%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU391+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n020.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 16:31:20 EDT 2023

% Result   : Theorem 0.20s 0.69s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU391+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n020.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 19:56:01 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.20/0.48  %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.69  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.rAvcUK2txb/cvc5---1.0.5_9747.p...
% 0.20/0.69  ------- get file name : TPTP file name is SEU391+1
% 0.20/0.69  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_9747.smt2...
% 0.20/0.69  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.69  % SZS status Theorem for SEU391+1
% 0.20/0.69  % SZS output start Proof for SEU391+1
% 0.20/0.69  (
% 0.20/0.69  (let ((_let_1 (not (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (forall ((B $$unsorted)) (=> (and (not (tptp.empty_carrier B)) (tptp.net_str B A)) (forall ((C $$unsorted)) (= (tptp.in C (tptp.filter_of_net_str A B)) (and (tptp.is_eventually_in A B C) (tptp.element C (tptp.powerset (tptp.the_carrier A))))))))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier B)) (tptp.one_sorted_str B) (not (tptp.empty_carrier C)) (tptp.net_str C B)) (= (tptp.in A (tptp.a_2_1_yellow19 B C)) (exists ((D $$unsorted)) (and (tptp.element D (tptp.powerset (tptp.the_carrier B))) (= A D) (tptp.is_eventually_in B C D)))))))) (let ((_let_3 (tptp.relation tptp.empty_set))) (let ((_let_4 (tptp.empty tptp.empty_set))) (let ((_let_5 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (forall ((B $$unsorted)) (=> (and (not (tptp.empty_carrier B)) (tptp.net_str B A)) (= (tptp.filter_of_net_str A B) (tptp.a_2_1_yellow19 A B)))))))) (let ((_let_6 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 (tptp.powerset (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))))) (let ((_let_7 (tptp.is_eventually_in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_8 (and _let_7 _let_6))) (let ((_let_9 (tptp.filter_of_net_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_10 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 _let_9))) (let ((_let_11 (= _let_10 _let_8))) (let ((_let_12 (not _let_8))) (let ((_let_13 (and _let_6 _let_7))) (let ((_let_14 (tptp.a_2_1_yellow19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_15 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 _let_14))) (let ((_let_16 (= _let_15 _let_13))) (let ((_let_17 (= _let_9 _let_14))) (let ((_let_18 (tptp.net_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_19 (not _let_18))) (let ((_let_20 (tptp.empty_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_21 (tptp.one_sorted_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_22 (not _let_21))) (let ((_let_23 (tptp.empty_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_24 (or _let_23 _let_22 _let_20 _let_19 _let_11))) (let ((_let_25 (forall ((A $$unsorted) (BOUND_VARIABLE_2928 $$unsorted) (BOUND_VARIABLE_2926 $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.one_sorted_str A)) (tptp.empty_carrier BOUND_VARIABLE_2926) (not (tptp.net_str BOUND_VARIABLE_2926 A)) (= (tptp.in BOUND_VARIABLE_2928 (tptp.filter_of_net_str A BOUND_VARIABLE_2926)) (and (tptp.is_eventually_in A BOUND_VARIABLE_2926 BOUND_VARIABLE_2928) (tptp.element BOUND_VARIABLE_2928 (tptp.powerset (tptp.the_carrier A))))))))) (let ((_let_26 (not _let_24))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (or))) (let ((_let_29 (not _let_25))) (let ((_let_30 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_27) :args (_let_29))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_25))) (REFL :args (_let_26)) :args _let_28)) _let_27 :args (_let_26 true _let_25)))) (let ((_let_31 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_24 4)) _let_30 :args ((not _let_11) true _let_24)))) (let ((_let_32 (_let_11))) (let ((_let_33 (or _let_23 _let_22 _let_20 _let_19 _let_16))) (let ((_let_34 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier B) (not (tptp.one_sorted_str B)) (tptp.empty_carrier C) (not (tptp.net_str C B)) (= (tptp.in A (tptp.a_2_1_yellow19 B C)) (and (tptp.element A (tptp.powerset (tptp.the_carrier B))) (tptp.is_eventually_in B C A))))))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (REFL :args (_let_24)))) (let ((_let_37 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_24 3)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) :args _let_28)) :args ((or _let_18 _let_24))) _let_30 :args (_let_18 true _let_24)))) (let ((_let_38 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_24 2)) _let_30 :args ((not _let_20) true _let_24)))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_24 1)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_28)) :args ((or _let_21 _let_24))) _let_30 :args (_let_21 true _let_24)))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_24 0)) _let_30 :args ((not _let_23) true _let_24)))) (let ((_let_41 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_33)) :args ((or _let_23 _let_22 _let_20 _let_19 _let_16 (not _let_33)))) _let_40 _let_39 _let_38 _let_37 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.is_eventually_in B C A)))) :args (_let_34))) _let_35 :args (_let_33 false _let_34)) :args (_let_16 true _let_23 false _let_21 true _let_20 false _let_18 false _let_33)))) (let ((_let_42 (not _let_16))) (let ((_let_43 (not _let_13))) (let ((_let_44 (_let_16))) (let ((_let_45 (or _let_23 _let_22 _let_20 _let_19 _let_17))) (let ((_let_46 (forall ((A $$unsorted) (BOUND_VARIABLE_1966 $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.one_sorted_str A)) (tptp.empty_carrier BOUND_VARIABLE_1966) (not (tptp.net_str BOUND_VARIABLE_1966 A)) (= (tptp.filter_of_net_str A BOUND_VARIABLE_1966) (tptp.a_2_1_yellow19 A BOUND_VARIABLE_1966)))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_45)) :args ((or _let_23 _let_22 _let_20 _let_19 _let_17 (not _let_45)))) _let_40 _let_39 _let_38 _let_37 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.net_str BOUND_VARIABLE_1966 A) false))))) :args (_let_46))) _let_47 :args (_let_45 false _let_46)) :args (_let_17 true _let_23 false _let_21 true _let_20 false _let_18 false _let_45)))) (let ((_let_49 (not _let_15))) (let ((_let_50 (not _let_17))) (let ((_let_51 (not _let_10))) (let ((_let_52 (and _let_51 _let_17))) (let ((_let_53 (_let_51 _let_17))) (let ((_let_54 (ASSUME :args (_let_51)))) (let ((_let_55 (ASSUME :args (_let_17)))) (let ((_let_56 (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18)) (SYMM _let_55) :args (APPLY_UF tptp.in)))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_52)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_54 _let_55) (SCOPE (FALSE_ELIM (TRANS _let_56 (FALSE_INTRO _let_54))) :args _let_53)) :args _let_53)) :args (true _let_52)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_10))) (REFL :args (_let_50)) (REFL :args (_let_49)) :args _let_28)) _let_48 (REORDERING (CNF_EQUIV_POS2 :args _let_44) :args ((or _let_15 _let_43 _let_42))) _let_41 (REORDERING (CNF_AND_NEG :args (_let_13)) :args ((or (not _let_7) (not _let_6) _let_13))) (REORDERING (CNF_AND_POS :args (_let_8 1)) :args ((or _let_6 _let_12))) (REORDERING (CNF_AND_POS :args (_let_8 0)) :args ((or _let_7 _let_12))) (REORDERING (CNF_EQUIV_NEG1 :args _let_32) :args ((or _let_10 _let_8 _let_11))) _let_31 :args (_let_10 false _let_17 false _let_15 false _let_16 false _let_13 false _let_6 false _let_7 false _let_8 true _let_11)))) (let ((_let_58 (and _let_10 _let_17))) (let ((_let_59 (_let_10 _let_17))) (let ((_let_60 (ASSUME :args (_let_10)))) (let ((_let_61 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_44) :args ((or _let_13 _let_49 _let_42))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_58)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_60 _let_55) (SCOPE (TRUE_ELIM (TRANS _let_56 (TRUE_INTRO _let_60))) :args _let_59)) :args _let_59)) :args (true _let_58)) :args ((or _let_51 _let_15 _let_50))) _let_57 _let_48 :args (_let_15 false _let_10 false _let_17)) _let_41 :args (_let_13 false _let_15 false _let_16)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_8)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_13 1)) :args ((or _let_7 _let_43))) _let_61 :args (_let_7 false _let_13)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_13 0)) :args ((or _let_6 _let_43))) _let_61 :args (_let_6 false _let_13)) (MACRO_RESOLUTION_TRUST (CNF_EQUIV_NEG2 :args _let_32) _let_31 _let_57 :args (_let_12 true _let_11 false _let_10)) :args (false false _let_7 false _let_6 true _let_8)) :args ((forall ((A $$unsorted)) (=> (tptp.rel_str A) (=> (tptp.strict_rel_str A) (= A (tptp.rel_str_of (tptp.the_carrier A) (tptp.the_InternalRel A)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.reflexive_relstr A))) (let ((_let_2 (not (tptp.empty_carrier A)))) (=> (tptp.rel_str A) (=> (and _let_2 _let_1 (tptp.complete_relstr A)) (and _let_2 _let_1 (tptp.up_complete_relstr A) (tptp.join_complete_relstr A))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.reflexive_relstr A))) (let ((_let_2 (not (tptp.empty_carrier A)))) (=> (tptp.rel_str A) (=> (and _let_2 _let_1 (tptp.join_complete_relstr A)) (and _let_2 _let_1 (tptp.lower_bounded_relstr A))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.lower_bounded_relstr A))) (let ((_let_2 (tptp.with_suprema_relstr A))) (let ((_let_3 (tptp.antisymmetric_relstr A))) (let ((_let_4 (tptp.transitive_relstr A))) (let ((_let_5 (tptp.reflexive_relstr A))) (let ((_let_6 (not (tptp.empty_carrier A)))) (=> (tptp.rel_str A) (=> (and _let_6 _let_5 _let_4 _let_3 _let_2 _let_1 (tptp.up_complete_relstr A)) (and _let_6 _let_5 _let_4 _let_3 _let_2 (tptp.with_infima_relstr A) (tptp.complete_relstr A) _let_1 (tptp.upper_bounded_relstr A) (tptp.bounded_relstr A))))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.antisymmetric_relstr A))) (let ((_let_2 (tptp.reflexive_relstr A))) (let ((_let_3 (not (tptp.empty_carrier A)))) (=> (tptp.rel_str A) (=> (and _let_3 _let_2 _let_1 (tptp.join_complete_relstr A)) (and _let_3 _let_2 _let_1 (tptp.with_infima_relstr A)))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.upper_bounded_relstr A))) (let ((_let_2 (tptp.antisymmetric_relstr A))) (let ((_let_3 (tptp.reflexive_relstr A))) (let ((_let_4 (not (tptp.empty_carrier A)))) (=> (tptp.rel_str A) (=> (and _let_4 _let_3 _let_2 _let_1 (tptp.join_complete_relstr A)) (and _let_4 _let_3 _let_2 (tptp.with_suprema_relstr A) _let_1)))))))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.finite A))) (forall ((A $$unsorted)) (=> (tptp.rel_str A) (=> (tptp.with_suprema_relstr A) (not (tptp.empty_carrier A))))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.relation A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))) (tptp.relation C))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.empty_carrier A)))) (=> (tptp.rel_str A) (=> (and _let_1 (tptp.complete_relstr A)) (and _let_1 (tptp.with_suprema_relstr A) (tptp.with_infima_relstr A)))))) (forall ((A $$unsorted)) (=> (tptp.finite A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (tptp.finite B))))) (forall ((A $$unsorted)) (=> (tptp.rel_str A) (=> (tptp.with_infima_relstr A) (not (tptp.empty_carrier A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.reflexive_relstr A))) (let ((_let_2 (not (tptp.empty_carrier A)))) (=> (tptp.rel_str A) (=> (and _let_2 _let_1 (tptp.trivial_carrier A)) (and _let_2 _let_1 (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.complete_relstr A))))))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.empty_carrier A)))) (=> (tptp.rel_str A) (=> (and _let_1 (tptp.complete_relstr A)) (and _let_1 (tptp.bounded_relstr A)))))) (forall ((A $$unsorted)) (=> (tptp.rel_str A) (=> (tptp.bounded_relstr A) (and (tptp.lower_bounded_relstr A) (tptp.upper_bounded_relstr A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.reflexive_relstr A))) (let ((_let_2 (not (tptp.empty_carrier A)))) (=> (tptp.rel_str A) (=> (and _let_2 _let_1 (tptp.trivial_carrier A)) (and _let_2 _let_1 (tptp.connected_relstr A))))))) (forall ((A $$unsorted)) (=> (tptp.rel_str A) (=> (and (tptp.lower_bounded_relstr A) (tptp.upper_bounded_relstr A)) (tptp.bounded_relstr A)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.with_suprema_relstr A))) (let ((_let_2 (tptp.reflexive_relstr A))) (=> (tptp.rel_str A) (=> (and _let_2 _let_1 (tptp.up_complete_relstr A)) (and (not (tptp.empty_carrier A)) _let_2 _let_1 (tptp.upper_bounded_relstr A))))))) _let_5 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.rel_str_of A B))) (=> (tptp.relation_of2 B A A) (and (tptp.strict_rel_str _let_1) (tptp.rel_str _let_1))))) true true (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (tptp.element (tptp.cast_as_carrier_subset A) (tptp.powerset (tptp.the_carrier A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.net_str B A)) (tptp.element (tptp.filter_of_net_str A B) (tptp.powerset (tptp.the_carrier (tptp.boole_POSet (tptp.cast_as_carrier_subset A))))))) true (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_POSet A))) (and (tptp.strict_rel_str _let_1) (tptp.rel_str _let_1)))) (forall ((A $$unsorted)) (=> (tptp.rel_str A) (tptp.one_sorted_str A))) true (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (forall ((B $$unsorted)) (=> (tptp.net_str B A) (tptp.rel_str B))))) true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2_as_subset C A B) (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (tptp.rel_str A) (tptp.relation_of2_as_subset (tptp.the_InternalRel A) _let_1 _let_1)))) true (exists ((A $$unsorted)) (tptp.rel_str A)) (exists ((A $$unsorted)) (tptp.one_sorted_str A)) (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (exists ((B $$unsorted)) (tptp.net_str B 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))) (and _let_4 _let_3 (tptp.relation_empty_yielding tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.finite A) (tptp.finite B)) (tptp.finite (tptp.cartesian_product2 A B)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.cast_as_carrier_subset A))) (=> (and (not (tptp.empty_carrier A)) (tptp.rel_str A)) (and (not (tptp.empty _let_1)) (tptp.lower_relstr_subset _let_1 A) (tptp.upper_relstr_subset _let_1 A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (not (tptp.empty (tptp.the_carrier A))))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_POSet A))) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1) (tptp.lower_bounded_relstr _let_1) (tptp.upper_bounded_relstr _let_1) (tptp.bounded_relstr _let_1) (tptp.up_complete_relstr _let_1) (tptp.join_complete_relstr _let_1) (not (tptp.v1_yellow_3 _let_1)) (tptp.distributive_relstr _let_1) (tptp.heyting_relstr _let_1) (tptp.complemented_relstr _let_1) (tptp.boolean_relstr _let_1) (tptp.with_suprema_relstr _let_1) (tptp.with_infima_relstr _let_1) (tptp.complete_relstr _let_1)))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (not (tptp.empty (tptp.cast_as_carrier_subset A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.cast_as_carrier_subset A))) (=> (and (tptp.with_suprema_relstr A) (tptp.rel_str A)) (and (not (tptp.empty _let_1)) (tptp.directed_subset _let_1 A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_POSet A))) (=> (not (tptp.empty A)) (and (not (tptp.empty_carrier _let_1)) (not (tptp.trivial_carrier _let_1)) (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1) (tptp.lower_bounded_relstr _let_1) (tptp.upper_bounded_relstr _let_1) (tptp.bounded_relstr _let_1) (tptp.up_complete_relstr _let_1) (tptp.join_complete_relstr _let_1) (not (tptp.v1_yellow_3 _let_1)) (tptp.distributive_relstr _let_1) (tptp.heyting_relstr _let_1) (tptp.complemented_relstr _let_1) (tptp.boolean_relstr _let_1) (tptp.with_suprema_relstr _let_1) (tptp.with_infima_relstr _let_1) (tptp.complete_relstr _let_1))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.rel_str A)) (not (tptp.empty (tptp.cast_as_carrier_subset A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.cast_as_carrier_subset A))) (=> (and (not (tptp.empty_carrier A)) (tptp.upper_bounded_relstr A) (tptp.rel_str A)) (and (not (tptp.empty _let_1)) (tptp.directed_subset _let_1 A))))) (and _let_4 _let_3) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B))) (not (tptp.empty (tptp.cartesian_product2 A B))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.cast_as_carrier_subset A))) (=> (and (tptp.with_infima_relstr A) (tptp.rel_str A)) (and (not (tptp.empty _let_1)) (tptp.filtered_subset _let_1 A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.cast_as_carrier_subset A))) (=> (and (not (tptp.empty_carrier A)) (tptp.lower_bounded_relstr A) (tptp.rel_str A)) (and (not (tptp.empty _let_1)) (tptp.filtered_subset _let_1 A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_POSet A))) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_POSet A))) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1) (tptp.lower_bounded_relstr _let_1) (tptp.upper_bounded_relstr _let_1) (tptp.bounded_relstr _let_1) (tptp.with_suprema_relstr _let_1) (tptp.with_infima_relstr _let_1) (tptp.complete_relstr _let_1)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_POSet A))) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1) (tptp.lower_bounded_relstr _let_1) (tptp.upper_bounded_relstr _let_1) (tptp.bounded_relstr _let_1) (tptp.directed_relstr _let_1) (tptp.up_complete_relstr _let_1) (tptp.join_complete_relstr _let_1) (not (tptp.v1_yellow_3 _let_1)) (tptp.with_suprema_relstr _let_1) (tptp.with_infima_relstr _let_1) (tptp.complete_relstr _let_1)))) _let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation_of2 B A A) (forall ((C $$unsorted) (D $$unsorted)) (=> (= (tptp.rel_str_of A B) (tptp.rel_str_of C D)) (and (= A C) (= B D)))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.rel_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)) (tptp.filtered_subset B A) (tptp.upper_relstr_subset B A))))) (forall ((A $$unsorted)) (=> (and (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.with_suprema_relstr A) (tptp.with_infima_relstr A) (tptp.rel_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)) (tptp.directed_subset B A) (tptp.filtered_subset B A) (tptp.lower_relstr_subset B A) (tptp.upper_relstr_subset B A))))) (exists ((A $$unsorted)) (and (tptp.rel_str A) (not (tptp.empty_carrier A)) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.connected_relstr A))) (exists ((A $$unsorted)) (and (tptp.rel_str A) (not (tptp.empty_carrier A)) (tptp.strict_rel_str A) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.with_suprema_relstr A) (tptp.with_infima_relstr A) (tptp.complete_relstr A) (tptp.lower_bounded_relstr A) (tptp.upper_bounded_relstr A) (tptp.bounded_relstr A) (tptp.up_complete_relstr A) (tptp.join_complete_relstr A))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.finite A))) (exists ((A $$unsorted)) (and (tptp.rel_str A) (not (tptp.empty_carrier A)) (tptp.strict_rel_str A) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.complete_relstr A))) (exists ((A $$unsorted)) (and (tptp.empty A) (tptp.relation A))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (forall ((A $$unsorted)) (=> (tptp.rel_str A) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.directed_subset B A) (tptp.filtered_subset B A))))) (exists ((A $$unsorted)) (and (tptp.rel_str A) (not (tptp.empty_carrier A)) (not (tptp.trivial_carrier A)) (tptp.strict_rel_str A) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.lower_bounded_relstr A) (tptp.upper_bounded_relstr A) (tptp.bounded_relstr A) (not (tptp.v1_yellow_3 A)) (tptp.distributive_relstr A) (tptp.heyting_relstr A) (tptp.complemented_relstr A) (tptp.boolean_relstr A) (tptp.with_suprema_relstr A) (tptp.with_infima_relstr A))) (exists ((A $$unsorted)) (and (tptp.rel_str A) (not (tptp.empty_carrier A)) (tptp.strict_rel_str A) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.with_suprema_relstr A) (tptp.with_infima_relstr A) (tptp.complete_relstr A) (tptp.trivial_carrier A))) (exists ((A $$unsorted)) (and (tptp.rel_str A) (not (tptp.empty_carrier A)) (tptp.strict_rel_str A) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.with_suprema_relstr A) (tptp.with_infima_relstr A) (tptp.complete_relstr A))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.relation A))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.reflexive_relstr A) (tptp.rel_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)) (tptp.finite B) (tptp.directed_subset B A) (tptp.filtered_subset B A))))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.powerset A))) (not (tptp.empty B)) (tptp.finite B)))) (exists ((A $$unsorted)) (and (tptp.rel_str A) (not (tptp.empty_carrier A)) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.with_suprema_relstr A) (tptp.with_infima_relstr A) (tptp.complete_relstr A) (tptp.lower_bounded_relstr A) (tptp.upper_bounded_relstr A) (tptp.bounded_relstr 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))))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A))) (exists ((A $$unsorted)) (and (tptp.one_sorted_str A) (not (tptp.empty_carrier A)))) (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier 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))))) (exists ((A $$unsorted)) (and (tptp.rel_str A) (not (tptp.empty_carrier A)) (tptp.strict_rel_str A) (tptp.transitive_relstr A) (tptp.directed_relstr A))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)))))) (forall ((A $$unsorted)) (=> (tptp.rel_str A) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.lower_relstr_subset B A) (tptp.upper_relstr_subset B A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.rel_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)) (tptp.lower_relstr_subset B A) (tptp.upper_relstr_subset B A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.rel_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)) (tptp.directed_subset B A) (tptp.lower_relstr_subset B A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.relation_of2_as_subset C A B) (tptp.relation_of2 C A B))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) _let_1 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) (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) (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)))) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.69  )
% 0.20/0.69  % SZS output end Proof for SEU391+1
% 0.20/0.69  % cvc5---1.0.5 exiting
% 0.20/0.70  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------