%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU353+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n024.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 16:31:07 EDT 2023

% Result   : Theorem 0.19s 0.56s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU353+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13  % Command    : do_cvc5 %s %d
% 0.13/0.34  % Computer : n024.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Thu Aug 24 01:07:09 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.19/0.48  %----Proving TF0_NAR, FOF, or CNF
% 0.19/0.56  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.WKaJQCff8c/cvc5---1.0.5_21180.p...
% 0.19/0.56  ------- get file name : TPTP file name is SEU353+1
% 0.19/0.56  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_21180.smt2...
% 0.19/0.56  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.19/0.56  % SZS status Theorem for SEU353+1
% 0.19/0.56  % SZS output start Proof for SEU353+1
% 0.19/0.56  (
% 0.19/0.56  (let ((_let_1 (not (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (tptp.element B _let_1) (= (tptp.apply_as_element _let_1 _let_1 (tptp.identity_on_carrier A) B) B))))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in B A) (= (tptp.apply (tptp.identity_relation A) B) B))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.relation_of2_as_subset C A B) (tptp.relation_of2 C A B))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.function C) (tptp.quasi_total C A B) (tptp.relation_of2 C A B) (tptp.element D A)) (= (tptp.apply_as_element A B C D) (tptp.apply C D)))))) (let ((_let_6 (forall ((A $$unsorted)) (= (tptp.identity_as_relation_of A) (tptp.identity_relation A))))) (let ((_let_7 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (not (tptp.empty (tptp.the_carrier A))))))) (let ((_let_8 (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.identity_on_carrier A))) (=> (tptp.one_sorted_str A) (and (tptp.function _let_2) (tptp.quasi_total _let_2 _let_1 _let_1) (tptp.relation_of2_as_subset _let_2 _let_1 _let_1)))))))) (let ((_let_9 (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (= (tptp.identity_on_carrier A) (tptp.identity_as_relation_of (tptp.the_carrier A))))))) (let ((_let_10 (tptp.identity_on_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_11 (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_12 (tptp.apply_as_element _let_11 _let_11 _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_13 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_12))) (let ((_let_14 (tptp.identity_as_relation_of _let_11))) (let ((_let_15 (= _let_10 _let_14))) (let ((_let_16 (tptp.identity_relation _let_11))) (let ((_let_17 (= _let_14 _let_16))) (let ((_let_18 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (tptp.apply _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)))) (let ((_let_19 (= _let_12 (tptp.apply _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)))) (let ((_let_20 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_11))) (let ((_let_21 (not _let_20))) (let ((_let_22 (tptp.one_sorted_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.empty_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_25 (or _let_24 _let_23 _let_21 _let_13))) (let ((_let_26 (forall ((A $$unsorted) (BOUND_VARIABLE_1522 $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (or (tptp.empty_carrier A) (not (tptp.one_sorted_str A)) (not (tptp.element BOUND_VARIABLE_1522 _let_1)) (= BOUND_VARIABLE_1522 (tptp.apply_as_element _let_1 _let_1 (tptp.identity_on_carrier A) BOUND_VARIABLE_1522))))))) (let ((_let_27 (not _let_25))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (or))) (let ((_let_30 (not _let_26))) (let ((_let_31 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_28) :args (_let_30))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_26))) (REFL :args (_let_27)) :args _let_29)) _let_28 :args (_let_27 true _let_26)))) (let ((_let_32 (or _let_23 _let_15))) (let ((_let_33 (forall ((A $$unsorted)) (or (not (tptp.one_sorted_str A)) (= (tptp.identity_on_carrier A) (tptp.identity_as_relation_of (tptp.the_carrier A))))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (REFL :args (_let_25)))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 1)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_29)) :args ((or _let_22 _let_25))) _let_31 :args (_let_22 true _let_25)))) (let ((_let_37 (_let_6))) (let ((_let_38 (ASSUME :args _let_37))) (let ((_let_39 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_11))) (let ((_let_40 (not _let_39))) (let ((_let_41 (or _let_40 _let_18))) (let ((_let_42 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.in B A)) (= B (tptp.apply (tptp.identity_relation A) B)))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (tptp.empty _let_11))) (let ((_let_45 (or _let_21 _let_44 _let_39))) (let ((_let_46 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.element A B)) (tptp.empty B) (tptp.in A B))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (not _let_44))) (let ((_let_49 (or _let_24 _let_23 _let_48))) (let ((_let_50 (forall ((A $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.one_sorted_str A)) (not (tptp.empty (tptp.the_carrier A))))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_24 _let_23 _let_48 (not _let_49)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_25 0)) _let_31 :args ((not _let_24) true _let_25)) _let_36 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.empty_carrier A) true))))) :args (_let_50))) _let_51 :args (_let_49 false _let_50)) :args (_let_48 true _let_24 false _let_22 false _let_49)))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 2)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_29)) :args ((or _let_20 _let_25))) _let_31 :args (_let_20 true _let_25)))) (let ((_let_54 (tptp.relation_of2 _let_10 _let_11 _let_11))) (let ((_let_55 (not _let_54))) (let ((_let_56 (tptp.quasi_total _let_10 _let_11 _let_11))) (let ((_let_57 (not _let_56))) (let ((_let_58 (tptp.function _let_10))) (let ((_let_59 (not _let_58))) (let ((_let_60 (or _let_44 _let_59 _let_57 _let_55 _let_21 _let_19))) (let ((_let_61 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (or (tptp.empty A) (not (tptp.function C)) (not (tptp.quasi_total C A B)) (not (tptp.relation_of2 C A B)) (not (tptp.element D A)) (= (tptp.apply_as_element A B C D) (tptp.apply C D)))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (tptp.relation_of2_as_subset _let_10 _let_11 _let_11))) (let ((_let_64 (= _let_63 _let_54))) (let ((_let_65 (_let_4))) (let ((_let_66 (ASSUME :args _let_65))) (let ((_let_67 (and _let_58 _let_56 _let_63))) (let ((_let_68 (or _let_23 _let_67))) (let ((_let_69 (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.identity_on_carrier A))) (or (not (tptp.one_sorted_str A)) (and (tptp.function _let_2) (tptp.quasi_total _let_2 _let_1 _let_1) (tptp.relation_of2_as_subset _let_2 _let_1 _let_1)))))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_23 _let_67 (not _let_68)))) _let_36 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_70 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.one_sorted_str A) false))))) :args (_let_69))) _let_70 :args (_let_68 false _let_69)) :args (_let_67 false _let_22 false _let_68)))) (let ((_let_72 (not _let_67))) (let ((_let_73 (and _let_15 _let_19 _let_17 _let_18))) (let ((_let_74 (ASSUME :args (_let_19)))) (let ((_let_75 (ASSUME :args (_let_15)))) (let ((_let_76 (ASSUME :args (_let_17)))) (let ((_let_77 (ASSUME :args (_let_18)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_73)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_74 _let_75 _let_76 _let_77) (SCOPE (TRANS (SYMM (SYMM _let_77)) (CONG (TRANS (SYMM _let_76) (SYMM _let_75)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) :args (APPLY_UF tptp.apply)) (SYMM _let_74)) :args (_let_19 _let_15 _let_17 _let_18))) :args (_let_15 _let_19 _let_17 _let_18))) :args (true _let_73)) :args ((or _let_13 (not _let_15) (not _let_19) (not _let_17) (not _let_18)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_21 _let_44 _let_59 _let_57 _let_55 _let_19 (not _let_60)))) _let_53 _let_52 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_67 0)) :args ((or _let_58 _let_72))) _let_71 :args (_let_58 false _let_67)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_67 1)) :args ((or _let_56 _let_72))) _let_71 :args (_let_56 false _let_67)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_64)) :args ((or _let_54 (not _let_63) (not _let_64)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_67 2)) :args ((or _let_63 _let_72))) _let_71 :args (_let_63 false _let_67)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (_let_11 _let_11 _let_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.relation_of2_as_subset C A B)))) :args _let_65)) _let_66 :args (_let_64 false _let_4)) :args (_let_54 false _let_63 false _let_64)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (_let_11 _let_11 _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.apply_as_element A B C D)))) :args (_let_61))) _let_62 :args (_let_60 false _let_61)) :args (_let_19 false _let_20 true _let_44 false _let_58 false _let_56 false _let_54 false _let_60)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_40 _let_18 (not _let_41)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_45)) :args ((or _let_21 _let_44 _let_39 (not _let_45)))) _let_53 _let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.element A B) false))))) :args (_let_46))) _let_47 :args (_let_45 false _let_46)) :args (_let_39 false _let_20 true _let_44 false _let_45)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (_let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.in B A) false))))) :args (_let_42))) _let_43 :args (_let_41 false _let_42)) :args (_let_18 false _let_39 false _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (_let_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.identity_as_relation_of A)))) :args _let_37)) _let_38 :args (_let_17 false _let_6)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_23 _let_15 (not _let_32)))) _let_36 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.one_sorted_str A) false))))) :args (_let_33))) _let_34 :args (_let_32 false _let_33)) :args (_let_15 false _let_22 false _let_32)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_25 3)) _let_31 :args ((not _let_13) true _let_25)) :args (false false _let_19 false _let_18 false _let_17 false _let_15 true _let_13)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.function C))) (=> (tptp.relation_of2 C A B) (=> (and _let_1 (tptp.v1_partfun1 C A B)) (and _let_1 (tptp.quasi_total C A B)))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation A))) (=> (and _let_1 (tptp.symmetric A) (tptp.transitive A)) (and _let_1 (tptp.reflexive A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))) (tptp.relation C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.quasi_total C A B))) (let ((_let_2 (tptp.function C))) (=> (tptp.relation_of2 C A B) (=> (and _let_2 _let_1 (tptp.bijective C A B)) (and _let_2 (tptp.one_to_one C) _let_1 (tptp.onto C A B))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.quasi_total C A B))) (let ((_let_2 (tptp.function C))) (=> (tptp.relation_of2 C A B) (=> (and _let_2 (tptp.one_to_one C) _let_1 (tptp.onto C A B)) (and _let_2 _let_1 (tptp.bijective C A B))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.quasi_total B A A))) (let ((_let_2 (tptp.function B))) (=> (tptp.relation_of2 B A A) (=> (and _let_2 (tptp.v1_partfun1 B A A) (tptp.reflexive B) _let_1) (and _let_2 (tptp.one_to_one B) _let_1 (tptp.onto B A A) (tptp.bijective B A A))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty B)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.quasi_total C A B))) (let ((_let_2 (tptp.function C))) (=> (tptp.relation_of2 C A B) (=> (and _let_2 _let_1) (and _let_2 (tptp.v1_partfun1 C A B) _let_1)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B))) (forall ((C $$unsorted)) (let ((_let_1 (tptp.quasi_total C A B))) (let ((_let_2 (tptp.function C))) (=> (tptp.relation_of2 C A B) (=> (and _let_2 _let_1) (and _let_2 (not (tptp.empty C)) (tptp.v1_partfun1 C A B) _let_1)))))))) _let_9 true true true true (forall ((A $$unsorted)) (let ((_let_1 (tptp.identity_as_relation_of A))) (and (tptp.v1_partfun1 _let_1 A A) (tptp.relation_of2_as_subset _let_1 A A)))) (forall ((A $$unsorted)) (tptp.relation (tptp.identity_relation A))) _let_8 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.function C) (tptp.quasi_total C A B) (tptp.relation_of2 C A B) (tptp.element D A)) (tptp.element (tptp.apply_as_element A B C D) B))) true true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2_as_subset C A B) (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))))) true (exists ((A $$unsorted)) (tptp.one_sorted_str A)) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.relation_of2 C A B))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.relation_of2_as_subset C A B))) _let_7 (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) (tptp.empty tptp.empty_set) (forall ((A $$unsorted)) (let ((_let_1 (tptp.identity_relation A))) (and (tptp.relation _let_1) (tptp.function _let_1) (tptp.reflexive _let_1) (tptp.symmetric _let_1) (tptp.antisymmetric _let_1) (tptp.transitive _let_1)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B))) (not (tptp.empty (tptp.cartesian_product2 A B))))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (and (tptp.relation_of2 C A B) (tptp.relation C) (tptp.function C) (tptp.quasi_total C A B)))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A) (tptp.empty A))) (forall ((A $$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.relation_of2 B A A) (tptp.relation B) (tptp.function B) (tptp.one_to_one B) (tptp.quasi_total B A A) (tptp.onto B A A) (tptp.bijective B A A)))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (and (tptp.relation_of2 C A B) (tptp.relation C) (tptp.function C)))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (exists ((A $$unsorted)) (not (tptp.empty A))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.relation_of2 B A A) (tptp.relation B) (tptp.reflexive B) (tptp.symmetric B) (tptp.antisymmetric B) (tptp.transitive B) (tptp.v1_partfun1 B A A)))) (exists ((A $$unsorted)) (and (tptp.one_sorted_str A) (not (tptp.empty_carrier A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)))))) _let_6 _let_5 _let_4 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) _let_3 _let_2 (forall ((A $$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 $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))) (forall ((A $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.19/0.56  )
% 0.19/0.56  % SZS output end Proof for SEU353+1
% 0.19/0.56  % cvc5---1.0.5 exiting
% 0.19/0.56  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------