptp.ordered_pair C D) A)))))))) (forall ((A $$unsorted)) (= (tptp.cast_to_subset A) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.union A)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (and (tptp.in C D) (tptp.in D A))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_difference A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (not (tptp.in D B))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (= B (tptp.relation_rng A)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (tptp.in (tptp.ordered_pair D C) A)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (= (tptp.subset_complement A B) (tptp.set_difference A B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.ordered_pair A B) (tptp.unordered_pair (tptp.unordered_pair A B) (tptp.singleton A)))) _let_8 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= (tptp.set_intersection2 A B) tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.powerset A))) (= (= C (tptp.complements_of_subsets A B)) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.powerset A)) (= (tptp.in D C) (tptp.in (tptp.subset_complement A D) B))))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.proper_subset A B) (and (tptp.subset A B) (not (= A B))))) true true true true true true (forall ((A $$unsorted)) (tptp.element (tptp.cast_to_subset A) (tptp.powerset A))) true true true true (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (tptp.element B _let_1) (tptp.element (tptp.subset_complement A B) _let_1)))) true true true true (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (tptp.element B (tptp.powerset _let_1)) (tptp.element (tptp.union_of_subsets A B) _let_1)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (tptp.element B (tptp.powerset _let_1)) (tptp.element (tptp.meet_of_subsets A B) _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (tptp.element (tptp.subset_difference A B C) _let_1)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset (tptp.powerset A)))) (=> (tptp.element B _let_1) (tptp.element (tptp.complements_of_subsets A B) _let_1)))) true (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) (tptp.empty tptp.empty_set) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.empty (tptp.ordered_pair A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.set_union2 A B)))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.singleton A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 A B))))) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.empty (tptp.unordered_pair A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 B A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B))) (not (tptp.empty (tptp.cartesian_product2 A B))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A A) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A A) A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (= (tptp.subset_complement A (tptp.subset_complement A B)) B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (= (tptp.complements_of_subsets A (tptp.complements_of_subsets A B)) B))) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.proper_subset A A))) (forall ((A $$unsorted)) (not (= (tptp.singleton A) tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (= (tptp.set_union2 (tptp.singleton A) B) B))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.disjoint (tptp.singleton A) B) (tptp.in A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.in A B)) (tptp.disjoint (tptp.singleton A) B))) _let_7 (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B))) _let_6 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (or (tptp.in C A) (tptp.subset A (tptp.set_difference B (tptp.singleton C)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.singleton B))) (= (tptp.subset A _let_1) (or (= A tptp.empty_set) (= A _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.subset A (tptp.union B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.in (tptp.ordered_pair A B) (tptp.cartesian_product2 C D)) (and (tptp.in A C) (tptp.in B D)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted)) (=> (tptp.in C A) (tptp.in C B))) (tptp.element A (tptp.powerset B)))) (exists ((A $$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 $$unsorted)) (tptp.empty A)) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (exists ((A $$unsorted)) (not (tptp.empty A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (= (tptp.union_of_subsets A B) (tptp.union B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (= (tptp.meet_of_subsets A B) (tptp.set_meet B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.subset_difference A B C) (tptp.set_difference B C))))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.disjoint A B) (tptp.disjoint B A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.in (tptp.ordered_pair A B) (tptp.cartesian_product2 C D)) (and (tptp.in A C) (tptp.in B D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (not (and (= (tptp.unordered_pair A B) (tptp.unordered_pair C D)) (not (= A C)) (not (= A D))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (and (tptp.subset (tptp.cartesian_product2 A C) (tptp.cartesian_product2 B C)) (tptp.subset (tptp.cartesian_product2 C A) (tptp.cartesian_product2 C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset C D)) (tptp.subset (tptp.cartesian_product2 A C) (tptp.cartesian_product2 B D)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= (tptp.set_union2 A B) B))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.in A B) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.in C B) (tptp.subset D C)) (tptp.in D B))) (forall ((C $$unsorted)) (=> (tptp.in C B) (tptp.in (tptp.powerset C) B))) (forall ((C $$unsorted)) (not (and (tptp.subset C B) (not (tptp.are_equipotent C B)) (not (tptp.in C B)))))))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_intersection2 A B) A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset A C)) (tptp.subset A (tptp.set_intersection2 B C)))) (forall ((A $$unsorted)) (= (tptp.set_union2 A tptp.empty_set) A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) _let_5 (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set)) _let_4 (forall ((A $$unsorted)) (=> (tptp.relation A) (tptp.subset A (tptp.cartesian_product2 (tptp.relation_dom A) (tptp.relation_rng A))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (=> (tptp.subset A B) (and (tptp.subset (tptp.relation_dom A) (tptp.relation_dom B)) (tptp.subset (tptp.relation_rng A) (tptp.relation_rng B)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (tptp.subset (tptp.set_intersection2 A C) (tptp.set_intersection2 B C)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= (tptp.set_intersection2 A B) A))) (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 $$unsorted)) (=> (forall ((C $$unsorted)) (= (tptp.in C A) (tptp.in C B))) (= A B))) (forall ((A $$unsorted)) (tptp.subset tptp.empty_set A)) _let_3 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (tptp.subset (tptp.set_difference A C) (tptp.set_difference B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (= (tptp.ordered_pair A B) (tptp.ordered_pair C D)) (and (= A C) (= B D)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_difference A B) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset (tptp.singleton A) B) (tptp.in A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.subset (tptp.unordered_pair A B) C) (and (tptp.in A C) (tptp.in B C)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A (tptp.set_difference B A)) (tptp.set_union2 A B))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.singleton B))) (= (tptp.subset A _let_1) (or (= A tptp.empty_set) (= A _let_1))))) (forall ((A $$unsorted)) (= (tptp.set_difference A tptp.empty_set) A)) _let_2 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.disjoint A B))) (and (not (and (not _let_1) (forall ((C $$unsorted)) (not (and (tptp.in C A) (tptp.in C B)))))) (not (and (exists ((C $$unsorted)) (and (tptp.in C A) (tptp.in C B))) _let_1))))) (forall ((A $$unsorted)) (=> (tptp.subset A tptp.empty_set) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_difference (tptp.set_union2 A B) B) (tptp.set_difference A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset A)) (= (tptp.disjoint B C) (tptp.subset B (tptp.subset_complement A C))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= B (tptp.set_union2 A (tptp.set_difference B A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (not (and (not (= B tptp.empty_set)) (= (tptp.complements_of_subsets A B) tptp.empty_set))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (= (tptp.set_union2 (tptp.singleton A) B) B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (=> (not (= B tptp.empty_set)) (= (tptp.subset_difference A (tptp.cast_to_subset A) (tptp.union_of_subsets A B)) (tptp.meet_of_subsets A (tptp.complements_of_subsets A B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (=> (not (= B tptp.empty_set)) (= (tptp.union_of_subsets A (tptp.complements_of_subsets A B)) (tptp.subset_difference A (tptp.cast_to_subset A) (tptp.meet_of_subsets A B)))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_difference A (tptp.set_difference A B)) (tptp.set_intersection2 A B))) (forall ((A $$unsorted)) (= (tptp.set_difference tptp.empty_set A) tptp.empty_set)) (forall ((A $$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)) (let ((_let_1 (tptp.disjoint A B))) (and (not (and (not _let_1) (forall ((C $$unsorted)) (not (tptp.in C (tptp.set_intersection2 A B)))))) (not (and (exists ((C $$unsorted)) (tptp.in C (tptp.set_intersection2 A B))) _let_1))))) (forall ((A $$unsorted)) (=> (not (= A tptp.empty_set)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (forall ((C $$unsorted)) (=> (tptp.element C A) (=> (not (tptp.in C B)) (tptp.in C (tptp.subset_complement A B))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.powerset A)) (not (and (tptp.in B (tptp.subset_complement A C)) (tptp.in B C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.subset A B) (tptp.proper_subset B A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.disjoint B C)) (tptp.disjoint A C))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A (tptp.singleton B)) A) (not (tptp.in B A)))) (forall ((A $$unsorted)) (= (tptp.unordered_pair A A) (tptp.singleton A))) (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset (tptp.singleton A) (tptp.singleton B)) (= A B))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))) _let_1 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= (tptp.set_difference A B) A))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset C B)) (tptp.subset (tptp.set_union2 A C) B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (= (tptp.singleton A) (tptp.unordered_pair B C)) (= A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.subset A (tptp.union B)))) (forall ((A $$unsorted)) (= (tptp.union (tptp.powerset A)) A)) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.in A B) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.in C B) (tptp.subset D C)) (tptp.in D B))) (forall ((C $$unsorted)) (not (and (tptp.in C B) (forall ((D $$unsorted)) (not (and (tptp.in D B) (forall ((E $$unsorted)) (=> (tptp.subset E C) (tptp.in E D))))))))) (forall ((C $$unsorted)) (not (and (tptp.subset C B) (not (tptp.are_equipotent C B)) (not (tptp.in C B)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (= (tptp.singleton A) (tptp.unordered_pair B C)) (= B C))) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 4.12/4.36  )
% 4.12/4.36  % SZS output end Proof for SEU180+2
% 4.12/4.36  % cvc5---1.0.5 exiting
% 4.12/4.36  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------