%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU254+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n028.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 16:30:26 EDT 2023

% Result   : Theorem 0.22s 0.60s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : SEU254+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n028.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Wed Aug 23 19:50:03 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.22/0.51  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.60  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.vQwieYj2xi/cvc5---1.0.5_16756.p...
% 0.22/0.60  ------- get file name : TPTP file name is SEU254+1
% 0.22/0.60  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_16756.smt2...
% 0.22/0.60  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.60  % SZS status Theorem for SEU254+1
% 0.22/0.60  % SZS output start Proof for SEU254+1
% 0.22/0.60  (
% 0.22/0.60  (let ((_let_1 (not (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.transitive B) (tptp.transitive (tptp.relation_restriction B A)))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (= (tptp.in A (tptp.relation_restriction C B)) (and (tptp.in A C) (tptp.in A (tptp.cartesian_product2 B B)))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.in (tptp.ordered_pair A B) (tptp.cartesian_product2 C D)) (and (tptp.in A C) (tptp.in B D)))))) (let ((_let_4 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.transitive A) (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.in (tptp.ordered_pair B C) A) (tptp.in (tptp.ordered_pair C D) A)) (tptp.in (tptp.ordered_pair B D) A)))))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation A) (tptp.relation (tptp.relation_restriction A B)))))) (let ((_let_6 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_7 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_8 (and _let_7 _let_6))) (let ((_let_9 (tptp.cartesian_product2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_10 (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_11 (tptp.in _let_10 _let_9))) (let ((_let_12 (= _let_11 _let_8))) (let ((_let_13 (not _let_8))) (let ((_let_14 (_let_3))) (let ((_let_15 (ASSUME :args _let_14))) (let ((_let_16 ((tptp.in (tptp.ordered_pair A B) (tptp.cartesian_product2 C D))))) (let ((_let_17 (tptp.in _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_18 (and _let_17 _let_11))) (let ((_let_19 (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_20 (tptp.in _let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_21 (not _let_20))) (let ((_let_22 (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_23 (tptp.in _let_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or _let_24 _let_21 _let_17))) (let ((_let_26 (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (or (not (tptp.in (tptp.ordered_pair B C) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) (not (tptp.in (tptp.ordered_pair C D) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) (tptp.in (tptp.ordered_pair B D) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))))) (let ((_let_27 (tptp.transitive SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_28 (= _let_27 _let_26))) (let ((_let_29 (tptp.relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_30 (not _let_29))) (let ((_let_31 (or _let_30 _let_28))) (let ((_let_32 (forall ((A $$unsorted)) (or (not (tptp.relation A)) (= (tptp.transitive A) (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (or (not (tptp.in (tptp.ordered_pair B C) A)) (not (tptp.in (tptp.ordered_pair C D) A)) (tptp.in (tptp.ordered_pair B D) A)))))))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (_let_32))) (let ((_let_35 (tptp.relation_restriction SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_36 (tptp.transitive _let_35))) (let ((_let_37 (not _let_27))) (let ((_let_38 (or _let_30 _let_37 _let_36))) (let ((_let_39 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.relation B)) (not (tptp.transitive B)) (tptp.transitive (tptp.relation_restriction B A)))))) (let ((_let_40 (not _let_38))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (or))) (let ((_let_43 (not _let_39))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_41) :args (_let_43))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_39))) (REFL :args (_let_40)) :args _let_42)) _let_41 :args (_let_40 true _let_39)))) (let ((_let_45 (REFL :args (_let_38)))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 0)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_42)) :args ((or _let_29 _let_38))) _let_44 :args (_let_29 true _let_38)))) (let ((_let_47 (_let_26))) (let ((_let_48 (tptp.in _let_19 _let_9))) (let ((_let_49 (and _let_20 _let_48))) (let ((_let_50 (tptp.in _let_19 _let_35))) (let ((_let_51 (= _let_50 _let_49))) (let ((_let_52 (or _let_30 _let_51))) (let ((_let_53 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.relation C)) (= (tptp.in A (tptp.relation_restriction C B)) (and (tptp.in A C) (tptp.in A (tptp.cartesian_product2 B B)))))))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (_let_53))) (let ((_let_56 ((tptp.in A (tptp.relation_restriction C B))))) (let ((_let_57 (tptp.in _let_10 _let_35))) (let ((_let_58 (not _let_50))) (let ((_let_59 (tptp.in _let_22 _let_35))) (let ((_let_60 (not _let_59))) (let ((_let_61 (or _let_60 _let_58 _let_57))) (let ((_let_62 (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.relation_restriction SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (or (not (tptp.in (tptp.ordered_pair B C) _let_1)) (not (tptp.in (tptp.ordered_pair C D) _let_1)) (tptp.in (tptp.ordered_pair B D) _let_1)))))) (let ((_let_63 (not _let_61))) (let ((_let_64 (= _let_36 _let_62))) (let ((_let_65 (not _let_62))) (let ((_let_66 (tptp.relation _let_35))) (let ((_let_67 (not _let_66))) (let ((_let_68 (or _let_67 _let_64))) (let ((_let_69 (or _let_30 _let_66))) (let ((_let_70 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.relation A)) (tptp.relation (tptp.relation_restriction A B)))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (_let_65))) (let ((_let_73 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_72)) :args _let_72)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_62))) (REFL :args (_let_63)) :args _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_64)) :args ((or _let_36 _let_65 (not _let_64)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_38 2)) _let_44 :args ((not _let_36) true _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_67 _let_64 (not _let_68)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_30 _let_66 (not _let_69)))) _let_46 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.relation_restriction A B)))) :args (_let_70))) _let_71 :args (_let_69 false _let_70)) :args (_let_66 false _let_29 false _let_69)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (_let_35 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.transitive A)))) :args _let_34)) _let_33 :args (_let_68 false _let_32)) :args (_let_64 false _let_66 false _let_68)) :args (_let_65 true _let_36 false _let_64)) :args (_let_63 true _let_62)))) (let ((_let_74 (REFL :args (_let_61)))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_51)) :args ((or _let_58 _let_49 (not _let_51)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_61 1)) (CONG _let_74 (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_50))) :args _let_42)) :args ((or _let_50 _let_61))) _let_73 :args (_let_50 true _let_61)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_30 _let_51 (not _let_52)))) _let_46 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (_let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING _let_56)) :args _let_55)) _let_54 :args (_let_52 false _let_53)) :args (_let_51 false _let_29 false _let_52)) :args (_let_49 false _let_50 false _let_51)))) (let ((_let_76 (not _let_49))) (let ((_let_77 (tptp.in _let_22 _let_9))) (let ((_let_78 (and _let_23 _let_77))) (let ((_let_79 (= _let_59 _let_78))) (let ((_let_80 (or _let_30 _let_79))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_79)) :args ((or _let_60 _let_78 (not _let_79)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_61 0)) (CONG _let_74 (MACRO_SR_PRED_INTRO :args ((= (not _let_60) _let_59))) :args _let_42)) :args ((or _let_59 _let_61))) _let_73 :args (_let_59 true _let_61)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_80)) :args ((or _let_30 _let_79 (not _let_80)))) _let_46 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (_let_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING _let_56)) :args _let_55)) _let_54 :args (_let_80 false _let_53)) :args (_let_79 false _let_29 false _let_80)) :args (_let_78 false _let_59 false _let_79)))) (let ((_let_82 (not _let_78))) (let ((_let_83 (= _let_57 _let_18))) (let ((_let_84 (not _let_18))) (let ((_let_85 (or _let_30 _let_83))) (let ((_let_86 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_87 (and _let_86 _let_6))) (let ((_let_88 (= _let_48 _let_87))) (let ((_let_89 (and _let_7 _let_86))) (let ((_let_90 (= _let_77 _let_89))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_8)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_89 0)) :args ((or _let_7 (not _let_89)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_90)) :args ((or (not _let_77) _let_89 (not _let_90)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_78 1)) :args ((or _let_77 _let_82))) _let_81 :args (_let_77 false _let_78)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_15 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING _let_16)) :args _let_14)) _let_15 :args (_let_90 false _let_3)) :args (_let_89 false _let_77 false _let_90)) :args (_let_7 false _let_89)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_87 1)) :args ((or _let_6 (not _let_87)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_88)) :args ((or (not _let_48) _let_87 (not _let_88)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_49 1)) :args ((or _let_48 _let_76))) _let_75 :args (_let_48 false _let_49)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_15 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING _let_16)) :args _let_14)) _let_15 :args (_let_88 false _let_3)) :args (_let_87 false _let_48 false _let_88)) :args (_let_6 false _let_87)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_12)) :args ((or _let_11 _let_13 (not _let_12)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_18)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_83)) :args ((or _let_57 _let_84 (not _let_83)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_61 2)) _let_73 :args ((not _let_57) true _let_61)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_85)) :args ((or _let_30 _let_83 (not _let_85)))) _let_46 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (_let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING _let_56)) :args _let_55)) _let_54 :args (_let_85 false _let_53)) :args (_let_83 false _let_29 false _let_85)) :args (_let_84 true _let_57 false _let_83)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_17 _let_24 _let_21 (not _let_25)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_78 0)) :args ((or _let_23 _let_82))) _let_81 :args (_let_23 false _let_78)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_49 0)) :args ((or _let_20 _let_76))) _let_75 :args (_let_20 false _let_49)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_47) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_E_MATCHING ((tptp.ordered_pair B C) (tptp.ordered_pair C D)))) :args _let_47)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_28)) :args ((or _let_37 _let_26 (not _let_28)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 1)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_27))) :args _let_42)) :args ((or _let_27 _let_38))) _let_44 :args (_let_27 true _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_31)) :args ((or _let_30 _let_28 (not _let_31)))) _let_46 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.relation A) false))))) :args _let_34)) _let_33 :args (_let_31 false _let_32)) :args (_let_28 false _let_29 false _let_31)) :args (_let_26 false _let_27 false _let_28)) :args (_let_25 false _let_26)) :args (_let_17 false _let_23 false _let_20 false _let_25)) :args ((not _let_11) true _let_18 false _let_17)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_15 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING _let_16)) :args _let_14)) _let_15 :args (_let_12 false _let_3)) :args (_let_13 true _let_11 false _let_12)) :args (false false _let_7 false _let_6 true _let_8)) :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)) (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))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A B) (tptp.set_intersection2 B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.ordered_pair A B) (tptp.unordered_pair (tptp.unordered_pair A B) (tptp.singleton A)))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (tptp.relation_restriction A B) (tptp.set_intersection2 A (tptp.cartesian_product2 B B)))))) true true true _let_5 true true true true (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (tptp.empty tptp.empty_set) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.empty (tptp.ordered_pair A B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A A) A)) _let_4 (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A))) (exists ((A $$unsorted)) (tptp.empty A)) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.empty A) (tptp.function A))) (exists ((A $$unsorted)) (not (tptp.empty A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A))) _let_3 _let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) _let_1 (forall ((A $$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 $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) (forall ((A $$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)))) true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.60  )
% 0.22/0.60  % SZS output end Proof for SEU254+1
% 0.22/0.60  % cvc5---1.0.5 exiting
% 0.22/0.60  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------