%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU105+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n011.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 16:29:17 EDT 2023

% Result   : Theorem 0.22s 0.72s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU105+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n011.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Wed Aug 23 13:36:06 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.22/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.72  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.5Q9VduoZrh/cvc5---1.0.5_4245.p...
% 0.22/0.72  ------- get file name : TPTP file name is SEU105+1
% 0.22/0.72  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_4245.smt2...
% 0.22/0.72  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.72  % SZS status Theorem for SEU105+1
% 0.22/0.72  % SZS output start Proof for SEU105+1
% 0.22/0.72  (
% 0.22/0.72  (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A B) (tptp.symmetric_difference (tptp.symmetric_difference A B) (tptp.set_intersection2 A B)))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))))) (let ((_let_3 (not (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (=> (forall ((B $$unsorted)) (=> (tptp.element B A) (forall ((C $$unsorted)) (=> (tptp.element C A) (and (tptp.in (tptp.symmetric_difference B C) A) (tptp.in (tptp.set_intersection2 B C) A)))))) (tptp.preboolean A))))))) (let ((_let_4 (forall ((A $$unsorted)) (= (tptp.preboolean A) (forall ((B $$unsorted) (C $$unsorted)) (=> (and (tptp.in B A) (tptp.in C A)) (and (tptp.in (tptp.set_union2 B C) A) (tptp.in (tptp.set_difference B C) A)))))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_difference A B) (tptp.symmetric_difference A (tptp.set_intersection2 A B)))))) (let ((_let_6 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_7 (tptp.in _let_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_8 (tptp.set_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_9 (tptp.in _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_10 (and _let_9 _let_7))) (let ((_let_11 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_12 (not _let_11))) (let ((_let_13 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_14 (not _let_13))) (let ((_let_15 (or _let_14 _let_12 _let_10))) (let ((_let_16 (forall ((B $$unsorted) (C $$unsorted)) (or (not (tptp.in B SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.in C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (and (tptp.in (tptp.set_union2 B C) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) (tptp.in (tptp.set_difference B C) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))))) (let ((_let_17 (not _let_15))) (let ((_let_18 (tptp.preboolean SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_19 (= _let_18 _let_16))) (let ((_let_20 (not _let_16))) (let ((_let_21 (forall ((A $$unsorted)) (= (tptp.preboolean A) (forall ((B $$unsorted) (C $$unsorted)) (or (not (tptp.in B A)) (not (tptp.in C A)) (and (tptp.in (tptp.set_union2 B C) A) (tptp.in (tptp.set_difference B C) A)))))))) (let ((_let_22 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_23 (forall ((B $$unsorted) (BOUND_VARIABLE_1216 $$unsorted)) (or (not (tptp.element B SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.element BOUND_VARIABLE_1216 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (and (tptp.in (tptp.symmetric_difference B BOUND_VARIABLE_1216) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) (tptp.in (tptp.set_intersection2 B BOUND_VARIABLE_1216) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or (tptp.empty SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) _let_24 _let_18))) (let ((_let_26 (forall ((A $$unsorted)) (or (tptp.empty A) (not (forall ((B $$unsorted) (BOUND_VARIABLE_1216 $$unsorted)) (or (not (tptp.element B A)) (not (tptp.element BOUND_VARIABLE_1216 A)) (and (tptp.in (tptp.symmetric_difference B BOUND_VARIABLE_1216) A) (tptp.in (tptp.set_intersection2 B BOUND_VARIABLE_1216) A))))) (tptp.preboolean A))))) (let ((_let_27 (not _let_25))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (or))) (let ((_let_30 (not _let_26))) (let ((_let_31 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_28) :args (_let_30))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_26))) (REFL :args (_let_27)) :args _let_29)) _let_28 :args (_let_27 true _let_26)))) (let ((_let_32 (_let_20))) (let ((_let_33 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_32)) :args _let_32)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_16))) (REFL :args (_let_17)) :args _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_19)) :args ((or _let_18 _let_20 (not _let_19)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_25 2)) _let_31 :args ((not _let_18) true _let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_22 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.preboolean A)))) :args (_let_21))) _let_22 :args (_let_19 false _let_21)) :args (_let_20 true _let_18 false _let_19)) :args (_let_17 true _let_16)))) (let ((_let_34 (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_35 (tptp.symmetric_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 _let_34))) (let ((_let_36 (tptp.in _let_35 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_37 (= _let_6 _let_35))) (let ((_let_38 (and _let_36 (tptp.in (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 _let_34) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_39 (tptp.element _let_34 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_40 (not _let_39))) (let ((_let_41 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_42 (not _let_41))) (let ((_let_43 (or _let_42 _let_40 _let_38))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 1)) (CONG (REFL :args (_let_25)) (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_29)) :args ((or _let_23 _let_25))) _let_31 :args (_let_23 true _let_25)))) (let ((_let_45 (_let_23))) (let ((_let_46 ((tptp.symmetric_difference B BOUND_VARIABLE_1216)))) (let ((_let_47 (ASSUME :args _let_45))) (let ((_let_48 (tptp.in _let_34 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_49 (not _let_48))) (let ((_let_50 (or _let_49 _let_39))) (let ((_let_51 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.in A B)) (tptp.element A B))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (_let_51))) (let ((_let_54 ((not (= (tptp.element A B) true))))) (let ((_let_55 (tptp.symmetric_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_56 (tptp.in _let_55 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_57 (and _let_56 _let_48))) (let ((_let_58 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_59 (not _let_58))) (let ((_let_60 (or _let_42 _let_59 _let_57))) (let ((_let_61 (or _let_12 _let_58))) (let ((_let_62 ((not (= (tptp.in A B) false))))) (let ((_let_63 (REFL :args (_let_15)))) (let ((_let_64 (or _let_14 _let_41))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_64)) :args ((or _let_14 _let_41 (not _let_64)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_15 0)) (CONG _let_63 (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) :args _let_29)) :args ((or _let_13 _let_15))) _let_33 :args (_let_13 true _let_15)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_62)) :args _let_53)) _let_52 :args (_let_64 false _let_51)) :args (_let_41 false _let_13 false _let_64)))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_42 _let_59 _let_57 (not _let_60)))) _let_65 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_61)) :args ((or _let_12 _let_58 (not _let_61)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_15 1)) (CONG _let_63 (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_11))) :args _let_29)) :args ((or _let_11 _let_15))) _let_33 :args (_let_11 true _let_15)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_62)) :args _let_53)) _let_52 :args (_let_61 false _let_51)) :args (_let_58 false _let_11 false _let_61)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_46)) :args _let_45)) _let_44 :args (_let_60 false _let_23)) :args (_let_57 false _let_41 false _let_58 false _let_60)))) (let ((_let_67 (not _let_57))) (let ((_let_68 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_39 _let_49 (not _let_50)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_57 1)) :args ((or _let_48 _let_67))) _let_66 :args (_let_48 false _let_57)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (_let_34 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_54)) :args _let_53)) _let_52 :args (_let_50 false _let_51)) :args (_let_39 false _let_48 false _let_50)))) (let ((_let_69 (_let_5))) (let ((_let_70 (ASSUME :args _let_69))) (let ((_let_71 (and _let_37 _let_36))) (let ((_let_72 (ASSUME :args (_let_36)))) (let ((_let_73 (APPLY_UF tptp.in))) (let ((_let_74 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_75 (ASSUME :args (_let_37)))) (let ((_let_76 (tptp.symmetric_difference _let_55 _let_34))) (let ((_let_77 (tptp.in _let_76 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_78 (= _let_8 _let_76))) (let ((_let_79 (and _let_77 (tptp.in (tptp.set_intersection2 _let_55 _let_34) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_80 (tptp.element _let_55 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_81 (not _let_80))) (let ((_let_82 (or _let_81 _let_40 _let_79))) (let ((_let_83 (not _let_56))) (let ((_let_84 (or _let_83 _let_80))) (let ((_let_85 (_let_1))) (let ((_let_86 (ASSUME :args _let_85))) (let ((_let_87 (and _let_78 _let_77))) (let ((_let_88 (ASSUME :args (_let_77)))) (let ((_let_89 (ASSUME :args (_let_78)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_10)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_87)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_88 _let_89) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM (SYMM _let_89)) _let_74 :args _let_73) (TRUE_INTRO _let_88))) :args (_let_77 _let_78))) :args (_let_78 _let_77))) :args (true _let_87)) :args ((or _let_9 (not _let_78) (not _let_77)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_86 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_union2 A B)))) :args _let_85)) _let_86 :args (_let_78 false _let_1)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_79 0)) :args ((or _let_77 (not _let_79)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_40 _let_81 _let_79 (not _let_82)))) _let_68 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_84)) :args ((or _let_80 _let_83 (not _let_84)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_57 0)) :args ((or _let_56 _let_67))) _let_66 :args (_let_56 false _let_57)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (_let_55 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_54)) :args _let_53)) _let_52 :args (_let_84 false _let_51)) :args (_let_80 false _let_56 false _let_84)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (_let_55 _let_34 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_46)) :args _let_45)) _let_44 :args (_let_82 false _let_23)) :args (_let_79 false _let_39 false _let_80 false _let_82)) :args (_let_77 false _let_79)) :args (_let_9 false _let_78 false _let_77)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_71)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_72 _let_75) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM (SYMM _let_75)) _let_74 :args _let_73) (TRUE_INTRO _let_72))) :args (_let_36 _let_37))) :args (_let_37 _let_36))) :args (true _let_71)) :args ((or _let_7 (not _let_37) (not _let_36)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_70 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_difference A B)))) :args _let_69)) _let_70 :args (_let_37 false _let_5)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_38 0)) :args ((or _let_36 (not _let_38)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_42 _let_40 _let_38 (not _let_43)))) _let_65 _let_68 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 _let_34 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_46)) :args _let_45)) _let_44 :args (_let_43 false _let_23)) :args (_let_38 false _let_41 false _let_39 false _let_43)) :args (_let_36 false _let_38)) :args (_let_7 false _let_37 false _let_36)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_15 2)) _let_33 :args ((not _let_10) true _let_15)) :args (false false _let_9 false _let_7 true _let_10)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.finite A))) (forall ((A $$unsorted)) (=> (tptp.preboolean A) (and (tptp.cup_closed A) (tptp.diff_closed A)))) (forall ((A $$unsorted)) (=> (tptp.finite A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (tptp.finite B))))) (forall ((A $$unsorted)) (=> (and (tptp.cup_closed A) (tptp.diff_closed A)) (tptp.preboolean A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A B) (tptp.set_union2 B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A B) (tptp.set_intersection2 B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.symmetric_difference A B) (tptp.symmetric_difference B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.symmetric_difference A B) (tptp.set_union2 (tptp.set_difference A B) (tptp.set_difference B A)))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.finite B) (tptp.finite (tptp.set_intersection2 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.finite A) (tptp.finite (tptp.set_intersection2 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.finite A) (tptp.finite (tptp.set_difference A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.finite A) (tptp.finite B)) (tptp.finite (tptp.symmetric_difference A B)))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) (tptp.empty tptp.empty_set) (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 A)) (not (tptp.empty (tptp.set_union2 B A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.finite A) (tptp.finite B)) (tptp.finite (tptp.set_union2 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A A) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A A) A)) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.finite A))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.cup_closed A) (tptp.cap_closed A) (tptp.diff_closed A) (tptp.preboolean 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 $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B) (tptp.relation B) (tptp.function B) (tptp.one_to_one B) (tptp.epsilon_transitive B) (tptp.epsilon_connected B) (tptp.ordinal B) (tptp.natural B) (tptp.finite B)))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (exists ((A $$unsorted)) (not (tptp.empty A))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)) (tptp.finite B))))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)) (tptp.finite B))))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) _let_5 _let_4 _let_3 (forall ((A $$unsorted)) (= (tptp.set_union2 A tptp.empty_set) A)) _let_2 (forall ((A $$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 $$unsorted)) (= (tptp.set_difference A tptp.empty_set) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))) (forall ((A $$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)) (= (tptp.symmetric_difference A tptp.empty_set) A)) (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)) (=> (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)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.72  )
% 0.22/0.72  % SZS output end Proof for SEU105+1
% 0.22/0.72  % cvc5---1.0.5 exiting
% 0.22/0.72  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------